id	sid	tid	token	lemma	pos
ejpam-6008	1	1	european	european	PROPN
ejpam-6008	1	2	journal	journal	PROPN
ejpam-6008	1	3	of	of	ADP
ejpam-6008	1	4	pure	pure	ADJ
ejpam-6008	1	5	and	and	CCONJ
ejpam-6008	1	6	applied	applied	ADJ
ejpam-6008	1	7	mathematics	mathematic	NOUN
ejpam-6008	1	8	2025	2025	NUM
ejpam-6008	1	9	,	,	PUNCT
ejpam-6008	1	10	vol	vol	NOUN
ejpam-6008	1	11	.	.	PROPN
ejpam-6008	1	12	18	18	NUM
ejpam-6008	1	13	,	,	PUNCT
ejpam-6008	1	14	issue	issue	NOUN
ejpam-6008	1	15	2	2	NUM
ejpam-6008	1	16	,	,	PUNCT
ejpam-6008	1	17	article	article	NOUN
ejpam-6008	1	18	number	number	NOUN
ejpam-6008	1	19	6008	6008	NUM
ejpam-6008	1	20	issn	issn	PROPN
ejpam-6008	1	21	1307	1307	NUM
ejpam-6008	1	22	-	-	SYM
ejpam-6008	1	23	5543	5543	NUM
ejpam-6008	1	24	–	–	PUNCT
ejpam-6008	1	25	ejpam.com	ejpam.com	X
ejpam-6008	1	26	published	publish	VERB
ejpam-6008	1	27	by	by	ADP
ejpam-6008	1	28	new	new	PROPN
ejpam-6008	1	29	york	york	PROPN
ejpam-6008	1	30	business	business	PROPN
ejpam-6008	1	31	global	global	PROPN
ejpam-6008	1	32	upper	upper	ADJ
ejpam-6008	1	33	and	and	CCONJ
ejpam-6008	1	34	lower	low	ADJ
ejpam-6008	1	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	1	36	,	,	PUNCT
ejpam-6008	1	37	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	1	38	nongluk	nongluk	PROPN
ejpam-6008	1	39	viriyapong1	viriyapong1	PROPN
ejpam-6008	1	40	,	,	PUNCT
ejpam-6008	1	41	areeyuth	areeyuth	NOUN
ejpam-6008	1	42	sama	sama	NOUN
ejpam-6008	1	43	-	-	PUNCT
ejpam-6008	1	44	ae2	ae2	PROPN
ejpam-6008	1	45	,	,	PUNCT
ejpam-6008	1	46	chawalit	chawalit	VERB
ejpam-6008	1	47	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6008	1	48	1	1	NUM
ejpam-6008	1	49	mathematics	mathematic	NOUN
ejpam-6008	1	50	and	and	CCONJ
ejpam-6008	1	51	applied	apply	VERB
ejpam-6008	1	52	mathematics	mathematics	PROPN
ejpam-6008	1	53	research	research	NOUN
ejpam-6008	1	54	unit	unit	NOUN
ejpam-6008	1	55	,	,	PUNCT
ejpam-6008	1	56	department	department	NOUN
ejpam-6008	1	57	of	of	ADP
ejpam-6008	1	58	mathematics	mathematic	NOUN
ejpam-6008	1	59	,	,	PUNCT
ejpam-6008	1	60	faculty	faculty	NOUN
ejpam-6008	1	61	of	of	ADP
ejpam-6008	1	62	science	science	NOUN
ejpam-6008	1	63	,	,	PUNCT
ejpam-6008	1	64	mahasarakham	mahasarakham	PROPN
ejpam-6008	1	65	university	university	PROPN
ejpam-6008	1	66	,	,	PUNCT
ejpam-6008	1	67	maha	maha	PROPN
ejpam-6008	1	68	sarakham	sarakham	PROPN
ejpam-6008	1	69	,	,	PUNCT
ejpam-6008	1	70	44150	44150	NUM
ejpam-6008	1	71	,	,	PUNCT
ejpam-6008	1	72	thailand	thailand	PROPN
ejpam-6008	1	73	2	2	NUM
ejpam-6008	1	74	department	department	NOUN
ejpam-6008	1	75	of	of	ADP
ejpam-6008	1	76	mathematics	mathematic	NOUN
ejpam-6008	1	77	and	and	CCONJ
ejpam-6008	1	78	computer	computer	NOUN
ejpam-6008	1	79	science	science	NOUN
ejpam-6008	1	80	,	,	PUNCT
ejpam-6008	1	81	faculty	faculty	NOUN
ejpam-6008	1	82	of	of	ADP
ejpam-6008	1	83	science	science	NOUN
ejpam-6008	1	84	and	and	CCONJ
ejpam-6008	1	85	technology	technology	NOUN
ejpam-6008	1	86	,	,	PUNCT
ejpam-6008	1	87	prince	prince	NOUN
ejpam-6008	1	88	of	of	ADP
ejpam-6008	1	89	songkla	songkla	PROPN
ejpam-6008	1	90	university	university	PROPN
ejpam-6008	1	91	,	,	PUNCT
ejpam-6008	1	92	pattani	pattani	NOUN
ejpam-6008	1	93	campus	campus	NOUN
ejpam-6008	1	94	,	,	PUNCT
ejpam-6008	1	95	pattani	pattani	NOUN
ejpam-6008	1	96	,	,	PUNCT
ejpam-6008	1	97	94000	94000	NUM
ejpam-6008	1	98	,	,	PUNCT
ejpam-6008	1	99	thailand	thailand	PROPN
ejpam-6008	1	100	abstract	abstract	PROPN
ejpam-6008	1	101	.	.	PUNCT
ejpam-6008	2	1	this	this	DET
ejpam-6008	2	2	paper	paper	NOUN
ejpam-6008	2	3	presents	present	VERB
ejpam-6008	2	4	new	new	ADJ
ejpam-6008	2	5	classes	class	NOUN
ejpam-6008	2	6	of	of	ADP
ejpam-6008	2	7	multifunctions	multifunction	NOUN
ejpam-6008	2	8	between	between	ADP
ejpam-6008	2	9	bitopological	bitopological	ADJ
ejpam-6008	2	10	spaces	space	NOUN
ejpam-6008	2	11	,	,	PUNCT
ejpam-6008	2	12	namely	namely	ADV
ejpam-6008	2	13	upper	upper	ADJ
ejpam-6008	2	14	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	2	15	,	,	PUNCT
ejpam-6008	2	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	2	17	multifunctions	multifunction	NOUN
ejpam-6008	2	18	and	and	CCONJ
ejpam-6008	2	19	lower	low	ADJ
ejpam-6008	2	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	2	21	,	,	PUNCT
ejpam-6008	2	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	2	23	multifunctions	multifunction	NOUN
ejpam-6008	2	24	.	.	PUNCT
ejpam-6008	3	1	moreover	moreover	ADV
ejpam-6008	3	2	,	,	PUNCT
ejpam-6008	3	3	several	several	ADJ
ejpam-6008	3	4	characterizations	characterization	NOUN
ejpam-6008	3	5	and	and	CCONJ
ejpam-6008	3	6	some	some	DET
ejpam-6008	3	7	properties	property	NOUN
ejpam-6008	3	8	concerning	concern	VERB
ejpam-6008	3	9	upper	upper	ADJ
ejpam-6008	3	10	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	3	11	,	,	PUNCT
ejpam-6008	3	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	3	13	multifunctions	multifunction	NOUN
ejpam-6008	3	14	and	and	CCONJ
ejpam-6008	3	15	lower	low	ADJ
ejpam-6008	3	16	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	3	17	,	,	PUNCT
ejpam-6008	3	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	3	19	multifunctions	multifunction	NOUN
ejpam-6008	3	20	are	be	AUX
ejpam-6008	3	21	investigated	investigate	VERB
ejpam-6008	3	22	.	.	PUNCT
ejpam-6008	4	1	2020	2020	NUM
ejpam-6008	4	2	mathematics	mathematic	NOUN
ejpam-6008	4	3	subject	subject	NOUN
ejpam-6008	4	4	classifications	classification	NOUN
ejpam-6008	4	5	:	:	PUNCT
ejpam-6008	4	6	54c08	54c08	NUM
ejpam-6008	4	7	,	,	PUNCT
ejpam-6008	4	8	54c60	54c60	NUM
ejpam-6008	4	9	key	key	ADJ
ejpam-6008	4	10	words	word	NOUN
ejpam-6008	4	11	and	and	CCONJ
ejpam-6008	4	12	phrases	phrase	NOUN
ejpam-6008	4	13	:	:	PUNCT
ejpam-6008	4	14	upper	upper	ADJ
ejpam-6008	4	15	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	4	16	,	,	PUNCT
ejpam-6008	4	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	4	18	multifunction	multifunction	NOUN
ejpam-6008	4	19	,	,	PUNCT
ejpam-6008	4	20	lower	low	ADJ
ejpam-6008	4	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	4	22	,	,	PUNCT
ejpam-6008	4	23	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	4	24	multifunction	multifunction	NOUN
ejpam-6008	4	25	1	1	NUM
ejpam-6008	4	26	.	.	PUNCT
ejpam-6008	5	1	introduction	introduction	NOUN
ejpam-6008	5	2	weaker	weak	ADJ
ejpam-6008	5	3	and	and	CCONJ
ejpam-6008	5	4	stronger	strong	ADJ
ejpam-6008	5	5	forms	form	NOUN
ejpam-6008	5	6	of	of	ADP
ejpam-6008	5	7	open	open	ADJ
ejpam-6008	5	8	sets	set	NOUN
ejpam-6008	5	9	in	in	ADP
ejpam-6008	5	10	topological	topological	ADJ
ejpam-6008	5	11	spaces	space	NOUN
ejpam-6008	5	12	such	such	ADJ
ejpam-6008	5	13	as	as	ADP
ejpam-6008	5	14	semi	semi	ADJ
ejpam-6008	5	15	-	-	ADJ
ejpam-6008	5	16	open	open	ADJ
ejpam-6008	5	17	sets	set	NOUN
ejpam-6008	5	18	,	,	PUNCT
ejpam-6008	5	19	preopen	preopen	ADJ
ejpam-6008	5	20	sets	set	NOUN
ejpam-6008	5	21	,	,	PUNCT
ejpam-6008	5	22	α	α	NOUN
ejpam-6008	5	23	-	-	ADJ
ejpam-6008	5	24	open	open	ADJ
ejpam-6008	5	25	sets	set	NOUN
ejpam-6008	5	26	,	,	PUNCT
ejpam-6008	5	27	β	β	ADJ
ejpam-6008	5	28	-	-	ADJ
ejpam-6008	5	29	open	open	ADJ
ejpam-6008	5	30	sets	set	NOUN
ejpam-6008	5	31	,	,	PUNCT
ejpam-6008	5	32	δ	δ	NOUN
ejpam-6008	5	33	-	-	ADJ
ejpam-6008	5	34	open	open	ADJ
ejpam-6008	5	35	sets	set	NOUN
ejpam-6008	5	36	and	and	CCONJ
ejpam-6008	5	37	θ	θ	ADJ
ejpam-6008	5	38	-	-	ADJ
ejpam-6008	5	39	open	open	ADJ
ejpam-6008	5	40	sets	set	NOUN
ejpam-6008	5	41	play	play	VERB
ejpam-6008	5	42	an	an	DET
ejpam-6008	5	43	important	important	ADJ
ejpam-6008	5	44	role	role	NOUN
ejpam-6008	5	45	in	in	ADP
ejpam-6008	5	46	the	the	DET
ejpam-6008	5	47	researches	research	NOUN
ejpam-6008	5	48	of	of	ADP
ejpam-6008	5	49	generalizations	generalization	NOUN
ejpam-6008	5	50	of	of	ADP
ejpam-6008	5	51	continuity	continuity	NOUN
ejpam-6008	5	52	.	.	PUNCT
ejpam-6008	6	1	by	by	ADP
ejpam-6008	6	2	using	use	VERB
ejpam-6008	6	3	these	these	DET
ejpam-6008	6	4	sets	set	NOUN
ejpam-6008	6	5	many	many	ADJ
ejpam-6008	6	6	authors	author	NOUN
ejpam-6008	6	7	introduced	introduce	VERB
ejpam-6008	6	8	and	and	CCONJ
ejpam-6008	6	9	investigated	investigate	VERB
ejpam-6008	6	10	various	various	ADJ
ejpam-6008	6	11	types	type	NOUN
ejpam-6008	6	12	of	of	ADP
ejpam-6008	6	13	continuity	continuity	NOUN
ejpam-6008	6	14	.	.	PUNCT
ejpam-6008	7	1	viriyapong	viriyapong	PROPN
ejpam-6008	8	1	and	and	CCONJ
ejpam-6008	8	2	boonpok	boonpok	VERB
ejpam-6008	9	1	[	[	X
ejpam-6008	9	2	1	1	NUM
ejpam-6008	9	3	]	]	PUNCT
ejpam-6008	9	4	investigated	investigate	VERB
ejpam-6008	9	5	some	some	DET
ejpam-6008	9	6	characterizations	characterization	NOUN
ejpam-6008	9	7	of	of	ADP
ejpam-6008	9	8	(	(	PUNCT
ejpam-6008	9	9	λ	λ	PROPN
ejpam-6008	9	10	,	,	PUNCT
ejpam-6008	9	11	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	9	12	functions	function	NOUN
ejpam-6008	9	13	by	by	ADP
ejpam-6008	9	14	utilizing	utilize	VERB
ejpam-6008	9	15	the	the	DET
ejpam-6008	9	16	notions	notion	NOUN
ejpam-6008	9	17	of	of	ADP
ejpam-6008	9	18	(	(	PUNCT
ejpam-6008	9	19	λ	λ	PROPN
ejpam-6008	9	20	,	,	PUNCT
ejpam-6008	9	21	sp)-open	sp)-open	ADJ
ejpam-6008	9	22	sets	set	NOUN
ejpam-6008	9	23	and	and	CCONJ
ejpam-6008	9	24	(	(	PUNCT
ejpam-6008	9	25	λ	λ	PROPN
ejpam-6008	9	26	,	,	PUNCT
ejpam-6008	9	27	sp)-closed	sp)-close	VERB
ejpam-6008	9	28	sets	set	NOUN
ejpam-6008	9	29	due	due	ADP
ejpam-6008	9	30	to	to	ADP
ejpam-6008	9	31	boonpok	boonpok	NOUN
ejpam-6008	9	32	and	and	CCONJ
ejpam-6008	9	33	khampakdee	khampakdee	NOUN
ejpam-6008	9	34	[	[	X
ejpam-6008	9	35	2	2	NUM
ejpam-6008	9	36	]	]	PUNCT
ejpam-6008	9	37	.	.	PUNCT
ejpam-6008	10	1	dungthaisong	dungthaisong	NOUN
ejpam-6008	10	2	et	et	PROPN
ejpam-6008	10	3	al	al	PROPN
ejpam-6008	10	4	.	.	PUNCT
ejpam-6008	11	1	[	[	X
ejpam-6008	11	2	3	3	NUM
ejpam-6008	11	3	]	]	PUNCT
ejpam-6008	11	4	introduced	introduce	VERB
ejpam-6008	11	5	and	and	CCONJ
ejpam-6008	11	6	studied	study	VERB
ejpam-6008	11	7	the	the	DET
ejpam-6008	11	8	concept	concept	NOUN
ejpam-6008	11	9	of	of	ADP
ejpam-6008	11	10	g(m	g(m	ADJ
ejpam-6008	11	11	,	,	PUNCT
ejpam-6008	11	12	n)-continuous	n)-continuous	ADJ
ejpam-6008	11	13	functions	function	NOUN
ejpam-6008	11	14	.	.	PUNCT
ejpam-6008	12	1	duangphui	duangphui	NOUN
ejpam-6008	12	2	et	et	PROPN
ejpam-6008	12	3	al	al	PROPN
ejpam-6008	12	4	.	.	PUNCT
ejpam-6008	13	1	[	[	X
ejpam-6008	13	2	4	4	X
ejpam-6008	13	3	]	]	PUNCT
ejpam-6008	13	4	introduced	introduce	VERB
ejpam-6008	13	5	and	and	CCONJ
ejpam-6008	13	6	investigated	investigate	VERB
ejpam-6008	13	7	the	the	DET
ejpam-6008	13	8	notion	notion	NOUN
ejpam-6008	13	9	of	of	ADP
ejpam-6008	13	10	(	(	PUNCT
ejpam-6008	13	11	µ	µ	NOUN
ejpam-6008	13	12	,	,	PUNCT
ejpam-6008	13	13	µ′)(m	µ′)(m	VERB
ejpam-6008	13	14	,	,	PUNCT
ejpam-6008	13	15	n)continuous	n)continuous	ADJ
ejpam-6008	13	16	functions	function	NOUN
ejpam-6008	13	17	.	.	PUNCT
ejpam-6008	14	1	furthermore	furthermore	ADV
ejpam-6008	14	2	,	,	PUNCT
ejpam-6008	14	3	several	several	ADJ
ejpam-6008	14	4	characterizations	characterization	NOUN
ejpam-6008	14	5	of	of	ADP
ejpam-6008	14	6	almost	almost	ADV
ejpam-6008	14	7	(	(	PUNCT
ejpam-6008	14	8	λ	λ	PROPN
ejpam-6008	14	9	,	,	PUNCT
ejpam-6008	14	10	p)-continuous	p)-continuous	ADJ
ejpam-6008	14	11	functions	function	NOUN
ejpam-6008	14	12	,	,	PUNCT
ejpam-6008	14	13	strongly	strongly	ADV
ejpam-6008	14	14	θ(λ	θ(λ	PROPN
ejpam-6008	14	15	,	,	PUNCT
ejpam-6008	14	16	p)-continuous	p)-continuous	ADJ
ejpam-6008	14	17	functions	function	NOUN
ejpam-6008	14	18	,	,	PUNCT
ejpam-6008	14	19	almost	almost	ADV
ejpam-6008	14	20	strongly	strongly	ADV
ejpam-6008	14	21	θ(λ	θ(λ	VERB
ejpam-6008	14	22	,	,	PUNCT
ejpam-6008	14	23	p)-continuous	p)-continuous	ADJ
ejpam-6008	14	24	functions	function	NOUN
ejpam-6008	14	25	,	,	PUNCT
ejpam-6008	14	26	θ(λ	θ(λ	PROPN
ejpam-6008	14	27	,	,	PUNCT
ejpam-6008	14	28	p)-continuous	p)-continuous	ADJ
ejpam-6008	14	29	functions	function	NOUN
ejpam-6008	14	30	,	,	PUNCT
ejpam-6008	14	31	weakly	weakly	ADJ
ejpam-6008	14	32	(	(	PUNCT
ejpam-6008	14	33	λ	λ	PROPN
ejpam-6008	14	34	,	,	PUNCT
ejpam-6008	14	35	b)-continuous	b)-continuous	ADJ
ejpam-6008	14	36	functions	function	NOUN
ejpam-6008	14	37	,	,	PUNCT
ejpam-6008	14	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-6008	14	39	functions	function	NOUN
ejpam-6008	14	40	,	,	PUNCT
ejpam-6008	14	41	(	(	PUNCT
ejpam-6008	14	42	λ	λ	NOUN
ejpam-6008	14	43	,	,	PUNCT
ejpam-6008	14	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-6008	14	45	functions	function	NOUN
ejpam-6008	14	46	,	,	PUNCT
ejpam-6008	14	47	⋆-continuous	⋆-continuous	ADJ
ejpam-6008	14	48	functions	function	NOUN
ejpam-6008	14	49	,	,	PUNCT
ejpam-6008	14	50	θ	θ	PROPN
ejpam-6008	14	51	-	-	ADJ
ejpam-6008	14	52	i	i	NOUN
ejpam-6008	14	53	-continuous	-continuous	ADJ
ejpam-6008	14	54	functions	function	NOUN
ejpam-6008	14	55	,	,	PUNCT
ejpam-6008	14	56	almost	almost	ADV
ejpam-6008	14	57	(	(	PUNCT
ejpam-6008	14	58	g	g	NOUN
ejpam-6008	14	59	,	,	PUNCT
ejpam-6008	14	60	m)-continuous	m)-continuous	ADJ
ejpam-6008	14	61	functions	function	NOUN
ejpam-6008	14	62	,	,	PUNCT
ejpam-6008	14	63	pairwise	pairwise	NOUN
ejpam-6008	14	64	almostm	almostm	NOUN
ejpam-6008	14	65	-continuous	-continuous	ADJ
ejpam-6008	14	66	functions	function	NOUN
ejpam-6008	14	67	,	,	PUNCT
ejpam-6008	14	68	(	(	PUNCT
ejpam-6008	14	69	τ1	τ1	NOUN
ejpam-6008	14	70	,	,	PUNCT
ejpam-6008	14	71	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	14	72	functions	function	NOUN
ejpam-6008	14	73	,	,	PUNCT
ejpam-6008	14	74	almost	almost	ADV
ejpam-6008	14	75	(	(	PUNCT
ejpam-6008	14	76	τ1	τ1	NOUN
ejpam-6008	14	77	,	,	PUNCT
ejpam-6008	14	78	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	14	79	functions	function	NOUN
ejpam-6008	14	80	,	,	PUNCT
ejpam-6008	14	81	weakly	weakly	ADJ
ejpam-6008	14	82	(	(	PUNCT
ejpam-6008	14	83	τ1	τ1	NOUN
ejpam-6008	14	84	,	,	PUNCT
ejpam-6008	14	85	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	14	86	functions	function	NOUN
ejpam-6008	14	87	and	and	CCONJ
ejpam-6008	14	88	slightly	slightly	ADV
ejpam-6008	14	89	(	(	PUNCT
ejpam-6008	14	90	τ1	τ1	NOUN
ejpam-6008	14	91	,	,	PUNCT
ejpam-6008	14	92	τ2)s	τ2)s	ADJ
ejpam-6008	14	93	-	-	PUNCT
ejpam-6008	14	94	continuous	continuous	ADJ
ejpam-6008	14	95	functions	function	NOUN
ejpam-6008	14	96	were	be	AUX
ejpam-6008	14	97	presented	present	VERB
ejpam-6008	14	98	in	in	ADP
ejpam-6008	14	99	[	[	X
ejpam-6008	14	100	5	5	NUM
ejpam-6008	14	101	]	]	PUNCT
ejpam-6008	14	102	,	,	PUNCT
ejpam-6008	14	103	[	[	X
ejpam-6008	14	104	6	6	NUM
ejpam-6008	14	105	]	]	PUNCT
ejpam-6008	14	106	,	,	PUNCT
ejpam-6008	14	107	[	[	X
ejpam-6008	14	108	7	7	NUM
ejpam-6008	14	109	]	]	PUNCT
ejpam-6008	14	110	,	,	PUNCT
ejpam-6008	14	111	[	[	X
ejpam-6008	14	112	8	8	NUM
ejpam-6008	14	113	]	]	PUNCT
ejpam-6008	14	114	,	,	PUNCT
ejpam-6008	15	1	[	[	X
ejpam-6008	15	2	9	9	NUM
ejpam-6008	15	3	]	]	PUNCT
ejpam-6008	15	4	,	,	PUNCT
ejpam-6008	15	5	∗corresponding	∗corresponde	VERB
ejpam-6008	15	6	author	author	NOUN
ejpam-6008	15	7	.	.	PUNCT
ejpam-6008	16	1	doi	doi	NOUN
ejpam-6008	16	2	:	:	PUNCT
ejpam-6008	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6008	https://doi.org/10.29020/nybg.ejpam.v18i2.6008	NOUN
ejpam-6008	16	4	email	email	NOUN
ejpam-6008	16	5	addresses	address	NOUN
ejpam-6008	16	6	:	:	PUNCT
ejpam-6008	16	7	nongluk.h@msu.ac.th	nongluk.h@msu.ac.th	PROPN
ejpam-6008	16	8	(	(	PUNCT
ejpam-6008	16	9	n.	n.	NOUN
ejpam-6008	16	10	viriyapong	viriyapong	PROPN
ejpam-6008	16	11	)	)	PUNCT
ejpam-6008	16	12	,	,	PUNCT
ejpam-6008	16	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-6008	16	14	(	(	PUNCT
ejpam-6008	16	15	a.	a.	PROPN
ejpam-6008	16	16	sama	sama	PROPN
ejpam-6008	16	17	-	-	PUNCT
ejpam-6008	16	18	ae	ae	PROPN
ejpam-6008	16	19	)	)	PUNCT
ejpam-6008	16	20	,	,	PUNCT
ejpam-6008	16	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6008	16	22	(	(	PUNCT
ejpam-6008	16	23	c.	c.	PROPN
ejpam-6008	16	24	boonpok	boonpok	PROPN
ejpam-6008	16	25	)	)	PUNCT
ejpam-6008	16	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6008	17	1	1	1	NUM
ejpam-6008	17	2	copyright	copyright	NOUN
ejpam-6008	17	3	:	:	PUNCT
ejpam-6008	17	4	©	©	PROPN
ejpam-6008	17	5	2025	2025	NUM
ejpam-6008	17	6	the	the	DET
ejpam-6008	17	7	author(s	author(s	NOUN
ejpam-6008	17	8	)	)	PUNCT
ejpam-6008	17	9	.	.	PUNCT
ejpam-6008	18	1	(	(	PUNCT
ejpam-6008	18	2	cc	cc	NOUN
ejpam-6008	18	3	by	by	ADP
ejpam-6008	18	4	-	-	PUNCT
ejpam-6008	18	5	nc	nc	PROPN
ejpam-6008	18	6	4.0	4.0	NUM
ejpam-6008	18	7	)	)	PUNCT
ejpam-6008	18	8	n.	n.	NOUN
ejpam-6008	18	9	viriyapong	viriyapong	PROPN
ejpam-6008	18	10	,	,	PUNCT
ejpam-6008	18	11	a.	a.	PROPN
ejpam-6008	18	12	sama	sama	PROPN
ejpam-6008	18	13	-	-	PUNCT
ejpam-6008	18	14	ae	ae	PROPN
ejpam-6008	18	15	,	,	PUNCT
ejpam-6008	18	16	c.	c.	PROPN
ejpam-6008	18	17	boonpok	boonpok	PROPN
ejpam-6008	18	18	/	/	SYM
ejpam-6008	18	19	eur	eur	PROPN
ejpam-6008	18	20	.	.	PUNCT
ejpam-6008	19	1	j.	j.	PROPN
ejpam-6008	19	2	pure	pure	PROPN
ejpam-6008	19	3	appl	appl	PROPN
ejpam-6008	19	4	.	.	PROPN
ejpam-6008	19	5	math	math	PROPN
ejpam-6008	19	6	,	,	PUNCT
ejpam-6008	19	7	18	18	NUM
ejpam-6008	19	8	(	(	PUNCT
ejpam-6008	19	9	2	2	NUM
ejpam-6008	19	10	)	)	PUNCT
ejpam-6008	19	11	(	(	PUNCT
ejpam-6008	19	12	2025	2025	NUM
ejpam-6008	19	13	)	)	PUNCT
ejpam-6008	19	14	,	,	PUNCT
ejpam-6008	19	15	6008	6008	NUM
ejpam-6008	19	16	2	2	NUM
ejpam-6008	19	17	of	of	ADP
ejpam-6008	19	18	15	15	NUM
ejpam-6008	19	19	[	[	SYM
ejpam-6008	19	20	10	10	NUM
ejpam-6008	19	21	]	]	PUNCT
ejpam-6008	19	22	,	,	PUNCT
ejpam-6008	20	1	[	[	X
ejpam-6008	20	2	11	11	NUM
ejpam-6008	20	3	]	]	PUNCT
ejpam-6008	20	4	,	,	PUNCT
ejpam-6008	20	5	[	[	X
ejpam-6008	20	6	12	12	NUM
ejpam-6008	20	7	]	]	PUNCT
ejpam-6008	20	8	,	,	PUNCT
ejpam-6008	21	1	[	[	X
ejpam-6008	21	2	13	13	NUM
ejpam-6008	21	3	]	]	PUNCT
ejpam-6008	21	4	,	,	PUNCT
ejpam-6008	21	5	[	[	X
ejpam-6008	21	6	14	14	NUM
ejpam-6008	21	7	]	]	PUNCT
ejpam-6008	21	8	,	,	PUNCT
ejpam-6008	21	9	[	[	X
ejpam-6008	21	10	15	15	NUM
ejpam-6008	21	11	]	]	PUNCT
ejpam-6008	21	12	,	,	PUNCT
ejpam-6008	21	13	[	[	X
ejpam-6008	21	14	16	16	NUM
ejpam-6008	21	15	]	]	PUNCT
ejpam-6008	21	16	,	,	PUNCT
ejpam-6008	22	1	[	[	X
ejpam-6008	22	2	17	17	NUM
ejpam-6008	22	3	]	]	PUNCT
ejpam-6008	22	4	,	,	PUNCT
ejpam-6008	22	5	[	[	X
ejpam-6008	22	6	18	18	NUM
ejpam-6008	22	7	]	]	PUNCT
ejpam-6008	22	8	and	and	CCONJ
ejpam-6008	22	9	[	[	X
ejpam-6008	22	10	19	19	NUM
ejpam-6008	22	11	]	]	PUNCT
ejpam-6008	22	12	,	,	PUNCT
ejpam-6008	22	13	respectively	respectively	ADV
ejpam-6008	22	14	.	.	PUNCT
ejpam-6008	23	1	kong	kong	PROPN
ejpam-6008	23	2	-	-	PUNCT
ejpam-6008	23	3	ied	ied	PROPN
ejpam-6008	23	4	at	at	ADP
ejpam-6008	23	5	al	al	PROPN
ejpam-6008	23	6	.	.	PUNCT
ejpam-6008	24	1	[	[	X
ejpam-6008	24	2	20	20	NUM
ejpam-6008	24	3	]	]	PUNCT
ejpam-6008	24	4	introduced	introduce	VERB
ejpam-6008	24	5	and	and	CCONJ
ejpam-6008	24	6	studied	study	VERB
ejpam-6008	24	7	the	the	DET
ejpam-6008	24	8	concept	concept	NOUN
ejpam-6008	24	9	of	of	ADP
ejpam-6008	24	10	almost	almost	ADV
ejpam-6008	24	11	quasi	quasi	X
ejpam-6008	24	12	(	(	PUNCT
ejpam-6008	24	13	τ1	τ1	NOUN
ejpam-6008	24	14	,	,	PUNCT
ejpam-6008	24	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	24	16	functions	function	NOUN
ejpam-6008	24	17	.	.	PUNCT
ejpam-6008	25	1	chiangpradit	chiangpradit	NOUN
ejpam-6008	25	2	et	et	PROPN
ejpam-6008	25	3	al	al	PROPN
ejpam-6008	25	4	.	.	PUNCT
ejpam-6008	26	1	[	[	X
ejpam-6008	26	2	21	21	NUM
ejpam-6008	26	3	]	]	PUNCT
ejpam-6008	26	4	introduced	introduce	VERB
ejpam-6008	26	5	and	and	CCONJ
ejpam-6008	26	6	investigated	investigate	VERB
ejpam-6008	26	7	the	the	DET
ejpam-6008	26	8	notion	notion	NOUN
ejpam-6008	26	9	of	of	ADP
ejpam-6008	26	10	weakly	weakly	ADJ
ejpam-6008	26	11	quasi	quasi	NOUN
ejpam-6008	26	12	(	(	PUNCT
ejpam-6008	26	13	τ1	τ1	NOUN
ejpam-6008	26	14	,	,	PUNCT
ejpam-6008	26	15	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	26	16	functions	function	NOUN
ejpam-6008	26	17	.	.	PUNCT
ejpam-6008	27	1	thongmoon	thongmoon	NOUN
ejpam-6008	27	2	et	et	PROPN
ejpam-6008	27	3	al	al	PROPN
ejpam-6008	27	4	.	.	PUNCT
ejpam-6008	28	1	[	[	X
ejpam-6008	28	2	22	22	NUM
ejpam-6008	28	3	]	]	PUNCT
ejpam-6008	28	4	introduced	introduce	VERB
ejpam-6008	28	5	and	and	CCONJ
ejpam-6008	28	6	studied	study	VERB
ejpam-6008	28	7	the	the	DET
ejpam-6008	28	8	notion	notion	NOUN
ejpam-6008	28	9	of	of	ADP
ejpam-6008	28	10	rarely	rarely	ADV
ejpam-6008	28	11	(	(	PUNCT
ejpam-6008	28	12	τ1	τ1	NOUN
ejpam-6008	28	13	,	,	PUNCT
ejpam-6008	28	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	28	15	functions	function	NOUN
ejpam-6008	28	16	.	.	PUNCT
ejpam-6008	29	1	srisarakham	srisarakham	PROPN
ejpam-6008	29	2	et	et	PROPN
ejpam-6008	29	3	al	al	PROPN
ejpam-6008	29	4	.	.	PUNCT
ejpam-6008	30	1	[	[	X
ejpam-6008	30	2	23	23	NUM
ejpam-6008	30	3	]	]	PUNCT
ejpam-6008	30	4	introduced	introduce	VERB
ejpam-6008	30	5	and	and	CCONJ
ejpam-6008	30	6	investigated	investigate	VERB
ejpam-6008	30	7	the	the	DET
ejpam-6008	30	8	concept	concept	NOUN
ejpam-6008	30	9	of	of	ADP
ejpam-6008	30	10	faintly	faintly	ADV
ejpam-6008	30	11	(	(	PUNCT
ejpam-6008	30	12	τ1	τ1	PROPN
ejpam-6008	30	13	,	,	PUNCT
ejpam-6008	30	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	30	15	functions	function	NOUN
ejpam-6008	30	16	.	.	PUNCT
ejpam-6008	31	1	on	on	ADP
ejpam-6008	31	2	the	the	DET
ejpam-6008	31	3	other	other	ADJ
ejpam-6008	31	4	hand	hand	NOUN
ejpam-6008	31	5	,	,	PUNCT
ejpam-6008	31	6	the	the	DET
ejpam-6008	31	7	present	present	ADJ
ejpam-6008	31	8	authors	author	NOUN
ejpam-6008	31	9	introduced	introduce	VERB
ejpam-6008	31	10	and	and	CCONJ
ejpam-6008	31	11	studied	study	VERB
ejpam-6008	31	12	the	the	DET
ejpam-6008	31	13	notions	notion	NOUN
ejpam-6008	31	14	of	of	ADP
ejpam-6008	31	15	δ(τ1	δ(τ1	NOUN
ejpam-6008	31	16	,	,	PUNCT
ejpam-6008	31	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	31	18	functions	function	NOUN
ejpam-6008	31	19	[	[	X
ejpam-6008	31	20	24	24	NUM
ejpam-6008	31	21	]	]	PUNCT
ejpam-6008	31	22	,	,	PUNCT
ejpam-6008	31	23	quasi	quasi	NOUN
ejpam-6008	31	24	θ(τ1	θ(τ1	PROPN
ejpam-6008	31	25	,	,	PUNCT
ejpam-6008	31	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	31	27	functions	function	NOUN
ejpam-6008	31	28	[	[	X
ejpam-6008	31	29	25	25	NUM
ejpam-6008	31	30	]	]	PUNCT
ejpam-6008	31	31	,	,	PUNCT
ejpam-6008	31	32	almost	almost	ADV
ejpam-6008	31	33	weakly	weakly	ADJ
ejpam-6008	31	34	(	(	PUNCT
ejpam-6008	31	35	τ1	τ1	NOUN
ejpam-6008	31	36	,	,	PUNCT
ejpam-6008	31	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	31	38	functions	function	NOUN
ejpam-6008	31	39	[	[	X
ejpam-6008	31	40	26	26	NUM
ejpam-6008	31	41	]	]	PUNCT
ejpam-6008	31	42	and	and	CCONJ
ejpam-6008	31	43	almost	almost	ADV
ejpam-6008	31	44	nearly	nearly	ADV
ejpam-6008	31	45	(	(	PUNCT
ejpam-6008	31	46	τ1	τ1	NOUN
ejpam-6008	31	47	,	,	PUNCT
ejpam-6008	31	48	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	31	49	functions	function	NOUN
ejpam-6008	31	50	[	[	X
ejpam-6008	31	51	27	27	NUM
ejpam-6008	31	52	]	]	PUNCT
ejpam-6008	31	53	.	.	PUNCT
ejpam-6008	32	1	in	in	ADP
ejpam-6008	32	2	1966	1966	NUM
ejpam-6008	32	3	,	,	PUNCT
ejpam-6008	32	4	dontchev	dontchev	ADJ
ejpam-6008	32	5	[	[	X
ejpam-6008	32	6	28	28	NUM
ejpam-6008	32	7	]	]	PUNCT
ejpam-6008	32	8	introduced	introduce	VERB
ejpam-6008	32	9	the	the	DET
ejpam-6008	32	10	notion	notion	NOUN
ejpam-6008	32	11	of	of	ADP
ejpam-6008	32	12	contra	contra	PROPN
ejpam-6008	32	13	-	-	NOUN
ejpam-6008	32	14	continuity	continuity	NOUN
ejpam-6008	32	15	in	in	ADP
ejpam-6008	32	16	topological	topological	ADJ
ejpam-6008	32	17	spaces	space	NOUN
ejpam-6008	32	18	.	.	PUNCT
ejpam-6008	33	1	dontchev	dontchev	NOUN
ejpam-6008	33	2	and	and	CCONJ
ejpam-6008	33	3	noiri	noiri	ADV
ejpam-6008	34	1	[	[	X
ejpam-6008	34	2	29	29	NUM
ejpam-6008	34	3	]	]	PUNCT
ejpam-6008	34	4	introduced	introduce	VERB
ejpam-6008	34	5	and	and	CCONJ
ejpam-6008	34	6	studied	study	VERB
ejpam-6008	34	7	the	the	DET
ejpam-6008	34	8	concept	concept	NOUN
ejpam-6008	34	9	of	of	ADP
ejpam-6008	34	10	rc	rc	NOUN
ejpam-6008	34	11	-	-	NOUN
ejpam-6008	34	12	continuity	continuity	NOUN
ejpam-6008	34	13	between	between	ADP
ejpam-6008	34	14	topological	topological	ADJ
ejpam-6008	34	15	spaces	space	NOUN
ejpam-6008	34	16	which	which	PRON
ejpam-6008	34	17	is	be	AUX
ejpam-6008	34	18	weaker	weak	ADJ
ejpam-6008	34	19	than	than	ADP
ejpam-6008	34	20	contra	contra	NOUN
ejpam-6008	34	21	-	-	NOUN
ejpam-6008	34	22	continuity	continuity	NOUN
ejpam-6008	34	23	.	.	PUNCT
ejpam-6008	35	1	jafari	jafari	PROPN
ejpam-6008	35	2	and	and	CCONJ
ejpam-6008	35	3	noiri	noiri	ADV
ejpam-6008	36	1	[	[	X
ejpam-6008	36	2	30	30	NUM
ejpam-6008	36	3	]	]	PUNCT
ejpam-6008	36	4	introduced	introduce	VERB
ejpam-6008	36	5	a	a	DET
ejpam-6008	36	6	new	new	ADJ
ejpam-6008	36	7	class	class	NOUN
ejpam-6008	36	8	of	of	ADP
ejpam-6008	36	9	function	function	NOUN
ejpam-6008	36	10	called	call	VERB
ejpam-6008	36	11	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6008	36	12	functions	function	NOUN
ejpam-6008	36	13	which	which	PRON
ejpam-6008	36	14	is	be	AUX
ejpam-6008	36	15	weaker	weak	ADJ
ejpam-6008	36	16	than	than	ADP
ejpam-6008	36	17	contra	contra	ADJ
ejpam-6008	36	18	-	-	ADJ
ejpam-6008	36	19	continuous	continuous	ADJ
ejpam-6008	36	20	functions	function	NOUN
ejpam-6008	36	21	and	and	CCONJ
ejpam-6008	36	22	studied	study	VERB
ejpam-6008	36	23	several	several	ADJ
ejpam-6008	36	24	basic	basic	ADJ
ejpam-6008	36	25	properties	property	NOUN
ejpam-6008	36	26	of	of	ADP
ejpam-6008	36	27	contra	contra	ADJ
ejpam-6008	36	28	-	-	ADJ
ejpam-6008	36	29	precontinuous	precontinuous	ADJ
ejpam-6008	36	30	functions	function	NOUN
ejpam-6008	36	31	.	.	PUNCT
ejpam-6008	37	1	ekici	ekici	NOUN
ejpam-6008	38	1	[	[	X
ejpam-6008	38	2	31	31	NUM
ejpam-6008	38	3	]	]	PUNCT
ejpam-6008	38	4	introduced	introduce	VERB
ejpam-6008	38	5	and	and	CCONJ
ejpam-6008	38	6	studied	study	VERB
ejpam-6008	38	7	a	a	DET
ejpam-6008	38	8	new	new	ADJ
ejpam-6008	38	9	class	class	NOUN
ejpam-6008	38	10	of	of	ADP
ejpam-6008	38	11	functions	function	NOUN
ejpam-6008	38	12	called	call	VERB
ejpam-6008	38	13	almost	almost	ADV
ejpam-6008	38	14	contra	contra	ADJ
ejpam-6008	38	15	-	-	ADJ
ejpam-6008	38	16	precontinuous	precontinuous	ADJ
ejpam-6008	38	17	functions	function	NOUN
ejpam-6008	38	18	which	which	PRON
ejpam-6008	38	19	generalize	generalize	VERB
ejpam-6008	38	20	classes	class	NOUN
ejpam-6008	38	21	of	of	ADP
ejpam-6008	38	22	regular	regular	ADJ
ejpam-6008	38	23	set	set	NOUN
ejpam-6008	38	24	-	-	PUNCT
ejpam-6008	38	25	connected	connect	VERB
ejpam-6008	38	26	functions	function	NOUN
ejpam-6008	38	27	[	[	X
ejpam-6008	38	28	32	32	NUM
ejpam-6008	38	29	]	]	PUNCT
ejpam-6008	38	30	,	,	PUNCT
ejpam-6008	38	31	contra	contra	ADJ
ejpam-6008	38	32	-	-	ADJ
ejpam-6008	38	33	precontinuous	precontinuous	ADJ
ejpam-6008	38	34	functions	function	NOUN
ejpam-6008	38	35	[	[	X
ejpam-6008	38	36	30	30	NUM
ejpam-6008	38	37	]	]	PUNCT
ejpam-6008	38	38	,	,	PUNCT
ejpam-6008	38	39	contra	contra	ADJ
ejpam-6008	38	40	-	-	ADJ
ejpam-6008	38	41	continuous	continuous	ADJ
ejpam-6008	38	42	functions	function	NOUN
ejpam-6008	38	43	[	[	X
ejpam-6008	38	44	28	28	NUM
ejpam-6008	38	45	]	]	X
ejpam-6008	38	46	,	,	PUNCT
ejpam-6008	38	47	almost	almost	ADV
ejpam-6008	38	48	s	s	NOUN
ejpam-6008	38	49	-	-	PUNCT
ejpam-6008	38	50	continuous	continuous	ADJ
ejpam-6008	38	51	functions	function	NOUN
ejpam-6008	38	52	[	[	X
ejpam-6008	38	53	33	33	NUM
ejpam-6008	38	54	]	]	PUNCT
ejpam-6008	38	55	and	and	CCONJ
ejpam-6008	38	56	perfectly	perfectly	ADV
ejpam-6008	38	57	continuous	continuous	ADJ
ejpam-6008	38	58	functions	function	NOUN
ejpam-6008	38	59	[	[	X
ejpam-6008	38	60	34	34	NUM
ejpam-6008	38	61	]	]	PUNCT
ejpam-6008	38	62	.	.	PUNCT
ejpam-6008	39	1	in	in	ADP
ejpam-6008	39	2	2008	2008	NUM
ejpam-6008	39	3	,	,	PUNCT
ejpam-6008	39	4	ekici	ekici	NOUN
ejpam-6008	39	5	et	et	PROPN
ejpam-6008	39	6	al	al	PROPN
ejpam-6008	39	7	.	.	PUNCT
ejpam-6008	40	1	[	[	X
ejpam-6008	40	2	35	35	NUM
ejpam-6008	40	3	]	]	PUNCT
ejpam-6008	40	4	extended	extend	VERB
ejpam-6008	40	5	the	the	DET
ejpam-6008	40	6	notion	notion	NOUN
ejpam-6008	40	7	of	of	ADP
ejpam-6008	40	8	contra	contra	ADJ
ejpam-6008	40	9	-	-	ADJ
ejpam-6008	40	10	continuous	continuous	ADJ
ejpam-6008	40	11	functions	function	NOUN
ejpam-6008	40	12	to	to	ADP
ejpam-6008	40	13	the	the	DET
ejpam-6008	40	14	setting	setting	NOUN
ejpam-6008	40	15	of	of	ADP
ejpam-6008	40	16	multifunctions	multifunction	NOUN
ejpam-6008	40	17	.	.	PUNCT
ejpam-6008	41	1	noiri	noiri	PROPN
ejpam-6008	41	2	and	and	CCONJ
ejpam-6008	41	3	popa	popa	NOUN
ejpam-6008	41	4	[	[	X
ejpam-6008	41	5	36	36	NUM
ejpam-6008	41	6	]	]	PUNCT
ejpam-6008	41	7	introduced	introduce	VERB
ejpam-6008	41	8	the	the	DET
ejpam-6008	41	9	notion	notion	NOUN
ejpam-6008	41	10	of	of	ADP
ejpam-6008	41	11	weakly	weakly	ADJ
ejpam-6008	41	12	precontinuous	precontinuous	ADJ
ejpam-6008	41	13	multifunctions	multifunction	NOUN
ejpam-6008	41	14	.	.	PUNCT
ejpam-6008	42	1	moreover	moreover	ADV
ejpam-6008	42	2	,	,	PUNCT
ejpam-6008	42	3	several	several	ADJ
ejpam-6008	42	4	characterizations	characterization	NOUN
ejpam-6008	42	5	and	and	CCONJ
ejpam-6008	42	6	some	some	DET
ejpam-6008	42	7	properties	property	NOUN
ejpam-6008	42	8	concerning	concern	VERB
ejpam-6008	42	9	(	(	PUNCT
ejpam-6008	42	10	τ1	τ1	NOUN
ejpam-6008	42	11	,	,	PUNCT
ejpam-6008	42	12	τ2)δ	τ2)δ	ADJ
ejpam-6008	42	13	-	-	PUNCT
ejpam-6008	42	14	semicontinuous	semicontinuous	ADJ
ejpam-6008	42	15	multifunctions	multifunction	NOUN
ejpam-6008	42	16	,	,	PUNCT
ejpam-6008	42	17	almost	almost	ADV
ejpam-6008	42	18	weakly	weakly	ADJ
ejpam-6008	42	19	(	(	PUNCT
ejpam-6008	42	20	τ1	τ1	NOUN
ejpam-6008	42	21	,	,	PUNCT
ejpam-6008	42	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	23	multifunctions	multifunction	NOUN
ejpam-6008	42	24	,	,	PUNCT
ejpam-6008	42	25	weakly	weakly	ADJ
ejpam-6008	42	26	quasi	quasi	NOUN
ejpam-6008	42	27	(	(	PUNCT
ejpam-6008	42	28	λ	λ	PROPN
ejpam-6008	42	29	,	,	PUNCT
ejpam-6008	42	30	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	31	multifunctions	multifunction	NOUN
ejpam-6008	42	32	,	,	PUNCT
ejpam-6008	42	33	⋆-continuous	⋆-continuous	ADJ
ejpam-6008	42	34	multifunctions	multifunction	NOUN
ejpam-6008	42	35	,	,	PUNCT
ejpam-6008	42	36	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-6008	42	37	multifunctions	multifunction	NOUN
ejpam-6008	42	38	,	,	PUNCT
ejpam-6008	42	39	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6008	42	40	multifunctions	multifunction	NOUN
ejpam-6008	42	41	,	,	PUNCT
ejpam-6008	42	42	almost	almost	ADV
ejpam-6008	42	43	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6008	42	44	multifunctions	multifunction	NOUN
ejpam-6008	42	45	,	,	PUNCT
ejpam-6008	42	46	almost	almost	ADV
ejpam-6008	42	47	quasi	quasi	VERB
ejpam-6008	42	48	⋆-continuous	⋆-continuous	ADJ
ejpam-6008	42	49	multifunctions	multifunction	NOUN
ejpam-6008	42	50	,	,	PUNCT
ejpam-6008	42	51	weakly	weakly	ADJ
ejpam-6008	42	52	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6008	42	53	multifunctions	multifunction	NOUN
ejpam-6008	42	54	,	,	PUNCT
ejpam-6008	42	55	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6008	42	56	multifunctions	multifunction	NOUN
ejpam-6008	42	57	,	,	PUNCT
ejpam-6008	42	58	weakly	weakly	ADJ
ejpam-6008	42	59	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6008	42	60	multifunctions	multifunction	NOUN
ejpam-6008	42	61	,	,	PUNCT
ejpam-6008	42	62	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-6008	42	63	continuous	continuous	ADJ
ejpam-6008	42	64	multifunctions	multifunction	NOUN
ejpam-6008	42	65	,	,	PUNCT
ejpam-6008	42	66	almost	almost	ADV
ejpam-6008	42	67	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-6008	42	68	multifunctions	multifunction	NOUN
ejpam-6008	42	69	,	,	PUNCT
ejpam-6008	42	70	weakly	weakly	ADJ
ejpam-6008	42	71	(	(	PUNCT
ejpam-6008	42	72	λ	λ	NOUN
ejpam-6008	42	73	,	,	PUNCT
ejpam-6008	42	74	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	75	multifunctions	multifunction	NOUN
ejpam-6008	42	76	,	,	PUNCT
ejpam-6008	42	77	α(λ	α(λ	PROPN
ejpam-6008	42	78	,	,	PUNCT
ejpam-6008	42	79	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	80	multifunctions	multifunction	NOUN
ejpam-6008	42	81	,	,	PUNCT
ejpam-6008	42	82	almost	almost	ADV
ejpam-6008	42	83	α(λ	α(λ	PROPN
ejpam-6008	42	84	,	,	PUNCT
ejpam-6008	42	85	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	86	multifunctions	multifunction	NOUN
ejpam-6008	42	87	,	,	PUNCT
ejpam-6008	42	88	weakly	weakly	ADJ
ejpam-6008	42	89	α(λ	α(λ	PROPN
ejpam-6008	42	90	,	,	PUNCT
ejpam-6008	42	91	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	92	multifunctions	multifunction	NOUN
ejpam-6008	42	93	,	,	PUNCT
ejpam-6008	42	94	almost	almost	ADV
ejpam-6008	42	95	β(λ	β(λ	NOUN
ejpam-6008	42	96	,	,	PUNCT
ejpam-6008	42	97	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	98	multifunctions	multifunction	NOUN
ejpam-6008	42	99	,	,	PUNCT
ejpam-6008	42	100	slightly	slightly	ADV
ejpam-6008	42	101	(	(	PUNCT
ejpam-6008	42	102	λ	λ	NOUN
ejpam-6008	42	103	,	,	PUNCT
ejpam-6008	42	104	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	42	105	multifunctions	multifunction	NOUN
ejpam-6008	42	106	,	,	PUNCT
ejpam-6008	42	107	(	(	PUNCT
ejpam-6008	42	108	τ1	τ1	NOUN
ejpam-6008	42	109	,	,	PUNCT
ejpam-6008	42	110	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	111	multifunctions	multifunction	NOUN
ejpam-6008	42	112	,	,	PUNCT
ejpam-6008	42	113	almost	almost	ADV
ejpam-6008	42	114	(	(	PUNCT
ejpam-6008	42	115	τ1	τ1	NOUN
ejpam-6008	42	116	,	,	PUNCT
ejpam-6008	42	117	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	118	multifunctions	multifunction	NOUN
ejpam-6008	42	119	,	,	PUNCT
ejpam-6008	42	120	weakly	weakly	ADJ
ejpam-6008	42	121	(	(	PUNCT
ejpam-6008	42	122	τ1	τ1	NOUN
ejpam-6008	42	123	,	,	PUNCT
ejpam-6008	42	124	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	125	multifunctions	multifunction	NOUN
ejpam-6008	42	126	,	,	PUNCT
ejpam-6008	42	127	weakly	weakly	ADJ
ejpam-6008	42	128	quasi	quasi	NOUN
ejpam-6008	42	129	(	(	PUNCT
ejpam-6008	42	130	τ1	τ1	PROPN
ejpam-6008	42	131	,	,	PUNCT
ejpam-6008	42	132	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	133	multifunctions	multifunction	NOUN
ejpam-6008	42	134	,	,	PUNCT
ejpam-6008	42	135	almost	almost	ADV
ejpam-6008	42	136	quasi	quasi	NOUN
ejpam-6008	42	137	(	(	PUNCT
ejpam-6008	42	138	τ1	τ1	NOUN
ejpam-6008	42	139	,	,	PUNCT
ejpam-6008	42	140	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	141	multifunctions	multifunction	NOUN
ejpam-6008	42	142	,	,	PUNCT
ejpam-6008	42	143	c-(τ1	c-(τ1	PROPN
ejpam-6008	42	144	,	,	PUNCT
ejpam-6008	42	145	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	146	multifunctions	multifunction	NOUN
ejpam-6008	42	147	,	,	PUNCT
ejpam-6008	42	148	c	c	NOUN
ejpam-6008	42	149	-	-	PUNCT
ejpam-6008	42	150	quasi	quasi	NOUN
ejpam-6008	42	151	(	(	PUNCT
ejpam-6008	42	152	τ1	τ1	PROPN
ejpam-6008	42	153	,	,	PUNCT
ejpam-6008	42	154	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	155	multifunctions	multifunction	NOUN
ejpam-6008	42	156	,	,	PUNCT
ejpam-6008	42	157	s-(τ1	s-(τ1	PROPN
ejpam-6008	42	158	,	,	PUNCT
ejpam-6008	42	159	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6008	42	160	multifunctions	multifunction	NOUN
ejpam-6008	42	161	,	,	PUNCT
ejpam-6008	42	162	slightly	slightly	ADV
ejpam-6008	42	163	α(τ1	α(τ1	NOUN
ejpam-6008	42	164	,	,	PUNCT
ejpam-6008	42	165	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	42	166	multifunctions	multifunction	NOUN
ejpam-6008	42	167	and	and	CCONJ
ejpam-6008	42	168	slightly	slightly	ADV
ejpam-6008	42	169	(	(	PUNCT
ejpam-6008	42	170	τ1	τ1	NOUN
ejpam-6008	42	171	,	,	PUNCT
ejpam-6008	42	172	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6008	42	173	multifunctions	multifunction	NOUN
ejpam-6008	42	174	were	be	AUX
ejpam-6008	42	175	established	establish	VERB
ejpam-6008	42	176	in	in	ADP
ejpam-6008	42	177	[	[	X
ejpam-6008	42	178	37	37	NUM
ejpam-6008	42	179	]	]	PUNCT
ejpam-6008	42	180	,	,	PUNCT
ejpam-6008	42	181	[	[	X
ejpam-6008	42	182	38	38	NUM
ejpam-6008	42	183	]	]	PUNCT
ejpam-6008	42	184	,	,	PUNCT
ejpam-6008	42	185	[	[	X
ejpam-6008	42	186	39	39	NUM
ejpam-6008	42	187	]	]	PUNCT
ejpam-6008	42	188	,	,	PUNCT
ejpam-6008	42	189	[	[	X
ejpam-6008	42	190	40	40	NUM
ejpam-6008	42	191	]	]	PUNCT
ejpam-6008	42	192	,	,	PUNCT
ejpam-6008	42	193	[	[	X
ejpam-6008	42	194	41	41	NUM
ejpam-6008	42	195	]	]	PUNCT
ejpam-6008	42	196	,	,	PUNCT
ejpam-6008	42	197	[	[	X
ejpam-6008	42	198	42	42	NUM
ejpam-6008	42	199	]	]	PUNCT
ejpam-6008	42	200	,	,	PUNCT
ejpam-6008	42	201	[	[	X
ejpam-6008	42	202	43	43	NUM
ejpam-6008	42	203	]	]	PUNCT
ejpam-6008	42	204	,	,	PUNCT
ejpam-6008	42	205	[	[	X
ejpam-6008	42	206	44	44	NUM
ejpam-6008	42	207	]	]	PUNCT
ejpam-6008	42	208	,	,	PUNCT
ejpam-6008	42	209	[	[	X
ejpam-6008	42	210	45	45	NUM
ejpam-6008	42	211	]	]	PUNCT
ejpam-6008	42	212	,	,	PUNCT
ejpam-6008	42	213	[	[	X
ejpam-6008	42	214	46	46	NUM
ejpam-6008	42	215	]	]	PUNCT
ejpam-6008	42	216	,	,	PUNCT
ejpam-6008	42	217	[	[	X
ejpam-6008	42	218	47	47	NUM
ejpam-6008	42	219	]	]	PUNCT
ejpam-6008	42	220	,	,	PUNCT
ejpam-6008	42	221	[	[	X
ejpam-6008	42	222	48	48	NUM
ejpam-6008	42	223	]	]	PUNCT
ejpam-6008	42	224	,	,	PUNCT
ejpam-6008	42	225	[	[	X
ejpam-6008	42	226	49	49	NUM
ejpam-6008	42	227	]	]	PUNCT
ejpam-6008	42	228	,	,	PUNCT
ejpam-6008	42	229	[	[	X
ejpam-6008	42	230	50	50	NUM
ejpam-6008	42	231	]	]	PUNCT
ejpam-6008	42	232	,	,	PUNCT
ejpam-6008	42	233	[	[	X
ejpam-6008	42	234	51	51	NUM
ejpam-6008	42	235	]	]	PUNCT
ejpam-6008	42	236	,	,	PUNCT
ejpam-6008	42	237	[	[	X
ejpam-6008	42	238	52	52	NUM
ejpam-6008	42	239	]	]	PUNCT
ejpam-6008	42	240	,	,	PUNCT
ejpam-6008	42	241	[	[	X
ejpam-6008	42	242	53	53	NUM
ejpam-6008	42	243	]	]	PUNCT
ejpam-6008	42	244	,	,	PUNCT
ejpam-6008	42	245	[	[	X
ejpam-6008	42	246	54	54	NUM
ejpam-6008	42	247	]	]	PUNCT
ejpam-6008	42	248	,	,	PUNCT
ejpam-6008	42	249	[	[	X
ejpam-6008	42	250	55	55	NUM
ejpam-6008	42	251	]	]	PUNCT
ejpam-6008	42	252	,	,	PUNCT
ejpam-6008	42	253	[	[	X
ejpam-6008	42	254	56	56	NUM
ejpam-6008	42	255	]	]	PUNCT
ejpam-6008	42	256	,	,	PUNCT
ejpam-6008	42	257	[	[	X
ejpam-6008	42	258	57	57	NUM
ejpam-6008	42	259	]	]	PUNCT
ejpam-6008	42	260	,	,	PUNCT
ejpam-6008	42	261	[	[	X
ejpam-6008	42	262	58	58	NUM
ejpam-6008	42	263	]	]	PUNCT
ejpam-6008	42	264	,	,	PUNCT
ejpam-6008	42	265	[	[	X
ejpam-6008	42	266	59	59	NUM
ejpam-6008	42	267	]	]	PUNCT
ejpam-6008	42	268	,	,	PUNCT
ejpam-6008	42	269	[	[	X
ejpam-6008	42	270	60	60	NUM
ejpam-6008	42	271	]	]	PUNCT
ejpam-6008	42	272	,	,	PUNCT
ejpam-6008	42	273	[	[	X
ejpam-6008	42	274	61	61	NUM
ejpam-6008	42	275	]	]	PUNCT
ejpam-6008	42	276	,	,	PUNCT
ejpam-6008	42	277	[	[	X
ejpam-6008	42	278	62	62	NUM
ejpam-6008	42	279	]	]	PUNCT
ejpam-6008	42	280	,	,	PUNCT
ejpam-6008	42	281	[	[	X
ejpam-6008	42	282	63	63	NUM
ejpam-6008	42	283	]	]	PUNCT
ejpam-6008	42	284	,	,	PUNCT
ejpam-6008	42	285	[	[	X
ejpam-6008	42	286	64	64	NUM
ejpam-6008	42	287	]	]	PUNCT
ejpam-6008	42	288	and	and	CCONJ
ejpam-6008	42	289	[	[	X
ejpam-6008	42	290	65	65	NUM
ejpam-6008	42	291	]	]	PUNCT
ejpam-6008	42	292	,	,	PUNCT
ejpam-6008	42	293	respectively	respectively	ADV
ejpam-6008	42	294	.	.	PUNCT
ejpam-6008	43	1	on	on	ADP
ejpam-6008	43	2	the	the	DET
ejpam-6008	43	3	other	other	ADJ
ejpam-6008	43	4	hand	hand	NOUN
ejpam-6008	43	5	,	,	PUNCT
ejpam-6008	43	6	the	the	DET
ejpam-6008	43	7	present	present	ADJ
ejpam-6008	43	8	authors	author	NOUN
ejpam-6008	43	9	introduced	introduce	VERB
ejpam-6008	43	10	and	and	CCONJ
ejpam-6008	43	11	investigated	investigate	VERB
ejpam-6008	43	12	the	the	DET
ejpam-6008	43	13	notions	notion	NOUN
ejpam-6008	43	14	of	of	ADP
ejpam-6008	43	15	rarely	rarely	ADV
ejpam-6008	43	16	s-(τ1	s-(τ1	NOUN
ejpam-6008	43	17	,	,	PUNCT
ejpam-6008	43	18	τ2)p	τ2)p	ADJ
ejpam-6008	43	19	-	-	ADJ
ejpam-6008	43	20	continuous	continuous	ADJ
ejpam-6008	43	21	multifunctions	multifunction	NOUN
ejpam-6008	44	1	[	[	X
ejpam-6008	44	2	66	66	NUM
ejpam-6008	44	3	]	]	PUNCT
ejpam-6008	44	4	,	,	PUNCT
ejpam-6008	44	5	almost	almost	ADV
ejpam-6008	44	6	nearly	nearly	ADV
ejpam-6008	44	7	(	(	PUNCT
ejpam-6008	44	8	τ1	τ1	NOUN
ejpam-6008	44	9	,	,	PUNCT
ejpam-6008	44	10	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	44	11	multifunctions	multifunction	NOUN
ejpam-6008	44	12	[	[	X
ejpam-6008	44	13	67	67	NUM
ejpam-6008	44	14	]	]	PUNCT
ejpam-6008	44	15	,	,	PUNCT
ejpam-6008	44	16	s-(τ1	s-(τ1	PROPN
ejpam-6008	44	17	,	,	PUNCT
ejpam-6008	44	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	44	19	multifunctions	multifunction	NOUN
ejpam-6008	45	1	[	[	X
ejpam-6008	45	2	68	68	NUM
ejpam-6008	45	3	]	]	PUNCT
ejpam-6008	45	4	,	,	PUNCT
ejpam-6008	45	5	quasi	quasi	NOUN
ejpam-6008	45	6	θ(τ1	θ(τ1	NOUN
ejpam-6008	45	7	,	,	PUNCT
ejpam-6008	45	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	45	9	multifunctions	multifunction	NOUN
ejpam-6008	46	1	[	[	X
ejpam-6008	46	2	69	69	NUM
ejpam-6008	46	3	]	]	X
ejpam-6008	46	4	,	,	PUNCT
ejpam-6008	46	5	almost	almost	ADV
ejpam-6008	46	6	nearly	nearly	ADV
ejpam-6008	46	7	quasi	quasi	NOUN
ejpam-6008	46	8	(	(	PUNCT
ejpam-6008	46	9	τ1	τ1	NOUN
ejpam-6008	46	10	,	,	PUNCT
ejpam-6008	46	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	46	12	multifunctions	multifunction	NOUN
ejpam-6008	47	1	[	[	X
ejpam-6008	47	2	70	70	NUM
ejpam-6008	47	3	]	]	PUNCT
ejpam-6008	47	4	,	,	PUNCT
ejpam-6008	47	5	weakly	weakly	ADJ
ejpam-6008	47	6	s-(τ1	s-(τ1	PROPN
ejpam-6008	47	7	,	,	PUNCT
ejpam-6008	47	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	47	9	multifunctions	multifunction	NOUN
ejpam-6008	48	1	[	[	X
ejpam-6008	48	2	71	71	NUM
ejpam-6008	48	3	]	]	X
ejpam-6008	48	4	,	,	PUNCT
ejpam-6008	48	5	nearly	nearly	ADV
ejpam-6008	48	6	(	(	PUNCT
ejpam-6008	48	7	τ1	τ1	NOUN
ejpam-6008	48	8	,	,	PUNCT
ejpam-6008	48	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	48	10	multifunctions	multifunction	NOUN
ejpam-6008	49	1	[	[	X
ejpam-6008	49	2	72	72	NUM
ejpam-6008	49	3	]	]	PUNCT
ejpam-6008	49	4	and	and	CCONJ
ejpam-6008	49	5	almost	almost	ADV
ejpam-6008	49	6	quasi	quasi	X
ejpam-6008	49	7	(	(	PUNCT
ejpam-6008	49	8	τ1	τ1	NOUN
ejpam-6008	49	9	,	,	PUNCT
ejpam-6008	49	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	49	11	multifunctions	multifunction	NOUN
ejpam-6008	50	1	[	[	X
ejpam-6008	50	2	73	73	NUM
ejpam-6008	50	3	]	]	PUNCT
ejpam-6008	50	4	.	.	PUNCT
ejpam-6008	51	1	ekici	ekici	PROPN
ejpam-6008	51	2	et	et	PROPN
ejpam-6008	51	3	al	al	PROPN
ejpam-6008	51	4	.	.	PUNCT
ejpam-6008	52	1	[	[	X
ejpam-6008	52	2	74	74	NUM
ejpam-6008	52	3	]	]	PUNCT
ejpam-6008	52	4	introduced	introduce	VERB
ejpam-6008	52	5	and	and	CCONJ
ejpam-6008	52	6	studied	study	VERB
ejpam-6008	52	7	two	two	NUM
ejpam-6008	52	8	new	new	ADJ
ejpam-6008	52	9	concepts	concept	NOUN
ejpam-6008	52	10	namely	namely	ADV
ejpam-6008	52	11	contra	contra	ADJ
ejpam-6008	52	12	-	-	ADJ
ejpam-6008	52	13	precontinuous	precontinuous	ADJ
ejpam-6008	52	14	multifunctions	multifunction	NOUN
ejpam-6008	52	15	and	and	CCONJ
ejpam-6008	52	16	almost	almost	ADV
ejpam-6008	52	17	n.	n.	PROPN
ejpam-6008	52	18	viriyapong	viriyapong	PROPN
ejpam-6008	52	19	,	,	PUNCT
ejpam-6008	52	20	a.	a.	PROPN
ejpam-6008	52	21	sama	sama	PROPN
ejpam-6008	52	22	-	-	PUNCT
ejpam-6008	52	23	ae	ae	PROPN
ejpam-6008	52	24	,	,	PUNCT
ejpam-6008	52	25	c.	c.	PROPN
ejpam-6008	52	26	boonpok	boonpok	PROPN
ejpam-6008	52	27	/	/	SYM
ejpam-6008	52	28	eur	eur	PROPN
ejpam-6008	52	29	.	.	PUNCT
ejpam-6008	53	1	j.	j.	PROPN
ejpam-6008	53	2	pure	pure	PROPN
ejpam-6008	53	3	appl	appl	PROPN
ejpam-6008	53	4	.	.	PROPN
ejpam-6008	53	5	math	math	PROPN
ejpam-6008	53	6	,	,	PUNCT
ejpam-6008	53	7	18	18	NUM
ejpam-6008	53	8	(	(	PUNCT
ejpam-6008	53	9	2	2	NUM
ejpam-6008	53	10	)	)	PUNCT
ejpam-6008	53	11	(	(	PUNCT
ejpam-6008	53	12	2025	2025	NUM
ejpam-6008	53	13	)	)	PUNCT
ejpam-6008	53	14	,	,	PUNCT
ejpam-6008	53	15	6008	6008	NUM
ejpam-6008	53	16	3	3	NUM
ejpam-6008	53	17	of	of	ADP
ejpam-6008	53	18	15	15	NUM
ejpam-6008	53	19	contra	contra	ADJ
ejpam-6008	53	20	-	-	ADJ
ejpam-6008	53	21	precontinuous	precontinuous	ADJ
ejpam-6008	53	22	multifunctions	multifunction	NOUN
ejpam-6008	53	23	which	which	PRON
ejpam-6008	53	24	are	be	AUX
ejpam-6008	53	25	containing	contain	VERB
ejpam-6008	53	26	the	the	DET
ejpam-6008	53	27	class	class	NOUN
ejpam-6008	53	28	of	of	ADP
ejpam-6008	53	29	contra	contra	ADJ
ejpam-6008	53	30	-	-	ADJ
ejpam-6008	53	31	continuous	continuous	ADJ
ejpam-6008	53	32	multifunctions	multifunction	NOUN
ejpam-6008	53	33	[	[	X
ejpam-6008	53	34	35	35	NUM
ejpam-6008	53	35	]	]	PUNCT
ejpam-6008	53	36	and	and	CCONJ
ejpam-6008	53	37	contained	contain	VERB
ejpam-6008	53	38	in	in	ADP
ejpam-6008	53	39	the	the	DET
ejpam-6008	53	40	class	class	NOUN
ejpam-6008	53	41	of	of	ADP
ejpam-6008	53	42	weakly	weakly	ADJ
ejpam-6008	53	43	precontinuous	precontinuous	ADJ
ejpam-6008	53	44	multifunctions	multifunction	NOUN
ejpam-6008	53	45	.	.	PUNCT
ejpam-6008	54	1	ekici	ekici	NOUN
ejpam-6008	54	2	et	et	PROPN
ejpam-6008	54	3	al	al	PROPN
ejpam-6008	54	4	.	.	PUNCT
ejpam-6008	55	1	[	[	X
ejpam-6008	55	2	75	75	NUM
ejpam-6008	55	3	]	]	PUNCT
ejpam-6008	55	4	introduced	introduce	VERB
ejpam-6008	55	5	and	and	CCONJ
ejpam-6008	55	6	studied	study	VERB
ejpam-6008	55	7	a	a	DET
ejpam-6008	55	8	new	new	ADJ
ejpam-6008	55	9	generalization	generalization	NOUN
ejpam-6008	55	10	of	of	ADP
ejpam-6008	55	11	contra	contra	ADJ
ejpam-6008	55	12	-	-	ADJ
ejpam-6008	55	13	continuous	continuous	ADJ
ejpam-6008	55	14	multifunctions	multifunction	NOUN
ejpam-6008	55	15	called	call	VERB
ejpam-6008	55	16	almost	almost	ADV
ejpam-6008	55	17	contra	contra	ADJ
ejpam-6008	55	18	-	-	ADJ
ejpam-6008	55	19	continuous	continuous	ADJ
ejpam-6008	55	20	multifunctions	multifunction	NOUN
ejpam-6008	55	21	.	.	PUNCT
ejpam-6008	56	1	recently	recently	ADV
ejpam-6008	56	2	,	,	PUNCT
ejpam-6008	56	3	the	the	DET
ejpam-6008	56	4	present	present	ADJ
ejpam-6008	56	5	authors	author	NOUN
ejpam-6008	56	6	[	[	X
ejpam-6008	56	7	76	76	NUM
ejpam-6008	56	8	]	]	PUNCT
ejpam-6008	56	9	introduced	introduce	VERB
ejpam-6008	56	10	and	and	CCONJ
ejpam-6008	56	11	investigated	investigate	VERB
ejpam-6008	56	12	the	the	DET
ejpam-6008	56	13	notions	notion	NOUN
ejpam-6008	56	14	of	of	ADP
ejpam-6008	56	15	upper	upper	ADJ
ejpam-6008	56	16	almost	almost	ADV
ejpam-6008	56	17	contra-(λ	contra-(λ	PROPN
ejpam-6008	56	18	,	,	PUNCT
ejpam-6008	56	19	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	56	20	multifunctions	multifunction	NOUN
ejpam-6008	56	21	and	and	CCONJ
ejpam-6008	56	22	lower	low	ADJ
ejpam-6008	56	23	almost	almost	ADV
ejpam-6008	56	24	contra-(λ	contra-(λ	PROPN
ejpam-6008	56	25	,	,	PUNCT
ejpam-6008	56	26	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	56	27	multifunctions	multifunction	NOUN
ejpam-6008	56	28	.	.	PUNCT
ejpam-6008	57	1	in	in	ADP
ejpam-6008	57	2	this	this	DET
ejpam-6008	57	3	paper	paper	NOUN
ejpam-6008	57	4	,	,	PUNCT
ejpam-6008	57	5	we	we	PRON
ejpam-6008	57	6	introduce	introduce	VERB
ejpam-6008	57	7	the	the	DET
ejpam-6008	57	8	concepts	concept	NOUN
ejpam-6008	57	9	of	of	ADP
ejpam-6008	57	10	upper	upper	ADJ
ejpam-6008	57	11	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	57	12	,	,	PUNCT
ejpam-6008	57	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	57	14	multifunctions	multifunction	NOUN
ejpam-6008	57	15	and	and	CCONJ
ejpam-6008	57	16	lower	low	ADJ
ejpam-6008	57	17	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	57	18	,	,	PUNCT
ejpam-6008	57	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	57	20	multifunctions	multifunction	NOUN
ejpam-6008	57	21	.	.	PUNCT
ejpam-6008	58	1	we	we	PRON
ejpam-6008	58	2	also	also	ADV
ejpam-6008	58	3	investigate	investigate	VERB
ejpam-6008	58	4	several	several	ADJ
ejpam-6008	58	5	characterizations	characterization	NOUN
ejpam-6008	58	6	of	of	ADP
ejpam-6008	58	7	upper	upper	ADJ
ejpam-6008	58	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	58	9	,	,	PUNCT
ejpam-6008	58	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	58	11	multifunctions	multifunction	NOUN
ejpam-6008	58	12	and	and	CCONJ
ejpam-6008	58	13	lower	low	ADJ
ejpam-6008	58	14	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	58	15	,	,	PUNCT
ejpam-6008	58	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	58	17	multifunctions	multifunction	NOUN
ejpam-6008	58	18	.	.	PUNCT
ejpam-6008	59	1	2	2	X
ejpam-6008	59	2	.	.	X
ejpam-6008	59	3	preliminaries	preliminary	NOUN
ejpam-6008	59	4	throughout	throughout	ADP
ejpam-6008	59	5	the	the	DET
ejpam-6008	59	6	present	present	ADJ
ejpam-6008	59	7	paper	paper	NOUN
ejpam-6008	59	8	,	,	PUNCT
ejpam-6008	59	9	spaces	space	NOUN
ejpam-6008	59	10	(	(	PUNCT
ejpam-6008	59	11	x	x	NOUN
ejpam-6008	59	12	,	,	PUNCT
ejpam-6008	59	13	τ1	τ1	NOUN
ejpam-6008	59	14	,	,	PUNCT
ejpam-6008	59	15	τ2	τ2	NOUN
ejpam-6008	59	16	)	)	PUNCT
ejpam-6008	59	17	and	and	CCONJ
ejpam-6008	59	18	(	(	PUNCT
ejpam-6008	59	19	y	y	PROPN
ejpam-6008	59	20	,	,	PUNCT
ejpam-6008	59	21	σ1	σ1	PROPN
ejpam-6008	59	22	,	,	PUNCT
ejpam-6008	59	23	σ2	σ2	NOUN
ejpam-6008	59	24	)	)	PUNCT
ejpam-6008	59	25	(	(	PUNCT
ejpam-6008	59	26	or	or	CCONJ
ejpam-6008	59	27	simply	simply	ADV
ejpam-6008	59	28	x	x	X
ejpam-6008	59	29	and	and	CCONJ
ejpam-6008	59	30	y	y	PROPN
ejpam-6008	59	31	)	)	PUNCT
ejpam-6008	59	32	always	always	ADV
ejpam-6008	59	33	mean	mean	VERB
ejpam-6008	59	34	bitopological	bitopological	ADJ
ejpam-6008	59	35	spaces	space	NOUN
ejpam-6008	59	36	on	on	ADP
ejpam-6008	59	37	which	which	PRON
ejpam-6008	59	38	no	no	DET
ejpam-6008	59	39	separation	separation	NOUN
ejpam-6008	59	40	axioms	axiom	NOUN
ejpam-6008	59	41	are	be	AUX
ejpam-6008	59	42	assumed	assume	VERB
ejpam-6008	59	43	unless	unless	SCONJ
ejpam-6008	59	44	explicitly	explicitly	ADV
ejpam-6008	59	45	stated	state	VERB
ejpam-6008	59	46	.	.	PUNCT
ejpam-6008	60	1	let	let	VERB
ejpam-6008	60	2	a	a	DET
ejpam-6008	60	3	be	be	AUX
ejpam-6008	60	4	a	a	DET
ejpam-6008	60	5	subset	subset	NOUN
ejpam-6008	60	6	of	of	ADP
ejpam-6008	60	7	a	a	DET
ejpam-6008	60	8	bitopological	bitopological	ADJ
ejpam-6008	60	9	space	space	NOUN
ejpam-6008	60	10	(	(	PUNCT
ejpam-6008	60	11	x	x	NOUN
ejpam-6008	60	12	,	,	PUNCT
ejpam-6008	60	13	τ1	τ1	NOUN
ejpam-6008	60	14	,	,	PUNCT
ejpam-6008	60	15	τ2	τ2	NOUN
ejpam-6008	60	16	)	)	PUNCT
ejpam-6008	60	17	.	.	PUNCT
ejpam-6008	61	1	the	the	DET
ejpam-6008	61	2	closure	closure	NOUN
ejpam-6008	61	3	of	of	ADP
ejpam-6008	61	4	a	a	PRON
ejpam-6008	61	5	and	and	CCONJ
ejpam-6008	61	6	the	the	DET
ejpam-6008	61	7	interior	interior	NOUN
ejpam-6008	61	8	of	of	ADP
ejpam-6008	61	9	a	a	PRON
ejpam-6008	61	10	with	with	ADP
ejpam-6008	61	11	respect	respect	NOUN
ejpam-6008	61	12	to	to	ADP
ejpam-6008	61	13	τi	τi	PROPN
ejpam-6008	61	14	are	be	AUX
ejpam-6008	61	15	denoted	denote	VERB
ejpam-6008	61	16	by	by	ADP
ejpam-6008	61	17	τi	τi	NOUN
ejpam-6008	61	18	-	-	PUNCT
ejpam-6008	61	19	cl(a	cl(a	NUM
ejpam-6008	61	20	)	)	PUNCT
ejpam-6008	61	21	and	and	CCONJ
ejpam-6008	61	22	τi	τi	NOUN
ejpam-6008	61	23	-	-	PUNCT
ejpam-6008	61	24	int(a	int(a	NOUN
ejpam-6008	61	25	)	)	PUNCT
ejpam-6008	61	26	,	,	PUNCT
ejpam-6008	61	27	respectively	respectively	ADV
ejpam-6008	61	28	,	,	PUNCT
ejpam-6008	61	29	for	for	ADP
ejpam-6008	61	30	i	i	PROPN
ejpam-6008	61	31	=	=	SYM
ejpam-6008	61	32	1	1	NUM
ejpam-6008	61	33	,	,	PUNCT
ejpam-6008	61	34	2	2	NUM
ejpam-6008	61	35	.	.	X
ejpam-6008	61	36	a	a	DET
ejpam-6008	61	37	subset	subset	NOUN
ejpam-6008	61	38	a	a	PRON
ejpam-6008	61	39	of	of	ADP
ejpam-6008	61	40	a	a	DET
ejpam-6008	61	41	bitopological	bitopological	ADJ
ejpam-6008	61	42	space	space	NOUN
ejpam-6008	61	43	(	(	PUNCT
ejpam-6008	61	44	x	x	NOUN
ejpam-6008	61	45	,	,	PUNCT
ejpam-6008	61	46	τ1	τ1	NOUN
ejpam-6008	61	47	,	,	PUNCT
ejpam-6008	61	48	τ2	τ2	NOUN
ejpam-6008	61	49	)	)	PUNCT
ejpam-6008	61	50	is	be	AUX
ejpam-6008	61	51	called	call	VERB
ejpam-6008	61	52	τ1τ2	τ1τ2	VERB
ejpam-6008	61	53	-	-	ADJ
ejpam-6008	61	54	closed	closed	ADJ
ejpam-6008	61	55	[	[	X
ejpam-6008	61	56	77	77	NUM
ejpam-6008	61	57	]	]	X
ejpam-6008	61	58	if	if	SCONJ
ejpam-6008	61	59	a	a	DET
ejpam-6008	61	60	=	=	NOUN
ejpam-6008	61	61	τ1	τ1	NOUN
ejpam-6008	61	62	-	-	PUNCT
ejpam-6008	61	63	cl(τ2	cl(τ2	NOUN
ejpam-6008	61	64	-	-	PUNCT
ejpam-6008	61	65	cl(a	cl(a	NUM
ejpam-6008	61	66	)	)	PUNCT
ejpam-6008	61	67	)	)	PUNCT
ejpam-6008	61	68	.	.	PUNCT
ejpam-6008	62	1	the	the	DET
ejpam-6008	62	2	complement	complement	NOUN
ejpam-6008	62	3	of	of	ADP
ejpam-6008	62	4	a	a	DET
ejpam-6008	62	5	τ1τ2	τ1τ2	ADJ
ejpam-6008	62	6	-	-	ADJ
ejpam-6008	62	7	closed	closed	ADJ
ejpam-6008	62	8	set	set	NOUN
ejpam-6008	62	9	is	be	AUX
ejpam-6008	62	10	called	call	VERB
ejpam-6008	62	11	τ1τ2	τ1τ2	NOUN
ejpam-6008	62	12	-	-	ADJ
ejpam-6008	62	13	open	open	ADJ
ejpam-6008	62	14	.	.	PUNCT
ejpam-6008	63	1	the	the	DET
ejpam-6008	63	2	intersection	intersection	NOUN
ejpam-6008	63	3	of	of	ADP
ejpam-6008	63	4	all	all	DET
ejpam-6008	63	5	τ1τ2	τ1τ2	ADJ
ejpam-6008	63	6	-	-	ADJ
ejpam-6008	63	7	closed	closed	ADJ
ejpam-6008	63	8	sets	set	NOUN
ejpam-6008	63	9	of	of	ADP
ejpam-6008	63	10	x	x	PUNCT
ejpam-6008	63	11	containing	contain	VERB
ejpam-6008	63	12	a	a	PRON
ejpam-6008	63	13	is	be	AUX
ejpam-6008	63	14	called	call	VERB
ejpam-6008	63	15	the	the	DET
ejpam-6008	63	16	τ1τ2	τ1τ2	NOUN
ejpam-6008	63	17	-	-	NOUN
ejpam-6008	63	18	closure	closure	NOUN
ejpam-6008	63	19	[	[	X
ejpam-6008	63	20	77	77	NUM
ejpam-6008	63	21	]	]	PUNCT
ejpam-6008	63	22	of	of	ADP
ejpam-6008	63	23	a	a	PRON
ejpam-6008	63	24	and	and	CCONJ
ejpam-6008	63	25	is	be	AUX
ejpam-6008	63	26	denoted	denote	VERB
ejpam-6008	63	27	by	by	ADP
ejpam-6008	63	28	τ1τ2	τ1τ2	NOUN
ejpam-6008	63	29	-	-	NUM
ejpam-6008	63	30	cl(a	cl(a	NUM
ejpam-6008	63	31	)	)	PUNCT
ejpam-6008	63	32	.	.	PUNCT
ejpam-6008	64	1	the	the	DET
ejpam-6008	64	2	union	union	NOUN
ejpam-6008	64	3	of	of	ADP
ejpam-6008	64	4	all	all	DET
ejpam-6008	64	5	τ1τ2	τ1τ2	ADJ
ejpam-6008	64	6	-	-	ADJ
ejpam-6008	64	7	open	open	ADJ
ejpam-6008	64	8	sets	set	NOUN
ejpam-6008	64	9	of	of	ADP
ejpam-6008	64	10	x	x	PUNCT
ejpam-6008	64	11	contained	contain	VERB
ejpam-6008	64	12	in	in	ADP
ejpam-6008	64	13	a	a	PRON
ejpam-6008	64	14	is	be	AUX
ejpam-6008	64	15	called	call	VERB
ejpam-6008	64	16	the	the	DET
ejpam-6008	64	17	τ1τ2	τ1τ2	NOUN
ejpam-6008	64	18	-	-	ADJ
ejpam-6008	64	19	interior	interior	ADJ
ejpam-6008	64	20	[	[	X
ejpam-6008	64	21	77	77	NUM
ejpam-6008	64	22	]	]	PUNCT
ejpam-6008	64	23	of	of	ADP
ejpam-6008	64	24	a	a	PRON
ejpam-6008	64	25	and	and	CCONJ
ejpam-6008	64	26	is	be	AUX
ejpam-6008	64	27	denoted	denote	VERB
ejpam-6008	64	28	by	by	ADP
ejpam-6008	64	29	τ1τ2	τ1τ2	NOUN
ejpam-6008	64	30	-	-	ADJ
ejpam-6008	64	31	int(a	int(a	NOUN
ejpam-6008	64	32	)	)	PUNCT
ejpam-6008	64	33	.	.	PUNCT
ejpam-6008	65	1	lemma	lemma	PROPN
ejpam-6008	65	2	1	1	NUM
ejpam-6008	65	3	.	.	PUNCT
ejpam-6008	66	1	[	[	X
ejpam-6008	66	2	77	77	NUM
ejpam-6008	66	3	]	]	PUNCT
ejpam-6008	66	4	let	let	VERB
ejpam-6008	66	5	a	a	PRON
ejpam-6008	66	6	and	and	CCONJ
ejpam-6008	66	7	b	b	NOUN
ejpam-6008	66	8	be	be	AUX
ejpam-6008	66	9	subsets	subset	NOUN
ejpam-6008	66	10	of	of	ADP
ejpam-6008	66	11	a	a	DET
ejpam-6008	66	12	bitopological	bitopological	ADJ
ejpam-6008	66	13	space	space	NOUN
ejpam-6008	66	14	(	(	PUNCT
ejpam-6008	66	15	x	x	NOUN
ejpam-6008	66	16	,	,	PUNCT
ejpam-6008	66	17	τ1	τ1	NOUN
ejpam-6008	66	18	,	,	PUNCT
ejpam-6008	66	19	τ2	τ2	NOUN
ejpam-6008	66	20	)	)	PUNCT
ejpam-6008	66	21	.	.	PUNCT
ejpam-6008	67	1	for	for	ADP
ejpam-6008	67	2	the	the	DET
ejpam-6008	67	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-6008	67	4	,	,	PUNCT
ejpam-6008	67	5	the	the	DET
ejpam-6008	67	6	following	follow	VERB
ejpam-6008	67	7	properties	property	NOUN
ejpam-6008	67	8	hold	hold	VERB
ejpam-6008	67	9	:	:	PUNCT
ejpam-6008	67	10	(	(	PUNCT
ejpam-6008	67	11	1	1	X
ejpam-6008	67	12	)	)	PUNCT
ejpam-6008	67	13	a	a	DET
ejpam-6008	67	14	⊆	⊆	NUM
ejpam-6008	67	15	τ1τ2	τ1τ2	NOUN
ejpam-6008	67	16	-	-	NUM
ejpam-6008	67	17	cl(a	cl(a	NUM
ejpam-6008	67	18	)	)	PUNCT
ejpam-6008	67	19	and	and	CCONJ
ejpam-6008	67	20	τ1τ2	τ1τ2	NOUN
ejpam-6008	67	21	-	-	ADJ
ejpam-6008	67	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6008	67	23	-	-	PUNCT
ejpam-6008	67	24	cl(a	cl(a	NUM
ejpam-6008	67	25	)	)	PUNCT
ejpam-6008	67	26	)	)	PUNCT
ejpam-6008	68	1	=	=	PUNCT
ejpam-6008	68	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	68	3	-	-	NUM
ejpam-6008	68	4	cl(a	cl(a	NUM
ejpam-6008	68	5	)	)	PUNCT
ejpam-6008	68	6	.	.	PUNCT
ejpam-6008	69	1	(	(	PUNCT
ejpam-6008	69	2	2	2	X
ejpam-6008	69	3	)	)	PUNCT
ejpam-6008	69	4	if	if	SCONJ
ejpam-6008	69	5	a	a	DET
ejpam-6008	69	6	⊆	⊆	NUM
ejpam-6008	69	7	b	b	NOUN
ejpam-6008	69	8	,	,	PUNCT
ejpam-6008	69	9	then	then	ADV
ejpam-6008	69	10	τ1τ2	τ1τ2	NOUN
ejpam-6008	69	11	-	-	NUM
ejpam-6008	69	12	cl(a	cl(a	NUM
ejpam-6008	69	13	)	)	PUNCT
ejpam-6008	69	14	⊆	⊆	NUM
ejpam-6008	69	15	τ1τ2	τ1τ2	NOUN
ejpam-6008	69	16	-	-	NOUN
ejpam-6008	69	17	cl(b	cl(b	NOUN
ejpam-6008	69	18	)	)	PUNCT
ejpam-6008	69	19	.	.	PUNCT
ejpam-6008	70	1	(	(	PUNCT
ejpam-6008	70	2	3	3	X
ejpam-6008	70	3	)	)	PUNCT
ejpam-6008	70	4	τ1τ2	τ1τ2	NOUN
ejpam-6008	70	5	-	-	NUM
ejpam-6008	70	6	cl(a	cl(a	NUM
ejpam-6008	70	7	)	)	PUNCT
ejpam-6008	70	8	is	be	AUX
ejpam-6008	70	9	τ1τ2	τ1τ2	NOUN
ejpam-6008	70	10	-	-	ADJ
ejpam-6008	70	11	closed	closed	ADJ
ejpam-6008	70	12	.	.	PUNCT
ejpam-6008	71	1	(	(	PUNCT
ejpam-6008	71	2	4	4	X
ejpam-6008	71	3	)	)	PUNCT
ejpam-6008	71	4	a	a	PRON
ejpam-6008	71	5	is	be	AUX
ejpam-6008	71	6	τ1τ2	τ1τ2	NOUN
ejpam-6008	71	7	-	-	ADJ
ejpam-6008	71	8	closed	closed	ADJ
ejpam-6008	71	9	if	if	SCONJ
ejpam-6008	71	10	and	and	CCONJ
ejpam-6008	71	11	only	only	ADV
ejpam-6008	71	12	if	if	SCONJ
ejpam-6008	71	13	a	a	DET
ejpam-6008	71	14	=	=	PUNCT
ejpam-6008	71	15	τ1τ2	τ1τ2	NOUN
ejpam-6008	71	16	-	-	NUM
ejpam-6008	71	17	cl(a	cl(a	NUM
ejpam-6008	71	18	)	)	PUNCT
ejpam-6008	71	19	.	.	PUNCT
ejpam-6008	72	1	(	(	PUNCT
ejpam-6008	72	2	5	5	X
ejpam-6008	72	3	)	)	PUNCT
ejpam-6008	72	4	τ1τ2	τ1τ2	NOUN
ejpam-6008	72	5	-	-	NOUN
ejpam-6008	72	6	cl(x	cl(x	X
ejpam-6008	72	7	−a	−a	NOUN
ejpam-6008	72	8	)	)	PUNCT
ejpam-6008	73	1	=	=	PUNCT
ejpam-6008	73	2	x	x	X
ejpam-6008	74	1	−	−	ADP
ejpam-6008	74	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	74	3	-	-	PUNCT
ejpam-6008	74	4	int(a	int(a	NOUN
ejpam-6008	74	5	)	)	PUNCT
ejpam-6008	74	6	.	.	PUNCT
ejpam-6008	75	1	a	a	DET
ejpam-6008	75	2	subset	subset	NOUN
ejpam-6008	75	3	a	a	PRON
ejpam-6008	75	4	of	of	ADP
ejpam-6008	75	5	a	a	DET
ejpam-6008	75	6	bitopological	bitopological	ADJ
ejpam-6008	75	7	space	space	NOUN
ejpam-6008	75	8	(	(	PUNCT
ejpam-6008	75	9	x	x	NOUN
ejpam-6008	75	10	,	,	PUNCT
ejpam-6008	75	11	τ1	τ1	NOUN
ejpam-6008	75	12	,	,	PUNCT
ejpam-6008	75	13	τ2	τ2	NOUN
ejpam-6008	75	14	)	)	PUNCT
ejpam-6008	75	15	is	be	AUX
ejpam-6008	75	16	called	call	VERB
ejpam-6008	75	17	α(τ1	α(τ1	NOUN
ejpam-6008	75	18	,	,	PUNCT
ejpam-6008	75	19	τ2)-open	τ2)-open	ADJ
ejpam-6008	75	20	[	[	X
ejpam-6008	75	21	78	78	NUM
ejpam-6008	75	22	]	]	PUNCT
ejpam-6008	75	23	if	if	SCONJ
ejpam-6008	75	24	a	a	DET
ejpam-6008	75	25	⊆	⊆	NUM
ejpam-6008	75	26	τ1τ2	τ1τ2	NOUN
ejpam-6008	75	27	-	-	PUNCT
ejpam-6008	75	28	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6008	75	29	-	-	PUNCT
ejpam-6008	75	30	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6008	75	31	-	-	PUNCT
ejpam-6008	75	32	int(a	int(a	NOUN
ejpam-6008	75	33	)	)	PUNCT
ejpam-6008	75	34	)	)	PUNCT
ejpam-6008	75	35	)	)	PUNCT
ejpam-6008	75	36	.	.	PUNCT
ejpam-6008	76	1	the	the	DET
ejpam-6008	76	2	complement	complement	NOUN
ejpam-6008	76	3	of	of	ADP
ejpam-6008	76	4	an	an	DET
ejpam-6008	76	5	α(τ1	α(τ1	NOUN
ejpam-6008	76	6	,	,	PUNCT
ejpam-6008	76	7	τ2)-open	τ2)-open	ADJ
ejpam-6008	76	8	set	set	NOUN
ejpam-6008	76	9	is	be	AUX
ejpam-6008	76	10	called	call	VERB
ejpam-6008	76	11	α(τ1	α(τ1	NOUN
ejpam-6008	76	12	,	,	PUNCT
ejpam-6008	76	13	τ2)closed	τ2)close	VERB
ejpam-6008	76	14	.	.	PUNCT
ejpam-6008	77	1	a	a	DET
ejpam-6008	77	2	subset	subset	NOUN
ejpam-6008	77	3	a	a	PRON
ejpam-6008	77	4	of	of	ADP
ejpam-6008	77	5	a	a	DET
ejpam-6008	77	6	bitopological	bitopological	ADJ
ejpam-6008	77	7	space	space	NOUN
ejpam-6008	77	8	(	(	PUNCT
ejpam-6008	77	9	x	x	NOUN
ejpam-6008	77	10	,	,	PUNCT
ejpam-6008	77	11	τ1	τ1	NOUN
ejpam-6008	77	12	,	,	PUNCT
ejpam-6008	77	13	τ2	τ2	NOUN
ejpam-6008	77	14	)	)	PUNCT
ejpam-6008	77	15	is	be	AUX
ejpam-6008	77	16	called	call	VERB
ejpam-6008	77	17	(	(	PUNCT
ejpam-6008	77	18	τ1	τ1	NOUN
ejpam-6008	77	19	,	,	PUNCT
ejpam-6008	77	20	τ2)r	τ2)r	NOUN
ejpam-6008	77	21	-	-	PUNCT
ejpam-6008	77	22	open	open	ADJ
ejpam-6008	78	1	[	[	X
ejpam-6008	78	2	79	79	NUM
ejpam-6008	78	3	]	]	PUNCT
ejpam-6008	78	4	(	(	PUNCT
ejpam-6008	78	5	resp	resp	NOUN
ejpam-6008	78	6	.	.	PUNCT
ejpam-6008	79	1	(	(	PUNCT
ejpam-6008	79	2	τ1	τ1	NOUN
ejpam-6008	79	3	,	,	PUNCT
ejpam-6008	79	4	τ2)s	τ2)s	NOUN
ejpam-6008	79	5	-	-	PUNCT
ejpam-6008	79	6	open	open	ADJ
ejpam-6008	79	7	[	[	X
ejpam-6008	79	8	37	37	NUM
ejpam-6008	79	9	]	]	PUNCT
ejpam-6008	79	10	,	,	PUNCT
ejpam-6008	79	11	(	(	PUNCT
ejpam-6008	79	12	τ1	τ1	NOUN
ejpam-6008	79	13	,	,	PUNCT
ejpam-6008	79	14	τ2)p	τ2)p	NOUN
ejpam-6008	79	15	-	-	ADJ
ejpam-6008	79	16	open	open	ADJ
ejpam-6008	80	1	[	[	X
ejpam-6008	80	2	37	37	NUM
ejpam-6008	80	3	]	]	PUNCT
ejpam-6008	80	4	,	,	PUNCT
ejpam-6008	80	5	(	(	PUNCT
ejpam-6008	80	6	τ1	τ1	NOUN
ejpam-6008	80	7	,	,	PUNCT
ejpam-6008	80	8	τ2)β	τ2)β	ADJ
ejpam-6008	80	9	-	-	PUNCT
ejpam-6008	80	10	open	open	NOUN
ejpam-6008	81	1	[	[	X
ejpam-6008	81	2	37	37	NUM
ejpam-6008	81	3	]	]	SYM
ejpam-6008	81	4	)	)	PUNCT
ejpam-6008	81	5	if	if	SCONJ
ejpam-6008	81	6	a	a	DET
ejpam-6008	81	7	=	=	PUNCT
ejpam-6008	81	8	τ1τ2	τ1τ2	NOUN
ejpam-6008	81	9	-	-	NOUN
ejpam-6008	81	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6008	81	11	-	-	PUNCT
ejpam-6008	81	12	cl(a	cl(a	NUM
ejpam-6008	81	13	)	)	PUNCT
ejpam-6008	81	14	)	)	PUNCT
ejpam-6008	81	15	(	(	PUNCT
ejpam-6008	81	16	resp	resp	NOUN
ejpam-6008	81	17	.	.	PUNCT
ejpam-6008	82	1	a	a	DET
ejpam-6008	82	2	⊆	⊆	NUM
ejpam-6008	82	3	τ1τ2	τ1τ2	NOUN
ejpam-6008	82	4	-	-	ADJ
ejpam-6008	82	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6008	82	6	-	-	PUNCT
ejpam-6008	82	7	int(a	int(a	NOUN
ejpam-6008	82	8	)	)	PUNCT
ejpam-6008	82	9	)	)	PUNCT
ejpam-6008	82	10	,	,	PUNCT
ejpam-6008	82	11	a	a	DET
ejpam-6008	82	12	⊆	⊆	NUM
ejpam-6008	82	13	τ1τ2	τ1τ2	NOUN
ejpam-6008	82	14	-	-	NOUN
ejpam-6008	82	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6008	82	16	-	-	PUNCT
ejpam-6008	82	17	cl(a	cl(a	NUM
ejpam-6008	82	18	)	)	PUNCT
ejpam-6008	82	19	)	)	PUNCT
ejpam-6008	82	20	,	,	PUNCT
ejpam-6008	82	21	a	a	DET
ejpam-6008	82	22	⊆	⊆	NUM
ejpam-6008	82	23	τ1τ2	τ1τ2	NOUN
ejpam-6008	82	24	-	-	PUNCT
ejpam-6008	82	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6008	82	26	-	-	PUNCT
ejpam-6008	82	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6008	82	28	-	-	PUNCT
ejpam-6008	82	29	cl(a	cl(a	NUM
ejpam-6008	82	30	)	)	PUNCT
ejpam-6008	82	31	)	)	PUNCT
ejpam-6008	82	32	)	)	PUNCT
ejpam-6008	82	33	)	)	PUNCT
ejpam-6008	82	34	.	.	PUNCT
ejpam-6008	83	1	the	the	DET
ejpam-6008	83	2	complement	complement	NOUN
ejpam-6008	83	3	of	of	ADP
ejpam-6008	83	4	a	a	DET
ejpam-6008	83	5	(	(	PUNCT
ejpam-6008	83	6	τ1	τ1	NOUN
ejpam-6008	83	7	,	,	PUNCT
ejpam-6008	83	8	τ2)r	τ2)r	NOUN
ejpam-6008	83	9	-	-	PUNCT
ejpam-6008	83	10	open	open	ADJ
ejpam-6008	83	11	(	(	PUNCT
ejpam-6008	83	12	resp	resp	NOUN
ejpam-6008	83	13	.	.	PUNCT
ejpam-6008	84	1	(	(	PUNCT
ejpam-6008	84	2	τ1	τ1	NOUN
ejpam-6008	84	3	,	,	PUNCT
ejpam-6008	84	4	τ2)s	τ2)s	NOUN
ejpam-6008	84	5	-	-	PUNCT
ejpam-6008	84	6	open	open	ADJ
ejpam-6008	84	7	,	,	PUNCT
ejpam-6008	84	8	(	(	PUNCT
ejpam-6008	84	9	τ1	τ1	NOUN
ejpam-6008	84	10	,	,	PUNCT
ejpam-6008	84	11	τ2)p	τ2)p	NOUN
ejpam-6008	84	12	-	-	ADJ
ejpam-6008	84	13	open	open	ADJ
ejpam-6008	84	14	,	,	PUNCT
ejpam-6008	84	15	(	(	PUNCT
ejpam-6008	84	16	τ1	τ1	NOUN
ejpam-6008	84	17	,	,	PUNCT
ejpam-6008	84	18	τ2)β	τ2)β	ADJ
ejpam-6008	84	19	-	-	PUNCT
ejpam-6008	84	20	open	open	ADJ
ejpam-6008	84	21	,	,	PUNCT
ejpam-6008	84	22	α(τ1	α(τ1	NOUN
ejpam-6008	84	23	,	,	PUNCT
ejpam-6008	84	24	τ2)-open	τ2)-open	ADJ
ejpam-6008	84	25	)	)	PUNCT
ejpam-6008	84	26	set	set	NOUN
ejpam-6008	84	27	is	be	AUX
ejpam-6008	84	28	called	call	VERB
ejpam-6008	84	29	(	(	PUNCT
ejpam-6008	84	30	τ1	τ1	NOUN
ejpam-6008	84	31	,	,	PUNCT
ejpam-6008	84	32	τ2)r	τ2)r	NOUN
ejpam-6008	84	33	-	-	PUNCT
ejpam-6008	84	34	closed	closed	ADJ
ejpam-6008	84	35	(	(	PUNCT
ejpam-6008	84	36	resp	resp	NOUN
ejpam-6008	84	37	.	.	PUNCT
ejpam-6008	85	1	(	(	PUNCT
ejpam-6008	85	2	τ1	τ1	NOUN
ejpam-6008	85	3	,	,	PUNCT
ejpam-6008	85	4	τ2)s	τ2)s	NOUN
ejpam-6008	85	5	-	-	PUNCT
ejpam-6008	85	6	closed	closed	ADJ
ejpam-6008	85	7	,	,	PUNCT
ejpam-6008	85	8	(	(	PUNCT
ejpam-6008	85	9	τ1	τ1	NOUN
ejpam-6008	85	10	,	,	PUNCT
ejpam-6008	85	11	τ2)p	τ2)p	NOUN
ejpam-6008	85	12	-	-	PUNCT
ejpam-6008	85	13	closed	closed	ADJ
ejpam-6008	85	14	,	,	PUNCT
ejpam-6008	85	15	(	(	PUNCT
ejpam-6008	85	16	τ1	τ1	NOUN
ejpam-6008	85	17	,	,	PUNCT
ejpam-6008	85	18	τ2)βclosed	τ2)βclose	VERB
ejpam-6008	85	19	,	,	PUNCT
ejpam-6008	85	20	α(τ1	α(τ1	NOUN
ejpam-6008	85	21	,	,	PUNCT
ejpam-6008	85	22	τ2)-closed	τ2)-closed	ADJ
ejpam-6008	85	23	)	)	PUNCT
ejpam-6008	85	24	.	.	PUNCT
ejpam-6008	86	1	let	let	VERB
ejpam-6008	86	2	a	a	DET
ejpam-6008	86	3	be	be	AUX
ejpam-6008	86	4	a	a	DET
ejpam-6008	86	5	subset	subset	NOUN
ejpam-6008	86	6	of	of	ADP
ejpam-6008	86	7	a	a	DET
ejpam-6008	86	8	bitopological	bitopological	ADJ
ejpam-6008	86	9	space	space	NOUN
ejpam-6008	86	10	(	(	PUNCT
ejpam-6008	86	11	x	x	NOUN
ejpam-6008	86	12	,	,	PUNCT
ejpam-6008	86	13	τ1	τ1	NOUN
ejpam-6008	86	14	,	,	PUNCT
ejpam-6008	86	15	τ2	τ2	NOUN
ejpam-6008	86	16	)	)	PUNCT
ejpam-6008	86	17	.	.	PUNCT
ejpam-6008	87	1	the	the	DET
ejpam-6008	87	2	set	set	NOUN
ejpam-6008	87	3	∩{g	∩{g	INTJ
ejpam-6008	87	4	|	|	ADV
ejpam-6008	87	5	a	a	DET
ejpam-6008	87	6	⊆	⊆	NUM
ejpam-6008	87	7	g	g	NOUN
ejpam-6008	87	8	and	and	CCONJ
ejpam-6008	87	9	g	g	PROPN
ejpam-6008	87	10	is	be	AUX
ejpam-6008	87	11	τ1τ2	τ1τ2	VERB
ejpam-6008	87	12	-	-	ADJ
ejpam-6008	87	13	open	open	ADJ
ejpam-6008	87	14	}	}	PUNCT
ejpam-6008	87	15	is	be	AUX
ejpam-6008	87	16	called	call	VERB
ejpam-6008	87	17	the	the	DET
ejpam-6008	87	18	τ1τ2	τ1τ2	NOUN
ejpam-6008	87	19	-	-	NOUN
ejpam-6008	87	20	kernel	kernel	NOUN
ejpam-6008	88	1	[	[	X
ejpam-6008	88	2	77	77	NUM
ejpam-6008	88	3	]	]	PUNCT
ejpam-6008	88	4	of	of	ADP
ejpam-6008	88	5	a	a	PRON
ejpam-6008	88	6	and	and	CCONJ
ejpam-6008	88	7	is	be	AUX
ejpam-6008	88	8	denoted	denote	VERB
ejpam-6008	88	9	by	by	ADP
ejpam-6008	88	10	τ1τ2	τ1τ2	NOUN
ejpam-6008	88	11	-	-	ADJ
ejpam-6008	88	12	ker(a	ker(a	ADJ
ejpam-6008	88	13	)	)	PUNCT
ejpam-6008	88	14	.	.	PUNCT
ejpam-6008	89	1	n.	n.	PROPN
ejpam-6008	89	2	viriyapong	viriyapong	PROPN
ejpam-6008	89	3	,	,	PUNCT
ejpam-6008	89	4	a.	a.	PROPN
ejpam-6008	89	5	sama	sama	PROPN
ejpam-6008	89	6	-	-	PUNCT
ejpam-6008	89	7	ae	ae	PROPN
ejpam-6008	89	8	,	,	PUNCT
ejpam-6008	89	9	c.	c.	PROPN
ejpam-6008	89	10	boonpok	boonpok	PROPN
ejpam-6008	89	11	/	/	SYM
ejpam-6008	89	12	eur	eur	PROPN
ejpam-6008	89	13	.	.	PUNCT
ejpam-6008	90	1	j.	j.	PROPN
ejpam-6008	90	2	pure	pure	PROPN
ejpam-6008	90	3	appl	appl	PROPN
ejpam-6008	90	4	.	.	PROPN
ejpam-6008	90	5	math	math	PROPN
ejpam-6008	90	6	,	,	PUNCT
ejpam-6008	90	7	18	18	NUM
ejpam-6008	90	8	(	(	PUNCT
ejpam-6008	90	9	2	2	NUM
ejpam-6008	90	10	)	)	PUNCT
ejpam-6008	90	11	(	(	PUNCT
ejpam-6008	90	12	2025	2025	NUM
ejpam-6008	90	13	)	)	PUNCT
ejpam-6008	90	14	,	,	PUNCT
ejpam-6008	90	15	6008	6008	NUM
ejpam-6008	90	16	4	4	NUM
ejpam-6008	90	17	of	of	ADP
ejpam-6008	90	18	15	15	NUM
ejpam-6008	90	19	lemma	lemma	PROPN
ejpam-6008	90	20	2	2	NUM
ejpam-6008	90	21	.	.	PUNCT
ejpam-6008	91	1	[	[	X
ejpam-6008	91	2	77	77	NUM
ejpam-6008	91	3	]	]	PUNCT
ejpam-6008	91	4	for	for	ADP
ejpam-6008	91	5	subsets	subset	NOUN
ejpam-6008	91	6	a	a	DET
ejpam-6008	91	7	,	,	PUNCT
ejpam-6008	91	8	b	b	NOUN
ejpam-6008	91	9	of	of	ADP
ejpam-6008	91	10	a	a	DET
ejpam-6008	91	11	bitopological	bitopological	ADJ
ejpam-6008	91	12	space	space	NOUN
ejpam-6008	91	13	(	(	PUNCT
ejpam-6008	91	14	x	x	NOUN
ejpam-6008	91	15	,	,	PUNCT
ejpam-6008	91	16	τ1	τ1	NOUN
ejpam-6008	91	17	,	,	PUNCT
ejpam-6008	91	18	τ2	τ2	NOUN
ejpam-6008	91	19	)	)	PUNCT
ejpam-6008	91	20	,	,	PUNCT
ejpam-6008	91	21	the	the	DET
ejpam-6008	91	22	following	follow	VERB
ejpam-6008	91	23	properties	property	NOUN
ejpam-6008	91	24	hold	hold	VERB
ejpam-6008	91	25	:	:	PUNCT
ejpam-6008	91	26	(	(	PUNCT
ejpam-6008	91	27	1	1	X
ejpam-6008	91	28	)	)	PUNCT
ejpam-6008	91	29	a	a	DET
ejpam-6008	91	30	⊆	⊆	NUM
ejpam-6008	91	31	τ1τ2	τ1τ2	NOUN
ejpam-6008	91	32	-	-	ADJ
ejpam-6008	91	33	ker(a	ker(a	ADJ
ejpam-6008	91	34	)	)	PUNCT
ejpam-6008	91	35	.	.	PUNCT
ejpam-6008	92	1	(	(	PUNCT
ejpam-6008	92	2	2	2	X
ejpam-6008	92	3	)	)	PUNCT
ejpam-6008	92	4	if	if	SCONJ
ejpam-6008	92	5	a	a	DET
ejpam-6008	92	6	⊆	⊆	NUM
ejpam-6008	92	7	b	b	NOUN
ejpam-6008	92	8	,	,	PUNCT
ejpam-6008	92	9	then	then	ADV
ejpam-6008	92	10	τ1τ2	τ1τ2	NOUN
ejpam-6008	92	11	-	-	ADJ
ejpam-6008	92	12	ker(a	ker(a	ADJ
ejpam-6008	92	13	)	)	PUNCT
ejpam-6008	92	14	⊆	⊆	NUM
ejpam-6008	92	15	τ1τ2	τ1τ2	PROPN
ejpam-6008	92	16	-	-	ADJ
ejpam-6008	92	17	ker(b	ker(b	PROPN
ejpam-6008	92	18	)	)	PUNCT
ejpam-6008	92	19	.	.	PUNCT
ejpam-6008	93	1	(	(	PUNCT
ejpam-6008	93	2	3	3	X
ejpam-6008	93	3	)	)	PUNCT
ejpam-6008	93	4	if	if	SCONJ
ejpam-6008	93	5	a	a	PRON
ejpam-6008	93	6	is	be	AUX
ejpam-6008	93	7	τ1τ2	τ1τ2	NOUN
ejpam-6008	93	8	-	-	ADJ
ejpam-6008	93	9	open	open	ADJ
ejpam-6008	93	10	,	,	PUNCT
ejpam-6008	93	11	then	then	ADV
ejpam-6008	93	12	τ1τ2	τ1τ2	NOUN
ejpam-6008	93	13	-	-	ADJ
ejpam-6008	93	14	ker(a	ker(a	ADJ
ejpam-6008	93	15	)	)	PUNCT
ejpam-6008	93	16	=	=	SYM
ejpam-6008	93	17	a.	a.	NOUN
ejpam-6008	93	18	(	(	PUNCT
ejpam-6008	93	19	4	4	NUM
ejpam-6008	93	20	)	)	PUNCT
ejpam-6008	93	21	x	x	SYM
ejpam-6008	93	22	∈	∈	PROPN
ejpam-6008	93	23	τ1τ2	τ1τ2	NOUN
ejpam-6008	93	24	-	-	ADJ
ejpam-6008	93	25	ker(a	ker(a	ADJ
ejpam-6008	93	26	)	)	PUNCT
ejpam-6008	93	27	if	if	SCONJ
ejpam-6008	93	28	and	and	CCONJ
ejpam-6008	93	29	only	only	ADV
ejpam-6008	93	30	if	if	SCONJ
ejpam-6008	93	31	a	a	DET
ejpam-6008	93	32	∩h	∩h	ADJ
ejpam-6008	93	33	̸=	̸=	PROPN
ejpam-6008	93	34	∅	∅	NOUN
ejpam-6008	93	35	for	for	ADP
ejpam-6008	93	36	every	every	DET
ejpam-6008	93	37	τ1τ2	τ1τ2	ADJ
ejpam-6008	93	38	-	-	ADJ
ejpam-6008	93	39	closed	closed	ADJ
ejpam-6008	93	40	set	set	ADJ
ejpam-6008	93	41	h	h	NOUN
ejpam-6008	93	42	containing	contain	VERB
ejpam-6008	93	43	x.	x.	NOUN
ejpam-6008	93	44	by	by	ADP
ejpam-6008	93	45	a	a	DET
ejpam-6008	93	46	multifunction	multifunction	NOUN
ejpam-6008	94	1	f	f	NOUN
ejpam-6008	94	2	:	:	PUNCT
ejpam-6008	94	3	x	x	X
ejpam-6008	94	4	→	→	SYM
ejpam-6008	94	5	y	y	PROPN
ejpam-6008	94	6	,	,	PUNCT
ejpam-6008	94	7	we	we	PRON
ejpam-6008	94	8	mean	mean	VERB
ejpam-6008	94	9	a	a	DET
ejpam-6008	94	10	point	point	NOUN
ejpam-6008	94	11	-	-	PUNCT
ejpam-6008	94	12	to	to	ADP
ejpam-6008	94	13	-	-	PUNCT
ejpam-6008	94	14	set	set	VERB
ejpam-6008	94	15	correspondence	correspondence	NOUN
ejpam-6008	94	16	from	from	ADP
ejpam-6008	94	17	x	x	PUNCT
ejpam-6008	94	18	into	into	ADP
ejpam-6008	94	19	y	y	PROPN
ejpam-6008	94	20	,	,	PUNCT
ejpam-6008	94	21	and	and	CCONJ
ejpam-6008	94	22	we	we	PRON
ejpam-6008	94	23	always	always	ADV
ejpam-6008	94	24	assume	assume	VERB
ejpam-6008	94	25	that	that	SCONJ
ejpam-6008	94	26	f	f	PROPN
ejpam-6008	94	27	(	(	PUNCT
ejpam-6008	94	28	x	x	X
ejpam-6008	94	29	)	)	PUNCT
ejpam-6008	94	30	̸=	̸=	NOUN
ejpam-6008	94	31	∅	∅	NOUN
ejpam-6008	94	32	for	for	ADP
ejpam-6008	94	33	all	all	PRON
ejpam-6008	94	34	x	x	SYM
ejpam-6008	94	35	∈	∈	ADJ
ejpam-6008	94	36	x.	x.	NOUN
ejpam-6008	94	37	for	for	ADP
ejpam-6008	94	38	a	a	DET
ejpam-6008	94	39	multifunction	multifunction	NOUN
ejpam-6008	94	40	f	f	NOUN
ejpam-6008	94	41	:	:	PUNCT
ejpam-6008	94	42	x	x	X
ejpam-6008	94	43	→	→	SYM
ejpam-6008	94	44	y	y	PROPN
ejpam-6008	94	45	,	,	PUNCT
ejpam-6008	94	46	we	we	PRON
ejpam-6008	94	47	shall	shall	AUX
ejpam-6008	94	48	denote	denote	VERB
ejpam-6008	94	49	the	the	DET
ejpam-6008	94	50	upper	upper	ADJ
ejpam-6008	94	51	and	and	CCONJ
ejpam-6008	94	52	lower	low	ADJ
ejpam-6008	94	53	inverse	inverse	NOUN
ejpam-6008	94	54	of	of	ADP
ejpam-6008	94	55	a	a	DET
ejpam-6008	94	56	set	set	NOUN
ejpam-6008	94	57	b	b	PROPN
ejpam-6008	94	58	of	of	ADP
ejpam-6008	94	59	y	y	PROPN
ejpam-6008	94	60	by	by	ADP
ejpam-6008	94	61	f+(b	f+(b	NOUN
ejpam-6008	94	62	)	)	PUNCT
ejpam-6008	94	63	and	and	CCONJ
ejpam-6008	94	64	f−(b	f−(b	NOUN
ejpam-6008	94	65	)	)	PUNCT
ejpam-6008	94	66	,	,	PUNCT
ejpam-6008	94	67	respectively	respectively	ADV
ejpam-6008	94	68	,	,	PUNCT
ejpam-6008	94	69	that	that	ADV
ejpam-6008	94	70	is	is	ADV
ejpam-6008	94	71	,	,	PUNCT
ejpam-6008	94	72	f+(b	f+(b	NOUN
ejpam-6008	94	73	)	)	PUNCT
ejpam-6008	94	74	=	=	PRON
ejpam-6008	95	1	{	{	PUNCT
ejpam-6008	95	2	x	x	PUNCT
ejpam-6008	95	3	∈	∈	PROPN
ejpam-6008	95	4	x	x	INTJ
ejpam-6008	96	1	|	|	NOUN
ejpam-6008	96	2	f	f	X
ejpam-6008	96	3	(	(	PUNCT
ejpam-6008	96	4	x	x	NOUN
ejpam-6008	96	5	)	)	PUNCT
ejpam-6008	96	6	⊆	⊆	NUM
ejpam-6008	96	7	b	b	NOUN
ejpam-6008	96	8	}	}	PUNCT
ejpam-6008	96	9	and	and	CCONJ
ejpam-6008	96	10	f−(b	f−(b	PROPN
ejpam-6008	96	11	)	)	PUNCT
ejpam-6008	96	12	=	=	PRON
ejpam-6008	97	1	{	{	PUNCT
ejpam-6008	97	2	x	x	PUNCT
ejpam-6008	97	3	∈	∈	PROPN
ejpam-6008	97	4	x	x	INTJ
ejpam-6008	98	1	|	|	NOUN
ejpam-6008	98	2	f	f	X
ejpam-6008	98	3	(	(	PUNCT
ejpam-6008	98	4	x	x	NOUN
ejpam-6008	98	5	)	)	PUNCT
ejpam-6008	98	6	∩	∩	NOUN
ejpam-6008	98	7	b	b	PROPN
ejpam-6008	98	8	̸=	̸=	PROPN
ejpam-6008	98	9	∅	∅	NOUN
ejpam-6008	98	10	}	}	PUNCT
ejpam-6008	98	11	.	.	PUNCT
ejpam-6008	99	1	in	in	ADP
ejpam-6008	99	2	particular	particular	ADJ
ejpam-6008	99	3	,	,	PUNCT
ejpam-6008	99	4	f−(y	f−(y	NOUN
ejpam-6008	99	5	)	)	PUNCT
ejpam-6008	99	6	=	=	SYM
ejpam-6008	100	1	{	{	PUNCT
ejpam-6008	100	2	x	x	PUNCT
ejpam-6008	100	3	∈	∈	PROPN
ejpam-6008	100	4	x	x	INTJ
ejpam-6008	101	1	|	|	ADV
ejpam-6008	101	2	y	y	PROPN
ejpam-6008	101	3	∈	∈	PROPN
ejpam-6008	101	4	f	f	X
ejpam-6008	101	5	(	(	PUNCT
ejpam-6008	101	6	x	x	NOUN
ejpam-6008	101	7	)	)	PUNCT
ejpam-6008	101	8	}	}	PUNCT
ejpam-6008	101	9	for	for	ADP
ejpam-6008	101	10	each	each	DET
ejpam-6008	101	11	point	point	NOUN
ejpam-6008	101	12	y	y	PROPN
ejpam-6008	101	13	∈	∈	PROPN
ejpam-6008	101	14	y	y	PROPN
ejpam-6008	101	15	.	.	PUNCT
ejpam-6008	102	1	for	for	ADP
ejpam-6008	102	2	each	each	DET
ejpam-6008	102	3	a	a	DET
ejpam-6008	102	4	⊆	⊆	NUM
ejpam-6008	102	5	x	x	SYM
ejpam-6008	102	6	,	,	PUNCT
ejpam-6008	102	7	f	f	PROPN
ejpam-6008	102	8	(	(	PUNCT
ejpam-6008	102	9	a	a	NOUN
ejpam-6008	102	10	)	)	PUNCT
ejpam-6008	102	11	=	=	SYM
ejpam-6008	102	12	∪x∈af	∪x∈af	NOUN
ejpam-6008	102	13	(	(	PUNCT
ejpam-6008	102	14	x	x	NOUN
ejpam-6008	102	15	)	)	PUNCT
ejpam-6008	102	16	.	.	PUNCT
ejpam-6008	103	1	3	3	X
ejpam-6008	103	2	.	.	X
ejpam-6008	103	3	upper	upper	ADJ
ejpam-6008	103	4	and	and	CCONJ
ejpam-6008	103	5	lower	low	ADJ
ejpam-6008	103	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	103	7	,	,	PUNCT
ejpam-6008	103	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	103	9	multifunctions	multifunction	NOUN
ejpam-6008	103	10	in	in	ADP
ejpam-6008	103	11	this	this	DET
ejpam-6008	103	12	section	section	NOUN
ejpam-6008	103	13	,	,	PUNCT
ejpam-6008	103	14	we	we	PRON
ejpam-6008	103	15	introduce	introduce	VERB
ejpam-6008	103	16	the	the	DET
ejpam-6008	103	17	concepts	concept	NOUN
ejpam-6008	103	18	of	of	ADP
ejpam-6008	103	19	upper	upper	ADJ
ejpam-6008	103	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	103	21	,	,	PUNCT
ejpam-6008	103	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	103	23	multifunctions	multifunction	NOUN
ejpam-6008	103	24	and	and	CCONJ
ejpam-6008	103	25	lower	low	ADJ
ejpam-6008	103	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	103	27	,	,	PUNCT
ejpam-6008	103	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	103	29	multifunctions	multifunction	NOUN
ejpam-6008	103	30	.	.	PUNCT
ejpam-6008	104	1	furthermore	furthermore	ADV
ejpam-6008	104	2	,	,	PUNCT
ejpam-6008	104	3	several	several	ADJ
ejpam-6008	104	4	characterizations	characterization	NOUN
ejpam-6008	104	5	of	of	ADP
ejpam-6008	104	6	upper	upper	ADJ
ejpam-6008	104	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	104	8	,	,	PUNCT
ejpam-6008	104	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	104	10	multifunctions	multifunction	NOUN
ejpam-6008	104	11	and	and	CCONJ
ejpam-6008	104	12	lower	low	ADJ
ejpam-6008	104	13	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	104	14	,	,	PUNCT
ejpam-6008	104	15	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	104	16	multifunctions	multifunction	NOUN
ejpam-6008	104	17	are	be	AUX
ejpam-6008	104	18	discussed	discuss	VERB
ejpam-6008	104	19	.	.	PUNCT
ejpam-6008	105	1	definition	definition	NOUN
ejpam-6008	105	2	1	1	NUM
ejpam-6008	105	3	.	.	PUNCT
ejpam-6008	106	1	a	a	DET
ejpam-6008	106	2	multifunction	multifunction	NOUN
ejpam-6008	106	3	f	f	NOUN
ejpam-6008	106	4	:	:	PUNCT
ejpam-6008	106	5	(	(	PUNCT
ejpam-6008	106	6	x	x	NOUN
ejpam-6008	106	7	,	,	PUNCT
ejpam-6008	106	8	τ1	τ1	NOUN
ejpam-6008	106	9	,	,	PUNCT
ejpam-6008	106	10	τ2	τ2	NOUN
ejpam-6008	106	11	)	)	PUNCT
ejpam-6008	106	12	→	→	SYM
ejpam-6008	106	13	(	(	PUNCT
ejpam-6008	106	14	y	y	PROPN
ejpam-6008	106	15	,	,	PUNCT
ejpam-6008	106	16	σ1	σ1	PROPN
ejpam-6008	106	17	,	,	PUNCT
ejpam-6008	106	18	σ2	σ2	PROPN
ejpam-6008	106	19	)	)	PUNCT
ejpam-6008	106	20	is	be	AUX
ejpam-6008	106	21	called	call	VERB
ejpam-6008	106	22	upper	upper	ADJ
ejpam-6008	106	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	106	24	,	,	PUNCT
ejpam-6008	106	25	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	106	26	at	at	ADP
ejpam-6008	106	27	a	a	DET
ejpam-6008	106	28	point	point	NOUN
ejpam-6008	106	29	x	x	SYM
ejpam-6008	106	30	∈	∈	NOUN
ejpam-6008	106	31	x	x	PUNCT
ejpam-6008	106	32	if	if	SCONJ
ejpam-6008	106	33	for	for	ADP
ejpam-6008	106	34	each	each	DET
ejpam-6008	106	35	σ1σ2	σ1σ2	NUM
ejpam-6008	106	36	-	-	PUNCT
ejpam-6008	106	37	closed	closed	ADJ
ejpam-6008	106	38	set	set	NOUN
ejpam-6008	106	39	k	k	PROPN
ejpam-6008	106	40	of	of	ADP
ejpam-6008	106	41	y	y	PROPN
ejpam-6008	106	42	such	such	ADJ
ejpam-6008	106	43	that	that	SCONJ
ejpam-6008	106	44	x	x	SYM
ejpam-6008	106	45	∈	∈	PROPN
ejpam-6008	106	46	f+(k	f+(k	NOUN
ejpam-6008	106	47	)	)	PUNCT
ejpam-6008	106	48	,	,	PUNCT
ejpam-6008	106	49	there	there	PRON
ejpam-6008	106	50	exists	exist	VERB
ejpam-6008	106	51	a	a	DET
ejpam-6008	106	52	τ1τ2	τ1τ2	NOUN
ejpam-6008	106	53	-	-	ADJ
ejpam-6008	106	54	open	open	ADJ
ejpam-6008	106	55	set	set	ADJ
ejpam-6008	106	56	u	u	NOUN
ejpam-6008	106	57	of	of	ADP
ejpam-6008	106	58	x	x	PUNCT
ejpam-6008	106	59	containing	contain	VERB
ejpam-6008	106	60	x	x	PUNCT
ejpam-6008	106	61	such	such	ADJ
ejpam-6008	106	62	that	that	SCONJ
ejpam-6008	106	63	u	u	PROPN
ejpam-6008	106	64	⊆	⊆	NUM
ejpam-6008	106	65	f+(k	f+(k	NUM
ejpam-6008	106	66	)	)	PUNCT
ejpam-6008	106	67	.	.	PUNCT
ejpam-6008	107	1	a	a	DET
ejpam-6008	107	2	multifunction	multifunction	NOUN
ejpam-6008	107	3	f	f	NOUN
ejpam-6008	107	4	:	:	PUNCT
ejpam-6008	107	5	(	(	PUNCT
ejpam-6008	107	6	x	x	NOUN
ejpam-6008	107	7	,	,	PUNCT
ejpam-6008	107	8	τ1	τ1	NOUN
ejpam-6008	107	9	,	,	PUNCT
ejpam-6008	107	10	τ2	τ2	NOUN
ejpam-6008	107	11	)	)	PUNCT
ejpam-6008	107	12	→	→	SYM
ejpam-6008	107	13	(	(	PUNCT
ejpam-6008	107	14	y	y	PROPN
ejpam-6008	107	15	,	,	PUNCT
ejpam-6008	107	16	σ1	σ1	PROPN
ejpam-6008	107	17	,	,	PUNCT
ejpam-6008	107	18	σ2	σ2	PROPN
ejpam-6008	107	19	)	)	PUNCT
ejpam-6008	107	20	is	be	AUX
ejpam-6008	107	21	called	call	VERB
ejpam-6008	107	22	upper	upper	ADJ
ejpam-6008	107	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	107	24	,	,	PUNCT
ejpam-6008	107	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	107	26	if	if	SCONJ
ejpam-6008	107	27	f	f	PROPN
ejpam-6008	107	28	is	be	AUX
ejpam-6008	107	29	upper	upper	ADJ
ejpam-6008	107	30	contra(τ1	contra(τ1	NOUN
ejpam-6008	107	31	,	,	PUNCT
ejpam-6008	107	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	107	33	at	at	ADP
ejpam-6008	107	34	each	each	DET
ejpam-6008	107	35	point	point	NOUN
ejpam-6008	107	36	x	x	PUNCT
ejpam-6008	107	37	of	of	ADP
ejpam-6008	107	38	x.	x.	PROPN
ejpam-6008	107	39	theorem	theorem	VERB
ejpam-6008	107	40	1	1	NUM
ejpam-6008	107	41	.	.	X
ejpam-6008	107	42	for	for	ADP
ejpam-6008	107	43	a	a	DET
ejpam-6008	107	44	multifunction	multifunction	NOUN
ejpam-6008	107	45	f	f	NOUN
ejpam-6008	107	46	:	:	PUNCT
ejpam-6008	107	47	(	(	PUNCT
ejpam-6008	107	48	x	x	NOUN
ejpam-6008	107	49	,	,	PUNCT
ejpam-6008	107	50	τ1	τ1	NOUN
ejpam-6008	107	51	,	,	PUNCT
ejpam-6008	107	52	τ2	τ2	NOUN
ejpam-6008	107	53	)	)	PUNCT
ejpam-6008	107	54	→	→	SYM
ejpam-6008	107	55	(	(	PUNCT
ejpam-6008	107	56	y	y	PROPN
ejpam-6008	107	57	,	,	PUNCT
ejpam-6008	107	58	σ1	σ1	PROPN
ejpam-6008	107	59	,	,	PUNCT
ejpam-6008	107	60	σ2	σ2	NOUN
ejpam-6008	107	61	)	)	PUNCT
ejpam-6008	107	62	,	,	PUNCT
ejpam-6008	107	63	the	the	DET
ejpam-6008	107	64	following	follow	VERB
ejpam-6008	107	65	properties	property	NOUN
ejpam-6008	107	66	are	be	AUX
ejpam-6008	107	67	equivalent	equivalent	ADJ
ejpam-6008	107	68	:	:	PUNCT
ejpam-6008	107	69	(	(	PUNCT
ejpam-6008	107	70	1	1	X
ejpam-6008	107	71	)	)	PUNCT
ejpam-6008	107	72	f	f	PROPN
ejpam-6008	107	73	is	be	AUX
ejpam-6008	107	74	upper	upper	ADJ
ejpam-6008	107	75	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	107	76	,	,	PUNCT
ejpam-6008	107	77	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	107	78	;	;	PUNCT
ejpam-6008	107	79	(	(	PUNCT
ejpam-6008	107	80	2	2	X
ejpam-6008	107	81	)	)	PUNCT
ejpam-6008	107	82	f+(k	f+(k	NOUN
ejpam-6008	107	83	)	)	PUNCT
ejpam-6008	107	84	is	be	AUX
ejpam-6008	107	85	τ1τ2	τ1τ2	NOUN
ejpam-6008	107	86	-	-	ADJ
ejpam-6008	107	87	open	open	ADJ
ejpam-6008	107	88	in	in	ADP
ejpam-6008	107	89	x	x	PUNCT
ejpam-6008	107	90	for	for	ADP
ejpam-6008	107	91	every	every	DET
ejpam-6008	107	92	σ1σ2	σ1σ2	NUM
ejpam-6008	107	93	-	-	PUNCT
ejpam-6008	107	94	closed	closed	ADJ
ejpam-6008	107	95	set	set	NOUN
ejpam-6008	107	96	k	k	PROPN
ejpam-6008	107	97	of	of	ADP
ejpam-6008	107	98	y	y	PROPN
ejpam-6008	107	99	;	;	PUNCT
ejpam-6008	107	100	(	(	PUNCT
ejpam-6008	107	101	3	3	X
ejpam-6008	107	102	)	)	PUNCT
ejpam-6008	107	103	f−(v	f−(v	NOUN
ejpam-6008	107	104	)	)	PUNCT
ejpam-6008	107	105	is	be	AUX
ejpam-6008	107	106	τ1τ2	τ1τ2	NOUN
ejpam-6008	107	107	-	-	ADJ
ejpam-6008	107	108	closed	closed	ADJ
ejpam-6008	107	109	in	in	ADP
ejpam-6008	107	110	x	x	PUNCT
ejpam-6008	107	111	for	for	ADP
ejpam-6008	107	112	every	every	DET
ejpam-6008	107	113	σ1σ2	σ1σ2	NOUN
ejpam-6008	107	114	-	-	ADJ
ejpam-6008	107	115	open	open	ADJ
ejpam-6008	107	116	set	set	NOUN
ejpam-6008	107	117	v	v	NOUN
ejpam-6008	107	118	of	of	ADP
ejpam-6008	107	119	y	y	PROPN
ejpam-6008	107	120	;	;	PUNCT
ejpam-6008	107	121	(	(	PUNCT
ejpam-6008	107	122	4	4	X
ejpam-6008	107	123	)	)	PUNCT
ejpam-6008	107	124	for	for	ADP
ejpam-6008	107	125	each	each	DET
ejpam-6008	107	126	x	x	SYM
ejpam-6008	107	127	∈	∈	PROPN
ejpam-6008	107	128	x	x	X
ejpam-6008	107	129	and	and	CCONJ
ejpam-6008	107	130	each	each	PRON
ejpam-6008	107	131	σ1σ2	σ1σ2	VERB
ejpam-6008	107	132	-	-	PUNCT
ejpam-6008	107	133	closed	closed	ADJ
ejpam-6008	107	134	set	set	NOUN
ejpam-6008	107	135	k	k	PROPN
ejpam-6008	107	136	of	of	ADP
ejpam-6008	107	137	y	y	PROPN
ejpam-6008	107	138	containing	contain	VERB
ejpam-6008	107	139	f	f	PROPN
ejpam-6008	107	140	(	(	PUNCT
ejpam-6008	107	141	x	x	NOUN
ejpam-6008	107	142	)	)	PUNCT
ejpam-6008	107	143	,	,	PUNCT
ejpam-6008	107	144	there	there	PRON
ejpam-6008	107	145	exists	exist	VERB
ejpam-6008	107	146	a	a	DET
ejpam-6008	107	147	τ1τ2	τ1τ2	NOUN
ejpam-6008	107	148	-	-	ADJ
ejpam-6008	107	149	open	open	ADJ
ejpam-6008	107	150	set	set	ADJ
ejpam-6008	107	151	u	u	NOUN
ejpam-6008	107	152	of	of	ADP
ejpam-6008	107	153	x	x	PUNCT
ejpam-6008	107	154	containing	contain	VERB
ejpam-6008	107	155	x	x	PUNCT
ejpam-6008	107	156	such	such	ADJ
ejpam-6008	107	157	that	that	SCONJ
ejpam-6008	107	158	if	if	SCONJ
ejpam-6008	107	159	y	y	PROPN
ejpam-6008	107	160	∈	∈	PROPN
ejpam-6008	107	161	u	u	PROPN
ejpam-6008	107	162	,	,	PUNCT
ejpam-6008	107	163	then	then	ADV
ejpam-6008	107	164	f	f	PROPN
ejpam-6008	107	165	(	(	PUNCT
ejpam-6008	107	166	y	y	PROPN
ejpam-6008	107	167	)	)	PUNCT
ejpam-6008	107	168	⊆	⊆	NUM
ejpam-6008	107	169	k.	k.	NOUN
ejpam-6008	107	170	proof	proof	NOUN
ejpam-6008	107	171	.	.	PUNCT
ejpam-6008	108	1	(	(	PUNCT
ejpam-6008	108	2	1	1	X
ejpam-6008	108	3	)	)	PUNCT
ejpam-6008	108	4	⇔	⇔	X
ejpam-6008	108	5	(	(	PUNCT
ejpam-6008	108	6	2	2	NUM
ejpam-6008	108	7	):	):	PUNCT
ejpam-6008	108	8	let	let	VERB
ejpam-6008	108	9	k	k	PRON
ejpam-6008	108	10	be	be	AUX
ejpam-6008	108	11	any	any	DET
ejpam-6008	108	12	σ1σ2	σ1σ2	NUM
ejpam-6008	108	13	-	-	PUNCT
ejpam-6008	108	14	closed	closed	ADJ
ejpam-6008	108	15	set	set	NOUN
ejpam-6008	108	16	of	of	ADP
ejpam-6008	108	17	y	y	PROPN
ejpam-6008	108	18	and	and	CCONJ
ejpam-6008	108	19	x	x	PUNCT
ejpam-6008	108	20	∈	∈	PROPN
ejpam-6008	108	21	f+(k	f+(k	PROPN
ejpam-6008	108	22	)	)	PUNCT
ejpam-6008	108	23	.	.	PUNCT
ejpam-6008	109	1	since	since	SCONJ
ejpam-6008	109	2	f	f	PROPN
ejpam-6008	109	3	is	be	AUX
ejpam-6008	109	4	upper	upper	ADJ
ejpam-6008	109	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	109	6	,	,	PUNCT
ejpam-6008	109	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	109	8	,	,	PUNCT
ejpam-6008	109	9	there	there	PRON
ejpam-6008	109	10	exists	exist	VERB
ejpam-6008	109	11	a	a	DET
ejpam-6008	109	12	τ1τ2	τ1τ2	NOUN
ejpam-6008	109	13	-	-	ADJ
ejpam-6008	109	14	open	open	ADJ
ejpam-6008	109	15	set	set	ADJ
ejpam-6008	109	16	u	u	NOUN
ejpam-6008	109	17	of	of	ADP
ejpam-6008	109	18	x	x	PUNCT
ejpam-6008	109	19	containing	contain	VERB
ejpam-6008	109	20	x	x	PUNCT
ejpam-6008	109	21	such	such	ADJ
ejpam-6008	109	22	that	that	SCONJ
ejpam-6008	109	23	u	u	PROPN
ejpam-6008	109	24	⊆	⊆	NUM
ejpam-6008	109	25	f+(k	f+(k	NUM
ejpam-6008	109	26	)	)	PUNCT
ejpam-6008	109	27	.	.	PUNCT
ejpam-6008	110	1	thus	thus	ADV
ejpam-6008	110	2	,	,	PUNCT
ejpam-6008	110	3	f+(k	f+(k	PRON
ejpam-6008	110	4	)	)	PUNCT
ejpam-6008	110	5	is	be	AUX
ejpam-6008	110	6	τ1τ2	τ1τ2	NOUN
ejpam-6008	110	7	-	-	ADJ
ejpam-6008	110	8	open	open	ADJ
ejpam-6008	110	9	in	in	ADP
ejpam-6008	110	10	x.	x.	NOUN
ejpam-6008	110	11	the	the	DET
ejpam-6008	110	12	converse	converse	NOUN
ejpam-6008	110	13	of	of	ADP
ejpam-6008	110	14	the	the	DET
ejpam-6008	110	15	proof	proof	NOUN
ejpam-6008	110	16	is	be	AUX
ejpam-6008	110	17	similar	similar	ADJ
ejpam-6008	110	18	.	.	PUNCT
ejpam-6008	111	1	(	(	PUNCT
ejpam-6008	111	2	2	2	X
ejpam-6008	111	3	)	)	PUNCT
ejpam-6008	111	4	⇔	⇔	X
ejpam-6008	111	5	(	(	PUNCT
ejpam-6008	111	6	3	3	NUM
ejpam-6008	111	7	):	):	PUNCT
ejpam-6008	111	8	this	this	PRON
ejpam-6008	111	9	follows	follow	VERB
ejpam-6008	111	10	from	from	ADP
ejpam-6008	111	11	the	the	DET
ejpam-6008	111	12	fact	fact	NOUN
ejpam-6008	111	13	that	that	SCONJ
ejpam-6008	111	14	f+(y	f+(y	PROPN
ejpam-6008	111	15	−b	−b	ADV
ejpam-6008	111	16	)	)	PUNCT
ejpam-6008	111	17	=	=	PUNCT
ejpam-6008	112	1	x	x	X
ejpam-6008	112	2	−	−	PROPN
ejpam-6008	112	3	f−(b	f−(b	PROPN
ejpam-6008	112	4	)	)	PUNCT
ejpam-6008	112	5	for	for	ADP
ejpam-6008	112	6	every	every	DET
ejpam-6008	112	7	subset	subset	NOUN
ejpam-6008	112	8	b	b	PROPN
ejpam-6008	112	9	of	of	ADP
ejpam-6008	112	10	y	y	PROPN
ejpam-6008	112	11	.	.	PUNCT
ejpam-6008	113	1	(	(	PUNCT
ejpam-6008	113	2	1	1	X
ejpam-6008	113	3	)	)	PUNCT
ejpam-6008	113	4	⇔	⇔	X
ejpam-6008	113	5	(	(	PUNCT
ejpam-6008	113	6	4	4	NUM
ejpam-6008	113	7	):	):	PUNCT
ejpam-6008	113	8	obvious	obvious	ADJ
ejpam-6008	113	9	.	.	PUNCT
ejpam-6008	114	1	n.	n.	PROPN
ejpam-6008	114	2	viriyapong	viriyapong	PROPN
ejpam-6008	114	3	,	,	PUNCT
ejpam-6008	114	4	a.	a.	PROPN
ejpam-6008	114	5	sama	sama	PROPN
ejpam-6008	114	6	-	-	PUNCT
ejpam-6008	114	7	ae	ae	PROPN
ejpam-6008	114	8	,	,	PUNCT
ejpam-6008	114	9	c.	c.	PROPN
ejpam-6008	114	10	boonpok	boonpok	PROPN
ejpam-6008	114	11	/	/	SYM
ejpam-6008	114	12	eur	eur	PROPN
ejpam-6008	114	13	.	.	PUNCT
ejpam-6008	115	1	j.	j.	PROPN
ejpam-6008	115	2	pure	pure	PROPN
ejpam-6008	115	3	appl	appl	PROPN
ejpam-6008	115	4	.	.	PROPN
ejpam-6008	115	5	math	math	PROPN
ejpam-6008	115	6	,	,	PUNCT
ejpam-6008	115	7	18	18	NUM
ejpam-6008	115	8	(	(	PUNCT
ejpam-6008	115	9	2	2	NUM
ejpam-6008	115	10	)	)	PUNCT
ejpam-6008	115	11	(	(	PUNCT
ejpam-6008	115	12	2025	2025	NUM
ejpam-6008	115	13	)	)	PUNCT
ejpam-6008	115	14	,	,	PUNCT
ejpam-6008	115	15	6008	6008	NUM
ejpam-6008	115	16	5	5	NUM
ejpam-6008	115	17	of	of	ADP
ejpam-6008	115	18	15	15	NUM
ejpam-6008	115	19	definition	definition	NOUN
ejpam-6008	115	20	2	2	NUM
ejpam-6008	115	21	.	.	PUNCT
ejpam-6008	115	22	a	a	DET
ejpam-6008	115	23	multifunction	multifunction	NOUN
ejpam-6008	115	24	f	f	NOUN
ejpam-6008	115	25	:	:	PUNCT
ejpam-6008	115	26	(	(	PUNCT
ejpam-6008	115	27	x	x	NOUN
ejpam-6008	115	28	,	,	PUNCT
ejpam-6008	115	29	τ1	τ1	NOUN
ejpam-6008	115	30	,	,	PUNCT
ejpam-6008	115	31	τ2	τ2	NOUN
ejpam-6008	115	32	)	)	PUNCT
ejpam-6008	115	33	→	→	SYM
ejpam-6008	115	34	(	(	PUNCT
ejpam-6008	115	35	y	y	PROPN
ejpam-6008	115	36	,	,	PUNCT
ejpam-6008	115	37	σ1	σ1	PROPN
ejpam-6008	115	38	,	,	PUNCT
ejpam-6008	115	39	σ2	σ2	PROPN
ejpam-6008	115	40	)	)	PUNCT
ejpam-6008	115	41	is	be	AUX
ejpam-6008	115	42	called	call	VERB
ejpam-6008	115	43	lower	low	ADJ
ejpam-6008	115	44	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	115	45	,	,	PUNCT
ejpam-6008	115	46	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	115	47	at	at	ADP
ejpam-6008	115	48	a	a	DET
ejpam-6008	115	49	point	point	NOUN
ejpam-6008	115	50	x	x	SYM
ejpam-6008	115	51	∈	∈	NOUN
ejpam-6008	115	52	x	x	PUNCT
ejpam-6008	115	53	if	if	SCONJ
ejpam-6008	115	54	for	for	ADP
ejpam-6008	115	55	each	each	DET
ejpam-6008	115	56	σ1σ2	σ1σ2	NUM
ejpam-6008	115	57	-	-	PUNCT
ejpam-6008	115	58	closed	closed	ADJ
ejpam-6008	115	59	set	set	NOUN
ejpam-6008	115	60	k	k	PROPN
ejpam-6008	115	61	of	of	ADP
ejpam-6008	115	62	y	y	PROPN
ejpam-6008	115	63	such	such	ADJ
ejpam-6008	115	64	that	that	SCONJ
ejpam-6008	115	65	x	x	SYM
ejpam-6008	115	66	∈	∈	PROPN
ejpam-6008	115	67	f−(k	f−(k	PROPN
ejpam-6008	115	68	)	)	PUNCT
ejpam-6008	115	69	,	,	PUNCT
ejpam-6008	115	70	there	there	PRON
ejpam-6008	115	71	exists	exist	VERB
ejpam-6008	115	72	a	a	DET
ejpam-6008	115	73	τ1τ2	τ1τ2	NOUN
ejpam-6008	115	74	-	-	ADJ
ejpam-6008	115	75	open	open	ADJ
ejpam-6008	115	76	set	set	ADJ
ejpam-6008	115	77	u	u	NOUN
ejpam-6008	115	78	of	of	ADP
ejpam-6008	115	79	x	x	PUNCT
ejpam-6008	115	80	containing	contain	VERB
ejpam-6008	115	81	x	x	PUNCT
ejpam-6008	115	82	such	such	ADJ
ejpam-6008	115	83	that	that	SCONJ
ejpam-6008	115	84	u	u	PROPN
ejpam-6008	115	85	⊆	⊆	NUM
ejpam-6008	115	86	f−(k	f−(k	PROPN
ejpam-6008	115	87	)	)	PUNCT
ejpam-6008	115	88	.	.	PUNCT
ejpam-6008	116	1	a	a	DET
ejpam-6008	116	2	multifunction	multifunction	NOUN
ejpam-6008	116	3	f	f	NOUN
ejpam-6008	116	4	:	:	PUNCT
ejpam-6008	116	5	(	(	PUNCT
ejpam-6008	116	6	x	x	NOUN
ejpam-6008	116	7	,	,	PUNCT
ejpam-6008	116	8	τ1	τ1	NOUN
ejpam-6008	116	9	,	,	PUNCT
ejpam-6008	116	10	τ2	τ2	NOUN
ejpam-6008	116	11	)	)	PUNCT
ejpam-6008	116	12	→	→	SYM
ejpam-6008	116	13	(	(	PUNCT
ejpam-6008	116	14	y	y	PROPN
ejpam-6008	116	15	,	,	PUNCT
ejpam-6008	116	16	σ1	σ1	PROPN
ejpam-6008	116	17	,	,	PUNCT
ejpam-6008	116	18	σ2	σ2	PROPN
ejpam-6008	116	19	)	)	PUNCT
ejpam-6008	116	20	is	be	AUX
ejpam-6008	116	21	called	call	VERB
ejpam-6008	116	22	lower	low	ADJ
ejpam-6008	116	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	116	24	,	,	PUNCT
ejpam-6008	116	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	116	26	if	if	SCONJ
ejpam-6008	116	27	f	f	PROPN
ejpam-6008	116	28	is	be	AUX
ejpam-6008	116	29	lower	low	ADJ
ejpam-6008	116	30	contra(τ1	contra(τ1	NOUN
ejpam-6008	116	31	,	,	PUNCT
ejpam-6008	116	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	116	33	at	at	ADP
ejpam-6008	116	34	each	each	DET
ejpam-6008	116	35	point	point	NOUN
ejpam-6008	116	36	x	x	PUNCT
ejpam-6008	116	37	of	of	ADP
ejpam-6008	116	38	x.	x.	PROPN
ejpam-6008	116	39	theorem	theorem	VERB
ejpam-6008	116	40	2	2	NUM
ejpam-6008	116	41	.	.	X
ejpam-6008	116	42	for	for	ADP
ejpam-6008	116	43	a	a	DET
ejpam-6008	116	44	multifunction	multifunction	NOUN
ejpam-6008	116	45	f	f	NOUN
ejpam-6008	116	46	:	:	PUNCT
ejpam-6008	116	47	(	(	PUNCT
ejpam-6008	116	48	x	x	NOUN
ejpam-6008	116	49	,	,	PUNCT
ejpam-6008	116	50	τ1	τ1	NOUN
ejpam-6008	116	51	,	,	PUNCT
ejpam-6008	116	52	τ2	τ2	NOUN
ejpam-6008	116	53	)	)	PUNCT
ejpam-6008	116	54	→	→	SYM
ejpam-6008	116	55	(	(	PUNCT
ejpam-6008	116	56	y	y	PROPN
ejpam-6008	116	57	,	,	PUNCT
ejpam-6008	116	58	σ1	σ1	PROPN
ejpam-6008	116	59	,	,	PUNCT
ejpam-6008	116	60	σ2	σ2	NOUN
ejpam-6008	116	61	)	)	PUNCT
ejpam-6008	116	62	,	,	PUNCT
ejpam-6008	116	63	the	the	DET
ejpam-6008	116	64	following	follow	VERB
ejpam-6008	116	65	properties	property	NOUN
ejpam-6008	116	66	are	be	AUX
ejpam-6008	116	67	equivalent	equivalent	ADJ
ejpam-6008	116	68	:	:	PUNCT
ejpam-6008	116	69	(	(	PUNCT
ejpam-6008	116	70	1	1	X
ejpam-6008	116	71	)	)	PUNCT
ejpam-6008	116	72	f	f	PROPN
ejpam-6008	116	73	is	be	AUX
ejpam-6008	116	74	lower	low	ADJ
ejpam-6008	116	75	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	116	76	,	,	PUNCT
ejpam-6008	116	77	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	116	78	;	;	PUNCT
ejpam-6008	116	79	(	(	PUNCT
ejpam-6008	116	80	2	2	X
ejpam-6008	116	81	)	)	PUNCT
ejpam-6008	116	82	f−(k	f−(k	PROPN
ejpam-6008	116	83	)	)	PUNCT
ejpam-6008	116	84	is	be	AUX
ejpam-6008	116	85	τ1τ2	τ1τ2	NOUN
ejpam-6008	116	86	-	-	ADJ
ejpam-6008	116	87	open	open	ADJ
ejpam-6008	116	88	in	in	ADP
ejpam-6008	116	89	x	x	PUNCT
ejpam-6008	116	90	for	for	ADP
ejpam-6008	116	91	every	every	DET
ejpam-6008	116	92	σ1σ2	σ1σ2	NUM
ejpam-6008	116	93	-	-	PUNCT
ejpam-6008	116	94	closed	closed	ADJ
ejpam-6008	116	95	set	set	NOUN
ejpam-6008	116	96	k	k	PROPN
ejpam-6008	116	97	of	of	ADP
ejpam-6008	116	98	y	y	PROPN
ejpam-6008	116	99	;	;	PUNCT
ejpam-6008	116	100	(	(	PUNCT
ejpam-6008	116	101	3	3	X
ejpam-6008	116	102	)	)	PUNCT
ejpam-6008	116	103	f+(v	f+(v	NOUN
ejpam-6008	116	104	)	)	PUNCT
ejpam-6008	117	1	is	be	AUX
ejpam-6008	117	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	117	3	-	-	ADJ
ejpam-6008	117	4	closed	closed	ADJ
ejpam-6008	117	5	in	in	ADP
ejpam-6008	117	6	x	x	PUNCT
ejpam-6008	117	7	for	for	ADP
ejpam-6008	117	8	every	every	DET
ejpam-6008	117	9	σ1σ2	σ1σ2	NOUN
ejpam-6008	117	10	-	-	ADJ
ejpam-6008	117	11	open	open	ADJ
ejpam-6008	117	12	set	set	NOUN
ejpam-6008	117	13	v	v	NOUN
ejpam-6008	117	14	of	of	ADP
ejpam-6008	117	15	y	y	PROPN
ejpam-6008	117	16	;	;	PUNCT
ejpam-6008	117	17	(	(	PUNCT
ejpam-6008	117	18	4	4	X
ejpam-6008	117	19	)	)	PUNCT
ejpam-6008	117	20	for	for	ADP
ejpam-6008	117	21	each	each	DET
ejpam-6008	117	22	x	x	SYM
ejpam-6008	117	23	∈	∈	PROPN
ejpam-6008	117	24	x	x	X
ejpam-6008	117	25	and	and	CCONJ
ejpam-6008	117	26	each	each	DET
ejpam-6008	117	27	σ1σ2	σ1σ2	VERB
ejpam-6008	117	28	-	-	PUNCT
ejpam-6008	117	29	closed	closed	ADJ
ejpam-6008	117	30	set	set	NOUN
ejpam-6008	117	31	k	k	PROPN
ejpam-6008	117	32	of	of	ADP
ejpam-6008	117	33	y	y	PRON
ejpam-6008	117	34	such	such	ADJ
ejpam-6008	117	35	that	that	SCONJ
ejpam-6008	117	36	f	f	PROPN
ejpam-6008	117	37	(	(	PUNCT
ejpam-6008	117	38	x)∩k	x)∩k	PROPN
ejpam-6008	117	39	̸=	̸=	PROPN
ejpam-6008	117	40	∅	∅	NOUN
ejpam-6008	117	41	,	,	PUNCT
ejpam-6008	117	42	there	there	PRON
ejpam-6008	117	43	exists	exist	VERB
ejpam-6008	117	44	a	a	DET
ejpam-6008	117	45	τ1τ2	τ1τ2	NOUN
ejpam-6008	117	46	-	-	ADJ
ejpam-6008	117	47	open	open	ADJ
ejpam-6008	117	48	set	set	ADJ
ejpam-6008	117	49	u	u	NOUN
ejpam-6008	117	50	of	of	ADP
ejpam-6008	117	51	x	x	PUNCT
ejpam-6008	117	52	containing	contain	VERB
ejpam-6008	117	53	x	x	PUNCT
ejpam-6008	117	54	such	such	ADJ
ejpam-6008	117	55	that	that	SCONJ
ejpam-6008	117	56	if	if	SCONJ
ejpam-6008	117	57	y	y	PROPN
ejpam-6008	117	58	∈	∈	PROPN
ejpam-6008	117	59	u	u	PROPN
ejpam-6008	117	60	,	,	PUNCT
ejpam-6008	117	61	then	then	ADV
ejpam-6008	117	62	f	f	PROPN
ejpam-6008	117	63	(	(	PUNCT
ejpam-6008	117	64	y	y	NOUN
ejpam-6008	117	65	)	)	PUNCT
ejpam-6008	117	66	∩k	∩k	NOUN
ejpam-6008	117	67	̸=	̸=	PROPN
ejpam-6008	117	68	∅.	∅.	ADP
ejpam-6008	117	69	proof	proof	NOUN
ejpam-6008	117	70	.	.	PUNCT
ejpam-6008	118	1	the	the	DET
ejpam-6008	118	2	proof	proof	NOUN
ejpam-6008	118	3	is	be	AUX
ejpam-6008	118	4	similar	similar	ADJ
ejpam-6008	118	5	to	to	ADP
ejpam-6008	118	6	that	that	PRON
ejpam-6008	118	7	of	of	ADP
ejpam-6008	118	8	theorem	theorem	ADJ
ejpam-6008	118	9	1	1	NUM
ejpam-6008	118	10	.	.	PUNCT
ejpam-6008	118	11	theorem	theorem	NOUN
ejpam-6008	118	12	3	3	X
ejpam-6008	118	13	.	.	PUNCT
ejpam-6008	119	1	let	let	VERB
ejpam-6008	119	2	f	f	NOUN
ejpam-6008	119	3	:	:	PUNCT
ejpam-6008	119	4	(	(	PUNCT
ejpam-6008	119	5	x	x	NOUN
ejpam-6008	119	6	,	,	PUNCT
ejpam-6008	119	7	τ1	τ1	NOUN
ejpam-6008	119	8	,	,	PUNCT
ejpam-6008	119	9	τ2	τ2	NOUN
ejpam-6008	119	10	)	)	PUNCT
ejpam-6008	119	11	→	→	SYM
ejpam-6008	119	12	(	(	PUNCT
ejpam-6008	119	13	y	y	PROPN
ejpam-6008	119	14	,	,	PUNCT
ejpam-6008	119	15	σ1	σ1	PROPN
ejpam-6008	119	16	,	,	PUNCT
ejpam-6008	119	17	σ2	σ2	PROPN
ejpam-6008	119	18	)	)	PUNCT
ejpam-6008	119	19	be	be	AUX
ejpam-6008	119	20	a	a	DET
ejpam-6008	119	21	multifunction	multifunction	NOUN
ejpam-6008	119	22	.	.	PUNCT
ejpam-6008	120	1	if	if	SCONJ
ejpam-6008	120	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	120	3	-	-	NOUN
ejpam-6008	120	4	cl(f	cl(f	NOUN
ejpam-6008	120	5	−(b	−(b	PROPN
ejpam-6008	120	6	)	)	PUNCT
ejpam-6008	120	7	)	)	PUNCT
ejpam-6008	121	1	⊆	⊆	X
ejpam-6008	121	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	121	3	-	-	PUNCT
ejpam-6008	121	4	ker(b	ker(b	PROPN
ejpam-6008	121	5	)	)	PUNCT
ejpam-6008	121	6	)	)	PUNCT
ejpam-6008	121	7	for	for	ADP
ejpam-6008	121	8	every	every	DET
ejpam-6008	121	9	subset	subset	NOUN
ejpam-6008	121	10	b	b	PROPN
ejpam-6008	121	11	of	of	ADP
ejpam-6008	121	12	y	y	PROPN
ejpam-6008	121	13	,	,	PUNCT
ejpam-6008	121	14	then	then	ADV
ejpam-6008	121	15	f	f	PROPN
ejpam-6008	121	16	is	be	AUX
ejpam-6008	121	17	upper	upper	ADJ
ejpam-6008	121	18	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	121	19	,	,	PUNCT
ejpam-6008	121	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	121	21	.	.	PUNCT
ejpam-6008	122	1	proof	proof	NOUN
ejpam-6008	122	2	.	.	PUNCT
ejpam-6008	123	1	suppose	suppose	VERB
ejpam-6008	123	2	that	that	SCONJ
ejpam-6008	123	3	τ1τ2	τ1τ2	NOUN
ejpam-6008	123	4	-	-	PROPN
ejpam-6008	123	5	cl(f	cl(f	NOUN
ejpam-6008	123	6	−(b	−(b	PROPN
ejpam-6008	123	7	)	)	PUNCT
ejpam-6008	123	8	)	)	PUNCT
ejpam-6008	123	9	⊆	⊆	X
ejpam-6008	123	10	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	123	11	-	-	PUNCT
ejpam-6008	123	12	ker(b	ker(b	PROPN
ejpam-6008	123	13	)	)	PUNCT
ejpam-6008	123	14	)	)	PUNCT
ejpam-6008	123	15	for	for	ADP
ejpam-6008	123	16	every	every	DET
ejpam-6008	123	17	subset	subset	NOUN
ejpam-6008	123	18	b	b	PROPN
ejpam-6008	123	19	of	of	ADP
ejpam-6008	123	20	y	y	PROPN
ejpam-6008	123	21	.	.	PUNCT
ejpam-6008	124	1	let	let	VERB
ejpam-6008	124	2	v	v	PART
ejpam-6008	124	3	be	be	AUX
ejpam-6008	124	4	any	any	DET
ejpam-6008	124	5	σ1σ2	σ1σ2	NOUN
ejpam-6008	124	6	-	-	ADJ
ejpam-6008	124	7	open	open	ADJ
ejpam-6008	124	8	set	set	NOUN
ejpam-6008	124	9	of	of	ADP
ejpam-6008	124	10	y	y	PROPN
ejpam-6008	124	11	.	.	PUNCT
ejpam-6008	125	1	by	by	ADP
ejpam-6008	125	2	lemma	lemma	PROPN
ejpam-6008	125	3	2	2	NUM
ejpam-6008	125	4	,	,	PUNCT
ejpam-6008	125	5	we	we	PRON
ejpam-6008	125	6	have	have	VERB
ejpam-6008	125	7	τ1τ2	τ1τ2	NOUN
ejpam-6008	125	8	-	-	ADJ
ejpam-6008	125	9	cl(f	cl(f	NUM
ejpam-6008	125	10	−(v	−(v	NOUN
ejpam-6008	125	11	)	)	PUNCT
ejpam-6008	125	12	)	)	PUNCT
ejpam-6008	126	1	⊆	⊆	X
ejpam-6008	126	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	126	3	-	-	PUNCT
ejpam-6008	126	4	ker(v	ker(v	NOUN
ejpam-6008	126	5	)	)	PUNCT
ejpam-6008	126	6	)	)	PUNCT
ejpam-6008	127	1	=	=	SYM
ejpam-6008	127	2	f−(v	f−(v	ADJ
ejpam-6008	127	3	)	)	PUNCT
ejpam-6008	127	4	and	and	CCONJ
ejpam-6008	127	5	hence	hence	ADV
ejpam-6008	127	6	f−(v	f−(v	ADJ
ejpam-6008	127	7	)	)	PUNCT
ejpam-6008	127	8	is	be	AUX
ejpam-6008	127	9	τ1τ2	τ1τ2	VERB
ejpam-6008	127	10	-	-	ADJ
ejpam-6008	127	11	closed	closed	ADJ
ejpam-6008	127	12	inx	inx	NOUN
ejpam-6008	127	13	.	.	PUNCT
ejpam-6008	127	14	by	by	ADP
ejpam-6008	127	15	theorem	theorem	NOUN
ejpam-6008	127	16	1	1	NUM
ejpam-6008	127	17	,	,	PUNCT
ejpam-6008	127	18	f	f	PROPN
ejpam-6008	127	19	is	be	AUX
ejpam-6008	127	20	upper	upper	ADJ
ejpam-6008	127	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	127	22	,	,	PUNCT
ejpam-6008	127	23	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	127	24	.	.	PUNCT
ejpam-6008	128	1	theorem	theorem	NOUN
ejpam-6008	128	2	4	4	NUM
ejpam-6008	128	3	.	.	PUNCT
ejpam-6008	129	1	let	let	VERB
ejpam-6008	129	2	f	f	NOUN
ejpam-6008	129	3	:	:	PUNCT
ejpam-6008	129	4	(	(	PUNCT
ejpam-6008	129	5	x	x	NOUN
ejpam-6008	129	6	,	,	PUNCT
ejpam-6008	129	7	τ1	τ1	NOUN
ejpam-6008	129	8	,	,	PUNCT
ejpam-6008	129	9	τ2	τ2	NOUN
ejpam-6008	129	10	)	)	PUNCT
ejpam-6008	129	11	→	→	SYM
ejpam-6008	129	12	(	(	PUNCT
ejpam-6008	129	13	y	y	PROPN
ejpam-6008	129	14	,	,	PUNCT
ejpam-6008	129	15	σ1	σ1	PROPN
ejpam-6008	129	16	,	,	PUNCT
ejpam-6008	129	17	σ2	σ2	PROPN
ejpam-6008	129	18	)	)	PUNCT
ejpam-6008	129	19	be	be	AUX
ejpam-6008	129	20	a	a	DET
ejpam-6008	129	21	multifunction	multifunction	NOUN
ejpam-6008	129	22	.	.	PUNCT
ejpam-6008	130	1	if	if	SCONJ
ejpam-6008	130	2	f	f	PROPN
ejpam-6008	130	3	(	(	PUNCT
ejpam-6008	130	4	τ1τ2	τ1τ2	NOUN
ejpam-6008	130	5	-	-	NUM
ejpam-6008	130	6	cl(a	cl(a	NUM
ejpam-6008	130	7	)	)	PUNCT
ejpam-6008	130	8	)	)	PUNCT
ejpam-6008	130	9	⊆	⊆	X
ejpam-6008	130	10	σ1σ2	σ1σ2	NUM
ejpam-6008	130	11	-	-	PUNCT
ejpam-6008	130	12	ker(f	ker(f	PROPN
ejpam-6008	130	13	(	(	PUNCT
ejpam-6008	130	14	a	a	NOUN
ejpam-6008	130	15	)	)	PUNCT
ejpam-6008	130	16	)	)	PUNCT
ejpam-6008	130	17	for	for	ADP
ejpam-6008	130	18	every	every	DET
ejpam-6008	130	19	subset	subset	NOUN
ejpam-6008	130	20	a	a	PRON
ejpam-6008	130	21	of	of	ADP
ejpam-6008	130	22	x	x	PRON
ejpam-6008	130	23	,	,	PUNCT
ejpam-6008	130	24	then	then	ADV
ejpam-6008	130	25	f	f	PROPN
ejpam-6008	130	26	is	be	AUX
ejpam-6008	130	27	lower	low	ADJ
ejpam-6008	130	28	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	130	29	,	,	PUNCT
ejpam-6008	130	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	130	31	.	.	PUNCT
ejpam-6008	130	32	proof	proof	NOUN
ejpam-6008	130	33	.	.	PUNCT
ejpam-6008	131	1	let	let	VERB
ejpam-6008	131	2	v	v	PART
ejpam-6008	131	3	be	be	AUX
ejpam-6008	131	4	any	any	DET
ejpam-6008	131	5	σ1σ2	σ1σ2	NOUN
ejpam-6008	131	6	-	-	ADJ
ejpam-6008	131	7	open	open	ADJ
ejpam-6008	131	8	set	set	NOUN
ejpam-6008	131	9	of	of	ADP
ejpam-6008	131	10	y	y	PROPN
ejpam-6008	131	11	.	.	PUNCT
ejpam-6008	132	1	then	then	ADV
ejpam-6008	132	2	,	,	PUNCT
ejpam-6008	132	3	f	f	PROPN
ejpam-6008	132	4	(	(	PUNCT
ejpam-6008	132	5	τ1τ2	τ1τ2	NOUN
ejpam-6008	132	6	-	-	NOUN
ejpam-6008	132	7	cl(f	cl(f	NOUN
ejpam-6008	132	8	+	+	NOUN
ejpam-6008	132	9	(	(	PUNCT
ejpam-6008	132	10	v	v	NOUN
ejpam-6008	132	11	)	)	PUNCT
ejpam-6008	132	12	)	)	PUNCT
ejpam-6008	132	13	)	)	PUNCT
ejpam-6008	132	14	⊆	⊆	X
ejpam-6008	132	15	σ1σ2	σ1σ2	X
ejpam-6008	132	16	-	-	PUNCT
ejpam-6008	132	17	ker(v	ker(v	NOUN
ejpam-6008	132	18	)	)	PUNCT
ejpam-6008	132	19	and	and	CCONJ
ejpam-6008	132	20	hence	hence	ADV
ejpam-6008	132	21	τ1τ2	τ1τ2	NOUN
ejpam-6008	132	22	-	-	NOUN
ejpam-6008	132	23	cl(f	cl(f	NOUN
ejpam-6008	132	24	+	+	NOUN
ejpam-6008	132	25	(	(	PUNCT
ejpam-6008	132	26	v	v	NOUN
ejpam-6008	132	27	)	)	PUNCT
ejpam-6008	132	28	)	)	PUNCT
ejpam-6008	132	29	⊆	⊆	NUM
ejpam-6008	132	30	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	132	31	-	-	PUNCT
ejpam-6008	132	32	ker(v	ker(v	NOUN
ejpam-6008	132	33	)	)	PUNCT
ejpam-6008	132	34	)	)	PUNCT
ejpam-6008	132	35	.	.	PUNCT
ejpam-6008	133	1	by	by	ADP
ejpam-6008	133	2	lemma	lemma	PROPN
ejpam-6008	133	3	2	2	NUM
ejpam-6008	133	4	,	,	PUNCT
ejpam-6008	133	5	we	we	PRON
ejpam-6008	133	6	have	have	VERB
ejpam-6008	133	7	τ1τ2	τ1τ2	NOUN
ejpam-6008	133	8	-	-	NOUN
ejpam-6008	133	9	cl(f	cl(f	NOUN
ejpam-6008	133	10	+	+	NOUN
ejpam-6008	133	11	(	(	PUNCT
ejpam-6008	133	12	v	v	NOUN
ejpam-6008	133	13	)	)	PUNCT
ejpam-6008	133	14	)	)	PUNCT
ejpam-6008	134	1	⊆	⊆	NUM
ejpam-6008	134	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	134	3	-	-	PUNCT
ejpam-6008	134	4	ker(v	ker(v	NOUN
ejpam-6008	134	5	)	)	PUNCT
ejpam-6008	134	6	)	)	PUNCT
ejpam-6008	134	7	=	=	PUNCT
ejpam-6008	135	1	f+(v	f+(v	NOUN
ejpam-6008	135	2	)	)	PUNCT
ejpam-6008	135	3	and	and	CCONJ
ejpam-6008	135	4	hence	hence	ADV
ejpam-6008	135	5	f+(v	f+(v	PROPN
ejpam-6008	135	6	)	)	PUNCT
ejpam-6008	135	7	is	be	AUX
ejpam-6008	135	8	τ1τ2	τ1τ2	NOUN
ejpam-6008	135	9	-	-	ADJ
ejpam-6008	135	10	closed	closed	ADJ
ejpam-6008	135	11	in	in	ADP
ejpam-6008	135	12	x.	x.	NOUN
ejpam-6008	135	13	by	by	ADP
ejpam-6008	135	14	theorem	theorem	NOUN
ejpam-6008	135	15	2	2	NUM
ejpam-6008	135	16	,	,	PUNCT
ejpam-6008	135	17	f	f	PROPN
ejpam-6008	135	18	is	be	AUX
ejpam-6008	135	19	lower	low	ADJ
ejpam-6008	135	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	135	21	,	,	PUNCT
ejpam-6008	135	22	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	135	23	.	.	PUNCT
ejpam-6008	136	1	theorem	theorem	NOUN
ejpam-6008	136	2	5	5	NUM
ejpam-6008	136	3	.	.	PUNCT
ejpam-6008	137	1	let	let	VERB
ejpam-6008	137	2	f	f	NOUN
ejpam-6008	137	3	:	:	PUNCT
ejpam-6008	137	4	(	(	PUNCT
ejpam-6008	137	5	x	x	NOUN
ejpam-6008	137	6	,	,	PUNCT
ejpam-6008	137	7	τ1	τ1	NOUN
ejpam-6008	137	8	,	,	PUNCT
ejpam-6008	137	9	τ2	τ2	NOUN
ejpam-6008	137	10	)	)	PUNCT
ejpam-6008	137	11	→	→	SYM
ejpam-6008	137	12	(	(	PUNCT
ejpam-6008	137	13	y	y	PROPN
ejpam-6008	137	14	,	,	PUNCT
ejpam-6008	137	15	σ1	σ1	PROPN
ejpam-6008	137	16	,	,	PUNCT
ejpam-6008	137	17	σ2	σ2	PROPN
ejpam-6008	137	18	)	)	PUNCT
ejpam-6008	137	19	be	be	AUX
ejpam-6008	137	20	a	a	DET
ejpam-6008	137	21	multifunction	multifunction	NOUN
ejpam-6008	137	22	.	.	PUNCT
ejpam-6008	138	1	if	if	SCONJ
ejpam-6008	138	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	138	3	-	-	NOUN
ejpam-6008	138	4	cl(f	cl(f	NOUN
ejpam-6008	138	5	+	+	NOUN
ejpam-6008	138	6	(	(	PUNCT
ejpam-6008	138	7	b	b	NOUN
ejpam-6008	138	8	)	)	PUNCT
ejpam-6008	138	9	)	)	PUNCT
ejpam-6008	138	10	⊆	⊆	NUM
ejpam-6008	138	11	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	138	12	-	-	PUNCT
ejpam-6008	138	13	ker(b	ker(b	NOUN
ejpam-6008	138	14	)	)	PUNCT
ejpam-6008	138	15	)	)	PUNCT
ejpam-6008	138	16	for	for	ADP
ejpam-6008	138	17	every	every	DET
ejpam-6008	138	18	subset	subset	NOUN
ejpam-6008	138	19	b	b	PROPN
ejpam-6008	138	20	of	of	ADP
ejpam-6008	138	21	y	y	PROPN
ejpam-6008	138	22	,	,	PUNCT
ejpam-6008	138	23	then	then	ADV
ejpam-6008	138	24	f	f	PROPN
ejpam-6008	138	25	is	be	AUX
ejpam-6008	138	26	lower	low	ADJ
ejpam-6008	138	27	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	138	28	,	,	PUNCT
ejpam-6008	138	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	138	30	.	.	PUNCT
ejpam-6008	139	1	proof	proof	NOUN
ejpam-6008	139	2	.	.	PUNCT
ejpam-6008	140	1	let	let	VERB
ejpam-6008	140	2	v	v	PART
ejpam-6008	140	3	be	be	AUX
ejpam-6008	140	4	any	any	DET
ejpam-6008	140	5	σ1σ2	σ1σ2	NOUN
ejpam-6008	140	6	-	-	ADJ
ejpam-6008	140	7	open	open	ADJ
ejpam-6008	140	8	set	set	NOUN
ejpam-6008	140	9	of	of	ADP
ejpam-6008	140	10	y	y	PROPN
ejpam-6008	140	11	.	.	PUNCT
ejpam-6008	141	1	then	then	ADV
ejpam-6008	141	2	,	,	PUNCT
ejpam-6008	141	3	τ1τ2	τ1τ2	NOUN
ejpam-6008	141	4	-	-	NOUN
ejpam-6008	141	5	cl(f	cl(f	NOUN
ejpam-6008	141	6	+	+	NOUN
ejpam-6008	141	7	(	(	PUNCT
ejpam-6008	141	8	v	v	NOUN
ejpam-6008	141	9	)	)	PUNCT
ejpam-6008	141	10	)	)	PUNCT
ejpam-6008	141	11	⊆	⊆	NUM
ejpam-6008	141	12	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	141	13	-	-	PUNCT
ejpam-6008	141	14	ker(v	ker(v	NOUN
ejpam-6008	141	15	)	)	PUNCT
ejpam-6008	141	16	)	)	PUNCT
ejpam-6008	141	17	and	and	CCONJ
ejpam-6008	141	18	by	by	ADP
ejpam-6008	141	19	lemma	lemma	PROPN
ejpam-6008	141	20	2	2	NUM
ejpam-6008	141	21	,	,	PUNCT
ejpam-6008	141	22	τ1τ2	τ1τ2	NOUN
ejpam-6008	141	23	-	-	NOUN
ejpam-6008	141	24	cl(f	cl(f	NOUN
ejpam-6008	141	25	+	+	NOUN
ejpam-6008	141	26	(	(	PUNCT
ejpam-6008	141	27	v	v	NOUN
ejpam-6008	141	28	)	)	PUNCT
ejpam-6008	141	29	)	)	PUNCT
ejpam-6008	141	30	⊆	⊆	NUM
ejpam-6008	141	31	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	141	32	-	-	PUNCT
ejpam-6008	141	33	ker(v	ker(v	NOUN
ejpam-6008	141	34	)	)	PUNCT
ejpam-6008	141	35	)	)	PUNCT
ejpam-6008	141	36	=	=	PUNCT
ejpam-6008	141	37	f+(v	f+(v	NOUN
ejpam-6008	141	38	)	)	PUNCT
ejpam-6008	141	39	.	.	PUNCT
ejpam-6008	142	1	this	this	PRON
ejpam-6008	142	2	implies	imply	VERB
ejpam-6008	142	3	that	that	SCONJ
ejpam-6008	142	4	f+(v	f+(v	PROPN
ejpam-6008	142	5	)	)	PUNCT
ejpam-6008	142	6	is	be	AUX
ejpam-6008	142	7	τ1τ2	τ1τ2	NOUN
ejpam-6008	142	8	-	-	ADJ
ejpam-6008	142	9	closed	closed	ADJ
ejpam-6008	142	10	in	in	ADP
ejpam-6008	142	11	x.	x.	NOUN
ejpam-6008	142	12	by	by	ADP
ejpam-6008	142	13	theorem	theorem	NOUN
ejpam-6008	142	14	2	2	NUM
ejpam-6008	142	15	,	,	PUNCT
ejpam-6008	142	16	f	f	PROPN
ejpam-6008	142	17	is	be	AUX
ejpam-6008	142	18	lower	low	ADJ
ejpam-6008	142	19	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	142	20	,	,	PUNCT
ejpam-6008	142	21	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	142	22	.	.	PUNCT
ejpam-6008	143	1	n.	n.	PROPN
ejpam-6008	143	2	viriyapong	viriyapong	PROPN
ejpam-6008	143	3	,	,	PUNCT
ejpam-6008	143	4	a.	a.	PROPN
ejpam-6008	143	5	sama	sama	PROPN
ejpam-6008	143	6	-	-	PUNCT
ejpam-6008	143	7	ae	ae	PROPN
ejpam-6008	143	8	,	,	PUNCT
ejpam-6008	143	9	c.	c.	PROPN
ejpam-6008	143	10	boonpok	boonpok	PROPN
ejpam-6008	143	11	/	/	SYM
ejpam-6008	143	12	eur	eur	PROPN
ejpam-6008	143	13	.	.	PUNCT
ejpam-6008	144	1	j.	j.	PROPN
ejpam-6008	144	2	pure	pure	PROPN
ejpam-6008	144	3	appl	appl	PROPN
ejpam-6008	144	4	.	.	PROPN
ejpam-6008	144	5	math	math	PROPN
ejpam-6008	144	6	,	,	PUNCT
ejpam-6008	144	7	18	18	NUM
ejpam-6008	144	8	(	(	PUNCT
ejpam-6008	144	9	2	2	NUM
ejpam-6008	144	10	)	)	PUNCT
ejpam-6008	144	11	(	(	PUNCT
ejpam-6008	144	12	2025	2025	NUM
ejpam-6008	144	13	)	)	PUNCT
ejpam-6008	144	14	,	,	PUNCT
ejpam-6008	144	15	6008	6008	NUM
ejpam-6008	144	16	6	6	NUM
ejpam-6008	144	17	of	of	ADP
ejpam-6008	144	18	15	15	NUM
ejpam-6008	144	19	definition	definition	NOUN
ejpam-6008	144	20	3	3	NUM
ejpam-6008	144	21	.	.	PUNCT
ejpam-6008	145	1	[	[	X
ejpam-6008	145	2	6	6	NUM
ejpam-6008	145	3	]	]	PUNCT
ejpam-6008	145	4	a	a	DET
ejpam-6008	145	5	multifunction	multifunction	NOUN
ejpam-6008	145	6	f	f	NOUN
ejpam-6008	145	7	:	:	PUNCT
ejpam-6008	145	8	(	(	PUNCT
ejpam-6008	145	9	x	x	NOUN
ejpam-6008	145	10	,	,	PUNCT
ejpam-6008	145	11	τ1	τ1	NOUN
ejpam-6008	145	12	,	,	PUNCT
ejpam-6008	145	13	τ2	τ2	NOUN
ejpam-6008	145	14	)	)	PUNCT
ejpam-6008	145	15	→	→	SYM
ejpam-6008	145	16	(	(	PUNCT
ejpam-6008	145	17	y	y	PROPN
ejpam-6008	145	18	,	,	PUNCT
ejpam-6008	145	19	σ1	σ1	PROPN
ejpam-6008	145	20	,	,	PUNCT
ejpam-6008	145	21	σ2	σ2	PROPN
ejpam-6008	145	22	)	)	PUNCT
ejpam-6008	145	23	is	be	AUX
ejpam-6008	145	24	said	say	VERB
ejpam-6008	145	25	to	to	PART
ejpam-6008	145	26	be	be	AUX
ejpam-6008	145	27	upper	upper	ADJ
ejpam-6008	145	28	weakly	weakly	ADJ
ejpam-6008	145	29	(	(	PUNCT
ejpam-6008	145	30	τ1	τ1	NOUN
ejpam-6008	145	31	,	,	PUNCT
ejpam-6008	145	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	145	33	if	if	SCONJ
ejpam-6008	145	34	for	for	ADP
ejpam-6008	145	35	each	each	DET
ejpam-6008	145	36	x	x	SYM
ejpam-6008	145	37	∈	∈	PROPN
ejpam-6008	145	38	x	x	X
ejpam-6008	145	39	and	and	CCONJ
ejpam-6008	145	40	each	each	DET
ejpam-6008	145	41	σ1σ2	σ1σ2	VERB
ejpam-6008	145	42	-	-	ADJ
ejpam-6008	145	43	open	open	ADJ
ejpam-6008	145	44	set	set	NOUN
ejpam-6008	145	45	v	v	NOUN
ejpam-6008	145	46	of	of	ADP
ejpam-6008	145	47	y	y	PROPN
ejpam-6008	145	48	containing	contain	VERB
ejpam-6008	145	49	f	f	PROPN
ejpam-6008	145	50	(	(	PUNCT
ejpam-6008	145	51	x	x	NOUN
ejpam-6008	145	52	)	)	PUNCT
ejpam-6008	145	53	,	,	PUNCT
ejpam-6008	145	54	there	there	PRON
ejpam-6008	145	55	exists	exist	VERB
ejpam-6008	145	56	a	a	DET
ejpam-6008	145	57	τ1τ2	τ1τ2	NOUN
ejpam-6008	145	58	-	-	ADJ
ejpam-6008	145	59	open	open	ADJ
ejpam-6008	145	60	set	set	ADJ
ejpam-6008	145	61	u	u	NOUN
ejpam-6008	145	62	of	of	ADP
ejpam-6008	145	63	x	x	PUNCT
ejpam-6008	145	64	containing	contain	VERB
ejpam-6008	145	65	x	x	PUNCT
ejpam-6008	145	66	such	such	ADJ
ejpam-6008	145	67	that	that	SCONJ
ejpam-6008	145	68	f	f	PROPN
ejpam-6008	145	69	(	(	PUNCT
ejpam-6008	145	70	u	u	NOUN
ejpam-6008	145	71	)	)	PUNCT
ejpam-6008	145	72	⊆	⊆	NUM
ejpam-6008	145	73	σ1σ2	σ1σ2	NOUN
ejpam-6008	145	74	-	-	NUM
ejpam-6008	145	75	cl(v	cl(v	NOUN
ejpam-6008	145	76	)	)	PUNCT
ejpam-6008	145	77	.	.	PUNCT
ejpam-6008	146	1	theorem	theorem	NOUN
ejpam-6008	146	2	6	6	NUM
ejpam-6008	146	3	.	.	PUNCT
ejpam-6008	147	1	if	if	SCONJ
ejpam-6008	147	2	f	f	PROPN
ejpam-6008	147	3	:	:	PUNCT
ejpam-6008	147	4	(	(	PUNCT
ejpam-6008	147	5	x	x	NOUN
ejpam-6008	147	6	,	,	PUNCT
ejpam-6008	147	7	τ1	τ1	NOUN
ejpam-6008	147	8	,	,	PUNCT
ejpam-6008	147	9	τ2	τ2	NOUN
ejpam-6008	147	10	)	)	PUNCT
ejpam-6008	147	11	→	→	SYM
ejpam-6008	147	12	(	(	PUNCT
ejpam-6008	147	13	y	y	PROPN
ejpam-6008	147	14	,	,	PUNCT
ejpam-6008	147	15	σ1	σ1	PROPN
ejpam-6008	147	16	,	,	PUNCT
ejpam-6008	147	17	σ2	σ2	PROPN
ejpam-6008	147	18	)	)	PUNCT
ejpam-6008	147	19	is	be	AUX
ejpam-6008	147	20	an	an	DET
ejpam-6008	147	21	upper	upper	ADJ
ejpam-6008	147	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	147	23	,	,	PUNCT
ejpam-6008	147	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	147	25	multifunction	multifunction	NOUN
ejpam-6008	147	26	,	,	PUNCT
ejpam-6008	147	27	then	then	ADV
ejpam-6008	147	28	f	f	PROPN
ejpam-6008	147	29	is	be	AUX
ejpam-6008	147	30	upper	upper	ADJ
ejpam-6008	147	31	weakly	weakly	ADJ
ejpam-6008	147	32	(	(	PUNCT
ejpam-6008	147	33	τ1	τ1	NOUN
ejpam-6008	147	34	,	,	PUNCT
ejpam-6008	147	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	147	36	.	.	PUNCT
ejpam-6008	148	1	proof	proof	NOUN
ejpam-6008	148	2	.	.	PUNCT
ejpam-6008	149	1	let	let	VERB
ejpam-6008	149	2	x	x	PUNCT
ejpam-6008	149	3	∈	∈	PROPN
ejpam-6008	149	4	x	x	X
ejpam-6008	149	5	and	and	CCONJ
ejpam-6008	149	6	v	v	X
ejpam-6008	149	7	be	be	AUX
ejpam-6008	149	8	any	any	DET
ejpam-6008	149	9	σ1σ2	σ1σ2	NOUN
ejpam-6008	149	10	-	-	ADJ
ejpam-6008	149	11	open	open	ADJ
ejpam-6008	149	12	set	set	NOUN
ejpam-6008	149	13	of	of	ADP
ejpam-6008	149	14	y	y	PROPN
ejpam-6008	149	15	containing	contain	VERB
ejpam-6008	149	16	f	f	PROPN
ejpam-6008	149	17	(	(	PUNCT
ejpam-6008	149	18	x	x	NOUN
ejpam-6008	149	19	)	)	PUNCT
ejpam-6008	149	20	.	.	PUNCT
ejpam-6008	150	1	then	then	ADV
ejpam-6008	150	2	,	,	PUNCT
ejpam-6008	150	3	σ1σ2	σ1σ2	NOUN
ejpam-6008	150	4	-	-	NUM
ejpam-6008	150	5	cl(v	cl(v	NOUN
ejpam-6008	150	6	)	)	PUNCT
ejpam-6008	150	7	is	be	AUX
ejpam-6008	150	8	a	a	DET
ejpam-6008	150	9	σ1σ2	σ1σ2	NUM
ejpam-6008	150	10	-	-	PUNCT
ejpam-6008	150	11	closed	closed	ADJ
ejpam-6008	150	12	set	set	NOUN
ejpam-6008	150	13	y	y	NOUN
ejpam-6008	150	14	containing	contain	VERB
ejpam-6008	150	15	f	f	PROPN
ejpam-6008	150	16	(	(	PUNCT
ejpam-6008	150	17	x	x	NOUN
ejpam-6008	150	18	)	)	PUNCT
ejpam-6008	150	19	.	.	PUNCT
ejpam-6008	151	1	since	since	SCONJ
ejpam-6008	151	2	f	f	PROPN
ejpam-6008	151	3	is	be	AUX
ejpam-6008	151	4	upper	upper	ADJ
ejpam-6008	151	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	151	6	,	,	PUNCT
ejpam-6008	151	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	151	8	,	,	PUNCT
ejpam-6008	151	9	by	by	ADP
ejpam-6008	151	10	theorem	theorem	NOUN
ejpam-6008	151	11	1	1	NUM
ejpam-6008	151	12	there	there	ADV
ejpam-6008	151	13	exists	exist	VERB
ejpam-6008	151	14	a	a	DET
ejpam-6008	151	15	τ1τ2	τ1τ2	NOUN
ejpam-6008	151	16	-	-	ADJ
ejpam-6008	151	17	open	open	ADJ
ejpam-6008	151	18	set	set	NOUN
ejpam-6008	151	19	u	u	PRON
ejpam-6008	151	20	ofx	ofx	NOUN
ejpam-6008	151	21	containing	contain	VERB
ejpam-6008	151	22	x	x	PUNCT
ejpam-6008	151	23	such	such	ADJ
ejpam-6008	151	24	that	that	SCONJ
ejpam-6008	151	25	u	u	NOUN
ejpam-6008	151	26	⊆	⊆	NUM
ejpam-6008	151	27	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	151	28	-	-	PUNCT
ejpam-6008	151	29	cl(v	cl(v	NOUN
ejpam-6008	151	30	)	)	PUNCT
ejpam-6008	151	31	)	)	PUNCT
ejpam-6008	151	32	;	;	PUNCT
ejpam-6008	151	33	hence	hence	ADV
ejpam-6008	151	34	f	f	PROPN
ejpam-6008	151	35	(	(	PUNCT
ejpam-6008	151	36	u	u	NOUN
ejpam-6008	151	37	)	)	PUNCT
ejpam-6008	151	38	⊆	⊆	NUM
ejpam-6008	151	39	σ1σ2	σ1σ2	NOUN
ejpam-6008	151	40	-	-	NUM
ejpam-6008	151	41	cl(v	cl(v	NOUN
ejpam-6008	151	42	)	)	PUNCT
ejpam-6008	151	43	.	.	PUNCT
ejpam-6008	152	1	this	this	PRON
ejpam-6008	152	2	shows	show	VERB
ejpam-6008	152	3	that	that	SCONJ
ejpam-6008	152	4	f	f	PROPN
ejpam-6008	152	5	is	be	AUX
ejpam-6008	152	6	upper	upper	ADJ
ejpam-6008	152	7	weakly	weakly	ADJ
ejpam-6008	152	8	(	(	PUNCT
ejpam-6008	152	9	τ1	τ1	NOUN
ejpam-6008	152	10	,	,	PUNCT
ejpam-6008	152	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	152	12	.	.	PUNCT
ejpam-6008	153	1	the	the	DET
ejpam-6008	153	2	converse	converse	NOUN
ejpam-6008	153	3	of	of	ADP
ejpam-6008	153	4	theorem	theorem	NOUN
ejpam-6008	153	5	6	6	NUM
ejpam-6008	153	6	is	be	AUX
ejpam-6008	153	7	not	not	PART
ejpam-6008	153	8	true	true	ADJ
ejpam-6008	153	9	in	in	ADP
ejpam-6008	153	10	general	general	ADJ
ejpam-6008	153	11	as	as	SCONJ
ejpam-6008	153	12	shown	show	VERB
ejpam-6008	153	13	in	in	ADP
ejpam-6008	153	14	the	the	DET
ejpam-6008	153	15	following	follow	VERB
ejpam-6008	153	16	example	example	NOUN
ejpam-6008	153	17	.	.	PUNCT
ejpam-6008	154	1	example	example	NOUN
ejpam-6008	155	1	1	1	NUM
ejpam-6008	155	2	.	.	PUNCT
ejpam-6008	155	3	let	let	VERB
ejpam-6008	155	4	x	x	PUNCT
ejpam-6008	155	5	=	=	PRON
ejpam-6008	155	6	{	{	PUNCT
ejpam-6008	155	7	a	a	PRON
ejpam-6008	155	8	,	,	PUNCT
ejpam-6008	155	9	b	b	NOUN
ejpam-6008	155	10	,	,	PUNCT
ejpam-6008	155	11	c	c	NOUN
ejpam-6008	155	12	,	,	PUNCT
ejpam-6008	155	13	d	d	NOUN
ejpam-6008	155	14	}	}	PUNCT
ejpam-6008	155	15	with	with	ADP
ejpam-6008	155	16	topologies	topology	NOUN
ejpam-6008	155	17	τ1	τ1	NOUN
ejpam-6008	155	18	=	=	SYM
ejpam-6008	155	19	{	{	PUNCT
ejpam-6008	155	20	∅	∅	NOUN
ejpam-6008	155	21	,	,	PUNCT
ejpam-6008	155	22	{	{	PUNCT
ejpam-6008	155	23	a	a	X
ejpam-6008	155	24	}	}	PUNCT
ejpam-6008	155	25	,	,	PUNCT
ejpam-6008	155	26	{	{	PUNCT
ejpam-6008	155	27	a	a	DET
ejpam-6008	155	28	,	,	PUNCT
ejpam-6008	155	29	b	b	NOUN
ejpam-6008	155	30	}	}	PUNCT
ejpam-6008	155	31	,	,	PUNCT
ejpam-6008	155	32	{	{	PUNCT
ejpam-6008	155	33	a	a	PRON
ejpam-6008	155	34	,	,	PUNCT
ejpam-6008	155	35	b	b	NOUN
ejpam-6008	155	36	,	,	PUNCT
ejpam-6008	155	37	c	c	NOUN
ejpam-6008	155	38	}	}	PUNCT
ejpam-6008	155	39	,	,	PUNCT
ejpam-6008	155	40	x	x	NOUN
ejpam-6008	155	41	}	}	PUNCT
ejpam-6008	155	42	and	and	CCONJ
ejpam-6008	155	43	τ2	τ2	NOUN
ejpam-6008	155	44	=	=	SYM
ejpam-6008	155	45	{	{	PUNCT
ejpam-6008	155	46	∅	∅	NOUN
ejpam-6008	155	47	,	,	PUNCT
ejpam-6008	155	48	{	{	PUNCT
ejpam-6008	155	49	a	a	X
ejpam-6008	155	50	}	}	PUNCT
ejpam-6008	155	51	,	,	PUNCT
ejpam-6008	155	52	{	{	PUNCT
ejpam-6008	155	53	a	a	DET
ejpam-6008	155	54	,	,	PUNCT
ejpam-6008	155	55	b	b	NOUN
ejpam-6008	155	56	}	}	PUNCT
ejpam-6008	155	57	,	,	PUNCT
ejpam-6008	155	58	{	{	PUNCT
ejpam-6008	155	59	a	a	DET
ejpam-6008	155	60	,	,	PUNCT
ejpam-6008	155	61	b	b	NOUN
ejpam-6008	155	62	,	,	PUNCT
ejpam-6008	155	63	c	c	NOUN
ejpam-6008	155	64	}	}	PUNCT
ejpam-6008	155	65	,	,	PUNCT
ejpam-6008	155	66	{	{	PUNCT
ejpam-6008	155	67	a	a	PRON
ejpam-6008	155	68	,	,	PUNCT
ejpam-6008	155	69	b	b	NOUN
ejpam-6008	155	70	,	,	PUNCT
ejpam-6008	155	71	d	d	NOUN
ejpam-6008	155	72	}	}	PUNCT
ejpam-6008	155	73	,	,	PUNCT
ejpam-6008	155	74	x	x	NOUN
ejpam-6008	155	75	}	}	PUNCT
ejpam-6008	155	76	.	.	PUNCT
ejpam-6008	156	1	let	let	VERB
ejpam-6008	156	2	y	y	PROPN
ejpam-6008	156	3	=	=	PUNCT
ejpam-6008	156	4	{	{	PUNCT
ejpam-6008	156	5	1	1	NUM
ejpam-6008	156	6	,	,	PUNCT
ejpam-6008	156	7	2	2	NUM
ejpam-6008	156	8	,	,	PUNCT
ejpam-6008	156	9	3	3	NUM
ejpam-6008	156	10	,	,	PUNCT
ejpam-6008	156	11	4	4	NUM
ejpam-6008	156	12	}	}	PUNCT
ejpam-6008	156	13	with	with	ADP
ejpam-6008	156	14	topologies	topology	NOUN
ejpam-6008	156	15	σ1	σ1	NOUN
ejpam-6008	156	16	=	=	SYM
ejpam-6008	156	17	{	{	PUNCT
ejpam-6008	156	18	∅	∅	NOUN
ejpam-6008	156	19	,	,	PUNCT
ejpam-6008	156	20	{	{	PUNCT
ejpam-6008	156	21	1	1	NUM
ejpam-6008	156	22	}	}	PUNCT
ejpam-6008	156	23	,	,	PUNCT
ejpam-6008	156	24	{	{	PUNCT
ejpam-6008	156	25	1	1	NUM
ejpam-6008	156	26	,	,	PUNCT
ejpam-6008	156	27	2	2	NUM
ejpam-6008	156	28	}	}	PUNCT
ejpam-6008	156	29	,	,	PUNCT
ejpam-6008	156	30	{	{	PUNCT
ejpam-6008	156	31	1	1	NUM
ejpam-6008	156	32	,	,	PUNCT
ejpam-6008	156	33	2	2	NUM
ejpam-6008	156	34	,	,	PUNCT
ejpam-6008	156	35	3	3	NUM
ejpam-6008	156	36	}	}	PUNCT
ejpam-6008	156	37	,	,	PUNCT
ejpam-6008	156	38	{	{	PUNCT
ejpam-6008	156	39	1	1	NUM
ejpam-6008	156	40	,	,	PUNCT
ejpam-6008	156	41	2	2	NUM
ejpam-6008	156	42	,	,	PUNCT
ejpam-6008	156	43	4	4	NUM
ejpam-6008	156	44	}	}	PUNCT
ejpam-6008	156	45	,	,	PUNCT
ejpam-6008	156	46	y	y	PROPN
ejpam-6008	156	47	}	}	PUNCT
ejpam-6008	156	48	and	and	CCONJ
ejpam-6008	156	49	σ2	σ2	PROPN
ejpam-6008	156	50	=	=	SYM
ejpam-6008	156	51	{	{	PUNCT
ejpam-6008	156	52	∅	∅	NOUN
ejpam-6008	156	53	,	,	PUNCT
ejpam-6008	156	54	{	{	PUNCT
ejpam-6008	156	55	1	1	NUM
ejpam-6008	156	56	}	}	PUNCT
ejpam-6008	156	57	,	,	PUNCT
ejpam-6008	156	58	{	{	PUNCT
ejpam-6008	156	59	1	1	NUM
ejpam-6008	156	60	,	,	PUNCT
ejpam-6008	156	61	2	2	NUM
ejpam-6008	156	62	}	}	PUNCT
ejpam-6008	156	63	,	,	PUNCT
ejpam-6008	156	64	{	{	PUNCT
ejpam-6008	156	65	1	1	NUM
ejpam-6008	156	66	,	,	PUNCT
ejpam-6008	156	67	2	2	NUM
ejpam-6008	156	68	,	,	PUNCT
ejpam-6008	156	69	3	3	NUM
ejpam-6008	156	70	}	}	PUNCT
ejpam-6008	156	71	,	,	PUNCT
ejpam-6008	156	72	y	y	PROPN
ejpam-6008	156	73	}	}	PUNCT
ejpam-6008	156	74	.	.	PUNCT
ejpam-6008	157	1	a	a	DET
ejpam-6008	157	2	multifunction	multifunction	NOUN
ejpam-6008	157	3	f	f	NOUN
ejpam-6008	157	4	:	:	PUNCT
ejpam-6008	157	5	(	(	PUNCT
ejpam-6008	157	6	x	x	NOUN
ejpam-6008	157	7	,	,	PUNCT
ejpam-6008	157	8	τ1	τ1	NOUN
ejpam-6008	157	9	,	,	PUNCT
ejpam-6008	157	10	τ2	τ2	NOUN
ejpam-6008	157	11	)	)	PUNCT
ejpam-6008	157	12	→	→	SYM
ejpam-6008	157	13	(	(	PUNCT
ejpam-6008	157	14	y	y	PROPN
ejpam-6008	157	15	,	,	PUNCT
ejpam-6008	157	16	σ1	σ1	PROPN
ejpam-6008	157	17	,	,	PUNCT
ejpam-6008	157	18	σ2	σ2	PROPN
ejpam-6008	157	19	)	)	PUNCT
ejpam-6008	157	20	is	be	AUX
ejpam-6008	157	21	defined	define	VERB
ejpam-6008	157	22	as	as	SCONJ
ejpam-6008	157	23	follows	follow	VERB
ejpam-6008	157	24	:	:	PUNCT
ejpam-6008	157	25	f	f	X
ejpam-6008	157	26	(	(	PUNCT
ejpam-6008	157	27	a	a	X
ejpam-6008	157	28	)	)	PUNCT
ejpam-6008	157	29	=	=	SYM
ejpam-6008	157	30	{	{	PUNCT
ejpam-6008	157	31	1	1	NUM
ejpam-6008	157	32	,	,	PUNCT
ejpam-6008	157	33	2	2	NUM
ejpam-6008	157	34	}	}	PUNCT
ejpam-6008	157	35	,	,	PUNCT
ejpam-6008	157	36	f	f	PROPN
ejpam-6008	157	37	(	(	PUNCT
ejpam-6008	157	38	b	b	X
ejpam-6008	157	39	)	)	PUNCT
ejpam-6008	157	40	=	=	SYM
ejpam-6008	157	41	{	{	PUNCT
ejpam-6008	157	42	2	2	NUM
ejpam-6008	157	43	}	}	PUNCT
ejpam-6008	157	44	,	,	PUNCT
ejpam-6008	157	45	f	f	PROPN
ejpam-6008	157	46	(	(	PUNCT
ejpam-6008	157	47	c	c	X
ejpam-6008	157	48	)	)	PUNCT
ejpam-6008	157	49	=	=	SYM
ejpam-6008	157	50	{	{	PUNCT
ejpam-6008	157	51	1	1	NUM
ejpam-6008	157	52	,	,	PUNCT
ejpam-6008	157	53	2	2	NUM
ejpam-6008	157	54	}	}	PUNCT
ejpam-6008	157	55	and	and	CCONJ
ejpam-6008	157	56	f	f	PROPN
ejpam-6008	157	57	(	(	PUNCT
ejpam-6008	157	58	d	d	X
ejpam-6008	157	59	)	)	PUNCT
ejpam-6008	157	60	=	=	SYM
ejpam-6008	157	61	{	{	PUNCT
ejpam-6008	157	62	4	4	NUM
ejpam-6008	157	63	}	}	PUNCT
ejpam-6008	157	64	.	.	PUNCT
ejpam-6008	158	1	then	then	ADV
ejpam-6008	158	2	,	,	PUNCT
ejpam-6008	158	3	f	f	PROPN
ejpam-6008	158	4	is	be	AUX
ejpam-6008	158	5	upper	upper	ADJ
ejpam-6008	158	6	weakly	weakly	ADJ
ejpam-6008	158	7	(	(	PUNCT
ejpam-6008	158	8	τ1	τ1	NOUN
ejpam-6008	158	9	,	,	PUNCT
ejpam-6008	158	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	159	1	but	but	CCONJ
ejpam-6008	159	2	f	f	PROPN
ejpam-6008	159	3	is	be	AUX
ejpam-6008	159	4	not	not	PART
ejpam-6008	159	5	upper	upper	ADJ
ejpam-6008	159	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	159	7	,	,	PUNCT
ejpam-6008	159	8	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	159	9	.	.	PUNCT
ejpam-6008	160	1	definition	definition	NOUN
ejpam-6008	160	2	4	4	NUM
ejpam-6008	160	3	.	.	PUNCT
ejpam-6008	161	1	[	[	X
ejpam-6008	161	2	6	6	NUM
ejpam-6008	161	3	]	]	PUNCT
ejpam-6008	161	4	a	a	DET
ejpam-6008	161	5	multifunction	multifunction	NOUN
ejpam-6008	161	6	f	f	NOUN
ejpam-6008	161	7	:	:	PUNCT
ejpam-6008	161	8	(	(	PUNCT
ejpam-6008	161	9	x	x	NOUN
ejpam-6008	161	10	,	,	PUNCT
ejpam-6008	161	11	τ1	τ1	NOUN
ejpam-6008	161	12	,	,	PUNCT
ejpam-6008	161	13	τ2	τ2	NOUN
ejpam-6008	161	14	)	)	PUNCT
ejpam-6008	161	15	→	→	SYM
ejpam-6008	161	16	(	(	PUNCT
ejpam-6008	161	17	y	y	PROPN
ejpam-6008	161	18	,	,	PUNCT
ejpam-6008	161	19	σ1	σ1	PROPN
ejpam-6008	161	20	,	,	PUNCT
ejpam-6008	161	21	σ2	σ2	PROPN
ejpam-6008	161	22	)	)	PUNCT
ejpam-6008	161	23	is	be	AUX
ejpam-6008	161	24	said	say	VERB
ejpam-6008	161	25	to	to	PART
ejpam-6008	161	26	be	be	AUX
ejpam-6008	161	27	lower	low	ADJ
ejpam-6008	161	28	weakly	weakly	ADJ
ejpam-6008	161	29	(	(	PUNCT
ejpam-6008	161	30	τ1	τ1	NOUN
ejpam-6008	161	31	,	,	PUNCT
ejpam-6008	161	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	161	33	if	if	SCONJ
ejpam-6008	161	34	for	for	ADP
ejpam-6008	161	35	each	each	DET
ejpam-6008	161	36	x	x	SYM
ejpam-6008	161	37	∈	∈	PROPN
ejpam-6008	161	38	x	x	X
ejpam-6008	161	39	and	and	CCONJ
ejpam-6008	161	40	each	each	DET
ejpam-6008	161	41	σ1σ2	σ1σ2	VERB
ejpam-6008	161	42	-	-	ADJ
ejpam-6008	161	43	open	open	ADJ
ejpam-6008	161	44	set	set	NOUN
ejpam-6008	161	45	v	v	NOUN
ejpam-6008	161	46	of	of	ADP
ejpam-6008	161	47	y	y	PRON
ejpam-6008	161	48	such	such	ADJ
ejpam-6008	161	49	that	that	SCONJ
ejpam-6008	161	50	f	f	PROPN
ejpam-6008	161	51	(	(	PUNCT
ejpam-6008	161	52	x)∩v	x)∩v	PROPN
ejpam-6008	161	53	̸=	̸=	PROPN
ejpam-6008	161	54	∅	∅	NOUN
ejpam-6008	161	55	,	,	PUNCT
ejpam-6008	161	56	there	there	PRON
ejpam-6008	161	57	exists	exist	VERB
ejpam-6008	161	58	a	a	DET
ejpam-6008	161	59	τ1τ2	τ1τ2	NOUN
ejpam-6008	161	60	-	-	ADJ
ejpam-6008	161	61	open	open	ADJ
ejpam-6008	161	62	set	set	ADJ
ejpam-6008	161	63	u	u	NOUN
ejpam-6008	161	64	of	of	ADP
ejpam-6008	161	65	x	x	PUNCT
ejpam-6008	161	66	containing	contain	VERB
ejpam-6008	161	67	x	x	PUNCT
ejpam-6008	162	1	such	such	ADJ
ejpam-6008	162	2	that	that	SCONJ
ejpam-6008	162	3	σ1σ2	σ1σ2	NOUN
ejpam-6008	162	4	-	-	NUM
ejpam-6008	162	5	cl(v	cl(v	PUNCT
ejpam-6008	162	6	)	)	PUNCT
ejpam-6008	162	7	∩f	∩f	NOUN
ejpam-6008	162	8	(	(	PUNCT
ejpam-6008	162	9	z	z	X
ejpam-6008	162	10	)	)	PUNCT
ejpam-6008	162	11	̸=	̸=	NOUN
ejpam-6008	162	12	∅	∅	NOUN
ejpam-6008	162	13	for	for	ADP
ejpam-6008	162	14	each	each	DET
ejpam-6008	162	15	z	z	NOUN
ejpam-6008	162	16	∈	∈	PROPN
ejpam-6008	162	17	u	u	PROPN
ejpam-6008	162	18	.	.	PUNCT
ejpam-6008	162	19	theorem	theorem	VERB
ejpam-6008	162	20	7	7	NUM
ejpam-6008	162	21	.	.	PUNCT
ejpam-6008	163	1	if	if	SCONJ
ejpam-6008	163	2	f	f	PROPN
ejpam-6008	163	3	:	:	PUNCT
ejpam-6008	163	4	(	(	PUNCT
ejpam-6008	163	5	x	x	NOUN
ejpam-6008	163	6	,	,	PUNCT
ejpam-6008	163	7	τ1	τ1	NOUN
ejpam-6008	163	8	,	,	PUNCT
ejpam-6008	163	9	τ2	τ2	NOUN
ejpam-6008	163	10	)	)	PUNCT
ejpam-6008	163	11	→	→	SYM
ejpam-6008	163	12	(	(	PUNCT
ejpam-6008	163	13	y	y	PROPN
ejpam-6008	163	14	,	,	PUNCT
ejpam-6008	163	15	σ1	σ1	PROPN
ejpam-6008	163	16	,	,	PUNCT
ejpam-6008	163	17	σ2	σ2	PROPN
ejpam-6008	163	18	)	)	PUNCT
ejpam-6008	163	19	is	be	AUX
ejpam-6008	163	20	a	a	DET
ejpam-6008	163	21	lower	low	ADJ
ejpam-6008	163	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	163	23	,	,	PUNCT
ejpam-6008	163	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	163	25	multifunction	multifunction	NOUN
ejpam-6008	163	26	,	,	PUNCT
ejpam-6008	163	27	then	then	ADV
ejpam-6008	163	28	f	f	PROPN
ejpam-6008	163	29	is	be	AUX
ejpam-6008	163	30	lower	low	ADJ
ejpam-6008	163	31	weakly	weakly	ADJ
ejpam-6008	163	32	(	(	PUNCT
ejpam-6008	163	33	τ1	τ1	NOUN
ejpam-6008	163	34	,	,	PUNCT
ejpam-6008	163	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	163	36	.	.	PUNCT
ejpam-6008	164	1	proof	proof	NOUN
ejpam-6008	164	2	.	.	PUNCT
ejpam-6008	165	1	the	the	DET
ejpam-6008	165	2	proof	proof	NOUN
ejpam-6008	165	3	is	be	AUX
ejpam-6008	165	4	similar	similar	ADJ
ejpam-6008	165	5	to	to	ADP
ejpam-6008	165	6	that	that	PRON
ejpam-6008	165	7	of	of	ADP
ejpam-6008	165	8	theorem	theorem	ADJ
ejpam-6008	165	9	6	6	NUM
ejpam-6008	165	10	.	.	PUNCT
ejpam-6008	165	11	recall	recall	VERB
ejpam-6008	165	12	that	that	SCONJ
ejpam-6008	165	13	a	a	DET
ejpam-6008	165	14	bitopological	bitopological	ADJ
ejpam-6008	165	15	space	space	NOUN
ejpam-6008	165	16	(	(	PUNCT
ejpam-6008	165	17	x	x	NOUN
ejpam-6008	165	18	,	,	PUNCT
ejpam-6008	165	19	τ1	τ1	NOUN
ejpam-6008	165	20	,	,	PUNCT
ejpam-6008	165	21	τ2	τ2	NOUN
ejpam-6008	165	22	)	)	PUNCT
ejpam-6008	165	23	is	be	AUX
ejpam-6008	165	24	said	say	VERB
ejpam-6008	165	25	to	to	PART
ejpam-6008	165	26	be	be	AUX
ejpam-6008	165	27	τ1τ2	τ1τ2	NOUN
ejpam-6008	165	28	-	-	ADJ
ejpam-6008	165	29	connected	connected	ADJ
ejpam-6008	166	1	[	[	X
ejpam-6008	166	2	77	77	NUM
ejpam-6008	166	3	]	]	X
ejpam-6008	166	4	if	if	SCONJ
ejpam-6008	166	5	x	x	PRON
ejpam-6008	166	6	can	can	AUX
ejpam-6008	166	7	not	not	PART
ejpam-6008	166	8	be	be	AUX
ejpam-6008	166	9	written	write	VERB
ejpam-6008	166	10	as	as	ADP
ejpam-6008	166	11	the	the	DET
ejpam-6008	166	12	union	union	NOUN
ejpam-6008	166	13	of	of	ADP
ejpam-6008	166	14	two	two	NUM
ejpam-6008	166	15	nonempty	nonempty	ADV
ejpam-6008	166	16	disjoint	disjoint	NOUN
ejpam-6008	166	17	τ1τ2	τ1τ2	ADJ
ejpam-6008	166	18	-	-	ADJ
ejpam-6008	166	19	open	open	ADJ
ejpam-6008	166	20	sets	set	NOUN
ejpam-6008	166	21	.	.	PUNCT
ejpam-6008	167	1	lemma	lemma	PROPN
ejpam-6008	167	2	3	3	NUM
ejpam-6008	167	3	.	.	PUNCT
ejpam-6008	168	1	[	[	X
ejpam-6008	168	2	6	6	NUM
ejpam-6008	168	3	]	]	PUNCT
ejpam-6008	168	4	for	for	ADP
ejpam-6008	168	5	a	a	DET
ejpam-6008	168	6	multifunction	multifunction	NOUN
ejpam-6008	168	7	f	f	NOUN
ejpam-6008	168	8	:	:	PUNCT
ejpam-6008	168	9	(	(	PUNCT
ejpam-6008	168	10	x	x	NOUN
ejpam-6008	168	11	,	,	PUNCT
ejpam-6008	168	12	τ1	τ1	NOUN
ejpam-6008	168	13	,	,	PUNCT
ejpam-6008	168	14	τ2	τ2	NOUN
ejpam-6008	168	15	)	)	PUNCT
ejpam-6008	168	16	→	→	SYM
ejpam-6008	168	17	(	(	PUNCT
ejpam-6008	168	18	y	y	PROPN
ejpam-6008	168	19	,	,	PUNCT
ejpam-6008	168	20	σ1	σ1	PROPN
ejpam-6008	168	21	,	,	PUNCT
ejpam-6008	168	22	σ2	σ2	NOUN
ejpam-6008	168	23	)	)	PUNCT
ejpam-6008	168	24	,	,	PUNCT
ejpam-6008	168	25	the	the	DET
ejpam-6008	168	26	following	follow	VERB
ejpam-6008	168	27	properties	property	NOUN
ejpam-6008	168	28	are	be	AUX
ejpam-6008	168	29	equivalent	equivalent	ADJ
ejpam-6008	168	30	:	:	PUNCT
ejpam-6008	168	31	(	(	PUNCT
ejpam-6008	168	32	1	1	X
ejpam-6008	168	33	)	)	PUNCT
ejpam-6008	168	34	f	f	PROPN
ejpam-6008	168	35	is	be	AUX
ejpam-6008	168	36	upper	upper	ADJ
ejpam-6008	168	37	weakly	weakly	ADJ
ejpam-6008	168	38	(	(	PUNCT
ejpam-6008	168	39	τ1	τ1	NOUN
ejpam-6008	168	40	,	,	PUNCT
ejpam-6008	168	41	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	168	42	;	;	PUNCT
ejpam-6008	168	43	(	(	PUNCT
ejpam-6008	168	44	2	2	NUM
ejpam-6008	168	45	)	)	PUNCT
ejpam-6008	168	46	f+(v	f+(v	NOUN
ejpam-6008	168	47	)	)	PUNCT
ejpam-6008	169	1	⊆	⊆	X
ejpam-6008	169	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	169	3	-	-	NUM
ejpam-6008	169	4	int(f	int(f	VERB
ejpam-6008	169	5	+	+	ADJ
ejpam-6008	169	6	(	(	PUNCT
ejpam-6008	169	7	σ1σ2	σ1σ2	NOUN
ejpam-6008	169	8	-	-	NUM
ejpam-6008	169	9	cl(v	cl(v	NOUN
ejpam-6008	169	10	)	)	PUNCT
ejpam-6008	169	11	)	)	PUNCT
ejpam-6008	169	12	)	)	PUNCT
ejpam-6008	169	13	for	for	ADP
ejpam-6008	169	14	every	every	DET
ejpam-6008	169	15	σ1σ2	σ1σ2	NOUN
ejpam-6008	169	16	-	-	ADJ
ejpam-6008	169	17	open	open	ADJ
ejpam-6008	169	18	set	set	NOUN
ejpam-6008	169	19	v	v	NOUN
ejpam-6008	169	20	of	of	ADP
ejpam-6008	169	21	y	y	PROPN
ejpam-6008	169	22	;	;	PUNCT
ejpam-6008	169	23	(	(	PUNCT
ejpam-6008	169	24	3	3	X
ejpam-6008	169	25	)	)	PUNCT
ejpam-6008	169	26	τ1τ2	τ1τ2	NOUN
ejpam-6008	169	27	-	-	NOUN
ejpam-6008	169	28	cl(f	cl(f	NOUN
ejpam-6008	169	29	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6008	169	30	-	-	PUNCT
ejpam-6008	169	31	int(k	int(k	NUM
ejpam-6008	169	32	)	)	PUNCT
ejpam-6008	169	33	)	)	PUNCT
ejpam-6008	169	34	)	)	PUNCT
ejpam-6008	170	1	⊆	⊆	X
ejpam-6008	170	2	f−(k	f−(k	PROPN
ejpam-6008	170	3	)	)	PUNCT
ejpam-6008	170	4	for	for	ADP
ejpam-6008	170	5	every	every	DET
ejpam-6008	170	6	σ1σ2	σ1σ2	NUM
ejpam-6008	170	7	-	-	PUNCT
ejpam-6008	170	8	closed	closed	ADJ
ejpam-6008	170	9	set	set	NOUN
ejpam-6008	170	10	k	k	PROPN
ejpam-6008	170	11	of	of	ADP
ejpam-6008	170	12	y	y	PROPN
ejpam-6008	170	13	;	;	PUNCT
ejpam-6008	170	14	(	(	PUNCT
ejpam-6008	170	15	4	4	X
ejpam-6008	170	16	)	)	PUNCT
ejpam-6008	170	17	τ1τ2	τ1τ2	NOUN
ejpam-6008	170	18	-	-	NOUN
ejpam-6008	170	19	cl(f	cl(f	NOUN
ejpam-6008	170	20	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6008	170	21	-	-	PUNCT
ejpam-6008	170	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6008	170	23	-	-	PUNCT
ejpam-6008	170	24	cl(b	cl(b	NOUN
ejpam-6008	170	25	)	)	PUNCT
ejpam-6008	170	26	)	)	PUNCT
ejpam-6008	170	27	)	)	PUNCT
ejpam-6008	170	28	)	)	PUNCT
ejpam-6008	171	1	⊆	⊆	X
ejpam-6008	171	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6008	171	3	-	-	PUNCT
ejpam-6008	171	4	cl(b	cl(b	NOUN
ejpam-6008	171	5	)	)	PUNCT
ejpam-6008	171	6	)	)	PUNCT
ejpam-6008	172	1	for	for	ADP
ejpam-6008	172	2	every	every	DET
ejpam-6008	172	3	subset	subset	NOUN
ejpam-6008	172	4	b	b	PROPN
ejpam-6008	172	5	of	of	ADP
ejpam-6008	172	6	y	y	PROPN
ejpam-6008	172	7	;	;	PUNCT
ejpam-6008	172	8	(	(	PUNCT
ejpam-6008	172	9	5	5	X
ejpam-6008	172	10	)	)	PUNCT
ejpam-6008	172	11	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	172	12	-	-	PUNCT
ejpam-6008	172	13	int(b	int(b	NOUN
ejpam-6008	172	14	)	)	PUNCT
ejpam-6008	172	15	)	)	PUNCT
ejpam-6008	173	1	⊆	⊆	X
ejpam-6008	173	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	173	3	-	-	NUM
ejpam-6008	173	4	int(f	int(f	VERB
ejpam-6008	173	5	+	+	ADJ
ejpam-6008	173	6	(	(	PUNCT
ejpam-6008	173	7	σ1σ2	σ1σ2	NUM
ejpam-6008	173	8	-	-	PUNCT
ejpam-6008	173	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6008	173	10	-	-	PUNCT
ejpam-6008	173	11	int(b	int(b	NOUN
ejpam-6008	173	12	)	)	PUNCT
ejpam-6008	173	13	)	)	PUNCT
ejpam-6008	173	14	)	)	PUNCT
ejpam-6008	173	15	)	)	PUNCT
ejpam-6008	173	16	for	for	ADP
ejpam-6008	173	17	every	every	DET
ejpam-6008	173	18	subset	subset	NOUN
ejpam-6008	173	19	b	b	PROPN
ejpam-6008	173	20	of	of	ADP
ejpam-6008	173	21	y	y	PROPN
ejpam-6008	173	22	;	;	PUNCT
ejpam-6008	173	23	n.	n.	PROPN
ejpam-6008	173	24	viriyapong	viriyapong	PROPN
ejpam-6008	173	25	,	,	PUNCT
ejpam-6008	173	26	a.	a.	PROPN
ejpam-6008	173	27	sama	sama	PROPN
ejpam-6008	173	28	-	-	PUNCT
ejpam-6008	173	29	ae	ae	PROPN
ejpam-6008	173	30	,	,	PUNCT
ejpam-6008	173	31	c.	c.	PROPN
ejpam-6008	173	32	boonpok	boonpok	PROPN
ejpam-6008	173	33	/	/	SYM
ejpam-6008	173	34	eur	eur	PROPN
ejpam-6008	173	35	.	.	PUNCT
ejpam-6008	174	1	j.	j.	PROPN
ejpam-6008	174	2	pure	pure	PROPN
ejpam-6008	174	3	appl	appl	PROPN
ejpam-6008	174	4	.	.	PROPN
ejpam-6008	174	5	math	math	PROPN
ejpam-6008	174	6	,	,	PUNCT
ejpam-6008	174	7	18	18	NUM
ejpam-6008	174	8	(	(	PUNCT
ejpam-6008	174	9	2	2	NUM
ejpam-6008	174	10	)	)	PUNCT
ejpam-6008	174	11	(	(	PUNCT
ejpam-6008	174	12	2025	2025	NUM
ejpam-6008	174	13	)	)	PUNCT
ejpam-6008	174	14	,	,	PUNCT
ejpam-6008	174	15	6008	6008	NUM
ejpam-6008	174	16	7	7	NUM
ejpam-6008	174	17	of	of	ADP
ejpam-6008	174	18	15	15	NUM
ejpam-6008	174	19	(	(	PUNCT
ejpam-6008	174	20	6	6	NUM
ejpam-6008	174	21	)	)	PUNCT
ejpam-6008	174	22	τ1τ2	τ1τ2	NOUN
ejpam-6008	174	23	-	-	NOUN
ejpam-6008	174	24	cl(f	cl(f	NOUN
ejpam-6008	174	25	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6008	174	26	-	-	PUNCT
ejpam-6008	174	27	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6008	174	28	-	-	PUNCT
ejpam-6008	174	29	cl(v	cl(v	NOUN
ejpam-6008	174	30	)	)	PUNCT
ejpam-6008	174	31	)	)	PUNCT
ejpam-6008	174	32	)	)	PUNCT
ejpam-6008	174	33	)	)	PUNCT
ejpam-6008	175	1	⊆	⊆	X
ejpam-6008	175	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	175	3	-	-	PUNCT
ejpam-6008	175	4	cl(v	cl(v	NOUN
ejpam-6008	175	5	)	)	PUNCT
ejpam-6008	175	6	)	)	PUNCT
ejpam-6008	175	7	for	for	ADP
ejpam-6008	175	8	every	every	DET
ejpam-6008	175	9	σ1σ2	σ1σ2	NOUN
ejpam-6008	175	10	-	-	ADJ
ejpam-6008	175	11	open	open	ADJ
ejpam-6008	175	12	set	set	NOUN
ejpam-6008	175	13	v	v	NOUN
ejpam-6008	175	14	of	of	ADP
ejpam-6008	175	15	y	y	PROPN
ejpam-6008	175	16	;	;	PUNCT
ejpam-6008	175	17	(	(	PUNCT
ejpam-6008	175	18	7	7	X
ejpam-6008	175	19	)	)	PUNCT
ejpam-6008	175	20	τ1τ2	τ1τ2	NOUN
ejpam-6008	175	21	-	-	NOUN
ejpam-6008	175	22	cl(f	cl(f	NUM
ejpam-6008	175	23	−(v	−(v	NOUN
ejpam-6008	175	24	)	)	PUNCT
ejpam-6008	175	25	)	)	PUNCT
ejpam-6008	176	1	⊆	⊆	X
ejpam-6008	176	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	176	3	-	-	PUNCT
ejpam-6008	176	4	cl(v	cl(v	NOUN
ejpam-6008	176	5	)	)	PUNCT
ejpam-6008	176	6	)	)	PUNCT
ejpam-6008	176	7	for	for	ADP
ejpam-6008	176	8	every	every	DET
ejpam-6008	176	9	σ1σ2	σ1σ2	NOUN
ejpam-6008	176	10	-	-	ADJ
ejpam-6008	176	11	open	open	ADJ
ejpam-6008	176	12	set	set	NOUN
ejpam-6008	176	13	v	v	NOUN
ejpam-6008	176	14	of	of	ADP
ejpam-6008	176	15	y	y	PROPN
ejpam-6008	176	16	;	;	PUNCT
ejpam-6008	176	17	(	(	PUNCT
ejpam-6008	176	18	8)	8)	NUM
ejpam-6008	176	19	τ1τ2	τ1τ2	NOUN
ejpam-6008	176	20	-	-	NOUN
ejpam-6008	176	21	cl(f	cl(f	NOUN
ejpam-6008	176	22	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6008	176	23	-	-	PUNCT
ejpam-6008	176	24	int(k	int(k	NUM
ejpam-6008	176	25	)	)	PUNCT
ejpam-6008	176	26	)	)	PUNCT
ejpam-6008	176	27	)	)	PUNCT
ejpam-6008	176	28	⊆	⊆	X
ejpam-6008	176	29	f−(k	f−(k	PROPN
ejpam-6008	176	30	)	)	PUNCT
ejpam-6008	176	31	for	for	ADP
ejpam-6008	176	32	every	every	DET
ejpam-6008	176	33	(	(	PUNCT
ejpam-6008	176	34	σ1	σ1	PROPN
ejpam-6008	176	35	,	,	PUNCT
ejpam-6008	176	36	σ2)r	σ2)r	NOUN
ejpam-6008	176	37	-	-	PUNCT
ejpam-6008	176	38	closed	close	VERB
ejpam-6008	176	39	set	set	ADJ
ejpam-6008	176	40	k	k	PROPN
ejpam-6008	176	41	of	of	ADP
ejpam-6008	176	42	y	y	PROPN
ejpam-6008	176	43	.	.	PUNCT
ejpam-6008	177	1	lemma	lemma	PROPN
ejpam-6008	177	2	4	4	NUM
ejpam-6008	177	3	.	.	PUNCT
ejpam-6008	178	1	[	[	X
ejpam-6008	178	2	6	6	NUM
ejpam-6008	178	3	]	]	PUNCT
ejpam-6008	178	4	for	for	ADP
ejpam-6008	178	5	a	a	DET
ejpam-6008	178	6	multifunction	multifunction	NOUN
ejpam-6008	178	7	f	f	NOUN
ejpam-6008	178	8	:	:	PUNCT
ejpam-6008	178	9	(	(	PUNCT
ejpam-6008	178	10	x	x	NOUN
ejpam-6008	178	11	,	,	PUNCT
ejpam-6008	178	12	τ1	τ1	NOUN
ejpam-6008	178	13	,	,	PUNCT
ejpam-6008	178	14	τ2	τ2	NOUN
ejpam-6008	178	15	)	)	PUNCT
ejpam-6008	178	16	→	→	SYM
ejpam-6008	178	17	(	(	PUNCT
ejpam-6008	178	18	y	y	PROPN
ejpam-6008	178	19	,	,	PUNCT
ejpam-6008	178	20	σ1	σ1	PROPN
ejpam-6008	178	21	,	,	PUNCT
ejpam-6008	178	22	σ2	σ2	NOUN
ejpam-6008	178	23	)	)	PUNCT
ejpam-6008	178	24	,	,	PUNCT
ejpam-6008	178	25	the	the	DET
ejpam-6008	178	26	following	follow	VERB
ejpam-6008	178	27	properties	property	NOUN
ejpam-6008	178	28	are	be	AUX
ejpam-6008	178	29	equivalent	equivalent	ADJ
ejpam-6008	178	30	:	:	PUNCT
ejpam-6008	178	31	(	(	PUNCT
ejpam-6008	178	32	1	1	X
ejpam-6008	178	33	)	)	PUNCT
ejpam-6008	178	34	f	f	PROPN
ejpam-6008	178	35	is	be	AUX
ejpam-6008	178	36	lower	low	ADJ
ejpam-6008	178	37	weakly	weakly	ADJ
ejpam-6008	178	38	(	(	PUNCT
ejpam-6008	178	39	τ1	τ1	NOUN
ejpam-6008	178	40	,	,	PUNCT
ejpam-6008	178	41	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	178	42	;	;	PUNCT
ejpam-6008	178	43	(	(	PUNCT
ejpam-6008	178	44	2	2	X
ejpam-6008	178	45	)	)	PUNCT
ejpam-6008	178	46	f−(v	f−(v	NOUN
ejpam-6008	178	47	)	)	PUNCT
ejpam-6008	178	48	⊆	⊆	NUM
ejpam-6008	178	49	τ1τ2	τ1τ2	NOUN
ejpam-6008	178	50	-	-	NUM
ejpam-6008	178	51	int(f	int(f	PRON
ejpam-6008	178	52	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6008	178	53	-	-	NOUN
ejpam-6008	178	54	cl(v	cl(v	NOUN
ejpam-6008	178	55	)	)	PUNCT
ejpam-6008	178	56	)	)	PUNCT
ejpam-6008	178	57	)	)	PUNCT
ejpam-6008	179	1	for	for	ADP
ejpam-6008	179	2	every	every	DET
ejpam-6008	179	3	σ1σ2	σ1σ2	NOUN
ejpam-6008	179	4	-	-	ADJ
ejpam-6008	179	5	open	open	ADJ
ejpam-6008	179	6	set	set	NOUN
ejpam-6008	179	7	v	v	NOUN
ejpam-6008	179	8	of	of	ADP
ejpam-6008	179	9	y	y	PROPN
ejpam-6008	179	10	;	;	PUNCT
ejpam-6008	179	11	(	(	PUNCT
ejpam-6008	179	12	3	3	X
ejpam-6008	179	13	)	)	PUNCT
ejpam-6008	179	14	τ1τ2	τ1τ2	NOUN
ejpam-6008	179	15	-	-	NOUN
ejpam-6008	179	16	cl(f	cl(f	NOUN
ejpam-6008	179	17	+	+	NOUN
ejpam-6008	179	18	(	(	PUNCT
ejpam-6008	179	19	σ1σ2	σ1σ2	NUM
ejpam-6008	179	20	-	-	PUNCT
ejpam-6008	179	21	int(k	int(k	NUM
ejpam-6008	179	22	)	)	PUNCT
ejpam-6008	179	23	)	)	PUNCT
ejpam-6008	179	24	)	)	PUNCT
ejpam-6008	179	25	⊆	⊆	NUM
ejpam-6008	179	26	f+(k	f+(k	NOUN
ejpam-6008	179	27	)	)	PUNCT
ejpam-6008	179	28	for	for	ADP
ejpam-6008	179	29	every	every	DET
ejpam-6008	179	30	σ1σ2	σ1σ2	NUM
ejpam-6008	179	31	-	-	PUNCT
ejpam-6008	179	32	closed	closed	ADJ
ejpam-6008	179	33	set	set	NOUN
ejpam-6008	179	34	k	k	PROPN
ejpam-6008	179	35	of	of	ADP
ejpam-6008	179	36	y	y	PROPN
ejpam-6008	179	37	;	;	PUNCT
ejpam-6008	179	38	(	(	PUNCT
ejpam-6008	179	39	4	4	X
ejpam-6008	179	40	)	)	PUNCT
ejpam-6008	179	41	τ1τ2	τ1τ2	NOUN
ejpam-6008	179	42	-	-	NOUN
ejpam-6008	179	43	cl(f	cl(f	NOUN
ejpam-6008	179	44	+	+	NOUN
ejpam-6008	179	45	(	(	PUNCT
ejpam-6008	179	46	σ1σ2	σ1σ2	NUM
ejpam-6008	179	47	-	-	PUNCT
ejpam-6008	179	48	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6008	179	49	-	-	PUNCT
ejpam-6008	179	50	cl(b	cl(b	NOUN
ejpam-6008	179	51	)	)	PUNCT
ejpam-6008	179	52	)	)	PUNCT
ejpam-6008	179	53	)	)	PUNCT
ejpam-6008	179	54	)	)	PUNCT
ejpam-6008	179	55	⊆	⊆	X
ejpam-6008	179	56	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	179	57	-	-	PUNCT
ejpam-6008	179	58	cl(b	cl(b	NOUN
ejpam-6008	179	59	)	)	PUNCT
ejpam-6008	179	60	)	)	PUNCT
ejpam-6008	179	61	for	for	ADP
ejpam-6008	179	62	every	every	DET
ejpam-6008	179	63	subset	subset	NOUN
ejpam-6008	179	64	b	b	PROPN
ejpam-6008	179	65	of	of	ADP
ejpam-6008	179	66	y	y	PROPN
ejpam-6008	179	67	;	;	PUNCT
ejpam-6008	179	68	(	(	PUNCT
ejpam-6008	179	69	5	5	X
ejpam-6008	179	70	)	)	PUNCT
ejpam-6008	179	71	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	179	72	-	-	PUNCT
ejpam-6008	179	73	int(b	int(b	NOUN
ejpam-6008	179	74	)	)	PUNCT
ejpam-6008	179	75	)	)	PUNCT
ejpam-6008	179	76	⊆	⊆	X
ejpam-6008	179	77	τ1τ2	τ1τ2	NOUN
ejpam-6008	179	78	-	-	NUM
ejpam-6008	179	79	int(f	int(f	PRON
ejpam-6008	179	80	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6008	179	81	-	-	PUNCT
ejpam-6008	179	82	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6008	179	83	-	-	PUNCT
ejpam-6008	179	84	int(b	int(b	NOUN
ejpam-6008	179	85	)	)	PUNCT
ejpam-6008	179	86	)	)	PUNCT
ejpam-6008	179	87	)	)	PUNCT
ejpam-6008	179	88	)	)	PUNCT
ejpam-6008	179	89	for	for	ADP
ejpam-6008	179	90	every	every	DET
ejpam-6008	179	91	subset	subset	NOUN
ejpam-6008	179	92	b	b	PROPN
ejpam-6008	179	93	of	of	ADP
ejpam-6008	179	94	y	y	PROPN
ejpam-6008	179	95	;	;	PUNCT
ejpam-6008	179	96	(	(	PUNCT
ejpam-6008	179	97	6	6	X
ejpam-6008	179	98	)	)	PUNCT
ejpam-6008	179	99	τ1τ2	τ1τ2	NOUN
ejpam-6008	179	100	-	-	NOUN
ejpam-6008	179	101	cl(f	cl(f	NOUN
ejpam-6008	179	102	+	+	NOUN
ejpam-6008	179	103	(	(	PUNCT
ejpam-6008	179	104	σ1σ2	σ1σ2	NUM
ejpam-6008	179	105	-	-	PUNCT
ejpam-6008	179	106	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6008	179	107	-	-	PUNCT
ejpam-6008	179	108	cl(v	cl(v	NOUN
ejpam-6008	179	109	)	)	PUNCT
ejpam-6008	179	110	)	)	PUNCT
ejpam-6008	179	111	)	)	PUNCT
ejpam-6008	179	112	)	)	PUNCT
ejpam-6008	179	113	⊆	⊆	X
ejpam-6008	179	114	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	179	115	-	-	PUNCT
ejpam-6008	179	116	cl(v	cl(v	NOUN
ejpam-6008	179	117	)	)	PUNCT
ejpam-6008	179	118	)	)	PUNCT
ejpam-6008	179	119	for	for	ADP
ejpam-6008	179	120	every	every	DET
ejpam-6008	179	121	σ1σ2	σ1σ2	NOUN
ejpam-6008	179	122	-	-	ADJ
ejpam-6008	179	123	open	open	ADJ
ejpam-6008	179	124	set	set	NOUN
ejpam-6008	179	125	v	v	NOUN
ejpam-6008	179	126	of	of	ADP
ejpam-6008	179	127	y	y	PROPN
ejpam-6008	179	128	;	;	PUNCT
ejpam-6008	179	129	(	(	PUNCT
ejpam-6008	179	130	7	7	X
ejpam-6008	179	131	)	)	PUNCT
ejpam-6008	179	132	τ1τ2	τ1τ2	NOUN
ejpam-6008	179	133	-	-	NOUN
ejpam-6008	179	134	cl(f	cl(f	NOUN
ejpam-6008	179	135	+	+	NOUN
ejpam-6008	179	136	(	(	PUNCT
ejpam-6008	179	137	v	v	NOUN
ejpam-6008	179	138	)	)	PUNCT
ejpam-6008	179	139	)	)	PUNCT
ejpam-6008	179	140	⊆	⊆	NUM
ejpam-6008	179	141	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	179	142	-	-	PUNCT
ejpam-6008	179	143	cl(v	cl(v	NOUN
ejpam-6008	179	144	)	)	PUNCT
ejpam-6008	179	145	)	)	PUNCT
ejpam-6008	179	146	for	for	ADP
ejpam-6008	179	147	every	every	DET
ejpam-6008	179	148	σ1σ2	σ1σ2	NOUN
ejpam-6008	179	149	-	-	ADJ
ejpam-6008	179	150	open	open	ADJ
ejpam-6008	179	151	set	set	NOUN
ejpam-6008	179	152	v	v	NOUN
ejpam-6008	179	153	of	of	ADP
ejpam-6008	179	154	y	y	PROPN
ejpam-6008	179	155	;	;	PUNCT
ejpam-6008	179	156	(	(	PUNCT
ejpam-6008	179	157	8)	8)	NUM
ejpam-6008	179	158	τ1τ2	τ1τ2	NOUN
ejpam-6008	179	159	-	-	NOUN
ejpam-6008	179	160	cl(f	cl(f	NOUN
ejpam-6008	179	161	+	+	NOUN
ejpam-6008	179	162	(	(	PUNCT
ejpam-6008	179	163	σ1σ2	σ1σ2	NUM
ejpam-6008	179	164	-	-	PUNCT
ejpam-6008	179	165	int(k	int(k	NUM
ejpam-6008	179	166	)	)	PUNCT
ejpam-6008	179	167	)	)	PUNCT
ejpam-6008	179	168	)	)	PUNCT
ejpam-6008	179	169	⊆	⊆	NUM
ejpam-6008	179	170	f+(k	f+(k	NOUN
ejpam-6008	179	171	)	)	PUNCT
ejpam-6008	179	172	for	for	ADP
ejpam-6008	179	173	every	every	DET
ejpam-6008	179	174	(	(	PUNCT
ejpam-6008	179	175	σ1	σ1	PROPN
ejpam-6008	179	176	,	,	PUNCT
ejpam-6008	179	177	σ2)r	σ2)r	NOUN
ejpam-6008	179	178	-	-	PUNCT
ejpam-6008	179	179	closed	close	VERB
ejpam-6008	179	180	set	set	ADJ
ejpam-6008	179	181	k	k	PROPN
ejpam-6008	179	182	of	of	ADP
ejpam-6008	179	183	y	y	PROPN
ejpam-6008	179	184	.	.	PUNCT
ejpam-6008	180	1	theorem	theorem	VERB
ejpam-6008	180	2	8	8	NUM
ejpam-6008	180	3	.	.	PUNCT
ejpam-6008	181	1	if	if	SCONJ
ejpam-6008	181	2	f	f	PROPN
ejpam-6008	181	3	:	:	PUNCT
ejpam-6008	181	4	(	(	PUNCT
ejpam-6008	181	5	x	x	NOUN
ejpam-6008	181	6	,	,	PUNCT
ejpam-6008	181	7	τ1	τ1	NOUN
ejpam-6008	181	8	,	,	PUNCT
ejpam-6008	181	9	τ2	τ2	NOUN
ejpam-6008	181	10	)	)	PUNCT
ejpam-6008	181	11	→	→	SYM
ejpam-6008	181	12	(	(	PUNCT
ejpam-6008	181	13	y	y	PROPN
ejpam-6008	181	14	,	,	PUNCT
ejpam-6008	181	15	σ1	σ1	PROPN
ejpam-6008	181	16	,	,	PUNCT
ejpam-6008	181	17	σ2	σ2	PROPN
ejpam-6008	181	18	)	)	PUNCT
ejpam-6008	181	19	is	be	AUX
ejpam-6008	181	20	an	an	DET
ejpam-6008	181	21	upper	upper	ADJ
ejpam-6008	181	22	or	or	CCONJ
ejpam-6008	181	23	lower	low	ADJ
ejpam-6008	181	24	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	181	25	,	,	PUNCT
ejpam-6008	181	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	181	27	surjective	surjective	ADJ
ejpam-6008	181	28	multifunction	multifunction	NOUN
ejpam-6008	181	29	such	such	ADJ
ejpam-6008	181	30	that	that	SCONJ
ejpam-6008	181	31	f	f	PROPN
ejpam-6008	181	32	(	(	PUNCT
ejpam-6008	181	33	x	x	X
ejpam-6008	181	34	)	)	PUNCT
ejpam-6008	181	35	is	be	AUX
ejpam-6008	181	36	σ1σ2	σ1σ2	NOUN
ejpam-6008	181	37	-	-	PUNCT
ejpam-6008	181	38	connected	connected	ADJ
ejpam-6008	181	39	for	for	ADP
ejpam-6008	181	40	each	each	DET
ejpam-6008	181	41	x	x	SYM
ejpam-6008	181	42	∈	∈	PROPN
ejpam-6008	181	43	x	x	X
ejpam-6008	181	44	and	and	CCONJ
ejpam-6008	181	45	(	(	PUNCT
ejpam-6008	181	46	x	x	NOUN
ejpam-6008	181	47	,	,	PUNCT
ejpam-6008	181	48	τ1	τ1	NOUN
ejpam-6008	181	49	,	,	PUNCT
ejpam-6008	181	50	τ2	τ2	NOUN
ejpam-6008	181	51	)	)	PUNCT
ejpam-6008	181	52	is	be	AUX
ejpam-6008	181	53	τ1τ2	τ1τ2	NOUN
ejpam-6008	181	54	-	-	ADJ
ejpam-6008	181	55	connected	connected	ADJ
ejpam-6008	181	56	,	,	PUNCT
ejpam-6008	181	57	then	then	ADV
ejpam-6008	181	58	(	(	PUNCT
ejpam-6008	181	59	y	y	PROPN
ejpam-6008	181	60	,	,	PUNCT
ejpam-6008	181	61	σ1	σ1	PROPN
ejpam-6008	181	62	,	,	PUNCT
ejpam-6008	181	63	σ2	σ2	PROPN
ejpam-6008	181	64	)	)	PUNCT
ejpam-6008	181	65	is	be	AUX
ejpam-6008	181	66	σ1σ2	σ1σ2	NOUN
ejpam-6008	181	67	-	-	PUNCT
ejpam-6008	181	68	connected	connected	ADJ
ejpam-6008	181	69	.	.	PUNCT
ejpam-6008	182	1	proof	proof	NOUN
ejpam-6008	182	2	.	.	PUNCT
ejpam-6008	183	1	suppose	suppose	VERB
ejpam-6008	183	2	that	that	SCONJ
ejpam-6008	183	3	(	(	PUNCT
ejpam-6008	183	4	y	y	PROPN
ejpam-6008	183	5	,	,	PUNCT
ejpam-6008	183	6	σ1	σ1	PROPN
ejpam-6008	183	7	,	,	PUNCT
ejpam-6008	183	8	σ2	σ2	PROPN
ejpam-6008	183	9	)	)	PUNCT
ejpam-6008	183	10	is	be	AUX
ejpam-6008	183	11	not	not	PART
ejpam-6008	183	12	σ1σ2	σ1σ2	VERB
ejpam-6008	183	13	-	-	PUNCT
ejpam-6008	183	14	connected	connect	VERB
ejpam-6008	183	15	.	.	PUNCT
ejpam-6008	184	1	there	there	PRON
ejpam-6008	184	2	exist	exist	VERB
ejpam-6008	184	3	nonempty	nonempty	ADJ
ejpam-6008	184	4	σ1σ2open	σ1σ2open	PUNCT
ejpam-6008	184	5	sets	set	VERB
ejpam-6008	184	6	u	u	NOUN
ejpam-6008	184	7	and	and	CCONJ
ejpam-6008	184	8	v	v	NOUN
ejpam-6008	184	9	of	of	ADP
ejpam-6008	184	10	y	y	PRON
ejpam-6008	184	11	such	such	ADJ
ejpam-6008	184	12	that	that	SCONJ
ejpam-6008	184	13	u	u	NOUN
ejpam-6008	184	14	∩v	∩v	NOUN
ejpam-6008	184	15	=	=	SYM
ejpam-6008	184	16	∅	∅	NOUN
ejpam-6008	184	17	and	and	CCONJ
ejpam-6008	184	18	u	u	NOUN
ejpam-6008	184	19	∪v	∪v	ADP
ejpam-6008	184	20	=	=	SYM
ejpam-6008	184	21	y	y	PROPN
ejpam-6008	184	22	.	.	PUNCT
ejpam-6008	185	1	since	since	SCONJ
ejpam-6008	185	2	f	f	PROPN
ejpam-6008	185	3	(	(	PUNCT
ejpam-6008	185	4	x	x	X
ejpam-6008	185	5	)	)	PUNCT
ejpam-6008	185	6	is	be	AUX
ejpam-6008	185	7	σ1σ2	σ1σ2	NOUN
ejpam-6008	185	8	-	-	PUNCT
ejpam-6008	185	9	connected	connected	ADJ
ejpam-6008	185	10	for	for	ADP
ejpam-6008	185	11	each	each	DET
ejpam-6008	185	12	x	x	SYM
ejpam-6008	185	13	∈	∈	PROPN
ejpam-6008	185	14	x	x	NOUN
ejpam-6008	185	15	,	,	PUNCT
ejpam-6008	185	16	either	either	CCONJ
ejpam-6008	185	17	f	f	PROPN
ejpam-6008	185	18	(	(	PUNCT
ejpam-6008	185	19	x	x	X
ejpam-6008	185	20	)	)	PUNCT
ejpam-6008	185	21	⊆	⊆	NUM
ejpam-6008	185	22	u	u	NOUN
ejpam-6008	185	23	or	or	CCONJ
ejpam-6008	185	24	f	f	PROPN
ejpam-6008	185	25	(	(	PUNCT
ejpam-6008	185	26	x	x	NOUN
ejpam-6008	185	27	)	)	PUNCT
ejpam-6008	185	28	⊆	⊆	NUM
ejpam-6008	185	29	v	v	NOUN
ejpam-6008	185	30	.	.	PUNCT
ejpam-6008	186	1	if	if	SCONJ
ejpam-6008	186	2	x	x	SYM
ejpam-6008	186	3	∈	∈	NOUN
ejpam-6008	186	4	f+(u	f+(u	PUNCT
ejpam-6008	186	5	∪v	∪v	NUM
ejpam-6008	186	6	)	)	PUNCT
ejpam-6008	186	7	,	,	PUNCT
ejpam-6008	186	8	then	then	ADV
ejpam-6008	186	9	f	f	X
ejpam-6008	186	10	(	(	PUNCT
ejpam-6008	186	11	x	x	NOUN
ejpam-6008	186	12	)	)	PUNCT
ejpam-6008	186	13	⊆	⊆	NUM
ejpam-6008	186	14	u	u	NOUN
ejpam-6008	186	15	∪v	∪v	PUNCT
ejpam-6008	186	16	and	and	CCONJ
ejpam-6008	186	17	hence	hence	ADV
ejpam-6008	186	18	x	x	PART
ejpam-6008	186	19	∈	∈	NOUN
ejpam-6008	186	20	f+(u)∪f+(v	f+(u)∪f+(v	NOUN
ejpam-6008	186	21	)	)	PUNCT
ejpam-6008	186	22	.	.	PUNCT
ejpam-6008	187	1	moreover	moreover	ADV
ejpam-6008	187	2	,	,	PUNCT
ejpam-6008	187	3	since	since	SCONJ
ejpam-6008	187	4	f	f	PROPN
ejpam-6008	187	5	is	be	AUX
ejpam-6008	187	6	surjective	surjective	ADJ
ejpam-6008	187	7	,	,	PUNCT
ejpam-6008	187	8	there	there	PRON
ejpam-6008	187	9	exist	exist	VERB
ejpam-6008	187	10	x	x	PUNCT
ejpam-6008	187	11	and	and	CCONJ
ejpam-6008	187	12	y	y	PROPN
ejpam-6008	187	13	in	in	ADP
ejpam-6008	187	14	x	x	PUNCT
ejpam-6008	187	15	such	such	ADJ
ejpam-6008	187	16	that	that	SCONJ
ejpam-6008	187	17	f	f	PROPN
ejpam-6008	187	18	(	(	PUNCT
ejpam-6008	187	19	x	x	X
ejpam-6008	187	20	)	)	PUNCT
ejpam-6008	187	21	⊆	⊆	NUM
ejpam-6008	187	22	u	u	NOUN
ejpam-6008	187	23	and	and	CCONJ
ejpam-6008	187	24	f	f	PROPN
ejpam-6008	187	25	(	(	PUNCT
ejpam-6008	187	26	y	y	PROPN
ejpam-6008	187	27	)	)	PUNCT
ejpam-6008	187	28	⊆	⊆	NUM
ejpam-6008	187	29	v	v	NOUN
ejpam-6008	187	30	;	;	PUNCT
ejpam-6008	187	31	hence	hence	ADV
ejpam-6008	187	32	x	x	SYM
ejpam-6008	187	33	∈	∈	PROPN
ejpam-6008	187	34	f+(u	f+(u	NUM
ejpam-6008	187	35	)	)	PUNCT
ejpam-6008	187	36	and	and	CCONJ
ejpam-6008	187	37	y	y	PROPN
ejpam-6008	187	38	∈	∈	PROPN
ejpam-6008	187	39	f+(v	f+(v	PROPN
ejpam-6008	187	40	)	)	PUNCT
ejpam-6008	187	41	.	.	PUNCT
ejpam-6008	188	1	therefore	therefore	ADV
ejpam-6008	188	2	,	,	PUNCT
ejpam-6008	188	3	we	we	PRON
ejpam-6008	188	4	obtain	obtain	VERB
ejpam-6008	188	5	the	the	DET
ejpam-6008	188	6	following	following	NOUN
ejpam-6008	188	7	:	:	PUNCT
ejpam-6008	188	8	(	(	PUNCT
ejpam-6008	188	9	1	1	X
ejpam-6008	188	10	)	)	PUNCT
ejpam-6008	188	11	f+(u	f+(u	NUM
ejpam-6008	188	12	)	)	PUNCT
ejpam-6008	188	13	∪	∪	ADP
ejpam-6008	188	14	f+(v	f+(v	NOUN
ejpam-6008	188	15	)	)	PUNCT
ejpam-6008	189	1	=	=	PUNCT
ejpam-6008	190	1	f+(u	f+(u	PUNCT
ejpam-6008	190	2	∪	∪	ADP
ejpam-6008	190	3	v	v	NOUN
ejpam-6008	190	4	)	)	PUNCT
ejpam-6008	190	5	=	=	SYM
ejpam-6008	191	1	x	x	X
ejpam-6008	191	2	;	;	PUNCT
ejpam-6008	191	3	(	(	PUNCT
ejpam-6008	191	4	2	2	X
ejpam-6008	191	5	)	)	PUNCT
ejpam-6008	191	6	f+(u	f+(u	NUM
ejpam-6008	191	7	)	)	PUNCT
ejpam-6008	191	8	∩	∩	NOUN
ejpam-6008	191	9	f+(v	f+(v	NOUN
ejpam-6008	191	10	)	)	PUNCT
ejpam-6008	191	11	=	=	SYM
ejpam-6008	192	1	f+(u	f+(u	NUM
ejpam-6008	192	2	∩	∩	NOUN
ejpam-6008	192	3	v	v	NOUN
ejpam-6008	192	4	)	)	PUNCT
ejpam-6008	192	5	=	=	NOUN
ejpam-6008	192	6	∅	∅	NOUN
ejpam-6008	192	7	;	;	PUNCT
ejpam-6008	192	8	(	(	PUNCT
ejpam-6008	192	9	3	3	X
ejpam-6008	192	10	)	)	PUNCT
ejpam-6008	192	11	f+(u	f+(u	NUM
ejpam-6008	192	12	)	)	PUNCT
ejpam-6008	192	13	̸=	̸=	PROPN
ejpam-6008	192	14	∅	∅	NOUN
ejpam-6008	192	15	and	and	CCONJ
ejpam-6008	192	16	f+(v	f+(v	NUM
ejpam-6008	192	17	)	)	PUNCT
ejpam-6008	193	1	̸=	̸=	PROPN
ejpam-6008	193	2	∅.	∅.	ADP
ejpam-6008	193	3	next	next	ADV
ejpam-6008	193	4	,	,	PUNCT
ejpam-6008	193	5	we	we	PRON
ejpam-6008	193	6	show	show	VERB
ejpam-6008	193	7	that	that	PRON
ejpam-6008	193	8	f+(u	f+(u	NUM
ejpam-6008	193	9	)	)	PUNCT
ejpam-6008	193	10	and	and	CCONJ
ejpam-6008	193	11	f+(v	f+(v	NUM
ejpam-6008	193	12	)	)	PUNCT
ejpam-6008	193	13	are	be	AUX
ejpam-6008	193	14	τ1τ2	τ1τ2	NOUN
ejpam-6008	193	15	-	-	ADJ
ejpam-6008	193	16	open	open	ADJ
ejpam-6008	193	17	in	in	ADP
ejpam-6008	193	18	x.	x.	PROPN
ejpam-6008	193	19	(	(	PUNCT
ejpam-6008	193	20	i	i	NOUN
ejpam-6008	193	21	)	)	PUNCT
ejpam-6008	193	22	let	let	VERB
ejpam-6008	193	23	f	f	PRON
ejpam-6008	193	24	be	be	AUX
ejpam-6008	193	25	upper	upper	ADJ
ejpam-6008	193	26	contra(τ1	contra(τ1	NOUN
ejpam-6008	193	27	,	,	PUNCT
ejpam-6008	193	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	193	29	,	,	PUNCT
ejpam-6008	193	30	by	by	ADP
ejpam-6008	193	31	theorem	theorem	NOUN
ejpam-6008	193	32	6	6	NUM
ejpam-6008	193	33	we	we	PRON
ejpam-6008	193	34	have	have	VERB
ejpam-6008	193	35	f	f	PROPN
ejpam-6008	193	36	is	be	AUX
ejpam-6008	193	37	upper	upper	ADJ
ejpam-6008	193	38	weakly	weakly	ADJ
ejpam-6008	193	39	(	(	PUNCT
ejpam-6008	193	40	τ1	τ1	NOUN
ejpam-6008	193	41	,	,	PUNCT
ejpam-6008	193	42	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	193	43	.	.	PUNCT
ejpam-6008	194	1	by	by	ADP
ejpam-6008	194	2	lemma	lemma	PROPN
ejpam-6008	194	3	3	3	NUM
ejpam-6008	194	4	,	,	PUNCT
ejpam-6008	194	5	f+(v	f+(v	PROPN
ejpam-6008	194	6	)	)	PUNCT
ejpam-6008	195	1	⊆	⊆	X
ejpam-6008	195	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	195	3	-	-	NUM
ejpam-6008	195	4	int(f	int(f	VERB
ejpam-6008	195	5	+	+	ADJ
ejpam-6008	195	6	(	(	PUNCT
ejpam-6008	195	7	σ1σ2	σ1σ2	NOUN
ejpam-6008	195	8	-	-	NUM
ejpam-6008	195	9	cl(v	cl(v	NOUN
ejpam-6008	195	10	)	)	PUNCT
ejpam-6008	195	11	)	)	PUNCT
ejpam-6008	195	12	)	)	PUNCT
ejpam-6008	196	1	=	=	PUNCT
ejpam-6008	196	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	196	3	-	-	NUM
ejpam-6008	196	4	int(f	int(f	VERB
ejpam-6008	196	5	+	+	ADJ
ejpam-6008	196	6	(	(	PUNCT
ejpam-6008	196	7	v	v	NOUN
ejpam-6008	196	8	)	)	PUNCT
ejpam-6008	196	9	)	)	PUNCT
ejpam-6008	196	10	since	since	SCONJ
ejpam-6008	196	11	v	v	NUM
ejpam-6008	196	12	is	be	AUX
ejpam-6008	196	13	σ1σ2	σ1σ2	NOUN
ejpam-6008	196	14	-	-	PUNCT
ejpam-6008	196	15	clopen	clopen	ADJ
ejpam-6008	196	16	.	.	PUNCT
ejpam-6008	197	1	thus	thus	ADV
ejpam-6008	197	2	,	,	PUNCT
ejpam-6008	197	3	f+(v	f+(v	PROPN
ejpam-6008	197	4	)	)	PUNCT
ejpam-6008	198	1	=	=	PUNCT
ejpam-6008	198	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	198	3	-	-	NUM
ejpam-6008	198	4	int(f	int(f	VERB
ejpam-6008	198	5	+	+	ADJ
ejpam-6008	198	6	(	(	PUNCT
ejpam-6008	198	7	v	v	NOUN
ejpam-6008	198	8	)	)	PUNCT
ejpam-6008	198	9	)	)	PUNCT
ejpam-6008	198	10	and	and	CCONJ
ejpam-6008	198	11	hence	hence	ADV
ejpam-6008	198	12	f+(v	f+(v	PROPN
ejpam-6008	198	13	)	)	PUNCT
ejpam-6008	198	14	is	be	AUX
ejpam-6008	198	15	τ1τ2	τ1τ2	NOUN
ejpam-6008	198	16	-	-	ADJ
ejpam-6008	198	17	open	open	ADJ
ejpam-6008	198	18	in	in	ADP
ejpam-6008	198	19	x.	x.	NOUN
ejpam-6008	198	20	similarly	similarly	ADV
ejpam-6008	198	21	,	,	PUNCT
ejpam-6008	198	22	we	we	PRON
ejpam-6008	198	23	obtain	obtain	VERB
ejpam-6008	198	24	f+(u	f+(u	PUNCT
ejpam-6008	198	25	)	)	PUNCT
ejpam-6008	198	26	is	be	AUX
ejpam-6008	198	27	τ1τ2	τ1τ2	NOUN
ejpam-6008	198	28	-	-	ADJ
ejpam-6008	198	29	open	open	ADJ
ejpam-6008	198	30	in	in	ADP
ejpam-6008	198	31	x.	x.	NOUN
ejpam-6008	198	32	consequently	consequently	ADV
ejpam-6008	198	33	,	,	PUNCT
ejpam-6008	198	34	this	this	PRON
ejpam-6008	198	35	shows	show	VERB
ejpam-6008	198	36	that	that	SCONJ
ejpam-6008	198	37	(	(	PUNCT
ejpam-6008	198	38	x	x	NOUN
ejpam-6008	198	39	,	,	PUNCT
ejpam-6008	198	40	τ1	τ1	NOUN
ejpam-6008	198	41	,	,	PUNCT
ejpam-6008	198	42	τ2	τ2	NOUN
ejpam-6008	198	43	)	)	PUNCT
ejpam-6008	198	44	is	be	AUX
ejpam-6008	198	45	not	not	PART
ejpam-6008	198	46	τ1τ2	τ1τ2	ADJ
ejpam-6008	198	47	-	-	VERB
ejpam-6008	198	48	connected	connected	ADJ
ejpam-6008	198	49	.	.	PUNCT
ejpam-6008	199	1	n.	n.	PROPN
ejpam-6008	199	2	viriyapong	viriyapong	PROPN
ejpam-6008	199	3	,	,	PUNCT
ejpam-6008	199	4	a.	a.	PROPN
ejpam-6008	199	5	sama	sama	PROPN
ejpam-6008	199	6	-	-	PUNCT
ejpam-6008	199	7	ae	ae	PROPN
ejpam-6008	199	8	,	,	PUNCT
ejpam-6008	199	9	c.	c.	PROPN
ejpam-6008	199	10	boonpok	boonpok	PROPN
ejpam-6008	199	11	/	/	SYM
ejpam-6008	199	12	eur	eur	PROPN
ejpam-6008	199	13	.	.	PUNCT
ejpam-6008	200	1	j.	j.	PROPN
ejpam-6008	200	2	pure	pure	PROPN
ejpam-6008	200	3	appl	appl	PROPN
ejpam-6008	200	4	.	.	PROPN
ejpam-6008	200	5	math	math	PROPN
ejpam-6008	200	6	,	,	PUNCT
ejpam-6008	200	7	18	18	NUM
ejpam-6008	200	8	(	(	PUNCT
ejpam-6008	200	9	2	2	NUM
ejpam-6008	200	10	)	)	PUNCT
ejpam-6008	200	11	(	(	PUNCT
ejpam-6008	200	12	2025	2025	NUM
ejpam-6008	200	13	)	)	PUNCT
ejpam-6008	200	14	,	,	PUNCT
ejpam-6008	200	15	6008	6008	NUM
ejpam-6008	200	16	8	8	NUM
ejpam-6008	200	17	of	of	ADP
ejpam-6008	200	18	15	15	NUM
ejpam-6008	200	19	(	(	PUNCT
ejpam-6008	200	20	ii	ii	NOUN
ejpam-6008	200	21	)	)	PUNCT
ejpam-6008	200	22	let	let	VERB
ejpam-6008	200	23	f	f	PRON
ejpam-6008	200	24	be	be	AUX
ejpam-6008	200	25	lower	low	ADJ
ejpam-6008	200	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	200	27	,	,	PUNCT
ejpam-6008	200	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	200	29	,	,	PUNCT
ejpam-6008	200	30	by	by	ADP
ejpam-6008	200	31	theorem	theorem	NOUN
ejpam-6008	200	32	7	7	NUM
ejpam-6008	200	33	we	we	PRON
ejpam-6008	200	34	have	have	VERB
ejpam-6008	200	35	f	f	PROPN
ejpam-6008	200	36	is	be	AUX
ejpam-6008	200	37	lower	low	ADJ
ejpam-6008	200	38	weakly	weakly	ADJ
ejpam-6008	200	39	(	(	PUNCT
ejpam-6008	200	40	τ1	τ1	NOUN
ejpam-6008	200	41	,	,	PUNCT
ejpam-6008	200	42	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	200	43	.	.	PUNCT
ejpam-6008	201	1	by	by	ADP
ejpam-6008	201	2	lemma	lemma	PROPN
ejpam-6008	201	3	4	4	NUM
ejpam-6008	201	4	,	,	PUNCT
ejpam-6008	201	5	τ1τ2	τ1τ2	NOUN
ejpam-6008	201	6	-	-	NOUN
ejpam-6008	201	7	cl(f	cl(f	NOUN
ejpam-6008	201	8	+	+	NOUN
ejpam-6008	201	9	(	(	PUNCT
ejpam-6008	201	10	v	v	NOUN
ejpam-6008	201	11	)	)	PUNCT
ejpam-6008	201	12	)	)	PUNCT
ejpam-6008	202	1	⊆	⊆	NUM
ejpam-6008	202	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	202	3	-	-	PUNCT
ejpam-6008	202	4	cl(v	cl(v	NOUN
ejpam-6008	202	5	)	)	PUNCT
ejpam-6008	202	6	)	)	PUNCT
ejpam-6008	203	1	=	=	PUNCT
ejpam-6008	203	2	f+(v	f+(v	NOUN
ejpam-6008	203	3	)	)	PUNCT
ejpam-6008	203	4	since	since	SCONJ
ejpam-6008	203	5	v	v	NUM
ejpam-6008	203	6	is	be	AUX
ejpam-6008	203	7	σ1σ2	σ1σ2	NOUN
ejpam-6008	203	8	-	-	PUNCT
ejpam-6008	203	9	clopen	clopen	ADJ
ejpam-6008	203	10	.	.	PUNCT
ejpam-6008	204	1	therefore	therefore	ADV
ejpam-6008	204	2	,	,	PUNCT
ejpam-6008	204	3	f+(v	f+(v	PROPN
ejpam-6008	204	4	)	)	PUNCT
ejpam-6008	205	1	=	=	PUNCT
ejpam-6008	205	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	205	3	-	-	NOUN
ejpam-6008	205	4	cl(f	cl(f	NOUN
ejpam-6008	205	5	+	+	NOUN
ejpam-6008	205	6	(	(	PUNCT
ejpam-6008	205	7	v	v	NOUN
ejpam-6008	205	8	)	)	PUNCT
ejpam-6008	205	9	)	)	PUNCT
ejpam-6008	205	10	and	and	CCONJ
ejpam-6008	205	11	so	so	ADV
ejpam-6008	205	12	f+(v	f+(v	PROPN
ejpam-6008	205	13	)	)	PUNCT
ejpam-6008	205	14	is	be	AUX
ejpam-6008	205	15	τ1τ2	τ1τ2	NOUN
ejpam-6008	205	16	-	-	ADJ
ejpam-6008	205	17	closed	closed	ADJ
ejpam-6008	205	18	in	in	ADP
ejpam-6008	205	19	x.	x.	NOUN
ejpam-6008	205	20	thus	thus	ADV
ejpam-6008	205	21	,	,	PUNCT
ejpam-6008	205	22	we	we	PRON
ejpam-6008	205	23	have	have	AUX
ejpam-6008	205	24	f+(u	f+(u	PUNCT
ejpam-6008	205	25	)	)	PUNCT
ejpam-6008	205	26	is	be	AUX
ejpam-6008	205	27	τ1τ2	τ1τ2	NOUN
ejpam-6008	205	28	-	-	ADJ
ejpam-6008	205	29	open	open	ADJ
ejpam-6008	205	30	in	in	ADP
ejpam-6008	205	31	x.	x.	NOUN
ejpam-6008	205	32	similarly	similarly	ADV
ejpam-6008	205	33	,	,	PUNCT
ejpam-6008	205	34	we	we	PRON
ejpam-6008	205	35	obtain	obtain	VERB
ejpam-6008	205	36	f+(v	f+(v	NOUN
ejpam-6008	205	37	)	)	PUNCT
ejpam-6008	205	38	is	be	AUX
ejpam-6008	205	39	τ1τ2	τ1τ2	NOUN
ejpam-6008	205	40	-	-	ADJ
ejpam-6008	205	41	open	open	ADJ
ejpam-6008	205	42	in	in	ADP
ejpam-6008	205	43	x.	x.	NOUN
ejpam-6008	205	44	consequently	consequently	ADV
ejpam-6008	205	45	,	,	PUNCT
ejpam-6008	205	46	this	this	PRON
ejpam-6008	205	47	shows	show	VERB
ejpam-6008	205	48	that	that	SCONJ
ejpam-6008	205	49	(	(	PUNCT
ejpam-6008	205	50	x	x	NOUN
ejpam-6008	205	51	,	,	PUNCT
ejpam-6008	205	52	τ1	τ1	NOUN
ejpam-6008	205	53	,	,	PUNCT
ejpam-6008	205	54	τ2	τ2	NOUN
ejpam-6008	205	55	)	)	PUNCT
ejpam-6008	205	56	is	be	AUX
ejpam-6008	205	57	not	not	PART
ejpam-6008	205	58	τ1τ2	τ1τ2	ADJ
ejpam-6008	205	59	-	-	VERB
ejpam-6008	205	60	connected	connected	ADJ
ejpam-6008	205	61	.	.	PUNCT
ejpam-6008	206	1	this	this	PRON
ejpam-6008	206	2	completes	complete	VERB
ejpam-6008	206	3	the	the	DET
ejpam-6008	206	4	proof	proof	NOUN
ejpam-6008	206	5	.	.	PUNCT
ejpam-6008	207	1	recall	recall	VERB
ejpam-6008	207	2	that	that	SCONJ
ejpam-6008	207	3	a	a	DET
ejpam-6008	207	4	bitopological	bitopological	ADJ
ejpam-6008	207	5	space	space	NOUN
ejpam-6008	207	6	(	(	PUNCT
ejpam-6008	207	7	x	x	NOUN
ejpam-6008	207	8	,	,	PUNCT
ejpam-6008	207	9	τ1	τ1	NOUN
ejpam-6008	207	10	,	,	PUNCT
ejpam-6008	207	11	τ2	τ2	NOUN
ejpam-6008	207	12	)	)	PUNCT
ejpam-6008	207	13	is	be	AUX
ejpam-6008	207	14	said	say	VERB
ejpam-6008	207	15	to	to	PART
ejpam-6008	207	16	be	be	AUX
ejpam-6008	207	17	τ1τ2	τ1τ2	NOUN
ejpam-6008	207	18	-	-	ADJ
ejpam-6008	208	1	compact	compact	ADJ
ejpam-6008	208	2	[	[	X
ejpam-6008	208	3	77	77	NUM
ejpam-6008	208	4	]	]	X
ejpam-6008	208	5	if	if	SCONJ
ejpam-6008	208	6	every	every	DET
ejpam-6008	208	7	cover	cover	NOUN
ejpam-6008	208	8	of	of	ADP
ejpam-6008	208	9	x	x	PUNCT
ejpam-6008	208	10	by	by	ADP
ejpam-6008	208	11	τ1τ2	τ1τ2	ADJ
ejpam-6008	208	12	-	-	ADJ
ejpam-6008	208	13	open	open	ADJ
ejpam-6008	208	14	sets	set	NOUN
ejpam-6008	208	15	of	of	ADP
ejpam-6008	208	16	x	x	PUNCT
ejpam-6008	208	17	has	have	VERB
ejpam-6008	208	18	a	a	DET
ejpam-6008	208	19	finite	finite	ADJ
ejpam-6008	208	20	subcover	subcover	PROPN
ejpam-6008	208	21	.	.	PUNCT
ejpam-6008	209	1	definition	definition	NOUN
ejpam-6008	209	2	5	5	NUM
ejpam-6008	209	3	.	.	PUNCT
ejpam-6008	210	1	[	[	X
ejpam-6008	210	2	80	80	NUM
ejpam-6008	210	3	]	]	PUNCT
ejpam-6008	210	4	a	a	DET
ejpam-6008	210	5	bitopological	bitopological	ADJ
ejpam-6008	210	6	space	space	NOUN
ejpam-6008	210	7	(	(	PUNCT
ejpam-6008	210	8	x	x	NOUN
ejpam-6008	210	9	,	,	PUNCT
ejpam-6008	210	10	τ1	τ1	NOUN
ejpam-6008	210	11	,	,	PUNCT
ejpam-6008	210	12	τ2	τ2	NOUN
ejpam-6008	210	13	)	)	PUNCT
ejpam-6008	210	14	is	be	AUX
ejpam-6008	210	15	said	say	VERB
ejpam-6008	210	16	to	to	PART
ejpam-6008	210	17	be	be	AUX
ejpam-6008	210	18	strongly	strongly	ADV
ejpam-6008	210	19	s	s	NOUN
ejpam-6008	210	20	-	-	PUNCT
ejpam-6008	210	21	τ1τ2	τ1τ2	ADJ
ejpam-6008	210	22	-	-	ADJ
ejpam-6008	210	23	closed	closed	ADJ
ejpam-6008	210	24	if	if	SCONJ
ejpam-6008	210	25	every	every	DET
ejpam-6008	210	26	cover	cover	NOUN
ejpam-6008	210	27	of	of	ADP
ejpam-6008	210	28	x	x	PUNCT
ejpam-6008	210	29	by	by	ADP
ejpam-6008	210	30	τ1τ2	τ1τ2	ADJ
ejpam-6008	210	31	-	-	ADJ
ejpam-6008	210	32	closed	closed	ADJ
ejpam-6008	210	33	sets	set	NOUN
ejpam-6008	210	34	of	of	ADP
ejpam-6008	210	35	x	x	PUNCT
ejpam-6008	210	36	has	have	VERB
ejpam-6008	210	37	a	a	DET
ejpam-6008	210	38	finite	finite	ADJ
ejpam-6008	210	39	subcover	subcover	PROPN
ejpam-6008	210	40	.	.	PUNCT
ejpam-6008	211	1	theorem	theorem	VERB
ejpam-6008	211	2	9	9	NUM
ejpam-6008	211	3	.	.	PUNCT
ejpam-6008	212	1	let	let	VERB
ejpam-6008	212	2	f	f	NOUN
ejpam-6008	212	3	:	:	PUNCT
ejpam-6008	212	4	(	(	PUNCT
ejpam-6008	212	5	x	x	NOUN
ejpam-6008	212	6	,	,	PUNCT
ejpam-6008	212	7	τ1	τ1	NOUN
ejpam-6008	212	8	,	,	PUNCT
ejpam-6008	212	9	τ2	τ2	NOUN
ejpam-6008	212	10	)	)	PUNCT
ejpam-6008	212	11	→	→	SYM
ejpam-6008	212	12	(	(	PUNCT
ejpam-6008	212	13	y	y	PROPN
ejpam-6008	212	14	,	,	PUNCT
ejpam-6008	212	15	σ1	σ1	PROPN
ejpam-6008	212	16	,	,	PUNCT
ejpam-6008	212	17	σ2	σ2	PROPN
ejpam-6008	212	18	)	)	PUNCT
ejpam-6008	212	19	be	be	AUX
ejpam-6008	212	20	a	a	DET
ejpam-6008	212	21	surjective	surjective	ADJ
ejpam-6008	212	22	multifunction	multifunction	NOUN
ejpam-6008	212	23	and	and	CCONJ
ejpam-6008	212	24	f	f	PROPN
ejpam-6008	212	25	(	(	PUNCT
ejpam-6008	212	26	x	x	X
ejpam-6008	212	27	)	)	PUNCT
ejpam-6008	212	28	is	be	AUX
ejpam-6008	212	29	strongly	strongly	ADV
ejpam-6008	212	30	s	s	NOUN
ejpam-6008	212	31	-	-	PUNCT
ejpam-6008	212	32	σ1σ2	σ1σ2	VERB
ejpam-6008	212	33	-	-	PUNCT
ejpam-6008	212	34	closed	closed	ADJ
ejpam-6008	212	35	for	for	ADP
ejpam-6008	212	36	each	each	DET
ejpam-6008	212	37	x	x	SYM
ejpam-6008	212	38	∈	∈	PROPN
ejpam-6008	212	39	x.	x.	NOUN
ejpam-6008	213	1	if	if	SCONJ
ejpam-6008	213	2	f	f	PROPN
ejpam-6008	213	3	is	be	AUX
ejpam-6008	213	4	upper	upper	ADJ
ejpam-6008	213	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	213	6	,	,	PUNCT
ejpam-6008	213	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	213	8	and	and	CCONJ
ejpam-6008	213	9	(	(	PUNCT
ejpam-6008	213	10	x	x	NOUN
ejpam-6008	213	11	,	,	PUNCT
ejpam-6008	213	12	τ1	τ1	NOUN
ejpam-6008	213	13	,	,	PUNCT
ejpam-6008	213	14	τ2	τ2	NOUN
ejpam-6008	213	15	)	)	PUNCT
ejpam-6008	213	16	is	be	AUX
ejpam-6008	213	17	τ1τ2	τ1τ2	NOUN
ejpam-6008	213	18	-	-	ADJ
ejpam-6008	213	19	compact	compact	ADJ
ejpam-6008	213	20	,	,	PUNCT
ejpam-6008	213	21	then	then	ADV
ejpam-6008	213	22	(	(	PUNCT
ejpam-6008	213	23	y	y	PROPN
ejpam-6008	213	24	,	,	PUNCT
ejpam-6008	213	25	σ1	σ1	PROPN
ejpam-6008	213	26	,	,	PUNCT
ejpam-6008	213	27	σ2	σ2	PROPN
ejpam-6008	213	28	)	)	PUNCT
ejpam-6008	213	29	is	be	AUX
ejpam-6008	213	30	strongly	strongly	ADV
ejpam-6008	213	31	s	s	NOUN
ejpam-6008	213	32	-	-	PUNCT
ejpam-6008	213	33	σ1σ2	σ1σ2	VERB
ejpam-6008	213	34	-	-	PUNCT
ejpam-6008	213	35	closed	closed	ADJ
ejpam-6008	213	36	.	.	PUNCT
ejpam-6008	214	1	proof	proof	NOUN
ejpam-6008	214	2	.	.	PUNCT
ejpam-6008	215	1	suppose	suppose	VERB
ejpam-6008	215	2	that	that	SCONJ
ejpam-6008	215	3	(	(	PUNCT
ejpam-6008	215	4	x	x	NOUN
ejpam-6008	215	5	,	,	PUNCT
ejpam-6008	215	6	τ1	τ1	NOUN
ejpam-6008	215	7	,	,	PUNCT
ejpam-6008	215	8	τ2	τ2	NOUN
ejpam-6008	215	9	)	)	PUNCT
ejpam-6008	215	10	is	be	AUX
ejpam-6008	215	11	τ1τ2	τ1τ2	NOUN
ejpam-6008	215	12	-	-	ADJ
ejpam-6008	215	13	compact	compact	ADJ
ejpam-6008	215	14	.	.	PUNCT
ejpam-6008	216	1	let	let	VERB
ejpam-6008	216	2	{	{	PUNCT
ejpam-6008	216	3	vγ	vγ	VERB
ejpam-6008	216	4	|	|	ADV
ejpam-6008	216	5	γ	γ	X
ejpam-6008	216	6	∈	∈	PROPN
ejpam-6008	216	7	∇	∇	X
ejpam-6008	216	8	}	}	PUNCT
ejpam-6008	216	9	be	be	AUX
ejpam-6008	216	10	any	any	DET
ejpam-6008	216	11	cover	cover	NOUN
ejpam-6008	216	12	of	of	ADP
ejpam-6008	216	13	y	y	PRON
ejpam-6008	216	14	by	by	ADP
ejpam-6008	216	15	σ1σ2	σ1σ2	NOUN
ejpam-6008	216	16	-	-	PUNCT
ejpam-6008	216	17	closed	closed	ADJ
ejpam-6008	216	18	sets	set	NOUN
ejpam-6008	216	19	of	of	ADP
ejpam-6008	216	20	y	y	PROPN
ejpam-6008	216	21	.	.	PUNCT
ejpam-6008	217	1	since	since	SCONJ
ejpam-6008	217	2	f	f	PROPN
ejpam-6008	217	3	(	(	PUNCT
ejpam-6008	217	4	x	x	X
ejpam-6008	217	5	)	)	PUNCT
ejpam-6008	217	6	is	be	AUX
ejpam-6008	217	7	strongly	strongly	ADV
ejpam-6008	217	8	s	s	NOUN
ejpam-6008	217	9	-	-	PUNCT
ejpam-6008	217	10	σ1σ2	σ1σ2	VERB
ejpam-6008	217	11	-	-	PUNCT
ejpam-6008	217	12	closed	closed	ADJ
ejpam-6008	217	13	for	for	ADP
ejpam-6008	217	14	each	each	DET
ejpam-6008	217	15	x	x	SYM
ejpam-6008	217	16	∈	∈	PROPN
ejpam-6008	217	17	x	x	X
ejpam-6008	217	18	,	,	PUNCT
ejpam-6008	217	19	there	there	PRON
ejpam-6008	217	20	exists	exist	VERB
ejpam-6008	217	21	a	a	DET
ejpam-6008	217	22	finite	finite	NOUN
ejpam-6008	217	23	subset	subset	NOUN
ejpam-6008	217	24	∇(x	∇(x	NOUN
ejpam-6008	217	25	)	)	PUNCT
ejpam-6008	217	26	of	of	ADP
ejpam-6008	217	27	∇	∇	NOUN
ejpam-6008	217	28	such	such	ADJ
ejpam-6008	217	29	that	that	SCONJ
ejpam-6008	217	30	f	f	PROPN
ejpam-6008	217	31	(	(	PUNCT
ejpam-6008	217	32	x	x	X
ejpam-6008	217	33	)	)	PUNCT
ejpam-6008	217	34	⊆	⊆	NUM
ejpam-6008	217	35	∪{vγ	∪{vγ	PROPN
ejpam-6008	217	36	|	|	ADV
ejpam-6008	217	37	γ	γ	PROPN
ejpam-6008	217	38	∈	∈	PROPN
ejpam-6008	217	39	∇(x	∇(x	NUM
ejpam-6008	217	40	)	)	PUNCT
ejpam-6008	217	41	}	}	PUNCT
ejpam-6008	217	42	.	.	PUNCT
ejpam-6008	218	1	put	put	VERB
ejpam-6008	218	2	v	v	NOUN
ejpam-6008	218	3	(	(	PUNCT
ejpam-6008	218	4	x	x	NOUN
ejpam-6008	218	5	)	)	PUNCT
ejpam-6008	218	6	=	=	SYM
ejpam-6008	218	7	∪{vγ	∪{vγ	PROPN
ejpam-6008	218	8	|	|	ADV
ejpam-6008	218	9	γ	γ	PROPN
ejpam-6008	218	10	∈	∈	PROPN
ejpam-6008	218	11	∇(x	∇(x	NUM
ejpam-6008	218	12	)	)	PUNCT
ejpam-6008	218	13	}	}	PUNCT
ejpam-6008	218	14	.	.	PUNCT
ejpam-6008	219	1	then	then	ADV
ejpam-6008	219	2	,	,	PUNCT
ejpam-6008	219	3	v	v	INTJ
ejpam-6008	219	4	(	(	PUNCT
ejpam-6008	219	5	x	x	X
ejpam-6008	219	6	)	)	PUNCT
ejpam-6008	219	7	is	be	AUX
ejpam-6008	219	8	σ1σ2	σ1σ2	NOUN
ejpam-6008	219	9	-	-	ADJ
ejpam-6008	219	10	closed	closed	ADJ
ejpam-6008	219	11	in	in	ADP
ejpam-6008	219	12	y	y	PROPN
ejpam-6008	219	13	and	and	CCONJ
ejpam-6008	219	14	f	f	PROPN
ejpam-6008	219	15	(	(	PUNCT
ejpam-6008	219	16	x	x	X
ejpam-6008	219	17	)	)	PUNCT
ejpam-6008	219	18	⊆	⊆	NUM
ejpam-6008	219	19	v	v	NOUN
ejpam-6008	219	20	(	(	PUNCT
ejpam-6008	219	21	x	x	NOUN
ejpam-6008	219	22	)	)	PUNCT
ejpam-6008	219	23	.	.	PUNCT
ejpam-6008	220	1	since	since	SCONJ
ejpam-6008	220	2	f	f	PROPN
ejpam-6008	220	3	is	be	AUX
ejpam-6008	220	4	upper	upper	ADJ
ejpam-6008	220	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	220	6	,	,	PUNCT
ejpam-6008	220	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	220	8	,	,	PUNCT
ejpam-6008	220	9	there	there	PRON
ejpam-6008	220	10	exists	exist	VERB
ejpam-6008	220	11	a	a	DET
ejpam-6008	220	12	τ1τ2	τ1τ2	NOUN
ejpam-6008	220	13	-	-	ADJ
ejpam-6008	220	14	open	open	ADJ
ejpam-6008	220	15	set	set	ADJ
ejpam-6008	220	16	u(x	u(x	NOUN
ejpam-6008	220	17	)	)	PUNCT
ejpam-6008	220	18	of	of	ADP
ejpam-6008	220	19	x	x	SYM
ejpam-6008	220	20	containing	contain	VERB
ejpam-6008	220	21	x	x	PUNCT
ejpam-6008	220	22	such	such	ADJ
ejpam-6008	220	23	that	that	SCONJ
ejpam-6008	220	24	f	f	PROPN
ejpam-6008	220	25	(	(	PUNCT
ejpam-6008	220	26	u(x	u(x	PROPN
ejpam-6008	220	27	)	)	PUNCT
ejpam-6008	220	28	)	)	PUNCT
ejpam-6008	221	1	⊆	⊆	NUM
ejpam-6008	221	2	v	v	X
ejpam-6008	221	3	(	(	PUNCT
ejpam-6008	221	4	x	x	NOUN
ejpam-6008	221	5	)	)	PUNCT
ejpam-6008	221	6	.	.	PUNCT
ejpam-6008	222	1	the	the	DET
ejpam-6008	222	2	family	family	NOUN
ejpam-6008	222	3	{	{	PUNCT
ejpam-6008	222	4	u(x	u(x	PROPN
ejpam-6008	222	5	)	)	PUNCT
ejpam-6008	222	6	|	|	ADV
ejpam-6008	222	7	x	x	SYM
ejpam-6008	222	8	∈	∈	NOUN
ejpam-6008	222	9	x	x	X
ejpam-6008	222	10	}	}	PUNCT
ejpam-6008	222	11	is	be	AUX
ejpam-6008	222	12	a	a	DET
ejpam-6008	222	13	τ1τ2	τ1τ2	ADJ
ejpam-6008	222	14	-	-	ADJ
ejpam-6008	222	15	open	open	ADJ
ejpam-6008	222	16	cover	cover	NOUN
ejpam-6008	222	17	of	of	ADP
ejpam-6008	222	18	x.	x.	NOUN
ejpam-6008	222	19	since	since	SCONJ
ejpam-6008	222	20	(	(	PUNCT
ejpam-6008	222	21	x	x	NOUN
ejpam-6008	222	22	,	,	PUNCT
ejpam-6008	222	23	τ1	τ1	NOUN
ejpam-6008	222	24	,	,	PUNCT
ejpam-6008	222	25	τ2	τ2	NOUN
ejpam-6008	222	26	)	)	PUNCT
ejpam-6008	222	27	is	be	AUX
ejpam-6008	222	28	τ1τ2	τ1τ2	NOUN
ejpam-6008	222	29	-	-	ADJ
ejpam-6008	222	30	compact	compact	ADJ
ejpam-6008	222	31	,	,	PUNCT
ejpam-6008	222	32	there	there	PRON
ejpam-6008	222	33	exists	exist	VERB
ejpam-6008	222	34	a	a	DET
ejpam-6008	222	35	finite	finite	ADJ
ejpam-6008	222	36	number	number	NOUN
ejpam-6008	222	37	of	of	ADP
ejpam-6008	222	38	pints	pint	NOUN
ejpam-6008	222	39	,	,	PUNCT
ejpam-6008	222	40	say	say	INTJ
ejpam-6008	222	41	,	,	PUNCT
ejpam-6008	222	42	x1	x1	PROPN
ejpam-6008	222	43	,	,	PUNCT
ejpam-6008	222	44	x2	x2	PROPN
ejpam-6008	222	45	,	,	PUNCT
ejpam-6008	222	46	x3	x3	ADJ
ejpam-6008	222	47	,	,	PUNCT
ejpam-6008	222	48	...	...	PUNCT
ejpam-6008	222	49	,	,	PUNCT
ejpam-6008	222	50	xn	xn	PROPN
ejpam-6008	223	1	in	in	ADP
ejpam-6008	223	2	x	x	X
ejpam-6008	223	3	such	such	ADJ
ejpam-6008	223	4	that	that	SCONJ
ejpam-6008	223	5	x	x	PART
ejpam-6008	223	6	=	=	SYM
ejpam-6008	223	7	∪{u(xk	∪{u(xk	X
ejpam-6008	223	8	)	)	PUNCT
ejpam-6008	223	9	|	|	ADV
ejpam-6008	223	10	xk	xk	PROPN
ejpam-6008	223	11	∈	∈	PROPN
ejpam-6008	223	12	x	x	X
ejpam-6008	223	13	;	;	PUNCT
ejpam-6008	223	14	1	1	NUM
ejpam-6008	223	15	≤	≤	NUM
ejpam-6008	223	16	k	k	X
ejpam-6008	223	17	≤	≤	PROPN
ejpam-6008	223	18	n	n	CCONJ
ejpam-6008	223	19	}	}	PUNCT
ejpam-6008	223	20	.	.	PUNCT
ejpam-6008	224	1	thus	thus	ADV
ejpam-6008	224	2	,	,	PUNCT
ejpam-6008	224	3	y	y	PROPN
ejpam-6008	224	4	=	=	SYM
ejpam-6008	224	5	f	f	PROPN
ejpam-6008	224	6	(	(	PUNCT
ejpam-6008	224	7	x	x	NOUN
ejpam-6008	224	8	)	)	PUNCT
ejpam-6008	224	9	=	=	SYM
ejpam-6008	224	10	∪{f	∪{f	PROPN
ejpam-6008	224	11	(	(	PUNCT
ejpam-6008	224	12	u(xk	u(xk	PROPN
ejpam-6008	224	13	)	)	PUNCT
ejpam-6008	224	14	)	)	PUNCT
ejpam-6008	224	15	|	|	ADV
ejpam-6008	224	16	xk	xk	PROPN
ejpam-6008	224	17	∈	∈	PROPN
ejpam-6008	224	18	x	x	X
ejpam-6008	224	19	;	;	PUNCT
ejpam-6008	224	20	1	1	NUM
ejpam-6008	224	21	≤	≤	NUM
ejpam-6008	224	22	k	k	X
ejpam-6008	224	23	≤	≤	PROPN
ejpam-6008	224	24	n	n	CCONJ
ejpam-6008	224	25	}	}	PUNCT
ejpam-6008	224	26	⊆	⊆	NUM
ejpam-6008	224	27	∪{vγ(xk	∪{vγ(xk	NOUN
ejpam-6008	224	28	)	)	PUNCT
ejpam-6008	224	29	|	|	ADV
ejpam-6008	224	30	xk	xk	PROPN
ejpam-6008	224	31	∈	∈	PROPN
ejpam-6008	224	32	x	x	X
ejpam-6008	224	33	;	;	PUNCT
ejpam-6008	224	34	1	1	NUM
ejpam-6008	224	35	≤	≤	NUM
ejpam-6008	224	36	k	k	X
ejpam-6008	224	37	≤	≤	PROPN
ejpam-6008	224	38	n	n	CCONJ
ejpam-6008	224	39	}	}	PUNCT
ejpam-6008	224	40	.	.	PUNCT
ejpam-6008	225	1	this	this	PRON
ejpam-6008	225	2	shows	show	VERB
ejpam-6008	225	3	that	that	SCONJ
ejpam-6008	225	4	(	(	PUNCT
ejpam-6008	225	5	y	y	PROPN
ejpam-6008	225	6	,	,	PUNCT
ejpam-6008	225	7	σ1	σ1	PROPN
ejpam-6008	225	8	,	,	PUNCT
ejpam-6008	225	9	σ2	σ2	PROPN
ejpam-6008	225	10	)	)	PUNCT
ejpam-6008	225	11	is	be	AUX
ejpam-6008	225	12	strongly	strongly	ADV
ejpam-6008	225	13	s	s	NOUN
ejpam-6008	225	14	-	-	PUNCT
ejpam-6008	225	15	σ1σ2	σ1σ2	VERB
ejpam-6008	225	16	-	-	PUNCT
ejpam-6008	225	17	closed	closed	ADJ
ejpam-6008	225	18	.	.	PUNCT
ejpam-6008	226	1	definition	definition	NOUN
ejpam-6008	226	2	6	6	NUM
ejpam-6008	226	3	.	.	PUNCT
ejpam-6008	227	1	[	[	X
ejpam-6008	227	2	56	56	NUM
ejpam-6008	227	3	]	]	PUNCT
ejpam-6008	227	4	a	a	DET
ejpam-6008	227	5	multifunction	multifunction	NOUN
ejpam-6008	227	6	f	f	NOUN
ejpam-6008	227	7	:	:	PUNCT
ejpam-6008	227	8	(	(	PUNCT
ejpam-6008	227	9	x	x	NOUN
ejpam-6008	227	10	,	,	PUNCT
ejpam-6008	227	11	τ1	τ1	NOUN
ejpam-6008	227	12	,	,	PUNCT
ejpam-6008	227	13	τ2	τ2	NOUN
ejpam-6008	227	14	)	)	PUNCT
ejpam-6008	227	15	→	→	SYM
ejpam-6008	227	16	(	(	PUNCT
ejpam-6008	227	17	y	y	PROPN
ejpam-6008	227	18	,	,	PUNCT
ejpam-6008	227	19	σ1	σ1	PROPN
ejpam-6008	227	20	,	,	PUNCT
ejpam-6008	227	21	σ2	σ2	PROPN
ejpam-6008	227	22	)	)	PUNCT
ejpam-6008	227	23	is	be	AUX
ejpam-6008	227	24	said	say	VERB
ejpam-6008	227	25	to	to	PART
ejpam-6008	227	26	be	be	AUX
ejpam-6008	227	27	:	:	PUNCT
ejpam-6008	227	28	(	(	PUNCT
ejpam-6008	227	29	1	1	X
ejpam-6008	227	30	)	)	PUNCT
ejpam-6008	227	31	upper	upper	ADJ
ejpam-6008	227	32	(	(	PUNCT
ejpam-6008	227	33	τ1	τ1	NOUN
ejpam-6008	227	34	,	,	PUNCT
ejpam-6008	227	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	227	36	if	if	SCONJ
ejpam-6008	227	37	for	for	ADP
ejpam-6008	227	38	each	each	DET
ejpam-6008	227	39	x	x	SYM
ejpam-6008	227	40	∈	∈	PROPN
ejpam-6008	227	41	x	x	X
ejpam-6008	227	42	and	and	CCONJ
ejpam-6008	227	43	each	each	DET
ejpam-6008	227	44	σ1σ2	σ1σ2	VERB
ejpam-6008	227	45	-	-	ADJ
ejpam-6008	227	46	open	open	ADJ
ejpam-6008	227	47	set	set	NOUN
ejpam-6008	227	48	v	v	NOUN
ejpam-6008	227	49	of	of	ADP
ejpam-6008	227	50	y	y	PRON
ejpam-6008	227	51	such	such	ADJ
ejpam-6008	227	52	that	that	SCONJ
ejpam-6008	227	53	f	f	PROPN
ejpam-6008	227	54	(	(	PUNCT
ejpam-6008	227	55	x	x	X
ejpam-6008	227	56	)	)	PUNCT
ejpam-6008	227	57	⊆	⊆	NUM
ejpam-6008	227	58	v	v	NOUN
ejpam-6008	227	59	,	,	PUNCT
ejpam-6008	227	60	there	there	PRON
ejpam-6008	227	61	exists	exist	VERB
ejpam-6008	227	62	a	a	DET
ejpam-6008	227	63	τ1τ2	τ1τ2	NOUN
ejpam-6008	227	64	-	-	ADJ
ejpam-6008	227	65	open	open	ADJ
ejpam-6008	227	66	set	set	ADJ
ejpam-6008	227	67	u	u	NOUN
ejpam-6008	227	68	of	of	ADP
ejpam-6008	227	69	x	x	PUNCT
ejpam-6008	227	70	containing	contain	VERB
ejpam-6008	227	71	x	x	PUNCT
ejpam-6008	228	1	such	such	ADJ
ejpam-6008	228	2	that	that	SCONJ
ejpam-6008	228	3	f	f	PROPN
ejpam-6008	228	4	(	(	PUNCT
ejpam-6008	228	5	u	u	NOUN
ejpam-6008	228	6	)	)	PUNCT
ejpam-6008	228	7	⊆	⊆	NUM
ejpam-6008	228	8	v	v	NOUN
ejpam-6008	228	9	;	;	PUNCT
ejpam-6008	228	10	(	(	PUNCT
ejpam-6008	228	11	2	2	X
ejpam-6008	228	12	)	)	PUNCT
ejpam-6008	228	13	lower	low	ADJ
ejpam-6008	228	14	(	(	PUNCT
ejpam-6008	228	15	τ1	τ1	NOUN
ejpam-6008	228	16	,	,	PUNCT
ejpam-6008	228	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	228	18	if	if	SCONJ
ejpam-6008	228	19	for	for	ADP
ejpam-6008	228	20	each	each	DET
ejpam-6008	228	21	x	x	SYM
ejpam-6008	228	22	∈	∈	PROPN
ejpam-6008	228	23	x	x	X
ejpam-6008	228	24	and	and	CCONJ
ejpam-6008	228	25	each	each	DET
ejpam-6008	228	26	σ1σ2	σ1σ2	VERB
ejpam-6008	228	27	-	-	ADJ
ejpam-6008	228	28	open	open	ADJ
ejpam-6008	228	29	set	set	NOUN
ejpam-6008	228	30	v	v	NOUN
ejpam-6008	228	31	of	of	ADP
ejpam-6008	228	32	y	y	PRON
ejpam-6008	228	33	such	such	ADJ
ejpam-6008	228	34	that	that	SCONJ
ejpam-6008	228	35	f	f	PROPN
ejpam-6008	228	36	(	(	PUNCT
ejpam-6008	228	37	x)∩v	x)∩v	PROPN
ejpam-6008	228	38	̸=	̸=	PROPN
ejpam-6008	228	39	∅	∅	NOUN
ejpam-6008	228	40	,	,	PUNCT
ejpam-6008	228	41	there	there	PRON
ejpam-6008	228	42	exists	exist	VERB
ejpam-6008	228	43	a	a	DET
ejpam-6008	228	44	τ1τ2	τ1τ2	NOUN
ejpam-6008	228	45	-	-	ADJ
ejpam-6008	228	46	open	open	ADJ
ejpam-6008	228	47	set	set	ADJ
ejpam-6008	228	48	u	u	NOUN
ejpam-6008	228	49	of	of	ADP
ejpam-6008	228	50	x	x	PUNCT
ejpam-6008	228	51	containing	contain	VERB
ejpam-6008	228	52	x	x	PUNCT
ejpam-6008	228	53	such	such	ADJ
ejpam-6008	228	54	that	that	SCONJ
ejpam-6008	228	55	f	f	PROPN
ejpam-6008	228	56	(	(	PUNCT
ejpam-6008	228	57	z)∩v	z)∩v	PROPN
ejpam-6008	228	58	̸=	̸=	PROPN
ejpam-6008	228	59	∅	∅	NOUN
ejpam-6008	228	60	for	for	ADP
ejpam-6008	228	61	each	each	DET
ejpam-6008	228	62	z	z	NOUN
ejpam-6008	228	63	∈	∈	PROPN
ejpam-6008	228	64	u	u	PROPN
ejpam-6008	228	65	.	.	PUNCT
ejpam-6008	229	1	lemma	lemma	PROPN
ejpam-6008	229	2	5	5	NUM
ejpam-6008	229	3	.	.	PUNCT
ejpam-6008	230	1	[	[	X
ejpam-6008	230	2	56	56	NUM
ejpam-6008	230	3	]	]	PUNCT
ejpam-6008	230	4	for	for	ADP
ejpam-6008	230	5	a	a	DET
ejpam-6008	230	6	multifunction	multifunction	NOUN
ejpam-6008	230	7	f	f	NOUN
ejpam-6008	230	8	:	:	PUNCT
ejpam-6008	230	9	(	(	PUNCT
ejpam-6008	230	10	x	x	NOUN
ejpam-6008	230	11	,	,	PUNCT
ejpam-6008	230	12	τ1	τ1	NOUN
ejpam-6008	230	13	,	,	PUNCT
ejpam-6008	230	14	τ2	τ2	NOUN
ejpam-6008	230	15	)	)	PUNCT
ejpam-6008	230	16	→	→	SYM
ejpam-6008	230	17	(	(	PUNCT
ejpam-6008	230	18	y	y	PROPN
ejpam-6008	230	19	,	,	PUNCT
ejpam-6008	230	20	σ1	σ1	PROPN
ejpam-6008	230	21	,	,	PUNCT
ejpam-6008	230	22	σ2	σ2	NOUN
ejpam-6008	230	23	)	)	PUNCT
ejpam-6008	230	24	,	,	PUNCT
ejpam-6008	230	25	the	the	DET
ejpam-6008	230	26	following	follow	VERB
ejpam-6008	230	27	properties	property	NOUN
ejpam-6008	230	28	are	be	AUX
ejpam-6008	230	29	equivalent	equivalent	ADJ
ejpam-6008	230	30	:	:	PUNCT
ejpam-6008	230	31	(	(	PUNCT
ejpam-6008	230	32	1	1	X
ejpam-6008	230	33	)	)	PUNCT
ejpam-6008	230	34	f	f	PROPN
ejpam-6008	230	35	is	be	AUX
ejpam-6008	230	36	upper	upper	ADJ
ejpam-6008	230	37	(	(	PUNCT
ejpam-6008	230	38	τ1	τ1	NOUN
ejpam-6008	230	39	,	,	PUNCT
ejpam-6008	230	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	230	41	;	;	PUNCT
ejpam-6008	230	42	(	(	PUNCT
ejpam-6008	230	43	2	2	NUM
ejpam-6008	230	44	)	)	PUNCT
ejpam-6008	230	45	f+(v	f+(v	NOUN
ejpam-6008	230	46	)	)	PUNCT
ejpam-6008	230	47	is	be	AUX
ejpam-6008	230	48	τ1τ2	τ1τ2	NOUN
ejpam-6008	230	49	-	-	ADJ
ejpam-6008	230	50	open	open	ADJ
ejpam-6008	230	51	in	in	ADP
ejpam-6008	230	52	x	x	PUNCT
ejpam-6008	230	53	for	for	ADP
ejpam-6008	230	54	every	every	DET
ejpam-6008	230	55	σ1σ2	σ1σ2	NOUN
ejpam-6008	230	56	-	-	ADJ
ejpam-6008	230	57	open	open	ADJ
ejpam-6008	230	58	set	set	NOUN
ejpam-6008	230	59	v	v	NOUN
ejpam-6008	230	60	of	of	ADP
ejpam-6008	230	61	y	y	PROPN
ejpam-6008	230	62	;	;	PUNCT
ejpam-6008	230	63	(	(	PUNCT
ejpam-6008	230	64	3	3	X
ejpam-6008	230	65	)	)	PUNCT
ejpam-6008	230	66	f−(k	f−(k	PROPN
ejpam-6008	230	67	)	)	PUNCT
ejpam-6008	230	68	is	be	AUX
ejpam-6008	230	69	τ1τ2	τ1τ2	NOUN
ejpam-6008	230	70	-	-	ADJ
ejpam-6008	230	71	closed	closed	ADJ
ejpam-6008	230	72	in	in	ADP
ejpam-6008	230	73	x	x	PUNCT
ejpam-6008	230	74	for	for	ADP
ejpam-6008	230	75	every	every	DET
ejpam-6008	230	76	σ1σ2	σ1σ2	NUM
ejpam-6008	230	77	-	-	PUNCT
ejpam-6008	230	78	closed	closed	ADJ
ejpam-6008	230	79	set	set	NOUN
ejpam-6008	230	80	k	k	PROPN
ejpam-6008	230	81	of	of	ADP
ejpam-6008	230	82	y	y	PROPN
ejpam-6008	230	83	;	;	PUNCT
ejpam-6008	230	84	(	(	PUNCT
ejpam-6008	230	85	4	4	X
ejpam-6008	230	86	)	)	PUNCT
ejpam-6008	230	87	τ1τ2	τ1τ2	NOUN
ejpam-6008	230	88	-	-	NOUN
ejpam-6008	230	89	cl(f	cl(f	NOUN
ejpam-6008	230	90	−(b	−(b	PROPN
ejpam-6008	230	91	)	)	PUNCT
ejpam-6008	230	92	)	)	PUNCT
ejpam-6008	231	1	⊆	⊆	X
ejpam-6008	231	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6008	231	3	-	-	PUNCT
ejpam-6008	231	4	cl(b	cl(b	NOUN
ejpam-6008	231	5	)	)	PUNCT
ejpam-6008	231	6	)	)	PUNCT
ejpam-6008	232	1	for	for	ADP
ejpam-6008	232	2	every	every	DET
ejpam-6008	232	3	subset	subset	NOUN
ejpam-6008	232	4	b	b	PROPN
ejpam-6008	232	5	of	of	ADP
ejpam-6008	232	6	y	y	PROPN
ejpam-6008	232	7	;	;	PUNCT
ejpam-6008	232	8	n.	n.	PROPN
ejpam-6008	232	9	viriyapong	viriyapong	PROPN
ejpam-6008	232	10	,	,	PUNCT
ejpam-6008	232	11	a.	a.	PROPN
ejpam-6008	232	12	sama	sama	PROPN
ejpam-6008	232	13	-	-	PUNCT
ejpam-6008	232	14	ae	ae	PROPN
ejpam-6008	232	15	,	,	PUNCT
ejpam-6008	232	16	c.	c.	PROPN
ejpam-6008	232	17	boonpok	boonpok	PROPN
ejpam-6008	232	18	/	/	SYM
ejpam-6008	232	19	eur	eur	PROPN
ejpam-6008	232	20	.	.	PUNCT
ejpam-6008	233	1	j.	j.	PROPN
ejpam-6008	233	2	pure	pure	PROPN
ejpam-6008	233	3	appl	appl	PROPN
ejpam-6008	233	4	.	.	PROPN
ejpam-6008	233	5	math	math	PROPN
ejpam-6008	233	6	,	,	PUNCT
ejpam-6008	233	7	18	18	NUM
ejpam-6008	233	8	(	(	PUNCT
ejpam-6008	233	9	2	2	NUM
ejpam-6008	233	10	)	)	PUNCT
ejpam-6008	233	11	(	(	PUNCT
ejpam-6008	233	12	2025	2025	NUM
ejpam-6008	233	13	)	)	PUNCT
ejpam-6008	233	14	,	,	PUNCT
ejpam-6008	233	15	6008	6008	NUM
ejpam-6008	233	16	9	9	NUM
ejpam-6008	233	17	of	of	ADP
ejpam-6008	233	18	15	15	NUM
ejpam-6008	233	19	(	(	PUNCT
ejpam-6008	233	20	5	5	NUM
ejpam-6008	233	21	)	)	PUNCT
ejpam-6008	233	22	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	233	23	-	-	PUNCT
ejpam-6008	233	24	int(b	int(b	NOUN
ejpam-6008	233	25	)	)	PUNCT
ejpam-6008	233	26	)	)	PUNCT
ejpam-6008	234	1	⊆	⊆	X
ejpam-6008	234	2	τ1τ2	τ1τ2	NOUN
ejpam-6008	234	3	-	-	NUM
ejpam-6008	234	4	int(f	int(f	VERB
ejpam-6008	234	5	+	+	ADJ
ejpam-6008	234	6	(	(	PUNCT
ejpam-6008	234	7	b	b	NOUN
ejpam-6008	234	8	)	)	PUNCT
ejpam-6008	234	9	)	)	PUNCT
ejpam-6008	234	10	for	for	ADP
ejpam-6008	234	11	every	every	DET
ejpam-6008	234	12	subset	subset	NOUN
ejpam-6008	234	13	b	b	PROPN
ejpam-6008	234	14	of	of	ADP
ejpam-6008	234	15	y	y	PROPN
ejpam-6008	234	16	.	.	PUNCT
ejpam-6008	235	1	theorem	theorem	ADJ
ejpam-6008	235	2	10	10	NUM
ejpam-6008	235	3	.	.	PUNCT
ejpam-6008	236	1	if	if	SCONJ
ejpam-6008	236	2	f	f	PROPN
ejpam-6008	236	3	:	:	PUNCT
ejpam-6008	236	4	(	(	PUNCT
ejpam-6008	236	5	x	x	NOUN
ejpam-6008	236	6	,	,	PUNCT
ejpam-6008	236	7	τ1	τ1	NOUN
ejpam-6008	236	8	,	,	PUNCT
ejpam-6008	236	9	τ2	τ2	NOUN
ejpam-6008	236	10	)	)	PUNCT
ejpam-6008	236	11	→	→	SYM
ejpam-6008	236	12	(	(	PUNCT
ejpam-6008	236	13	y	y	PROPN
ejpam-6008	236	14	,	,	PUNCT
ejpam-6008	236	15	σ1	σ1	PROPN
ejpam-6008	236	16	,	,	PUNCT
ejpam-6008	236	17	σ2	σ2	PROPN
ejpam-6008	236	18	)	)	PUNCT
ejpam-6008	236	19	is	be	AUX
ejpam-6008	236	20	upper	upper	ADJ
ejpam-6008	236	21	(	(	PUNCT
ejpam-6008	236	22	τ1	τ1	NOUN
ejpam-6008	236	23	,	,	PUNCT
ejpam-6008	236	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	236	25	and	and	CCONJ
ejpam-6008	236	26	g	g	NOUN
ejpam-6008	236	27	:	:	PUNCT
ejpam-6008	236	28	(	(	PUNCT
ejpam-6008	236	29	y	y	PROPN
ejpam-6008	236	30	,	,	PUNCT
ejpam-6008	236	31	σ1	σ1	PROPN
ejpam-6008	236	32	,	,	PUNCT
ejpam-6008	236	33	σ2	σ2	NOUN
ejpam-6008	236	34	)	)	PUNCT
ejpam-6008	236	35	→	→	SYM
ejpam-6008	236	36	(	(	PUNCT
ejpam-6008	236	37	z	z	NOUN
ejpam-6008	236	38	,	,	PUNCT
ejpam-6008	236	39	ρ1	ρ1	NOUN
ejpam-6008	236	40	,	,	PUNCT
ejpam-6008	236	41	ρ2	ρ2	NOUN
ejpam-6008	236	42	)	)	PUNCT
ejpam-6008	236	43	is	be	AUX
ejpam-6008	236	44	upper	upper	ADJ
ejpam-6008	236	45	contra-(σ1	contra-(σ1	NOUN
ejpam-6008	236	46	,	,	PUNCT
ejpam-6008	236	47	σ2)-continuous	σ2)-continuous	PROPN
ejpam-6008	236	48	,	,	PUNCT
ejpam-6008	236	49	then	then	ADV
ejpam-6008	236	50	g	g	PROPN
ejpam-6008	236	51	◦	◦	NOUN
ejpam-6008	236	52	f	f	X
ejpam-6008	236	53	:	:	PUNCT
ejpam-6008	236	54	(	(	PUNCT
ejpam-6008	236	55	x	x	NOUN
ejpam-6008	236	56	,	,	PUNCT
ejpam-6008	236	57	τ1	τ1	NOUN
ejpam-6008	236	58	,	,	PUNCT
ejpam-6008	236	59	τ2	τ2	NOUN
ejpam-6008	236	60	)	)	PUNCT
ejpam-6008	236	61	→	→	SYM
ejpam-6008	236	62	(	(	PUNCT
ejpam-6008	236	63	z	z	NOUN
ejpam-6008	236	64	,	,	PUNCT
ejpam-6008	236	65	ρ1	ρ1	NOUN
ejpam-6008	236	66	,	,	PUNCT
ejpam-6008	236	67	ρ2	ρ2	NOUN
ejpam-6008	236	68	)	)	PUNCT
ejpam-6008	236	69	is	be	AUX
ejpam-6008	236	70	upper	upper	ADJ
ejpam-6008	236	71	contra(τ1	contra(τ1	NOUN
ejpam-6008	236	72	,	,	PUNCT
ejpam-6008	236	73	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	236	74	.	.	PUNCT
ejpam-6008	237	1	proof	proof	NOUN
ejpam-6008	237	2	.	.	PUNCT
ejpam-6008	238	1	let	let	VERB
ejpam-6008	238	2	k	k	PRON
ejpam-6008	238	3	be	be	AUX
ejpam-6008	238	4	any	any	DET
ejpam-6008	238	5	ρ1ρ2	ρ1ρ2	NOUN
ejpam-6008	238	6	-	-	PUNCT
ejpam-6008	238	7	closed	closed	ADJ
ejpam-6008	238	8	set	set	NOUN
ejpam-6008	238	9	of	of	ADP
ejpam-6008	238	10	z.	z.	PROPN
ejpam-6008	238	11	since	since	SCONJ
ejpam-6008	238	12	g	g	PROPN
ejpam-6008	238	13	is	be	AUX
ejpam-6008	238	14	upper	upper	ADJ
ejpam-6008	238	15	contra-(σ1	contra-(σ1	NOUN
ejpam-6008	238	16	,	,	PUNCT
ejpam-6008	238	17	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6008	238	18	,	,	PUNCT
ejpam-6008	238	19	by	by	ADP
ejpam-6008	238	20	theorem	theorem	NOUN
ejpam-6008	238	21	1	1	NUM
ejpam-6008	238	22	we	we	PRON
ejpam-6008	238	23	have	have	VERB
ejpam-6008	238	24	f+(k	f+(k	NOUN
ejpam-6008	238	25	)	)	PUNCT
ejpam-6008	238	26	is	be	AUX
ejpam-6008	238	27	σ1σ2	σ1σ2	NOUN
ejpam-6008	238	28	-	-	ADJ
ejpam-6008	238	29	open	open	ADJ
ejpam-6008	238	30	in	in	ADP
ejpam-6008	238	31	y	y	PROPN
ejpam-6008	238	32	.	.	PUNCT
ejpam-6008	239	1	since	since	SCONJ
ejpam-6008	239	2	f	f	PROPN
ejpam-6008	239	3	is	be	AUX
ejpam-6008	239	4	upper	upper	ADJ
ejpam-6008	239	5	(	(	PUNCT
ejpam-6008	239	6	τ1	τ1	NOUN
ejpam-6008	239	7	,	,	PUNCT
ejpam-6008	239	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	239	9	,	,	PUNCT
ejpam-6008	239	10	by	by	ADP
ejpam-6008	239	11	lemma	lemma	PROPN
ejpam-6008	239	12	5	5	NUM
ejpam-6008	239	13	we	we	PRON
ejpam-6008	239	14	have	have	VERB
ejpam-6008	239	15	(	(	PUNCT
ejpam-6008	239	16	g	g	NOUN
ejpam-6008	239	17	◦	◦	NOUN
ejpam-6008	239	18	f	f	PROPN
ejpam-6008	239	19	)	)	PUNCT
ejpam-6008	240	1	+	+	ADJ
ejpam-6008	240	2	(	(	PUNCT
ejpam-6008	240	3	k	k	NOUN
ejpam-6008	240	4	)	)	PUNCT
ejpam-6008	240	5	=	=	SYM
ejpam-6008	240	6	f+(g+(k	f+(g+(k	NOUN
ejpam-6008	240	7	)	)	PUNCT
ejpam-6008	240	8	)	)	PUNCT
ejpam-6008	240	9	is	be	AUX
ejpam-6008	240	10	τ1τ2	τ1τ2	NOUN
ejpam-6008	240	11	-	-	ADJ
ejpam-6008	240	12	open	open	ADJ
ejpam-6008	240	13	in	in	ADP
ejpam-6008	240	14	x.	x.	NOUN
ejpam-6008	240	15	thus	thus	ADV
ejpam-6008	240	16	by	by	ADP
ejpam-6008	240	17	theorem	theorem	NOUN
ejpam-6008	240	18	1	1	NUM
ejpam-6008	240	19	,	,	PUNCT
ejpam-6008	240	20	g	g	NOUN
ejpam-6008	240	21	◦	◦	NOUN
ejpam-6008	240	22	f	f	PROPN
ejpam-6008	240	23	is	be	AUX
ejpam-6008	240	24	upper	upper	ADJ
ejpam-6008	240	25	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	240	26	,	,	PUNCT
ejpam-6008	240	27	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	240	28	.	.	PUNCT
ejpam-6008	241	1	lemma	lemma	PROPN
ejpam-6008	241	2	6	6	NUM
ejpam-6008	241	3	.	.	PUNCT
ejpam-6008	242	1	[	[	X
ejpam-6008	242	2	56	56	NUM
ejpam-6008	242	3	]	]	PUNCT
ejpam-6008	242	4	for	for	ADP
ejpam-6008	242	5	a	a	DET
ejpam-6008	242	6	multifunction	multifunction	NOUN
ejpam-6008	242	7	f	f	NOUN
ejpam-6008	242	8	:	:	PUNCT
ejpam-6008	242	9	(	(	PUNCT
ejpam-6008	242	10	x	x	NOUN
ejpam-6008	242	11	,	,	PUNCT
ejpam-6008	242	12	τ1	τ1	NOUN
ejpam-6008	242	13	,	,	PUNCT
ejpam-6008	242	14	τ2	τ2	NOUN
ejpam-6008	242	15	)	)	PUNCT
ejpam-6008	242	16	→	→	SYM
ejpam-6008	242	17	(	(	PUNCT
ejpam-6008	242	18	y	y	PROPN
ejpam-6008	242	19	,	,	PUNCT
ejpam-6008	242	20	σ1	σ1	PROPN
ejpam-6008	242	21	,	,	PUNCT
ejpam-6008	242	22	σ2	σ2	NOUN
ejpam-6008	242	23	)	)	PUNCT
ejpam-6008	242	24	,	,	PUNCT
ejpam-6008	242	25	the	the	DET
ejpam-6008	242	26	following	follow	VERB
ejpam-6008	242	27	properties	property	NOUN
ejpam-6008	242	28	are	be	AUX
ejpam-6008	242	29	equivalent	equivalent	ADJ
ejpam-6008	242	30	:	:	PUNCT
ejpam-6008	242	31	(	(	PUNCT
ejpam-6008	242	32	1	1	X
ejpam-6008	242	33	)	)	PUNCT
ejpam-6008	242	34	f	f	PROPN
ejpam-6008	242	35	is	be	AUX
ejpam-6008	242	36	lower	low	ADJ
ejpam-6008	242	37	(	(	PUNCT
ejpam-6008	242	38	τ1	τ1	NOUN
ejpam-6008	242	39	,	,	PUNCT
ejpam-6008	242	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	242	41	;	;	PUNCT
ejpam-6008	242	42	(	(	PUNCT
ejpam-6008	242	43	2	2	X
ejpam-6008	242	44	)	)	PUNCT
ejpam-6008	242	45	f−(v	f−(v	NOUN
ejpam-6008	242	46	)	)	PUNCT
ejpam-6008	242	47	is	be	AUX
ejpam-6008	242	48	τ1τ2	τ1τ2	NOUN
ejpam-6008	242	49	-	-	ADJ
ejpam-6008	242	50	open	open	ADJ
ejpam-6008	242	51	in	in	ADP
ejpam-6008	242	52	x	x	PUNCT
ejpam-6008	242	53	for	for	ADP
ejpam-6008	242	54	every	every	DET
ejpam-6008	242	55	σ1σ2	σ1σ2	NOUN
ejpam-6008	242	56	-	-	ADJ
ejpam-6008	242	57	open	open	ADJ
ejpam-6008	242	58	set	set	NOUN
ejpam-6008	242	59	v	v	NOUN
ejpam-6008	242	60	of	of	ADP
ejpam-6008	242	61	y	y	PROPN
ejpam-6008	242	62	;	;	PUNCT
ejpam-6008	242	63	(	(	PUNCT
ejpam-6008	242	64	3	3	X
ejpam-6008	242	65	)	)	PUNCT
ejpam-6008	242	66	f+(k	f+(k	NOUN
ejpam-6008	242	67	)	)	PUNCT
ejpam-6008	242	68	is	be	AUX
ejpam-6008	242	69	τ1τ2	τ1τ2	NOUN
ejpam-6008	242	70	-	-	ADJ
ejpam-6008	242	71	closed	closed	ADJ
ejpam-6008	242	72	in	in	ADP
ejpam-6008	242	73	x	x	PUNCT
ejpam-6008	242	74	for	for	ADP
ejpam-6008	242	75	every	every	DET
ejpam-6008	242	76	σ1σ2	σ1σ2	NUM
ejpam-6008	242	77	-	-	PUNCT
ejpam-6008	242	78	closed	closed	ADJ
ejpam-6008	242	79	set	set	NOUN
ejpam-6008	242	80	k	k	PROPN
ejpam-6008	242	81	of	of	ADP
ejpam-6008	242	82	y	y	PROPN
ejpam-6008	242	83	;	;	PUNCT
ejpam-6008	242	84	(	(	PUNCT
ejpam-6008	242	85	4	4	X
ejpam-6008	242	86	)	)	PUNCT
ejpam-6008	242	87	τ1τ2	τ1τ2	NOUN
ejpam-6008	242	88	-	-	NOUN
ejpam-6008	242	89	cl(f	cl(f	NOUN
ejpam-6008	242	90	+	+	NOUN
ejpam-6008	242	91	(	(	PUNCT
ejpam-6008	242	92	b	b	NOUN
ejpam-6008	242	93	)	)	PUNCT
ejpam-6008	242	94	)	)	PUNCT
ejpam-6008	242	95	⊆	⊆	NUM
ejpam-6008	242	96	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6008	242	97	-	-	PUNCT
ejpam-6008	242	98	cl(b	cl(b	NOUN
ejpam-6008	242	99	)	)	PUNCT
ejpam-6008	242	100	)	)	PUNCT
ejpam-6008	242	101	for	for	ADP
ejpam-6008	242	102	every	every	DET
ejpam-6008	242	103	subset	subset	NOUN
ejpam-6008	242	104	b	b	PROPN
ejpam-6008	242	105	of	of	ADP
ejpam-6008	242	106	y	y	PROPN
ejpam-6008	242	107	;	;	PUNCT
ejpam-6008	242	108	(	(	PUNCT
ejpam-6008	242	109	5	5	X
ejpam-6008	242	110	)	)	PUNCT
ejpam-6008	242	111	f	f	NOUN
ejpam-6008	242	112	(	(	PUNCT
ejpam-6008	242	113	τ1τ2	τ1τ2	NOUN
ejpam-6008	242	114	-	-	NUM
ejpam-6008	242	115	cl(a	cl(a	NUM
ejpam-6008	242	116	)	)	PUNCT
ejpam-6008	242	117	)	)	PUNCT
ejpam-6008	243	1	⊆	⊆	X
ejpam-6008	243	2	σ1σ2	σ1σ2	X
ejpam-6008	243	3	-	-	NUM
ejpam-6008	243	4	cl(f	cl(f	NOUN
ejpam-6008	243	5	(	(	PUNCT
ejpam-6008	243	6	a	a	NOUN
ejpam-6008	243	7	)	)	PUNCT
ejpam-6008	243	8	)	)	PUNCT
ejpam-6008	243	9	for	for	ADP
ejpam-6008	243	10	every	every	DET
ejpam-6008	243	11	subset	subset	NOUN
ejpam-6008	243	12	a	a	PRON
ejpam-6008	243	13	of	of	ADP
ejpam-6008	243	14	x	x	PRON
ejpam-6008	243	15	;	;	PUNCT
ejpam-6008	243	16	(	(	PUNCT
ejpam-6008	243	17	6	6	X
ejpam-6008	243	18	)	)	PUNCT
ejpam-6008	243	19	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6008	243	20	-	-	PUNCT
ejpam-6008	243	21	int(b	int(b	NOUN
ejpam-6008	243	22	)	)	PUNCT
ejpam-6008	243	23	)	)	PUNCT
ejpam-6008	243	24	⊆	⊆	X
ejpam-6008	243	25	τ1τ2	τ1τ2	NOUN
ejpam-6008	243	26	-	-	NUM
ejpam-6008	243	27	int(f	int(f	VERB
ejpam-6008	243	28	−(b	−(b	NOUN
ejpam-6008	243	29	)	)	PUNCT
ejpam-6008	243	30	)	)	PUNCT
ejpam-6008	243	31	for	for	ADP
ejpam-6008	243	32	every	every	DET
ejpam-6008	243	33	subset	subset	NOUN
ejpam-6008	243	34	b	b	PROPN
ejpam-6008	243	35	of	of	ADP
ejpam-6008	243	36	y	y	PROPN
ejpam-6008	243	37	.	.	PUNCT
ejpam-6008	244	1	theorem	theorem	VERB
ejpam-6008	244	2	11	11	NUM
ejpam-6008	244	3	.	.	PUNCT
ejpam-6008	245	1	if	if	SCONJ
ejpam-6008	245	2	f	f	PROPN
ejpam-6008	245	3	:	:	PUNCT
ejpam-6008	245	4	(	(	PUNCT
ejpam-6008	245	5	x	x	NOUN
ejpam-6008	245	6	,	,	PUNCT
ejpam-6008	245	7	τ1	τ1	NOUN
ejpam-6008	245	8	,	,	PUNCT
ejpam-6008	245	9	τ2	τ2	NOUN
ejpam-6008	245	10	)	)	PUNCT
ejpam-6008	245	11	→	→	SYM
ejpam-6008	245	12	(	(	PUNCT
ejpam-6008	245	13	y	y	PROPN
ejpam-6008	245	14	,	,	PUNCT
ejpam-6008	245	15	σ1	σ1	PROPN
ejpam-6008	245	16	,	,	PUNCT
ejpam-6008	245	17	σ2	σ2	NOUN
ejpam-6008	245	18	)	)	PUNCT
ejpam-6008	245	19	is	be	AUX
ejpam-6008	245	20	lower	low	ADJ
ejpam-6008	245	21	(	(	PUNCT
ejpam-6008	245	22	τ1	τ1	NOUN
ejpam-6008	245	23	,	,	PUNCT
ejpam-6008	245	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	245	25	and	and	CCONJ
ejpam-6008	245	26	g	g	NOUN
ejpam-6008	245	27	:	:	PUNCT
ejpam-6008	245	28	(	(	PUNCT
ejpam-6008	245	29	y	y	PROPN
ejpam-6008	245	30	,	,	PUNCT
ejpam-6008	245	31	σ1	σ1	PROPN
ejpam-6008	245	32	,	,	PUNCT
ejpam-6008	245	33	σ2	σ2	NOUN
ejpam-6008	245	34	)	)	PUNCT
ejpam-6008	245	35	→	→	SYM
ejpam-6008	245	36	(	(	PUNCT
ejpam-6008	245	37	z	z	NOUN
ejpam-6008	245	38	,	,	PUNCT
ejpam-6008	245	39	ρ1	ρ1	NOUN
ejpam-6008	245	40	,	,	PUNCT
ejpam-6008	245	41	ρ2	ρ2	NOUN
ejpam-6008	245	42	)	)	PUNCT
ejpam-6008	245	43	is	be	AUX
ejpam-6008	245	44	lower	low	ADJ
ejpam-6008	245	45	contra-(σ1	contra-(σ1	NOUN
ejpam-6008	245	46	,	,	PUNCT
ejpam-6008	245	47	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6008	245	48	,	,	PUNCT
ejpam-6008	245	49	then	then	ADV
ejpam-6008	245	50	g	g	PROPN
ejpam-6008	245	51	◦	◦	NOUN
ejpam-6008	245	52	f	f	X
ejpam-6008	245	53	:	:	PUNCT
ejpam-6008	245	54	(	(	PUNCT
ejpam-6008	245	55	x	x	NOUN
ejpam-6008	245	56	,	,	PUNCT
ejpam-6008	245	57	τ1	τ1	NOUN
ejpam-6008	245	58	,	,	PUNCT
ejpam-6008	245	59	τ2	τ2	NOUN
ejpam-6008	245	60	)	)	PUNCT
ejpam-6008	245	61	→	→	SYM
ejpam-6008	245	62	(	(	PUNCT
ejpam-6008	245	63	z	z	NOUN
ejpam-6008	245	64	,	,	PUNCT
ejpam-6008	245	65	ρ1	ρ1	NOUN
ejpam-6008	245	66	,	,	PUNCT
ejpam-6008	245	67	ρ2	ρ2	NOUN
ejpam-6008	245	68	)	)	PUNCT
ejpam-6008	245	69	is	be	AUX
ejpam-6008	245	70	lower	low	ADJ
ejpam-6008	245	71	contra(τ1	contra(τ1	NOUN
ejpam-6008	245	72	,	,	PUNCT
ejpam-6008	245	73	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	245	74	.	.	PUNCT
ejpam-6008	246	1	proof	proof	NOUN
ejpam-6008	246	2	.	.	PUNCT
ejpam-6008	247	1	the	the	DET
ejpam-6008	247	2	proof	proof	NOUN
ejpam-6008	247	3	is	be	AUX
ejpam-6008	247	4	similar	similar	ADJ
ejpam-6008	247	5	to	to	ADP
ejpam-6008	247	6	that	that	PRON
ejpam-6008	247	7	of	of	ADP
ejpam-6008	247	8	theorem	theorem	ADJ
ejpam-6008	247	9	10	10	NUM
ejpam-6008	247	10	.	.	PUNCT
ejpam-6008	248	1	for	for	ADP
ejpam-6008	248	2	a	a	DET
ejpam-6008	248	3	multifunction	multifunction	NOUN
ejpam-6008	248	4	f	f	NOUN
ejpam-6008	248	5	:	:	PUNCT
ejpam-6008	248	6	(	(	PUNCT
ejpam-6008	248	7	x	x	NOUN
ejpam-6008	248	8	,	,	PUNCT
ejpam-6008	248	9	τ1	τ1	NOUN
ejpam-6008	248	10	,	,	PUNCT
ejpam-6008	248	11	τ2	τ2	NOUN
ejpam-6008	248	12	)	)	PUNCT
ejpam-6008	248	13	→	→	SYM
ejpam-6008	248	14	(	(	PUNCT
ejpam-6008	248	15	y	y	PROPN
ejpam-6008	248	16	,	,	PUNCT
ejpam-6008	248	17	σ1	σ1	PROPN
ejpam-6008	248	18	,	,	PUNCT
ejpam-6008	248	19	σ2	σ2	PROPN
ejpam-6008	248	20	)	)	PUNCT
ejpam-6008	248	21	,	,	PUNCT
ejpam-6008	248	22	a	a	DET
ejpam-6008	248	23	multifunction	multifunction	NOUN
ejpam-6008	248	24	clf⊛	clf⊛	NOUN
ejpam-6008	248	25	:	:	PUNCT
ejpam-6008	248	26	(	(	PUNCT
ejpam-6008	248	27	x	x	NOUN
ejpam-6008	248	28	,	,	PUNCT
ejpam-6008	248	29	τ1	τ1	NOUN
ejpam-6008	248	30	,	,	PUNCT
ejpam-6008	248	31	τ2	τ2	NOUN
ejpam-6008	248	32	)	)	PUNCT
ejpam-6008	248	33	→	→	SYM
ejpam-6008	248	34	(	(	PUNCT
ejpam-6008	248	35	y	y	PROPN
ejpam-6008	248	36	,	,	PUNCT
ejpam-6008	248	37	σ1	σ1	PROPN
ejpam-6008	248	38	,	,	PUNCT
ejpam-6008	248	39	σ2	σ2	PROPN
ejpam-6008	248	40	)	)	PUNCT
ejpam-6008	248	41	is	be	AUX
ejpam-6008	248	42	defined	define	VERB
ejpam-6008	248	43	in	in	ADP
ejpam-6008	248	44	[	[	X
ejpam-6008	248	45	77	77	NUM
ejpam-6008	248	46	]	]	PUNCT
ejpam-6008	248	47	as	as	SCONJ
ejpam-6008	248	48	follows	follow	VERB
ejpam-6008	248	49	:	:	PUNCT
ejpam-6008	248	50	clf⊛(x	clf⊛(x	PROPN
ejpam-6008	248	51	)	)	PUNCT
ejpam-6008	248	52	=	=	PUNCT
ejpam-6008	249	1	σ1σ2	σ1σ2	X
ejpam-6008	249	2	-	-	NUM
ejpam-6008	249	3	cl(f	cl(f	NOUN
ejpam-6008	249	4	(	(	PUNCT
ejpam-6008	249	5	x	x	NOUN
ejpam-6008	249	6	)	)	PUNCT
ejpam-6008	249	7	)	)	PUNCT
ejpam-6008	249	8	for	for	ADP
ejpam-6008	249	9	each	each	DET
ejpam-6008	249	10	x	x	SYM
ejpam-6008	249	11	∈	∈	PROPN
ejpam-6008	249	12	x.	x.	NOUN
ejpam-6008	249	13	definition	definition	NOUN
ejpam-6008	249	14	7	7	NUM
ejpam-6008	249	15	.	.	PUNCT
ejpam-6008	250	1	[	[	X
ejpam-6008	250	2	77	77	NUM
ejpam-6008	250	3	]	]	X
ejpam-6008	250	4	a	a	DET
ejpam-6008	250	5	subset	subset	NOUN
ejpam-6008	250	6	a	a	PRON
ejpam-6008	250	7	of	of	ADP
ejpam-6008	250	8	a	a	DET
ejpam-6008	250	9	bitopological	bitopological	ADJ
ejpam-6008	250	10	space	space	NOUN
ejpam-6008	250	11	(	(	PUNCT
ejpam-6008	250	12	x	x	NOUN
ejpam-6008	250	13	,	,	PUNCT
ejpam-6008	250	14	τ1	τ1	NOUN
ejpam-6008	250	15	,	,	PUNCT
ejpam-6008	250	16	τ2	τ2	NOUN
ejpam-6008	250	17	)	)	PUNCT
ejpam-6008	250	18	is	be	AUX
ejpam-6008	250	19	said	say	VERB
ejpam-6008	250	20	to	to	PART
ejpam-6008	250	21	be	be	AUX
ejpam-6008	250	22	:	:	PUNCT
ejpam-6008	250	23	(	(	PUNCT
ejpam-6008	250	24	1	1	X
ejpam-6008	250	25	)	)	PUNCT
ejpam-6008	250	26	τ1τ2	τ1τ2	NOUN
ejpam-6008	250	27	-	-	NOUN
ejpam-6008	250	28	paracompact	paracompact	ADJ
ejpam-6008	250	29	if	if	SCONJ
ejpam-6008	250	30	every	every	DET
ejpam-6008	250	31	cover	cover	NOUN
ejpam-6008	250	32	of	of	ADP
ejpam-6008	250	33	a	a	PRON
ejpam-6008	250	34	by	by	ADP
ejpam-6008	250	35	τ1τ2	τ1τ2	ADJ
ejpam-6008	250	36	-	-	ADJ
ejpam-6008	250	37	open	open	ADJ
ejpam-6008	250	38	sets	set	NOUN
ejpam-6008	250	39	of	of	ADP
ejpam-6008	250	40	x	x	VERB
ejpam-6008	250	41	is	be	AUX
ejpam-6008	250	42	refined	refine	VERB
ejpam-6008	250	43	by	by	ADP
ejpam-6008	250	44	a	a	DET
ejpam-6008	250	45	cover	cover	NOUN
ejpam-6008	250	46	of	of	ADP
ejpam-6008	250	47	a	a	PRON
ejpam-6008	250	48	which	which	PRON
ejpam-6008	250	49	consists	consist	VERB
ejpam-6008	250	50	of	of	ADP
ejpam-6008	250	51	τ1τ2	τ1τ2	ADJ
ejpam-6008	250	52	-	-	ADJ
ejpam-6008	250	53	open	open	ADJ
ejpam-6008	250	54	sets	set	NOUN
ejpam-6008	250	55	of	of	ADP
ejpam-6008	250	56	x	x	PUNCT
ejpam-6008	250	57	and	and	CCONJ
ejpam-6008	250	58	is	be	AUX
ejpam-6008	250	59	τ1τ2	τ1τ2	NOUN
ejpam-6008	250	60	-	-	ADJ
ejpam-6008	250	61	locally	locally	ADV
ejpam-6008	250	62	finite	finite	NOUN
ejpam-6008	250	63	in	in	ADP
ejpam-6008	250	64	x	x	PROPN
ejpam-6008	250	65	;	;	PUNCT
ejpam-6008	250	66	n.	n.	PROPN
ejpam-6008	250	67	viriyapong	viriyapong	PROPN
ejpam-6008	250	68	,	,	PUNCT
ejpam-6008	250	69	a.	a.	PROPN
ejpam-6008	250	70	sama	sama	PROPN
ejpam-6008	250	71	-	-	PUNCT
ejpam-6008	250	72	ae	ae	PROPN
ejpam-6008	250	73	,	,	PUNCT
ejpam-6008	250	74	c.	c.	PROPN
ejpam-6008	250	75	boonpok	boonpok	PROPN
ejpam-6008	250	76	/	/	SYM
ejpam-6008	250	77	eur	eur	PROPN
ejpam-6008	250	78	.	.	PUNCT
ejpam-6008	251	1	j.	j.	PROPN
ejpam-6008	251	2	pure	pure	PROPN
ejpam-6008	251	3	appl	appl	PROPN
ejpam-6008	251	4	.	.	PROPN
ejpam-6008	251	5	math	math	PROPN
ejpam-6008	251	6	,	,	PUNCT
ejpam-6008	251	7	18	18	NUM
ejpam-6008	251	8	(	(	PUNCT
ejpam-6008	251	9	2	2	NUM
ejpam-6008	251	10	)	)	PUNCT
ejpam-6008	251	11	(	(	PUNCT
ejpam-6008	251	12	2025	2025	NUM
ejpam-6008	251	13	)	)	PUNCT
ejpam-6008	251	14	,	,	PUNCT
ejpam-6008	251	15	6008	6008	NUM
ejpam-6008	251	16	10	10	NUM
ejpam-6008	251	17	of	of	ADP
ejpam-6008	251	18	15	15	NUM
ejpam-6008	251	19	(	(	PUNCT
ejpam-6008	251	20	2	2	NUM
ejpam-6008	251	21	)	)	PUNCT
ejpam-6008	251	22	τ1τ2	τ1τ2	NOUN
ejpam-6008	251	23	-	-	NOUN
ejpam-6008	251	24	regular	regular	ADJ
ejpam-6008	251	25	if	if	SCONJ
ejpam-6008	251	26	for	for	ADP
ejpam-6008	251	27	each	each	DET
ejpam-6008	251	28	x	x	SYM
ejpam-6008	251	29	∈	∈	PROPN
ejpam-6008	251	30	a	a	PRON
ejpam-6008	251	31	and	and	CCONJ
ejpam-6008	251	32	each	each	DET
ejpam-6008	251	33	τ1τ2	τ1τ2	ADJ
ejpam-6008	251	34	-	-	ADJ
ejpam-6008	251	35	open	open	ADJ
ejpam-6008	251	36	set	set	ADJ
ejpam-6008	251	37	u	u	NOUN
ejpam-6008	251	38	of	of	ADP
ejpam-6008	251	39	x	x	PUNCT
ejpam-6008	251	40	containing	contain	VERB
ejpam-6008	251	41	x	x	PRON
ejpam-6008	251	42	,	,	PUNCT
ejpam-6008	251	43	there	there	PRON
ejpam-6008	251	44	exists	exist	VERB
ejpam-6008	251	45	a	a	DET
ejpam-6008	251	46	τ1τ2	τ1τ2	NOUN
ejpam-6008	251	47	-	-	ADJ
ejpam-6008	251	48	open	open	ADJ
ejpam-6008	251	49	set	set	NOUN
ejpam-6008	251	50	v	v	NOUN
ejpam-6008	251	51	of	of	ADP
ejpam-6008	251	52	x	x	PUNCT
ejpam-6008	251	53	such	such	ADJ
ejpam-6008	251	54	that	that	SCONJ
ejpam-6008	251	55	x	x	SYM
ejpam-6008	251	56	∈	∈	NOUN
ejpam-6008	251	57	v	v	ADP
ejpam-6008	251	58	⊆	⊆	NUM
ejpam-6008	251	59	τ1τ2	τ1τ2	NOUN
ejpam-6008	251	60	-	-	NOUN
ejpam-6008	251	61	cl(v	cl(v	X
ejpam-6008	251	62	)	)	PUNCT
ejpam-6008	251	63	⊆	⊆	NUM
ejpam-6008	251	64	u	u	NOUN
ejpam-6008	251	65	.	.	PUNCT
ejpam-6008	252	1	lemma	lemma	PROPN
ejpam-6008	252	2	7	7	NUM
ejpam-6008	252	3	.	.	PUNCT
ejpam-6008	253	1	[	[	X
ejpam-6008	253	2	77	77	X
ejpam-6008	253	3	]	]	X
ejpam-6008	253	4	if	if	SCONJ
ejpam-6008	253	5	f	f	PROPN
ejpam-6008	253	6	:	:	PUNCT
ejpam-6008	253	7	(	(	PUNCT
ejpam-6008	253	8	x	x	NOUN
ejpam-6008	253	9	,	,	PUNCT
ejpam-6008	253	10	τ1	τ1	NOUN
ejpam-6008	253	11	,	,	PUNCT
ejpam-6008	253	12	τ2	τ2	NOUN
ejpam-6008	253	13	)	)	PUNCT
ejpam-6008	253	14	→	→	SYM
ejpam-6008	253	15	(	(	PUNCT
ejpam-6008	253	16	y	y	PROPN
ejpam-6008	253	17	,	,	PUNCT
ejpam-6008	253	18	σ1	σ1	PROPN
ejpam-6008	253	19	,	,	PUNCT
ejpam-6008	253	20	σ2	σ2	PROPN
ejpam-6008	253	21	)	)	PUNCT
ejpam-6008	253	22	is	be	AUX
ejpam-6008	253	23	a	a	DET
ejpam-6008	253	24	multifunction	multifunction	NOUN
ejpam-6008	253	25	such	such	ADJ
ejpam-6008	253	26	that	that	SCONJ
ejpam-6008	253	27	f	f	PROPN
ejpam-6008	253	28	(	(	PUNCT
ejpam-6008	253	29	x	x	X
ejpam-6008	253	30	)	)	PUNCT
ejpam-6008	253	31	is	be	AUX
ejpam-6008	253	32	σ1σ2regular	σ1σ2regular	PROPN
ejpam-6008	253	33	and	and	CCONJ
ejpam-6008	253	34	σ1σ2	σ1σ2	NOUN
ejpam-6008	253	35	-	-	ADJ
ejpam-6008	253	36	paracompact	paracompact	NOUN
ejpam-6008	253	37	for	for	ADP
ejpam-6008	253	38	each	each	DET
ejpam-6008	253	39	x	x	SYM
ejpam-6008	253	40	∈	∈	PROPN
ejpam-6008	253	41	x	x	NOUN
ejpam-6008	253	42	,	,	PUNCT
ejpam-6008	253	43	then	then	ADV
ejpam-6008	253	44	clf+	clf+	PROPN
ejpam-6008	253	45	⊛	⊛	X
ejpam-6008	253	46	(	(	PUNCT
ejpam-6008	253	47	v	v	NOUN
ejpam-6008	253	48	)	)	PUNCT
ejpam-6008	253	49	=	=	PUNCT
ejpam-6008	253	50	f+(v	f+(v	NOUN
ejpam-6008	253	51	)	)	PUNCT
ejpam-6008	253	52	for	for	ADP
ejpam-6008	253	53	each	each	DET
ejpam-6008	253	54	σ1σ2	σ1σ2	VERB
ejpam-6008	253	55	-	-	ADJ
ejpam-6008	253	56	open	open	ADJ
ejpam-6008	253	57	set	set	NOUN
ejpam-6008	253	58	v	v	NOUN
ejpam-6008	253	59	of	of	ADP
ejpam-6008	253	60	y	y	PROPN
ejpam-6008	253	61	.	.	PUNCT
ejpam-6008	254	1	lemma	lemma	PROPN
ejpam-6008	254	2	8	8	NUM
ejpam-6008	254	3	.	.	PUNCT
ejpam-6008	255	1	if	if	SCONJ
ejpam-6008	255	2	f	f	PROPN
ejpam-6008	255	3	:	:	PUNCT
ejpam-6008	255	4	(	(	PUNCT
ejpam-6008	255	5	x	x	NOUN
ejpam-6008	255	6	,	,	PUNCT
ejpam-6008	255	7	τ1	τ1	NOUN
ejpam-6008	255	8	,	,	PUNCT
ejpam-6008	255	9	τ2	τ2	NOUN
ejpam-6008	255	10	)	)	PUNCT
ejpam-6008	255	11	→	→	SYM
ejpam-6008	255	12	(	(	PUNCT
ejpam-6008	255	13	y	y	PROPN
ejpam-6008	255	14	,	,	PUNCT
ejpam-6008	255	15	σ1	σ1	PROPN
ejpam-6008	255	16	,	,	PUNCT
ejpam-6008	255	17	σ2	σ2	PROPN
ejpam-6008	255	18	)	)	PUNCT
ejpam-6008	255	19	is	be	AUX
ejpam-6008	255	20	a	a	DET
ejpam-6008	255	21	multifunction	multifunction	NOUN
ejpam-6008	255	22	such	such	ADJ
ejpam-6008	255	23	that	that	SCONJ
ejpam-6008	255	24	f	f	PROPN
ejpam-6008	255	25	(	(	PUNCT
ejpam-6008	255	26	x	x	X
ejpam-6008	255	27	)	)	PUNCT
ejpam-6008	255	28	is	be	AUX
ejpam-6008	255	29	σ1σ2	σ1σ2	NOUN
ejpam-6008	255	30	-	-	ADJ
ejpam-6008	255	31	regular	regular	ADJ
ejpam-6008	255	32	and	and	CCONJ
ejpam-6008	255	33	σ1σ2	σ1σ2	NOUN
ejpam-6008	255	34	-	-	ADJ
ejpam-6008	255	35	paracompact	paracompact	NOUN
ejpam-6008	255	36	for	for	ADP
ejpam-6008	255	37	each	each	DET
ejpam-6008	255	38	x	x	SYM
ejpam-6008	255	39	∈	∈	PROPN
ejpam-6008	255	40	x	x	NOUN
ejpam-6008	255	41	,	,	PUNCT
ejpam-6008	255	42	then	then	ADV
ejpam-6008	255	43	clf−	clf−	PROPN
ejpam-6008	255	44	⊛	⊛	ADJ
ejpam-6008	255	45	(	(	PUNCT
ejpam-6008	255	46	k	k	X
ejpam-6008	255	47	)	)	PUNCT
ejpam-6008	255	48	=	=	SYM
ejpam-6008	255	49	f−(k	f−(k	PROPN
ejpam-6008	255	50	)	)	PUNCT
ejpam-6008	255	51	for	for	ADP
ejpam-6008	255	52	each	each	DET
ejpam-6008	255	53	σ1σ2	σ1σ2	NUM
ejpam-6008	255	54	-	-	PUNCT
ejpam-6008	255	55	closed	closed	ADJ
ejpam-6008	255	56	set	set	NOUN
ejpam-6008	255	57	k	k	PROPN
ejpam-6008	255	58	of	of	ADP
ejpam-6008	255	59	y	y	PROPN
ejpam-6008	255	60	.	.	PUNCT
ejpam-6008	256	1	proof	proof	NOUN
ejpam-6008	256	2	.	.	PUNCT
ejpam-6008	257	1	it	it	PRON
ejpam-6008	257	2	follows	follow	VERB
ejpam-6008	257	3	from	from	ADP
ejpam-6008	257	4	lemma	lemma	PROPN
ejpam-6008	257	5	7	7	PROPN
ejpam-6008	257	6	.	.	PUNCT
ejpam-6008	258	1	lemma	lemma	PROPN
ejpam-6008	258	2	9	9	NUM
ejpam-6008	258	3	.	.	PUNCT
ejpam-6008	259	1	[	[	X
ejpam-6008	259	2	77	77	NUM
ejpam-6008	259	3	]	]	PUNCT
ejpam-6008	259	4	for	for	ADP
ejpam-6008	259	5	a	a	DET
ejpam-6008	259	6	multifunction	multifunction	NOUN
ejpam-6008	259	7	f	f	NOUN
ejpam-6008	259	8	:	:	PUNCT
ejpam-6008	259	9	(	(	PUNCT
ejpam-6008	259	10	x	x	NOUN
ejpam-6008	259	11	,	,	PUNCT
ejpam-6008	259	12	τ1	τ1	NOUN
ejpam-6008	259	13	,	,	PUNCT
ejpam-6008	259	14	τ2	τ2	NOUN
ejpam-6008	259	15	)	)	PUNCT
ejpam-6008	259	16	→	→	SYM
ejpam-6008	259	17	(	(	PUNCT
ejpam-6008	259	18	y	y	PROPN
ejpam-6008	259	19	,	,	PUNCT
ejpam-6008	259	20	σ1	σ1	PROPN
ejpam-6008	259	21	,	,	PUNCT
ejpam-6008	259	22	σ2	σ2	NOUN
ejpam-6008	259	23	)	)	PUNCT
ejpam-6008	259	24	,	,	PUNCT
ejpam-6008	259	25	clf	clf	PROPN
ejpam-6008	259	26	−	−	PROPN
ejpam-6008	259	27	⊛	⊛	NUM
ejpam-6008	259	28	(	(	PUNCT
ejpam-6008	259	29	v	v	NOUN
ejpam-6008	259	30	)	)	PUNCT
ejpam-6008	259	31	=	=	SYM
ejpam-6008	259	32	f−(v	f−(v	ADJ
ejpam-6008	259	33	)	)	PUNCT
ejpam-6008	259	34	for	for	ADP
ejpam-6008	259	35	each	each	DET
ejpam-6008	259	36	σ1σ2	σ1σ2	VERB
ejpam-6008	259	37	-	-	ADJ
ejpam-6008	259	38	open	open	ADJ
ejpam-6008	259	39	set	set	NOUN
ejpam-6008	259	40	v	v	NOUN
ejpam-6008	259	41	of	of	ADP
ejpam-6008	259	42	y	y	PROPN
ejpam-6008	259	43	.	.	PUNCT
ejpam-6008	260	1	lemma	lemma	PROPN
ejpam-6008	260	2	10	10	NUM
ejpam-6008	260	3	.	.	PUNCT
ejpam-6008	261	1	for	for	ADP
ejpam-6008	261	2	a	a	DET
ejpam-6008	261	3	multifunction	multifunction	NOUN
ejpam-6008	261	4	f	f	NOUN
ejpam-6008	261	5	:	:	PUNCT
ejpam-6008	261	6	(	(	PUNCT
ejpam-6008	261	7	x	x	NOUN
ejpam-6008	261	8	,	,	PUNCT
ejpam-6008	261	9	τ1	τ1	NOUN
ejpam-6008	261	10	,	,	PUNCT
ejpam-6008	261	11	τ2	τ2	NOUN
ejpam-6008	261	12	)	)	PUNCT
ejpam-6008	261	13	→	→	SYM
ejpam-6008	261	14	(	(	PUNCT
ejpam-6008	261	15	y	y	PROPN
ejpam-6008	261	16	,	,	PUNCT
ejpam-6008	261	17	σ1	σ1	PROPN
ejpam-6008	261	18	,	,	PUNCT
ejpam-6008	261	19	σ2	σ2	NOUN
ejpam-6008	261	20	)	)	PUNCT
ejpam-6008	261	21	,	,	PUNCT
ejpam-6008	261	22	clf+	clf+	NOUN
ejpam-6008	261	23	⊛	⊛	X
ejpam-6008	261	24	(	(	PUNCT
ejpam-6008	261	25	k	k	X
ejpam-6008	261	26	)	)	PUNCT
ejpam-6008	261	27	=	=	SYM
ejpam-6008	261	28	f+(k	f+(k	X
ejpam-6008	261	29	)	)	PUNCT
ejpam-6008	261	30	for	for	ADP
ejpam-6008	261	31	each	each	DET
ejpam-6008	261	32	σ1σ2	σ1σ2	NUM
ejpam-6008	261	33	-	-	PUNCT
ejpam-6008	261	34	closed	closed	ADJ
ejpam-6008	261	35	set	set	NOUN
ejpam-6008	261	36	k	k	PROPN
ejpam-6008	261	37	of	of	ADP
ejpam-6008	261	38	y	y	PROPN
ejpam-6008	261	39	.	.	PUNCT
ejpam-6008	262	1	proof	proof	NOUN
ejpam-6008	262	2	.	.	PUNCT
ejpam-6008	263	1	it	it	PRON
ejpam-6008	263	2	follows	follow	VERB
ejpam-6008	263	3	from	from	ADP
ejpam-6008	263	4	lemma	lemma	PROPN
ejpam-6008	263	5	9	9	NUM
ejpam-6008	263	6	.	.	PUNCT
ejpam-6008	263	7	theorem	theorem	NOUN
ejpam-6008	263	8	12	12	NUM
ejpam-6008	263	9	.	.	PUNCT
ejpam-6008	264	1	a	a	DET
ejpam-6008	264	2	multifunction	multifunction	NOUN
ejpam-6008	264	3	f	f	NOUN
ejpam-6008	264	4	:	:	PUNCT
ejpam-6008	264	5	(	(	PUNCT
ejpam-6008	264	6	x	x	NOUN
ejpam-6008	264	7	,	,	PUNCT
ejpam-6008	264	8	τ1	τ1	NOUN
ejpam-6008	264	9	,	,	PUNCT
ejpam-6008	264	10	τ2	τ2	NOUN
ejpam-6008	264	11	)	)	PUNCT
ejpam-6008	264	12	→	→	SYM
ejpam-6008	264	13	(	(	PUNCT
ejpam-6008	264	14	y	y	PROPN
ejpam-6008	264	15	,	,	PUNCT
ejpam-6008	264	16	σ1	σ1	PROPN
ejpam-6008	264	17	,	,	PUNCT
ejpam-6008	264	18	σ2	σ2	PROPN
ejpam-6008	264	19	)	)	PUNCT
ejpam-6008	264	20	is	be	AUX
ejpam-6008	264	21	upper	upper	ADJ
ejpam-6008	264	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	264	23	,	,	PUNCT
ejpam-6008	264	24	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	264	25	if	if	SCONJ
ejpam-6008	264	26	and	and	CCONJ
ejpam-6008	264	27	only	only	ADV
ejpam-6008	264	28	if	if	SCONJ
ejpam-6008	264	29	clf⊛	clf⊛	PROPN
ejpam-6008	264	30	:	:	PUNCT
ejpam-6008	264	31	(	(	PUNCT
ejpam-6008	264	32	x	x	NOUN
ejpam-6008	264	33	,	,	PUNCT
ejpam-6008	264	34	τ1	τ1	NOUN
ejpam-6008	264	35	,	,	PUNCT
ejpam-6008	264	36	τ2	τ2	NOUN
ejpam-6008	264	37	)	)	PUNCT
ejpam-6008	264	38	→	→	SYM
ejpam-6008	264	39	(	(	PUNCT
ejpam-6008	264	40	y	y	PROPN
ejpam-6008	264	41	,	,	PUNCT
ejpam-6008	264	42	σ1	σ1	PROPN
ejpam-6008	264	43	,	,	PUNCT
ejpam-6008	264	44	σ2	σ2	PROPN
ejpam-6008	264	45	)	)	PUNCT
ejpam-6008	264	46	is	be	AUX
ejpam-6008	264	47	upper	upper	ADJ
ejpam-6008	264	48	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	264	49	,	,	PUNCT
ejpam-6008	264	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	264	51	.	.	PUNCT
ejpam-6008	265	1	proof	proof	NOUN
ejpam-6008	265	2	.	.	PUNCT
ejpam-6008	266	1	suppose	suppose	VERB
ejpam-6008	266	2	that	that	SCONJ
ejpam-6008	266	3	f	f	PROPN
ejpam-6008	266	4	is	be	AUX
ejpam-6008	266	5	upper	upper	ADJ
ejpam-6008	266	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	266	7	,	,	PUNCT
ejpam-6008	266	8	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	266	9	.	.	PUNCT
ejpam-6008	267	1	let	let	VERB
ejpam-6008	267	2	k	k	PRON
ejpam-6008	267	3	be	be	AUX
ejpam-6008	267	4	any	any	DET
ejpam-6008	267	5	σ1σ2	σ1σ2	NUM
ejpam-6008	267	6	-	-	PUNCT
ejpam-6008	267	7	closed	closed	ADJ
ejpam-6008	267	8	set	set	NOUN
ejpam-6008	267	9	of	of	ADP
ejpam-6008	267	10	y	y	PROPN
ejpam-6008	267	11	.	.	PUNCT
ejpam-6008	268	1	it	it	PRON
ejpam-6008	268	2	follows	follow	VERB
ejpam-6008	268	3	from	from	ADP
ejpam-6008	268	4	lemma	lemma	PROPN
ejpam-6008	268	5	9	9	NUM
ejpam-6008	268	6	,	,	PUNCT
ejpam-6008	268	7	lemma	lemma	PROPN
ejpam-6008	268	8	10	10	NUM
ejpam-6008	268	9	and	and	CCONJ
ejpam-6008	268	10	theorem	theorem	VERB
ejpam-6008	268	11	1	1	NUM
ejpam-6008	268	12	,	,	PUNCT
ejpam-6008	268	13	clf+	clf+	NOUN
ejpam-6008	268	14	⊛	⊛	X
ejpam-6008	268	15	(	(	PUNCT
ejpam-6008	268	16	k	k	X
ejpam-6008	268	17	)	)	PUNCT
ejpam-6008	268	18	=	=	SYM
ejpam-6008	268	19	f+(k	f+(k	X
ejpam-6008	268	20	)	)	PUNCT
ejpam-6008	268	21	is	be	AUX
ejpam-6008	268	22	τ1τ2	τ1τ2	NOUN
ejpam-6008	268	23	-	-	ADJ
ejpam-6008	268	24	open	open	ADJ
ejpam-6008	268	25	in	in	ADP
ejpam-6008	268	26	x.	x.	PROPN
ejpam-6008	268	27	thus	thus	ADV
ejpam-6008	268	28	,	,	PUNCT
ejpam-6008	268	29	clf⊛	clf⊛	PROPN
ejpam-6008	268	30	is	be	AUX
ejpam-6008	268	31	upper	upper	ADJ
ejpam-6008	268	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	268	33	,	,	PUNCT
ejpam-6008	268	34	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	268	35	.	.	PUNCT
ejpam-6008	269	1	conversely	conversely	ADV
ejpam-6008	269	2	,	,	PUNCT
ejpam-6008	269	3	suppose	suppose	VERB
ejpam-6008	269	4	that	that	SCONJ
ejpam-6008	269	5	clf⊛	clf⊛	PROPN
ejpam-6008	269	6	is	be	AUX
ejpam-6008	269	7	upper	upper	ADJ
ejpam-6008	269	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	269	9	,	,	PUNCT
ejpam-6008	269	10	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	269	11	.	.	PUNCT
ejpam-6008	270	1	let	let	VERB
ejpam-6008	270	2	k	k	X
ejpam-6008	270	3	be	be	AUX
ejpam-6008	270	4	any	any	DET
ejpam-6008	270	5	σ1σ2closed	σ1σ2closed	ADJ
ejpam-6008	270	6	set	set	NOUN
ejpam-6008	270	7	of	of	ADP
ejpam-6008	270	8	y	y	PROPN
ejpam-6008	270	9	.	.	PUNCT
ejpam-6008	271	1	by	by	ADP
ejpam-6008	271	2	lemma	lemma	PROPN
ejpam-6008	271	3	9	9	NUM
ejpam-6008	271	4	,	,	PUNCT
ejpam-6008	271	5	lemma	lemma	PROPN
ejpam-6008	271	6	10	10	NUM
ejpam-6008	271	7	and	and	CCONJ
ejpam-6008	271	8	theorem	theorem	VERB
ejpam-6008	271	9	1	1	NUM
ejpam-6008	271	10	,	,	PUNCT
ejpam-6008	271	11	f+(k	f+(k	NUM
ejpam-6008	271	12	)	)	PUNCT
ejpam-6008	271	13	=	=	PUNCT
ejpam-6008	271	14	clf+	clf+	NOUN
ejpam-6008	271	15	⊛	⊛	NUM
ejpam-6008	271	16	(	(	PUNCT
ejpam-6008	271	17	k	k	X
ejpam-6008	271	18	)	)	PUNCT
ejpam-6008	271	19	is	be	AUX
ejpam-6008	271	20	τ1τ2	τ1τ2	NOUN
ejpam-6008	271	21	-	-	ADJ
ejpam-6008	271	22	open	open	ADJ
ejpam-6008	271	23	in	in	ADP
ejpam-6008	271	24	x.	x.	PROPN
ejpam-6008	271	25	thus	thus	ADV
ejpam-6008	271	26	,	,	PUNCT
ejpam-6008	271	27	f	f	PROPN
ejpam-6008	271	28	is	be	AUX
ejpam-6008	271	29	upper	upper	ADJ
ejpam-6008	271	30	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	271	31	,	,	PUNCT
ejpam-6008	271	32	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	271	33	.	.	PUNCT
ejpam-6008	272	1	theorem	theorem	VERB
ejpam-6008	272	2	13	13	NUM
ejpam-6008	272	3	.	.	PUNCT
ejpam-6008	273	1	let	let	VERB
ejpam-6008	273	2	f	f	NOUN
ejpam-6008	273	3	:	:	PUNCT
ejpam-6008	273	4	(	(	PUNCT
ejpam-6008	273	5	x	x	NOUN
ejpam-6008	273	6	,	,	PUNCT
ejpam-6008	273	7	τ1	τ1	NOUN
ejpam-6008	273	8	,	,	PUNCT
ejpam-6008	273	9	τ2	τ2	NOUN
ejpam-6008	273	10	)	)	PUNCT
ejpam-6008	273	11	→	→	SYM
ejpam-6008	273	12	(	(	PUNCT
ejpam-6008	273	13	y	y	PROPN
ejpam-6008	273	14	,	,	PUNCT
ejpam-6008	273	15	σ1	σ1	PROPN
ejpam-6008	273	16	,	,	PUNCT
ejpam-6008	273	17	σ2	σ2	PROPN
ejpam-6008	273	18	)	)	PUNCT
ejpam-6008	273	19	be	be	VERB
ejpam-6008	273	20	a	a	DET
ejpam-6008	273	21	multifunction	multifunction	NOUN
ejpam-6008	273	22	such	such	ADJ
ejpam-6008	273	23	that	that	SCONJ
ejpam-6008	273	24	f	f	PROPN
ejpam-6008	273	25	(	(	PUNCT
ejpam-6008	273	26	x	x	X
ejpam-6008	273	27	)	)	PUNCT
ejpam-6008	273	28	is	be	AUX
ejpam-6008	273	29	σ1σ2paracompact	σ1σ2paracompact	NUM
ejpam-6008	273	30	and	and	CCONJ
ejpam-6008	273	31	σ1σ2	σ1σ2	NOUN
ejpam-6008	273	32	-	-	ADJ
ejpam-6008	273	33	regular	regular	ADJ
ejpam-6008	273	34	for	for	ADP
ejpam-6008	273	35	each	each	DET
ejpam-6008	273	36	x	x	SYM
ejpam-6008	273	37	∈	∈	PROPN
ejpam-6008	273	38	x.	x.	NOUN
ejpam-6008	273	39	then	then	ADV
ejpam-6008	273	40	,	,	PUNCT
ejpam-6008	273	41	f	f	PROPN
ejpam-6008	273	42	is	be	AUX
ejpam-6008	273	43	lower	low	ADJ
ejpam-6008	273	44	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	273	45	,	,	PUNCT
ejpam-6008	273	46	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	273	47	if	if	SCONJ
ejpam-6008	273	48	and	and	CCONJ
ejpam-6008	273	49	only	only	ADV
ejpam-6008	273	50	if	if	SCONJ
ejpam-6008	273	51	clf⊛	clf⊛	PROPN
ejpam-6008	273	52	:	:	PUNCT
ejpam-6008	273	53	(	(	PUNCT
ejpam-6008	273	54	x	x	NOUN
ejpam-6008	273	55	,	,	PUNCT
ejpam-6008	273	56	τ1	τ1	NOUN
ejpam-6008	273	57	,	,	PUNCT
ejpam-6008	273	58	τ2	τ2	NOUN
ejpam-6008	273	59	)	)	PUNCT
ejpam-6008	273	60	→	→	SYM
ejpam-6008	273	61	(	(	PUNCT
ejpam-6008	273	62	y	y	PROPN
ejpam-6008	273	63	,	,	PUNCT
ejpam-6008	273	64	σ1	σ1	PROPN
ejpam-6008	273	65	,	,	PUNCT
ejpam-6008	273	66	σ2	σ2	NOUN
ejpam-6008	273	67	)	)	PUNCT
ejpam-6008	273	68	is	be	AUX
ejpam-6008	273	69	lower	low	ADJ
ejpam-6008	273	70	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	273	71	,	,	PUNCT
ejpam-6008	273	72	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	273	73	.	.	PUNCT
ejpam-6008	274	1	proof	proof	NOUN
ejpam-6008	274	2	.	.	PUNCT
ejpam-6008	275	1	suppose	suppose	VERB
ejpam-6008	275	2	that	that	SCONJ
ejpam-6008	275	3	f	f	PROPN
ejpam-6008	275	4	is	be	AUX
ejpam-6008	275	5	lower	low	ADJ
ejpam-6008	275	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	275	7	,	,	PUNCT
ejpam-6008	275	8	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	275	9	.	.	PUNCT
ejpam-6008	276	1	let	let	VERB
ejpam-6008	276	2	k	k	PRON
ejpam-6008	276	3	be	be	AUX
ejpam-6008	276	4	any	any	DET
ejpam-6008	276	5	σ1σ2	σ1σ2	NUM
ejpam-6008	276	6	-	-	PUNCT
ejpam-6008	276	7	closed	closed	ADJ
ejpam-6008	276	8	set	set	NOUN
ejpam-6008	276	9	of	of	ADP
ejpam-6008	276	10	y	y	PROPN
ejpam-6008	276	11	.	.	PUNCT
ejpam-6008	277	1	it	it	PRON
ejpam-6008	277	2	follows	follow	VERB
ejpam-6008	277	3	from	from	ADP
ejpam-6008	277	4	lemma	lemma	PROPN
ejpam-6008	277	5	7	7	NUM
ejpam-6008	277	6	,	,	PUNCT
ejpam-6008	277	7	lemma	lemma	X
ejpam-6008	277	8	8	8	NUM
ejpam-6008	277	9	and	and	CCONJ
ejpam-6008	277	10	theorem	theorem	VERB
ejpam-6008	277	11	2	2	NUM
ejpam-6008	277	12	that	that	SCONJ
ejpam-6008	277	13	clf−	clf−	PROPN
ejpam-6008	277	14	⊛	⊛	X
ejpam-6008	277	15	(	(	PUNCT
ejpam-6008	277	16	k	k	X
ejpam-6008	277	17	)	)	PUNCT
ejpam-6008	277	18	=	=	SYM
ejpam-6008	277	19	f−(k	f−(k	PROPN
ejpam-6008	277	20	)	)	PUNCT
ejpam-6008	277	21	is	be	AUX
ejpam-6008	277	22	τ1τ2	τ1τ2	NOUN
ejpam-6008	277	23	-	-	ADJ
ejpam-6008	277	24	open	open	ADJ
ejpam-6008	277	25	in	in	ADP
ejpam-6008	277	26	x.	x.	NOUN
ejpam-6008	277	27	this	this	PRON
ejpam-6008	277	28	shows	show	VERB
ejpam-6008	277	29	that	that	SCONJ
ejpam-6008	277	30	clf⊛	clf⊛	PROPN
ejpam-6008	277	31	is	be	AUX
ejpam-6008	277	32	lower	low	ADJ
ejpam-6008	277	33	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	277	34	,	,	PUNCT
ejpam-6008	277	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	277	36	.	.	PUNCT
ejpam-6008	278	1	conversely	conversely	ADV
ejpam-6008	278	2	,	,	PUNCT
ejpam-6008	278	3	suppose	suppose	VERB
ejpam-6008	278	4	that	that	SCONJ
ejpam-6008	278	5	clf⊛	clf⊛	PROPN
ejpam-6008	278	6	is	be	AUX
ejpam-6008	278	7	lower	low	ADJ
ejpam-6008	278	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	278	9	,	,	PUNCT
ejpam-6008	278	10	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	278	11	.	.	PUNCT
ejpam-6008	279	1	let	let	VERB
ejpam-6008	279	2	k	k	X
ejpam-6008	279	3	be	be	AUX
ejpam-6008	279	4	any	any	DET
ejpam-6008	279	5	σ1σ2closed	σ1σ2closed	ADJ
ejpam-6008	279	6	set	set	NOUN
ejpam-6008	279	7	of	of	ADP
ejpam-6008	279	8	y	y	PROPN
ejpam-6008	279	9	.	.	PUNCT
ejpam-6008	280	1	by	by	ADP
ejpam-6008	280	2	lemma	lemma	PROPN
ejpam-6008	280	3	7	7	NUM
ejpam-6008	280	4	,	,	PUNCT
ejpam-6008	280	5	lemma	lemma	X
ejpam-6008	280	6	8	8	NUM
ejpam-6008	280	7	and	and	CCONJ
ejpam-6008	280	8	theorem	theorem	VERB
ejpam-6008	280	9	2	2	NUM
ejpam-6008	280	10	,	,	PUNCT
ejpam-6008	280	11	f−(k	f−(k	PROPN
ejpam-6008	280	12	)	)	PUNCT
ejpam-6008	280	13	=	=	SYM
ejpam-6008	280	14	clf−	clf−	PROPN
ejpam-6008	280	15	⊛	⊛	X
ejpam-6008	280	16	(	(	PUNCT
ejpam-6008	280	17	k	k	X
ejpam-6008	280	18	)	)	PUNCT
ejpam-6008	280	19	is	be	AUX
ejpam-6008	280	20	τ1τ2	τ1τ2	NOUN
ejpam-6008	280	21	-	-	ADJ
ejpam-6008	280	22	open	open	ADJ
ejpam-6008	280	23	in	in	ADP
ejpam-6008	280	24	x.	x.	NOUN
ejpam-6008	280	25	this	this	PRON
ejpam-6008	280	26	shows	show	VERB
ejpam-6008	280	27	that	that	SCONJ
ejpam-6008	280	28	f	f	PROPN
ejpam-6008	280	29	is	be	AUX
ejpam-6008	280	30	lower	low	ADJ
ejpam-6008	280	31	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	280	32	,	,	PUNCT
ejpam-6008	280	33	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6008	280	34	.	.	PUNCT
ejpam-6008	281	1	acknowledgements	acknowledgement	NOUN
ejpam-6008	281	2	this	this	DET
ejpam-6008	281	3	research	research	NOUN
ejpam-6008	281	4	project	project	NOUN
ejpam-6008	281	5	was	be	AUX
ejpam-6008	281	6	financially	financially	ADV
ejpam-6008	281	7	supported	support	VERB
ejpam-6008	281	8	by	by	ADP
ejpam-6008	281	9	mahasarakham	mahasarakham	PROPN
ejpam-6008	281	10	university	university	PROPN
ejpam-6008	281	11	.	.	PUNCT
ejpam-6008	282	1	n.	n.	PROPN
ejpam-6008	282	2	viriyapong	viriyapong	PROPN
ejpam-6008	282	3	,	,	PUNCT
ejpam-6008	282	4	a.	a.	PROPN
ejpam-6008	282	5	sama	sama	PROPN
ejpam-6008	282	6	-	-	PUNCT
ejpam-6008	282	7	ae	ae	PROPN
ejpam-6008	282	8	,	,	PUNCT
ejpam-6008	282	9	c.	c.	PROPN
ejpam-6008	282	10	boonpok	boonpok	PROPN
ejpam-6008	282	11	/	/	SYM
ejpam-6008	282	12	eur	eur	PROPN
ejpam-6008	282	13	.	.	PUNCT
ejpam-6008	283	1	j.	j.	PROPN
ejpam-6008	283	2	pure	pure	PROPN
ejpam-6008	283	3	appl	appl	PROPN
ejpam-6008	283	4	.	.	PROPN
ejpam-6008	283	5	math	math	PROPN
ejpam-6008	283	6	,	,	PUNCT
ejpam-6008	283	7	18	18	NUM
ejpam-6008	283	8	(	(	PUNCT
ejpam-6008	283	9	2	2	NUM
ejpam-6008	283	10	)	)	PUNCT
ejpam-6008	283	11	(	(	PUNCT
ejpam-6008	283	12	2025	2025	NUM
ejpam-6008	283	13	)	)	PUNCT
ejpam-6008	283	14	,	,	PUNCT
ejpam-6008	283	15	6008	6008	NUM
ejpam-6008	283	16	11	11	NUM
ejpam-6008	283	17	of	of	ADP
ejpam-6008	283	18	15	15	NUM
ejpam-6008	283	19	references	reference	NOUN
ejpam-6008	283	20	[	[	X
ejpam-6008	283	21	1	1	NUM
ejpam-6008	283	22	]	]	PUNCT
ejpam-6008	283	23	c.	c.	PROPN
ejpam-6008	283	24	viriyapong	viriyapong	PROPN
ejpam-6008	283	25	and	and	CCONJ
ejpam-6008	283	26	c.	c.	PROPN
ejpam-6008	283	27	boonpok	boonpok	PROPN
ejpam-6008	283	28	.	.	PUNCT
ejpam-6008	284	1	(	(	PUNCT
ejpam-6008	284	2	λ	λ	X
ejpam-6008	284	3	,	,	PUNCT
ejpam-6008	284	4	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	284	5	functions	function	NOUN
ejpam-6008	284	6	.	.	PUNCT
ejpam-6008	285	1	wseas	wseas	VERB
ejpam-6008	285	2	transactions	transaction	NOUN
ejpam-6008	285	3	on	on	ADP
ejpam-6008	285	4	mathematics	mathematic	NOUN
ejpam-6008	285	5	,	,	PUNCT
ejpam-6008	285	6	21:380–385	21:380–385	NUM
ejpam-6008	285	7	,	,	PUNCT
ejpam-6008	285	8	2022	2022	NUM
ejpam-6008	285	9	.	.	PUNCT
ejpam-6008	286	1	[	[	X
ejpam-6008	286	2	2	2	NUM
ejpam-6008	286	3	]	]	PUNCT
ejpam-6008	286	4	c.	c.	PROPN
ejpam-6008	286	5	boonpok	boonpok	PROPN
ejpam-6008	286	6	and	and	CCONJ
ejpam-6008	286	7	j.	j.	PROPN
ejpam-6008	286	8	khampakdee	khampakdee	PROPN
ejpam-6008	286	9	.	.	PUNCT
ejpam-6008	287	1	(	(	PUNCT
ejpam-6008	287	2	λ	λ	NOUN
ejpam-6008	287	3	,	,	PUNCT
ejpam-6008	287	4	sp)-open	sp)-open	ADJ
ejpam-6008	287	5	sets	set	NOUN
ejpam-6008	287	6	in	in	ADP
ejpam-6008	287	7	topological	topological	ADJ
ejpam-6008	287	8	spaces	space	NOUN
ejpam-6008	287	9	.	.	PUNCT
ejpam-6008	288	1	european	european	ADJ
ejpam-6008	288	2	journal	journal	PROPN
ejpam-6008	288	3	of	of	ADP
ejpam-6008	288	4	pure	pure	ADJ
ejpam-6008	288	5	and	and	CCONJ
ejpam-6008	288	6	applied	applied	ADJ
ejpam-6008	288	7	mathematics	mathematic	NOUN
ejpam-6008	288	8	,	,	PUNCT
ejpam-6008	288	9	15(2):572–588	15(2):572–588	NUM
ejpam-6008	288	10	,	,	PUNCT
ejpam-6008	288	11	2022	2022	NUM
ejpam-6008	288	12	.	.	PUNCT
ejpam-6008	289	1	[	[	X
ejpam-6008	289	2	3	3	X
ejpam-6008	289	3	]	]	PUNCT
ejpam-6008	289	4	t.	t.	NOUN
ejpam-6008	289	5	dungthaisong	dungthaisong	PROPN
ejpam-6008	289	6	,	,	PUNCT
ejpam-6008	289	7	c.	c.	PROPN
ejpam-6008	289	8	boonpok	boonpok	PROPN
ejpam-6008	289	9	,	,	PUNCT
ejpam-6008	289	10	and	and	CCONJ
ejpam-6008	289	11	c.	c.	PROPN
ejpam-6008	289	12	viriyapong	viriyapong	PROPN
ejpam-6008	289	13	.	.	PUNCT
ejpam-6008	290	1	generalized	generalize	VERB
ejpam-6008	290	2	closed	close	VERB
ejpam-6008	290	3	sets	set	NOUN
ejpam-6008	290	4	in	in	ADP
ejpam-6008	290	5	bigeneralized	bigeneralize	VERB
ejpam-6008	290	6	topological	topological	ADJ
ejpam-6008	290	7	spaces	space	NOUN
ejpam-6008	290	8	.	.	PUNCT
ejpam-6008	291	1	international	international	ADJ
ejpam-6008	291	2	journal	journal	PROPN
ejpam-6008	291	3	of	of	ADP
ejpam-6008	291	4	mathematical	mathematical	ADJ
ejpam-6008	291	5	analysis	analysis	NOUN
ejpam-6008	291	6	,	,	PUNCT
ejpam-6008	291	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-6008	291	8	,	,	PUNCT
ejpam-6008	291	9	2011	2011	NUM
ejpam-6008	291	10	.	.	PUNCT
ejpam-6008	292	1	[	[	X
ejpam-6008	292	2	4	4	X
ejpam-6008	292	3	]	]	PUNCT
ejpam-6008	292	4	t.	t.	PROPN
ejpam-6008	292	5	duangphui	duangphui	PROPN
ejpam-6008	292	6	,	,	PUNCT
ejpam-6008	292	7	c.	c.	PROPN
ejpam-6008	292	8	boonpok	boonpok	PROPN
ejpam-6008	292	9	,	,	PUNCT
ejpam-6008	292	10	and	and	CCONJ
ejpam-6008	292	11	c.	c.	PROPN
ejpam-6008	292	12	viriyapong	viriyapong	PROPN
ejpam-6008	292	13	.	.	PUNCT
ejpam-6008	293	1	continuous	continuous	ADJ
ejpam-6008	293	2	functions	function	NOUN
ejpam-6008	293	3	on	on	ADP
ejpam-6008	293	4	bigeneralized	bigeneralize	VERB
ejpam-6008	293	5	topological	topological	ADJ
ejpam-6008	293	6	spaces	space	NOUN
ejpam-6008	293	7	.	.	PUNCT
ejpam-6008	294	1	international	international	ADJ
ejpam-6008	294	2	journal	journal	PROPN
ejpam-6008	294	3	of	of	ADP
ejpam-6008	294	4	mathematical	mathematical	ADJ
ejpam-6008	294	5	analysis	analysis	NOUN
ejpam-6008	294	6	,	,	PUNCT
ejpam-6008	294	7	5(24):1165	5(24):1165	NUM
ejpam-6008	294	8	–	–	PUNCT
ejpam-6008	294	9	1174	1174	NUM
ejpam-6008	294	10	,	,	PUNCT
ejpam-6008	294	11	2011	2011	NUM
ejpam-6008	294	12	.	.	PUNCT
ejpam-6008	295	1	[	[	X
ejpam-6008	295	2	5	5	NUM
ejpam-6008	295	3	]	]	X
ejpam-6008	295	4	n.	n.	NOUN
ejpam-6008	295	5	srisarakham	srisarakham	PROPN
ejpam-6008	295	6	and	and	CCONJ
ejpam-6008	295	7	c.	c.	PROPN
ejpam-6008	295	8	boonpok	boonpok	PROPN
ejpam-6008	295	9	.	.	PUNCT
ejpam-6008	296	1	almost	almost	ADV
ejpam-6008	296	2	(	(	PUNCT
ejpam-6008	296	3	λ	λ	NOUN
ejpam-6008	296	4	,	,	PUNCT
ejpam-6008	296	5	p)-continuous	p)-continuous	ADJ
ejpam-6008	296	6	functions	function	NOUN
ejpam-6008	296	7	.	.	PUNCT
ejpam-6008	297	1	international	international	ADJ
ejpam-6008	297	2	journal	journal	PROPN
ejpam-6008	297	3	of	of	ADP
ejpam-6008	297	4	mathematics	mathematic	NOUN
ejpam-6008	297	5	and	and	CCONJ
ejpam-6008	297	6	computer	computer	NOUN
ejpam-6008	297	7	science	science	NOUN
ejpam-6008	297	8	,	,	PUNCT
ejpam-6008	297	9	18(2):255–259	18(2):255–259	NUM
ejpam-6008	297	10	,	,	PUNCT
ejpam-6008	297	11	2023	2023	NUM
ejpam-6008	297	12	.	.	PUNCT
ejpam-6008	298	1	[	[	X
ejpam-6008	298	2	6	6	NUM
ejpam-6008	298	3	]	]	PUNCT
ejpam-6008	298	4	m.	m.	NOUN
ejpam-6008	298	5	thongmoon	thongmoon	NOUN
ejpam-6008	298	6	and	and	CCONJ
ejpam-6008	298	7	c.	c.	PROPN
ejpam-6008	298	8	boonpok	boonpok	PROPN
ejpam-6008	298	9	.	.	PUNCT
ejpam-6008	299	1	strongly	strongly	ADV
ejpam-6008	299	2	θ(λ	θ(λ	PROPN
ejpam-6008	299	3	,	,	PUNCT
ejpam-6008	299	4	p)-continuous	p)-continuous	ADJ
ejpam-6008	299	5	functions	function	NOUN
ejpam-6008	299	6	.	.	PUNCT
ejpam-6008	300	1	international	international	ADJ
ejpam-6008	300	2	journal	journal	PROPN
ejpam-6008	300	3	of	of	ADP
ejpam-6008	300	4	mathematics	mathematic	NOUN
ejpam-6008	300	5	and	and	CCONJ
ejpam-6008	300	6	computer	computer	NOUN
ejpam-6008	300	7	science	science	NOUN
ejpam-6008	300	8	,	,	PUNCT
ejpam-6008	300	9	19(2):475–479	19(2):475–479	PROPN
ejpam-6008	300	10	,	,	PUNCT
ejpam-6008	300	11	2024	2024	NUM
ejpam-6008	300	12	.	.	PUNCT
ejpam-6008	301	1	[	[	X
ejpam-6008	301	2	7	7	X
ejpam-6008	301	3	]	]	X
ejpam-6008	301	4	c.	c.	PROPN
ejpam-6008	301	5	boonpok	boonpok	PROPN
ejpam-6008	301	6	and	and	CCONJ
ejpam-6008	301	7	j.	j.	PROPN
ejpam-6008	301	8	khampakdee	khampakdee	PROPN
ejpam-6008	301	9	.	.	PUNCT
ejpam-6008	302	1	almost	almost	ADV
ejpam-6008	302	2	strong	strong	ADJ
ejpam-6008	302	3	θ(λ	θ(λ	PROPN
ejpam-6008	302	4	,	,	PUNCT
ejpam-6008	302	5	p)-continuity	p)-continuity	NOUN
ejpam-6008	302	6	for	for	ADP
ejpam-6008	302	7	functions	function	NOUN
ejpam-6008	302	8	.	.	PUNCT
ejpam-6008	303	1	european	european	ADJ
ejpam-6008	303	2	journal	journal	PROPN
ejpam-6008	303	3	of	of	ADP
ejpam-6008	303	4	pure	pure	ADJ
ejpam-6008	303	5	and	and	CCONJ
ejpam-6008	303	6	applied	applied	ADJ
ejpam-6008	303	7	mathematics	mathematic	NOUN
ejpam-6008	303	8	,	,	PUNCT
ejpam-6008	303	9	17(1):300–309	17(1):300–309	PROPN
ejpam-6008	303	10	,	,	PUNCT
ejpam-6008	303	11	2024	2024	NUM
ejpam-6008	303	12	.	.	PUNCT
ejpam-6008	304	1	[	[	X
ejpam-6008	304	2	8	8	NUM
ejpam-6008	304	3	]	]	X
ejpam-6008	304	4	p.	p.	NOUN
ejpam-6008	304	5	pue	pue	NOUN
ejpam-6008	304	6	-	-	PUNCT
ejpam-6008	304	7	on	on	ADP
ejpam-6008	304	8	and	and	CCONJ
ejpam-6008	304	9	c.	c.	PROPN
ejpam-6008	304	10	boonpok	boonpok	PROPN
ejpam-6008	304	11	.	.	PUNCT
ejpam-6008	305	1	θ(λ	θ(λ	PROPN
ejpam-6008	305	2	,	,	PUNCT
ejpam-6008	305	3	p)-continuity	p)-continuity	NOUN
ejpam-6008	305	4	for	for	ADP
ejpam-6008	305	5	functions	function	NOUN
ejpam-6008	305	6	.	.	PUNCT
ejpam-6008	306	1	international	international	ADJ
ejpam-6008	306	2	journal	journal	NOUN
ejpam-6008	306	3	of	of	ADP
ejpam-6008	306	4	mathematics	mathematic	NOUN
ejpam-6008	306	5	and	and	CCONJ
ejpam-6008	306	6	computer	computer	NOUN
ejpam-6008	306	7	science	science	NOUN
ejpam-6008	306	8	,	,	PUNCT
ejpam-6008	306	9	19(2):491–495	19(2):491–495	NUM
ejpam-6008	306	10	,	,	PUNCT
ejpam-6008	306	11	2024	2024	NUM
ejpam-6008	306	12	.	.	PUNCT
ejpam-6008	307	1	[	[	X
ejpam-6008	307	2	9	9	NUM
ejpam-6008	307	3	]	]	PUNCT
ejpam-6008	307	4	c.	c.	NOUN
ejpam-6008	307	5	boonpok	boonpok	PROPN
ejpam-6008	307	6	and	and	CCONJ
ejpam-6008	307	7	n.	n.	PROPN
ejpam-6008	307	8	srisarakham	srisarakham	PROPN
ejpam-6008	307	9	.	.	PUNCT
ejpam-6008	308	1	weak	weak	ADJ
ejpam-6008	308	2	forms	form	NOUN
ejpam-6008	308	3	of	of	ADP
ejpam-6008	308	4	(	(	PUNCT
ejpam-6008	308	5	λ	λ	PROPN
ejpam-6008	308	6	,	,	PUNCT
ejpam-6008	308	7	b)-open	b)-open	VERB
ejpam-6008	308	8	sets	set	NOUN
ejpam-6008	308	9	and	and	CCONJ
ejpam-6008	308	10	weak	weak	ADJ
ejpam-6008	308	11	(	(	PUNCT
ejpam-6008	308	12	λ	λ	NOUN
ejpam-6008	308	13	,	,	PUNCT
ejpam-6008	308	14	b)continuity	b)continuity	NOUN
ejpam-6008	308	15	.	.	PUNCT
ejpam-6008	309	1	european	european	PROPN
ejpam-6008	309	2	journal	journal	PROPN
ejpam-6008	309	3	of	of	ADP
ejpam-6008	309	4	pure	pure	ADJ
ejpam-6008	309	5	and	and	CCONJ
ejpam-6008	309	6	applied	applied	ADJ
ejpam-6008	309	7	mathematics	mathematic	NOUN
ejpam-6008	309	8	,	,	PUNCT
ejpam-6008	309	9	16(1):29–43	16(1):29–43	NUM
ejpam-6008	309	10	,	,	PUNCT
ejpam-6008	309	11	2023	2023	NUM
ejpam-6008	309	12	.	.	PUNCT
ejpam-6008	310	1	[	[	X
ejpam-6008	310	2	10	10	NUM
ejpam-6008	310	3	]	]	X
ejpam-6008	310	4	c.	c.	PROPN
ejpam-6008	310	5	boonpok	boonpok	PROPN
ejpam-6008	310	6	.	.	PUNCT
ejpam-6008	311	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-6008	311	2	.	.	PUNCT
ejpam-6008	312	1	mathematica	mathematica	PROPN
ejpam-6008	312	2	,	,	PUNCT
ejpam-6008	312	3	65(1):31–42	65(1):31–42	NUM
ejpam-6008	312	4	,	,	PUNCT
ejpam-6008	312	5	2023	2023	NUM
ejpam-6008	312	6	.	.	PUNCT
ejpam-6008	313	1	[	[	X
ejpam-6008	313	2	11	11	NUM
ejpam-6008	313	3	]	]	PUNCT
ejpam-6008	313	4	c.	c.	PROPN
ejpam-6008	313	5	boonpok	boonpok	PROPN
ejpam-6008	313	6	.	.	PUNCT
ejpam-6008	314	1	on	on	ADP
ejpam-6008	314	2	some	some	DET
ejpam-6008	314	3	closed	closed	ADJ
ejpam-6008	314	4	sets	set	NOUN
ejpam-6008	314	5	and	and	CCONJ
ejpam-6008	314	6	low	low	ADJ
ejpam-6008	314	7	separation	separation	NOUN
ejpam-6008	314	8	axioms	axiom	NOUN
ejpam-6008	314	9	via	via	ADP
ejpam-6008	314	10	topological	topological	ADJ
ejpam-6008	314	11	ideals	ideal	NOUN
ejpam-6008	314	12	.	.	PUNCT
ejpam-6008	315	1	european	european	ADJ
ejpam-6008	315	2	journal	journal	PROPN
ejpam-6008	315	3	of	of	ADP
ejpam-6008	315	4	pure	pure	ADJ
ejpam-6008	315	5	and	and	CCONJ
ejpam-6008	315	6	applied	applied	ADJ
ejpam-6008	315	7	mathematics	mathematic	NOUN
ejpam-6008	315	8	,	,	PUNCT
ejpam-6008	315	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-6008	315	10	,	,	PUNCT
ejpam-6008	315	11	2022	2022	NUM
ejpam-6008	315	12	.	.	PUNCT
ejpam-6008	316	1	[	[	X
ejpam-6008	316	2	12	12	NUM
ejpam-6008	316	3	]	]	PUNCT
ejpam-6008	316	4	c.	c.	PROPN
ejpam-6008	316	5	boonpok	boonpok	PROPN
ejpam-6008	316	6	.	.	PUNCT
ejpam-6008	317	1	on	on	ADP
ejpam-6008	317	2	some	some	DET
ejpam-6008	317	3	spaces	space	NOUN
ejpam-6008	317	4	via	via	ADP
ejpam-6008	317	5	topological	topological	ADJ
ejpam-6008	317	6	ideals	ideal	NOUN
ejpam-6008	317	7	.	.	PUNCT
ejpam-6008	318	1	open	open	ADJ
ejpam-6008	318	2	mathematics	mathematic	NOUN
ejpam-6008	318	3	,	,	PUNCT
ejpam-6008	318	4	21:20230118	21:20230118	NUM
ejpam-6008	318	5	,	,	PUNCT
ejpam-6008	318	6	2023	2023	NUM
ejpam-6008	318	7	.	.	PUNCT
ejpam-6008	319	1	[	[	X
ejpam-6008	319	2	13	13	NUM
ejpam-6008	319	3	]	]	PUNCT
ejpam-6008	319	4	c.	c.	PROPN
ejpam-6008	319	5	boonpok	boonpok	PROPN
ejpam-6008	319	6	.	.	PUNCT
ejpam-6008	320	1	on	on	ADP
ejpam-6008	320	2	characterizations	characterization	NOUN
ejpam-6008	320	3	of	of	ADP
ejpam-6008	320	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-6008	320	5	ideal	ideal	ADJ
ejpam-6008	320	6	topological	topological	ADJ
ejpam-6008	320	7	spaces	space	NOUN
ejpam-6008	320	8	.	.	PUNCT
ejpam-6008	321	1	journal	journal	NOUN
ejpam-6008	321	2	of	of	ADP
ejpam-6008	321	3	mathematics	mathematic	NOUN
ejpam-6008	321	4	,	,	PUNCT
ejpam-6008	321	5	2020:9387601	2020:9387601	NUM
ejpam-6008	321	6	,	,	PUNCT
ejpam-6008	321	7	2020	2020	NUM
ejpam-6008	321	8	.	.	PUNCT
ejpam-6008	322	1	[	[	X
ejpam-6008	322	2	14	14	NUM
ejpam-6008	322	3	]	]	X
ejpam-6008	322	4	c.	c.	PROPN
ejpam-6008	322	5	boonpok	boonpok	PROPN
ejpam-6008	322	6	.	.	PUNCT
ejpam-6008	323	1	almost	almost	ADV
ejpam-6008	323	2	(	(	PUNCT
ejpam-6008	323	3	g	g	NOUN
ejpam-6008	323	4	,	,	PUNCT
ejpam-6008	323	5	m)-continuous	m)-continuous	ADJ
ejpam-6008	323	6	functions	function	NOUN
ejpam-6008	323	7	.	.	PUNCT
ejpam-6008	324	1	international	international	ADJ
ejpam-6008	324	2	journal	journal	PROPN
ejpam-6008	324	3	of	of	ADP
ejpam-6008	324	4	mathematical	mathematical	ADJ
ejpam-6008	324	5	analysis	analysis	NOUN
ejpam-6008	324	6	,	,	PUNCT
ejpam-6008	324	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-6008	324	8	,	,	PUNCT
ejpam-6008	324	9	2010	2010	NUM
ejpam-6008	324	10	.	.	PUNCT
ejpam-6008	325	1	[	[	X
ejpam-6008	325	2	15	15	NUM
ejpam-6008	325	3	]	]	X
ejpam-6008	325	4	c.	c.	PROPN
ejpam-6008	325	5	boonpok	boonpok	PROPN
ejpam-6008	325	6	.	.	PUNCT
ejpam-6008	326	1	m	m	VERB
ejpam-6008	326	2	-continuous	-continuous	ADJ
ejpam-6008	326	3	functions	function	NOUN
ejpam-6008	326	4	in	in	ADP
ejpam-6008	326	5	biminimal	biminimal	NOUN
ejpam-6008	326	6	structure	structure	NOUN
ejpam-6008	326	7	spaces	space	NOUN
ejpam-6008	326	8	.	.	PUNCT
ejpam-6008	327	1	far	far	PROPN
ejpam-6008	327	2	east	east	PROPN
ejpam-6008	327	3	journal	journal	PROPN
ejpam-6008	327	4	of	of	ADP
ejpam-6008	327	5	mathematical	mathematical	ADJ
ejpam-6008	327	6	sciences	science	NOUN
ejpam-6008	327	7	,	,	PUNCT
ejpam-6008	327	8	43(1):41–58	43(1):41–58	NUM
ejpam-6008	327	9	,	,	PUNCT
ejpam-6008	327	10	2010	2010	NUM
ejpam-6008	327	11	.	.	PUNCT
ejpam-6008	328	1	[	[	X
ejpam-6008	328	2	16	16	NUM
ejpam-6008	328	3	]	]	X
ejpam-6008	328	4	c.	c.	PROPN
ejpam-6008	328	5	boonpok	boonpok	PROPN
ejpam-6008	328	6	and	and	CCONJ
ejpam-6008	328	7	n.	n.	PROPN
ejpam-6008	328	8	srisarakham	srisarakham	PROPN
ejpam-6008	328	9	.	.	PUNCT
ejpam-6008	329	1	(	(	PUNCT
ejpam-6008	329	2	τ1	τ1	NOUN
ejpam-6008	329	3	,	,	PUNCT
ejpam-6008	329	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	329	5	for	for	ADP
ejpam-6008	329	6	functions	function	NOUN
ejpam-6008	329	7	.	.	PUNCT
ejpam-6008	330	1	asia	asia	PROPN
ejpam-6008	330	2	pacific	pacific	PROPN
ejpam-6008	330	3	journal	journal	PROPN
ejpam-6008	330	4	of	of	ADP
ejpam-6008	330	5	mathematics	mathematic	NOUN
ejpam-6008	330	6	,	,	PUNCT
ejpam-6008	330	7	11:21	11:21	NUM
ejpam-6008	330	8	,	,	PUNCT
ejpam-6008	330	9	2024	2024	NUM
ejpam-6008	330	10	.	.	PUNCT
ejpam-6008	331	1	[	[	X
ejpam-6008	331	2	17	17	NUM
ejpam-6008	331	3	]	]	X
ejpam-6008	331	4	c.	c.	PROPN
ejpam-6008	331	5	boonpok	boonpok	PROPN
ejpam-6008	331	6	and	and	CCONJ
ejpam-6008	331	7	p.	p.	NOUN
ejpam-6008	331	8	pue	pue	NOUN
ejpam-6008	331	9	-	-	PUNCT
ejpam-6008	331	10	on	on	ADP
ejpam-6008	331	11	.	.	PUNCT
ejpam-6008	332	1	characterizations	characterization	NOUN
ejpam-6008	332	2	of	of	ADP
ejpam-6008	332	3	almost	almost	ADV
ejpam-6008	332	4	(	(	PUNCT
ejpam-6008	332	5	τ1	τ1	NOUN
ejpam-6008	332	6	,	,	PUNCT
ejpam-6008	332	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	332	8	functions	function	NOUN
ejpam-6008	332	9	.	.	PUNCT
ejpam-6008	333	1	international	international	ADJ
ejpam-6008	333	2	journal	journal	NOUN
ejpam-6008	333	3	of	of	ADP
ejpam-6008	333	4	analysis	analysis	NOUN
ejpam-6008	333	5	and	and	CCONJ
ejpam-6008	333	6	applications	application	NOUN
ejpam-6008	333	7	,	,	PUNCT
ejpam-6008	333	8	22:33	22:33	NUM
ejpam-6008	333	9	,	,	PUNCT
ejpam-6008	333	10	2024	2024	NUM
ejpam-6008	333	11	.	.	PUNCT
ejpam-6008	334	1	[	[	X
ejpam-6008	334	2	18	18	NUM
ejpam-6008	334	3	]	]	PUNCT
ejpam-6008	334	4	c.	c.	PROPN
ejpam-6008	334	5	boonpok	boonpok	PROPN
ejpam-6008	334	6	and	and	CCONJ
ejpam-6008	334	7	c.	c.	PROPN
ejpam-6008	334	8	klanarong	klanarong	PROPN
ejpam-6008	334	9	.	.	PUNCT
ejpam-6008	335	1	on	on	ADP
ejpam-6008	335	2	weakly	weakly	ADJ
ejpam-6008	335	3	(	(	PUNCT
ejpam-6008	335	4	τ1	τ1	NOUN
ejpam-6008	335	5	,	,	PUNCT
ejpam-6008	335	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	335	7	functions	function	NOUN
ejpam-6008	335	8	.	.	PUNCT
ejpam-6008	336	1	european	european	ADJ
ejpam-6008	336	2	journal	journal	PROPN
ejpam-6008	336	3	of	of	ADP
ejpam-6008	336	4	pure	pure	ADJ
ejpam-6008	336	5	and	and	CCONJ
ejpam-6008	336	6	applied	applied	ADJ
ejpam-6008	336	7	mathematics	mathematic	NOUN
ejpam-6008	336	8	,	,	PUNCT
ejpam-6008	336	9	17(1):416–425	17(1):416–425	NUM
ejpam-6008	336	10	,	,	PUNCT
ejpam-6008	336	11	2024	2024	NUM
ejpam-6008	336	12	.	.	PUNCT
ejpam-6008	337	1	[	[	X
ejpam-6008	337	2	19	19	NUM
ejpam-6008	337	3	]	]	X
ejpam-6008	337	4	p.	p.	NOUN
ejpam-6008	337	5	pue	pue	NOUN
ejpam-6008	337	6	-	-	PUNCT
ejpam-6008	337	7	on	on	ADP
ejpam-6008	337	8	,	,	PUNCT
ejpam-6008	337	9	s.	s.	PROPN
ejpam-6008	337	10	sompong	sompong	PROPN
ejpam-6008	337	11	,	,	PUNCT
ejpam-6008	337	12	and	and	CCONJ
ejpam-6008	337	13	c.	c.	PROPN
ejpam-6008	337	14	boonpok	boonpok	PROPN
ejpam-6008	337	15	.	.	PUNCT
ejpam-6008	338	1	slightly	slightly	ADV
ejpam-6008	338	2	(	(	PUNCT
ejpam-6008	338	3	τ1	τ1	NOUN
ejpam-6008	338	4	,	,	PUNCT
ejpam-6008	338	5	τ2)s	τ2)s	ADJ
ejpam-6008	338	6	-	-	PUNCT
ejpam-6008	338	7	continuous	continuous	ADJ
ejpam-6008	338	8	functions	function	NOUN
ejpam-6008	338	9	.	.	PUNCT
ejpam-6008	339	1	international	international	ADJ
ejpam-6008	339	2	journal	journal	NOUN
ejpam-6008	339	3	of	of	ADP
ejpam-6008	339	4	mathematics	mathematic	NOUN
ejpam-6008	339	5	and	and	CCONJ
ejpam-6008	339	6	computer	computer	NOUN
ejpam-6008	339	7	science	science	NOUN
ejpam-6008	339	8	,	,	PUNCT
ejpam-6008	339	9	20(1):217–221	20(1):217–221	PROPN
ejpam-6008	339	10	,	,	PUNCT
ejpam-6008	339	11	2025	2025	NUM
ejpam-6008	339	12	.	.	PUNCT
ejpam-6008	340	1	[	[	X
ejpam-6008	340	2	20	20	NUM
ejpam-6008	340	3	]	]	PUNCT
ejpam-6008	340	4	b.	b.	PROPN
ejpam-6008	340	5	kong	kong	PROPN
ejpam-6008	340	6	-	-	PUNCT
ejpam-6008	340	7	ied	ied	PROPN
ejpam-6008	340	8	,	,	PUNCT
ejpam-6008	340	9	s.	s.	PROPN
ejpam-6008	340	10	sompong	sompong	PROPN
ejpam-6008	340	11	,	,	PUNCT
ejpam-6008	340	12	and	and	CCONJ
ejpam-6008	340	13	c.	c.	PROPN
ejpam-6008	340	14	boonpok	boonpok	PROPN
ejpam-6008	340	15	.	.	PUNCT
ejpam-6008	341	1	almost	almost	ADV
ejpam-6008	341	2	quasi	quasi	X
ejpam-6008	341	3	(	(	PUNCT
ejpam-6008	341	4	τ1	τ1	NOUN
ejpam-6008	341	5	,	,	PUNCT
ejpam-6008	341	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	341	7	functions	function	NOUN
ejpam-6008	341	8	.	.	PUNCT
ejpam-6008	342	1	asia	asia	PROPN
ejpam-6008	342	2	pacific	pacific	PROPN
ejpam-6008	342	3	journal	journal	PROPN
ejpam-6008	342	4	of	of	ADP
ejpam-6008	342	5	mathematics	mathematic	NOUN
ejpam-6008	342	6	,	,	PUNCT
ejpam-6008	342	7	11:64	11:64	NUM
ejpam-6008	342	8	,	,	PUNCT
ejpam-6008	342	9	2024	2024	NUM
ejpam-6008	342	10	.	.	PUNCT
ejpam-6008	343	1	n.	n.	PROPN
ejpam-6008	343	2	viriyapong	viriyapong	PROPN
ejpam-6008	343	3	,	,	PUNCT
ejpam-6008	343	4	a.	a.	PROPN
ejpam-6008	343	5	sama	sama	PROPN
ejpam-6008	343	6	-	-	PUNCT
ejpam-6008	343	7	ae	ae	PROPN
ejpam-6008	343	8	,	,	PUNCT
ejpam-6008	343	9	c.	c.	PROPN
ejpam-6008	343	10	boonpok	boonpok	PROPN
ejpam-6008	343	11	/	/	SYM
ejpam-6008	343	12	eur	eur	PROPN
ejpam-6008	343	13	.	.	PUNCT
ejpam-6008	344	1	j.	j.	PROPN
ejpam-6008	344	2	pure	pure	PROPN
ejpam-6008	344	3	appl	appl	PROPN
ejpam-6008	344	4	.	.	PROPN
ejpam-6008	344	5	math	math	PROPN
ejpam-6008	344	6	,	,	PUNCT
ejpam-6008	344	7	18	18	NUM
ejpam-6008	344	8	(	(	PUNCT
ejpam-6008	344	9	2	2	NUM
ejpam-6008	344	10	)	)	PUNCT
ejpam-6008	344	11	(	(	PUNCT
ejpam-6008	344	12	2025	2025	NUM
ejpam-6008	344	13	)	)	PUNCT
ejpam-6008	344	14	,	,	PUNCT
ejpam-6008	344	15	6008	6008	NUM
ejpam-6008	344	16	12	12	NUM
ejpam-6008	344	17	of	of	ADP
ejpam-6008	344	18	15	15	NUM
ejpam-6008	344	19	[	[	SYM
ejpam-6008	344	20	21	21	NUM
ejpam-6008	344	21	]	]	PUNCT
ejpam-6008	344	22	m.	m.	NOUN
ejpam-6008	344	23	chiangpradit	chiangpradit	NOUN
ejpam-6008	344	24	,	,	PUNCT
ejpam-6008	344	25	s.	s.	PROPN
ejpam-6008	344	26	sompong	sompong	PROPN
ejpam-6008	344	27	,	,	PUNCT
ejpam-6008	344	28	and	and	CCONJ
ejpam-6008	344	29	c.	c.	PROPN
ejpam-6008	344	30	boonpok	boonpok	PROPN
ejpam-6008	344	31	.	.	PUNCT
ejpam-6008	345	1	weakly	weakly	ADJ
ejpam-6008	345	2	quasi	quasi	NOUN
ejpam-6008	345	3	(	(	PUNCT
ejpam-6008	345	4	τ1	τ1	PROPN
ejpam-6008	345	5	,	,	PUNCT
ejpam-6008	345	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	345	7	functions	function	NOUN
ejpam-6008	345	8	.	.	PUNCT
ejpam-6008	346	1	international	international	ADJ
ejpam-6008	346	2	journal	journal	NOUN
ejpam-6008	346	3	of	of	ADP
ejpam-6008	346	4	analysis	analysis	NOUN
ejpam-6008	346	5	and	and	CCONJ
ejpam-6008	346	6	applications	application	NOUN
ejpam-6008	346	7	,	,	PUNCT
ejpam-6008	346	8	22:125	22:125	NUM
ejpam-6008	346	9	,	,	PUNCT
ejpam-6008	346	10	2024	2024	NUM
ejpam-6008	346	11	.	.	PUNCT
ejpam-6008	347	1	[	[	X
ejpam-6008	347	2	22	22	NUM
ejpam-6008	347	3	]	]	PUNCT
ejpam-6008	347	4	m.	m.	NOUN
ejpam-6008	347	5	thongmoon	thongmoon	NOUN
ejpam-6008	347	6	,	,	PUNCT
ejpam-6008	347	7	s.	s.	PROPN
ejpam-6008	347	8	sompong	sompong	PROPN
ejpam-6008	347	9	,	,	PUNCT
ejpam-6008	347	10	and	and	CCONJ
ejpam-6008	347	11	c.	c.	PROPN
ejpam-6008	347	12	boonpok	boonpok	PROPN
ejpam-6008	347	13	.	.	PUNCT
ejpam-6008	348	1	rarely	rarely	ADV
ejpam-6008	348	2	(	(	PUNCT
ejpam-6008	348	3	τ1	τ1	NOUN
ejpam-6008	348	4	,	,	PUNCT
ejpam-6008	348	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	348	6	functions	function	NOUN
ejpam-6008	348	7	.	.	PUNCT
ejpam-6008	349	1	international	international	ADJ
ejpam-6008	349	2	journal	journal	NOUN
ejpam-6008	349	3	of	of	ADP
ejpam-6008	349	4	mathematics	mathematic	NOUN
ejpam-6008	349	5	and	and	CCONJ
ejpam-6008	349	6	computer	computer	NOUN
ejpam-6008	349	7	science	science	NOUN
ejpam-6008	349	8	,	,	PUNCT
ejpam-6008	349	9	20(1):423–427	20(1):423–427	NUM
ejpam-6008	349	10	,	,	PUNCT
ejpam-6008	349	11	2025	2025	NUM
ejpam-6008	349	12	.	.	PUNCT
ejpam-6008	350	1	[	[	X
ejpam-6008	350	2	23	23	NUM
ejpam-6008	350	3	]	]	X
ejpam-6008	350	4	n.	n.	PROPN
ejpam-6008	350	5	srisarakham	srisarakham	PROPN
ejpam-6008	350	6	,	,	PUNCT
ejpam-6008	350	7	a.	a.	PROPN
ejpam-6008	350	8	sama	sama	PROPN
ejpam-6008	350	9	-	-	PUNCT
ejpam-6008	350	10	ae	ae	PROPN
ejpam-6008	350	11	,	,	PUNCT
ejpam-6008	350	12	and	and	CCONJ
ejpam-6008	350	13	c.	c.	PROPN
ejpam-6008	350	14	boonpok	boonpok	PROPN
ejpam-6008	350	15	.	.	PUNCT
ejpam-6008	351	1	characterizations	characterization	NOUN
ejpam-6008	351	2	of	of	ADP
ejpam-6008	351	3	faintly	faintly	ADV
ejpam-6008	351	4	(	(	PUNCT
ejpam-6008	351	5	τ1	τ1	PROPN
ejpam-6008	351	6	,	,	PUNCT
ejpam-6008	351	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	351	8	functions	function	NOUN
ejpam-6008	351	9	.	.	PUNCT
ejpam-6008	352	1	european	european	ADJ
ejpam-6008	352	2	journal	journal	PROPN
ejpam-6008	352	3	of	of	ADP
ejpam-6008	352	4	pure	pure	ADJ
ejpam-6008	352	5	and	and	CCONJ
ejpam-6008	352	6	applied	applied	ADJ
ejpam-6008	352	7	mathematics	mathematic	NOUN
ejpam-6008	352	8	,	,	PUNCT
ejpam-6008	352	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-6008	352	10	,	,	PUNCT
ejpam-6008	352	11	2024	2024	NUM
ejpam-6008	352	12	.	.	PUNCT
ejpam-6008	353	1	[	[	X
ejpam-6008	353	2	24	24	NUM
ejpam-6008	353	3	]	]	PUNCT
ejpam-6008	353	4	c.	c.	NOUN
ejpam-6008	353	5	prachanpol	prachanpol	NOUN
ejpam-6008	353	6	,	,	PUNCT
ejpam-6008	353	7	c.	c.	PROPN
ejpam-6008	353	8	boonpok	boonpok	PROPN
ejpam-6008	353	9	,	,	PUNCT
ejpam-6008	353	10	and	and	CCONJ
ejpam-6008	353	11	c.	c.	PROPN
ejpam-6008	353	12	viriyapong	viriyapong	PROPN
ejpam-6008	353	13	.	.	PUNCT
ejpam-6008	354	1	δ(τ1	δ(τ1	PROPN
ejpam-6008	354	2	,	,	PUNCT
ejpam-6008	354	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	354	4	functions	function	NOUN
ejpam-6008	354	5	.	.	PUNCT
ejpam-6008	355	1	european	european	ADJ
ejpam-6008	355	2	journal	journal	PROPN
ejpam-6008	355	3	of	of	ADP
ejpam-6008	355	4	pure	pure	ADJ
ejpam-6008	355	5	and	and	CCONJ
ejpam-6008	355	6	applied	applied	ADJ
ejpam-6008	355	7	mathematics	mathematic	NOUN
ejpam-6008	355	8	,	,	PUNCT
ejpam-6008	355	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-6008	355	10	,	,	PUNCT
ejpam-6008	355	11	2024	2024	NUM
ejpam-6008	355	12	.	.	PUNCT
ejpam-6008	356	1	[	[	X
ejpam-6008	356	2	25	25	NUM
ejpam-6008	356	3	]	]	X
ejpam-6008	356	4	n.	n.	NOUN
ejpam-6008	356	5	srisarakham	srisarakham	PROPN
ejpam-6008	356	6	,	,	PUNCT
ejpam-6008	356	7	s.	s.	PROPN
ejpam-6008	356	8	sompong	sompong	PROPN
ejpam-6008	356	9	,	,	PUNCT
ejpam-6008	356	10	and	and	CCONJ
ejpam-6008	356	11	c.	c.	PROPN
ejpam-6008	356	12	boonpok	boonpok	PROPN
ejpam-6008	356	13	.	.	PUNCT
ejpam-6008	357	1	quasi	quasi	PROPN
ejpam-6008	357	2	θ(τ1	θ(τ1	PROPN
ejpam-6008	357	3	,	,	PUNCT
ejpam-6008	357	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	357	5	functions	function	NOUN
ejpam-6008	357	6	.	.	PUNCT
ejpam-6008	358	1	european	european	ADJ
ejpam-6008	358	2	journal	journal	PROPN
ejpam-6008	358	3	of	of	ADP
ejpam-6008	358	4	pure	pure	ADJ
ejpam-6008	358	5	and	and	CCONJ
ejpam-6008	358	6	applied	applied	ADJ
ejpam-6008	358	7	mathematics	mathematic	NOUN
ejpam-6008	358	8	,	,	PUNCT
ejpam-6008	358	9	18(1):5722	18(1):5722	NUM
ejpam-6008	358	10	,	,	PUNCT
ejpam-6008	358	11	2025	2025	NUM
ejpam-6008	358	12	.	.	PUNCT
ejpam-6008	359	1	[	[	X
ejpam-6008	359	2	26	26	NUM
ejpam-6008	359	3	]	]	X
ejpam-6008	359	4	j.	j.	PROPN
ejpam-6008	359	5	khampakdee	khampakdee	PROPN
ejpam-6008	359	6	,	,	PUNCT
ejpam-6008	359	7	s.	s.	PROPN
ejpam-6008	359	8	sompong	sompong	PROPN
ejpam-6008	359	9	,	,	PUNCT
ejpam-6008	359	10	and	and	CCONJ
ejpam-6008	359	11	c.	c.	PROPN
ejpam-6008	359	12	boonpok	boonpok	PROPN
ejpam-6008	359	13	.	.	PUNCT
ejpam-6008	360	1	almost	almost	ADV
ejpam-6008	360	2	weakly	weakly	ADJ
ejpam-6008	360	3	(	(	PUNCT
ejpam-6008	360	4	τ1	τ1	NOUN
ejpam-6008	360	5	,	,	PUNCT
ejpam-6008	360	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	360	7	functions	function	NOUN
ejpam-6008	360	8	.	.	PUNCT
ejpam-6008	361	1	european	european	ADJ
ejpam-6008	361	2	journal	journal	PROPN
ejpam-6008	361	3	of	of	ADP
ejpam-6008	361	4	pure	pure	ADJ
ejpam-6008	361	5	and	and	CCONJ
ejpam-6008	361	6	applied	applied	ADJ
ejpam-6008	361	7	mathematics	mathematic	NOUN
ejpam-6008	361	8	,	,	PUNCT
ejpam-6008	361	9	18(1):5721	18(1):5721	NUM
ejpam-6008	361	10	,	,	PUNCT
ejpam-6008	361	11	2025	2025	NUM
ejpam-6008	361	12	.	.	PUNCT
ejpam-6008	362	1	[	[	X
ejpam-6008	362	2	27	27	NUM
ejpam-6008	362	3	]	]	X
ejpam-6008	362	4	b.	b.	PROPN
ejpam-6008	362	5	kong	kong	PROPN
ejpam-6008	362	6	-	-	PUNCT
ejpam-6008	362	7	ied	ied	PROPN
ejpam-6008	362	8	,	,	PUNCT
ejpam-6008	362	9	a.	a.	PROPN
ejpam-6008	362	10	sama	sama	PROPN
ejpam-6008	362	11	-	-	PUNCT
ejpam-6008	362	12	ae	ae	PROPN
ejpam-6008	362	13	,	,	PUNCT
ejpam-6008	362	14	and	and	CCONJ
ejpam-6008	362	15	c.	c.	PROPN
ejpam-6008	362	16	boonpok	boonpok	PROPN
ejpam-6008	362	17	.	.	PUNCT
ejpam-6008	363	1	almost	almost	ADV
ejpam-6008	363	2	nearly	nearly	ADV
ejpam-6008	363	3	(	(	PUNCT
ejpam-6008	363	4	τ1	τ1	NOUN
ejpam-6008	363	5	,	,	PUNCT
ejpam-6008	363	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	363	7	functions	function	NOUN
ejpam-6008	363	8	.	.	PUNCT
ejpam-6008	364	1	international	international	ADJ
ejpam-6008	364	2	journal	journal	NOUN
ejpam-6008	364	3	of	of	ADP
ejpam-6008	364	4	analysis	analysis	NOUN
ejpam-6008	364	5	and	and	CCONJ
ejpam-6008	364	6	applications	application	NOUN
ejpam-6008	364	7	,	,	PUNCT
ejpam-6008	364	8	23:14	23:14	NUM
ejpam-6008	364	9	,	,	PUNCT
ejpam-6008	364	10	2025	2025	NUM
ejpam-6008	364	11	.	.	PUNCT
ejpam-6008	365	1	[	[	X
ejpam-6008	365	2	28	28	NUM
ejpam-6008	365	3	]	]	X
ejpam-6008	365	4	j.	j.	PROPN
ejpam-6008	365	5	dontchev	dontchev	PROPN
ejpam-6008	365	6	.	.	PUNCT
ejpam-6008	366	1	contra	contra	ADJ
ejpam-6008	366	2	-	-	ADJ
ejpam-6008	366	3	continuous	continuous	ADJ
ejpam-6008	366	4	functions	function	NOUN
ejpam-6008	366	5	and	and	CCONJ
ejpam-6008	366	6	strongly	strongly	ADV
ejpam-6008	366	7	s	s	NOUN
ejpam-6008	366	8	-	-	PUNCT
ejpam-6008	366	9	closed	closed	ADJ
ejpam-6008	366	10	spaces	space	NOUN
ejpam-6008	366	11	.	.	PUNCT
ejpam-6008	367	1	international	international	ADJ
ejpam-6008	367	2	journal	journal	PROPN
ejpam-6008	367	3	of	of	ADP
ejpam-6008	367	4	mathematics	mathematics	PROPN
ejpam-6008	367	5	and	and	CCONJ
ejpam-6008	367	6	mathematical	mathematical	ADJ
ejpam-6008	367	7	sciences	science	NOUN
ejpam-6008	367	8	,	,	PUNCT
ejpam-6008	367	9	19:303–310	19:303–310	PROPN
ejpam-6008	367	10	,	,	PUNCT
ejpam-6008	367	11	1966	1966	NUM
ejpam-6008	367	12	.	.	PUNCT
ejpam-6008	368	1	[	[	X
ejpam-6008	368	2	29	29	NUM
ejpam-6008	368	3	]	]	X
ejpam-6008	368	4	j.	j.	PROPN
ejpam-6008	368	5	dontchev	dontchev	PROPN
ejpam-6008	368	6	and	and	CCONJ
ejpam-6008	368	7	t.	t.	PROPN
ejpam-6008	368	8	noiri	noiri	PROPN
ejpam-6008	368	9	.	.	PUNCT
ejpam-6008	369	1	contra	contra	ADJ
ejpam-6008	369	2	-	-	ADJ
ejpam-6008	369	3	semicontinuous	semicontinuous	ADJ
ejpam-6008	369	4	functions	function	NOUN
ejpam-6008	369	5	.	.	PUNCT
ejpam-6008	370	1	mathematica	mathematica	PROPN
ejpam-6008	370	2	pannonica	pannonica	PROPN
ejpam-6008	370	3	,	,	PUNCT
ejpam-6008	370	4	10:159–168	10:159–168	NOUN
ejpam-6008	370	5	,	,	PUNCT
ejpam-6008	370	6	1999	1999	NUM
ejpam-6008	370	7	.	.	PUNCT
ejpam-6008	371	1	[	[	X
ejpam-6008	371	2	30	30	NUM
ejpam-6008	371	3	]	]	X
ejpam-6008	371	4	s.	s.	PROPN
ejpam-6008	371	5	jafari	jafari	PROPN
ejpam-6008	371	6	and	and	CCONJ
ejpam-6008	371	7	t.	t.	PROPN
ejpam-6008	371	8	noiri	noiri	PROPN
ejpam-6008	371	9	.	.	PUNCT
ejpam-6008	372	1	on	on	ADP
ejpam-6008	372	2	contra	contra	ADJ
ejpam-6008	372	3	-	-	ADJ
ejpam-6008	372	4	precontinuous	precontinuous	ADJ
ejpam-6008	372	5	functions	function	NOUN
ejpam-6008	372	6	.	.	PUNCT
ejpam-6008	373	1	bulletin	bulletin	NOUN
ejpam-6008	373	2	of	of	ADP
ejpam-6008	373	3	the	the	DET
ejpam-6008	373	4	malaysian	malaysian	PROPN
ejpam-6008	373	5	mathematical	mathematical	PROPN
ejpam-6008	373	6	sciences	sciences	PROPN
ejpam-6008	373	7	society	society	NOUN
ejpam-6008	373	8	,	,	PUNCT
ejpam-6008	373	9	25:115–128	25:115–128	PROPN
ejpam-6008	373	10	,	,	PUNCT
ejpam-6008	373	11	2002	2002	NUM
ejpam-6008	373	12	.	.	PUNCT
ejpam-6008	374	1	[	[	X
ejpam-6008	374	2	31	31	NUM
ejpam-6008	374	3	]	]	PUNCT
ejpam-6008	374	4	e.	e.	PROPN
ejpam-6008	374	5	ekici	ekici	PROPN
ejpam-6008	374	6	.	.	PUNCT
ejpam-6008	375	1	almost	almost	ADV
ejpam-6008	375	2	contra	contra	ADJ
ejpam-6008	375	3	-	-	ADJ
ejpam-6008	375	4	precontinuous	precontinuous	ADJ
ejpam-6008	375	5	functions	function	NOUN
ejpam-6008	375	6	.	.	PUNCT
ejpam-6008	376	1	bulletin	bulletin	NOUN
ejpam-6008	376	2	of	of	ADP
ejpam-6008	376	3	the	the	DET
ejpam-6008	376	4	malaysian	malaysian	PROPN
ejpam-6008	376	5	mathematical	mathematical	PROPN
ejpam-6008	376	6	sciences	sciences	PROPN
ejpam-6008	376	7	society	society	NOUN
ejpam-6008	376	8	,	,	PUNCT
ejpam-6008	376	9	27:53–65	27:53–65	NUM
ejpam-6008	376	10	,	,	PUNCT
ejpam-6008	376	11	2004	2004	NUM
ejpam-6008	376	12	.	.	PUNCT
ejpam-6008	377	1	[	[	X
ejpam-6008	377	2	32	32	NUM
ejpam-6008	377	3	]	]	PUNCT
ejpam-6008	377	4	j.	j.	PROPN
ejpam-6008	377	5	dontchev	dontchev	PROPN
ejpam-6008	377	6	,	,	PUNCT
ejpam-6008	377	7	m.	m.	NOUN
ejpam-6008	377	8	ganster	ganster	NOUN
ejpam-6008	377	9	,	,	PUNCT
ejpam-6008	377	10	and	and	CCONJ
ejpam-6008	377	11	i.	i.	PROPN
ejpam-6008	377	12	reilly	reilly	PROPN
ejpam-6008	377	13	.	.	PUNCT
ejpam-6008	378	1	more	more	ADV
ejpam-6008	378	2	on	on	ADP
ejpam-6008	378	3	almost	almost	ADV
ejpam-6008	378	4	s	s	NOUN
ejpam-6008	378	5	-	-	NOUN
ejpam-6008	378	6	continuity	continuity	NOUN
ejpam-6008	378	7	.	.	PUNCT
ejpam-6008	379	1	indian	indian	ADJ
ejpam-6008	379	2	journal	journal	PROPN
ejpam-6008	379	3	of	of	ADP
ejpam-6008	379	4	mathematics	mathematics	PROPN
ejpam-6008	379	5	,	,	PUNCT
ejpam-6008	379	6	41:139–146	41:139–146	PROPN
ejpam-6008	379	7	,	,	PUNCT
ejpam-6008	379	8	1999	1999	NUM
ejpam-6008	379	9	.	.	PUNCT
ejpam-6008	380	1	[	[	X
ejpam-6008	380	2	33	33	NUM
ejpam-6008	380	3	]	]	PUNCT
ejpam-6008	380	4	t.	t.	PROPN
ejpam-6008	380	5	noiri	noiri	PROPN
ejpam-6008	380	6	,	,	PUNCT
ejpam-6008	380	7	b.	b.	PROPN
ejpam-6008	380	8	ahmad	ahmad	PROPN
ejpam-6008	380	9	,	,	PUNCT
ejpam-6008	380	10	and	and	CCONJ
ejpam-6008	380	11	m.	m.	PROPN
ejpam-6008	380	12	khan	khan	PROPN
ejpam-6008	380	13	.	.	PUNCT
ejpam-6008	381	1	almost	almost	ADV
ejpam-6008	381	2	s	s	NOUN
ejpam-6008	381	3	-	-	PUNCT
ejpam-6008	381	4	continuous	continuous	ADJ
ejpam-6008	381	5	functions	function	NOUN
ejpam-6008	381	6	.	.	PUNCT
ejpam-6008	382	1	kyungpook	kyungpook	PROPN
ejpam-6008	382	2	mathematical	mathematical	PROPN
ejpam-6008	382	3	journal	journal	PROPN
ejpam-6008	382	4	,	,	PUNCT
ejpam-6008	382	5	35:311–322	35:311–322	PROPN
ejpam-6008	382	6	,	,	PUNCT
ejpam-6008	382	7	1995	1995	NUM
ejpam-6008	382	8	.	.	PUNCT
ejpam-6008	383	1	[	[	X
ejpam-6008	383	2	34	34	NUM
ejpam-6008	383	3	]	]	PUNCT
ejpam-6008	383	4	t.	t.	PROPN
ejpam-6008	383	5	noiri	noiri	PROPN
ejpam-6008	383	6	.	.	PUNCT
ejpam-6008	384	1	super	super	ADJ
ejpam-6008	384	2	-	-	NOUN
ejpam-6008	384	3	continuity	continuity	NOUN
ejpam-6008	384	4	and	and	CCONJ
ejpam-6008	384	5	some	some	DET
ejpam-6008	384	6	strong	strong	ADJ
ejpam-6008	384	7	forms	form	NOUN
ejpam-6008	384	8	of	of	ADP
ejpam-6008	384	9	continuity	continuity	NOUN
ejpam-6008	384	10	.	.	PUNCT
ejpam-6008	385	1	indian	indian	ADJ
ejpam-6008	385	2	journal	journal	PROPN
ejpam-6008	385	3	of	of	ADP
ejpam-6008	385	4	pure	pure	ADJ
ejpam-6008	385	5	and	and	CCONJ
ejpam-6008	385	6	applied	applied	ADJ
ejpam-6008	385	7	mathematics	mathematic	NOUN
ejpam-6008	385	8	,	,	PUNCT
ejpam-6008	385	9	15:241–250	15:241–250	NUM
ejpam-6008	385	10	,	,	PUNCT
ejpam-6008	385	11	1984	1984	NUM
ejpam-6008	385	12	.	.	PUNCT
ejpam-6008	386	1	[	[	X
ejpam-6008	386	2	35	35	NUM
ejpam-6008	386	3	]	]	X
ejpam-6008	386	4	e.	e.	PROPN
ejpam-6008	386	5	ekici	ekici	PROPN
ejpam-6008	386	6	,	,	PUNCT
ejpam-6008	386	7	s.	s.	PROPN
ejpam-6008	386	8	jafari	jafari	PROPN
ejpam-6008	386	9	,	,	PUNCT
ejpam-6008	386	10	and	and	CCONJ
ejpam-6008	386	11	t.	t.	PROPN
ejpam-6008	386	12	noiri	noiri	PROPN
ejpam-6008	386	13	.	.	PUNCT
ejpam-6008	387	1	on	on	ADP
ejpam-6008	387	2	upper	upper	ADJ
ejpam-6008	387	3	and	and	CCONJ
ejpam-6008	387	4	lower	low	ADJ
ejpam-6008	387	5	contra	contra	ADJ
ejpam-6008	387	6	-	-	ADJ
ejpam-6008	387	7	continuous	continuous	ADJ
ejpam-6008	387	8	multifunctions	multifunction	NOUN
ejpam-6008	387	9	.	.	PUNCT
ejpam-6008	388	1	analele	analele	ADP
ejpam-6008	388	2	ştiinţifice	ştiinţifice	PROPN
ejpam-6008	388	3	ale	ale	NOUN
ejpam-6008	388	4	universităţii	universităţii	AUX
ejpam-6008	388	5	al	al	PROPN
ejpam-6008	388	6	.	.	PROPN
ejpam-6008	388	7	i.	i.	PROPN
ejpam-6008	388	8	cuza	cuza	AUX
ejpam-6008	388	9	din	din	PROPN
ejpam-6008	388	10	iaşi	iaşi	VERB
ejpam-6008	388	11	matematică	matematică	NOUN
ejpam-6008	388	12	,	,	PUNCT
ejpam-6008	388	13	54(1):75	54(1):75	NUM
ejpam-6008	388	14	–	–	PUNCT
ejpam-6008	388	15	85	85	NUM
ejpam-6008	388	16	,	,	PUNCT
ejpam-6008	388	17	2008	2008	NUM
ejpam-6008	388	18	.	.	PUNCT
ejpam-6008	389	1	[	[	X
ejpam-6008	389	2	36	36	NUM
ejpam-6008	389	3	]	]	PUNCT
ejpam-6008	389	4	t.	t.	PROPN
ejpam-6008	389	5	noiri	noiri	PROPN
ejpam-6008	389	6	and	and	CCONJ
ejpam-6008	389	7	v.	v.	ADP
ejpam-6008	389	8	popa	popa	NOUN
ejpam-6008	389	9	.	.	PUNCT
ejpam-6008	390	1	almost	almost	ADV
ejpam-6008	390	2	weakly	weakly	ADJ
ejpam-6008	390	3	continuous	continuous	ADJ
ejpam-6008	390	4	multifunctions	multifunction	NOUN
ejpam-6008	390	5	.	.	PUNCT
ejpam-6008	391	1	demonstratio	demonstratio	PROPN
ejpam-6008	391	2	mathematica	mathematica	PROPN
ejpam-6008	391	3	,	,	PUNCT
ejpam-6008	391	4	26:363–380	26:363–380	PROPN
ejpam-6008	391	5	,	,	PUNCT
ejpam-6008	391	6	1993	1993	NUM
ejpam-6008	391	7	.	.	PUNCT
ejpam-6008	392	1	[	[	X
ejpam-6008	392	2	37	37	NUM
ejpam-6008	392	3	]	]	PUNCT
ejpam-6008	392	4	c.	c.	PROPN
ejpam-6008	392	5	boonpok	boonpok	PROPN
ejpam-6008	392	6	.	.	PUNCT
ejpam-6008	393	1	(	(	PUNCT
ejpam-6008	393	2	τ1	τ1	NOUN
ejpam-6008	393	3	,	,	PUNCT
ejpam-6008	393	4	τ2)δ	τ2)δ	ADJ
ejpam-6008	393	5	-	-	PUNCT
ejpam-6008	393	6	semicontinuous	semicontinuous	ADJ
ejpam-6008	393	7	multifunctions	multifunction	NOUN
ejpam-6008	393	8	.	.	PUNCT
ejpam-6008	394	1	heliyon	heliyon	NOUN
ejpam-6008	394	2	,	,	PUNCT
ejpam-6008	394	3	6	6	NUM
ejpam-6008	394	4	:	:	SYM
ejpam-6008	394	5	e05367	e05367	PROPN
ejpam-6008	394	6	,	,	PUNCT
ejpam-6008	394	7	2020	2020	NUM
ejpam-6008	394	8	.	.	PUNCT
ejpam-6008	395	1	[	[	X
ejpam-6008	395	2	38	38	NUM
ejpam-6008	395	3	]	]	PUNCT
ejpam-6008	395	4	c.	c.	PROPN
ejpam-6008	395	5	boonpok	boonpok	PROPN
ejpam-6008	395	6	and	and	CCONJ
ejpam-6008	395	7	c.	c.	PROPN
ejpam-6008	395	8	viriyapong	viriyapong	PROPN
ejpam-6008	395	9	.	.	PUNCT
ejpam-6008	396	1	upper	upper	ADJ
ejpam-6008	396	2	and	and	CCONJ
ejpam-6008	396	3	lower	low	ADJ
ejpam-6008	396	4	almost	almost	ADV
ejpam-6008	396	5	weak	weak	ADJ
ejpam-6008	396	6	(	(	PUNCT
ejpam-6008	396	7	τ1	τ1	NOUN
ejpam-6008	396	8	,	,	PUNCT
ejpam-6008	396	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	396	10	.	.	PUNCT
ejpam-6008	397	1	european	european	PROPN
ejpam-6008	397	2	journal	journal	PROPN
ejpam-6008	397	3	of	of	ADP
ejpam-6008	397	4	pure	pure	ADJ
ejpam-6008	397	5	and	and	CCONJ
ejpam-6008	397	6	applied	applied	ADJ
ejpam-6008	397	7	mathematics	mathematic	NOUN
ejpam-6008	397	8	,	,	PUNCT
ejpam-6008	397	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-6008	397	10	,	,	PUNCT
ejpam-6008	397	11	2021	2021	NUM
ejpam-6008	397	12	.	.	PUNCT
ejpam-6008	398	1	[	[	X
ejpam-6008	398	2	39	39	NUM
ejpam-6008	398	3	]	]	PUNCT
ejpam-6008	398	4	c.	c.	PROPN
ejpam-6008	398	5	viriyapong	viriyapong	PROPN
ejpam-6008	398	6	and	and	CCONJ
ejpam-6008	398	7	c.	c.	PROPN
ejpam-6008	398	8	boonpok	boonpok	PROPN
ejpam-6008	398	9	.	.	PUNCT
ejpam-6008	399	1	weak	weak	ADJ
ejpam-6008	399	2	quasi	quasi	NOUN
ejpam-6008	399	3	(	(	PUNCT
ejpam-6008	399	4	λ	λ	PROPN
ejpam-6008	399	5	,	,	PUNCT
ejpam-6008	399	6	sp)-continuity	sp)-continuity	NOUN
ejpam-6008	399	7	for	for	ADP
ejpam-6008	399	8	multifunctions	multifunction	NOUN
ejpam-6008	399	9	.	.	PUNCT
ejpam-6008	400	1	international	international	ADJ
ejpam-6008	400	2	journal	journal	PROPN
ejpam-6008	400	3	of	of	ADP
ejpam-6008	400	4	mathematics	mathematic	NOUN
ejpam-6008	400	5	and	and	CCONJ
ejpam-6008	400	6	computer	computer	NOUN
ejpam-6008	400	7	science	science	NOUN
ejpam-6008	400	8	,	,	PUNCT
ejpam-6008	400	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-6008	400	10	,	,	PUNCT
ejpam-6008	400	11	2022	2022	NUM
ejpam-6008	400	12	.	.	PUNCT
ejpam-6008	401	1	[	[	X
ejpam-6008	401	2	40	40	NUM
ejpam-6008	401	3	]	]	PUNCT
ejpam-6008	401	4	c.	c.	PROPN
ejpam-6008	401	5	boonpok	boonpok	PROPN
ejpam-6008	401	6	.	.	PUNCT
ejpam-6008	402	1	on	on	ADP
ejpam-6008	402	2	continuous	continuous	ADJ
ejpam-6008	402	3	multifunctions	multifunction	NOUN
ejpam-6008	402	4	in	in	ADP
ejpam-6008	402	5	ideal	ideal	ADJ
ejpam-6008	402	6	topological	topological	ADJ
ejpam-6008	402	7	spaces	space	NOUN
ejpam-6008	402	8	.	.	PUNCT
ejpam-6008	403	1	lobachevskii	lobachevskii	PROPN
ejpam-6008	403	2	journal	journal	PROPN
ejpam-6008	403	3	of	of	ADP
ejpam-6008	403	4	mathematics	mathematic	NOUN
ejpam-6008	403	5	,	,	PUNCT
ejpam-6008	403	6	40(1):24–35	40(1):24–35	NUM
ejpam-6008	403	7	,	,	PUNCT
ejpam-6008	403	8	2019	2019	NUM
ejpam-6008	403	9	.	.	PUNCT
ejpam-6008	404	1	[	[	X
ejpam-6008	404	2	41	41	NUM
ejpam-6008	404	3	]	]	PUNCT
ejpam-6008	404	4	c.	c.	PROPN
ejpam-6008	404	5	boonpok	boonpok	PROPN
ejpam-6008	404	6	.	.	PUNCT
ejpam-6008	405	1	upper	upper	ADJ
ejpam-6008	405	2	and	and	CCONJ
ejpam-6008	405	3	lower	low	ADJ
ejpam-6008	405	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-6008	405	5	.	.	PUNCT
ejpam-6008	405	6	heliyon	heliyon	NOUN
ejpam-6008	405	7	,	,	PUNCT
ejpam-6008	405	8	7	7	NUM
ejpam-6008	405	9	:	:	PUNCT
ejpam-6008	405	10	e05986	e05986	PROPN
ejpam-6008	405	11	,	,	PUNCT
ejpam-6008	405	12	2021	2021	NUM
ejpam-6008	405	13	.	.	PUNCT
ejpam-6008	406	1	[	[	X
ejpam-6008	406	2	42	42	NUM
ejpam-6008	406	3	]	]	PUNCT
ejpam-6008	406	4	c.	c.	PROPN
ejpam-6008	406	5	boonpok	boonpok	PROPN
ejpam-6008	406	6	and	and	CCONJ
ejpam-6008	406	7	j.	j.	PROPN
ejpam-6008	406	8	khampakdee	khampakdee	PROPN
ejpam-6008	406	9	.	.	PUNCT
ejpam-6008	407	1	upper	upper	ADJ
ejpam-6008	407	2	and	and	CCONJ
ejpam-6008	407	3	lower	low	ADJ
ejpam-6008	407	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-6008	407	5	.	.	PUNCT
ejpam-6008	407	6	european	european	PROPN
ejpam-6008	407	7	journal	journal	PROPN
ejpam-6008	407	8	n.	n.	PROPN
ejpam-6008	407	9	viriyapong	viriyapong	PROPN
ejpam-6008	407	10	,	,	PUNCT
ejpam-6008	407	11	a.	a.	PROPN
ejpam-6008	407	12	sama	sama	PROPN
ejpam-6008	407	13	-	-	PUNCT
ejpam-6008	407	14	ae	ae	PROPN
ejpam-6008	407	15	,	,	PUNCT
ejpam-6008	407	16	c.	c.	PROPN
ejpam-6008	407	17	boonpok	boonpok	PROPN
ejpam-6008	407	18	/	/	SYM
ejpam-6008	407	19	eur	eur	PROPN
ejpam-6008	407	20	.	.	PUNCT
ejpam-6008	408	1	j.	j.	PROPN
ejpam-6008	408	2	pure	pure	PROPN
ejpam-6008	408	3	appl	appl	PROPN
ejpam-6008	408	4	.	.	PROPN
ejpam-6008	408	5	math	math	PROPN
ejpam-6008	408	6	,	,	PUNCT
ejpam-6008	408	7	18	18	NUM
ejpam-6008	408	8	(	(	PUNCT
ejpam-6008	408	9	2	2	NUM
ejpam-6008	408	10	)	)	PUNCT
ejpam-6008	408	11	(	(	PUNCT
ejpam-6008	408	12	2025	2025	NUM
ejpam-6008	408	13	)	)	PUNCT
ejpam-6008	408	14	,	,	PUNCT
ejpam-6008	408	15	6008	6008	NUM
ejpam-6008	408	16	13	13	NUM
ejpam-6008	408	17	of	of	ADP
ejpam-6008	408	18	15	15	NUM
ejpam-6008	408	19	of	of	ADP
ejpam-6008	408	20	pure	pure	ADJ
ejpam-6008	408	21	and	and	CCONJ
ejpam-6008	408	22	applied	applied	ADJ
ejpam-6008	408	23	mathematics	mathematic	NOUN
ejpam-6008	408	24	,	,	PUNCT
ejpam-6008	408	25	17(1):201–211	17(1):201–211	NUM
ejpam-6008	408	26	,	,	PUNCT
ejpam-6008	408	27	2024	2024	NUM
ejpam-6008	408	28	.	.	PUNCT
ejpam-6008	409	1	[	[	X
ejpam-6008	409	2	43	43	NUM
ejpam-6008	409	3	]	]	X
ejpam-6008	409	4	c.	c.	PROPN
ejpam-6008	409	5	boonpok	boonpok	PROPN
ejpam-6008	409	6	and	and	CCONJ
ejpam-6008	409	7	n.	n.	PROPN
ejpam-6008	409	8	srisarakham	srisarakham	PROPN
ejpam-6008	409	9	.	.	PUNCT
ejpam-6008	410	1	almost	almost	ADV
ejpam-6008	410	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-6008	410	3	for	for	ADP
ejpam-6008	410	4	multifunctions	multifunction	NOUN
ejpam-6008	410	5	.	.	PUNCT
ejpam-6008	411	1	international	international	ADJ
ejpam-6008	411	2	journal	journal	NOUN
ejpam-6008	411	3	of	of	ADP
ejpam-6008	411	4	analysis	analysis	NOUN
ejpam-6008	411	5	and	and	CCONJ
ejpam-6008	411	6	applications	application	NOUN
ejpam-6008	411	7	,	,	PUNCT
ejpam-6008	411	8	21:107	21:107	NUM
ejpam-6008	411	9	,	,	PUNCT
ejpam-6008	411	10	2023	2023	NUM
ejpam-6008	411	11	.	.	PUNCT
ejpam-6008	412	1	[	[	X
ejpam-6008	412	2	44	44	NUM
ejpam-6008	412	3	]	]	PUNCT
ejpam-6008	412	4	c.	c.	PROPN
ejpam-6008	412	5	boonpok	boonpok	PROPN
ejpam-6008	412	6	.	.	PUNCT
ejpam-6008	413	1	weak	weak	ADJ
ejpam-6008	413	2	quasi	quasi	ADJ
ejpam-6008	413	3	continuity	continuity	NOUN
ejpam-6008	413	4	for	for	ADP
ejpam-6008	413	5	multifunctions	multifunction	NOUN
ejpam-6008	413	6	in	in	ADP
ejpam-6008	413	7	ideal	ideal	ADJ
ejpam-6008	413	8	topological	topological	ADJ
ejpam-6008	413	9	spaces	space	NOUN
ejpam-6008	413	10	.	.	PUNCT
ejpam-6008	414	1	advances	advance	NOUN
ejpam-6008	414	2	in	in	ADP
ejpam-6008	414	3	mathematics	mathematic	NOUN
ejpam-6008	414	4	:	:	PUNCT
ejpam-6008	414	5	scientific	scientific	ADJ
ejpam-6008	414	6	journal	journal	NOUN
ejpam-6008	414	7	,	,	PUNCT
ejpam-6008	414	8	9(1):339–355	9(1):339–355	NUM
ejpam-6008	414	9	,	,	PUNCT
ejpam-6008	414	10	2020	2020	NUM
ejpam-6008	414	11	.	.	PUNCT
ejpam-6008	415	1	[	[	X
ejpam-6008	415	2	45	45	NUM
ejpam-6008	415	3	]	]	PUNCT
ejpam-6008	415	4	c.	c.	PROPN
ejpam-6008	415	5	boonpok	boonpok	PROPN
ejpam-6008	415	6	and	and	CCONJ
ejpam-6008	415	7	p.	p.	NOUN
ejpam-6008	415	8	pue	pue	NOUN
ejpam-6008	415	9	-	-	PUNCT
ejpam-6008	415	10	on	on	ADP
ejpam-6008	415	11	.	.	PUNCT
ejpam-6008	416	1	upper	upper	ADJ
ejpam-6008	416	2	and	and	CCONJ
ejpam-6008	416	3	lower	low	ADJ
ejpam-6008	416	4	weakly	weakly	ADJ
ejpam-6008	416	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6008	416	6	multifunctions	multifunction	NOUN
ejpam-6008	416	7	.	.	PUNCT
ejpam-6008	417	1	international	international	ADJ
ejpam-6008	417	2	journal	journal	NOUN
ejpam-6008	417	3	of	of	ADP
ejpam-6008	417	4	analysis	analysis	NOUN
ejpam-6008	417	5	and	and	CCONJ
ejpam-6008	417	6	applications	application	NOUN
ejpam-6008	417	7	,	,	PUNCT
ejpam-6008	417	8	21:90	21:90	NUM
ejpam-6008	417	9	,	,	PUNCT
ejpam-6008	417	10	2023	2023	NUM
ejpam-6008	417	11	.	.	PUNCT
ejpam-6008	418	1	[	[	X
ejpam-6008	418	2	46	46	NUM
ejpam-6008	418	3	]	]	X
ejpam-6008	418	4	c.	c.	PROPN
ejpam-6008	418	5	boonpok	boonpok	PROPN
ejpam-6008	418	6	and	and	CCONJ
ejpam-6008	418	7	p.	p.	NOUN
ejpam-6008	418	8	pue	pue	NOUN
ejpam-6008	418	9	-	-	PUNCT
ejpam-6008	418	10	on	on	ADP
ejpam-6008	418	11	.	.	PUNCT
ejpam-6008	419	1	upper	upper	ADJ
ejpam-6008	419	2	and	and	CCONJ
ejpam-6008	419	3	lower	low	ADJ
ejpam-6008	419	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6008	419	5	multifunctions	multifunction	NOUN
ejpam-6008	419	6	.	.	PUNCT
ejpam-6008	420	1	european	european	ADJ
ejpam-6008	420	2	journal	journal	PROPN
ejpam-6008	420	3	of	of	ADP
ejpam-6008	420	4	pure	pure	ADJ
ejpam-6008	420	5	and	and	CCONJ
ejpam-6008	420	6	applied	applied	ADJ
ejpam-6008	420	7	mathematics	mathematic	NOUN
ejpam-6008	420	8	,	,	PUNCT
ejpam-6008	420	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-6008	420	10	,	,	PUNCT
ejpam-6008	420	11	2023	2023	NUM
ejpam-6008	420	12	.	.	PUNCT
ejpam-6008	421	1	[	[	X
ejpam-6008	421	2	47	47	NUM
ejpam-6008	421	3	]	]	X
ejpam-6008	421	4	c.	c.	PROPN
ejpam-6008	421	5	boonpok	boonpok	PROPN
ejpam-6008	421	6	and	and	CCONJ
ejpam-6008	421	7	j.	j.	PROPN
ejpam-6008	421	8	khampakdee	khampakdee	PROPN
ejpam-6008	421	9	.	.	PUNCT
ejpam-6008	422	1	upper	upper	ADJ
ejpam-6008	422	2	and	and	CCONJ
ejpam-6008	422	3	lower	low	ADJ
ejpam-6008	422	4	weak	weak	ADJ
ejpam-6008	422	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-6008	422	6	.	.	PUNCT
ejpam-6008	423	1	european	european	PROPN
ejpam-6008	423	2	journal	journal	PROPN
ejpam-6008	423	3	of	of	ADP
ejpam-6008	423	4	pure	pure	ADJ
ejpam-6008	423	5	and	and	CCONJ
ejpam-6008	423	6	applied	applied	ADJ
ejpam-6008	423	7	mathematics	mathematic	NOUN
ejpam-6008	423	8	,	,	PUNCT
ejpam-6008	423	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-6008	423	10	,	,	PUNCT
ejpam-6008	423	11	2023	2023	NUM
ejpam-6008	423	12	.	.	PUNCT
ejpam-6008	424	1	[	[	X
ejpam-6008	424	2	48	48	NUM
ejpam-6008	424	3	]	]	PUNCT
ejpam-6008	424	4	c.	c.	PROPN
ejpam-6008	424	5	boonpok	boonpok	PROPN
ejpam-6008	424	6	.	.	PUNCT
ejpam-6008	425	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-6008	425	2	continuity	continuity	NOUN
ejpam-6008	425	3	for	for	ADP
ejpam-6008	425	4	multifunctions	multifunction	NOUN
ejpam-6008	425	5	.	.	PUNCT
ejpam-6008	426	1	wseas	wseas	PROPN
ejpam-6008	426	2	transactions	transaction	NOUN
ejpam-6008	426	3	on	on	ADP
ejpam-6008	426	4	mathematics	mathematic	NOUN
ejpam-6008	426	5	,	,	PUNCT
ejpam-6008	426	6	21:245–251	21:245–251	NUM
ejpam-6008	426	7	,	,	PUNCT
ejpam-6008	426	8	2022	2022	NUM
ejpam-6008	426	9	.	.	PUNCT
ejpam-6008	427	1	[	[	X
ejpam-6008	427	2	49	49	NUM
ejpam-6008	427	3	]	]	PUNCT
ejpam-6008	427	4	c.	c.	PROPN
ejpam-6008	427	5	boonpok	boonpok	PROPN
ejpam-6008	427	6	and	and	CCONJ
ejpam-6008	427	7	p.	p.	NOUN
ejpam-6008	427	8	pue	pue	NOUN
ejpam-6008	427	9	-	-	PUNCT
ejpam-6008	427	10	on	on	ADP
ejpam-6008	427	11	.	.	PUNCT
ejpam-6008	428	1	continuity	continuity	NOUN
ejpam-6008	428	2	for	for	ADP
ejpam-6008	428	3	multifunctions	multifunction	NOUN
ejpam-6008	428	4	in	in	ADP
ejpam-6008	428	5	ideal	ideal	ADJ
ejpam-6008	428	6	topological	topological	ADJ
ejpam-6008	428	7	spaces	space	NOUN
ejpam-6008	428	8	.	.	PUNCT
ejpam-6008	429	1	wseas	wseas	VERB
ejpam-6008	429	2	transactions	transaction	NOUN
ejpam-6008	429	3	on	on	ADP
ejpam-6008	429	4	mathematics	mathematic	NOUN
ejpam-6008	429	5	,	,	PUNCT
ejpam-6008	429	6	19:624–631	19:624–631	NUM
ejpam-6008	429	7	,	,	PUNCT
ejpam-6008	429	8	2020	2020	NUM
ejpam-6008	429	9	.	.	PUNCT
ejpam-6008	430	1	[	[	X
ejpam-6008	430	2	50	50	NUM
ejpam-6008	430	3	]	]	PUNCT
ejpam-6008	430	4	c.	c.	PROPN
ejpam-6008	430	5	boonpok	boonpok	PROPN
ejpam-6008	430	6	and	and	CCONJ
ejpam-6008	430	7	p.	p.	NOUN
ejpam-6008	430	8	pue	pue	NOUN
ejpam-6008	430	9	-	-	PUNCT
ejpam-6008	430	10	on	on	ADP
ejpam-6008	430	11	.	.	PUNCT
ejpam-6008	431	1	upper	upper	ADJ
ejpam-6008	431	2	and	and	CCONJ
ejpam-6008	431	3	lower	low	ADJ
ejpam-6008	431	4	weakly	weakly	ADJ
ejpam-6008	431	5	(	(	PUNCT
ejpam-6008	431	6	λ	λ	NOUN
ejpam-6008	431	7	,	,	PUNCT
ejpam-6008	431	8	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	431	9	multifunctions	multifunction	NOUN
ejpam-6008	431	10	.	.	PUNCT
ejpam-6008	432	1	european	european	PROPN
ejpam-6008	432	2	journal	journal	PROPN
ejpam-6008	432	3	of	of	ADP
ejpam-6008	432	4	pure	pure	ADJ
ejpam-6008	432	5	and	and	CCONJ
ejpam-6008	432	6	applied	applied	ADJ
ejpam-6008	432	7	mathematics	mathematic	NOUN
ejpam-6008	432	8	,	,	PUNCT
ejpam-6008	432	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-6008	432	10	,	,	PUNCT
ejpam-6008	432	11	2023	2023	NUM
ejpam-6008	432	12	.	.	PUNCT
ejpam-6008	433	1	[	[	X
ejpam-6008	433	2	51	51	NUM
ejpam-6008	433	3	]	]	X
ejpam-6008	433	4	j.	j.	PROPN
ejpam-6008	433	5	khampakdee	khampakdee	PROPN
ejpam-6008	433	6	and	and	CCONJ
ejpam-6008	433	7	c.	c.	PROPN
ejpam-6008	433	8	boonpok	boonpok	PROPN
ejpam-6008	433	9	.	.	PUNCT
ejpam-6008	434	1	upper	upper	ADJ
ejpam-6008	434	2	and	and	CCONJ
ejpam-6008	434	3	lower	low	ADJ
ejpam-6008	434	4	α(λ	α(λ	PROPN
ejpam-6008	434	5	,	,	PUNCT
ejpam-6008	434	6	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	434	7	multifunctions	multifunction	NOUN
ejpam-6008	434	8	.	.	PUNCT
ejpam-6008	435	1	wseas	wseas	VERB
ejpam-6008	435	2	transactions	transaction	NOUN
ejpam-6008	435	3	on	on	ADP
ejpam-6008	435	4	mathematics	mathematic	NOUN
ejpam-6008	435	5	,	,	PUNCT
ejpam-6008	435	6	21:684–690	21:684–690	NUM
ejpam-6008	435	7	,	,	PUNCT
ejpam-6008	435	8	2022	2022	NUM
ejpam-6008	435	9	.	.	PUNCT
ejpam-6008	436	1	[	[	X
ejpam-6008	436	2	52	52	NUM
ejpam-6008	436	3	]	]	PUNCT
ejpam-6008	436	4	c.	c.	PROPN
ejpam-6008	436	5	boonpok	boonpok	PROPN
ejpam-6008	436	6	and	and	CCONJ
ejpam-6008	436	7	j.	j.	PROPN
ejpam-6008	436	8	khampakdee	khampakdee	PROPN
ejpam-6008	436	9	.	.	PUNCT
ejpam-6008	437	1	on	on	ADP
ejpam-6008	437	2	almost	almost	ADV
ejpam-6008	437	3	α(λ	α(λ	PROPN
ejpam-6008	437	4	,	,	PUNCT
ejpam-6008	437	5	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	437	6	multifunctions	multifunction	NOUN
ejpam-6008	437	7	.	.	PUNCT
ejpam-6008	438	1	european	european	PROPN
ejpam-6008	438	2	journal	journal	PROPN
ejpam-6008	438	3	of	of	ADP
ejpam-6008	438	4	pure	pure	ADJ
ejpam-6008	438	5	and	and	CCONJ
ejpam-6008	438	6	applied	applied	ADJ
ejpam-6008	438	7	mathematics	mathematic	NOUN
ejpam-6008	438	8	,	,	PUNCT
ejpam-6008	438	9	15(2):626–634	15(2):626–634	PROPN
ejpam-6008	438	10	,	,	PUNCT
ejpam-6008	438	11	2022	2022	NUM
ejpam-6008	438	12	.	.	PUNCT
ejpam-6008	439	1	[	[	X
ejpam-6008	439	2	53	53	NUM
ejpam-6008	439	3	]	]	PUNCT
ejpam-6008	439	4	c.	c.	PROPN
ejpam-6008	439	5	boonpok	boonpok	PROPN
ejpam-6008	439	6	and	and	CCONJ
ejpam-6008	439	7	m.	m.	NOUN
ejpam-6008	439	8	thongmoon	thongmoon	NOUN
ejpam-6008	439	9	.	.	PUNCT
ejpam-6008	440	1	weak	weak	ADJ
ejpam-6008	440	2	α(λ	α(λ	PROPN
ejpam-6008	440	3	,	,	PUNCT
ejpam-6008	440	4	sp)-continuity	sp)-continuity	NOUN
ejpam-6008	440	5	for	for	ADP
ejpam-6008	440	6	multifunctions	multifunction	NOUN
ejpam-6008	440	7	.	.	PUNCT
ejpam-6008	441	1	european	european	ADJ
ejpam-6008	441	2	journal	journal	PROPN
ejpam-6008	441	3	of	of	ADP
ejpam-6008	441	4	pure	pure	ADJ
ejpam-6008	441	5	and	and	CCONJ
ejpam-6008	441	6	applied	applied	ADJ
ejpam-6008	441	7	mathematics	mathematic	NOUN
ejpam-6008	441	8	,	,	PUNCT
ejpam-6008	441	9	16(1):465–478	16(1):465–478	NUM
ejpam-6008	441	10	,	,	PUNCT
ejpam-6008	441	11	2023	2023	NUM
ejpam-6008	441	12	.	.	PUNCT
ejpam-6008	442	1	[	[	X
ejpam-6008	442	2	54	54	NUM
ejpam-6008	442	3	]	]	PUNCT
ejpam-6008	442	4	m.	m.	NOUN
ejpam-6008	442	5	thongmoon	thongmoon	NOUN
ejpam-6008	442	6	and	and	CCONJ
ejpam-6008	442	7	c.	c.	PROPN
ejpam-6008	442	8	boonpok	boonpok	PROPN
ejpam-6008	442	9	.	.	PUNCT
ejpam-6008	443	1	upper	upper	ADJ
ejpam-6008	443	2	and	and	CCONJ
ejpam-6008	443	3	lower	low	ADJ
ejpam-6008	443	4	almost	almost	ADV
ejpam-6008	443	5	β(λ	β(λ	NOUN
ejpam-6008	443	6	,	,	PUNCT
ejpam-6008	443	7	sp)-continuous	sp)-continuous	ADJ
ejpam-6008	443	8	multifunctions	multifunction	NOUN
ejpam-6008	443	9	.	.	PUNCT
ejpam-6008	444	1	wseas	wseas	VERB
ejpam-6008	444	2	transactions	transaction	NOUN
ejpam-6008	444	3	on	on	ADP
ejpam-6008	444	4	mathematics	mathematic	NOUN
ejpam-6008	444	5	,	,	PUNCT
ejpam-6008	444	6	21:844–853	21:844–853	NUM
ejpam-6008	444	7	,	,	PUNCT
ejpam-6008	444	8	2022	2022	NUM
ejpam-6008	444	9	.	.	PUNCT
ejpam-6008	445	1	[	[	X
ejpam-6008	445	2	55	55	NUM
ejpam-6008	445	3	]	]	PUNCT
ejpam-6008	445	4	c.	c.	PROPN
ejpam-6008	445	5	boonpok	boonpok	PROPN
ejpam-6008	445	6	and	and	CCONJ
ejpam-6008	445	7	j.	j.	PROPN
ejpam-6008	445	8	khampakdee	khampakdee	PROPN
ejpam-6008	445	9	.	.	PUNCT
ejpam-6008	446	1	slight	slight	PROPN
ejpam-6008	446	2	(	(	PUNCT
ejpam-6008	446	3	λ	λ	NOUN
ejpam-6008	446	4	,	,	PUNCT
ejpam-6008	446	5	sp)-continuity	sp)-continuity	NOUN
ejpam-6008	446	6	and	and	CCONJ
ejpam-6008	446	7	λsp	λsp	NOUN
ejpam-6008	446	8	-	-	PUNCT
ejpam-6008	446	9	extremally	extremally	ADV
ejpam-6008	446	10	disconnectedness	disconnectedness	NOUN
ejpam-6008	446	11	.	.	PUNCT
ejpam-6008	447	1	european	european	ADJ
ejpam-6008	447	2	journal	journal	PROPN
ejpam-6008	447	3	of	of	ADP
ejpam-6008	447	4	pure	pure	ADJ
ejpam-6008	447	5	and	and	CCONJ
ejpam-6008	447	6	applied	applied	ADJ
ejpam-6008	447	7	mathematics	mathematic	NOUN
ejpam-6008	447	8	,	,	PUNCT
ejpam-6008	447	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-6008	447	10	,	,	PUNCT
ejpam-6008	447	11	2022	2022	NUM
ejpam-6008	447	12	.	.	PUNCT
ejpam-6008	448	1	[	[	X
ejpam-6008	448	2	56	56	NUM
ejpam-6008	448	3	]	]	X
ejpam-6008	448	4	p.	p.	NOUN
ejpam-6008	448	5	pue	pue	NOUN
ejpam-6008	448	6	-	-	PUNCT
ejpam-6008	448	7	on	on	ADP
ejpam-6008	448	8	,	,	PUNCT
ejpam-6008	448	9	s.	s.	PROPN
ejpam-6008	448	10	sompong	sompong	PROPN
ejpam-6008	448	11	,	,	PUNCT
ejpam-6008	448	12	and	and	CCONJ
ejpam-6008	448	13	c.	c.	PROPN
ejpam-6008	448	14	boonpok	boonpok	PROPN
ejpam-6008	448	15	.	.	PUNCT
ejpam-6008	449	1	upper	upper	ADJ
ejpam-6008	449	2	and	and	CCONJ
ejpam-6008	449	3	lower	low	ADJ
ejpam-6008	449	4	(	(	PUNCT
ejpam-6008	449	5	τ1	τ1	NOUN
ejpam-6008	449	6	,	,	PUNCT
ejpam-6008	449	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	449	8	mulfunctions	mulfunction	NOUN
ejpam-6008	449	9	.	.	PUNCT
ejpam-6008	450	1	international	international	ADJ
ejpam-6008	450	2	journal	journal	NOUN
ejpam-6008	450	3	of	of	ADP
ejpam-6008	450	4	mathematics	mathematic	NOUN
ejpam-6008	450	5	and	and	CCONJ
ejpam-6008	450	6	computer	computer	NOUN
ejpam-6008	450	7	science	science	NOUN
ejpam-6008	450	8	,	,	PUNCT
ejpam-6008	450	9	19(4):1305	19(4):1305	NUM
ejpam-6008	450	10	–	–	PUNCT
ejpam-6008	450	11	1310	1310	NUM
ejpam-6008	450	12	,	,	PUNCT
ejpam-6008	450	13	2024	2024	NUM
ejpam-6008	450	14	.	.	PUNCT
ejpam-6008	451	1	[	[	X
ejpam-6008	451	2	57	57	NUM
ejpam-6008	451	3	]	]	X
ejpam-6008	451	4	c.	c.	PROPN
ejpam-6008	451	5	klanarong	klanarong	PROPN
ejpam-6008	451	6	,	,	PUNCT
ejpam-6008	451	7	s.	s.	PROPN
ejpam-6008	451	8	sompong	sompong	PROPN
ejpam-6008	451	9	,	,	PUNCT
ejpam-6008	451	10	and	and	CCONJ
ejpam-6008	451	11	c.	c.	PROPN
ejpam-6008	451	12	boonpok	boonpok	PROPN
ejpam-6008	451	13	.	.	PUNCT
ejpam-6008	452	1	upper	upper	ADJ
ejpam-6008	452	2	and	and	CCONJ
ejpam-6008	452	3	lower	low	ADJ
ejpam-6008	452	4	almost	almost	ADV
ejpam-6008	452	5	(	(	PUNCT
ejpam-6008	452	6	τ1	τ1	NOUN
ejpam-6008	452	7	,	,	PUNCT
ejpam-6008	452	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	452	9	multifunctions	multifunction	NOUN
ejpam-6008	452	10	.	.	PUNCT
ejpam-6008	453	1	european	european	ADJ
ejpam-6008	453	2	journal	journal	PROPN
ejpam-6008	453	3	of	of	ADP
ejpam-6008	453	4	pure	pure	ADJ
ejpam-6008	453	5	and	and	CCONJ
ejpam-6008	453	6	applied	applied	ADJ
ejpam-6008	453	7	mathematics	mathematic	NOUN
ejpam-6008	453	8	,	,	PUNCT
ejpam-6008	453	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-6008	453	10	,	,	PUNCT
ejpam-6008	453	11	2024	2024	NUM
ejpam-6008	453	12	.	.	PUNCT
ejpam-6008	454	1	[	[	X
ejpam-6008	454	2	58	58	NUM
ejpam-6008	454	3	]	]	PUNCT
ejpam-6008	454	4	m.	m.	NOUN
ejpam-6008	454	5	thongmoon	thongmoon	NOUN
ejpam-6008	454	6	,	,	PUNCT
ejpam-6008	454	7	s.	s.	PROPN
ejpam-6008	454	8	sompong	sompong	PROPN
ejpam-6008	454	9	,	,	PUNCT
ejpam-6008	454	10	and	and	CCONJ
ejpam-6008	454	11	c.	c.	PROPN
ejpam-6008	454	12	boonpok	boonpok	PROPN
ejpam-6008	454	13	.	.	PUNCT
ejpam-6008	455	1	upper	upper	ADJ
ejpam-6008	455	2	and	and	CCONJ
ejpam-6008	455	3	lower	low	ADJ
ejpam-6008	455	4	weak	weak	ADJ
ejpam-6008	455	5	(	(	PUNCT
ejpam-6008	455	6	τ1	τ1	NOUN
ejpam-6008	455	7	,	,	PUNCT
ejpam-6008	455	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6008	455	9	.	.	PUNCT
ejpam-6008	456	1	european	european	PROPN
ejpam-6008	456	2	journal	journal	PROPN
ejpam-6008	456	3	of	of	ADP
ejpam-6008	456	4	pure	pure	ADJ
ejpam-6008	456	5	and	and	CCONJ
ejpam-6008	456	6	applied	applied	ADJ
ejpam-6008	456	7	mathematics	mathematic	NOUN
ejpam-6008	456	8	,	,	PUNCT
ejpam-6008	456	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-6008	456	10	,	,	PUNCT
ejpam-6008	456	11	2024	2024	NUM
ejpam-6008	456	12	.	.	PUNCT
ejpam-6008	457	1	[	[	X
ejpam-6008	457	2	59	59	NUM
ejpam-6008	457	3	]	]	X
ejpam-6008	457	4	p.	p.	NOUN
ejpam-6008	457	5	pue	pue	NOUN
ejpam-6008	457	6	-	-	PUNCT
ejpam-6008	457	7	on	on	ADP
ejpam-6008	457	8	,	,	PUNCT
ejpam-6008	457	9	s.	s.	PROPN
ejpam-6008	457	10	sompong	sompong	PROPN
ejpam-6008	457	11	,	,	PUNCT
ejpam-6008	457	12	and	and	CCONJ
ejpam-6008	457	13	c.	c.	PROPN
ejpam-6008	457	14	boonpok	boonpok	PROPN
ejpam-6008	457	15	.	.	PUNCT
ejpam-6008	458	1	weakly	weakly	ADJ
ejpam-6008	458	2	quasi	quasi	NOUN
ejpam-6008	458	3	(	(	PUNCT
ejpam-6008	458	4	τ1	τ1	PROPN
ejpam-6008	458	5	,	,	PUNCT
ejpam-6008	458	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	458	7	multifunctions	multifunction	NOUN
ejpam-6008	458	8	.	.	PUNCT
ejpam-6008	459	1	european	european	ADJ
ejpam-6008	459	2	journal	journal	PROPN
ejpam-6008	459	3	of	of	ADP
ejpam-6008	459	4	pure	pure	ADJ
ejpam-6008	459	5	and	and	CCONJ
ejpam-6008	459	6	applied	applied	ADJ
ejpam-6008	459	7	mathematics	mathematic	NOUN
ejpam-6008	459	8	,	,	PUNCT
ejpam-6008	459	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-6008	459	10	,	,	PUNCT
ejpam-6008	459	11	2024	2024	NUM
ejpam-6008	459	12	.	.	PUNCT
ejpam-6008	460	1	[	[	X
ejpam-6008	460	2	60	60	NUM
ejpam-6008	460	3	]	]	X
ejpam-6008	460	4	p.	p.	NOUN
ejpam-6008	460	5	pue	pue	NOUN
ejpam-6008	460	6	-	-	PUNCT
ejpam-6008	460	7	on	on	ADP
ejpam-6008	460	8	,	,	PUNCT
ejpam-6008	460	9	s.	s.	PROPN
ejpam-6008	460	10	sompong	sompong	PROPN
ejpam-6008	460	11	,	,	PUNCT
ejpam-6008	460	12	and	and	CCONJ
ejpam-6008	460	13	c.	c.	PROPN
ejpam-6008	460	14	boonpok	boonpok	PROPN
ejpam-6008	460	15	.	.	PUNCT
ejpam-6008	461	1	almost	almost	ADV
ejpam-6008	461	2	quasi	quasi	X
ejpam-6008	461	3	(	(	PUNCT
ejpam-6008	461	4	τ1	τ1	NOUN
ejpam-6008	461	5	,	,	PUNCT
ejpam-6008	461	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	461	7	for	for	ADP
ejpam-6008	461	8	multifunctions	multifunction	NOUN
ejpam-6008	461	9	.	.	PUNCT
ejpam-6008	462	1	international	international	ADJ
ejpam-6008	462	2	journal	journal	NOUN
ejpam-6008	462	3	of	of	ADP
ejpam-6008	462	4	analysis	analysis	NOUN
ejpam-6008	462	5	and	and	CCONJ
ejpam-6008	462	6	applications	application	NOUN
ejpam-6008	462	7	,	,	PUNCT
ejpam-6008	462	8	22:97	22:97	NUM
ejpam-6008	462	9	,	,	PUNCT
ejpam-6008	462	10	2024	2024	NUM
ejpam-6008	462	11	.	.	PUNCT
ejpam-6008	463	1	[	[	X
ejpam-6008	463	2	61	61	NUM
ejpam-6008	463	3	]	]	PUNCT
ejpam-6008	463	4	j.	j.	PROPN
ejpam-6008	463	5	khampakdee	khampakdee	PROPN
ejpam-6008	463	6	,	,	PUNCT
ejpam-6008	463	7	s.	s.	PROPN
ejpam-6008	463	8	sompong	sompong	PROPN
ejpam-6008	463	9	,	,	PUNCT
ejpam-6008	463	10	and	and	CCONJ
ejpam-6008	463	11	c.	c.	PROPN
ejpam-6008	463	12	boonpok	boonpok	PROPN
ejpam-6008	463	13	.	.	PUNCT
ejpam-6008	464	1	c-(τ1	c-(τ1	PROPN
ejpam-6008	464	2	,	,	PUNCT
ejpam-6008	464	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	464	4	for	for	ADP
ejpam-6008	464	5	multifunctions	multifunction	NOUN
ejpam-6008	464	6	.	.	PUNCT
ejpam-6008	465	1	european	european	ADJ
ejpam-6008	465	2	journal	journal	PROPN
ejpam-6008	465	3	of	of	ADP
ejpam-6008	465	4	pure	pure	ADJ
ejpam-6008	465	5	and	and	CCONJ
ejpam-6008	465	6	applied	applied	ADJ
ejpam-6008	465	7	mathematics	mathematic	NOUN
ejpam-6008	465	8	,	,	PUNCT
ejpam-6008	465	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-6008	465	10	,	,	PUNCT
ejpam-6008	465	11	2024	2024	NUM
ejpam-6008	465	12	.	.	PUNCT
ejpam-6008	466	1	n.	n.	PROPN
ejpam-6008	466	2	viriyapong	viriyapong	PROPN
ejpam-6008	466	3	,	,	PUNCT
ejpam-6008	466	4	a.	a.	PROPN
ejpam-6008	466	5	sama	sama	PROPN
ejpam-6008	466	6	-	-	PUNCT
ejpam-6008	466	7	ae	ae	PROPN
ejpam-6008	466	8	,	,	PUNCT
ejpam-6008	466	9	c.	c.	PROPN
ejpam-6008	466	10	boonpok	boonpok	PROPN
ejpam-6008	466	11	/	/	SYM
ejpam-6008	466	12	eur	eur	PROPN
ejpam-6008	466	13	.	.	PUNCT
ejpam-6008	467	1	j.	j.	PROPN
ejpam-6008	467	2	pure	pure	PROPN
ejpam-6008	467	3	appl	appl	PROPN
ejpam-6008	467	4	.	.	PROPN
ejpam-6008	467	5	math	math	PROPN
ejpam-6008	467	6	,	,	PUNCT
ejpam-6008	467	7	18	18	NUM
ejpam-6008	467	8	(	(	PUNCT
ejpam-6008	467	9	2	2	NUM
ejpam-6008	467	10	)	)	PUNCT
ejpam-6008	467	11	(	(	PUNCT
ejpam-6008	467	12	2025	2025	NUM
ejpam-6008	467	13	)	)	PUNCT
ejpam-6008	467	14	,	,	PUNCT
ejpam-6008	467	15	6008	6008	NUM
ejpam-6008	467	16	14	14	NUM
ejpam-6008	467	17	of	of	ADP
ejpam-6008	467	18	15	15	NUM
ejpam-6008	467	19	[	[	SYM
ejpam-6008	467	20	62	62	NUM
ejpam-6008	467	21	]	]	PUNCT
ejpam-6008	467	22	p.	p.	NOUN
ejpam-6008	467	23	pue	pue	NOUN
ejpam-6008	467	24	-	-	PUNCT
ejpam-6008	467	25	on	on	ADP
ejpam-6008	467	26	,	,	PUNCT
ejpam-6008	467	27	a.	a.	PROPN
ejpam-6008	467	28	sama	sama	PROPN
ejpam-6008	467	29	-	-	PUNCT
ejpam-6008	467	30	ae	ae	PROPN
ejpam-6008	467	31	,	,	PUNCT
ejpam-6008	467	32	and	and	CCONJ
ejpam-6008	467	33	c.	c.	PROPN
ejpam-6008	467	34	boonpok	boonpok	PROPN
ejpam-6008	467	35	.	.	PUNCT
ejpam-6008	468	1	c	c	X
ejpam-6008	468	2	-	-	PUNCT
ejpam-6008	468	3	quasi	quasi	X
ejpam-6008	468	4	(	(	PUNCT
ejpam-6008	468	5	τ1	τ1	PROPN
ejpam-6008	468	6	,	,	PUNCT
ejpam-6008	468	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6008	468	8	multifunctions	multifunction	NOUN
ejpam-6008	468	9	.	.	PUNCT
ejpam-6008	469	1	european	european	ADJ
ejpam-6008	469	2	journal	journal	PROPN
ejpam-6008	469	3	of	of	ADP
ejpam-6008	469	4	pure	pure	ADJ
ejpam-6008	469	5	and	and	CCONJ
ejpam-6008	469	6	applied	applied	ADJ
ejpam-6008	469	7	mathematics	mathematic	NOUN
ejpam-6008	469	8	,	,	PUNCT
ejpam-6008	469	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-6008	469	10	,	,	PUNCT
ejpam-6008	469	11	2024	2024	NUM
ejpam-6008	469	12	.	.	PUNCT
ejpam-6008	470	1	[	[	X
ejpam-6008	470	2	63	63	NUM
ejpam-6008	470	3	]	]	PUNCT
ejpam-6008	470	4	n.	n.	PROPN
ejpam-6008	470	5	viriyapong	viriyapong	PROPN
ejpam-6008	470	6	,	,	PUNCT
ejpam-6008	470	7	s.	s.	PROPN
ejpam-6008	470	8	sompong	sompong	PROPN
ejpam-6008	470	9	,	,	PUNCT
ejpam-6008	470	10	and	and	CCONJ
ejpam-6008	470	11	c.	c.	PROPN
ejpam-6008	470	12	boonpok	boonpok	PROPN
ejpam-6008	470	13	.	.	PUNCT
ejpam-6008	471	1	upper	upper	ADJ
ejpam-6008	471	2	and	and	CCONJ
ejpam-6008	471	3	lower	low	ADJ
ejpam-6008	471	4	s-(τ1	s-(τ1	NOUN
ejpam-6008	471	5	,	,	PUNCT
ejpam-6008	471	6	τ2)p	τ2)p	ADJ
ejpam-6008	471	7	-	-	PUNCT
ejpam-6008	471	8	continuous	continuous	ADJ
ejpam-6008	471	9	multifunctions	multifunction	NOUN
ejpam-6008	471	10	.	.	PUNCT
ejpam-6008	472	1	european	european	ADJ
ejpam-6008	472	2	journal	journal	PROPN
ejpam-6008	472	3	of	of	ADP
ejpam-6008	472	4	pure	pure	ADJ
ejpam-6008	472	5	and	and	CCONJ
ejpam-6008	472	6	applied	applied	ADJ
ejpam-6008	472	7	mathematics	mathematic	NOUN
ejpam-6008	472	8	,	,	PUNCT
ejpam-6008	472	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-6008	472	10	,	,	PUNCT
ejpam-6008	472	11	2024	2024	NUM
ejpam-6008	472	12	.	.	PUNCT
ejpam-6008	473	1	[	[	X
ejpam-6008	473	2	64	64	NUM
ejpam-6008	473	3	]	]	PUNCT
ejpam-6008	473	4	c.	c.	PROPN
ejpam-6008	473	5	viriyapong	viriyapong	PROPN
ejpam-6008	473	6	,	,	PUNCT
ejpam-6008	473	7	s.	s.	PROPN
ejpam-6008	473	8	sompong	sompong	PROPN
ejpam-6008	473	9	,	,	PUNCT
ejpam-6008	473	10	and	and	CCONJ
ejpam-6008	473	11	c.	c.	PROPN
ejpam-6008	473	12	boonpok	boonpok	PROPN
ejpam-6008	473	13	.	.	PUNCT
ejpam-6008	474	1	upper	upper	ADJ
ejpam-6008	474	2	and	and	CCONJ
ejpam-6008	474	3	lower	low	ADJ
ejpam-6008	474	4	slight	slight	ADJ
ejpam-6008	474	5	α(τ1	α(τ1	NOUN
ejpam-6008	474	6	,	,	PUNCT
ejpam-6008	474	7	τ2)continuity	τ2)continuity	PROPN
ejpam-6008	474	8	.	.	PUNCT
ejpam-6008	475	1	european	european	PROPN
ejpam-6008	475	2	journal	journal	PROPN
ejpam-6008	475	3	of	of	ADP
ejpam-6008	475	4	pure	pure	ADJ
ejpam-6008	475	5	and	and	CCONJ
ejpam-6008	475	6	applied	applied	ADJ
ejpam-6008	475	7	mathematics	mathematic	NOUN
ejpam-6008	475	8	,	,	PUNCT
ejpam-6008	475	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-6008	475	10	,	,	PUNCT
ejpam-6008	475	11	2024	2024	NUM
ejpam-6008	475	12	.	.	PUNCT
ejpam-6008	476	1	[	[	X
ejpam-6008	476	2	65	65	NUM
ejpam-6008	476	3	]	]	X
ejpam-6008	476	4	n.	n.	PROPN
ejpam-6008	476	5	viriyapong	viriyapong	PROPN
ejpam-6008	476	6	,	,	PUNCT
ejpam-6008	476	7	s.	s.	PROPN
ejpam-6008	476	8	sompong	sompong	PROPN
ejpam-6008	476	9	,	,	PUNCT
ejpam-6008	476	10	and	and	CCONJ
ejpam-6008	476	11	c.	c.	PROPN
ejpam-6008	476	12	boonpok	boonpok	PROPN
ejpam-6008	476	13	.	.	PUNCT
ejpam-6008	477	1	slightly	slightly	ADV
ejpam-6008	477	2	(	(	PUNCT
ejpam-6008	477	3	τ1	τ1	NOUN
ejpam-6008	477	4	,	,	PUNCT
ejpam-6008	477	5	τ2)p	τ2)p	ADJ
ejpam-6008	477	6	-	-	ADJ
ejpam-6008	477	7	continuous	continuous	ADJ
ejpam-6008	477	8	multifunctions	multifunction	NOUN
ejpam-6008	477	9	.	.	PUNCT
ejpam-6008	478	1	international	international	ADJ
ejpam-6008	478	2	journal	journal	NOUN
ejpam-6008	478	3	of	of	ADP
ejpam-6008	478	4	analysis	analysis	NOUN
ejpam-6008	478	5	and	and	CCONJ
ejpam-6008	478	6	applications	application	NOUN
ejpam-6008	478	7	,	,	PUNCT
ejpam-6008	478	8	22:152	22:152	NUM
ejpam-6008	478	9	,	,	PUNCT
ejpam-6008	478	10	2024	2024	NUM
ejpam-6008	478	11	.	.	PUNCT
ejpam-6008	479	1	[	[	X
ejpam-6008	479	2	66	66	NUM
ejpam-6008	479	3	]	]	PUNCT
ejpam-6008	479	4	b.	b.	PROPN
ejpam-6008	479	5	kong	kong	PROPN
ejpam-6008	479	6	-	-	PUNCT
ejpam-6008	479	7	ied	ied	PROPN
ejpam-6008	479	8	,	,	PUNCT
ejpam-6008	479	9	s.	s.	PROPN
ejpam-6008	479	10	sompong	sompong	PROPN
ejpam-6008	479	11	,	,	PUNCT
ejpam-6008	479	12	and	and	CCONJ
ejpam-6008	479	13	c.	c.	PROPN
ejpam-6008	479	14	boonpok	boonpok	PROPN
ejpam-6008	479	15	.	.	PUNCT
ejpam-6008	480	1	rarely	rarely	ADV
ejpam-6008	480	2	s-(τ1	s-(τ1	VERB
ejpam-6008	480	3	,	,	PUNCT
ejpam-6008	480	4	τ2)p	τ2)p	ADJ
ejpam-6008	480	5	-	-	PUNCT
ejpam-6008	480	6	continuous	continuous	ADJ
ejpam-6008	480	7	multifunctions	multifunction	NOUN
ejpam-6008	480	8	.	.	PUNCT
ejpam-6008	481	1	european	european	ADJ
ejpam-6008	481	2	journal	journal	PROPN
ejpam-6008	481	3	of	of	ADP
ejpam-6008	481	4	pure	pure	ADJ
ejpam-6008	481	5	and	and	CCONJ
ejpam-6008	481	6	applied	applied	ADJ
ejpam-6008	481	7	mathematics	mathematic	NOUN
ejpam-6008	481	8	,	,	PUNCT
ejpam-6008	481	9	18(1):5649	18(1):5649	NUM
ejpam-6008	481	10	,	,	PUNCT
ejpam-6008	481	11	2025	2025	NUM
ejpam-6008	481	12	.	.	PUNCT
ejpam-6008	482	1	[	[	X
ejpam-6008	482	2	67	67	NUM
ejpam-6008	482	3	]	]	X
ejpam-6008	482	4	n.	n.	NOUN
ejpam-6008	482	5	chutiman	chutiman	NOUN
ejpam-6008	482	6	,	,	PUNCT
ejpam-6008	482	7	a.	a.	PROPN
ejpam-6008	482	8	sama	sama	PROPN
ejpam-6008	482	9	-	-	PUNCT
ejpam-6008	482	10	ae	ae	PROPN
ejpam-6008	482	11	,	,	PUNCT
ejpam-6008	482	12	and	and	CCONJ
ejpam-6008	482	13	c.	c.	PROPN
ejpam-6008	482	14	boonpok	boonpok	PROPN
ejpam-6008	482	15	.	.	PUNCT
ejpam-6008	483	1	almost	almost	ADV
ejpam-6008	483	2	near	near	ADV
ejpam-6008	483	3	(	(	PUNCT
ejpam-6008	483	4	τ1	τ1	NOUN
ejpam-6008	483	5	,	,	PUNCT
ejpam-6008	483	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	483	7	for	for	ADP
ejpam-6008	483	8	multifunctions	multifunction	NOUN
ejpam-6008	483	9	.	.	PUNCT
ejpam-6008	484	1	european	european	ADJ
ejpam-6008	484	2	journal	journal	PROPN
ejpam-6008	484	3	of	of	ADP
ejpam-6008	484	4	pure	pure	ADJ
ejpam-6008	484	5	and	and	CCONJ
ejpam-6008	484	6	applied	applied	ADJ
ejpam-6008	484	7	mathematics	mathematic	NOUN
ejpam-6008	484	8	,	,	PUNCT
ejpam-6008	484	9	18(1):5650	18(1):5650	NUM
ejpam-6008	484	10	,	,	PUNCT
ejpam-6008	484	11	2025	2025	NUM
ejpam-6008	484	12	.	.	PUNCT
ejpam-6008	485	1	[	[	X
ejpam-6008	485	2	68	68	NUM
ejpam-6008	485	3	]	]	PUNCT
ejpam-6008	485	4	m.	m.	NOUN
ejpam-6008	485	5	chiangpradit	chiangpradit	NOUN
ejpam-6008	485	6	,	,	PUNCT
ejpam-6008	485	7	a.	a.	PROPN
ejpam-6008	485	8	sama	sama	PROPN
ejpam-6008	485	9	-	-	PUNCT
ejpam-6008	485	10	ae	ae	PROPN
ejpam-6008	485	11	,	,	PUNCT
ejpam-6008	485	12	and	and	CCONJ
ejpam-6008	485	13	c.	c.	PROPN
ejpam-6008	485	14	boonpok	boonpok	PROPN
ejpam-6008	485	15	.	.	PUNCT
ejpam-6008	486	1	s-(τ1	s-(τ1	PROPN
ejpam-6008	486	2	,	,	PUNCT
ejpam-6008	486	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	486	4	for	for	ADP
ejpam-6008	486	5	multifunctions	multifunction	NOUN
ejpam-6008	486	6	.	.	PUNCT
ejpam-6008	487	1	european	european	ADJ
ejpam-6008	487	2	journal	journal	PROPN
ejpam-6008	487	3	of	of	ADP
ejpam-6008	487	4	pure	pure	ADJ
ejpam-6008	487	5	and	and	CCONJ
ejpam-6008	487	6	applied	applied	ADJ
ejpam-6008	487	7	mathematics	mathematic	NOUN
ejpam-6008	487	8	,	,	PUNCT
ejpam-6008	487	9	18(1):5634	18(1):5634	NUM
ejpam-6008	487	10	,	,	PUNCT
ejpam-6008	487	11	2025	2025	NUM
ejpam-6008	487	12	.	.	PUNCT
ejpam-6008	488	1	[	[	X
ejpam-6008	488	2	69	69	NUM
ejpam-6008	488	3	]	]	PUNCT
ejpam-6008	488	4	p.	p.	NOUN
ejpam-6008	488	5	pue	pue	NOUN
ejpam-6008	488	6	-	-	PUNCT
ejpam-6008	488	7	on	on	ADP
ejpam-6008	488	8	,	,	PUNCT
ejpam-6008	488	9	a.	a.	PROPN
ejpam-6008	488	10	sama	sama	PROPN
ejpam-6008	488	11	-	-	PUNCT
ejpam-6008	488	12	ae	ae	PROPN
ejpam-6008	488	13	,	,	PUNCT
ejpam-6008	488	14	and	and	CCONJ
ejpam-6008	488	15	c.	c.	PROPN
ejpam-6008	488	16	boonpok	boonpok	PROPN
ejpam-6008	488	17	.	.	PUNCT
ejpam-6008	489	1	quasi	quasi	PROPN
ejpam-6008	489	2	θ(τ1	θ(τ1	PROPN
ejpam-6008	489	3	,	,	PUNCT
ejpam-6008	489	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	489	5	for	for	ADP
ejpam-6008	489	6	multifunctions	multifunction	NOUN
ejpam-6008	489	7	.	.	PUNCT
ejpam-6008	490	1	european	european	ADJ
ejpam-6008	490	2	journal	journal	PROPN
ejpam-6008	490	3	of	of	ADP
ejpam-6008	490	4	pure	pure	ADJ
ejpam-6008	490	5	and	and	CCONJ
ejpam-6008	490	6	applied	applied	ADJ
ejpam-6008	490	7	mathematics	mathematic	NOUN
ejpam-6008	490	8	,	,	PUNCT
ejpam-6008	490	9	18(1):5717	18(1):5717	NUM
ejpam-6008	490	10	,	,	PUNCT
ejpam-6008	490	11	2025	2025	NUM
ejpam-6008	490	12	.	.	PUNCT
ejpam-6008	491	1	[	[	X
ejpam-6008	491	2	70	70	NUM
ejpam-6008	491	3	]	]	X
ejpam-6008	491	4	j.	j.	PROPN
ejpam-6008	491	5	khampakdee	khampakdee	PROPN
ejpam-6008	491	6	,	,	PUNCT
ejpam-6008	491	7	a.	a.	PROPN
ejpam-6008	491	8	sama	sama	PROPN
ejpam-6008	491	9	-	-	PUNCT
ejpam-6008	491	10	ae	ae	PROPN
ejpam-6008	491	11	,	,	PUNCT
ejpam-6008	491	12	and	and	CCONJ
ejpam-6008	491	13	c.	c.	PROPN
ejpam-6008	491	14	boonpok	boonpok	PROPN
ejpam-6008	491	15	.	.	PUNCT
ejpam-6008	492	1	almost	almost	ADV
ejpam-6008	492	2	nearly	nearly	ADV
ejpam-6008	492	3	quasi	quasi	NOUN
ejpam-6008	492	4	(	(	PUNCT
ejpam-6008	492	5	τ1	τ1	NOUN
ejpam-6008	492	6	,	,	PUNCT
ejpam-6008	492	7	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	492	8	multifunctions	multifunction	NOUN
ejpam-6008	492	9	.	.	PUNCT
ejpam-6008	493	1	european	european	ADJ
ejpam-6008	493	2	journal	journal	PROPN
ejpam-6008	493	3	of	of	ADP
ejpam-6008	493	4	pure	pure	ADJ
ejpam-6008	493	5	and	and	CCONJ
ejpam-6008	493	6	applied	applied	ADJ
ejpam-6008	493	7	mathematics	mathematic	NOUN
ejpam-6008	493	8	,	,	PUNCT
ejpam-6008	493	9	18(1):5720	18(1):5720	NUM
ejpam-6008	493	10	,	,	PUNCT
ejpam-6008	493	11	2025	2025	NUM
ejpam-6008	493	12	.	.	PUNCT
ejpam-6008	494	1	[	[	X
ejpam-6008	494	2	71	71	NUM
ejpam-6008	494	3	]	]	X
ejpam-6008	494	4	p.	p.	NOUN
ejpam-6008	494	5	pue	pue	NOUN
ejpam-6008	494	6	-	-	PUNCT
ejpam-6008	494	7	on	on	ADP
ejpam-6008	494	8	,	,	PUNCT
ejpam-6008	494	9	a.	a.	PROPN
ejpam-6008	494	10	sama	sama	PROPN
ejpam-6008	494	11	-	-	PUNCT
ejpam-6008	494	12	ae	ae	PROPN
ejpam-6008	494	13	,	,	PUNCT
ejpam-6008	494	14	and	and	CCONJ
ejpam-6008	494	15	c.	c.	PROPN
ejpam-6008	494	16	boonpok	boonpok	PROPN
ejpam-6008	494	17	.	.	PUNCT
ejpam-6008	495	1	upper	upper	ADJ
ejpam-6008	495	2	and	and	CCONJ
ejpam-6008	495	3	lower	low	ADJ
ejpam-6008	495	4	weakly	weakly	ADJ
ejpam-6008	495	5	s-(τ1	s-(τ1	PROPN
ejpam-6008	495	6	,	,	PUNCT
ejpam-6008	495	7	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	495	8	multifunctions	multifunction	NOUN
ejpam-6008	495	9	.	.	PUNCT
ejpam-6008	496	1	european	european	ADJ
ejpam-6008	496	2	journal	journal	PROPN
ejpam-6008	496	3	of	of	ADP
ejpam-6008	496	4	pure	pure	ADJ
ejpam-6008	496	5	and	and	CCONJ
ejpam-6008	496	6	applied	applied	ADJ
ejpam-6008	496	7	mathematics	mathematic	NOUN
ejpam-6008	496	8	,	,	PUNCT
ejpam-6008	496	9	18(1):5718	18(1):5718	NUM
ejpam-6008	496	10	,	,	PUNCT
ejpam-6008	496	11	2025	2025	NUM
ejpam-6008	496	12	.	.	PUNCT
ejpam-6008	497	1	[	[	X
ejpam-6008	497	2	72	72	NUM
ejpam-6008	497	3	]	]	PUNCT
ejpam-6008	497	4	m.	m.	NOUN
ejpam-6008	497	5	thongmoon	thongmoon	NOUN
ejpam-6008	497	6	,	,	PUNCT
ejpam-6008	497	7	a.	a.	PROPN
ejpam-6008	497	8	sama	sama	PROPN
ejpam-6008	497	9	-	-	PUNCT
ejpam-6008	497	10	ae	ae	PROPN
ejpam-6008	497	11	,	,	PUNCT
ejpam-6008	497	12	and	and	CCONJ
ejpam-6008	497	13	c.	c.	PROPN
ejpam-6008	497	14	boonpok	boonpok	PROPN
ejpam-6008	497	15	.	.	PUNCT
ejpam-6008	498	1	upper	upper	ADJ
ejpam-6008	498	2	and	and	CCONJ
ejpam-6008	498	3	lower	low	ADJ
ejpam-6008	498	4	near	near	ADV
ejpam-6008	498	5	(	(	PUNCT
ejpam-6008	498	6	τ1	τ1	NOUN
ejpam-6008	498	7	,	,	PUNCT
ejpam-6008	498	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6008	498	9	.	.	PUNCT
ejpam-6008	499	1	european	european	PROPN
ejpam-6008	499	2	journal	journal	PROPN
ejpam-6008	499	3	of	of	ADP
ejpam-6008	499	4	pure	pure	ADJ
ejpam-6008	499	5	and	and	CCONJ
ejpam-6008	499	6	applied	applied	ADJ
ejpam-6008	499	7	mathematics	mathematic	NOUN
ejpam-6008	499	8	,	,	PUNCT
ejpam-6008	499	9	18(1):5633	18(1):5633	NUM
ejpam-6008	499	10	,	,	PUNCT
ejpam-6008	499	11	2025	2025	NUM
ejpam-6008	499	12	.	.	PUNCT
ejpam-6008	500	1	[	[	X
ejpam-6008	500	2	73	73	NUM
ejpam-6008	500	3	]	]	PUNCT
ejpam-6008	500	4	m.	m.	NOUN
ejpam-6008	500	5	chiangpradit	chiangpradit	NOUN
ejpam-6008	500	6	,	,	PUNCT
ejpam-6008	500	7	s.	s.	PROPN
ejpam-6008	500	8	sompong	sompong	PROPN
ejpam-6008	500	9	,	,	PUNCT
ejpam-6008	500	10	and	and	CCONJ
ejpam-6008	500	11	c.	c.	PROPN
ejpam-6008	500	12	boonpok	boonpok	PROPN
ejpam-6008	500	13	.	.	PUNCT
ejpam-6008	501	1	upper	upper	ADJ
ejpam-6008	501	2	and	and	CCONJ
ejpam-6008	501	3	lower	low	ADJ
ejpam-6008	501	4	almost	almost	ADV
ejpam-6008	501	5	quasi	quasi	NOUN
ejpam-6008	501	6	(	(	PUNCT
ejpam-6008	501	7	τ1	τ1	NOUN
ejpam-6008	501	8	,	,	PUNCT
ejpam-6008	501	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6008	501	10	.	.	PUNCT
ejpam-6008	501	11	asia	asia	PROPN
ejpam-6008	501	12	pacific	pacific	PROPN
ejpam-6008	501	13	journal	journal	PROPN
ejpam-6008	501	14	of	of	ADP
ejpam-6008	501	15	mathematics	mathematic	NOUN
ejpam-6008	501	16	,	,	PUNCT
ejpam-6008	501	17	12:12	12:12	NUM
ejpam-6008	501	18	,	,	PUNCT
ejpam-6008	501	19	2025	2025	NUM
ejpam-6008	501	20	.	.	PUNCT
ejpam-6008	502	1	[	[	X
ejpam-6008	502	2	74	74	NUM
ejpam-6008	502	3	]	]	PUNCT
ejpam-6008	502	4	e.	e.	PROPN
ejpam-6008	502	5	ekici	ekici	PROPN
ejpam-6008	502	6	,	,	PUNCT
ejpam-6008	502	7	s.	s.	PROPN
ejpam-6008	502	8	jafari	jafari	PROPN
ejpam-6008	502	9	,	,	PUNCT
ejpam-6008	502	10	and	and	CCONJ
ejpam-6008	502	11	v.	v.	ADP
ejpam-6008	502	12	popa	popa	NOUN
ejpam-6008	502	13	.	.	PUNCT
ejpam-6008	503	1	on	on	ADP
ejpam-6008	503	2	contra	contra	PROPN
ejpam-6008	503	3	-	-	ADJ
ejpam-6008	503	4	precontinuous	precontinuous	ADJ
ejpam-6008	503	5	and	and	CCONJ
ejpam-6008	503	6	almost	almost	ADV
ejpam-6008	503	7	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6008	503	8	multifunctions	multifunction	NOUN
ejpam-6008	503	9	.	.	PUNCT
ejpam-6008	504	1	journal	journal	PROPN
ejpam-6008	504	2	of	of	ADP
ejpam-6008	504	3	advanced	advanced	ADJ
ejpam-6008	504	4	research	research	NOUN
ejpam-6008	504	5	in	in	ADP
ejpam-6008	504	6	pure	pure	ADJ
ejpam-6008	504	7	mathematics	mathematic	NOUN
ejpam-6008	504	8	,	,	PUNCT
ejpam-6008	504	9	2(1):11–25	2(1):11–25	NUM
ejpam-6008	504	10	,	,	PUNCT
ejpam-6008	504	11	2010	2010	NUM
ejpam-6008	504	12	.	.	PUNCT
ejpam-6008	505	1	[	[	X
ejpam-6008	505	2	75	75	NUM
ejpam-6008	505	3	]	]	PUNCT
ejpam-6008	505	4	e.	e.	PROPN
ejpam-6008	505	5	ekici	ekici	PROPN
ejpam-6008	505	6	,	,	PUNCT
ejpam-6008	505	7	s.	s.	PROPN
ejpam-6008	505	8	jafari	jafari	PROPN
ejpam-6008	505	9	,	,	PUNCT
ejpam-6008	505	10	and	and	CCONJ
ejpam-6008	505	11	v.	v.	ADP
ejpam-6008	505	12	popa	popa	NOUN
ejpam-6008	505	13	.	.	PUNCT
ejpam-6008	506	1	on	on	ADP
ejpam-6008	506	2	almost	almost	ADV
ejpam-6008	506	3	contra	contra	ADJ
ejpam-6008	506	4	-	-	ADJ
ejpam-6008	506	5	continuous	continuous	ADJ
ejpam-6008	506	6	multifunctions	multifunction	NOUN
ejpam-6008	506	7	.	.	PUNCT
ejpam-6008	507	1	lobachevskii	lobachevskii	PROPN
ejpam-6008	507	2	journal	journal	PROPN
ejpam-6008	507	3	of	of	ADP
ejpam-6008	507	4	mathematics	mathematic	NOUN
ejpam-6008	507	5	,	,	PUNCT
ejpam-6008	507	6	30(2):124–131	30(2):124–131	PROPN
ejpam-6008	507	7	,	,	PUNCT
ejpam-6008	507	8	2009	2009	NUM
ejpam-6008	507	9	.	.	PUNCT
ejpam-6008	508	1	[	[	X
ejpam-6008	508	2	76	76	NUM
ejpam-6008	508	3	]	]	X
ejpam-6008	508	4	c.	c.	PROPN
ejpam-6008	508	5	boonpok	boonpok	PROPN
ejpam-6008	508	6	and	and	CCONJ
ejpam-6008	508	7	j.	j.	PROPN
ejpam-6008	508	8	khampakdee	khampakdee	PROPN
ejpam-6008	508	9	.	.	PUNCT
ejpam-6008	509	1	upper	upper	ADJ
ejpam-6008	509	2	and	and	CCONJ
ejpam-6008	509	3	lower	low	ADJ
ejpam-6008	509	4	almost	almost	ADV
ejpam-6008	509	5	contra-(λ	contra-(λ	PROPN
ejpam-6008	509	6	,	,	PUNCT
ejpam-6008	509	7	sp)-continuity	sp)-continuity	NOUN
ejpam-6008	509	8	.	.	PUNCT
ejpam-6008	510	1	european	european	PROPN
ejpam-6008	510	2	journal	journal	PROPN
ejpam-6008	510	3	of	of	ADP
ejpam-6008	510	4	pure	pure	ADJ
ejpam-6008	510	5	and	and	CCONJ
ejpam-6008	510	6	applied	applied	ADJ
ejpam-6008	510	7	mathematics	mathematic	NOUN
ejpam-6008	510	8	,	,	PUNCT
ejpam-6008	510	9	16(1):156–168	16(1):156–168	PROPN
ejpam-6008	510	10	,	,	PUNCT
ejpam-6008	510	11	2023	2023	NUM
ejpam-6008	510	12	.	.	PUNCT
ejpam-6008	511	1	[	[	X
ejpam-6008	511	2	77	77	NUM
ejpam-6008	511	3	]	]	X
ejpam-6008	511	4	c.	c.	PROPN
ejpam-6008	511	5	boonpok	boonpok	PROPN
ejpam-6008	511	6	,	,	PUNCT
ejpam-6008	511	7	c.	c.	PROPN
ejpam-6008	511	8	viriyapong	viriyapong	PROPN
ejpam-6008	511	9	,	,	PUNCT
ejpam-6008	511	10	and	and	CCONJ
ejpam-6008	511	11	m.	m.	NOUN
ejpam-6008	511	12	thongmoon	thongmoon	NOUN
ejpam-6008	511	13	.	.	PUNCT
ejpam-6008	512	1	on	on	ADP
ejpam-6008	512	2	upper	upper	ADJ
ejpam-6008	512	3	and	and	CCONJ
ejpam-6008	512	4	lower	low	ADJ
ejpam-6008	512	5	(	(	PUNCT
ejpam-6008	512	6	τ1	τ1	NOUN
ejpam-6008	512	7	,	,	PUNCT
ejpam-6008	512	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6008	512	9	multifunctions	multifunction	NOUN
ejpam-6008	512	10	.	.	PUNCT
ejpam-6008	513	1	journal	journal	PROPN
ejpam-6008	513	2	of	of	ADP
ejpam-6008	513	3	mathematics	mathematics	PROPN
ejpam-6008	513	4	and	and	CCONJ
ejpam-6008	513	5	computer	computer	NOUN
ejpam-6008	513	6	science	science	NOUN
ejpam-6008	513	7	,	,	PUNCT
ejpam-6008	513	8	18:282–293	18:282–293	NUM
ejpam-6008	513	9	,	,	PUNCT
ejpam-6008	513	10	2018	2018	NUM
ejpam-6008	513	11	.	.	PUNCT
ejpam-6008	514	1	[	[	X
ejpam-6008	514	2	78	78	NUM
ejpam-6008	514	3	]	]	X
ejpam-6008	514	4	n.	n.	PROPN
ejpam-6008	514	5	viriyapong	viriyapong	PROPN
ejpam-6008	514	6	,	,	PUNCT
ejpam-6008	514	7	s.	s.	PROPN
ejpam-6008	514	8	sompong	sompong	PROPN
ejpam-6008	514	9	,	,	PUNCT
ejpam-6008	514	10	and	and	CCONJ
ejpam-6008	514	11	c.	c.	PROPN
ejpam-6008	514	12	boonpok	boonpok	PROPN
ejpam-6008	514	13	.	.	PUNCT
ejpam-6008	515	1	(	(	PUNCT
ejpam-6008	515	2	τ1	τ1	NOUN
ejpam-6008	515	3	,	,	PUNCT
ejpam-6008	515	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6008	515	5	disconnectedness	disconnectedness	NOUN
ejpam-6008	515	6	in	in	ADP
ejpam-6008	515	7	bitopological	bitopological	ADJ
ejpam-6008	515	8	spaces	space	NOUN
ejpam-6008	515	9	.	.	PUNCT
ejpam-6008	516	1	international	international	ADJ
ejpam-6008	516	2	journal	journal	PROPN
ejpam-6008	516	3	of	of	ADP
ejpam-6008	516	4	mathematics	mathematic	NOUN
ejpam-6008	516	5	and	and	CCONJ
ejpam-6008	516	6	computer	computer	NOUN
ejpam-6008	516	7	science	science	NOUN
ejpam-6008	516	8	,	,	PUNCT
ejpam-6008	516	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6008	516	10	,	,	PUNCT
ejpam-6008	516	11	2024	2024	NUM
ejpam-6008	516	12	.	.	PUNCT
ejpam-6008	517	1	[	[	X
ejpam-6008	517	2	79	79	NUM
ejpam-6008	517	3	]	]	X
ejpam-6008	517	4	c.	c.	PROPN
ejpam-6008	517	5	viriyapong	viriyapong	PROPN
ejpam-6008	517	6	and	and	CCONJ
ejpam-6008	517	7	c.	c.	PROPN
ejpam-6008	517	8	boonpok	boonpok	PROPN
ejpam-6008	517	9	.	.	PUNCT
ejpam-6008	518	1	(	(	PUNCT
ejpam-6008	518	2	τ1	τ1	NOUN
ejpam-6008	518	3	,	,	PUNCT
ejpam-6008	518	4	τ2)α	τ2)α	NOUN
ejpam-6008	518	5	-	-	PUNCT
ejpam-6008	518	6	continuity	continuity	NOUN
ejpam-6008	518	7	for	for	ADP
ejpam-6008	518	8	multifunctions	multifunction	NOUN
ejpam-6008	518	9	.	.	PUNCT
ejpam-6008	519	1	journal	journal	PROPN
ejpam-6008	519	2	of	of	ADP
ejpam-6008	519	3	mathematics	mathematic	NOUN
ejpam-6008	519	4	,	,	PUNCT
ejpam-6008	519	5	2020:6285763	2020:6285763	NUM
ejpam-6008	519	6	,	,	PUNCT
ejpam-6008	519	7	2020	2020	NUM
ejpam-6008	519	8	.	.	PUNCT
ejpam-6008	520	1	n.	n.	PROPN
ejpam-6008	520	2	viriyapong	viriyapong	PROPN
ejpam-6008	520	3	,	,	PUNCT
ejpam-6008	520	4	a.	a.	PROPN
ejpam-6008	520	5	sama	sama	PROPN
ejpam-6008	520	6	-	-	PUNCT
ejpam-6008	520	7	ae	ae	PROPN
ejpam-6008	520	8	,	,	PUNCT
ejpam-6008	520	9	c.	c.	PROPN
ejpam-6008	520	10	boonpok	boonpok	PROPN
ejpam-6008	520	11	/	/	SYM
ejpam-6008	520	12	eur	eur	PROPN
ejpam-6008	520	13	.	.	PUNCT
ejpam-6008	521	1	j.	j.	PROPN
ejpam-6008	521	2	pure	pure	PROPN
ejpam-6008	521	3	appl	appl	PROPN
ejpam-6008	521	4	.	.	PROPN
ejpam-6008	521	5	math	math	PROPN
ejpam-6008	521	6	,	,	PUNCT
ejpam-6008	521	7	18	18	NUM
ejpam-6008	521	8	(	(	PUNCT
ejpam-6008	521	9	2	2	NUM
ejpam-6008	521	10	)	)	PUNCT
ejpam-6008	521	11	(	(	PUNCT
ejpam-6008	521	12	2025	2025	NUM
ejpam-6008	521	13	)	)	PUNCT
ejpam-6008	521	14	,	,	PUNCT
ejpam-6008	521	15	6008	6008	NUM
ejpam-6008	521	16	15	15	NUM
ejpam-6008	521	17	of	of	ADP
ejpam-6008	521	18	15	15	NUM
ejpam-6008	521	19	[	[	SYM
ejpam-6008	521	20	80	80	NUM
ejpam-6008	521	21	]	]	X
ejpam-6008	521	22	n.	n.	NOUN
ejpam-6008	521	23	srisarakham	srisarakham	PROPN
ejpam-6008	521	24	,	,	PUNCT
ejpam-6008	521	25	s.	s.	PROPN
ejpam-6008	521	26	sompong	sompong	PROPN
ejpam-6008	521	27	,	,	PUNCT
ejpam-6008	521	28	and	and	CCONJ
ejpam-6008	521	29	c.	c.	PROPN
ejpam-6008	521	30	boonpok	boonpok	PROPN
ejpam-6008	521	31	.	.	PUNCT
ejpam-6008	522	1	characterizations	characterization	NOUN
ejpam-6008	522	2	of	of	ADP
ejpam-6008	522	3	contra-(τ1	contra-(τ1	NOUN
ejpam-6008	522	4	,	,	PUNCT
ejpam-6008	522	5	τ2)continuous	τ2)continuous	ADJ
ejpam-6008	522	6	functions	function	NOUN
ejpam-6008	522	7	.	.	PUNCT
ejpam-6008	523	1	(	(	PUNCT
ejpam-6008	523	2	submitted	submit	VERB
ejpam-6008	523	3	)	)	PUNCT
ejpam-6008	523	4	.	.	PUNCT