id	sid	tid	token	lemma	pos
ejpam-5649	1	1	european	european	PROPN
ejpam-5649	1	2	journal	journal	PROPN
ejpam-5649	1	3	of	of	ADP
ejpam-5649	1	4	pure	pure	ADJ
ejpam-5649	1	5	and	and	CCONJ
ejpam-5649	1	6	applied	applied	ADJ
ejpam-5649	1	7	mathematics	mathematic	NOUN
ejpam-5649	1	8	2025	2025	NUM
ejpam-5649	1	9	,	,	PUNCT
ejpam-5649	1	10	vol	vol	NOUN
ejpam-5649	1	11	.	.	PROPN
ejpam-5649	1	12	18	18	NUM
ejpam-5649	1	13	,	,	PUNCT
ejpam-5649	1	14	issue	issue	NOUN
ejpam-5649	1	15	1	1	NUM
ejpam-5649	1	16	,	,	PUNCT
ejpam-5649	1	17	article	article	NOUN
ejpam-5649	1	18	number	number	NOUN
ejpam-5649	1	19	5649	5649	NUM
ejpam-5649	1	20	issn	issn	PROPN
ejpam-5649	1	21	1307	1307	NUM
ejpam-5649	1	22	-	-	SYM
ejpam-5649	1	23	5543	5543	NUM
ejpam-5649	1	24	–	–	PUNCT
ejpam-5649	1	25	ejpam.com	ejpam.com	X
ejpam-5649	1	26	published	publish	VERB
ejpam-5649	1	27	by	by	ADP
ejpam-5649	1	28	new	new	PROPN
ejpam-5649	1	29	york	york	PROPN
ejpam-5649	1	30	business	business	PROPN
ejpam-5649	1	31	global	global	PROPN
ejpam-5649	1	32	rarely	rarely	ADV
ejpam-5649	1	33	s-(τ1	s-(τ1	NOUN
ejpam-5649	1	34	,	,	PUNCT
ejpam-5649	1	35	τ2)p	τ2)p	ADJ
ejpam-5649	1	36	-	-	PUNCT
ejpam-5649	1	37	continuous	continuous	ADJ
ejpam-5649	1	38	multifunctions	multifunction	NOUN
ejpam-5649	1	39	butsakorn	butsakorn	PROPN
ejpam-5649	1	40	kong	kong	PROPN
ejpam-5649	1	41	-	-	PUNCT
ejpam-5649	1	42	ied1	ied1	PROPN
ejpam-5649	1	43	,	,	PUNCT
ejpam-5649	1	44	supunnee	supunnee	PROPN
ejpam-5649	1	45	sompong2	sompong2	PROPN
ejpam-5649	1	46	,	,	PUNCT
ejpam-5649	1	47	chawalit	chawalit	VERB
ejpam-5649	1	48	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5649	1	49	1	1	NUM
ejpam-5649	1	50	mathematics	mathematic	NOUN
ejpam-5649	1	51	and	and	CCONJ
ejpam-5649	1	52	applied	apply	VERB
ejpam-5649	1	53	mathematics	mathematics	PROPN
ejpam-5649	1	54	research	research	NOUN
ejpam-5649	1	55	unit	unit	NOUN
ejpam-5649	1	56	,	,	PUNCT
ejpam-5649	1	57	department	department	NOUN
ejpam-5649	1	58	of	of	ADP
ejpam-5649	1	59	mathematics	mathematic	NOUN
ejpam-5649	1	60	,	,	PUNCT
ejpam-5649	1	61	faculty	faculty	NOUN
ejpam-5649	1	62	of	of	ADP
ejpam-5649	1	63	science	science	NOUN
ejpam-5649	1	64	,	,	PUNCT
ejpam-5649	1	65	mahasarakham	mahasarakham	PROPN
ejpam-5649	1	66	university	university	PROPN
ejpam-5649	1	67	,	,	PUNCT
ejpam-5649	1	68	maha	maha	PROPN
ejpam-5649	1	69	sarakham	sarakham	PROPN
ejpam-5649	1	70	,	,	PUNCT
ejpam-5649	1	71	44150	44150	NUM
ejpam-5649	1	72	,	,	PUNCT
ejpam-5649	1	73	thailand	thailand	PROPN
ejpam-5649	1	74	2	2	NUM
ejpam-5649	1	75	department	department	NOUN
ejpam-5649	1	76	of	of	ADP
ejpam-5649	1	77	mathematics	mathematic	NOUN
ejpam-5649	1	78	and	and	CCONJ
ejpam-5649	1	79	statistics	statistic	NOUN
ejpam-5649	1	80	,	,	PUNCT
ejpam-5649	1	81	faculty	faculty	NOUN
ejpam-5649	1	82	of	of	ADP
ejpam-5649	1	83	science	science	NOUN
ejpam-5649	1	84	and	and	CCONJ
ejpam-5649	1	85	technology	technology	NOUN
ejpam-5649	1	86	,	,	PUNCT
ejpam-5649	1	87	sakon	sakon	PROPN
ejpam-5649	1	88	nakhon	nakhon	PROPN
ejpam-5649	1	89	rajbhat	rajbhat	PROPN
ejpam-5649	1	90	university	university	PROPN
ejpam-5649	1	91	,	,	PUNCT
ejpam-5649	1	92	sakon	sakon	PROPN
ejpam-5649	1	93	nakhon	nakhon	PROPN
ejpam-5649	1	94	,	,	PUNCT
ejpam-5649	1	95	47000	47000	NUM
ejpam-5649	1	96	,	,	PUNCT
ejpam-5649	1	97	thailand	thailand	PROPN
ejpam-5649	1	98	abstract	abstract	NOUN
ejpam-5649	1	99	.	.	PUNCT
ejpam-5649	2	1	this	this	DET
ejpam-5649	2	2	paper	paper	NOUN
ejpam-5649	2	3	is	be	AUX
ejpam-5649	2	4	concerned	concern	VERB
ejpam-5649	2	5	with	with	ADP
ejpam-5649	2	6	the	the	DET
ejpam-5649	2	7	concepts	concept	NOUN
ejpam-5649	2	8	of	of	ADP
ejpam-5649	2	9	upper	upper	ADJ
ejpam-5649	2	10	rarely	rarely	ADV
ejpam-5649	2	11	s-(τ1	s-(τ1	NOUN
ejpam-5649	2	12	,	,	PUNCT
ejpam-5649	2	13	τ2)p	τ2)p	ADJ
ejpam-5649	2	14	-	-	ADJ
ejpam-5649	2	15	continuous	continuous	ADJ
ejpam-5649	2	16	multifunctions	multifunction	NOUN
ejpam-5649	2	17	and	and	CCONJ
ejpam-5649	2	18	lower	low	ADJ
ejpam-5649	2	19	rarely	rarely	ADV
ejpam-5649	2	20	s-(τ1	s-(τ1	NOUN
ejpam-5649	2	21	,	,	PUNCT
ejpam-5649	2	22	τ2)p	τ2)p	ADJ
ejpam-5649	2	23	-	-	PUNCT
ejpam-5649	2	24	continuous	continuous	ADJ
ejpam-5649	2	25	multifunctions	multifunction	NOUN
ejpam-5649	2	26	.	.	PUNCT
ejpam-5649	3	1	furthermore	furthermore	ADV
ejpam-5649	3	2	,	,	PUNCT
ejpam-5649	3	3	some	some	DET
ejpam-5649	3	4	characterizations	characterization	NOUN
ejpam-5649	3	5	and	and	CCONJ
ejpam-5649	3	6	several	several	ADJ
ejpam-5649	3	7	properties	property	NOUN
ejpam-5649	3	8	concerning	concern	VERB
ejpam-5649	3	9	upper	upper	ADJ
ejpam-5649	3	10	rarely	rarely	ADV
ejpam-5649	3	11	s-(τ1	s-(τ1	NOUN
ejpam-5649	3	12	,	,	PUNCT
ejpam-5649	3	13	τ2)p	τ2)p	ADJ
ejpam-5649	3	14	-	-	ADJ
ejpam-5649	3	15	continuous	continuous	ADJ
ejpam-5649	3	16	multifunctions	multifunction	NOUN
ejpam-5649	3	17	and	and	CCONJ
ejpam-5649	3	18	lower	low	ADJ
ejpam-5649	3	19	rarely	rarely	ADV
ejpam-5649	3	20	s-(τ1	s-(τ1	NOUN
ejpam-5649	3	21	,	,	PUNCT
ejpam-5649	3	22	τ2)p	τ2)p	ADJ
ejpam-5649	3	23	-	-	PUNCT
ejpam-5649	3	24	continuous	continuous	ADJ
ejpam-5649	3	25	multifunctions	multifunction	NOUN
ejpam-5649	3	26	are	be	AUX
ejpam-5649	3	27	established	establish	VERB
ejpam-5649	3	28	.	.	PUNCT
ejpam-5649	4	1	2020	2020	NUM
ejpam-5649	4	2	mathematics	mathematics	PROPN
ejpam-5649	4	3	subject	subject	NOUN
ejpam-5649	4	4	classifications	classification	NOUN
ejpam-5649	4	5	:	:	PUNCT
ejpam-5649	4	6	54c08	54c08	NUM
ejpam-5649	4	7	,	,	PUNCT
ejpam-5649	4	8	54c60	54c60	NUM
ejpam-5649	4	9	key	key	ADJ
ejpam-5649	4	10	words	word	NOUN
ejpam-5649	4	11	and	and	CCONJ
ejpam-5649	4	12	phrases	phrase	NOUN
ejpam-5649	4	13	:	:	PUNCT
ejpam-5649	4	14	(	(	PUNCT
ejpam-5649	4	15	τ1	τ1	NOUN
ejpam-5649	4	16	,	,	PUNCT
ejpam-5649	4	17	τ2)p	τ2)p	ADJ
ejpam-5649	4	18	-	-	PUNCT
ejpam-5649	4	19	open	open	ADJ
ejpam-5649	4	20	set	set	NOUN
ejpam-5649	4	21	,	,	PUNCT
ejpam-5649	4	22	upper	upper	ADJ
ejpam-5649	4	23	rarely	rarely	ADV
ejpam-5649	4	24	s-(τ1	s-(τ1	NOUN
ejpam-5649	4	25	,	,	PUNCT
ejpam-5649	4	26	τ2)p	τ2)p	ADJ
ejpam-5649	4	27	-	-	PUNCT
ejpam-5649	4	28	continuous	continuous	ADJ
ejpam-5649	4	29	multifunction	multifunction	NOUN
ejpam-5649	4	30	,	,	PUNCT
ejpam-5649	4	31	lower	low	ADJ
ejpam-5649	4	32	rarely	rarely	ADV
ejpam-5649	4	33	s-(τ1	s-(τ1	NOUN
ejpam-5649	4	34	,	,	PUNCT
ejpam-5649	4	35	τ2)p	τ2)p	ADJ
ejpam-5649	4	36	-	-	PUNCT
ejpam-5649	4	37	continuous	continuous	ADJ
ejpam-5649	4	38	multifunction	multifunction	NOUN
ejpam-5649	4	39	1	1	NUM
ejpam-5649	4	40	.	.	PUNCT
ejpam-5649	5	1	introduction	introduction	NOUN
ejpam-5649	5	2	weaker	weak	ADJ
ejpam-5649	5	3	and	and	CCONJ
ejpam-5649	5	4	stronger	strong	ADJ
ejpam-5649	5	5	forms	form	NOUN
ejpam-5649	5	6	of	of	ADP
ejpam-5649	5	7	open	open	ADJ
ejpam-5649	5	8	sets	set	NOUN
ejpam-5649	5	9	such	such	ADJ
ejpam-5649	5	10	as	as	ADP
ejpam-5649	5	11	semi	semi	ADJ
ejpam-5649	5	12	-	-	ADJ
ejpam-5649	5	13	open	open	ADJ
ejpam-5649	5	14	sets	set	NOUN
ejpam-5649	5	15	[	[	X
ejpam-5649	5	16	48	48	NUM
ejpam-5649	5	17	]	]	PUNCT
ejpam-5649	5	18	,	,	PUNCT
ejpam-5649	5	19	preopen	preopen	ADJ
ejpam-5649	5	20	sets	set	NOUN
ejpam-5649	5	21	[	[	X
ejpam-5649	5	22	50	50	NUM
ejpam-5649	5	23	]	]	PUNCT
ejpam-5649	5	24	,	,	PUNCT
ejpam-5649	5	25	α	α	X
ejpam-5649	5	26	-	-	ADJ
ejpam-5649	5	27	open	open	ADJ
ejpam-5649	5	28	sets	set	NOUN
ejpam-5649	5	29	[	[	X
ejpam-5649	5	30	51	51	NUM
ejpam-5649	5	31	]	]	PUNCT
ejpam-5649	5	32	,	,	PUNCT
ejpam-5649	5	33	β	β	X
ejpam-5649	5	34	-	-	ADJ
ejpam-5649	5	35	open	open	ADJ
ejpam-5649	5	36	sets	set	NOUN
ejpam-5649	5	37	[	[	X
ejpam-5649	5	38	38	38	NUM
ejpam-5649	5	39	]	]	PUNCT
ejpam-5649	5	40	,	,	PUNCT
ejpam-5649	5	41	δ	δ	PROPN
ejpam-5649	5	42	-	-	ADJ
ejpam-5649	5	43	open	open	ADJ
ejpam-5649	5	44	sets	set	NOUN
ejpam-5649	5	45	[	[	X
ejpam-5649	5	46	67	67	NUM
ejpam-5649	5	47	]	]	PUNCT
ejpam-5649	5	48	and	and	CCONJ
ejpam-5649	5	49	θ	θ	ADJ
ejpam-5649	5	50	-	-	ADJ
ejpam-5649	5	51	open	open	ADJ
ejpam-5649	5	52	sets	set	NOUN
ejpam-5649	5	53	[	[	X
ejpam-5649	5	54	67	67	NUM
ejpam-5649	5	55	]	]	PUNCT
ejpam-5649	5	56	play	play	VERB
ejpam-5649	5	57	an	an	DET
ejpam-5649	5	58	important	important	ADJ
ejpam-5649	5	59	role	role	NOUN
ejpam-5649	5	60	in	in	ADP
ejpam-5649	5	61	the	the	DET
ejpam-5649	5	62	research	research	NOUN
ejpam-5649	5	63	of	of	ADP
ejpam-5649	5	64	generalizations	generalization	NOUN
ejpam-5649	5	65	of	of	ADP
ejpam-5649	5	66	continuity	continuity	NOUN
ejpam-5649	5	67	in	in	ADP
ejpam-5649	5	68	topological	topological	ADJ
ejpam-5649	5	69	spaces	space	NOUN
ejpam-5649	5	70	.	.	PUNCT
ejpam-5649	6	1	by	by	ADP
ejpam-5649	6	2	using	use	VERB
ejpam-5649	6	3	these	these	DET
ejpam-5649	6	4	sets	set	NOUN
ejpam-5649	6	5	,	,	PUNCT
ejpam-5649	6	6	many	many	ADJ
ejpam-5649	6	7	authors	author	NOUN
ejpam-5649	6	8	introduced	introduce	VERB
ejpam-5649	6	9	and	and	CCONJ
ejpam-5649	6	10	studied	study	VERB
ejpam-5649	6	11	various	various	ADJ
ejpam-5649	6	12	types	type	NOUN
ejpam-5649	6	13	of	of	ADP
ejpam-5649	6	14	continuity	continuity	NOUN
ejpam-5649	6	15	for	for	ADP
ejpam-5649	6	16	functions	function	NOUN
ejpam-5649	6	17	and	and	CCONJ
ejpam-5649	6	18	multifunctions	multifunction	NOUN
ejpam-5649	6	19	.	.	PUNCT
ejpam-5649	7	1	viriyapong	viriyapong	PROPN
ejpam-5649	7	2	and	and	CCONJ
ejpam-5649	7	3	boonpok	boonpok	VERB
ejpam-5649	8	1	[	[	X
ejpam-5649	8	2	69	69	NUM
ejpam-5649	8	3	]	]	PUNCT
ejpam-5649	8	4	investigated	investigate	VERB
ejpam-5649	8	5	some	some	DET
ejpam-5649	8	6	characterizations	characterization	NOUN
ejpam-5649	8	7	of	of	ADP
ejpam-5649	8	8	(	(	PUNCT
ejpam-5649	8	9	λ	λ	PROPN
ejpam-5649	8	10	,	,	PUNCT
ejpam-5649	8	11	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	8	12	functions	function	NOUN
ejpam-5649	8	13	by	by	ADP
ejpam-5649	8	14	utilizing	utilize	VERB
ejpam-5649	8	15	the	the	DET
ejpam-5649	8	16	notions	notion	NOUN
ejpam-5649	8	17	of	of	ADP
ejpam-5649	8	18	(	(	PUNCT
ejpam-5649	8	19	λ	λ	PROPN
ejpam-5649	8	20	,	,	PUNCT
ejpam-5649	8	21	sp)-open	sp)-open	ADJ
ejpam-5649	8	22	sets	set	NOUN
ejpam-5649	8	23	and	and	CCONJ
ejpam-5649	8	24	(	(	PUNCT
ejpam-5649	8	25	λ	λ	PROPN
ejpam-5649	8	26	,	,	PUNCT
ejpam-5649	8	27	sp)closed	sp)close	VERB
ejpam-5649	8	28	sets	set	NOUN
ejpam-5649	8	29	due	due	ADP
ejpam-5649	8	30	to	to	ADP
ejpam-5649	8	31	boonpok	boonpok	NOUN
ejpam-5649	8	32	and	and	CCONJ
ejpam-5649	8	33	khampakdee	khampakdee	NOUN
ejpam-5649	8	34	[	[	X
ejpam-5649	8	35	12	12	NUM
ejpam-5649	8	36	]	]	PUNCT
ejpam-5649	8	37	.	.	PUNCT
ejpam-5649	9	1	dungthaisong	dungthaisong	NOUN
ejpam-5649	9	2	et	et	PROPN
ejpam-5649	9	3	al	al	PROPN
ejpam-5649	9	4	.	.	PUNCT
ejpam-5649	10	1	[	[	X
ejpam-5649	10	2	35	35	NUM
ejpam-5649	10	3	]	]	PUNCT
ejpam-5649	10	4	introduced	introduce	VERB
ejpam-5649	10	5	and	and	CCONJ
ejpam-5649	10	6	studied	study	VERB
ejpam-5649	10	7	the	the	DET
ejpam-5649	10	8	concept	concept	NOUN
ejpam-5649	10	9	of	of	ADP
ejpam-5649	10	10	g(m	g(m	ADJ
ejpam-5649	10	11	,	,	PUNCT
ejpam-5649	10	12	n)-continuous	n)-continuous	ADJ
ejpam-5649	10	13	functions	function	NOUN
ejpam-5649	10	14	.	.	PUNCT
ejpam-5649	11	1	duangphui	duangphui	NOUN
ejpam-5649	11	2	et	et	PROPN
ejpam-5649	11	3	al	al	PROPN
ejpam-5649	11	4	.	.	PUNCT
ejpam-5649	12	1	[	[	X
ejpam-5649	12	2	34	34	NUM
ejpam-5649	12	3	]	]	PUNCT
ejpam-5649	12	4	introduced	introduce	VERB
ejpam-5649	12	5	and	and	CCONJ
ejpam-5649	12	6	investigated	investigate	VERB
ejpam-5649	12	7	the	the	DET
ejpam-5649	12	8	notion	notion	NOUN
ejpam-5649	12	9	of	of	ADP
ejpam-5649	12	10	(	(	PUNCT
ejpam-5649	12	11	µ	µ	NOUN
ejpam-5649	12	12	,	,	PUNCT
ejpam-5649	12	13	µ′)(m	µ′)(m	VERB
ejpam-5649	12	14	,	,	PUNCT
ejpam-5649	12	15	n)-continuous	n)-continuous	ADJ
ejpam-5649	12	16	functions	function	NOUN
ejpam-5649	12	17	.	.	PUNCT
ejpam-5649	13	1	moreover	moreover	ADV
ejpam-5649	13	2	,	,	PUNCT
ejpam-5649	13	3	some	some	DET
ejpam-5649	13	4	characterizations	characterization	NOUN
ejpam-5649	13	5	of	of	ADP
ejpam-5649	13	6	almost	almost	ADV
ejpam-5649	13	7	(	(	PUNCT
ejpam-5649	13	8	λ	λ	PROPN
ejpam-5649	13	9	,	,	PUNCT
ejpam-5649	13	10	p)-continuous	p)-continuous	ADJ
ejpam-5649	13	11	functions	function	NOUN
ejpam-5649	13	12	,	,	PUNCT
ejpam-5649	13	13	strongly	strongly	ADV
ejpam-5649	13	14	θ(λ	θ(λ	PROPN
ejpam-5649	13	15	,	,	PUNCT
ejpam-5649	13	16	p)-continuous	p)-continuous	ADJ
ejpam-5649	13	17	functions	function	NOUN
ejpam-5649	13	18	,	,	PUNCT
ejpam-5649	13	19	almost	almost	ADV
ejpam-5649	13	20	strongly	strongly	ADV
ejpam-5649	13	21	θ(λ	θ(λ	VERB
ejpam-5649	13	22	,	,	PUNCT
ejpam-5649	13	23	p)-continuous	p)-continuous	ADJ
ejpam-5649	13	24	functions	function	NOUN
ejpam-5649	13	25	,	,	PUNCT
ejpam-5649	13	26	θ(λ	θ(λ	PROPN
ejpam-5649	13	27	,	,	PUNCT
ejpam-5649	13	28	p)-continuous	p)-continuous	ADJ
ejpam-5649	13	29	functions	function	NOUN
ejpam-5649	13	30	,	,	PUNCT
ejpam-5649	13	31	weakly	weakly	ADJ
ejpam-5649	13	32	(	(	PUNCT
ejpam-5649	13	33	λ	λ	PROPN
ejpam-5649	13	34	,	,	PUNCT
ejpam-5649	13	35	b)-continuous	b)-continuous	ADJ
ejpam-5649	13	36	functions	function	NOUN
ejpam-5649	13	37	,	,	PUNCT
ejpam-5649	13	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5649	13	39	functions	function	NOUN
ejpam-5649	13	40	,	,	PUNCT
ejpam-5649	13	41	(	(	PUNCT
ejpam-5649	13	42	λ	λ	NOUN
ejpam-5649	13	43	,	,	PUNCT
ejpam-5649	13	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5649	13	45	functions	function	NOUN
ejpam-5649	13	46	,	,	PUNCT
ejpam-5649	13	47	⋆-continuous	⋆-continuous	ADJ
ejpam-5649	13	48	functions	function	NOUN
ejpam-5649	13	49	,	,	PUNCT
ejpam-5649	13	50	θ	θ	PROPN
ejpam-5649	13	51	-	-	ADJ
ejpam-5649	13	52	i	i	NOUN
ejpam-5649	13	53	-continuous	-continuous	ADJ
ejpam-5649	13	54	functions	function	NOUN
ejpam-5649	13	55	,	,	PUNCT
ejpam-5649	13	56	almost	almost	ADV
ejpam-5649	13	57	(	(	PUNCT
ejpam-5649	13	58	g	g	NOUN
ejpam-5649	13	59	,	,	PUNCT
ejpam-5649	13	60	m)-continuous	m)-continuous	ADJ
ejpam-5649	13	61	functions	function	NOUN
ejpam-5649	13	62	,	,	PUNCT
ejpam-5649	13	63	∗corresponding	∗corresponde	VERB
ejpam-5649	13	64	author	author	NOUN
ejpam-5649	13	65	.	.	PUNCT
ejpam-5649	14	1	doi	doi	NOUN
ejpam-5649	14	2	:	:	PUNCT
ejpam-5649	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5649	https://doi.org/10.29020/nybg.ejpam.v18i1.5649	VERB
ejpam-5649	14	4	email	email	NOUN
ejpam-5649	14	5	addresses	address	VERB
ejpam-5649	14	6	:	:	PUNCT
ejpam-5649	14	7	butsakorn.k@msu.ac.th	butsakorn.k@msu.ac.th	ADP
ejpam-5649	14	8	(	(	PUNCT
ejpam-5649	14	9	b.	b.	PROPN
ejpam-5649	14	10	kong	kong	PROPN
ejpam-5649	14	11	-	-	PUNCT
ejpam-5649	14	12	ied	ied	PROPN
ejpam-5649	14	13	)	)	PUNCT
ejpam-5649	14	14	,	,	PUNCT
ejpam-5649	14	15	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-5649	14	16	(	(	PUNCT
ejpam-5649	14	17	s.	s.	PROPN
ejpam-5649	14	18	sompong	sompong	PROPN
ejpam-5649	14	19	)	)	PUNCT
ejpam-5649	14	20	,	,	PUNCT
ejpam-5649	15	1	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5649	15	2	(	(	PUNCT
ejpam-5649	15	3	c.	c.	PROPN
ejpam-5649	15	4	boonpok	boonpok	PROPN
ejpam-5649	15	5	)	)	PUNCT
ejpam-5649	15	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5649	15	7	1	1	NUM
ejpam-5649	15	8	copyright	copyright	NOUN
ejpam-5649	15	9	:	:	PUNCT
ejpam-5649	15	10	©	©	PROPN
ejpam-5649	15	11	2025	2025	NUM
ejpam-5649	15	12	the	the	DET
ejpam-5649	15	13	author(s	author(s	NOUN
ejpam-5649	15	14	)	)	PUNCT
ejpam-5649	15	15	.	.	PUNCT
ejpam-5649	16	1	(	(	PUNCT
ejpam-5649	16	2	cc	cc	NOUN
ejpam-5649	16	3	by	by	ADP
ejpam-5649	16	4	-	-	PUNCT
ejpam-5649	16	5	nc	nc	PROPN
ejpam-5649	16	6	4.0	4.0	NUM
ejpam-5649	16	7	)	)	PUNCT
ejpam-5649	16	8	b.	b.	PROPN
ejpam-5649	16	9	kong	kong	PROPN
ejpam-5649	16	10	-	-	PUNCT
ejpam-5649	16	11	ied	ied	PROPN
ejpam-5649	16	12	,	,	PUNCT
ejpam-5649	16	13	s.	s.	PROPN
ejpam-5649	16	14	sompong	sompong	PROPN
ejpam-5649	16	15	,	,	PUNCT
ejpam-5649	16	16	c.	c.	PROPN
ejpam-5649	16	17	boonpok	boonpok	PROPN
ejpam-5649	16	18	/	/	SYM
ejpam-5649	16	19	eur	eur	PROPN
ejpam-5649	16	20	.	.	PUNCT
ejpam-5649	17	1	j.	j.	PROPN
ejpam-5649	17	2	pure	pure	PROPN
ejpam-5649	17	3	appl	appl	PROPN
ejpam-5649	17	4	.	.	PROPN
ejpam-5649	17	5	math	math	PROPN
ejpam-5649	17	6	,	,	PUNCT
ejpam-5649	17	7	18	18	NUM
ejpam-5649	17	8	(	(	PUNCT
ejpam-5649	17	9	1	1	NUM
ejpam-5649	17	10	)	)	PUNCT
ejpam-5649	17	11	(	(	PUNCT
ejpam-5649	17	12	2025	2025	NUM
ejpam-5649	17	13	)	)	PUNCT
ejpam-5649	17	14	,	,	PUNCT
ejpam-5649	17	15	5649	5649	NUM
ejpam-5649	17	16	2	2	NUM
ejpam-5649	17	17	of	of	ADP
ejpam-5649	17	18	13	13	NUM
ejpam-5649	17	19	pairwise	pairwise	NOUN
ejpam-5649	17	20	almost	almost	ADV
ejpam-5649	17	21	m	m	VERB
ejpam-5649	17	22	-continuous	-continuous	ADJ
ejpam-5649	17	23	functions	function	NOUN
ejpam-5649	17	24	,	,	PUNCT
ejpam-5649	17	25	(	(	PUNCT
ejpam-5649	17	26	τ1	τ1	NOUN
ejpam-5649	17	27	,	,	PUNCT
ejpam-5649	17	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	17	29	functions	function	NOUN
ejpam-5649	17	30	,	,	PUNCT
ejpam-5649	17	31	almost	almost	ADV
ejpam-5649	17	32	(	(	PUNCT
ejpam-5649	17	33	τ1	τ1	NOUN
ejpam-5649	17	34	,	,	PUNCT
ejpam-5649	17	35	τ2)continuous	τ2)continuous	ADJ
ejpam-5649	17	36	functions	function	NOUN
ejpam-5649	17	37	,	,	PUNCT
ejpam-5649	17	38	weakly	weakly	ADJ
ejpam-5649	17	39	(	(	PUNCT
ejpam-5649	17	40	τ1	τ1	NOUN
ejpam-5649	17	41	,	,	PUNCT
ejpam-5649	17	42	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	17	43	functions	function	NOUN
ejpam-5649	17	44	,	,	PUNCT
ejpam-5649	17	45	faintly	faintly	ADV
ejpam-5649	17	46	(	(	PUNCT
ejpam-5649	17	47	τ1	τ1	PROPN
ejpam-5649	17	48	,	,	PUNCT
ejpam-5649	17	49	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	17	50	functions	function	NOUN
ejpam-5649	17	51	,	,	PUNCT
ejpam-5649	17	52	almost	almost	ADV
ejpam-5649	17	53	quasi	quasi	NOUN
ejpam-5649	17	54	(	(	PUNCT
ejpam-5649	17	55	τ1	τ1	NOUN
ejpam-5649	17	56	,	,	PUNCT
ejpam-5649	17	57	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	17	58	functions	function	NOUN
ejpam-5649	17	59	and	and	CCONJ
ejpam-5649	17	60	weakly	weakly	ADJ
ejpam-5649	17	61	quasi	quasi	NOUN
ejpam-5649	17	62	(	(	PUNCT
ejpam-5649	17	63	τ1	τ1	PROPN
ejpam-5649	17	64	,	,	PUNCT
ejpam-5649	17	65	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	17	66	functions	function	NOUN
ejpam-5649	17	67	were	be	AUX
ejpam-5649	17	68	presented	present	VERB
ejpam-5649	17	69	in	in	ADP
ejpam-5649	17	70	[	[	X
ejpam-5649	17	71	61	61	NUM
ejpam-5649	17	72	]	]	PUNCT
ejpam-5649	17	73	,	,	PUNCT
ejpam-5649	17	74	[	[	X
ejpam-5649	17	75	64	64	NUM
ejpam-5649	17	76	]	]	PUNCT
ejpam-5649	17	77	,	,	PUNCT
ejpam-5649	17	78	[	[	X
ejpam-5649	17	79	16	16	NUM
ejpam-5649	17	80	]	]	PUNCT
ejpam-5649	17	81	,	,	PUNCT
ejpam-5649	17	82	[	[	X
ejpam-5649	17	83	56	56	NUM
ejpam-5649	17	84	]	]	PUNCT
ejpam-5649	17	85	,	,	PUNCT
ejpam-5649	17	86	[	[	X
ejpam-5649	17	87	25	25	NUM
ejpam-5649	17	88	]	]	PUNCT
ejpam-5649	17	89	,	,	PUNCT
ejpam-5649	17	90	[	[	X
ejpam-5649	17	91	11	11	NUM
ejpam-5649	17	92	]	]	PUNCT
ejpam-5649	17	93	,	,	PUNCT
ejpam-5649	17	94	[	[	X
ejpam-5649	17	95	8	8	NUM
ejpam-5649	17	96	]	]	PUNCT
ejpam-5649	17	97	,	,	PUNCT
ejpam-5649	17	98	[	[	X
ejpam-5649	17	99	10	10	NUM
ejpam-5649	17	100	]	]	PUNCT
ejpam-5649	17	101	,	,	PUNCT
ejpam-5649	17	102	[	[	X
ejpam-5649	17	103	4	4	NUM
ejpam-5649	17	104	]	]	PUNCT
ejpam-5649	17	105	,	,	PUNCT
ejpam-5649	17	106	[	[	X
ejpam-5649	17	107	1	1	NUM
ejpam-5649	17	108	]	]	PUNCT
ejpam-5649	17	109	,	,	PUNCT
ejpam-5649	17	110	[	[	X
ejpam-5649	17	111	2	2	NUM
ejpam-5649	17	112	]	]	PUNCT
ejpam-5649	17	113	,	,	PUNCT
ejpam-5649	17	114	[	[	X
ejpam-5649	17	115	26	26	NUM
ejpam-5649	17	116	]	]	PUNCT
ejpam-5649	17	117	,	,	PUNCT
ejpam-5649	17	118	[	[	X
ejpam-5649	17	119	23	23	NUM
ejpam-5649	17	120	]	]	PUNCT
ejpam-5649	17	121	,	,	PUNCT
ejpam-5649	17	122	[	[	X
ejpam-5649	17	123	18	18	NUM
ejpam-5649	17	124	]	]	PUNCT
ejpam-5649	17	125	,	,	PUNCT
ejpam-5649	17	126	[	[	X
ejpam-5649	17	127	62	62	NUM
ejpam-5649	17	128	]	]	PUNCT
ejpam-5649	17	129	,	,	PUNCT
ejpam-5649	17	130	[	[	X
ejpam-5649	17	131	46	46	NUM
ejpam-5649	17	132	]	]	PUNCT
ejpam-5649	17	133	and	and	CCONJ
ejpam-5649	17	134	[	[	X
ejpam-5649	17	135	33	33	NUM
ejpam-5649	17	136	]	]	PUNCT
ejpam-5649	17	137	,	,	PUNCT
ejpam-5649	17	138	respectively	respectively	ADV
ejpam-5649	17	139	.	.	PUNCT
ejpam-5649	18	1	popa	popa	NOUN
ejpam-5649	18	2	[	[	X
ejpam-5649	18	3	54	54	NUM
ejpam-5649	18	4	]	]	PUNCT
ejpam-5649	18	5	introduced	introduce	VERB
ejpam-5649	18	6	the	the	DET
ejpam-5649	18	7	concept	concept	NOUN
ejpam-5649	18	8	of	of	ADP
ejpam-5649	18	9	rare	rare	ADJ
ejpam-5649	18	10	continuity	continuity	NOUN
ejpam-5649	18	11	as	as	ADP
ejpam-5649	18	12	a	a	DET
ejpam-5649	18	13	generalization	generalization	NOUN
ejpam-5649	18	14	of	of	ADP
ejpam-5649	18	15	weak	weak	ADJ
ejpam-5649	18	16	continuity	continuity	NOUN
ejpam-5649	18	17	[	[	X
ejpam-5649	18	18	47	47	NUM
ejpam-5649	18	19	]	]	PUNCT
ejpam-5649	18	20	which	which	PRON
ejpam-5649	18	21	has	have	AUX
ejpam-5649	18	22	been	be	AUX
ejpam-5649	18	23	further	far	ADV
ejpam-5649	18	24	investigated	investigate	VERB
ejpam-5649	18	25	by	by	ADP
ejpam-5649	18	26	long	long	ADV
ejpam-5649	18	27	and	and	CCONJ
ejpam-5649	18	28	herrington	herrington	PROPN
ejpam-5649	19	1	[	[	X
ejpam-5649	19	2	49	49	NUM
ejpam-5649	19	3	]	]	PUNCT
ejpam-5649	19	4	and	and	CCONJ
ejpam-5649	19	5	jafari	jafari	ADJ
ejpam-5649	20	1	[	[	X
ejpam-5649	20	2	39	39	NUM
ejpam-5649	20	3	,	,	PUNCT
ejpam-5649	20	4	40	40	NUM
ejpam-5649	20	5	]	]	PUNCT
ejpam-5649	20	6	.	.	PUNCT
ejpam-5649	21	1	jafari	jafari	PROPN
ejpam-5649	21	2	[	[	X
ejpam-5649	21	3	41	41	NUM
ejpam-5649	21	4	]	]	PUNCT
ejpam-5649	21	5	also	also	ADV
ejpam-5649	21	6	generalized	generalize	VERB
ejpam-5649	21	7	the	the	DET
ejpam-5649	21	8	concept	concept	NOUN
ejpam-5649	21	9	of	of	ADP
ejpam-5649	21	10	rare	rare	ADJ
ejpam-5649	21	11	continuity	continuity	NOUN
ejpam-5649	21	12	to	to	PART
ejpam-5649	21	13	rare	rare	VERB
ejpam-5649	21	14	β	β	NOUN
ejpam-5649	21	15	-	-	NOUN
ejpam-5649	21	16	continuity	continuity	NOUN
ejpam-5649	21	17	by	by	ADP
ejpam-5649	21	18	involving	involve	VERB
ejpam-5649	21	19	the	the	DET
ejpam-5649	21	20	notion	notion	NOUN
ejpam-5649	21	21	of	of	ADP
ejpam-5649	21	22	β	β	ADJ
ejpam-5649	21	23	-	-	ADJ
ejpam-5649	21	24	open	open	ADJ
ejpam-5649	21	25	sets	set	NOUN
ejpam-5649	21	26	.	.	PUNCT
ejpam-5649	22	1	caldas	caldas	PROPN
ejpam-5649	22	2	[	[	X
ejpam-5649	22	3	30	30	NUM
ejpam-5649	22	4	]	]	PUNCT
ejpam-5649	22	5	introduced	introduce	VERB
ejpam-5649	22	6	a	a	DET
ejpam-5649	22	7	new	new	ADJ
ejpam-5649	22	8	class	class	NOUN
ejpam-5649	22	9	of	of	ADP
ejpam-5649	22	10	functions	function	NOUN
ejpam-5649	22	11	called	call	VERB
ejpam-5649	22	12	rarely	rarely	ADV
ejpam-5649	22	13	βθ	βθ	ADJ
ejpam-5649	22	14	-	-	PUNCT
ejpam-5649	22	15	continuous	continuous	ADJ
ejpam-5649	22	16	functions	function	NOUN
ejpam-5649	22	17	by	by	ADP
ejpam-5649	22	18	utilizing	utilize	VERB
ejpam-5649	22	19	the	the	DET
ejpam-5649	22	20	notion	notion	NOUN
ejpam-5649	22	21	of	of	ADP
ejpam-5649	22	22	β	β	NOUN
ejpam-5649	22	23	-	-	PUNCT
ejpam-5649	22	24	θ	θ	ADJ
ejpam-5649	22	25	-	-	ADJ
ejpam-5649	22	26	open	open	ADJ
ejpam-5649	22	27	sets	set	NOUN
ejpam-5649	22	28	and	and	CCONJ
ejpam-5649	22	29	investigated	investigate	VERB
ejpam-5649	22	30	some	some	DET
ejpam-5649	22	31	characterizations	characterization	NOUN
ejpam-5649	22	32	of	of	ADP
ejpam-5649	22	33	rarely	rarely	ADV
ejpam-5649	22	34	βθ	βθ	ADJ
ejpam-5649	22	35	-	-	PUNCT
ejpam-5649	22	36	continuous	continuous	ADJ
ejpam-5649	22	37	functions	function	NOUN
ejpam-5649	22	38	.	.	PUNCT
ejpam-5649	23	1	jafari	jafari	PROPN
ejpam-5649	23	2	[	[	X
ejpam-5649	23	3	42	42	NUM
ejpam-5649	23	4	]	]	PUNCT
ejpam-5649	23	5	introduced	introduce	VERB
ejpam-5649	23	6	and	and	CCONJ
ejpam-5649	23	7	studied	study	VERB
ejpam-5649	23	8	the	the	DET
ejpam-5649	23	9	concept	concept	NOUN
ejpam-5649	23	10	of	of	ADP
ejpam-5649	23	11	rare	rare	ADJ
ejpam-5649	23	12	α	α	NOUN
ejpam-5649	23	13	-	-	NOUN
ejpam-5649	23	14	continuity	continuity	NOUN
ejpam-5649	23	15	as	as	ADP
ejpam-5649	23	16	a	a	DET
ejpam-5649	23	17	generalization	generalization	NOUN
ejpam-5649	23	18	of	of	ADP
ejpam-5649	23	19	rare	rare	ADJ
ejpam-5649	23	20	continuity	continuity	NOUN
ejpam-5649	23	21	and	and	CCONJ
ejpam-5649	23	22	weak	weak	ADJ
ejpam-5649	23	23	α	α	NOUN
ejpam-5649	23	24	-	-	NOUN
ejpam-5649	23	25	continuity	continuity	NOUN
ejpam-5649	23	26	[	[	X
ejpam-5649	23	27	52	52	NUM
ejpam-5649	23	28	]	]	PUNCT
ejpam-5649	23	29	.	.	PUNCT
ejpam-5649	24	1	caldas	caldas	PROPN
ejpam-5649	24	2	and	and	CCONJ
ejpam-5649	24	3	jafari	jafari	PROPN
ejpam-5649	24	4	[	[	X
ejpam-5649	24	5	31	31	NUM
ejpam-5649	24	6	]	]	PUNCT
ejpam-5649	24	7	introduced	introduce	VERB
ejpam-5649	24	8	and	and	CCONJ
ejpam-5649	24	9	investigated	investigate	VERB
ejpam-5649	24	10	a	a	DET
ejpam-5649	24	11	new	new	ADJ
ejpam-5649	24	12	class	class	NOUN
ejpam-5649	24	13	of	of	ADP
ejpam-5649	24	14	functions	function	NOUN
ejpam-5649	24	15	called	call	VERB
ejpam-5649	24	16	rarely	rarely	ADV
ejpam-5649	24	17	g	g	NOUN
ejpam-5649	24	18	-	-	PUNCT
ejpam-5649	24	19	continuous	continuous	ADJ
ejpam-5649	24	20	functions	function	NOUN
ejpam-5649	24	21	which	which	PRON
ejpam-5649	24	22	is	be	AUX
ejpam-5649	24	23	a	a	DET
ejpam-5649	24	24	generalization	generalization	NOUN
ejpam-5649	24	25	of	of	ADP
ejpam-5649	24	26	both	both	CCONJ
ejpam-5649	24	27	the	the	DET
ejpam-5649	24	28	class	class	NOUN
ejpam-5649	24	29	of	of	ADP
ejpam-5649	24	30	rarely	rarely	ADV
ejpam-5649	24	31	continuous	continuous	ADJ
ejpam-5649	24	32	functions	function	NOUN
ejpam-5649	24	33	and	and	CCONJ
ejpam-5649	24	34	the	the	DET
ejpam-5649	24	35	class	class	NOUN
ejpam-5649	24	36	of	of	ADP
ejpam-5649	24	37	weakly	weakly	ADJ
ejpam-5649	24	38	g	g	NOUN
ejpam-5649	24	39	-	-	PUNCT
ejpam-5649	24	40	continuous	continuous	ADJ
ejpam-5649	24	41	functions	function	NOUN
ejpam-5649	24	42	.	.	PUNCT
ejpam-5649	25	1	quite	quite	ADV
ejpam-5649	25	2	recently	recently	ADV
ejpam-5649	25	3	,	,	PUNCT
ejpam-5649	25	4	thongmoon	thongmoon	NOUN
ejpam-5649	25	5	et	et	PROPN
ejpam-5649	25	6	al	al	PROPN
ejpam-5649	25	7	.	.	PUNCT
ejpam-5649	26	1	[	[	X
ejpam-5649	26	2	66	66	NUM
ejpam-5649	26	3	]	]	PUNCT
ejpam-5649	26	4	introduced	introduce	VERB
ejpam-5649	26	5	and	and	CCONJ
ejpam-5649	26	6	studied	study	VERB
ejpam-5649	26	7	the	the	DET
ejpam-5649	26	8	concept	concept	NOUN
ejpam-5649	26	9	of	of	ADP
ejpam-5649	26	10	rarely	rarely	ADV
ejpam-5649	26	11	(	(	PUNCT
ejpam-5649	26	12	τ1	τ1	NOUN
ejpam-5649	26	13	,	,	PUNCT
ejpam-5649	26	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	26	15	functions	function	NOUN
ejpam-5649	26	16	.	.	PUNCT
ejpam-5649	27	1	in	in	ADP
ejpam-5649	27	2	2005	2005	NUM
ejpam-5649	27	3	,	,	PUNCT
ejpam-5649	27	4	caldas	caldas	PROPN
ejpam-5649	27	5	et	et	PROPN
ejpam-5649	27	6	al	al	PROPN
ejpam-5649	27	7	.	.	PUNCT
ejpam-5649	28	1	[	[	X
ejpam-5649	28	2	32	32	NUM
ejpam-5649	28	3	]	]	PUNCT
ejpam-5649	28	4	introduced	introduce	VERB
ejpam-5649	28	5	and	and	CCONJ
ejpam-5649	28	6	studied	study	VERB
ejpam-5649	28	7	the	the	DET
ejpam-5649	28	8	new	new	ADJ
ejpam-5649	28	9	notion	notion	NOUN
ejpam-5649	28	10	of	of	ADP
ejpam-5649	28	11	rarely	rarely	ADV
ejpam-5649	28	12	g	g	NOUN
ejpam-5649	28	13	-	-	PUNCT
ejpam-5649	28	14	continuous	continuous	ADJ
ejpam-5649	28	15	multifunctions	multifunction	NOUN
ejpam-5649	28	16	is	be	AUX
ejpam-5649	28	17	a	a	DET
ejpam-5649	28	18	generalization	generalization	NOUN
ejpam-5649	28	19	of	of	ADP
ejpam-5649	28	20	weakly	weakly	ADJ
ejpam-5649	28	21	continuous	continuous	ADJ
ejpam-5649	28	22	multifunctions	multifunction	NOUN
ejpam-5649	29	1	[	[	X
ejpam-5649	29	2	53	53	NUM
ejpam-5649	29	3	]	]	PUNCT
ejpam-5649	29	4	.	.	PUNCT
ejpam-5649	30	1	viriyapong	viriyapong	PROPN
ejpam-5649	30	2	and	and	CCONJ
ejpam-5649	30	3	boonpok	boonpok	VERB
ejpam-5649	31	1	[	[	X
ejpam-5649	31	2	70	70	NUM
ejpam-5649	31	3	]	]	PUNCT
ejpam-5649	31	4	introduced	introduce	VERB
ejpam-5649	31	5	and	and	CCONJ
ejpam-5649	31	6	studied	study	VERB
ejpam-5649	31	7	the	the	DET
ejpam-5649	31	8	concept	concept	NOUN
ejpam-5649	31	9	of	of	ADP
ejpam-5649	31	10	weakly	weakly	ADJ
ejpam-5649	31	11	quasi	quasi	NOUN
ejpam-5649	31	12	(	(	PUNCT
ejpam-5649	31	13	λ	λ	PROPN
ejpam-5649	31	14	,	,	PUNCT
ejpam-5649	31	15	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	31	16	multifunctions	multifunction	NOUN
ejpam-5649	31	17	.	.	PUNCT
ejpam-5649	32	1	furthermore	furthermore	ADV
ejpam-5649	32	2	,	,	PUNCT
ejpam-5649	32	3	several	several	ADJ
ejpam-5649	32	4	characterizations	characterization	NOUN
ejpam-5649	32	5	of	of	ADP
ejpam-5649	32	6	(	(	PUNCT
ejpam-5649	32	7	τ1	τ1	NOUN
ejpam-5649	32	8	,	,	PUNCT
ejpam-5649	32	9	τ2)δ	τ2)δ	ADJ
ejpam-5649	32	10	-	-	PUNCT
ejpam-5649	32	11	semicontinuous	semicontinuous	ADJ
ejpam-5649	32	12	multifunctions	multifunction	NOUN
ejpam-5649	32	13	,	,	PUNCT
ejpam-5649	32	14	almost	almost	ADV
ejpam-5649	32	15	weakly	weakly	ADJ
ejpam-5649	32	16	(	(	PUNCT
ejpam-5649	32	17	τ1	τ1	NOUN
ejpam-5649	32	18	,	,	PUNCT
ejpam-5649	32	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	20	multifunctions	multifunction	NOUN
ejpam-5649	32	21	,	,	PUNCT
ejpam-5649	32	22	⋆-continuous	⋆-continuous	ADJ
ejpam-5649	32	23	multifunctions	multifunction	NOUN
ejpam-5649	32	24	,	,	PUNCT
ejpam-5649	32	25	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-5649	32	26	multifunctions	multifunction	NOUN
ejpam-5649	32	27	,	,	PUNCT
ejpam-5649	32	28	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5649	32	29	multifunctions	multifunction	NOUN
ejpam-5649	32	30	,	,	PUNCT
ejpam-5649	32	31	almost	almost	ADV
ejpam-5649	32	32	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5649	32	33	multifunctions	multifunction	NOUN
ejpam-5649	32	34	,	,	PUNCT
ejpam-5649	32	35	almost	almost	ADV
ejpam-5649	32	36	quasi	quasi	VERB
ejpam-5649	32	37	⋆-continuous	⋆-continuous	ADJ
ejpam-5649	32	38	multifunctions	multifunction	NOUN
ejpam-5649	32	39	,	,	PUNCT
ejpam-5649	32	40	weakly	weakly	ADJ
ejpam-5649	32	41	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5649	32	42	multifunctions	multifunction	NOUN
ejpam-5649	32	43	,	,	PUNCT
ejpam-5649	32	44	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5649	32	45	multifunctions	multifunction	NOUN
ejpam-5649	32	46	,	,	PUNCT
ejpam-5649	32	47	weakly	weakly	ADJ
ejpam-5649	32	48	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5649	32	49	multifunctions	multifunction	NOUN
ejpam-5649	32	50	,	,	PUNCT
ejpam-5649	32	51	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-5649	32	52	continuous	continuous	ADJ
ejpam-5649	32	53	multifunctions	multifunction	NOUN
ejpam-5649	32	54	,	,	PUNCT
ejpam-5649	32	55	almost	almost	ADV
ejpam-5649	32	56	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5649	32	57	multifunctions	multifunction	NOUN
ejpam-5649	32	58	,	,	PUNCT
ejpam-5649	32	59	weakly	weakly	ADJ
ejpam-5649	32	60	(	(	PUNCT
ejpam-5649	32	61	λ	λ	NOUN
ejpam-5649	32	62	,	,	PUNCT
ejpam-5649	32	63	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	32	64	multifunctions	multifunction	NOUN
ejpam-5649	32	65	,	,	PUNCT
ejpam-5649	32	66	α(λ	α(λ	PROPN
ejpam-5649	32	67	,	,	PUNCT
ejpam-5649	32	68	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	32	69	multifunctions	multifunction	NOUN
ejpam-5649	32	70	,	,	PUNCT
ejpam-5649	32	71	almost	almost	ADV
ejpam-5649	32	72	α(λ	α(λ	PROPN
ejpam-5649	32	73	,	,	PUNCT
ejpam-5649	32	74	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	32	75	multifunctions	multifunction	NOUN
ejpam-5649	32	76	,	,	PUNCT
ejpam-5649	32	77	weakly	weakly	ADJ
ejpam-5649	32	78	α(λ	α(λ	PROPN
ejpam-5649	32	79	,	,	PUNCT
ejpam-5649	32	80	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	32	81	multifunctions	multifunction	NOUN
ejpam-5649	32	82	,	,	PUNCT
ejpam-5649	32	83	almost	almost	ADV
ejpam-5649	32	84	β(λ	β(λ	NOUN
ejpam-5649	32	85	,	,	PUNCT
ejpam-5649	32	86	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	32	87	multifunctions	multifunction	NOUN
ejpam-5649	32	88	,	,	PUNCT
ejpam-5649	32	89	slightly	slightly	ADV
ejpam-5649	32	90	(	(	PUNCT
ejpam-5649	32	91	λ	λ	NOUN
ejpam-5649	32	92	,	,	PUNCT
ejpam-5649	32	93	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	32	94	multifunctions	multifunction	NOUN
ejpam-5649	32	95	,	,	PUNCT
ejpam-5649	32	96	(	(	PUNCT
ejpam-5649	32	97	τ1	τ1	NOUN
ejpam-5649	32	98	,	,	PUNCT
ejpam-5649	32	99	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	100	multifunctions	multifunction	NOUN
ejpam-5649	32	101	,	,	PUNCT
ejpam-5649	32	102	almost	almost	ADV
ejpam-5649	32	103	(	(	PUNCT
ejpam-5649	32	104	τ1	τ1	NOUN
ejpam-5649	32	105	,	,	PUNCT
ejpam-5649	32	106	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	107	multifunctions	multifunction	NOUN
ejpam-5649	32	108	,	,	PUNCT
ejpam-5649	32	109	weakly	weakly	ADJ
ejpam-5649	32	110	(	(	PUNCT
ejpam-5649	32	111	τ1	τ1	NOUN
ejpam-5649	32	112	,	,	PUNCT
ejpam-5649	32	113	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	114	multifunctions	multifunction	NOUN
ejpam-5649	32	115	,	,	PUNCT
ejpam-5649	32	116	weakly	weakly	ADJ
ejpam-5649	32	117	quasi	quasi	NOUN
ejpam-5649	32	118	(	(	PUNCT
ejpam-5649	32	119	τ1	τ1	PROPN
ejpam-5649	32	120	,	,	PUNCT
ejpam-5649	32	121	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	122	multifunctions	multifunction	NOUN
ejpam-5649	32	123	,	,	PUNCT
ejpam-5649	32	124	almost	almost	ADV
ejpam-5649	32	125	quasi	quasi	NOUN
ejpam-5649	32	126	(	(	PUNCT
ejpam-5649	32	127	τ1	τ1	NOUN
ejpam-5649	32	128	,	,	PUNCT
ejpam-5649	32	129	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	130	multifunctions	multifunction	NOUN
ejpam-5649	32	131	,	,	PUNCT
ejpam-5649	32	132	c-(τ1	c-(τ1	PROPN
ejpam-5649	32	133	,	,	PUNCT
ejpam-5649	32	134	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	135	multifunctions	multifunction	NOUN
ejpam-5649	32	136	and	and	CCONJ
ejpam-5649	32	137	c	c	NOUN
ejpam-5649	32	138	-	-	PUNCT
ejpam-5649	32	139	quasi	quasi	NOUN
ejpam-5649	32	140	(	(	PUNCT
ejpam-5649	32	141	τ1	τ1	PROPN
ejpam-5649	32	142	,	,	PUNCT
ejpam-5649	32	143	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	32	144	multifunctions	multifunction	NOUN
ejpam-5649	32	145	were	be	AUX
ejpam-5649	32	146	established	establish	VERB
ejpam-5649	32	147	in	in	ADP
ejpam-5649	32	148	[	[	X
ejpam-5649	32	149	5	5	NUM
ejpam-5649	32	150	]	]	PUNCT
ejpam-5649	32	151	,	,	PUNCT
ejpam-5649	32	152	[	[	X
ejpam-5649	32	153	28	28	NUM
ejpam-5649	32	154	]	]	PUNCT
ejpam-5649	32	155	,	,	PUNCT
ejpam-5649	32	156	[	[	X
ejpam-5649	32	157	3	3	NUM
ejpam-5649	32	158	]	]	PUNCT
ejpam-5649	32	159	,	,	PUNCT
ejpam-5649	32	160	[	[	X
ejpam-5649	32	161	7	7	NUM
ejpam-5649	32	162	]	]	PUNCT
ejpam-5649	32	163	,	,	PUNCT
ejpam-5649	32	164	[	[	X
ejpam-5649	32	165	17	17	NUM
ejpam-5649	32	166	]	]	PUNCT
ejpam-5649	32	167	,	,	PUNCT
ejpam-5649	32	168	[	[	X
ejpam-5649	32	169	24	24	NUM
ejpam-5649	32	170	]	]	PUNCT
ejpam-5649	32	171	,	,	PUNCT
ejpam-5649	32	172	[	[	X
ejpam-5649	32	173	6	6	NUM
ejpam-5649	32	174	]	]	PUNCT
ejpam-5649	32	175	,	,	PUNCT
ejpam-5649	32	176	[	[	X
ejpam-5649	32	177	21	21	NUM
ejpam-5649	32	178	]	]	PUNCT
ejpam-5649	32	179	,	,	PUNCT
ejpam-5649	32	180	[	[	X
ejpam-5649	32	181	20	20	NUM
ejpam-5649	32	182	]	]	PUNCT
ejpam-5649	32	183	,	,	PUNCT
ejpam-5649	32	184	[	[	X
ejpam-5649	32	185	15	15	NUM
ejpam-5649	32	186	]	]	PUNCT
ejpam-5649	32	187	,	,	PUNCT
ejpam-5649	32	188	[	[	X
ejpam-5649	32	189	9	9	NUM
ejpam-5649	32	190	]	]	PUNCT
ejpam-5649	32	191	,	,	PUNCT
ejpam-5649	32	192	[	[	X
ejpam-5649	32	193	19	19	NUM
ejpam-5649	32	194	]	]	PUNCT
ejpam-5649	32	195	,	,	PUNCT
ejpam-5649	32	196	[	[	X
ejpam-5649	32	197	22	22	NUM
ejpam-5649	32	198	]	]	PUNCT
ejpam-5649	32	199	,	,	PUNCT
ejpam-5649	32	200	[	[	X
ejpam-5649	32	201	43	43	NUM
ejpam-5649	32	202	]	]	PUNCT
ejpam-5649	32	203	,	,	PUNCT
ejpam-5649	32	204	[	[	X
ejpam-5649	32	205	13	13	NUM
ejpam-5649	32	206	]	]	PUNCT
ejpam-5649	32	207	,	,	PUNCT
ejpam-5649	32	208	[	[	X
ejpam-5649	32	209	27	27	NUM
ejpam-5649	32	210	]	]	PUNCT
ejpam-5649	32	211	,	,	PUNCT
ejpam-5649	32	212	[	[	X
ejpam-5649	32	213	63	63	NUM
ejpam-5649	32	214	]	]	PUNCT
ejpam-5649	32	215	,	,	PUNCT
ejpam-5649	32	216	[	[	X
ejpam-5649	32	217	14	14	NUM
ejpam-5649	32	218	]	]	PUNCT
ejpam-5649	32	219	,	,	PUNCT
ejpam-5649	32	220	[	[	X
ejpam-5649	32	221	59	59	NUM
ejpam-5649	32	222	]	]	PUNCT
ejpam-5649	32	223	,	,	PUNCT
ejpam-5649	32	224	[	[	X
ejpam-5649	32	225	45	45	NUM
ejpam-5649	32	226	]	]	PUNCT
ejpam-5649	32	227	,	,	PUNCT
ejpam-5649	32	228	[	[	X
ejpam-5649	32	229	65	65	NUM
ejpam-5649	32	230	]	]	PUNCT
ejpam-5649	32	231	,	,	PUNCT
ejpam-5649	32	232	[	[	X
ejpam-5649	32	233	60	60	NUM
ejpam-5649	32	234	]	]	PUNCT
ejpam-5649	32	235	,	,	PUNCT
ejpam-5649	32	236	[	[	X
ejpam-5649	32	237	58	58	NUM
ejpam-5649	32	238	]	]	PUNCT
ejpam-5649	32	239	,	,	PUNCT
ejpam-5649	32	240	[	[	X
ejpam-5649	32	241	44	44	NUM
ejpam-5649	32	242	]	]	PUNCT
ejpam-5649	32	243	and	and	CCONJ
ejpam-5649	32	244	[	[	X
ejpam-5649	32	245	57	57	NUM
ejpam-5649	32	246	]	]	PUNCT
ejpam-5649	32	247	,	,	PUNCT
ejpam-5649	32	248	respectively	respectively	ADV
ejpam-5649	32	249	.	.	PUNCT
ejpam-5649	33	1	popa	popa	NOUN
ejpam-5649	33	2	and	and	CCONJ
ejpam-5649	33	3	noiri	noiri	ADV
ejpam-5649	34	1	[	[	X
ejpam-5649	34	2	55	55	NUM
ejpam-5649	34	3	]	]	PUNCT
ejpam-5649	34	4	introduced	introduce	VERB
ejpam-5649	34	5	and	and	CCONJ
ejpam-5649	34	6	studied	study	VERB
ejpam-5649	34	7	the	the	DET
ejpam-5649	34	8	notion	notion	NOUN
ejpam-5649	34	9	of	of	ADP
ejpam-5649	34	10	s	s	NOUN
ejpam-5649	34	11	-	-	ADJ
ejpam-5649	34	12	precontinuous	precontinuous	ADJ
ejpam-5649	34	13	multifunctions	multifunction	NOUN
ejpam-5649	34	14	is	be	AUX
ejpam-5649	34	15	a	a	DET
ejpam-5649	34	16	generalization	generalization	NOUN
ejpam-5649	34	17	of	of	ADP
ejpam-5649	34	18	s	s	NOUN
ejpam-5649	34	19	-	-	ADJ
ejpam-5649	34	20	continuous	continuous	ADJ
ejpam-5649	34	21	multifunctions	multifunction	NOUN
ejpam-5649	34	22	and	and	CCONJ
ejpam-5649	34	23	precontinuous	precontinuous	ADJ
ejpam-5649	34	24	multifunctions	multifunction	NOUN
ejpam-5649	34	25	.	.	PUNCT
ejpam-5649	35	1	ekici	ekici	NOUN
ejpam-5649	35	2	and	and	CCONJ
ejpam-5649	35	3	park	park	NOUN
ejpam-5649	36	1	[	[	X
ejpam-5649	36	2	37	37	NUM
ejpam-5649	36	3	]	]	PUNCT
ejpam-5649	36	4	introduced	introduce	VERB
ejpam-5649	36	5	and	and	CCONJ
ejpam-5649	36	6	investigated	investigate	VERB
ejpam-5649	36	7	the	the	DET
ejpam-5649	36	8	concept	concept	NOUN
ejpam-5649	36	9	of	of	ADP
ejpam-5649	36	10	weakly	weakly	ADJ
ejpam-5649	36	11	s	s	NOUN
ejpam-5649	36	12	-	-	ADJ
ejpam-5649	36	13	precontinuous	precontinuous	ADJ
ejpam-5649	36	14	multifunctions	multifunction	NOUN
ejpam-5649	36	15	.	.	PUNCT
ejpam-5649	37	1	the	the	DET
ejpam-5649	37	2	notion	notion	NOUN
ejpam-5649	37	3	of	of	ADP
ejpam-5649	37	4	weakly	weakly	ADJ
ejpam-5649	37	5	s	s	NOUN
ejpam-5649	37	6	-	-	ADJ
ejpam-5649	37	7	precontinuous	precontinuous	ADJ
ejpam-5649	37	8	multifunctions	multifunction	NOUN
ejpam-5649	37	9	is	be	AUX
ejpam-5649	37	10	a	a	DET
ejpam-5649	37	11	generalization	generalization	NOUN
ejpam-5649	37	12	of	of	ADP
ejpam-5649	37	13	s	s	ADJ
ejpam-5649	37	14	-	-	ADJ
ejpam-5649	37	15	precontinuous	precontinuous	ADJ
ejpam-5649	37	16	multifunctions	multifunction	NOUN
ejpam-5649	37	17	due	due	ADP
ejpam-5649	37	18	to	to	ADP
ejpam-5649	37	19	popa	popa	NOUN
ejpam-5649	37	20	and	and	CCONJ
ejpam-5649	37	21	noiri	noiri	ADV
ejpam-5649	37	22	[	[	X
ejpam-5649	37	23	55	55	NUM
ejpam-5649	37	24	]	]	PUNCT
ejpam-5649	37	25	.	.	PUNCT
ejpam-5649	38	1	ekici	ekici	PROPN
ejpam-5649	38	2	and	and	CCONJ
ejpam-5649	38	3	jafari	jafari	PROPN
ejpam-5649	39	1	[	[	X
ejpam-5649	39	2	36	36	NUM
ejpam-5649	39	3	]	]	PUNCT
ejpam-5649	39	4	introduced	introduce	VERB
ejpam-5649	39	5	and	and	CCONJ
ejpam-5649	39	6	investigated	investigate	VERB
ejpam-5649	39	7	the	the	DET
ejpam-5649	39	8	notion	notion	NOUN
ejpam-5649	39	9	of	of	ADP
ejpam-5649	39	10	rarely	rarely	ADV
ejpam-5649	39	11	s	s	NOUN
ejpam-5649	39	12	-	-	ADJ
ejpam-5649	39	13	precontinuous	precontinuous	ADJ
ejpam-5649	39	14	multifunctions	multifunction	NOUN
ejpam-5649	39	15	which	which	PRON
ejpam-5649	39	16	is	be	AUX
ejpam-5649	39	17	a	a	DET
ejpam-5649	39	18	generalization	generalization	NOUN
ejpam-5649	39	19	of	of	ADP
ejpam-5649	39	20	weakly	weakly	ADJ
ejpam-5649	39	21	s	s	NOUN
ejpam-5649	39	22	-	-	ADJ
ejpam-5649	39	23	precontinuous	precontinuous	ADJ
ejpam-5649	39	24	multifunctions	multifunction	NOUN
ejpam-5649	39	25	due	due	ADP
ejpam-5649	39	26	to	to	PART
ejpam-5649	39	27	ekici	ekici	VERB
ejpam-5649	39	28	and	and	CCONJ
ejpam-5649	39	29	park	park	NOUN
ejpam-5649	39	30	[	[	X
ejpam-5649	39	31	37	37	NUM
ejpam-5649	39	32	]	]	PUNCT
ejpam-5649	39	33	.	.	PUNCT
ejpam-5649	40	1	in	in	ADP
ejpam-5649	40	2	this	this	DET
ejpam-5649	40	3	paper	paper	NOUN
ejpam-5649	40	4	,	,	PUNCT
ejpam-5649	40	5	we	we	PRON
ejpam-5649	40	6	introduce	introduce	VERB
ejpam-5649	40	7	the	the	DET
ejpam-5649	40	8	notions	notion	NOUN
ejpam-5649	40	9	of	of	ADP
ejpam-5649	40	10	upper	upper	ADJ
ejpam-5649	40	11	rarely	rarely	ADV
ejpam-5649	40	12	s-(τ1	s-(τ1	NOUN
ejpam-5649	40	13	,	,	PUNCT
ejpam-5649	40	14	τ2)p	τ2)p	ADJ
ejpam-5649	40	15	-	-	ADJ
ejpam-5649	40	16	continuous	continuous	ADJ
ejpam-5649	40	17	multifunctions	multifunction	NOUN
ejpam-5649	40	18	and	and	CCONJ
ejpam-5649	40	19	lower	low	ADJ
ejpam-5649	40	20	rarely	rarely	ADV
ejpam-5649	40	21	s-(τ1	s-(τ1	NOUN
ejpam-5649	40	22	,	,	PUNCT
ejpam-5649	40	23	τ2)p	τ2)p	ADJ
ejpam-5649	40	24	-	-	PUNCT
ejpam-5649	40	25	continuous	continuous	ADJ
ejpam-5649	40	26	multifunctions	multifunction	NOUN
ejpam-5649	40	27	.	.	PUNCT
ejpam-5649	41	1	we	we	PRON
ejpam-5649	41	2	also	also	ADV
ejpam-5649	41	3	investigate	investigate	VERB
ejpam-5649	41	4	several	several	ADJ
ejpam-5649	41	5	characterizations	characterization	NOUN
ejpam-5649	41	6	of	of	ADP
ejpam-5649	41	7	upper	upper	ADJ
ejpam-5649	41	8	rarely	rarely	ADV
ejpam-5649	41	9	s-(τ1	s-(τ1	NOUN
ejpam-5649	41	10	,	,	PUNCT
ejpam-5649	41	11	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5649	41	12	multifunctions	multifunction	NOUN
ejpam-5649	41	13	and	and	CCONJ
ejpam-5649	41	14	lower	low	ADJ
ejpam-5649	41	15	rarely	rarely	ADV
ejpam-5649	41	16	s-(τ1	s-(τ1	NOUN
ejpam-5649	41	17	,	,	PUNCT
ejpam-5649	41	18	τ2)p	τ2)p	ADJ
ejpam-5649	41	19	-	-	PUNCT
ejpam-5649	41	20	continuous	continuous	ADJ
ejpam-5649	41	21	multifunctions	multifunction	NOUN
ejpam-5649	41	22	.	.	PUNCT
ejpam-5649	42	1	b.	b.	PROPN
ejpam-5649	42	2	kong	kong	PROPN
ejpam-5649	42	3	-	-	PUNCT
ejpam-5649	42	4	ied	ied	PROPN
ejpam-5649	42	5	,	,	PUNCT
ejpam-5649	42	6	s.	s.	PROPN
ejpam-5649	42	7	sompong	sompong	PROPN
ejpam-5649	42	8	,	,	PUNCT
ejpam-5649	42	9	c.	c.	PROPN
ejpam-5649	42	10	boonpok	boonpok	PROPN
ejpam-5649	42	11	/	/	SYM
ejpam-5649	42	12	eur	eur	PROPN
ejpam-5649	42	13	.	.	PUNCT
ejpam-5649	43	1	j.	j.	PROPN
ejpam-5649	43	2	pure	pure	PROPN
ejpam-5649	43	3	appl	appl	PROPN
ejpam-5649	43	4	.	.	PROPN
ejpam-5649	43	5	math	math	PROPN
ejpam-5649	43	6	,	,	PUNCT
ejpam-5649	43	7	18	18	NUM
ejpam-5649	43	8	(	(	PUNCT
ejpam-5649	43	9	1	1	NUM
ejpam-5649	43	10	)	)	PUNCT
ejpam-5649	43	11	(	(	PUNCT
ejpam-5649	43	12	2025	2025	NUM
ejpam-5649	43	13	)	)	PUNCT
ejpam-5649	43	14	,	,	PUNCT
ejpam-5649	43	15	5649	5649	NUM
ejpam-5649	43	16	3	3	NUM
ejpam-5649	43	17	of	of	ADP
ejpam-5649	43	18	13	13	NUM
ejpam-5649	43	19	2	2	NUM
ejpam-5649	43	20	.	.	PUNCT
ejpam-5649	43	21	preliminaries	preliminary	NOUN
ejpam-5649	43	22	throughout	throughout	ADP
ejpam-5649	43	23	the	the	DET
ejpam-5649	43	24	present	present	ADJ
ejpam-5649	43	25	paper	paper	NOUN
ejpam-5649	43	26	,	,	PUNCT
ejpam-5649	43	27	spaces	space	NOUN
ejpam-5649	43	28	(	(	PUNCT
ejpam-5649	43	29	x	x	NOUN
ejpam-5649	43	30	,	,	PUNCT
ejpam-5649	43	31	τ1	τ1	NOUN
ejpam-5649	43	32	,	,	PUNCT
ejpam-5649	43	33	τ2	τ2	NOUN
ejpam-5649	43	34	)	)	PUNCT
ejpam-5649	43	35	and	and	CCONJ
ejpam-5649	43	36	(	(	PUNCT
ejpam-5649	43	37	y	y	PROPN
ejpam-5649	43	38	,	,	PUNCT
ejpam-5649	43	39	σ1	σ1	PROPN
ejpam-5649	43	40	,	,	PUNCT
ejpam-5649	43	41	σ2	σ2	NOUN
ejpam-5649	43	42	)	)	PUNCT
ejpam-5649	43	43	(	(	PUNCT
ejpam-5649	43	44	or	or	CCONJ
ejpam-5649	43	45	simply	simply	ADV
ejpam-5649	43	46	x	x	X
ejpam-5649	43	47	and	and	CCONJ
ejpam-5649	43	48	y	y	PROPN
ejpam-5649	43	49	)	)	PUNCT
ejpam-5649	43	50	always	always	ADV
ejpam-5649	43	51	mean	mean	VERB
ejpam-5649	43	52	bitopological	bitopological	ADJ
ejpam-5649	43	53	spaces	space	NOUN
ejpam-5649	43	54	on	on	ADP
ejpam-5649	43	55	which	which	PRON
ejpam-5649	43	56	no	no	DET
ejpam-5649	43	57	separation	separation	NOUN
ejpam-5649	43	58	axioms	axiom	NOUN
ejpam-5649	43	59	are	be	AUX
ejpam-5649	43	60	assumed	assume	VERB
ejpam-5649	43	61	unless	unless	SCONJ
ejpam-5649	43	62	explicitly	explicitly	ADV
ejpam-5649	43	63	stated	state	VERB
ejpam-5649	43	64	.	.	PUNCT
ejpam-5649	44	1	let	let	VERB
ejpam-5649	44	2	a	a	DET
ejpam-5649	44	3	be	be	AUX
ejpam-5649	44	4	a	a	DET
ejpam-5649	44	5	subset	subset	NOUN
ejpam-5649	44	6	of	of	ADP
ejpam-5649	44	7	a	a	DET
ejpam-5649	44	8	bitopological	bitopological	ADJ
ejpam-5649	44	9	space	space	NOUN
ejpam-5649	44	10	(	(	PUNCT
ejpam-5649	44	11	x	x	NOUN
ejpam-5649	44	12	,	,	PUNCT
ejpam-5649	44	13	τ1	τ1	NOUN
ejpam-5649	44	14	,	,	PUNCT
ejpam-5649	44	15	τ2	τ2	NOUN
ejpam-5649	44	16	)	)	PUNCT
ejpam-5649	44	17	.	.	PUNCT
ejpam-5649	45	1	the	the	DET
ejpam-5649	45	2	closure	closure	NOUN
ejpam-5649	45	3	of	of	ADP
ejpam-5649	45	4	a	a	PRON
ejpam-5649	45	5	and	and	CCONJ
ejpam-5649	45	6	the	the	DET
ejpam-5649	45	7	interior	interior	NOUN
ejpam-5649	45	8	of	of	ADP
ejpam-5649	45	9	a	a	PRON
ejpam-5649	45	10	with	with	ADP
ejpam-5649	45	11	respect	respect	NOUN
ejpam-5649	45	12	to	to	ADP
ejpam-5649	45	13	τi	τi	PROPN
ejpam-5649	45	14	are	be	AUX
ejpam-5649	45	15	denoted	denote	VERB
ejpam-5649	45	16	by	by	ADP
ejpam-5649	45	17	τi	τi	NOUN
ejpam-5649	45	18	-	-	PUNCT
ejpam-5649	45	19	cl(a	cl(a	NUM
ejpam-5649	45	20	)	)	PUNCT
ejpam-5649	45	21	and	and	CCONJ
ejpam-5649	45	22	τi	τi	NOUN
ejpam-5649	45	23	-	-	PUNCT
ejpam-5649	45	24	int(a	int(a	NOUN
ejpam-5649	45	25	)	)	PUNCT
ejpam-5649	45	26	,	,	PUNCT
ejpam-5649	45	27	respectively	respectively	ADV
ejpam-5649	45	28	,	,	PUNCT
ejpam-5649	45	29	for	for	ADP
ejpam-5649	45	30	i	i	PROPN
ejpam-5649	45	31	=	=	SYM
ejpam-5649	45	32	1	1	NUM
ejpam-5649	45	33	,	,	PUNCT
ejpam-5649	45	34	2	2	NUM
ejpam-5649	45	35	.	.	X
ejpam-5649	45	36	a	a	DET
ejpam-5649	45	37	subset	subset	NOUN
ejpam-5649	45	38	a	a	PRON
ejpam-5649	45	39	of	of	ADP
ejpam-5649	45	40	a	a	DET
ejpam-5649	45	41	bitopological	bitopological	ADJ
ejpam-5649	45	42	space	space	NOUN
ejpam-5649	45	43	(	(	PUNCT
ejpam-5649	45	44	x	x	NOUN
ejpam-5649	45	45	,	,	PUNCT
ejpam-5649	45	46	τ1	τ1	NOUN
ejpam-5649	45	47	,	,	PUNCT
ejpam-5649	45	48	τ2	τ2	NOUN
ejpam-5649	45	49	)	)	PUNCT
ejpam-5649	45	50	is	be	AUX
ejpam-5649	45	51	called	call	VERB
ejpam-5649	45	52	τ1τ2	τ1τ2	VERB
ejpam-5649	45	53	-	-	ADJ
ejpam-5649	45	54	closed	closed	ADJ
ejpam-5649	45	55	[	[	X
ejpam-5649	45	56	29	29	NUM
ejpam-5649	45	57	]	]	X
ejpam-5649	45	58	if	if	SCONJ
ejpam-5649	45	59	a	a	DET
ejpam-5649	45	60	=	=	NOUN
ejpam-5649	45	61	τ1	τ1	NOUN
ejpam-5649	45	62	-	-	PUNCT
ejpam-5649	45	63	cl(τ2	cl(τ2	NOUN
ejpam-5649	45	64	-	-	PUNCT
ejpam-5649	45	65	cl(a	cl(a	NUM
ejpam-5649	45	66	)	)	PUNCT
ejpam-5649	45	67	)	)	PUNCT
ejpam-5649	45	68	.	.	PUNCT
ejpam-5649	46	1	the	the	DET
ejpam-5649	46	2	complement	complement	NOUN
ejpam-5649	46	3	of	of	ADP
ejpam-5649	46	4	a	a	DET
ejpam-5649	46	5	τ1τ2	τ1τ2	ADJ
ejpam-5649	46	6	-	-	ADJ
ejpam-5649	46	7	closed	closed	ADJ
ejpam-5649	46	8	set	set	NOUN
ejpam-5649	46	9	is	be	AUX
ejpam-5649	46	10	called	call	VERB
ejpam-5649	46	11	τ1τ2	τ1τ2	NOUN
ejpam-5649	46	12	-	-	ADJ
ejpam-5649	46	13	open	open	ADJ
ejpam-5649	46	14	.	.	PUNCT
ejpam-5649	47	1	the	the	DET
ejpam-5649	47	2	intersection	intersection	NOUN
ejpam-5649	47	3	of	of	ADP
ejpam-5649	47	4	all	all	DET
ejpam-5649	47	5	τ1τ2	τ1τ2	ADJ
ejpam-5649	47	6	-	-	ADJ
ejpam-5649	47	7	closed	closed	ADJ
ejpam-5649	47	8	sets	set	NOUN
ejpam-5649	47	9	of	of	ADP
ejpam-5649	47	10	x	x	PUNCT
ejpam-5649	47	11	containing	contain	VERB
ejpam-5649	47	12	a	a	PRON
ejpam-5649	47	13	is	be	AUX
ejpam-5649	47	14	called	call	VERB
ejpam-5649	47	15	the	the	DET
ejpam-5649	47	16	τ1τ2	τ1τ2	NOUN
ejpam-5649	47	17	-	-	NOUN
ejpam-5649	47	18	closure	closure	NOUN
ejpam-5649	47	19	[	[	X
ejpam-5649	47	20	29	29	NUM
ejpam-5649	47	21	]	]	PUNCT
ejpam-5649	47	22	of	of	ADP
ejpam-5649	47	23	a	a	PRON
ejpam-5649	47	24	and	and	CCONJ
ejpam-5649	47	25	is	be	AUX
ejpam-5649	47	26	denoted	denote	VERB
ejpam-5649	47	27	by	by	ADP
ejpam-5649	47	28	τ1τ2	τ1τ2	NOUN
ejpam-5649	47	29	-	-	NUM
ejpam-5649	47	30	cl(a	cl(a	NUM
ejpam-5649	47	31	)	)	PUNCT
ejpam-5649	47	32	.	.	PUNCT
ejpam-5649	48	1	the	the	DET
ejpam-5649	48	2	union	union	NOUN
ejpam-5649	48	3	of	of	ADP
ejpam-5649	48	4	all	all	DET
ejpam-5649	48	5	τ1τ2	τ1τ2	ADJ
ejpam-5649	48	6	-	-	ADJ
ejpam-5649	48	7	open	open	ADJ
ejpam-5649	48	8	sets	set	NOUN
ejpam-5649	48	9	of	of	ADP
ejpam-5649	48	10	x	x	PUNCT
ejpam-5649	48	11	contained	contain	VERB
ejpam-5649	48	12	in	in	ADP
ejpam-5649	48	13	a	a	PRON
ejpam-5649	48	14	is	be	AUX
ejpam-5649	48	15	called	call	VERB
ejpam-5649	48	16	the	the	DET
ejpam-5649	48	17	τ1τ2	τ1τ2	NOUN
ejpam-5649	48	18	-	-	ADJ
ejpam-5649	48	19	interior	interior	ADJ
ejpam-5649	48	20	[	[	X
ejpam-5649	48	21	29	29	NUM
ejpam-5649	48	22	]	]	PUNCT
ejpam-5649	48	23	of	of	ADP
ejpam-5649	48	24	a	a	PRON
ejpam-5649	48	25	and	and	CCONJ
ejpam-5649	48	26	is	be	AUX
ejpam-5649	48	27	denoted	denote	VERB
ejpam-5649	48	28	by	by	ADP
ejpam-5649	48	29	τ1τ2	τ1τ2	NOUN
ejpam-5649	48	30	-	-	ADJ
ejpam-5649	48	31	int(a	int(a	NOUN
ejpam-5649	48	32	)	)	PUNCT
ejpam-5649	48	33	.	.	PUNCT
ejpam-5649	49	1	lemma	lemma	PROPN
ejpam-5649	49	2	1	1	NUM
ejpam-5649	49	3	.	.	PUNCT
ejpam-5649	50	1	[	[	X
ejpam-5649	50	2	29	29	NUM
ejpam-5649	50	3	]	]	PUNCT
ejpam-5649	50	4	let	let	VERB
ejpam-5649	50	5	a	a	PRON
ejpam-5649	50	6	and	and	CCONJ
ejpam-5649	50	7	b	b	NOUN
ejpam-5649	50	8	be	be	AUX
ejpam-5649	50	9	subsets	subset	NOUN
ejpam-5649	50	10	of	of	ADP
ejpam-5649	50	11	a	a	DET
ejpam-5649	50	12	bitopological	bitopological	ADJ
ejpam-5649	50	13	space	space	NOUN
ejpam-5649	50	14	(	(	PUNCT
ejpam-5649	50	15	x	x	NOUN
ejpam-5649	50	16	,	,	PUNCT
ejpam-5649	50	17	τ1	τ1	NOUN
ejpam-5649	50	18	,	,	PUNCT
ejpam-5649	50	19	τ2	τ2	NOUN
ejpam-5649	50	20	)	)	PUNCT
ejpam-5649	50	21	.	.	PUNCT
ejpam-5649	51	1	for	for	ADP
ejpam-5649	51	2	the	the	DET
ejpam-5649	51	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5649	51	4	,	,	PUNCT
ejpam-5649	51	5	the	the	DET
ejpam-5649	51	6	following	follow	VERB
ejpam-5649	51	7	properties	property	NOUN
ejpam-5649	51	8	hold	hold	VERB
ejpam-5649	51	9	:	:	PUNCT
ejpam-5649	51	10	(	(	PUNCT
ejpam-5649	51	11	1	1	X
ejpam-5649	51	12	)	)	PUNCT
ejpam-5649	51	13	a	a	DET
ejpam-5649	51	14	⊆	⊆	NUM
ejpam-5649	51	15	τ1τ2	τ1τ2	NOUN
ejpam-5649	51	16	-	-	NUM
ejpam-5649	51	17	cl(a	cl(a	NUM
ejpam-5649	51	18	)	)	PUNCT
ejpam-5649	51	19	and	and	CCONJ
ejpam-5649	51	20	τ1τ2	τ1τ2	NOUN
ejpam-5649	51	21	-	-	ADJ
ejpam-5649	51	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5649	51	23	-	-	PUNCT
ejpam-5649	51	24	cl(a	cl(a	NUM
ejpam-5649	51	25	)	)	PUNCT
ejpam-5649	51	26	)	)	PUNCT
ejpam-5649	52	1	=	=	PUNCT
ejpam-5649	52	2	τ1τ2	τ1τ2	NOUN
ejpam-5649	52	3	-	-	NUM
ejpam-5649	52	4	cl(a	cl(a	NUM
ejpam-5649	52	5	)	)	PUNCT
ejpam-5649	52	6	.	.	PUNCT
ejpam-5649	53	1	(	(	PUNCT
ejpam-5649	53	2	2	2	X
ejpam-5649	53	3	)	)	PUNCT
ejpam-5649	53	4	if	if	SCONJ
ejpam-5649	53	5	a	a	DET
ejpam-5649	53	6	⊆	⊆	NUM
ejpam-5649	53	7	b	b	NOUN
ejpam-5649	53	8	,	,	PUNCT
ejpam-5649	53	9	then	then	ADV
ejpam-5649	53	10	τ1τ2	τ1τ2	NOUN
ejpam-5649	53	11	-	-	NUM
ejpam-5649	53	12	cl(a	cl(a	NUM
ejpam-5649	53	13	)	)	PUNCT
ejpam-5649	53	14	⊆	⊆	NUM
ejpam-5649	53	15	τ1τ2	τ1τ2	NOUN
ejpam-5649	53	16	-	-	NOUN
ejpam-5649	53	17	cl(b	cl(b	NOUN
ejpam-5649	53	18	)	)	PUNCT
ejpam-5649	53	19	.	.	PUNCT
ejpam-5649	54	1	(	(	PUNCT
ejpam-5649	54	2	3	3	X
ejpam-5649	54	3	)	)	PUNCT
ejpam-5649	54	4	τ1τ2	τ1τ2	NOUN
ejpam-5649	54	5	-	-	NUM
ejpam-5649	54	6	cl(a	cl(a	NUM
ejpam-5649	54	7	)	)	PUNCT
ejpam-5649	54	8	is	be	AUX
ejpam-5649	54	9	τ1τ2	τ1τ2	NOUN
ejpam-5649	54	10	-	-	ADJ
ejpam-5649	54	11	closed	closed	ADJ
ejpam-5649	54	12	.	.	PUNCT
ejpam-5649	55	1	(	(	PUNCT
ejpam-5649	55	2	4	4	X
ejpam-5649	55	3	)	)	PUNCT
ejpam-5649	55	4	a	a	PRON
ejpam-5649	55	5	is	be	AUX
ejpam-5649	55	6	τ1τ2	τ1τ2	NOUN
ejpam-5649	55	7	-	-	ADJ
ejpam-5649	55	8	closed	closed	ADJ
ejpam-5649	55	9	if	if	SCONJ
ejpam-5649	55	10	and	and	CCONJ
ejpam-5649	55	11	only	only	ADV
ejpam-5649	55	12	if	if	SCONJ
ejpam-5649	55	13	a	a	DET
ejpam-5649	55	14	=	=	PUNCT
ejpam-5649	55	15	τ1τ2	τ1τ2	NOUN
ejpam-5649	55	16	-	-	NUM
ejpam-5649	55	17	cl(a	cl(a	NUM
ejpam-5649	55	18	)	)	PUNCT
ejpam-5649	55	19	.	.	PUNCT
ejpam-5649	56	1	(	(	PUNCT
ejpam-5649	56	2	5	5	X
ejpam-5649	56	3	)	)	PUNCT
ejpam-5649	56	4	τ1τ2	τ1τ2	NOUN
ejpam-5649	56	5	-	-	NOUN
ejpam-5649	56	6	cl(x	cl(x	X
ejpam-5649	56	7	−a	−a	NOUN
ejpam-5649	56	8	)	)	PUNCT
ejpam-5649	57	1	=	=	PUNCT
ejpam-5649	57	2	x	x	X
ejpam-5649	58	1	−	−	ADP
ejpam-5649	58	2	τ1τ2	τ1τ2	NOUN
ejpam-5649	58	3	-	-	PUNCT
ejpam-5649	58	4	int(a	int(a	NOUN
ejpam-5649	58	5	)	)	PUNCT
ejpam-5649	58	6	.	.	PUNCT
ejpam-5649	59	1	a	a	DET
ejpam-5649	59	2	bitopological	bitopological	ADJ
ejpam-5649	59	3	space	space	NOUN
ejpam-5649	59	4	(	(	PUNCT
ejpam-5649	59	5	x	x	NOUN
ejpam-5649	59	6	,	,	PUNCT
ejpam-5649	59	7	τ1	τ1	NOUN
ejpam-5649	59	8	,	,	PUNCT
ejpam-5649	59	9	τ2	τ2	NOUN
ejpam-5649	59	10	)	)	PUNCT
ejpam-5649	59	11	is	be	AUX
ejpam-5649	59	12	said	say	VERB
ejpam-5649	59	13	to	to	PART
ejpam-5649	59	14	be	be	AUX
ejpam-5649	59	15	τ1τ2	τ1τ2	NOUN
ejpam-5649	59	16	-	-	ADJ
ejpam-5649	59	17	connected	connected	ADJ
ejpam-5649	59	18	[	[	X
ejpam-5649	59	19	29	29	NUM
ejpam-5649	59	20	]	]	X
ejpam-5649	59	21	if	if	SCONJ
ejpam-5649	59	22	x	x	PRON
ejpam-5649	59	23	can	can	AUX
ejpam-5649	59	24	not	not	PART
ejpam-5649	59	25	be	be	AUX
ejpam-5649	59	26	written	write	VERB
ejpam-5649	59	27	as	as	ADP
ejpam-5649	59	28	the	the	DET
ejpam-5649	59	29	union	union	NOUN
ejpam-5649	59	30	of	of	ADP
ejpam-5649	59	31	two	two	NUM
ejpam-5649	59	32	nonempty	nonempty	ADV
ejpam-5649	59	33	disjoint	disjoint	NOUN
ejpam-5649	59	34	τ1τ2	τ1τ2	ADJ
ejpam-5649	59	35	-	-	ADJ
ejpam-5649	59	36	open	open	ADJ
ejpam-5649	59	37	sets	set	NOUN
ejpam-5649	59	38	.	.	PUNCT
ejpam-5649	60	1	a	a	DET
ejpam-5649	60	2	subset	subset	NOUN
ejpam-5649	60	3	a	a	PRON
ejpam-5649	60	4	of	of	ADP
ejpam-5649	60	5	a	a	DET
ejpam-5649	60	6	bitopological	bitopological	ADJ
ejpam-5649	60	7	space	space	NOUN
ejpam-5649	60	8	(	(	PUNCT
ejpam-5649	60	9	x	x	NOUN
ejpam-5649	60	10	,	,	PUNCT
ejpam-5649	60	11	τ1	τ1	NOUN
ejpam-5649	60	12	,	,	PUNCT
ejpam-5649	60	13	τ2	τ2	NOUN
ejpam-5649	60	14	)	)	PUNCT
ejpam-5649	60	15	is	be	AUX
ejpam-5649	60	16	called	call	VERB
ejpam-5649	60	17	(	(	PUNCT
ejpam-5649	60	18	τ1	τ1	NOUN
ejpam-5649	60	19	,	,	PUNCT
ejpam-5649	60	20	τ2)r	τ2)r	NOUN
ejpam-5649	60	21	-	-	PUNCT
ejpam-5649	60	22	open	open	NOUN
ejpam-5649	61	1	[	[	X
ejpam-5649	61	2	68	68	NUM
ejpam-5649	61	3	]	]	PUNCT
ejpam-5649	61	4	(	(	PUNCT
ejpam-5649	61	5	resp	resp	NOUN
ejpam-5649	61	6	.	.	PUNCT
ejpam-5649	62	1	(	(	PUNCT
ejpam-5649	62	2	τ1	τ1	NOUN
ejpam-5649	62	3	,	,	PUNCT
ejpam-5649	62	4	τ2)s	τ2)s	NOUN
ejpam-5649	62	5	-	-	PUNCT
ejpam-5649	62	6	open	open	ADJ
ejpam-5649	62	7	[	[	X
ejpam-5649	62	8	5	5	NUM
ejpam-5649	62	9	]	]	PUNCT
ejpam-5649	62	10	,	,	PUNCT
ejpam-5649	62	11	(	(	PUNCT
ejpam-5649	62	12	τ1	τ1	NOUN
ejpam-5649	62	13	,	,	PUNCT
ejpam-5649	62	14	τ2)popen	τ2)popen	ADJ
ejpam-5649	62	15	[	[	PUNCT
ejpam-5649	62	16	5	5	NUM
ejpam-5649	62	17	]	]	PUNCT
ejpam-5649	62	18	,	,	PUNCT
ejpam-5649	62	19	(	(	PUNCT
ejpam-5649	62	20	τ1	τ1	NOUN
ejpam-5649	62	21	,	,	PUNCT
ejpam-5649	62	22	τ2)β	τ2)β	ADJ
ejpam-5649	62	23	-	-	PUNCT
ejpam-5649	62	24	open	open	NOUN
ejpam-5649	63	1	[	[	X
ejpam-5649	63	2	5	5	NUM
ejpam-5649	63	3	]	]	PUNCT
ejpam-5649	63	4	,	,	PUNCT
ejpam-5649	63	5	α(τ1	α(τ1	NOUN
ejpam-5649	63	6	,	,	PUNCT
ejpam-5649	63	7	τ2)-open	τ2)-open	ADJ
ejpam-5649	63	8	)	)	PUNCT
ejpam-5649	64	1	[	[	X
ejpam-5649	64	2	71	71	NUM
ejpam-5649	64	3	]	]	SYM
ejpam-5649	64	4	)	)	PUNCT
ejpam-5649	64	5	if	if	SCONJ
ejpam-5649	64	6	a	a	DET
ejpam-5649	64	7	=	=	PUNCT
ejpam-5649	64	8	τ1τ2	τ1τ2	NOUN
ejpam-5649	64	9	-	-	NOUN
ejpam-5649	64	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	64	11	-	-	PUNCT
ejpam-5649	64	12	cl(a	cl(a	NUM
ejpam-5649	64	13	)	)	PUNCT
ejpam-5649	64	14	)	)	PUNCT
ejpam-5649	64	15	(	(	PUNCT
ejpam-5649	64	16	resp	resp	NOUN
ejpam-5649	64	17	.	.	PUNCT
ejpam-5649	65	1	a	a	DET
ejpam-5649	65	2	⊆	⊆	NUM
ejpam-5649	65	3	τ1τ2	τ1τ2	NOUN
ejpam-5649	65	4	-	-	ADJ
ejpam-5649	65	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5649	65	6	-	-	PUNCT
ejpam-5649	65	7	int(a	int(a	NOUN
ejpam-5649	65	8	)	)	PUNCT
ejpam-5649	65	9	)	)	PUNCT
ejpam-5649	65	10	,	,	PUNCT
ejpam-5649	65	11	a	a	DET
ejpam-5649	65	12	⊆	⊆	NUM
ejpam-5649	65	13	τ1τ2	τ1τ2	NOUN
ejpam-5649	65	14	-	-	NOUN
ejpam-5649	65	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	65	16	-	-	PUNCT
ejpam-5649	65	17	cl(a	cl(a	NUM
ejpam-5649	65	18	)	)	PUNCT
ejpam-5649	65	19	)	)	PUNCT
ejpam-5649	65	20	,	,	PUNCT
ejpam-5649	65	21	a	a	DET
ejpam-5649	65	22	⊆	⊆	NUM
ejpam-5649	65	23	τ1τ2	τ1τ2	NOUN
ejpam-5649	65	24	-	-	PUNCT
ejpam-5649	65	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5649	65	26	-	-	PUNCT
ejpam-5649	65	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	65	28	-	-	PUNCT
ejpam-5649	65	29	cl(a	cl(a	NUM
ejpam-5649	65	30	)	)	PUNCT
ejpam-5649	65	31	)	)	PUNCT
ejpam-5649	65	32	)	)	PUNCT
ejpam-5649	65	33	,	,	PUNCT
ejpam-5649	65	34	a	a	DET
ejpam-5649	65	35	⊆	⊆	NUM
ejpam-5649	65	36	τ1τ2	τ1τ2	NOUN
ejpam-5649	65	37	-	-	PUNCT
ejpam-5649	65	38	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	65	39	-	-	PUNCT
ejpam-5649	65	40	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5649	65	41	-	-	PUNCT
ejpam-5649	65	42	int(a	int(a	NOUN
ejpam-5649	65	43	)	)	PUNCT
ejpam-5649	65	44	)	)	PUNCT
ejpam-5649	65	45	)	)	PUNCT
ejpam-5649	65	46	)	)	PUNCT
ejpam-5649	65	47	.	.	PUNCT
ejpam-5649	66	1	the	the	DET
ejpam-5649	66	2	complement	complement	NOUN
ejpam-5649	66	3	of	of	ADP
ejpam-5649	66	4	a	a	DET
ejpam-5649	66	5	(	(	PUNCT
ejpam-5649	66	6	τ1	τ1	NOUN
ejpam-5649	66	7	,	,	PUNCT
ejpam-5649	66	8	τ2)r	τ2)r	NOUN
ejpam-5649	66	9	-	-	PUNCT
ejpam-5649	66	10	open	open	ADJ
ejpam-5649	66	11	(	(	PUNCT
ejpam-5649	66	12	resp	resp	NOUN
ejpam-5649	66	13	.	.	PUNCT
ejpam-5649	67	1	(	(	PUNCT
ejpam-5649	67	2	τ1	τ1	NOUN
ejpam-5649	67	3	,	,	PUNCT
ejpam-5649	67	4	τ2)s	τ2)s	NOUN
ejpam-5649	67	5	-	-	PUNCT
ejpam-5649	67	6	open	open	ADJ
ejpam-5649	67	7	,	,	PUNCT
ejpam-5649	67	8	(	(	PUNCT
ejpam-5649	67	9	τ1	τ1	NOUN
ejpam-5649	67	10	,	,	PUNCT
ejpam-5649	67	11	τ2)p	τ2)p	NOUN
ejpam-5649	67	12	-	-	ADJ
ejpam-5649	67	13	open	open	ADJ
ejpam-5649	67	14	,	,	PUNCT
ejpam-5649	67	15	(	(	PUNCT
ejpam-5649	67	16	τ1	τ1	NOUN
ejpam-5649	67	17	,	,	PUNCT
ejpam-5649	67	18	τ2)β	τ2)β	ADJ
ejpam-5649	67	19	-	-	PUNCT
ejpam-5649	67	20	open	open	ADJ
ejpam-5649	67	21	,	,	PUNCT
ejpam-5649	67	22	α(τ1	α(τ1	NOUN
ejpam-5649	67	23	,	,	PUNCT
ejpam-5649	67	24	τ2)-open	τ2)-open	ADJ
ejpam-5649	67	25	)	)	PUNCT
ejpam-5649	67	26	set	set	NOUN
ejpam-5649	67	27	is	be	AUX
ejpam-5649	67	28	called	call	VERB
ejpam-5649	67	29	(	(	PUNCT
ejpam-5649	67	30	τ1	τ1	NOUN
ejpam-5649	67	31	,	,	PUNCT
ejpam-5649	67	32	τ2)r	τ2)r	NOUN
ejpam-5649	67	33	-	-	PUNCT
ejpam-5649	67	34	closed	closed	ADJ
ejpam-5649	67	35	(	(	PUNCT
ejpam-5649	67	36	resp	resp	NOUN
ejpam-5649	67	37	.	.	PUNCT
ejpam-5649	68	1	(	(	PUNCT
ejpam-5649	68	2	τ1	τ1	NOUN
ejpam-5649	68	3	,	,	PUNCT
ejpam-5649	68	4	τ2)sclosed	τ2)sclose	VERB
ejpam-5649	68	5	,	,	PUNCT
ejpam-5649	68	6	(	(	PUNCT
ejpam-5649	68	7	τ1	τ1	NOUN
ejpam-5649	68	8	,	,	PUNCT
ejpam-5649	68	9	τ2)p	τ2)p	NOUN
ejpam-5649	68	10	-	-	PUNCT
ejpam-5649	68	11	closed	closed	ADJ
ejpam-5649	68	12	,	,	PUNCT
ejpam-5649	68	13	(	(	PUNCT
ejpam-5649	68	14	τ1	τ1	NOUN
ejpam-5649	68	15	,	,	PUNCT
ejpam-5649	68	16	τ2)β	τ2)β	ADJ
ejpam-5649	68	17	-	-	PUNCT
ejpam-5649	68	18	closed	closed	ADJ
ejpam-5649	68	19	,	,	PUNCT
ejpam-5649	68	20	α(τ1	α(τ1	NOUN
ejpam-5649	68	21	,	,	PUNCT
ejpam-5649	68	22	τ2)-closed	τ2)-closed	ADJ
ejpam-5649	68	23	)	)	PUNCT
ejpam-5649	68	24	.	.	PUNCT
ejpam-5649	69	1	a	a	DET
ejpam-5649	69	2	subset	subset	ADJ
ejpam-5649	69	3	r	r	NOUN
ejpam-5649	69	4	of	of	ADP
ejpam-5649	69	5	a	a	DET
ejpam-5649	69	6	bitopological	bitopological	ADJ
ejpam-5649	69	7	space	space	NOUN
ejpam-5649	69	8	(	(	PUNCT
ejpam-5649	69	9	x	x	NOUN
ejpam-5649	69	10	,	,	PUNCT
ejpam-5649	69	11	τ1	τ1	NOUN
ejpam-5649	69	12	,	,	PUNCT
ejpam-5649	69	13	τ2	τ2	NOUN
ejpam-5649	69	14	)	)	PUNCT
ejpam-5649	69	15	is	be	AUX
ejpam-5649	69	16	said	say	VERB
ejpam-5649	69	17	to	to	PART
ejpam-5649	69	18	be	be	AUX
ejpam-5649	69	19	τ1τ2	τ1τ2	NOUN
ejpam-5649	69	20	-	-	ADJ
ejpam-5649	69	21	rare	rare	ADJ
ejpam-5649	69	22	set	set	NOUN
ejpam-5649	69	23	[	[	X
ejpam-5649	69	24	66	66	NUM
ejpam-5649	69	25	]	]	PUNCT
ejpam-5649	69	26	if	if	SCONJ
ejpam-5649	69	27	τ1τ2	τ1τ2	NOUN
ejpam-5649	69	28	-	-	PUNCT
ejpam-5649	69	29	int(r	int(r	NOUN
ejpam-5649	69	30	)	)	PUNCT
ejpam-5649	69	31	=	=	VERB
ejpam-5649	69	32	∅.	∅.	AUX
ejpam-5649	69	33	let	let	VERB
ejpam-5649	69	34	a	a	DET
ejpam-5649	69	35	be	be	AUX
ejpam-5649	69	36	a	a	DET
ejpam-5649	69	37	subset	subset	NOUN
ejpam-5649	69	38	of	of	ADP
ejpam-5649	69	39	a	a	DET
ejpam-5649	69	40	bitopological	bitopological	ADJ
ejpam-5649	69	41	space	space	NOUN
ejpam-5649	69	42	(	(	PUNCT
ejpam-5649	69	43	x	x	NOUN
ejpam-5649	69	44	,	,	PUNCT
ejpam-5649	69	45	τ1	τ1	NOUN
ejpam-5649	69	46	,	,	PUNCT
ejpam-5649	69	47	τ2	τ2	NOUN
ejpam-5649	69	48	)	)	PUNCT
ejpam-5649	69	49	.	.	PUNCT
ejpam-5649	70	1	the	the	DET
ejpam-5649	70	2	intersection	intersection	NOUN
ejpam-5649	70	3	of	of	ADP
ejpam-5649	70	4	all	all	DET
ejpam-5649	70	5	(	(	PUNCT
ejpam-5649	70	6	τ1	τ1	NOUN
ejpam-5649	70	7	,	,	PUNCT
ejpam-5649	70	8	τ2)p	τ2)p	ADJ
ejpam-5649	70	9	-	-	PUNCT
ejpam-5649	70	10	closed	closed	ADJ
ejpam-5649	70	11	sets	set	NOUN
ejpam-5649	70	12	of	of	ADP
ejpam-5649	70	13	x	x	PUNCT
ejpam-5649	70	14	containing	contain	VERB
ejpam-5649	70	15	a	a	PRON
ejpam-5649	70	16	is	be	AUX
ejpam-5649	70	17	called	call	VERB
ejpam-5649	70	18	the	the	DET
ejpam-5649	70	19	(	(	PUNCT
ejpam-5649	70	20	τ1	τ1	NOUN
ejpam-5649	70	21	,	,	PUNCT
ejpam-5649	70	22	τ2)p	τ2)p	NOUN
ejpam-5649	70	23	-	-	PUNCT
ejpam-5649	70	24	closure	closure	NOUN
ejpam-5649	70	25	of	of	ADP
ejpam-5649	70	26	a	a	PRON
ejpam-5649	70	27	and	and	CCONJ
ejpam-5649	70	28	is	be	AUX
ejpam-5649	70	29	denoted	denote	VERB
ejpam-5649	70	30	by	by	ADP
ejpam-5649	70	31	(	(	PUNCT
ejpam-5649	70	32	τ1	τ1	PROPN
ejpam-5649	70	33	,	,	PUNCT
ejpam-5649	70	34	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-5649	70	35	)	)	PUNCT
ejpam-5649	70	36	.	.	PUNCT
ejpam-5649	71	1	the	the	DET
ejpam-5649	71	2	union	union	NOUN
ejpam-5649	71	3	of	of	ADP
ejpam-5649	71	4	all	all	DET
ejpam-5649	71	5	(	(	PUNCT
ejpam-5649	71	6	τ1	τ1	NOUN
ejpam-5649	71	7	,	,	PUNCT
ejpam-5649	71	8	τ2)p	τ2)p	ADJ
ejpam-5649	71	9	-	-	PUNCT
ejpam-5649	71	10	open	open	ADJ
ejpam-5649	71	11	sets	set	NOUN
ejpam-5649	71	12	of	of	ADP
ejpam-5649	71	13	x	x	PUNCT
ejpam-5649	71	14	contained	contain	VERB
ejpam-5649	71	15	in	in	ADP
ejpam-5649	71	16	a	a	PRON
ejpam-5649	71	17	is	be	AUX
ejpam-5649	71	18	called	call	VERB
ejpam-5649	71	19	the	the	DET
ejpam-5649	71	20	(	(	PUNCT
ejpam-5649	71	21	τ1	τ1	NOUN
ejpam-5649	71	22	,	,	PUNCT
ejpam-5649	71	23	τ2)p	τ2)p	ADJ
ejpam-5649	71	24	-	-	NOUN
ejpam-5649	71	25	interior	interior	NOUN
ejpam-5649	71	26	of	of	ADP
ejpam-5649	71	27	a	a	PRON
ejpam-5649	71	28	and	and	CCONJ
ejpam-5649	71	29	is	be	AUX
ejpam-5649	71	30	denoted	denote	VERB
ejpam-5649	71	31	by	by	ADP
ejpam-5649	71	32	(	(	PUNCT
ejpam-5649	71	33	τ1	τ1	NOUN
ejpam-5649	71	34	,	,	PUNCT
ejpam-5649	71	35	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-5649	71	36	)	)	PUNCT
ejpam-5649	71	37	.	.	PUNCT
ejpam-5649	72	1	lemma	lemma	PROPN
ejpam-5649	72	2	2	2	NUM
ejpam-5649	72	3	.	.	PUNCT
ejpam-5649	73	1	[	[	X
ejpam-5649	73	2	72	72	NUM
ejpam-5649	73	3	]	]	PUNCT
ejpam-5649	73	4	for	for	ADP
ejpam-5649	73	5	a	a	DET
ejpam-5649	73	6	subset	subset	NOUN
ejpam-5649	73	7	a	a	PRON
ejpam-5649	73	8	of	of	ADP
ejpam-5649	73	9	a	a	DET
ejpam-5649	73	10	bitopological	bitopological	ADJ
ejpam-5649	73	11	space	space	NOUN
ejpam-5649	73	12	(	(	PUNCT
ejpam-5649	73	13	x	x	NOUN
ejpam-5649	73	14	,	,	PUNCT
ejpam-5649	73	15	τ1	τ1	NOUN
ejpam-5649	73	16	,	,	PUNCT
ejpam-5649	73	17	τ2	τ2	NOUN
ejpam-5649	73	18	)	)	PUNCT
ejpam-5649	73	19	,	,	PUNCT
ejpam-5649	73	20	the	the	DET
ejpam-5649	73	21	following	follow	VERB
ejpam-5649	73	22	properties	property	NOUN
ejpam-5649	73	23	hold	hold	VERB
ejpam-5649	73	24	:	:	PUNCT
ejpam-5649	73	25	(	(	PUNCT
ejpam-5649	73	26	1	1	X
ejpam-5649	73	27	)	)	PUNCT
ejpam-5649	73	28	a	a	PRON
ejpam-5649	73	29	is	is	NOUN
ejpam-5649	73	30	(	(	PUNCT
ejpam-5649	73	31	τ1	τ1	NOUN
ejpam-5649	73	32	,	,	PUNCT
ejpam-5649	73	33	τ2)p	τ2)p	NOUN
ejpam-5649	73	34	-	-	PUNCT
ejpam-5649	73	35	closed	closed	ADJ
ejpam-5649	73	36	if	if	SCONJ
ejpam-5649	73	37	and	and	CCONJ
ejpam-5649	74	1	only	only	ADV
ejpam-5649	74	2	if	if	SCONJ
ejpam-5649	74	3	(	(	PUNCT
ejpam-5649	74	4	τ1	τ1	NOUN
ejpam-5649	74	5	,	,	PUNCT
ejpam-5649	74	6	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-5649	74	7	)	)	PUNCT
ejpam-5649	74	8	=	=	SYM
ejpam-5649	74	9	a	a	X
ejpam-5649	74	10	;	;	PUNCT
ejpam-5649	74	11	(	(	PUNCT
ejpam-5649	74	12	2	2	NUM
ejpam-5649	74	13	)	)	PUNCT
ejpam-5649	74	14	(	(	PUNCT
ejpam-5649	74	15	τ1	τ1	NOUN
ejpam-5649	74	16	,	,	PUNCT
ejpam-5649	74	17	τ2)-pcl(a	τ2)-pcl(a	ADJ
ejpam-5649	74	18	)	)	PUNCT
ejpam-5649	74	19	=	=	SYM
ejpam-5649	74	20	τ1τ2cl(τ1τ2int(a	τ1τ2cl(τ1τ2int(a	NOUN
ejpam-5649	74	21	)	)	PUNCT
ejpam-5649	74	22	)	)	PUNCT
ejpam-5649	75	1	∪a	∪a	NUM
ejpam-5649	75	2	;	;	PUNCT
ejpam-5649	75	3	(	(	PUNCT
ejpam-5649	75	4	3	3	X
ejpam-5649	75	5	)	)	PUNCT
ejpam-5649	75	6	(	(	PUNCT
ejpam-5649	75	7	τ1	τ1	NOUN
ejpam-5649	75	8	,	,	PUNCT
ejpam-5649	75	9	τ2)-pcl((τ1	τ2)-pcl((τ1	PROPN
ejpam-5649	75	10	,	,	PUNCT
ejpam-5649	75	11	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-5649	75	12	)	)	PUNCT
ejpam-5649	75	13	)	)	PUNCT
ejpam-5649	76	1	=	=	PRON
ejpam-5649	76	2	(	(	PUNCT
ejpam-5649	76	3	τ1	τ1	PROPN
ejpam-5649	76	4	,	,	PUNCT
ejpam-5649	76	5	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-5649	76	6	)	)	PUNCT
ejpam-5649	76	7	.	.	PUNCT
ejpam-5649	77	1	b.	b.	PROPN
ejpam-5649	77	2	kong	kong	PROPN
ejpam-5649	77	3	-	-	PUNCT
ejpam-5649	77	4	ied	ied	PROPN
ejpam-5649	77	5	,	,	PUNCT
ejpam-5649	77	6	s.	s.	PROPN
ejpam-5649	77	7	sompong	sompong	PROPN
ejpam-5649	77	8	,	,	PUNCT
ejpam-5649	77	9	c.	c.	PROPN
ejpam-5649	77	10	boonpok	boonpok	PROPN
ejpam-5649	77	11	/	/	SYM
ejpam-5649	77	12	eur	eur	PROPN
ejpam-5649	77	13	.	.	PUNCT
ejpam-5649	78	1	j.	j.	PROPN
ejpam-5649	78	2	pure	pure	PROPN
ejpam-5649	78	3	appl	appl	PROPN
ejpam-5649	78	4	.	.	PROPN
ejpam-5649	78	5	math	math	PROPN
ejpam-5649	78	6	,	,	PUNCT
ejpam-5649	78	7	18	18	NUM
ejpam-5649	78	8	(	(	PUNCT
ejpam-5649	78	9	1	1	NUM
ejpam-5649	78	10	)	)	PUNCT
ejpam-5649	78	11	(	(	PUNCT
ejpam-5649	78	12	2025	2025	NUM
ejpam-5649	78	13	)	)	PUNCT
ejpam-5649	78	14	,	,	PUNCT
ejpam-5649	78	15	5649	5649	NUM
ejpam-5649	78	16	4	4	NUM
ejpam-5649	78	17	of	of	ADP
ejpam-5649	78	18	13	13	NUM
ejpam-5649	78	19	by	by	ADP
ejpam-5649	78	20	a	a	DET
ejpam-5649	78	21	multifunction	multifunction	NOUN
ejpam-5649	78	22	f	f	NOUN
ejpam-5649	78	23	:	:	PUNCT
ejpam-5649	78	24	x	x	X
ejpam-5649	78	25	→	→	SYM
ejpam-5649	78	26	y	y	PROPN
ejpam-5649	78	27	,	,	PUNCT
ejpam-5649	78	28	we	we	PRON
ejpam-5649	78	29	mean	mean	VERB
ejpam-5649	78	30	a	a	DET
ejpam-5649	78	31	point	point	NOUN
ejpam-5649	78	32	-	-	PUNCT
ejpam-5649	78	33	to	to	ADP
ejpam-5649	78	34	-	-	PUNCT
ejpam-5649	78	35	set	set	VERB
ejpam-5649	78	36	correspondence	correspondence	NOUN
ejpam-5649	78	37	from	from	ADP
ejpam-5649	78	38	x	x	PUNCT
ejpam-5649	78	39	into	into	ADP
ejpam-5649	78	40	y	y	PROPN
ejpam-5649	78	41	,	,	PUNCT
ejpam-5649	78	42	and	and	CCONJ
ejpam-5649	78	43	we	we	PRON
ejpam-5649	78	44	always	always	ADV
ejpam-5649	78	45	assume	assume	VERB
ejpam-5649	78	46	that	that	SCONJ
ejpam-5649	78	47	f	f	PROPN
ejpam-5649	78	48	(	(	PUNCT
ejpam-5649	78	49	x	x	X
ejpam-5649	78	50	)	)	PUNCT
ejpam-5649	78	51	̸=	̸=	NOUN
ejpam-5649	78	52	∅	∅	NOUN
ejpam-5649	78	53	for	for	ADP
ejpam-5649	78	54	all	all	PRON
ejpam-5649	78	55	x	x	SYM
ejpam-5649	78	56	∈	∈	ADJ
ejpam-5649	78	57	x.	x.	NOUN
ejpam-5649	78	58	for	for	ADP
ejpam-5649	78	59	a	a	DET
ejpam-5649	78	60	multifunction	multifunction	NOUN
ejpam-5649	78	61	f	f	NOUN
ejpam-5649	78	62	:	:	PUNCT
ejpam-5649	78	63	x	x	X
ejpam-5649	78	64	→	→	SYM
ejpam-5649	78	65	y	y	PROPN
ejpam-5649	78	66	,	,	PUNCT
ejpam-5649	78	67	we	we	PRON
ejpam-5649	78	68	shall	shall	AUX
ejpam-5649	78	69	denote	denote	VERB
ejpam-5649	78	70	the	the	DET
ejpam-5649	78	71	upper	upper	ADJ
ejpam-5649	78	72	and	and	CCONJ
ejpam-5649	78	73	lower	low	ADJ
ejpam-5649	78	74	inverse	inverse	NOUN
ejpam-5649	78	75	of	of	ADP
ejpam-5649	78	76	a	a	DET
ejpam-5649	78	77	set	set	NOUN
ejpam-5649	78	78	b	b	PROPN
ejpam-5649	78	79	of	of	ADP
ejpam-5649	78	80	y	y	PROPN
ejpam-5649	78	81	by	by	ADP
ejpam-5649	78	82	f+(b	f+(b	NOUN
ejpam-5649	78	83	)	)	PUNCT
ejpam-5649	78	84	and	and	CCONJ
ejpam-5649	78	85	f−(b	f−(b	NOUN
ejpam-5649	78	86	)	)	PUNCT
ejpam-5649	78	87	,	,	PUNCT
ejpam-5649	78	88	respectively	respectively	ADV
ejpam-5649	78	89	,	,	PUNCT
ejpam-5649	78	90	that	that	ADV
ejpam-5649	78	91	is	is	ADV
ejpam-5649	78	92	,	,	PUNCT
ejpam-5649	78	93	f+(b	f+(b	NOUN
ejpam-5649	78	94	)	)	PUNCT
ejpam-5649	78	95	=	=	PRON
ejpam-5649	79	1	{	{	PUNCT
ejpam-5649	79	2	x	x	PUNCT
ejpam-5649	79	3	∈	∈	PROPN
ejpam-5649	79	4	x	x	INTJ
ejpam-5649	80	1	|	|	NOUN
ejpam-5649	80	2	f	f	X
ejpam-5649	80	3	(	(	PUNCT
ejpam-5649	80	4	x	x	NOUN
ejpam-5649	80	5	)	)	PUNCT
ejpam-5649	80	6	⊆	⊆	NUM
ejpam-5649	80	7	b	b	NOUN
ejpam-5649	80	8	}	}	PUNCT
ejpam-5649	80	9	and	and	CCONJ
ejpam-5649	80	10	f−(b	f−(b	PROPN
ejpam-5649	80	11	)	)	PUNCT
ejpam-5649	80	12	=	=	PRON
ejpam-5649	81	1	{	{	PUNCT
ejpam-5649	81	2	x	x	PUNCT
ejpam-5649	81	3	∈	∈	PROPN
ejpam-5649	81	4	x	x	INTJ
ejpam-5649	82	1	|	|	NOUN
ejpam-5649	82	2	f	f	X
ejpam-5649	82	3	(	(	PUNCT
ejpam-5649	82	4	x	x	NOUN
ejpam-5649	82	5	)	)	PUNCT
ejpam-5649	82	6	∩	∩	NOUN
ejpam-5649	82	7	b	b	PROPN
ejpam-5649	82	8	̸=	̸=	PROPN
ejpam-5649	82	9	∅	∅	NOUN
ejpam-5649	82	10	}	}	PUNCT
ejpam-5649	82	11	.	.	PUNCT
ejpam-5649	83	1	in	in	ADP
ejpam-5649	83	2	particular	particular	ADJ
ejpam-5649	83	3	,	,	PUNCT
ejpam-5649	83	4	f−(y	f−(y	NOUN
ejpam-5649	83	5	)	)	PUNCT
ejpam-5649	83	6	=	=	SYM
ejpam-5649	84	1	{	{	PUNCT
ejpam-5649	84	2	x	x	PUNCT
ejpam-5649	84	3	∈	∈	PROPN
ejpam-5649	84	4	x	x	INTJ
ejpam-5649	85	1	|	|	ADV
ejpam-5649	85	2	y	y	PROPN
ejpam-5649	85	3	∈	∈	PROPN
ejpam-5649	85	4	f	f	X
ejpam-5649	85	5	(	(	PUNCT
ejpam-5649	85	6	x	x	NOUN
ejpam-5649	85	7	)	)	PUNCT
ejpam-5649	85	8	}	}	PUNCT
ejpam-5649	85	9	for	for	ADP
ejpam-5649	85	10	each	each	DET
ejpam-5649	85	11	point	point	NOUN
ejpam-5649	85	12	y	y	PROPN
ejpam-5649	85	13	∈	∈	PROPN
ejpam-5649	85	14	y	y	PROPN
ejpam-5649	85	15	.	.	PUNCT
ejpam-5649	86	1	for	for	ADP
ejpam-5649	86	2	each	each	DET
ejpam-5649	86	3	a	a	DET
ejpam-5649	86	4	⊆	⊆	NUM
ejpam-5649	86	5	x	x	SYM
ejpam-5649	86	6	,	,	PUNCT
ejpam-5649	86	7	f	f	PROPN
ejpam-5649	86	8	(	(	PUNCT
ejpam-5649	86	9	a	a	NOUN
ejpam-5649	86	10	)	)	PUNCT
ejpam-5649	86	11	=	=	SYM
ejpam-5649	86	12	∪x∈af	∪x∈af	NOUN
ejpam-5649	86	13	(	(	PUNCT
ejpam-5649	86	14	x	x	NOUN
ejpam-5649	86	15	)	)	PUNCT
ejpam-5649	86	16	.	.	PUNCT
ejpam-5649	87	1	3	3	X
ejpam-5649	87	2	.	.	X
ejpam-5649	87	3	upper	upper	ADJ
ejpam-5649	87	4	and	and	CCONJ
ejpam-5649	87	5	lower	low	ADJ
ejpam-5649	87	6	rarely	rarely	ADV
ejpam-5649	87	7	s-(τ1	s-(τ1	NOUN
ejpam-5649	87	8	,	,	PUNCT
ejpam-5649	87	9	τ2)p	τ2)p	ADJ
ejpam-5649	87	10	-	-	ADJ
ejpam-5649	87	11	continuous	continuous	ADJ
ejpam-5649	87	12	multifunctions	multifunction	NOUN
ejpam-5649	87	13	in	in	ADP
ejpam-5649	87	14	this	this	DET
ejpam-5649	87	15	section	section	NOUN
ejpam-5649	87	16	,	,	PUNCT
ejpam-5649	87	17	we	we	PRON
ejpam-5649	87	18	introduce	introduce	VERB
ejpam-5649	87	19	the	the	DET
ejpam-5649	87	20	notions	notion	NOUN
ejpam-5649	87	21	of	of	ADP
ejpam-5649	87	22	upper	upper	ADJ
ejpam-5649	87	23	rarely	rarely	ADV
ejpam-5649	87	24	s-(τ1	s-(τ1	NOUN
ejpam-5649	87	25	,	,	PUNCT
ejpam-5649	87	26	τ2)p	τ2)p	ADJ
ejpam-5649	87	27	-	-	ADJ
ejpam-5649	87	28	continuous	continuous	ADJ
ejpam-5649	87	29	multifunctions	multifunction	NOUN
ejpam-5649	87	30	and	and	CCONJ
ejpam-5649	87	31	lower	low	ADJ
ejpam-5649	87	32	rarely	rarely	ADV
ejpam-5649	87	33	s-(τ1	s-(τ1	NOUN
ejpam-5649	87	34	,	,	PUNCT
ejpam-5649	87	35	τ2)p	τ2)p	ADJ
ejpam-5649	87	36	-	-	PUNCT
ejpam-5649	87	37	continuous	continuous	ADJ
ejpam-5649	87	38	multifunctions	multifunction	NOUN
ejpam-5649	87	39	.	.	PUNCT
ejpam-5649	88	1	moreover	moreover	ADV
ejpam-5649	88	2	,	,	PUNCT
ejpam-5649	88	3	some	some	DET
ejpam-5649	88	4	characterizations	characterization	NOUN
ejpam-5649	88	5	of	of	ADP
ejpam-5649	88	6	upper	upper	ADJ
ejpam-5649	88	7	rarely	rarely	ADV
ejpam-5649	88	8	s-(τ1	s-(τ1	NOUN
ejpam-5649	88	9	,	,	PUNCT
ejpam-5649	88	10	τ2)p	τ2)p	ADJ
ejpam-5649	88	11	-	-	ADJ
ejpam-5649	88	12	continuous	continuous	ADJ
ejpam-5649	88	13	multifunctions	multifunction	NOUN
ejpam-5649	88	14	and	and	CCONJ
ejpam-5649	88	15	lower	low	ADJ
ejpam-5649	88	16	rarely	rarely	ADV
ejpam-5649	88	17	s(τ1	s(τ1	VERB
ejpam-5649	88	18	,	,	PUNCT
ejpam-5649	88	19	τ2)p	τ2)p	ADJ
ejpam-5649	88	20	-	-	PUNCT
ejpam-5649	88	21	continuous	continuous	ADJ
ejpam-5649	88	22	multifunctions	multifunction	NOUN
ejpam-5649	88	23	are	be	AUX
ejpam-5649	88	24	discussed	discuss	VERB
ejpam-5649	88	25	.	.	PUNCT
ejpam-5649	89	1	definition	definition	NOUN
ejpam-5649	89	2	1	1	NUM
ejpam-5649	89	3	.	.	PUNCT
ejpam-5649	90	1	a	a	DET
ejpam-5649	90	2	multifunction	multifunction	NOUN
ejpam-5649	90	3	f	f	NOUN
ejpam-5649	90	4	:	:	PUNCT
ejpam-5649	90	5	(	(	PUNCT
ejpam-5649	90	6	x	x	NOUN
ejpam-5649	90	7	,	,	PUNCT
ejpam-5649	90	8	τ1	τ1	NOUN
ejpam-5649	90	9	,	,	PUNCT
ejpam-5649	90	10	τ2	τ2	NOUN
ejpam-5649	90	11	)	)	PUNCT
ejpam-5649	90	12	→	→	SYM
ejpam-5649	90	13	(	(	PUNCT
ejpam-5649	90	14	y	y	PROPN
ejpam-5649	90	15	,	,	PUNCT
ejpam-5649	90	16	σ1	σ1	PROPN
ejpam-5649	90	17	,	,	PUNCT
ejpam-5649	90	18	σ2	σ2	PROPN
ejpam-5649	90	19	)	)	PUNCT
ejpam-5649	90	20	is	be	AUX
ejpam-5649	90	21	said	say	VERB
ejpam-5649	90	22	to	to	PART
ejpam-5649	90	23	be	be	AUX
ejpam-5649	90	24	upper	upper	ADJ
ejpam-5649	90	25	rarely	rarely	ADV
ejpam-5649	90	26	s-(τ1	s-(τ1	NOUN
ejpam-5649	90	27	,	,	PUNCT
ejpam-5649	90	28	τ2)p	τ2)p	ADJ
ejpam-5649	90	29	-	-	ADJ
ejpam-5649	90	30	continuous	continuous	ADJ
ejpam-5649	90	31	at	at	ADP
ejpam-5649	90	32	x	x	X
ejpam-5649	90	33	∈	∈	PROPN
ejpam-5649	90	34	x	x	SYM
ejpam-5649	90	35	if	if	SCONJ
ejpam-5649	90	36	for	for	ADP
ejpam-5649	90	37	each	each	DET
ejpam-5649	90	38	σ1σ2	σ1σ2	VERB
ejpam-5649	90	39	-	-	ADJ
ejpam-5649	90	40	open	open	ADJ
ejpam-5649	90	41	set	set	NOUN
ejpam-5649	90	42	v	v	NOUN
ejpam-5649	90	43	of	of	ADP
ejpam-5649	90	44	y	y	PROPN
ejpam-5649	90	45	having	have	VERB
ejpam-5649	90	46	σ1σ2	σ1σ2	ADV
ejpam-5649	90	47	-	-	PUNCT
ejpam-5649	90	48	connected	connected	ADJ
ejpam-5649	90	49	complement	complement	NOUN
ejpam-5649	90	50	such	such	ADJ
ejpam-5649	90	51	that	that	SCONJ
ejpam-5649	90	52	f	f	PROPN
ejpam-5649	90	53	(	(	PUNCT
ejpam-5649	90	54	x	x	X
ejpam-5649	90	55	)	)	PUNCT
ejpam-5649	90	56	⊆	⊆	NUM
ejpam-5649	90	57	v	v	NOUN
ejpam-5649	90	58	,	,	PUNCT
ejpam-5649	90	59	there	there	PRON
ejpam-5649	90	60	exists	exist	VERB
ejpam-5649	90	61	a	a	DET
ejpam-5649	90	62	σ1σ2	σ1σ2	NUM
ejpam-5649	90	63	-	-	ADJ
ejpam-5649	90	64	rare	rare	ADJ
ejpam-5649	90	65	set	set	NOUN
ejpam-5649	90	66	rv	rv	PROPN
ejpam-5649	90	67	with	with	ADP
ejpam-5649	90	68	τ1τ2	τ1τ2	NOUN
ejpam-5649	90	69	-	-	ADJ
ejpam-5649	90	70	cl(rv	cl(rv	ADJ
ejpam-5649	90	71	)	)	PUNCT
ejpam-5649	91	1	∩v	∩v	NOUN
ejpam-5649	91	2	=	=	PUNCT
ejpam-5649	92	1	∅	∅	NOUN
ejpam-5649	92	2	and	and	CCONJ
ejpam-5649	92	3	a	a	DET
ejpam-5649	92	4	(	(	PUNCT
ejpam-5649	92	5	τ1	τ1	NOUN
ejpam-5649	92	6	,	,	PUNCT
ejpam-5649	92	7	τ2)p	τ2)p	ADJ
ejpam-5649	92	8	-	-	PUNCT
ejpam-5649	92	9	open	open	ADJ
ejpam-5649	92	10	set	set	NOUN
ejpam-5649	92	11	u	u	NOUN
ejpam-5649	92	12	of	of	ADP
ejpam-5649	92	13	x	x	PUNCT
ejpam-5649	92	14	containing	contain	VERB
ejpam-5649	92	15	x	x	PUNCT
ejpam-5649	92	16	such	such	ADJ
ejpam-5649	92	17	that	that	SCONJ
ejpam-5649	92	18	f	f	PROPN
ejpam-5649	92	19	(	(	PUNCT
ejpam-5649	92	20	u	u	NOUN
ejpam-5649	92	21	)	)	PUNCT
ejpam-5649	92	22	⊆	⊆	NUM
ejpam-5649	92	23	v	v	ADP
ejpam-5649	92	24	∪rv	∪rv	NOUN
ejpam-5649	92	25	.	.	PUNCT
ejpam-5649	93	1	a	a	DET
ejpam-5649	93	2	multifunction	multifunction	NOUN
ejpam-5649	93	3	f	f	NOUN
ejpam-5649	93	4	:	:	PUNCT
ejpam-5649	93	5	(	(	PUNCT
ejpam-5649	93	6	x	x	NOUN
ejpam-5649	93	7	,	,	PUNCT
ejpam-5649	93	8	τ1	τ1	NOUN
ejpam-5649	93	9	,	,	PUNCT
ejpam-5649	93	10	τ2	τ2	NOUN
ejpam-5649	93	11	)	)	PUNCT
ejpam-5649	93	12	→	→	SYM
ejpam-5649	93	13	(	(	PUNCT
ejpam-5649	93	14	y	y	PROPN
ejpam-5649	93	15	,	,	PUNCT
ejpam-5649	93	16	σ1	σ1	PROPN
ejpam-5649	93	17	,	,	PUNCT
ejpam-5649	93	18	σ2	σ2	PROPN
ejpam-5649	93	19	)	)	PUNCT
ejpam-5649	93	20	is	be	AUX
ejpam-5649	93	21	said	say	VERB
ejpam-5649	93	22	to	to	PART
ejpam-5649	93	23	be	be	AUX
ejpam-5649	93	24	upper	upper	ADJ
ejpam-5649	93	25	rarely	rarely	ADV
ejpam-5649	93	26	s-(τ1	s-(τ1	NOUN
ejpam-5649	93	27	,	,	PUNCT
ejpam-5649	93	28	τ2)p	τ2)p	ADJ
ejpam-5649	93	29	-	-	ADJ
ejpam-5649	93	30	continuous	continuous	ADJ
ejpam-5649	93	31	if	if	SCONJ
ejpam-5649	93	32	f	f	PROPN
ejpam-5649	93	33	is	be	AUX
ejpam-5649	93	34	upper	upper	ADJ
ejpam-5649	93	35	rarely	rarely	ADV
ejpam-5649	93	36	s-(τ1	s-(τ1	NOUN
ejpam-5649	93	37	,	,	PUNCT
ejpam-5649	93	38	τ2)p	τ2)p	ADJ
ejpam-5649	93	39	-	-	ADJ
ejpam-5649	93	40	continuous	continuous	ADJ
ejpam-5649	93	41	at	at	ADP
ejpam-5649	93	42	each	each	DET
ejpam-5649	93	43	point	point	NOUN
ejpam-5649	93	44	x	x	PUNCT
ejpam-5649	93	45	of	of	ADP
ejpam-5649	93	46	x.	x.	PROPN
ejpam-5649	93	47	theorem	theorem	VERB
ejpam-5649	93	48	1	1	NUM
ejpam-5649	93	49	.	.	X
ejpam-5649	93	50	for	for	ADP
ejpam-5649	93	51	a	a	DET
ejpam-5649	93	52	multifunction	multifunction	NOUN
ejpam-5649	93	53	f	f	NOUN
ejpam-5649	93	54	:	:	PUNCT
ejpam-5649	93	55	(	(	PUNCT
ejpam-5649	93	56	x	x	NOUN
ejpam-5649	93	57	,	,	PUNCT
ejpam-5649	93	58	τ1	τ1	NOUN
ejpam-5649	93	59	,	,	PUNCT
ejpam-5649	93	60	τ2	τ2	NOUN
ejpam-5649	93	61	)	)	PUNCT
ejpam-5649	93	62	→	→	SYM
ejpam-5649	93	63	(	(	PUNCT
ejpam-5649	93	64	y	y	PROPN
ejpam-5649	93	65	,	,	PUNCT
ejpam-5649	93	66	σ1	σ1	PROPN
ejpam-5649	93	67	,	,	PUNCT
ejpam-5649	93	68	σ2	σ2	NOUN
ejpam-5649	93	69	)	)	PUNCT
ejpam-5649	93	70	,	,	PUNCT
ejpam-5649	93	71	the	the	DET
ejpam-5649	93	72	following	follow	VERB
ejpam-5649	93	73	properties	property	NOUN
ejpam-5649	93	74	are	be	AUX
ejpam-5649	93	75	equivalent	equivalent	ADJ
ejpam-5649	93	76	:	:	PUNCT
ejpam-5649	93	77	(	(	PUNCT
ejpam-5649	93	78	1	1	X
ejpam-5649	93	79	)	)	PUNCT
ejpam-5649	93	80	f	f	PROPN
ejpam-5649	93	81	is	be	AUX
ejpam-5649	93	82	upper	upper	ADJ
ejpam-5649	93	83	rarely	rarely	ADV
ejpam-5649	93	84	s-(τ1	s-(τ1	NOUN
ejpam-5649	93	85	,	,	PUNCT
ejpam-5649	93	86	τ2)p	τ2)p	ADJ
ejpam-5649	93	87	-	-	ADJ
ejpam-5649	93	88	continuous	continuous	ADJ
ejpam-5649	93	89	at	at	ADP
ejpam-5649	93	90	x	x	X
ejpam-5649	93	91	∈	∈	PROPN
ejpam-5649	93	92	x	x	X
ejpam-5649	93	93	;	;	PUNCT
ejpam-5649	93	94	(	(	PUNCT
ejpam-5649	93	95	2	2	X
ejpam-5649	93	96	)	)	PUNCT
ejpam-5649	93	97	for	for	ADP
ejpam-5649	93	98	every	every	DET
ejpam-5649	93	99	σ1σ2	σ1σ2	NOUN
ejpam-5649	93	100	-	-	ADJ
ejpam-5649	93	101	open	open	ADJ
ejpam-5649	93	102	set	set	NOUN
ejpam-5649	93	103	v	v	NOUN
ejpam-5649	93	104	of	of	ADP
ejpam-5649	93	105	y	y	PROPN
ejpam-5649	93	106	having	have	VERB
ejpam-5649	93	107	σ1σ2	σ1σ2	ADV
ejpam-5649	93	108	-	-	PUNCT
ejpam-5649	93	109	connected	connect	VERB
ejpam-5649	93	110	complement	complement	NOUN
ejpam-5649	93	111	with	with	ADP
ejpam-5649	93	112	f	f	PROPN
ejpam-5649	93	113	(	(	PUNCT
ejpam-5649	93	114	x	x	NOUN
ejpam-5649	93	115	)	)	PUNCT
ejpam-5649	93	116	⊆	⊆	NUM
ejpam-5649	93	117	v	v	NOUN
ejpam-5649	93	118	,	,	PUNCT
ejpam-5649	93	119	there	there	PRON
ejpam-5649	93	120	exists	exist	VERB
ejpam-5649	93	121	a	a	DET
ejpam-5649	93	122	σ1σ2	σ1σ2	NUM
ejpam-5649	93	123	-	-	ADJ
ejpam-5649	93	124	rare	rare	ADJ
ejpam-5649	93	125	set	set	ADJ
ejpam-5649	93	126	rv	rv	PROPN
ejpam-5649	93	127	with	with	ADP
ejpam-5649	93	128	σ1σ2	σ1σ2	NOUN
ejpam-5649	93	129	-	-	PUNCT
ejpam-5649	93	130	cl(rv	cl(rv	ADJ
ejpam-5649	93	131	)	)	PUNCT
ejpam-5649	94	1	∩	∩	NOUN
ejpam-5649	94	2	v	v	NOUN
ejpam-5649	94	3	=	=	NOUN
ejpam-5649	94	4	∅	∅	NOUN
ejpam-5649	94	5	such	such	ADJ
ejpam-5649	94	6	that	that	SCONJ
ejpam-5649	94	7	x	x	SYM
ejpam-5649	94	8	∈	∈	PROPN
ejpam-5649	94	9	(	(	PUNCT
ejpam-5649	94	10	τ1	τ1	NOUN
ejpam-5649	94	11	,	,	PUNCT
ejpam-5649	94	12	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	95	1	+	+	ADJ
ejpam-5649	95	2	(	(	PUNCT
ejpam-5649	95	3	v	v	NOUN
ejpam-5649	95	4	∪rv	∪rv	NOUN
ejpam-5649	95	5	)	)	PUNCT
ejpam-5649	95	6	)	)	PUNCT
ejpam-5649	95	7	;	;	PUNCT
ejpam-5649	95	8	(	(	PUNCT
ejpam-5649	95	9	3	3	X
ejpam-5649	95	10	)	)	PUNCT
ejpam-5649	95	11	for	for	ADP
ejpam-5649	95	12	every	every	DET
ejpam-5649	95	13	σ1σ2	σ1σ2	NOUN
ejpam-5649	95	14	-	-	ADJ
ejpam-5649	95	15	open	open	ADJ
ejpam-5649	95	16	set	set	NOUN
ejpam-5649	95	17	v	v	NOUN
ejpam-5649	95	18	of	of	ADP
ejpam-5649	95	19	y	y	PROPN
ejpam-5649	95	20	having	have	VERB
ejpam-5649	95	21	σ1σ2	σ1σ2	ADV
ejpam-5649	95	22	-	-	PUNCT
ejpam-5649	95	23	connected	connect	VERB
ejpam-5649	95	24	complement	complement	NOUN
ejpam-5649	95	25	with	with	ADP
ejpam-5649	95	26	f	f	PROPN
ejpam-5649	95	27	(	(	PUNCT
ejpam-5649	95	28	x	x	NOUN
ejpam-5649	95	29	)	)	PUNCT
ejpam-5649	95	30	⊆	⊆	NUM
ejpam-5649	95	31	v	v	NOUN
ejpam-5649	95	32	,	,	PUNCT
ejpam-5649	95	33	there	there	PRON
ejpam-5649	95	34	exists	exist	VERB
ejpam-5649	95	35	a	a	DET
ejpam-5649	95	36	σ1σ2	σ1σ2	NUM
ejpam-5649	95	37	-	-	ADJ
ejpam-5649	95	38	rare	rare	ADJ
ejpam-5649	95	39	set	set	ADJ
ejpam-5649	95	40	rv	rv	NOUN
ejpam-5649	95	41	with	with	ADP
ejpam-5649	95	42	σ1σ2	σ1σ2	NOUN
ejpam-5649	95	43	-	-	PUNCT
ejpam-5649	95	44	cl(v	cl(v	NOUN
ejpam-5649	95	45	)	)	PUNCT
ejpam-5649	95	46	∩rv	∩rv	NOUN
ejpam-5649	95	47	=	=	PUNCT
ejpam-5649	95	48	∅	∅	NOUN
ejpam-5649	95	49	such	such	ADJ
ejpam-5649	95	50	that	that	SCONJ
ejpam-5649	95	51	x	x	SYM
ejpam-5649	95	52	∈	∈	PROPN
ejpam-5649	95	53	(	(	PUNCT
ejpam-5649	95	54	τ1	τ1	NOUN
ejpam-5649	95	55	,	,	PUNCT
ejpam-5649	95	56	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	95	57	+	+	ADJ
ejpam-5649	95	58	(	(	PUNCT
ejpam-5649	95	59	σ1σ2	σ1σ2	NOUN
ejpam-5649	95	60	-	-	PUNCT
ejpam-5649	95	61	cl(v	cl(v	NOUN
ejpam-5649	95	62	)	)	PUNCT
ejpam-5649	95	63	∪rv	∪rv	NOUN
ejpam-5649	95	64	)	)	PUNCT
ejpam-5649	95	65	)	)	PUNCT
ejpam-5649	95	66	;	;	PUNCT
ejpam-5649	95	67	(	(	PUNCT
ejpam-5649	95	68	4	4	X
ejpam-5649	95	69	)	)	PUNCT
ejpam-5649	95	70	for	for	ADP
ejpam-5649	95	71	every	every	DET
ejpam-5649	95	72	σ1σ2	σ1σ2	NOUN
ejpam-5649	95	73	-	-	ADJ
ejpam-5649	95	74	open	open	ADJ
ejpam-5649	95	75	set	set	NOUN
ejpam-5649	95	76	v	v	NOUN
ejpam-5649	95	77	of	of	ADP
ejpam-5649	95	78	y	y	PROPN
ejpam-5649	95	79	having	have	VERB
ejpam-5649	95	80	σ1σ2	σ1σ2	ADV
ejpam-5649	95	81	-	-	PUNCT
ejpam-5649	95	82	connected	connect	VERB
ejpam-5649	95	83	complement	complement	NOUN
ejpam-5649	95	84	with	with	ADP
ejpam-5649	95	85	f	f	PROPN
ejpam-5649	95	86	(	(	PUNCT
ejpam-5649	95	87	x	x	NOUN
ejpam-5649	95	88	)	)	PUNCT
ejpam-5649	95	89	⊆	⊆	NUM
ejpam-5649	95	90	v	v	NOUN
ejpam-5649	95	91	,	,	PUNCT
ejpam-5649	95	92	there	there	PRON
ejpam-5649	95	93	exists	exist	VERB
ejpam-5649	95	94	a	a	DET
ejpam-5649	95	95	(	(	PUNCT
ejpam-5649	95	96	τ1	τ1	NOUN
ejpam-5649	95	97	,	,	PUNCT
ejpam-5649	95	98	τ2)p	τ2)p	ADJ
ejpam-5649	95	99	-	-	PUNCT
ejpam-5649	95	100	open	open	ADJ
ejpam-5649	95	101	set	set	NOUN
ejpam-5649	95	102	u	u	NOUN
ejpam-5649	95	103	of	of	ADP
ejpam-5649	95	104	x	x	PUNCT
ejpam-5649	95	105	containing	contain	VERB
ejpam-5649	95	106	x	x	PUNCT
ejpam-5649	95	107	such	such	ADJ
ejpam-5649	95	108	that	that	SCONJ
ejpam-5649	95	109	σ1σ2	σ1σ2	NOUN
ejpam-5649	95	110	-	-	PUNCT
ejpam-5649	95	111	int(f	int(f	PROPN
ejpam-5649	95	112	(	(	PUNCT
ejpam-5649	95	113	u	u	NOUN
ejpam-5649	95	114	)	)	PUNCT
ejpam-5649	95	115	∩	∩	NOUN
ejpam-5649	95	116	(	(	PUNCT
ejpam-5649	95	117	y	y	PROPN
ejpam-5649	95	118	−	−	PROPN
ejpam-5649	95	119	v	v	NOUN
ejpam-5649	95	120	)	)	PUNCT
ejpam-5649	95	121	)	)	PUNCT
ejpam-5649	96	1	=	=	NOUN
ejpam-5649	96	2	∅	∅	NOUN
ejpam-5649	96	3	;	;	PUNCT
ejpam-5649	96	4	(	(	PUNCT
ejpam-5649	96	5	5	5	X
ejpam-5649	96	6	)	)	PUNCT
ejpam-5649	96	7	for	for	ADP
ejpam-5649	96	8	every	every	DET
ejpam-5649	96	9	σ1σ2	σ1σ2	NOUN
ejpam-5649	96	10	-	-	ADJ
ejpam-5649	96	11	open	open	ADJ
ejpam-5649	96	12	set	set	NOUN
ejpam-5649	96	13	v	v	NOUN
ejpam-5649	96	14	of	of	ADP
ejpam-5649	96	15	y	y	PROPN
ejpam-5649	96	16	having	have	VERB
ejpam-5649	96	17	σ1σ2	σ1σ2	ADV
ejpam-5649	96	18	-	-	PUNCT
ejpam-5649	96	19	connected	connect	VERB
ejpam-5649	96	20	complement	complement	NOUN
ejpam-5649	96	21	with	with	ADP
ejpam-5649	96	22	f	f	PROPN
ejpam-5649	96	23	(	(	PUNCT
ejpam-5649	96	24	x	x	NOUN
ejpam-5649	96	25	)	)	PUNCT
ejpam-5649	96	26	⊆	⊆	NUM
ejpam-5649	96	27	v	v	NOUN
ejpam-5649	96	28	,	,	PUNCT
ejpam-5649	96	29	there	there	PRON
ejpam-5649	96	30	exists	exist	VERB
ejpam-5649	96	31	a	a	DET
ejpam-5649	96	32	(	(	PUNCT
ejpam-5649	96	33	τ1	τ1	NOUN
ejpam-5649	96	34	,	,	PUNCT
ejpam-5649	96	35	τ2)p	τ2)p	ADJ
ejpam-5649	96	36	-	-	PUNCT
ejpam-5649	96	37	open	open	ADJ
ejpam-5649	96	38	set	set	NOUN
ejpam-5649	96	39	u	u	NOUN
ejpam-5649	96	40	of	of	ADP
ejpam-5649	96	41	x	x	PUNCT
ejpam-5649	96	42	containing	contain	VERB
ejpam-5649	96	43	x	x	PUNCT
ejpam-5649	96	44	such	such	ADJ
ejpam-5649	96	45	that	that	SCONJ
ejpam-5649	96	46	σ1σ2	σ1σ2	NOUN
ejpam-5649	96	47	-	-	PUNCT
ejpam-5649	96	48	int(f	int(f	PROPN
ejpam-5649	96	49	(	(	PUNCT
ejpam-5649	96	50	u	u	NOUN
ejpam-5649	96	51	)	)	PUNCT
ejpam-5649	96	52	)	)	PUNCT
ejpam-5649	97	1	⊆	⊆	X
ejpam-5649	97	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	97	3	-	-	NUM
ejpam-5649	97	4	cl(v	cl(v	NOUN
ejpam-5649	97	5	)	)	PUNCT
ejpam-5649	97	6	;	;	PUNCT
ejpam-5649	97	7	b.	b.	PROPN
ejpam-5649	97	8	kong	kong	PROPN
ejpam-5649	97	9	-	-	PUNCT
ejpam-5649	97	10	ied	ied	PROPN
ejpam-5649	97	11	,	,	PUNCT
ejpam-5649	97	12	s.	s.	PROPN
ejpam-5649	97	13	sompong	sompong	PROPN
ejpam-5649	97	14	,	,	PUNCT
ejpam-5649	97	15	c.	c.	PROPN
ejpam-5649	97	16	boonpok	boonpok	PROPN
ejpam-5649	97	17	/	/	SYM
ejpam-5649	97	18	eur	eur	PROPN
ejpam-5649	97	19	.	.	PUNCT
ejpam-5649	98	1	j.	j.	PROPN
ejpam-5649	98	2	pure	pure	PROPN
ejpam-5649	98	3	appl	appl	PROPN
ejpam-5649	98	4	.	.	PROPN
ejpam-5649	98	5	math	math	PROPN
ejpam-5649	98	6	,	,	PUNCT
ejpam-5649	98	7	18	18	NUM
ejpam-5649	98	8	(	(	PUNCT
ejpam-5649	98	9	1	1	NUM
ejpam-5649	98	10	)	)	PUNCT
ejpam-5649	98	11	(	(	PUNCT
ejpam-5649	98	12	2025	2025	NUM
ejpam-5649	98	13	)	)	PUNCT
ejpam-5649	98	14	,	,	PUNCT
ejpam-5649	98	15	5649	5649	NUM
ejpam-5649	98	16	5	5	NUM
ejpam-5649	98	17	of	of	ADP
ejpam-5649	98	18	13	13	NUM
ejpam-5649	98	19	(	(	PUNCT
ejpam-5649	98	20	6	6	NUM
ejpam-5649	98	21	)	)	PUNCT
ejpam-5649	98	22	for	for	ADP
ejpam-5649	98	23	every	every	DET
ejpam-5649	98	24	σ1σ2	σ1σ2	NOUN
ejpam-5649	98	25	-	-	ADJ
ejpam-5649	98	26	open	open	ADJ
ejpam-5649	98	27	set	set	NOUN
ejpam-5649	98	28	v	v	NOUN
ejpam-5649	98	29	of	of	ADP
ejpam-5649	98	30	y	y	PROPN
ejpam-5649	98	31	having	have	VERB
ejpam-5649	98	32	σ1σ2	σ1σ2	ADV
ejpam-5649	98	33	-	-	PUNCT
ejpam-5649	98	34	connected	connect	VERB
ejpam-5649	98	35	complement	complement	NOUN
ejpam-5649	98	36	with	with	ADP
ejpam-5649	98	37	f	f	PROPN
ejpam-5649	98	38	(	(	PUNCT
ejpam-5649	98	39	x	x	NOUN
ejpam-5649	98	40	)	)	PUNCT
ejpam-5649	98	41	⊆	⊆	NUM
ejpam-5649	98	42	v	v	NOUN
ejpam-5649	98	43	,	,	PUNCT
ejpam-5649	98	44	there	there	PRON
ejpam-5649	98	45	exists	exist	VERB
ejpam-5649	98	46	a	a	DET
ejpam-5649	98	47	σ1σ2	σ1σ2	NUM
ejpam-5649	98	48	-	-	ADJ
ejpam-5649	98	49	rare	rare	ADJ
ejpam-5649	98	50	set	set	ADJ
ejpam-5649	98	51	rv	rv	PROPN
ejpam-5649	98	52	with	with	ADP
ejpam-5649	98	53	σ1σ2	σ1σ2	NOUN
ejpam-5649	98	54	-	-	PUNCT
ejpam-5649	98	55	cl(rv	cl(rv	ADJ
ejpam-5649	98	56	)	)	PUNCT
ejpam-5649	99	1	∩	∩	NOUN
ejpam-5649	99	2	v	v	NOUN
ejpam-5649	99	3	=	=	NOUN
ejpam-5649	99	4	∅	∅	NOUN
ejpam-5649	99	5	such	such	ADJ
ejpam-5649	99	6	that	that	SCONJ
ejpam-5649	99	7	x	x	SYM
ejpam-5649	99	8	∈	∈	NOUN
ejpam-5649	99	9	f+(v	f+(v	NOUN
ejpam-5649	99	10	∪rv	∪rv	NOUN
ejpam-5649	99	11	)	)	PUNCT
ejpam-5649	99	12	∩	∩	NOUN
ejpam-5649	99	13	τ1τ2	τ1τ2	NOUN
ejpam-5649	99	14	-	-	NOUN
ejpam-5649	99	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	99	16	-	-	PUNCT
ejpam-5649	99	17	cl(f	cl(f	NOUN
ejpam-5649	99	18	+	+	NOUN
ejpam-5649	99	19	(	(	PUNCT
ejpam-5649	99	20	v	v	NOUN
ejpam-5649	99	21	∪rv	∪rv	NOUN
ejpam-5649	99	22	)	)	PUNCT
ejpam-5649	99	23	)	)	PUNCT
ejpam-5649	99	24	)	)	PUNCT
ejpam-5649	99	25	.	.	PUNCT
ejpam-5649	100	1	proof	proof	NOUN
ejpam-5649	100	2	.	.	PUNCT
ejpam-5649	101	1	(	(	PUNCT
ejpam-5649	101	2	1	1	X
ejpam-5649	101	3	)	)	PUNCT
ejpam-5649	101	4	⇒	⇒	NOUN
ejpam-5649	101	5	(	(	PUNCT
ejpam-5649	101	6	2	2	NUM
ejpam-5649	101	7	):	):	PUNCT
ejpam-5649	101	8	let	let	VERB
ejpam-5649	101	9	v	v	PART
ejpam-5649	101	10	be	be	AUX
ejpam-5649	101	11	any	any	DET
ejpam-5649	101	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	101	13	-	-	ADJ
ejpam-5649	101	14	open	open	ADJ
ejpam-5649	101	15	set	set	NOUN
ejpam-5649	101	16	of	of	ADP
ejpam-5649	101	17	y	y	PROPN
ejpam-5649	101	18	having	have	VERB
ejpam-5649	101	19	σ1σ2	σ1σ2	ADV
ejpam-5649	101	20	-	-	PUNCT
ejpam-5649	101	21	connected	connected	ADJ
ejpam-5649	101	22	complement	complement	NOUN
ejpam-5649	101	23	such	such	ADJ
ejpam-5649	101	24	that	that	SCONJ
ejpam-5649	101	25	f	f	PROPN
ejpam-5649	101	26	(	(	PUNCT
ejpam-5649	101	27	x	x	X
ejpam-5649	101	28	)	)	PUNCT
ejpam-5649	101	29	⊆	⊆	NUM
ejpam-5649	101	30	v	v	NOUN
ejpam-5649	101	31	.	.	PUNCT
ejpam-5649	102	1	since	since	SCONJ
ejpam-5649	102	2	f	f	PROPN
ejpam-5649	102	3	is	be	AUX
ejpam-5649	102	4	upper	upper	ADJ
ejpam-5649	102	5	rarely	rarely	ADV
ejpam-5649	102	6	s-(τ1	s-(τ1	NOUN
ejpam-5649	102	7	,	,	PUNCT
ejpam-5649	102	8	τ2)p	τ2)p	ADJ
ejpam-5649	102	9	-	-	ADJ
ejpam-5649	102	10	continuous	continuous	ADJ
ejpam-5649	102	11	at	at	ADP
ejpam-5649	102	12	x	x	X
ejpam-5649	102	13	∈	∈	PROPN
ejpam-5649	102	14	x	x	NOUN
ejpam-5649	102	15	,	,	PUNCT
ejpam-5649	102	16	there	there	PRON
ejpam-5649	102	17	exists	exist	VERB
ejpam-5649	102	18	a	a	DET
ejpam-5649	102	19	σ1σ2	σ1σ2	NUM
ejpam-5649	102	20	-	-	ADJ
ejpam-5649	102	21	rare	rare	ADJ
ejpam-5649	102	22	set	set	ADJ
ejpam-5649	102	23	rv	rv	PROPN
ejpam-5649	102	24	with	with	ADP
ejpam-5649	102	25	σ1σ2	σ1σ2	NOUN
ejpam-5649	102	26	-	-	PUNCT
ejpam-5649	102	27	cl(rv	cl(rv	ADJ
ejpam-5649	102	28	)	)	PUNCT
ejpam-5649	103	1	∩	∩	NOUN
ejpam-5649	103	2	v	v	NOUN
ejpam-5649	103	3	=	=	NOUN
ejpam-5649	103	4	∅	∅	NOUN
ejpam-5649	103	5	and	and	CCONJ
ejpam-5649	103	6	a	a	DET
ejpam-5649	103	7	(	(	PUNCT
ejpam-5649	103	8	τ1	τ1	NOUN
ejpam-5649	103	9	,	,	PUNCT
ejpam-5649	103	10	τ2)p	τ2)p	ADJ
ejpam-5649	103	11	-	-	PUNCT
ejpam-5649	103	12	open	open	ADJ
ejpam-5649	103	13	set	set	NOUN
ejpam-5649	103	14	u	u	NOUN
ejpam-5649	103	15	of	of	ADP
ejpam-5649	103	16	x	x	PUNCT
ejpam-5649	103	17	containing	contain	VERB
ejpam-5649	103	18	x	x	PUNCT
ejpam-5649	103	19	such	such	ADJ
ejpam-5649	103	20	that	that	SCONJ
ejpam-5649	103	21	f	f	PROPN
ejpam-5649	103	22	(	(	PUNCT
ejpam-5649	103	23	u	u	NOUN
ejpam-5649	103	24	)	)	PUNCT
ejpam-5649	103	25	⊆	⊆	NUM
ejpam-5649	103	26	v	v	ADP
ejpam-5649	103	27	∪rv	∪rv	NOUN
ejpam-5649	103	28	.	.	PUNCT
ejpam-5649	104	1	thus	thus	ADV
ejpam-5649	104	2	,	,	PUNCT
ejpam-5649	104	3	x	x	PUNCT
ejpam-5649	104	4	∈	∈	PROPN
ejpam-5649	104	5	u	u	NOUN
ejpam-5649	104	6	⊆	⊆	NUM
ejpam-5649	104	7	f+(v	f+(v	NOUN
ejpam-5649	104	8	∪rv	∪rv	NOUN
ejpam-5649	104	9	)	)	PUNCT
ejpam-5649	104	10	and	and	CCONJ
ejpam-5649	104	11	hence	hence	ADV
ejpam-5649	104	12	x	x	X
ejpam-5649	104	13	∈	∈	PROPN
ejpam-5649	104	14	(	(	PUNCT
ejpam-5649	104	15	τ1	τ1	NOUN
ejpam-5649	104	16	,	,	PUNCT
ejpam-5649	104	17	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	105	1	+	+	ADJ
ejpam-5649	105	2	(	(	PUNCT
ejpam-5649	105	3	v	v	NOUN
ejpam-5649	105	4	∪rv	∪rv	NOUN
ejpam-5649	105	5	)	)	PUNCT
ejpam-5649	105	6	)	)	PUNCT
ejpam-5649	105	7	.	.	PUNCT
ejpam-5649	106	1	(	(	PUNCT
ejpam-5649	106	2	2	2	X
ejpam-5649	106	3	)	)	PUNCT
ejpam-5649	106	4	⇒	⇒	NOUN
ejpam-5649	106	5	(	(	PUNCT
ejpam-5649	106	6	3	3	NUM
ejpam-5649	106	7	):	):	PUNCT
ejpam-5649	106	8	let	let	VERB
ejpam-5649	106	9	v	v	PART
ejpam-5649	106	10	be	be	AUX
ejpam-5649	106	11	any	any	DET
ejpam-5649	106	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	106	13	-	-	ADJ
ejpam-5649	106	14	open	open	ADJ
ejpam-5649	106	15	set	set	NOUN
ejpam-5649	106	16	of	of	ADP
ejpam-5649	106	17	y	y	PROPN
ejpam-5649	106	18	having	have	VERB
ejpam-5649	106	19	σ1σ2	σ1σ2	ADV
ejpam-5649	106	20	-	-	PUNCT
ejpam-5649	106	21	connected	connected	ADJ
ejpam-5649	106	22	complement	complement	NOUN
ejpam-5649	106	23	such	such	ADJ
ejpam-5649	106	24	that	that	SCONJ
ejpam-5649	106	25	f	f	PROPN
ejpam-5649	106	26	(	(	PUNCT
ejpam-5649	106	27	x	x	X
ejpam-5649	106	28	)	)	PUNCT
ejpam-5649	106	29	⊆	⊆	NUM
ejpam-5649	106	30	v	v	NOUN
ejpam-5649	106	31	.	.	PUNCT
ejpam-5649	107	1	by	by	ADP
ejpam-5649	107	2	(	(	PUNCT
ejpam-5649	107	3	2	2	NUM
ejpam-5649	107	4	)	)	PUNCT
ejpam-5649	107	5	,	,	PUNCT
ejpam-5649	107	6	there	there	PRON
ejpam-5649	107	7	exists	exist	VERB
ejpam-5649	107	8	a	a	DET
ejpam-5649	107	9	σ1σ2	σ1σ2	NUM
ejpam-5649	107	10	-	-	ADJ
ejpam-5649	107	11	rare	rare	ADJ
ejpam-5649	107	12	set	set	ADJ
ejpam-5649	107	13	rv	rv	PROPN
ejpam-5649	107	14	with	with	ADP
ejpam-5649	107	15	σ1σ2	σ1σ2	NOUN
ejpam-5649	107	16	-	-	PUNCT
ejpam-5649	107	17	cl(rv	cl(rv	ADJ
ejpam-5649	107	18	)	)	PUNCT
ejpam-5649	108	1	∩	∩	NOUN
ejpam-5649	108	2	v	v	NOUN
ejpam-5649	108	3	=	=	NOUN
ejpam-5649	108	4	∅	∅	NOUN
ejpam-5649	108	5	such	such	ADJ
ejpam-5649	108	6	that	that	SCONJ
ejpam-5649	108	7	x	x	SYM
ejpam-5649	108	8	∈	∈	PROPN
ejpam-5649	108	9	(	(	PUNCT
ejpam-5649	108	10	τ1	τ1	NOUN
ejpam-5649	108	11	,	,	PUNCT
ejpam-5649	108	12	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	109	1	+	+	ADJ
ejpam-5649	109	2	(	(	PUNCT
ejpam-5649	109	3	v	v	NOUN
ejpam-5649	109	4	∪	∪	X
ejpam-5649	109	5	rv	rv	PROPN
ejpam-5649	109	6	)	)	PUNCT
ejpam-5649	109	7	)	)	PUNCT
ejpam-5649	109	8	.	.	PUNCT
ejpam-5649	110	1	since	since	SCONJ
ejpam-5649	110	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	110	3	-	-	PUNCT
ejpam-5649	110	4	cl(rv	cl(rv	ADJ
ejpam-5649	110	5	)	)	PUNCT
ejpam-5649	110	6	∩	∩	PROPN
ejpam-5649	110	7	v	v	NOUN
ejpam-5649	110	8	=	=	SYM
ejpam-5649	110	9	∅	∅	NOUN
ejpam-5649	110	10	,	,	PUNCT
ejpam-5649	110	11	we	we	PRON
ejpam-5649	110	12	have	have	VERB
ejpam-5649	110	13	rv	rv	PROPN
ejpam-5649	110	14	⊆	⊆	NUM
ejpam-5649	110	15	y	y	PROPN
ejpam-5649	110	16	−	−	PROPN
ejpam-5649	110	17	v	v	NOUN
ejpam-5649	111	1	and	and	CCONJ
ejpam-5649	111	2	y	y	PROPN
ejpam-5649	111	3	−	−	PROPN
ejpam-5649	111	4	v	v	NOUN
ejpam-5649	111	5	=	=	SYM
ejpam-5649	112	1	[	[	X
ejpam-5649	112	2	y	y	NOUN
ejpam-5649	112	3	−	−	NOUN
ejpam-5649	112	4	σ1σ2	σ1σ2	NOUN
ejpam-5649	112	5	-	-	NUM
ejpam-5649	112	6	cl(v	cl(v	NOUN
ejpam-5649	112	7	)	)	PUNCT
ejpam-5649	112	8	]	]	PUNCT
ejpam-5649	112	9	∪	∪	ADP
ejpam-5649	112	10	[	[	PUNCT
ejpam-5649	112	11	σ1σ2	σ1σ2	NOUN
ejpam-5649	112	12	-	-	NOUN
ejpam-5649	112	13	cl(v	cl(v	NOUN
ejpam-5649	112	14	)	)	PUNCT
ejpam-5649	112	15	−	−	PROPN
ejpam-5649	112	16	v	v	ADP
ejpam-5649	112	17	]	]	PUNCT
ejpam-5649	112	18	.	.	PUNCT
ejpam-5649	113	1	thus	thus	ADV
ejpam-5649	113	2	,	,	PUNCT
ejpam-5649	113	3	rv	rv	PROPN
ejpam-5649	113	4	⊆	⊆	NUM
ejpam-5649	114	1	[	[	X
ejpam-5649	114	2	rv	rv	X
ejpam-5649	114	3	∩	∩	NOUN
ejpam-5649	114	4	(	(	PUNCT
ejpam-5649	114	5	y	y	PROPN
ejpam-5649	114	6	−	−	PROPN
ejpam-5649	114	7	σ1σ2	σ1σ2	NOUN
ejpam-5649	114	8	-	-	NUM
ejpam-5649	114	9	cl(v	cl(v	NOUN
ejpam-5649	114	10	)	)	PUNCT
ejpam-5649	114	11	)	)	PUNCT
ejpam-5649	114	12	]	]	PUNCT
ejpam-5649	114	13	∪	∪	ADP
ejpam-5649	114	14	[	[	PUNCT
ejpam-5649	114	15	σ1σ2	σ1σ2	NOUN
ejpam-5649	114	16	-	-	NOUN
ejpam-5649	114	17	cl(v	cl(v	NOUN
ejpam-5649	114	18	)	)	PUNCT
ejpam-5649	114	19	−	−	PROPN
ejpam-5649	114	20	v	v	ADP
ejpam-5649	114	21	]	]	PUNCT
ejpam-5649	114	22	.	.	PUNCT
ejpam-5649	115	1	put	put	VERB
ejpam-5649	115	2	wv	wv	PROPN
ejpam-5649	115	3	=	=	SYM
ejpam-5649	115	4	rv	rv	PROPN
ejpam-5649	115	5	∩(y	∩(y	PROPN
ejpam-5649	115	6	−σ1σ2	−σ1σ2	X
ejpam-5649	115	7	-	-	NOUN
ejpam-5649	115	8	cl(v	cl(v	NOUN
ejpam-5649	115	9	)	)	PUNCT
ejpam-5649	115	10	)	)	PUNCT
ejpam-5649	115	11	.	.	PUNCT
ejpam-5649	116	1	then	then	ADV
ejpam-5649	116	2	,	,	PUNCT
ejpam-5649	116	3	wv	wv	PROPN
ejpam-5649	116	4	is	be	AUX
ejpam-5649	116	5	a	a	DET
ejpam-5649	116	6	τ1τ2	τ1τ2	ADJ
ejpam-5649	116	7	-	-	ADJ
ejpam-5649	116	8	rare	rare	ADJ
ejpam-5649	116	9	set	set	NOUN
ejpam-5649	116	10	with	with	ADP
ejpam-5649	116	11	σ1σ2	σ1σ2	NOUN
ejpam-5649	116	12	-	-	PUNCT
ejpam-5649	116	13	cl(v	cl(v	PUNCT
ejpam-5649	116	14	)	)	PUNCT
ejpam-5649	116	15	∩wv	∩wv	NOUN
ejpam-5649	116	16	=	=	PUNCT
ejpam-5649	116	17	∅.	∅.	VERB
ejpam-5649	116	18	therefore	therefore	ADV
ejpam-5649	116	19	,	,	PUNCT
ejpam-5649	116	20	x	x	SYM
ejpam-5649	116	21	∈	∈	PROPN
ejpam-5649	116	22	(	(	PUNCT
ejpam-5649	116	23	τ1	τ1	NOUN
ejpam-5649	116	24	,	,	PUNCT
ejpam-5649	116	25	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	117	1	+	+	ADJ
ejpam-5649	117	2	(	(	PUNCT
ejpam-5649	117	3	v	v	NOUN
ejpam-5649	117	4	∪rv	∪rv	NOUN
ejpam-5649	117	5	)	)	PUNCT
ejpam-5649	117	6	)	)	PUNCT
ejpam-5649	118	1	⊆	⊆	NUM
ejpam-5649	118	2	(	(	PUNCT
ejpam-5649	118	3	τ1	τ1	NOUN
ejpam-5649	118	4	,	,	PUNCT
ejpam-5649	118	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	118	6	+	+	ADJ
ejpam-5649	118	7	(	(	PUNCT
ejpam-5649	118	8	σ1σ2	σ1σ2	NOUN
ejpam-5649	118	9	-	-	PUNCT
ejpam-5649	118	10	cl(v	cl(v	NOUN
ejpam-5649	118	11	)	)	PUNCT
ejpam-5649	118	12	∪wv	∪wv	NOUN
ejpam-5649	118	13	)	)	PUNCT
ejpam-5649	118	14	)	)	PUNCT
ejpam-5649	118	15	.	.	PUNCT
ejpam-5649	119	1	(	(	PUNCT
ejpam-5649	119	2	3	3	X
ejpam-5649	119	3	)	)	PUNCT
ejpam-5649	119	4	⇒	⇒	NOUN
ejpam-5649	119	5	(	(	PUNCT
ejpam-5649	119	6	4	4	NUM
ejpam-5649	119	7	):	):	PUNCT
ejpam-5649	119	8	let	let	VERB
ejpam-5649	119	9	v	v	PART
ejpam-5649	119	10	be	be	AUX
ejpam-5649	119	11	any	any	DET
ejpam-5649	119	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	119	13	-	-	ADJ
ejpam-5649	119	14	open	open	ADJ
ejpam-5649	119	15	set	set	NOUN
ejpam-5649	119	16	of	of	ADP
ejpam-5649	119	17	y	y	PROPN
ejpam-5649	119	18	having	have	VERB
ejpam-5649	119	19	σ1σ2	σ1σ2	ADV
ejpam-5649	119	20	-	-	PUNCT
ejpam-5649	119	21	connected	connected	ADJ
ejpam-5649	119	22	complement	complement	NOUN
ejpam-5649	119	23	such	such	ADJ
ejpam-5649	119	24	that	that	SCONJ
ejpam-5649	119	25	f	f	PROPN
ejpam-5649	119	26	(	(	PUNCT
ejpam-5649	119	27	x	x	X
ejpam-5649	119	28	)	)	PUNCT
ejpam-5649	119	29	⊆	⊆	NUM
ejpam-5649	119	30	v	v	NOUN
ejpam-5649	119	31	.	.	PUNCT
ejpam-5649	120	1	by	by	ADP
ejpam-5649	120	2	(	(	PUNCT
ejpam-5649	120	3	3	3	NUM
ejpam-5649	120	4	)	)	PUNCT
ejpam-5649	120	5	,	,	PUNCT
ejpam-5649	120	6	there	there	PRON
ejpam-5649	120	7	exists	exist	VERB
ejpam-5649	120	8	a	a	DET
ejpam-5649	120	9	σ1σ2	σ1σ2	NUM
ejpam-5649	120	10	-	-	ADJ
ejpam-5649	120	11	rare	rare	ADJ
ejpam-5649	120	12	set	set	ADJ
ejpam-5649	120	13	rv	rv	NOUN
ejpam-5649	120	14	with	with	ADP
ejpam-5649	120	15	σ1σ2	σ1σ2	NOUN
ejpam-5649	120	16	-	-	PUNCT
ejpam-5649	120	17	cl(v	cl(v	NOUN
ejpam-5649	120	18	)	)	PUNCT
ejpam-5649	120	19	∩rv	∩rv	NOUN
ejpam-5649	120	20	=	=	PUNCT
ejpam-5649	120	21	∅	∅	NOUN
ejpam-5649	120	22	such	such	ADJ
ejpam-5649	120	23	that	that	SCONJ
ejpam-5649	120	24	x	x	SYM
ejpam-5649	120	25	∈	∈	PROPN
ejpam-5649	120	26	(	(	PUNCT
ejpam-5649	120	27	τ1	τ1	NOUN
ejpam-5649	120	28	,	,	PUNCT
ejpam-5649	120	29	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	120	30	+	+	ADJ
ejpam-5649	120	31	(	(	PUNCT
ejpam-5649	120	32	σ1σ2	σ1σ2	NOUN
ejpam-5649	120	33	-	-	PUNCT
ejpam-5649	120	34	cl(v	cl(v	NOUN
ejpam-5649	120	35	)	)	PUNCT
ejpam-5649	120	36	∪	∪	ADP
ejpam-5649	120	37	rv	rv	PROPN
ejpam-5649	120	38	)	)	PUNCT
ejpam-5649	120	39	)	)	PUNCT
ejpam-5649	120	40	.	.	PUNCT
ejpam-5649	121	1	let	let	VERB
ejpam-5649	121	2	u	u	PRON
ejpam-5649	121	3	=	=	PUNCT
ejpam-5649	121	4	(	(	PUNCT
ejpam-5649	121	5	τ1	τ1	PROPN
ejpam-5649	121	6	,	,	PUNCT
ejpam-5649	121	7	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	122	1	+	+	ADJ
ejpam-5649	122	2	(	(	PUNCT
ejpam-5649	122	3	σ1σ2	σ1σ2	NOUN
ejpam-5649	122	4	-	-	PUNCT
ejpam-5649	122	5	cl(v	cl(v	NOUN
ejpam-5649	122	6	)	)	PUNCT
ejpam-5649	122	7	∪	∪	ADP
ejpam-5649	122	8	rv	rv	PROPN
ejpam-5649	122	9	)	)	PUNCT
ejpam-5649	122	10	)	)	PUNCT
ejpam-5649	122	11	.	.	PUNCT
ejpam-5649	123	1	then	then	ADV
ejpam-5649	123	2	,	,	PUNCT
ejpam-5649	123	3	u	u	NOUN
ejpam-5649	123	4	is	be	AUX
ejpam-5649	123	5	a	a	DET
ejpam-5649	123	6	(	(	PUNCT
ejpam-5649	123	7	τ1	τ1	NOUN
ejpam-5649	123	8	,	,	PUNCT
ejpam-5649	123	9	τ2)p	τ2)p	ADJ
ejpam-5649	123	10	-	-	PUNCT
ejpam-5649	123	11	open	open	ADJ
ejpam-5649	123	12	set	set	NOUN
ejpam-5649	123	13	of	of	ADP
ejpam-5649	123	14	x	x	PUNCT
ejpam-5649	123	15	containing	contain	VERB
ejpam-5649	123	16	x	x	PROPN
ejpam-5649	123	17	and	and	CCONJ
ejpam-5649	123	18	f	f	PROPN
ejpam-5649	123	19	(	(	PUNCT
ejpam-5649	123	20	u	u	NOUN
ejpam-5649	123	21	)	)	PUNCT
ejpam-5649	123	22	⊆	⊆	NUM
ejpam-5649	123	23	σ1σ2	σ1σ2	NOUN
ejpam-5649	123	24	-	-	PUNCT
ejpam-5649	123	25	cl(v	cl(v	NOUN
ejpam-5649	123	26	)	)	PUNCT
ejpam-5649	123	27	∪rv	∪rv	NOUN
ejpam-5649	123	28	.	.	PUNCT
ejpam-5649	124	1	thus	thus	ADV
ejpam-5649	124	2	,	,	PUNCT
ejpam-5649	124	3	σ1σ2	σ1σ2	NOUN
ejpam-5649	124	4	-	-	PUNCT
ejpam-5649	124	5	int(f	int(f	NUM
ejpam-5649	124	6	(	(	PUNCT
ejpam-5649	124	7	u	u	NOUN
ejpam-5649	124	8	)	)	PUNCT
ejpam-5649	124	9	∩	∩	NOUN
ejpam-5649	124	10	(	(	PUNCT
ejpam-5649	124	11	y	y	PROPN
ejpam-5649	124	12	−	−	PROPN
ejpam-5649	124	13	v	v	NOUN
ejpam-5649	124	14	)	)	PUNCT
ejpam-5649	124	15	)	)	PUNCT
ejpam-5649	125	1	=	=	PUNCT
ejpam-5649	125	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	125	3	-	-	PUNCT
ejpam-5649	125	4	int(f	int(f	PROPN
ejpam-5649	125	5	(	(	PUNCT
ejpam-5649	125	6	u	u	NOUN
ejpam-5649	125	7	)	)	PUNCT
ejpam-5649	125	8	)	)	PUNCT
ejpam-5649	125	9	∩	∩	NOUN
ejpam-5649	125	10	σ1σ2	σ1σ2	X
ejpam-5649	125	11	-	-	PUNCT
ejpam-5649	125	12	int(y	int(y	ADJ
ejpam-5649	125	13	−	−	NOUN
ejpam-5649	125	14	v	v	NOUN
ejpam-5649	125	15	)	)	PUNCT
ejpam-5649	125	16	⊆	⊆	NUM
ejpam-5649	125	17	σ1σ2	σ1σ2	X
ejpam-5649	125	18	-	-	PUNCT
ejpam-5649	125	19	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5649	125	20	-	-	PUNCT
ejpam-5649	125	21	cl(v	cl(v	NOUN
ejpam-5649	125	22	)	)	PUNCT
ejpam-5649	125	23	∪rv	∪rv	PROPN
ejpam-5649	125	24	)	)	PUNCT
ejpam-5649	125	25	∩	∩	NOUN
ejpam-5649	125	26	(	(	PUNCT
ejpam-5649	125	27	y	y	PROPN
ejpam-5649	125	28	−	−	PROPN
ejpam-5649	125	29	σ1σ2	σ1σ2	NOUN
ejpam-5649	125	30	-	-	NUM
ejpam-5649	125	31	cl(v	cl(v	NOUN
ejpam-5649	125	32	)	)	PUNCT
ejpam-5649	125	33	)	)	PUNCT
ejpam-5649	126	1	=	=	SYM
ejpam-5649	126	2	σ1σ2	σ1σ2	X
ejpam-5649	126	3	-	-	PUNCT
ejpam-5649	126	4	int([σ1σ2	int([σ1σ2	NOUN
ejpam-5649	126	5	-	-	PUNCT
ejpam-5649	126	6	cl(v	cl(v	NOUN
ejpam-5649	126	7	)	)	PUNCT
ejpam-5649	126	8	∪rv	∪rv	NOUN
ejpam-5649	126	9	]	]	PUNCT
ejpam-5649	126	10	∩	∩	NOUN
ejpam-5649	127	1	[	[	X
ejpam-5649	127	2	y	y	NOUN
ejpam-5649	127	3	−	−	VERB
ejpam-5649	127	4	σ1σ2	σ1σ2	NOUN
ejpam-5649	127	5	-	-	NUM
ejpam-5649	127	6	cl(v	cl(v	NOUN
ejpam-5649	127	7	)	)	PUNCT
ejpam-5649	127	8	]	]	PUNCT
ejpam-5649	127	9	)	)	PUNCT
ejpam-5649	127	10	=	=	PUNCT
ejpam-5649	127	11	σ1σ2	σ1σ2	X
ejpam-5649	127	12	-	-	PUNCT
ejpam-5649	127	13	int([σ1σ2	int([σ1σ2	NOUN
ejpam-5649	127	14	-	-	PUNCT
ejpam-5649	127	15	cl(v	cl(v	NOUN
ejpam-5649	127	16	)	)	PUNCT
ejpam-5649	127	17	∩	∩	NOUN
ejpam-5649	127	18	(	(	PUNCT
ejpam-5649	127	19	y	y	PROPN
ejpam-5649	127	20	−	−	PROPN
ejpam-5649	127	21	σ1σ2	σ1σ2	NOUN
ejpam-5649	127	22	-	-	NUM
ejpam-5649	127	23	cl(v	cl(v	NOUN
ejpam-5649	127	24	)	)	PUNCT
ejpam-5649	127	25	)	)	PUNCT
ejpam-5649	127	26	]	]	PUNCT
ejpam-5649	127	27	∪	∪	ADP
ejpam-5649	127	28	[	[	X
ejpam-5649	127	29	rv	rv	X
ejpam-5649	127	30	∩	∩	NOUN
ejpam-5649	127	31	(	(	PUNCT
ejpam-5649	127	32	y	y	PROPN
ejpam-5649	127	33	−	−	PROPN
ejpam-5649	127	34	σ1σ2	σ1σ2	NOUN
ejpam-5649	127	35	-	-	NUM
ejpam-5649	127	36	cl(v	cl(v	NOUN
ejpam-5649	127	37	)	)	PUNCT
ejpam-5649	127	38	)	)	PUNCT
ejpam-5649	127	39	]	]	PUNCT
ejpam-5649	127	40	)	)	PUNCT
ejpam-5649	127	41	=	=	SYM
ejpam-5649	127	42	σ1σ2	σ1σ2	X
ejpam-5649	127	43	-	-	PUNCT
ejpam-5649	127	44	int(rv	int(rv	NOUN
ejpam-5649	127	45	∩	∩	NOUN
ejpam-5649	127	46	(	(	PUNCT
ejpam-5649	127	47	y	y	PROPN
ejpam-5649	127	48	−	−	PROPN
ejpam-5649	127	49	σ1σ2	σ1σ2	NOUN
ejpam-5649	127	50	-	-	NUM
ejpam-5649	127	51	cl(v	cl(v	NOUN
ejpam-5649	127	52	)	)	PUNCT
ejpam-5649	127	53	)	)	PUNCT
ejpam-5649	127	54	)	)	PUNCT
ejpam-5649	128	1	=	=	SYM
ejpam-5649	128	2	σ1σ2	σ1σ2	X
ejpam-5649	128	3	-	-	PUNCT
ejpam-5649	128	4	int(rv	int(rv	NOUN
ejpam-5649	128	5	)	)	PUNCT
ejpam-5649	128	6	∩	∩	NOUN
ejpam-5649	128	7	σ1σ2	σ1σ2	X
ejpam-5649	128	8	-	-	PUNCT
ejpam-5649	128	9	int(y	int(y	ADJ
ejpam-5649	128	10	−	−	NOUN
ejpam-5649	128	11	σ1σ2	σ1σ2	NOUN
ejpam-5649	128	12	-	-	NUM
ejpam-5649	128	13	cl(v	cl(v	NOUN
ejpam-5649	128	14	)	)	PUNCT
ejpam-5649	128	15	)	)	PUNCT
ejpam-5649	129	1	=	=	PUNCT
ejpam-5649	129	2	∅.	∅.	X
ejpam-5649	129	3	(	(	PUNCT
ejpam-5649	129	4	4	4	NUM
ejpam-5649	129	5	)	)	PUNCT
ejpam-5649	129	6	⇒	⇒	NOUN
ejpam-5649	129	7	(	(	PUNCT
ejpam-5649	129	8	5	5	NUM
ejpam-5649	129	9	):	):	PUNCT
ejpam-5649	129	10	let	let	VERB
ejpam-5649	129	11	v	v	PART
ejpam-5649	129	12	be	be	AUX
ejpam-5649	129	13	any	any	DET
ejpam-5649	129	14	σ1σ2	σ1σ2	NOUN
ejpam-5649	129	15	-	-	ADJ
ejpam-5649	129	16	open	open	ADJ
ejpam-5649	129	17	set	set	NOUN
ejpam-5649	129	18	of	of	ADP
ejpam-5649	129	19	y	y	PROPN
ejpam-5649	129	20	having	have	VERB
ejpam-5649	129	21	σ1σ2	σ1σ2	ADV
ejpam-5649	129	22	-	-	PUNCT
ejpam-5649	129	23	connected	connected	ADJ
ejpam-5649	129	24	complement	complement	NOUN
ejpam-5649	129	25	such	such	ADJ
ejpam-5649	129	26	that	that	SCONJ
ejpam-5649	129	27	f	f	PROPN
ejpam-5649	129	28	(	(	PUNCT
ejpam-5649	129	29	x	x	X
ejpam-5649	129	30	)	)	PUNCT
ejpam-5649	129	31	⊆	⊆	NUM
ejpam-5649	129	32	v	v	NOUN
ejpam-5649	129	33	.	.	PUNCT
ejpam-5649	130	1	by	by	ADP
ejpam-5649	130	2	(	(	PUNCT
ejpam-5649	130	3	4	4	NUM
ejpam-5649	130	4	)	)	PUNCT
ejpam-5649	130	5	,	,	PUNCT
ejpam-5649	130	6	there	there	PRON
ejpam-5649	130	7	exists	exist	VERB
ejpam-5649	130	8	a	a	DET
ejpam-5649	130	9	(	(	PUNCT
ejpam-5649	130	10	τ1	τ1	NOUN
ejpam-5649	130	11	,	,	PUNCT
ejpam-5649	130	12	τ2)p	τ2)p	ADJ
ejpam-5649	130	13	-	-	PUNCT
ejpam-5649	130	14	open	open	ADJ
ejpam-5649	130	15	set	set	NOUN
ejpam-5649	130	16	u	u	NOUN
ejpam-5649	130	17	of	of	ADP
ejpam-5649	130	18	x	x	PUNCT
ejpam-5649	130	19	containing	contain	VERB
ejpam-5649	130	20	x	x	PUNCT
ejpam-5649	130	21	such	such	ADJ
ejpam-5649	130	22	that	that	SCONJ
ejpam-5649	130	23	σ1σ2	σ1σ2	NOUN
ejpam-5649	130	24	-	-	PUNCT
ejpam-5649	130	25	int(f	int(f	PROPN
ejpam-5649	130	26	(	(	PUNCT
ejpam-5649	130	27	u	u	NOUN
ejpam-5649	130	28	)	)	PUNCT
ejpam-5649	130	29	∩	∩	NOUN
ejpam-5649	130	30	(	(	PUNCT
ejpam-5649	130	31	y	y	PROPN
ejpam-5649	130	32	−	−	PROPN
ejpam-5649	130	33	v	v	NOUN
ejpam-5649	130	34	)	)	PUNCT
ejpam-5649	130	35	)	)	PUNCT
ejpam-5649	131	1	=	=	PUNCT
ejpam-5649	131	2	∅.	∅.	NOUN
ejpam-5649	131	3	since	since	SCONJ
ejpam-5649	131	4	σ1σ2	σ1σ2	NOUN
ejpam-5649	131	5	-	-	PUNCT
ejpam-5649	131	6	int(f	int(f	NUM
ejpam-5649	131	7	(	(	PUNCT
ejpam-5649	131	8	u	u	NOUN
ejpam-5649	131	9	)	)	PUNCT
ejpam-5649	131	10	∩	∩	NOUN
ejpam-5649	131	11	(	(	PUNCT
ejpam-5649	131	12	y	y	PROPN
ejpam-5649	131	13	−	−	PROPN
ejpam-5649	131	14	v	v	NOUN
ejpam-5649	131	15	)	)	PUNCT
ejpam-5649	131	16	)	)	PUNCT
ejpam-5649	132	1	=	=	NOUN
ejpam-5649	132	2	∅	∅	NOUN
ejpam-5649	132	3	,	,	PUNCT
ejpam-5649	132	4	we	we	PRON
ejpam-5649	132	5	have	have	VERB
ejpam-5649	132	6	σ1σ2	σ1σ2	NOUN
ejpam-5649	132	7	-	-	NUM
ejpam-5649	132	8	int(f	int(f	PROPN
ejpam-5649	132	9	(	(	PUNCT
ejpam-5649	132	10	u	u	NOUN
ejpam-5649	132	11	)	)	PUNCT
ejpam-5649	132	12	)	)	PUNCT
ejpam-5649	133	1	⊆	⊆	NUM
ejpam-5649	133	2	v	v	ADP
ejpam-5649	133	3	⊆	⊆	NUM
ejpam-5649	133	4	σ1σ2	σ1σ2	NOUN
ejpam-5649	133	5	-	-	NUM
ejpam-5649	133	6	cl(v	cl(v	NOUN
ejpam-5649	133	7	)	)	PUNCT
ejpam-5649	133	8	.	.	PUNCT
ejpam-5649	134	1	(	(	PUNCT
ejpam-5649	134	2	5	5	X
ejpam-5649	134	3	)	)	PUNCT
ejpam-5649	134	4	⇒	⇒	NOUN
ejpam-5649	134	5	(	(	PUNCT
ejpam-5649	134	6	1	1	NUM
ejpam-5649	134	7	):	):	PUNCT
ejpam-5649	134	8	let	let	VERB
ejpam-5649	134	9	v	v	PART
ejpam-5649	134	10	be	be	AUX
ejpam-5649	134	11	any	any	DET
ejpam-5649	134	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	134	13	-	-	ADJ
ejpam-5649	134	14	open	open	ADJ
ejpam-5649	134	15	set	set	NOUN
ejpam-5649	134	16	of	of	ADP
ejpam-5649	134	17	y	y	PROPN
ejpam-5649	134	18	having	have	VERB
ejpam-5649	134	19	σ1σ2	σ1σ2	ADV
ejpam-5649	134	20	-	-	PUNCT
ejpam-5649	134	21	connected	connect	VERB
ejpam-5649	134	22	complement	complement	NOUN
ejpam-5649	134	23	with	with	ADP
ejpam-5649	134	24	f	f	PROPN
ejpam-5649	134	25	(	(	PUNCT
ejpam-5649	134	26	x	x	NOUN
ejpam-5649	134	27	)	)	PUNCT
ejpam-5649	134	28	⊆	⊆	NUM
ejpam-5649	134	29	v	v	NOUN
ejpam-5649	134	30	.	.	PUNCT
ejpam-5649	135	1	by	by	ADP
ejpam-5649	135	2	(	(	PUNCT
ejpam-5649	135	3	5	5	NUM
ejpam-5649	135	4	)	)	PUNCT
ejpam-5649	135	5	,	,	PUNCT
ejpam-5649	135	6	there	there	PRON
ejpam-5649	135	7	exists	exist	VERB
ejpam-5649	135	8	a	a	DET
ejpam-5649	135	9	(	(	PUNCT
ejpam-5649	135	10	τ1	τ1	NOUN
ejpam-5649	135	11	,	,	PUNCT
ejpam-5649	135	12	τ2)p	τ2)p	ADJ
ejpam-5649	135	13	-	-	PUNCT
ejpam-5649	135	14	open	open	ADJ
ejpam-5649	135	15	set	set	NOUN
ejpam-5649	135	16	u	u	NOUN
ejpam-5649	135	17	of	of	ADP
ejpam-5649	135	18	x	x	PUNCT
ejpam-5649	135	19	containing	contain	VERB
ejpam-5649	135	20	x	x	PUNCT
ejpam-5649	135	21	such	such	ADJ
ejpam-5649	135	22	that	that	SCONJ
ejpam-5649	135	23	σ1σ2	σ1σ2	NOUN
ejpam-5649	135	24	-	-	PUNCT
ejpam-5649	135	25	int(f	int(f	PROPN
ejpam-5649	135	26	(	(	PUNCT
ejpam-5649	135	27	u	u	NOUN
ejpam-5649	135	28	)	)	PUNCT
ejpam-5649	135	29	)	)	PUNCT
ejpam-5649	136	1	⊆	⊆	X
ejpam-5649	136	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	136	3	-	-	NUM
ejpam-5649	136	4	cl(v	cl(v	NOUN
ejpam-5649	136	5	)	)	PUNCT
ejpam-5649	136	6	.	.	PUNCT
ejpam-5649	137	1	thus	thus	ADV
ejpam-5649	137	2	,	,	PUNCT
ejpam-5649	137	3	f	f	PROPN
ejpam-5649	137	4	(	(	PUNCT
ejpam-5649	137	5	u	u	NOUN
ejpam-5649	137	6	)	)	PUNCT
ejpam-5649	137	7	=	=	SYM
ejpam-5649	137	8	(	(	PUNCT
ejpam-5649	137	9	f	f	X
ejpam-5649	137	10	(	(	PUNCT
ejpam-5649	137	11	u)−	u)−	PROPN
ejpam-5649	137	12	σ1σ2	σ1σ2	PROPN
ejpam-5649	137	13	-	-	NUM
ejpam-5649	137	14	int(f	int(f	PROPN
ejpam-5649	137	15	(	(	PUNCT
ejpam-5649	137	16	u	u	NOUN
ejpam-5649	137	17	)	)	PUNCT
ejpam-5649	137	18	)	)	PUNCT
ejpam-5649	137	19	)	)	PUNCT
ejpam-5649	137	20	∪	∪	ADP
ejpam-5649	137	21	σ1σ2	σ1σ2	NOUN
ejpam-5649	137	22	-	-	NUM
ejpam-5649	137	23	int(f	int(f	NOUN
ejpam-5649	137	24	(	(	PUNCT
ejpam-5649	137	25	u	u	NOUN
ejpam-5649	137	26	)	)	PUNCT
ejpam-5649	137	27	)	)	PUNCT
ejpam-5649	137	28	b.	b.	PROPN
ejpam-5649	137	29	kong	kong	PROPN
ejpam-5649	137	30	-	-	PUNCT
ejpam-5649	137	31	ied	ied	PROPN
ejpam-5649	137	32	,	,	PUNCT
ejpam-5649	137	33	s.	s.	PROPN
ejpam-5649	137	34	sompong	sompong	PROPN
ejpam-5649	137	35	,	,	PUNCT
ejpam-5649	137	36	c.	c.	PROPN
ejpam-5649	137	37	boonpok	boonpok	PROPN
ejpam-5649	137	38	/	/	SYM
ejpam-5649	137	39	eur	eur	PROPN
ejpam-5649	137	40	.	.	PUNCT
ejpam-5649	138	1	j.	j.	PROPN
ejpam-5649	138	2	pure	pure	PROPN
ejpam-5649	138	3	appl	appl	PROPN
ejpam-5649	138	4	.	.	PROPN
ejpam-5649	138	5	math	math	PROPN
ejpam-5649	138	6	,	,	PUNCT
ejpam-5649	138	7	18	18	NUM
ejpam-5649	138	8	(	(	PUNCT
ejpam-5649	138	9	1	1	NUM
ejpam-5649	138	10	)	)	PUNCT
ejpam-5649	138	11	(	(	PUNCT
ejpam-5649	138	12	2025	2025	NUM
ejpam-5649	138	13	)	)	PUNCT
ejpam-5649	138	14	,	,	PUNCT
ejpam-5649	138	15	5649	5649	NUM
ejpam-5649	138	16	6	6	NUM
ejpam-5649	138	17	of	of	ADP
ejpam-5649	138	18	13	13	NUM
ejpam-5649	138	19	⊆	⊆	NUM
ejpam-5649	138	20	(	(	PUNCT
ejpam-5649	138	21	f	f	PROPN
ejpam-5649	138	22	(	(	PUNCT
ejpam-5649	138	23	u)−	u)−	PROPN
ejpam-5649	138	24	σ1σ2	σ1σ2	PROPN
ejpam-5649	138	25	-	-	NUM
ejpam-5649	138	26	int(f	int(f	PROPN
ejpam-5649	138	27	(	(	PUNCT
ejpam-5649	138	28	u	u	NOUN
ejpam-5649	138	29	)	)	PUNCT
ejpam-5649	138	30	)	)	PUNCT
ejpam-5649	138	31	)	)	PUNCT
ejpam-5649	138	32	∪	∪	ADP
ejpam-5649	138	33	σ1σ2	σ1σ2	NOUN
ejpam-5649	138	34	-	-	NOUN
ejpam-5649	138	35	cl(v	cl(v	NOUN
ejpam-5649	138	36	)	)	PUNCT
ejpam-5649	138	37	=	=	SYM
ejpam-5649	139	1	(	(	PUNCT
ejpam-5649	139	2	f	f	X
ejpam-5649	139	3	(	(	PUNCT
ejpam-5649	139	4	u)−	u)−	PROPN
ejpam-5649	139	5	σ1σ2	σ1σ2	PROPN
ejpam-5649	139	6	-	-	NUM
ejpam-5649	139	7	int(f	int(f	PROPN
ejpam-5649	139	8	(	(	PUNCT
ejpam-5649	139	9	u	u	NOUN
ejpam-5649	139	10	)	)	PUNCT
ejpam-5649	139	11	)	)	PUNCT
ejpam-5649	139	12	)	)	PUNCT
ejpam-5649	139	13	∪	∪	ADP
ejpam-5649	139	14	v	v	ADP
ejpam-5649	139	15	∪	∪	X
ejpam-5649	139	16	(	(	PUNCT
ejpam-5649	139	17	σ1σ2	σ1σ2	NOUN
ejpam-5649	139	18	-	-	NUM
ejpam-5649	139	19	cl(v	cl(v	NOUN
ejpam-5649	139	20	)	)	PUNCT
ejpam-5649	139	21	−	−	PROPN
ejpam-5649	139	22	v	v	NOUN
ejpam-5649	139	23	)	)	PUNCT
ejpam-5649	140	1	=	=	PUNCT
ejpam-5649	141	1	[	[	X
ejpam-5649	141	2	(	(	PUNCT
ejpam-5649	141	3	f	f	X
ejpam-5649	141	4	(	(	PUNCT
ejpam-5649	141	5	u)−	u)−	PROPN
ejpam-5649	141	6	σ1σ2	σ1σ2	PROPN
ejpam-5649	141	7	-	-	NUM
ejpam-5649	141	8	int(f	int(f	PROPN
ejpam-5649	141	9	(	(	PUNCT
ejpam-5649	141	10	u	u	NOUN
ejpam-5649	141	11	)	)	PUNCT
ejpam-5649	141	12	)	)	PUNCT
ejpam-5649	141	13	)	)	PUNCT
ejpam-5649	141	14	∩	∩	NOUN
ejpam-5649	141	15	(	(	PUNCT
ejpam-5649	141	16	y	y	PROPN
ejpam-5649	141	17	−	−	PROPN
ejpam-5649	141	18	v	v	NOUN
ejpam-5649	141	19	)	)	PUNCT
ejpam-5649	141	20	]	]	PUNCT
ejpam-5649	141	21	∪	∪	ADP
ejpam-5649	141	22	v	v	ADP
ejpam-5649	141	23	∪	∪	X
ejpam-5649	141	24	(	(	PUNCT
ejpam-5649	141	25	σ1σ2	σ1σ2	NOUN
ejpam-5649	141	26	-	-	NUM
ejpam-5649	141	27	cl(v	cl(v	NOUN
ejpam-5649	141	28	)	)	PUNCT
ejpam-5649	141	29	−	−	PROPN
ejpam-5649	141	30	v	v	NOUN
ejpam-5649	141	31	)	)	PUNCT
ejpam-5649	141	32	.	.	PUNCT
ejpam-5649	142	1	let	let	VERB
ejpam-5649	142	2	wv	wv	PROPN
ejpam-5649	142	3	=	=	PUNCT
ejpam-5649	142	4	(	(	PUNCT
ejpam-5649	142	5	f	f	X
ejpam-5649	142	6	(	(	PUNCT
ejpam-5649	142	7	u)−σ1σ2	u)−σ1σ2	NOUN
ejpam-5649	142	8	-	-	PUNCT
ejpam-5649	142	9	int(f	int(f	NOUN
ejpam-5649	142	10	(	(	PUNCT
ejpam-5649	142	11	u)))∩	u)))∩	PROPN
ejpam-5649	142	12	(	(	PUNCT
ejpam-5649	142	13	y	y	PROPN
ejpam-5649	142	14	−v	−v	PROPN
ejpam-5649	142	15	)	)	PUNCT
ejpam-5649	142	16	and	and	CCONJ
ejpam-5649	143	1	w	w	NOUN
ejpam-5649	143	2	′	′	NUM
ejpam-5649	143	3	v	v	NOUN
ejpam-5649	143	4	=	=	SYM
ejpam-5649	143	5	σ1σ2	σ1σ2	NOUN
ejpam-5649	143	6	-	-	PUNCT
ejpam-5649	143	7	cl(v	cl(v	PUNCT
ejpam-5649	143	8	)	)	PUNCT
ejpam-5649	143	9	−v	−v	NOUN
ejpam-5649	143	10	.	.	PUNCT
ejpam-5649	144	1	then	then	ADV
ejpam-5649	144	2	,	,	PUNCT
ejpam-5649	144	3	wv	wv	PROPN
ejpam-5649	144	4	and	and	CCONJ
ejpam-5649	144	5	w	w	PROPN
ejpam-5649	144	6	′	′	NUM
ejpam-5649	144	7	v	v	NOUN
ejpam-5649	144	8	are	be	AUX
ejpam-5649	144	9	σ1σ2	σ1σ2	NOUN
ejpam-5649	144	10	-	-	ADJ
ejpam-5649	144	11	rare	rare	ADJ
ejpam-5649	144	12	sets	set	NOUN
ejpam-5649	144	13	and	and	CCONJ
ejpam-5649	144	14	rv	rv	NOUN
ejpam-5649	144	15	=	=	PROPN
ejpam-5649	144	16	wv	wv	PROPN
ejpam-5649	144	17	∪w	∪w	PROPN
ejpam-5649	144	18	′	′	NUM
ejpam-5649	144	19	v	v	NOUN
ejpam-5649	144	20	is	be	AUX
ejpam-5649	144	21	a	a	DET
ejpam-5649	144	22	σ1σ2	σ1σ2	NOUN
ejpam-5649	144	23	-	-	ADJ
ejpam-5649	144	24	rare	rare	ADJ
ejpam-5649	144	25	set	set	NOUN
ejpam-5649	144	26	such	such	ADJ
ejpam-5649	144	27	that	that	SCONJ
ejpam-5649	144	28	σ1σ2	σ1σ2	NOUN
ejpam-5649	144	29	-	-	PUNCT
ejpam-5649	144	30	cl(rv	cl(rv	ADJ
ejpam-5649	144	31	)	)	PUNCT
ejpam-5649	145	1	∩v	∩v	NOUN
ejpam-5649	145	2	=	=	PUNCT
ejpam-5649	146	1	∅	∅	NOUN
ejpam-5649	146	2	and	and	CCONJ
ejpam-5649	146	3	f	f	PROPN
ejpam-5649	146	4	(	(	PUNCT
ejpam-5649	146	5	u	u	NOUN
ejpam-5649	146	6	)	)	PUNCT
ejpam-5649	146	7	⊆	⊆	NUM
ejpam-5649	146	8	v	v	ADP
ejpam-5649	146	9	∪rv	∪rv	NOUN
ejpam-5649	146	10	.	.	PUNCT
ejpam-5649	147	1	thus	thus	ADV
ejpam-5649	147	2	,	,	PUNCT
ejpam-5649	147	3	f	f	PROPN
ejpam-5649	147	4	is	be	AUX
ejpam-5649	147	5	upper	upper	ADJ
ejpam-5649	147	6	rarely	rarely	ADV
ejpam-5649	147	7	s-(τ1	s-(τ1	NOUN
ejpam-5649	147	8	,	,	PUNCT
ejpam-5649	147	9	τ2)p	τ2)p	ADJ
ejpam-5649	147	10	-	-	ADJ
ejpam-5649	147	11	continuous	continuous	ADJ
ejpam-5649	147	12	at	at	ADP
ejpam-5649	147	13	x.	x.	NOUN
ejpam-5649	147	14	(	(	PUNCT
ejpam-5649	147	15	2	2	X
ejpam-5649	147	16	)	)	PUNCT
ejpam-5649	147	17	⇔	⇔	X
ejpam-5649	147	18	(	(	PUNCT
ejpam-5649	147	19	6	6	NUM
ejpam-5649	147	20	):	):	PUNCT
ejpam-5649	147	21	it	it	PRON
ejpam-5649	147	22	follows	follow	VERB
ejpam-5649	147	23	from	from	ADP
ejpam-5649	147	24	the	the	DET
ejpam-5649	147	25	fact	fact	NOUN
ejpam-5649	147	26	that	that	SCONJ
ejpam-5649	147	27	(	(	PUNCT
ejpam-5649	147	28	τ1	τ1	NOUN
ejpam-5649	147	29	,	,	PUNCT
ejpam-5649	147	30	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	148	1	+	+	ADJ
ejpam-5649	148	2	(	(	PUNCT
ejpam-5649	148	3	v	v	NOUN
ejpam-5649	148	4	∪rv	∪rv	NOUN
ejpam-5649	148	5	)	)	PUNCT
ejpam-5649	148	6	)	)	PUNCT
ejpam-5649	149	1	=	=	PUNCT
ejpam-5649	150	1	τ1τ2	τ1τ2	NOUN
ejpam-5649	150	2	-	-	NOUN
ejpam-5649	150	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	150	4	-	-	PUNCT
ejpam-5649	150	5	cl(f	cl(f	NOUN
ejpam-5649	150	6	+	+	NOUN
ejpam-5649	150	7	(	(	PUNCT
ejpam-5649	150	8	v	v	NOUN
ejpam-5649	150	9	∪rv	∪rv	NOUN
ejpam-5649	150	10	)	)	PUNCT
ejpam-5649	150	11	)	)	PUNCT
ejpam-5649	150	12	)	)	PUNCT
ejpam-5649	150	13	∩	∩	NOUN
ejpam-5649	150	14	f+(v	f+(v	NOUN
ejpam-5649	150	15	∪rv	∪rv	NOUN
ejpam-5649	150	16	)	)	PUNCT
ejpam-5649	150	17	.	.	PUNCT
ejpam-5649	151	1	definition	definition	NOUN
ejpam-5649	151	2	2	2	NUM
ejpam-5649	151	3	.	.	PUNCT
ejpam-5649	151	4	a	a	DET
ejpam-5649	151	5	multifunction	multifunction	NOUN
ejpam-5649	151	6	f	f	NOUN
ejpam-5649	151	7	:	:	PUNCT
ejpam-5649	151	8	(	(	PUNCT
ejpam-5649	151	9	x	x	NOUN
ejpam-5649	151	10	,	,	PUNCT
ejpam-5649	151	11	τ1	τ1	NOUN
ejpam-5649	151	12	,	,	PUNCT
ejpam-5649	151	13	τ2	τ2	NOUN
ejpam-5649	151	14	)	)	PUNCT
ejpam-5649	151	15	→	→	SYM
ejpam-5649	151	16	(	(	PUNCT
ejpam-5649	151	17	y	y	PROPN
ejpam-5649	151	18	,	,	PUNCT
ejpam-5649	151	19	σ1	σ1	PROPN
ejpam-5649	151	20	,	,	PUNCT
ejpam-5649	151	21	σ2	σ2	PROPN
ejpam-5649	151	22	)	)	PUNCT
ejpam-5649	151	23	is	be	AUX
ejpam-5649	151	24	said	say	VERB
ejpam-5649	151	25	to	to	PART
ejpam-5649	151	26	be	be	AUX
ejpam-5649	151	27	upper	upper	ADJ
ejpam-5649	151	28	weakly	weakly	ADJ
ejpam-5649	151	29	s-(τ1	s-(τ1	PROPN
ejpam-5649	151	30	,	,	PUNCT
ejpam-5649	151	31	τ2)p	τ2)p	ADJ
ejpam-5649	151	32	-	-	ADJ
ejpam-5649	151	33	continuous	continuous	ADJ
ejpam-5649	151	34	at	at	ADP
ejpam-5649	151	35	x	x	X
ejpam-5649	151	36	∈	∈	PROPN
ejpam-5649	151	37	x	x	SYM
ejpam-5649	151	38	if	if	SCONJ
ejpam-5649	151	39	for	for	ADP
ejpam-5649	151	40	each	each	DET
ejpam-5649	151	41	σ1σ2	σ1σ2	VERB
ejpam-5649	151	42	-	-	ADJ
ejpam-5649	151	43	open	open	ADJ
ejpam-5649	151	44	set	set	NOUN
ejpam-5649	151	45	v	v	NOUN
ejpam-5649	151	46	of	of	ADP
ejpam-5649	151	47	y	y	PROPN
ejpam-5649	151	48	having	have	VERB
ejpam-5649	151	49	σ1σ2	σ1σ2	ADV
ejpam-5649	151	50	-	-	PUNCT
ejpam-5649	151	51	connected	connected	ADJ
ejpam-5649	151	52	complement	complement	NOUN
ejpam-5649	151	53	such	such	ADJ
ejpam-5649	151	54	that	that	SCONJ
ejpam-5649	151	55	x	x	SYM
ejpam-5649	151	56	∈	∈	PROPN
ejpam-5649	151	57	f+(v	f+(v	NOUN
ejpam-5649	151	58	)	)	PUNCT
ejpam-5649	151	59	,	,	PUNCT
ejpam-5649	151	60	there	there	PRON
ejpam-5649	151	61	exists	exist	VERB
ejpam-5649	151	62	a	a	DET
ejpam-5649	151	63	(	(	PUNCT
ejpam-5649	151	64	τ1	τ1	NOUN
ejpam-5649	151	65	,	,	PUNCT
ejpam-5649	151	66	τ2)p	τ2)p	ADJ
ejpam-5649	151	67	-	-	PUNCT
ejpam-5649	151	68	open	open	ADJ
ejpam-5649	151	69	set	set	NOUN
ejpam-5649	151	70	u	u	NOUN
ejpam-5649	151	71	of	of	ADP
ejpam-5649	151	72	x	x	PUNCT
ejpam-5649	151	73	containing	contain	VERB
ejpam-5649	151	74	x	x	PUNCT
ejpam-5649	151	75	such	such	ADJ
ejpam-5649	151	76	that	that	SCONJ
ejpam-5649	151	77	u	u	NOUN
ejpam-5649	151	78	⊆	⊆	NUM
ejpam-5649	151	79	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5649	151	80	-	-	PUNCT
ejpam-5649	151	81	cl(v	cl(v	NOUN
ejpam-5649	151	82	)	)	PUNCT
ejpam-5649	151	83	)	)	PUNCT
ejpam-5649	151	84	.	.	PUNCT
ejpam-5649	152	1	a	a	DET
ejpam-5649	152	2	multifunction	multifunction	NOUN
ejpam-5649	152	3	f	f	NOUN
ejpam-5649	152	4	:	:	PUNCT
ejpam-5649	152	5	(	(	PUNCT
ejpam-5649	152	6	x	x	NOUN
ejpam-5649	152	7	,	,	PUNCT
ejpam-5649	152	8	τ1	τ1	NOUN
ejpam-5649	152	9	,	,	PUNCT
ejpam-5649	152	10	τ2	τ2	NOUN
ejpam-5649	152	11	)	)	PUNCT
ejpam-5649	152	12	→	→	SYM
ejpam-5649	152	13	(	(	PUNCT
ejpam-5649	152	14	y	y	PROPN
ejpam-5649	152	15	,	,	PUNCT
ejpam-5649	152	16	σ1	σ1	PROPN
ejpam-5649	152	17	,	,	PUNCT
ejpam-5649	152	18	σ2	σ2	PROPN
ejpam-5649	152	19	)	)	PUNCT
ejpam-5649	152	20	is	be	AUX
ejpam-5649	152	21	said	say	VERB
ejpam-5649	152	22	to	to	PART
ejpam-5649	152	23	be	be	AUX
ejpam-5649	152	24	upper	upper	ADJ
ejpam-5649	152	25	weakly	weakly	ADJ
ejpam-5649	152	26	s-(τ1	s-(τ1	PROPN
ejpam-5649	152	27	,	,	PUNCT
ejpam-5649	152	28	τ2)p	τ2)p	ADJ
ejpam-5649	152	29	-	-	ADJ
ejpam-5649	152	30	continuous	continuous	ADJ
ejpam-5649	152	31	if	if	SCONJ
ejpam-5649	152	32	f	f	PROPN
ejpam-5649	152	33	is	be	AUX
ejpam-5649	152	34	upper	upper	ADJ
ejpam-5649	152	35	weakly	weakly	ADJ
ejpam-5649	152	36	s-(τ1	s-(τ1	PROPN
ejpam-5649	152	37	,	,	PUNCT
ejpam-5649	152	38	τ2)p	τ2)p	ADJ
ejpam-5649	152	39	-	-	ADJ
ejpam-5649	152	40	continuous	continuous	ADJ
ejpam-5649	152	41	at	at	ADP
ejpam-5649	152	42	each	each	DET
ejpam-5649	152	43	point	point	NOUN
ejpam-5649	152	44	x	x	PUNCT
ejpam-5649	152	45	of	of	ADP
ejpam-5649	152	46	x.	x.	NOUN
ejpam-5649	152	47	definition	definition	NOUN
ejpam-5649	152	48	3	3	NUM
ejpam-5649	152	49	.	.	PUNCT
ejpam-5649	153	1	a	a	DET
ejpam-5649	153	2	multifunction	multifunction	NOUN
ejpam-5649	153	3	f	f	NOUN
ejpam-5649	153	4	:	:	PUNCT
ejpam-5649	153	5	(	(	PUNCT
ejpam-5649	153	6	x	x	NOUN
ejpam-5649	153	7	,	,	PUNCT
ejpam-5649	153	8	τ1	τ1	NOUN
ejpam-5649	153	9	,	,	PUNCT
ejpam-5649	153	10	τ2	τ2	NOUN
ejpam-5649	153	11	)	)	PUNCT
ejpam-5649	153	12	→	→	SYM
ejpam-5649	153	13	(	(	PUNCT
ejpam-5649	153	14	y	y	PROPN
ejpam-5649	153	15	,	,	PUNCT
ejpam-5649	153	16	σ1	σ1	PROPN
ejpam-5649	153	17	,	,	PUNCT
ejpam-5649	153	18	σ2	σ2	PROPN
ejpam-5649	153	19	)	)	PUNCT
ejpam-5649	153	20	is	be	AUX
ejpam-5649	153	21	said	say	VERB
ejpam-5649	153	22	to	to	PART
ejpam-5649	153	23	be	be	AUX
ejpam-5649	153	24	lower	low	ADJ
ejpam-5649	153	25	weakly	weakly	ADJ
ejpam-5649	153	26	s-(τ1	s-(τ1	NOUN
ejpam-5649	153	27	,	,	PUNCT
ejpam-5649	153	28	τ2)p	τ2)p	ADJ
ejpam-5649	153	29	-	-	ADJ
ejpam-5649	153	30	continuous	continuous	ADJ
ejpam-5649	153	31	at	at	ADP
ejpam-5649	153	32	x	x	X
ejpam-5649	153	33	∈	∈	PROPN
ejpam-5649	153	34	x	x	SYM
ejpam-5649	153	35	if	if	SCONJ
ejpam-5649	153	36	for	for	ADP
ejpam-5649	153	37	each	each	DET
ejpam-5649	153	38	σ1σ2	σ1σ2	VERB
ejpam-5649	153	39	-	-	ADJ
ejpam-5649	153	40	open	open	ADJ
ejpam-5649	153	41	set	set	NOUN
ejpam-5649	153	42	v	v	NOUN
ejpam-5649	153	43	of	of	ADP
ejpam-5649	153	44	y	y	PROPN
ejpam-5649	153	45	having	have	VERB
ejpam-5649	153	46	σ1σ2	σ1σ2	ADV
ejpam-5649	153	47	-	-	PUNCT
ejpam-5649	153	48	connected	connected	ADJ
ejpam-5649	153	49	complement	complement	NOUN
ejpam-5649	153	50	such	such	ADJ
ejpam-5649	153	51	that	that	SCONJ
ejpam-5649	153	52	x	x	SYM
ejpam-5649	153	53	∈	∈	PROPN
ejpam-5649	153	54	f−(v	f−(v	NOUN
ejpam-5649	153	55	)	)	PUNCT
ejpam-5649	153	56	,	,	PUNCT
ejpam-5649	153	57	there	there	PRON
ejpam-5649	153	58	exists	exist	VERB
ejpam-5649	153	59	a	a	DET
ejpam-5649	153	60	(	(	PUNCT
ejpam-5649	153	61	τ1	τ1	NOUN
ejpam-5649	153	62	,	,	PUNCT
ejpam-5649	153	63	τ2)p	τ2)p	ADJ
ejpam-5649	153	64	-	-	PUNCT
ejpam-5649	153	65	open	open	ADJ
ejpam-5649	153	66	set	set	NOUN
ejpam-5649	153	67	u	u	NOUN
ejpam-5649	153	68	of	of	ADP
ejpam-5649	153	69	x	x	PUNCT
ejpam-5649	153	70	containing	contain	VERB
ejpam-5649	153	71	x	x	PUNCT
ejpam-5649	153	72	such	such	ADJ
ejpam-5649	153	73	that	that	SCONJ
ejpam-5649	153	74	u	u	NOUN
ejpam-5649	153	75	⊆	⊆	NUM
ejpam-5649	153	76	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5649	153	77	-	-	PUNCT
ejpam-5649	153	78	cl(v	cl(v	NOUN
ejpam-5649	153	79	)	)	PUNCT
ejpam-5649	153	80	)	)	PUNCT
ejpam-5649	153	81	.	.	PUNCT
ejpam-5649	154	1	a	a	DET
ejpam-5649	154	2	multifunction	multifunction	NOUN
ejpam-5649	154	3	f	f	NOUN
ejpam-5649	154	4	:	:	PUNCT
ejpam-5649	154	5	(	(	PUNCT
ejpam-5649	154	6	x	x	NOUN
ejpam-5649	154	7	,	,	PUNCT
ejpam-5649	154	8	τ1	τ1	NOUN
ejpam-5649	154	9	,	,	PUNCT
ejpam-5649	154	10	τ2	τ2	NOUN
ejpam-5649	154	11	)	)	PUNCT
ejpam-5649	154	12	→	→	SYM
ejpam-5649	154	13	(	(	PUNCT
ejpam-5649	154	14	y	y	PROPN
ejpam-5649	154	15	,	,	PUNCT
ejpam-5649	154	16	σ1	σ1	PROPN
ejpam-5649	154	17	,	,	PUNCT
ejpam-5649	154	18	σ2	σ2	PROPN
ejpam-5649	154	19	)	)	PUNCT
ejpam-5649	154	20	is	be	AUX
ejpam-5649	154	21	said	say	VERB
ejpam-5649	154	22	to	to	PART
ejpam-5649	154	23	be	be	AUX
ejpam-5649	154	24	lower	low	ADJ
ejpam-5649	154	25	weakly	weakly	ADJ
ejpam-5649	154	26	s-(τ1	s-(τ1	NOUN
ejpam-5649	154	27	,	,	PUNCT
ejpam-5649	154	28	τ2)p	τ2)p	ADJ
ejpam-5649	154	29	-	-	ADJ
ejpam-5649	154	30	continuous	continuous	ADJ
ejpam-5649	154	31	if	if	SCONJ
ejpam-5649	154	32	f	f	PROPN
ejpam-5649	154	33	is	be	AUX
ejpam-5649	154	34	lower	low	ADJ
ejpam-5649	154	35	weakly	weakly	ADJ
ejpam-5649	154	36	s-(τ1	s-(τ1	NOUN
ejpam-5649	154	37	,	,	PUNCT
ejpam-5649	154	38	τ2)p	τ2)p	ADJ
ejpam-5649	154	39	-	-	ADJ
ejpam-5649	154	40	continuous	continuous	ADJ
ejpam-5649	154	41	at	at	ADP
ejpam-5649	154	42	each	each	DET
ejpam-5649	154	43	point	point	NOUN
ejpam-5649	154	44	x	x	PUNCT
ejpam-5649	154	45	of	of	ADP
ejpam-5649	154	46	x.	x.	NOUN
ejpam-5649	154	47	definition	definition	NOUN
ejpam-5649	154	48	4	4	NUM
ejpam-5649	154	49	.	.	PUNCT
ejpam-5649	155	1	a	a	DET
ejpam-5649	155	2	multifunction	multifunction	NOUN
ejpam-5649	155	3	f	f	NOUN
ejpam-5649	155	4	:	:	PUNCT
ejpam-5649	155	5	(	(	PUNCT
ejpam-5649	155	6	x	x	NOUN
ejpam-5649	155	7	,	,	PUNCT
ejpam-5649	155	8	τ1	τ1	NOUN
ejpam-5649	155	9	,	,	PUNCT
ejpam-5649	155	10	τ2	τ2	NOUN
ejpam-5649	155	11	)	)	PUNCT
ejpam-5649	155	12	→	→	SYM
ejpam-5649	155	13	(	(	PUNCT
ejpam-5649	155	14	y	y	PROPN
ejpam-5649	155	15	,	,	PUNCT
ejpam-5649	155	16	σ1	σ1	PROPN
ejpam-5649	155	17	,	,	PUNCT
ejpam-5649	155	18	σ2	σ2	PROPN
ejpam-5649	155	19	)	)	PUNCT
ejpam-5649	155	20	is	be	AUX
ejpam-5649	155	21	called	call	VERB
ejpam-5649	155	22	strongly	strongly	ADV
ejpam-5649	155	23	(	(	PUNCT
ejpam-5649	155	24	τ1	τ1	NOUN
ejpam-5649	155	25	,	,	PUNCT
ejpam-5649	155	26	τ2)p	τ2)p	NOUN
ejpam-5649	155	27	-	-	PUNCT
ejpam-5649	155	28	open	open	ADJ
ejpam-5649	155	29	if	if	SCONJ
ejpam-5649	155	30	f	f	PROPN
ejpam-5649	155	31	(	(	PUNCT
ejpam-5649	155	32	u	u	NOUN
ejpam-5649	155	33	)	)	PUNCT
ejpam-5649	155	34	is	be	AUX
ejpam-5649	155	35	σ1σ2	σ1σ2	NOUN
ejpam-5649	155	36	-	-	ADJ
ejpam-5649	155	37	open	open	ADJ
ejpam-5649	155	38	in	in	ADP
ejpam-5649	155	39	y	y	PROPN
ejpam-5649	155	40	for	for	ADP
ejpam-5649	155	41	every	every	DET
ejpam-5649	155	42	(	(	PUNCT
ejpam-5649	155	43	τ1	τ1	NOUN
ejpam-5649	155	44	,	,	PUNCT
ejpam-5649	155	45	τ2)p	τ2)p	ADJ
ejpam-5649	155	46	-	-	PUNCT
ejpam-5649	155	47	open	open	ADJ
ejpam-5649	155	48	set	set	NOUN
ejpam-5649	155	49	u	u	PROPN
ejpam-5649	155	50	of	of	ADP
ejpam-5649	155	51	x.	x.	PROPN
ejpam-5649	155	52	theorem	theorem	VERB
ejpam-5649	155	53	2	2	NUM
ejpam-5649	155	54	.	.	PUNCT
ejpam-5649	156	1	if	if	SCONJ
ejpam-5649	156	2	f	f	PROPN
ejpam-5649	156	3	:	:	PUNCT
ejpam-5649	156	4	(	(	PUNCT
ejpam-5649	156	5	x	x	NOUN
ejpam-5649	156	6	,	,	PUNCT
ejpam-5649	156	7	τ1	τ1	NOUN
ejpam-5649	156	8	,	,	PUNCT
ejpam-5649	156	9	τ2	τ2	NOUN
ejpam-5649	156	10	)	)	PUNCT
ejpam-5649	156	11	→	→	SYM
ejpam-5649	156	12	(	(	PUNCT
ejpam-5649	156	13	y	y	PROPN
ejpam-5649	156	14	,	,	PUNCT
ejpam-5649	156	15	σ1	σ1	PROPN
ejpam-5649	156	16	,	,	PUNCT
ejpam-5649	156	17	σ2	σ2	PROPN
ejpam-5649	156	18	)	)	PUNCT
ejpam-5649	156	19	is	be	AUX
ejpam-5649	156	20	upper	upper	ADJ
ejpam-5649	156	21	rarely	rarely	ADV
ejpam-5649	156	22	s-(τ1	s-(τ1	NOUN
ejpam-5649	156	23	,	,	PUNCT
ejpam-5649	156	24	τ2)p	τ2)p	ADJ
ejpam-5649	156	25	-	-	ADJ
ejpam-5649	156	26	continuous	continuous	ADJ
ejpam-5649	156	27	and	and	CCONJ
ejpam-5649	156	28	strongly	strongly	ADV
ejpam-5649	156	29	(	(	PUNCT
ejpam-5649	156	30	τ1	τ1	NOUN
ejpam-5649	156	31	,	,	PUNCT
ejpam-5649	156	32	τ2)p	τ2)p	NOUN
ejpam-5649	156	33	-	-	NOUN
ejpam-5649	156	34	open	open	ADJ
ejpam-5649	156	35	,	,	PUNCT
ejpam-5649	156	36	then	then	ADV
ejpam-5649	156	37	f	f	PROPN
ejpam-5649	156	38	is	be	AUX
ejpam-5649	156	39	upper	upper	ADJ
ejpam-5649	156	40	weakly	weakly	ADJ
ejpam-5649	156	41	s-(τ1	s-(τ1	PROPN
ejpam-5649	156	42	,	,	PUNCT
ejpam-5649	156	43	τ2)p	τ2)p	ADJ
ejpam-5649	156	44	-	-	ADJ
ejpam-5649	156	45	continuous	continuous	ADJ
ejpam-5649	156	46	.	.	PUNCT
ejpam-5649	157	1	proof	proof	NOUN
ejpam-5649	157	2	.	.	PUNCT
ejpam-5649	158	1	let	let	VERB
ejpam-5649	158	2	x	x	PUNCT
ejpam-5649	158	3	∈	∈	PROPN
ejpam-5649	158	4	x	x	X
ejpam-5649	158	5	and	and	CCONJ
ejpam-5649	158	6	v	v	X
ejpam-5649	158	7	be	be	AUX
ejpam-5649	158	8	any	any	DET
ejpam-5649	158	9	σ1σ2	σ1σ2	NOUN
ejpam-5649	158	10	-	-	ADJ
ejpam-5649	158	11	open	open	ADJ
ejpam-5649	158	12	set	set	NOUN
ejpam-5649	158	13	of	of	ADP
ejpam-5649	158	14	y	y	PROPN
ejpam-5649	158	15	having	have	VERB
ejpam-5649	158	16	σ1σ2	σ1σ2	ADV
ejpam-5649	158	17	-	-	PUNCT
ejpam-5649	158	18	connected	connect	VERB
ejpam-5649	158	19	complement	complement	NOUN
ejpam-5649	158	20	with	with	ADP
ejpam-5649	158	21	f	f	PROPN
ejpam-5649	158	22	(	(	PUNCT
ejpam-5649	158	23	x	x	NOUN
ejpam-5649	158	24	)	)	PUNCT
ejpam-5649	158	25	⊆	⊆	NUM
ejpam-5649	158	26	v	v	NOUN
ejpam-5649	158	27	.	.	PUNCT
ejpam-5649	159	1	since	since	SCONJ
ejpam-5649	159	2	f	f	PROPN
ejpam-5649	159	3	is	be	AUX
ejpam-5649	159	4	upper	upper	ADJ
ejpam-5649	159	5	rarely	rarely	ADV
ejpam-5649	159	6	s-(τ1	s-(τ1	NOUN
ejpam-5649	159	7	,	,	PUNCT
ejpam-5649	159	8	τ2)p	τ2)p	ADJ
ejpam-5649	159	9	-	-	ADJ
ejpam-5649	159	10	continuous	continuous	ADJ
ejpam-5649	159	11	,	,	PUNCT
ejpam-5649	159	12	there	there	PRON
ejpam-5649	159	13	exists	exist	VERB
ejpam-5649	159	14	a	a	DET
ejpam-5649	159	15	(	(	PUNCT
ejpam-5649	159	16	τ1	τ1	NOUN
ejpam-5649	159	17	,	,	PUNCT
ejpam-5649	159	18	τ2)p	τ2)p	ADJ
ejpam-5649	159	19	-	-	PUNCT
ejpam-5649	159	20	open	open	ADJ
ejpam-5649	159	21	set	set	NOUN
ejpam-5649	159	22	u	u	NOUN
ejpam-5649	159	23	of	of	ADP
ejpam-5649	159	24	x	x	PUNCT
ejpam-5649	159	25	containing	contain	VERB
ejpam-5649	159	26	x	x	PUNCT
ejpam-5649	159	27	such	such	ADJ
ejpam-5649	159	28	that	that	SCONJ
ejpam-5649	159	29	σ1σ2	σ1σ2	NOUN
ejpam-5649	159	30	-	-	PUNCT
ejpam-5649	159	31	int(f	int(f	PROPN
ejpam-5649	159	32	(	(	PUNCT
ejpam-5649	159	33	u	u	NOUN
ejpam-5649	159	34	)	)	PUNCT
ejpam-5649	159	35	)	)	PUNCT
ejpam-5649	160	1	⊆	⊆	X
ejpam-5649	160	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	160	3	-	-	NUM
ejpam-5649	160	4	cl(v	cl(v	NOUN
ejpam-5649	160	5	)	)	PUNCT
ejpam-5649	160	6	.	.	PUNCT
ejpam-5649	161	1	it	it	PRON
ejpam-5649	161	2	follows	follow	VERB
ejpam-5649	161	3	from	from	ADP
ejpam-5649	161	4	that	that	PRON
ejpam-5649	161	5	f	f	PROPN
ejpam-5649	161	6	(	(	PUNCT
ejpam-5649	161	7	u	u	NOUN
ejpam-5649	161	8	)	)	PUNCT
ejpam-5649	161	9	⊆	⊆	NUM
ejpam-5649	161	10	σ1σ2	σ1σ2	X
ejpam-5649	161	11	-	-	PUNCT
ejpam-5649	161	12	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5649	161	13	-	-	PUNCT
ejpam-5649	161	14	int(f	int(f	PROPN
ejpam-5649	161	15	(	(	PUNCT
ejpam-5649	161	16	u	u	NOUN
ejpam-5649	161	17	)	)	PUNCT
ejpam-5649	161	18	)	)	PUNCT
ejpam-5649	161	19	)	)	PUNCT
ejpam-5649	162	1	⊆	⊆	X
ejpam-5649	162	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	162	3	-	-	NUM
ejpam-5649	162	4	cl(v	cl(v	NOUN
ejpam-5649	162	5	)	)	PUNCT
ejpam-5649	162	6	.	.	PUNCT
ejpam-5649	163	1	thus	thus	ADV
ejpam-5649	163	2	,	,	PUNCT
ejpam-5649	163	3	f	f	PROPN
ejpam-5649	163	4	is	be	AUX
ejpam-5649	163	5	upper	upper	ADJ
ejpam-5649	163	6	weakly	weakly	ADJ
ejpam-5649	163	7	s-(τ1	s-(τ1	PROPN
ejpam-5649	163	8	,	,	PUNCT
ejpam-5649	163	9	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5649	163	10	.	.	PUNCT
ejpam-5649	164	1	definition	definition	NOUN
ejpam-5649	164	2	5	5	NUM
ejpam-5649	164	3	.	.	PUNCT
ejpam-5649	165	1	a	a	DET
ejpam-5649	165	2	multifunction	multifunction	NOUN
ejpam-5649	165	3	f	f	NOUN
ejpam-5649	165	4	:	:	PUNCT
ejpam-5649	165	5	(	(	PUNCT
ejpam-5649	165	6	x	x	NOUN
ejpam-5649	165	7	,	,	PUNCT
ejpam-5649	165	8	τ1	τ1	NOUN
ejpam-5649	165	9	,	,	PUNCT
ejpam-5649	165	10	τ2	τ2	NOUN
ejpam-5649	165	11	)	)	PUNCT
ejpam-5649	165	12	→	→	SYM
ejpam-5649	165	13	(	(	PUNCT
ejpam-5649	165	14	y	y	PROPN
ejpam-5649	165	15	,	,	PUNCT
ejpam-5649	165	16	σ1	σ1	PROPN
ejpam-5649	165	17	,	,	PUNCT
ejpam-5649	165	18	σ2	σ2	PROPN
ejpam-5649	165	19	)	)	PUNCT
ejpam-5649	165	20	is	be	AUX
ejpam-5649	165	21	said	say	VERB
ejpam-5649	165	22	to	to	PART
ejpam-5649	165	23	be	be	AUX
ejpam-5649	165	24	lower	low	ADJ
ejpam-5649	165	25	rarely	rarely	ADV
ejpam-5649	165	26	s-(τ1	s-(τ1	NOUN
ejpam-5649	165	27	,	,	PUNCT
ejpam-5649	165	28	τ2)p	τ2)p	ADJ
ejpam-5649	165	29	-	-	ADJ
ejpam-5649	165	30	continuous	continuous	ADJ
ejpam-5649	165	31	at	at	ADP
ejpam-5649	165	32	x	x	X
ejpam-5649	165	33	∈	∈	PROPN
ejpam-5649	165	34	x	x	SYM
ejpam-5649	165	35	if	if	SCONJ
ejpam-5649	165	36	for	for	ADP
ejpam-5649	165	37	each	each	DET
ejpam-5649	165	38	σ1σ2	σ1σ2	VERB
ejpam-5649	165	39	-	-	ADJ
ejpam-5649	165	40	open	open	ADJ
ejpam-5649	165	41	set	set	NOUN
ejpam-5649	165	42	v	v	NOUN
ejpam-5649	165	43	of	of	ADP
ejpam-5649	165	44	y	y	PROPN
ejpam-5649	165	45	having	have	VERB
ejpam-5649	165	46	σ1σ2	σ1σ2	ADV
ejpam-5649	165	47	-	-	PUNCT
ejpam-5649	165	48	connected	connected	ADJ
ejpam-5649	165	49	complement	complement	NOUN
ejpam-5649	165	50	such	such	ADJ
ejpam-5649	165	51	that	that	SCONJ
ejpam-5649	165	52	f	f	PROPN
ejpam-5649	165	53	(	(	PUNCT
ejpam-5649	165	54	x)∩v	x)∩v	PROPN
ejpam-5649	165	55	̸=	̸=	PROPN
ejpam-5649	165	56	∅	∅	NOUN
ejpam-5649	165	57	,	,	PUNCT
ejpam-5649	165	58	there	there	PRON
ejpam-5649	165	59	exists	exist	VERB
ejpam-5649	165	60	a	a	DET
ejpam-5649	165	61	σ1σ2	σ1σ2	NUM
ejpam-5649	165	62	-	-	ADJ
ejpam-5649	165	63	rare	rare	ADJ
ejpam-5649	165	64	set	set	ADJ
ejpam-5649	165	65	rv	rv	PROPN
ejpam-5649	165	66	with	with	ADP
ejpam-5649	165	67	σ1σ2	σ1σ2	NOUN
ejpam-5649	165	68	-	-	PUNCT
ejpam-5649	165	69	cl(rv	cl(rv	ADJ
ejpam-5649	165	70	)	)	PUNCT
ejpam-5649	166	1	∩v	∩v	NOUN
ejpam-5649	166	2	=	=	PUNCT
ejpam-5649	167	1	∅	∅	NOUN
ejpam-5649	167	2	and	and	CCONJ
ejpam-5649	167	3	a	a	DET
ejpam-5649	167	4	(	(	PUNCT
ejpam-5649	167	5	τ1	τ1	NOUN
ejpam-5649	167	6	,	,	PUNCT
ejpam-5649	167	7	τ2)p	τ2)p	ADJ
ejpam-5649	167	8	-	-	PUNCT
ejpam-5649	167	9	open	open	ADJ
ejpam-5649	167	10	set	set	NOUN
ejpam-5649	167	11	u	u	NOUN
ejpam-5649	167	12	of	of	ADP
ejpam-5649	167	13	x	x	PUNCT
ejpam-5649	167	14	containing	contain	VERB
ejpam-5649	167	15	x	x	PUNCT
ejpam-5649	167	16	such	such	ADJ
ejpam-5649	167	17	that	that	SCONJ
ejpam-5649	167	18	f	f	PROPN
ejpam-5649	167	19	(	(	PUNCT
ejpam-5649	167	20	z	z	NOUN
ejpam-5649	167	21	)	)	PUNCT
ejpam-5649	167	22	∩	∩	NOUN
ejpam-5649	167	23	(	(	PUNCT
ejpam-5649	167	24	v	v	X
ejpam-5649	167	25	∪	∪	X
ejpam-5649	167	26	rv	rv	NOUN
ejpam-5649	167	27	)	)	PUNCT
ejpam-5649	167	28	̸=	̸=	PROPN
ejpam-5649	167	29	∅	∅	NOUN
ejpam-5649	167	30	for	for	ADP
ejpam-5649	167	31	each	each	DET
ejpam-5649	167	32	z	z	NOUN
ejpam-5649	167	33	∈	∈	PROPN
ejpam-5649	167	34	u	u	NOUN
ejpam-5649	167	35	.	.	PUNCT
ejpam-5649	168	1	a	a	DET
ejpam-5649	168	2	multifunction	multifunction	NOUN
ejpam-5649	168	3	f	f	NOUN
ejpam-5649	168	4	:	:	PUNCT
ejpam-5649	168	5	(	(	PUNCT
ejpam-5649	168	6	x	x	NOUN
ejpam-5649	168	7	,	,	PUNCT
ejpam-5649	168	8	τ1	τ1	NOUN
ejpam-5649	168	9	,	,	PUNCT
ejpam-5649	168	10	τ2	τ2	NOUN
ejpam-5649	168	11	)	)	PUNCT
ejpam-5649	168	12	→	→	SYM
ejpam-5649	168	13	(	(	PUNCT
ejpam-5649	168	14	y	y	PROPN
ejpam-5649	168	15	,	,	PUNCT
ejpam-5649	168	16	σ1	σ1	PROPN
ejpam-5649	168	17	,	,	PUNCT
ejpam-5649	168	18	σ2	σ2	PROPN
ejpam-5649	168	19	)	)	PUNCT
ejpam-5649	168	20	is	be	AUX
ejpam-5649	168	21	said	say	VERB
ejpam-5649	168	22	to	to	PART
ejpam-5649	168	23	be	be	AUX
ejpam-5649	168	24	lower	low	ADJ
ejpam-5649	168	25	rarely	rarely	ADV
ejpam-5649	168	26	s-(τ1	s-(τ1	NOUN
ejpam-5649	168	27	,	,	PUNCT
ejpam-5649	168	28	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5649	168	29	if	if	SCONJ
ejpam-5649	168	30	f	f	PROPN
ejpam-5649	168	31	is	be	AUX
ejpam-5649	168	32	lower	low	ADJ
ejpam-5649	168	33	rarely	rarely	ADV
ejpam-5649	168	34	s-(τ1	s-(τ1	NOUN
ejpam-5649	168	35	,	,	PUNCT
ejpam-5649	168	36	τ2)p	τ2)p	ADJ
ejpam-5649	168	37	-	-	ADJ
ejpam-5649	168	38	continuous	continuous	ADJ
ejpam-5649	168	39	at	at	ADP
ejpam-5649	168	40	each	each	DET
ejpam-5649	168	41	point	point	NOUN
ejpam-5649	168	42	x	x	PUNCT
ejpam-5649	168	43	of	of	ADP
ejpam-5649	168	44	x.	x.	PROPN
ejpam-5649	168	45	b.	b.	PROPN
ejpam-5649	168	46	kong	kong	PROPN
ejpam-5649	168	47	-	-	PUNCT
ejpam-5649	168	48	ied	ied	PROPN
ejpam-5649	168	49	,	,	PUNCT
ejpam-5649	168	50	s.	s.	PROPN
ejpam-5649	168	51	sompong	sompong	PROPN
ejpam-5649	168	52	,	,	PUNCT
ejpam-5649	168	53	c.	c.	PROPN
ejpam-5649	168	54	boonpok	boonpok	PROPN
ejpam-5649	168	55	/	/	SYM
ejpam-5649	168	56	eur	eur	PROPN
ejpam-5649	168	57	.	.	PUNCT
ejpam-5649	169	1	j.	j.	PROPN
ejpam-5649	169	2	pure	pure	PROPN
ejpam-5649	169	3	appl	appl	PROPN
ejpam-5649	169	4	.	.	PROPN
ejpam-5649	169	5	math	math	PROPN
ejpam-5649	169	6	,	,	PUNCT
ejpam-5649	169	7	18	18	NUM
ejpam-5649	169	8	(	(	PUNCT
ejpam-5649	169	9	1	1	NUM
ejpam-5649	169	10	)	)	PUNCT
ejpam-5649	169	11	(	(	PUNCT
ejpam-5649	169	12	2025	2025	NUM
ejpam-5649	169	13	)	)	PUNCT
ejpam-5649	169	14	,	,	PUNCT
ejpam-5649	169	15	5649	5649	NUM
ejpam-5649	169	16	7	7	NUM
ejpam-5649	169	17	of	of	ADP
ejpam-5649	169	18	13	13	NUM
ejpam-5649	169	19	theorem	theorem	NOUN
ejpam-5649	169	20	3	3	NUM
ejpam-5649	169	21	.	.	X
ejpam-5649	169	22	for	for	ADP
ejpam-5649	169	23	a	a	DET
ejpam-5649	169	24	multifunction	multifunction	NOUN
ejpam-5649	169	25	f	f	NOUN
ejpam-5649	169	26	:	:	PUNCT
ejpam-5649	169	27	(	(	PUNCT
ejpam-5649	169	28	x	x	NOUN
ejpam-5649	169	29	,	,	PUNCT
ejpam-5649	169	30	τ1	τ1	NOUN
ejpam-5649	169	31	,	,	PUNCT
ejpam-5649	169	32	τ2	τ2	NOUN
ejpam-5649	169	33	)	)	PUNCT
ejpam-5649	169	34	→	→	SYM
ejpam-5649	169	35	(	(	PUNCT
ejpam-5649	169	36	y	y	PROPN
ejpam-5649	169	37	,	,	PUNCT
ejpam-5649	169	38	σ1	σ1	PROPN
ejpam-5649	169	39	,	,	PUNCT
ejpam-5649	169	40	σ2	σ2	NOUN
ejpam-5649	169	41	)	)	PUNCT
ejpam-5649	169	42	,	,	PUNCT
ejpam-5649	169	43	the	the	DET
ejpam-5649	169	44	following	follow	VERB
ejpam-5649	169	45	properties	property	NOUN
ejpam-5649	169	46	are	be	AUX
ejpam-5649	169	47	equivalent	equivalent	ADJ
ejpam-5649	169	48	:	:	PUNCT
ejpam-5649	169	49	(	(	PUNCT
ejpam-5649	169	50	1	1	X
ejpam-5649	169	51	)	)	PUNCT
ejpam-5649	169	52	f	f	PROPN
ejpam-5649	169	53	is	be	AUX
ejpam-5649	169	54	lower	low	ADJ
ejpam-5649	169	55	rarely	rarely	ADV
ejpam-5649	169	56	s-(τ1	s-(τ1	NOUN
ejpam-5649	169	57	,	,	PUNCT
ejpam-5649	169	58	τ2)p	τ2)p	ADJ
ejpam-5649	169	59	-	-	ADJ
ejpam-5649	169	60	continuous	continuous	ADJ
ejpam-5649	169	61	at	at	ADP
ejpam-5649	169	62	x	x	X
ejpam-5649	169	63	∈	∈	PROPN
ejpam-5649	169	64	x	x	X
ejpam-5649	169	65	;	;	PUNCT
ejpam-5649	169	66	(	(	PUNCT
ejpam-5649	169	67	2	2	X
ejpam-5649	169	68	)	)	PUNCT
ejpam-5649	169	69	for	for	ADP
ejpam-5649	169	70	every	every	DET
ejpam-5649	169	71	σ1σ2	σ1σ2	NOUN
ejpam-5649	169	72	-	-	ADJ
ejpam-5649	169	73	open	open	ADJ
ejpam-5649	169	74	set	set	NOUN
ejpam-5649	169	75	v	v	NOUN
ejpam-5649	169	76	of	of	ADP
ejpam-5649	169	77	y	y	PROPN
ejpam-5649	169	78	having	have	VERB
ejpam-5649	169	79	σ1σ2	σ1σ2	ADV
ejpam-5649	169	80	-	-	PUNCT
ejpam-5649	169	81	connected	connect	VERB
ejpam-5649	169	82	complement	complement	NOUN
ejpam-5649	169	83	with	with	ADP
ejpam-5649	169	84	f	f	PROPN
ejpam-5649	169	85	(	(	PUNCT
ejpam-5649	169	86	x)∩v	x)∩v	PROPN
ejpam-5649	169	87	̸=	̸=	PROPN
ejpam-5649	169	88	∅	∅	NOUN
ejpam-5649	169	89	,	,	PUNCT
ejpam-5649	169	90	there	there	PRON
ejpam-5649	169	91	exists	exist	VERB
ejpam-5649	169	92	a	a	DET
ejpam-5649	169	93	σ1σ2	σ1σ2	NUM
ejpam-5649	169	94	-	-	ADJ
ejpam-5649	169	95	rare	rare	ADJ
ejpam-5649	169	96	set	set	ADJ
ejpam-5649	169	97	rv	rv	PROPN
ejpam-5649	169	98	with	with	ADP
ejpam-5649	169	99	σ1σ2	σ1σ2	NOUN
ejpam-5649	169	100	-	-	PUNCT
ejpam-5649	169	101	cl(rv	cl(rv	ADJ
ejpam-5649	169	102	)	)	PUNCT
ejpam-5649	170	1	∩	∩	NOUN
ejpam-5649	170	2	v	v	NOUN
ejpam-5649	170	3	=	=	NOUN
ejpam-5649	170	4	∅	∅	NOUN
ejpam-5649	170	5	such	such	ADJ
ejpam-5649	170	6	that	that	SCONJ
ejpam-5649	170	7	x	x	SYM
ejpam-5649	170	8	∈	∈	PROPN
ejpam-5649	170	9	(	(	PUNCT
ejpam-5649	170	10	τ1	τ1	NOUN
ejpam-5649	170	11	,	,	PUNCT
ejpam-5649	170	12	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	170	13	−(v	−(v	NOUN
ejpam-5649	170	14	∪rv	∪rv	NOUN
ejpam-5649	170	15	)	)	PUNCT
ejpam-5649	170	16	)	)	PUNCT
ejpam-5649	170	17	;	;	PUNCT
ejpam-5649	170	18	(	(	PUNCT
ejpam-5649	170	19	3	3	X
ejpam-5649	170	20	)	)	PUNCT
ejpam-5649	170	21	for	for	ADP
ejpam-5649	170	22	every	every	DET
ejpam-5649	170	23	σ1σ2	σ1σ2	NOUN
ejpam-5649	170	24	-	-	ADJ
ejpam-5649	170	25	open	open	ADJ
ejpam-5649	170	26	set	set	NOUN
ejpam-5649	170	27	v	v	NOUN
ejpam-5649	170	28	of	of	ADP
ejpam-5649	170	29	y	y	PROPN
ejpam-5649	170	30	having	have	VERB
ejpam-5649	170	31	σ1σ2	σ1σ2	ADV
ejpam-5649	170	32	-	-	PUNCT
ejpam-5649	170	33	connected	connect	VERB
ejpam-5649	170	34	complement	complement	NOUN
ejpam-5649	170	35	with	with	ADP
ejpam-5649	170	36	f	f	PROPN
ejpam-5649	170	37	(	(	PUNCT
ejpam-5649	170	38	x)∩v	x)∩v	PROPN
ejpam-5649	170	39	̸=	̸=	PROPN
ejpam-5649	170	40	∅	∅	NOUN
ejpam-5649	170	41	,	,	PUNCT
ejpam-5649	170	42	there	there	PRON
ejpam-5649	170	43	exists	exist	VERB
ejpam-5649	170	44	a	a	DET
ejpam-5649	170	45	σ1σ2	σ1σ2	NUM
ejpam-5649	170	46	-	-	ADJ
ejpam-5649	170	47	rare	rare	ADJ
ejpam-5649	170	48	set	set	ADJ
ejpam-5649	170	49	rv	rv	PROPN
ejpam-5649	170	50	with	with	ADP
ejpam-5649	170	51	σ1σ2	σ1σ2	NOUN
ejpam-5649	170	52	-	-	PUNCT
ejpam-5649	170	53	cl(rv	cl(rv	ADJ
ejpam-5649	170	54	)	)	PUNCT
ejpam-5649	171	1	∩	∩	NOUN
ejpam-5649	171	2	v	v	NOUN
ejpam-5649	171	3	=	=	NOUN
ejpam-5649	171	4	∅	∅	NOUN
ejpam-5649	171	5	such	such	ADJ
ejpam-5649	171	6	that	that	SCONJ
ejpam-5649	171	7	x	x	SYM
ejpam-5649	171	8	∈	∈	PROPN
ejpam-5649	171	9	f−(v	f−(v	NOUN
ejpam-5649	171	10	∪rv	∪rv	PROPN
ejpam-5649	171	11	)	)	PUNCT
ejpam-5649	171	12	∩	∩	NOUN
ejpam-5649	171	13	τ1τ2	τ1τ2	NOUN
ejpam-5649	171	14	-	-	NOUN
ejpam-5649	171	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	171	16	-	-	PUNCT
ejpam-5649	171	17	cl(f	cl(f	NUM
ejpam-5649	171	18	−(v	−(v	NOUN
ejpam-5649	171	19	∪rv	∪rv	PROPN
ejpam-5649	171	20	)	)	PUNCT
ejpam-5649	171	21	)	)	PUNCT
ejpam-5649	171	22	)	)	PUNCT
ejpam-5649	171	23	.	.	PUNCT
ejpam-5649	172	1	proof	proof	NOUN
ejpam-5649	172	2	.	.	PUNCT
ejpam-5649	173	1	(	(	PUNCT
ejpam-5649	173	2	1	1	X
ejpam-5649	173	3	)	)	PUNCT
ejpam-5649	173	4	⇒	⇒	NOUN
ejpam-5649	173	5	(	(	PUNCT
ejpam-5649	173	6	2	2	NUM
ejpam-5649	173	7	):	):	PUNCT
ejpam-5649	173	8	let	let	VERB
ejpam-5649	173	9	v	v	PART
ejpam-5649	173	10	be	be	AUX
ejpam-5649	173	11	any	any	DET
ejpam-5649	173	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	173	13	-	-	ADJ
ejpam-5649	173	14	open	open	ADJ
ejpam-5649	173	15	set	set	NOUN
ejpam-5649	173	16	of	of	ADP
ejpam-5649	173	17	y	y	PROPN
ejpam-5649	173	18	having	have	VERB
ejpam-5649	173	19	σ1σ2	σ1σ2	ADV
ejpam-5649	173	20	-	-	PUNCT
ejpam-5649	173	21	connected	connected	ADJ
ejpam-5649	173	22	complement	complement	NOUN
ejpam-5649	173	23	such	such	ADJ
ejpam-5649	173	24	that	that	SCONJ
ejpam-5649	173	25	f	f	PROPN
ejpam-5649	173	26	(	(	PUNCT
ejpam-5649	173	27	x	x	X
ejpam-5649	173	28	)	)	PUNCT
ejpam-5649	173	29	⊆	⊆	NUM
ejpam-5649	173	30	v	v	NOUN
ejpam-5649	173	31	.	.	PUNCT
ejpam-5649	174	1	since	since	SCONJ
ejpam-5649	174	2	f	f	PROPN
ejpam-5649	174	3	is	be	AUX
ejpam-5649	174	4	lower	low	ADJ
ejpam-5649	174	5	rarely	rarely	ADV
ejpam-5649	174	6	s-(τ1	s-(τ1	NOUN
ejpam-5649	174	7	,	,	PUNCT
ejpam-5649	174	8	τ2)p	τ2)p	ADJ
ejpam-5649	174	9	-	-	ADJ
ejpam-5649	174	10	continuous	continuous	ADJ
ejpam-5649	174	11	at	at	ADP
ejpam-5649	174	12	x	x	X
ejpam-5649	174	13	∈	∈	PROPN
ejpam-5649	174	14	x	x	NOUN
ejpam-5649	174	15	,	,	PUNCT
ejpam-5649	174	16	there	there	PRON
ejpam-5649	174	17	exists	exist	VERB
ejpam-5649	174	18	a	a	DET
ejpam-5649	174	19	σ1σ2	σ1σ2	NUM
ejpam-5649	174	20	-	-	ADJ
ejpam-5649	174	21	rare	rare	ADJ
ejpam-5649	174	22	set	set	ADJ
ejpam-5649	174	23	rv	rv	PROPN
ejpam-5649	174	24	with	with	ADP
ejpam-5649	174	25	σ1σ2	σ1σ2	NOUN
ejpam-5649	174	26	-	-	PUNCT
ejpam-5649	174	27	cl(rv	cl(rv	ADJ
ejpam-5649	174	28	)	)	PUNCT
ejpam-5649	175	1	∩	∩	NOUN
ejpam-5649	175	2	v	v	NOUN
ejpam-5649	175	3	=	=	NOUN
ejpam-5649	175	4	∅	∅	NOUN
ejpam-5649	175	5	and	and	CCONJ
ejpam-5649	175	6	a	a	DET
ejpam-5649	175	7	(	(	PUNCT
ejpam-5649	175	8	τ1	τ1	NOUN
ejpam-5649	175	9	,	,	PUNCT
ejpam-5649	175	10	τ2)p	τ2)p	ADJ
ejpam-5649	175	11	-	-	PUNCT
ejpam-5649	175	12	open	open	ADJ
ejpam-5649	175	13	set	set	NOUN
ejpam-5649	175	14	u	u	NOUN
ejpam-5649	175	15	of	of	ADP
ejpam-5649	175	16	x	x	PUNCT
ejpam-5649	175	17	containing	contain	VERB
ejpam-5649	175	18	x	x	PUNCT
ejpam-5649	175	19	such	such	ADJ
ejpam-5649	175	20	that	that	SCONJ
ejpam-5649	175	21	f	f	PROPN
ejpam-5649	175	22	(	(	PUNCT
ejpam-5649	175	23	z	z	NOUN
ejpam-5649	175	24	)	)	PUNCT
ejpam-5649	175	25	∩	∩	NOUN
ejpam-5649	175	26	(	(	PUNCT
ejpam-5649	175	27	v	v	NUM
ejpam-5649	175	28	∪rv	∪rv	NOUN
ejpam-5649	175	29	)	)	PUNCT
ejpam-5649	175	30	̸=	̸=	NOUN
ejpam-5649	175	31	∅	∅	NOUN
ejpam-5649	175	32	for	for	ADP
ejpam-5649	175	33	each	each	DET
ejpam-5649	175	34	z	z	NOUN
ejpam-5649	175	35	∈	∈	PROPN
ejpam-5649	175	36	u	u	NOUN
ejpam-5649	175	37	.	.	PUNCT
ejpam-5649	176	1	thus	thus	ADV
ejpam-5649	176	2	,	,	PUNCT
ejpam-5649	176	3	x	x	PUNCT
ejpam-5649	176	4	∈	∈	PROPN
ejpam-5649	176	5	u	u	NOUN
ejpam-5649	176	6	⊆	⊆	NUM
ejpam-5649	176	7	f−(v	f−(v	ADJ
ejpam-5649	176	8	∪rv	∪rv	NOUN
ejpam-5649	176	9	)	)	PUNCT
ejpam-5649	176	10	and	and	CCONJ
ejpam-5649	176	11	hence	hence	ADV
ejpam-5649	176	12	x	x	X
ejpam-5649	176	13	∈	∈	PROPN
ejpam-5649	176	14	(	(	PUNCT
ejpam-5649	176	15	τ1	τ1	NOUN
ejpam-5649	176	16	,	,	PUNCT
ejpam-5649	176	17	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	176	18	−(v	−(v	NOUN
ejpam-5649	176	19	∪rv	∪rv	NOUN
ejpam-5649	176	20	)	)	PUNCT
ejpam-5649	176	21	)	)	PUNCT
ejpam-5649	176	22	.	.	PUNCT
ejpam-5649	177	1	(	(	PUNCT
ejpam-5649	177	2	2	2	X
ejpam-5649	177	3	)	)	PUNCT
ejpam-5649	177	4	⇒	⇒	NOUN
ejpam-5649	177	5	(	(	PUNCT
ejpam-5649	177	6	1	1	NUM
ejpam-5649	177	7	):	):	PUNCT
ejpam-5649	177	8	let	let	VERB
ejpam-5649	177	9	v	v	PART
ejpam-5649	177	10	be	be	AUX
ejpam-5649	177	11	any	any	DET
ejpam-5649	177	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	177	13	-	-	ADJ
ejpam-5649	177	14	open	open	ADJ
ejpam-5649	177	15	set	set	NOUN
ejpam-5649	177	16	of	of	ADP
ejpam-5649	177	17	y	y	PROPN
ejpam-5649	177	18	having	have	VERB
ejpam-5649	177	19	σ1σ2	σ1σ2	ADV
ejpam-5649	177	20	-	-	PUNCT
ejpam-5649	177	21	connected	connect	VERB
ejpam-5649	177	22	complement	complement	NOUN
ejpam-5649	177	23	with	with	ADP
ejpam-5649	177	24	f	f	PROPN
ejpam-5649	177	25	(	(	PUNCT
ejpam-5649	177	26	x	x	NOUN
ejpam-5649	177	27	)	)	PUNCT
ejpam-5649	177	28	∩	∩	NOUN
ejpam-5649	177	29	v	v	ADP
ejpam-5649	177	30	̸=	̸=	PROPN
ejpam-5649	177	31	∅.	∅.	ADV
ejpam-5649	177	32	by	by	ADP
ejpam-5649	177	33	(	(	PUNCT
ejpam-5649	177	34	2	2	NUM
ejpam-5649	177	35	)	)	PUNCT
ejpam-5649	177	36	,	,	PUNCT
ejpam-5649	177	37	there	there	PRON
ejpam-5649	177	38	exists	exist	VERB
ejpam-5649	177	39	a	a	DET
ejpam-5649	177	40	σ1σ2	σ1σ2	NUM
ejpam-5649	177	41	-	-	ADJ
ejpam-5649	177	42	rare	rare	ADJ
ejpam-5649	177	43	set	set	ADJ
ejpam-5649	177	44	rv	rv	PROPN
ejpam-5649	177	45	with	with	ADP
ejpam-5649	177	46	σ1σ2	σ1σ2	NOUN
ejpam-5649	177	47	-	-	PUNCT
ejpam-5649	177	48	cl(rv	cl(rv	ADJ
ejpam-5649	177	49	)	)	PUNCT
ejpam-5649	178	1	∩	∩	NOUN
ejpam-5649	178	2	v	v	NOUN
ejpam-5649	178	3	=	=	NOUN
ejpam-5649	178	4	∅	∅	NOUN
ejpam-5649	178	5	such	such	ADJ
ejpam-5649	178	6	that	that	SCONJ
ejpam-5649	178	7	x	x	SYM
ejpam-5649	178	8	∈	∈	PROPN
ejpam-5649	178	9	(	(	PUNCT
ejpam-5649	178	10	τ1	τ1	NOUN
ejpam-5649	178	11	,	,	PUNCT
ejpam-5649	178	12	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	178	13	−(v	−(v	NOUN
ejpam-5649	178	14	∪	∪	PROPN
ejpam-5649	178	15	rv	rv	PROPN
ejpam-5649	178	16	)	)	PUNCT
ejpam-5649	178	17	)	)	PUNCT
ejpam-5649	178	18	.	.	PUNCT
ejpam-5649	179	1	let	let	VERB
ejpam-5649	179	2	u	u	PRON
ejpam-5649	179	3	=	=	PUNCT
ejpam-5649	179	4	(	(	PUNCT
ejpam-5649	179	5	τ1	τ1	PROPN
ejpam-5649	179	6	,	,	PUNCT
ejpam-5649	179	7	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	179	8	−(v	−(v	NOUN
ejpam-5649	179	9	∪	∪	PROPN
ejpam-5649	179	10	rv	rv	PROPN
ejpam-5649	179	11	)	)	PUNCT
ejpam-5649	179	12	)	)	PUNCT
ejpam-5649	179	13	.	.	PUNCT
ejpam-5649	180	1	then	then	ADV
ejpam-5649	180	2	,	,	PUNCT
ejpam-5649	180	3	u	u	NOUN
ejpam-5649	180	4	is	be	AUX
ejpam-5649	180	5	a	a	DET
ejpam-5649	180	6	(	(	PUNCT
ejpam-5649	180	7	τ1	τ1	NOUN
ejpam-5649	180	8	,	,	PUNCT
ejpam-5649	180	9	τ2)p	τ2)p	ADJ
ejpam-5649	180	10	-	-	PUNCT
ejpam-5649	180	11	open	open	ADJ
ejpam-5649	180	12	set	set	NOUN
ejpam-5649	180	13	u	u	NOUN
ejpam-5649	180	14	of	of	ADP
ejpam-5649	180	15	x	x	SYM
ejpam-5649	180	16	containing	contain	VERB
ejpam-5649	180	17	x.	x.	NOUN
ejpam-5649	180	18	furthermore	furthermore	ADV
ejpam-5649	180	19	,	,	PUNCT
ejpam-5649	180	20	f	f	PROPN
ejpam-5649	180	21	(	(	PUNCT
ejpam-5649	180	22	z)∩(v	z)∩(v	PROPN
ejpam-5649	180	23	∪rv	∪rv	PROPN
ejpam-5649	180	24	)	)	PUNCT
ejpam-5649	180	25	̸=	̸=	NOUN
ejpam-5649	180	26	∅	∅	NOUN
ejpam-5649	180	27	for	for	ADP
ejpam-5649	180	28	every	every	DET
ejpam-5649	180	29	z	z	NOUN
ejpam-5649	180	30	∈	∈	PROPN
ejpam-5649	180	31	u	u	NOUN
ejpam-5649	180	32	.	.	PUNCT
ejpam-5649	181	1	thus	thus	ADV
ejpam-5649	181	2	,	,	PUNCT
ejpam-5649	181	3	f	f	PROPN
ejpam-5649	181	4	is	be	AUX
ejpam-5649	181	5	lower	low	ADJ
ejpam-5649	181	6	rarely	rarely	ADV
ejpam-5649	181	7	s-(τ1	s-(τ1	NOUN
ejpam-5649	181	8	,	,	PUNCT
ejpam-5649	181	9	τ2)p	τ2)p	ADJ
ejpam-5649	181	10	-	-	ADJ
ejpam-5649	181	11	continuous	continuous	ADJ
ejpam-5649	181	12	at	at	ADP
ejpam-5649	181	13	x	x	PROPN
ejpam-5649	181	14	∈	∈	PROPN
ejpam-5649	181	15	x.	x.	NOUN
ejpam-5649	181	16	(	(	PUNCT
ejpam-5649	181	17	2	2	X
ejpam-5649	181	18	)	)	PUNCT
ejpam-5649	181	19	⇔	⇔	X
ejpam-5649	181	20	(	(	PUNCT
ejpam-5649	181	21	3	3	NUM
ejpam-5649	181	22	):	):	PUNCT
ejpam-5649	181	23	it	it	PRON
ejpam-5649	181	24	follows	follow	VERB
ejpam-5649	181	25	from	from	ADP
ejpam-5649	181	26	the	the	DET
ejpam-5649	181	27	fact	fact	NOUN
ejpam-5649	181	28	that	that	SCONJ
ejpam-5649	181	29	(	(	PUNCT
ejpam-5649	181	30	τ1	τ1	NOUN
ejpam-5649	181	31	,	,	PUNCT
ejpam-5649	181	32	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	181	33	−(v	−(v	NOUN
ejpam-5649	181	34	∪rv	∪rv	NOUN
ejpam-5649	181	35	)	)	PUNCT
ejpam-5649	181	36	)	)	PUNCT
ejpam-5649	182	1	=	=	PUNCT
ejpam-5649	183	1	τ1τ2	τ1τ2	NOUN
ejpam-5649	183	2	-	-	NOUN
ejpam-5649	183	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	183	4	-	-	PUNCT
ejpam-5649	183	5	cl(f	cl(f	NUM
ejpam-5649	183	6	−(v	−(v	NOUN
ejpam-5649	183	7	∪rv	∪rv	PROPN
ejpam-5649	183	8	)	)	PUNCT
ejpam-5649	183	9	)	)	PUNCT
ejpam-5649	183	10	)	)	PUNCT
ejpam-5649	183	11	∩	∩	NOUN
ejpam-5649	183	12	f−(v	f−(v	VERB
ejpam-5649	183	13	∪rv	∪rv	NOUN
ejpam-5649	183	14	)	)	PUNCT
ejpam-5649	183	15	.	.	PUNCT
ejpam-5649	184	1	definition	definition	NOUN
ejpam-5649	184	2	6	6	NUM
ejpam-5649	184	3	.	.	PUNCT
ejpam-5649	185	1	a	a	DET
ejpam-5649	185	2	function	function	NOUN
ejpam-5649	185	3	f	f	NOUN
ejpam-5649	185	4	:	:	PUNCT
ejpam-5649	185	5	(	(	PUNCT
ejpam-5649	185	6	x	x	NOUN
ejpam-5649	185	7	,	,	PUNCT
ejpam-5649	185	8	τ1	τ1	NOUN
ejpam-5649	185	9	,	,	PUNCT
ejpam-5649	185	10	τ2	τ2	NOUN
ejpam-5649	185	11	)	)	PUNCT
ejpam-5649	185	12	→	→	SYM
ejpam-5649	185	13	(	(	PUNCT
ejpam-5649	185	14	y	y	PROPN
ejpam-5649	185	15	,	,	PUNCT
ejpam-5649	185	16	σ1	σ1	PROPN
ejpam-5649	185	17	,	,	PUNCT
ejpam-5649	185	18	σ2	σ2	PROPN
ejpam-5649	185	19	)	)	PUNCT
ejpam-5649	185	20	is	be	AUX
ejpam-5649	185	21	called	call	VERB
ejpam-5649	185	22	rarely	rarely	ADV
ejpam-5649	185	23	s-(τ1	s-(τ1	NOUN
ejpam-5649	185	24	,	,	PUNCT
ejpam-5649	185	25	τ2)p	τ2)p	ADJ
ejpam-5649	185	26	-	-	ADJ
ejpam-5649	185	27	continuous	continuous	ADJ
ejpam-5649	185	28	at	at	ADP
ejpam-5649	185	29	x	x	X
ejpam-5649	185	30	∈	∈	PROPN
ejpam-5649	185	31	x	x	SYM
ejpam-5649	185	32	if	if	SCONJ
ejpam-5649	185	33	for	for	ADP
ejpam-5649	185	34	each	each	DET
ejpam-5649	185	35	σ1σ2	σ1σ2	VERB
ejpam-5649	185	36	-	-	ADJ
ejpam-5649	185	37	open	open	ADJ
ejpam-5649	185	38	set	set	NOUN
ejpam-5649	185	39	v	v	NOUN
ejpam-5649	185	40	of	of	ADP
ejpam-5649	185	41	y	y	NOUN
ejpam-5649	185	42	containing	contain	VERB
ejpam-5649	185	43	f(x	f(x	PROPN
ejpam-5649	185	44	)	)	PUNCT
ejpam-5649	185	45	and	and	CCONJ
ejpam-5649	185	46	having	have	VERB
ejpam-5649	185	47	σ1σ2	σ1σ2	NOUN
ejpam-5649	185	48	-	-	PUNCT
ejpam-5649	185	49	connected	connect	VERB
ejpam-5649	185	50	complement	complement	NOUN
ejpam-5649	185	51	,	,	PUNCT
ejpam-5649	185	52	there	there	PRON
ejpam-5649	185	53	exists	exist	VERB
ejpam-5649	185	54	a	a	DET
ejpam-5649	185	55	σ1σ2	σ1σ2	NUM
ejpam-5649	185	56	-	-	ADJ
ejpam-5649	185	57	rare	rare	ADJ
ejpam-5649	185	58	set	set	ADJ
ejpam-5649	185	59	rv	rv	PROPN
ejpam-5649	185	60	with	with	ADP
ejpam-5649	185	61	σ1σ2	σ1σ2	NOUN
ejpam-5649	185	62	-	-	PUNCT
ejpam-5649	185	63	cl(rv	cl(rv	ADJ
ejpam-5649	185	64	)	)	PUNCT
ejpam-5649	186	1	∩v	∩v	NOUN
ejpam-5649	186	2	=	=	PUNCT
ejpam-5649	187	1	∅	∅	NOUN
ejpam-5649	187	2	and	and	CCONJ
ejpam-5649	187	3	a	a	DET
ejpam-5649	187	4	(	(	PUNCT
ejpam-5649	187	5	τ1	τ1	NOUN
ejpam-5649	187	6	,	,	PUNCT
ejpam-5649	187	7	τ2)p	τ2)p	ADJ
ejpam-5649	187	8	-	-	PUNCT
ejpam-5649	187	9	open	open	ADJ
ejpam-5649	187	10	set	set	NOUN
ejpam-5649	187	11	u	u	NOUN
ejpam-5649	187	12	of	of	ADP
ejpam-5649	187	13	x	x	PUNCT
ejpam-5649	187	14	containing	contain	VERB
ejpam-5649	187	15	x	x	PUNCT
ejpam-5649	187	16	such	such	ADJ
ejpam-5649	187	17	that	that	DET
ejpam-5649	187	18	f(u	f(u	PROPN
ejpam-5649	187	19	)	)	PUNCT
ejpam-5649	188	1	⊆	⊆	NUM
ejpam-5649	188	2	v	v	ADP
ejpam-5649	188	3	∪rv	∪rv	NOUN
ejpam-5649	188	4	.	.	PUNCT
ejpam-5649	189	1	a	a	DET
ejpam-5649	189	2	function	function	NOUN
ejpam-5649	189	3	f	f	NOUN
ejpam-5649	189	4	:	:	PUNCT
ejpam-5649	189	5	(	(	PUNCT
ejpam-5649	189	6	x	x	NOUN
ejpam-5649	189	7	,	,	PUNCT
ejpam-5649	189	8	τ1	τ1	NOUN
ejpam-5649	189	9	,	,	PUNCT
ejpam-5649	189	10	τ2	τ2	NOUN
ejpam-5649	189	11	)	)	PUNCT
ejpam-5649	189	12	→	→	SYM
ejpam-5649	189	13	(	(	PUNCT
ejpam-5649	189	14	y	y	PROPN
ejpam-5649	189	15	,	,	PUNCT
ejpam-5649	189	16	σ1	σ1	PROPN
ejpam-5649	189	17	,	,	PUNCT
ejpam-5649	189	18	σ2	σ2	PROPN
ejpam-5649	189	19	)	)	PUNCT
ejpam-5649	189	20	is	be	AUX
ejpam-5649	189	21	called	call	VERB
ejpam-5649	189	22	rarely	rarely	ADV
ejpam-5649	189	23	s-(τ1	s-(τ1	NOUN
ejpam-5649	189	24	,	,	PUNCT
ejpam-5649	189	25	τ2)p	τ2)p	ADJ
ejpam-5649	189	26	-	-	ADJ
ejpam-5649	189	27	continuous	continuous	ADJ
ejpam-5649	189	28	if	if	SCONJ
ejpam-5649	189	29	f	f	PROPN
ejpam-5649	189	30	is	be	AUX
ejpam-5649	189	31	rarely	rarely	ADV
ejpam-5649	189	32	s-(τ1	s-(τ1	NOUN
ejpam-5649	189	33	,	,	PUNCT
ejpam-5649	189	34	τ2)p	τ2)p	ADJ
ejpam-5649	189	35	-	-	ADJ
ejpam-5649	189	36	continuous	continuous	ADJ
ejpam-5649	189	37	at	at	ADP
ejpam-5649	189	38	each	each	DET
ejpam-5649	189	39	point	point	NOUN
ejpam-5649	189	40	x	x	PUNCT
ejpam-5649	189	41	of	of	ADP
ejpam-5649	189	42	x.	x.	PROPN
ejpam-5649	189	43	corollary	corollary	NOUN
ejpam-5649	189	44	1	1	NUM
ejpam-5649	189	45	.	.	PUNCT
ejpam-5649	190	1	for	for	ADP
ejpam-5649	190	2	a	a	DET
ejpam-5649	190	3	function	function	NOUN
ejpam-5649	190	4	f	f	NOUN
ejpam-5649	190	5	:	:	PUNCT
ejpam-5649	190	6	(	(	PUNCT
ejpam-5649	190	7	x	x	NOUN
ejpam-5649	190	8	,	,	PUNCT
ejpam-5649	190	9	τ1	τ1	NOUN
ejpam-5649	190	10	,	,	PUNCT
ejpam-5649	190	11	τ2	τ2	NOUN
ejpam-5649	190	12	)	)	PUNCT
ejpam-5649	190	13	→	→	SYM
ejpam-5649	190	14	(	(	PUNCT
ejpam-5649	190	15	y	y	PROPN
ejpam-5649	190	16	,	,	PUNCT
ejpam-5649	190	17	σ1	σ1	PROPN
ejpam-5649	190	18	,	,	PUNCT
ejpam-5649	190	19	σ2	σ2	NOUN
ejpam-5649	190	20	)	)	PUNCT
ejpam-5649	190	21	,	,	PUNCT
ejpam-5649	190	22	the	the	DET
ejpam-5649	190	23	following	follow	VERB
ejpam-5649	190	24	properties	property	NOUN
ejpam-5649	190	25	are	be	AUX
ejpam-5649	190	26	equivalent	equivalent	ADJ
ejpam-5649	190	27	:	:	PUNCT
ejpam-5649	190	28	(	(	PUNCT
ejpam-5649	190	29	1	1	X
ejpam-5649	190	30	)	)	PUNCT
ejpam-5649	190	31	f	f	PROPN
ejpam-5649	190	32	is	be	AUX
ejpam-5649	190	33	rarely	rarely	ADV
ejpam-5649	190	34	s-(τ1	s-(τ1	NOUN
ejpam-5649	190	35	,	,	PUNCT
ejpam-5649	190	36	τ2)p	τ2)p	ADJ
ejpam-5649	190	37	-	-	ADJ
ejpam-5649	190	38	continuous	continuous	ADJ
ejpam-5649	190	39	at	at	ADP
ejpam-5649	190	40	x	x	X
ejpam-5649	190	41	∈	∈	PROPN
ejpam-5649	190	42	x	x	X
ejpam-5649	190	43	;	;	PUNCT
ejpam-5649	190	44	(	(	PUNCT
ejpam-5649	190	45	2	2	X
ejpam-5649	190	46	)	)	PUNCT
ejpam-5649	190	47	for	for	ADP
ejpam-5649	190	48	every	every	DET
ejpam-5649	190	49	σ1σ2	σ1σ2	NOUN
ejpam-5649	190	50	-	-	ADJ
ejpam-5649	190	51	open	open	ADJ
ejpam-5649	190	52	set	set	NOUN
ejpam-5649	190	53	v	v	NOUN
ejpam-5649	190	54	of	of	ADP
ejpam-5649	190	55	y	y	NOUN
ejpam-5649	190	56	containing	contain	VERB
ejpam-5649	190	57	f(x	f(x	PROPN
ejpam-5649	190	58	)	)	PUNCT
ejpam-5649	190	59	and	and	CCONJ
ejpam-5649	190	60	having	have	VERB
ejpam-5649	190	61	σ1σ2	σ1σ2	NOUN
ejpam-5649	190	62	-	-	PUNCT
ejpam-5649	190	63	connected	connect	VERB
ejpam-5649	190	64	complement	complement	NOUN
ejpam-5649	190	65	,	,	PUNCT
ejpam-5649	190	66	there	there	PRON
ejpam-5649	190	67	exists	exist	VERB
ejpam-5649	190	68	a	a	DET
ejpam-5649	190	69	σ1σ2	σ1σ2	NUM
ejpam-5649	190	70	-	-	ADJ
ejpam-5649	190	71	rare	rare	ADJ
ejpam-5649	190	72	set	set	ADJ
ejpam-5649	190	73	rv	rv	PROPN
ejpam-5649	190	74	with	with	ADP
ejpam-5649	190	75	σ1σ2	σ1σ2	NOUN
ejpam-5649	190	76	-	-	PUNCT
ejpam-5649	190	77	cl(rv	cl(rv	ADJ
ejpam-5649	190	78	)	)	PUNCT
ejpam-5649	191	1	∩	∩	NOUN
ejpam-5649	191	2	v	v	NOUN
ejpam-5649	191	3	=	=	NOUN
ejpam-5649	191	4	∅	∅	NOUN
ejpam-5649	191	5	such	such	ADJ
ejpam-5649	191	6	that	that	SCONJ
ejpam-5649	191	7	x	x	SYM
ejpam-5649	191	8	∈	∈	PROPN
ejpam-5649	191	9	(	(	PUNCT
ejpam-5649	191	10	τ1	τ1	NOUN
ejpam-5649	191	11	,	,	PUNCT
ejpam-5649	191	12	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	191	13	−1(v	−1(v	PRON
ejpam-5649	191	14	∪rv	∪rv	NOUN
ejpam-5649	191	15	)	)	PUNCT
ejpam-5649	191	16	)	)	PUNCT
ejpam-5649	191	17	;	;	PUNCT
ejpam-5649	191	18	b.	b.	PROPN
ejpam-5649	191	19	kong	kong	PROPN
ejpam-5649	191	20	-	-	PUNCT
ejpam-5649	191	21	ied	ied	PROPN
ejpam-5649	191	22	,	,	PUNCT
ejpam-5649	191	23	s.	s.	PROPN
ejpam-5649	191	24	sompong	sompong	PROPN
ejpam-5649	191	25	,	,	PUNCT
ejpam-5649	191	26	c.	c.	PROPN
ejpam-5649	191	27	boonpok	boonpok	PROPN
ejpam-5649	191	28	/	/	SYM
ejpam-5649	191	29	eur	eur	PROPN
ejpam-5649	191	30	.	.	PUNCT
ejpam-5649	192	1	j.	j.	PROPN
ejpam-5649	192	2	pure	pure	PROPN
ejpam-5649	192	3	appl	appl	PROPN
ejpam-5649	192	4	.	.	PROPN
ejpam-5649	192	5	math	math	PROPN
ejpam-5649	192	6	,	,	PUNCT
ejpam-5649	192	7	18	18	NUM
ejpam-5649	192	8	(	(	PUNCT
ejpam-5649	192	9	1	1	NUM
ejpam-5649	192	10	)	)	PUNCT
ejpam-5649	192	11	(	(	PUNCT
ejpam-5649	192	12	2025	2025	NUM
ejpam-5649	192	13	)	)	PUNCT
ejpam-5649	192	14	,	,	PUNCT
ejpam-5649	192	15	5649	5649	NUM
ejpam-5649	192	16	8	8	NUM
ejpam-5649	192	17	of	of	ADP
ejpam-5649	192	18	13	13	NUM
ejpam-5649	192	19	(	(	PUNCT
ejpam-5649	192	20	3	3	NUM
ejpam-5649	192	21	)	)	PUNCT
ejpam-5649	192	22	for	for	ADP
ejpam-5649	192	23	every	every	DET
ejpam-5649	192	24	σ1σ2	σ1σ2	NOUN
ejpam-5649	192	25	-	-	ADJ
ejpam-5649	192	26	open	open	ADJ
ejpam-5649	192	27	set	set	NOUN
ejpam-5649	192	28	v	v	NOUN
ejpam-5649	192	29	of	of	ADP
ejpam-5649	192	30	y	y	NOUN
ejpam-5649	192	31	containing	contain	VERB
ejpam-5649	192	32	f(x	f(x	PROPN
ejpam-5649	192	33	)	)	PUNCT
ejpam-5649	192	34	and	and	CCONJ
ejpam-5649	192	35	having	have	VERB
ejpam-5649	192	36	σ1σ2	σ1σ2	NOUN
ejpam-5649	192	37	-	-	PUNCT
ejpam-5649	192	38	connected	connect	VERB
ejpam-5649	192	39	complement	complement	NOUN
ejpam-5649	193	1	,	,	PUNCT
ejpam-5649	193	2	there	there	PRON
ejpam-5649	193	3	exists	exist	VERB
ejpam-5649	193	4	a	a	DET
ejpam-5649	193	5	σ1σ2	σ1σ2	NUM
ejpam-5649	193	6	-	-	ADJ
ejpam-5649	193	7	rare	rare	ADJ
ejpam-5649	193	8	set	set	ADJ
ejpam-5649	193	9	rv	rv	NOUN
ejpam-5649	193	10	with	with	ADP
ejpam-5649	193	11	σ1σ2	σ1σ2	NOUN
ejpam-5649	193	12	-	-	PUNCT
ejpam-5649	193	13	cl(v	cl(v	NOUN
ejpam-5649	193	14	)	)	PUNCT
ejpam-5649	193	15	∩rv	∩rv	NOUN
ejpam-5649	193	16	=	=	PUNCT
ejpam-5649	193	17	∅	∅	NOUN
ejpam-5649	193	18	such	such	ADJ
ejpam-5649	193	19	that	that	SCONJ
ejpam-5649	193	20	x	x	SYM
ejpam-5649	193	21	∈	∈	PROPN
ejpam-5649	193	22	(	(	PUNCT
ejpam-5649	193	23	τ1	τ1	NOUN
ejpam-5649	193	24	,	,	PUNCT
ejpam-5649	193	25	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	193	26	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5649	193	27	-	-	PUNCT
ejpam-5649	193	28	cl(v	cl(v	X
ejpam-5649	193	29	)	)	PUNCT
ejpam-5649	193	30	∪rv	∪rv	NOUN
ejpam-5649	193	31	)	)	PUNCT
ejpam-5649	193	32	)	)	PUNCT
ejpam-5649	193	33	;	;	PUNCT
ejpam-5649	193	34	(	(	PUNCT
ejpam-5649	193	35	4	4	X
ejpam-5649	193	36	)	)	PUNCT
ejpam-5649	193	37	for	for	ADP
ejpam-5649	193	38	every	every	DET
ejpam-5649	193	39	σ1σ2	σ1σ2	NOUN
ejpam-5649	193	40	-	-	ADJ
ejpam-5649	193	41	open	open	ADJ
ejpam-5649	193	42	set	set	NOUN
ejpam-5649	193	43	v	v	NOUN
ejpam-5649	193	44	of	of	ADP
ejpam-5649	193	45	y	y	NOUN
ejpam-5649	193	46	containing	contain	VERB
ejpam-5649	193	47	f(x	f(x	PROPN
ejpam-5649	193	48	)	)	PUNCT
ejpam-5649	193	49	and	and	CCONJ
ejpam-5649	193	50	having	have	VERB
ejpam-5649	193	51	σ1σ2	σ1σ2	NOUN
ejpam-5649	193	52	-	-	PUNCT
ejpam-5649	193	53	connected	connect	VERB
ejpam-5649	193	54	complement	complement	NOUN
ejpam-5649	193	55	,	,	PUNCT
ejpam-5649	193	56	there	there	PRON
ejpam-5649	193	57	exists	exist	VERB
ejpam-5649	193	58	a	a	DET
ejpam-5649	193	59	(	(	PUNCT
ejpam-5649	193	60	τ1	τ1	NOUN
ejpam-5649	193	61	,	,	PUNCT
ejpam-5649	193	62	τ2)p	τ2)p	ADJ
ejpam-5649	193	63	-	-	PUNCT
ejpam-5649	193	64	open	open	ADJ
ejpam-5649	193	65	set	set	NOUN
ejpam-5649	193	66	u	u	NOUN
ejpam-5649	193	67	of	of	ADP
ejpam-5649	193	68	x	x	PUNCT
ejpam-5649	193	69	containing	contain	VERB
ejpam-5649	193	70	x	x	PUNCT
ejpam-5649	193	71	such	such	ADJ
ejpam-5649	193	72	that	that	SCONJ
ejpam-5649	193	73	σ1σ2	σ1σ2	ADJ
ejpam-5649	193	74	-	-	PUNCT
ejpam-5649	193	75	int(f(u	int(f(u	ADJ
ejpam-5649	193	76	)	)	PUNCT
ejpam-5649	193	77	∩	∩	NOUN
ejpam-5649	193	78	(	(	PUNCT
ejpam-5649	193	79	y	y	PROPN
ejpam-5649	193	80	−	−	PROPN
ejpam-5649	193	81	v	v	NOUN
ejpam-5649	193	82	)	)	PUNCT
ejpam-5649	193	83	)	)	PUNCT
ejpam-5649	194	1	=	=	NOUN
ejpam-5649	194	2	∅	∅	NOUN
ejpam-5649	194	3	;	;	PUNCT
ejpam-5649	194	4	(	(	PUNCT
ejpam-5649	194	5	5	5	X
ejpam-5649	194	6	)	)	PUNCT
ejpam-5649	194	7	for	for	ADP
ejpam-5649	194	8	every	every	DET
ejpam-5649	194	9	σ1σ2	σ1σ2	NOUN
ejpam-5649	194	10	-	-	ADJ
ejpam-5649	194	11	open	open	ADJ
ejpam-5649	194	12	set	set	NOUN
ejpam-5649	194	13	v	v	NOUN
ejpam-5649	194	14	of	of	ADP
ejpam-5649	194	15	y	y	NOUN
ejpam-5649	194	16	containing	contain	VERB
ejpam-5649	194	17	f(x	f(x	PROPN
ejpam-5649	194	18	)	)	PUNCT
ejpam-5649	194	19	and	and	CCONJ
ejpam-5649	194	20	having	have	VERB
ejpam-5649	194	21	σ1σ2	σ1σ2	NOUN
ejpam-5649	194	22	-	-	PUNCT
ejpam-5649	194	23	connected	connect	VERB
ejpam-5649	194	24	complement	complement	NOUN
ejpam-5649	194	25	,	,	PUNCT
ejpam-5649	194	26	there	there	PRON
ejpam-5649	194	27	exists	exist	VERB
ejpam-5649	194	28	a	a	DET
ejpam-5649	194	29	(	(	PUNCT
ejpam-5649	194	30	τ1	τ1	NOUN
ejpam-5649	194	31	,	,	PUNCT
ejpam-5649	194	32	τ2)p	τ2)p	ADJ
ejpam-5649	194	33	-	-	PUNCT
ejpam-5649	194	34	open	open	ADJ
ejpam-5649	194	35	set	set	NOUN
ejpam-5649	194	36	u	u	NOUN
ejpam-5649	194	37	of	of	ADP
ejpam-5649	194	38	x	x	PUNCT
ejpam-5649	194	39	containing	contain	VERB
ejpam-5649	194	40	x	x	PUNCT
ejpam-5649	194	41	such	such	ADJ
ejpam-5649	194	42	that	that	SCONJ
ejpam-5649	194	43	σ1σ2	σ1σ2	NOUN
ejpam-5649	194	44	-	-	NUM
ejpam-5649	194	45	int(f(u	int(f(u	NOUN
ejpam-5649	194	46	)	)	PUNCT
ejpam-5649	194	47	)	)	PUNCT
ejpam-5649	195	1	⊆	⊆	X
ejpam-5649	195	2	σ1σ2	σ1σ2	NOUN
ejpam-5649	195	3	-	-	NUM
ejpam-5649	195	4	cl(v	cl(v	NOUN
ejpam-5649	195	5	)	)	PUNCT
ejpam-5649	195	6	;	;	PUNCT
ejpam-5649	195	7	(	(	PUNCT
ejpam-5649	195	8	6	6	X
ejpam-5649	195	9	)	)	PUNCT
ejpam-5649	195	10	for	for	ADP
ejpam-5649	195	11	every	every	DET
ejpam-5649	195	12	σ1σ2	σ1σ2	NOUN
ejpam-5649	195	13	-	-	ADJ
ejpam-5649	195	14	open	open	ADJ
ejpam-5649	195	15	set	set	NOUN
ejpam-5649	195	16	v	v	NOUN
ejpam-5649	195	17	of	of	ADP
ejpam-5649	195	18	y	y	NOUN
ejpam-5649	195	19	containing	contain	VERB
ejpam-5649	195	20	f(x	f(x	PROPN
ejpam-5649	195	21	)	)	PUNCT
ejpam-5649	195	22	and	and	CCONJ
ejpam-5649	195	23	having	have	VERB
ejpam-5649	195	24	σ1σ2	σ1σ2	NOUN
ejpam-5649	195	25	-	-	PUNCT
ejpam-5649	195	26	connected	connect	VERB
ejpam-5649	195	27	complement	complement	NOUN
ejpam-5649	195	28	,	,	PUNCT
ejpam-5649	195	29	there	there	PRON
ejpam-5649	195	30	exists	exist	VERB
ejpam-5649	195	31	a	a	DET
ejpam-5649	195	32	σ1σ2	σ1σ2	NUM
ejpam-5649	195	33	-	-	ADJ
ejpam-5649	195	34	rare	rare	ADJ
ejpam-5649	195	35	set	set	ADJ
ejpam-5649	195	36	rv	rv	PROPN
ejpam-5649	195	37	with	with	ADP
ejpam-5649	195	38	σ1σ2	σ1σ2	NOUN
ejpam-5649	195	39	-	-	PUNCT
ejpam-5649	195	40	cl(rv	cl(rv	ADJ
ejpam-5649	195	41	)	)	PUNCT
ejpam-5649	196	1	∩	∩	NOUN
ejpam-5649	196	2	v	v	NOUN
ejpam-5649	196	3	=	=	NOUN
ejpam-5649	196	4	∅	∅	NOUN
ejpam-5649	196	5	such	such	ADJ
ejpam-5649	196	6	that	that	SCONJ
ejpam-5649	196	7	x	x	SYM
ejpam-5649	196	8	∈	∈	PROPN
ejpam-5649	196	9	f−1(v	f−1(v	NOUN
ejpam-5649	196	10	∪rv	∪rv	PROPN
ejpam-5649	196	11	)	)	PUNCT
ejpam-5649	196	12	∩	∩	NOUN
ejpam-5649	196	13	τ1τ2	τ1τ2	NOUN
ejpam-5649	196	14	-	-	NOUN
ejpam-5649	196	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5649	196	16	-	-	PUNCT
ejpam-5649	196	17	cl(f	cl(f	PRON
ejpam-5649	196	18	−1(v	−1(v	NOUN
ejpam-5649	196	19	∪rv	∪rv	NOUN
ejpam-5649	196	20	)	)	PUNCT
ejpam-5649	196	21	)	)	PUNCT
ejpam-5649	196	22	)	)	PUNCT
ejpam-5649	196	23	.	.	PUNCT
ejpam-5649	197	1	theorem	theorem	VERB
ejpam-5649	197	2	4	4	NUM
ejpam-5649	197	3	.	.	PUNCT
ejpam-5649	198	1	a	a	DET
ejpam-5649	198	2	function	function	NOUN
ejpam-5649	198	3	f	f	NOUN
ejpam-5649	198	4	:	:	PUNCT
ejpam-5649	198	5	(	(	PUNCT
ejpam-5649	198	6	x	x	NOUN
ejpam-5649	198	7	,	,	PUNCT
ejpam-5649	198	8	τ1	τ1	NOUN
ejpam-5649	198	9	,	,	PUNCT
ejpam-5649	198	10	τ2	τ2	NOUN
ejpam-5649	198	11	)	)	PUNCT
ejpam-5649	198	12	→	→	SYM
ejpam-5649	198	13	(	(	PUNCT
ejpam-5649	198	14	y	y	PROPN
ejpam-5649	198	15	,	,	PUNCT
ejpam-5649	198	16	σ1	σ1	PROPN
ejpam-5649	198	17	,	,	PUNCT
ejpam-5649	198	18	σ2	σ2	PROPN
ejpam-5649	198	19	)	)	PUNCT
ejpam-5649	198	20	is	be	AUX
ejpam-5649	198	21	rarely	rarely	ADV
ejpam-5649	198	22	s-(τ1	s-(τ1	NOUN
ejpam-5649	198	23	,	,	PUNCT
ejpam-5649	198	24	τ2)p	τ2)p	ADJ
ejpam-5649	198	25	-	-	ADJ
ejpam-5649	198	26	continuous	continuous	ADJ
ejpam-5649	198	27	if	if	SCONJ
ejpam-5649	198	28	and	and	CCONJ
ejpam-5649	198	29	only	only	ADV
ejpam-5649	198	30	if	if	SCONJ
ejpam-5649	198	31	for	for	ADP
ejpam-5649	198	32	every	every	DET
ejpam-5649	198	33	σ1σ2	σ1σ2	NUM
ejpam-5649	198	34	-	-	ADJ
ejpam-5649	198	35	open	open	ADJ
ejpam-5649	198	36	set	set	NOUN
ejpam-5649	198	37	v	v	NOUN
ejpam-5649	198	38	of	of	ADP
ejpam-5649	198	39	y	y	PROPN
ejpam-5649	198	40	,	,	PUNCT
ejpam-5649	198	41	there	there	PRON
ejpam-5649	198	42	exists	exist	VERB
ejpam-5649	198	43	a	a	DET
ejpam-5649	198	44	σ1σ2	σ1σ2	NUM
ejpam-5649	198	45	-	-	ADJ
ejpam-5649	198	46	rare	rare	ADJ
ejpam-5649	198	47	set	set	ADJ
ejpam-5649	198	48	rv	rv	PROPN
ejpam-5649	198	49	with	with	ADP
ejpam-5649	198	50	σ1σ2	σ1σ2	NOUN
ejpam-5649	198	51	-	-	PUNCT
ejpam-5649	198	52	cl(rv	cl(rv	ADJ
ejpam-5649	198	53	)	)	PUNCT
ejpam-5649	199	1	∩	∩	NOUN
ejpam-5649	199	2	v	v	NOUN
ejpam-5649	199	3	=	=	NOUN
ejpam-5649	199	4	∅	∅	NOUN
ejpam-5649	199	5	such	such	ADJ
ejpam-5649	199	6	that	that	DET
ejpam-5649	199	7	f−1(v	f−1(v	NOUN
ejpam-5649	199	8	)	)	PUNCT
ejpam-5649	200	1	⊆	⊆	NUM
ejpam-5649	200	2	(	(	PUNCT
ejpam-5649	200	3	τ1	τ1	NOUN
ejpam-5649	200	4	,	,	PUNCT
ejpam-5649	200	5	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	200	6	−1(v	−1(v	PRON
ejpam-5649	200	7	∪rv	∪rv	NOUN
ejpam-5649	200	8	)	)	PUNCT
ejpam-5649	200	9	)	)	PUNCT
ejpam-5649	200	10	.	.	PUNCT
ejpam-5649	201	1	proof	proof	NOUN
ejpam-5649	201	2	.	.	PUNCT
ejpam-5649	202	1	it	it	PRON
ejpam-5649	202	2	is	be	AUX
ejpam-5649	202	3	an	an	DET
ejpam-5649	202	4	immediate	immediate	ADJ
ejpam-5649	202	5	consequence	consequence	NOUN
ejpam-5649	202	6	of	of	ADP
ejpam-5649	202	7	the	the	DET
ejpam-5649	202	8	above	above	ADJ
ejpam-5649	202	9	corollary	corollary	NOUN
ejpam-5649	202	10	.	.	PUNCT
ejpam-5649	203	1	definition	definition	NOUN
ejpam-5649	203	2	7	7	NUM
ejpam-5649	203	3	.	.	PUNCT
ejpam-5649	204	1	a	a	DET
ejpam-5649	204	2	bitopologcal	bitopologcal	ADJ
ejpam-5649	204	3	space	space	NOUN
ejpam-5649	204	4	(	(	PUNCT
ejpam-5649	204	5	x	x	NOUN
ejpam-5649	204	6	,	,	PUNCT
ejpam-5649	204	7	τ1	τ1	NOUN
ejpam-5649	204	8	,	,	PUNCT
ejpam-5649	204	9	τ2	τ2	NOUN
ejpam-5649	204	10	)	)	PUNCT
ejpam-5649	204	11	is	be	AUX
ejpam-5649	204	12	said	say	VERB
ejpam-5649	204	13	to	to	PART
ejpam-5649	204	14	be	be	AUX
ejpam-5649	204	15	τ1τ2	τ1τ2	NOUN
ejpam-5649	204	16	-	-	ADJ
ejpam-5649	204	17	rarely	rarely	ADV
ejpam-5649	204	18	separate	separate	ADJ
ejpam-5649	204	19	if	if	SCONJ
ejpam-5649	204	20	for	for	ADP
ejpam-5649	204	21	every	every	DET
ejpam-5649	204	22	pair	pair	NOUN
ejpam-5649	204	23	of	of	ADP
ejpam-5649	204	24	distinct	distinct	ADJ
ejpam-5649	204	25	points	point	NOUN
ejpam-5649	204	26	x	x	PUNCT
ejpam-5649	204	27	and	and	CCONJ
ejpam-5649	204	28	y	y	PROPN
ejpam-5649	204	29	in	in	ADP
ejpam-5649	204	30	x	x	SYM
ejpam-5649	204	31	,	,	PUNCT
ejpam-5649	204	32	there	there	PRON
ejpam-5649	204	33	exist	exist	VERB
ejpam-5649	204	34	τ1τ2	τ1τ2	ADJ
ejpam-5649	204	35	-	-	ADJ
ejpam-5649	204	36	open	open	ADJ
ejpam-5649	204	37	sets	set	NOUN
ejpam-5649	204	38	vx	vx	PROPN
ejpam-5649	204	39	and	and	CCONJ
ejpam-5649	204	40	vy	vy	ADV
ejpam-5649	204	41	containing	contain	VERB
ejpam-5649	204	42	x	x	PROPN
ejpam-5649	204	43	and	and	CCONJ
ejpam-5649	204	44	y	y	PROPN
ejpam-5649	204	45	,	,	PUNCT
ejpam-5649	204	46	respectively	respectively	ADV
ejpam-5649	204	47	,	,	PUNCT
ejpam-5649	204	48	and	and	CCONJ
ejpam-5649	204	49	τ1τ2	τ1τ2	VERB
ejpam-5649	204	50	-	-	ADJ
ejpam-5649	204	51	rare	rare	ADJ
ejpam-5649	204	52	sets	set	NOUN
ejpam-5649	204	53	rvx	rvx	ADJ
ejpam-5649	204	54	,	,	PUNCT
ejpam-5649	204	55	rvy	rvy	VERB
ejpam-5649	204	56	with	with	ADP
ejpam-5649	204	57	τ1τ2	τ1τ2	NOUN
ejpam-5649	204	58	-	-	ADJ
ejpam-5649	204	59	cl(rvx	cl(rvx	NOUN
ejpam-5649	204	60	)	)	PUNCT
ejpam-5649	204	61	∩	∩	NOUN
ejpam-5649	204	62	vx	vx	PROPN
ejpam-5649	204	63	=	=	NOUN
ejpam-5649	204	64	∅	∅	NOUN
ejpam-5649	204	65	and	and	CCONJ
ejpam-5649	204	66	τ1τ2	τ1τ2	NOUN
ejpam-5649	204	67	-	-	ADJ
ejpam-5649	204	68	cl(rvy	cl(rvy	ADJ
ejpam-5649	204	69	)	)	PUNCT
ejpam-5649	204	70	∩	∩	NOUN
ejpam-5649	204	71	vy	vy	NOUN
ejpam-5649	204	72	=	=	NOUN
ejpam-5649	204	73	∅	∅	NOUN
ejpam-5649	204	74	such	such	ADJ
ejpam-5649	204	75	that	that	DET
ejpam-5649	204	76	(	(	PUNCT
ejpam-5649	204	77	vx	vx	PROPN
ejpam-5649	204	78	∪rvx	∪rvx	PROPN
ejpam-5649	204	79	)	)	PUNCT
ejpam-5649	204	80	∩	∩	NOUN
ejpam-5649	204	81	(	(	PUNCT
ejpam-5649	204	82	vy	vy	NOUN
ejpam-5649	204	83	∪rvy	∪rvy	NOUN
ejpam-5649	204	84	)	)	PUNCT
ejpam-5649	204	85	=	=	PUNCT
ejpam-5649	204	86	∅.	∅.	PRON
ejpam-5649	204	87	definition	definition	NOUN
ejpam-5649	204	88	8	8	NUM
ejpam-5649	204	89	.	.	PUNCT
ejpam-5649	205	1	a	a	DET
ejpam-5649	205	2	bitopologcal	bitopologcal	ADJ
ejpam-5649	205	3	space	space	NOUN
ejpam-5649	205	4	(	(	PUNCT
ejpam-5649	205	5	x	x	NOUN
ejpam-5649	205	6	,	,	PUNCT
ejpam-5649	205	7	τ1	τ1	NOUN
ejpam-5649	205	8	,	,	PUNCT
ejpam-5649	205	9	τ2	τ2	NOUN
ejpam-5649	205	10	)	)	PUNCT
ejpam-5649	205	11	is	be	AUX
ejpam-5649	205	12	said	say	VERB
ejpam-5649	205	13	to	to	PART
ejpam-5649	205	14	be	be	AUX
ejpam-5649	205	15	(	(	PUNCT
ejpam-5649	205	16	τ1	τ1	NOUN
ejpam-5649	205	17	,	,	PUNCT
ejpam-5649	205	18	τ2)p	τ2)p	ADJ
ejpam-5649	205	19	-	-	PUNCT
ejpam-5649	205	20	hausdorff	hausdorff	NOUN
ejpam-5649	205	21	if	if	SCONJ
ejpam-5649	205	22	for	for	ADP
ejpam-5649	205	23	any	any	DET
ejpam-5649	205	24	distinct	distinct	ADJ
ejpam-5649	205	25	pair	pair	NOUN
ejpam-5649	205	26	of	of	ADP
ejpam-5649	205	27	points	point	NOUN
ejpam-5649	205	28	x	x	PUNCT
ejpam-5649	205	29	and	and	CCONJ
ejpam-5649	205	30	y	y	PROPN
ejpam-5649	205	31	in	in	ADP
ejpam-5649	205	32	x	x	SYM
ejpam-5649	205	33	,	,	PUNCT
ejpam-5649	205	34	there	there	PRON
ejpam-5649	205	35	exist	exist	VERB
ejpam-5649	205	36	(	(	PUNCT
ejpam-5649	205	37	τ1	τ1	NOUN
ejpam-5649	205	38	,	,	PUNCT
ejpam-5649	205	39	τ2)p	τ2)p	ADJ
ejpam-5649	205	40	-	-	PUNCT
ejpam-5649	205	41	open	open	ADJ
ejpam-5649	205	42	sets	set	VERB
ejpam-5649	205	43	u	u	NOUN
ejpam-5649	205	44	and	and	CCONJ
ejpam-5649	205	45	v	v	NOUN
ejpam-5649	205	46	of	of	ADP
ejpam-5649	205	47	x	x	PUNCT
ejpam-5649	205	48	containing	contain	VERB
ejpam-5649	205	49	x	x	PROPN
ejpam-5649	205	50	and	and	CCONJ
ejpam-5649	205	51	y	y	PROPN
ejpam-5649	205	52	,	,	PUNCT
ejpam-5649	205	53	respectively	respectively	ADV
ejpam-5649	205	54	,	,	PUNCT
ejpam-5649	205	55	such	such	ADJ
ejpam-5649	205	56	that	that	SCONJ
ejpam-5649	205	57	u	u	PROPN
ejpam-5649	205	58	∩	∩	NOUN
ejpam-5649	205	59	v	v	NOUN
ejpam-5649	205	60	=	=	PUNCT
ejpam-5649	205	61	∅.	∅.	NOUN
ejpam-5649	205	62	theorem	theorem	VERB
ejpam-5649	205	63	5	5	NUM
ejpam-5649	205	64	.	.	PUNCT
ejpam-5649	206	1	if	if	SCONJ
ejpam-5649	206	2	(	(	PUNCT
ejpam-5649	206	3	y	y	PROPN
ejpam-5649	206	4	,	,	PUNCT
ejpam-5649	206	5	σ1	σ1	PROPN
ejpam-5649	206	6	,	,	PUNCT
ejpam-5649	206	7	σ2	σ2	PROPN
ejpam-5649	206	8	)	)	PUNCT
ejpam-5649	206	9	is	be	AUX
ejpam-5649	206	10	σ1σ2	σ1σ2	NOUN
ejpam-5649	206	11	-	-	PUNCT
ejpam-5649	206	12	rarely	rarely	ADV
ejpam-5649	206	13	separate	separate	ADJ
ejpam-5649	206	14	and	and	CCONJ
ejpam-5649	206	15	f	f	X
ejpam-5649	206	16	:	:	PUNCT
ejpam-5649	206	17	(	(	PUNCT
ejpam-5649	206	18	x	x	NOUN
ejpam-5649	206	19	,	,	PUNCT
ejpam-5649	206	20	τ1	τ1	NOUN
ejpam-5649	206	21	,	,	PUNCT
ejpam-5649	206	22	τ2	τ2	NOUN
ejpam-5649	206	23	)	)	PUNCT
ejpam-5649	206	24	→	→	SYM
ejpam-5649	206	25	(	(	PUNCT
ejpam-5649	206	26	y	y	PROPN
ejpam-5649	206	27	,	,	PUNCT
ejpam-5649	206	28	σ1	σ1	PROPN
ejpam-5649	206	29	,	,	PUNCT
ejpam-5649	206	30	σ2	σ2	PROPN
ejpam-5649	206	31	)	)	PUNCT
ejpam-5649	206	32	is	be	AUX
ejpam-5649	206	33	a	a	DET
ejpam-5649	206	34	rarely	rarely	ADV
ejpam-5649	206	35	s-(τ1	s-(τ1	ADJ
ejpam-5649	206	36	,	,	PUNCT
ejpam-5649	206	37	τ2)p	τ2)p	ADJ
ejpam-5649	206	38	-	-	ADJ
ejpam-5649	206	39	continuous	continuous	ADJ
ejpam-5649	206	40	injection	injection	NOUN
ejpam-5649	206	41	,	,	PUNCT
ejpam-5649	206	42	then	then	ADV
ejpam-5649	206	43	(	(	PUNCT
ejpam-5649	206	44	x	x	NOUN
ejpam-5649	206	45	,	,	PUNCT
ejpam-5649	206	46	τ1	τ1	NOUN
ejpam-5649	206	47	,	,	PUNCT
ejpam-5649	206	48	τ2	τ2	NOUN
ejpam-5649	206	49	)	)	PUNCT
ejpam-5649	206	50	is	be	AUX
ejpam-5649	206	51	(	(	PUNCT
ejpam-5649	206	52	τ1	τ1	NOUN
ejpam-5649	206	53	,	,	PUNCT
ejpam-5649	206	54	τ2)p	τ2)p	ADJ
ejpam-5649	206	55	-	-	PUNCT
ejpam-5649	206	56	hausdorff	hausdorff	NOUN
ejpam-5649	206	57	.	.	PUNCT
ejpam-5649	207	1	b.	b.	PROPN
ejpam-5649	207	2	kong	kong	PROPN
ejpam-5649	207	3	-	-	PUNCT
ejpam-5649	207	4	ied	ied	PROPN
ejpam-5649	207	5	,	,	PUNCT
ejpam-5649	207	6	s.	s.	PROPN
ejpam-5649	207	7	sompong	sompong	PROPN
ejpam-5649	207	8	,	,	PUNCT
ejpam-5649	207	9	c.	c.	PROPN
ejpam-5649	207	10	boonpok	boonpok	PROPN
ejpam-5649	207	11	/	/	SYM
ejpam-5649	207	12	eur	eur	PROPN
ejpam-5649	207	13	.	.	PUNCT
ejpam-5649	208	1	j.	j.	PROPN
ejpam-5649	208	2	pure	pure	PROPN
ejpam-5649	208	3	appl	appl	PROPN
ejpam-5649	208	4	.	.	PROPN
ejpam-5649	208	5	math	math	PROPN
ejpam-5649	208	6	,	,	PUNCT
ejpam-5649	208	7	18	18	NUM
ejpam-5649	208	8	(	(	PUNCT
ejpam-5649	208	9	1	1	NUM
ejpam-5649	208	10	)	)	PUNCT
ejpam-5649	208	11	(	(	PUNCT
ejpam-5649	208	12	2025	2025	NUM
ejpam-5649	208	13	)	)	PUNCT
ejpam-5649	208	14	,	,	PUNCT
ejpam-5649	208	15	5649	5649	NUM
ejpam-5649	208	16	9	9	NUM
ejpam-5649	208	17	of	of	ADP
ejpam-5649	208	18	13	13	NUM
ejpam-5649	208	19	proof	proof	NOUN
ejpam-5649	208	20	.	.	PUNCT
ejpam-5649	209	1	let	let	VERB
ejpam-5649	209	2	x	x	PRON
ejpam-5649	209	3	and	and	CCONJ
ejpam-5649	209	4	y	y	PROPN
ejpam-5649	209	5	be	be	AUX
ejpam-5649	209	6	any	any	DET
ejpam-5649	209	7	distinct	distinct	ADJ
ejpam-5649	209	8	points	point	NOUN
ejpam-5649	209	9	in	in	ADP
ejpam-5649	209	10	x.	x.	NOUN
ejpam-5649	209	11	then	then	ADV
ejpam-5649	209	12	,	,	PUNCT
ejpam-5649	209	13	f(x	f(x	PROPN
ejpam-5649	209	14	)	)	PUNCT
ejpam-5649	209	15	̸=	̸=	PROPN
ejpam-5649	209	16	f(y	f(y	NOUN
ejpam-5649	209	17	)	)	PUNCT
ejpam-5649	209	18	.	.	PUNCT
ejpam-5649	210	1	since	since	SCONJ
ejpam-5649	210	2	(	(	PUNCT
ejpam-5649	210	3	y	y	PROPN
ejpam-5649	210	4	,	,	PUNCT
ejpam-5649	210	5	σ1	σ1	PROPN
ejpam-5649	210	6	,	,	PUNCT
ejpam-5649	210	7	σ2	σ2	PROPN
ejpam-5649	210	8	)	)	PUNCT
ejpam-5649	210	9	is	be	AUX
ejpam-5649	210	10	σ1σ2	σ1σ2	NOUN
ejpam-5649	210	11	-	-	PUNCT
ejpam-5649	210	12	rarely	rarely	ADV
ejpam-5649	210	13	separate	separate	ADJ
ejpam-5649	210	14	,	,	PUNCT
ejpam-5649	210	15	there	there	PRON
ejpam-5649	210	16	exist	exist	VERB
ejpam-5649	210	17	σ1σ2	σ1σ2	NOUN
ejpam-5649	210	18	-	-	ADJ
ejpam-5649	210	19	open	open	ADJ
ejpam-5649	210	20	sets	set	NOUN
ejpam-5649	210	21	v	v	ADP
ejpam-5649	210	22	and	and	CCONJ
ejpam-5649	210	23	w	w	PROPN
ejpam-5649	210	24	of	of	ADP
ejpam-5649	210	25	y	y	PROPN
ejpam-5649	210	26	containing	contain	VERB
ejpam-5649	210	27	f(x	f(x	PROPN
ejpam-5649	210	28	)	)	PUNCT
ejpam-5649	210	29	and	and	CCONJ
ejpam-5649	210	30	f(y	f(y	NOUN
ejpam-5649	210	31	)	)	PUNCT
ejpam-5649	210	32	,	,	PUNCT
ejpam-5649	210	33	respectively	respectively	ADV
ejpam-5649	210	34	,	,	PUNCT
ejpam-5649	210	35	and	and	CCONJ
ejpam-5649	210	36	σ1σ2	σ1σ2	NOUN
ejpam-5649	210	37	-	-	ADJ
ejpam-5649	210	38	rare	rare	ADJ
ejpam-5649	210	39	sets	set	NOUN
ejpam-5649	210	40	rv	rv	PROPN
ejpam-5649	210	41	and	and	CCONJ
ejpam-5649	210	42	rw	rw	VERB
ejpam-5649	210	43	with	with	ADP
ejpam-5649	210	44	σ1σ2	σ1σ2	NOUN
ejpam-5649	210	45	-	-	PUNCT
ejpam-5649	210	46	cl(rv	cl(rv	ADJ
ejpam-5649	210	47	)	)	PUNCT
ejpam-5649	211	1	∩	∩	NOUN
ejpam-5649	211	2	v	v	NOUN
ejpam-5649	211	3	=	=	NOUN
ejpam-5649	211	4	∅	∅	NOUN
ejpam-5649	211	5	and	and	CCONJ
ejpam-5649	211	6	σ1σ2	σ1σ2	NOUN
ejpam-5649	211	7	-	-	ADJ
ejpam-5649	211	8	cl(rw	cl(rw	NOUN
ejpam-5649	211	9	)	)	PUNCT
ejpam-5649	211	10	∩w	∩w	NOUN
ejpam-5649	212	1	=	=	PUNCT
ejpam-5649	212	2	∅	∅	NOUN
ejpam-5649	212	3	such	such	ADJ
ejpam-5649	212	4	that	that	PRON
ejpam-5649	212	5	(	(	PUNCT
ejpam-5649	212	6	v	v	NUM
ejpam-5649	212	7	∪rv	∪rv	NOUN
ejpam-5649	212	8	)	)	PUNCT
ejpam-5649	212	9	∩	∩	NOUN
ejpam-5649	212	10	(	(	PUNCT
ejpam-5649	212	11	w	w	PROPN
ejpam-5649	212	12	∪rw	∪rw	NOUN
ejpam-5649	212	13	)	)	PUNCT
ejpam-5649	212	14	=	=	PUNCT
ejpam-5649	212	15	∅.	∅.	ADP
ejpam-5649	212	16	thus	thus	ADV
ejpam-5649	212	17	,	,	PUNCT
ejpam-5649	212	18	(	(	PUNCT
ejpam-5649	212	19	τ1	τ1	NOUN
ejpam-5649	212	20	,	,	PUNCT
ejpam-5649	212	21	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	212	22	−1(v	−1(v	PRON
ejpam-5649	212	23	∪rv	∪rv	NOUN
ejpam-5649	212	24	)	)	PUNCT
ejpam-5649	212	25	)	)	PUNCT
ejpam-5649	212	26	∩	∩	NOUN
ejpam-5649	212	27	(	(	PUNCT
ejpam-5649	212	28	τ1	τ1	NOUN
ejpam-5649	212	29	,	,	PUNCT
ejpam-5649	212	30	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	212	31	−1(w	−1(w	X
ejpam-5649	212	32	∪rw	∪rw	NOUN
ejpam-5649	212	33	)	)	PUNCT
ejpam-5649	212	34	)	)	PUNCT
ejpam-5649	213	1	=	=	PUNCT
ejpam-5649	213	2	∅.	∅.	VERB
ejpam-5649	213	3	by	by	ADP
ejpam-5649	213	4	theorem	theorem	NOUN
ejpam-5649	213	5	4	4	NUM
ejpam-5649	213	6	,	,	PUNCT
ejpam-5649	213	7	we	we	PRON
ejpam-5649	213	8	have	have	VERB
ejpam-5649	213	9	x	x	X
ejpam-5649	213	10	∈	∈	PROPN
ejpam-5649	213	11	f−1(v	f−1(v	NOUN
ejpam-5649	213	12	)	)	PUNCT
ejpam-5649	214	1	⊆	⊆	NUM
ejpam-5649	214	2	(	(	PUNCT
ejpam-5649	214	3	τ1	τ1	NOUN
ejpam-5649	214	4	,	,	PUNCT
ejpam-5649	214	5	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	214	6	−1(v	−1(v	PRON
ejpam-5649	214	7	∪rv	∪rv	NOUN
ejpam-5649	214	8	)	)	PUNCT
ejpam-5649	214	9	)	)	PUNCT
ejpam-5649	214	10	and	and	CCONJ
ejpam-5649	214	11	y	y	PROPN
ejpam-5649	214	12	∈	∈	PROPN
ejpam-5649	214	13	f−1(w	f−1(w	PROPN
ejpam-5649	214	14	)	)	PUNCT
ejpam-5649	214	15	⊆	⊆	NUM
ejpam-5649	214	16	(	(	PUNCT
ejpam-5649	214	17	τ1	τ1	NOUN
ejpam-5649	214	18	,	,	PUNCT
ejpam-5649	214	19	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-5649	214	20	−1(w	−1(w	X
ejpam-5649	214	21	∪rw	∪rw	NOUN
ejpam-5649	214	22	)	)	PUNCT
ejpam-5649	214	23	)	)	PUNCT
ejpam-5649	214	24	.	.	PUNCT
ejpam-5649	215	1	since	since	SCONJ
ejpam-5649	215	2	(	(	PUNCT
ejpam-5649	215	3	τ1	τ1	NOUN
ejpam-5649	215	4	,	,	PUNCT
ejpam-5649	215	5	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	215	6	−1(v	−1(v	PROPN
ejpam-5649	215	7	∪	∪	PROPN
ejpam-5649	215	8	rv	rv	PROPN
ejpam-5649	215	9	)	)	PUNCT
ejpam-5649	215	10	)	)	PUNCT
ejpam-5649	215	11	and	and	CCONJ
ejpam-5649	215	12	(	(	PUNCT
ejpam-5649	215	13	τ1	τ1	NOUN
ejpam-5649	215	14	,	,	PUNCT
ejpam-5649	215	15	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-5649	215	16	−1(w	−1(w	ADV
ejpam-5649	215	17	∪	∪	ADJ
ejpam-5649	215	18	rw	rw	NOUN
ejpam-5649	215	19	)	)	PUNCT
ejpam-5649	215	20	)	)	PUNCT
ejpam-5649	215	21	are	be	AUX
ejpam-5649	215	22	(	(	PUNCT
ejpam-5649	215	23	τ1	τ1	NOUN
ejpam-5649	215	24	,	,	PUNCT
ejpam-5649	215	25	τ2)p	τ2)p	ADJ
ejpam-5649	215	26	-	-	PUNCT
ejpam-5649	215	27	open	open	ADJ
ejpam-5649	215	28	sets	set	NOUN
ejpam-5649	215	29	,	,	PUNCT
ejpam-5649	215	30	(	(	PUNCT
ejpam-5649	215	31	x	x	NOUN
ejpam-5649	215	32	,	,	PUNCT
ejpam-5649	215	33	τ1	τ1	NOUN
ejpam-5649	215	34	,	,	PUNCT
ejpam-5649	215	35	τ2	τ2	NOUN
ejpam-5649	215	36	)	)	PUNCT
ejpam-5649	215	37	is	be	AUX
ejpam-5649	215	38	a	a	DET
ejpam-5649	215	39	(	(	PUNCT
ejpam-5649	215	40	τ1	τ1	NOUN
ejpam-5649	215	41	,	,	PUNCT
ejpam-5649	215	42	τ2)p	τ2)p	ADJ
ejpam-5649	215	43	-	-	PUNCT
ejpam-5649	215	44	hausdorff	hausdorff	NOUN
ejpam-5649	215	45	space	space	NOUN
ejpam-5649	215	46	.	.	PUNCT
ejpam-5649	216	1	acknowledgements	acknowledgement	NOUN
ejpam-5649	216	2	this	this	DET
ejpam-5649	216	3	research	research	NOUN
ejpam-5649	216	4	project	project	NOUN
ejpam-5649	216	5	was	be	AUX
ejpam-5649	216	6	financially	financially	ADV
ejpam-5649	216	7	supported	support	VERB
ejpam-5649	216	8	by	by	ADP
ejpam-5649	216	9	mahasarakham	mahasarakham	PROPN
ejpam-5649	216	10	university	university	PROPN
ejpam-5649	216	11	.	.	PUNCT
ejpam-5649	217	1	references	reference	NOUN
ejpam-5649	217	2	[	[	X
ejpam-5649	217	3	1	1	NUM
ejpam-5649	217	4	]	]	PUNCT
ejpam-5649	217	5	c.	c.	PROPN
ejpam-5649	217	6	boonpok	boonpok	PROPN
ejpam-5649	217	7	.	.	PUNCT
ejpam-5649	218	1	almost	almost	ADV
ejpam-5649	218	2	(	(	PUNCT
ejpam-5649	218	3	g	g	NOUN
ejpam-5649	218	4	,	,	PUNCT
ejpam-5649	218	5	m)-continuous	m)-continuous	ADJ
ejpam-5649	218	6	functions	function	NOUN
ejpam-5649	218	7	.	.	PUNCT
ejpam-5649	219	1	international	international	ADJ
ejpam-5649	219	2	journal	journal	PROPN
ejpam-5649	219	3	of	of	ADP
ejpam-5649	219	4	mathematical	mathematical	ADJ
ejpam-5649	219	5	analysis	analysis	NOUN
ejpam-5649	219	6	,	,	PUNCT
ejpam-5649	219	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5649	219	8	,	,	PUNCT
ejpam-5649	219	9	2010	2010	NUM
ejpam-5649	219	10	.	.	PUNCT
ejpam-5649	220	1	[	[	X
ejpam-5649	220	2	2	2	NUM
ejpam-5649	220	3	]	]	PUNCT
ejpam-5649	220	4	c.	c.	PROPN
ejpam-5649	220	5	boonpok	boonpok	PROPN
ejpam-5649	220	6	.	.	PUNCT
ejpam-5649	221	1	m	m	VERB
ejpam-5649	221	2	-continuous	-continuous	ADJ
ejpam-5649	221	3	functions	function	NOUN
ejpam-5649	221	4	in	in	ADP
ejpam-5649	221	5	biminimal	biminimal	NOUN
ejpam-5649	221	6	structure	structure	NOUN
ejpam-5649	221	7	spaces	space	NOUN
ejpam-5649	221	8	.	.	PUNCT
ejpam-5649	222	1	far	far	PROPN
ejpam-5649	222	2	east	east	PROPN
ejpam-5649	222	3	journal	journal	PROPN
ejpam-5649	222	4	of	of	ADP
ejpam-5649	222	5	mathematical	mathematical	ADJ
ejpam-5649	222	6	sciences	science	NOUN
ejpam-5649	222	7	,	,	PUNCT
ejpam-5649	222	8	43(1):41–58	43(1):41–58	NUM
ejpam-5649	222	9	,	,	PUNCT
ejpam-5649	222	10	2010	2010	NUM
ejpam-5649	222	11	.	.	PUNCT
ejpam-5649	223	1	[	[	X
ejpam-5649	223	2	3	3	X
ejpam-5649	223	3	]	]	PUNCT
ejpam-5649	223	4	c.	c.	PROPN
ejpam-5649	223	5	boonpok	boonpok	PROPN
ejpam-5649	223	6	.	.	PUNCT
ejpam-5649	224	1	on	on	ADP
ejpam-5649	224	2	continuous	continuous	ADJ
ejpam-5649	224	3	multifunctions	multifunction	NOUN
ejpam-5649	224	4	in	in	ADP
ejpam-5649	224	5	ideal	ideal	ADJ
ejpam-5649	224	6	topological	topological	ADJ
ejpam-5649	224	7	spaces	space	NOUN
ejpam-5649	224	8	.	.	PUNCT
ejpam-5649	225	1	lobachevskii	lobachevskii	PROPN
ejpam-5649	225	2	journal	journal	PROPN
ejpam-5649	225	3	of	of	ADP
ejpam-5649	225	4	mathematics	mathematic	NOUN
ejpam-5649	225	5	,	,	PUNCT
ejpam-5649	225	6	40(1):24–35	40(1):24–35	NUM
ejpam-5649	225	7	,	,	PUNCT
ejpam-5649	225	8	2019	2019	NUM
ejpam-5649	225	9	.	.	PUNCT
ejpam-5649	226	1	[	[	X
ejpam-5649	226	2	4	4	NUM
ejpam-5649	226	3	]	]	PUNCT
ejpam-5649	226	4	c.	c.	PROPN
ejpam-5649	226	5	boonpok	boonpok	PROPN
ejpam-5649	226	6	.	.	PUNCT
ejpam-5649	227	1	on	on	ADP
ejpam-5649	227	2	characterizations	characterization	NOUN
ejpam-5649	227	3	of	of	ADP
ejpam-5649	227	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5649	227	5	ideal	ideal	ADJ
ejpam-5649	227	6	topological	topological	ADJ
ejpam-5649	227	7	spaces	space	NOUN
ejpam-5649	227	8	.	.	PUNCT
ejpam-5649	228	1	journal	journal	NOUN
ejpam-5649	228	2	of	of	ADP
ejpam-5649	228	3	mathematics	mathematic	NOUN
ejpam-5649	228	4	,	,	PUNCT
ejpam-5649	228	5	2020:9387601	2020:9387601	NUM
ejpam-5649	228	6	,	,	PUNCT
ejpam-5649	228	7	2020	2020	NUM
ejpam-5649	228	8	.	.	PUNCT
ejpam-5649	229	1	[	[	X
ejpam-5649	229	2	5	5	X
ejpam-5649	229	3	]	]	PUNCT
ejpam-5649	229	4	c.	c.	PROPN
ejpam-5649	229	5	boonpok	boonpok	PROPN
ejpam-5649	229	6	.	.	PUNCT
ejpam-5649	230	1	(	(	PUNCT
ejpam-5649	230	2	τ1	τ1	NOUN
ejpam-5649	230	3	,	,	PUNCT
ejpam-5649	230	4	τ2)δ	τ2)δ	ADJ
ejpam-5649	230	5	-	-	PUNCT
ejpam-5649	230	6	semicontinuous	semicontinuous	ADJ
ejpam-5649	230	7	multifunctions	multifunction	NOUN
ejpam-5649	230	8	.	.	PUNCT
ejpam-5649	231	1	heliyon	heliyon	NOUN
ejpam-5649	231	2	,	,	PUNCT
ejpam-5649	231	3	6	6	NUM
ejpam-5649	231	4	:	:	SYM
ejpam-5649	231	5	e05367	e05367	PROPN
ejpam-5649	231	6	,	,	PUNCT
ejpam-5649	231	7	2020	2020	NUM
ejpam-5649	231	8	.	.	PUNCT
ejpam-5649	232	1	[	[	X
ejpam-5649	232	2	6	6	NUM
ejpam-5649	232	3	]	]	PUNCT
ejpam-5649	232	4	c.	c.	PROPN
ejpam-5649	232	5	boonpok	boonpok	PROPN
ejpam-5649	232	6	.	.	PUNCT
ejpam-5649	233	1	weak	weak	ADJ
ejpam-5649	233	2	quasi	quasi	ADJ
ejpam-5649	233	3	continuity	continuity	NOUN
ejpam-5649	233	4	for	for	ADP
ejpam-5649	233	5	multifunctions	multifunction	NOUN
ejpam-5649	233	6	in	in	ADP
ejpam-5649	233	7	ideal	ideal	ADJ
ejpam-5649	233	8	topological	topological	ADJ
ejpam-5649	233	9	spaces	space	NOUN
ejpam-5649	233	10	.	.	PUNCT
ejpam-5649	234	1	advances	advance	NOUN
ejpam-5649	234	2	in	in	ADP
ejpam-5649	234	3	mathematics	mathematic	NOUN
ejpam-5649	234	4	:	:	PUNCT
ejpam-5649	234	5	scientific	scientific	ADJ
ejpam-5649	234	6	journal	journal	NOUN
ejpam-5649	234	7	,	,	PUNCT
ejpam-5649	234	8	9(1):339–355	9(1):339–355	NUM
ejpam-5649	234	9	,	,	PUNCT
ejpam-5649	234	10	2020	2020	NUM
ejpam-5649	234	11	.	.	PUNCT
ejpam-5649	235	1	[	[	X
ejpam-5649	235	2	7	7	X
ejpam-5649	235	3	]	]	X
ejpam-5649	235	4	c.	c.	PROPN
ejpam-5649	235	5	boonpok	boonpok	PROPN
ejpam-5649	235	6	.	.	PUNCT
ejpam-5649	236	1	upper	upper	ADJ
ejpam-5649	236	2	and	and	CCONJ
ejpam-5649	236	3	lower	low	ADJ
ejpam-5649	236	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5649	236	5	.	.	PUNCT
ejpam-5649	236	6	heliyon	heliyon	NOUN
ejpam-5649	236	7	,	,	PUNCT
ejpam-5649	236	8	7	7	NUM
ejpam-5649	236	9	:	:	PUNCT
ejpam-5649	236	10	e05986	e05986	PROPN
ejpam-5649	236	11	,	,	PUNCT
ejpam-5649	236	12	2021	2021	NUM
ejpam-5649	236	13	.	.	PUNCT
ejpam-5649	237	1	[	[	X
ejpam-5649	237	2	8	8	NUM
ejpam-5649	237	3	]	]	X
ejpam-5649	237	4	c.	c.	PROPN
ejpam-5649	237	5	boonpok	boonpok	PROPN
ejpam-5649	237	6	.	.	PUNCT
ejpam-5649	238	1	on	on	ADP
ejpam-5649	238	2	some	some	DET
ejpam-5649	238	3	closed	closed	ADJ
ejpam-5649	238	4	sets	set	NOUN
ejpam-5649	238	5	and	and	CCONJ
ejpam-5649	238	6	low	low	ADJ
ejpam-5649	238	7	separation	separation	NOUN
ejpam-5649	238	8	axioms	axiom	NOUN
ejpam-5649	238	9	via	via	ADP
ejpam-5649	238	10	topological	topological	ADJ
ejpam-5649	238	11	ideals	ideal	NOUN
ejpam-5649	238	12	.	.	PUNCT
ejpam-5649	239	1	european	european	ADJ
ejpam-5649	239	2	journal	journal	PROPN
ejpam-5649	239	3	of	of	ADP
ejpam-5649	239	4	pure	pure	ADJ
ejpam-5649	239	5	and	and	CCONJ
ejpam-5649	239	6	applied	applied	ADJ
ejpam-5649	239	7	mathematics	mathematic	NOUN
ejpam-5649	239	8	,	,	PUNCT
ejpam-5649	239	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5649	239	10	,	,	PUNCT
ejpam-5649	239	11	2022	2022	NUM
ejpam-5649	239	12	.	.	PUNCT
ejpam-5649	240	1	[	[	X
ejpam-5649	240	2	9	9	NUM
ejpam-5649	240	3	]	]	PUNCT
ejpam-5649	240	4	c.	c.	PROPN
ejpam-5649	240	5	boonpok	boonpok	PROPN
ejpam-5649	240	6	.	.	PUNCT
ejpam-5649	241	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-5649	241	2	continuity	continuity	NOUN
ejpam-5649	241	3	for	for	ADP
ejpam-5649	241	4	multifunctions	multifunction	NOUN
ejpam-5649	241	5	.	.	PUNCT
ejpam-5649	242	1	wseas	wseas	PROPN
ejpam-5649	242	2	transactions	transaction	NOUN
ejpam-5649	242	3	on	on	ADP
ejpam-5649	242	4	mathematics	mathematic	NOUN
ejpam-5649	242	5	,	,	PUNCT
ejpam-5649	242	6	21:245–251	21:245–251	NUM
ejpam-5649	242	7	,	,	PUNCT
ejpam-5649	242	8	2022	2022	NUM
ejpam-5649	242	9	.	.	PUNCT
ejpam-5649	243	1	[	[	X
ejpam-5649	243	2	10	10	NUM
ejpam-5649	243	3	]	]	X
ejpam-5649	243	4	c.	c.	PROPN
ejpam-5649	243	5	boonpok	boonpok	PROPN
ejpam-5649	243	6	.	.	PUNCT
ejpam-5649	244	1	on	on	ADP
ejpam-5649	244	2	some	some	DET
ejpam-5649	244	3	spaces	space	NOUN
ejpam-5649	244	4	via	via	ADP
ejpam-5649	244	5	topological	topological	ADJ
ejpam-5649	244	6	ideals	ideal	NOUN
ejpam-5649	244	7	.	.	PUNCT
ejpam-5649	245	1	open	open	ADJ
ejpam-5649	245	2	mathematics	mathematic	NOUN
ejpam-5649	245	3	,	,	PUNCT
ejpam-5649	245	4	21:20230118	21:20230118	NUM
ejpam-5649	245	5	,	,	PUNCT
ejpam-5649	245	6	2023	2023	NUM
ejpam-5649	245	7	.	.	PUNCT
ejpam-5649	246	1	[	[	X
ejpam-5649	246	2	11	11	NUM
ejpam-5649	246	3	]	]	PUNCT
ejpam-5649	246	4	c.	c.	PROPN
ejpam-5649	246	5	boonpok	boonpok	PROPN
ejpam-5649	246	6	.	.	PUNCT
ejpam-5649	247	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5649	247	2	.	.	PUNCT
ejpam-5649	248	1	mathematica	mathematica	PROPN
ejpam-5649	248	2	,	,	PUNCT
ejpam-5649	248	3	65(1):31–42	65(1):31–42	NUM
ejpam-5649	248	4	,	,	PUNCT
ejpam-5649	248	5	2023	2023	NUM
ejpam-5649	248	6	.	.	PUNCT
ejpam-5649	249	1	[	[	X
ejpam-5649	249	2	12	12	NUM
ejpam-5649	249	3	]	]	X
ejpam-5649	249	4	c.	c.	PROPN
ejpam-5649	249	5	boonpok	boonpok	PROPN
ejpam-5649	249	6	and	and	CCONJ
ejpam-5649	249	7	j.	j.	PROPN
ejpam-5649	249	8	khampakdee	khampakdee	PROPN
ejpam-5649	249	9	.	.	PUNCT
ejpam-5649	250	1	(	(	PUNCT
ejpam-5649	250	2	λ	λ	NOUN
ejpam-5649	250	3	,	,	PUNCT
ejpam-5649	250	4	sp)-open	sp)-open	ADJ
ejpam-5649	250	5	sets	set	NOUN
ejpam-5649	250	6	in	in	ADP
ejpam-5649	250	7	topological	topological	ADJ
ejpam-5649	250	8	spaces	space	NOUN
ejpam-5649	250	9	.	.	PUNCT
ejpam-5649	251	1	european	european	ADJ
ejpam-5649	251	2	journal	journal	PROPN
ejpam-5649	251	3	of	of	ADP
ejpam-5649	251	4	pure	pure	ADJ
ejpam-5649	251	5	and	and	CCONJ
ejpam-5649	251	6	applied	applied	ADJ
ejpam-5649	251	7	mathematics	mathematic	NOUN
ejpam-5649	251	8	,	,	PUNCT
ejpam-5649	251	9	15(2):572–588	15(2):572–588	NUM
ejpam-5649	251	10	,	,	PUNCT
ejpam-5649	251	11	2022	2022	NUM
ejpam-5649	251	12	.	.	PUNCT
ejpam-5649	252	1	b.	b.	PROPN
ejpam-5649	252	2	kong	kong	PROPN
ejpam-5649	252	3	-	-	PUNCT
ejpam-5649	252	4	ied	ied	PROPN
ejpam-5649	252	5	,	,	PUNCT
ejpam-5649	252	6	s.	s.	PROPN
ejpam-5649	252	7	sompong	sompong	PROPN
ejpam-5649	252	8	,	,	PUNCT
ejpam-5649	252	9	c.	c.	PROPN
ejpam-5649	252	10	boonpok	boonpok	PROPN
ejpam-5649	252	11	/	/	SYM
ejpam-5649	252	12	eur	eur	PROPN
ejpam-5649	252	13	.	.	PUNCT
ejpam-5649	253	1	j.	j.	PROPN
ejpam-5649	253	2	pure	pure	PROPN
ejpam-5649	253	3	appl	appl	PROPN
ejpam-5649	253	4	.	.	PROPN
ejpam-5649	253	5	math	math	PROPN
ejpam-5649	253	6	,	,	PUNCT
ejpam-5649	253	7	18	18	NUM
ejpam-5649	253	8	(	(	PUNCT
ejpam-5649	253	9	1	1	NUM
ejpam-5649	253	10	)	)	PUNCT
ejpam-5649	253	11	(	(	PUNCT
ejpam-5649	253	12	2025	2025	NUM
ejpam-5649	253	13	)	)	PUNCT
ejpam-5649	253	14	,	,	PUNCT
ejpam-5649	253	15	5649	5649	NUM
ejpam-5649	253	16	10	10	NUM
ejpam-5649	253	17	of	of	ADP
ejpam-5649	253	18	13	13	NUM
ejpam-5649	253	19	[	[	SYM
ejpam-5649	253	20	13	13	NUM
ejpam-5649	253	21	]	]	PUNCT
ejpam-5649	253	22	c.	c.	PROPN
ejpam-5649	253	23	boonpok	boonpok	PROPN
ejpam-5649	253	24	and	and	CCONJ
ejpam-5649	253	25	j.	j.	PROPN
ejpam-5649	253	26	khampakdee	khampakdee	PROPN
ejpam-5649	253	27	.	.	PUNCT
ejpam-5649	254	1	on	on	ADP
ejpam-5649	254	2	almost	almost	ADV
ejpam-5649	254	3	α(λ	α(λ	PROPN
ejpam-5649	254	4	,	,	PUNCT
ejpam-5649	254	5	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	254	6	multifunctions	multifunction	NOUN
ejpam-5649	254	7	.	.	PUNCT
ejpam-5649	255	1	european	european	PROPN
ejpam-5649	255	2	journal	journal	PROPN
ejpam-5649	255	3	of	of	ADP
ejpam-5649	255	4	pure	pure	ADJ
ejpam-5649	255	5	and	and	CCONJ
ejpam-5649	255	6	applied	applied	ADJ
ejpam-5649	255	7	mathematics	mathematic	NOUN
ejpam-5649	255	8	,	,	PUNCT
ejpam-5649	255	9	15(2):626–634	15(2):626–634	PROPN
ejpam-5649	255	10	,	,	PUNCT
ejpam-5649	255	11	2022	2022	NUM
ejpam-5649	255	12	.	.	PUNCT
ejpam-5649	256	1	[	[	X
ejpam-5649	256	2	14	14	NUM
ejpam-5649	256	3	]	]	X
ejpam-5649	256	4	c.	c.	PROPN
ejpam-5649	256	5	boonpok	boonpok	PROPN
ejpam-5649	256	6	and	and	CCONJ
ejpam-5649	256	7	j.	j.	PROPN
ejpam-5649	256	8	khampakdee	khampakdee	PROPN
ejpam-5649	256	9	.	.	PUNCT
ejpam-5649	257	1	slight	slight	PROPN
ejpam-5649	257	2	(	(	PUNCT
ejpam-5649	257	3	λ	λ	NOUN
ejpam-5649	257	4	,	,	PUNCT
ejpam-5649	257	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5649	257	6	and	and	CCONJ
ejpam-5649	257	7	λsp	λsp	NOUN
ejpam-5649	257	8	-	-	PUNCT
ejpam-5649	257	9	extremally	extremally	ADV
ejpam-5649	257	10	disconnectedness	disconnectedness	NOUN
ejpam-5649	257	11	.	.	PUNCT
ejpam-5649	258	1	european	european	ADJ
ejpam-5649	258	2	journal	journal	PROPN
ejpam-5649	258	3	of	of	ADP
ejpam-5649	258	4	pure	pure	ADJ
ejpam-5649	258	5	and	and	CCONJ
ejpam-5649	258	6	applied	applied	ADJ
ejpam-5649	258	7	mathematics	mathematic	NOUN
ejpam-5649	258	8	,	,	PUNCT
ejpam-5649	258	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-5649	258	10	,	,	PUNCT
ejpam-5649	258	11	2022	2022	NUM
ejpam-5649	258	12	.	.	PUNCT
ejpam-5649	259	1	[	[	X
ejpam-5649	259	2	15	15	NUM
ejpam-5649	259	3	]	]	X
ejpam-5649	259	4	c.	c.	PROPN
ejpam-5649	259	5	boonpok	boonpok	PROPN
ejpam-5649	259	6	and	and	CCONJ
ejpam-5649	259	7	j.	j.	PROPN
ejpam-5649	259	8	khampakdee	khampakdee	PROPN
ejpam-5649	259	9	.	.	PUNCT
ejpam-5649	260	1	upper	upper	ADJ
ejpam-5649	260	2	and	and	CCONJ
ejpam-5649	260	3	lower	low	ADJ
ejpam-5649	260	4	weak	weak	ADJ
ejpam-5649	260	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-5649	260	6	.	.	PUNCT
ejpam-5649	261	1	european	european	PROPN
ejpam-5649	261	2	journal	journal	PROPN
ejpam-5649	261	3	of	of	ADP
ejpam-5649	261	4	pure	pure	ADJ
ejpam-5649	261	5	and	and	CCONJ
ejpam-5649	261	6	applied	applied	ADJ
ejpam-5649	261	7	mathematics	mathematic	NOUN
ejpam-5649	261	8	,	,	PUNCT
ejpam-5649	261	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-5649	261	10	,	,	PUNCT
ejpam-5649	261	11	2023	2023	NUM
ejpam-5649	261	12	.	.	PUNCT
ejpam-5649	262	1	[	[	X
ejpam-5649	262	2	16	16	NUM
ejpam-5649	262	3	]	]	X
ejpam-5649	262	4	c.	c.	PROPN
ejpam-5649	262	5	boonpok	boonpok	PROPN
ejpam-5649	262	6	and	and	CCONJ
ejpam-5649	262	7	j.	j.	PROPN
ejpam-5649	262	8	khampakdee	khampakdee	PROPN
ejpam-5649	262	9	.	.	PUNCT
ejpam-5649	263	1	almost	almost	ADV
ejpam-5649	263	2	strong	strong	ADJ
ejpam-5649	263	3	θ(λ	θ(λ	PROPN
ejpam-5649	263	4	,	,	PUNCT
ejpam-5649	263	5	p)-continuity	p)-continuity	NOUN
ejpam-5649	263	6	for	for	ADP
ejpam-5649	263	7	functions	function	NOUN
ejpam-5649	263	8	.	.	PUNCT
ejpam-5649	264	1	european	european	ADJ
ejpam-5649	264	2	journal	journal	PROPN
ejpam-5649	264	3	of	of	ADP
ejpam-5649	264	4	pure	pure	ADJ
ejpam-5649	264	5	and	and	CCONJ
ejpam-5649	264	6	applied	applied	ADJ
ejpam-5649	264	7	mathematics	mathematic	NOUN
ejpam-5649	264	8	,	,	PUNCT
ejpam-5649	264	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5649	264	10	,	,	PUNCT
ejpam-5649	264	11	2024	2024	NUM
ejpam-5649	264	12	.	.	PUNCT
ejpam-5649	265	1	[	[	X
ejpam-5649	265	2	17	17	NUM
ejpam-5649	265	3	]	]	X
ejpam-5649	265	4	c.	c.	PROPN
ejpam-5649	265	5	boonpok	boonpok	PROPN
ejpam-5649	265	6	and	and	CCONJ
ejpam-5649	265	7	j.	j.	PROPN
ejpam-5649	265	8	khampakdee	khampakdee	PROPN
ejpam-5649	265	9	.	.	PUNCT
ejpam-5649	266	1	upper	upper	ADJ
ejpam-5649	266	2	and	and	CCONJ
ejpam-5649	266	3	lower	low	ADJ
ejpam-5649	266	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5649	266	5	.	.	PUNCT
ejpam-5649	266	6	european	european	PROPN
ejpam-5649	266	7	journal	journal	PROPN
ejpam-5649	266	8	of	of	ADP
ejpam-5649	266	9	pure	pure	ADJ
ejpam-5649	266	10	and	and	CCONJ
ejpam-5649	266	11	applied	applied	ADJ
ejpam-5649	266	12	mathematics	mathematic	NOUN
ejpam-5649	266	13	,	,	PUNCT
ejpam-5649	266	14	17(1):201–211	17(1):201–211	NUM
ejpam-5649	266	15	,	,	PUNCT
ejpam-5649	266	16	2024	2024	NUM
ejpam-5649	266	17	.	.	PUNCT
ejpam-5649	267	1	[	[	X
ejpam-5649	267	2	18	18	NUM
ejpam-5649	267	3	]	]	PUNCT
ejpam-5649	267	4	c.	c.	PROPN
ejpam-5649	267	5	boonpok	boonpok	PROPN
ejpam-5649	267	6	and	and	CCONJ
ejpam-5649	267	7	c.	c.	PROPN
ejpam-5649	267	8	klanarong	klanarong	PROPN
ejpam-5649	267	9	.	.	PUNCT
ejpam-5649	268	1	on	on	ADP
ejpam-5649	268	2	weakly	weakly	ADJ
ejpam-5649	268	3	(	(	PUNCT
ejpam-5649	268	4	τ1	τ1	NOUN
ejpam-5649	268	5	,	,	PUNCT
ejpam-5649	268	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	268	7	functions	function	NOUN
ejpam-5649	268	8	.	.	PUNCT
ejpam-5649	269	1	european	european	ADJ
ejpam-5649	269	2	journal	journal	PROPN
ejpam-5649	269	3	of	of	ADP
ejpam-5649	269	4	pure	pure	ADJ
ejpam-5649	269	5	and	and	CCONJ
ejpam-5649	269	6	applied	applied	ADJ
ejpam-5649	269	7	mathematics	mathematic	NOUN
ejpam-5649	269	8	,	,	PUNCT
ejpam-5649	269	9	17(1):416–425	17(1):416–425	NUM
ejpam-5649	269	10	,	,	PUNCT
ejpam-5649	269	11	2024	2024	NUM
ejpam-5649	269	12	.	.	PUNCT
ejpam-5649	270	1	[	[	X
ejpam-5649	270	2	19	19	NUM
ejpam-5649	270	3	]	]	X
ejpam-5649	270	4	c.	c.	PROPN
ejpam-5649	270	5	boonpok	boonpok	PROPN
ejpam-5649	270	6	and	and	CCONJ
ejpam-5649	270	7	p.	p.	NOUN
ejpam-5649	270	8	pue	pue	NOUN
ejpam-5649	270	9	-	-	PUNCT
ejpam-5649	270	10	on	on	ADP
ejpam-5649	270	11	.	.	PUNCT
ejpam-5649	271	1	continuity	continuity	NOUN
ejpam-5649	271	2	for	for	ADP
ejpam-5649	271	3	multifunctions	multifunction	NOUN
ejpam-5649	271	4	in	in	ADP
ejpam-5649	271	5	ideal	ideal	ADJ
ejpam-5649	271	6	topological	topological	ADJ
ejpam-5649	271	7	spaces	space	NOUN
ejpam-5649	271	8	.	.	PUNCT
ejpam-5649	272	1	wseas	wseas	VERB
ejpam-5649	272	2	transactions	transaction	NOUN
ejpam-5649	272	3	on	on	ADP
ejpam-5649	272	4	mathematics	mathematic	NOUN
ejpam-5649	272	5	,	,	PUNCT
ejpam-5649	272	6	19:624–631	19:624–631	NUM
ejpam-5649	272	7	,	,	PUNCT
ejpam-5649	272	8	2020	2020	NUM
ejpam-5649	272	9	.	.	PUNCT
ejpam-5649	273	1	[	[	X
ejpam-5649	273	2	20	20	NUM
ejpam-5649	273	3	]	]	PUNCT
ejpam-5649	273	4	c.	c.	PROPN
ejpam-5649	273	5	boonpok	boonpok	PROPN
ejpam-5649	273	6	and	and	CCONJ
ejpam-5649	273	7	p.	p.	NOUN
ejpam-5649	273	8	pue	pue	NOUN
ejpam-5649	273	9	-	-	PUNCT
ejpam-5649	273	10	on	on	ADP
ejpam-5649	273	11	.	.	PUNCT
ejpam-5649	274	1	upper	upper	ADJ
ejpam-5649	274	2	and	and	CCONJ
ejpam-5649	274	3	lower	low	ADJ
ejpam-5649	274	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5649	274	5	multifunctions	multifunction	NOUN
ejpam-5649	274	6	.	.	PUNCT
ejpam-5649	275	1	european	european	ADJ
ejpam-5649	275	2	journal	journal	PROPN
ejpam-5649	275	3	of	of	ADP
ejpam-5649	275	4	pure	pure	ADJ
ejpam-5649	275	5	and	and	CCONJ
ejpam-5649	275	6	applied	applied	ADJ
ejpam-5649	275	7	mathematics	mathematic	NOUN
ejpam-5649	275	8	,	,	PUNCT
ejpam-5649	275	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-5649	275	10	,	,	PUNCT
ejpam-5649	275	11	2023	2023	NUM
ejpam-5649	275	12	.	.	PUNCT
ejpam-5649	276	1	[	[	X
ejpam-5649	276	2	21	21	NUM
ejpam-5649	276	3	]	]	X
ejpam-5649	276	4	c.	c.	PROPN
ejpam-5649	276	5	boonpok	boonpok	PROPN
ejpam-5649	276	6	and	and	CCONJ
ejpam-5649	276	7	p.	p.	NOUN
ejpam-5649	276	8	pue	pue	NOUN
ejpam-5649	276	9	-	-	PUNCT
ejpam-5649	276	10	on	on	ADP
ejpam-5649	276	11	.	.	PUNCT
ejpam-5649	277	1	upper	upper	ADJ
ejpam-5649	277	2	and	and	CCONJ
ejpam-5649	277	3	lower	low	ADJ
ejpam-5649	277	4	weakly	weakly	ADJ
ejpam-5649	277	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5649	277	6	multifunctions	multifunction	NOUN
ejpam-5649	277	7	.	.	PUNCT
ejpam-5649	278	1	international	international	ADJ
ejpam-5649	278	2	journal	journal	NOUN
ejpam-5649	278	3	of	of	ADP
ejpam-5649	278	4	analysis	analysis	NOUN
ejpam-5649	278	5	and	and	CCONJ
ejpam-5649	278	6	applications	application	NOUN
ejpam-5649	278	7	,	,	PUNCT
ejpam-5649	278	8	21:90	21:90	NUM
ejpam-5649	278	9	,	,	PUNCT
ejpam-5649	278	10	2023	2023	NUM
ejpam-5649	278	11	.	.	PUNCT
ejpam-5649	279	1	[	[	X
ejpam-5649	279	2	22	22	NUM
ejpam-5649	279	3	]	]	PUNCT
ejpam-5649	279	4	c.	c.	PROPN
ejpam-5649	279	5	boonpok	boonpok	PROPN
ejpam-5649	279	6	and	and	CCONJ
ejpam-5649	279	7	p.	p.	NOUN
ejpam-5649	279	8	pue	pue	NOUN
ejpam-5649	279	9	-	-	PUNCT
ejpam-5649	279	10	on	on	ADP
ejpam-5649	279	11	.	.	PUNCT
ejpam-5649	280	1	upper	upper	ADJ
ejpam-5649	280	2	and	and	CCONJ
ejpam-5649	280	3	lower	low	ADJ
ejpam-5649	280	4	weakly	weakly	ADJ
ejpam-5649	280	5	(	(	PUNCT
ejpam-5649	280	6	λ	λ	NOUN
ejpam-5649	280	7	,	,	PUNCT
ejpam-5649	280	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	280	9	multifunctions	multifunction	NOUN
ejpam-5649	280	10	.	.	PUNCT
ejpam-5649	281	1	european	european	PROPN
ejpam-5649	281	2	journal	journal	PROPN
ejpam-5649	281	3	of	of	ADP
ejpam-5649	281	4	pure	pure	ADJ
ejpam-5649	281	5	and	and	CCONJ
ejpam-5649	281	6	applied	applied	ADJ
ejpam-5649	281	7	mathematics	mathematic	NOUN
ejpam-5649	281	8	,	,	PUNCT
ejpam-5649	281	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5649	281	10	,	,	PUNCT
ejpam-5649	281	11	2023	2023	NUM
ejpam-5649	281	12	.	.	PUNCT
ejpam-5649	282	1	[	[	X
ejpam-5649	282	2	23	23	NUM
ejpam-5649	282	3	]	]	X
ejpam-5649	282	4	c.	c.	PROPN
ejpam-5649	282	5	boonpok	boonpok	PROPN
ejpam-5649	282	6	and	and	CCONJ
ejpam-5649	282	7	p.	p.	NOUN
ejpam-5649	282	8	pue	pue	NOUN
ejpam-5649	282	9	-	-	PUNCT
ejpam-5649	282	10	on	on	ADP
ejpam-5649	282	11	.	.	PUNCT
ejpam-5649	283	1	characterizations	characterization	NOUN
ejpam-5649	283	2	of	of	ADP
ejpam-5649	283	3	almost	almost	ADV
ejpam-5649	283	4	(	(	PUNCT
ejpam-5649	283	5	τ1	τ1	NOUN
ejpam-5649	283	6	,	,	PUNCT
ejpam-5649	283	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	283	8	functions	function	NOUN
ejpam-5649	283	9	.	.	PUNCT
ejpam-5649	284	1	international	international	ADJ
ejpam-5649	284	2	journal	journal	NOUN
ejpam-5649	284	3	of	of	ADP
ejpam-5649	284	4	analysis	analysis	NOUN
ejpam-5649	284	5	and	and	CCONJ
ejpam-5649	284	6	applications	application	NOUN
ejpam-5649	284	7	,	,	PUNCT
ejpam-5649	284	8	22:33	22:33	NUM
ejpam-5649	284	9	,	,	PUNCT
ejpam-5649	284	10	2024	2024	NUM
ejpam-5649	284	11	.	.	PUNCT
ejpam-5649	285	1	[	[	X
ejpam-5649	285	2	24	24	NUM
ejpam-5649	285	3	]	]	PUNCT
ejpam-5649	285	4	c.	c.	PROPN
ejpam-5649	285	5	boonpok	boonpok	PROPN
ejpam-5649	285	6	and	and	CCONJ
ejpam-5649	285	7	n.	n.	PROPN
ejpam-5649	285	8	srisarakham	srisarakham	PROPN
ejpam-5649	285	9	.	.	PUNCT
ejpam-5649	286	1	almost	almost	ADV
ejpam-5649	286	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5649	286	3	for	for	ADP
ejpam-5649	286	4	multifunctions	multifunction	NOUN
ejpam-5649	286	5	.	.	PUNCT
ejpam-5649	287	1	international	international	ADJ
ejpam-5649	287	2	journal	journal	NOUN
ejpam-5649	287	3	of	of	ADP
ejpam-5649	287	4	analysis	analysis	NOUN
ejpam-5649	287	5	and	and	CCONJ
ejpam-5649	287	6	applications	application	NOUN
ejpam-5649	287	7	,	,	PUNCT
ejpam-5649	287	8	21:107	21:107	NUM
ejpam-5649	287	9	,	,	PUNCT
ejpam-5649	287	10	2023	2023	NUM
ejpam-5649	287	11	.	.	PUNCT
ejpam-5649	288	1	[	[	X
ejpam-5649	288	2	25	25	NUM
ejpam-5649	288	3	]	]	PUNCT
ejpam-5649	288	4	c.	c.	PROPN
ejpam-5649	288	5	boonpok	boonpok	PROPN
ejpam-5649	288	6	and	and	CCONJ
ejpam-5649	288	7	n.	n.	PROPN
ejpam-5649	288	8	srisarakham	srisarakham	PROPN
ejpam-5649	288	9	.	.	PUNCT
ejpam-5649	289	1	weak	weak	ADJ
ejpam-5649	289	2	forms	form	NOUN
ejpam-5649	289	3	of	of	ADP
ejpam-5649	289	4	(	(	PUNCT
ejpam-5649	289	5	λ	λ	PROPN
ejpam-5649	289	6	,	,	PUNCT
ejpam-5649	289	7	b)-open	b)-open	VERB
ejpam-5649	289	8	sets	set	NOUN
ejpam-5649	289	9	and	and	CCONJ
ejpam-5649	289	10	weak	weak	ADJ
ejpam-5649	289	11	(	(	PUNCT
ejpam-5649	289	12	λ	λ	NOUN
ejpam-5649	289	13	,	,	PUNCT
ejpam-5649	289	14	b)continuity	b)continuity	NOUN
ejpam-5649	289	15	.	.	PUNCT
ejpam-5649	290	1	european	european	PROPN
ejpam-5649	290	2	journal	journal	PROPN
ejpam-5649	290	3	of	of	ADP
ejpam-5649	290	4	pure	pure	ADJ
ejpam-5649	290	5	and	and	CCONJ
ejpam-5649	290	6	applied	applied	ADJ
ejpam-5649	290	7	mathematics	mathematic	NOUN
ejpam-5649	290	8	,	,	PUNCT
ejpam-5649	290	9	16(1):29–43	16(1):29–43	NUM
ejpam-5649	290	10	,	,	PUNCT
ejpam-5649	290	11	2023	2023	NUM
ejpam-5649	290	12	.	.	PUNCT
ejpam-5649	291	1	[	[	X
ejpam-5649	291	2	26	26	NUM
ejpam-5649	291	3	]	]	X
ejpam-5649	291	4	c.	c.	PROPN
ejpam-5649	291	5	boonpok	boonpok	PROPN
ejpam-5649	291	6	and	and	CCONJ
ejpam-5649	291	7	n.	n.	PROPN
ejpam-5649	291	8	srisarakham	srisarakham	PROPN
ejpam-5649	291	9	.	.	PUNCT
ejpam-5649	292	1	(	(	PUNCT
ejpam-5649	292	2	τ1	τ1	NOUN
ejpam-5649	292	3	,	,	PUNCT
ejpam-5649	292	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5649	292	5	for	for	ADP
ejpam-5649	292	6	functions	function	NOUN
ejpam-5649	292	7	.	.	PUNCT
ejpam-5649	293	1	asia	asia	PROPN
ejpam-5649	293	2	pacific	pacific	PROPN
ejpam-5649	293	3	journal	journal	PROPN
ejpam-5649	293	4	of	of	ADP
ejpam-5649	293	5	mathematics	mathematic	NOUN
ejpam-5649	293	6	,	,	PUNCT
ejpam-5649	293	7	11:21	11:21	NUM
ejpam-5649	293	8	,	,	PUNCT
ejpam-5649	293	9	2024	2024	NUM
ejpam-5649	293	10	.	.	PUNCT
ejpam-5649	294	1	[	[	X
ejpam-5649	294	2	27	27	NUM
ejpam-5649	294	3	]	]	X
ejpam-5649	294	4	c.	c.	PROPN
ejpam-5649	294	5	boonpok	boonpok	PROPN
ejpam-5649	294	6	and	and	CCONJ
ejpam-5649	294	7	m.	m.	NOUN
ejpam-5649	294	8	thongmoon	thongmoon	NOUN
ejpam-5649	294	9	.	.	PUNCT
ejpam-5649	295	1	weak	weak	ADJ
ejpam-5649	295	2	α(λ	α(λ	PROPN
ejpam-5649	295	3	,	,	PUNCT
ejpam-5649	295	4	sp)-continuity	sp)-continuity	NOUN
ejpam-5649	295	5	for	for	ADP
ejpam-5649	295	6	multifunctions	multifunction	NOUN
ejpam-5649	295	7	.	.	PUNCT
ejpam-5649	296	1	european	european	ADJ
ejpam-5649	296	2	journal	journal	PROPN
ejpam-5649	296	3	of	of	ADP
ejpam-5649	296	4	pure	pure	ADJ
ejpam-5649	296	5	and	and	CCONJ
ejpam-5649	296	6	applied	applied	ADJ
ejpam-5649	296	7	mathematics	mathematic	NOUN
ejpam-5649	296	8	,	,	PUNCT
ejpam-5649	296	9	16(1):465–478	16(1):465–478	NUM
ejpam-5649	296	10	,	,	PUNCT
ejpam-5649	296	11	2023	2023	NUM
ejpam-5649	296	12	.	.	PUNCT
ejpam-5649	297	1	[	[	X
ejpam-5649	297	2	28	28	NUM
ejpam-5649	297	3	]	]	X
ejpam-5649	297	4	c.	c.	PROPN
ejpam-5649	297	5	boonpok	boonpok	PROPN
ejpam-5649	297	6	and	and	CCONJ
ejpam-5649	297	7	c.	c.	PROPN
ejpam-5649	297	8	viriyapong	viriyapong	PROPN
ejpam-5649	297	9	.	.	PUNCT
ejpam-5649	298	1	upper	upper	ADJ
ejpam-5649	298	2	and	and	CCONJ
ejpam-5649	298	3	lower	low	ADJ
ejpam-5649	298	4	almost	almost	ADV
ejpam-5649	298	5	weak	weak	ADJ
ejpam-5649	298	6	(	(	PUNCT
ejpam-5649	298	7	τ1	τ1	NOUN
ejpam-5649	298	8	,	,	PUNCT
ejpam-5649	298	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5649	298	10	.	.	PUNCT
ejpam-5649	299	1	european	european	PROPN
ejpam-5649	299	2	journal	journal	PROPN
ejpam-5649	299	3	of	of	ADP
ejpam-5649	299	4	pure	pure	ADJ
ejpam-5649	299	5	and	and	CCONJ
ejpam-5649	299	6	applied	applied	ADJ
ejpam-5649	299	7	mathematics	mathematic	NOUN
ejpam-5649	299	8	,	,	PUNCT
ejpam-5649	299	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5649	299	10	,	,	PUNCT
ejpam-5649	299	11	2021	2021	NUM
ejpam-5649	299	12	.	.	PUNCT
ejpam-5649	300	1	[	[	X
ejpam-5649	300	2	29	29	NUM
ejpam-5649	300	3	]	]	X
ejpam-5649	300	4	c.	c.	PROPN
ejpam-5649	300	5	boonpok	boonpok	PROPN
ejpam-5649	300	6	,	,	PUNCT
ejpam-5649	300	7	c.	c.	PROPN
ejpam-5649	300	8	viriyapong	viriyapong	PROPN
ejpam-5649	300	9	,	,	PUNCT
ejpam-5649	300	10	and	and	CCONJ
ejpam-5649	300	11	m.	m.	NOUN
ejpam-5649	300	12	thongmoon	thongmoon	NOUN
ejpam-5649	300	13	.	.	PUNCT
ejpam-5649	301	1	on	on	ADP
ejpam-5649	301	2	upper	upper	ADJ
ejpam-5649	301	3	and	and	CCONJ
ejpam-5649	301	4	lower	low	ADJ
ejpam-5649	301	5	(	(	PUNCT
ejpam-5649	301	6	τ1	τ1	NOUN
ejpam-5649	301	7	,	,	PUNCT
ejpam-5649	301	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5649	301	9	multifunctions	multifunction	NOUN
ejpam-5649	301	10	.	.	PUNCT
ejpam-5649	302	1	journal	journal	PROPN
ejpam-5649	302	2	of	of	ADP
ejpam-5649	302	3	mathematics	mathematics	PROPN
ejpam-5649	302	4	and	and	CCONJ
ejpam-5649	302	5	computer	computer	NOUN
ejpam-5649	302	6	science	science	NOUN
ejpam-5649	302	7	,	,	PUNCT
ejpam-5649	302	8	18:282–293	18:282–293	NUM
ejpam-5649	302	9	,	,	PUNCT
ejpam-5649	302	10	2018	2018	NUM
ejpam-5649	302	11	.	.	PUNCT
ejpam-5649	303	1	[	[	X
ejpam-5649	303	2	30	30	NUM
ejpam-5649	303	3	]	]	X
ejpam-5649	303	4	m.	m.	NOUN
ejpam-5649	303	5	caldas	caldas	PROPN
ejpam-5649	303	6	.	.	PUNCT
ejpam-5649	304	1	on	on	ADP
ejpam-5649	304	2	rarely	rarely	ADV
ejpam-5649	304	3	βθ	βθ	ADJ
ejpam-5649	304	4	-	-	PUNCT
ejpam-5649	304	5	continuous	continuous	ADJ
ejpam-5649	304	6	functions	function	NOUN
ejpam-5649	304	7	.	.	PUNCT
ejpam-5649	305	1	pro	pro	PROPN
ejpam-5649	305	2	mathematica	mathematica	PROPN
ejpam-5649	305	3	,	,	PUNCT
ejpam-5649	305	4	26(51	26(51	NUM
ejpam-5649	305	5	-	-	SYM
ejpam-5649	305	6	52):75–85	52):75–85	NUM
ejpam-5649	305	7	,	,	PUNCT
ejpam-5649	305	8	2012	2012	NUM
ejpam-5649	305	9	.	.	PUNCT
ejpam-5649	306	1	[	[	X
ejpam-5649	306	2	31	31	NUM
ejpam-5649	306	3	]	]	PUNCT
ejpam-5649	306	4	m.	m.	NOUN
ejpam-5649	306	5	caldas	caldas	PROPN
ejpam-5649	306	6	and	and	CCONJ
ejpam-5649	306	7	s.	s.	PROPN
ejpam-5649	306	8	jafari	jafari	PROPN
ejpam-5649	306	9	.	.	PUNCT
ejpam-5649	307	1	on	on	ADP
ejpam-5649	307	2	rarely	rarely	ADV
ejpam-5649	307	3	g	g	NOUN
ejpam-5649	307	4	-	-	PUNCT
ejpam-5649	307	5	continuous	continuous	ADJ
ejpam-5649	307	6	functions	function	NOUN
ejpam-5649	307	7	.	.	PUNCT
ejpam-5649	308	1	glasnik	glasnik	PROPN
ejpam-5649	308	2	matematički	matematički	PROPN
ejpam-5649	308	3	,	,	PUNCT
ejpam-5649	308	4	40(60):317–322	40(60):317–322	PROPN
ejpam-5649	308	5	,	,	PUNCT
ejpam-5649	308	6	2005	2005	NUM
ejpam-5649	308	7	.	.	PUNCT
ejpam-5649	309	1	[	[	X
ejpam-5649	309	2	32	32	NUM
ejpam-5649	309	3	]	]	PUNCT
ejpam-5649	309	4	m.	m.	NOUN
ejpam-5649	309	5	caldas	caldas	PROPN
ejpam-5649	309	6	,	,	PUNCT
ejpam-5649	309	7	s.	s.	PROPN
ejpam-5649	309	8	jafari	jafari	PROPN
ejpam-5649	309	9	,	,	PUNCT
ejpam-5649	309	10	and	and	CCONJ
ejpam-5649	309	11	t.	t.	PROPN
ejpam-5649	309	12	noiri	noiri	PROPN
ejpam-5649	309	13	.	.	PUNCT
ejpam-5649	310	1	characterizations	characterization	NOUN
ejpam-5649	310	2	of	of	ADP
ejpam-5649	310	3	rarely	rarely	ADV
ejpam-5649	310	4	g	g	NOUN
ejpam-5649	310	5	-	-	PUNCT
ejpam-5649	310	6	continuous	continuous	ADJ
ejpam-5649	310	7	multifunctions	multifunction	NOUN
ejpam-5649	310	8	.	.	PUNCT
ejpam-5649	311	1	sarajevo	sarajevo	PROPN
ejpam-5649	311	2	journal	journal	PROPN
ejpam-5649	311	3	of	of	ADP
ejpam-5649	311	4	mathematics	mathematic	NOUN
ejpam-5649	311	5	,	,	PUNCT
ejpam-5649	311	6	1(13):129–133	1(13):129–133	NUM
ejpam-5649	311	7	,	,	PUNCT
ejpam-5649	311	8	2005	2005	NUM
ejpam-5649	311	9	.	.	PUNCT
ejpam-5649	312	1	[	[	X
ejpam-5649	312	2	33	33	NUM
ejpam-5649	312	3	]	]	PUNCT
ejpam-5649	312	4	m.	m.	NOUN
ejpam-5649	312	5	chiangpradit	chiangpradit	NOUN
ejpam-5649	312	6	,	,	PUNCT
ejpam-5649	312	7	s.	s.	PROPN
ejpam-5649	312	8	sompong	sompong	PROPN
ejpam-5649	312	9	,	,	PUNCT
ejpam-5649	312	10	and	and	CCONJ
ejpam-5649	312	11	c.	c.	PROPN
ejpam-5649	312	12	boonpok	boonpok	PROPN
ejpam-5649	312	13	.	.	PUNCT
ejpam-5649	313	1	weakly	weakly	ADJ
ejpam-5649	313	2	quasi	quasi	NOUN
ejpam-5649	313	3	(	(	PUNCT
ejpam-5649	313	4	τ1	τ1	PROPN
ejpam-5649	313	5	,	,	PUNCT
ejpam-5649	313	6	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5649	313	7	b.	b.	PROPN
ejpam-5649	313	8	kong	kong	PROPN
ejpam-5649	313	9	-	-	PUNCT
ejpam-5649	313	10	ied	ied	PROPN
ejpam-5649	313	11	,	,	PUNCT
ejpam-5649	313	12	s.	s.	PROPN
ejpam-5649	313	13	sompong	sompong	PROPN
ejpam-5649	313	14	,	,	PUNCT
ejpam-5649	313	15	c.	c.	PROPN
ejpam-5649	313	16	boonpok	boonpok	PROPN
ejpam-5649	313	17	/	/	SYM
ejpam-5649	313	18	eur	eur	PROPN
ejpam-5649	313	19	.	.	PUNCT
ejpam-5649	314	1	j.	j.	PROPN
ejpam-5649	314	2	pure	pure	PROPN
ejpam-5649	314	3	appl	appl	PROPN
ejpam-5649	314	4	.	.	PROPN
ejpam-5649	314	5	math	math	PROPN
ejpam-5649	314	6	,	,	PUNCT
ejpam-5649	314	7	18	18	NUM
ejpam-5649	314	8	(	(	PUNCT
ejpam-5649	314	9	1	1	NUM
ejpam-5649	314	10	)	)	PUNCT
ejpam-5649	314	11	(	(	PUNCT
ejpam-5649	314	12	2025	2025	NUM
ejpam-5649	314	13	)	)	PUNCT
ejpam-5649	314	14	,	,	PUNCT
ejpam-5649	314	15	5649	5649	NUM
ejpam-5649	314	16	11	11	NUM
ejpam-5649	314	17	of	of	ADP
ejpam-5649	314	18	13	13	NUM
ejpam-5649	314	19	functions	function	NOUN
ejpam-5649	314	20	.	.	PUNCT
ejpam-5649	315	1	international	international	ADJ
ejpam-5649	315	2	journal	journal	NOUN
ejpam-5649	315	3	of	of	ADP
ejpam-5649	315	4	analysis	analysis	NOUN
ejpam-5649	315	5	and	and	CCONJ
ejpam-5649	315	6	applications	application	NOUN
ejpam-5649	315	7	,	,	PUNCT
ejpam-5649	315	8	22:125	22:125	NUM
ejpam-5649	315	9	,	,	PUNCT
ejpam-5649	315	10	2024	2024	NUM
ejpam-5649	315	11	.	.	PUNCT
ejpam-5649	316	1	[	[	X
ejpam-5649	316	2	34	34	NUM
ejpam-5649	316	3	]	]	X
ejpam-5649	316	4	t.	t.	PROPN
ejpam-5649	316	5	duangphui	duangphui	PROPN
ejpam-5649	316	6	,	,	PUNCT
ejpam-5649	316	7	c.	c.	PROPN
ejpam-5649	316	8	boonpok	boonpok	PROPN
ejpam-5649	316	9	,	,	PUNCT
ejpam-5649	316	10	and	and	CCONJ
ejpam-5649	316	11	c.	c.	PROPN
ejpam-5649	316	12	viriyapong	viriyapong	PROPN
ejpam-5649	316	13	.	.	PUNCT
ejpam-5649	317	1	continuous	continuous	ADJ
ejpam-5649	317	2	functions	function	NOUN
ejpam-5649	317	3	on	on	ADP
ejpam-5649	317	4	bigeneralized	bigeneralize	VERB
ejpam-5649	317	5	topological	topological	ADJ
ejpam-5649	317	6	spaces	space	NOUN
ejpam-5649	317	7	.	.	PUNCT
ejpam-5649	318	1	international	international	ADJ
ejpam-5649	318	2	journal	journal	PROPN
ejpam-5649	318	3	of	of	ADP
ejpam-5649	318	4	mathematical	mathematical	ADJ
ejpam-5649	318	5	analysis	analysis	NOUN
ejpam-5649	318	6	,	,	PUNCT
ejpam-5649	318	7	5(24):1165	5(24):1165	NUM
ejpam-5649	318	8	–	–	PUNCT
ejpam-5649	318	9	1174	1174	NUM
ejpam-5649	318	10	,	,	PUNCT
ejpam-5649	318	11	2011	2011	NUM
ejpam-5649	318	12	.	.	PUNCT
ejpam-5649	319	1	[	[	X
ejpam-5649	319	2	35	35	NUM
ejpam-5649	319	3	]	]	PUNCT
ejpam-5649	319	4	t.	t.	NOUN
ejpam-5649	319	5	dungthaisong	dungthaisong	PROPN
ejpam-5649	319	6	,	,	PUNCT
ejpam-5649	319	7	c.	c.	PROPN
ejpam-5649	319	8	boonpok	boonpok	PROPN
ejpam-5649	319	9	,	,	PUNCT
ejpam-5649	319	10	and	and	CCONJ
ejpam-5649	319	11	c.	c.	PROPN
ejpam-5649	319	12	viriyapong	viriyapong	PROPN
ejpam-5649	319	13	.	.	PUNCT
ejpam-5649	320	1	generalized	generalize	VERB
ejpam-5649	320	2	closed	close	VERB
ejpam-5649	320	3	sets	set	NOUN
ejpam-5649	320	4	in	in	ADP
ejpam-5649	320	5	bigeneralized	bigeneralize	VERB
ejpam-5649	320	6	topological	topological	ADJ
ejpam-5649	320	7	spaces	space	NOUN
ejpam-5649	320	8	.	.	PUNCT
ejpam-5649	321	1	international	international	ADJ
ejpam-5649	321	2	journal	journal	PROPN
ejpam-5649	321	3	of	of	ADP
ejpam-5649	321	4	mathematical	mathematical	ADJ
ejpam-5649	321	5	analysis	analysis	NOUN
ejpam-5649	321	6	,	,	PUNCT
ejpam-5649	321	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5649	321	8	,	,	PUNCT
ejpam-5649	321	9	2011	2011	NUM
ejpam-5649	321	10	.	.	PUNCT
ejpam-5649	322	1	[	[	X
ejpam-5649	322	2	36	36	NUM
ejpam-5649	322	3	]	]	X
ejpam-5649	322	4	e.	e.	PROPN
ejpam-5649	322	5	ekici	ekici	PROPN
ejpam-5649	322	6	and	and	CCONJ
ejpam-5649	322	7	s.	s.	PROPN
ejpam-5649	322	8	jafari	jafari	PROPN
ejpam-5649	322	9	.	.	PUNCT
ejpam-5649	323	1	on	on	ADP
ejpam-5649	323	2	rare	rare	ADJ
ejpam-5649	323	3	s	s	NOUN
ejpam-5649	323	4	-	-	NOUN
ejpam-5649	323	5	precontinuity	precontinuity	NOUN
ejpam-5649	323	6	for	for	ADP
ejpam-5649	323	7	multifunctions	multifunction	NOUN
ejpam-5649	323	8	.	.	PUNCT
ejpam-5649	324	1	demonstratio	demonstratio	PROPN
ejpam-5649	324	2	mathematica	mathematica	PROPN
ejpam-5649	324	3	,	,	PUNCT
ejpam-5649	324	4	46(2):395–403	46(2):395–403	PROPN
ejpam-5649	324	5	,	,	PUNCT
ejpam-5649	324	6	2013	2013	NUM
ejpam-5649	324	7	.	.	PUNCT
ejpam-5649	325	1	[	[	X
ejpam-5649	325	2	37	37	NUM
ejpam-5649	325	3	]	]	PUNCT
ejpam-5649	325	4	e.	e.	PROPN
ejpam-5649	325	5	ekici	ekici	PROPN
ejpam-5649	325	6	and	and	CCONJ
ejpam-5649	325	7	j.	j.	PROPN
ejpam-5649	325	8	h.	h.	PROPN
ejpam-5649	325	9	park	park	PROPN
ejpam-5649	325	10	.	.	PUNCT
ejpam-5649	326	1	on	on	ADP
ejpam-5649	326	2	weakly	weakly	ADJ
ejpam-5649	326	3	s	s	NOUN
ejpam-5649	326	4	-	-	ADJ
ejpam-5649	326	5	precontinuous	precontinuous	ADJ
ejpam-5649	326	6	multifunctions	multifunction	NOUN
ejpam-5649	326	7	.	.	PUNCT
ejpam-5649	327	1	arabian	arabian	ADJ
ejpam-5649	327	2	journal	journal	PROPN
ejpam-5649	327	3	science	science	NOUN
ejpam-5649	327	4	and	and	CCONJ
ejpam-5649	327	5	engineering	engineering	NOUN
ejpam-5649	327	6	,	,	PUNCT
ejpam-5649	327	7	32(1a):83–92	32(1a):83–92	NUM
ejpam-5649	327	8	,	,	PUNCT
ejpam-5649	327	9	2009	2009	NUM
ejpam-5649	327	10	.	.	PUNCT
ejpam-5649	328	1	[	[	X
ejpam-5649	328	2	38	38	NUM
ejpam-5649	328	3	]	]	PUNCT
ejpam-5649	328	4	m.	m.	NOUN
ejpam-5649	328	5	e.	e.	PROPN
ejpam-5649	328	6	abd	abd	PROPN
ejpam-5649	329	1	el	el	PROPN
ejpam-5649	329	2	-	-	PROPN
ejpam-5649	329	3	monsef	monsef	PROPN
ejpam-5649	329	4	,	,	PUNCT
ejpam-5649	329	5	s.	s.	PROPN
ejpam-5649	329	6	n.	n.	PROPN
ejpam-5649	329	7	el	el	PROPN
ejpam-5649	329	8	-	-	PROPN
ejpam-5649	329	9	deeb	deeb	PROPN
ejpam-5649	329	10	,	,	PUNCT
ejpam-5649	329	11	and	and	CCONJ
ejpam-5649	329	12	r.	r.	PROPN
ejpam-5649	329	13	a.	a.	PROPN
ejpam-5649	329	14	mahmoud	mahmoud	PROPN
ejpam-5649	329	15	.	.	PUNCT
ejpam-5649	330	1	β	β	X
ejpam-5649	330	2	-	-	ADJ
ejpam-5649	330	3	open	open	ADJ
ejpam-5649	330	4	sets	set	NOUN
ejpam-5649	330	5	and	and	CCONJ
ejpam-5649	330	6	βcontinuous	βcontinuous	ADJ
ejpam-5649	330	7	mappings	mapping	NOUN
ejpam-5649	330	8	.	.	PUNCT
ejpam-5649	331	1	bulletin	bulletin	NOUN
ejpam-5649	331	2	of	of	ADP
ejpam-5649	331	3	the	the	DET
ejpam-5649	331	4	faculty	faculty	NOUN
ejpam-5649	331	5	of	of	ADP
ejpam-5649	331	6	science	science	NOUN
ejpam-5649	331	7	,	,	PUNCT
ejpam-5649	331	8	assiut	assiut	NOUN
ejpam-5649	331	9	university	university	NOUN
ejpam-5649	331	10	,	,	PUNCT
ejpam-5649	331	11	12:77–90	12:77–90	NUM
ejpam-5649	331	12	,	,	PUNCT
ejpam-5649	331	13	1983	1983	NUM
ejpam-5649	331	14	.	.	PUNCT
ejpam-5649	332	1	[	[	X
ejpam-5649	332	2	39	39	NUM
ejpam-5649	332	3	]	]	PUNCT
ejpam-5649	332	4	s.	s.	PROPN
ejpam-5649	332	5	jafari	jafari	PROPN
ejpam-5649	332	6	.	.	PUNCT
ejpam-5649	333	1	a	a	DET
ejpam-5649	333	2	note	note	NOUN
ejpam-5649	333	3	on	on	ADP
ejpam-5649	333	4	rarely	rarely	ADV
ejpam-5649	333	5	continuous	continuous	ADJ
ejpam-5649	333	6	functions	function	NOUN
ejpam-5649	333	7	.	.	PUNCT
ejpam-5649	334	1	universitatea	universitatea	PROPN
ejpam-5649	334	2	din	din	PROPN
ejpam-5649	334	3	bacǎu	bacǎu	PROPN
ejpam-5649	334	4	,	,	PUNCT
ejpam-5649	334	5	studii	studii	PROPN
ejpam-5649	334	6	si	si	PROPN
ejpam-5649	334	7	cercetari	cercetari	PROPN
ejpam-5649	334	8	stiintific	stiintific	PROPN
ejpam-5649	334	9	,	,	PUNCT
ejpam-5649	334	10	seria	seria	PROPN
ejpam-5649	334	11	:	:	PUNCT
ejpam-5649	334	12	matematica	matematica	PROPN
ejpam-5649	334	13	,	,	PUNCT
ejpam-5649	334	14	5:29–34	5:29–34	NUM
ejpam-5649	334	15	,	,	PUNCT
ejpam-5649	334	16	1995	1995	NUM
ejpam-5649	334	17	.	.	PUNCT
ejpam-5649	335	1	[	[	X
ejpam-5649	335	2	40	40	NUM
ejpam-5649	335	3	]	]	PUNCT
ejpam-5649	335	4	s.	s.	PROPN
ejpam-5649	335	5	jafari	jafari	PROPN
ejpam-5649	335	6	.	.	PUNCT
ejpam-5649	336	1	on	on	ADP
ejpam-5649	336	2	some	some	DET
ejpam-5649	336	3	properties	property	NOUN
ejpam-5649	336	4	of	of	ADP
ejpam-5649	336	5	rarely	rarely	ADV
ejpam-5649	336	6	continuous	continuous	ADJ
ejpam-5649	336	7	functions	function	NOUN
ejpam-5649	336	8	.	.	PUNCT
ejpam-5649	337	1	universitatea	universitatea	PROPN
ejpam-5649	337	2	din	din	PROPN
ejpam-5649	337	3	bacǎu	bacǎu	PROPN
ejpam-5649	337	4	,	,	PUNCT
ejpam-5649	337	5	studii	studii	PROPN
ejpam-5649	337	6	si	si	PROPN
ejpam-5649	337	7	cercetari	cercetari	PROPN
ejpam-5649	337	8	stiintific	stiintific	PROPN
ejpam-5649	337	9	,	,	PUNCT
ejpam-5649	337	10	seria	seria	PROPN
ejpam-5649	337	11	:	:	PUNCT
ejpam-5649	337	12	matematica	matematica	PROPN
ejpam-5649	337	13	,	,	PUNCT
ejpam-5649	337	14	7:65–73	7:65–73	PROPN
ejpam-5649	337	15	,	,	PUNCT
ejpam-5649	337	16	1997	1997	NUM
ejpam-5649	337	17	.	.	PUNCT
ejpam-5649	338	1	[	[	X
ejpam-5649	338	2	41	41	NUM
ejpam-5649	338	3	]	]	X
ejpam-5649	338	4	s.	s.	PROPN
ejpam-5649	338	5	jafari	jafari	PROPN
ejpam-5649	338	6	.	.	PUNCT
ejpam-5649	339	1	on	on	ADP
ejpam-5649	339	2	rarely	rarely	ADV
ejpam-5649	339	3	β	β	ADJ
ejpam-5649	339	4	-	-	ADJ
ejpam-5649	339	5	continuous	continuous	ADJ
ejpam-5649	339	6	functions	function	NOUN
ejpam-5649	339	7	.	.	PUNCT
ejpam-5649	340	1	journal	journal	PROPN
ejpam-5649	340	2	of	of	ADP
ejpam-5649	340	3	institute	institute	PROPN
ejpam-5649	340	4	of	of	ADP
ejpam-5649	340	5	mathematics	mathematics	PROPN
ejpam-5649	340	6	and	and	CCONJ
ejpam-5649	340	7	computer	computer	NOUN
ejpam-5649	340	8	science	science	NOUN
ejpam-5649	340	9	,	,	PUNCT
ejpam-5649	340	10	13(2):247–251	13(2):247–251	PROPN
ejpam-5649	340	11	,	,	PUNCT
ejpam-5649	340	12	2000	2000	NUM
ejpam-5649	340	13	.	.	PUNCT
ejpam-5649	341	1	[	[	X
ejpam-5649	341	2	42	42	NUM
ejpam-5649	341	3	]	]	PUNCT
ejpam-5649	341	4	s.	s.	PROPN
ejpam-5649	341	5	jafari	jafari	PROPN
ejpam-5649	341	6	.	.	PUNCT
ejpam-5649	342	1	rarely	rarely	ADV
ejpam-5649	342	2	α	α	NOUN
ejpam-5649	342	3	-	-	NOUN
ejpam-5649	342	4	continuity	continuity	NOUN
ejpam-5649	342	5	.	.	PUNCT
ejpam-5649	343	1	bulletin	bulletin	NOUN
ejpam-5649	343	2	of	of	ADP
ejpam-5649	343	3	the	the	DET
ejpam-5649	343	4	malaysian	malaysian	PROPN
ejpam-5649	343	5	mathematical	mathematical	PROPN
ejpam-5649	343	6	sciences	sciences	PROPN
ejpam-5649	343	7	society	society	NOUN
ejpam-5649	343	8	,	,	PUNCT
ejpam-5649	343	9	28(2):157–161	28(2):157–161	PROPN
ejpam-5649	343	10	,	,	PUNCT
ejpam-5649	343	11	2005	2005	NUM
ejpam-5649	343	12	.	.	PUNCT
ejpam-5649	344	1	[	[	X
ejpam-5649	344	2	43	43	NUM
ejpam-5649	344	3	]	]	X
ejpam-5649	344	4	j.	j.	PROPN
ejpam-5649	344	5	khampakdee	khampakdee	PROPN
ejpam-5649	344	6	and	and	CCONJ
ejpam-5649	344	7	c.	c.	PROPN
ejpam-5649	344	8	boonpok	boonpok	PROPN
ejpam-5649	344	9	.	.	PUNCT
ejpam-5649	345	1	upper	upper	ADJ
ejpam-5649	345	2	and	and	CCONJ
ejpam-5649	345	3	lower	low	ADJ
ejpam-5649	345	4	α(λ	α(λ	PROPN
ejpam-5649	345	5	,	,	PUNCT
ejpam-5649	345	6	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	345	7	multifunctions	multifunction	NOUN
ejpam-5649	345	8	.	.	PUNCT
ejpam-5649	346	1	wseas	wseas	VERB
ejpam-5649	346	2	transactions	transaction	NOUN
ejpam-5649	346	3	on	on	ADP
ejpam-5649	346	4	mathematics	mathematic	NOUN
ejpam-5649	346	5	,	,	PUNCT
ejpam-5649	346	6	21:684–690	21:684–690	NUM
ejpam-5649	346	7	,	,	PUNCT
ejpam-5649	346	8	2022	2022	NUM
ejpam-5649	346	9	.	.	PUNCT
ejpam-5649	347	1	[	[	X
ejpam-5649	347	2	44	44	NUM
ejpam-5649	347	3	]	]	PUNCT
ejpam-5649	347	4	j.	j.	PROPN
ejpam-5649	347	5	khampakdee	khampakdee	PROPN
ejpam-5649	347	6	,	,	PUNCT
ejpam-5649	347	7	s.	s.	PROPN
ejpam-5649	347	8	sompong	sompong	PROPN
ejpam-5649	347	9	,	,	PUNCT
ejpam-5649	347	10	and	and	CCONJ
ejpam-5649	347	11	c.	c.	PROPN
ejpam-5649	347	12	boonpok	boonpok	PROPN
ejpam-5649	347	13	.	.	PUNCT
ejpam-5649	348	1	c-(τ1	c-(τ1	PROPN
ejpam-5649	348	2	,	,	PUNCT
ejpam-5649	348	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5649	348	4	for	for	ADP
ejpam-5649	348	5	multifunctions	multifunction	NOUN
ejpam-5649	348	6	.	.	PUNCT
ejpam-5649	349	1	european	european	ADJ
ejpam-5649	349	2	journal	journal	PROPN
ejpam-5649	349	3	of	of	ADP
ejpam-5649	349	4	pure	pure	ADJ
ejpam-5649	349	5	and	and	CCONJ
ejpam-5649	349	6	applied	applied	ADJ
ejpam-5649	349	7	mathematics	mathematic	NOUN
ejpam-5649	349	8	,	,	PUNCT
ejpam-5649	349	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-5649	349	10	,	,	PUNCT
ejpam-5649	349	11	2024	2024	NUM
ejpam-5649	349	12	.	.	PUNCT
ejpam-5649	350	1	[	[	X
ejpam-5649	350	2	45	45	NUM
ejpam-5649	350	3	]	]	PUNCT
ejpam-5649	350	4	c.	c.	PROPN
ejpam-5649	350	5	klanarong	klanarong	PROPN
ejpam-5649	350	6	,	,	PUNCT
ejpam-5649	350	7	s.	s.	PROPN
ejpam-5649	350	8	sompong	sompong	PROPN
ejpam-5649	350	9	,	,	PUNCT
ejpam-5649	350	10	and	and	CCONJ
ejpam-5649	350	11	c.	c.	PROPN
ejpam-5649	350	12	boonpok	boonpok	PROPN
ejpam-5649	350	13	.	.	PUNCT
ejpam-5649	351	1	upper	upper	ADJ
ejpam-5649	351	2	and	and	CCONJ
ejpam-5649	351	3	lower	low	ADJ
ejpam-5649	351	4	almost	almost	ADV
ejpam-5649	351	5	(	(	PUNCT
ejpam-5649	351	6	τ1	τ1	NOUN
ejpam-5649	351	7	,	,	PUNCT
ejpam-5649	351	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5649	351	9	multifunctions	multifunction	NOUN
ejpam-5649	351	10	.	.	PUNCT
ejpam-5649	352	1	european	european	ADJ
ejpam-5649	352	2	journal	journal	PROPN
ejpam-5649	352	3	of	of	ADP
ejpam-5649	352	4	pure	pure	ADJ
ejpam-5649	352	5	and	and	CCONJ
ejpam-5649	352	6	applied	applied	ADJ
ejpam-5649	352	7	mathematics	mathematic	NOUN
ejpam-5649	352	8	,	,	PUNCT
ejpam-5649	352	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5649	352	10	,	,	PUNCT
ejpam-5649	352	11	2024	2024	NUM
ejpam-5649	352	12	.	.	PUNCT
ejpam-5649	353	1	[	[	X
ejpam-5649	353	2	46	46	NUM
ejpam-5649	353	3	]	]	X
ejpam-5649	353	4	b.	b.	PROPN
ejpam-5649	353	5	kong	kong	PROPN
ejpam-5649	353	6	-	-	PUNCT
ejpam-5649	353	7	ied	ied	PROPN
ejpam-5649	353	8	,	,	PUNCT
ejpam-5649	353	9	s.	s.	PROPN
ejpam-5649	353	10	sompong	sompong	PROPN
ejpam-5649	353	11	,	,	PUNCT
ejpam-5649	353	12	and	and	CCONJ
ejpam-5649	353	13	c.	c.	PROPN
ejpam-5649	353	14	boonpok	boonpok	PROPN
ejpam-5649	353	15	.	.	PUNCT
ejpam-5649	354	1	almost	almost	ADV
ejpam-5649	354	2	quasi	quasi	X
ejpam-5649	354	3	(	(	PUNCT
ejpam-5649	354	4	τ1	τ1	NOUN
ejpam-5649	354	5	,	,	PUNCT
ejpam-5649	354	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	354	7	functions	function	NOUN
ejpam-5649	354	8	.	.	PUNCT
ejpam-5649	355	1	asia	asia	PROPN
ejpam-5649	355	2	pacific	pacific	PROPN
ejpam-5649	355	3	journal	journal	PROPN
ejpam-5649	355	4	of	of	ADP
ejpam-5649	355	5	mathematics	mathematic	NOUN
ejpam-5649	355	6	,	,	PUNCT
ejpam-5649	355	7	11:64	11:64	NUM
ejpam-5649	355	8	,	,	PUNCT
ejpam-5649	355	9	2024	2024	NUM
ejpam-5649	355	10	.	.	PUNCT
ejpam-5649	356	1	[	[	X
ejpam-5649	356	2	47	47	NUM
ejpam-5649	356	3	]	]	X
ejpam-5649	356	4	n.	n.	PROPN
ejpam-5649	356	5	levine	levine	PROPN
ejpam-5649	356	6	.	.	PUNCT
ejpam-5649	357	1	a	a	DET
ejpam-5649	357	2	decomposition	decomposition	NOUN
ejpam-5649	357	3	of	of	ADP
ejpam-5649	357	4	continuity	continuity	NOUN
ejpam-5649	357	5	in	in	ADP
ejpam-5649	357	6	topological	topological	ADJ
ejpam-5649	357	7	spaces	space	NOUN
ejpam-5649	357	8	.	.	PUNCT
ejpam-5649	358	1	the	the	DET
ejpam-5649	358	2	american	american	PROPN
ejpam-5649	358	3	mathematical	mathematical	PROPN
ejpam-5649	358	4	monthly	monthly	ADV
ejpam-5649	358	5	,	,	PUNCT
ejpam-5649	358	6	60:44–46	60:44–46	NUM
ejpam-5649	358	7	,	,	PUNCT
ejpam-5649	358	8	1961	1961	NUM
ejpam-5649	358	9	.	.	PUNCT
ejpam-5649	359	1	[	[	X
ejpam-5649	359	2	48	48	NUM
ejpam-5649	359	3	]	]	X
ejpam-5649	359	4	n.	n.	PROPN
ejpam-5649	359	5	levine	levine	PROPN
ejpam-5649	359	6	.	.	PUNCT
ejpam-5649	360	1	semi	semi	ADJ
ejpam-5649	360	2	-	-	ADJ
ejpam-5649	360	3	open	open	ADJ
ejpam-5649	360	4	sets	set	NOUN
ejpam-5649	360	5	and	and	CCONJ
ejpam-5649	360	6	semi	semi	ADJ
ejpam-5649	360	7	-	-	NOUN
ejpam-5649	360	8	continuity	continuity	NOUN
ejpam-5649	360	9	in	in	ADP
ejpam-5649	360	10	topological	topological	ADJ
ejpam-5649	360	11	spaces	space	NOUN
ejpam-5649	360	12	.	.	PUNCT
ejpam-5649	361	1	the	the	DET
ejpam-5649	361	2	american	american	PROPN
ejpam-5649	361	3	mathematical	mathematical	PROPN
ejpam-5649	361	4	monthly	monthly	ADV
ejpam-5649	361	5	,	,	PUNCT
ejpam-5649	361	6	70:36–41	70:36–41	NUM
ejpam-5649	361	7	,	,	PUNCT
ejpam-5649	361	8	1963	1963	NUM
ejpam-5649	361	9	.	.	PUNCT
ejpam-5649	362	1	[	[	X
ejpam-5649	362	2	49	49	NUM
ejpam-5649	362	3	]	]	PUNCT
ejpam-5649	363	1	p.	p.	NOUN
ejpam-5649	363	2	e.	e.	PROPN
ejpam-5649	364	1	long	long	PROPN
ejpam-5649	364	2	and	and	CCONJ
ejpam-5649	364	3	l.	l.	PROPN
ejpam-5649	364	4	l.	l.	PROPN
ejpam-5649	364	5	herrington	herrington	PROPN
ejpam-5649	364	6	.	.	PUNCT
ejpam-5649	365	1	properties	property	NOUN
ejpam-5649	365	2	of	of	ADP
ejpam-5649	365	3	rarely	rarely	ADV
ejpam-5649	365	4	continuous	continuous	ADJ
ejpam-5649	365	5	functions	function	NOUN
ejpam-5649	365	6	.	.	PUNCT
ejpam-5649	366	1	glasnik	glasnik	PROPN
ejpam-5649	366	2	matematički	matematički	PROPN
ejpam-5649	366	3	,	,	PUNCT
ejpam-5649	366	4	17(37):147–153	17(37):147–153	NUM
ejpam-5649	366	5	,	,	PUNCT
ejpam-5649	366	6	1982	1982	NUM
ejpam-5649	366	7	.	.	PUNCT
ejpam-5649	367	1	[	[	X
ejpam-5649	367	2	50	50	NUM
ejpam-5649	367	3	]	]	PUNCT
ejpam-5649	367	4	a.	a.	NOUN
ejpam-5649	367	5	s.	s.	PROPN
ejpam-5649	367	6	mashhour	mashhour	PROPN
ejpam-5649	367	7	,	,	PUNCT
ejpam-5649	367	8	m.	m.	PROPN
ejpam-5649	367	9	e.	e.	PROPN
ejpam-5649	367	10	abd	abd	PROPN
ejpam-5649	368	1	el	el	PROPN
ejpam-5649	368	2	-	-	PROPN
ejpam-5649	368	3	monsef	monsef	ADJ
ejpam-5649	368	4	,	,	PUNCT
ejpam-5649	368	5	and	and	CCONJ
ejpam-5649	368	6	s.	s.	PROPN
ejpam-5649	368	7	n.	n.	PROPN
ejpam-5649	368	8	el	el	PROPN
ejpam-5649	368	9	-	-	PROPN
ejpam-5649	368	10	deeb	deeb	PROPN
ejpam-5649	368	11	.	.	PUNCT
ejpam-5649	369	1	on	on	ADP
ejpam-5649	369	2	precontinuous	precontinuous	ADJ
ejpam-5649	369	3	and	and	CCONJ
ejpam-5649	369	4	weak	weak	ADJ
ejpam-5649	369	5	precontinuous	precontinuous	ADJ
ejpam-5649	369	6	mappings	mapping	NOUN
ejpam-5649	369	7	.	.	PUNCT
ejpam-5649	370	1	proceedings	proceeding	NOUN
ejpam-5649	370	2	of	of	ADP
ejpam-5649	370	3	the	the	DET
ejpam-5649	370	4	mathematical	mathematical	ADJ
ejpam-5649	370	5	and	and	CCONJ
ejpam-5649	370	6	physical	physical	ADJ
ejpam-5649	370	7	society	society	NOUN
ejpam-5649	370	8	of	of	ADP
ejpam-5649	370	9	egypt	egypt	PROPN
ejpam-5649	370	10	,	,	PUNCT
ejpam-5649	370	11	53:47–53	53:47–53	NUM
ejpam-5649	370	12	,	,	PUNCT
ejpam-5649	370	13	1982	1982	NUM
ejpam-5649	370	14	.	.	PUNCT
ejpam-5649	371	1	[	[	X
ejpam-5649	371	2	51	51	NUM
ejpam-5649	371	3	]	]	X
ejpam-5649	371	4	o.	o.	NOUN
ejpam-5649	371	5	nj̊astad	nj̊astad	NOUN
ejpam-5649	371	6	.	.	PUNCT
ejpam-5649	372	1	on	on	ADP
ejpam-5649	372	2	some	some	DET
ejpam-5649	372	3	classes	class	NOUN
ejpam-5649	372	4	of	of	ADP
ejpam-5649	372	5	nearly	nearly	ADV
ejpam-5649	372	6	open	open	ADJ
ejpam-5649	372	7	sets	set	NOUN
ejpam-5649	372	8	.	.	PUNCT
ejpam-5649	373	1	pacific	pacific	PROPN
ejpam-5649	373	2	journal	journal	PROPN
ejpam-5649	373	3	of	of	ADP
ejpam-5649	373	4	mathematics	mathematic	NOUN
ejpam-5649	373	5	,	,	PUNCT
ejpam-5649	373	6	15:961–970	15:961–970	PROPN
ejpam-5649	373	7	,	,	PUNCT
ejpam-5649	373	8	1965	1965	NUM
ejpam-5649	373	9	.	.	PUNCT
ejpam-5649	374	1	[	[	X
ejpam-5649	374	2	52	52	NUM
ejpam-5649	374	3	]	]	PUNCT
ejpam-5649	374	4	t.	t.	PROPN
ejpam-5649	374	5	noiri	noiri	PROPN
ejpam-5649	374	6	.	.	PUNCT
ejpam-5649	375	1	weakly	weakly	ADJ
ejpam-5649	375	2	α	α	X
ejpam-5649	375	3	-	-	ADJ
ejpam-5649	375	4	continuous	continuous	ADJ
ejpam-5649	375	5	functions	function	NOUN
ejpam-5649	375	6	.	.	PUNCT
ejpam-5649	376	1	international	international	ADJ
ejpam-5649	376	2	journal	journal	NOUN
ejpam-5649	376	3	of	of	ADP
ejpam-5649	376	4	mathematics	mathematics	PROPN
ejpam-5649	376	5	and	and	CCONJ
ejpam-5649	376	6	b.	b.	PROPN
ejpam-5649	376	7	kong	kong	PROPN
ejpam-5649	376	8	-	-	PUNCT
ejpam-5649	376	9	ied	ied	PROPN
ejpam-5649	376	10	,	,	PUNCT
ejpam-5649	376	11	s.	s.	PROPN
ejpam-5649	376	12	sompong	sompong	PROPN
ejpam-5649	376	13	,	,	PUNCT
ejpam-5649	376	14	c.	c.	PROPN
ejpam-5649	376	15	boonpok	boonpok	PROPN
ejpam-5649	376	16	/	/	SYM
ejpam-5649	376	17	eur	eur	PROPN
ejpam-5649	376	18	.	.	PUNCT
ejpam-5649	377	1	j.	j.	PROPN
ejpam-5649	377	2	pure	pure	PROPN
ejpam-5649	377	3	appl	appl	PROPN
ejpam-5649	377	4	.	.	PROPN
ejpam-5649	377	5	math	math	PROPN
ejpam-5649	377	6	,	,	PUNCT
ejpam-5649	377	7	18	18	NUM
ejpam-5649	377	8	(	(	PUNCT
ejpam-5649	377	9	1	1	NUM
ejpam-5649	377	10	)	)	PUNCT
ejpam-5649	377	11	(	(	PUNCT
ejpam-5649	377	12	2025	2025	NUM
ejpam-5649	377	13	)	)	PUNCT
ejpam-5649	377	14	,	,	PUNCT
ejpam-5649	377	15	5649	5649	NUM
ejpam-5649	377	16	12	12	NUM
ejpam-5649	377	17	of	of	ADP
ejpam-5649	377	18	13	13	NUM
ejpam-5649	377	19	mathematical	mathematical	ADJ
ejpam-5649	377	20	sciences	science	NOUN
ejpam-5649	377	21	,	,	PUNCT
ejpam-5649	377	22	10(3):483–490	10(3):483–490	NUM
ejpam-5649	377	23	,	,	PUNCT
ejpam-5649	377	24	1987	1987	NUM
ejpam-5649	377	25	.	.	PUNCT
ejpam-5649	378	1	[	[	X
ejpam-5649	378	2	53	53	NUM
ejpam-5649	378	3	]	]	PUNCT
ejpam-5649	378	4	v.	v.	CCONJ
ejpam-5649	378	5	popa	popa	NOUN
ejpam-5649	378	6	.	.	PUNCT
ejpam-5649	379	1	weakly	weakly	ADJ
ejpam-5649	379	2	continuous	continuous	ADJ
ejpam-5649	379	3	multifunctions	multifunction	NOUN
ejpam-5649	379	4	.	.	PUNCT
ejpam-5649	380	1	bollettino	bollettino	PROPN
ejpam-5649	380	2	dell	dell	PROPN
ejpam-5649	380	3	’	'	PUNCT
ejpam-5649	380	4	unione	unione	PROPN
ejpam-5649	380	5	matematica	matematica	PROPN
ejpam-5649	380	6	italiana	italiana	PROPN
ejpam-5649	380	7	,	,	PUNCT
ejpam-5649	380	8	15(2):379–388	15(2):379–388	NUM
ejpam-5649	380	9	,	,	PUNCT
ejpam-5649	380	10	1978	1978	NUM
ejpam-5649	380	11	.	.	PUNCT
ejpam-5649	381	1	[	[	X
ejpam-5649	381	2	54	54	NUM
ejpam-5649	381	3	]	]	PUNCT
ejpam-5649	381	4	v.	v.	CCONJ
ejpam-5649	381	5	popa	popa	NOUN
ejpam-5649	381	6	.	.	PUNCT
ejpam-5649	382	1	sur	sur	VERB
ejpam-5649	382	2	certain	certain	ADJ
ejpam-5649	382	3	decomposition	decomposition	NOUN
ejpam-5649	382	4	de	de	X
ejpam-5649	382	5	la	la	X
ejpam-5649	382	6	continuité	continuité	ADJ
ejpam-5649	382	7	dans	dans	PROPN
ejpam-5649	382	8	les	les	PROPN
ejpam-5649	382	9	espaces	espaces	PROPN
ejpam-5649	382	10	topologiques	topologique	NOUN
ejpam-5649	382	11	.	.	PUNCT
ejpam-5649	383	1	glasnik	glasnik	PROPN
ejpam-5649	383	2	matematički	matematički	PROPN
ejpam-5649	383	3	,	,	PUNCT
ejpam-5649	383	4	14(34):359–362	14(34):359–362	NUM
ejpam-5649	383	5	,	,	PUNCT
ejpam-5649	383	6	1979	1979	NUM
ejpam-5649	383	7	.	.	PUNCT
ejpam-5649	384	1	[	[	X
ejpam-5649	384	2	55	55	NUM
ejpam-5649	384	3	]	]	PUNCT
ejpam-5649	384	4	v.	v.	CCONJ
ejpam-5649	384	5	popa	popa	NOUN
ejpam-5649	384	6	and	and	CCONJ
ejpam-5649	384	7	t.	t.	PROPN
ejpam-5649	384	8	noiri	noiri	PROPN
ejpam-5649	384	9	.	.	PUNCT
ejpam-5649	385	1	on	on	ADP
ejpam-5649	385	2	s	s	NOUN
ejpam-5649	385	3	-	-	ADJ
ejpam-5649	385	4	precontinuous	precontinuous	ADJ
ejpam-5649	385	5	multifunctions	multifunction	NOUN
ejpam-5649	385	6	.	.	PUNCT
ejpam-5649	386	1	demonstratio	demonstratio	PROPN
ejpam-5649	386	2	mathematica	mathematica	PROPN
ejpam-5649	386	3	,	,	PUNCT
ejpam-5649	386	4	33(3):679–687	33(3):679–687	PROPN
ejpam-5649	386	5	,	,	PUNCT
ejpam-5649	386	6	2000	2000	NUM
ejpam-5649	386	7	.	.	PUNCT
ejpam-5649	387	1	[	[	X
ejpam-5649	387	2	56	56	NUM
ejpam-5649	387	3	]	]	X
ejpam-5649	387	4	p.	p.	NOUN
ejpam-5649	387	5	pue	pue	NOUN
ejpam-5649	387	6	-	-	PUNCT
ejpam-5649	387	7	on	on	ADP
ejpam-5649	387	8	and	and	CCONJ
ejpam-5649	387	9	c.	c.	PROPN
ejpam-5649	387	10	boonpok	boonpok	PROPN
ejpam-5649	387	11	.	.	PUNCT
ejpam-5649	388	1	θ(λ	θ(λ	PROPN
ejpam-5649	388	2	,	,	PUNCT
ejpam-5649	388	3	p)-continuity	p)-continuity	NOUN
ejpam-5649	388	4	for	for	ADP
ejpam-5649	388	5	functions	function	NOUN
ejpam-5649	388	6	.	.	PUNCT
ejpam-5649	389	1	international	international	ADJ
ejpam-5649	389	2	journal	journal	NOUN
ejpam-5649	389	3	of	of	ADP
ejpam-5649	389	4	mathematics	mathematic	NOUN
ejpam-5649	389	5	and	and	CCONJ
ejpam-5649	389	6	computer	computer	NOUN
ejpam-5649	389	7	science	science	NOUN
ejpam-5649	389	8	,	,	PUNCT
ejpam-5649	389	9	19(2):491–495	19(2):491–495	NUM
ejpam-5649	389	10	,	,	PUNCT
ejpam-5649	389	11	2024	2024	NUM
ejpam-5649	389	12	.	.	PUNCT
ejpam-5649	390	1	[	[	X
ejpam-5649	390	2	57	57	NUM
ejpam-5649	390	3	]	]	X
ejpam-5649	390	4	p.	p.	NOUN
ejpam-5649	390	5	pue	pue	NOUN
ejpam-5649	390	6	-	-	PUNCT
ejpam-5649	390	7	on	on	ADP
ejpam-5649	390	8	,	,	PUNCT
ejpam-5649	390	9	a.	a.	PROPN
ejpam-5649	390	10	sama	sama	PROPN
ejpam-5649	390	11	-	-	PUNCT
ejpam-5649	390	12	ae	ae	PROPN
ejpam-5649	390	13	,	,	PUNCT
ejpam-5649	390	14	and	and	CCONJ
ejpam-5649	390	15	c.	c.	PROPN
ejpam-5649	390	16	boonpok	boonpok	PROPN
ejpam-5649	390	17	.	.	PUNCT
ejpam-5649	391	1	c	c	X
ejpam-5649	391	2	-	-	PUNCT
ejpam-5649	391	3	quasi	quasi	X
ejpam-5649	391	4	(	(	PUNCT
ejpam-5649	391	5	τ1	τ1	PROPN
ejpam-5649	391	6	,	,	PUNCT
ejpam-5649	391	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	391	8	multifunctions	multifunction	NOUN
ejpam-5649	391	9	.	.	PUNCT
ejpam-5649	392	1	european	european	ADJ
ejpam-5649	392	2	journal	journal	PROPN
ejpam-5649	392	3	of	of	ADP
ejpam-5649	392	4	pure	pure	ADJ
ejpam-5649	392	5	and	and	CCONJ
ejpam-5649	392	6	applied	applied	ADJ
ejpam-5649	392	7	mathematics	mathematic	NOUN
ejpam-5649	392	8	,	,	PUNCT
ejpam-5649	392	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-5649	392	10	,	,	PUNCT
ejpam-5649	392	11	2024	2024	NUM
ejpam-5649	392	12	.	.	PUNCT
ejpam-5649	393	1	[	[	X
ejpam-5649	393	2	58	58	NUM
ejpam-5649	393	3	]	]	PUNCT
ejpam-5649	393	4	p.	p.	NOUN
ejpam-5649	393	5	pue	pue	NOUN
ejpam-5649	393	6	-	-	PUNCT
ejpam-5649	393	7	on	on	ADP
ejpam-5649	393	8	,	,	PUNCT
ejpam-5649	393	9	s.	s.	PROPN
ejpam-5649	393	10	sompong	sompong	PROPN
ejpam-5649	393	11	,	,	PUNCT
ejpam-5649	393	12	and	and	CCONJ
ejpam-5649	393	13	c.	c.	PROPN
ejpam-5649	393	14	boonpok	boonpok	PROPN
ejpam-5649	393	15	.	.	PUNCT
ejpam-5649	394	1	almost	almost	ADV
ejpam-5649	394	2	quasi	quasi	X
ejpam-5649	394	3	(	(	PUNCT
ejpam-5649	394	4	τ1	τ1	NOUN
ejpam-5649	394	5	,	,	PUNCT
ejpam-5649	394	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5649	394	7	for	for	ADP
ejpam-5649	394	8	multifunctions	multifunction	NOUN
ejpam-5649	394	9	.	.	PUNCT
ejpam-5649	395	1	international	international	ADJ
ejpam-5649	395	2	journal	journal	NOUN
ejpam-5649	395	3	of	of	ADP
ejpam-5649	395	4	analysis	analysis	NOUN
ejpam-5649	395	5	and	and	CCONJ
ejpam-5649	395	6	applications	application	NOUN
ejpam-5649	395	7	,	,	PUNCT
ejpam-5649	395	8	22:97	22:97	NUM
ejpam-5649	395	9	,	,	PUNCT
ejpam-5649	395	10	2024	2024	NUM
ejpam-5649	395	11	.	.	PUNCT
ejpam-5649	396	1	[	[	X
ejpam-5649	396	2	59	59	NUM
ejpam-5649	396	3	]	]	X
ejpam-5649	396	4	p.	p.	NOUN
ejpam-5649	396	5	pue	pue	NOUN
ejpam-5649	396	6	-	-	PUNCT
ejpam-5649	396	7	on	on	ADP
ejpam-5649	396	8	,	,	PUNCT
ejpam-5649	396	9	s.	s.	PROPN
ejpam-5649	396	10	sompong	sompong	PROPN
ejpam-5649	396	11	,	,	PUNCT
ejpam-5649	396	12	and	and	CCONJ
ejpam-5649	396	13	c.	c.	PROPN
ejpam-5649	396	14	boonpok	boonpok	PROPN
ejpam-5649	396	15	.	.	PUNCT
ejpam-5649	397	1	upper	upper	ADJ
ejpam-5649	397	2	and	and	CCONJ
ejpam-5649	397	3	lower	low	ADJ
ejpam-5649	397	4	(	(	PUNCT
ejpam-5649	397	5	τ1	τ1	NOUN
ejpam-5649	397	6	,	,	PUNCT
ejpam-5649	397	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	397	8	mulfunctions	mulfunction	NOUN
ejpam-5649	397	9	.	.	PUNCT
ejpam-5649	398	1	international	international	ADJ
ejpam-5649	398	2	journal	journal	NOUN
ejpam-5649	398	3	of	of	ADP
ejpam-5649	398	4	mathematics	mathematic	NOUN
ejpam-5649	398	5	and	and	CCONJ
ejpam-5649	398	6	computer	computer	NOUN
ejpam-5649	398	7	science	science	NOUN
ejpam-5649	398	8	,	,	PUNCT
ejpam-5649	398	9	19(4):1305	19(4):1305	NUM
ejpam-5649	398	10	–	–	PUNCT
ejpam-5649	398	11	1310	1310	NUM
ejpam-5649	398	12	,	,	PUNCT
ejpam-5649	398	13	2024	2024	NUM
ejpam-5649	398	14	.	.	PUNCT
ejpam-5649	399	1	[	[	X
ejpam-5649	399	2	60	60	NUM
ejpam-5649	399	3	]	]	X
ejpam-5649	399	4	p.	p.	NOUN
ejpam-5649	399	5	pue	pue	NOUN
ejpam-5649	399	6	-	-	PUNCT
ejpam-5649	399	7	on	on	ADP
ejpam-5649	399	8	,	,	PUNCT
ejpam-5649	399	9	s.	s.	PROPN
ejpam-5649	399	10	sompong	sompong	PROPN
ejpam-5649	399	11	,	,	PUNCT
ejpam-5649	399	12	and	and	CCONJ
ejpam-5649	399	13	c.	c.	PROPN
ejpam-5649	399	14	boonpok	boonpok	PROPN
ejpam-5649	399	15	.	.	PUNCT
ejpam-5649	400	1	weakly	weakly	ADJ
ejpam-5649	400	2	quasi	quasi	NOUN
ejpam-5649	400	3	(	(	PUNCT
ejpam-5649	400	4	τ1	τ1	PROPN
ejpam-5649	400	5	,	,	PUNCT
ejpam-5649	400	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	400	7	multifunctions	multifunction	NOUN
ejpam-5649	400	8	.	.	PUNCT
ejpam-5649	401	1	european	european	ADJ
ejpam-5649	401	2	journal	journal	PROPN
ejpam-5649	401	3	of	of	ADP
ejpam-5649	401	4	pure	pure	ADJ
ejpam-5649	401	5	and	and	CCONJ
ejpam-5649	401	6	applied	applied	ADJ
ejpam-5649	401	7	mathematics	mathematic	NOUN
ejpam-5649	401	8	,	,	PUNCT
ejpam-5649	401	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-5649	401	10	,	,	PUNCT
ejpam-5649	401	11	2024	2024	NUM
ejpam-5649	401	12	.	.	PUNCT
ejpam-5649	402	1	[	[	X
ejpam-5649	402	2	61	61	NUM
ejpam-5649	402	3	]	]	X
ejpam-5649	402	4	n.	n.	NOUN
ejpam-5649	402	5	srisarakham	srisarakham	PROPN
ejpam-5649	402	6	and	and	CCONJ
ejpam-5649	402	7	c.	c.	PROPN
ejpam-5649	402	8	boonpok	boonpok	PROPN
ejpam-5649	402	9	.	.	PUNCT
ejpam-5649	403	1	almost	almost	ADV
ejpam-5649	403	2	(	(	PUNCT
ejpam-5649	403	3	λ	λ	NOUN
ejpam-5649	403	4	,	,	PUNCT
ejpam-5649	403	5	p)-continuous	p)-continuous	ADJ
ejpam-5649	403	6	functions	function	NOUN
ejpam-5649	403	7	.	.	PUNCT
ejpam-5649	404	1	international	international	ADJ
ejpam-5649	404	2	journal	journal	PROPN
ejpam-5649	404	3	of	of	ADP
ejpam-5649	404	4	mathematics	mathematic	NOUN
ejpam-5649	404	5	and	and	CCONJ
ejpam-5649	404	6	computer	computer	NOUN
ejpam-5649	404	7	science	science	NOUN
ejpam-5649	404	8	,	,	PUNCT
ejpam-5649	404	9	18(2):255–259	18(2):255–259	NUM
ejpam-5649	404	10	,	,	PUNCT
ejpam-5649	404	11	2023	2023	NUM
ejpam-5649	404	12	.	.	PUNCT
ejpam-5649	405	1	[	[	X
ejpam-5649	405	2	62	62	NUM
ejpam-5649	405	3	]	]	X
ejpam-5649	405	4	n.	n.	NOUN
ejpam-5649	405	5	srisarakham	srisarakham	PROPN
ejpam-5649	405	6	,	,	PUNCT
ejpam-5649	405	7	a.	a.	PROPN
ejpam-5649	405	8	sama	sama	PROPN
ejpam-5649	405	9	-	-	PUNCT
ejpam-5649	405	10	ae	ae	PROPN
ejpam-5649	405	11	,	,	PUNCT
ejpam-5649	405	12	and	and	CCONJ
ejpam-5649	405	13	c.	c.	PROPN
ejpam-5649	405	14	boonpok	boonpok	PROPN
ejpam-5649	405	15	.	.	PUNCT
ejpam-5649	406	1	characterizations	characterization	NOUN
ejpam-5649	406	2	of	of	ADP
ejpam-5649	406	3	faintly	faintly	ADV
ejpam-5649	406	4	(	(	PUNCT
ejpam-5649	406	5	τ1	τ1	PROPN
ejpam-5649	406	6	,	,	PUNCT
ejpam-5649	406	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	406	8	functions	function	NOUN
ejpam-5649	406	9	.	.	PUNCT
ejpam-5649	407	1	european	european	ADJ
ejpam-5649	407	2	journal	journal	PROPN
ejpam-5649	407	3	of	of	ADP
ejpam-5649	407	4	pure	pure	ADJ
ejpam-5649	407	5	and	and	CCONJ
ejpam-5649	407	6	applied	applied	ADJ
ejpam-5649	407	7	mathematics	mathematic	NOUN
ejpam-5649	407	8	,	,	PUNCT
ejpam-5649	407	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-5649	407	10	,	,	PUNCT
ejpam-5649	407	11	2024	2024	NUM
ejpam-5649	407	12	.	.	PUNCT
ejpam-5649	408	1	[	[	X
ejpam-5649	408	2	63	63	NUM
ejpam-5649	408	3	]	]	PUNCT
ejpam-5649	408	4	m.	m.	NOUN
ejpam-5649	408	5	thongmoon	thongmoon	NOUN
ejpam-5649	408	6	and	and	CCONJ
ejpam-5649	408	7	c.	c.	PROPN
ejpam-5649	408	8	boonpok	boonpok	PROPN
ejpam-5649	408	9	.	.	PUNCT
ejpam-5649	409	1	upper	upper	ADJ
ejpam-5649	409	2	and	and	CCONJ
ejpam-5649	409	3	lower	low	ADJ
ejpam-5649	409	4	almost	almost	ADV
ejpam-5649	409	5	β(λ	β(λ	NOUN
ejpam-5649	409	6	,	,	PUNCT
ejpam-5649	409	7	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	409	8	multifunctions	multifunction	NOUN
ejpam-5649	409	9	.	.	PUNCT
ejpam-5649	410	1	wseas	wseas	VERB
ejpam-5649	410	2	transactions	transaction	NOUN
ejpam-5649	410	3	on	on	ADP
ejpam-5649	410	4	mathematics	mathematic	NOUN
ejpam-5649	410	5	,	,	PUNCT
ejpam-5649	410	6	21:844–853	21:844–853	NUM
ejpam-5649	410	7	,	,	PUNCT
ejpam-5649	410	8	2022	2022	NUM
ejpam-5649	410	9	.	.	PUNCT
ejpam-5649	411	1	[	[	X
ejpam-5649	411	2	64	64	NUM
ejpam-5649	411	3	]	]	PUNCT
ejpam-5649	411	4	m.	m.	NOUN
ejpam-5649	411	5	thongmoon	thongmoon	NOUN
ejpam-5649	411	6	and	and	CCONJ
ejpam-5649	411	7	c.	c.	PROPN
ejpam-5649	411	8	boonpok	boonpok	PROPN
ejpam-5649	411	9	.	.	PUNCT
ejpam-5649	412	1	strongly	strongly	ADV
ejpam-5649	412	2	θ(λ	θ(λ	PROPN
ejpam-5649	412	3	,	,	PUNCT
ejpam-5649	412	4	p)-continuous	p)-continuous	ADJ
ejpam-5649	412	5	functions	function	NOUN
ejpam-5649	412	6	.	.	PUNCT
ejpam-5649	413	1	international	international	ADJ
ejpam-5649	413	2	journal	journal	PROPN
ejpam-5649	413	3	of	of	ADP
ejpam-5649	413	4	mathematics	mathematic	NOUN
ejpam-5649	413	5	and	and	CCONJ
ejpam-5649	413	6	computer	computer	NOUN
ejpam-5649	413	7	science	science	NOUN
ejpam-5649	413	8	,	,	PUNCT
ejpam-5649	413	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5649	413	10	,	,	PUNCT
ejpam-5649	413	11	2024	2024	NUM
ejpam-5649	413	12	.	.	PUNCT
ejpam-5649	414	1	[	[	X
ejpam-5649	414	2	65	65	NUM
ejpam-5649	414	3	]	]	X
ejpam-5649	414	4	m.	m.	NOUN
ejpam-5649	414	5	thongmoon	thongmoon	NOUN
ejpam-5649	414	6	,	,	PUNCT
ejpam-5649	414	7	s.	s.	PROPN
ejpam-5649	414	8	sompong	sompong	PROPN
ejpam-5649	414	9	,	,	PUNCT
ejpam-5649	414	10	and	and	CCONJ
ejpam-5649	414	11	c.	c.	PROPN
ejpam-5649	414	12	boonpok	boonpok	PROPN
ejpam-5649	414	13	.	.	PUNCT
ejpam-5649	415	1	upper	upper	ADJ
ejpam-5649	415	2	and	and	CCONJ
ejpam-5649	415	3	lower	low	ADJ
ejpam-5649	415	4	weak	weak	ADJ
ejpam-5649	415	5	(	(	PUNCT
ejpam-5649	415	6	τ1	τ1	NOUN
ejpam-5649	415	7	,	,	PUNCT
ejpam-5649	415	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5649	415	9	.	.	PUNCT
ejpam-5649	416	1	european	european	PROPN
ejpam-5649	416	2	journal	journal	PROPN
ejpam-5649	416	3	of	of	ADP
ejpam-5649	416	4	pure	pure	ADJ
ejpam-5649	416	5	and	and	CCONJ
ejpam-5649	416	6	applied	applied	ADJ
ejpam-5649	416	7	mathematics	mathematic	NOUN
ejpam-5649	416	8	,	,	PUNCT
ejpam-5649	416	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5649	416	10	,	,	PUNCT
ejpam-5649	416	11	2024	2024	NUM
ejpam-5649	416	12	.	.	PUNCT
ejpam-5649	417	1	[	[	X
ejpam-5649	417	2	66	66	NUM
ejpam-5649	417	3	]	]	PUNCT
ejpam-5649	417	4	m.	m.	NOUN
ejpam-5649	417	5	thongmoon	thongmoon	NOUN
ejpam-5649	417	6	,	,	PUNCT
ejpam-5649	417	7	s.	s.	PROPN
ejpam-5649	417	8	sompong	sompong	PROPN
ejpam-5649	417	9	,	,	PUNCT
ejpam-5649	417	10	and	and	CCONJ
ejpam-5649	417	11	c.	c.	PROPN
ejpam-5649	417	12	boonpok	boonpok	PROPN
ejpam-5649	417	13	.	.	PUNCT
ejpam-5649	418	1	rarely	rarely	ADV
ejpam-5649	418	2	(	(	PUNCT
ejpam-5649	418	3	τ1	τ1	NOUN
ejpam-5649	418	4	,	,	PUNCT
ejpam-5649	418	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5649	418	6	functions	function	NOUN
ejpam-5649	418	7	.	.	PUNCT
ejpam-5649	419	1	international	international	ADJ
ejpam-5649	419	2	journal	journal	NOUN
ejpam-5649	419	3	of	of	ADP
ejpam-5649	419	4	mathematics	mathematic	NOUN
ejpam-5649	419	5	and	and	CCONJ
ejpam-5649	419	6	computer	computer	NOUN
ejpam-5649	419	7	science	science	NOUN
ejpam-5649	419	8	,	,	PUNCT
ejpam-5649	419	9	20(1):423–427	20(1):423–427	NUM
ejpam-5649	419	10	,	,	PUNCT
ejpam-5649	419	11	2025	2025	NUM
ejpam-5649	419	12	.	.	PUNCT
ejpam-5649	420	1	[	[	X
ejpam-5649	420	2	67	67	NUM
ejpam-5649	420	3	]	]	X
ejpam-5649	420	4	n.	n.	PROPN
ejpam-5649	420	5	v.	v.	PROPN
ejpam-5649	420	6	veličko	veličko	PROPN
ejpam-5649	420	7	.	.	PUNCT
ejpam-5649	421	1	h	h	NOUN
ejpam-5649	421	2	-	-	PUNCT
ejpam-5649	421	3	closed	close	VERB
ejpam-5649	421	4	topological	topological	ADJ
ejpam-5649	421	5	spaces	space	NOUN
ejpam-5649	421	6	.	.	PUNCT
ejpam-5649	422	1	american	american	PROPN
ejpam-5649	422	2	mathematical	mathematical	ADJ
ejpam-5649	422	3	society	society	NOUN
ejpam-5649	422	4	translations	translation	NOUN
ejpam-5649	422	5	,	,	PUNCT
ejpam-5649	422	6	78(2):102–118	78(2):102–118	NUM
ejpam-5649	422	7	,	,	PUNCT
ejpam-5649	422	8	1968	1968	NUM
ejpam-5649	422	9	.	.	PUNCT
ejpam-5649	423	1	[	[	X
ejpam-5649	423	2	68	68	NUM
ejpam-5649	423	3	]	]	X
ejpam-5649	423	4	c.	c.	PROPN
ejpam-5649	423	5	viriyapong	viriyapong	PROPN
ejpam-5649	423	6	and	and	CCONJ
ejpam-5649	423	7	c.	c.	PROPN
ejpam-5649	423	8	boonpok	boonpok	PROPN
ejpam-5649	423	9	.	.	PUNCT
ejpam-5649	424	1	(	(	PUNCT
ejpam-5649	424	2	τ1	τ1	NOUN
ejpam-5649	424	3	,	,	PUNCT
ejpam-5649	424	4	τ2)α	τ2)α	NOUN
ejpam-5649	424	5	-	-	PUNCT
ejpam-5649	424	6	continuity	continuity	NOUN
ejpam-5649	424	7	for	for	ADP
ejpam-5649	424	8	multifunctions	multifunction	NOUN
ejpam-5649	424	9	.	.	PUNCT
ejpam-5649	425	1	journal	journal	PROPN
ejpam-5649	425	2	of	of	ADP
ejpam-5649	425	3	mathematics	mathematic	NOUN
ejpam-5649	425	4	,	,	PUNCT
ejpam-5649	425	5	2020:6285763	2020:6285763	NUM
ejpam-5649	425	6	,	,	PUNCT
ejpam-5649	425	7	2020	2020	NUM
ejpam-5649	425	8	.	.	PUNCT
ejpam-5649	426	1	[	[	X
ejpam-5649	426	2	69	69	NUM
ejpam-5649	426	3	]	]	X
ejpam-5649	426	4	c.	c.	PROPN
ejpam-5649	426	5	viriyapong	viriyapong	PROPN
ejpam-5649	426	6	and	and	CCONJ
ejpam-5649	426	7	c.	c.	PROPN
ejpam-5649	426	8	boonpok	boonpok	PROPN
ejpam-5649	426	9	.	.	PUNCT
ejpam-5649	427	1	(	(	PUNCT
ejpam-5649	427	2	λ	λ	X
ejpam-5649	427	3	,	,	PUNCT
ejpam-5649	427	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5649	427	5	functions	function	NOUN
ejpam-5649	427	6	.	.	PUNCT
ejpam-5649	428	1	wseas	wseas	VERB
ejpam-5649	428	2	transactions	transaction	NOUN
ejpam-5649	428	3	on	on	ADP
ejpam-5649	428	4	mathematics	mathematic	NOUN
ejpam-5649	428	5	,	,	PUNCT
ejpam-5649	428	6	21:380–385	21:380–385	NUM
ejpam-5649	428	7	,	,	PUNCT
ejpam-5649	428	8	2022	2022	NUM
ejpam-5649	428	9	.	.	PUNCT
ejpam-5649	429	1	[	[	X
ejpam-5649	429	2	70	70	NUM
ejpam-5649	429	3	]	]	X
ejpam-5649	429	4	c.	c.	PROPN
ejpam-5649	429	5	viriyapong	viriyapong	PROPN
ejpam-5649	429	6	and	and	CCONJ
ejpam-5649	429	7	c.	c.	PROPN
ejpam-5649	429	8	boonpok	boonpok	PROPN
ejpam-5649	429	9	.	.	PUNCT
ejpam-5649	430	1	weak	weak	ADJ
ejpam-5649	430	2	quasi	quasi	NOUN
ejpam-5649	430	3	(	(	PUNCT
ejpam-5649	430	4	λ	λ	PROPN
ejpam-5649	430	5	,	,	PUNCT
ejpam-5649	430	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5649	430	7	for	for	ADP
ejpam-5649	430	8	multifunctions	multifunction	NOUN
ejpam-5649	430	9	.	.	PUNCT
ejpam-5649	431	1	international	international	ADJ
ejpam-5649	431	2	journal	journal	PROPN
ejpam-5649	431	3	of	of	ADP
ejpam-5649	431	4	mathematics	mathematic	NOUN
ejpam-5649	431	5	and	and	CCONJ
ejpam-5649	431	6	computer	computer	NOUN
ejpam-5649	431	7	science	science	NOUN
ejpam-5649	431	8	,	,	PUNCT
ejpam-5649	431	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5649	431	10	,	,	PUNCT
ejpam-5649	431	11	2022	2022	NUM
ejpam-5649	431	12	.	.	PUNCT
ejpam-5649	432	1	[	[	X
ejpam-5649	432	2	71	71	NUM
ejpam-5649	432	3	]	]	X
ejpam-5649	432	4	n.	n.	PROPN
ejpam-5649	432	5	viriyapong	viriyapong	PROPN
ejpam-5649	432	6	,	,	PUNCT
ejpam-5649	432	7	s.	s.	PROPN
ejpam-5649	432	8	sompong	sompong	PROPN
ejpam-5649	432	9	,	,	PUNCT
ejpam-5649	432	10	and	and	CCONJ
ejpam-5649	432	11	c.	c.	PROPN
ejpam-5649	432	12	boonpok	boonpok	PROPN
ejpam-5649	432	13	.	.	PUNCT
ejpam-5649	433	1	(	(	PUNCT
ejpam-5649	433	2	τ1	τ1	NOUN
ejpam-5649	433	3	,	,	PUNCT
ejpam-5649	433	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5649	433	5	disconnectedness	disconnectedness	NOUN
ejpam-5649	433	6	in	in	ADP
ejpam-5649	433	7	bitopological	bitopological	ADJ
ejpam-5649	433	8	spaces	space	NOUN
ejpam-5649	433	9	.	.	PUNCT
ejpam-5649	434	1	international	international	ADJ
ejpam-5649	434	2	journal	journal	PROPN
ejpam-5649	434	3	of	of	ADP
ejpam-5649	434	4	mathematics	mathematic	NOUN
ejpam-5649	434	5	and	and	CCONJ
ejpam-5649	434	6	computer	computer	NOUN
ejpam-5649	434	7	science	science	NOUN
ejpam-5649	434	8	,	,	PUNCT
ejpam-5649	434	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5649	434	10	,	,	PUNCT
ejpam-5649	434	11	2024	2024	NUM
ejpam-5649	434	12	.	.	PUNCT
ejpam-5649	435	1	b.	b.	PROPN
ejpam-5649	435	2	kong	kong	PROPN
ejpam-5649	435	3	-	-	PUNCT
ejpam-5649	435	4	ied	ied	PROPN
ejpam-5649	435	5	,	,	PUNCT
ejpam-5649	435	6	s.	s.	PROPN
ejpam-5649	435	7	sompong	sompong	PROPN
ejpam-5649	435	8	,	,	PUNCT
ejpam-5649	435	9	c.	c.	PROPN
ejpam-5649	435	10	boonpok	boonpok	PROPN
ejpam-5649	435	11	/	/	SYM
ejpam-5649	435	12	eur	eur	PROPN
ejpam-5649	435	13	.	.	PUNCT
ejpam-5649	436	1	j.	j.	PROPN
ejpam-5649	436	2	pure	pure	PROPN
ejpam-5649	436	3	appl	appl	PROPN
ejpam-5649	436	4	.	.	PROPN
ejpam-5649	436	5	math	math	PROPN
ejpam-5649	436	6	,	,	PUNCT
ejpam-5649	436	7	18	18	NUM
ejpam-5649	436	8	(	(	PUNCT
ejpam-5649	436	9	1	1	NUM
ejpam-5649	436	10	)	)	PUNCT
ejpam-5649	436	11	(	(	PUNCT
ejpam-5649	436	12	2025	2025	NUM
ejpam-5649	436	13	)	)	PUNCT
ejpam-5649	436	14	,	,	PUNCT
ejpam-5649	436	15	5649	5649	NUM
ejpam-5649	436	16	13	13	NUM
ejpam-5649	436	17	of	of	ADP
ejpam-5649	436	18	13	13	NUM
ejpam-5649	436	19	[	[	SYM
ejpam-5649	436	20	72	72	NUM
ejpam-5649	436	21	]	]	X
ejpam-5649	436	22	n.	n.	PROPN
ejpam-5649	436	23	viriyapong	viriyapong	PROPN
ejpam-5649	436	24	,	,	PUNCT
ejpam-5649	436	25	s.	s.	PROPN
ejpam-5649	436	26	sompong	sompong	PROPN
ejpam-5649	436	27	,	,	PUNCT
ejpam-5649	436	28	and	and	CCONJ
ejpam-5649	436	29	c.	c.	PROPN
ejpam-5649	436	30	boonpok	boonpok	PROPN
ejpam-5649	436	31	.	.	PUNCT
ejpam-5649	437	1	upper	upper	ADJ
ejpam-5649	437	2	and	and	CCONJ
ejpam-5649	437	3	lower	low	ADJ
ejpam-5649	437	4	s-(τ1	s-(τ1	NOUN
ejpam-5649	437	5	,	,	PUNCT
ejpam-5649	437	6	τ2)p	τ2)p	ADJ
ejpam-5649	437	7	-	-	PUNCT
ejpam-5649	437	8	continuous	continuous	ADJ
ejpam-5649	437	9	multifunctions	multifunction	NOUN
ejpam-5649	437	10	.	.	PUNCT
ejpam-5649	438	1	european	european	ADJ
ejpam-5649	438	2	journal	journal	PROPN
ejpam-5649	438	3	of	of	ADP
ejpam-5649	438	4	pure	pure	ADJ
ejpam-5649	438	5	and	and	CCONJ
ejpam-5649	438	6	applied	applied	ADJ
ejpam-5649	438	7	mathematics	mathematic	NOUN
ejpam-5649	438	8	,	,	PUNCT
ejpam-5649	438	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-5649	438	10	,	,	PUNCT
ejpam-5649	438	11	2024	2024	NUM
ejpam-5649	438	12	.	.	PUNCT