id	sid	tid	token	lemma	pos
ejpam-6010	1	1	european	european	PROPN
ejpam-6010	1	2	journal	journal	PROPN
ejpam-6010	1	3	of	of	ADP
ejpam-6010	1	4	pure	pure	ADJ
ejpam-6010	1	5	and	and	CCONJ
ejpam-6010	1	6	applied	applied	ADJ
ejpam-6010	1	7	mathematics	mathematic	NOUN
ejpam-6010	1	8	2025	2025	NUM
ejpam-6010	1	9	,	,	PUNCT
ejpam-6010	1	10	vol	vol	NOUN
ejpam-6010	1	11	.	.	PROPN
ejpam-6010	1	12	18	18	NUM
ejpam-6010	1	13	,	,	PUNCT
ejpam-6010	1	14	issue	issue	NOUN
ejpam-6010	1	15	2	2	NUM
ejpam-6010	1	16	,	,	PUNCT
ejpam-6010	1	17	article	article	NOUN
ejpam-6010	1	18	number	number	NOUN
ejpam-6010	1	19	6010	6010	NUM
ejpam-6010	1	20	issn	issn	PROPN
ejpam-6010	1	21	1307	1307	NUM
ejpam-6010	1	22	-	-	SYM
ejpam-6010	1	23	5543	5543	NUM
ejpam-6010	1	24	–	–	PUNCT
ejpam-6010	1	25	ejpam.com	ejpam.com	X
ejpam-6010	1	26	published	publish	VERB
ejpam-6010	1	27	by	by	ADP
ejpam-6010	1	28	new	new	PROPN
ejpam-6010	1	29	york	york	PROPN
ejpam-6010	1	30	business	business	PROPN
ejpam-6010	1	31	global	global	PROPN
ejpam-6010	1	32	upper	upper	ADJ
ejpam-6010	1	33	and	and	CCONJ
ejpam-6010	1	34	lower	low	ADJ
ejpam-6010	1	35	almost	almost	ADV
ejpam-6010	1	36	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	1	37	,	,	PUNCT
ejpam-6010	1	38	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	1	39	jeeranunt	jeeranunt	NOUN
ejpam-6010	1	40	khampakdee1	khampakdee1	PROPN
ejpam-6010	1	41	,	,	PUNCT
ejpam-6010	1	42	areeyuth	areeyuth	NOUN
ejpam-6010	1	43	sama	sama	NOUN
ejpam-6010	1	44	-	-	PUNCT
ejpam-6010	1	45	ae2	ae2	PROPN
ejpam-6010	1	46	,	,	PUNCT
ejpam-6010	1	47	chawalit	chawalit	VERB
ejpam-6010	1	48	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6010	1	49	1	1	NUM
ejpam-6010	1	50	mathematics	mathematic	NOUN
ejpam-6010	1	51	and	and	CCONJ
ejpam-6010	1	52	applied	apply	VERB
ejpam-6010	1	53	mathematics	mathematics	PROPN
ejpam-6010	1	54	research	research	NOUN
ejpam-6010	1	55	unit	unit	NOUN
ejpam-6010	1	56	,	,	PUNCT
ejpam-6010	1	57	department	department	NOUN
ejpam-6010	1	58	of	of	ADP
ejpam-6010	1	59	mathematics	mathematic	NOUN
ejpam-6010	1	60	,	,	PUNCT
ejpam-6010	1	61	faculty	faculty	NOUN
ejpam-6010	1	62	of	of	ADP
ejpam-6010	1	63	science	science	NOUN
ejpam-6010	1	64	,	,	PUNCT
ejpam-6010	1	65	mahasarakham	mahasarakham	PROPN
ejpam-6010	1	66	university	university	PROPN
ejpam-6010	1	67	,	,	PUNCT
ejpam-6010	1	68	maha	maha	PROPN
ejpam-6010	1	69	sarakham	sarakham	PROPN
ejpam-6010	1	70	,	,	PUNCT
ejpam-6010	1	71	44150	44150	NUM
ejpam-6010	1	72	,	,	PUNCT
ejpam-6010	1	73	thailand	thailand	PROPN
ejpam-6010	1	74	2	2	NUM
ejpam-6010	1	75	department	department	NOUN
ejpam-6010	1	76	of	of	ADP
ejpam-6010	1	77	mathematics	mathematic	NOUN
ejpam-6010	1	78	and	and	CCONJ
ejpam-6010	1	79	computer	computer	NOUN
ejpam-6010	1	80	science	science	NOUN
ejpam-6010	1	81	,	,	PUNCT
ejpam-6010	1	82	faculty	faculty	NOUN
ejpam-6010	1	83	of	of	ADP
ejpam-6010	1	84	science	science	NOUN
ejpam-6010	1	85	and	and	CCONJ
ejpam-6010	1	86	technology	technology	NOUN
ejpam-6010	1	87	,	,	PUNCT
ejpam-6010	1	88	prince	prince	NOUN
ejpam-6010	1	89	of	of	ADP
ejpam-6010	1	90	songkla	songkla	PROPN
ejpam-6010	1	91	university	university	PROPN
ejpam-6010	1	92	,	,	PUNCT
ejpam-6010	1	93	pattani	pattani	NOUN
ejpam-6010	1	94	campus	campus	NOUN
ejpam-6010	1	95	,	,	PUNCT
ejpam-6010	1	96	pattani	pattani	NOUN
ejpam-6010	1	97	,	,	PUNCT
ejpam-6010	1	98	94000	94000	NUM
ejpam-6010	1	99	,	,	PUNCT
ejpam-6010	1	100	thailand	thailand	PROPN
ejpam-6010	1	101	abstract	abstract	PROPN
ejpam-6010	1	102	.	.	PUNCT
ejpam-6010	2	1	this	this	DET
ejpam-6010	2	2	paper	paper	NOUN
ejpam-6010	2	3	introduces	introduce	VERB
ejpam-6010	2	4	new	new	ADJ
ejpam-6010	2	5	classes	class	NOUN
ejpam-6010	2	6	of	of	ADP
ejpam-6010	2	7	multifunctions	multifunction	NOUN
ejpam-6010	2	8	between	between	ADP
ejpam-6010	2	9	bitopological	bitopological	ADJ
ejpam-6010	2	10	spaces	space	NOUN
ejpam-6010	2	11	,	,	PUNCT
ejpam-6010	2	12	namely	namely	ADV
ejpam-6010	2	13	upper	upper	ADJ
ejpam-6010	2	14	almost	almost	ADV
ejpam-6010	2	15	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	2	16	,	,	PUNCT
ejpam-6010	2	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	2	18	multifunctions	multifunction	NOUN
ejpam-6010	2	19	and	and	CCONJ
ejpam-6010	2	20	lower	low	ADJ
ejpam-6010	2	21	almost	almost	ADV
ejpam-6010	2	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	2	23	,	,	PUNCT
ejpam-6010	2	24	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	2	25	multifunctions	multifunction	NOUN
ejpam-6010	2	26	.	.	PUNCT
ejpam-6010	3	1	furthermore	furthermore	ADV
ejpam-6010	3	2	,	,	PUNCT
ejpam-6010	3	3	several	several	ADJ
ejpam-6010	3	4	characterizations	characterization	NOUN
ejpam-6010	3	5	of	of	ADP
ejpam-6010	3	6	upper	upper	ADJ
ejpam-6010	3	7	almost	almost	ADV
ejpam-6010	3	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	3	9	,	,	PUNCT
ejpam-6010	3	10	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	3	11	multifunctions	multifunction	NOUN
ejpam-6010	3	12	and	and	CCONJ
ejpam-6010	3	13	lower	low	ADJ
ejpam-6010	3	14	almost	almost	ADV
ejpam-6010	3	15	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	3	16	,	,	PUNCT
ejpam-6010	3	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	3	18	multifunctions	multifunction	NOUN
ejpam-6010	3	19	are	be	AUX
ejpam-6010	3	20	considered	consider	VERB
ejpam-6010	3	21	.	.	PUNCT
ejpam-6010	4	1	2020	2020	NUM
ejpam-6010	4	2	mathematics	mathematic	NOUN
ejpam-6010	4	3	subject	subject	NOUN
ejpam-6010	4	4	classifications	classification	NOUN
ejpam-6010	4	5	:	:	PUNCT
ejpam-6010	4	6	54c08	54c08	NUM
ejpam-6010	4	7	,	,	PUNCT
ejpam-6010	4	8	54c60	54c60	NUM
ejpam-6010	4	9	key	key	ADJ
ejpam-6010	4	10	words	word	NOUN
ejpam-6010	4	11	and	and	CCONJ
ejpam-6010	4	12	phrases	phrase	NOUN
ejpam-6010	4	13	:	:	PUNCT
ejpam-6010	4	14	upper	upper	ADJ
ejpam-6010	4	15	almost	almost	ADV
ejpam-6010	4	16	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	4	17	,	,	PUNCT
ejpam-6010	4	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	4	19	multifunction	multifunction	NOUN
ejpam-6010	4	20	,	,	PUNCT
ejpam-6010	4	21	lower	low	ADJ
ejpam-6010	4	22	almost	almost	ADV
ejpam-6010	4	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	4	24	,	,	PUNCT
ejpam-6010	4	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	4	26	multifunction	multifunction	NOUN
ejpam-6010	4	27	1	1	NUM
ejpam-6010	4	28	.	.	PUNCT
ejpam-6010	5	1	introduction	introduction	NOUN
ejpam-6010	5	2	it	it	PRON
ejpam-6010	5	3	is	be	AUX
ejpam-6010	5	4	well	well	ADV
ejpam-6010	5	5	-	-	PUNCT
ejpam-6010	5	6	known	know	VERB
ejpam-6010	5	7	that	that	SCONJ
ejpam-6010	5	8	the	the	DET
ejpam-6010	5	9	branch	branch	NOUN
ejpam-6010	5	10	of	of	ADP
ejpam-6010	5	11	mathematics	mathematic	NOUN
ejpam-6010	5	12	called	call	VERB
ejpam-6010	5	13	topology	topology	NOUN
ejpam-6010	5	14	is	be	AUX
ejpam-6010	5	15	concerned	concern	VERB
ejpam-6010	5	16	with	with	ADP
ejpam-6010	5	17	all	all	DET
ejpam-6010	5	18	questions	question	NOUN
ejpam-6010	5	19	directly	directly	ADV
ejpam-6010	5	20	or	or	CCONJ
ejpam-6010	5	21	indirectly	indirectly	ADV
ejpam-6010	5	22	related	relate	VERB
ejpam-6010	5	23	to	to	ADP
ejpam-6010	5	24	continuity	continuity	NOUN
ejpam-6010	5	25	.	.	PUNCT
ejpam-6010	6	1	stronger	strong	ADJ
ejpam-6010	6	2	and	and	CCONJ
ejpam-6010	6	3	weaker	weak	ADJ
ejpam-6010	6	4	forms	form	NOUN
ejpam-6010	6	5	of	of	ADP
ejpam-6010	6	6	open	open	ADJ
ejpam-6010	6	7	sets	set	NOUN
ejpam-6010	6	8	play	play	VERB
ejpam-6010	6	9	an	an	DET
ejpam-6010	6	10	important	important	ADJ
ejpam-6010	6	11	role	role	NOUN
ejpam-6010	6	12	in	in	ADP
ejpam-6010	6	13	the	the	DET
ejpam-6010	6	14	generalization	generalization	NOUN
ejpam-6010	6	15	of	of	ADP
ejpam-6010	6	16	different	different	ADJ
ejpam-6010	6	17	forms	form	NOUN
ejpam-6010	6	18	of	of	ADP
ejpam-6010	6	19	continuity	continuity	NOUN
ejpam-6010	6	20	.	.	PUNCT
ejpam-6010	7	1	using	use	VERB
ejpam-6010	7	2	different	different	ADJ
ejpam-6010	7	3	forms	form	NOUN
ejpam-6010	7	4	of	of	ADP
ejpam-6010	7	5	open	open	ADJ
ejpam-6010	7	6	sets	set	NOUN
ejpam-6010	7	7	,	,	PUNCT
ejpam-6010	7	8	many	many	ADJ
ejpam-6010	7	9	authors	author	NOUN
ejpam-6010	7	10	have	have	AUX
ejpam-6010	7	11	introduced	introduce	VERB
ejpam-6010	7	12	and	and	CCONJ
ejpam-6010	7	13	studied	study	VERB
ejpam-6010	7	14	various	various	ADJ
ejpam-6010	7	15	types	type	NOUN
ejpam-6010	7	16	of	of	ADP
ejpam-6010	7	17	continuity	continuity	NOUN
ejpam-6010	7	18	for	for	ADP
ejpam-6010	7	19	functions	function	NOUN
ejpam-6010	7	20	and	and	CCONJ
ejpam-6010	7	21	multifunctions	multifunction	NOUN
ejpam-6010	7	22	.	.	PUNCT
ejpam-6010	8	1	in	in	ADP
ejpam-6010	8	2	[	[	X
ejpam-6010	8	3	1	1	NUM
ejpam-6010	8	4	]	]	PUNCT
ejpam-6010	8	5	,	,	PUNCT
ejpam-6010	8	6	the	the	DET
ejpam-6010	8	7	present	present	ADJ
ejpam-6010	8	8	authors	author	NOUN
ejpam-6010	8	9	studied	study	VERB
ejpam-6010	8	10	some	some	DET
ejpam-6010	8	11	properties	property	NOUN
ejpam-6010	8	12	of	of	ADP
ejpam-6010	8	13	(	(	PUNCT
ejpam-6010	8	14	λ	λ	PROPN
ejpam-6010	8	15	,	,	PUNCT
ejpam-6010	8	16	sp)-open	sp)-open	ADJ
ejpam-6010	8	17	sets	set	NOUN
ejpam-6010	8	18	,	,	PUNCT
ejpam-6010	8	19	r(λ	r(λ	NOUN
ejpam-6010	8	20	,	,	PUNCT
ejpam-6010	8	21	sp)-open	sp)-open	ADJ
ejpam-6010	8	22	sets	set	NOUN
ejpam-6010	8	23	,	,	PUNCT
ejpam-6010	8	24	s(λ	s(λ	PROPN
ejpam-6010	8	25	,	,	PUNCT
ejpam-6010	8	26	sp)-open	sp)-open	ADJ
ejpam-6010	8	27	sets	set	NOUN
ejpam-6010	8	28	,	,	PUNCT
ejpam-6010	8	29	p(λ	p(λ	NOUN
ejpam-6010	8	30	,	,	PUNCT
ejpam-6010	8	31	sp)-open	sp)-open	ADJ
ejpam-6010	8	32	sets	set	NOUN
ejpam-6010	8	33	,	,	PUNCT
ejpam-6010	8	34	α(λ	α(λ	PROPN
ejpam-6010	8	35	,	,	PUNCT
ejpam-6010	8	36	sp)-open	sp)-open	ADJ
ejpam-6010	8	37	sets	set	NOUN
ejpam-6010	8	38	,	,	PUNCT
ejpam-6010	8	39	β(λ	β(λ	X
ejpam-6010	8	40	,	,	PUNCT
ejpam-6010	8	41	sp)-open	sp)-open	ADJ
ejpam-6010	8	42	sets	set	NOUN
ejpam-6010	8	43	and	and	CCONJ
ejpam-6010	8	44	b(λ	b(λ	NOUN
ejpam-6010	8	45	,	,	PUNCT
ejpam-6010	8	46	sp)-open	sp)-open	ADJ
ejpam-6010	8	47	sets	set	NOUN
ejpam-6010	8	48	.	.	PUNCT
ejpam-6010	9	1	viriyapong	viriyapong	VERB
ejpam-6010	9	2	and	and	CCONJ
ejpam-6010	9	3	boonpok	boonpok	VERB
ejpam-6010	10	1	[	[	X
ejpam-6010	10	2	2	2	NUM
ejpam-6010	10	3	]	]	PUNCT
ejpam-6010	10	4	investigated	investigate	VERB
ejpam-6010	10	5	some	some	DET
ejpam-6010	10	6	characterizations	characterization	NOUN
ejpam-6010	10	7	of	of	ADP
ejpam-6010	10	8	(	(	PUNCT
ejpam-6010	10	9	λ	λ	PROPN
ejpam-6010	10	10	,	,	PUNCT
ejpam-6010	10	11	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	10	12	functions	function	NOUN
ejpam-6010	10	13	by	by	ADP
ejpam-6010	10	14	utilizing	utilize	VERB
ejpam-6010	10	15	the	the	DET
ejpam-6010	10	16	notions	notion	NOUN
ejpam-6010	10	17	of	of	ADP
ejpam-6010	10	18	(	(	PUNCT
ejpam-6010	10	19	λ	λ	PROPN
ejpam-6010	10	20	,	,	PUNCT
ejpam-6010	10	21	sp)-open	sp)-open	ADJ
ejpam-6010	10	22	sets	set	NOUN
ejpam-6010	10	23	and	and	CCONJ
ejpam-6010	10	24	(	(	PUNCT
ejpam-6010	10	25	λ	λ	PROPN
ejpam-6010	10	26	,	,	PUNCT
ejpam-6010	10	27	sp)-closed	sp)-close	VERB
ejpam-6010	10	28	sets	set	NOUN
ejpam-6010	10	29	.	.	PUNCT
ejpam-6010	11	1	dungthaisong	dungthaisong	NOUN
ejpam-6010	11	2	et	et	PROPN
ejpam-6010	11	3	al	al	PROPN
ejpam-6010	11	4	.	.	PUNCT
ejpam-6010	12	1	[	[	X
ejpam-6010	12	2	3	3	NUM
ejpam-6010	12	3	]	]	PUNCT
ejpam-6010	12	4	introduced	introduce	VERB
ejpam-6010	12	5	and	and	CCONJ
ejpam-6010	12	6	studied	study	VERB
ejpam-6010	12	7	the	the	DET
ejpam-6010	12	8	concept	concept	NOUN
ejpam-6010	12	9	of	of	ADP
ejpam-6010	12	10	g(m	g(m	ADJ
ejpam-6010	12	11	,	,	PUNCT
ejpam-6010	12	12	n)-continuous	n)-continuous	ADJ
ejpam-6010	12	13	functions	function	NOUN
ejpam-6010	12	14	.	.	PUNCT
ejpam-6010	13	1	duangphui	duangphui	NOUN
ejpam-6010	13	2	et	et	PROPN
ejpam-6010	13	3	al	al	PROPN
ejpam-6010	13	4	.	.	PUNCT
ejpam-6010	14	1	[	[	X
ejpam-6010	14	2	4	4	X
ejpam-6010	14	3	]	]	PUNCT
ejpam-6010	14	4	introduced	introduce	VERB
ejpam-6010	14	5	and	and	CCONJ
ejpam-6010	14	6	investigated	investigate	VERB
ejpam-6010	14	7	the	the	DET
ejpam-6010	14	8	notion	notion	NOUN
ejpam-6010	14	9	of	of	ADP
ejpam-6010	14	10	almost	almost	ADV
ejpam-6010	14	11	(	(	PUNCT
ejpam-6010	14	12	µ	µ	NUM
ejpam-6010	14	13	,	,	PUNCT
ejpam-6010	14	14	µ′)(m	µ′)(m	VERB
ejpam-6010	14	15	,	,	PUNCT
ejpam-6010	14	16	n)-continuous	n)-continuous	ADJ
ejpam-6010	14	17	functions	function	NOUN
ejpam-6010	14	18	.	.	PUNCT
ejpam-6010	15	1	furthermore	furthermore	ADV
ejpam-6010	15	2	,	,	PUNCT
ejpam-6010	15	3	several	several	ADJ
ejpam-6010	15	4	characterizations	characterization	NOUN
ejpam-6010	15	5	of	of	ADP
ejpam-6010	15	6	almost	almost	ADV
ejpam-6010	15	7	(	(	PUNCT
ejpam-6010	15	8	λ	λ	PROPN
ejpam-6010	15	9	,	,	PUNCT
ejpam-6010	15	10	p)-continuous	p)-continuous	ADJ
ejpam-6010	15	11	functions	function	NOUN
ejpam-6010	15	12	,	,	PUNCT
ejpam-6010	15	13	strongly	strongly	ADV
ejpam-6010	15	14	θ(λ	θ(λ	PROPN
ejpam-6010	15	15	,	,	PUNCT
ejpam-6010	15	16	p)-continuous	p)-continuous	ADJ
ejpam-6010	15	17	functions	function	NOUN
ejpam-6010	15	18	,	,	PUNCT
ejpam-6010	15	19	almost	almost	ADV
ejpam-6010	15	20	strongly	strongly	ADV
ejpam-6010	15	21	θ(λ	θ(λ	VERB
ejpam-6010	15	22	,	,	PUNCT
ejpam-6010	15	23	p)-continuous	p)-continuous	ADJ
ejpam-6010	15	24	functions	function	NOUN
ejpam-6010	15	25	,	,	PUNCT
ejpam-6010	15	26	θ(λ	θ(λ	PROPN
ejpam-6010	15	27	,	,	PUNCT
ejpam-6010	15	28	p)-continuous	p)-continuous	ADJ
ejpam-6010	15	29	functions	function	NOUN
ejpam-6010	15	30	,	,	PUNCT
ejpam-6010	15	31	weakly	weakly	ADJ
ejpam-6010	15	32	(	(	PUNCT
ejpam-6010	15	33	λ	λ	PROPN
ejpam-6010	15	34	,	,	PUNCT
ejpam-6010	15	35	b)-continuous	b)-continuous	ADJ
ejpam-6010	15	36	functions	function	NOUN
ejpam-6010	15	37	,	,	PUNCT
ejpam-6010	15	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-6010	15	39	functions	function	NOUN
ejpam-6010	15	40	,	,	PUNCT
ejpam-6010	15	41	(	(	PUNCT
ejpam-6010	15	42	λ	λ	NOUN
ejpam-6010	15	43	,	,	PUNCT
ejpam-6010	15	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-6010	15	45	functions	function	NOUN
ejpam-6010	15	46	,	,	PUNCT
ejpam-6010	15	47	∗corresponding	∗corresponde	VERB
ejpam-6010	15	48	author	author	NOUN
ejpam-6010	15	49	.	.	PUNCT
ejpam-6010	16	1	doi	doi	NOUN
ejpam-6010	16	2	:	:	PUNCT
ejpam-6010	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6010	https://doi.org/10.29020/nybg.ejpam.v18i2.6010	NOUN
ejpam-6010	16	4	email	email	NOUN
ejpam-6010	16	5	addresses	address	VERB
ejpam-6010	16	6	:	:	PUNCT
ejpam-6010	16	7	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-6010	16	8	(	(	PUNCT
ejpam-6010	16	9	j.	j.	PROPN
ejpam-6010	16	10	khampakdee	khampakdee	PROPN
ejpam-6010	16	11	)	)	PUNCT
ejpam-6010	16	12	,	,	PUNCT
ejpam-6010	16	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-6010	16	14	(	(	PUNCT
ejpam-6010	16	15	a.	a.	PROPN
ejpam-6010	16	16	sama	sama	PROPN
ejpam-6010	16	17	-	-	PUNCT
ejpam-6010	16	18	ae	ae	PROPN
ejpam-6010	16	19	)	)	PUNCT
ejpam-6010	16	20	,	,	PUNCT
ejpam-6010	16	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6010	16	22	(	(	PUNCT
ejpam-6010	16	23	c.	c.	PROPN
ejpam-6010	16	24	boonpok	boonpok	PROPN
ejpam-6010	16	25	)	)	PUNCT
ejpam-6010	16	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6010	17	1	1	1	NUM
ejpam-6010	17	2	copyright	copyright	NOUN
ejpam-6010	17	3	:	:	PUNCT
ejpam-6010	17	4	©	©	PROPN
ejpam-6010	17	5	2025	2025	NUM
ejpam-6010	17	6	the	the	DET
ejpam-6010	17	7	author(s	author(s	NOUN
ejpam-6010	17	8	)	)	PUNCT
ejpam-6010	17	9	.	.	PUNCT
ejpam-6010	18	1	(	(	PUNCT
ejpam-6010	18	2	cc	cc	NOUN
ejpam-6010	18	3	by	by	ADP
ejpam-6010	18	4	-	-	PUNCT
ejpam-6010	18	5	nc	nc	PROPN
ejpam-6010	18	6	4.0	4.0	NUM
ejpam-6010	18	7	)	)	PUNCT
ejpam-6010	18	8	j.	j.	PROPN
ejpam-6010	18	9	khampakdee	khampakdee	PROPN
ejpam-6010	18	10	,	,	PUNCT
ejpam-6010	18	11	a.	a.	PROPN
ejpam-6010	18	12	sama	sama	PROPN
ejpam-6010	18	13	-	-	PUNCT
ejpam-6010	18	14	ae	ae	PROPN
ejpam-6010	18	15	,	,	PUNCT
ejpam-6010	18	16	c.	c.	PROPN
ejpam-6010	18	17	boonpok	boonpok	PROPN
ejpam-6010	18	18	/	/	SYM
ejpam-6010	18	19	eur	eur	PROPN
ejpam-6010	18	20	.	.	PUNCT
ejpam-6010	19	1	j.	j.	PROPN
ejpam-6010	19	2	pure	pure	PROPN
ejpam-6010	19	3	appl	appl	PROPN
ejpam-6010	19	4	.	.	PROPN
ejpam-6010	19	5	math	math	PROPN
ejpam-6010	19	6	,	,	PUNCT
ejpam-6010	19	7	18	18	NUM
ejpam-6010	19	8	(	(	PUNCT
ejpam-6010	19	9	2	2	NUM
ejpam-6010	19	10	)	)	PUNCT
ejpam-6010	19	11	(	(	PUNCT
ejpam-6010	19	12	2025	2025	NUM
ejpam-6010	19	13	)	)	PUNCT
ejpam-6010	19	14	,	,	PUNCT
ejpam-6010	19	15	6010	6010	NUM
ejpam-6010	19	16	2	2	NUM
ejpam-6010	19	17	of	of	ADP
ejpam-6010	19	18	19	19	NUM
ejpam-6010	19	19	⋆-continuous	⋆-continuous	ADJ
ejpam-6010	19	20	functions	function	NOUN
ejpam-6010	19	21	,	,	PUNCT
ejpam-6010	19	22	θ	θ	PROPN
ejpam-6010	19	23	-	-	ADJ
ejpam-6010	19	24	i	i	NOUN
ejpam-6010	19	25	-continuous	-continuous	ADJ
ejpam-6010	19	26	functions	function	NOUN
ejpam-6010	19	27	,	,	PUNCT
ejpam-6010	19	28	almost	almost	ADV
ejpam-6010	19	29	(	(	PUNCT
ejpam-6010	19	30	g	g	NOUN
ejpam-6010	19	31	,	,	PUNCT
ejpam-6010	19	32	m)-continuous	m)-continuous	ADJ
ejpam-6010	19	33	functions	function	NOUN
ejpam-6010	19	34	,	,	PUNCT
ejpam-6010	19	35	pairwise	pairwise	NOUN
ejpam-6010	19	36	almost	almost	ADV
ejpam-6010	19	37	m	m	VERB
ejpam-6010	19	38	-continuous	-continuous	ADJ
ejpam-6010	19	39	functions	function	NOUN
ejpam-6010	19	40	,	,	PUNCT
ejpam-6010	19	41	(	(	PUNCT
ejpam-6010	19	42	τ1	τ1	NOUN
ejpam-6010	19	43	,	,	PUNCT
ejpam-6010	19	44	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	19	45	functions	function	NOUN
ejpam-6010	19	46	,	,	PUNCT
ejpam-6010	19	47	almost	almost	ADV
ejpam-6010	19	48	(	(	PUNCT
ejpam-6010	19	49	τ1	τ1	NOUN
ejpam-6010	19	50	,	,	PUNCT
ejpam-6010	19	51	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	19	52	functions	function	NOUN
ejpam-6010	19	53	,	,	PUNCT
ejpam-6010	19	54	weakly	weakly	ADJ
ejpam-6010	19	55	(	(	PUNCT
ejpam-6010	19	56	τ1	τ1	NOUN
ejpam-6010	19	57	,	,	PUNCT
ejpam-6010	19	58	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	19	59	functions	function	NOUN
ejpam-6010	19	60	and	and	CCONJ
ejpam-6010	19	61	slightly	slightly	ADV
ejpam-6010	19	62	(	(	PUNCT
ejpam-6010	19	63	τ1	τ1	NOUN
ejpam-6010	19	64	,	,	PUNCT
ejpam-6010	19	65	τ2)s	τ2)s	ADJ
ejpam-6010	19	66	-	-	PUNCT
ejpam-6010	19	67	continuous	continuous	ADJ
ejpam-6010	19	68	functions	function	NOUN
ejpam-6010	19	69	were	be	AUX
ejpam-6010	19	70	presented	present	VERB
ejpam-6010	19	71	in	in	ADP
ejpam-6010	19	72	[	[	X
ejpam-6010	19	73	5	5	NUM
ejpam-6010	19	74	]	]	PUNCT
ejpam-6010	19	75	,	,	PUNCT
ejpam-6010	19	76	[	[	X
ejpam-6010	19	77	6	6	NUM
ejpam-6010	19	78	]	]	PUNCT
ejpam-6010	19	79	,	,	PUNCT
ejpam-6010	19	80	[	[	X
ejpam-6010	19	81	7	7	NUM
ejpam-6010	19	82	]	]	PUNCT
ejpam-6010	19	83	,	,	PUNCT
ejpam-6010	19	84	[	[	X
ejpam-6010	19	85	8	8	NUM
ejpam-6010	19	86	]	]	PUNCT
ejpam-6010	19	87	,	,	PUNCT
ejpam-6010	19	88	[	[	X
ejpam-6010	19	89	9	9	NUM
ejpam-6010	19	90	]	]	PUNCT
ejpam-6010	19	91	,	,	PUNCT
ejpam-6010	19	92	[	[	X
ejpam-6010	19	93	10	10	NUM
ejpam-6010	19	94	]	]	PUNCT
ejpam-6010	19	95	,	,	PUNCT
ejpam-6010	19	96	[	[	X
ejpam-6010	19	97	11	11	NUM
ejpam-6010	19	98	]	]	PUNCT
ejpam-6010	19	99	,	,	PUNCT
ejpam-6010	19	100	[	[	X
ejpam-6010	19	101	12	12	NUM
ejpam-6010	19	102	]	]	PUNCT
ejpam-6010	19	103	,	,	PUNCT
ejpam-6010	19	104	[	[	X
ejpam-6010	19	105	13	13	NUM
ejpam-6010	19	106	]	]	PUNCT
ejpam-6010	19	107	,	,	PUNCT
ejpam-6010	19	108	[	[	X
ejpam-6010	19	109	14	14	NUM
ejpam-6010	19	110	]	]	PUNCT
ejpam-6010	19	111	,	,	PUNCT
ejpam-6010	19	112	[	[	X
ejpam-6010	19	113	15	15	NUM
ejpam-6010	19	114	]	]	PUNCT
ejpam-6010	19	115	,	,	PUNCT
ejpam-6010	19	116	[	[	X
ejpam-6010	19	117	16	16	NUM
ejpam-6010	19	118	]	]	PUNCT
ejpam-6010	19	119	,	,	PUNCT
ejpam-6010	19	120	[	[	X
ejpam-6010	19	121	17	17	NUM
ejpam-6010	19	122	]	]	PUNCT
ejpam-6010	19	123	,	,	PUNCT
ejpam-6010	19	124	[	[	X
ejpam-6010	19	125	18	18	NUM
ejpam-6010	19	126	]	]	PUNCT
ejpam-6010	19	127	and	and	CCONJ
ejpam-6010	19	128	[	[	X
ejpam-6010	19	129	19	19	NUM
ejpam-6010	19	130	]	]	PUNCT
ejpam-6010	19	131	,	,	PUNCT
ejpam-6010	19	132	respectively	respectively	ADV
ejpam-6010	19	133	.	.	PUNCT
ejpam-6010	20	1	kong	kong	PROPN
ejpam-6010	20	2	-	-	PUNCT
ejpam-6010	20	3	ied	ied	PROPN
ejpam-6010	20	4	at	at	ADP
ejpam-6010	20	5	al	al	PROPN
ejpam-6010	20	6	.	.	PUNCT
ejpam-6010	21	1	[	[	X
ejpam-6010	21	2	20	20	NUM
ejpam-6010	21	3	]	]	PUNCT
ejpam-6010	21	4	introduced	introduce	VERB
ejpam-6010	21	5	and	and	CCONJ
ejpam-6010	21	6	studied	study	VERB
ejpam-6010	21	7	the	the	DET
ejpam-6010	21	8	concept	concept	NOUN
ejpam-6010	21	9	of	of	ADP
ejpam-6010	21	10	almost	almost	ADV
ejpam-6010	21	11	quasi	quasi	X
ejpam-6010	21	12	(	(	PUNCT
ejpam-6010	21	13	τ1	τ1	NOUN
ejpam-6010	21	14	,	,	PUNCT
ejpam-6010	21	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	21	16	functions	function	NOUN
ejpam-6010	21	17	.	.	PUNCT
ejpam-6010	22	1	chiangpradit	chiangpradit	NOUN
ejpam-6010	22	2	et	et	PROPN
ejpam-6010	22	3	al	al	PROPN
ejpam-6010	22	4	.	.	PUNCT
ejpam-6010	23	1	[	[	X
ejpam-6010	23	2	21	21	NUM
ejpam-6010	23	3	]	]	PUNCT
ejpam-6010	23	4	introduced	introduce	VERB
ejpam-6010	23	5	and	and	CCONJ
ejpam-6010	23	6	investigated	investigate	VERB
ejpam-6010	23	7	the	the	DET
ejpam-6010	23	8	notion	notion	NOUN
ejpam-6010	23	9	of	of	ADP
ejpam-6010	23	10	weakly	weakly	ADJ
ejpam-6010	23	11	quasi	quasi	NOUN
ejpam-6010	23	12	(	(	PUNCT
ejpam-6010	23	13	τ1	τ1	PROPN
ejpam-6010	23	14	,	,	PUNCT
ejpam-6010	23	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	23	16	functions	function	NOUN
ejpam-6010	23	17	.	.	PUNCT
ejpam-6010	24	1	thongmoon	thongmoon	NOUN
ejpam-6010	24	2	et	et	PROPN
ejpam-6010	24	3	al	al	PROPN
ejpam-6010	24	4	.	.	PUNCT
ejpam-6010	25	1	[	[	X
ejpam-6010	25	2	22	22	NUM
ejpam-6010	25	3	]	]	PUNCT
ejpam-6010	25	4	introduced	introduce	VERB
ejpam-6010	25	5	and	and	CCONJ
ejpam-6010	25	6	studied	study	VERB
ejpam-6010	25	7	the	the	DET
ejpam-6010	25	8	notion	notion	NOUN
ejpam-6010	25	9	of	of	ADP
ejpam-6010	25	10	rarely	rarely	ADV
ejpam-6010	25	11	(	(	PUNCT
ejpam-6010	25	12	τ1	τ1	NOUN
ejpam-6010	25	13	,	,	PUNCT
ejpam-6010	25	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	25	15	functions	function	NOUN
ejpam-6010	25	16	.	.	PUNCT
ejpam-6010	26	1	srisarakham	srisarakham	PROPN
ejpam-6010	26	2	et	et	PROPN
ejpam-6010	26	3	al	al	PROPN
ejpam-6010	26	4	.	.	PUNCT
ejpam-6010	27	1	[	[	X
ejpam-6010	27	2	23	23	NUM
ejpam-6010	27	3	]	]	PUNCT
ejpam-6010	27	4	introduced	introduce	VERB
ejpam-6010	27	5	and	and	CCONJ
ejpam-6010	27	6	investigated	investigate	VERB
ejpam-6010	27	7	the	the	DET
ejpam-6010	27	8	concept	concept	NOUN
ejpam-6010	27	9	of	of	ADP
ejpam-6010	27	10	faintly	faintly	ADV
ejpam-6010	27	11	(	(	PUNCT
ejpam-6010	27	12	τ1	τ1	PROPN
ejpam-6010	27	13	,	,	PUNCT
ejpam-6010	27	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	27	15	functions	function	NOUN
ejpam-6010	27	16	.	.	PUNCT
ejpam-6010	28	1	on	on	ADP
ejpam-6010	28	2	the	the	DET
ejpam-6010	28	3	other	other	ADJ
ejpam-6010	28	4	hand	hand	NOUN
ejpam-6010	28	5	,	,	PUNCT
ejpam-6010	28	6	the	the	DET
ejpam-6010	28	7	present	present	ADJ
ejpam-6010	28	8	authors	author	NOUN
ejpam-6010	28	9	introduced	introduce	VERB
ejpam-6010	28	10	and	and	CCONJ
ejpam-6010	28	11	studied	study	VERB
ejpam-6010	28	12	the	the	DET
ejpam-6010	28	13	notions	notion	NOUN
ejpam-6010	28	14	of	of	ADP
ejpam-6010	28	15	δ(τ1	δ(τ1	NOUN
ejpam-6010	28	16	,	,	PUNCT
ejpam-6010	28	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	28	18	functions	function	NOUN
ejpam-6010	28	19	[	[	X
ejpam-6010	28	20	24	24	NUM
ejpam-6010	28	21	]	]	PUNCT
ejpam-6010	28	22	,	,	PUNCT
ejpam-6010	28	23	quasi	quasi	NOUN
ejpam-6010	28	24	θ(τ1	θ(τ1	PROPN
ejpam-6010	28	25	,	,	PUNCT
ejpam-6010	28	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	28	27	functions	function	NOUN
ejpam-6010	28	28	[	[	X
ejpam-6010	28	29	25	25	NUM
ejpam-6010	28	30	]	]	PUNCT
ejpam-6010	28	31	,	,	PUNCT
ejpam-6010	28	32	almost	almost	ADV
ejpam-6010	28	33	weakly	weakly	ADJ
ejpam-6010	28	34	(	(	PUNCT
ejpam-6010	28	35	τ1	τ1	NOUN
ejpam-6010	28	36	,	,	PUNCT
ejpam-6010	28	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	28	38	functions	function	NOUN
ejpam-6010	28	39	[	[	X
ejpam-6010	28	40	26	26	NUM
ejpam-6010	28	41	]	]	PUNCT
ejpam-6010	28	42	and	and	CCONJ
ejpam-6010	28	43	almost	almost	ADV
ejpam-6010	28	44	nearly	nearly	ADV
ejpam-6010	28	45	(	(	PUNCT
ejpam-6010	28	46	τ1	τ1	NOUN
ejpam-6010	28	47	,	,	PUNCT
ejpam-6010	28	48	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	28	49	functions	function	NOUN
ejpam-6010	28	50	[	[	X
ejpam-6010	28	51	27	27	NUM
ejpam-6010	28	52	]	]	PUNCT
ejpam-6010	28	53	.	.	PUNCT
ejpam-6010	29	1	the	the	DET
ejpam-6010	29	2	notion	notion	NOUN
ejpam-6010	29	3	of	of	ADP
ejpam-6010	29	4	contracontinuity	contracontinuity	NOUN
ejpam-6010	29	5	in	in	ADP
ejpam-6010	29	6	topological	topological	ADJ
ejpam-6010	29	7	spaces	space	NOUN
ejpam-6010	29	8	was	be	AUX
ejpam-6010	29	9	introduced	introduce	VERB
ejpam-6010	29	10	by	by	ADP
ejpam-6010	29	11	dontchev	dontchev	NOUN
ejpam-6010	29	12	[	[	X
ejpam-6010	29	13	28	28	NUM
ejpam-6010	29	14	]	]	PUNCT
ejpam-6010	29	15	.	.	PUNCT
ejpam-6010	30	1	dontchev	dontchev	NOUN
ejpam-6010	30	2	and	and	CCONJ
ejpam-6010	30	3	noiri	noiri	ADV
ejpam-6010	31	1	[	[	X
ejpam-6010	31	2	29	29	NUM
ejpam-6010	31	3	]	]	PUNCT
ejpam-6010	31	4	introduced	introduce	VERB
ejpam-6010	31	5	and	and	CCONJ
ejpam-6010	31	6	studied	study	VERB
ejpam-6010	31	7	the	the	DET
ejpam-6010	31	8	concept	concept	NOUN
ejpam-6010	31	9	of	of	ADP
ejpam-6010	31	10	rc	rc	NOUN
ejpam-6010	31	11	-	-	NOUN
ejpam-6010	31	12	continuity	continuity	NOUN
ejpam-6010	31	13	between	between	ADP
ejpam-6010	31	14	topological	topological	ADJ
ejpam-6010	31	15	spaces	space	NOUN
ejpam-6010	31	16	which	which	PRON
ejpam-6010	31	17	is	be	AUX
ejpam-6010	31	18	weaker	weak	ADJ
ejpam-6010	31	19	than	than	ADP
ejpam-6010	31	20	contra	contra	NOUN
ejpam-6010	31	21	-	-	NOUN
ejpam-6010	31	22	continuity	continuity	NOUN
ejpam-6010	31	23	.	.	PUNCT
ejpam-6010	32	1	jafari	jafari	PROPN
ejpam-6010	32	2	and	and	CCONJ
ejpam-6010	32	3	noiri	noiri	ADV
ejpam-6010	33	1	[	[	X
ejpam-6010	33	2	30	30	NUM
ejpam-6010	33	3	]	]	PUNCT
ejpam-6010	33	4	introduced	introduce	VERB
ejpam-6010	33	5	a	a	DET
ejpam-6010	33	6	new	new	ADJ
ejpam-6010	33	7	class	class	NOUN
ejpam-6010	33	8	of	of	ADP
ejpam-6010	33	9	functions	function	NOUN
ejpam-6010	33	10	called	call	VERB
ejpam-6010	33	11	contra	contra	ADJ
ejpam-6010	33	12	-	-	ADJ
ejpam-6010	33	13	precontinuous	precontinuous	ADJ
ejpam-6010	33	14	functions	function	NOUN
ejpam-6010	33	15	which	which	PRON
ejpam-6010	33	16	is	be	AUX
ejpam-6010	33	17	weaker	weak	ADJ
ejpam-6010	33	18	than	than	ADP
ejpam-6010	33	19	contra	contra	ADJ
ejpam-6010	33	20	-	-	ADJ
ejpam-6010	33	21	continuous	continuous	ADJ
ejpam-6010	33	22	functions	function	NOUN
ejpam-6010	33	23	and	and	CCONJ
ejpam-6010	33	24	studied	study	VERB
ejpam-6010	33	25	several	several	ADJ
ejpam-6010	33	26	basic	basic	ADJ
ejpam-6010	33	27	properties	property	NOUN
ejpam-6010	33	28	of	of	ADP
ejpam-6010	33	29	contra	contra	ADJ
ejpam-6010	33	30	-	-	ADJ
ejpam-6010	33	31	precontinuous	precontinuous	ADJ
ejpam-6010	33	32	functions	function	NOUN
ejpam-6010	33	33	.	.	PUNCT
ejpam-6010	34	1	ekici	ekici	NOUN
ejpam-6010	35	1	[	[	X
ejpam-6010	35	2	31	31	NUM
ejpam-6010	35	3	]	]	PUNCT
ejpam-6010	35	4	introduced	introduce	VERB
ejpam-6010	35	5	and	and	CCONJ
ejpam-6010	35	6	studied	study	VERB
ejpam-6010	35	7	a	a	DET
ejpam-6010	35	8	new	new	ADJ
ejpam-6010	35	9	class	class	NOUN
ejpam-6010	35	10	of	of	ADP
ejpam-6010	35	11	functions	function	NOUN
ejpam-6010	35	12	called	call	VERB
ejpam-6010	35	13	almost	almost	ADV
ejpam-6010	35	14	contra	contra	ADJ
ejpam-6010	35	15	-	-	ADJ
ejpam-6010	35	16	precontinuous	precontinuous	ADJ
ejpam-6010	35	17	functions	function	NOUN
ejpam-6010	35	18	which	which	PRON
ejpam-6010	35	19	generalize	generalize	VERB
ejpam-6010	35	20	classes	class	NOUN
ejpam-6010	35	21	of	of	ADP
ejpam-6010	35	22	regular	regular	ADJ
ejpam-6010	35	23	set	set	NOUN
ejpam-6010	35	24	-	-	PUNCT
ejpam-6010	35	25	connected	connect	VERB
ejpam-6010	35	26	functions	function	NOUN
ejpam-6010	35	27	[	[	X
ejpam-6010	35	28	32	32	NUM
ejpam-6010	35	29	]	]	PUNCT
ejpam-6010	35	30	,	,	PUNCT
ejpam-6010	35	31	contra	contra	ADJ
ejpam-6010	35	32	-	-	ADJ
ejpam-6010	35	33	precontinuous	precontinuous	ADJ
ejpam-6010	35	34	functions	function	NOUN
ejpam-6010	35	35	[	[	X
ejpam-6010	35	36	30	30	NUM
ejpam-6010	35	37	]	]	PUNCT
ejpam-6010	35	38	,	,	PUNCT
ejpam-6010	35	39	contra	contra	ADJ
ejpam-6010	35	40	-	-	ADJ
ejpam-6010	35	41	continuous	continuous	ADJ
ejpam-6010	35	42	functions	function	NOUN
ejpam-6010	35	43	[	[	X
ejpam-6010	35	44	28	28	NUM
ejpam-6010	35	45	]	]	X
ejpam-6010	35	46	,	,	PUNCT
ejpam-6010	35	47	almost	almost	ADV
ejpam-6010	35	48	s	s	NOUN
ejpam-6010	35	49	-	-	PUNCT
ejpam-6010	35	50	continuous	continuous	ADJ
ejpam-6010	35	51	functions	function	NOUN
ejpam-6010	35	52	[	[	X
ejpam-6010	35	53	33	33	NUM
ejpam-6010	35	54	]	]	PUNCT
ejpam-6010	35	55	and	and	CCONJ
ejpam-6010	35	56	perfectly	perfectly	ADV
ejpam-6010	35	57	continuous	continuous	ADJ
ejpam-6010	35	58	functions	function	NOUN
ejpam-6010	35	59	[	[	X
ejpam-6010	35	60	34	34	NUM
ejpam-6010	35	61	]	]	PUNCT
ejpam-6010	35	62	.	.	PUNCT
ejpam-6010	36	1	in	in	ADP
ejpam-6010	36	2	2008	2008	NUM
ejpam-6010	36	3	,	,	PUNCT
ejpam-6010	36	4	ekici	ekici	NOUN
ejpam-6010	36	5	et	et	PROPN
ejpam-6010	36	6	al	al	PROPN
ejpam-6010	36	7	.	.	PUNCT
ejpam-6010	37	1	[	[	X
ejpam-6010	37	2	35	35	NUM
ejpam-6010	37	3	]	]	PUNCT
ejpam-6010	37	4	extended	extend	VERB
ejpam-6010	37	5	the	the	DET
ejpam-6010	37	6	notion	notion	NOUN
ejpam-6010	37	7	of	of	ADP
ejpam-6010	37	8	contra	contra	ADJ
ejpam-6010	37	9	-	-	ADJ
ejpam-6010	37	10	continuous	continuous	ADJ
ejpam-6010	37	11	functions	function	NOUN
ejpam-6010	37	12	to	to	ADP
ejpam-6010	37	13	the	the	DET
ejpam-6010	37	14	setting	setting	NOUN
ejpam-6010	37	15	of	of	ADP
ejpam-6010	37	16	multifunctions	multifunction	NOUN
ejpam-6010	37	17	.	.	PUNCT
ejpam-6010	38	1	noiri	noiri	PROPN
ejpam-6010	38	2	and	and	CCONJ
ejpam-6010	38	3	popa	popa	NOUN
ejpam-6010	38	4	[	[	X
ejpam-6010	38	5	36	36	NUM
ejpam-6010	38	6	]	]	PUNCT
ejpam-6010	38	7	introduced	introduce	VERB
ejpam-6010	38	8	the	the	DET
ejpam-6010	38	9	notion	notion	NOUN
ejpam-6010	38	10	of	of	ADP
ejpam-6010	38	11	weakly	weakly	ADJ
ejpam-6010	38	12	precontinuous	precontinuous	ADJ
ejpam-6010	38	13	multifunctions	multifunction	NOUN
ejpam-6010	38	14	.	.	PUNCT
ejpam-6010	39	1	ekici	ekici	NOUN
ejpam-6010	39	2	et	et	PROPN
ejpam-6010	39	3	al	al	PROPN
ejpam-6010	39	4	.	.	PUNCT
ejpam-6010	40	1	[	[	X
ejpam-6010	40	2	37	37	NUM
ejpam-6010	40	3	]	]	PUNCT
ejpam-6010	40	4	introduced	introduce	VERB
ejpam-6010	40	5	and	and	CCONJ
ejpam-6010	40	6	studied	study	VERB
ejpam-6010	40	7	two	two	NUM
ejpam-6010	40	8	new	new	ADJ
ejpam-6010	40	9	concepts	concept	NOUN
ejpam-6010	40	10	namely	namely	ADV
ejpam-6010	40	11	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6010	40	12	multifunctions	multifunction	NOUN
ejpam-6010	40	13	and	and	CCONJ
ejpam-6010	40	14	almost	almost	ADV
ejpam-6010	40	15	contra	contra	ADJ
ejpam-6010	40	16	-	-	ADJ
ejpam-6010	40	17	precontinuous	precontinuous	ADJ
ejpam-6010	40	18	multifunctions	multifunction	NOUN
ejpam-6010	40	19	which	which	PRON
ejpam-6010	40	20	are	be	AUX
ejpam-6010	40	21	containing	contain	VERB
ejpam-6010	40	22	the	the	DET
ejpam-6010	40	23	class	class	NOUN
ejpam-6010	40	24	of	of	ADP
ejpam-6010	40	25	contra	contra	ADJ
ejpam-6010	40	26	-	-	ADJ
ejpam-6010	40	27	continuous	continuous	ADJ
ejpam-6010	40	28	multifunctions	multifunction	NOUN
ejpam-6010	40	29	[	[	X
ejpam-6010	40	30	35	35	NUM
ejpam-6010	40	31	]	]	PUNCT
ejpam-6010	40	32	and	and	CCONJ
ejpam-6010	40	33	contained	contain	VERB
ejpam-6010	40	34	in	in	ADP
ejpam-6010	40	35	the	the	DET
ejpam-6010	40	36	class	class	NOUN
ejpam-6010	40	37	of	of	ADP
ejpam-6010	40	38	weakly	weakly	ADJ
ejpam-6010	40	39	precontinuous	precontinuous	ADJ
ejpam-6010	40	40	multifunctions	multifunction	NOUN
ejpam-6010	40	41	.	.	PUNCT
ejpam-6010	41	1	laprom	laprom	ADP
ejpam-6010	41	2	et	et	PROPN
ejpam-6010	41	3	al	al	PROPN
ejpam-6010	41	4	.	.	PUNCT
ejpam-6010	42	1	[	[	X
ejpam-6010	42	2	38	38	NUM
ejpam-6010	42	3	]	]	PUNCT
ejpam-6010	42	4	introduced	introduce	VERB
ejpam-6010	42	5	and	and	CCONJ
ejpam-6010	42	6	investigated	investigate	VERB
ejpam-6010	42	7	the	the	DET
ejpam-6010	42	8	notion	notion	NOUN
ejpam-6010	42	9	of	of	ADP
ejpam-6010	42	10	almost	almost	ADV
ejpam-6010	42	11	β(τ1	β(τ1	NOUN
ejpam-6010	42	12	,	,	PUNCT
ejpam-6010	42	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	42	14	multifunctions	multifunction	NOUN
ejpam-6010	42	15	.	.	PUNCT
ejpam-6010	43	1	moreover	moreover	ADV
ejpam-6010	43	2	,	,	PUNCT
ejpam-6010	43	3	some	some	DET
ejpam-6010	43	4	characterizations	characterization	NOUN
ejpam-6010	43	5	of	of	ADP
ejpam-6010	43	6	(	(	PUNCT
ejpam-6010	43	7	τ1	τ1	NOUN
ejpam-6010	43	8	,	,	PUNCT
ejpam-6010	43	9	τ2)δ	τ2)δ	ADJ
ejpam-6010	43	10	-	-	PUNCT
ejpam-6010	43	11	semicontinuous	semicontinuous	ADJ
ejpam-6010	43	12	multifunctions	multifunction	NOUN
ejpam-6010	43	13	,	,	PUNCT
ejpam-6010	43	14	almost	almost	ADV
ejpam-6010	43	15	weakly	weakly	ADJ
ejpam-6010	43	16	(	(	PUNCT
ejpam-6010	43	17	τ1	τ1	NOUN
ejpam-6010	43	18	,	,	PUNCT
ejpam-6010	43	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	20	multifunctions	multifunction	NOUN
ejpam-6010	43	21	,	,	PUNCT
ejpam-6010	43	22	weakly	weakly	ADJ
ejpam-6010	43	23	quasi	quasi	NOUN
ejpam-6010	43	24	(	(	PUNCT
ejpam-6010	43	25	λ	λ	PROPN
ejpam-6010	43	26	,	,	PUNCT
ejpam-6010	43	27	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	28	multifunctions	multifunction	NOUN
ejpam-6010	43	29	,	,	PUNCT
ejpam-6010	43	30	⋆-continuous	⋆-continuous	ADJ
ejpam-6010	43	31	multifunctions	multifunction	NOUN
ejpam-6010	43	32	,	,	PUNCT
ejpam-6010	43	33	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-6010	43	34	multifunctions	multifunction	NOUN
ejpam-6010	43	35	,	,	PUNCT
ejpam-6010	43	36	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6010	43	37	multifunctions	multifunction	NOUN
ejpam-6010	43	38	,	,	PUNCT
ejpam-6010	43	39	almost	almost	ADV
ejpam-6010	43	40	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6010	43	41	multifunctions	multifunction	NOUN
ejpam-6010	43	42	,	,	PUNCT
ejpam-6010	43	43	almost	almost	ADV
ejpam-6010	43	44	quasi	quasi	VERB
ejpam-6010	43	45	⋆-continuous	⋆-continuous	ADJ
ejpam-6010	43	46	multifunctions	multifunction	NOUN
ejpam-6010	43	47	,	,	PUNCT
ejpam-6010	43	48	weakly	weakly	ADJ
ejpam-6010	43	49	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6010	43	50	multifunctions	multifunction	NOUN
ejpam-6010	43	51	,	,	PUNCT
ejpam-6010	43	52	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6010	43	53	multifunctions	multifunction	NOUN
ejpam-6010	43	54	,	,	PUNCT
ejpam-6010	43	55	weakly	weakly	ADJ
ejpam-6010	43	56	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6010	43	57	multifunctions	multifunction	NOUN
ejpam-6010	43	58	,	,	PUNCT
ejpam-6010	43	59	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-6010	43	60	continuous	continuous	ADJ
ejpam-6010	43	61	multifunctions	multifunction	NOUN
ejpam-6010	43	62	,	,	PUNCT
ejpam-6010	43	63	almost	almost	ADV
ejpam-6010	43	64	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-6010	43	65	multifunctions	multifunction	NOUN
ejpam-6010	43	66	,	,	PUNCT
ejpam-6010	43	67	weakly	weakly	ADJ
ejpam-6010	43	68	(	(	PUNCT
ejpam-6010	43	69	λ	λ	NOUN
ejpam-6010	43	70	,	,	PUNCT
ejpam-6010	43	71	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	72	multifunctions	multifunction	NOUN
ejpam-6010	43	73	,	,	PUNCT
ejpam-6010	43	74	α(λ	α(λ	PROPN
ejpam-6010	43	75	,	,	PUNCT
ejpam-6010	43	76	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	77	multifunctions	multifunction	NOUN
ejpam-6010	43	78	,	,	PUNCT
ejpam-6010	43	79	almost	almost	ADV
ejpam-6010	43	80	α(λ	α(λ	PROPN
ejpam-6010	43	81	,	,	PUNCT
ejpam-6010	43	82	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	83	multifunctions	multifunction	NOUN
ejpam-6010	43	84	,	,	PUNCT
ejpam-6010	43	85	weakly	weakly	ADJ
ejpam-6010	43	86	α(λ	α(λ	PROPN
ejpam-6010	43	87	,	,	PUNCT
ejpam-6010	43	88	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	89	multifunctions	multifunction	NOUN
ejpam-6010	43	90	,	,	PUNCT
ejpam-6010	43	91	almost	almost	ADV
ejpam-6010	43	92	β(λ	β(λ	NOUN
ejpam-6010	43	93	,	,	PUNCT
ejpam-6010	43	94	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	95	multifunctions	multifunction	NOUN
ejpam-6010	43	96	,	,	PUNCT
ejpam-6010	43	97	slightly	slightly	ADV
ejpam-6010	43	98	(	(	PUNCT
ejpam-6010	43	99	λ	λ	NOUN
ejpam-6010	43	100	,	,	PUNCT
ejpam-6010	43	101	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	43	102	multifunctions	multifunction	NOUN
ejpam-6010	43	103	,	,	PUNCT
ejpam-6010	43	104	(	(	PUNCT
ejpam-6010	43	105	τ1	τ1	NOUN
ejpam-6010	43	106	,	,	PUNCT
ejpam-6010	43	107	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	108	multifunctions	multifunction	NOUN
ejpam-6010	43	109	,	,	PUNCT
ejpam-6010	43	110	almost	almost	ADV
ejpam-6010	43	111	(	(	PUNCT
ejpam-6010	43	112	τ1	τ1	NOUN
ejpam-6010	43	113	,	,	PUNCT
ejpam-6010	43	114	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	115	multifunctions	multifunction	NOUN
ejpam-6010	43	116	,	,	PUNCT
ejpam-6010	43	117	weakly	weakly	ADJ
ejpam-6010	43	118	(	(	PUNCT
ejpam-6010	43	119	τ1	τ1	NOUN
ejpam-6010	43	120	,	,	PUNCT
ejpam-6010	43	121	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	122	multifunctions	multifunction	NOUN
ejpam-6010	43	123	,	,	PUNCT
ejpam-6010	43	124	weakly	weakly	ADJ
ejpam-6010	43	125	quasi	quasi	NOUN
ejpam-6010	43	126	(	(	PUNCT
ejpam-6010	43	127	τ1	τ1	PROPN
ejpam-6010	43	128	,	,	PUNCT
ejpam-6010	43	129	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	130	multifunctions	multifunction	NOUN
ejpam-6010	43	131	,	,	PUNCT
ejpam-6010	43	132	almost	almost	ADV
ejpam-6010	43	133	quasi	quasi	NOUN
ejpam-6010	43	134	(	(	PUNCT
ejpam-6010	43	135	τ1	τ1	NOUN
ejpam-6010	43	136	,	,	PUNCT
ejpam-6010	43	137	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	138	multifunctions	multifunction	NOUN
ejpam-6010	43	139	,	,	PUNCT
ejpam-6010	43	140	c-(τ1	c-(τ1	PROPN
ejpam-6010	43	141	,	,	PUNCT
ejpam-6010	43	142	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	143	multifunctions	multifunction	NOUN
ejpam-6010	43	144	,	,	PUNCT
ejpam-6010	43	145	c	c	NOUN
ejpam-6010	43	146	-	-	PUNCT
ejpam-6010	43	147	quasi	quasi	NOUN
ejpam-6010	43	148	(	(	PUNCT
ejpam-6010	43	149	τ1	τ1	PROPN
ejpam-6010	43	150	,	,	PUNCT
ejpam-6010	43	151	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	152	multifunctions	multifunction	NOUN
ejpam-6010	43	153	,	,	PUNCT
ejpam-6010	43	154	s-(τ1	s-(τ1	PROPN
ejpam-6010	43	155	,	,	PUNCT
ejpam-6010	43	156	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6010	43	157	multifunctions	multifunction	NOUN
ejpam-6010	43	158	,	,	PUNCT
ejpam-6010	43	159	slightly	slightly	ADV
ejpam-6010	43	160	α(τ1	α(τ1	NOUN
ejpam-6010	43	161	,	,	PUNCT
ejpam-6010	43	162	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	43	163	multifunctions	multifunction	NOUN
ejpam-6010	43	164	and	and	CCONJ
ejpam-6010	43	165	slightly	slightly	ADV
ejpam-6010	43	166	(	(	PUNCT
ejpam-6010	43	167	τ1	τ1	NOUN
ejpam-6010	43	168	,	,	PUNCT
ejpam-6010	43	169	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6010	43	170	multifunctions	multifunction	NOUN
ejpam-6010	43	171	were	be	AUX
ejpam-6010	43	172	established	establish	VERB
ejpam-6010	43	173	in	in	ADP
ejpam-6010	43	174	[	[	X
ejpam-6010	43	175	39	39	NUM
ejpam-6010	43	176	]	]	PUNCT
ejpam-6010	43	177	,	,	PUNCT
ejpam-6010	44	1	[	[	X
ejpam-6010	44	2	40	40	NUM
ejpam-6010	44	3	]	]	PUNCT
ejpam-6010	44	4	,	,	PUNCT
ejpam-6010	44	5	[	[	X
ejpam-6010	44	6	41	41	NUM
ejpam-6010	44	7	]	]	PUNCT
ejpam-6010	44	8	,	,	PUNCT
ejpam-6010	45	1	[	[	X
ejpam-6010	45	2	42	42	NUM
ejpam-6010	45	3	]	]	PUNCT
ejpam-6010	45	4	,	,	PUNCT
ejpam-6010	45	5	[	[	X
ejpam-6010	45	6	43	43	NUM
ejpam-6010	45	7	]	]	PUNCT
ejpam-6010	45	8	,	,	PUNCT
ejpam-6010	45	9	[	[	X
ejpam-6010	45	10	44	44	NUM
ejpam-6010	45	11	]	]	PUNCT
ejpam-6010	45	12	,	,	PUNCT
ejpam-6010	45	13	[	[	X
ejpam-6010	45	14	45	45	NUM
ejpam-6010	45	15	]	]	PUNCT
ejpam-6010	45	16	,	,	PUNCT
ejpam-6010	45	17	[	[	X
ejpam-6010	45	18	46	46	NUM
ejpam-6010	45	19	]	]	PUNCT
ejpam-6010	45	20	,	,	PUNCT
ejpam-6010	46	1	[	[	X
ejpam-6010	46	2	47	47	NUM
ejpam-6010	46	3	]	]	PUNCT
ejpam-6010	46	4	,	,	PUNCT
ejpam-6010	46	5	[	[	X
ejpam-6010	46	6	48	48	NUM
ejpam-6010	46	7	]	]	PUNCT
ejpam-6010	46	8	,	,	PUNCT
ejpam-6010	46	9	[	[	X
ejpam-6010	46	10	49	49	NUM
ejpam-6010	46	11	]	]	PUNCT
ejpam-6010	46	12	,	,	PUNCT
ejpam-6010	46	13	[	[	X
ejpam-6010	46	14	50	50	NUM
ejpam-6010	46	15	]	]	PUNCT
ejpam-6010	46	16	,	,	PUNCT
ejpam-6010	46	17	[	[	X
ejpam-6010	46	18	51	51	NUM
ejpam-6010	46	19	]	]	PUNCT
ejpam-6010	46	20	,	,	PUNCT
ejpam-6010	46	21	[	[	X
ejpam-6010	46	22	52	52	NUM
ejpam-6010	46	23	]	]	PUNCT
ejpam-6010	46	24	,	,	PUNCT
ejpam-6010	46	25	[	[	X
ejpam-6010	46	26	53	53	NUM
ejpam-6010	46	27	]	]	PUNCT
ejpam-6010	46	28	,	,	PUNCT
ejpam-6010	46	29	[	[	X
ejpam-6010	46	30	54	54	NUM
ejpam-6010	46	31	]	]	PUNCT
ejpam-6010	46	32	,	,	PUNCT
ejpam-6010	46	33	[	[	X
ejpam-6010	46	34	55	55	NUM
ejpam-6010	46	35	]	]	PUNCT
ejpam-6010	46	36	,	,	PUNCT
ejpam-6010	46	37	[	[	X
ejpam-6010	46	38	56	56	NUM
ejpam-6010	46	39	]	]	PUNCT
ejpam-6010	46	40	,	,	PUNCT
ejpam-6010	46	41	[	[	X
ejpam-6010	46	42	57	57	NUM
ejpam-6010	46	43	]	]	PUNCT
ejpam-6010	46	44	,	,	PUNCT
ejpam-6010	46	45	[	[	X
ejpam-6010	46	46	58	58	NUM
ejpam-6010	46	47	]	]	PUNCT
ejpam-6010	46	48	,	,	PUNCT
ejpam-6010	46	49	[	[	X
ejpam-6010	46	50	59	59	NUM
ejpam-6010	46	51	]	]	PUNCT
ejpam-6010	46	52	,	,	PUNCT
ejpam-6010	46	53	[	[	X
ejpam-6010	46	54	60	60	NUM
ejpam-6010	46	55	]	]	PUNCT
ejpam-6010	46	56	,	,	PUNCT
ejpam-6010	46	57	[	[	X
ejpam-6010	46	58	61	61	NUM
ejpam-6010	46	59	]	]	PUNCT
ejpam-6010	46	60	,	,	PUNCT
ejpam-6010	46	61	[	[	X
ejpam-6010	46	62	62	62	NUM
ejpam-6010	46	63	]	]	PUNCT
ejpam-6010	46	64	,	,	PUNCT
ejpam-6010	46	65	[	[	X
ejpam-6010	46	66	63	63	NUM
ejpam-6010	46	67	]	]	PUNCT
ejpam-6010	46	68	,	,	PUNCT
ejpam-6010	46	69	[	[	X
ejpam-6010	46	70	64	64	NUM
ejpam-6010	46	71	]	]	PUNCT
ejpam-6010	46	72	,	,	PUNCT
ejpam-6010	46	73	[	[	X
ejpam-6010	46	74	65	65	NUM
ejpam-6010	46	75	]	]	PUNCT
ejpam-6010	46	76	,	,	PUNCT
ejpam-6010	46	77	j.	j.	PROPN
ejpam-6010	46	78	khampakdee	khampakdee	PROPN
ejpam-6010	46	79	,	,	PUNCT
ejpam-6010	46	80	a.	a.	PROPN
ejpam-6010	46	81	sama	sama	PROPN
ejpam-6010	46	82	-	-	PUNCT
ejpam-6010	46	83	ae	ae	PROPN
ejpam-6010	46	84	,	,	PUNCT
ejpam-6010	46	85	c.	c.	PROPN
ejpam-6010	46	86	boonpok	boonpok	PROPN
ejpam-6010	46	87	/	/	SYM
ejpam-6010	46	88	eur	eur	PROPN
ejpam-6010	46	89	.	.	PUNCT
ejpam-6010	47	1	j.	j.	PROPN
ejpam-6010	47	2	pure	pure	PROPN
ejpam-6010	47	3	appl	appl	PROPN
ejpam-6010	47	4	.	.	PROPN
ejpam-6010	47	5	math	math	PROPN
ejpam-6010	47	6	,	,	PUNCT
ejpam-6010	47	7	18	18	NUM
ejpam-6010	47	8	(	(	PUNCT
ejpam-6010	47	9	2	2	NUM
ejpam-6010	47	10	)	)	PUNCT
ejpam-6010	47	11	(	(	PUNCT
ejpam-6010	47	12	2025	2025	NUM
ejpam-6010	47	13	)	)	PUNCT
ejpam-6010	47	14	,	,	PUNCT
ejpam-6010	47	15	6010	6010	NUM
ejpam-6010	47	16	3	3	NUM
ejpam-6010	47	17	of	of	ADP
ejpam-6010	47	18	19	19	NUM
ejpam-6010	48	1	[	[	X
ejpam-6010	48	2	66	66	NUM
ejpam-6010	48	3	]	]	PUNCT
ejpam-6010	48	4	and	and	CCONJ
ejpam-6010	48	5	[	[	X
ejpam-6010	48	6	67	67	NUM
ejpam-6010	48	7	]	]	X
ejpam-6010	48	8	,	,	PUNCT
ejpam-6010	48	9	respectively	respectively	ADV
ejpam-6010	48	10	.	.	PUNCT
ejpam-6010	49	1	on	on	ADP
ejpam-6010	49	2	the	the	DET
ejpam-6010	49	3	other	other	ADJ
ejpam-6010	49	4	hand	hand	NOUN
ejpam-6010	49	5	,	,	PUNCT
ejpam-6010	49	6	the	the	DET
ejpam-6010	49	7	present	present	ADJ
ejpam-6010	49	8	authors	author	NOUN
ejpam-6010	49	9	introduced	introduce	VERB
ejpam-6010	49	10	and	and	CCONJ
ejpam-6010	49	11	investigated	investigate	VERB
ejpam-6010	49	12	the	the	DET
ejpam-6010	49	13	notions	notion	NOUN
ejpam-6010	49	14	of	of	ADP
ejpam-6010	49	15	rarely	rarely	ADV
ejpam-6010	49	16	s-(τ1	s-(τ1	NOUN
ejpam-6010	49	17	,	,	PUNCT
ejpam-6010	49	18	τ2)p	τ2)p	ADJ
ejpam-6010	49	19	-	-	ADJ
ejpam-6010	49	20	continuous	continuous	ADJ
ejpam-6010	49	21	multifunctions	multifunction	NOUN
ejpam-6010	50	1	[	[	X
ejpam-6010	50	2	68	68	NUM
ejpam-6010	50	3	]	]	X
ejpam-6010	50	4	,	,	PUNCT
ejpam-6010	50	5	almost	almost	ADV
ejpam-6010	50	6	nearly	nearly	ADV
ejpam-6010	50	7	(	(	PUNCT
ejpam-6010	50	8	τ1	τ1	NOUN
ejpam-6010	50	9	,	,	PUNCT
ejpam-6010	50	10	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	50	11	multifunctions	multifunction	NOUN
ejpam-6010	51	1	[	[	X
ejpam-6010	51	2	69	69	NUM
ejpam-6010	51	3	]	]	PUNCT
ejpam-6010	51	4	,	,	PUNCT
ejpam-6010	51	5	s-(τ1	s-(τ1	PROPN
ejpam-6010	51	6	,	,	PUNCT
ejpam-6010	51	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	51	8	multifunctions	multifunction	NOUN
ejpam-6010	52	1	[	[	X
ejpam-6010	52	2	70	70	NUM
ejpam-6010	52	3	]	]	PUNCT
ejpam-6010	52	4	,	,	PUNCT
ejpam-6010	52	5	quasi	quasi	NOUN
ejpam-6010	52	6	θ(τ1	θ(τ1	NOUN
ejpam-6010	52	7	,	,	PUNCT
ejpam-6010	52	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	52	9	multifunctions	multifunction	NOUN
ejpam-6010	53	1	[	[	X
ejpam-6010	53	2	71	71	NUM
ejpam-6010	53	3	]	]	PUNCT
ejpam-6010	53	4	,	,	PUNCT
ejpam-6010	53	5	almost	almost	ADV
ejpam-6010	53	6	nearly	nearly	ADV
ejpam-6010	53	7	quasi	quasi	NOUN
ejpam-6010	53	8	(	(	PUNCT
ejpam-6010	53	9	τ1	τ1	NOUN
ejpam-6010	53	10	,	,	PUNCT
ejpam-6010	53	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	53	12	multifunctions	multifunction	NOUN
ejpam-6010	54	1	[	[	X
ejpam-6010	54	2	72	72	NUM
ejpam-6010	54	3	]	]	X
ejpam-6010	54	4	,	,	PUNCT
ejpam-6010	54	5	weakly	weakly	ADJ
ejpam-6010	54	6	s-(τ1	s-(τ1	PROPN
ejpam-6010	54	7	,	,	PUNCT
ejpam-6010	54	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	54	9	multifunctions	multifunction	NOUN
ejpam-6010	55	1	[	[	X
ejpam-6010	55	2	73	73	NUM
ejpam-6010	55	3	]	]	PUNCT
ejpam-6010	55	4	,	,	PUNCT
ejpam-6010	55	5	nearly	nearly	ADV
ejpam-6010	55	6	(	(	PUNCT
ejpam-6010	55	7	τ1	τ1	NOUN
ejpam-6010	55	8	,	,	PUNCT
ejpam-6010	55	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	55	10	multifunctions	multifunction	NOUN
ejpam-6010	56	1	[	[	X
ejpam-6010	56	2	74	74	NUM
ejpam-6010	56	3	]	]	PUNCT
ejpam-6010	56	4	and	and	CCONJ
ejpam-6010	56	5	almost	almost	ADV
ejpam-6010	56	6	quasi	quasi	X
ejpam-6010	56	7	(	(	PUNCT
ejpam-6010	56	8	τ1	τ1	NOUN
ejpam-6010	56	9	,	,	PUNCT
ejpam-6010	56	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	56	11	multifunctions	multifunction	NOUN
ejpam-6010	57	1	[	[	X
ejpam-6010	57	2	75	75	NUM
ejpam-6010	57	3	]	]	PUNCT
ejpam-6010	57	4	.	.	PUNCT
ejpam-6010	58	1	ekici	ekici	PROPN
ejpam-6010	58	2	et	et	PROPN
ejpam-6010	58	3	al	al	PROPN
ejpam-6010	58	4	.	.	PUNCT
ejpam-6010	59	1	[	[	X
ejpam-6010	59	2	76	76	NUM
ejpam-6010	59	3	]	]	PUNCT
ejpam-6010	59	4	introduced	introduce	VERB
ejpam-6010	59	5	and	and	CCONJ
ejpam-6010	59	6	studied	study	VERB
ejpam-6010	59	7	a	a	DET
ejpam-6010	59	8	new	new	ADJ
ejpam-6010	59	9	generalization	generalization	NOUN
ejpam-6010	59	10	of	of	ADP
ejpam-6010	59	11	contra	contra	ADJ
ejpam-6010	59	12	-	-	ADJ
ejpam-6010	59	13	continuous	continuous	ADJ
ejpam-6010	59	14	multifunctions	multifunction	NOUN
ejpam-6010	59	15	called	call	VERB
ejpam-6010	59	16	almost	almost	ADV
ejpam-6010	59	17	contracontinuous	contracontinuous	ADJ
ejpam-6010	59	18	multifunctions	multifunction	NOUN
ejpam-6010	59	19	.	.	PUNCT
ejpam-6010	60	1	boonpok	boonpok	PROPN
ejpam-6010	60	2	and	and	CCONJ
ejpam-6010	60	3	khampakdee	khampakdee	NOUN
ejpam-6010	60	4	[	[	X
ejpam-6010	60	5	77	77	NUM
ejpam-6010	60	6	]	]	PUNCT
ejpam-6010	60	7	introduced	introduce	VERB
ejpam-6010	60	8	and	and	CCONJ
ejpam-6010	60	9	investigated	investigate	VERB
ejpam-6010	60	10	the	the	DET
ejpam-6010	60	11	notions	notion	NOUN
ejpam-6010	60	12	of	of	ADP
ejpam-6010	60	13	upper	upper	ADJ
ejpam-6010	60	14	almost	almost	ADV
ejpam-6010	60	15	contra-(λ	contra-(λ	PROPN
ejpam-6010	60	16	,	,	PUNCT
ejpam-6010	60	17	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	60	18	multifunctions	multifunction	NOUN
ejpam-6010	60	19	and	and	CCONJ
ejpam-6010	60	20	lower	low	ADJ
ejpam-6010	60	21	almost	almost	ADV
ejpam-6010	60	22	contra-(λ	contra-(λ	PROPN
ejpam-6010	60	23	,	,	PUNCT
ejpam-6010	60	24	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	60	25	multifunctions	multifunction	NOUN
ejpam-6010	60	26	.	.	PUNCT
ejpam-6010	61	1	in	in	ADP
ejpam-6010	61	2	this	this	DET
ejpam-6010	61	3	paper	paper	NOUN
ejpam-6010	61	4	,	,	PUNCT
ejpam-6010	61	5	we	we	PRON
ejpam-6010	61	6	introduce	introduce	VERB
ejpam-6010	61	7	the	the	DET
ejpam-6010	61	8	concepts	concept	NOUN
ejpam-6010	61	9	of	of	ADP
ejpam-6010	61	10	upper	upper	ADJ
ejpam-6010	61	11	almost	almost	ADV
ejpam-6010	61	12	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	61	13	,	,	PUNCT
ejpam-6010	61	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	61	15	multifunctions	multifunction	NOUN
ejpam-6010	61	16	and	and	CCONJ
ejpam-6010	61	17	lower	low	ADJ
ejpam-6010	61	18	almost	almost	ADV
ejpam-6010	61	19	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	61	20	,	,	PUNCT
ejpam-6010	61	21	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	61	22	multifunctions	multifunction	NOUN
ejpam-6010	61	23	.	.	PUNCT
ejpam-6010	62	1	we	we	PRON
ejpam-6010	62	2	also	also	ADV
ejpam-6010	62	3	investigate	investigate	VERB
ejpam-6010	62	4	some	some	DET
ejpam-6010	62	5	characterizations	characterization	NOUN
ejpam-6010	62	6	of	of	ADP
ejpam-6010	62	7	upper	upper	ADJ
ejpam-6010	62	8	almost	almost	ADV
ejpam-6010	62	9	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	62	10	,	,	PUNCT
ejpam-6010	62	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	62	12	multifunctions	multifunction	NOUN
ejpam-6010	62	13	and	and	CCONJ
ejpam-6010	62	14	lower	low	ADJ
ejpam-6010	62	15	almost	almost	ADV
ejpam-6010	62	16	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	62	17	,	,	PUNCT
ejpam-6010	62	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	62	19	multifunctions	multifunction	NOUN
ejpam-6010	62	20	.	.	PUNCT
ejpam-6010	63	1	2	2	X
ejpam-6010	63	2	.	.	X
ejpam-6010	63	3	preliminaries	preliminary	NOUN
ejpam-6010	63	4	throughout	throughout	ADP
ejpam-6010	63	5	the	the	DET
ejpam-6010	63	6	present	present	ADJ
ejpam-6010	63	7	paper	paper	NOUN
ejpam-6010	63	8	,	,	PUNCT
ejpam-6010	63	9	spaces	space	NOUN
ejpam-6010	63	10	(	(	PUNCT
ejpam-6010	63	11	x	x	NOUN
ejpam-6010	63	12	,	,	PUNCT
ejpam-6010	63	13	τ1	τ1	NOUN
ejpam-6010	63	14	,	,	PUNCT
ejpam-6010	63	15	τ2	τ2	NOUN
ejpam-6010	63	16	)	)	PUNCT
ejpam-6010	63	17	and	and	CCONJ
ejpam-6010	63	18	(	(	PUNCT
ejpam-6010	63	19	y	y	PROPN
ejpam-6010	63	20	,	,	PUNCT
ejpam-6010	63	21	σ1	σ1	PROPN
ejpam-6010	63	22	,	,	PUNCT
ejpam-6010	63	23	σ2	σ2	NOUN
ejpam-6010	63	24	)	)	PUNCT
ejpam-6010	63	25	(	(	PUNCT
ejpam-6010	63	26	or	or	CCONJ
ejpam-6010	63	27	simply	simply	ADV
ejpam-6010	63	28	x	x	X
ejpam-6010	63	29	and	and	CCONJ
ejpam-6010	63	30	y	y	PROPN
ejpam-6010	63	31	)	)	PUNCT
ejpam-6010	63	32	always	always	ADV
ejpam-6010	63	33	mean	mean	VERB
ejpam-6010	63	34	bitopological	bitopological	ADJ
ejpam-6010	63	35	spaces	space	NOUN
ejpam-6010	63	36	on	on	ADP
ejpam-6010	63	37	which	which	PRON
ejpam-6010	63	38	no	no	DET
ejpam-6010	63	39	separation	separation	NOUN
ejpam-6010	63	40	axioms	axiom	NOUN
ejpam-6010	63	41	are	be	AUX
ejpam-6010	63	42	assumed	assume	VERB
ejpam-6010	63	43	unless	unless	SCONJ
ejpam-6010	63	44	explicitly	explicitly	ADV
ejpam-6010	63	45	stated	state	VERB
ejpam-6010	63	46	.	.	PUNCT
ejpam-6010	64	1	let	let	VERB
ejpam-6010	64	2	a	a	DET
ejpam-6010	64	3	be	be	AUX
ejpam-6010	64	4	a	a	DET
ejpam-6010	64	5	subset	subset	NOUN
ejpam-6010	64	6	of	of	ADP
ejpam-6010	64	7	a	a	DET
ejpam-6010	64	8	bitopological	bitopological	ADJ
ejpam-6010	64	9	space	space	NOUN
ejpam-6010	64	10	(	(	PUNCT
ejpam-6010	64	11	x	x	NOUN
ejpam-6010	64	12	,	,	PUNCT
ejpam-6010	64	13	τ1	τ1	NOUN
ejpam-6010	64	14	,	,	PUNCT
ejpam-6010	64	15	τ2	τ2	NOUN
ejpam-6010	64	16	)	)	PUNCT
ejpam-6010	64	17	.	.	PUNCT
ejpam-6010	65	1	the	the	DET
ejpam-6010	65	2	closure	closure	NOUN
ejpam-6010	65	3	of	of	ADP
ejpam-6010	65	4	a	a	PRON
ejpam-6010	65	5	and	and	CCONJ
ejpam-6010	65	6	the	the	DET
ejpam-6010	65	7	interior	interior	NOUN
ejpam-6010	65	8	of	of	ADP
ejpam-6010	65	9	a	a	PRON
ejpam-6010	65	10	with	with	ADP
ejpam-6010	65	11	respect	respect	NOUN
ejpam-6010	65	12	to	to	ADP
ejpam-6010	65	13	τi	τi	PROPN
ejpam-6010	65	14	are	be	AUX
ejpam-6010	65	15	denoted	denote	VERB
ejpam-6010	65	16	by	by	ADP
ejpam-6010	65	17	τi	τi	NOUN
ejpam-6010	65	18	-	-	PUNCT
ejpam-6010	65	19	cl(a	cl(a	NUM
ejpam-6010	65	20	)	)	PUNCT
ejpam-6010	65	21	and	and	CCONJ
ejpam-6010	65	22	τi	τi	NOUN
ejpam-6010	65	23	-	-	PUNCT
ejpam-6010	65	24	int(a	int(a	NOUN
ejpam-6010	65	25	)	)	PUNCT
ejpam-6010	65	26	,	,	PUNCT
ejpam-6010	65	27	respectively	respectively	ADV
ejpam-6010	65	28	,	,	PUNCT
ejpam-6010	65	29	for	for	ADP
ejpam-6010	65	30	i	i	PROPN
ejpam-6010	65	31	=	=	SYM
ejpam-6010	65	32	1	1	NUM
ejpam-6010	65	33	,	,	PUNCT
ejpam-6010	65	34	2	2	NUM
ejpam-6010	65	35	.	.	X
ejpam-6010	65	36	a	a	DET
ejpam-6010	65	37	subset	subset	NOUN
ejpam-6010	65	38	a	a	PRON
ejpam-6010	65	39	of	of	ADP
ejpam-6010	65	40	a	a	DET
ejpam-6010	65	41	bitopological	bitopological	ADJ
ejpam-6010	65	42	space	space	NOUN
ejpam-6010	65	43	(	(	PUNCT
ejpam-6010	65	44	x	x	NOUN
ejpam-6010	65	45	,	,	PUNCT
ejpam-6010	65	46	τ1	τ1	NOUN
ejpam-6010	65	47	,	,	PUNCT
ejpam-6010	65	48	τ2	τ2	NOUN
ejpam-6010	65	49	)	)	PUNCT
ejpam-6010	65	50	is	be	AUX
ejpam-6010	65	51	called	call	VERB
ejpam-6010	65	52	τ1τ2	τ1τ2	VERB
ejpam-6010	65	53	-	-	ADJ
ejpam-6010	65	54	closed	closed	ADJ
ejpam-6010	65	55	[	[	X
ejpam-6010	65	56	78	78	NUM
ejpam-6010	65	57	]	]	PUNCT
ejpam-6010	65	58	if	if	SCONJ
ejpam-6010	65	59	a	a	DET
ejpam-6010	65	60	=	=	NOUN
ejpam-6010	65	61	τ1	τ1	NOUN
ejpam-6010	65	62	-	-	PUNCT
ejpam-6010	65	63	cl(τ2	cl(τ2	NOUN
ejpam-6010	65	64	-	-	PUNCT
ejpam-6010	65	65	cl(a	cl(a	NUM
ejpam-6010	65	66	)	)	PUNCT
ejpam-6010	65	67	)	)	PUNCT
ejpam-6010	65	68	.	.	PUNCT
ejpam-6010	66	1	the	the	DET
ejpam-6010	66	2	complement	complement	NOUN
ejpam-6010	66	3	of	of	ADP
ejpam-6010	66	4	a	a	DET
ejpam-6010	66	5	τ1τ2	τ1τ2	ADJ
ejpam-6010	66	6	-	-	ADJ
ejpam-6010	66	7	closed	closed	ADJ
ejpam-6010	66	8	set	set	NOUN
ejpam-6010	66	9	is	be	AUX
ejpam-6010	66	10	called	call	VERB
ejpam-6010	66	11	τ1τ2	τ1τ2	NOUN
ejpam-6010	66	12	-	-	ADJ
ejpam-6010	66	13	open	open	ADJ
ejpam-6010	66	14	.	.	PUNCT
ejpam-6010	67	1	the	the	DET
ejpam-6010	67	2	intersection	intersection	NOUN
ejpam-6010	67	3	of	of	ADP
ejpam-6010	67	4	all	all	DET
ejpam-6010	67	5	τ1τ2	τ1τ2	ADJ
ejpam-6010	67	6	-	-	ADJ
ejpam-6010	67	7	closed	closed	ADJ
ejpam-6010	67	8	sets	set	NOUN
ejpam-6010	67	9	of	of	ADP
ejpam-6010	67	10	x	x	PUNCT
ejpam-6010	67	11	containing	contain	VERB
ejpam-6010	67	12	a	a	PRON
ejpam-6010	67	13	is	be	AUX
ejpam-6010	67	14	called	call	VERB
ejpam-6010	67	15	the	the	DET
ejpam-6010	67	16	τ1τ2	τ1τ2	NOUN
ejpam-6010	67	17	-	-	NOUN
ejpam-6010	67	18	closure	closure	NOUN
ejpam-6010	67	19	[	[	X
ejpam-6010	67	20	78	78	NUM
ejpam-6010	67	21	]	]	PUNCT
ejpam-6010	67	22	of	of	ADP
ejpam-6010	67	23	a	a	PRON
ejpam-6010	67	24	and	and	CCONJ
ejpam-6010	67	25	is	be	AUX
ejpam-6010	67	26	denoted	denote	VERB
ejpam-6010	67	27	by	by	ADP
ejpam-6010	67	28	τ1τ2	τ1τ2	NOUN
ejpam-6010	67	29	-	-	NUM
ejpam-6010	67	30	cl(a	cl(a	NUM
ejpam-6010	67	31	)	)	PUNCT
ejpam-6010	67	32	.	.	PUNCT
ejpam-6010	68	1	the	the	DET
ejpam-6010	68	2	union	union	NOUN
ejpam-6010	68	3	of	of	ADP
ejpam-6010	68	4	all	all	DET
ejpam-6010	68	5	τ1τ2	τ1τ2	ADJ
ejpam-6010	68	6	-	-	ADJ
ejpam-6010	68	7	open	open	ADJ
ejpam-6010	68	8	sets	set	NOUN
ejpam-6010	68	9	of	of	ADP
ejpam-6010	68	10	x	x	PUNCT
ejpam-6010	68	11	contained	contain	VERB
ejpam-6010	68	12	in	in	ADP
ejpam-6010	68	13	a	a	PRON
ejpam-6010	68	14	is	be	AUX
ejpam-6010	68	15	called	call	VERB
ejpam-6010	68	16	the	the	DET
ejpam-6010	68	17	τ1τ2	τ1τ2	NOUN
ejpam-6010	68	18	-	-	ADJ
ejpam-6010	68	19	interior	interior	ADJ
ejpam-6010	68	20	[	[	X
ejpam-6010	68	21	78	78	NUM
ejpam-6010	68	22	]	]	PUNCT
ejpam-6010	68	23	of	of	ADP
ejpam-6010	68	24	a	a	PRON
ejpam-6010	68	25	and	and	CCONJ
ejpam-6010	68	26	is	be	AUX
ejpam-6010	68	27	denoted	denote	VERB
ejpam-6010	68	28	by	by	ADP
ejpam-6010	68	29	τ1τ2	τ1τ2	NOUN
ejpam-6010	68	30	-	-	ADJ
ejpam-6010	68	31	int(a	int(a	NOUN
ejpam-6010	68	32	)	)	PUNCT
ejpam-6010	68	33	.	.	PUNCT
ejpam-6010	69	1	lemma	lemma	PROPN
ejpam-6010	69	2	1	1	NUM
ejpam-6010	69	3	.	.	PUNCT
ejpam-6010	70	1	[	[	X
ejpam-6010	70	2	78	78	NUM
ejpam-6010	70	3	]	]	PUNCT
ejpam-6010	70	4	let	let	VERB
ejpam-6010	70	5	a	a	PRON
ejpam-6010	70	6	and	and	CCONJ
ejpam-6010	70	7	b	b	NOUN
ejpam-6010	70	8	be	be	AUX
ejpam-6010	70	9	subsets	subset	NOUN
ejpam-6010	70	10	of	of	ADP
ejpam-6010	70	11	a	a	DET
ejpam-6010	70	12	bitopological	bitopological	ADJ
ejpam-6010	70	13	space	space	NOUN
ejpam-6010	70	14	(	(	PUNCT
ejpam-6010	70	15	x	x	NOUN
ejpam-6010	70	16	,	,	PUNCT
ejpam-6010	70	17	τ1	τ1	NOUN
ejpam-6010	70	18	,	,	PUNCT
ejpam-6010	70	19	τ2	τ2	NOUN
ejpam-6010	70	20	)	)	PUNCT
ejpam-6010	70	21	.	.	PUNCT
ejpam-6010	71	1	for	for	ADP
ejpam-6010	71	2	the	the	DET
ejpam-6010	71	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-6010	71	4	,	,	PUNCT
ejpam-6010	71	5	the	the	DET
ejpam-6010	71	6	following	follow	VERB
ejpam-6010	71	7	properties	property	NOUN
ejpam-6010	71	8	hold	hold	VERB
ejpam-6010	71	9	:	:	PUNCT
ejpam-6010	71	10	(	(	PUNCT
ejpam-6010	71	11	1	1	X
ejpam-6010	71	12	)	)	PUNCT
ejpam-6010	71	13	a	a	DET
ejpam-6010	71	14	⊆	⊆	NUM
ejpam-6010	71	15	τ1τ2	τ1τ2	NOUN
ejpam-6010	71	16	-	-	NUM
ejpam-6010	71	17	cl(a	cl(a	NUM
ejpam-6010	71	18	)	)	PUNCT
ejpam-6010	71	19	and	and	CCONJ
ejpam-6010	71	20	τ1τ2	τ1τ2	NOUN
ejpam-6010	71	21	-	-	ADJ
ejpam-6010	71	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6010	71	23	-	-	PUNCT
ejpam-6010	71	24	cl(a	cl(a	NUM
ejpam-6010	71	25	)	)	PUNCT
ejpam-6010	71	26	)	)	PUNCT
ejpam-6010	72	1	=	=	PUNCT
ejpam-6010	72	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	72	3	-	-	NUM
ejpam-6010	72	4	cl(a	cl(a	NUM
ejpam-6010	72	5	)	)	PUNCT
ejpam-6010	72	6	.	.	PUNCT
ejpam-6010	73	1	(	(	PUNCT
ejpam-6010	73	2	2	2	X
ejpam-6010	73	3	)	)	PUNCT
ejpam-6010	73	4	if	if	SCONJ
ejpam-6010	73	5	a	a	DET
ejpam-6010	73	6	⊆	⊆	NUM
ejpam-6010	73	7	b	b	NOUN
ejpam-6010	73	8	,	,	PUNCT
ejpam-6010	73	9	then	then	ADV
ejpam-6010	73	10	τ1τ2	τ1τ2	NOUN
ejpam-6010	73	11	-	-	NUM
ejpam-6010	73	12	cl(a	cl(a	NUM
ejpam-6010	73	13	)	)	PUNCT
ejpam-6010	73	14	⊆	⊆	NUM
ejpam-6010	73	15	τ1τ2	τ1τ2	NOUN
ejpam-6010	73	16	-	-	NOUN
ejpam-6010	73	17	cl(b	cl(b	NOUN
ejpam-6010	73	18	)	)	PUNCT
ejpam-6010	73	19	.	.	PUNCT
ejpam-6010	74	1	(	(	PUNCT
ejpam-6010	74	2	3	3	X
ejpam-6010	74	3	)	)	PUNCT
ejpam-6010	74	4	τ1τ2	τ1τ2	NOUN
ejpam-6010	74	5	-	-	NUM
ejpam-6010	74	6	cl(a	cl(a	NUM
ejpam-6010	74	7	)	)	PUNCT
ejpam-6010	74	8	is	be	AUX
ejpam-6010	74	9	τ1τ2	τ1τ2	NOUN
ejpam-6010	74	10	-	-	ADJ
ejpam-6010	74	11	closed	closed	ADJ
ejpam-6010	74	12	.	.	PUNCT
ejpam-6010	75	1	(	(	PUNCT
ejpam-6010	75	2	4	4	X
ejpam-6010	75	3	)	)	PUNCT
ejpam-6010	75	4	a	a	PRON
ejpam-6010	75	5	is	be	AUX
ejpam-6010	75	6	τ1τ2	τ1τ2	NOUN
ejpam-6010	75	7	-	-	ADJ
ejpam-6010	75	8	closed	closed	ADJ
ejpam-6010	75	9	if	if	SCONJ
ejpam-6010	75	10	and	and	CCONJ
ejpam-6010	75	11	only	only	ADV
ejpam-6010	75	12	if	if	SCONJ
ejpam-6010	75	13	a	a	DET
ejpam-6010	75	14	=	=	PUNCT
ejpam-6010	75	15	τ1τ2	τ1τ2	NOUN
ejpam-6010	75	16	-	-	NUM
ejpam-6010	75	17	cl(a	cl(a	NUM
ejpam-6010	75	18	)	)	PUNCT
ejpam-6010	75	19	.	.	PUNCT
ejpam-6010	76	1	(	(	PUNCT
ejpam-6010	76	2	5	5	X
ejpam-6010	76	3	)	)	PUNCT
ejpam-6010	76	4	τ1τ2	τ1τ2	NOUN
ejpam-6010	76	5	-	-	NOUN
ejpam-6010	76	6	cl(x	cl(x	X
ejpam-6010	76	7	−a	−a	NOUN
ejpam-6010	76	8	)	)	PUNCT
ejpam-6010	77	1	=	=	PUNCT
ejpam-6010	77	2	x	x	X
ejpam-6010	78	1	−	−	ADP
ejpam-6010	78	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	78	3	-	-	PUNCT
ejpam-6010	78	4	int(a	int(a	NOUN
ejpam-6010	78	5	)	)	PUNCT
ejpam-6010	78	6	.	.	PUNCT
ejpam-6010	79	1	a	a	DET
ejpam-6010	79	2	subseta	subseta	NOUN
ejpam-6010	79	3	of	of	ADP
ejpam-6010	79	4	a	a	DET
ejpam-6010	79	5	bitopological	bitopological	ADJ
ejpam-6010	79	6	space	space	NOUN
ejpam-6010	79	7	(	(	PUNCT
ejpam-6010	79	8	x	x	NOUN
ejpam-6010	79	9	,	,	PUNCT
ejpam-6010	79	10	τ1	τ1	NOUN
ejpam-6010	79	11	,	,	PUNCT
ejpam-6010	79	12	τ2	τ2	NOUN
ejpam-6010	79	13	)	)	PUNCT
ejpam-6010	79	14	is	be	AUX
ejpam-6010	79	15	called	call	VERB
ejpam-6010	79	16	(	(	PUNCT
ejpam-6010	79	17	τ1	τ1	NOUN
ejpam-6010	79	18	,	,	PUNCT
ejpam-6010	79	19	τ2)r	τ2)r	NOUN
ejpam-6010	79	20	-	-	PUNCT
ejpam-6010	79	21	open	open	ADJ
ejpam-6010	80	1	[	[	X
ejpam-6010	80	2	79	79	NUM
ejpam-6010	80	3	]	]	PUNCT
ejpam-6010	80	4	(	(	PUNCT
ejpam-6010	80	5	resp	resp	NOUN
ejpam-6010	80	6	.	.	PUNCT
ejpam-6010	81	1	(	(	PUNCT
ejpam-6010	81	2	τ1	τ1	NOUN
ejpam-6010	81	3	,	,	PUNCT
ejpam-6010	81	4	τ2)sopen	τ2)sopen	VERB
ejpam-6010	81	5	[	[	X
ejpam-6010	81	6	39	39	NUM
ejpam-6010	81	7	]	]	PUNCT
ejpam-6010	81	8	,	,	PUNCT
ejpam-6010	81	9	(	(	PUNCT
ejpam-6010	81	10	τ1	τ1	NOUN
ejpam-6010	81	11	,	,	PUNCT
ejpam-6010	81	12	τ2)p	τ2)p	NOUN
ejpam-6010	81	13	-	-	ADJ
ejpam-6010	81	14	open	open	ADJ
ejpam-6010	81	15	[	[	X
ejpam-6010	81	16	39	39	NUM
ejpam-6010	81	17	]	]	PUNCT
ejpam-6010	81	18	,	,	PUNCT
ejpam-6010	81	19	(	(	PUNCT
ejpam-6010	81	20	τ1	τ1	NOUN
ejpam-6010	81	21	,	,	PUNCT
ejpam-6010	81	22	τ2)β	τ2)β	ADJ
ejpam-6010	81	23	-	-	PUNCT
ejpam-6010	81	24	open	open	NOUN
ejpam-6010	82	1	[	[	X
ejpam-6010	82	2	39	39	NUM
ejpam-6010	82	3	]	]	PUNCT
ejpam-6010	82	4	)	)	PUNCT
ejpam-6010	82	5	if	if	SCONJ
ejpam-6010	82	6	a	a	DET
ejpam-6010	82	7	=	=	PUNCT
ejpam-6010	82	8	τ1τ2	τ1τ2	NOUN
ejpam-6010	82	9	-	-	NOUN
ejpam-6010	82	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	82	11	-	-	PUNCT
ejpam-6010	82	12	cl(a	cl(a	NUM
ejpam-6010	82	13	)	)	PUNCT
ejpam-6010	82	14	)	)	PUNCT
ejpam-6010	82	15	(	(	PUNCT
ejpam-6010	82	16	resp	resp	NOUN
ejpam-6010	82	17	.	.	PUNCT
ejpam-6010	83	1	a	a	DET
ejpam-6010	83	2	⊆	⊆	NUM
ejpam-6010	83	3	τ1τ2	τ1τ2	NOUN
ejpam-6010	83	4	-	-	ADJ
ejpam-6010	83	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6010	83	6	-	-	PUNCT
ejpam-6010	83	7	int(a	int(a	NOUN
ejpam-6010	83	8	)	)	PUNCT
ejpam-6010	83	9	)	)	PUNCT
ejpam-6010	83	10	,	,	PUNCT
ejpam-6010	83	11	a	a	DET
ejpam-6010	83	12	⊆	⊆	NUM
ejpam-6010	83	13	τ1τ2	τ1τ2	NOUN
ejpam-6010	83	14	-	-	NOUN
ejpam-6010	83	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	83	16	-	-	PUNCT
ejpam-6010	83	17	cl(a	cl(a	NUM
ejpam-6010	83	18	)	)	PUNCT
ejpam-6010	83	19	)	)	PUNCT
ejpam-6010	83	20	,	,	PUNCT
ejpam-6010	83	21	a	a	DET
ejpam-6010	83	22	⊆	⊆	NUM
ejpam-6010	83	23	τ1τ2	τ1τ2	NOUN
ejpam-6010	83	24	-	-	PUNCT
ejpam-6010	83	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6010	83	26	-	-	PUNCT
ejpam-6010	83	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	83	28	-	-	PUNCT
ejpam-6010	83	29	cl(a	cl(a	NUM
ejpam-6010	83	30	)	)	PUNCT
ejpam-6010	83	31	)	)	PUNCT
ejpam-6010	83	32	)	)	PUNCT
ejpam-6010	83	33	)	)	PUNCT
ejpam-6010	83	34	.	.	PUNCT
ejpam-6010	84	1	the	the	DET
ejpam-6010	84	2	complement	complement	NOUN
ejpam-6010	84	3	of	of	ADP
ejpam-6010	84	4	a	a	DET
ejpam-6010	84	5	(	(	PUNCT
ejpam-6010	84	6	τ1	τ1	NOUN
ejpam-6010	84	7	,	,	PUNCT
ejpam-6010	84	8	τ2)r	τ2)r	NOUN
ejpam-6010	84	9	-	-	PUNCT
ejpam-6010	84	10	open	open	ADJ
ejpam-6010	84	11	(	(	PUNCT
ejpam-6010	84	12	resp	resp	NOUN
ejpam-6010	84	13	.	.	PUNCT
ejpam-6010	85	1	(	(	PUNCT
ejpam-6010	85	2	τ1	τ1	NOUN
ejpam-6010	85	3	,	,	PUNCT
ejpam-6010	85	4	τ2)s	τ2)s	NOUN
ejpam-6010	85	5	-	-	PUNCT
ejpam-6010	85	6	open	open	ADJ
ejpam-6010	85	7	,	,	PUNCT
ejpam-6010	85	8	(	(	PUNCT
ejpam-6010	85	9	τ1	τ1	NOUN
ejpam-6010	85	10	,	,	PUNCT
ejpam-6010	85	11	τ2)p	τ2)p	NOUN
ejpam-6010	85	12	-	-	ADJ
ejpam-6010	85	13	open	open	ADJ
ejpam-6010	85	14	,	,	PUNCT
ejpam-6010	85	15	(	(	PUNCT
ejpam-6010	85	16	τ1	τ1	NOUN
ejpam-6010	85	17	,	,	PUNCT
ejpam-6010	85	18	τ2)β	τ2)β	ADJ
ejpam-6010	85	19	-	-	PUNCT
ejpam-6010	85	20	open	open	ADJ
ejpam-6010	85	21	)	)	PUNCT
ejpam-6010	85	22	set	set	NOUN
ejpam-6010	85	23	is	be	AUX
ejpam-6010	85	24	called	call	VERB
ejpam-6010	85	25	(	(	PUNCT
ejpam-6010	85	26	τ1	τ1	NOUN
ejpam-6010	85	27	,	,	PUNCT
ejpam-6010	85	28	τ2)r	τ2)r	NOUN
ejpam-6010	85	29	-	-	PUNCT
ejpam-6010	85	30	closed	closed	ADJ
ejpam-6010	85	31	(	(	PUNCT
ejpam-6010	85	32	resp	resp	NOUN
ejpam-6010	85	33	.	.	PUNCT
ejpam-6010	86	1	(	(	PUNCT
ejpam-6010	86	2	τ1	τ1	NOUN
ejpam-6010	86	3	,	,	PUNCT
ejpam-6010	86	4	τ2)s	τ2)s	NOUN
ejpam-6010	86	5	-	-	PUNCT
ejpam-6010	86	6	closed	closed	ADJ
ejpam-6010	86	7	,	,	PUNCT
ejpam-6010	86	8	(	(	PUNCT
ejpam-6010	86	9	τ1	τ1	NOUN
ejpam-6010	86	10	,	,	PUNCT
ejpam-6010	86	11	τ2)p	τ2)p	NOUN
ejpam-6010	86	12	-	-	PUNCT
ejpam-6010	86	13	closed	closed	ADJ
ejpam-6010	86	14	,	,	PUNCT
ejpam-6010	86	15	(	(	PUNCT
ejpam-6010	86	16	τ1	τ1	NOUN
ejpam-6010	86	17	,	,	PUNCT
ejpam-6010	86	18	τ2)β	τ2)β	ADJ
ejpam-6010	86	19	-	-	PUNCT
ejpam-6010	86	20	closed	closed	ADJ
ejpam-6010	86	21	)	)	PUNCT
ejpam-6010	86	22	.	.	PUNCT
ejpam-6010	87	1	let	let	VERB
ejpam-6010	87	2	a	a	DET
ejpam-6010	87	3	be	be	AUX
ejpam-6010	87	4	a	a	DET
ejpam-6010	87	5	subset	subset	NOUN
ejpam-6010	87	6	of	of	ADP
ejpam-6010	87	7	a	a	DET
ejpam-6010	87	8	bitopological	bitopological	ADJ
ejpam-6010	87	9	space	space	NOUN
ejpam-6010	87	10	(	(	PUNCT
ejpam-6010	87	11	x	x	NOUN
ejpam-6010	87	12	,	,	PUNCT
ejpam-6010	87	13	τ1	τ1	NOUN
ejpam-6010	87	14	,	,	PUNCT
ejpam-6010	87	15	τ2	τ2	NOUN
ejpam-6010	87	16	)	)	PUNCT
ejpam-6010	87	17	.	.	PUNCT
ejpam-6010	88	1	the	the	DET
ejpam-6010	88	2	set	set	NOUN
ejpam-6010	88	3	∩{v	∩{v	PROPN
ejpam-6010	89	1	|	|	ADV
ejpam-6010	89	2	v	v	NOUN
ejpam-6010	89	3	is	be	AUX
ejpam-6010	89	4	(	(	PUNCT
ejpam-6010	89	5	τ1	τ1	NOUN
ejpam-6010	89	6	,	,	PUNCT
ejpam-6010	89	7	τ2)r	τ2)r	NOUN
ejpam-6010	89	8	-	-	PUNCT
ejpam-6010	89	9	open	open	ADJ
ejpam-6010	89	10	and	and	CCONJ
ejpam-6010	89	11	a	a	DET
ejpam-6010	89	12	⊆	⊆	NUM
ejpam-6010	89	13	v	v	NOUN
ejpam-6010	89	14	}	}	PUNCT
ejpam-6010	89	15	is	be	AUX
ejpam-6010	89	16	called	call	VERB
ejpam-6010	89	17	the	the	DET
ejpam-6010	89	18	(	(	PUNCT
ejpam-6010	89	19	τ1	τ1	NOUN
ejpam-6010	89	20	,	,	PUNCT
ejpam-6010	89	21	τ2)r	τ2)r	ADJ
ejpam-6010	89	22	-	-	PUNCT
ejpam-6010	89	23	kernel	kernel	NOUN
ejpam-6010	89	24	of	of	ADP
ejpam-6010	89	25	a	a	PRON
ejpam-6010	89	26	and	and	CCONJ
ejpam-6010	89	27	is	be	AUX
ejpam-6010	89	28	denoted	denote	VERB
ejpam-6010	89	29	by	by	ADP
ejpam-6010	89	30	(	(	PUNCT
ejpam-6010	89	31	τ1	τ1	NOUN
ejpam-6010	89	32	,	,	PUNCT
ejpam-6010	89	33	τ2)r	τ2)r	NOUN
ejpam-6010	89	34	-	-	PUNCT
ejpam-6010	89	35	ker(a	ker(a	NOUN
ejpam-6010	89	36	)	)	PUNCT
ejpam-6010	89	37	.	.	PUNCT
ejpam-6010	90	1	j.	j.	PROPN
ejpam-6010	90	2	khampakdee	khampakdee	PROPN
ejpam-6010	90	3	,	,	PUNCT
ejpam-6010	90	4	a.	a.	PROPN
ejpam-6010	90	5	sama	sama	PROPN
ejpam-6010	90	6	-	-	PUNCT
ejpam-6010	90	7	ae	ae	PROPN
ejpam-6010	90	8	,	,	PUNCT
ejpam-6010	90	9	c.	c.	PROPN
ejpam-6010	90	10	boonpok	boonpok	PROPN
ejpam-6010	90	11	/	/	SYM
ejpam-6010	90	12	eur	eur	PROPN
ejpam-6010	90	13	.	.	PUNCT
ejpam-6010	91	1	j.	j.	PROPN
ejpam-6010	91	2	pure	pure	PROPN
ejpam-6010	91	3	appl	appl	PROPN
ejpam-6010	91	4	.	.	PROPN
ejpam-6010	91	5	math	math	PROPN
ejpam-6010	91	6	,	,	PUNCT
ejpam-6010	91	7	18	18	NUM
ejpam-6010	91	8	(	(	PUNCT
ejpam-6010	91	9	2	2	NUM
ejpam-6010	91	10	)	)	PUNCT
ejpam-6010	91	11	(	(	PUNCT
ejpam-6010	91	12	2025	2025	NUM
ejpam-6010	91	13	)	)	PUNCT
ejpam-6010	91	14	,	,	PUNCT
ejpam-6010	91	15	6010	6010	NUM
ejpam-6010	91	16	4	4	NUM
ejpam-6010	91	17	of	of	ADP
ejpam-6010	91	18	19	19	NUM
ejpam-6010	91	19	lemma	lemma	PROPN
ejpam-6010	91	20	2	2	NUM
ejpam-6010	91	21	.	.	X
ejpam-6010	92	1	for	for	ADP
ejpam-6010	92	2	subsets	subset	NOUN
ejpam-6010	92	3	a	a	DET
ejpam-6010	92	4	,	,	PUNCT
ejpam-6010	92	5	b	b	NOUN
ejpam-6010	92	6	of	of	ADP
ejpam-6010	92	7	a	a	DET
ejpam-6010	92	8	bitopological	bitopological	ADJ
ejpam-6010	92	9	space	space	NOUN
ejpam-6010	92	10	(	(	PUNCT
ejpam-6010	92	11	x	x	NOUN
ejpam-6010	92	12	,	,	PUNCT
ejpam-6010	92	13	τ1	τ1	NOUN
ejpam-6010	92	14	,	,	PUNCT
ejpam-6010	92	15	τ2	τ2	NOUN
ejpam-6010	92	16	)	)	PUNCT
ejpam-6010	92	17	,	,	PUNCT
ejpam-6010	92	18	the	the	DET
ejpam-6010	92	19	following	follow	VERB
ejpam-6010	92	20	properties	property	NOUN
ejpam-6010	92	21	hold	hold	VERB
ejpam-6010	92	22	:	:	PUNCT
ejpam-6010	92	23	(	(	PUNCT
ejpam-6010	92	24	1	1	X
ejpam-6010	92	25	)	)	PUNCT
ejpam-6010	92	26	a	a	DET
ejpam-6010	92	27	⊆	⊆	NUM
ejpam-6010	92	28	(	(	PUNCT
ejpam-6010	92	29	τ1	τ1	NOUN
ejpam-6010	92	30	,	,	PUNCT
ejpam-6010	92	31	τ2)r	τ2)r	NOUN
ejpam-6010	92	32	-	-	PUNCT
ejpam-6010	92	33	ker(a	ker(a	NOUN
ejpam-6010	92	34	)	)	PUNCT
ejpam-6010	92	35	.	.	PUNCT
ejpam-6010	93	1	(	(	PUNCT
ejpam-6010	93	2	2	2	X
ejpam-6010	93	3	)	)	PUNCT
ejpam-6010	93	4	if	if	SCONJ
ejpam-6010	93	5	a	a	DET
ejpam-6010	93	6	⊆	⊆	NUM
ejpam-6010	93	7	b	b	NOUN
ejpam-6010	93	8	,	,	PUNCT
ejpam-6010	93	9	then	then	ADV
ejpam-6010	93	10	(	(	PUNCT
ejpam-6010	93	11	τ1	τ1	NOUN
ejpam-6010	93	12	,	,	PUNCT
ejpam-6010	93	13	τ2)r	τ2)r	NOUN
ejpam-6010	93	14	-	-	PUNCT
ejpam-6010	93	15	ker(a	ker(a	NOUN
ejpam-6010	93	16	)	)	PUNCT
ejpam-6010	93	17	⊆	⊆	NUM
ejpam-6010	93	18	(	(	PUNCT
ejpam-6010	93	19	τ1	τ1	NOUN
ejpam-6010	93	20	,	,	PUNCT
ejpam-6010	93	21	τ2)r	τ2)r	PROPN
ejpam-6010	93	22	-	-	PUNCT
ejpam-6010	93	23	ker(b	ker(b	PROPN
ejpam-6010	93	24	)	)	PUNCT
ejpam-6010	93	25	.	.	PUNCT
ejpam-6010	94	1	(	(	PUNCT
ejpam-6010	94	2	3	3	X
ejpam-6010	94	3	)	)	PUNCT
ejpam-6010	94	4	if	if	SCONJ
ejpam-6010	94	5	a	a	PRON
ejpam-6010	94	6	is	be	AUX
ejpam-6010	94	7	(	(	PUNCT
ejpam-6010	94	8	τ1	τ1	NOUN
ejpam-6010	94	9	,	,	PUNCT
ejpam-6010	94	10	τ2)r	τ2)r	NOUN
ejpam-6010	94	11	-	-	PUNCT
ejpam-6010	94	12	open	open	ADJ
ejpam-6010	94	13	,	,	PUNCT
ejpam-6010	94	14	then	then	ADV
ejpam-6010	94	15	(	(	PUNCT
ejpam-6010	94	16	τ1	τ1	NOUN
ejpam-6010	94	17	,	,	PUNCT
ejpam-6010	94	18	τ2)r	τ2)r	NOUN
ejpam-6010	94	19	-	-	PUNCT
ejpam-6010	94	20	ker(a	ker(a	NOUN
ejpam-6010	94	21	)	)	PUNCT
ejpam-6010	94	22	=	=	SYM
ejpam-6010	94	23	a.	a.	NOUN
ejpam-6010	94	24	(	(	PUNCT
ejpam-6010	94	25	4	4	NUM
ejpam-6010	94	26	)	)	PUNCT
ejpam-6010	94	27	x	x	SYM
ejpam-6010	95	1	∈	∈	PROPN
ejpam-6010	95	2	(	(	PUNCT
ejpam-6010	95	3	τ1	τ1	NOUN
ejpam-6010	95	4	,	,	PUNCT
ejpam-6010	95	5	τ2)r	τ2)r	NOUN
ejpam-6010	95	6	-	-	PUNCT
ejpam-6010	95	7	ker(a	ker(a	NOUN
ejpam-6010	95	8	)	)	PUNCT
ejpam-6010	95	9	if	if	SCONJ
ejpam-6010	95	10	and	and	CCONJ
ejpam-6010	95	11	only	only	ADV
ejpam-6010	95	12	if	if	SCONJ
ejpam-6010	95	13	a	a	DET
ejpam-6010	95	14	∩	∩	NOUN
ejpam-6010	95	15	k	k	PROPN
ejpam-6010	95	16	̸=	̸=	PROPN
ejpam-6010	95	17	∅	∅	NOUN
ejpam-6010	95	18	for	for	ADP
ejpam-6010	95	19	every	every	PRON
ejpam-6010	95	20	(	(	PUNCT
ejpam-6010	95	21	τ1	τ1	NOUN
ejpam-6010	95	22	,	,	PUNCT
ejpam-6010	95	23	τ2)r	τ2)r	NOUN
ejpam-6010	95	24	-	-	PUNCT
ejpam-6010	95	25	closed	close	VERB
ejpam-6010	95	26	set	set	NOUN
ejpam-6010	95	27	k	k	NOUN
ejpam-6010	95	28	containing	contain	VERB
ejpam-6010	95	29	x.	x.	NOUN
ejpam-6010	95	30	a	a	DET
ejpam-6010	95	31	subset	subset	NOUN
ejpam-6010	95	32	a	a	PRON
ejpam-6010	95	33	of	of	ADP
ejpam-6010	95	34	a	a	DET
ejpam-6010	95	35	bitopological	bitopological	ADJ
ejpam-6010	95	36	space	space	NOUN
ejpam-6010	95	37	(	(	PUNCT
ejpam-6010	95	38	x	x	NOUN
ejpam-6010	95	39	,	,	PUNCT
ejpam-6010	95	40	τ1	τ1	NOUN
ejpam-6010	95	41	,	,	PUNCT
ejpam-6010	95	42	τ2	τ2	NOUN
ejpam-6010	95	43	)	)	PUNCT
ejpam-6010	95	44	is	be	AUX
ejpam-6010	95	45	said	say	VERB
ejpam-6010	95	46	to	to	PART
ejpam-6010	95	47	be	be	AUX
ejpam-6010	95	48	α(τ1	α(τ1	NOUN
ejpam-6010	95	49	,	,	PUNCT
ejpam-6010	95	50	τ2)-open	τ2)-open	ADJ
ejpam-6010	95	51	[	[	X
ejpam-6010	95	52	80	80	NUM
ejpam-6010	95	53	]	]	X
ejpam-6010	95	54	if	if	SCONJ
ejpam-6010	95	55	a	a	DET
ejpam-6010	95	56	⊆	⊆	NUM
ejpam-6010	95	57	τ1τ2	τ1τ2	NOUN
ejpam-6010	95	58	-	-	PUNCT
ejpam-6010	95	59	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	95	60	-	-	PUNCT
ejpam-6010	95	61	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6010	95	62	-	-	PUNCT
ejpam-6010	95	63	int(a	int(a	NOUN
ejpam-6010	95	64	)	)	PUNCT
ejpam-6010	95	65	)	)	PUNCT
ejpam-6010	95	66	)	)	PUNCT
ejpam-6010	95	67	.	.	PUNCT
ejpam-6010	96	1	the	the	DET
ejpam-6010	96	2	complement	complement	NOUN
ejpam-6010	96	3	of	of	ADP
ejpam-6010	96	4	an	an	DET
ejpam-6010	96	5	α(τ1	α(τ1	NOUN
ejpam-6010	96	6	,	,	PUNCT
ejpam-6010	96	7	τ2)-open	τ2)-open	ADJ
ejpam-6010	96	8	set	set	NOUN
ejpam-6010	96	9	is	be	AUX
ejpam-6010	96	10	called	call	VERB
ejpam-6010	96	11	α(τ1	α(τ1	NOUN
ejpam-6010	96	12	,	,	PUNCT
ejpam-6010	96	13	τ2)closed	τ2)close	VERB
ejpam-6010	96	14	.	.	PUNCT
ejpam-6010	97	1	let	let	VERB
ejpam-6010	97	2	a	a	DET
ejpam-6010	97	3	be	be	AUX
ejpam-6010	97	4	a	a	DET
ejpam-6010	97	5	subset	subset	NOUN
ejpam-6010	97	6	of	of	ADP
ejpam-6010	97	7	a	a	DET
ejpam-6010	97	8	bitopological	bitopological	ADJ
ejpam-6010	97	9	space	space	NOUN
ejpam-6010	97	10	(	(	PUNCT
ejpam-6010	97	11	x	x	NOUN
ejpam-6010	97	12	,	,	PUNCT
ejpam-6010	97	13	τ1	τ1	NOUN
ejpam-6010	97	14	,	,	PUNCT
ejpam-6010	97	15	τ2	τ2	NOUN
ejpam-6010	97	16	)	)	PUNCT
ejpam-6010	97	17	.	.	PUNCT
ejpam-6010	98	1	the	the	DET
ejpam-6010	98	2	intersection	intersection	NOUN
ejpam-6010	98	3	of	of	ADP
ejpam-6010	98	4	all	all	DET
ejpam-6010	98	5	(	(	PUNCT
ejpam-6010	98	6	τ1	τ1	NOUN
ejpam-6010	98	7	,	,	PUNCT
ejpam-6010	98	8	τ2)p	τ2)p	NOUN
ejpam-6010	98	9	-	-	PUNCT
ejpam-6010	98	10	closed	closed	ADJ
ejpam-6010	98	11	(	(	PUNCT
ejpam-6010	98	12	resp	resp	NOUN
ejpam-6010	98	13	.	.	PUNCT
ejpam-6010	99	1	(	(	PUNCT
ejpam-6010	99	2	τ1	τ1	NOUN
ejpam-6010	99	3	,	,	PUNCT
ejpam-6010	99	4	τ2)s	τ2)s	NOUN
ejpam-6010	99	5	-	-	PUNCT
ejpam-6010	99	6	closed	closed	ADJ
ejpam-6010	99	7	,	,	PUNCT
ejpam-6010	99	8	α(τ1	α(τ1	NOUN
ejpam-6010	99	9	,	,	PUNCT
ejpam-6010	99	10	τ2)-closed	τ2)-closed	ADJ
ejpam-6010	99	11	)	)	PUNCT
ejpam-6010	99	12	sets	set	NOUN
ejpam-6010	99	13	of	of	ADP
ejpam-6010	99	14	x	x	PUNCT
ejpam-6010	99	15	containing	contain	VERB
ejpam-6010	99	16	a	a	PRON
ejpam-6010	99	17	is	be	AUX
ejpam-6010	99	18	called	call	VERB
ejpam-6010	99	19	the	the	DET
ejpam-6010	99	20	(	(	PUNCT
ejpam-6010	99	21	τ1	τ1	NOUN
ejpam-6010	99	22	,	,	PUNCT
ejpam-6010	99	23	τ2)p	τ2)p	NOUN
ejpam-6010	99	24	-	-	NOUN
ejpam-6010	99	25	closure	closure	NOUN
ejpam-6010	99	26	[	[	X
ejpam-6010	99	27	65	65	NUM
ejpam-6010	99	28	]	]	X
ejpam-6010	99	29	(	(	PUNCT
ejpam-6010	99	30	resp	resp	NOUN
ejpam-6010	99	31	.	.	PUNCT
ejpam-6010	100	1	(	(	PUNCT
ejpam-6010	100	2	τ1	τ1	NOUN
ejpam-6010	100	3	,	,	PUNCT
ejpam-6010	100	4	τ2)s	τ2)s	NOUN
ejpam-6010	100	5	-	-	PUNCT
ejpam-6010	100	6	closure	closure	NOUN
ejpam-6010	100	7	[	[	X
ejpam-6010	100	8	39	39	NUM
ejpam-6010	100	9	]	]	PUNCT
ejpam-6010	100	10	,	,	PUNCT
ejpam-6010	100	11	α(τ1	α(τ1	NOUN
ejpam-6010	100	12	,	,	PUNCT
ejpam-6010	100	13	τ2)-closure	τ2)-closure	NOUN
ejpam-6010	100	14	[	[	X
ejpam-6010	100	15	66	66	NUM
ejpam-6010	100	16	]	]	PUNCT
ejpam-6010	100	17	)	)	PUNCT
ejpam-6010	100	18	of	of	ADP
ejpam-6010	100	19	a	a	PRON
ejpam-6010	100	20	and	and	CCONJ
ejpam-6010	100	21	is	be	AUX
ejpam-6010	100	22	denoted	denote	VERB
ejpam-6010	100	23	by	by	ADP
ejpam-6010	100	24	(	(	PUNCT
ejpam-6010	100	25	τ1	τ1	NOUN
ejpam-6010	100	26	,	,	PUNCT
ejpam-6010	100	27	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6010	100	28	)	)	PUNCT
ejpam-6010	100	29	(	(	PUNCT
ejpam-6010	100	30	resp	resp	NOUN
ejpam-6010	100	31	.	.	PUNCT
ejpam-6010	101	1	(	(	PUNCT
ejpam-6010	101	2	τ1	τ1	NOUN
ejpam-6010	101	3	,	,	PUNCT
ejpam-6010	101	4	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6010	101	5	)	)	PUNCT
ejpam-6010	101	6	,	,	PUNCT
ejpam-6010	101	7	α(τ1	α(τ1	NOUN
ejpam-6010	101	8	,	,	PUNCT
ejpam-6010	101	9	τ2)-cl(a	τ2)-cl(a	NUM
ejpam-6010	101	10	)	)	PUNCT
ejpam-6010	101	11	)	)	PUNCT
ejpam-6010	101	12	.	.	PUNCT
ejpam-6010	102	1	the	the	DET
ejpam-6010	102	2	union	union	NOUN
ejpam-6010	102	3	of	of	ADP
ejpam-6010	102	4	all	all	DET
ejpam-6010	102	5	(	(	PUNCT
ejpam-6010	102	6	τ1	τ1	NOUN
ejpam-6010	102	7	,	,	PUNCT
ejpam-6010	102	8	τ2)p	τ2)p	NOUN
ejpam-6010	102	9	-	-	ADJ
ejpam-6010	102	10	open	open	ADJ
ejpam-6010	102	11	(	(	PUNCT
ejpam-6010	102	12	resp	resp	NOUN
ejpam-6010	102	13	.	.	PUNCT
ejpam-6010	103	1	(	(	PUNCT
ejpam-6010	103	2	τ1	τ1	NOUN
ejpam-6010	103	3	,	,	PUNCT
ejpam-6010	103	4	τ2)s	τ2)s	NOUN
ejpam-6010	103	5	-	-	PUNCT
ejpam-6010	103	6	open	open	ADJ
ejpam-6010	103	7	,	,	PUNCT
ejpam-6010	103	8	α(τ1	α(τ1	NOUN
ejpam-6010	103	9	,	,	PUNCT
ejpam-6010	103	10	τ2)-open	τ2)-open	ADJ
ejpam-6010	103	11	)	)	PUNCT
ejpam-6010	103	12	sets	set	NOUN
ejpam-6010	103	13	of	of	ADP
ejpam-6010	103	14	x	x	PUNCT
ejpam-6010	103	15	contained	contain	VERB
ejpam-6010	103	16	in	in	ADP
ejpam-6010	103	17	a	a	PRON
ejpam-6010	103	18	is	be	AUX
ejpam-6010	103	19	called	call	VERB
ejpam-6010	103	20	the	the	DET
ejpam-6010	103	21	(	(	PUNCT
ejpam-6010	103	22	τ1	τ1	PROPN
ejpam-6010	103	23	,	,	PUNCT
ejpam-6010	103	24	τ2)pinterior	τ2)pinterior	PROPN
ejpam-6010	104	1	[	[	X
ejpam-6010	104	2	65	65	NUM
ejpam-6010	104	3	]	]	X
ejpam-6010	104	4	(	(	PUNCT
ejpam-6010	104	5	resp	resp	NOUN
ejpam-6010	104	6	.	.	PUNCT
ejpam-6010	105	1	(	(	PUNCT
ejpam-6010	105	2	τ1	τ1	NOUN
ejpam-6010	105	3	,	,	PUNCT
ejpam-6010	105	4	τ2)s	τ2)s	NOUN
ejpam-6010	105	5	-	-	NOUN
ejpam-6010	105	6	interior	interior	NOUN
ejpam-6010	105	7	[	[	X
ejpam-6010	105	8	39	39	NUM
ejpam-6010	105	9	]	]	PUNCT
ejpam-6010	105	10	,	,	PUNCT
ejpam-6010	105	11	α(τ1	α(τ1	NOUN
ejpam-6010	105	12	,	,	PUNCT
ejpam-6010	105	13	τ2)-interior	τ2)-interior	PROPN
ejpam-6010	105	14	[	[	X
ejpam-6010	105	15	66	66	NUM
ejpam-6010	105	16	]	]	PUNCT
ejpam-6010	105	17	)	)	PUNCT
ejpam-6010	105	18	of	of	ADP
ejpam-6010	105	19	a	a	PRON
ejpam-6010	105	20	and	and	CCONJ
ejpam-6010	105	21	is	be	AUX
ejpam-6010	105	22	denoted	denote	VERB
ejpam-6010	105	23	by	by	ADP
ejpam-6010	105	24	(	(	PUNCT
ejpam-6010	105	25	τ1	τ1	NOUN
ejpam-6010	105	26	,	,	PUNCT
ejpam-6010	105	27	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6010	105	28	)	)	PUNCT
ejpam-6010	105	29	(	(	PUNCT
ejpam-6010	105	30	resp	resp	NOUN
ejpam-6010	105	31	.	.	PUNCT
ejpam-6010	106	1	(	(	PUNCT
ejpam-6010	106	2	τ1	τ1	NOUN
ejpam-6010	106	3	,	,	PUNCT
ejpam-6010	106	4	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6010	106	5	)	)	PUNCT
ejpam-6010	106	6	,	,	PUNCT
ejpam-6010	106	7	α(τ1	α(τ1	NOUN
ejpam-6010	106	8	,	,	PUNCT
ejpam-6010	106	9	τ2)-int(a	τ2)-int(a	NOUN
ejpam-6010	106	10	)	)	PUNCT
ejpam-6010	106	11	)	)	PUNCT
ejpam-6010	106	12	.	.	PUNCT
ejpam-6010	107	1	lemma	lemma	PROPN
ejpam-6010	107	2	3	3	X
ejpam-6010	107	3	.	.	X
ejpam-6010	108	1	for	for	ADP
ejpam-6010	108	2	a	a	DET
ejpam-6010	108	3	subset	subset	NOUN
ejpam-6010	108	4	a	a	PRON
ejpam-6010	108	5	of	of	ADP
ejpam-6010	108	6	a	a	DET
ejpam-6010	108	7	bitopological	bitopological	ADJ
ejpam-6010	108	8	space	space	NOUN
ejpam-6010	108	9	(	(	PUNCT
ejpam-6010	108	10	x	x	NOUN
ejpam-6010	108	11	,	,	PUNCT
ejpam-6010	108	12	τ1	τ1	NOUN
ejpam-6010	108	13	,	,	PUNCT
ejpam-6010	108	14	τ2	τ2	NOUN
ejpam-6010	108	15	)	)	PUNCT
ejpam-6010	108	16	,	,	PUNCT
ejpam-6010	108	17	the	the	DET
ejpam-6010	108	18	following	follow	VERB
ejpam-6010	108	19	properties	property	NOUN
ejpam-6010	108	20	hold	hold	VERB
ejpam-6010	108	21	:	:	PUNCT
ejpam-6010	108	22	(	(	PUNCT
ejpam-6010	108	23	1	1	X
ejpam-6010	108	24	)	)	PUNCT
ejpam-6010	108	25	(	(	PUNCT
ejpam-6010	108	26	τ1	τ1	NOUN
ejpam-6010	108	27	,	,	PUNCT
ejpam-6010	108	28	τ2)-pcl(a	τ2)-pcl(a	ADJ
ejpam-6010	108	29	)	)	PUNCT
ejpam-6010	108	30	=	=	PUNCT
ejpam-6010	109	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	109	2	-	-	ADJ
ejpam-6010	109	3	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6010	109	4	-	-	PUNCT
ejpam-6010	109	5	int(a	int(a	NOUN
ejpam-6010	109	6	)	)	PUNCT
ejpam-6010	109	7	)	)	PUNCT
ejpam-6010	110	1	∪a	∪a	X
ejpam-6010	111	1	[	[	X
ejpam-6010	111	2	65	65	NUM
ejpam-6010	111	3	]	]	PUNCT
ejpam-6010	111	4	.	.	PUNCT
ejpam-6010	112	1	(	(	PUNCT
ejpam-6010	112	2	2	2	NUM
ejpam-6010	112	3	)	)	PUNCT
ejpam-6010	112	4	(	(	PUNCT
ejpam-6010	112	5	τ1	τ1	NOUN
ejpam-6010	112	6	,	,	PUNCT
ejpam-6010	112	7	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6010	112	8	)	)	PUNCT
ejpam-6010	113	1	=	=	PUNCT
ejpam-6010	113	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	113	3	-	-	NOUN
ejpam-6010	113	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	113	5	-	-	PUNCT
ejpam-6010	113	6	cl(a	cl(a	NUM
ejpam-6010	113	7	)	)	PUNCT
ejpam-6010	113	8	)	)	PUNCT
ejpam-6010	114	1	∩a	∩a	PROPN
ejpam-6010	115	1	[	[	X
ejpam-6010	115	2	26	26	NUM
ejpam-6010	115	3	]	]	PUNCT
ejpam-6010	115	4	.	.	PUNCT
ejpam-6010	116	1	(	(	PUNCT
ejpam-6010	116	2	3	3	X
ejpam-6010	116	3	)	)	PUNCT
ejpam-6010	116	4	(	(	PUNCT
ejpam-6010	116	5	τ1	τ1	NOUN
ejpam-6010	116	6	,	,	PUNCT
ejpam-6010	116	7	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6010	116	8	)	)	PUNCT
ejpam-6010	116	9	=	=	PUNCT
ejpam-6010	117	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	117	2	-	-	NOUN
ejpam-6010	117	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	117	4	-	-	PUNCT
ejpam-6010	117	5	cl(a	cl(a	NUM
ejpam-6010	117	6	)	)	PUNCT
ejpam-6010	117	7	)	)	PUNCT
ejpam-6010	118	1	∪a	∪a	X
ejpam-6010	119	1	[	[	X
ejpam-6010	119	2	39	39	NUM
ejpam-6010	119	3	]	]	PUNCT
ejpam-6010	119	4	.	.	PUNCT
ejpam-6010	120	1	(	(	PUNCT
ejpam-6010	120	2	4	4	NUM
ejpam-6010	120	3	)	)	PUNCT
ejpam-6010	120	4	(	(	PUNCT
ejpam-6010	120	5	τ1	τ1	NOUN
ejpam-6010	120	6	,	,	PUNCT
ejpam-6010	120	7	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6010	120	8	)	)	PUNCT
ejpam-6010	121	1	=	=	PUNCT
ejpam-6010	121	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	121	3	-	-	ADJ
ejpam-6010	121	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6010	121	5	-	-	PUNCT
ejpam-6010	121	6	int(a	int(a	NOUN
ejpam-6010	121	7	)	)	PUNCT
ejpam-6010	121	8	)	)	PUNCT
ejpam-6010	122	1	∩a	∩a	PROPN
ejpam-6010	123	1	[	[	X
ejpam-6010	123	2	62	62	NUM
ejpam-6010	123	3	]	]	PUNCT
ejpam-6010	123	4	.	.	PUNCT
ejpam-6010	124	1	for	for	ADP
ejpam-6010	124	2	a	a	DET
ejpam-6010	124	3	subset	subset	NOUN
ejpam-6010	124	4	a	a	PRON
ejpam-6010	124	5	of	of	ADP
ejpam-6010	124	6	a	a	DET
ejpam-6010	124	7	bitopological	bitopological	ADJ
ejpam-6010	124	8	space	space	NOUN
ejpam-6010	124	9	(	(	PUNCT
ejpam-6010	124	10	x	x	NOUN
ejpam-6010	124	11	,	,	PUNCT
ejpam-6010	124	12	τ1	τ1	NOUN
ejpam-6010	124	13	,	,	PUNCT
ejpam-6010	124	14	τ2	τ2	PROPN
ejpam-6010	124	15	)	)	PUNCT
ejpam-6010	124	16	,	,	PUNCT
ejpam-6010	124	17	a	a	DET
ejpam-6010	124	18	point	point	NOUN
ejpam-6010	124	19	x	x	X
ejpam-6010	124	20	∈	∈	NOUN
ejpam-6010	124	21	x	x	PUNCT
ejpam-6010	124	22	is	be	AUX
ejpam-6010	124	23	called	call	VERB
ejpam-6010	124	24	a	a	DET
ejpam-6010	124	25	s(τ1	s(τ1	NOUN
ejpam-6010	124	26	,	,	PUNCT
ejpam-6010	124	27	τ2)θcluster	τ2)θcluster	NOUN
ejpam-6010	124	28	point	point	NOUN
ejpam-6010	124	29	[	[	X
ejpam-6010	124	30	81	81	NUM
ejpam-6010	124	31	]	]	PUNCT
ejpam-6010	124	32	of	of	ADP
ejpam-6010	124	33	a	a	DET
ejpam-6010	124	34	if	if	SCONJ
ejpam-6010	124	35	τ1τ2	τ1τ2	NOUN
ejpam-6010	124	36	-	-	NOUN
ejpam-6010	124	37	cl(u	cl(u	NOUN
ejpam-6010	124	38	)	)	PUNCT
ejpam-6010	124	39	∩	∩	NOUN
ejpam-6010	124	40	a	a	DET
ejpam-6010	124	41	̸=	̸=	PROPN
ejpam-6010	124	42	∅	∅	NOUN
ejpam-6010	124	43	for	for	ADP
ejpam-6010	124	44	every	every	DET
ejpam-6010	124	45	(	(	PUNCT
ejpam-6010	124	46	τ1	τ1	NOUN
ejpam-6010	124	47	,	,	PUNCT
ejpam-6010	124	48	τ2)s	τ2)s	NOUN
ejpam-6010	124	49	-	-	PUNCT
ejpam-6010	124	50	open	open	ADJ
ejpam-6010	124	51	set	set	NOUN
ejpam-6010	124	52	u	u	NOUN
ejpam-6010	124	53	containing	contain	VERB
ejpam-6010	124	54	x.	x.	NOUN
ejpam-6010	124	55	the	the	DET
ejpam-6010	124	56	set	set	NOUN
ejpam-6010	124	57	of	of	ADP
ejpam-6010	124	58	all	all	DET
ejpam-6010	124	59	s(τ1	s(τ1	NOUN
ejpam-6010	124	60	,	,	PUNCT
ejpam-6010	124	61	τ2)θ	τ2)θ	ADJ
ejpam-6010	124	62	-	-	PUNCT
ejpam-6010	124	63	cluster	cluster	NOUN
ejpam-6010	124	64	points	point	NOUN
ejpam-6010	124	65	of	of	ADP
ejpam-6010	124	66	a	a	PRON
ejpam-6010	124	67	is	be	AUX
ejpam-6010	124	68	called	call	VERB
ejpam-6010	124	69	the	the	DET
ejpam-6010	124	70	s(τ1	s(τ1	NOUN
ejpam-6010	124	71	,	,	PUNCT
ejpam-6010	124	72	τ2)θ	τ2)θ	NOUN
ejpam-6010	124	73	-	-	PUNCT
ejpam-6010	124	74	closure	closure	NOUN
ejpam-6010	124	75	[	[	X
ejpam-6010	124	76	81	81	NUM
ejpam-6010	124	77	]	]	PUNCT
ejpam-6010	124	78	of	of	ADP
ejpam-6010	124	79	a	a	PRON
ejpam-6010	124	80	and	and	CCONJ
ejpam-6010	124	81	is	be	AUX
ejpam-6010	124	82	denoted	denote	VERB
ejpam-6010	124	83	by	by	ADP
ejpam-6010	124	84	s(τ1	s(τ1	NOUN
ejpam-6010	124	85	,	,	PUNCT
ejpam-6010	124	86	τ2)θ	τ2)θ	NOUN
ejpam-6010	124	87	-	-	PUNCT
ejpam-6010	124	88	cl(a	cl(a	NUM
ejpam-6010	124	89	)	)	PUNCT
ejpam-6010	124	90	.	.	PUNCT
ejpam-6010	125	1	a	a	DET
ejpam-6010	125	2	subset	subset	NOUN
ejpam-6010	125	3	a	a	PRON
ejpam-6010	125	4	of	of	ADP
ejpam-6010	125	5	a	a	DET
ejpam-6010	125	6	bitopological	bitopological	ADJ
ejpam-6010	125	7	space	space	NOUN
ejpam-6010	125	8	(	(	PUNCT
ejpam-6010	125	9	x	x	NOUN
ejpam-6010	125	10	,	,	PUNCT
ejpam-6010	125	11	τ1	τ1	NOUN
ejpam-6010	125	12	,	,	PUNCT
ejpam-6010	125	13	τ2	τ2	NOUN
ejpam-6010	125	14	)	)	PUNCT
ejpam-6010	125	15	is	be	AUX
ejpam-6010	125	16	called	call	VERB
ejpam-6010	125	17	s(τ1	s(τ1	NOUN
ejpam-6010	125	18	,	,	PUNCT
ejpam-6010	125	19	τ2)θ	τ2)θ	NOUN
ejpam-6010	125	20	-	-	PUNCT
ejpam-6010	125	21	closed	closed	ADJ
ejpam-6010	125	22	[	[	X
ejpam-6010	125	23	81	81	NUM
ejpam-6010	125	24	]	]	PUNCT
ejpam-6010	125	25	if	if	SCONJ
ejpam-6010	125	26	s(τ1	s(τ1	NOUN
ejpam-6010	125	27	,	,	PUNCT
ejpam-6010	125	28	τ2)θ	τ2)θ	NOUN
ejpam-6010	125	29	-	-	PUNCT
ejpam-6010	125	30	cl(a	cl(a	NUM
ejpam-6010	125	31	)	)	PUNCT
ejpam-6010	125	32	=	=	PUNCT
ejpam-6010	125	33	a.	a.	NOUN
ejpam-6010	125	34	the	the	DET
ejpam-6010	125	35	complement	complement	NOUN
ejpam-6010	125	36	of	of	ADP
ejpam-6010	125	37	a	a	DET
ejpam-6010	125	38	s(τ1	s(τ1	NOUN
ejpam-6010	125	39	,	,	PUNCT
ejpam-6010	125	40	τ2)θ	τ2)θ	ADJ
ejpam-6010	125	41	-	-	PUNCT
ejpam-6010	125	42	closed	close	VERB
ejpam-6010	125	43	set	set	NOUN
ejpam-6010	125	44	is	be	AUX
ejpam-6010	125	45	said	say	VERB
ejpam-6010	125	46	to	to	PART
ejpam-6010	125	47	be	be	AUX
ejpam-6010	125	48	s(τ1	s(τ1	NOUN
ejpam-6010	125	49	,	,	PUNCT
ejpam-6010	125	50	τ2)θ	τ2)θ	ADJ
ejpam-6010	125	51	-	-	PUNCT
ejpam-6010	125	52	open	open	NOUN
ejpam-6010	126	1	[	[	X
ejpam-6010	126	2	81	81	NUM
ejpam-6010	126	3	]	]	PUNCT
ejpam-6010	126	4	.	.	PUNCT
ejpam-6010	127	1	the	the	DET
ejpam-6010	127	2	union	union	NOUN
ejpam-6010	127	3	of	of	ADP
ejpam-6010	127	4	all	all	DET
ejpam-6010	127	5	s(τ1	s(τ1	NOUN
ejpam-6010	127	6	,	,	PUNCT
ejpam-6010	127	7	τ2)θ	τ2)θ	ADJ
ejpam-6010	127	8	-	-	PUNCT
ejpam-6010	127	9	open	open	ADJ
ejpam-6010	127	10	sets	set	NOUN
ejpam-6010	127	11	of	of	ADP
ejpam-6010	127	12	x	x	PUNCT
ejpam-6010	127	13	contained	contain	VERB
ejpam-6010	127	14	in	in	ADP
ejpam-6010	127	15	a	a	PRON
ejpam-6010	127	16	is	be	AUX
ejpam-6010	127	17	called	call	VERB
ejpam-6010	127	18	the	the	DET
ejpam-6010	127	19	s(τ1	s(τ1	NOUN
ejpam-6010	127	20	,	,	PUNCT
ejpam-6010	127	21	τ2)θ	τ2)θ	ADJ
ejpam-6010	127	22	-	-	PUNCT
ejpam-6010	127	23	interior	interior	NOUN
ejpam-6010	127	24	[	[	X
ejpam-6010	127	25	81	81	NUM
ejpam-6010	127	26	]	]	PUNCT
ejpam-6010	127	27	of	of	ADP
ejpam-6010	127	28	a	a	PRON
ejpam-6010	127	29	and	and	CCONJ
ejpam-6010	127	30	is	be	AUX
ejpam-6010	127	31	denoted	denote	VERB
ejpam-6010	127	32	by	by	ADP
ejpam-6010	127	33	s(τ1	s(τ1	NOUN
ejpam-6010	127	34	,	,	PUNCT
ejpam-6010	127	35	τ2)θ	τ2)θ	NOUN
ejpam-6010	127	36	-	-	PUNCT
ejpam-6010	127	37	int(a	int(a	NOUN
ejpam-6010	127	38	)	)	PUNCT
ejpam-6010	127	39	.	.	PUNCT
ejpam-6010	128	1	by	by	ADP
ejpam-6010	128	2	a	a	DET
ejpam-6010	128	3	multifunction	multifunction	NOUN
ejpam-6010	128	4	f	f	NOUN
ejpam-6010	128	5	:	:	PUNCT
ejpam-6010	128	6	x	x	X
ejpam-6010	128	7	→	→	SYM
ejpam-6010	128	8	y	y	PROPN
ejpam-6010	128	9	,	,	PUNCT
ejpam-6010	128	10	we	we	PRON
ejpam-6010	128	11	mean	mean	VERB
ejpam-6010	128	12	a	a	DET
ejpam-6010	128	13	point	point	NOUN
ejpam-6010	128	14	-	-	PUNCT
ejpam-6010	128	15	to	to	ADP
ejpam-6010	128	16	-	-	PUNCT
ejpam-6010	128	17	set	set	VERB
ejpam-6010	128	18	correspondence	correspondence	NOUN
ejpam-6010	128	19	from	from	ADP
ejpam-6010	128	20	x	x	PUNCT
ejpam-6010	128	21	into	into	ADP
ejpam-6010	128	22	y	y	PROPN
ejpam-6010	128	23	,	,	PUNCT
ejpam-6010	128	24	and	and	CCONJ
ejpam-6010	128	25	we	we	PRON
ejpam-6010	128	26	always	always	ADV
ejpam-6010	128	27	assume	assume	VERB
ejpam-6010	128	28	that	that	SCONJ
ejpam-6010	128	29	f	f	PROPN
ejpam-6010	128	30	(	(	PUNCT
ejpam-6010	128	31	x	x	X
ejpam-6010	128	32	)	)	PUNCT
ejpam-6010	128	33	̸=	̸=	NOUN
ejpam-6010	128	34	∅	∅	NOUN
ejpam-6010	128	35	for	for	ADP
ejpam-6010	128	36	all	all	PRON
ejpam-6010	128	37	x	x	SYM
ejpam-6010	128	38	∈	∈	ADJ
ejpam-6010	128	39	x.	x.	NOUN
ejpam-6010	128	40	for	for	ADP
ejpam-6010	128	41	a	a	DET
ejpam-6010	128	42	multifunction	multifunction	NOUN
ejpam-6010	128	43	f	f	NOUN
ejpam-6010	128	44	:	:	PUNCT
ejpam-6010	128	45	x	x	X
ejpam-6010	128	46	→	→	SYM
ejpam-6010	128	47	y	y	PROPN
ejpam-6010	128	48	,	,	PUNCT
ejpam-6010	128	49	we	we	PRON
ejpam-6010	128	50	shall	shall	AUX
ejpam-6010	128	51	denote	denote	VERB
ejpam-6010	128	52	the	the	DET
ejpam-6010	128	53	upper	upper	ADJ
ejpam-6010	128	54	and	and	CCONJ
ejpam-6010	128	55	lower	low	ADJ
ejpam-6010	128	56	inverse	inverse	NOUN
ejpam-6010	128	57	of	of	ADP
ejpam-6010	128	58	a	a	DET
ejpam-6010	128	59	set	set	NOUN
ejpam-6010	128	60	b	b	PROPN
ejpam-6010	128	61	of	of	ADP
ejpam-6010	128	62	y	y	PROPN
ejpam-6010	128	63	by	by	ADP
ejpam-6010	128	64	f+(b	f+(b	NOUN
ejpam-6010	128	65	)	)	PUNCT
ejpam-6010	128	66	and	and	CCONJ
ejpam-6010	128	67	f−(b	f−(b	NOUN
ejpam-6010	128	68	)	)	PUNCT
ejpam-6010	128	69	,	,	PUNCT
ejpam-6010	128	70	respectively	respectively	ADV
ejpam-6010	128	71	,	,	PUNCT
ejpam-6010	128	72	that	that	ADV
ejpam-6010	128	73	is	is	ADV
ejpam-6010	128	74	,	,	PUNCT
ejpam-6010	128	75	f+(b	f+(b	NOUN
ejpam-6010	128	76	)	)	PUNCT
ejpam-6010	128	77	=	=	PRON
ejpam-6010	129	1	{	{	PUNCT
ejpam-6010	129	2	x	x	PUNCT
ejpam-6010	129	3	∈	∈	PROPN
ejpam-6010	129	4	x	x	INTJ
ejpam-6010	130	1	|	|	NOUN
ejpam-6010	130	2	f	f	X
ejpam-6010	130	3	(	(	PUNCT
ejpam-6010	130	4	x	x	NOUN
ejpam-6010	130	5	)	)	PUNCT
ejpam-6010	130	6	⊆	⊆	NUM
ejpam-6010	130	7	b	b	NOUN
ejpam-6010	130	8	}	}	PUNCT
ejpam-6010	130	9	and	and	CCONJ
ejpam-6010	130	10	f−(b	f−(b	PROPN
ejpam-6010	130	11	)	)	PUNCT
ejpam-6010	130	12	=	=	PRON
ejpam-6010	131	1	{	{	PUNCT
ejpam-6010	131	2	x	x	PUNCT
ejpam-6010	131	3	∈	∈	PROPN
ejpam-6010	131	4	x	x	INTJ
ejpam-6010	132	1	|	|	NOUN
ejpam-6010	132	2	f	f	X
ejpam-6010	132	3	(	(	PUNCT
ejpam-6010	132	4	x	x	NOUN
ejpam-6010	132	5	)	)	PUNCT
ejpam-6010	132	6	∩	∩	NOUN
ejpam-6010	132	7	b	b	PROPN
ejpam-6010	132	8	̸=	̸=	PROPN
ejpam-6010	132	9	∅	∅	NOUN
ejpam-6010	132	10	}	}	PUNCT
ejpam-6010	132	11	.	.	PUNCT
ejpam-6010	133	1	in	in	ADP
ejpam-6010	133	2	particular	particular	ADJ
ejpam-6010	133	3	,	,	PUNCT
ejpam-6010	133	4	f−(y	f−(y	NOUN
ejpam-6010	133	5	)	)	PUNCT
ejpam-6010	133	6	=	=	SYM
ejpam-6010	134	1	{	{	PUNCT
ejpam-6010	134	2	x	x	PUNCT
ejpam-6010	134	3	∈	∈	PROPN
ejpam-6010	134	4	x	x	INTJ
ejpam-6010	135	1	|	|	ADV
ejpam-6010	135	2	y	y	PROPN
ejpam-6010	135	3	∈	∈	PROPN
ejpam-6010	135	4	f	f	X
ejpam-6010	135	5	(	(	PUNCT
ejpam-6010	135	6	x	x	NOUN
ejpam-6010	135	7	)	)	PUNCT
ejpam-6010	135	8	}	}	PUNCT
ejpam-6010	135	9	for	for	ADP
ejpam-6010	135	10	each	each	DET
ejpam-6010	135	11	point	point	NOUN
ejpam-6010	135	12	y	y	PROPN
ejpam-6010	135	13	∈	∈	PROPN
ejpam-6010	135	14	y	y	PROPN
ejpam-6010	135	15	.	.	PUNCT
ejpam-6010	136	1	for	for	ADP
ejpam-6010	136	2	each	each	PRON
ejpam-6010	136	3	a	a	DET
ejpam-6010	136	4	⊆	⊆	NUM
ejpam-6010	136	5	x	x	SYM
ejpam-6010	136	6	,	,	PUNCT
ejpam-6010	136	7	f	f	PROPN
ejpam-6010	136	8	(	(	PUNCT
ejpam-6010	136	9	a	a	NOUN
ejpam-6010	136	10	)	)	PUNCT
ejpam-6010	136	11	=	=	SYM
ejpam-6010	136	12	∪x∈af	∪x∈af	NOUN
ejpam-6010	136	13	(	(	PUNCT
ejpam-6010	136	14	x	x	NOUN
ejpam-6010	136	15	)	)	PUNCT
ejpam-6010	136	16	.	.	PUNCT
ejpam-6010	137	1	j.	j.	PROPN
ejpam-6010	137	2	khampakdee	khampakdee	PROPN
ejpam-6010	137	3	,	,	PUNCT
ejpam-6010	137	4	a.	a.	PROPN
ejpam-6010	137	5	sama	sama	PROPN
ejpam-6010	137	6	-	-	PUNCT
ejpam-6010	137	7	ae	ae	PROPN
ejpam-6010	137	8	,	,	PUNCT
ejpam-6010	137	9	c.	c.	PROPN
ejpam-6010	137	10	boonpok	boonpok	PROPN
ejpam-6010	137	11	/	/	SYM
ejpam-6010	137	12	eur	eur	PROPN
ejpam-6010	137	13	.	.	PUNCT
ejpam-6010	138	1	j.	j.	PROPN
ejpam-6010	138	2	pure	pure	PROPN
ejpam-6010	138	3	appl	appl	PROPN
ejpam-6010	138	4	.	.	PROPN
ejpam-6010	138	5	math	math	PROPN
ejpam-6010	138	6	,	,	PUNCT
ejpam-6010	138	7	18	18	NUM
ejpam-6010	138	8	(	(	PUNCT
ejpam-6010	138	9	2	2	NUM
ejpam-6010	138	10	)	)	PUNCT
ejpam-6010	138	11	(	(	PUNCT
ejpam-6010	138	12	2025	2025	NUM
ejpam-6010	138	13	)	)	PUNCT
ejpam-6010	138	14	,	,	PUNCT
ejpam-6010	138	15	6010	6010	NUM
ejpam-6010	138	16	5	5	NUM
ejpam-6010	138	17	of	of	ADP
ejpam-6010	138	18	19	19	NUM
ejpam-6010	138	19	3	3	NUM
ejpam-6010	138	20	.	.	PUNCT
ejpam-6010	138	21	upper	upper	ADJ
ejpam-6010	138	22	and	and	CCONJ
ejpam-6010	138	23	lower	low	ADJ
ejpam-6010	138	24	almost	almost	ADV
ejpam-6010	138	25	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	138	26	,	,	PUNCT
ejpam-6010	138	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	138	28	multifunctions	multifunction	NOUN
ejpam-6010	138	29	in	in	ADP
ejpam-6010	138	30	this	this	DET
ejpam-6010	138	31	section	section	NOUN
ejpam-6010	138	32	,	,	PUNCT
ejpam-6010	138	33	we	we	PRON
ejpam-6010	138	34	introduce	introduce	VERB
ejpam-6010	138	35	the	the	DET
ejpam-6010	138	36	concepts	concept	NOUN
ejpam-6010	138	37	of	of	ADP
ejpam-6010	138	38	upper	upper	ADJ
ejpam-6010	138	39	almost	almost	ADV
ejpam-6010	138	40	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	138	41	,	,	PUNCT
ejpam-6010	138	42	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	138	43	multifunctions	multifunction	NOUN
ejpam-6010	138	44	and	and	CCONJ
ejpam-6010	138	45	lower	low	ADJ
ejpam-6010	138	46	almost	almost	ADV
ejpam-6010	138	47	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	138	48	,	,	PUNCT
ejpam-6010	138	49	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	138	50	multifunctions	multifunction	NOUN
ejpam-6010	138	51	.	.	PUNCT
ejpam-6010	139	1	moreover	moreover	ADV
ejpam-6010	139	2	,	,	PUNCT
ejpam-6010	139	3	some	some	DET
ejpam-6010	139	4	characterizations	characterization	NOUN
ejpam-6010	139	5	of	of	ADP
ejpam-6010	139	6	upper	upper	ADJ
ejpam-6010	139	7	almost	almost	ADV
ejpam-6010	139	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	139	9	,	,	PUNCT
ejpam-6010	139	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	139	11	multifunctions	multifunction	NOUN
ejpam-6010	139	12	and	and	CCONJ
ejpam-6010	139	13	lower	low	ADJ
ejpam-6010	139	14	almost	almost	ADV
ejpam-6010	139	15	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	139	16	,	,	PUNCT
ejpam-6010	139	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	139	18	multifunctions	multifunction	NOUN
ejpam-6010	139	19	are	be	AUX
ejpam-6010	139	20	considered	consider	VERB
ejpam-6010	139	21	.	.	PUNCT
ejpam-6010	140	1	definition	definition	NOUN
ejpam-6010	140	2	1	1	NUM
ejpam-6010	140	3	.	.	PUNCT
ejpam-6010	141	1	a	a	DET
ejpam-6010	141	2	multifunction	multifunction	NOUN
ejpam-6010	141	3	f	f	NOUN
ejpam-6010	141	4	:	:	PUNCT
ejpam-6010	141	5	(	(	PUNCT
ejpam-6010	141	6	x	x	NOUN
ejpam-6010	141	7	,	,	PUNCT
ejpam-6010	141	8	τ1	τ1	NOUN
ejpam-6010	141	9	,	,	PUNCT
ejpam-6010	141	10	τ2	τ2	NOUN
ejpam-6010	141	11	)	)	PUNCT
ejpam-6010	141	12	→	→	SYM
ejpam-6010	141	13	(	(	PUNCT
ejpam-6010	141	14	y	y	PROPN
ejpam-6010	141	15	,	,	PUNCT
ejpam-6010	141	16	σ1	σ1	PROPN
ejpam-6010	141	17	,	,	PUNCT
ejpam-6010	141	18	σ2	σ2	PROPN
ejpam-6010	141	19	)	)	PUNCT
ejpam-6010	141	20	is	be	AUX
ejpam-6010	141	21	said	say	VERB
ejpam-6010	141	22	to	to	PART
ejpam-6010	141	23	be	be	AUX
ejpam-6010	141	24	upper	upper	ADJ
ejpam-6010	141	25	almost	almost	ADV
ejpam-6010	141	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	141	27	,	,	PUNCT
ejpam-6010	141	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	141	29	at	at	ADP
ejpam-6010	141	30	a	a	DET
ejpam-6010	141	31	point	point	NOUN
ejpam-6010	141	32	x	x	SYM
ejpam-6010	141	33	∈	∈	NOUN
ejpam-6010	141	34	x	x	INTJ
ejpam-6010	141	35	if	if	SCONJ
ejpam-6010	141	36	for	for	ADP
ejpam-6010	141	37	each	each	DET
ejpam-6010	141	38	(	(	PUNCT
ejpam-6010	141	39	σ1	σ1	PROPN
ejpam-6010	141	40	,	,	PUNCT
ejpam-6010	141	41	σ2)r	σ2)r	NOUN
ejpam-6010	141	42	-	-	PUNCT
ejpam-6010	141	43	closed	close	VERB
ejpam-6010	141	44	set	set	ADJ
ejpam-6010	141	45	k	k	PROPN
ejpam-6010	141	46	of	of	ADP
ejpam-6010	141	47	y	y	PROPN
ejpam-6010	141	48	with	with	ADP
ejpam-6010	141	49	x	x	PROPN
ejpam-6010	141	50	∈	∈	PROPN
ejpam-6010	141	51	f+(k	f+(k	PROPN
ejpam-6010	141	52	)	)	PUNCT
ejpam-6010	141	53	,	,	PUNCT
ejpam-6010	141	54	there	there	PRON
ejpam-6010	141	55	exists	exist	VERB
ejpam-6010	141	56	a	a	DET
ejpam-6010	141	57	τ1τ2	τ1τ2	NOUN
ejpam-6010	141	58	-	-	ADJ
ejpam-6010	141	59	open	open	ADJ
ejpam-6010	141	60	set	set	ADJ
ejpam-6010	141	61	u	u	NOUN
ejpam-6010	141	62	of	of	ADP
ejpam-6010	141	63	x	x	PUNCT
ejpam-6010	141	64	containing	contain	VERB
ejpam-6010	141	65	x	x	PUNCT
ejpam-6010	141	66	such	such	ADJ
ejpam-6010	141	67	that	that	SCONJ
ejpam-6010	141	68	u	u	PROPN
ejpam-6010	141	69	⊆	⊆	NUM
ejpam-6010	141	70	f+(k	f+(k	NUM
ejpam-6010	141	71	)	)	PUNCT
ejpam-6010	141	72	.	.	PUNCT
ejpam-6010	142	1	a	a	DET
ejpam-6010	142	2	multifunction	multifunction	NOUN
ejpam-6010	142	3	f	f	NOUN
ejpam-6010	142	4	:	:	PUNCT
ejpam-6010	142	5	(	(	PUNCT
ejpam-6010	142	6	x	x	NOUN
ejpam-6010	142	7	,	,	PUNCT
ejpam-6010	142	8	τ1	τ1	NOUN
ejpam-6010	142	9	,	,	PUNCT
ejpam-6010	142	10	τ2	τ2	NOUN
ejpam-6010	142	11	)	)	PUNCT
ejpam-6010	142	12	→	→	SYM
ejpam-6010	142	13	(	(	PUNCT
ejpam-6010	142	14	y	y	PROPN
ejpam-6010	142	15	,	,	PUNCT
ejpam-6010	142	16	σ1	σ1	PROPN
ejpam-6010	142	17	,	,	PUNCT
ejpam-6010	142	18	σ2	σ2	PROPN
ejpam-6010	142	19	)	)	PUNCT
ejpam-6010	142	20	is	be	AUX
ejpam-6010	142	21	said	say	VERB
ejpam-6010	142	22	to	to	PART
ejpam-6010	142	23	be	be	AUX
ejpam-6010	142	24	upper	upper	ADJ
ejpam-6010	142	25	almost	almost	ADV
ejpam-6010	142	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	142	27	,	,	PUNCT
ejpam-6010	142	28	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	142	29	if	if	SCONJ
ejpam-6010	142	30	f	f	PROPN
ejpam-6010	142	31	is	be	AUX
ejpam-6010	142	32	upper	upper	ADJ
ejpam-6010	142	33	almost	almost	ADV
ejpam-6010	142	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	142	35	,	,	PUNCT
ejpam-6010	142	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	142	37	at	at	ADP
ejpam-6010	142	38	each	each	DET
ejpam-6010	142	39	point	point	NOUN
ejpam-6010	142	40	x	x	PUNCT
ejpam-6010	142	41	of	of	ADP
ejpam-6010	142	42	x.	x.	PROPN
ejpam-6010	142	43	theorem	theorem	VERB
ejpam-6010	142	44	1	1	NUM
ejpam-6010	142	45	.	.	X
ejpam-6010	142	46	for	for	ADP
ejpam-6010	142	47	a	a	DET
ejpam-6010	142	48	multifunction	multifunction	NOUN
ejpam-6010	142	49	f	f	NOUN
ejpam-6010	142	50	:	:	PUNCT
ejpam-6010	142	51	(	(	PUNCT
ejpam-6010	142	52	x	x	NOUN
ejpam-6010	142	53	,	,	PUNCT
ejpam-6010	142	54	τ1	τ1	NOUN
ejpam-6010	142	55	,	,	PUNCT
ejpam-6010	142	56	τ2	τ2	NOUN
ejpam-6010	142	57	)	)	PUNCT
ejpam-6010	142	58	→	→	SYM
ejpam-6010	142	59	(	(	PUNCT
ejpam-6010	142	60	y	y	PROPN
ejpam-6010	142	61	,	,	PUNCT
ejpam-6010	142	62	σ1	σ1	PROPN
ejpam-6010	142	63	,	,	PUNCT
ejpam-6010	142	64	σ2	σ2	NOUN
ejpam-6010	142	65	)	)	PUNCT
ejpam-6010	142	66	,	,	PUNCT
ejpam-6010	142	67	the	the	DET
ejpam-6010	142	68	following	follow	VERB
ejpam-6010	142	69	properties	property	NOUN
ejpam-6010	142	70	are	be	AUX
ejpam-6010	142	71	equivalent	equivalent	ADJ
ejpam-6010	142	72	:	:	PUNCT
ejpam-6010	142	73	(	(	PUNCT
ejpam-6010	142	74	1	1	X
ejpam-6010	142	75	)	)	PUNCT
ejpam-6010	142	76	f	f	PROPN
ejpam-6010	142	77	is	be	AUX
ejpam-6010	142	78	upper	upper	ADJ
ejpam-6010	142	79	almost	almost	ADV
ejpam-6010	142	80	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	142	81	,	,	PUNCT
ejpam-6010	142	82	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	142	83	;	;	PUNCT
ejpam-6010	142	84	(	(	PUNCT
ejpam-6010	142	85	2	2	X
ejpam-6010	142	86	)	)	PUNCT
ejpam-6010	142	87	f+(k	f+(k	NOUN
ejpam-6010	142	88	)	)	PUNCT
ejpam-6010	142	89	is	be	AUX
ejpam-6010	142	90	τ1τ2	τ1τ2	NOUN
ejpam-6010	142	91	-	-	ADJ
ejpam-6010	142	92	open	open	ADJ
ejpam-6010	142	93	in	in	ADP
ejpam-6010	142	94	x	x	PUNCT
ejpam-6010	142	95	for	for	ADP
ejpam-6010	142	96	every	every	DET
ejpam-6010	142	97	(	(	PUNCT
ejpam-6010	142	98	σ1	σ1	PROPN
ejpam-6010	142	99	,	,	PUNCT
ejpam-6010	142	100	σ2)r	σ2)r	NOUN
ejpam-6010	142	101	-	-	PUNCT
ejpam-6010	142	102	closed	close	VERB
ejpam-6010	142	103	set	set	ADJ
ejpam-6010	142	104	k	k	PROPN
ejpam-6010	142	105	of	of	ADP
ejpam-6010	142	106	y	y	PROPN
ejpam-6010	142	107	;	;	PUNCT
ejpam-6010	142	108	(	(	PUNCT
ejpam-6010	142	109	3	3	X
ejpam-6010	142	110	)	)	PUNCT
ejpam-6010	142	111	f−(v	f−(v	NOUN
ejpam-6010	142	112	)	)	PUNCT
ejpam-6010	142	113	is	be	AUX
ejpam-6010	142	114	τ1τ2	τ1τ2	NOUN
ejpam-6010	142	115	-	-	ADJ
ejpam-6010	142	116	closed	closed	ADJ
ejpam-6010	142	117	in	in	ADP
ejpam-6010	142	118	x	x	PUNCT
ejpam-6010	142	119	for	for	ADP
ejpam-6010	142	120	every	every	DET
ejpam-6010	142	121	(	(	PUNCT
ejpam-6010	142	122	σ1	σ1	PROPN
ejpam-6010	142	123	,	,	PUNCT
ejpam-6010	142	124	σ2)r	σ2)r	NOUN
ejpam-6010	142	125	-	-	PUNCT
ejpam-6010	142	126	open	open	ADJ
ejpam-6010	142	127	set	set	VERB
ejpam-6010	142	128	v	v	NOUN
ejpam-6010	142	129	of	of	ADP
ejpam-6010	142	130	y	y	PROPN
ejpam-6010	142	131	;	;	PUNCT
ejpam-6010	142	132	(	(	PUNCT
ejpam-6010	142	133	4	4	X
ejpam-6010	142	134	)	)	PUNCT
ejpam-6010	142	135	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6010	142	136	-	-	PUNCT
ejpam-6010	142	137	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	142	138	-	-	PUNCT
ejpam-6010	142	139	cl(v	cl(v	NOUN
ejpam-6010	142	140	)	)	PUNCT
ejpam-6010	142	141	)	)	PUNCT
ejpam-6010	142	142	)	)	PUNCT
ejpam-6010	142	143	is	be	AUX
ejpam-6010	142	144	τ1τ2	τ1τ2	NOUN
ejpam-6010	142	145	-	-	ADJ
ejpam-6010	142	146	closed	closed	ADJ
ejpam-6010	142	147	in	in	ADP
ejpam-6010	142	148	x	x	PUNCT
ejpam-6010	142	149	for	for	ADP
ejpam-6010	142	150	every	every	DET
ejpam-6010	142	151	σ1σ2	σ1σ2	NOUN
ejpam-6010	142	152	-	-	ADJ
ejpam-6010	142	153	open	open	ADJ
ejpam-6010	142	154	set	set	NOUN
ejpam-6010	142	155	v	v	NOUN
ejpam-6010	142	156	of	of	ADP
ejpam-6010	142	157	y	y	PROPN
ejpam-6010	142	158	;	;	PUNCT
ejpam-6010	142	159	(	(	PUNCT
ejpam-6010	142	160	5	5	X
ejpam-6010	142	161	)	)	PUNCT
ejpam-6010	142	162	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	142	163	-	-	PUNCT
ejpam-6010	142	164	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6010	142	165	-	-	PUNCT
ejpam-6010	142	166	int(k	int(k	NOUN
ejpam-6010	142	167	)	)	PUNCT
ejpam-6010	142	168	)	)	PUNCT
ejpam-6010	142	169	)	)	PUNCT
ejpam-6010	142	170	is	be	AUX
ejpam-6010	142	171	τ1τ2	τ1τ2	NOUN
ejpam-6010	142	172	-	-	ADJ
ejpam-6010	142	173	open	open	ADJ
ejpam-6010	142	174	in	in	ADP
ejpam-6010	142	175	x	x	PUNCT
ejpam-6010	142	176	for	for	ADP
ejpam-6010	142	177	every	every	DET
ejpam-6010	142	178	σ1σ2	σ1σ2	NUM
ejpam-6010	142	179	-	-	PUNCT
ejpam-6010	142	180	closed	closed	ADJ
ejpam-6010	142	181	set	set	NOUN
ejpam-6010	142	182	k	k	PROPN
ejpam-6010	142	183	of	of	ADP
ejpam-6010	142	184	y	y	PROPN
ejpam-6010	142	185	;	;	PUNCT
ejpam-6010	142	186	(	(	PUNCT
ejpam-6010	142	187	6	6	NUM
ejpam-6010	142	188	)	)	PUNCT
ejpam-6010	142	189	for	for	ADP
ejpam-6010	142	190	each	each	DET
ejpam-6010	142	191	x	x	SYM
ejpam-6010	142	192	∈	∈	PROPN
ejpam-6010	142	193	x	x	X
ejpam-6010	142	194	and	and	CCONJ
ejpam-6010	142	195	each	each	DET
ejpam-6010	142	196	(	(	PUNCT
ejpam-6010	142	197	σ1	σ1	PROPN
ejpam-6010	142	198	,	,	PUNCT
ejpam-6010	142	199	σ2)s	σ2)s	NOUN
ejpam-6010	142	200	-	-	PUNCT
ejpam-6010	142	201	open	open	NOUN
ejpam-6010	142	202	set	set	NOUN
ejpam-6010	142	203	v	v	NOUN
ejpam-6010	142	204	of	of	ADP
ejpam-6010	142	205	y	y	PROPN
ejpam-6010	142	206	with	with	ADP
ejpam-6010	142	207	f	f	PROPN
ejpam-6010	142	208	(	(	PUNCT
ejpam-6010	142	209	x	x	NOUN
ejpam-6010	142	210	)	)	PUNCT
ejpam-6010	142	211	⊆	⊆	NUM
ejpam-6010	142	212	v	v	NOUN
ejpam-6010	142	213	,	,	PUNCT
ejpam-6010	142	214	there	there	PRON
ejpam-6010	142	215	exists	exist	VERB
ejpam-6010	142	216	a	a	DET
ejpam-6010	142	217	τ1τ2	τ1τ2	NOUN
ejpam-6010	142	218	-	-	ADJ
ejpam-6010	142	219	open	open	ADJ
ejpam-6010	142	220	set	set	ADJ
ejpam-6010	142	221	u	u	NOUN
ejpam-6010	142	222	of	of	ADP
ejpam-6010	142	223	x	x	PUNCT
ejpam-6010	142	224	containing	contain	VERB
ejpam-6010	142	225	x	x	PUNCT
ejpam-6010	142	226	such	such	ADJ
ejpam-6010	142	227	that	that	SCONJ
ejpam-6010	142	228	f	f	PROPN
ejpam-6010	142	229	(	(	PUNCT
ejpam-6010	142	230	u	u	NOUN
ejpam-6010	142	231	)	)	PUNCT
ejpam-6010	142	232	⊆	⊆	NUM
ejpam-6010	142	233	σ1σ2	σ1σ2	NOUN
ejpam-6010	142	234	-	-	NUM
ejpam-6010	142	235	cl(v	cl(v	NOUN
ejpam-6010	142	236	)	)	PUNCT
ejpam-6010	142	237	;	;	PUNCT
ejpam-6010	142	238	(	(	PUNCT
ejpam-6010	142	239	7	7	X
ejpam-6010	142	240	)	)	PUNCT
ejpam-6010	142	241	f+(v	f+(v	NOUN
ejpam-6010	142	242	)	)	PUNCT
ejpam-6010	143	1	⊆	⊆	X
ejpam-6010	143	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	143	3	-	-	NUM
ejpam-6010	143	4	int(f	int(f	VERB
ejpam-6010	143	5	+	+	ADJ
ejpam-6010	143	6	(	(	PUNCT
ejpam-6010	143	7	σ1σ2	σ1σ2	NOUN
ejpam-6010	143	8	-	-	NUM
ejpam-6010	143	9	cl(v	cl(v	NOUN
ejpam-6010	143	10	)	)	PUNCT
ejpam-6010	143	11	)	)	PUNCT
ejpam-6010	143	12	)	)	PUNCT
ejpam-6010	143	13	for	for	SCONJ
ejpam-6010	143	14	every	every	DET
ejpam-6010	143	15	(	(	PUNCT
ejpam-6010	143	16	σ1	σ1	PROPN
ejpam-6010	143	17	,	,	PUNCT
ejpam-6010	143	18	σ2)s	σ2)s	NOUN
ejpam-6010	143	19	-	-	PUNCT
ejpam-6010	143	20	open	open	NOUN
ejpam-6010	143	21	set	set	NOUN
ejpam-6010	143	22	v	v	NOUN
ejpam-6010	143	23	of	of	ADP
ejpam-6010	143	24	y	y	PROPN
ejpam-6010	143	25	.	.	PUNCT
ejpam-6010	144	1	proof	proof	NOUN
ejpam-6010	144	2	.	.	PUNCT
ejpam-6010	145	1	(	(	PUNCT
ejpam-6010	145	2	1	1	X
ejpam-6010	145	3	)	)	PUNCT
ejpam-6010	145	4	⇒	⇒	NOUN
ejpam-6010	145	5	(	(	PUNCT
ejpam-6010	145	6	2	2	NUM
ejpam-6010	145	7	):	):	PUNCT
ejpam-6010	145	8	let	let	VERB
ejpam-6010	145	9	k	k	PRON
ejpam-6010	145	10	be	be	AUX
ejpam-6010	145	11	any	any	DET
ejpam-6010	145	12	(	(	PUNCT
ejpam-6010	145	13	σ1	σ1	NOUN
ejpam-6010	145	14	,	,	PUNCT
ejpam-6010	145	15	σ2)r	σ2)r	NOUN
ejpam-6010	145	16	-	-	PUNCT
ejpam-6010	145	17	closed	close	VERB
ejpam-6010	145	18	set	set	NOUN
ejpam-6010	145	19	of	of	ADP
ejpam-6010	145	20	y	y	PROPN
ejpam-6010	145	21	and	and	CCONJ
ejpam-6010	145	22	x	x	PUNCT
ejpam-6010	145	23	∈	∈	PROPN
ejpam-6010	145	24	f+(k	f+(k	PROPN
ejpam-6010	145	25	)	)	PUNCT
ejpam-6010	145	26	.	.	PUNCT
ejpam-6010	146	1	since	since	SCONJ
ejpam-6010	146	2	f	f	PROPN
ejpam-6010	146	3	is	be	AUX
ejpam-6010	146	4	is	be	AUX
ejpam-6010	146	5	upper	upper	ADJ
ejpam-6010	146	6	almost	almost	ADV
ejpam-6010	146	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	146	8	,	,	PUNCT
ejpam-6010	146	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	146	10	,	,	PUNCT
ejpam-6010	146	11	there	there	PRON
ejpam-6010	146	12	exists	exist	VERB
ejpam-6010	146	13	a	a	DET
ejpam-6010	146	14	τ1τ2	τ1τ2	NOUN
ejpam-6010	146	15	-	-	ADJ
ejpam-6010	146	16	open	open	ADJ
ejpam-6010	146	17	set	set	ADJ
ejpam-6010	146	18	u	u	NOUN
ejpam-6010	146	19	of	of	ADP
ejpam-6010	146	20	x	x	PUNCT
ejpam-6010	146	21	containing	contain	VERB
ejpam-6010	146	22	x	x	PUNCT
ejpam-6010	146	23	such	such	ADJ
ejpam-6010	146	24	that	that	SCONJ
ejpam-6010	146	25	u	u	PROPN
ejpam-6010	146	26	⊆	⊆	NUM
ejpam-6010	146	27	f+(k	f+(k	NUM
ejpam-6010	146	28	)	)	PUNCT
ejpam-6010	146	29	.	.	PUNCT
ejpam-6010	147	1	it	it	PRON
ejpam-6010	147	2	follows	follow	VERB
ejpam-6010	147	3	that	that	SCONJ
ejpam-6010	147	4	f+(k	f+(k	NOUN
ejpam-6010	147	5	)	)	PUNCT
ejpam-6010	147	6	is	be	AUX
ejpam-6010	147	7	τ1τ2	τ1τ2	NOUN
ejpam-6010	147	8	-	-	ADJ
ejpam-6010	147	9	open	open	ADJ
ejpam-6010	147	10	in	in	ADP
ejpam-6010	147	11	x.	x.	NOUN
ejpam-6010	147	12	(	(	PUNCT
ejpam-6010	147	13	2	2	NUM
ejpam-6010	147	14	)	)	PUNCT
ejpam-6010	147	15	⇒	⇒	NOUN
ejpam-6010	147	16	(	(	PUNCT
ejpam-6010	147	17	1	1	NUM
ejpam-6010	147	18	):	):	PUNCT
ejpam-6010	147	19	the	the	DET
ejpam-6010	147	20	proof	proof	NOUN
ejpam-6010	147	21	is	be	AUX
ejpam-6010	147	22	obvious	obvious	ADJ
ejpam-6010	147	23	.	.	PUNCT
ejpam-6010	148	1	(	(	PUNCT
ejpam-6010	148	2	2	2	X
ejpam-6010	148	3	)	)	PUNCT
ejpam-6010	148	4	⇔	⇔	X
ejpam-6010	148	5	(	(	PUNCT
ejpam-6010	148	6	3	3	NUM
ejpam-6010	148	7	):	):	PUNCT
ejpam-6010	148	8	it	it	PRON
ejpam-6010	148	9	follows	follow	VERB
ejpam-6010	148	10	from	from	ADP
ejpam-6010	148	11	the	the	DET
ejpam-6010	148	12	fact	fact	NOUN
ejpam-6010	148	13	that	that	SCONJ
ejpam-6010	148	14	f+(y	f+(y	PROPN
ejpam-6010	148	15	−b	−b	ADV
ejpam-6010	148	16	)	)	PUNCT
ejpam-6010	148	17	=	=	PUNCT
ejpam-6010	149	1	x	x	X
ejpam-6010	149	2	−	−	PROPN
ejpam-6010	149	3	f−(b	f−(b	PROPN
ejpam-6010	149	4	)	)	PUNCT
ejpam-6010	149	5	for	for	ADP
ejpam-6010	149	6	every	every	DET
ejpam-6010	149	7	subset	subset	NOUN
ejpam-6010	149	8	b	b	PROPN
ejpam-6010	149	9	of	of	ADP
ejpam-6010	149	10	y	y	PROPN
ejpam-6010	149	11	.	.	PUNCT
ejpam-6010	150	1	(	(	PUNCT
ejpam-6010	150	2	3	3	X
ejpam-6010	150	3	)	)	PUNCT
ejpam-6010	150	4	⇔	⇔	X
ejpam-6010	150	5	(	(	PUNCT
ejpam-6010	150	6	4	4	NUM
ejpam-6010	150	7	):	):	PUNCT
ejpam-6010	150	8	let	let	VERB
ejpam-6010	150	9	v	v	PART
ejpam-6010	150	10	be	be	AUX
ejpam-6010	150	11	any	any	DET
ejpam-6010	150	12	σ1σ2	σ1σ2	NOUN
ejpam-6010	150	13	-	-	ADJ
ejpam-6010	150	14	open	open	ADJ
ejpam-6010	150	15	set	set	NOUN
ejpam-6010	150	16	of	of	ADP
ejpam-6010	150	17	y	y	PROPN
ejpam-6010	150	18	.	.	PUNCT
ejpam-6010	151	1	since	since	SCONJ
ejpam-6010	151	2	σ1σ2	σ1σ2	ADV
ejpam-6010	151	3	-	-	PUNCT
ejpam-6010	151	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	151	5	-	-	PUNCT
ejpam-6010	151	6	cl(v	cl(v	NOUN
ejpam-6010	151	7	)	)	PUNCT
ejpam-6010	151	8	)	)	PUNCT
ejpam-6010	151	9	is	be	AUX
ejpam-6010	151	10	(	(	PUNCT
ejpam-6010	151	11	σ1	σ1	PROPN
ejpam-6010	151	12	,	,	PUNCT
ejpam-6010	151	13	σ2)ropen	σ2)ropen	NOUN
ejpam-6010	151	14	in	in	ADP
ejpam-6010	151	15	y	y	PROPN
ejpam-6010	151	16	,	,	PUNCT
ejpam-6010	151	17	by	by	ADP
ejpam-6010	151	18	(	(	PUNCT
ejpam-6010	151	19	3	3	X
ejpam-6010	151	20	)	)	PUNCT
ejpam-6010	151	21	we	we	PRON
ejpam-6010	151	22	have	have	VERB
ejpam-6010	151	23	f−(σ1σ2	f−(σ1σ2	VERB
ejpam-6010	151	24	-	-	PUNCT
ejpam-6010	151	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	151	26	-	-	PUNCT
ejpam-6010	151	27	cl(v	cl(v	NOUN
ejpam-6010	151	28	)	)	PUNCT
ejpam-6010	151	29	)	)	PUNCT
ejpam-6010	151	30	)	)	PUNCT
ejpam-6010	151	31	is	be	AUX
ejpam-6010	151	32	τ1τ2	τ1τ2	NOUN
ejpam-6010	151	33	-	-	ADJ
ejpam-6010	151	34	closed	closed	ADJ
ejpam-6010	151	35	in	in	ADP
ejpam-6010	151	36	x.	x.	NOUN
ejpam-6010	151	37	the	the	DET
ejpam-6010	151	38	converse	converse	NOUN
ejpam-6010	151	39	is	be	AUX
ejpam-6010	151	40	obvious	obvious	ADJ
ejpam-6010	151	41	.	.	PUNCT
ejpam-6010	152	1	(	(	PUNCT
ejpam-6010	152	2	4	4	X
ejpam-6010	152	3	)	)	PUNCT
ejpam-6010	152	4	⇔	⇔	X
ejpam-6010	152	5	(	(	PUNCT
ejpam-6010	152	6	5	5	NUM
ejpam-6010	152	7	):	):	PUNCT
ejpam-6010	152	8	it	it	PRON
ejpam-6010	152	9	follows	follow	VERB
ejpam-6010	152	10	from	from	ADP
ejpam-6010	152	11	the	the	DET
ejpam-6010	152	12	fact	fact	NOUN
ejpam-6010	152	13	that	that	SCONJ
ejpam-6010	152	14	f+(y	f+(y	PROPN
ejpam-6010	152	15	−b	−b	ADV
ejpam-6010	152	16	)	)	PUNCT
ejpam-6010	152	17	=	=	PUNCT
ejpam-6010	153	1	x	x	X
ejpam-6010	153	2	−	−	PROPN
ejpam-6010	153	3	f−(b	f−(b	PROPN
ejpam-6010	153	4	)	)	PUNCT
ejpam-6010	153	5	for	for	ADP
ejpam-6010	153	6	every	every	DET
ejpam-6010	153	7	subset	subset	NOUN
ejpam-6010	153	8	b	b	PROPN
ejpam-6010	153	9	of	of	ADP
ejpam-6010	153	10	y	y	PROPN
ejpam-6010	153	11	.	.	PUNCT
ejpam-6010	154	1	(	(	PUNCT
ejpam-6010	154	2	5	5	X
ejpam-6010	154	3	)	)	PUNCT
ejpam-6010	154	4	⇔	⇔	X
ejpam-6010	154	5	(	(	PUNCT
ejpam-6010	154	6	2	2	NUM
ejpam-6010	154	7	):	):	PUNCT
ejpam-6010	154	8	it	it	PRON
ejpam-6010	154	9	is	be	AUX
ejpam-6010	154	10	similar	similar	ADJ
ejpam-6010	154	11	to	to	ADP
ejpam-6010	154	12	that	that	PRON
ejpam-6010	154	13	of	of	ADP
ejpam-6010	154	14	(	(	PUNCT
ejpam-6010	154	15	3	3	X
ejpam-6010	154	16	)	)	PUNCT
ejpam-6010	154	17	⇔	⇔	X
ejpam-6010	154	18	(	(	PUNCT
ejpam-6010	154	19	4	4	NUM
ejpam-6010	154	20	)	)	PUNCT
ejpam-6010	154	21	.	.	PUNCT
ejpam-6010	155	1	(	(	PUNCT
ejpam-6010	155	2	6	6	X
ejpam-6010	155	3	)	)	PUNCT
ejpam-6010	155	4	⇒	⇒	NOUN
ejpam-6010	155	5	(	(	PUNCT
ejpam-6010	155	6	7	7	NUM
ejpam-6010	155	7	):	):	PUNCT
ejpam-6010	155	8	let	let	VERB
ejpam-6010	155	9	v	v	PART
ejpam-6010	155	10	be	be	AUX
ejpam-6010	155	11	any	any	DET
ejpam-6010	155	12	(	(	PUNCT
ejpam-6010	155	13	σ1	σ1	NOUN
ejpam-6010	155	14	,	,	PUNCT
ejpam-6010	155	15	σ2)s	σ2)s	NOUN
ejpam-6010	155	16	-	-	PUNCT
ejpam-6010	155	17	open	open	ADJ
ejpam-6010	155	18	set	set	NOUN
ejpam-6010	155	19	of	of	ADP
ejpam-6010	155	20	y	y	PROPN
ejpam-6010	155	21	and	and	CCONJ
ejpam-6010	155	22	x	x	PROPN
ejpam-6010	155	23	∈	∈	PROPN
ejpam-6010	155	24	f+(v	f+(v	NOUN
ejpam-6010	155	25	)	)	PUNCT
ejpam-6010	155	26	.	.	PUNCT
ejpam-6010	156	1	then	then	ADV
ejpam-6010	156	2	,	,	PUNCT
ejpam-6010	156	3	f	f	PROPN
ejpam-6010	156	4	(	(	PUNCT
ejpam-6010	156	5	x	x	X
ejpam-6010	156	6	)	)	PUNCT
ejpam-6010	156	7	⊆	⊆	NUM
ejpam-6010	156	8	v	v	NOUN
ejpam-6010	156	9	.	.	PUNCT
ejpam-6010	157	1	by	by	ADP
ejpam-6010	157	2	(	(	PUNCT
ejpam-6010	157	3	6	6	NUM
ejpam-6010	157	4	)	)	PUNCT
ejpam-6010	157	5	,	,	PUNCT
ejpam-6010	157	6	there	there	PRON
ejpam-6010	157	7	exists	exist	VERB
ejpam-6010	157	8	a	a	DET
ejpam-6010	157	9	τ1τ2	τ1τ2	NOUN
ejpam-6010	157	10	-	-	ADJ
ejpam-6010	157	11	open	open	ADJ
ejpam-6010	157	12	set	set	ADJ
ejpam-6010	157	13	u	u	NOUN
ejpam-6010	157	14	of	of	ADP
ejpam-6010	157	15	x	x	PUNCT
ejpam-6010	157	16	containing	contain	VERB
ejpam-6010	157	17	x	x	PUNCT
ejpam-6010	157	18	such	such	ADJ
ejpam-6010	157	19	that	that	SCONJ
ejpam-6010	157	20	f	f	PROPN
ejpam-6010	157	21	(	(	PUNCT
ejpam-6010	157	22	u	u	NOUN
ejpam-6010	157	23	)	)	PUNCT
ejpam-6010	157	24	⊆	⊆	NUM
ejpam-6010	157	25	σ1σ2	σ1σ2	NOUN
ejpam-6010	157	26	-	-	NUM
ejpam-6010	157	27	cl(v	cl(v	NOUN
ejpam-6010	157	28	)	)	PUNCT
ejpam-6010	157	29	.	.	PUNCT
ejpam-6010	158	1	thus	thus	ADV
ejpam-6010	158	2	,	,	PUNCT
ejpam-6010	158	3	u	u	NOUN
ejpam-6010	158	4	⊆	⊆	NUM
ejpam-6010	158	5	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	158	6	-	-	PUNCT
ejpam-6010	158	7	cl(v	cl(v	NOUN
ejpam-6010	158	8	)	)	PUNCT
ejpam-6010	158	9	)	)	PUNCT
ejpam-6010	158	10	and	and	CCONJ
ejpam-6010	158	11	hence	hence	ADV
ejpam-6010	158	12	x	x	X
ejpam-6010	158	13	∈	∈	PRON
ejpam-6010	158	14	τ1τ2	τ1τ2	NOUN
ejpam-6010	158	15	-	-	NUM
ejpam-6010	158	16	int(f	int(f	VERB
ejpam-6010	158	17	+	+	ADJ
ejpam-6010	158	18	(	(	PUNCT
ejpam-6010	158	19	σ1σ2	σ1σ2	NOUN
ejpam-6010	158	20	-	-	NUM
ejpam-6010	158	21	cl(v	cl(v	NOUN
ejpam-6010	158	22	)	)	PUNCT
ejpam-6010	158	23	)	)	PUNCT
ejpam-6010	158	24	)	)	PUNCT
ejpam-6010	158	25	.	.	PUNCT
ejpam-6010	159	1	this	this	PRON
ejpam-6010	159	2	implies	imply	VERB
ejpam-6010	159	3	that	that	SCONJ
ejpam-6010	159	4	f+(v	f+(v	PROPN
ejpam-6010	159	5	)	)	PUNCT
ejpam-6010	160	1	⊆	⊆	X
ejpam-6010	160	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	160	3	-	-	NUM
ejpam-6010	160	4	int(f	int(f	VERB
ejpam-6010	160	5	+	+	ADJ
ejpam-6010	160	6	(	(	PUNCT
ejpam-6010	160	7	σ1σ2	σ1σ2	NOUN
ejpam-6010	160	8	-	-	NUM
ejpam-6010	160	9	cl(v	cl(v	NOUN
ejpam-6010	160	10	)	)	PUNCT
ejpam-6010	160	11	)	)	PUNCT
ejpam-6010	160	12	)	)	PUNCT
ejpam-6010	160	13	.	.	PUNCT
ejpam-6010	161	1	j.	j.	PROPN
ejpam-6010	161	2	khampakdee	khampakdee	PROPN
ejpam-6010	161	3	,	,	PUNCT
ejpam-6010	161	4	a.	a.	PROPN
ejpam-6010	161	5	sama	sama	PROPN
ejpam-6010	161	6	-	-	PUNCT
ejpam-6010	161	7	ae	ae	PROPN
ejpam-6010	161	8	,	,	PUNCT
ejpam-6010	161	9	c.	c.	PROPN
ejpam-6010	161	10	boonpok	boonpok	PROPN
ejpam-6010	161	11	/	/	SYM
ejpam-6010	161	12	eur	eur	PROPN
ejpam-6010	161	13	.	.	PUNCT
ejpam-6010	162	1	j.	j.	PROPN
ejpam-6010	162	2	pure	pure	PROPN
ejpam-6010	162	3	appl	appl	PROPN
ejpam-6010	162	4	.	.	PROPN
ejpam-6010	162	5	math	math	PROPN
ejpam-6010	162	6	,	,	PUNCT
ejpam-6010	162	7	18	18	NUM
ejpam-6010	162	8	(	(	PUNCT
ejpam-6010	162	9	2	2	NUM
ejpam-6010	162	10	)	)	PUNCT
ejpam-6010	162	11	(	(	PUNCT
ejpam-6010	162	12	2025	2025	NUM
ejpam-6010	162	13	)	)	PUNCT
ejpam-6010	162	14	,	,	PUNCT
ejpam-6010	162	15	6010	6010	NUM
ejpam-6010	162	16	6	6	NUM
ejpam-6010	162	17	of	of	ADP
ejpam-6010	162	18	19	19	NUM
ejpam-6010	162	19	(	(	PUNCT
ejpam-6010	162	20	7	7	NUM
ejpam-6010	162	21	)	)	PUNCT
ejpam-6010	162	22	⇒	⇒	NOUN
ejpam-6010	162	23	(	(	PUNCT
ejpam-6010	162	24	2	2	NUM
ejpam-6010	162	25	):	):	PUNCT
ejpam-6010	162	26	let	let	VERB
ejpam-6010	162	27	k	k	PRON
ejpam-6010	162	28	be	be	AUX
ejpam-6010	162	29	any	any	DET
ejpam-6010	162	30	(	(	PUNCT
ejpam-6010	162	31	σ1	σ1	NOUN
ejpam-6010	162	32	,	,	PUNCT
ejpam-6010	162	33	σ2)r	σ2)r	NOUN
ejpam-6010	162	34	-	-	PUNCT
ejpam-6010	162	35	closed	close	VERB
ejpam-6010	162	36	set	set	NOUN
ejpam-6010	162	37	of	of	ADP
ejpam-6010	162	38	y	y	PROPN
ejpam-6010	162	39	.	.	PUNCT
ejpam-6010	163	1	since	since	SCONJ
ejpam-6010	163	2	k	k	PROPN
ejpam-6010	163	3	is	be	AUX
ejpam-6010	163	4	(	(	PUNCT
ejpam-6010	163	5	σ1	σ1	PROPN
ejpam-6010	163	6	,	,	PUNCT
ejpam-6010	163	7	σ2)s	σ2)s	NOUN
ejpam-6010	163	8	-	-	PUNCT
ejpam-6010	163	9	open	open	ADJ
ejpam-6010	163	10	in	in	ADP
ejpam-6010	163	11	y	y	PROPN
ejpam-6010	163	12	,	,	PUNCT
ejpam-6010	163	13	by	by	ADP
ejpam-6010	163	14	(	(	PUNCT
ejpam-6010	163	15	7	7	X
ejpam-6010	163	16	)	)	PUNCT
ejpam-6010	163	17	we	we	PRON
ejpam-6010	163	18	have	have	VERB
ejpam-6010	163	19	f+(v	f+(v	NOUN
ejpam-6010	163	20	)	)	PUNCT
ejpam-6010	164	1	⊆	⊆	X
ejpam-6010	164	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	164	3	-	-	NUM
ejpam-6010	164	4	int(f	int(f	VERB
ejpam-6010	164	5	+	+	ADJ
ejpam-6010	164	6	(	(	PUNCT
ejpam-6010	164	7	σ1σ2	σ1σ2	NOUN
ejpam-6010	164	8	-	-	NUM
ejpam-6010	164	9	cl(v	cl(v	NOUN
ejpam-6010	164	10	)	)	PUNCT
ejpam-6010	164	11	)	)	PUNCT
ejpam-6010	164	12	)	)	PUNCT
ejpam-6010	165	1	=	=	PUNCT
ejpam-6010	165	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	165	3	-	-	NUM
ejpam-6010	165	4	int(f	int(f	VERB
ejpam-6010	165	5	+	+	ADJ
ejpam-6010	165	6	(	(	PUNCT
ejpam-6010	165	7	v	v	NOUN
ejpam-6010	165	8	)	)	PUNCT
ejpam-6010	165	9	)	)	PUNCT
ejpam-6010	165	10	.	.	PUNCT
ejpam-6010	166	1	thus	thus	ADV
ejpam-6010	166	2	,	,	PUNCT
ejpam-6010	166	3	f+(k	f+(k	PRON
ejpam-6010	166	4	)	)	PUNCT
ejpam-6010	166	5	is	be	AUX
ejpam-6010	166	6	τ1τ2	τ1τ2	NOUN
ejpam-6010	166	7	-	-	ADJ
ejpam-6010	166	8	open	open	ADJ
ejpam-6010	166	9	in	in	ADP
ejpam-6010	166	10	x.	x.	NOUN
ejpam-6010	166	11	(	(	PUNCT
ejpam-6010	166	12	2	2	NUM
ejpam-6010	166	13	)	)	PUNCT
ejpam-6010	166	14	⇒	⇒	NOUN
ejpam-6010	166	15	(	(	PUNCT
ejpam-6010	166	16	6	6	NUM
ejpam-6010	166	17	):	):	PUNCT
ejpam-6010	166	18	let	let	VERB
ejpam-6010	166	19	x	x	PUNCT
ejpam-6010	166	20	∈	∈	PROPN
ejpam-6010	166	21	x	x	X
ejpam-6010	166	22	and	and	CCONJ
ejpam-6010	166	23	v	v	AUX
ejpam-6010	166	24	be	be	AUX
ejpam-6010	166	25	any	any	DET
ejpam-6010	166	26	(	(	PUNCT
ejpam-6010	166	27	σ1	σ1	NOUN
ejpam-6010	166	28	,	,	PUNCT
ejpam-6010	166	29	σ2)s	σ2)s	NOUN
ejpam-6010	166	30	-	-	PUNCT
ejpam-6010	166	31	open	open	ADJ
ejpam-6010	166	32	set	set	NOUN
ejpam-6010	166	33	of	of	ADP
ejpam-6010	166	34	y	y	PROPN
ejpam-6010	166	35	with	with	ADP
ejpam-6010	166	36	f	f	PROPN
ejpam-6010	166	37	(	(	PUNCT
ejpam-6010	166	38	x	x	NOUN
ejpam-6010	166	39	)	)	PUNCT
ejpam-6010	166	40	⊆	⊆	NUM
ejpam-6010	166	41	v	v	NOUN
ejpam-6010	166	42	.	.	PUNCT
ejpam-6010	167	1	since	since	SCONJ
ejpam-6010	167	2	σ1σ2	σ1σ2	NOUN
ejpam-6010	167	3	-	-	NOUN
ejpam-6010	167	4	cl(v	cl(v	NOUN
ejpam-6010	167	5	)	)	PUNCT
ejpam-6010	167	6	is	be	AUX
ejpam-6010	167	7	(	(	PUNCT
ejpam-6010	167	8	σ1	σ1	NOUN
ejpam-6010	167	9	,	,	PUNCT
ejpam-6010	167	10	σ2)r	σ2)r	NOUN
ejpam-6010	167	11	-	-	PUNCT
ejpam-6010	167	12	closed	closed	ADJ
ejpam-6010	167	13	in	in	ADP
ejpam-6010	167	14	y	y	PROPN
ejpam-6010	167	15	,	,	PUNCT
ejpam-6010	167	16	by	by	ADP
ejpam-6010	167	17	(	(	PUNCT
ejpam-6010	167	18	2	2	X
ejpam-6010	167	19	)	)	PUNCT
ejpam-6010	167	20	we	we	PRON
ejpam-6010	167	21	have	have	AUX
ejpam-6010	167	22	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	167	23	-	-	NOUN
ejpam-6010	167	24	cl(v	cl(v	NOUN
ejpam-6010	167	25	)	)	PUNCT
ejpam-6010	167	26	)	)	PUNCT
ejpam-6010	167	27	is	be	AUX
ejpam-6010	167	28	τ1τ2	τ1τ2	NOUN
ejpam-6010	167	29	-	-	ADJ
ejpam-6010	167	30	open	open	ADJ
ejpam-6010	167	31	in	in	ADP
ejpam-6010	167	32	x.	x.	NOUN
ejpam-6010	167	33	then	then	ADV
ejpam-6010	167	34	,	,	PUNCT
ejpam-6010	167	35	there	there	PRON
ejpam-6010	167	36	exists	exist	VERB
ejpam-6010	167	37	a	a	DET
ejpam-6010	167	38	τ1τ2	τ1τ2	NOUN
ejpam-6010	167	39	-	-	ADJ
ejpam-6010	167	40	open	open	ADJ
ejpam-6010	167	41	set	set	ADJ
ejpam-6010	167	42	u	u	NOUN
ejpam-6010	167	43	of	of	ADP
ejpam-6010	167	44	x	x	PUNCT
ejpam-6010	167	45	containing	contain	VERB
ejpam-6010	167	46	x	x	PUNCT
ejpam-6010	167	47	such	such	ADJ
ejpam-6010	167	48	that	that	SCONJ
ejpam-6010	167	49	u	u	NOUN
ejpam-6010	167	50	⊆	⊆	NUM
ejpam-6010	167	51	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	167	52	-	-	PUNCT
ejpam-6010	167	53	cl(v	cl(v	NOUN
ejpam-6010	167	54	)	)	PUNCT
ejpam-6010	167	55	)	)	PUNCT
ejpam-6010	167	56	.	.	PUNCT
ejpam-6010	168	1	thus	thus	ADV
ejpam-6010	168	2	,	,	PUNCT
ejpam-6010	168	3	f	f	PROPN
ejpam-6010	168	4	(	(	PUNCT
ejpam-6010	168	5	u	u	NOUN
ejpam-6010	168	6	)	)	PUNCT
ejpam-6010	168	7	⊆	⊆	NUM
ejpam-6010	168	8	σ1σ2	σ1σ2	NOUN
ejpam-6010	168	9	-	-	NUM
ejpam-6010	168	10	cl(v	cl(v	NOUN
ejpam-6010	168	11	)	)	PUNCT
ejpam-6010	168	12	.	.	PUNCT
ejpam-6010	169	1	definition	definition	NOUN
ejpam-6010	169	2	2	2	NUM
ejpam-6010	169	3	.	.	PUNCT
ejpam-6010	169	4	a	a	DET
ejpam-6010	169	5	multifunction	multifunction	NOUN
ejpam-6010	169	6	f	f	NOUN
ejpam-6010	169	7	:	:	PUNCT
ejpam-6010	169	8	(	(	PUNCT
ejpam-6010	169	9	x	x	NOUN
ejpam-6010	169	10	,	,	PUNCT
ejpam-6010	169	11	τ1	τ1	NOUN
ejpam-6010	169	12	,	,	PUNCT
ejpam-6010	169	13	τ2	τ2	NOUN
ejpam-6010	169	14	)	)	PUNCT
ejpam-6010	169	15	→	→	SYM
ejpam-6010	169	16	(	(	PUNCT
ejpam-6010	169	17	y	y	PROPN
ejpam-6010	169	18	,	,	PUNCT
ejpam-6010	169	19	σ1	σ1	PROPN
ejpam-6010	169	20	,	,	PUNCT
ejpam-6010	169	21	σ2	σ2	PROPN
ejpam-6010	169	22	)	)	PUNCT
ejpam-6010	169	23	is	be	AUX
ejpam-6010	169	24	said	say	VERB
ejpam-6010	169	25	to	to	PART
ejpam-6010	169	26	be	be	AUX
ejpam-6010	169	27	lower	low	ADJ
ejpam-6010	169	28	almost	almost	ADV
ejpam-6010	169	29	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	169	30	,	,	PUNCT
ejpam-6010	169	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	169	32	at	at	ADP
ejpam-6010	169	33	a	a	DET
ejpam-6010	169	34	point	point	NOUN
ejpam-6010	169	35	x	x	SYM
ejpam-6010	169	36	∈	∈	NOUN
ejpam-6010	169	37	x	x	INTJ
ejpam-6010	169	38	if	if	SCONJ
ejpam-6010	169	39	for	for	ADP
ejpam-6010	169	40	each	each	DET
ejpam-6010	169	41	(	(	PUNCT
ejpam-6010	169	42	σ1	σ1	PROPN
ejpam-6010	169	43	,	,	PUNCT
ejpam-6010	169	44	σ2)r	σ2)r	NOUN
ejpam-6010	169	45	-	-	PUNCT
ejpam-6010	169	46	closed	close	VERB
ejpam-6010	169	47	set	set	ADJ
ejpam-6010	169	48	k	k	PROPN
ejpam-6010	169	49	of	of	ADP
ejpam-6010	169	50	y	y	PROPN
ejpam-6010	169	51	with	with	ADP
ejpam-6010	169	52	x	x	PROPN
ejpam-6010	169	53	∈	∈	PROPN
ejpam-6010	169	54	f−(k	f−(k	PROPN
ejpam-6010	169	55	)	)	PUNCT
ejpam-6010	169	56	,	,	PUNCT
ejpam-6010	169	57	there	there	PRON
ejpam-6010	169	58	exists	exist	VERB
ejpam-6010	169	59	a	a	DET
ejpam-6010	169	60	τ1τ2	τ1τ2	NOUN
ejpam-6010	169	61	-	-	ADJ
ejpam-6010	169	62	open	open	ADJ
ejpam-6010	169	63	set	set	ADJ
ejpam-6010	169	64	u	u	NOUN
ejpam-6010	169	65	of	of	ADP
ejpam-6010	169	66	x	x	PUNCT
ejpam-6010	169	67	containing	contain	VERB
ejpam-6010	169	68	x	x	PUNCT
ejpam-6010	169	69	such	such	ADJ
ejpam-6010	169	70	that	that	SCONJ
ejpam-6010	169	71	u	u	PROPN
ejpam-6010	169	72	⊆	⊆	NUM
ejpam-6010	169	73	f−(k	f−(k	PROPN
ejpam-6010	169	74	)	)	PUNCT
ejpam-6010	169	75	.	.	PUNCT
ejpam-6010	170	1	a	a	DET
ejpam-6010	170	2	multifunction	multifunction	NOUN
ejpam-6010	170	3	f	f	NOUN
ejpam-6010	170	4	:	:	PUNCT
ejpam-6010	170	5	(	(	PUNCT
ejpam-6010	170	6	x	x	NOUN
ejpam-6010	170	7	,	,	PUNCT
ejpam-6010	170	8	τ1	τ1	NOUN
ejpam-6010	170	9	,	,	PUNCT
ejpam-6010	170	10	τ2	τ2	NOUN
ejpam-6010	170	11	)	)	PUNCT
ejpam-6010	170	12	→	→	SYM
ejpam-6010	170	13	(	(	PUNCT
ejpam-6010	170	14	y	y	PROPN
ejpam-6010	170	15	,	,	PUNCT
ejpam-6010	170	16	σ1	σ1	PROPN
ejpam-6010	170	17	,	,	PUNCT
ejpam-6010	170	18	σ2	σ2	PROPN
ejpam-6010	170	19	)	)	PUNCT
ejpam-6010	170	20	is	be	AUX
ejpam-6010	170	21	said	say	VERB
ejpam-6010	170	22	to	to	PART
ejpam-6010	170	23	be	be	AUX
ejpam-6010	170	24	lower	low	ADJ
ejpam-6010	170	25	almost	almost	ADV
ejpam-6010	170	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	170	27	,	,	PUNCT
ejpam-6010	170	28	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	170	29	if	if	SCONJ
ejpam-6010	170	30	f	f	PROPN
ejpam-6010	170	31	is	be	AUX
ejpam-6010	170	32	lower	low	ADJ
ejpam-6010	170	33	almost	almost	ADV
ejpam-6010	170	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	170	35	,	,	PUNCT
ejpam-6010	170	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	170	37	at	at	ADP
ejpam-6010	170	38	each	each	DET
ejpam-6010	170	39	point	point	NOUN
ejpam-6010	170	40	x	x	PUNCT
ejpam-6010	170	41	of	of	ADP
ejpam-6010	170	42	x.	x.	PROPN
ejpam-6010	170	43	theorem	theorem	VERB
ejpam-6010	170	44	2	2	NUM
ejpam-6010	170	45	.	.	X
ejpam-6010	170	46	for	for	ADP
ejpam-6010	170	47	a	a	DET
ejpam-6010	170	48	multifunction	multifunction	NOUN
ejpam-6010	170	49	f	f	NOUN
ejpam-6010	170	50	:	:	PUNCT
ejpam-6010	170	51	(	(	PUNCT
ejpam-6010	170	52	x	x	NOUN
ejpam-6010	170	53	,	,	PUNCT
ejpam-6010	170	54	τ1	τ1	NOUN
ejpam-6010	170	55	,	,	PUNCT
ejpam-6010	170	56	τ2	τ2	NOUN
ejpam-6010	170	57	)	)	PUNCT
ejpam-6010	170	58	→	→	SYM
ejpam-6010	170	59	(	(	PUNCT
ejpam-6010	170	60	y	y	PROPN
ejpam-6010	170	61	,	,	PUNCT
ejpam-6010	170	62	σ1	σ1	PROPN
ejpam-6010	170	63	,	,	PUNCT
ejpam-6010	170	64	σ2	σ2	NOUN
ejpam-6010	170	65	)	)	PUNCT
ejpam-6010	170	66	,	,	PUNCT
ejpam-6010	170	67	the	the	DET
ejpam-6010	170	68	following	follow	VERB
ejpam-6010	170	69	properties	property	NOUN
ejpam-6010	170	70	are	be	AUX
ejpam-6010	170	71	equivalent	equivalent	ADJ
ejpam-6010	170	72	:	:	PUNCT
ejpam-6010	170	73	(	(	PUNCT
ejpam-6010	170	74	1	1	X
ejpam-6010	170	75	)	)	PUNCT
ejpam-6010	170	76	f	f	PROPN
ejpam-6010	170	77	is	be	AUX
ejpam-6010	170	78	lower	low	ADJ
ejpam-6010	170	79	almost	almost	ADV
ejpam-6010	170	80	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	170	81	,	,	PUNCT
ejpam-6010	170	82	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	170	83	;	;	PUNCT
ejpam-6010	170	84	(	(	PUNCT
ejpam-6010	170	85	2	2	X
ejpam-6010	170	86	)	)	PUNCT
ejpam-6010	170	87	f−(k	f−(k	PROPN
ejpam-6010	170	88	)	)	PUNCT
ejpam-6010	170	89	is	be	AUX
ejpam-6010	170	90	τ1τ2	τ1τ2	NOUN
ejpam-6010	170	91	-	-	ADJ
ejpam-6010	170	92	open	open	ADJ
ejpam-6010	170	93	in	in	ADP
ejpam-6010	170	94	x	x	PUNCT
ejpam-6010	170	95	for	for	ADP
ejpam-6010	170	96	every	every	DET
ejpam-6010	170	97	(	(	PUNCT
ejpam-6010	170	98	σ1	σ1	PROPN
ejpam-6010	170	99	,	,	PUNCT
ejpam-6010	170	100	σ2)r	σ2)r	NOUN
ejpam-6010	170	101	-	-	PUNCT
ejpam-6010	170	102	closed	close	VERB
ejpam-6010	170	103	set	set	ADJ
ejpam-6010	170	104	k	k	PROPN
ejpam-6010	170	105	of	of	ADP
ejpam-6010	170	106	y	y	PROPN
ejpam-6010	170	107	;	;	PUNCT
ejpam-6010	170	108	(	(	PUNCT
ejpam-6010	170	109	3	3	X
ejpam-6010	170	110	)	)	PUNCT
ejpam-6010	170	111	f+(v	f+(v	NOUN
ejpam-6010	170	112	)	)	PUNCT
ejpam-6010	170	113	is	be	AUX
ejpam-6010	170	114	τ1τ2	τ1τ2	NOUN
ejpam-6010	170	115	-	-	ADJ
ejpam-6010	170	116	closed	closed	ADJ
ejpam-6010	170	117	in	in	ADP
ejpam-6010	170	118	x	x	PUNCT
ejpam-6010	170	119	for	for	ADP
ejpam-6010	170	120	every	every	DET
ejpam-6010	170	121	(	(	PUNCT
ejpam-6010	170	122	σ1	σ1	PROPN
ejpam-6010	170	123	,	,	PUNCT
ejpam-6010	170	124	σ2)r	σ2)r	NOUN
ejpam-6010	170	125	-	-	PUNCT
ejpam-6010	170	126	open	open	ADJ
ejpam-6010	170	127	set	set	VERB
ejpam-6010	170	128	v	v	NOUN
ejpam-6010	170	129	of	of	ADP
ejpam-6010	170	130	y	y	PROPN
ejpam-6010	170	131	;	;	PUNCT
ejpam-6010	170	132	(	(	PUNCT
ejpam-6010	170	133	4	4	X
ejpam-6010	170	134	)	)	PUNCT
ejpam-6010	170	135	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	170	136	-	-	PUNCT
ejpam-6010	170	137	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	170	138	-	-	PUNCT
ejpam-6010	170	139	cl(v	cl(v	NOUN
ejpam-6010	170	140	)	)	PUNCT
ejpam-6010	170	141	)	)	PUNCT
ejpam-6010	170	142	)	)	PUNCT
ejpam-6010	171	1	is	be	AUX
ejpam-6010	171	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	171	3	-	-	ADJ
ejpam-6010	171	4	closed	closed	ADJ
ejpam-6010	171	5	in	in	ADP
ejpam-6010	171	6	x	x	PUNCT
ejpam-6010	171	7	for	for	ADP
ejpam-6010	171	8	every	every	DET
ejpam-6010	171	9	σ1σ2	σ1σ2	NOUN
ejpam-6010	171	10	-	-	ADJ
ejpam-6010	171	11	open	open	ADJ
ejpam-6010	171	12	set	set	NOUN
ejpam-6010	171	13	v	v	NOUN
ejpam-6010	171	14	of	of	ADP
ejpam-6010	171	15	y	y	PROPN
ejpam-6010	171	16	;	;	PUNCT
ejpam-6010	171	17	(	(	PUNCT
ejpam-6010	171	18	5	5	X
ejpam-6010	171	19	)	)	PUNCT
ejpam-6010	171	20	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	171	21	-	-	PUNCT
ejpam-6010	171	22	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6010	171	23	-	-	PUNCT
ejpam-6010	171	24	int(k	int(k	NOUN
ejpam-6010	171	25	)	)	PUNCT
ejpam-6010	171	26	)	)	PUNCT
ejpam-6010	171	27	)	)	PUNCT
ejpam-6010	172	1	is	be	AUX
ejpam-6010	172	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	172	3	-	-	ADJ
ejpam-6010	172	4	open	open	ADJ
ejpam-6010	172	5	in	in	ADP
ejpam-6010	172	6	x	x	PUNCT
ejpam-6010	172	7	for	for	ADP
ejpam-6010	172	8	every	every	DET
ejpam-6010	172	9	σ1σ2	σ1σ2	NUM
ejpam-6010	172	10	-	-	PUNCT
ejpam-6010	172	11	closed	closed	ADJ
ejpam-6010	172	12	set	set	NOUN
ejpam-6010	172	13	k	k	PROPN
ejpam-6010	172	14	of	of	ADP
ejpam-6010	172	15	y	y	PROPN
ejpam-6010	172	16	;	;	PUNCT
ejpam-6010	172	17	(	(	PUNCT
ejpam-6010	172	18	6	6	NUM
ejpam-6010	172	19	)	)	PUNCT
ejpam-6010	172	20	for	for	ADP
ejpam-6010	172	21	each	each	DET
ejpam-6010	172	22	x	x	SYM
ejpam-6010	172	23	∈	∈	PROPN
ejpam-6010	172	24	x	x	X
ejpam-6010	172	25	and	and	CCONJ
ejpam-6010	172	26	each	each	DET
ejpam-6010	172	27	(	(	PUNCT
ejpam-6010	172	28	σ1	σ1	PROPN
ejpam-6010	172	29	,	,	PUNCT
ejpam-6010	172	30	σ2)s	σ2)s	NOUN
ejpam-6010	172	31	-	-	PUNCT
ejpam-6010	172	32	open	open	NOUN
ejpam-6010	172	33	set	set	NOUN
ejpam-6010	172	34	v	v	NOUN
ejpam-6010	172	35	of	of	ADP
ejpam-6010	172	36	y	y	PROPN
ejpam-6010	172	37	with	with	ADP
ejpam-6010	172	38	f	f	PROPN
ejpam-6010	172	39	(	(	PUNCT
ejpam-6010	172	40	x)∩v	x)∩v	PROPN
ejpam-6010	172	41	̸=	̸=	PROPN
ejpam-6010	172	42	∅	∅	NOUN
ejpam-6010	172	43	,	,	PUNCT
ejpam-6010	172	44	there	there	PRON
ejpam-6010	172	45	exists	exist	VERB
ejpam-6010	172	46	a	a	DET
ejpam-6010	172	47	τ1τ2	τ1τ2	NOUN
ejpam-6010	172	48	-	-	ADJ
ejpam-6010	172	49	open	open	ADJ
ejpam-6010	172	50	set	set	ADJ
ejpam-6010	172	51	u	u	NOUN
ejpam-6010	172	52	of	of	ADP
ejpam-6010	172	53	x	x	PUNCT
ejpam-6010	172	54	containing	contain	VERB
ejpam-6010	172	55	x	x	PUNCT
ejpam-6010	172	56	such	such	ADJ
ejpam-6010	172	57	that	that	SCONJ
ejpam-6010	172	58	f	f	PROPN
ejpam-6010	172	59	(	(	PUNCT
ejpam-6010	172	60	z)∩	z)∩	X
ejpam-6010	172	61	σ1σ2	σ1σ2	NOUN
ejpam-6010	172	62	-	-	PUNCT
ejpam-6010	172	63	cl(v	cl(v	NOUN
ejpam-6010	172	64	)	)	PUNCT
ejpam-6010	172	65	̸=	̸=	NOUN
ejpam-6010	172	66	∅	∅	NOUN
ejpam-6010	172	67	for	for	ADP
ejpam-6010	172	68	each	each	DET
ejpam-6010	172	69	z	z	NOUN
ejpam-6010	172	70	∈	∈	PROPN
ejpam-6010	172	71	u	u	NOUN
ejpam-6010	172	72	;	;	PUNCT
ejpam-6010	172	73	(	(	PUNCT
ejpam-6010	172	74	7	7	X
ejpam-6010	172	75	)	)	PUNCT
ejpam-6010	172	76	f−(v	f−(v	NOUN
ejpam-6010	172	77	)	)	PUNCT
ejpam-6010	172	78	⊆	⊆	NUM
ejpam-6010	173	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	173	2	-	-	NUM
ejpam-6010	173	3	int(f	int(f	PRON
ejpam-6010	173	4	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	173	5	-	-	NOUN
ejpam-6010	173	6	cl(v	cl(v	NOUN
ejpam-6010	173	7	)	)	PUNCT
ejpam-6010	173	8	)	)	PUNCT
ejpam-6010	173	9	)	)	PUNCT
ejpam-6010	174	1	for	for	SCONJ
ejpam-6010	174	2	every	every	DET
ejpam-6010	174	3	(	(	PUNCT
ejpam-6010	174	4	σ1	σ1	PROPN
ejpam-6010	174	5	,	,	PUNCT
ejpam-6010	174	6	σ2)s	σ2)s	NOUN
ejpam-6010	174	7	-	-	PUNCT
ejpam-6010	174	8	open	open	NOUN
ejpam-6010	174	9	set	set	NOUN
ejpam-6010	174	10	v	v	NOUN
ejpam-6010	174	11	of	of	ADP
ejpam-6010	174	12	y	y	PROPN
ejpam-6010	174	13	.	.	PUNCT
ejpam-6010	175	1	proof	proof	NOUN
ejpam-6010	175	2	.	.	PUNCT
ejpam-6010	176	1	the	the	DET
ejpam-6010	176	2	proof	proof	NOUN
ejpam-6010	176	3	is	be	AUX
ejpam-6010	176	4	similar	similar	ADJ
ejpam-6010	176	5	to	to	ADP
ejpam-6010	176	6	that	that	PRON
ejpam-6010	176	7	of	of	ADP
ejpam-6010	176	8	theorem	theorem	ADJ
ejpam-6010	176	9	1	1	NUM
ejpam-6010	176	10	.	.	PUNCT
ejpam-6010	176	11	theorem	theorem	NOUN
ejpam-6010	176	12	3	3	NUM
ejpam-6010	176	13	.	.	X
ejpam-6010	176	14	for	for	ADP
ejpam-6010	176	15	a	a	DET
ejpam-6010	176	16	multifunction	multifunction	NOUN
ejpam-6010	176	17	f	f	NOUN
ejpam-6010	176	18	:	:	PUNCT
ejpam-6010	176	19	(	(	PUNCT
ejpam-6010	176	20	x	x	NOUN
ejpam-6010	176	21	,	,	PUNCT
ejpam-6010	176	22	τ1	τ1	NOUN
ejpam-6010	176	23	,	,	PUNCT
ejpam-6010	176	24	τ2	τ2	NOUN
ejpam-6010	176	25	)	)	PUNCT
ejpam-6010	176	26	→	→	SYM
ejpam-6010	176	27	(	(	PUNCT
ejpam-6010	176	28	y	y	PROPN
ejpam-6010	176	29	,	,	PUNCT
ejpam-6010	176	30	σ1	σ1	PROPN
ejpam-6010	176	31	,	,	PUNCT
ejpam-6010	176	32	σ2	σ2	NOUN
ejpam-6010	176	33	)	)	PUNCT
ejpam-6010	176	34	,	,	PUNCT
ejpam-6010	176	35	the	the	DET
ejpam-6010	176	36	following	follow	VERB
ejpam-6010	176	37	properties	property	NOUN
ejpam-6010	176	38	are	be	AUX
ejpam-6010	176	39	equivalent	equivalent	ADJ
ejpam-6010	176	40	:	:	PUNCT
ejpam-6010	176	41	(	(	PUNCT
ejpam-6010	176	42	1	1	X
ejpam-6010	176	43	)	)	PUNCT
ejpam-6010	176	44	f	f	PROPN
ejpam-6010	176	45	is	be	AUX
ejpam-6010	176	46	upper	upper	ADJ
ejpam-6010	176	47	almost	almost	ADV
ejpam-6010	176	48	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	176	49	,	,	PUNCT
ejpam-6010	176	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	176	51	;	;	PUNCT
ejpam-6010	176	52	(	(	PUNCT
ejpam-6010	176	53	2	2	X
ejpam-6010	176	54	)	)	PUNCT
ejpam-6010	176	55	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	176	56	-	-	PUNCT
ejpam-6010	176	57	cl(v	cl(v	NOUN
ejpam-6010	176	58	)	)	PUNCT
ejpam-6010	176	59	)	)	PUNCT
ejpam-6010	176	60	is	be	AUX
ejpam-6010	176	61	τ1τ2	τ1τ2	NOUN
ejpam-6010	176	62	-	-	ADJ
ejpam-6010	176	63	open	open	ADJ
ejpam-6010	176	64	in	in	ADP
ejpam-6010	176	65	x	x	PUNCT
ejpam-6010	176	66	for	for	ADP
ejpam-6010	176	67	every	every	DET
ejpam-6010	176	68	(	(	PUNCT
ejpam-6010	176	69	σ1	σ1	PROPN
ejpam-6010	176	70	,	,	PUNCT
ejpam-6010	176	71	σ2)β	σ2)β	NOUN
ejpam-6010	176	72	-	-	PUNCT
ejpam-6010	176	73	open	open	NOUN
ejpam-6010	176	74	set	set	NOUN
ejpam-6010	176	75	v	v	NOUN
ejpam-6010	176	76	of	of	ADP
ejpam-6010	176	77	y	y	PROPN
ejpam-6010	176	78	;	;	PUNCT
ejpam-6010	176	79	(	(	PUNCT
ejpam-6010	176	80	3	3	X
ejpam-6010	176	81	)	)	PUNCT
ejpam-6010	176	82	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	176	83	-	-	PUNCT
ejpam-6010	176	84	cl(v	cl(v	NOUN
ejpam-6010	176	85	)	)	PUNCT
ejpam-6010	176	86	)	)	PUNCT
ejpam-6010	177	1	is	be	AUX
ejpam-6010	177	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	177	3	-	-	ADJ
ejpam-6010	177	4	open	open	ADJ
ejpam-6010	177	5	in	in	ADP
ejpam-6010	177	6	x	x	PUNCT
ejpam-6010	177	7	for	for	ADP
ejpam-6010	177	8	every	every	DET
ejpam-6010	177	9	(	(	PUNCT
ejpam-6010	177	10	σ1	σ1	PROPN
ejpam-6010	177	11	,	,	PUNCT
ejpam-6010	177	12	σ2)s	σ2)s	NOUN
ejpam-6010	177	13	-	-	PUNCT
ejpam-6010	177	14	open	open	NOUN
ejpam-6010	177	15	set	set	NOUN
ejpam-6010	177	16	v	v	NOUN
ejpam-6010	177	17	of	of	ADP
ejpam-6010	177	18	y	y	PROPN
ejpam-6010	177	19	;	;	PUNCT
ejpam-6010	177	20	(	(	PUNCT
ejpam-6010	177	21	4	4	X
ejpam-6010	177	22	)	)	PUNCT
ejpam-6010	177	23	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6010	177	24	-	-	PUNCT
ejpam-6010	177	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	177	26	-	-	PUNCT
ejpam-6010	177	27	cl(v	cl(v	NOUN
ejpam-6010	177	28	)	)	PUNCT
ejpam-6010	177	29	)	)	PUNCT
ejpam-6010	177	30	)	)	PUNCT
ejpam-6010	178	1	is	be	AUX
ejpam-6010	178	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	178	3	-	-	ADJ
ejpam-6010	178	4	closed	closed	ADJ
ejpam-6010	178	5	in	in	ADP
ejpam-6010	178	6	x	x	PUNCT
ejpam-6010	178	7	for	for	ADP
ejpam-6010	178	8	every	every	DET
ejpam-6010	178	9	(	(	PUNCT
ejpam-6010	178	10	σ1	σ1	PROPN
ejpam-6010	178	11	,	,	PUNCT
ejpam-6010	178	12	σ2)p	σ2)p	NOUN
ejpam-6010	178	13	-	-	PUNCT
ejpam-6010	178	14	open	open	NOUN
ejpam-6010	178	15	set	set	NOUN
ejpam-6010	178	16	v	v	NOUN
ejpam-6010	178	17	of	of	ADP
ejpam-6010	178	18	y	y	PROPN
ejpam-6010	178	19	.	.	PUNCT
ejpam-6010	179	1	j.	j.	PROPN
ejpam-6010	179	2	khampakdee	khampakdee	PROPN
ejpam-6010	179	3	,	,	PUNCT
ejpam-6010	179	4	a.	a.	PROPN
ejpam-6010	179	5	sama	sama	PROPN
ejpam-6010	179	6	-	-	PUNCT
ejpam-6010	179	7	ae	ae	PROPN
ejpam-6010	179	8	,	,	PUNCT
ejpam-6010	179	9	c.	c.	PROPN
ejpam-6010	179	10	boonpok	boonpok	PROPN
ejpam-6010	179	11	/	/	SYM
ejpam-6010	179	12	eur	eur	PROPN
ejpam-6010	179	13	.	.	PUNCT
ejpam-6010	180	1	j.	j.	PROPN
ejpam-6010	180	2	pure	pure	PROPN
ejpam-6010	180	3	appl	appl	PROPN
ejpam-6010	180	4	.	.	PROPN
ejpam-6010	180	5	math	math	PROPN
ejpam-6010	180	6	,	,	PUNCT
ejpam-6010	180	7	18	18	NUM
ejpam-6010	180	8	(	(	PUNCT
ejpam-6010	180	9	2	2	NUM
ejpam-6010	180	10	)	)	PUNCT
ejpam-6010	180	11	(	(	PUNCT
ejpam-6010	180	12	2025	2025	NUM
ejpam-6010	180	13	)	)	PUNCT
ejpam-6010	180	14	,	,	PUNCT
ejpam-6010	180	15	6010	6010	NUM
ejpam-6010	180	16	7	7	NUM
ejpam-6010	180	17	of	of	ADP
ejpam-6010	180	18	19	19	NUM
ejpam-6010	180	19	proof	proof	NOUN
ejpam-6010	180	20	.	.	PUNCT
ejpam-6010	181	1	(	(	PUNCT
ejpam-6010	181	2	1	1	X
ejpam-6010	181	3	)	)	PUNCT
ejpam-6010	181	4	⇒	⇒	NOUN
ejpam-6010	181	5	(	(	PUNCT
ejpam-6010	181	6	2	2	NUM
ejpam-6010	181	7	):	):	PUNCT
ejpam-6010	181	8	let	let	VERB
ejpam-6010	181	9	v	v	PART
ejpam-6010	181	10	be	be	AUX
ejpam-6010	181	11	any	any	DET
ejpam-6010	181	12	(	(	PUNCT
ejpam-6010	181	13	σ1	σ1	PROPN
ejpam-6010	181	14	,	,	PUNCT
ejpam-6010	181	15	σ2)β	σ2)β	NOUN
ejpam-6010	181	16	-	-	PUNCT
ejpam-6010	181	17	open	open	ADJ
ejpam-6010	181	18	set	set	NOUN
ejpam-6010	181	19	of	of	ADP
ejpam-6010	181	20	y	y	PROPN
ejpam-6010	181	21	.	.	PUNCT
ejpam-6010	182	1	then	then	ADV
ejpam-6010	182	2	,	,	PUNCT
ejpam-6010	182	3	σ1σ2	σ1σ2	NOUN
ejpam-6010	182	4	-	-	NUM
ejpam-6010	182	5	cl(v	cl(v	NOUN
ejpam-6010	182	6	)	)	PUNCT
ejpam-6010	182	7	is	be	AUX
ejpam-6010	182	8	(	(	PUNCT
ejpam-6010	182	9	σ1	σ1	PROPN
ejpam-6010	182	10	,	,	PUNCT
ejpam-6010	182	11	σ2)rclosed	σ2)rclose	VERB
ejpam-6010	182	12	in	in	ADP
ejpam-6010	182	13	y	y	PROPN
ejpam-6010	182	14	,	,	PUNCT
ejpam-6010	182	15	by	by	ADP
ejpam-6010	182	16	theorem	theorem	NOUN
ejpam-6010	182	17	1	1	NUM
ejpam-6010	182	18	we	we	PRON
ejpam-6010	182	19	have	have	VERB
ejpam-6010	182	20	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	182	21	-	-	NOUN
ejpam-6010	182	22	cl(v	cl(v	NOUN
ejpam-6010	182	23	)	)	PUNCT
ejpam-6010	182	24	)	)	PUNCT
ejpam-6010	182	25	is	be	AUX
ejpam-6010	182	26	τ1τ2	τ1τ2	NOUN
ejpam-6010	182	27	-	-	ADJ
ejpam-6010	182	28	open	open	ADJ
ejpam-6010	182	29	in	in	ADP
ejpam-6010	182	30	x.	x.	NOUN
ejpam-6010	182	31	(	(	PUNCT
ejpam-6010	182	32	2	2	NUM
ejpam-6010	182	33	)	)	PUNCT
ejpam-6010	182	34	⇒	⇒	NOUN
ejpam-6010	182	35	(	(	PUNCT
ejpam-6010	182	36	3	3	NUM
ejpam-6010	182	37	):	):	PUNCT
ejpam-6010	182	38	this	this	PRON
ejpam-6010	182	39	is	be	AUX
ejpam-6010	182	40	obvious	obvious	ADJ
ejpam-6010	182	41	since	since	SCONJ
ejpam-6010	182	42	every	every	DET
ejpam-6010	182	43	(	(	PUNCT
ejpam-6010	182	44	σ1	σ1	PROPN
ejpam-6010	182	45	,	,	PUNCT
ejpam-6010	182	46	σ2)s	σ2)s	NOUN
ejpam-6010	182	47	-	-	PUNCT
ejpam-6010	182	48	open	open	ADJ
ejpam-6010	182	49	set	set	NOUN
ejpam-6010	182	50	is	be	AUX
ejpam-6010	182	51	(	(	PUNCT
ejpam-6010	182	52	σ1	σ1	PROPN
ejpam-6010	182	53	,	,	PUNCT
ejpam-6010	182	54	σ2)β	σ2)β	NOUN
ejpam-6010	182	55	-	-	PUNCT
ejpam-6010	182	56	open	open	ADJ
ejpam-6010	182	57	.	.	PUNCT
ejpam-6010	183	1	(	(	PUNCT
ejpam-6010	183	2	3	3	X
ejpam-6010	183	3	)	)	PUNCT
ejpam-6010	183	4	⇒	⇒	NOUN
ejpam-6010	183	5	(	(	PUNCT
ejpam-6010	183	6	4	4	NUM
ejpam-6010	183	7	):	):	PUNCT
ejpam-6010	183	8	let	let	VERB
ejpam-6010	183	9	v	v	PART
ejpam-6010	183	10	be	be	AUX
ejpam-6010	183	11	any	any	DET
ejpam-6010	183	12	(	(	PUNCT
ejpam-6010	183	13	σ1	σ1	PROPN
ejpam-6010	183	14	,	,	PUNCT
ejpam-6010	183	15	σ2)p	σ2)p	NOUN
ejpam-6010	183	16	-	-	PUNCT
ejpam-6010	183	17	open	open	ADJ
ejpam-6010	183	18	set	set	NOUN
ejpam-6010	183	19	of	of	ADP
ejpam-6010	183	20	y	y	PROPN
ejpam-6010	183	21	.	.	PUNCT
ejpam-6010	184	1	thus	thus	ADV
ejpam-6010	184	2	,	,	PUNCT
ejpam-6010	184	3	y	y	PROPN
ejpam-6010	184	4	−	−	NOUN
ejpam-6010	184	5	σ1σ2	σ1σ2	NUM
ejpam-6010	184	6	-	-	PUNCT
ejpam-6010	184	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	184	8	-	-	PUNCT
ejpam-6010	184	9	cl(v	cl(v	NOUN
ejpam-6010	184	10	)	)	PUNCT
ejpam-6010	184	11	)	)	PUNCT
ejpam-6010	184	12	is	be	AUX
ejpam-6010	184	13	(	(	PUNCT
ejpam-6010	184	14	σ1	σ1	NOUN
ejpam-6010	184	15	,	,	PUNCT
ejpam-6010	184	16	σ2)r	σ2)r	NOUN
ejpam-6010	184	17	-	-	PUNCT
ejpam-6010	184	18	closed	close	VERB
ejpam-6010	184	19	in	in	ADP
ejpam-6010	184	20	y	y	PROPN
ejpam-6010	184	21	and	and	CCONJ
ejpam-6010	184	22	hence	hence	ADV
ejpam-6010	184	23	y	y	NOUN
ejpam-6010	184	24	−	−	NUM
ejpam-6010	184	25	σ1σ2	σ1σ2	ADV
ejpam-6010	184	26	-	-	PUNCT
ejpam-6010	184	27	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	184	28	-	-	PUNCT
ejpam-6010	184	29	cl(v	cl(v	NOUN
ejpam-6010	184	30	)	)	PUNCT
ejpam-6010	184	31	)	)	PUNCT
ejpam-6010	185	1	is	be	AUX
ejpam-6010	185	2	(	(	PUNCT
ejpam-6010	185	3	σ1	σ1	PROPN
ejpam-6010	185	4	,	,	PUNCT
ejpam-6010	185	5	σ2)s	σ2)s	NOUN
ejpam-6010	185	6	-	-	PUNCT
ejpam-6010	185	7	open	open	ADJ
ejpam-6010	185	8	in	in	ADP
ejpam-6010	185	9	y	y	PROPN
ejpam-6010	185	10	.	.	PUNCT
ejpam-6010	186	1	by	by	ADP
ejpam-6010	186	2	(	(	PUNCT
ejpam-6010	186	3	3	3	NUM
ejpam-6010	186	4	)	)	PUNCT
ejpam-6010	186	5	,	,	PUNCT
ejpam-6010	186	6	x	x	PUNCT
ejpam-6010	186	7	−	−	ADP
ejpam-6010	186	8	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6010	186	9	-	-	PUNCT
ejpam-6010	186	10	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	186	11	-	-	PUNCT
ejpam-6010	186	12	cl(v	cl(v	NOUN
ejpam-6010	186	13	)	)	PUNCT
ejpam-6010	186	14	)	)	PUNCT
ejpam-6010	186	15	)	)	PUNCT
ejpam-6010	187	1	=	=	PUNCT
ejpam-6010	188	1	f+(y	f+(y	NOUN
ejpam-6010	188	2	−	−	NUM
ejpam-6010	188	3	σ1σ2	σ1σ2	X
ejpam-6010	188	4	-	-	PUNCT
ejpam-6010	188	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	188	6	-	-	PUNCT
ejpam-6010	188	7	cl(v	cl(v	NOUN
ejpam-6010	188	8	)	)	PUNCT
ejpam-6010	188	9	)	)	PUNCT
ejpam-6010	188	10	)	)	PUNCT
ejpam-6010	189	1	=	=	SYM
ejpam-6010	189	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	189	3	-	-	PUNCT
ejpam-6010	189	4	cl(y	cl(y	NOUN
ejpam-6010	189	5	−	−	NOUN
ejpam-6010	189	6	σ1σ2	σ1σ2	NUM
ejpam-6010	189	7	-	-	PUNCT
ejpam-6010	189	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	189	9	-	-	PUNCT
ejpam-6010	189	10	cl(v	cl(v	NOUN
ejpam-6010	189	11	)	)	PUNCT
ejpam-6010	189	12	)	)	PUNCT
ejpam-6010	189	13	)	)	PUNCT
ejpam-6010	189	14	)	)	PUNCT
ejpam-6010	189	15	is	be	AUX
ejpam-6010	189	16	τ1τ2	τ1τ2	NOUN
ejpam-6010	189	17	-	-	ADJ
ejpam-6010	189	18	open	open	ADJ
ejpam-6010	189	19	in	in	ADP
ejpam-6010	189	20	x.	x.	PROPN
ejpam-6010	189	21	thus	thus	ADV
ejpam-6010	189	22	,	,	PUNCT
ejpam-6010	189	23	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	189	24	-	-	PUNCT
ejpam-6010	189	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	189	26	-	-	PUNCT
ejpam-6010	189	27	cl(v	cl(v	NOUN
ejpam-6010	189	28	)	)	PUNCT
ejpam-6010	189	29	)	)	PUNCT
ejpam-6010	189	30	)	)	PUNCT
ejpam-6010	190	1	is	be	AUX
ejpam-6010	190	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	190	3	-	-	ADJ
ejpam-6010	190	4	closed	closed	ADJ
ejpam-6010	190	5	in	in	ADP
ejpam-6010	190	6	x.	x.	NOUN
ejpam-6010	190	7	(	(	PUNCT
ejpam-6010	190	8	4	4	NUM
ejpam-6010	190	9	)	)	PUNCT
ejpam-6010	190	10	⇒	⇒	NOUN
ejpam-6010	190	11	(	(	PUNCT
ejpam-6010	190	12	1	1	NUM
ejpam-6010	190	13	):	):	PUNCT
ejpam-6010	190	14	let	let	VERB
ejpam-6010	190	15	v	v	PART
ejpam-6010	190	16	be	be	AUX
ejpam-6010	190	17	any	any	DET
ejpam-6010	190	18	(	(	PUNCT
ejpam-6010	190	19	σ1	σ1	NOUN
ejpam-6010	190	20	,	,	PUNCT
ejpam-6010	190	21	σ2)r	σ2)r	NOUN
ejpam-6010	190	22	-	-	PUNCT
ejpam-6010	190	23	open	open	ADJ
ejpam-6010	190	24	set	set	NOUN
ejpam-6010	190	25	of	of	ADP
ejpam-6010	190	26	y	y	PROPN
ejpam-6010	190	27	.	.	PUNCT
ejpam-6010	191	1	then	then	ADV
ejpam-6010	191	2	,	,	PUNCT
ejpam-6010	191	3	v	v	NOUN
ejpam-6010	191	4	is	be	AUX
ejpam-6010	191	5	(	(	PUNCT
ejpam-6010	191	6	σ1	σ1	PROPN
ejpam-6010	191	7	,	,	PUNCT
ejpam-6010	191	8	σ2)p	σ2)p	NOUN
ejpam-6010	191	9	-	-	PUNCT
ejpam-6010	191	10	open	open	ADJ
ejpam-6010	191	11	in	in	ADP
ejpam-6010	191	12	y	y	PROPN
ejpam-6010	191	13	and	and	CCONJ
ejpam-6010	191	14	by	by	ADP
ejpam-6010	191	15	(	(	PUNCT
ejpam-6010	191	16	4	4	NUM
ejpam-6010	191	17	)	)	PUNCT
ejpam-6010	191	18	,	,	PUNCT
ejpam-6010	191	19	f−(v	f−(v	ADJ
ejpam-6010	191	20	)	)	PUNCT
ejpam-6010	191	21	=	=	SYM
ejpam-6010	191	22	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6010	191	23	-	-	PUNCT
ejpam-6010	191	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	191	25	-	-	PUNCT
ejpam-6010	191	26	cl(v	cl(v	NOUN
ejpam-6010	191	27	)	)	PUNCT
ejpam-6010	191	28	)	)	PUNCT
ejpam-6010	191	29	)	)	PUNCT
ejpam-6010	191	30	is	be	AUX
ejpam-6010	191	31	τ1τ2	τ1τ2	NOUN
ejpam-6010	191	32	-	-	ADJ
ejpam-6010	191	33	closed	closed	ADJ
ejpam-6010	191	34	in	in	ADP
ejpam-6010	191	35	x.	x.	NOUN
ejpam-6010	191	36	by	by	ADP
ejpam-6010	191	37	theorem	theorem	NOUN
ejpam-6010	191	38	1	1	NUM
ejpam-6010	191	39	,	,	PUNCT
ejpam-6010	191	40	f	f	PROPN
ejpam-6010	191	41	is	be	AUX
ejpam-6010	191	42	upper	upper	ADJ
ejpam-6010	191	43	almost	almost	ADV
ejpam-6010	191	44	almost	almost	ADV
ejpam-6010	191	45	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	191	46	,	,	PUNCT
ejpam-6010	191	47	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	191	48	.	.	PUNCT
ejpam-6010	192	1	theorem	theorem	NOUN
ejpam-6010	192	2	4	4	NUM
ejpam-6010	192	3	.	.	X
ejpam-6010	192	4	for	for	ADP
ejpam-6010	192	5	a	a	DET
ejpam-6010	192	6	multifunction	multifunction	NOUN
ejpam-6010	193	1	f	f	NOUN
ejpam-6010	193	2	:	:	PUNCT
ejpam-6010	193	3	(	(	PUNCT
ejpam-6010	193	4	x	x	NOUN
ejpam-6010	193	5	,	,	PUNCT
ejpam-6010	193	6	τ1	τ1	NOUN
ejpam-6010	193	7	,	,	PUNCT
ejpam-6010	193	8	τ2	τ2	NOUN
ejpam-6010	193	9	)	)	PUNCT
ejpam-6010	193	10	→	→	SYM
ejpam-6010	193	11	(	(	PUNCT
ejpam-6010	193	12	y	y	PROPN
ejpam-6010	193	13	,	,	PUNCT
ejpam-6010	193	14	σ1	σ1	PROPN
ejpam-6010	193	15	,	,	PUNCT
ejpam-6010	193	16	σ2	σ2	NOUN
ejpam-6010	193	17	)	)	PUNCT
ejpam-6010	193	18	,	,	PUNCT
ejpam-6010	193	19	the	the	DET
ejpam-6010	193	20	following	follow	VERB
ejpam-6010	193	21	properties	property	NOUN
ejpam-6010	193	22	are	be	AUX
ejpam-6010	193	23	equivalent	equivalent	ADJ
ejpam-6010	193	24	:	:	PUNCT
ejpam-6010	193	25	(	(	PUNCT
ejpam-6010	193	26	1	1	X
ejpam-6010	193	27	)	)	PUNCT
ejpam-6010	193	28	f	f	PROPN
ejpam-6010	193	29	is	be	AUX
ejpam-6010	193	30	lower	low	ADJ
ejpam-6010	193	31	almost	almost	ADV
ejpam-6010	193	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	193	33	,	,	PUNCT
ejpam-6010	193	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	193	35	;	;	PUNCT
ejpam-6010	193	36	(	(	PUNCT
ejpam-6010	193	37	2	2	X
ejpam-6010	193	38	)	)	PUNCT
ejpam-6010	193	39	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	193	40	-	-	PUNCT
ejpam-6010	193	41	cl(v	cl(v	NOUN
ejpam-6010	193	42	)	)	PUNCT
ejpam-6010	193	43	)	)	PUNCT
ejpam-6010	193	44	is	be	AUX
ejpam-6010	193	45	τ1τ2	τ1τ2	NOUN
ejpam-6010	193	46	-	-	ADJ
ejpam-6010	193	47	open	open	ADJ
ejpam-6010	193	48	in	in	ADP
ejpam-6010	193	49	x	x	PUNCT
ejpam-6010	193	50	for	for	ADP
ejpam-6010	193	51	every	every	DET
ejpam-6010	193	52	(	(	PUNCT
ejpam-6010	193	53	σ1	σ1	PROPN
ejpam-6010	193	54	,	,	PUNCT
ejpam-6010	193	55	σ2)β	σ2)β	NOUN
ejpam-6010	193	56	-	-	PUNCT
ejpam-6010	193	57	open	open	NOUN
ejpam-6010	193	58	set	set	NOUN
ejpam-6010	193	59	v	v	NOUN
ejpam-6010	193	60	of	of	ADP
ejpam-6010	193	61	y	y	PROPN
ejpam-6010	193	62	;	;	PUNCT
ejpam-6010	193	63	(	(	PUNCT
ejpam-6010	193	64	3	3	X
ejpam-6010	193	65	)	)	PUNCT
ejpam-6010	193	66	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	193	67	-	-	PUNCT
ejpam-6010	193	68	cl(v	cl(v	NOUN
ejpam-6010	193	69	)	)	PUNCT
ejpam-6010	193	70	)	)	PUNCT
ejpam-6010	194	1	is	be	AUX
ejpam-6010	194	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	194	3	-	-	ADJ
ejpam-6010	194	4	open	open	ADJ
ejpam-6010	194	5	in	in	ADP
ejpam-6010	194	6	x	x	PUNCT
ejpam-6010	194	7	for	for	ADP
ejpam-6010	194	8	every	every	DET
ejpam-6010	194	9	(	(	PUNCT
ejpam-6010	194	10	σ1	σ1	PROPN
ejpam-6010	194	11	,	,	PUNCT
ejpam-6010	194	12	σ2)s	σ2)s	NOUN
ejpam-6010	194	13	-	-	PUNCT
ejpam-6010	194	14	open	open	NOUN
ejpam-6010	194	15	set	set	NOUN
ejpam-6010	194	16	v	v	NOUN
ejpam-6010	194	17	of	of	ADP
ejpam-6010	194	18	y	y	PROPN
ejpam-6010	194	19	;	;	PUNCT
ejpam-6010	194	20	(	(	PUNCT
ejpam-6010	194	21	4	4	X
ejpam-6010	194	22	)	)	PUNCT
ejpam-6010	194	23	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	194	24	-	-	PUNCT
ejpam-6010	194	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	194	26	-	-	PUNCT
ejpam-6010	194	27	cl(v	cl(v	NOUN
ejpam-6010	194	28	)	)	PUNCT
ejpam-6010	194	29	)	)	PUNCT
ejpam-6010	194	30	)	)	PUNCT
ejpam-6010	195	1	is	be	AUX
ejpam-6010	195	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	195	3	-	-	ADJ
ejpam-6010	195	4	closed	closed	ADJ
ejpam-6010	195	5	in	in	ADP
ejpam-6010	195	6	x	x	PUNCT
ejpam-6010	195	7	for	for	ADP
ejpam-6010	195	8	every	every	DET
ejpam-6010	195	9	(	(	PUNCT
ejpam-6010	195	10	σ1	σ1	PROPN
ejpam-6010	195	11	,	,	PUNCT
ejpam-6010	195	12	σ2)p	σ2)p	NOUN
ejpam-6010	195	13	-	-	PUNCT
ejpam-6010	195	14	open	open	NOUN
ejpam-6010	195	15	set	set	NOUN
ejpam-6010	195	16	v	v	NOUN
ejpam-6010	195	17	of	of	ADP
ejpam-6010	195	18	y	y	PROPN
ejpam-6010	195	19	.	.	PUNCT
ejpam-6010	196	1	proof	proof	NOUN
ejpam-6010	196	2	.	.	PUNCT
ejpam-6010	197	1	the	the	DET
ejpam-6010	197	2	proof	proof	NOUN
ejpam-6010	197	3	is	be	AUX
ejpam-6010	197	4	similar	similar	ADJ
ejpam-6010	197	5	to	to	ADP
ejpam-6010	197	6	that	that	PRON
ejpam-6010	197	7	of	of	ADP
ejpam-6010	197	8	theorem	theorem	NOUN
ejpam-6010	197	9	3	3	X
ejpam-6010	197	10	.	.	PUNCT
ejpam-6010	197	11	lemma	lemma	PROPN
ejpam-6010	197	12	4	4	NUM
ejpam-6010	197	13	.	.	PUNCT
ejpam-6010	198	1	[	[	X
ejpam-6010	198	2	81	81	NUM
ejpam-6010	198	3	]	]	PUNCT
ejpam-6010	198	4	for	for	ADP
ejpam-6010	198	5	a	a	DET
ejpam-6010	198	6	bitopological	bitopological	ADJ
ejpam-6010	198	7	space	space	NOUN
ejpam-6010	198	8	(	(	PUNCT
ejpam-6010	198	9	x	x	NOUN
ejpam-6010	198	10	,	,	PUNCT
ejpam-6010	198	11	τ1	τ1	NOUN
ejpam-6010	198	12	,	,	PUNCT
ejpam-6010	198	13	τ2	τ2	NOUN
ejpam-6010	198	14	)	)	PUNCT
ejpam-6010	198	15	,	,	PUNCT
ejpam-6010	198	16	the	the	DET
ejpam-6010	198	17	following	follow	VERB
ejpam-6010	198	18	properties	property	NOUN
ejpam-6010	198	19	hold	hold	VERB
ejpam-6010	198	20	:	:	PUNCT
ejpam-6010	198	21	(	(	PUNCT
ejpam-6010	198	22	1	1	X
ejpam-6010	198	23	)	)	PUNCT
ejpam-6010	198	24	α(τ1	α(τ1	NOUN
ejpam-6010	198	25	,	,	PUNCT
ejpam-6010	198	26	τ2)-cl(v	τ2)-cl(v	NOUN
ejpam-6010	198	27	)	)	PUNCT
ejpam-6010	198	28	=	=	PUNCT
ejpam-6010	199	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	199	2	-	-	NOUN
ejpam-6010	199	3	cl(v	cl(v	X
ejpam-6010	199	4	)	)	PUNCT
ejpam-6010	199	5	for	for	ADP
ejpam-6010	199	6	every	every	DET
ejpam-6010	199	7	(	(	PUNCT
ejpam-6010	199	8	τ1	τ1	NOUN
ejpam-6010	199	9	,	,	PUNCT
ejpam-6010	199	10	τ2)β	τ2)β	ADJ
ejpam-6010	199	11	-	-	PUNCT
ejpam-6010	199	12	open	open	NOUN
ejpam-6010	199	13	set	set	NOUN
ejpam-6010	199	14	v	v	NOUN
ejpam-6010	199	15	of	of	ADP
ejpam-6010	199	16	x	x	PRON
ejpam-6010	199	17	;	;	PUNCT
ejpam-6010	199	18	(	(	PUNCT
ejpam-6010	199	19	2	2	X
ejpam-6010	199	20	)	)	PUNCT
ejpam-6010	199	21	(	(	PUNCT
ejpam-6010	199	22	τ1	τ1	NOUN
ejpam-6010	199	23	,	,	PUNCT
ejpam-6010	199	24	τ2)-pcl(v	τ2)-pcl(v	NOUN
ejpam-6010	199	25	)	)	PUNCT
ejpam-6010	199	26	=	=	PUNCT
ejpam-6010	200	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	200	2	-	-	NOUN
ejpam-6010	200	3	cl(v	cl(v	X
ejpam-6010	200	4	)	)	PUNCT
ejpam-6010	200	5	for	for	ADP
ejpam-6010	200	6	every	every	DET
ejpam-6010	200	7	(	(	PUNCT
ejpam-6010	200	8	τ1	τ1	NOUN
ejpam-6010	200	9	,	,	PUNCT
ejpam-6010	200	10	τ2)s	τ2)s	NOUN
ejpam-6010	200	11	-	-	PUNCT
ejpam-6010	200	12	open	open	ADJ
ejpam-6010	200	13	set	set	NOUN
ejpam-6010	200	14	v	v	NOUN
ejpam-6010	200	15	of	of	ADP
ejpam-6010	200	16	x	x	PRON
ejpam-6010	200	17	;	;	PUNCT
ejpam-6010	200	18	(	(	PUNCT
ejpam-6010	200	19	3	3	X
ejpam-6010	200	20	)	)	PUNCT
ejpam-6010	200	21	(	(	PUNCT
ejpam-6010	200	22	τ1	τ1	NOUN
ejpam-6010	200	23	,	,	PUNCT
ejpam-6010	200	24	τ2)-scl(v	τ2)-scl(v	NOUN
ejpam-6010	200	25	)	)	PUNCT
ejpam-6010	201	1	=	=	PUNCT
ejpam-6010	202	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	202	2	-	-	NOUN
ejpam-6010	202	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6010	202	4	-	-	PUNCT
ejpam-6010	202	5	cl(v	cl(v	NOUN
ejpam-6010	202	6	)	)	PUNCT
ejpam-6010	202	7	)	)	PUNCT
ejpam-6010	202	8	for	for	ADP
ejpam-6010	202	9	every	every	DET
ejpam-6010	202	10	(	(	PUNCT
ejpam-6010	202	11	τ1	τ1	NOUN
ejpam-6010	202	12	,	,	PUNCT
ejpam-6010	202	13	τ2)p	τ2)p	ADJ
ejpam-6010	202	14	-	-	PUNCT
ejpam-6010	202	15	open	open	ADJ
ejpam-6010	202	16	set	set	NOUN
ejpam-6010	202	17	v	v	NOUN
ejpam-6010	202	18	of	of	ADP
ejpam-6010	202	19	x.	x.	NOUN
ejpam-6010	202	20	corollary	corollary	NOUN
ejpam-6010	202	21	1	1	NUM
ejpam-6010	202	22	.	.	PUNCT
ejpam-6010	202	23	for	for	ADP
ejpam-6010	202	24	a	a	DET
ejpam-6010	202	25	multifunction	multifunction	NOUN
ejpam-6010	202	26	f	f	NOUN
ejpam-6010	202	27	:	:	PUNCT
ejpam-6010	202	28	(	(	PUNCT
ejpam-6010	202	29	x	x	NOUN
ejpam-6010	202	30	,	,	PUNCT
ejpam-6010	202	31	τ1	τ1	NOUN
ejpam-6010	202	32	,	,	PUNCT
ejpam-6010	202	33	τ2	τ2	NOUN
ejpam-6010	202	34	)	)	PUNCT
ejpam-6010	202	35	→	→	SYM
ejpam-6010	202	36	(	(	PUNCT
ejpam-6010	202	37	y	y	PROPN
ejpam-6010	202	38	,	,	PUNCT
ejpam-6010	202	39	σ1	σ1	PROPN
ejpam-6010	202	40	,	,	PUNCT
ejpam-6010	202	41	σ2	σ2	NOUN
ejpam-6010	202	42	)	)	PUNCT
ejpam-6010	202	43	,	,	PUNCT
ejpam-6010	202	44	the	the	DET
ejpam-6010	202	45	following	follow	VERB
ejpam-6010	202	46	properties	property	NOUN
ejpam-6010	202	47	are	be	AUX
ejpam-6010	202	48	equivalent	equivalent	ADJ
ejpam-6010	202	49	:	:	PUNCT
ejpam-6010	202	50	(	(	PUNCT
ejpam-6010	202	51	1	1	X
ejpam-6010	202	52	)	)	PUNCT
ejpam-6010	202	53	f	f	PROPN
ejpam-6010	202	54	is	be	AUX
ejpam-6010	202	55	upper	upper	ADJ
ejpam-6010	202	56	almost	almost	ADV
ejpam-6010	202	57	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	202	58	,	,	PUNCT
ejpam-6010	202	59	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	202	60	;	;	PUNCT
ejpam-6010	202	61	(	(	PUNCT
ejpam-6010	202	62	2	2	X
ejpam-6010	202	63	)	)	PUNCT
ejpam-6010	202	64	f+(α(σ1	f+(α(σ1	NOUN
ejpam-6010	202	65	,	,	PUNCT
ejpam-6010	202	66	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-6010	202	67	)	)	PUNCT
ejpam-6010	202	68	)	)	PUNCT
ejpam-6010	202	69	is	be	AUX
ejpam-6010	202	70	τ1τ2	τ1τ2	NOUN
ejpam-6010	202	71	-	-	ADJ
ejpam-6010	202	72	open	open	ADJ
ejpam-6010	202	73	in	in	ADP
ejpam-6010	202	74	x	x	PUNCT
ejpam-6010	202	75	for	for	ADP
ejpam-6010	202	76	every	every	DET
ejpam-6010	202	77	(	(	PUNCT
ejpam-6010	202	78	σ1	σ1	PROPN
ejpam-6010	202	79	,	,	PUNCT
ejpam-6010	202	80	σ2)β	σ2)β	NOUN
ejpam-6010	202	81	-	-	PUNCT
ejpam-6010	202	82	open	open	NOUN
ejpam-6010	202	83	set	set	NOUN
ejpam-6010	202	84	v	v	NOUN
ejpam-6010	202	85	of	of	ADP
ejpam-6010	202	86	y	y	PROPN
ejpam-6010	202	87	;	;	PUNCT
ejpam-6010	202	88	(	(	PUNCT
ejpam-6010	202	89	3	3	X
ejpam-6010	202	90	)	)	PUNCT
ejpam-6010	202	91	f+((σ1	f+((σ1	NOUN
ejpam-6010	202	92	,	,	PUNCT
ejpam-6010	202	93	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-6010	202	94	)	)	PUNCT
ejpam-6010	202	95	)	)	PUNCT
ejpam-6010	202	96	is	be	AUX
ejpam-6010	202	97	τ1τ2	τ1τ2	NOUN
ejpam-6010	202	98	-	-	ADJ
ejpam-6010	202	99	open	open	ADJ
ejpam-6010	202	100	in	in	ADP
ejpam-6010	202	101	x	x	PUNCT
ejpam-6010	202	102	for	for	ADP
ejpam-6010	202	103	every	every	DET
ejpam-6010	202	104	(	(	PUNCT
ejpam-6010	202	105	σ1	σ1	PROPN
ejpam-6010	202	106	,	,	PUNCT
ejpam-6010	202	107	σ2)s	σ2)s	NOUN
ejpam-6010	202	108	-	-	PUNCT
ejpam-6010	202	109	open	open	NOUN
ejpam-6010	202	110	set	set	NOUN
ejpam-6010	202	111	v	v	NOUN
ejpam-6010	202	112	of	of	ADP
ejpam-6010	202	113	y	y	PROPN
ejpam-6010	202	114	;	;	PUNCT
ejpam-6010	202	115	(	(	PUNCT
ejpam-6010	202	116	4	4	X
ejpam-6010	202	117	)	)	PUNCT
ejpam-6010	202	118	f−((σ1	f−((σ1	NOUN
ejpam-6010	202	119	,	,	PUNCT
ejpam-6010	202	120	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6010	202	121	)	)	PUNCT
ejpam-6010	202	122	)	)	PUNCT
ejpam-6010	202	123	is	be	AUX
ejpam-6010	202	124	τ1	τ1	NOUN
ejpam-6010	202	125	,	,	PUNCT
ejpam-6010	202	126	τ2	τ2	NOUN
ejpam-6010	202	127	-	-	PUNCT
ejpam-6010	202	128	closed	closed	ADJ
ejpam-6010	202	129	in	in	ADP
ejpam-6010	202	130	x	x	PUNCT
ejpam-6010	202	131	for	for	ADP
ejpam-6010	202	132	every	every	DET
ejpam-6010	202	133	(	(	PUNCT
ejpam-6010	202	134	σ1	σ1	PROPN
ejpam-6010	202	135	,	,	PUNCT
ejpam-6010	202	136	σ2)p	σ2)p	NOUN
ejpam-6010	202	137	-	-	PUNCT
ejpam-6010	202	138	open	open	NOUN
ejpam-6010	202	139	set	set	NOUN
ejpam-6010	202	140	v	v	NOUN
ejpam-6010	202	141	of	of	ADP
ejpam-6010	202	142	y	y	PROPN
ejpam-6010	202	143	.	.	PUNCT
ejpam-6010	203	1	corollary	corollary	ADJ
ejpam-6010	203	2	2	2	NUM
ejpam-6010	203	3	.	.	PUNCT
ejpam-6010	203	4	for	for	ADP
ejpam-6010	203	5	a	a	DET
ejpam-6010	203	6	multifunction	multifunction	NOUN
ejpam-6010	204	1	f	f	NOUN
ejpam-6010	204	2	:	:	PUNCT
ejpam-6010	204	3	(	(	PUNCT
ejpam-6010	204	4	x	x	NOUN
ejpam-6010	204	5	,	,	PUNCT
ejpam-6010	204	6	τ1	τ1	NOUN
ejpam-6010	204	7	,	,	PUNCT
ejpam-6010	204	8	τ2	τ2	NOUN
ejpam-6010	204	9	)	)	PUNCT
ejpam-6010	204	10	→	→	SYM
ejpam-6010	204	11	(	(	PUNCT
ejpam-6010	204	12	y	y	PROPN
ejpam-6010	204	13	,	,	PUNCT
ejpam-6010	204	14	σ1	σ1	PROPN
ejpam-6010	204	15	,	,	PUNCT
ejpam-6010	204	16	σ2	σ2	NOUN
ejpam-6010	204	17	)	)	PUNCT
ejpam-6010	204	18	,	,	PUNCT
ejpam-6010	204	19	the	the	DET
ejpam-6010	204	20	following	follow	VERB
ejpam-6010	204	21	properties	property	NOUN
ejpam-6010	204	22	are	be	AUX
ejpam-6010	204	23	equivalent	equivalent	ADJ
ejpam-6010	204	24	:	:	PUNCT
ejpam-6010	204	25	j.	j.	PROPN
ejpam-6010	204	26	khampakdee	khampakdee	PROPN
ejpam-6010	204	27	,	,	PUNCT
ejpam-6010	204	28	a.	a.	PROPN
ejpam-6010	204	29	sama	sama	PROPN
ejpam-6010	204	30	-	-	PUNCT
ejpam-6010	204	31	ae	ae	PROPN
ejpam-6010	204	32	,	,	PUNCT
ejpam-6010	204	33	c.	c.	PROPN
ejpam-6010	204	34	boonpok	boonpok	PROPN
ejpam-6010	204	35	/	/	SYM
ejpam-6010	204	36	eur	eur	PROPN
ejpam-6010	204	37	.	.	PUNCT
ejpam-6010	205	1	j.	j.	PROPN
ejpam-6010	205	2	pure	pure	PROPN
ejpam-6010	205	3	appl	appl	PROPN
ejpam-6010	205	4	.	.	PROPN
ejpam-6010	205	5	math	math	PROPN
ejpam-6010	205	6	,	,	PUNCT
ejpam-6010	205	7	18	18	NUM
ejpam-6010	205	8	(	(	PUNCT
ejpam-6010	205	9	2	2	NUM
ejpam-6010	205	10	)	)	PUNCT
ejpam-6010	205	11	(	(	PUNCT
ejpam-6010	205	12	2025	2025	NUM
ejpam-6010	205	13	)	)	PUNCT
ejpam-6010	205	14	,	,	PUNCT
ejpam-6010	205	15	6010	6010	NUM
ejpam-6010	205	16	8	8	NUM
ejpam-6010	205	17	of	of	ADP
ejpam-6010	205	18	19	19	NUM
ejpam-6010	205	19	(	(	PUNCT
ejpam-6010	205	20	1	1	NUM
ejpam-6010	205	21	)	)	PUNCT
ejpam-6010	205	22	f	f	PROPN
ejpam-6010	205	23	is	be	AUX
ejpam-6010	205	24	lower	low	ADJ
ejpam-6010	205	25	almost	almost	ADV
ejpam-6010	205	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	205	27	,	,	PUNCT
ejpam-6010	205	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	205	29	;	;	PUNCT
ejpam-6010	205	30	(	(	PUNCT
ejpam-6010	205	31	2	2	X
ejpam-6010	205	32	)	)	PUNCT
ejpam-6010	205	33	f−(α(σ1	f−(α(σ1	NOUN
ejpam-6010	205	34	,	,	PUNCT
ejpam-6010	205	35	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-6010	205	36	)	)	PUNCT
ejpam-6010	205	37	)	)	PUNCT
ejpam-6010	205	38	is	be	AUX
ejpam-6010	205	39	τ1τ2	τ1τ2	NOUN
ejpam-6010	205	40	-	-	ADJ
ejpam-6010	205	41	open	open	ADJ
ejpam-6010	205	42	in	in	ADP
ejpam-6010	205	43	x	x	PUNCT
ejpam-6010	205	44	for	for	ADP
ejpam-6010	205	45	every	every	DET
ejpam-6010	205	46	(	(	PUNCT
ejpam-6010	205	47	σ1	σ1	PROPN
ejpam-6010	205	48	,	,	PUNCT
ejpam-6010	206	1	σ2)β	σ2)β	NOUN
ejpam-6010	206	2	-	-	PUNCT
ejpam-6010	206	3	open	open	NOUN
ejpam-6010	206	4	set	set	NOUN
ejpam-6010	206	5	v	v	NOUN
ejpam-6010	206	6	of	of	ADP
ejpam-6010	206	7	y	y	PROPN
ejpam-6010	206	8	;	;	PUNCT
ejpam-6010	206	9	(	(	PUNCT
ejpam-6010	206	10	3	3	X
ejpam-6010	206	11	)	)	PUNCT
ejpam-6010	206	12	f−((σ1	f−((σ1	NOUN
ejpam-6010	206	13	,	,	PUNCT
ejpam-6010	206	14	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-6010	206	15	)	)	PUNCT
ejpam-6010	206	16	)	)	PUNCT
ejpam-6010	206	17	is	be	AUX
ejpam-6010	206	18	τ1τ2	τ1τ2	NOUN
ejpam-6010	206	19	-	-	ADJ
ejpam-6010	206	20	open	open	ADJ
ejpam-6010	206	21	in	in	ADP
ejpam-6010	206	22	x	x	PUNCT
ejpam-6010	206	23	for	for	ADP
ejpam-6010	206	24	every	every	DET
ejpam-6010	206	25	(	(	PUNCT
ejpam-6010	206	26	σ1	σ1	PROPN
ejpam-6010	206	27	,	,	PUNCT
ejpam-6010	206	28	σ2)s	σ2)s	NOUN
ejpam-6010	206	29	-	-	PUNCT
ejpam-6010	206	30	open	open	NOUN
ejpam-6010	206	31	set	set	NOUN
ejpam-6010	206	32	v	v	NOUN
ejpam-6010	206	33	of	of	ADP
ejpam-6010	206	34	y	y	PROPN
ejpam-6010	206	35	;	;	PUNCT
ejpam-6010	206	36	(	(	PUNCT
ejpam-6010	206	37	4	4	X
ejpam-6010	206	38	)	)	PUNCT
ejpam-6010	206	39	f+((σ1	f+((σ1	NOUN
ejpam-6010	206	40	,	,	PUNCT
ejpam-6010	206	41	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6010	206	42	)	)	PUNCT
ejpam-6010	206	43	)	)	PUNCT
ejpam-6010	207	1	is	be	AUX
ejpam-6010	207	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	207	3	-	-	ADJ
ejpam-6010	207	4	closed	closed	ADJ
ejpam-6010	207	5	in	in	ADP
ejpam-6010	207	6	x	x	PUNCT
ejpam-6010	207	7	for	for	ADP
ejpam-6010	207	8	every	every	DET
ejpam-6010	207	9	(	(	PUNCT
ejpam-6010	207	10	σ1	σ1	PROPN
ejpam-6010	207	11	,	,	PUNCT
ejpam-6010	207	12	σ2)p	σ2)p	NOUN
ejpam-6010	207	13	-	-	PUNCT
ejpam-6010	207	14	open	open	NOUN
ejpam-6010	207	15	set	set	NOUN
ejpam-6010	207	16	v	v	NOUN
ejpam-6010	207	17	of	of	ADP
ejpam-6010	207	18	y	y	PROPN
ejpam-6010	207	19	.	.	PUNCT
ejpam-6010	208	1	theorem	theorem	ADJ
ejpam-6010	208	2	5	5	NUM
ejpam-6010	208	3	.	.	X
ejpam-6010	208	4	for	for	ADP
ejpam-6010	208	5	a	a	DET
ejpam-6010	208	6	multifunction	multifunction	NOUN
ejpam-6010	209	1	f	f	NOUN
ejpam-6010	209	2	:	:	PUNCT
ejpam-6010	209	3	(	(	PUNCT
ejpam-6010	209	4	x	x	NOUN
ejpam-6010	209	5	,	,	PUNCT
ejpam-6010	209	6	τ1	τ1	NOUN
ejpam-6010	209	7	,	,	PUNCT
ejpam-6010	209	8	τ2	τ2	NOUN
ejpam-6010	209	9	)	)	PUNCT
ejpam-6010	209	10	→	→	SYM
ejpam-6010	209	11	(	(	PUNCT
ejpam-6010	209	12	y	y	PROPN
ejpam-6010	209	13	,	,	PUNCT
ejpam-6010	209	14	σ1	σ1	PROPN
ejpam-6010	209	15	,	,	PUNCT
ejpam-6010	209	16	σ2	σ2	NOUN
ejpam-6010	209	17	)	)	PUNCT
ejpam-6010	209	18	,	,	PUNCT
ejpam-6010	209	19	the	the	DET
ejpam-6010	209	20	following	follow	VERB
ejpam-6010	209	21	properties	property	NOUN
ejpam-6010	209	22	are	be	AUX
ejpam-6010	209	23	equivalent	equivalent	ADJ
ejpam-6010	209	24	:	:	PUNCT
ejpam-6010	209	25	(	(	PUNCT
ejpam-6010	209	26	1	1	X
ejpam-6010	209	27	)	)	PUNCT
ejpam-6010	209	28	f	f	PROPN
ejpam-6010	209	29	is	be	AUX
ejpam-6010	209	30	upper	upper	ADJ
ejpam-6010	209	31	almost	almost	ADV
ejpam-6010	209	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	209	33	,	,	PUNCT
ejpam-6010	209	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	209	35	;	;	PUNCT
ejpam-6010	209	36	(	(	PUNCT
ejpam-6010	209	37	2	2	X
ejpam-6010	209	38	)	)	PUNCT
ejpam-6010	209	39	τ1τ2	τ1τ2	NOUN
ejpam-6010	209	40	-	-	NOUN
ejpam-6010	209	41	cl(f	cl(f	NUM
ejpam-6010	209	42	−(v	−(v	NOUN
ejpam-6010	209	43	)	)	PUNCT
ejpam-6010	209	44	)	)	PUNCT
ejpam-6010	210	1	⊆	⊆	X
ejpam-6010	210	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6010	210	3	-	-	PUNCT
ejpam-6010	210	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	210	5	-	-	PUNCT
ejpam-6010	210	6	cl(v	cl(v	NOUN
ejpam-6010	210	7	)	)	PUNCT
ejpam-6010	210	8	)	)	PUNCT
ejpam-6010	210	9	)	)	PUNCT
ejpam-6010	210	10	for	for	ADP
ejpam-6010	210	11	every	every	DET
ejpam-6010	210	12	σ1σ2	σ1σ2	NOUN
ejpam-6010	210	13	-	-	ADJ
ejpam-6010	210	14	open	open	ADJ
ejpam-6010	210	15	set	set	NOUN
ejpam-6010	210	16	v	v	NOUN
ejpam-6010	210	17	of	of	ADP
ejpam-6010	210	18	y	y	PROPN
ejpam-6010	210	19	;	;	PUNCT
ejpam-6010	210	20	(	(	PUNCT
ejpam-6010	210	21	3	3	X
ejpam-6010	210	22	)	)	PUNCT
ejpam-6010	210	23	τ1τ2	τ1τ2	NOUN
ejpam-6010	210	24	-	-	NOUN
ejpam-6010	210	25	cl(f	cl(f	NUM
ejpam-6010	210	26	−(v	−(v	NOUN
ejpam-6010	210	27	)	)	PUNCT
ejpam-6010	210	28	)	)	PUNCT
ejpam-6010	211	1	⊆	⊆	NUM
ejpam-6010	211	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	211	3	,	,	PUNCT
ejpam-6010	211	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6010	211	5	)	)	PUNCT
ejpam-6010	211	6	)	)	PUNCT
ejpam-6010	211	7	for	for	ADP
ejpam-6010	211	8	every	every	DET
ejpam-6010	211	9	σ1σ2	σ1σ2	NOUN
ejpam-6010	211	10	-	-	ADJ
ejpam-6010	211	11	open	open	ADJ
ejpam-6010	211	12	set	set	NOUN
ejpam-6010	211	13	v	v	NOUN
ejpam-6010	211	14	of	of	ADP
ejpam-6010	211	15	y	y	PROPN
ejpam-6010	211	16	.	.	PUNCT
ejpam-6010	212	1	proof	proof	NOUN
ejpam-6010	212	2	.	.	PUNCT
ejpam-6010	213	1	(	(	PUNCT
ejpam-6010	213	2	1	1	X
ejpam-6010	213	3	)	)	PUNCT
ejpam-6010	213	4	⇒	⇒	NOUN
ejpam-6010	213	5	(	(	PUNCT
ejpam-6010	213	6	2	2	NUM
ejpam-6010	213	7	):	):	PUNCT
ejpam-6010	213	8	let	let	VERB
ejpam-6010	213	9	v	v	PART
ejpam-6010	213	10	be	be	AUX
ejpam-6010	213	11	any	any	DET
ejpam-6010	213	12	σ1σ2	σ1σ2	NOUN
ejpam-6010	213	13	-	-	ADJ
ejpam-6010	213	14	open	open	ADJ
ejpam-6010	213	15	set	set	NOUN
ejpam-6010	213	16	of	of	ADP
ejpam-6010	213	17	y	y	PROPN
ejpam-6010	213	18	.	.	PUNCT
ejpam-6010	214	1	then	then	ADV
ejpam-6010	214	2	,	,	PUNCT
ejpam-6010	214	3	σ1σ2	σ1σ2	X
ejpam-6010	214	4	-	-	PUNCT
ejpam-6010	214	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	214	6	-	-	PUNCT
ejpam-6010	214	7	cl(v	cl(v	NOUN
ejpam-6010	214	8	)	)	PUNCT
ejpam-6010	214	9	)	)	PUNCT
ejpam-6010	214	10	is	be	AUX
ejpam-6010	214	11	(	(	PUNCT
ejpam-6010	214	12	σ1	σ1	NOUN
ejpam-6010	214	13	,	,	PUNCT
ejpam-6010	214	14	σ2)r	σ2)r	NOUN
ejpam-6010	214	15	-	-	PUNCT
ejpam-6010	214	16	open	open	ADJ
ejpam-6010	214	17	in	in	ADP
ejpam-6010	214	18	y	y	PROPN
ejpam-6010	214	19	.	.	PUNCT
ejpam-6010	215	1	thus	thus	ADV
ejpam-6010	215	2	by	by	ADP
ejpam-6010	215	3	(	(	PUNCT
ejpam-6010	215	4	1	1	NUM
ejpam-6010	215	5	)	)	PUNCT
ejpam-6010	215	6	,	,	PUNCT
ejpam-6010	215	7	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	215	8	-	-	PUNCT
ejpam-6010	215	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	215	10	-	-	PUNCT
ejpam-6010	215	11	cl(v	cl(v	NOUN
ejpam-6010	215	12	)	)	PUNCT
ejpam-6010	215	13	)	)	PUNCT
ejpam-6010	215	14	)	)	PUNCT
ejpam-6010	215	15	is	be	AUX
ejpam-6010	215	16	τ1τ2	τ1τ2	NOUN
ejpam-6010	215	17	-	-	ADJ
ejpam-6010	215	18	closed	closed	ADJ
ejpam-6010	215	19	in	in	ADP
ejpam-6010	215	20	x.	x.	NOUN
ejpam-6010	215	21	since	since	SCONJ
ejpam-6010	215	22	v	v	NUM
ejpam-6010	215	23	⊆	⊆	NUM
ejpam-6010	215	24	σ1σ2	σ1σ2	NOUN
ejpam-6010	215	25	-	-	PUNCT
ejpam-6010	215	26	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	215	27	-	-	PUNCT
ejpam-6010	215	28	cl(v	cl(v	NOUN
ejpam-6010	215	29	)	)	PUNCT
ejpam-6010	215	30	)	)	PUNCT
ejpam-6010	215	31	,	,	PUNCT
ejpam-6010	215	32	we	we	PRON
ejpam-6010	215	33	have	have	VERB
ejpam-6010	215	34	f−(v	f−(v	NOUN
ejpam-6010	215	35	)	)	PUNCT
ejpam-6010	215	36	⊆	⊆	NUM
ejpam-6010	215	37	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6010	215	38	-	-	PUNCT
ejpam-6010	215	39	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	215	40	-	-	PUNCT
ejpam-6010	215	41	cl(v	cl(v	NOUN
ejpam-6010	215	42	)	)	PUNCT
ejpam-6010	215	43	)	)	PUNCT
ejpam-6010	215	44	)	)	PUNCT
ejpam-6010	215	45	and	and	CCONJ
ejpam-6010	215	46	hence	hence	ADV
ejpam-6010	215	47	τ1τ2	τ1τ2	NOUN
ejpam-6010	215	48	-	-	PROPN
ejpam-6010	215	49	cl(f	cl(f	NUM
ejpam-6010	215	50	−(v	−(v	NOUN
ejpam-6010	215	51	)	)	PUNCT
ejpam-6010	215	52	)	)	PUNCT
ejpam-6010	216	1	⊆	⊆	X
ejpam-6010	216	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6010	216	3	-	-	PUNCT
ejpam-6010	216	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	216	5	-	-	PUNCT
ejpam-6010	216	6	cl(v	cl(v	NOUN
ejpam-6010	216	7	)	)	PUNCT
ejpam-6010	216	8	)	)	PUNCT
ejpam-6010	216	9	)	)	PUNCT
ejpam-6010	216	10	.	.	PUNCT
ejpam-6010	217	1	(	(	PUNCT
ejpam-6010	217	2	2	2	X
ejpam-6010	217	3	)	)	PUNCT
ejpam-6010	217	4	⇒	⇒	NOUN
ejpam-6010	217	5	(	(	PUNCT
ejpam-6010	217	6	1	1	NUM
ejpam-6010	217	7	):	):	PUNCT
ejpam-6010	217	8	let	let	VERB
ejpam-6010	217	9	v	v	PART
ejpam-6010	217	10	be	be	AUX
ejpam-6010	217	11	any	any	DET
ejpam-6010	217	12	(	(	PUNCT
ejpam-6010	217	13	σ1	σ1	NOUN
ejpam-6010	217	14	,	,	PUNCT
ejpam-6010	217	15	σ2)r	σ2)r	NOUN
ejpam-6010	217	16	-	-	PUNCT
ejpam-6010	217	17	open	open	ADJ
ejpam-6010	217	18	set	set	NOUN
ejpam-6010	217	19	of	of	ADP
ejpam-6010	217	20	y	y	PROPN
ejpam-6010	217	21	.	.	PUNCT
ejpam-6010	218	1	by	by	ADP
ejpam-6010	218	2	(	(	PUNCT
ejpam-6010	218	3	2	2	NUM
ejpam-6010	218	4	)	)	PUNCT
ejpam-6010	218	5	,	,	PUNCT
ejpam-6010	218	6	we	we	PRON
ejpam-6010	218	7	have	have	VERB
ejpam-6010	218	8	τ1τ2	τ1τ2	NOUN
ejpam-6010	218	9	-	-	ADJ
ejpam-6010	218	10	cl(f	cl(f	NUM
ejpam-6010	218	11	−(v	−(v	NOUN
ejpam-6010	218	12	)	)	PUNCT
ejpam-6010	218	13	)	)	PUNCT
ejpam-6010	219	1	⊆	⊆	X
ejpam-6010	219	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6010	219	3	-	-	PUNCT
ejpam-6010	219	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	219	5	-	-	PUNCT
ejpam-6010	219	6	cl(v	cl(v	NOUN
ejpam-6010	219	7	)	)	PUNCT
ejpam-6010	219	8	)	)	PUNCT
ejpam-6010	219	9	)	)	PUNCT
ejpam-6010	220	1	=	=	SYM
ejpam-6010	220	2	f−(v	f−(v	ADJ
ejpam-6010	220	3	)	)	PUNCT
ejpam-6010	220	4	and	and	CCONJ
ejpam-6010	220	5	hence	hence	ADV
ejpam-6010	220	6	f−(v	f−(v	ADJ
ejpam-6010	220	7	)	)	PUNCT
ejpam-6010	220	8	is	be	AUX
ejpam-6010	220	9	τ1τ2	τ1τ2	NOUN
ejpam-6010	220	10	-	-	ADJ
ejpam-6010	220	11	closed	closed	ADJ
ejpam-6010	220	12	in	in	ADP
ejpam-6010	220	13	x	x	X
ejpam-6010	220	14	,	,	PUNCT
ejpam-6010	220	15	by	by	ADP
ejpam-6010	220	16	theorem	theorem	NOUN
ejpam-6010	220	17	1	1	NUM
ejpam-6010	220	18	we	we	PRON
ejpam-6010	220	19	have	have	VERB
ejpam-6010	220	20	f	f	PROPN
ejpam-6010	220	21	is	be	AUX
ejpam-6010	220	22	upper	upper	ADJ
ejpam-6010	220	23	almost	almost	ADV
ejpam-6010	220	24	contra(τ1	contra(τ1	NOUN
ejpam-6010	220	25	,	,	PUNCT
ejpam-6010	220	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	220	27	.	.	PUNCT
ejpam-6010	221	1	(	(	PUNCT
ejpam-6010	221	2	2	2	X
ejpam-6010	221	3	)	)	PUNCT
ejpam-6010	221	4	⇔	⇔	X
ejpam-6010	221	5	(	(	PUNCT
ejpam-6010	221	6	3	3	NUM
ejpam-6010	221	7	):	):	PUNCT
ejpam-6010	221	8	it	it	PRON
ejpam-6010	221	9	follows	follow	VERB
ejpam-6010	221	10	from	from	ADP
ejpam-6010	221	11	lemma	lemma	PROPN
ejpam-6010	221	12	4	4	NUM
ejpam-6010	221	13	.	.	PUNCT
ejpam-6010	221	14	theorem	theorem	VERB
ejpam-6010	221	15	6	6	NUM
ejpam-6010	221	16	.	.	PUNCT
ejpam-6010	221	17	for	for	ADP
ejpam-6010	221	18	a	a	DET
ejpam-6010	221	19	multifunction	multifunction	NOUN
ejpam-6010	221	20	f	f	NOUN
ejpam-6010	221	21	:	:	PUNCT
ejpam-6010	221	22	(	(	PUNCT
ejpam-6010	221	23	x	x	NOUN
ejpam-6010	221	24	,	,	PUNCT
ejpam-6010	221	25	τ1	τ1	NOUN
ejpam-6010	221	26	,	,	PUNCT
ejpam-6010	221	27	τ2	τ2	NOUN
ejpam-6010	221	28	)	)	PUNCT
ejpam-6010	221	29	→	→	SYM
ejpam-6010	221	30	(	(	PUNCT
ejpam-6010	221	31	y	y	PROPN
ejpam-6010	221	32	,	,	PUNCT
ejpam-6010	221	33	σ1	σ1	PROPN
ejpam-6010	221	34	,	,	PUNCT
ejpam-6010	221	35	σ2	σ2	NOUN
ejpam-6010	221	36	)	)	PUNCT
ejpam-6010	221	37	,	,	PUNCT
ejpam-6010	221	38	the	the	DET
ejpam-6010	221	39	following	follow	VERB
ejpam-6010	221	40	properties	property	NOUN
ejpam-6010	221	41	are	be	AUX
ejpam-6010	221	42	equivalent	equivalent	ADJ
ejpam-6010	221	43	:	:	PUNCT
ejpam-6010	221	44	(	(	PUNCT
ejpam-6010	221	45	1	1	X
ejpam-6010	221	46	)	)	PUNCT
ejpam-6010	221	47	f	f	PROPN
ejpam-6010	221	48	is	be	AUX
ejpam-6010	221	49	lower	low	ADJ
ejpam-6010	221	50	almost	almost	ADV
ejpam-6010	221	51	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	221	52	,	,	PUNCT
ejpam-6010	221	53	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	221	54	;	;	PUNCT
ejpam-6010	221	55	(	(	PUNCT
ejpam-6010	221	56	2	2	X
ejpam-6010	221	57	)	)	PUNCT
ejpam-6010	221	58	τ1τ2	τ1τ2	NOUN
ejpam-6010	221	59	-	-	NOUN
ejpam-6010	221	60	cl(f	cl(f	NOUN
ejpam-6010	221	61	+	+	NOUN
ejpam-6010	221	62	(	(	PUNCT
ejpam-6010	221	63	v	v	NOUN
ejpam-6010	221	64	)	)	PUNCT
ejpam-6010	221	65	)	)	PUNCT
ejpam-6010	222	1	⊆	⊆	X
ejpam-6010	222	2	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-6010	222	3	-	-	PUNCT
ejpam-6010	222	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	222	5	-	-	PUNCT
ejpam-6010	222	6	cl(v	cl(v	NOUN
ejpam-6010	222	7	)	)	PUNCT
ejpam-6010	222	8	)	)	PUNCT
ejpam-6010	222	9	)	)	PUNCT
ejpam-6010	222	10	for	for	ADP
ejpam-6010	222	11	every	every	DET
ejpam-6010	222	12	σ1σ2	σ1σ2	NOUN
ejpam-6010	222	13	-	-	ADJ
ejpam-6010	222	14	open	open	ADJ
ejpam-6010	222	15	set	set	NOUN
ejpam-6010	222	16	v	v	NOUN
ejpam-6010	222	17	of	of	ADP
ejpam-6010	222	18	y	y	PROPN
ejpam-6010	222	19	;	;	PUNCT
ejpam-6010	222	20	(	(	PUNCT
ejpam-6010	222	21	3	3	X
ejpam-6010	222	22	)	)	PUNCT
ejpam-6010	222	23	τ1τ2	τ1τ2	NOUN
ejpam-6010	222	24	-	-	NOUN
ejpam-6010	222	25	cl(f	cl(f	NOUN
ejpam-6010	222	26	+	+	NOUN
ejpam-6010	222	27	(	(	PUNCT
ejpam-6010	222	28	v	v	NOUN
ejpam-6010	222	29	)	)	PUNCT
ejpam-6010	222	30	)	)	PUNCT
ejpam-6010	222	31	⊆	⊆	NUM
ejpam-6010	222	32	f+((σ1	f+((σ1	NOUN
ejpam-6010	222	33	,	,	PUNCT
ejpam-6010	222	34	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6010	222	35	)	)	PUNCT
ejpam-6010	222	36	)	)	PUNCT
ejpam-6010	222	37	for	for	ADP
ejpam-6010	222	38	every	every	DET
ejpam-6010	222	39	σ1σ2	σ1σ2	NOUN
ejpam-6010	222	40	-	-	ADJ
ejpam-6010	222	41	open	open	ADJ
ejpam-6010	222	42	set	set	NOUN
ejpam-6010	222	43	v	v	NOUN
ejpam-6010	222	44	of	of	ADP
ejpam-6010	222	45	y	y	PROPN
ejpam-6010	222	46	.	.	PUNCT
ejpam-6010	223	1	proof	proof	NOUN
ejpam-6010	223	2	.	.	PUNCT
ejpam-6010	224	1	the	the	DET
ejpam-6010	224	2	proof	proof	NOUN
ejpam-6010	224	3	is	be	AUX
ejpam-6010	224	4	similar	similar	ADJ
ejpam-6010	224	5	to	to	ADP
ejpam-6010	224	6	that	that	PRON
ejpam-6010	224	7	of	of	ADP
ejpam-6010	224	8	theorem	theorem	ADJ
ejpam-6010	224	9	5	5	NUM
ejpam-6010	224	10	.	.	PUNCT
ejpam-6010	224	11	theorem	theorem	VERB
ejpam-6010	224	12	7	7	NUM
ejpam-6010	224	13	.	.	X
ejpam-6010	224	14	for	for	ADP
ejpam-6010	224	15	a	a	DET
ejpam-6010	224	16	multifunction	multifunction	NOUN
ejpam-6010	224	17	f	f	NOUN
ejpam-6010	224	18	:	:	PUNCT
ejpam-6010	224	19	(	(	PUNCT
ejpam-6010	224	20	x	x	NOUN
ejpam-6010	224	21	,	,	PUNCT
ejpam-6010	224	22	τ1	τ1	NOUN
ejpam-6010	224	23	,	,	PUNCT
ejpam-6010	224	24	τ2	τ2	NOUN
ejpam-6010	224	25	)	)	PUNCT
ejpam-6010	224	26	→	→	SYM
ejpam-6010	224	27	(	(	PUNCT
ejpam-6010	224	28	y	y	PROPN
ejpam-6010	224	29	,	,	PUNCT
ejpam-6010	224	30	σ1	σ1	PROPN
ejpam-6010	224	31	,	,	PUNCT
ejpam-6010	224	32	σ2	σ2	NOUN
ejpam-6010	224	33	)	)	PUNCT
ejpam-6010	224	34	,	,	PUNCT
ejpam-6010	224	35	the	the	DET
ejpam-6010	224	36	following	follow	VERB
ejpam-6010	224	37	properties	property	NOUN
ejpam-6010	224	38	are	be	AUX
ejpam-6010	224	39	equivalent	equivalent	ADJ
ejpam-6010	224	40	:	:	PUNCT
ejpam-6010	224	41	(	(	PUNCT
ejpam-6010	224	42	1	1	X
ejpam-6010	224	43	)	)	PUNCT
ejpam-6010	224	44	f	f	PROPN
ejpam-6010	224	45	is	be	AUX
ejpam-6010	224	46	lower	low	ADJ
ejpam-6010	224	47	almost	almost	ADV
ejpam-6010	224	48	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	224	49	,	,	PUNCT
ejpam-6010	224	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	224	51	;	;	PUNCT
ejpam-6010	224	52	(	(	PUNCT
ejpam-6010	224	53	2	2	X
ejpam-6010	224	54	)	)	PUNCT
ejpam-6010	224	55	f−(v	f−(v	NOUN
ejpam-6010	224	56	)	)	PUNCT
ejpam-6010	224	57	is	be	AUX
ejpam-6010	224	58	τ1τ2	τ1τ2	NOUN
ejpam-6010	224	59	-	-	ADJ
ejpam-6010	224	60	open	open	ADJ
ejpam-6010	224	61	in	in	ADP
ejpam-6010	224	62	x	x	PUNCT
ejpam-6010	224	63	for	for	ADP
ejpam-6010	224	64	every	every	DET
ejpam-6010	224	65	s(σ1	s(σ1	NOUN
ejpam-6010	224	66	,	,	PUNCT
ejpam-6010	224	67	σ2)θ	σ2)θ	NOUN
ejpam-6010	224	68	-	-	PUNCT
ejpam-6010	224	69	open	open	ADJ
ejpam-6010	224	70	set	set	NOUN
ejpam-6010	224	71	v	v	NOUN
ejpam-6010	224	72	of	of	ADP
ejpam-6010	224	73	y	y	PROPN
ejpam-6010	224	74	;	;	PUNCT
ejpam-6010	224	75	(	(	PUNCT
ejpam-6010	224	76	3	3	X
ejpam-6010	224	77	)	)	PUNCT
ejpam-6010	224	78	f+(k	f+(k	NOUN
ejpam-6010	224	79	)	)	PUNCT
ejpam-6010	224	80	is	be	AUX
ejpam-6010	224	81	τ1τ2	τ1τ2	NOUN
ejpam-6010	224	82	-	-	ADJ
ejpam-6010	224	83	closed	closed	ADJ
ejpam-6010	224	84	in	in	ADP
ejpam-6010	224	85	x	x	PUNCT
ejpam-6010	224	86	for	for	ADP
ejpam-6010	224	87	every	every	DET
ejpam-6010	224	88	s(σ1	s(σ1	NOUN
ejpam-6010	224	89	,	,	PUNCT
ejpam-6010	224	90	σ2)θ	σ2)θ	NOUN
ejpam-6010	224	91	-	-	PUNCT
ejpam-6010	224	92	closed	close	VERB
ejpam-6010	224	93	set	set	NOUN
ejpam-6010	224	94	k	k	PROPN
ejpam-6010	224	95	of	of	ADP
ejpam-6010	224	96	y	y	PROPN
ejpam-6010	224	97	;	;	PUNCT
ejpam-6010	224	98	j.	j.	PROPN
ejpam-6010	224	99	khampakdee	khampakdee	PROPN
ejpam-6010	224	100	,	,	PUNCT
ejpam-6010	224	101	a.	a.	PROPN
ejpam-6010	224	102	sama	sama	PROPN
ejpam-6010	224	103	-	-	PUNCT
ejpam-6010	224	104	ae	ae	PROPN
ejpam-6010	224	105	,	,	PUNCT
ejpam-6010	224	106	c.	c.	PROPN
ejpam-6010	224	107	boonpok	boonpok	PROPN
ejpam-6010	224	108	/	/	SYM
ejpam-6010	224	109	eur	eur	PROPN
ejpam-6010	224	110	.	.	PUNCT
ejpam-6010	225	1	j.	j.	PROPN
ejpam-6010	225	2	pure	pure	PROPN
ejpam-6010	225	3	appl	appl	PROPN
ejpam-6010	225	4	.	.	PROPN
ejpam-6010	225	5	math	math	PROPN
ejpam-6010	225	6	,	,	PUNCT
ejpam-6010	225	7	18	18	NUM
ejpam-6010	225	8	(	(	PUNCT
ejpam-6010	225	9	2	2	NUM
ejpam-6010	225	10	)	)	PUNCT
ejpam-6010	225	11	(	(	PUNCT
ejpam-6010	225	12	2025	2025	NUM
ejpam-6010	225	13	)	)	PUNCT
ejpam-6010	225	14	,	,	PUNCT
ejpam-6010	225	15	6010	6010	NUM
ejpam-6010	225	16	9	9	NUM
ejpam-6010	225	17	of	of	ADP
ejpam-6010	225	18	19	19	NUM
ejpam-6010	225	19	(	(	PUNCT
ejpam-6010	225	20	4	4	NUM
ejpam-6010	225	21	)	)	PUNCT
ejpam-6010	225	22	τ1τ2	τ1τ2	NOUN
ejpam-6010	225	23	-	-	NOUN
ejpam-6010	225	24	cl(f	cl(f	NOUN
ejpam-6010	225	25	+	+	NOUN
ejpam-6010	225	26	(	(	PUNCT
ejpam-6010	225	27	σ1σ2	σ1σ2	NUM
ejpam-6010	225	28	-	-	PUNCT
ejpam-6010	225	29	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	225	30	-	-	PUNCT
ejpam-6010	225	31	cl(b	cl(b	NOUN
ejpam-6010	225	32	)	)	PUNCT
ejpam-6010	225	33	)	)	PUNCT
ejpam-6010	225	34	)	)	PUNCT
ejpam-6010	225	35	)	)	PUNCT
ejpam-6010	226	1	⊆	⊆	NUM
ejpam-6010	226	2	f+((σ1	f+((σ1	NOUN
ejpam-6010	226	3	,	,	PUNCT
ejpam-6010	226	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	226	5	)	)	PUNCT
ejpam-6010	226	6	)	)	PUNCT
ejpam-6010	226	7	for	for	ADP
ejpam-6010	226	8	every	every	DET
ejpam-6010	226	9	subset	subset	NOUN
ejpam-6010	226	10	b	b	PROPN
ejpam-6010	226	11	of	of	ADP
ejpam-6010	226	12	y	y	PROPN
ejpam-6010	226	13	;	;	PUNCT
ejpam-6010	226	14	(	(	PUNCT
ejpam-6010	226	15	5	5	X
ejpam-6010	226	16	)	)	PUNCT
ejpam-6010	226	17	τ1τ2	τ1τ2	NOUN
ejpam-6010	226	18	-	-	NOUN
ejpam-6010	226	19	cl(f	cl(f	NOUN
ejpam-6010	226	20	+	+	NOUN
ejpam-6010	226	21	(	(	PUNCT
ejpam-6010	226	22	b	b	NOUN
ejpam-6010	226	23	)	)	PUNCT
ejpam-6010	226	24	)	)	PUNCT
ejpam-6010	226	25	⊆	⊆	NUM
ejpam-6010	226	26	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6010	226	27	,	,	PUNCT
ejpam-6010	226	28	σ2)θ	σ2)θ	NOUN
ejpam-6010	226	29	-	-	PUNCT
ejpam-6010	226	30	cl(b	cl(b	NOUN
ejpam-6010	226	31	)	)	PUNCT
ejpam-6010	226	32	)	)	PUNCT
ejpam-6010	226	33	for	for	ADP
ejpam-6010	226	34	every	every	DET
ejpam-6010	226	35	subset	subset	NOUN
ejpam-6010	226	36	b	b	PROPN
ejpam-6010	226	37	of	of	ADP
ejpam-6010	226	38	y	y	PROPN
ejpam-6010	226	39	;	;	PUNCT
ejpam-6010	226	40	(	(	PUNCT
ejpam-6010	226	41	6	6	X
ejpam-6010	226	42	)	)	PUNCT
ejpam-6010	226	43	f	f	NOUN
ejpam-6010	226	44	(	(	PUNCT
ejpam-6010	226	45	τ1τ2	τ1τ2	NOUN
ejpam-6010	226	46	-	-	NUM
ejpam-6010	226	47	cl(a	cl(a	NUM
ejpam-6010	226	48	)	)	PUNCT
ejpam-6010	226	49	)	)	PUNCT
ejpam-6010	226	50	⊆	⊆	NUM
ejpam-6010	226	51	s(σ1	s(σ1	NOUN
ejpam-6010	226	52	,	,	PUNCT
ejpam-6010	226	53	σ2)θ	σ2)θ	NOUN
ejpam-6010	226	54	-	-	PUNCT
ejpam-6010	226	55	cl(f	cl(f	PROPN
ejpam-6010	226	56	(	(	PUNCT
ejpam-6010	226	57	a	a	NOUN
ejpam-6010	226	58	)	)	PUNCT
ejpam-6010	226	59	)	)	PUNCT
ejpam-6010	226	60	for	for	ADP
ejpam-6010	226	61	every	every	DET
ejpam-6010	226	62	subset	subset	NOUN
ejpam-6010	226	63	a	a	PRON
ejpam-6010	226	64	of	of	ADP
ejpam-6010	226	65	x.	x.	NOUN
ejpam-6010	226	66	proof	proof	NOUN
ejpam-6010	226	67	.	.	PUNCT
ejpam-6010	227	1	(	(	PUNCT
ejpam-6010	227	2	1	1	X
ejpam-6010	227	3	)	)	PUNCT
ejpam-6010	227	4	⇒	⇒	NOUN
ejpam-6010	227	5	(	(	PUNCT
ejpam-6010	227	6	2	2	NUM
ejpam-6010	227	7	):	):	PUNCT
ejpam-6010	227	8	let	let	VERB
ejpam-6010	227	9	v	v	PART
ejpam-6010	227	10	be	be	AUX
ejpam-6010	227	11	any	any	DET
ejpam-6010	227	12	s(σ1	s(σ1	NOUN
ejpam-6010	227	13	,	,	PUNCT
ejpam-6010	227	14	σ2)θ	σ2)θ	ADJ
ejpam-6010	227	15	-	-	PUNCT
ejpam-6010	227	16	open	open	ADJ
ejpam-6010	227	17	set	set	NOUN
ejpam-6010	227	18	of	of	ADP
ejpam-6010	227	19	y	y	PROPN
ejpam-6010	227	20	.	.	PUNCT
ejpam-6010	228	1	there	there	PRON
ejpam-6010	228	2	exists	exist	VERB
ejpam-6010	228	3	a	a	DET
ejpam-6010	228	4	family	family	NOUN
ejpam-6010	228	5	of	of	ADP
ejpam-6010	228	6	(	(	PUNCT
ejpam-6010	228	7	σ1	σ1	PROPN
ejpam-6010	228	8	,	,	PUNCT
ejpam-6010	228	9	σ2)r	σ2)r	NOUN
ejpam-6010	228	10	-	-	PUNCT
ejpam-6010	228	11	closed	close	VERB
ejpam-6010	228	12	sets	set	NOUN
ejpam-6010	228	13	{	{	PUNCT
ejpam-6010	228	14	kγ	kγ	NOUN
ejpam-6010	228	15	|	|	ADV
ejpam-6010	228	16	γ	γ	PROPN
ejpam-6010	228	17	∈	∈	PROPN
ejpam-6010	228	18	∇	∇	X
ejpam-6010	228	19	}	}	PUNCT
ejpam-6010	229	1	such	such	ADJ
ejpam-6010	229	2	that	that	PRON
ejpam-6010	229	3	v	v	NOUN
ejpam-6010	229	4	=	=	SYM
ejpam-6010	229	5	∪{kγ	∪{kγ	PROPN
ejpam-6010	229	6	|	|	ADV
ejpam-6010	229	7	γ	γ	X
ejpam-6010	229	8	∈	∈	NOUN
ejpam-6010	229	9	∇	∇	X
ejpam-6010	229	10	}	}	PUNCT
ejpam-6010	229	11	.	.	PUNCT
ejpam-6010	230	1	it	it	PRON
ejpam-6010	230	2	follows	follow	VERB
ejpam-6010	230	3	from	from	ADP
ejpam-6010	230	4	theorem	theorem	ADJ
ejpam-6010	230	5	2	2	NUM
ejpam-6010	230	6	that	that	DET
ejpam-6010	230	7	f−(v	f−(v	VERB
ejpam-6010	230	8	)	)	PUNCT
ejpam-6010	230	9	=	=	SYM
ejpam-6010	230	10	∪{f−(kγ	∪{f−(kγ	PROPN
ejpam-6010	230	11	)	)	PUNCT
ejpam-6010	230	12	|	|	ADV
ejpam-6010	230	13	γ	γ	PROPN
ejpam-6010	230	14	∈	∈	PROPN
ejpam-6010	230	15	∇	∇	X
ejpam-6010	230	16	}	}	PUNCT
ejpam-6010	230	17	is	be	AUX
ejpam-6010	230	18	τ1τ2	τ1τ2	NOUN
ejpam-6010	230	19	-	-	ADJ
ejpam-6010	230	20	open	open	ADJ
ejpam-6010	230	21	in	in	ADP
ejpam-6010	230	22	x.	x.	NOUN
ejpam-6010	230	23	(	(	PUNCT
ejpam-6010	230	24	2	2	NUM
ejpam-6010	230	25	)	)	PUNCT
ejpam-6010	230	26	⇒	⇒	NOUN
ejpam-6010	230	27	(	(	PUNCT
ejpam-6010	230	28	3	3	NUM
ejpam-6010	230	29	):	):	PUNCT
ejpam-6010	230	30	the	the	DET
ejpam-6010	230	31	proof	proof	NOUN
ejpam-6010	230	32	is	be	AUX
ejpam-6010	230	33	obvious	obvious	ADJ
ejpam-6010	230	34	.	.	PUNCT
ejpam-6010	231	1	(	(	PUNCT
ejpam-6010	231	2	3	3	X
ejpam-6010	231	3	)	)	PUNCT
ejpam-6010	231	4	⇒	⇒	NOUN
ejpam-6010	231	5	(	(	PUNCT
ejpam-6010	231	6	4	4	NUM
ejpam-6010	231	7	):	):	PUNCT
ejpam-6010	231	8	let	let	VERB
ejpam-6010	231	9	b	b	X
ejpam-6010	231	10	be	be	AUX
ejpam-6010	231	11	any	any	DET
ejpam-6010	231	12	subset	subset	NOUN
ejpam-6010	231	13	of	of	ADP
ejpam-6010	231	14	y	y	PROPN
ejpam-6010	231	15	.	.	PUNCT
ejpam-6010	232	1	then	then	ADV
ejpam-6010	232	2	,	,	PUNCT
ejpam-6010	232	3	σ1σ2	σ1σ2	X
ejpam-6010	232	4	-	-	PUNCT
ejpam-6010	232	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	232	6	-	-	PUNCT
ejpam-6010	232	7	cl(b	cl(b	NOUN
ejpam-6010	232	8	)	)	PUNCT
ejpam-6010	232	9	)	)	PUNCT
ejpam-6010	232	10	is	be	AUX
ejpam-6010	232	11	(	(	PUNCT
ejpam-6010	232	12	σ1	σ1	NOUN
ejpam-6010	232	13	,	,	PUNCT
ejpam-6010	232	14	σ2)r	σ2)r	NOUN
ejpam-6010	232	15	-	-	PUNCT
ejpam-6010	232	16	open	open	ADJ
ejpam-6010	232	17	and	and	CCONJ
ejpam-6010	232	18	hence	hence	ADV
ejpam-6010	232	19	σ1σ2	σ1σ2	ADV
ejpam-6010	232	20	-	-	PUNCT
ejpam-6010	232	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	232	22	-	-	PUNCT
ejpam-6010	232	23	cl(b	cl(b	NOUN
ejpam-6010	232	24	)	)	PUNCT
ejpam-6010	232	25	)	)	PUNCT
ejpam-6010	233	1	is	be	AUX
ejpam-6010	233	2	s(σ1	s(σ1	ADV
ejpam-6010	233	3	,	,	PUNCT
ejpam-6010	233	4	σ2)θ	σ2)θ	NOUN
ejpam-6010	233	5	-	-	PUNCT
ejpam-6010	233	6	closed	closed	ADJ
ejpam-6010	233	7	in	in	ADP
ejpam-6010	233	8	y	y	PROPN
ejpam-6010	233	9	.	.	PUNCT
ejpam-6010	234	1	by	by	ADP
ejpam-6010	234	2	(	(	PUNCT
ejpam-6010	234	3	3	3	NUM
ejpam-6010	234	4	)	)	PUNCT
ejpam-6010	234	5	,	,	PUNCT
ejpam-6010	234	6	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	234	7	-	-	PUNCT
ejpam-6010	234	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	234	9	-	-	PUNCT
ejpam-6010	234	10	cl(b	cl(b	NOUN
ejpam-6010	234	11	)	)	PUNCT
ejpam-6010	234	12	)	)	PUNCT
ejpam-6010	234	13	)	)	PUNCT
ejpam-6010	234	14	is	be	AUX
ejpam-6010	234	15	τ1τ2	τ1τ2	NOUN
ejpam-6010	234	16	-	-	ADJ
ejpam-6010	234	17	closed	closed	ADJ
ejpam-6010	234	18	in	in	ADP
ejpam-6010	234	19	x.	x.	NOUN
ejpam-6010	234	20	thus	thus	ADV
ejpam-6010	234	21	,	,	PUNCT
ejpam-6010	234	22	τ1τ2	τ1τ2	NOUN
ejpam-6010	234	23	-	-	NOUN
ejpam-6010	234	24	cl(f	cl(f	NOUN
ejpam-6010	234	25	+	+	NOUN
ejpam-6010	234	26	(	(	PUNCT
ejpam-6010	234	27	σ1σ2	σ1σ2	NUM
ejpam-6010	234	28	-	-	PUNCT
ejpam-6010	234	29	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	234	30	-	-	PUNCT
ejpam-6010	234	31	cl(b	cl(b	NOUN
ejpam-6010	234	32	)	)	PUNCT
ejpam-6010	234	33	)	)	PUNCT
ejpam-6010	234	34	)	)	PUNCT
ejpam-6010	234	35	)	)	PUNCT
ejpam-6010	235	1	=	=	SYM
ejpam-6010	235	2	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-6010	235	3	-	-	PUNCT
ejpam-6010	235	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	235	5	-	-	PUNCT
ejpam-6010	235	6	cl(b	cl(b	NOUN
ejpam-6010	235	7	)	)	PUNCT
ejpam-6010	235	8	)	)	PUNCT
ejpam-6010	235	9	)	)	PUNCT
ejpam-6010	236	1	⊆	⊆	NUM
ejpam-6010	236	2	f+((σ1	f+((σ1	NOUN
ejpam-6010	236	3	,	,	PUNCT
ejpam-6010	236	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	236	5	)	)	PUNCT
ejpam-6010	236	6	)	)	PUNCT
ejpam-6010	236	7	.	.	PUNCT
ejpam-6010	237	1	(	(	PUNCT
ejpam-6010	237	2	4	4	X
ejpam-6010	237	3	)	)	PUNCT
ejpam-6010	237	4	⇒	⇒	NOUN
ejpam-6010	237	5	(	(	PUNCT
ejpam-6010	237	6	5	5	NUM
ejpam-6010	237	7	):	):	PUNCT
ejpam-6010	237	8	let	let	VERB
ejpam-6010	237	9	b	b	X
ejpam-6010	237	10	be	be	AUX
ejpam-6010	237	11	any	any	DET
ejpam-6010	237	12	subset	subset	NOUN
ejpam-6010	237	13	of	of	ADP
ejpam-6010	237	14	y	y	PROPN
ejpam-6010	237	15	.	.	PUNCT
ejpam-6010	238	1	for	for	ADP
ejpam-6010	238	2	any	any	DET
ejpam-6010	238	3	(	(	PUNCT
ejpam-6010	238	4	σ1	σ1	NOUN
ejpam-6010	238	5	,	,	PUNCT
ejpam-6010	238	6	σ2)r	σ2)r	NOUN
ejpam-6010	238	7	-	-	PUNCT
ejpam-6010	238	8	open	open	ADJ
ejpam-6010	238	9	set	set	VERB
ejpam-6010	238	10	v	v	NOUN
ejpam-6010	238	11	of	of	ADP
ejpam-6010	238	12	y	y	PROPN
ejpam-6010	238	13	with	with	ADP
ejpam-6010	238	14	b	b	PROPN
ejpam-6010	238	15	⊆	⊆	NUM
ejpam-6010	238	16	v	v	NOUN
ejpam-6010	238	17	,	,	PUNCT
ejpam-6010	238	18	by	by	ADP
ejpam-6010	238	19	(	(	PUNCT
ejpam-6010	238	20	4	4	NUM
ejpam-6010	238	21	)	)	PUNCT
ejpam-6010	238	22	and	and	CCONJ
ejpam-6010	238	23	lemma	lemma	PROPN
ejpam-6010	238	24	4	4	NUM
ejpam-6010	238	25	we	we	PRON
ejpam-6010	238	26	have	have	VERB
ejpam-6010	238	27	τ1τ2	τ1τ2	NOUN
ejpam-6010	238	28	-	-	NOUN
ejpam-6010	238	29	cl(f	cl(f	NOUN
ejpam-6010	238	30	+	+	PROPN
ejpam-6010	238	31	(	(	PUNCT
ejpam-6010	238	32	b	b	NOUN
ejpam-6010	238	33	)	)	PUNCT
ejpam-6010	238	34	)	)	PUNCT
ejpam-6010	239	1	⊆	⊆	X
ejpam-6010	239	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	239	3	-	-	NOUN
ejpam-6010	239	4	cl(f	cl(f	NOUN
ejpam-6010	239	5	+	+	NOUN
ejpam-6010	239	6	(	(	PUNCT
ejpam-6010	239	7	v	v	NOUN
ejpam-6010	239	8	)	)	PUNCT
ejpam-6010	239	9	)	)	PUNCT
ejpam-6010	240	1	=	=	PUNCT
ejpam-6010	240	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	240	3	-	-	NOUN
ejpam-6010	240	4	cl(f	cl(f	NOUN
ejpam-6010	240	5	+	+	NOUN
ejpam-6010	240	6	(	(	PUNCT
ejpam-6010	240	7	σ1σ2	σ1σ2	NUM
ejpam-6010	240	8	-	-	PUNCT
ejpam-6010	240	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6010	240	10	-	-	PUNCT
ejpam-6010	240	11	cl(v	cl(v	NOUN
ejpam-6010	240	12	)	)	PUNCT
ejpam-6010	240	13	)	)	PUNCT
ejpam-6010	240	14	)	)	PUNCT
ejpam-6010	240	15	)	)	PUNCT
ejpam-6010	241	1	⊆	⊆	NUM
ejpam-6010	241	2	f+((σ1	f+((σ1	NOUN
ejpam-6010	241	3	,	,	PUNCT
ejpam-6010	241	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6010	241	5	)	)	PUNCT
ejpam-6010	241	6	)	)	PUNCT
ejpam-6010	242	1	=	=	PUNCT
ejpam-6010	242	2	f+(v	f+(v	NOUN
ejpam-6010	242	3	)	)	PUNCT
ejpam-6010	242	4	.	.	PUNCT
ejpam-6010	243	1	thus	thus	ADV
ejpam-6010	243	2	,	,	PUNCT
ejpam-6010	243	3	τ1τ2	τ1τ2	NOUN
ejpam-6010	243	4	-	-	NOUN
ejpam-6010	243	5	cl(f	cl(f	NOUN
ejpam-6010	243	6	+	+	PROPN
ejpam-6010	243	7	(	(	PUNCT
ejpam-6010	243	8	b	b	NOUN
ejpam-6010	243	9	)	)	PUNCT
ejpam-6010	243	10	)	)	PUNCT
ejpam-6010	244	1	⊆	⊆	NUM
ejpam-6010	244	2	f+(∩{v	f+(∩{v	NOUN
ejpam-6010	244	3	|	|	ADV
ejpam-6010	244	4	v	v	NOUN
ejpam-6010	244	5	is	be	AUX
ejpam-6010	244	6	(	(	PUNCT
ejpam-6010	244	7	σ1	σ1	NOUN
ejpam-6010	244	8	,	,	PUNCT
ejpam-6010	244	9	σ2)r	σ2)r	NOUN
ejpam-6010	244	10	-	-	PUNCT
ejpam-6010	244	11	open	open	ADJ
ejpam-6010	244	12	in	in	ADP
ejpam-6010	244	13	y	y	PROPN
ejpam-6010	244	14	and	and	CCONJ
ejpam-6010	244	15	b	b	PROPN
ejpam-6010	244	16	⊆	⊆	NUM
ejpam-6010	244	17	v	v	NOUN
ejpam-6010	244	18	}	}	PUNCT
ejpam-6010	244	19	)	)	PUNCT
ejpam-6010	244	20	=	=	SYM
ejpam-6010	244	21	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6010	244	22	,	,	PUNCT
ejpam-6010	244	23	σ2)θ	σ2)θ	NOUN
ejpam-6010	244	24	-	-	PUNCT
ejpam-6010	244	25	cl(b	cl(b	NOUN
ejpam-6010	244	26	)	)	PUNCT
ejpam-6010	244	27	)	)	PUNCT
ejpam-6010	244	28	.	.	PUNCT
ejpam-6010	245	1	(	(	PUNCT
ejpam-6010	245	2	5	5	X
ejpam-6010	245	3	)	)	PUNCT
ejpam-6010	245	4	⇒	⇒	NOUN
ejpam-6010	245	5	(	(	PUNCT
ejpam-6010	245	6	1	1	NUM
ejpam-6010	245	7	):	):	PUNCT
ejpam-6010	245	8	let	let	VERB
ejpam-6010	245	9	v	v	PART
ejpam-6010	245	10	be	be	AUX
ejpam-6010	245	11	any	any	DET
ejpam-6010	245	12	(	(	PUNCT
ejpam-6010	245	13	σ1	σ1	NOUN
ejpam-6010	245	14	,	,	PUNCT
ejpam-6010	245	15	σ2)s	σ2)s	NOUN
ejpam-6010	245	16	-	-	PUNCT
ejpam-6010	245	17	open	open	ADJ
ejpam-6010	245	18	set	set	NOUN
ejpam-6010	245	19	of	of	ADP
ejpam-6010	245	20	y	y	PROPN
ejpam-6010	245	21	.	.	PUNCT
ejpam-6010	246	1	by	by	ADP
ejpam-6010	246	2	(	(	PUNCT
ejpam-6010	246	3	5	5	NUM
ejpam-6010	246	4	)	)	PUNCT
ejpam-6010	246	5	,	,	PUNCT
ejpam-6010	246	6	we	we	PRON
ejpam-6010	246	7	have	have	VERB
ejpam-6010	246	8	x	x	INTJ
ejpam-6010	246	9	−	−	ADP
ejpam-6010	246	10	τ1τ2	τ1τ2	NOUN
ejpam-6010	246	11	-	-	NUM
ejpam-6010	246	12	int(f	int(f	PRON
ejpam-6010	246	13	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	246	14	-	-	NOUN
ejpam-6010	246	15	cl(v	cl(v	NOUN
ejpam-6010	246	16	)	)	PUNCT
ejpam-6010	246	17	)	)	PUNCT
ejpam-6010	246	18	)	)	PUNCT
ejpam-6010	247	1	=	=	PUNCT
ejpam-6010	247	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	247	3	-	-	NOUN
ejpam-6010	247	4	cl(f	cl(f	NOUN
ejpam-6010	247	5	+	+	PROPN
ejpam-6010	247	6	(	(	PUNCT
ejpam-6010	247	7	y	y	PROPN
ejpam-6010	247	8	−	−	PROPN
ejpam-6010	247	9	σ1σ2	σ1σ2	NOUN
ejpam-6010	247	10	-	-	NUM
ejpam-6010	247	11	cl(v	cl(v	NOUN
ejpam-6010	247	12	)	)	PUNCT
ejpam-6010	247	13	)	)	PUNCT
ejpam-6010	247	14	)	)	PUNCT
ejpam-6010	248	1	⊆	⊆	NUM
ejpam-6010	248	2	f+((σ1	f+((σ1	NOUN
ejpam-6010	248	3	,	,	PUNCT
ejpam-6010	248	4	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6010	248	5	−	−	NOUN
ejpam-6010	248	6	σ1σ2	σ1σ2	NOUN
ejpam-6010	248	7	-	-	NUM
ejpam-6010	248	8	cl(v	cl(v	NOUN
ejpam-6010	248	9	)	)	PUNCT
ejpam-6010	248	10	)	)	PUNCT
ejpam-6010	248	11	)	)	PUNCT
ejpam-6010	249	1	=	=	PUNCT
ejpam-6010	250	1	f+(y	f+(y	NOUN
ejpam-6010	250	2	−	−	NUM
ejpam-6010	250	3	σ1σ2	σ1σ2	NOUN
ejpam-6010	250	4	-	-	NUM
ejpam-6010	250	5	cl(v	cl(v	NOUN
ejpam-6010	250	6	)	)	PUNCT
ejpam-6010	250	7	)	)	PUNCT
ejpam-6010	251	1	=	=	PUNCT
ejpam-6010	251	2	x	x	PUNCT
ejpam-6010	251	3	−	−	NOUN
ejpam-6010	251	4	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	251	5	-	-	PUNCT
ejpam-6010	251	6	cl(v	cl(v	NOUN
ejpam-6010	251	7	)	)	PUNCT
ejpam-6010	251	8	)	)	PUNCT
ejpam-6010	251	9	and	and	CCONJ
ejpam-6010	251	10	hence	hence	ADV
ejpam-6010	251	11	f−(v	f−(v	ADJ
ejpam-6010	251	12	)	)	PUNCT
ejpam-6010	251	13	⊆	⊆	NUM
ejpam-6010	251	14	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	251	15	-	-	PUNCT
ejpam-6010	251	16	cl(v	cl(v	NOUN
ejpam-6010	251	17	)	)	PUNCT
ejpam-6010	251	18	)	)	PUNCT
ejpam-6010	252	1	⊆	⊆	X
ejpam-6010	252	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	252	3	-	-	NUM
ejpam-6010	252	4	int(f	int(f	PRON
ejpam-6010	252	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	252	6	-	-	NOUN
ejpam-6010	252	7	cl(v	cl(v	NOUN
ejpam-6010	252	8	)	)	PUNCT
ejpam-6010	252	9	)	)	PUNCT
ejpam-6010	252	10	)	)	PUNCT
ejpam-6010	252	11	.	.	PUNCT
ejpam-6010	253	1	by	by	ADP
ejpam-6010	253	2	theorem	theorem	NOUN
ejpam-6010	253	3	2	2	NUM
ejpam-6010	253	4	,	,	PUNCT
ejpam-6010	253	5	f	f	PROPN
ejpam-6010	253	6	is	be	AUX
ejpam-6010	253	7	lower	low	ADJ
ejpam-6010	253	8	almost	almost	ADV
ejpam-6010	253	9	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	253	10	,	,	PUNCT
ejpam-6010	253	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	253	12	.	.	PUNCT
ejpam-6010	254	1	(	(	PUNCT
ejpam-6010	254	2	5	5	X
ejpam-6010	254	3	)	)	PUNCT
ejpam-6010	254	4	⇒	⇒	NOUN
ejpam-6010	254	5	(	(	PUNCT
ejpam-6010	254	6	6	6	NUM
ejpam-6010	254	7	):	):	PUNCT
ejpam-6010	254	8	let	let	VERB
ejpam-6010	254	9	a	a	PRON
ejpam-6010	254	10	be	be	AUX
ejpam-6010	254	11	any	any	DET
ejpam-6010	254	12	subset	subset	NOUN
ejpam-6010	254	13	of	of	ADP
ejpam-6010	254	14	x	x	PROPN
ejpam-6010	254	15	and	and	CCONJ
ejpam-6010	254	16	b	b	X
ejpam-6010	254	17	=	=	SYM
ejpam-6010	254	18	f	f	PROPN
ejpam-6010	254	19	(	(	PUNCT
ejpam-6010	254	20	a	a	NOUN
ejpam-6010	254	21	)	)	PUNCT
ejpam-6010	254	22	.	.	PUNCT
ejpam-6010	255	1	then	then	ADV
ejpam-6010	255	2	,	,	PUNCT
ejpam-6010	255	3	a	a	DET
ejpam-6010	255	4	⊆	⊆	NUM
ejpam-6010	255	5	f+(b	f+(b	NOUN
ejpam-6010	255	6	)	)	PUNCT
ejpam-6010	255	7	and	and	CCONJ
ejpam-6010	255	8	by	by	ADP
ejpam-6010	255	9	(	(	PUNCT
ejpam-6010	255	10	5	5	NUM
ejpam-6010	255	11	)	)	PUNCT
ejpam-6010	255	12	,	,	PUNCT
ejpam-6010	255	13	τ1τ2	τ1τ2	NOUN
ejpam-6010	255	14	-	-	NUM
ejpam-6010	255	15	cl(a	cl(a	NUM
ejpam-6010	255	16	)	)	PUNCT
ejpam-6010	255	17	⊆	⊆	NUM
ejpam-6010	255	18	τ1τ2	τ1τ2	NOUN
ejpam-6010	255	19	-	-	NOUN
ejpam-6010	255	20	cl(f	cl(f	NOUN
ejpam-6010	255	21	+	+	PROPN
ejpam-6010	255	22	(	(	PUNCT
ejpam-6010	255	23	b	b	NOUN
ejpam-6010	255	24	)	)	PUNCT
ejpam-6010	255	25	)	)	PUNCT
ejpam-6010	255	26	⊆	⊆	NUM
ejpam-6010	255	27	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6010	255	28	,	,	PUNCT
ejpam-6010	255	29	σ2)θ	σ2)θ	NOUN
ejpam-6010	255	30	-	-	PUNCT
ejpam-6010	255	31	cl(b	cl(b	NOUN
ejpam-6010	255	32	)	)	PUNCT
ejpam-6010	255	33	)	)	PUNCT
ejpam-6010	255	34	.	.	PUNCT
ejpam-6010	256	1	thus	thus	ADV
ejpam-6010	256	2	,	,	PUNCT
ejpam-6010	256	3	f	f	PROPN
ejpam-6010	256	4	(	(	PUNCT
ejpam-6010	256	5	τ1τ2	τ1τ2	NOUN
ejpam-6010	256	6	-	-	NUM
ejpam-6010	256	7	cl(a	cl(a	NUM
ejpam-6010	256	8	)	)	PUNCT
ejpam-6010	256	9	)	)	PUNCT
ejpam-6010	256	10	⊆	⊆	NUM
ejpam-6010	256	11	f	f	X
ejpam-6010	256	12	(	(	PUNCT
ejpam-6010	256	13	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6010	256	14	,	,	PUNCT
ejpam-6010	256	15	σ2)θ	σ2)θ	NOUN
ejpam-6010	256	16	-	-	PUNCT
ejpam-6010	256	17	cl(b	cl(b	NOUN
ejpam-6010	256	18	)	)	PUNCT
ejpam-6010	256	19	)	)	PUNCT
ejpam-6010	256	20	)	)	PUNCT
ejpam-6010	257	1	⊆	⊆	NUM
ejpam-6010	257	2	s(σ1	s(σ1	NOUN
ejpam-6010	257	3	,	,	PUNCT
ejpam-6010	257	4	σ2)θ	σ2)θ	NOUN
ejpam-6010	257	5	-	-	PUNCT
ejpam-6010	257	6	cl(b	cl(b	NOUN
ejpam-6010	257	7	)	)	PUNCT
ejpam-6010	257	8	j.	j.	PROPN
ejpam-6010	257	9	khampakdee	khampakdee	PROPN
ejpam-6010	257	10	,	,	PUNCT
ejpam-6010	257	11	a.	a.	PROPN
ejpam-6010	257	12	sama	sama	PROPN
ejpam-6010	257	13	-	-	PUNCT
ejpam-6010	257	14	ae	ae	PROPN
ejpam-6010	257	15	,	,	PUNCT
ejpam-6010	257	16	c.	c.	PROPN
ejpam-6010	257	17	boonpok	boonpok	PROPN
ejpam-6010	257	18	/	/	SYM
ejpam-6010	257	19	eur	eur	PROPN
ejpam-6010	257	20	.	.	PUNCT
ejpam-6010	258	1	j.	j.	PROPN
ejpam-6010	258	2	pure	pure	PROPN
ejpam-6010	258	3	appl	appl	PROPN
ejpam-6010	258	4	.	.	PROPN
ejpam-6010	258	5	math	math	PROPN
ejpam-6010	258	6	,	,	PUNCT
ejpam-6010	258	7	18	18	NUM
ejpam-6010	258	8	(	(	PUNCT
ejpam-6010	258	9	2	2	NUM
ejpam-6010	258	10	)	)	PUNCT
ejpam-6010	258	11	(	(	PUNCT
ejpam-6010	258	12	2025	2025	NUM
ejpam-6010	258	13	)	)	PUNCT
ejpam-6010	258	14	,	,	PUNCT
ejpam-6010	258	15	6010	6010	NUM
ejpam-6010	258	16	10	10	NUM
ejpam-6010	258	17	of	of	ADP
ejpam-6010	258	18	19	19	NUM
ejpam-6010	258	19	=	=	PUNCT
ejpam-6010	258	20	s(σ1	s(σ1	NOUN
ejpam-6010	258	21	,	,	PUNCT
ejpam-6010	258	22	σ2)θ	σ2)θ	NOUN
ejpam-6010	258	23	-	-	PUNCT
ejpam-6010	258	24	cl(f	cl(f	PROPN
ejpam-6010	258	25	(	(	PUNCT
ejpam-6010	258	26	a	a	NOUN
ejpam-6010	258	27	)	)	PUNCT
ejpam-6010	258	28	)	)	PUNCT
ejpam-6010	258	29	.	.	PUNCT
ejpam-6010	259	1	(	(	PUNCT
ejpam-6010	259	2	6	6	X
ejpam-6010	259	3	)	)	PUNCT
ejpam-6010	259	4	⇒	⇒	NOUN
ejpam-6010	259	5	(	(	PUNCT
ejpam-6010	259	6	5	5	NUM
ejpam-6010	259	7	):	):	PUNCT
ejpam-6010	259	8	let	let	VERB
ejpam-6010	259	9	b	b	X
ejpam-6010	259	10	be	be	AUX
ejpam-6010	259	11	any	any	DET
ejpam-6010	259	12	subset	subset	NOUN
ejpam-6010	259	13	of	of	ADP
ejpam-6010	259	14	y	y	PROPN
ejpam-6010	259	15	.	.	PUNCT
ejpam-6010	260	1	by	by	ADP
ejpam-6010	260	2	(	(	PUNCT
ejpam-6010	260	3	6	6	NUM
ejpam-6010	260	4	)	)	PUNCT
ejpam-6010	260	5	,	,	PUNCT
ejpam-6010	260	6	we	we	PRON
ejpam-6010	260	7	have	have	VERB
ejpam-6010	260	8	f	f	X
ejpam-6010	260	9	(	(	PUNCT
ejpam-6010	260	10	τ1τ2	τ1τ2	NOUN
ejpam-6010	260	11	-	-	NOUN
ejpam-6010	260	12	cl(f	cl(f	NOUN
ejpam-6010	260	13	+	+	PROPN
ejpam-6010	260	14	(	(	PUNCT
ejpam-6010	260	15	b	b	NOUN
ejpam-6010	260	16	)	)	PUNCT
ejpam-6010	260	17	)	)	PUNCT
ejpam-6010	260	18	)	)	PUNCT
ejpam-6010	261	1	⊆	⊆	NUM
ejpam-6010	261	2	s(σ1	s(σ1	NOUN
ejpam-6010	261	3	,	,	PUNCT
ejpam-6010	261	4	σ2)θ	σ2)θ	NOUN
ejpam-6010	261	5	-	-	PUNCT
ejpam-6010	261	6	cl(f	cl(f	PROPN
ejpam-6010	261	7	(	(	PUNCT
ejpam-6010	261	8	f+(b	f+(b	PROPN
ejpam-6010	261	9	)	)	PUNCT
ejpam-6010	261	10	)	)	PUNCT
ejpam-6010	261	11	)	)	PUNCT
ejpam-6010	262	1	⊆	⊆	NUM
ejpam-6010	262	2	s(σ1	s(σ1	NOUN
ejpam-6010	262	3	,	,	PUNCT
ejpam-6010	262	4	σ2)θ	σ2)θ	NOUN
ejpam-6010	262	5	-	-	PUNCT
ejpam-6010	262	6	cl(b	cl(b	NOUN
ejpam-6010	262	7	)	)	PUNCT
ejpam-6010	262	8	and	and	CCONJ
ejpam-6010	262	9	hence	hence	ADV
ejpam-6010	262	10	τ1τ2	τ1τ2	NOUN
ejpam-6010	262	11	-	-	NOUN
ejpam-6010	262	12	cl(f	cl(f	NOUN
ejpam-6010	262	13	+	+	NOUN
ejpam-6010	262	14	(	(	PUNCT
ejpam-6010	262	15	b	b	NOUN
ejpam-6010	262	16	)	)	PUNCT
ejpam-6010	262	17	)	)	PUNCT
ejpam-6010	263	1	⊆	⊆	NUM
ejpam-6010	263	2	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6010	263	3	,	,	PUNCT
ejpam-6010	263	4	σ2)θ	σ2)θ	NOUN
ejpam-6010	263	5	-	-	PUNCT
ejpam-6010	263	6	cl(b	cl(b	NOUN
ejpam-6010	263	7	)	)	PUNCT
ejpam-6010	263	8	)	)	PUNCT
ejpam-6010	263	9	.	.	PUNCT
ejpam-6010	264	1	theorem	theorem	ADJ
ejpam-6010	264	2	8	8	NUM
ejpam-6010	264	3	.	.	PUNCT
ejpam-6010	265	1	for	for	ADP
ejpam-6010	265	2	a	a	DET
ejpam-6010	265	3	multifunction	multifunction	NOUN
ejpam-6010	265	4	f	f	NOUN
ejpam-6010	265	5	:	:	PUNCT
ejpam-6010	265	6	(	(	PUNCT
ejpam-6010	265	7	x	x	NOUN
ejpam-6010	265	8	,	,	PUNCT
ejpam-6010	265	9	τ1	τ1	NOUN
ejpam-6010	265	10	,	,	PUNCT
ejpam-6010	265	11	τ2	τ2	NOUN
ejpam-6010	265	12	)	)	PUNCT
ejpam-6010	265	13	→	→	SYM
ejpam-6010	265	14	(	(	PUNCT
ejpam-6010	265	15	y	y	PROPN
ejpam-6010	265	16	,	,	PUNCT
ejpam-6010	265	17	σ1	σ1	PROPN
ejpam-6010	265	18	,	,	PUNCT
ejpam-6010	265	19	σ2	σ2	NOUN
ejpam-6010	265	20	)	)	PUNCT
ejpam-6010	265	21	,	,	PUNCT
ejpam-6010	265	22	the	the	DET
ejpam-6010	265	23	following	follow	VERB
ejpam-6010	265	24	properties	property	NOUN
ejpam-6010	265	25	are	be	AUX
ejpam-6010	265	26	equivalent	equivalent	ADJ
ejpam-6010	265	27	:	:	PUNCT
ejpam-6010	265	28	(	(	PUNCT
ejpam-6010	265	29	1	1	X
ejpam-6010	265	30	)	)	PUNCT
ejpam-6010	265	31	f	f	PROPN
ejpam-6010	265	32	is	be	AUX
ejpam-6010	265	33	upper	upper	ADJ
ejpam-6010	265	34	almost	almost	ADV
ejpam-6010	265	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	265	36	,	,	PUNCT
ejpam-6010	265	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	265	38	;	;	PUNCT
ejpam-6010	265	39	(	(	PUNCT
ejpam-6010	265	40	2	2	X
ejpam-6010	265	41	)	)	PUNCT
ejpam-6010	265	42	τ1τ2	τ1τ2	NOUN
ejpam-6010	265	43	-	-	NOUN
ejpam-6010	265	44	cl(f	cl(f	NOUN
ejpam-6010	265	45	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	265	46	-	-	PUNCT
ejpam-6010	265	47	int(k	int(k	NUM
ejpam-6010	265	48	)	)	PUNCT
ejpam-6010	265	49	)	)	PUNCT
ejpam-6010	265	50	)	)	PUNCT
ejpam-6010	266	1	⊆	⊆	X
ejpam-6010	266	2	f−(k	f−(k	PROPN
ejpam-6010	266	3	)	)	PUNCT
ejpam-6010	266	4	for	for	ADP
ejpam-6010	266	5	every	every	DET
ejpam-6010	266	6	(	(	PUNCT
ejpam-6010	266	7	σ1	σ1	PROPN
ejpam-6010	266	8	,	,	PUNCT
ejpam-6010	266	9	σ2)s	σ2)s	NOUN
ejpam-6010	266	10	-	-	PUNCT
ejpam-6010	266	11	closed	close	VERB
ejpam-6010	266	12	set	set	NOUN
ejpam-6010	266	13	k	k	PROPN
ejpam-6010	266	14	of	of	ADP
ejpam-6010	266	15	y	y	PROPN
ejpam-6010	266	16	;	;	PUNCT
ejpam-6010	266	17	(	(	PUNCT
ejpam-6010	266	18	3	3	X
ejpam-6010	266	19	)	)	PUNCT
ejpam-6010	266	20	τ1τ2	τ1τ2	NOUN
ejpam-6010	266	21	-	-	NOUN
ejpam-6010	266	22	cl(f	cl(f	NOUN
ejpam-6010	266	23	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	266	24	-	-	PUNCT
ejpam-6010	266	25	int((σ1	int((σ1	ADJ
ejpam-6010	266	26	,	,	PUNCT
ejpam-6010	266	27	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	266	28	)	)	PUNCT
ejpam-6010	266	29	)	)	PUNCT
ejpam-6010	266	30	)	)	PUNCT
ejpam-6010	266	31	)	)	PUNCT
ejpam-6010	267	1	⊆	⊆	NUM
ejpam-6010	267	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	267	3	,	,	PUNCT
ejpam-6010	267	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	267	5	)	)	PUNCT
ejpam-6010	267	6	)	)	PUNCT
ejpam-6010	267	7	for	for	ADP
ejpam-6010	267	8	every	every	DET
ejpam-6010	267	9	subset	subset	NOUN
ejpam-6010	267	10	b	b	PROPN
ejpam-6010	267	11	of	of	ADP
ejpam-6010	267	12	y	y	PROPN
ejpam-6010	267	13	;	;	PUNCT
ejpam-6010	267	14	(	(	PUNCT
ejpam-6010	267	15	4	4	X
ejpam-6010	267	16	)	)	PUNCT
ejpam-6010	267	17	f+((σ1	f+((σ1	NOUN
ejpam-6010	267	18	,	,	PUNCT
ejpam-6010	267	19	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	267	20	)	)	PUNCT
ejpam-6010	267	21	)	)	PUNCT
ejpam-6010	268	1	⊆	⊆	X
ejpam-6010	268	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	268	3	-	-	NUM
ejpam-6010	268	4	int(f	int(f	VERB
ejpam-6010	268	5	+	+	ADJ
ejpam-6010	268	6	(	(	PUNCT
ejpam-6010	268	7	σ1σ2	σ1σ2	NOUN
ejpam-6010	268	8	-	-	PUNCT
ejpam-6010	268	9	cl((σ1	cl((σ1	NOUN
ejpam-6010	268	10	,	,	PUNCT
ejpam-6010	268	11	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	268	12	)	)	PUNCT
ejpam-6010	268	13	)	)	PUNCT
ejpam-6010	268	14	)	)	PUNCT
ejpam-6010	268	15	)	)	PUNCT
ejpam-6010	268	16	for	for	ADP
ejpam-6010	268	17	every	every	DET
ejpam-6010	268	18	subset	subset	NOUN
ejpam-6010	268	19	b	b	PROPN
ejpam-6010	268	20	of	of	ADP
ejpam-6010	268	21	y	y	PROPN
ejpam-6010	268	22	.	.	PUNCT
ejpam-6010	269	1	proof	proof	NOUN
ejpam-6010	269	2	.	.	PUNCT
ejpam-6010	270	1	(	(	PUNCT
ejpam-6010	270	2	1	1	X
ejpam-6010	270	3	)	)	PUNCT
ejpam-6010	270	4	⇒	⇒	NOUN
ejpam-6010	270	5	(	(	PUNCT
ejpam-6010	270	6	2	2	NUM
ejpam-6010	270	7	):	):	PUNCT
ejpam-6010	270	8	letk	letk	ADJ
ejpam-6010	270	9	be	be	VERB
ejpam-6010	270	10	any	any	DET
ejpam-6010	270	11	(	(	PUNCT
ejpam-6010	270	12	σ1	σ1	NOUN
ejpam-6010	270	13	,	,	PUNCT
ejpam-6010	270	14	σ2)s	σ2)s	NOUN
ejpam-6010	270	15	-	-	PUNCT
ejpam-6010	270	16	closed	close	VERB
ejpam-6010	270	17	set	set	NOUN
ejpam-6010	270	18	of	of	ADP
ejpam-6010	270	19	y	y	PROPN
ejpam-6010	270	20	.	.	PUNCT
ejpam-6010	271	1	then	then	ADV
ejpam-6010	271	2	,	,	PUNCT
ejpam-6010	271	3	y	y	PROPN
ejpam-6010	271	4	−k	−k	PROPN
ejpam-6010	271	5	is	be	AUX
ejpam-6010	271	6	(	(	PUNCT
ejpam-6010	271	7	σ1	σ1	PROPN
ejpam-6010	271	8	,	,	PUNCT
ejpam-6010	271	9	σ2)s	σ2)s	NOUN
ejpam-6010	271	10	-	-	PUNCT
ejpam-6010	271	11	open	open	ADJ
ejpam-6010	271	12	in	in	ADP
ejpam-6010	271	13	y	y	PROPN
ejpam-6010	271	14	.	.	PUNCT
ejpam-6010	272	1	by	by	ADP
ejpam-6010	272	2	theorem	theorem	NOUN
ejpam-6010	272	3	1	1	NUM
ejpam-6010	272	4	,	,	PUNCT
ejpam-6010	272	5	f+(y	f+(y	PROPN
ejpam-6010	272	6	−k	−k	ADJ
ejpam-6010	272	7	)	)	PUNCT
ejpam-6010	272	8	⊆	⊆	NUM
ejpam-6010	272	9	τ1τ2)-int(f	τ1τ2)-int(f	NOUN
ejpam-6010	272	10	+	+	PROPN
ejpam-6010	272	11	(	(	PUNCT
ejpam-6010	272	12	y	y	PROPN
ejpam-6010	272	13	−	−	PROPN
ejpam-6010	272	14	σ1σ2	σ1σ2	NUM
ejpam-6010	272	15	-	-	PUNCT
ejpam-6010	272	16	int(k	int(k	NOUN
ejpam-6010	272	17	)	)	PUNCT
ejpam-6010	272	18	)	)	PUNCT
ejpam-6010	272	19	)	)	PUNCT
ejpam-6010	272	20	.	.	PUNCT
ejpam-6010	273	1	thus	thus	ADV
ejpam-6010	273	2	,	,	PUNCT
ejpam-6010	273	3	x	x	PUNCT
ejpam-6010	273	4	−	−	PRON
ejpam-6010	273	5	f−(k	f−(k	PROPN
ejpam-6010	273	6	)	)	PUNCT
ejpam-6010	273	7	⊆	⊆	NUM
ejpam-6010	273	8	τ1τ2	τ1τ2	NOUN
ejpam-6010	273	9	-	-	NUM
ejpam-6010	273	10	int(f	int(f	VERB
ejpam-6010	273	11	+	+	ADJ
ejpam-6010	273	12	(	(	PUNCT
ejpam-6010	273	13	y	y	PROPN
ejpam-6010	273	14	−	−	PROPN
ejpam-6010	273	15	σ1σ2	σ1σ2	NUM
ejpam-6010	273	16	-	-	PUNCT
ejpam-6010	273	17	int(k	int(k	NOUN
ejpam-6010	273	18	)	)	PUNCT
ejpam-6010	273	19	)	)	PUNCT
ejpam-6010	273	20	)	)	PUNCT
ejpam-6010	273	21	=	=	PUNCT
ejpam-6010	273	22	τ1τ2	τ1τ2	NOUN
ejpam-6010	273	23	-	-	ADJ
ejpam-6010	273	24	int(x	int(x	ADJ
ejpam-6010	273	25	−	−	NOUN
ejpam-6010	273	26	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	273	27	-	-	PUNCT
ejpam-6010	273	28	int(k	int(k	NOUN
ejpam-6010	273	29	)	)	PUNCT
ejpam-6010	273	30	)	)	PUNCT
ejpam-6010	273	31	)	)	PUNCT
ejpam-6010	274	1	=	=	PUNCT
ejpam-6010	275	1	x	x	X
ejpam-6010	275	2	−	−	ADP
ejpam-6010	275	3	τ1τ2	τ1τ2	NOUN
ejpam-6010	275	4	-	-	NOUN
ejpam-6010	275	5	cl(f	cl(f	NOUN
ejpam-6010	275	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	275	7	-	-	PUNCT
ejpam-6010	275	8	int(k	int(k	NUM
ejpam-6010	275	9	)	)	PUNCT
ejpam-6010	275	10	)	)	PUNCT
ejpam-6010	275	11	)	)	PUNCT
ejpam-6010	276	1	and	and	CCONJ
ejpam-6010	276	2	hence	hence	ADV
ejpam-6010	276	3	τ1τ2	τ1τ2	NOUN
ejpam-6010	276	4	-	-	ADJ
ejpam-6010	276	5	cl(f	cl(f	NOUN
ejpam-6010	276	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	276	7	-	-	PUNCT
ejpam-6010	276	8	int(k	int(k	NUM
ejpam-6010	276	9	)	)	PUNCT
ejpam-6010	276	10	)	)	PUNCT
ejpam-6010	276	11	)	)	PUNCT
ejpam-6010	277	1	⊆	⊆	NUM
ejpam-6010	277	2	f−(k	f−(k	PROPN
ejpam-6010	277	3	)	)	PUNCT
ejpam-6010	277	4	.	.	PUNCT
ejpam-6010	278	1	(	(	PUNCT
ejpam-6010	278	2	2	2	X
ejpam-6010	278	3	)	)	PUNCT
ejpam-6010	278	4	⇒	⇒	NOUN
ejpam-6010	278	5	(	(	PUNCT
ejpam-6010	278	6	3	3	NUM
ejpam-6010	278	7	):	):	PUNCT
ejpam-6010	278	8	let	let	VERB
ejpam-6010	278	9	b	b	X
ejpam-6010	278	10	be	be	AUX
ejpam-6010	278	11	any	any	DET
ejpam-6010	278	12	subset	subset	NOUN
ejpam-6010	278	13	of	of	ADP
ejpam-6010	278	14	y	y	PROPN
ejpam-6010	278	15	.	.	PUNCT
ejpam-6010	279	1	then	then	ADV
ejpam-6010	279	2	,	,	PUNCT
ejpam-6010	279	3	(	(	PUNCT
ejpam-6010	279	4	σ1	σ1	PROPN
ejpam-6010	279	5	,	,	PUNCT
ejpam-6010	279	6	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	279	7	)	)	PUNCT
ejpam-6010	279	8	)	)	PUNCT
ejpam-6010	279	9	is	be	AUX
ejpam-6010	279	10	(	(	PUNCT
ejpam-6010	279	11	σ1	σ1	PROPN
ejpam-6010	279	12	,	,	PUNCT
ejpam-6010	279	13	σ2)s	σ2)s	NOUN
ejpam-6010	279	14	-	-	PUNCT
ejpam-6010	279	15	closed	close	VERB
ejpam-6010	279	16	in	in	ADP
ejpam-6010	279	17	y	y	PROPN
ejpam-6010	279	18	,	,	PUNCT
ejpam-6010	279	19	by	by	ADP
ejpam-6010	279	20	(	(	PUNCT
ejpam-6010	279	21	2	2	X
ejpam-6010	279	22	)	)	PUNCT
ejpam-6010	279	23	we	we	PRON
ejpam-6010	279	24	have	have	VERB
ejpam-6010	279	25	τ1τ2	τ1τ2	NOUN
ejpam-6010	279	26	-	-	ADJ
ejpam-6010	279	27	cl(f	cl(f	NOUN
ejpam-6010	279	28	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	279	29	-	-	PUNCT
ejpam-6010	279	30	int((σ1	int((σ1	ADJ
ejpam-6010	279	31	,	,	PUNCT
ejpam-6010	279	32	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	279	33	)	)	PUNCT
ejpam-6010	279	34	)	)	PUNCT
ejpam-6010	279	35	)	)	PUNCT
ejpam-6010	279	36	)	)	PUNCT
ejpam-6010	280	1	⊆	⊆	NUM
ejpam-6010	280	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	280	3	,	,	PUNCT
ejpam-6010	280	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	280	5	)	)	PUNCT
ejpam-6010	280	6	)	)	PUNCT
ejpam-6010	280	7	.	.	PUNCT
ejpam-6010	281	1	(	(	PUNCT
ejpam-6010	281	2	3	3	X
ejpam-6010	281	3	)	)	PUNCT
ejpam-6010	281	4	⇒	⇒	NOUN
ejpam-6010	281	5	(	(	PUNCT
ejpam-6010	281	6	4	4	NUM
ejpam-6010	281	7	):	):	PUNCT
ejpam-6010	281	8	let	let	VERB
ejpam-6010	281	9	b	b	X
ejpam-6010	281	10	be	be	AUX
ejpam-6010	281	11	any	any	DET
ejpam-6010	281	12	subset	subset	NOUN
ejpam-6010	281	13	of	of	ADP
ejpam-6010	281	14	y	y	PROPN
ejpam-6010	281	15	.	.	PUNCT
ejpam-6010	282	1	by	by	ADP
ejpam-6010	282	2	(	(	PUNCT
ejpam-6010	282	3	3	3	NUM
ejpam-6010	282	4	)	)	PUNCT
ejpam-6010	282	5	,	,	PUNCT
ejpam-6010	282	6	we	we	PRON
ejpam-6010	282	7	have	have	VERB
ejpam-6010	282	8	x	x	X
ejpam-6010	282	9	−	−	NOUN
ejpam-6010	282	10	f+((σ1	f+((σ1	NOUN
ejpam-6010	282	11	,	,	PUNCT
ejpam-6010	282	12	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	282	13	)	)	PUNCT
ejpam-6010	282	14	)	)	PUNCT
ejpam-6010	283	1	=	=	SYM
ejpam-6010	283	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	283	3	,	,	PUNCT
ejpam-6010	283	4	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6010	283	5	−b	−b	ADJ
ejpam-6010	283	6	)	)	PUNCT
ejpam-6010	283	7	)	)	PUNCT
ejpam-6010	284	1	⊇	⊇	PROPN
ejpam-6010	284	2	τ1τ2	τ1τ2	PROPN
ejpam-6010	284	3	-	-	ADJ
ejpam-6010	284	4	cl(f	cl(f	NOUN
ejpam-6010	284	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	284	6	-	-	PUNCT
ejpam-6010	284	7	int((σ1	int((σ1	ADJ
ejpam-6010	284	8	,	,	PUNCT
ejpam-6010	284	9	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6010	284	10	−b	−b	NOUN
ejpam-6010	284	11	)	)	PUNCT
ejpam-6010	284	12	)	)	PUNCT
ejpam-6010	284	13	)	)	PUNCT
ejpam-6010	284	14	)	)	PUNCT
ejpam-6010	285	1	=	=	PUNCT
ejpam-6010	285	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	285	3	-	-	ADJ
ejpam-6010	285	4	cl(f	cl(f	NOUN
ejpam-6010	285	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	285	6	-	-	PUNCT
ejpam-6010	285	7	int(y	int(y	ADJ
ejpam-6010	285	8	−	−	PROPN
ejpam-6010	285	9	(	(	PUNCT
ejpam-6010	285	10	σ1	σ1	PROPN
ejpam-6010	285	11	,	,	PUNCT
ejpam-6010	285	12	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	285	13	)	)	PUNCT
ejpam-6010	285	14	)	)	PUNCT
ejpam-6010	285	15	)	)	PUNCT
ejpam-6010	285	16	)	)	PUNCT
ejpam-6010	286	1	=	=	PUNCT
ejpam-6010	287	1	τ1τ2	τ1τ2	NOUN
ejpam-6010	287	2	-	-	PROPN
ejpam-6010	287	3	cl(f	cl(f	NOUN
ejpam-6010	287	4	−(y	−(y	NOUN
ejpam-6010	287	5	−	−	NOUN
ejpam-6010	287	6	σ1σ2	σ1σ2	NOUN
ejpam-6010	287	7	-	-	PUNCT
ejpam-6010	287	8	cl((σ1	cl((σ1	NOUN
ejpam-6010	287	9	,	,	PUNCT
ejpam-6010	287	10	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	287	11	)	)	PUNCT
ejpam-6010	287	12	)	)	PUNCT
ejpam-6010	287	13	)	)	PUNCT
ejpam-6010	287	14	)	)	PUNCT
ejpam-6010	288	1	=	=	PUNCT
ejpam-6010	288	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	288	3	-	-	NOUN
ejpam-6010	288	4	cl(x	cl(x	SYM
ejpam-6010	288	5	−	−	ADP
ejpam-6010	288	6	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	288	7	-	-	PUNCT
ejpam-6010	288	8	cl((σ1	cl((σ1	NOUN
ejpam-6010	288	9	,	,	PUNCT
ejpam-6010	288	10	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	288	11	)	)	PUNCT
ejpam-6010	288	12	)	)	PUNCT
ejpam-6010	288	13	)	)	PUNCT
ejpam-6010	288	14	)	)	PUNCT
ejpam-6010	289	1	=	=	PUNCT
ejpam-6010	289	2	x	x	X
ejpam-6010	290	1	−	−	ADP
ejpam-6010	290	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	290	3	-	-	NUM
ejpam-6010	290	4	int(f	int(f	VERB
ejpam-6010	290	5	+	+	ADJ
ejpam-6010	290	6	(	(	PUNCT
ejpam-6010	290	7	σ1σ2	σ1σ2	NOUN
ejpam-6010	290	8	-	-	PUNCT
ejpam-6010	290	9	cl((σ1	cl((σ1	NOUN
ejpam-6010	290	10	,	,	PUNCT
ejpam-6010	290	11	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	290	12	)	)	PUNCT
ejpam-6010	290	13	)	)	PUNCT
ejpam-6010	290	14	)	)	PUNCT
ejpam-6010	290	15	)	)	PUNCT
ejpam-6010	290	16	and	and	CCONJ
ejpam-6010	290	17	hence	hence	ADV
ejpam-6010	290	18	f+((σ1	f+((σ1	ADV
ejpam-6010	290	19	,	,	PUNCT
ejpam-6010	290	20	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	290	21	)	)	PUNCT
ejpam-6010	290	22	)	)	PUNCT
ejpam-6010	290	23	⊆	⊆	X
ejpam-6010	290	24	τ1τ2	τ1τ2	NOUN
ejpam-6010	290	25	-	-	NUM
ejpam-6010	290	26	int(f	int(f	VERB
ejpam-6010	290	27	+	+	ADJ
ejpam-6010	290	28	(	(	PUNCT
ejpam-6010	290	29	σ1σ2	σ1σ2	NOUN
ejpam-6010	290	30	-	-	PUNCT
ejpam-6010	290	31	cl((σ1	cl((σ1	NOUN
ejpam-6010	290	32	,	,	PUNCT
ejpam-6010	290	33	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	290	34	)	)	PUNCT
ejpam-6010	290	35	)	)	PUNCT
ejpam-6010	290	36	)	)	PUNCT
ejpam-6010	290	37	)	)	PUNCT
ejpam-6010	290	38	.	.	PUNCT
ejpam-6010	291	1	(	(	PUNCT
ejpam-6010	291	2	4	4	X
ejpam-6010	291	3	)	)	PUNCT
ejpam-6010	291	4	⇒	⇒	NOUN
ejpam-6010	291	5	(	(	PUNCT
ejpam-6010	291	6	1	1	NUM
ejpam-6010	291	7	):	):	PUNCT
ejpam-6010	291	8	let	let	VERB
ejpam-6010	291	9	v	v	PART
ejpam-6010	291	10	be	be	AUX
ejpam-6010	291	11	any	any	DET
ejpam-6010	291	12	(	(	PUNCT
ejpam-6010	291	13	σ1	σ1	NOUN
ejpam-6010	291	14	,	,	PUNCT
ejpam-6010	291	15	σ2)s	σ2)s	NOUN
ejpam-6010	291	16	-	-	PUNCT
ejpam-6010	291	17	open	open	ADJ
ejpam-6010	291	18	set	set	NOUN
ejpam-6010	291	19	of	of	ADP
ejpam-6010	291	20	y	y	PROPN
ejpam-6010	291	21	.	.	PUNCT
ejpam-6010	292	1	then	then	ADV
ejpam-6010	292	2	,	,	PUNCT
ejpam-6010	292	3	v	v	NOUN
ejpam-6010	292	4	=	=	SYM
ejpam-6010	292	5	(	(	PUNCT
ejpam-6010	292	6	σ1	σ1	PROPN
ejpam-6010	292	7	,	,	PUNCT
ejpam-6010	292	8	σ2)-sint(v	σ2)-sint(v	PROPN
ejpam-6010	292	9	)	)	PUNCT
ejpam-6010	292	10	and	and	CCONJ
ejpam-6010	292	11	by	by	ADP
ejpam-6010	292	12	(	(	PUNCT
ejpam-6010	292	13	4	4	NUM
ejpam-6010	292	14	)	)	PUNCT
ejpam-6010	292	15	,	,	PUNCT
ejpam-6010	292	16	f+(v	f+(v	PROPN
ejpam-6010	292	17	)	)	PUNCT
ejpam-6010	293	1	⊆	⊆	X
ejpam-6010	293	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	293	3	-	-	NUM
ejpam-6010	293	4	int(f	int(f	VERB
ejpam-6010	293	5	+	+	ADJ
ejpam-6010	293	6	(	(	PUNCT
ejpam-6010	293	7	σ1σ2	σ1σ2	NOUN
ejpam-6010	293	8	-	-	NUM
ejpam-6010	293	9	cl(v	cl(v	NOUN
ejpam-6010	293	10	)	)	PUNCT
ejpam-6010	293	11	)	)	PUNCT
ejpam-6010	293	12	)	)	PUNCT
ejpam-6010	293	13	.	.	PUNCT
ejpam-6010	294	1	by	by	ADP
ejpam-6010	294	2	theorem	theorem	NOUN
ejpam-6010	294	3	5	5	NUM
ejpam-6010	294	4	,	,	PUNCT
ejpam-6010	294	5	f	f	PROPN
ejpam-6010	294	6	is	be	AUX
ejpam-6010	294	7	upper	upper	ADJ
ejpam-6010	294	8	almost	almost	ADV
ejpam-6010	294	9	contra(τ1	contra(τ1	NOUN
ejpam-6010	294	10	,	,	PUNCT
ejpam-6010	294	11	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	294	12	.	.	PUNCT
ejpam-6010	295	1	j.	j.	PROPN
ejpam-6010	295	2	khampakdee	khampakdee	PROPN
ejpam-6010	295	3	,	,	PUNCT
ejpam-6010	295	4	a.	a.	PROPN
ejpam-6010	295	5	sama	sama	PROPN
ejpam-6010	295	6	-	-	PUNCT
ejpam-6010	295	7	ae	ae	PROPN
ejpam-6010	295	8	,	,	PUNCT
ejpam-6010	295	9	c.	c.	PROPN
ejpam-6010	295	10	boonpok	boonpok	PROPN
ejpam-6010	295	11	/	/	SYM
ejpam-6010	295	12	eur	eur	PROPN
ejpam-6010	295	13	.	.	PUNCT
ejpam-6010	296	1	j.	j.	PROPN
ejpam-6010	296	2	pure	pure	PROPN
ejpam-6010	296	3	appl	appl	PROPN
ejpam-6010	296	4	.	.	PROPN
ejpam-6010	296	5	math	math	PROPN
ejpam-6010	296	6	,	,	PUNCT
ejpam-6010	296	7	18	18	NUM
ejpam-6010	296	8	(	(	PUNCT
ejpam-6010	296	9	2	2	NUM
ejpam-6010	296	10	)	)	PUNCT
ejpam-6010	296	11	(	(	PUNCT
ejpam-6010	296	12	2025	2025	NUM
ejpam-6010	296	13	)	)	PUNCT
ejpam-6010	296	14	,	,	PUNCT
ejpam-6010	296	15	6010	6010	NUM
ejpam-6010	296	16	11	11	NUM
ejpam-6010	296	17	of	of	ADP
ejpam-6010	296	18	19	19	NUM
ejpam-6010	296	19	theorem	theorem	NOUN
ejpam-6010	296	20	9	9	NUM
ejpam-6010	296	21	.	.	PUNCT
ejpam-6010	296	22	for	for	ADP
ejpam-6010	296	23	a	a	DET
ejpam-6010	296	24	multifunction	multifunction	NOUN
ejpam-6010	296	25	f	f	NOUN
ejpam-6010	296	26	:	:	PUNCT
ejpam-6010	296	27	(	(	PUNCT
ejpam-6010	296	28	x	x	NOUN
ejpam-6010	296	29	,	,	PUNCT
ejpam-6010	296	30	τ1	τ1	NOUN
ejpam-6010	296	31	,	,	PUNCT
ejpam-6010	296	32	τ2	τ2	NOUN
ejpam-6010	296	33	)	)	PUNCT
ejpam-6010	296	34	→	→	SYM
ejpam-6010	296	35	(	(	PUNCT
ejpam-6010	296	36	y	y	PROPN
ejpam-6010	296	37	,	,	PUNCT
ejpam-6010	296	38	σ1	σ1	PROPN
ejpam-6010	296	39	,	,	PUNCT
ejpam-6010	296	40	σ2	σ2	NOUN
ejpam-6010	296	41	)	)	PUNCT
ejpam-6010	296	42	,	,	PUNCT
ejpam-6010	296	43	the	the	DET
ejpam-6010	296	44	following	follow	VERB
ejpam-6010	296	45	properties	property	NOUN
ejpam-6010	296	46	are	be	AUX
ejpam-6010	296	47	equivalent	equivalent	ADJ
ejpam-6010	296	48	:	:	PUNCT
ejpam-6010	296	49	(	(	PUNCT
ejpam-6010	296	50	1	1	X
ejpam-6010	296	51	)	)	PUNCT
ejpam-6010	296	52	f	f	PROPN
ejpam-6010	296	53	is	be	AUX
ejpam-6010	296	54	lower	low	ADJ
ejpam-6010	296	55	almost	almost	ADV
ejpam-6010	296	56	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	296	57	,	,	PUNCT
ejpam-6010	296	58	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	296	59	;	;	PUNCT
ejpam-6010	296	60	(	(	PUNCT
ejpam-6010	296	61	2	2	X
ejpam-6010	296	62	)	)	PUNCT
ejpam-6010	296	63	τ1τ2	τ1τ2	NOUN
ejpam-6010	296	64	-	-	NOUN
ejpam-6010	296	65	cl(f	cl(f	NOUN
ejpam-6010	296	66	+	+	NOUN
ejpam-6010	296	67	(	(	PUNCT
ejpam-6010	296	68	σ1σ2	σ1σ2	NUM
ejpam-6010	296	69	-	-	PUNCT
ejpam-6010	296	70	int(k	int(k	NUM
ejpam-6010	296	71	)	)	PUNCT
ejpam-6010	296	72	)	)	PUNCT
ejpam-6010	296	73	)	)	PUNCT
ejpam-6010	297	1	⊆	⊆	NUM
ejpam-6010	297	2	f+(k	f+(k	NOUN
ejpam-6010	297	3	)	)	PUNCT
ejpam-6010	297	4	for	for	ADP
ejpam-6010	297	5	every	every	DET
ejpam-6010	297	6	(	(	PUNCT
ejpam-6010	297	7	σ1	σ1	PROPN
ejpam-6010	297	8	,	,	PUNCT
ejpam-6010	297	9	σ2)s	σ2)s	NOUN
ejpam-6010	297	10	-	-	PUNCT
ejpam-6010	297	11	closed	close	VERB
ejpam-6010	297	12	set	set	NOUN
ejpam-6010	297	13	k	k	PROPN
ejpam-6010	297	14	of	of	ADP
ejpam-6010	297	15	y	y	PROPN
ejpam-6010	297	16	;	;	PUNCT
ejpam-6010	297	17	(	(	PUNCT
ejpam-6010	297	18	3	3	X
ejpam-6010	297	19	)	)	PUNCT
ejpam-6010	297	20	τ1τ2	τ1τ2	NOUN
ejpam-6010	297	21	-	-	NOUN
ejpam-6010	297	22	cl(f	cl(f	NOUN
ejpam-6010	297	23	+	+	NOUN
ejpam-6010	297	24	(	(	PUNCT
ejpam-6010	297	25	σ1σ2	σ1σ2	NOUN
ejpam-6010	297	26	-	-	PUNCT
ejpam-6010	297	27	int((σ1	int((σ1	ADJ
ejpam-6010	297	28	,	,	PUNCT
ejpam-6010	297	29	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	297	30	)	)	PUNCT
ejpam-6010	297	31	)	)	PUNCT
ejpam-6010	297	32	)	)	PUNCT
ejpam-6010	297	33	)	)	PUNCT
ejpam-6010	297	34	⊆	⊆	NUM
ejpam-6010	297	35	f+((σ1	f+((σ1	NOUN
ejpam-6010	297	36	,	,	PUNCT
ejpam-6010	297	37	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6010	297	38	)	)	PUNCT
ejpam-6010	297	39	)	)	PUNCT
ejpam-6010	297	40	for	for	ADP
ejpam-6010	297	41	every	every	DET
ejpam-6010	297	42	subset	subset	NOUN
ejpam-6010	297	43	b	b	PROPN
ejpam-6010	297	44	of	of	ADP
ejpam-6010	297	45	y	y	PROPN
ejpam-6010	297	46	;	;	PUNCT
ejpam-6010	297	47	(	(	PUNCT
ejpam-6010	297	48	4	4	X
ejpam-6010	297	49	)	)	PUNCT
ejpam-6010	297	50	f−((σ1	f−((σ1	NOUN
ejpam-6010	297	51	,	,	PUNCT
ejpam-6010	297	52	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	297	53	)	)	PUNCT
ejpam-6010	297	54	)	)	PUNCT
ejpam-6010	298	1	⊆	⊆	X
ejpam-6010	298	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	298	3	-	-	NUM
ejpam-6010	298	4	int(f	int(f	PRON
ejpam-6010	298	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6010	298	6	-	-	PUNCT
ejpam-6010	298	7	cl((σ1	cl((σ1	NOUN
ejpam-6010	298	8	,	,	PUNCT
ejpam-6010	298	9	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6010	298	10	)	)	PUNCT
ejpam-6010	298	11	)	)	PUNCT
ejpam-6010	298	12	)	)	PUNCT
ejpam-6010	298	13	)	)	PUNCT
ejpam-6010	298	14	for	for	ADP
ejpam-6010	298	15	every	every	DET
ejpam-6010	298	16	subset	subset	NOUN
ejpam-6010	298	17	b	b	PROPN
ejpam-6010	298	18	of	of	ADP
ejpam-6010	298	19	y	y	PROPN
ejpam-6010	298	20	.	.	PUNCT
ejpam-6010	299	1	proof	proof	NOUN
ejpam-6010	299	2	.	.	PUNCT
ejpam-6010	300	1	the	the	DET
ejpam-6010	300	2	proof	proof	NOUN
ejpam-6010	300	3	is	be	AUX
ejpam-6010	300	4	similar	similar	ADJ
ejpam-6010	300	5	to	to	ADP
ejpam-6010	300	6	that	that	PRON
ejpam-6010	300	7	of	of	ADP
ejpam-6010	300	8	theorem	theorem	ADJ
ejpam-6010	300	9	8	8	NUM
ejpam-6010	300	10	.	.	PUNCT
ejpam-6010	300	11	theorem	theorem	NOUN
ejpam-6010	300	12	10	10	NUM
ejpam-6010	300	13	.	.	PUNCT
ejpam-6010	301	1	let	let	VERB
ejpam-6010	301	2	f	f	NOUN
ejpam-6010	301	3	:	:	PUNCT
ejpam-6010	301	4	(	(	PUNCT
ejpam-6010	301	5	x	x	NOUN
ejpam-6010	301	6	,	,	PUNCT
ejpam-6010	301	7	τ1	τ1	NOUN
ejpam-6010	301	8	,	,	PUNCT
ejpam-6010	301	9	τ2	τ2	NOUN
ejpam-6010	301	10	)	)	PUNCT
ejpam-6010	301	11	→	→	SYM
ejpam-6010	301	12	(	(	PUNCT
ejpam-6010	301	13	y	y	PROPN
ejpam-6010	301	14	,	,	PUNCT
ejpam-6010	301	15	σ1	σ1	PROPN
ejpam-6010	301	16	,	,	PUNCT
ejpam-6010	301	17	σ2	σ2	PROPN
ejpam-6010	301	18	)	)	PUNCT
ejpam-6010	301	19	be	be	AUX
ejpam-6010	301	20	a	a	DET
ejpam-6010	301	21	multifunction	multifunction	NOUN
ejpam-6010	301	22	.	.	PUNCT
ejpam-6010	302	1	if	if	SCONJ
ejpam-6010	302	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	302	3	-	-	NOUN
ejpam-6010	302	4	cl(f	cl(f	NOUN
ejpam-6010	302	5	−(b	−(b	PROPN
ejpam-6010	302	6	)	)	PUNCT
ejpam-6010	302	7	)	)	PUNCT
ejpam-6010	303	1	⊆	⊆	NUM
ejpam-6010	303	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	303	3	,	,	PUNCT
ejpam-6010	303	4	σ2)r	σ2)r	NOUN
ejpam-6010	303	5	-	-	PUNCT
ejpam-6010	303	6	ker(b	ker(b	PROPN
ejpam-6010	303	7	)	)	PUNCT
ejpam-6010	303	8	)	)	PUNCT
ejpam-6010	303	9	for	for	ADP
ejpam-6010	303	10	every	every	DET
ejpam-6010	303	11	subset	subset	NOUN
ejpam-6010	303	12	b	b	PROPN
ejpam-6010	303	13	of	of	ADP
ejpam-6010	303	14	y	y	PROPN
ejpam-6010	303	15	,	,	PUNCT
ejpam-6010	303	16	then	then	ADV
ejpam-6010	303	17	f	f	PROPN
ejpam-6010	303	18	is	be	AUX
ejpam-6010	303	19	upper	upper	ADJ
ejpam-6010	303	20	almost	almost	ADV
ejpam-6010	303	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	303	22	,	,	PUNCT
ejpam-6010	303	23	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	303	24	.	.	PUNCT
ejpam-6010	304	1	proof	proof	NOUN
ejpam-6010	304	2	.	.	PUNCT
ejpam-6010	305	1	suppose	suppose	VERB
ejpam-6010	305	2	that	that	SCONJ
ejpam-6010	305	3	τ1τ2	τ1τ2	NOUN
ejpam-6010	305	4	-	-	PROPN
ejpam-6010	305	5	cl(f	cl(f	NOUN
ejpam-6010	305	6	−(b	−(b	PROPN
ejpam-6010	305	7	)	)	PUNCT
ejpam-6010	305	8	)	)	PUNCT
ejpam-6010	306	1	⊆	⊆	NUM
ejpam-6010	306	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	306	3	,	,	PUNCT
ejpam-6010	306	4	σ2)r	σ2)r	NOUN
ejpam-6010	306	5	-	-	PUNCT
ejpam-6010	306	6	ker(b	ker(b	PROPN
ejpam-6010	306	7	)	)	PUNCT
ejpam-6010	306	8	)	)	PUNCT
ejpam-6010	306	9	for	for	ADP
ejpam-6010	306	10	every	every	DET
ejpam-6010	306	11	subset	subset	NOUN
ejpam-6010	306	12	b	b	PROPN
ejpam-6010	306	13	of	of	ADP
ejpam-6010	306	14	y	y	PROPN
ejpam-6010	306	15	.	.	PUNCT
ejpam-6010	307	1	let	let	VERB
ejpam-6010	307	2	v	v	PART
ejpam-6010	307	3	be	be	AUX
ejpam-6010	307	4	any	any	DET
ejpam-6010	307	5	(	(	PUNCT
ejpam-6010	307	6	σ1	σ1	NOUN
ejpam-6010	307	7	,	,	PUNCT
ejpam-6010	307	8	σ2)r	σ2)r	NOUN
ejpam-6010	307	9	-	-	PUNCT
ejpam-6010	307	10	open	open	ADJ
ejpam-6010	307	11	set	set	NOUN
ejpam-6010	307	12	of	of	ADP
ejpam-6010	307	13	y	y	PROPN
ejpam-6010	307	14	.	.	PUNCT
ejpam-6010	308	1	by	by	ADP
ejpam-6010	308	2	lemma	lemma	PROPN
ejpam-6010	308	3	2	2	NUM
ejpam-6010	308	4	,	,	PUNCT
ejpam-6010	308	5	we	we	PRON
ejpam-6010	308	6	have	have	VERB
ejpam-6010	308	7	τ1τ2	τ1τ2	NOUN
ejpam-6010	308	8	-	-	ADJ
ejpam-6010	308	9	cl(f	cl(f	NUM
ejpam-6010	308	10	−(v	−(v	NOUN
ejpam-6010	308	11	)	)	PUNCT
ejpam-6010	308	12	)	)	PUNCT
ejpam-6010	309	1	⊆	⊆	NUM
ejpam-6010	309	2	f−((σ1	f−((σ1	NOUN
ejpam-6010	309	3	,	,	PUNCT
ejpam-6010	309	4	σ2)r	σ2)r	NOUN
ejpam-6010	309	5	-	-	PUNCT
ejpam-6010	309	6	ker(v	ker(v	PROPN
ejpam-6010	309	7	)	)	PUNCT
ejpam-6010	309	8	)	)	PUNCT
ejpam-6010	310	1	=	=	SYM
ejpam-6010	310	2	f−(v	f−(v	ADJ
ejpam-6010	310	3	)	)	PUNCT
ejpam-6010	310	4	and	and	CCONJ
ejpam-6010	310	5	hence	hence	ADV
ejpam-6010	310	6	f−(v	f−(v	ADJ
ejpam-6010	310	7	)	)	PUNCT
ejpam-6010	310	8	is	be	AUX
ejpam-6010	310	9	τ1τ2	τ1τ2	NOUN
ejpam-6010	310	10	-	-	ADJ
ejpam-6010	310	11	closed	closed	ADJ
ejpam-6010	310	12	in	in	ADP
ejpam-6010	310	13	x.	x.	NOUN
ejpam-6010	310	14	by	by	ADP
ejpam-6010	310	15	theorem	theorem	NOUN
ejpam-6010	310	16	1	1	NUM
ejpam-6010	310	17	,	,	PUNCT
ejpam-6010	310	18	f	f	PROPN
ejpam-6010	310	19	is	be	AUX
ejpam-6010	310	20	upper	upper	ADJ
ejpam-6010	310	21	almost	almost	ADV
ejpam-6010	310	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	310	23	,	,	PUNCT
ejpam-6010	310	24	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	310	25	.	.	PUNCT
ejpam-6010	311	1	theorem	theorem	VERB
ejpam-6010	311	2	11	11	NUM
ejpam-6010	311	3	.	.	PUNCT
ejpam-6010	312	1	let	let	VERB
ejpam-6010	312	2	f	f	NOUN
ejpam-6010	312	3	:	:	PUNCT
ejpam-6010	312	4	(	(	PUNCT
ejpam-6010	312	5	x	x	NOUN
ejpam-6010	312	6	,	,	PUNCT
ejpam-6010	312	7	τ1	τ1	NOUN
ejpam-6010	312	8	,	,	PUNCT
ejpam-6010	312	9	τ2	τ2	NOUN
ejpam-6010	312	10	)	)	PUNCT
ejpam-6010	312	11	→	→	SYM
ejpam-6010	312	12	(	(	PUNCT
ejpam-6010	312	13	y	y	PROPN
ejpam-6010	312	14	,	,	PUNCT
ejpam-6010	312	15	σ1	σ1	PROPN
ejpam-6010	312	16	,	,	PUNCT
ejpam-6010	312	17	σ2	σ2	PROPN
ejpam-6010	312	18	)	)	PUNCT
ejpam-6010	312	19	be	be	AUX
ejpam-6010	312	20	a	a	DET
ejpam-6010	312	21	multifunction	multifunction	NOUN
ejpam-6010	312	22	.	.	PUNCT
ejpam-6010	313	1	if	if	SCONJ
ejpam-6010	313	2	f	f	PROPN
ejpam-6010	313	3	(	(	PUNCT
ejpam-6010	313	4	τ1τ2	τ1τ2	NOUN
ejpam-6010	313	5	-	-	NUM
ejpam-6010	313	6	cl(a	cl(a	NUM
ejpam-6010	313	7	)	)	PUNCT
ejpam-6010	313	8	)	)	PUNCT
ejpam-6010	314	1	⊆	⊆	NUM
ejpam-6010	314	2	(	(	PUNCT
ejpam-6010	314	3	σ1	σ1	PROPN
ejpam-6010	314	4	,	,	PUNCT
ejpam-6010	314	5	σ2)r	σ2)r	PROPN
ejpam-6010	314	6	-	-	PUNCT
ejpam-6010	314	7	ker(f	ker(f	PROPN
ejpam-6010	314	8	(	(	PUNCT
ejpam-6010	314	9	a	a	NOUN
ejpam-6010	314	10	)	)	PUNCT
ejpam-6010	314	11	)	)	PUNCT
ejpam-6010	314	12	for	for	ADP
ejpam-6010	314	13	every	every	DET
ejpam-6010	314	14	subset	subset	NOUN
ejpam-6010	314	15	a	a	PRON
ejpam-6010	314	16	of	of	ADP
ejpam-6010	314	17	x	x	PRON
ejpam-6010	314	18	,	,	PUNCT
ejpam-6010	314	19	then	then	ADV
ejpam-6010	314	20	f	f	PROPN
ejpam-6010	314	21	is	be	AUX
ejpam-6010	314	22	lower	low	ADJ
ejpam-6010	314	23	almost	almost	ADV
ejpam-6010	314	24	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	314	25	,	,	PUNCT
ejpam-6010	314	26	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	314	27	.	.	PUNCT
ejpam-6010	315	1	proof	proof	NOUN
ejpam-6010	315	2	.	.	PUNCT
ejpam-6010	316	1	let	let	VERB
ejpam-6010	316	2	v	v	PART
ejpam-6010	316	3	be	be	AUX
ejpam-6010	316	4	any	any	DET
ejpam-6010	316	5	(	(	PUNCT
ejpam-6010	316	6	σ1	σ1	NOUN
ejpam-6010	316	7	,	,	PUNCT
ejpam-6010	316	8	σ2)r	σ2)r	NOUN
ejpam-6010	316	9	-	-	PUNCT
ejpam-6010	316	10	open	open	ADJ
ejpam-6010	316	11	set	set	NOUN
ejpam-6010	316	12	of	of	ADP
ejpam-6010	316	13	y	y	PROPN
ejpam-6010	316	14	.	.	PUNCT
ejpam-6010	317	1	then	then	ADV
ejpam-6010	317	2	,	,	PUNCT
ejpam-6010	317	3	we	we	PRON
ejpam-6010	317	4	have	have	VERB
ejpam-6010	317	5	f	f	X
ejpam-6010	317	6	(	(	PUNCT
ejpam-6010	317	7	τ1τ2	τ1τ2	NOUN
ejpam-6010	317	8	-	-	NOUN
ejpam-6010	317	9	cl(f	cl(f	NOUN
ejpam-6010	317	10	+	+	NOUN
ejpam-6010	317	11	(	(	PUNCT
ejpam-6010	317	12	v	v	NOUN
ejpam-6010	317	13	)	)	PUNCT
ejpam-6010	317	14	)	)	PUNCT
ejpam-6010	317	15	)	)	PUNCT
ejpam-6010	318	1	⊆	⊆	X
ejpam-6010	318	2	(	(	PUNCT
ejpam-6010	318	3	σ1	σ1	PROPN
ejpam-6010	318	4	,	,	PUNCT
ejpam-6010	318	5	σ2)r	σ2)r	NOUN
ejpam-6010	318	6	-	-	PUNCT
ejpam-6010	318	7	ker(v	ker(v	PROPN
ejpam-6010	318	8	)	)	PUNCT
ejpam-6010	318	9	and	and	CCONJ
ejpam-6010	318	10	hence	hence	ADV
ejpam-6010	318	11	τ1τ2	τ1τ2	NOUN
ejpam-6010	318	12	-	-	NOUN
ejpam-6010	318	13	cl(f	cl(f	NOUN
ejpam-6010	318	14	+	+	NOUN
ejpam-6010	318	15	(	(	PUNCT
ejpam-6010	318	16	v	v	NOUN
ejpam-6010	318	17	)	)	PUNCT
ejpam-6010	318	18	)	)	PUNCT
ejpam-6010	318	19	⊆	⊆	NUM
ejpam-6010	318	20	f+((σ1	f+((σ1	NOUN
ejpam-6010	318	21	,	,	PUNCT
ejpam-6010	318	22	σ2)r	σ2)r	NOUN
ejpam-6010	318	23	-	-	PUNCT
ejpam-6010	318	24	ker(v	ker(v	PROPN
ejpam-6010	318	25	)	)	PUNCT
ejpam-6010	318	26	)	)	PUNCT
ejpam-6010	318	27	.	.	PUNCT
ejpam-6010	319	1	thus	thus	ADV
ejpam-6010	319	2	by	by	ADP
ejpam-6010	319	3	lemma	lemma	PROPN
ejpam-6010	319	4	2	2	NUM
ejpam-6010	319	5	,	,	PUNCT
ejpam-6010	319	6	τ1τ2	τ1τ2	NOUN
ejpam-6010	319	7	-	-	NOUN
ejpam-6010	319	8	cl(f	cl(f	NOUN
ejpam-6010	319	9	+	+	NOUN
ejpam-6010	319	10	(	(	PUNCT
ejpam-6010	319	11	v	v	NOUN
ejpam-6010	319	12	)	)	PUNCT
ejpam-6010	319	13	)	)	PUNCT
ejpam-6010	319	14	⊆	⊆	NUM
ejpam-6010	319	15	f+((σ1	f+((σ1	NOUN
ejpam-6010	319	16	,	,	PUNCT
ejpam-6010	319	17	σ2)r	σ2)r	NOUN
ejpam-6010	319	18	-	-	PUNCT
ejpam-6010	319	19	ker(v	ker(v	PROPN
ejpam-6010	319	20	)	)	PUNCT
ejpam-6010	319	21	)	)	PUNCT
ejpam-6010	320	1	=	=	PUNCT
ejpam-6010	320	2	f+(v	f+(v	NOUN
ejpam-6010	320	3	)	)	PUNCT
ejpam-6010	320	4	and	and	CCONJ
ejpam-6010	320	5	so	so	ADV
ejpam-6010	320	6	f+(v	f+(v	PROPN
ejpam-6010	320	7	)	)	PUNCT
ejpam-6010	320	8	is	be	AUX
ejpam-6010	320	9	τ1τ2	τ1τ2	NOUN
ejpam-6010	320	10	-	-	ADJ
ejpam-6010	320	11	closed	closed	ADJ
ejpam-6010	320	12	in	in	ADP
ejpam-6010	320	13	x.	x.	NOUN
ejpam-6010	320	14	by	by	ADP
ejpam-6010	320	15	theorem	theorem	NOUN
ejpam-6010	320	16	2	2	NUM
ejpam-6010	320	17	,	,	PUNCT
ejpam-6010	320	18	f	f	PROPN
ejpam-6010	320	19	is	be	AUX
ejpam-6010	320	20	lower	low	ADJ
ejpam-6010	320	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	320	22	,	,	PUNCT
ejpam-6010	320	23	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	320	24	.	.	PUNCT
ejpam-6010	321	1	theorem	theorem	NOUN
ejpam-6010	321	2	12	12	NUM
ejpam-6010	321	3	.	.	PUNCT
ejpam-6010	322	1	let	let	VERB
ejpam-6010	322	2	f	f	NOUN
ejpam-6010	322	3	:	:	PUNCT
ejpam-6010	322	4	(	(	PUNCT
ejpam-6010	322	5	x	x	NOUN
ejpam-6010	322	6	,	,	PUNCT
ejpam-6010	322	7	τ1	τ1	NOUN
ejpam-6010	322	8	,	,	PUNCT
ejpam-6010	322	9	τ2	τ2	NOUN
ejpam-6010	322	10	)	)	PUNCT
ejpam-6010	322	11	→	→	SYM
ejpam-6010	322	12	(	(	PUNCT
ejpam-6010	322	13	y	y	PROPN
ejpam-6010	322	14	,	,	PUNCT
ejpam-6010	322	15	σ1	σ1	PROPN
ejpam-6010	322	16	,	,	PUNCT
ejpam-6010	322	17	σ2	σ2	PROPN
ejpam-6010	322	18	)	)	PUNCT
ejpam-6010	322	19	be	be	AUX
ejpam-6010	322	20	a	a	DET
ejpam-6010	322	21	multifunction	multifunction	NOUN
ejpam-6010	322	22	.	.	PUNCT
ejpam-6010	323	1	if	if	SCONJ
ejpam-6010	323	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	323	3	-	-	NOUN
ejpam-6010	323	4	cl(f	cl(f	NOUN
ejpam-6010	323	5	+	+	NOUN
ejpam-6010	323	6	(	(	PUNCT
ejpam-6010	323	7	b	b	NOUN
ejpam-6010	323	8	)	)	PUNCT
ejpam-6010	323	9	)	)	PUNCT
ejpam-6010	323	10	⊆	⊆	NUM
ejpam-6010	323	11	f+((σ1	f+((σ1	NOUN
ejpam-6010	323	12	,	,	PUNCT
ejpam-6010	323	13	σ2)r	σ2)r	NOUN
ejpam-6010	323	14	-	-	PUNCT
ejpam-6010	323	15	ker(b	ker(b	PROPN
ejpam-6010	323	16	)	)	PUNCT
ejpam-6010	323	17	)	)	PUNCT
ejpam-6010	323	18	for	for	ADP
ejpam-6010	323	19	every	every	DET
ejpam-6010	323	20	subset	subset	NOUN
ejpam-6010	323	21	b	b	PROPN
ejpam-6010	323	22	of	of	ADP
ejpam-6010	323	23	y	y	PROPN
ejpam-6010	323	24	,	,	PUNCT
ejpam-6010	323	25	then	then	ADV
ejpam-6010	323	26	f	f	PROPN
ejpam-6010	323	27	is	be	AUX
ejpam-6010	323	28	lower	low	ADJ
ejpam-6010	323	29	almost	almost	ADV
ejpam-6010	323	30	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	323	31	,	,	PUNCT
ejpam-6010	323	32	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	323	33	.	.	PUNCT
ejpam-6010	324	1	j.	j.	PROPN
ejpam-6010	324	2	khampakdee	khampakdee	PROPN
ejpam-6010	324	3	,	,	PUNCT
ejpam-6010	324	4	a.	a.	PROPN
ejpam-6010	324	5	sama	sama	PROPN
ejpam-6010	324	6	-	-	PUNCT
ejpam-6010	324	7	ae	ae	PROPN
ejpam-6010	324	8	,	,	PUNCT
ejpam-6010	324	9	c.	c.	PROPN
ejpam-6010	324	10	boonpok	boonpok	PROPN
ejpam-6010	324	11	/	/	SYM
ejpam-6010	324	12	eur	eur	PROPN
ejpam-6010	324	13	.	.	PUNCT
ejpam-6010	325	1	j.	j.	PROPN
ejpam-6010	325	2	pure	pure	PROPN
ejpam-6010	325	3	appl	appl	PROPN
ejpam-6010	325	4	.	.	PROPN
ejpam-6010	325	5	math	math	PROPN
ejpam-6010	325	6	,	,	PUNCT
ejpam-6010	325	7	18	18	NUM
ejpam-6010	325	8	(	(	PUNCT
ejpam-6010	325	9	2	2	NUM
ejpam-6010	325	10	)	)	PUNCT
ejpam-6010	325	11	(	(	PUNCT
ejpam-6010	325	12	2025	2025	NUM
ejpam-6010	325	13	)	)	PUNCT
ejpam-6010	325	14	,	,	PUNCT
ejpam-6010	325	15	6010	6010	NUM
ejpam-6010	325	16	12	12	NUM
ejpam-6010	325	17	of	of	ADP
ejpam-6010	325	18	19	19	NUM
ejpam-6010	325	19	proof	proof	NOUN
ejpam-6010	325	20	.	.	PUNCT
ejpam-6010	326	1	let	let	VERB
ejpam-6010	326	2	v	v	PART
ejpam-6010	326	3	be	be	AUX
ejpam-6010	326	4	any	any	DET
ejpam-6010	326	5	(	(	PUNCT
ejpam-6010	326	6	σ1	σ1	NOUN
ejpam-6010	326	7	,	,	PUNCT
ejpam-6010	326	8	σ2)r	σ2)r	NOUN
ejpam-6010	326	9	-	-	PUNCT
ejpam-6010	326	10	open	open	ADJ
ejpam-6010	326	11	set	set	NOUN
ejpam-6010	326	12	of	of	ADP
ejpam-6010	326	13	y	y	PROPN
ejpam-6010	326	14	.	.	PUNCT
ejpam-6010	327	1	then	then	ADV
ejpam-6010	327	2	,	,	PUNCT
ejpam-6010	327	3	τ1τ2	τ1τ2	NOUN
ejpam-6010	327	4	-	-	NOUN
ejpam-6010	327	5	cl(f	cl(f	NOUN
ejpam-6010	327	6	+	+	NOUN
ejpam-6010	327	7	(	(	PUNCT
ejpam-6010	327	8	v	v	NOUN
ejpam-6010	327	9	)	)	PUNCT
ejpam-6010	327	10	)	)	PUNCT
ejpam-6010	327	11	⊆	⊆	NUM
ejpam-6010	327	12	f+((σ1	f+((σ1	NOUN
ejpam-6010	327	13	,	,	PUNCT
ejpam-6010	327	14	σ2)r	σ2)r	NOUN
ejpam-6010	327	15	-	-	PUNCT
ejpam-6010	327	16	ker(v	ker(v	PROPN
ejpam-6010	327	17	)	)	PUNCT
ejpam-6010	327	18	)	)	PUNCT
ejpam-6010	327	19	and	and	CCONJ
ejpam-6010	327	20	by	by	ADP
ejpam-6010	327	21	lemma	lemma	PROPN
ejpam-6010	327	22	2	2	NUM
ejpam-6010	327	23	,	,	PUNCT
ejpam-6010	327	24	τ1τ2	τ1τ2	NOUN
ejpam-6010	327	25	-	-	NOUN
ejpam-6010	327	26	cl(f	cl(f	NOUN
ejpam-6010	327	27	+	+	NOUN
ejpam-6010	327	28	(	(	PUNCT
ejpam-6010	327	29	v	v	NOUN
ejpam-6010	327	30	)	)	PUNCT
ejpam-6010	327	31	)	)	PUNCT
ejpam-6010	327	32	⊆	⊆	NUM
ejpam-6010	327	33	f+((σ1	f+((σ1	NOUN
ejpam-6010	327	34	,	,	PUNCT
ejpam-6010	327	35	σ2)r	σ2)r	NOUN
ejpam-6010	327	36	-	-	PUNCT
ejpam-6010	327	37	ker(v	ker(v	PROPN
ejpam-6010	327	38	)	)	PUNCT
ejpam-6010	327	39	)	)	PUNCT
ejpam-6010	327	40	=	=	PUNCT
ejpam-6010	328	1	f+(v	f+(v	NOUN
ejpam-6010	328	2	)	)	PUNCT
ejpam-6010	328	3	.	.	PUNCT
ejpam-6010	329	1	this	this	PRON
ejpam-6010	329	2	implies	imply	VERB
ejpam-6010	329	3	that	that	SCONJ
ejpam-6010	329	4	f+(v	f+(v	PROPN
ejpam-6010	329	5	)	)	PUNCT
ejpam-6010	329	6	is	be	AUX
ejpam-6010	329	7	τ1τ2	τ1τ2	NOUN
ejpam-6010	329	8	-	-	ADJ
ejpam-6010	329	9	closed	closed	ADJ
ejpam-6010	329	10	in	in	ADP
ejpam-6010	329	11	x.	x.	NOUN
ejpam-6010	329	12	by	by	ADP
ejpam-6010	329	13	theorem	theorem	NOUN
ejpam-6010	329	14	2	2	NUM
ejpam-6010	329	15	,	,	PUNCT
ejpam-6010	329	16	f	f	PROPN
ejpam-6010	329	17	is	be	AUX
ejpam-6010	329	18	lower	low	ADJ
ejpam-6010	329	19	almost	almost	ADV
ejpam-6010	329	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	329	21	,	,	PUNCT
ejpam-6010	329	22	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	329	23	.	.	PUNCT
ejpam-6010	330	1	definition	definition	NOUN
ejpam-6010	330	2	3	3	NUM
ejpam-6010	330	3	.	.	PUNCT
ejpam-6010	331	1	[	[	X
ejpam-6010	331	2	60	60	NUM
ejpam-6010	331	3	]	]	PUNCT
ejpam-6010	331	4	a	a	DET
ejpam-6010	331	5	multifunction	multifunction	NOUN
ejpam-6010	331	6	f	f	NOUN
ejpam-6010	331	7	:	:	PUNCT
ejpam-6010	331	8	(	(	PUNCT
ejpam-6010	331	9	x	x	NOUN
ejpam-6010	331	10	,	,	PUNCT
ejpam-6010	331	11	τ1	τ1	NOUN
ejpam-6010	331	12	,	,	PUNCT
ejpam-6010	331	13	τ2	τ2	NOUN
ejpam-6010	331	14	)	)	PUNCT
ejpam-6010	331	15	→	→	SYM
ejpam-6010	331	16	(	(	PUNCT
ejpam-6010	331	17	y	y	PROPN
ejpam-6010	331	18	,	,	PUNCT
ejpam-6010	331	19	σ1	σ1	PROPN
ejpam-6010	331	20	,	,	PUNCT
ejpam-6010	331	21	σ2	σ2	PROPN
ejpam-6010	331	22	)	)	PUNCT
ejpam-6010	331	23	is	be	AUX
ejpam-6010	331	24	said	say	VERB
ejpam-6010	331	25	to	to	PART
ejpam-6010	331	26	be	be	AUX
ejpam-6010	331	27	upper	upper	ADJ
ejpam-6010	331	28	weakly	weakly	ADJ
ejpam-6010	331	29	(	(	PUNCT
ejpam-6010	331	30	τ1	τ1	NOUN
ejpam-6010	331	31	,	,	PUNCT
ejpam-6010	331	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	331	33	if	if	SCONJ
ejpam-6010	331	34	for	for	ADP
ejpam-6010	331	35	each	each	DET
ejpam-6010	331	36	x	x	SYM
ejpam-6010	331	37	∈	∈	PROPN
ejpam-6010	331	38	x	x	X
ejpam-6010	331	39	and	and	CCONJ
ejpam-6010	331	40	each	each	DET
ejpam-6010	331	41	σ1σ2	σ1σ2	VERB
ejpam-6010	331	42	-	-	ADJ
ejpam-6010	331	43	open	open	ADJ
ejpam-6010	331	44	set	set	NOUN
ejpam-6010	331	45	v	v	NOUN
ejpam-6010	331	46	of	of	ADP
ejpam-6010	331	47	y	y	PROPN
ejpam-6010	331	48	containing	contain	VERB
ejpam-6010	331	49	f	f	PROPN
ejpam-6010	331	50	(	(	PUNCT
ejpam-6010	331	51	x	x	NOUN
ejpam-6010	331	52	)	)	PUNCT
ejpam-6010	331	53	,	,	PUNCT
ejpam-6010	331	54	there	there	PRON
ejpam-6010	331	55	exists	exist	VERB
ejpam-6010	331	56	a	a	DET
ejpam-6010	331	57	τ1τ2	τ1τ2	NOUN
ejpam-6010	331	58	-	-	ADJ
ejpam-6010	331	59	open	open	ADJ
ejpam-6010	331	60	set	set	ADJ
ejpam-6010	331	61	u	u	NOUN
ejpam-6010	331	62	of	of	ADP
ejpam-6010	331	63	x	x	PUNCT
ejpam-6010	331	64	containing	contain	VERB
ejpam-6010	331	65	x	x	PUNCT
ejpam-6010	331	66	such	such	ADJ
ejpam-6010	331	67	that	that	SCONJ
ejpam-6010	331	68	f	f	PROPN
ejpam-6010	331	69	(	(	PUNCT
ejpam-6010	331	70	u	u	NOUN
ejpam-6010	331	71	)	)	PUNCT
ejpam-6010	331	72	⊆	⊆	NUM
ejpam-6010	331	73	σ1σ2	σ1σ2	NOUN
ejpam-6010	331	74	-	-	NUM
ejpam-6010	331	75	cl(v	cl(v	NOUN
ejpam-6010	331	76	)	)	PUNCT
ejpam-6010	331	77	.	.	PUNCT
ejpam-6010	332	1	theorem	theorem	VERB
ejpam-6010	332	2	13	13	NUM
ejpam-6010	332	3	.	.	PUNCT
ejpam-6010	333	1	if	if	SCONJ
ejpam-6010	333	2	f	f	PROPN
ejpam-6010	333	3	:	:	PUNCT
ejpam-6010	333	4	(	(	PUNCT
ejpam-6010	333	5	x	x	NOUN
ejpam-6010	333	6	,	,	PUNCT
ejpam-6010	333	7	τ1	τ1	NOUN
ejpam-6010	333	8	,	,	PUNCT
ejpam-6010	333	9	τ2	τ2	NOUN
ejpam-6010	333	10	)	)	PUNCT
ejpam-6010	333	11	→	→	SYM
ejpam-6010	333	12	(	(	PUNCT
ejpam-6010	333	13	y	y	PROPN
ejpam-6010	333	14	,	,	PUNCT
ejpam-6010	333	15	σ1	σ1	PROPN
ejpam-6010	333	16	,	,	PUNCT
ejpam-6010	333	17	σ2	σ2	PROPN
ejpam-6010	333	18	)	)	PUNCT
ejpam-6010	333	19	is	be	AUX
ejpam-6010	333	20	an	an	DET
ejpam-6010	333	21	upper	upper	ADJ
ejpam-6010	333	22	almost	almost	ADV
ejpam-6010	333	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	333	24	,	,	PUNCT
ejpam-6010	333	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	333	26	multifunction	multifunction	NOUN
ejpam-6010	333	27	,	,	PUNCT
ejpam-6010	333	28	then	then	ADV
ejpam-6010	333	29	f	f	PROPN
ejpam-6010	333	30	is	be	AUX
ejpam-6010	333	31	upper	upper	ADJ
ejpam-6010	333	32	weakly	weakly	ADJ
ejpam-6010	333	33	(	(	PUNCT
ejpam-6010	333	34	τ1	τ1	NOUN
ejpam-6010	333	35	,	,	PUNCT
ejpam-6010	333	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	333	37	.	.	PUNCT
ejpam-6010	334	1	proof	proof	NOUN
ejpam-6010	334	2	.	.	PUNCT
ejpam-6010	335	1	let	let	VERB
ejpam-6010	335	2	x	x	PUNCT
ejpam-6010	335	3	∈	∈	PROPN
ejpam-6010	335	4	x	x	X
ejpam-6010	335	5	and	and	CCONJ
ejpam-6010	335	6	v	v	X
ejpam-6010	335	7	be	be	AUX
ejpam-6010	335	8	any	any	DET
ejpam-6010	335	9	σ1σ2	σ1σ2	NOUN
ejpam-6010	335	10	-	-	ADJ
ejpam-6010	335	11	open	open	ADJ
ejpam-6010	335	12	set	set	NOUN
ejpam-6010	335	13	of	of	ADP
ejpam-6010	335	14	y	y	PROPN
ejpam-6010	335	15	containing	contain	VERB
ejpam-6010	335	16	f	f	PROPN
ejpam-6010	335	17	(	(	PUNCT
ejpam-6010	335	18	x	x	NOUN
ejpam-6010	335	19	)	)	PUNCT
ejpam-6010	335	20	.	.	PUNCT
ejpam-6010	336	1	then	then	ADV
ejpam-6010	336	2	,	,	PUNCT
ejpam-6010	336	3	σ1σ2	σ1σ2	NOUN
ejpam-6010	336	4	-	-	NUM
ejpam-6010	336	5	cl(v	cl(v	NOUN
ejpam-6010	336	6	)	)	PUNCT
ejpam-6010	336	7	is	be	AUX
ejpam-6010	336	8	a	a	DET
ejpam-6010	336	9	(	(	PUNCT
ejpam-6010	336	10	σ1	σ1	NOUN
ejpam-6010	336	11	,	,	PUNCT
ejpam-6010	336	12	σ2)r	σ2)r	NOUN
ejpam-6010	336	13	-	-	PUNCT
ejpam-6010	336	14	closed	close	VERB
ejpam-6010	336	15	set	set	NOUN
ejpam-6010	336	16	y	y	NOUN
ejpam-6010	336	17	containing	contain	VERB
ejpam-6010	336	18	f	f	PROPN
ejpam-6010	336	19	(	(	PUNCT
ejpam-6010	336	20	x	x	NOUN
ejpam-6010	336	21	)	)	PUNCT
ejpam-6010	336	22	.	.	PUNCT
ejpam-6010	337	1	since	since	SCONJ
ejpam-6010	337	2	f	f	PROPN
ejpam-6010	337	3	is	be	AUX
ejpam-6010	337	4	upper	upper	ADJ
ejpam-6010	337	5	almost	almost	ADV
ejpam-6010	337	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	337	7	,	,	PUNCT
ejpam-6010	337	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	337	9	,	,	PUNCT
ejpam-6010	337	10	there	there	PRON
ejpam-6010	337	11	exists	exist	VERB
ejpam-6010	337	12	a	a	DET
ejpam-6010	337	13	τ1τ2	τ1τ2	NOUN
ejpam-6010	337	14	-	-	ADJ
ejpam-6010	337	15	open	open	ADJ
ejpam-6010	337	16	set	set	NOUN
ejpam-6010	337	17	u	u	PRON
ejpam-6010	337	18	ofx	ofx	NOUN
ejpam-6010	337	19	containing	contain	VERB
ejpam-6010	337	20	x	x	PUNCT
ejpam-6010	337	21	such	such	ADJ
ejpam-6010	337	22	that	that	SCONJ
ejpam-6010	337	23	u	u	NOUN
ejpam-6010	337	24	⊆	⊆	NUM
ejpam-6010	337	25	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	337	26	-	-	PUNCT
ejpam-6010	337	27	cl(v	cl(v	NOUN
ejpam-6010	337	28	)	)	PUNCT
ejpam-6010	337	29	)	)	PUNCT
ejpam-6010	337	30	;	;	PUNCT
ejpam-6010	337	31	hence	hence	ADV
ejpam-6010	337	32	f	f	PROPN
ejpam-6010	337	33	(	(	PUNCT
ejpam-6010	337	34	u	u	NOUN
ejpam-6010	337	35	)	)	PUNCT
ejpam-6010	337	36	⊆	⊆	NUM
ejpam-6010	337	37	σ1σ2	σ1σ2	NOUN
ejpam-6010	337	38	-	-	NUM
ejpam-6010	337	39	cl(v	cl(v	NOUN
ejpam-6010	337	40	)	)	PUNCT
ejpam-6010	337	41	.	.	PUNCT
ejpam-6010	338	1	thus	thus	ADV
ejpam-6010	338	2	,	,	PUNCT
ejpam-6010	338	3	f	f	PROPN
ejpam-6010	338	4	is	be	AUX
ejpam-6010	338	5	upper	upper	ADJ
ejpam-6010	338	6	weakly	weakly	ADJ
ejpam-6010	338	7	(	(	PUNCT
ejpam-6010	338	8	τ1	τ1	NOUN
ejpam-6010	338	9	,	,	PUNCT
ejpam-6010	338	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	338	11	.	.	PUNCT
ejpam-6010	339	1	definition	definition	NOUN
ejpam-6010	339	2	4	4	NUM
ejpam-6010	339	3	.	.	PUNCT
ejpam-6010	340	1	[	[	X
ejpam-6010	340	2	60	60	NUM
ejpam-6010	340	3	]	]	PUNCT
ejpam-6010	340	4	a	a	DET
ejpam-6010	340	5	multifunction	multifunction	NOUN
ejpam-6010	340	6	f	f	NOUN
ejpam-6010	340	7	:	:	PUNCT
ejpam-6010	340	8	(	(	PUNCT
ejpam-6010	340	9	x	x	NOUN
ejpam-6010	340	10	,	,	PUNCT
ejpam-6010	340	11	τ1	τ1	NOUN
ejpam-6010	340	12	,	,	PUNCT
ejpam-6010	340	13	τ2	τ2	NOUN
ejpam-6010	340	14	)	)	PUNCT
ejpam-6010	340	15	→	→	SYM
ejpam-6010	340	16	(	(	PUNCT
ejpam-6010	340	17	y	y	PROPN
ejpam-6010	340	18	,	,	PUNCT
ejpam-6010	340	19	σ1	σ1	PROPN
ejpam-6010	340	20	,	,	PUNCT
ejpam-6010	340	21	σ2	σ2	PROPN
ejpam-6010	340	22	)	)	PUNCT
ejpam-6010	340	23	is	be	AUX
ejpam-6010	340	24	said	say	VERB
ejpam-6010	340	25	to	to	PART
ejpam-6010	340	26	be	be	AUX
ejpam-6010	340	27	lower	low	ADJ
ejpam-6010	340	28	weakly	weakly	ADJ
ejpam-6010	340	29	(	(	PUNCT
ejpam-6010	340	30	τ1	τ1	NOUN
ejpam-6010	340	31	,	,	PUNCT
ejpam-6010	340	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	340	33	if	if	SCONJ
ejpam-6010	340	34	for	for	ADP
ejpam-6010	340	35	each	each	DET
ejpam-6010	340	36	x	x	SYM
ejpam-6010	340	37	∈	∈	PROPN
ejpam-6010	340	38	x	x	X
ejpam-6010	340	39	and	and	CCONJ
ejpam-6010	340	40	each	each	DET
ejpam-6010	340	41	σ1σ2	σ1σ2	VERB
ejpam-6010	340	42	-	-	ADJ
ejpam-6010	340	43	open	open	ADJ
ejpam-6010	340	44	set	set	NOUN
ejpam-6010	340	45	v	v	NOUN
ejpam-6010	340	46	of	of	ADP
ejpam-6010	340	47	y	y	PRON
ejpam-6010	340	48	such	such	ADJ
ejpam-6010	340	49	that	that	SCONJ
ejpam-6010	340	50	f	f	PROPN
ejpam-6010	340	51	(	(	PUNCT
ejpam-6010	340	52	x)∩v	x)∩v	PROPN
ejpam-6010	340	53	̸=	̸=	PROPN
ejpam-6010	340	54	∅	∅	NOUN
ejpam-6010	340	55	,	,	PUNCT
ejpam-6010	340	56	there	there	PRON
ejpam-6010	340	57	exists	exist	VERB
ejpam-6010	340	58	a	a	DET
ejpam-6010	340	59	τ1τ2	τ1τ2	NOUN
ejpam-6010	340	60	-	-	ADJ
ejpam-6010	340	61	open	open	ADJ
ejpam-6010	340	62	set	set	ADJ
ejpam-6010	340	63	u	u	NOUN
ejpam-6010	340	64	of	of	ADP
ejpam-6010	340	65	x	x	PUNCT
ejpam-6010	340	66	containing	contain	VERB
ejpam-6010	340	67	x	x	PUNCT
ejpam-6010	341	1	such	such	ADJ
ejpam-6010	341	2	that	that	SCONJ
ejpam-6010	341	3	σ1σ2	σ1σ2	NOUN
ejpam-6010	341	4	-	-	NUM
ejpam-6010	341	5	cl(v	cl(v	PUNCT
ejpam-6010	341	6	)	)	PUNCT
ejpam-6010	341	7	∩f	∩f	NOUN
ejpam-6010	341	8	(	(	PUNCT
ejpam-6010	341	9	z	z	X
ejpam-6010	341	10	)	)	PUNCT
ejpam-6010	341	11	̸=	̸=	NOUN
ejpam-6010	341	12	∅	∅	NOUN
ejpam-6010	341	13	for	for	ADP
ejpam-6010	341	14	each	each	DET
ejpam-6010	341	15	z	z	NOUN
ejpam-6010	341	16	∈	∈	PROPN
ejpam-6010	341	17	u	u	PROPN
ejpam-6010	341	18	.	.	PUNCT
ejpam-6010	341	19	theorem	theorem	VERB
ejpam-6010	341	20	14	14	NUM
ejpam-6010	341	21	.	.	PUNCT
ejpam-6010	342	1	if	if	SCONJ
ejpam-6010	342	2	f	f	PROPN
ejpam-6010	342	3	:	:	PUNCT
ejpam-6010	342	4	(	(	PUNCT
ejpam-6010	342	5	x	x	NOUN
ejpam-6010	342	6	,	,	PUNCT
ejpam-6010	342	7	τ1	τ1	NOUN
ejpam-6010	342	8	,	,	PUNCT
ejpam-6010	342	9	τ2	τ2	NOUN
ejpam-6010	342	10	)	)	PUNCT
ejpam-6010	342	11	→	→	SYM
ejpam-6010	342	12	(	(	PUNCT
ejpam-6010	342	13	y	y	PROPN
ejpam-6010	342	14	,	,	PUNCT
ejpam-6010	342	15	σ1	σ1	PROPN
ejpam-6010	342	16	,	,	PUNCT
ejpam-6010	342	17	σ2	σ2	PROPN
ejpam-6010	342	18	)	)	PUNCT
ejpam-6010	342	19	is	be	AUX
ejpam-6010	342	20	a	a	DET
ejpam-6010	342	21	lower	low	ADJ
ejpam-6010	342	22	almost	almost	ADV
ejpam-6010	342	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	342	24	,	,	PUNCT
ejpam-6010	342	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	342	26	multifunction	multifunction	NOUN
ejpam-6010	342	27	,	,	PUNCT
ejpam-6010	342	28	then	then	ADV
ejpam-6010	342	29	f	f	PROPN
ejpam-6010	342	30	is	be	AUX
ejpam-6010	342	31	lower	low	ADJ
ejpam-6010	342	32	weakly	weakly	ADJ
ejpam-6010	342	33	(	(	PUNCT
ejpam-6010	342	34	τ1	τ1	NOUN
ejpam-6010	342	35	,	,	PUNCT
ejpam-6010	342	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	342	37	.	.	PUNCT
ejpam-6010	343	1	proof	proof	NOUN
ejpam-6010	343	2	.	.	PUNCT
ejpam-6010	344	1	it	it	PRON
ejpam-6010	344	2	is	be	AUX
ejpam-6010	344	3	similar	similar	ADJ
ejpam-6010	344	4	to	to	ADP
ejpam-6010	344	5	that	that	PRON
ejpam-6010	344	6	of	of	ADP
ejpam-6010	344	7	theorem	theorem	ADJ
ejpam-6010	344	8	13	13	NUM
ejpam-6010	344	9	.	.	PUNCT
ejpam-6010	345	1	definition	definition	NOUN
ejpam-6010	345	2	5	5	NUM
ejpam-6010	345	3	.	.	PUNCT
ejpam-6010	346	1	[	[	X
ejpam-6010	346	2	82	82	NUM
ejpam-6010	346	3	]	]	SYM
ejpam-6010	346	4	a	a	DET
ejpam-6010	346	5	multifunction	multifunction	NOUN
ejpam-6010	346	6	f	f	NOUN
ejpam-6010	346	7	:	:	PUNCT
ejpam-6010	346	8	(	(	PUNCT
ejpam-6010	346	9	x	x	NOUN
ejpam-6010	346	10	,	,	PUNCT
ejpam-6010	346	11	τ1	τ1	NOUN
ejpam-6010	346	12	,	,	PUNCT
ejpam-6010	346	13	τ2	τ2	NOUN
ejpam-6010	346	14	)	)	PUNCT
ejpam-6010	346	15	→	→	SYM
ejpam-6010	346	16	(	(	PUNCT
ejpam-6010	346	17	y	y	PROPN
ejpam-6010	346	18	,	,	PUNCT
ejpam-6010	346	19	σ1	σ1	PROPN
ejpam-6010	346	20	,	,	PUNCT
ejpam-6010	346	21	σ2	σ2	PROPN
ejpam-6010	346	22	)	)	PUNCT
ejpam-6010	346	23	is	be	AUX
ejpam-6010	346	24	called	call	VERB
ejpam-6010	346	25	upper	upper	ADJ
ejpam-6010	346	26	contra(τ1	contra(τ1	NOUN
ejpam-6010	346	27	,	,	PUNCT
ejpam-6010	346	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	346	29	at	at	ADP
ejpam-6010	346	30	a	a	DET
ejpam-6010	346	31	point	point	NOUN
ejpam-6010	346	32	x	x	SYM
ejpam-6010	346	33	∈	∈	NOUN
ejpam-6010	346	34	x	x	PUNCT
ejpam-6010	346	35	if	if	SCONJ
ejpam-6010	346	36	for	for	ADP
ejpam-6010	346	37	each	each	DET
ejpam-6010	346	38	σ1σ2	σ1σ2	NUM
ejpam-6010	346	39	-	-	PUNCT
ejpam-6010	346	40	closed	closed	ADJ
ejpam-6010	346	41	set	set	NOUN
ejpam-6010	346	42	k	k	PROPN
ejpam-6010	346	43	of	of	ADP
ejpam-6010	346	44	y	y	PROPN
ejpam-6010	346	45	with	with	ADP
ejpam-6010	346	46	x	x	PROPN
ejpam-6010	346	47	∈	∈	PROPN
ejpam-6010	346	48	f+(k	f+(k	PROPN
ejpam-6010	346	49	)	)	PUNCT
ejpam-6010	346	50	,	,	PUNCT
ejpam-6010	346	51	there	there	PRON
ejpam-6010	346	52	exists	exist	VERB
ejpam-6010	346	53	a	a	DET
ejpam-6010	346	54	τ1τ2	τ1τ2	NOUN
ejpam-6010	346	55	-	-	ADJ
ejpam-6010	346	56	open	open	ADJ
ejpam-6010	346	57	set	set	ADJ
ejpam-6010	346	58	u	u	NOUN
ejpam-6010	346	59	of	of	ADP
ejpam-6010	346	60	x	x	PUNCT
ejpam-6010	346	61	containing	contain	VERB
ejpam-6010	346	62	x	x	PUNCT
ejpam-6010	346	63	such	such	ADJ
ejpam-6010	346	64	that	that	SCONJ
ejpam-6010	346	65	u	u	PROPN
ejpam-6010	346	66	⊆	⊆	NUM
ejpam-6010	346	67	f+(k	f+(k	NUM
ejpam-6010	346	68	)	)	PUNCT
ejpam-6010	346	69	.	.	PUNCT
ejpam-6010	347	1	a	a	DET
ejpam-6010	347	2	multifunction	multifunction	NOUN
ejpam-6010	347	3	f	f	NOUN
ejpam-6010	347	4	:	:	PUNCT
ejpam-6010	347	5	(	(	PUNCT
ejpam-6010	347	6	x	x	NOUN
ejpam-6010	347	7	,	,	PUNCT
ejpam-6010	347	8	τ1	τ1	NOUN
ejpam-6010	347	9	,	,	PUNCT
ejpam-6010	347	10	τ2	τ2	NOUN
ejpam-6010	347	11	)	)	PUNCT
ejpam-6010	347	12	→	→	SYM
ejpam-6010	347	13	(	(	PUNCT
ejpam-6010	347	14	y	y	PROPN
ejpam-6010	347	15	,	,	PUNCT
ejpam-6010	347	16	σ1	σ1	PROPN
ejpam-6010	347	17	,	,	PUNCT
ejpam-6010	347	18	σ2	σ2	PROPN
ejpam-6010	347	19	)	)	PUNCT
ejpam-6010	347	20	is	be	AUX
ejpam-6010	347	21	called	call	VERB
ejpam-6010	347	22	upper	upper	ADJ
ejpam-6010	347	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	347	24	,	,	PUNCT
ejpam-6010	347	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	347	26	if	if	SCONJ
ejpam-6010	347	27	f	f	PROPN
ejpam-6010	347	28	is	be	AUX
ejpam-6010	347	29	upper	upper	ADJ
ejpam-6010	347	30	contra(τ1	contra(τ1	NOUN
ejpam-6010	347	31	,	,	PUNCT
ejpam-6010	347	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	347	33	at	at	ADP
ejpam-6010	347	34	each	each	DET
ejpam-6010	347	35	point	point	NOUN
ejpam-6010	347	36	x	x	PUNCT
ejpam-6010	347	37	of	of	ADP
ejpam-6010	347	38	x.	x.	PROPN
ejpam-6010	347	39	theorem	theorem	VERB
ejpam-6010	347	40	15	15	NUM
ejpam-6010	347	41	.	.	PUNCT
ejpam-6010	348	1	if	if	SCONJ
ejpam-6010	348	2	f	f	PROPN
ejpam-6010	348	3	:	:	PUNCT
ejpam-6010	348	4	(	(	PUNCT
ejpam-6010	348	5	x	x	NOUN
ejpam-6010	348	6	,	,	PUNCT
ejpam-6010	348	7	τ1	τ1	NOUN
ejpam-6010	348	8	,	,	PUNCT
ejpam-6010	348	9	τ2	τ2	NOUN
ejpam-6010	348	10	)	)	PUNCT
ejpam-6010	348	11	→	→	SYM
ejpam-6010	348	12	(	(	PUNCT
ejpam-6010	348	13	y	y	PROPN
ejpam-6010	348	14	,	,	PUNCT
ejpam-6010	348	15	σ1	σ1	PROPN
ejpam-6010	348	16	,	,	PUNCT
ejpam-6010	348	17	σ2	σ2	PROPN
ejpam-6010	348	18	)	)	PUNCT
ejpam-6010	348	19	is	be	AUX
ejpam-6010	348	20	an	an	DET
ejpam-6010	348	21	upper	upper	ADJ
ejpam-6010	348	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	348	23	,	,	PUNCT
ejpam-6010	348	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	348	25	multifunction	multifunction	NOUN
ejpam-6010	348	26	,	,	PUNCT
ejpam-6010	348	27	then	then	ADV
ejpam-6010	348	28	f	f	PROPN
ejpam-6010	348	29	is	be	AUX
ejpam-6010	348	30	upper	upper	ADJ
ejpam-6010	348	31	almost	almost	ADV
ejpam-6010	348	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	348	33	,	,	PUNCT
ejpam-6010	348	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	348	35	.	.	PUNCT
ejpam-6010	349	1	proof	proof	NOUN
ejpam-6010	349	2	.	.	PUNCT
ejpam-6010	350	1	let	let	VERB
ejpam-6010	350	2	x	x	PUNCT
ejpam-6010	350	3	∈	∈	PROPN
ejpam-6010	350	4	x	x	X
ejpam-6010	350	5	and	and	CCONJ
ejpam-6010	350	6	k	k	PROPN
ejpam-6010	350	7	be	be	AUX
ejpam-6010	350	8	any	any	DET
ejpam-6010	350	9	(	(	PUNCT
ejpam-6010	350	10	σ1	σ1	NOUN
ejpam-6010	350	11	,	,	PUNCT
ejpam-6010	350	12	σ2)r	σ2)r	NOUN
ejpam-6010	350	13	-	-	PUNCT
ejpam-6010	350	14	closed	close	VERB
ejpam-6010	350	15	set	set	NOUN
ejpam-6010	350	16	of	of	ADP
ejpam-6010	350	17	y	y	PROPN
ejpam-6010	350	18	with	with	ADP
ejpam-6010	350	19	x	x	PROPN
ejpam-6010	350	20	∈	∈	PROPN
ejpam-6010	350	21	f+(k	f+(k	PROPN
ejpam-6010	350	22	)	)	PUNCT
ejpam-6010	350	23	.	.	PUNCT
ejpam-6010	351	1	then	then	ADV
ejpam-6010	351	2	,	,	PUNCT
ejpam-6010	351	3	k	k	PROPN
ejpam-6010	351	4	is	be	AUX
ejpam-6010	351	5	σ1σ2	σ1σ2	NOUN
ejpam-6010	351	6	-	-	ADJ
ejpam-6010	351	7	closed	closed	ADJ
ejpam-6010	351	8	in	in	ADP
ejpam-6010	351	9	y	y	PROPN
ejpam-6010	351	10	.	.	PUNCT
ejpam-6010	352	1	since	since	SCONJ
ejpam-6010	352	2	f	f	PROPN
ejpam-6010	352	3	is	be	AUX
ejpam-6010	352	4	upper	upper	ADJ
ejpam-6010	352	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	352	6	,	,	PUNCT
ejpam-6010	352	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	352	8	,	,	PUNCT
ejpam-6010	352	9	there	there	PRON
ejpam-6010	352	10	exists	exist	VERB
ejpam-6010	352	11	a	a	DET
ejpam-6010	352	12	τ1τ2	τ1τ2	NOUN
ejpam-6010	352	13	-	-	ADJ
ejpam-6010	352	14	open	open	ADJ
ejpam-6010	352	15	set	set	ADJ
ejpam-6010	352	16	u	u	NOUN
ejpam-6010	352	17	of	of	ADP
ejpam-6010	352	18	x	x	PUNCT
ejpam-6010	352	19	containing	contain	VERB
ejpam-6010	352	20	x	x	PUNCT
ejpam-6010	352	21	such	such	ADJ
ejpam-6010	352	22	that	that	SCONJ
ejpam-6010	352	23	u	u	PROPN
ejpam-6010	352	24	⊆	⊆	NUM
ejpam-6010	352	25	f+(k	f+(k	NUM
ejpam-6010	352	26	)	)	PUNCT
ejpam-6010	352	27	.	.	PUNCT
ejpam-6010	353	1	thus	thus	ADV
ejpam-6010	353	2	,	,	PUNCT
ejpam-6010	353	3	f	f	PROPN
ejpam-6010	353	4	is	be	AUX
ejpam-6010	353	5	upper	upper	ADJ
ejpam-6010	353	6	almost	almost	ADV
ejpam-6010	353	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	353	8	,	,	PUNCT
ejpam-6010	353	9	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	353	10	.	.	PUNCT
ejpam-6010	354	1	the	the	DET
ejpam-6010	354	2	converse	converse	NOUN
ejpam-6010	354	3	of	of	ADP
ejpam-6010	354	4	theorem	theorem	NOUN
ejpam-6010	354	5	15	15	NUM
ejpam-6010	354	6	is	be	AUX
ejpam-6010	354	7	not	not	PART
ejpam-6010	354	8	true	true	ADJ
ejpam-6010	354	9	in	in	ADP
ejpam-6010	354	10	general	general	ADJ
ejpam-6010	354	11	as	as	SCONJ
ejpam-6010	354	12	shown	show	VERB
ejpam-6010	354	13	in	in	ADP
ejpam-6010	354	14	the	the	DET
ejpam-6010	354	15	following	follow	VERB
ejpam-6010	354	16	example	example	NOUN
ejpam-6010	354	17	.	.	PUNCT
ejpam-6010	355	1	j.	j.	PROPN
ejpam-6010	355	2	khampakdee	khampakdee	PROPN
ejpam-6010	355	3	,	,	PUNCT
ejpam-6010	355	4	a.	a.	PROPN
ejpam-6010	355	5	sama	sama	PROPN
ejpam-6010	355	6	-	-	PUNCT
ejpam-6010	355	7	ae	ae	PROPN
ejpam-6010	355	8	,	,	PUNCT
ejpam-6010	355	9	c.	c.	PROPN
ejpam-6010	355	10	boonpok	boonpok	PROPN
ejpam-6010	355	11	/	/	SYM
ejpam-6010	355	12	eur	eur	PROPN
ejpam-6010	355	13	.	.	PUNCT
ejpam-6010	356	1	j.	j.	PROPN
ejpam-6010	356	2	pure	pure	PROPN
ejpam-6010	356	3	appl	appl	PROPN
ejpam-6010	356	4	.	.	PROPN
ejpam-6010	356	5	math	math	PROPN
ejpam-6010	356	6	,	,	PUNCT
ejpam-6010	356	7	18	18	NUM
ejpam-6010	356	8	(	(	PUNCT
ejpam-6010	356	9	2	2	NUM
ejpam-6010	356	10	)	)	PUNCT
ejpam-6010	356	11	(	(	PUNCT
ejpam-6010	356	12	2025	2025	NUM
ejpam-6010	356	13	)	)	PUNCT
ejpam-6010	356	14	,	,	PUNCT
ejpam-6010	356	15	6010	6010	NUM
ejpam-6010	356	16	13	13	NUM
ejpam-6010	356	17	of	of	ADP
ejpam-6010	356	18	19	19	NUM
ejpam-6010	356	19	example	example	NOUN
ejpam-6010	356	20	1	1	NUM
ejpam-6010	356	21	.	.	PUNCT
ejpam-6010	357	1	let	let	VERB
ejpam-6010	357	2	x	x	PUNCT
ejpam-6010	357	3	=	=	PRON
ejpam-6010	357	4	{	{	PUNCT
ejpam-6010	357	5	a	a	PRON
ejpam-6010	357	6	,	,	PUNCT
ejpam-6010	357	7	b	b	NOUN
ejpam-6010	357	8	,	,	PUNCT
ejpam-6010	357	9	c	c	NOUN
ejpam-6010	357	10	,	,	PUNCT
ejpam-6010	357	11	d	d	NOUN
ejpam-6010	357	12	}	}	PUNCT
ejpam-6010	357	13	with	with	ADP
ejpam-6010	357	14	topologies	topology	NOUN
ejpam-6010	357	15	τ1	τ1	NOUN
ejpam-6010	357	16	=	=	SYM
ejpam-6010	357	17	{	{	PUNCT
ejpam-6010	357	18	∅	∅	NOUN
ejpam-6010	357	19	,	,	PUNCT
ejpam-6010	357	20	{	{	PUNCT
ejpam-6010	357	21	a	a	X
ejpam-6010	357	22	}	}	PUNCT
ejpam-6010	357	23	,	,	PUNCT
ejpam-6010	357	24	{	{	PUNCT
ejpam-6010	357	25	c	c	X
ejpam-6010	357	26	}	}	PUNCT
ejpam-6010	357	27	,	,	PUNCT
ejpam-6010	357	28	{	{	PUNCT
ejpam-6010	357	29	a	a	DET
ejpam-6010	357	30	,	,	PUNCT
ejpam-6010	357	31	b	b	NOUN
ejpam-6010	357	32	}	}	PUNCT
ejpam-6010	357	33	,	,	PUNCT
ejpam-6010	357	34	{	{	PUNCT
ejpam-6010	357	35	a	a	X
ejpam-6010	357	36	,	,	PUNCT
ejpam-6010	357	37	c	c	NOUN
ejpam-6010	357	38	}	}	PUNCT
ejpam-6010	357	39	,	,	PUNCT
ejpam-6010	357	40	{	{	PUNCT
ejpam-6010	357	41	a	a	DET
ejpam-6010	357	42	,	,	PUNCT
ejpam-6010	357	43	d	d	NOUN
ejpam-6010	357	44	}	}	PUNCT
ejpam-6010	357	45	,	,	PUNCT
ejpam-6010	357	46	{	{	PUNCT
ejpam-6010	357	47	a	a	DET
ejpam-6010	357	48	,	,	PUNCT
ejpam-6010	357	49	b	b	NOUN
ejpam-6010	357	50	,	,	PUNCT
ejpam-6010	357	51	c	c	NOUN
ejpam-6010	357	52	}	}	PUNCT
ejpam-6010	357	53	,	,	PUNCT
ejpam-6010	357	54	{	{	PUNCT
ejpam-6010	357	55	a	a	PRON
ejpam-6010	357	56	,	,	PUNCT
ejpam-6010	357	57	c	c	NOUN
ejpam-6010	357	58	,	,	PUNCT
ejpam-6010	357	59	d	d	NOUN
ejpam-6010	357	60	}	}	PUNCT
ejpam-6010	357	61	,	,	PUNCT
ejpam-6010	357	62	{	{	PUNCT
ejpam-6010	357	63	a	a	DET
ejpam-6010	357	64	,	,	PUNCT
ejpam-6010	357	65	b	b	NOUN
ejpam-6010	357	66	,	,	PUNCT
ejpam-6010	357	67	d	d	NOUN
ejpam-6010	357	68	}	}	PUNCT
ejpam-6010	357	69	,	,	PUNCT
ejpam-6010	357	70	x	x	NOUN
ejpam-6010	357	71	}	}	PUNCT
ejpam-6010	357	72	and	and	CCONJ
ejpam-6010	357	73	τ2	τ2	NOUN
ejpam-6010	357	74	=	=	SYM
ejpam-6010	357	75	{	{	PUNCT
ejpam-6010	357	76	∅	∅	NOUN
ejpam-6010	357	77	,	,	PUNCT
ejpam-6010	357	78	{	{	PUNCT
ejpam-6010	357	79	a	a	X
ejpam-6010	357	80	}	}	PUNCT
ejpam-6010	357	81	,	,	PUNCT
ejpam-6010	357	82	{	{	PUNCT
ejpam-6010	357	83	c	c	X
ejpam-6010	357	84	}	}	PUNCT
ejpam-6010	357	85	,	,	PUNCT
ejpam-6010	357	86	{	{	PUNCT
ejpam-6010	357	87	a	a	DET
ejpam-6010	357	88	,	,	PUNCT
ejpam-6010	357	89	b	b	NOUN
ejpam-6010	357	90	}	}	PUNCT
ejpam-6010	357	91	,	,	PUNCT
ejpam-6010	357	92	{	{	PUNCT
ejpam-6010	357	93	a	a	X
ejpam-6010	357	94	,	,	PUNCT
ejpam-6010	357	95	c	c	NOUN
ejpam-6010	357	96	}	}	PUNCT
ejpam-6010	357	97	,	,	PUNCT
ejpam-6010	357	98	{	{	PUNCT
ejpam-6010	357	99	a	a	DET
ejpam-6010	357	100	,	,	PUNCT
ejpam-6010	357	101	b	b	NOUN
ejpam-6010	357	102	,	,	PUNCT
ejpam-6010	357	103	c	c	NOUN
ejpam-6010	357	104	}	}	PUNCT
ejpam-6010	357	105	,	,	PUNCT
ejpam-6010	357	106	{	{	PUNCT
ejpam-6010	357	107	a	a	PRON
ejpam-6010	357	108	,	,	PUNCT
ejpam-6010	357	109	c	c	NOUN
ejpam-6010	357	110	,	,	PUNCT
ejpam-6010	357	111	d	d	NOUN
ejpam-6010	357	112	}	}	PUNCT
ejpam-6010	357	113	,	,	PUNCT
ejpam-6010	357	114	x	x	NOUN
ejpam-6010	357	115	}	}	PUNCT
ejpam-6010	357	116	.	.	PUNCT
ejpam-6010	358	1	let	let	VERB
ejpam-6010	358	2	y	y	PROPN
ejpam-6010	358	3	=	=	PUNCT
ejpam-6010	358	4	{	{	PUNCT
ejpam-6010	358	5	1	1	NUM
ejpam-6010	358	6	,	,	PUNCT
ejpam-6010	358	7	2	2	NUM
ejpam-6010	358	8	,	,	PUNCT
ejpam-6010	358	9	3	3	NUM
ejpam-6010	358	10	,	,	PUNCT
ejpam-6010	358	11	4	4	NUM
ejpam-6010	358	12	}	}	PUNCT
ejpam-6010	358	13	with	with	ADP
ejpam-6010	358	14	topologies	topology	NOUN
ejpam-6010	358	15	σ1	σ1	NOUN
ejpam-6010	358	16	=	=	SYM
ejpam-6010	358	17	{	{	PUNCT
ejpam-6010	358	18	∅	∅	NOUN
ejpam-6010	358	19	,	,	PUNCT
ejpam-6010	358	20	{	{	PUNCT
ejpam-6010	358	21	1	1	NUM
ejpam-6010	358	22	}	}	PUNCT
ejpam-6010	358	23	,	,	PUNCT
ejpam-6010	358	24	{	{	PUNCT
ejpam-6010	358	25	3	3	NUM
ejpam-6010	358	26	}	}	PUNCT
ejpam-6010	358	27	,	,	PUNCT
ejpam-6010	358	28	{	{	PUNCT
ejpam-6010	358	29	1	1	NUM
ejpam-6010	358	30	,	,	PUNCT
ejpam-6010	358	31	2	2	NUM
ejpam-6010	358	32	}	}	PUNCT
ejpam-6010	358	33	,	,	PUNCT
ejpam-6010	358	34	{	{	PUNCT
ejpam-6010	358	35	1	1	NUM
ejpam-6010	358	36	,	,	PUNCT
ejpam-6010	358	37	3	3	NUM
ejpam-6010	358	38	}	}	PUNCT
ejpam-6010	358	39	,	,	PUNCT
ejpam-6010	358	40	{	{	PUNCT
ejpam-6010	358	41	1	1	NUM
ejpam-6010	358	42	,	,	PUNCT
ejpam-6010	358	43	2	2	NUM
ejpam-6010	358	44	,	,	PUNCT
ejpam-6010	358	45	3	3	NUM
ejpam-6010	358	46	}	}	PUNCT
ejpam-6010	358	47	,	,	PUNCT
ejpam-6010	358	48	{	{	PUNCT
ejpam-6010	358	49	1	1	NUM
ejpam-6010	358	50	,	,	PUNCT
ejpam-6010	358	51	3	3	NUM
ejpam-6010	358	52	,	,	PUNCT
ejpam-6010	358	53	4	4	NUM
ejpam-6010	358	54	}	}	PUNCT
ejpam-6010	358	55	,	,	PUNCT
ejpam-6010	358	56	y	y	PROPN
ejpam-6010	358	57	}	}	PUNCT
ejpam-6010	358	58	and	and	CCONJ
ejpam-6010	358	59	σ2	σ2	PROPN
ejpam-6010	358	60	=	=	SYM
ejpam-6010	358	61	{	{	PUNCT
ejpam-6010	358	62	∅	∅	NOUN
ejpam-6010	358	63	,	,	PUNCT
ejpam-6010	358	64	{	{	PUNCT
ejpam-6010	358	65	1	1	NUM
ejpam-6010	358	66	}	}	PUNCT
ejpam-6010	358	67	,	,	PUNCT
ejpam-6010	358	68	{	{	PUNCT
ejpam-6010	358	69	3	3	NUM
ejpam-6010	358	70	}	}	PUNCT
ejpam-6010	358	71	,	,	PUNCT
ejpam-6010	358	72	{	{	PUNCT
ejpam-6010	358	73	1	1	NUM
ejpam-6010	358	74	,	,	PUNCT
ejpam-6010	358	75	2	2	NUM
ejpam-6010	358	76	}	}	PUNCT
ejpam-6010	358	77	,	,	PUNCT
ejpam-6010	358	78	{	{	PUNCT
ejpam-6010	358	79	1	1	NUM
ejpam-6010	358	80	,	,	PUNCT
ejpam-6010	358	81	3	3	NUM
ejpam-6010	358	82	}	}	PUNCT
ejpam-6010	358	83	,	,	PUNCT
ejpam-6010	358	84	{	{	PUNCT
ejpam-6010	358	85	1	1	NUM
ejpam-6010	358	86	,	,	PUNCT
ejpam-6010	358	87	4	4	NUM
ejpam-6010	358	88	}	}	PUNCT
ejpam-6010	358	89	,	,	PUNCT
ejpam-6010	358	90	{	{	PUNCT
ejpam-6010	358	91	1	1	NUM
ejpam-6010	358	92	,	,	PUNCT
ejpam-6010	358	93	2	2	NUM
ejpam-6010	358	94	,	,	PUNCT
ejpam-6010	358	95	3	3	NUM
ejpam-6010	358	96	}	}	PUNCT
ejpam-6010	358	97	,	,	PUNCT
ejpam-6010	358	98	{	{	PUNCT
ejpam-6010	358	99	1	1	NUM
ejpam-6010	358	100	,	,	PUNCT
ejpam-6010	358	101	3	3	NUM
ejpam-6010	358	102	,	,	PUNCT
ejpam-6010	358	103	4	4	NUM
ejpam-6010	358	104	}	}	PUNCT
ejpam-6010	358	105	,	,	PUNCT
ejpam-6010	358	106	{	{	PUNCT
ejpam-6010	358	107	1	1	NUM
ejpam-6010	358	108	,	,	PUNCT
ejpam-6010	358	109	2	2	NUM
ejpam-6010	358	110	,	,	PUNCT
ejpam-6010	358	111	4	4	NUM
ejpam-6010	358	112	}	}	PUNCT
ejpam-6010	358	113	,	,	PUNCT
ejpam-6010	358	114	y	y	PROPN
ejpam-6010	358	115	}	}	PUNCT
ejpam-6010	358	116	.	.	PUNCT
ejpam-6010	359	1	a	a	DET
ejpam-6010	359	2	multifunction	multifunction	NOUN
ejpam-6010	359	3	f	f	NOUN
ejpam-6010	359	4	:	:	PUNCT
ejpam-6010	359	5	(	(	PUNCT
ejpam-6010	359	6	x	x	NOUN
ejpam-6010	359	7	,	,	PUNCT
ejpam-6010	359	8	τ1	τ1	NOUN
ejpam-6010	359	9	,	,	PUNCT
ejpam-6010	359	10	τ2	τ2	NOUN
ejpam-6010	359	11	)	)	PUNCT
ejpam-6010	359	12	→	→	SYM
ejpam-6010	359	13	(	(	PUNCT
ejpam-6010	359	14	y	y	PROPN
ejpam-6010	359	15	,	,	PUNCT
ejpam-6010	359	16	σ1	σ1	PROPN
ejpam-6010	359	17	,	,	PUNCT
ejpam-6010	359	18	σ2	σ2	PROPN
ejpam-6010	359	19	)	)	PUNCT
ejpam-6010	359	20	is	be	AUX
ejpam-6010	359	21	defined	define	VERB
ejpam-6010	359	22	as	as	SCONJ
ejpam-6010	359	23	follows	follow	VERB
ejpam-6010	359	24	:	:	PUNCT
ejpam-6010	359	25	f	f	X
ejpam-6010	359	26	(	(	PUNCT
ejpam-6010	359	27	a	a	X
ejpam-6010	359	28	)	)	PUNCT
ejpam-6010	359	29	=	=	PUNCT
ejpam-6010	359	30	{	{	PUNCT
ejpam-6010	359	31	4	4	NUM
ejpam-6010	359	32	}	}	PUNCT
ejpam-6010	359	33	,	,	PUNCT
ejpam-6010	359	34	f	f	PROPN
ejpam-6010	359	35	(	(	PUNCT
ejpam-6010	359	36	b	b	X
ejpam-6010	359	37	)	)	PUNCT
ejpam-6010	359	38	=	=	PUNCT
ejpam-6010	359	39	{	{	PUNCT
ejpam-6010	359	40	3	3	NUM
ejpam-6010	359	41	}	}	PUNCT
ejpam-6010	359	42	,	,	PUNCT
ejpam-6010	359	43	f	f	PROPN
ejpam-6010	359	44	(	(	PUNCT
ejpam-6010	359	45	c	c	X
ejpam-6010	359	46	)	)	PUNCT
ejpam-6010	359	47	=	=	PRON
ejpam-6010	359	48	{	{	PUNCT
ejpam-6010	359	49	1	1	NUM
ejpam-6010	359	50	}	}	PUNCT
ejpam-6010	359	51	and	and	CCONJ
ejpam-6010	359	52	f	f	PROPN
ejpam-6010	359	53	(	(	PUNCT
ejpam-6010	359	54	d	d	X
ejpam-6010	359	55	)	)	PUNCT
ejpam-6010	359	56	=	=	SYM
ejpam-6010	359	57	{	{	PUNCT
ejpam-6010	359	58	2	2	NUM
ejpam-6010	359	59	}	}	PUNCT
ejpam-6010	359	60	.	.	PUNCT
ejpam-6010	360	1	then	then	ADV
ejpam-6010	360	2	,	,	PUNCT
ejpam-6010	360	3	f	f	PROPN
ejpam-6010	360	4	is	be	AUX
ejpam-6010	360	5	upper	upper	ADJ
ejpam-6010	360	6	almost	almost	ADV
ejpam-6010	360	7	(	(	PUNCT
ejpam-6010	360	8	τ1	τ1	NOUN
ejpam-6010	360	9	,	,	PUNCT
ejpam-6010	360	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	360	11	but	but	CCONJ
ejpam-6010	360	12	f	f	PROPN
ejpam-6010	360	13	is	be	AUX
ejpam-6010	360	14	not	not	PART
ejpam-6010	360	15	upper	upper	ADJ
ejpam-6010	360	16	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	360	17	,	,	PUNCT
ejpam-6010	360	18	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	360	19	.	.	PUNCT
ejpam-6010	361	1	definition	definition	NOUN
ejpam-6010	361	2	6	6	NUM
ejpam-6010	361	3	.	.	PUNCT
ejpam-6010	362	1	[	[	X
ejpam-6010	362	2	82	82	NUM
ejpam-6010	362	3	]	]	SYM
ejpam-6010	362	4	a	a	DET
ejpam-6010	362	5	multifunction	multifunction	NOUN
ejpam-6010	362	6	f	f	NOUN
ejpam-6010	362	7	:	:	PUNCT
ejpam-6010	362	8	(	(	PUNCT
ejpam-6010	362	9	x	x	NOUN
ejpam-6010	362	10	,	,	PUNCT
ejpam-6010	362	11	τ1	τ1	NOUN
ejpam-6010	362	12	,	,	PUNCT
ejpam-6010	362	13	τ2	τ2	NOUN
ejpam-6010	362	14	)	)	PUNCT
ejpam-6010	362	15	→	→	SYM
ejpam-6010	362	16	(	(	PUNCT
ejpam-6010	362	17	y	y	PROPN
ejpam-6010	362	18	,	,	PUNCT
ejpam-6010	362	19	σ1	σ1	PROPN
ejpam-6010	362	20	,	,	PUNCT
ejpam-6010	362	21	σ2	σ2	PROPN
ejpam-6010	362	22	)	)	PUNCT
ejpam-6010	362	23	is	be	AUX
ejpam-6010	362	24	said	say	VERB
ejpam-6010	362	25	to	to	PART
ejpam-6010	362	26	be	be	AUX
ejpam-6010	362	27	lower	low	ADJ
ejpam-6010	362	28	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	362	29	,	,	PUNCT
ejpam-6010	362	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	362	31	at	at	ADP
ejpam-6010	362	32	a	a	DET
ejpam-6010	362	33	point	point	NOUN
ejpam-6010	362	34	x	x	SYM
ejpam-6010	362	35	∈	∈	NOUN
ejpam-6010	362	36	x	x	PUNCT
ejpam-6010	362	37	if	if	SCONJ
ejpam-6010	362	38	for	for	ADP
ejpam-6010	362	39	each	each	DET
ejpam-6010	362	40	σ1σ2	σ1σ2	NUM
ejpam-6010	362	41	-	-	PUNCT
ejpam-6010	362	42	closed	closed	ADJ
ejpam-6010	362	43	set	set	NOUN
ejpam-6010	362	44	k	k	PROPN
ejpam-6010	362	45	of	of	ADP
ejpam-6010	362	46	y	y	PROPN
ejpam-6010	362	47	such	such	ADJ
ejpam-6010	362	48	that	that	SCONJ
ejpam-6010	362	49	x	x	SYM
ejpam-6010	362	50	∈	∈	PROPN
ejpam-6010	362	51	f−(k	f−(k	PROPN
ejpam-6010	362	52	)	)	PUNCT
ejpam-6010	362	53	,	,	PUNCT
ejpam-6010	362	54	there	there	PRON
ejpam-6010	362	55	exists	exist	VERB
ejpam-6010	362	56	a	a	DET
ejpam-6010	362	57	τ1τ2	τ1τ2	NOUN
ejpam-6010	362	58	-	-	ADJ
ejpam-6010	362	59	open	open	ADJ
ejpam-6010	362	60	set	set	ADJ
ejpam-6010	362	61	u	u	NOUN
ejpam-6010	362	62	of	of	ADP
ejpam-6010	362	63	x	x	PUNCT
ejpam-6010	362	64	containing	contain	VERB
ejpam-6010	362	65	x	x	PUNCT
ejpam-6010	362	66	with	with	ADP
ejpam-6010	362	67	u	u	NOUN
ejpam-6010	362	68	⊆	⊆	NUM
ejpam-6010	362	69	f−(k	f−(k	PROPN
ejpam-6010	362	70	)	)	PUNCT
ejpam-6010	362	71	.	.	PUNCT
ejpam-6010	363	1	a	a	DET
ejpam-6010	363	2	multifunction	multifunction	NOUN
ejpam-6010	363	3	f	f	NOUN
ejpam-6010	363	4	:	:	PUNCT
ejpam-6010	363	5	(	(	PUNCT
ejpam-6010	363	6	x	x	NOUN
ejpam-6010	363	7	,	,	PUNCT
ejpam-6010	363	8	τ1	τ1	NOUN
ejpam-6010	363	9	,	,	PUNCT
ejpam-6010	363	10	τ2	τ2	NOUN
ejpam-6010	363	11	)	)	PUNCT
ejpam-6010	363	12	→	→	SYM
ejpam-6010	363	13	(	(	PUNCT
ejpam-6010	363	14	y	y	PROPN
ejpam-6010	363	15	,	,	PUNCT
ejpam-6010	363	16	σ1	σ1	PROPN
ejpam-6010	363	17	,	,	PUNCT
ejpam-6010	363	18	σ2	σ2	PROPN
ejpam-6010	363	19	)	)	PUNCT
ejpam-6010	363	20	is	be	AUX
ejpam-6010	363	21	called	call	VERB
ejpam-6010	363	22	lower	low	ADJ
ejpam-6010	363	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	363	24	,	,	PUNCT
ejpam-6010	363	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	363	26	if	if	SCONJ
ejpam-6010	363	27	f	f	PROPN
ejpam-6010	363	28	is	be	AUX
ejpam-6010	363	29	lower	low	ADJ
ejpam-6010	363	30	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	363	31	,	,	PUNCT
ejpam-6010	363	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	363	33	at	at	ADP
ejpam-6010	363	34	each	each	DET
ejpam-6010	363	35	point	point	NOUN
ejpam-6010	363	36	x	x	PUNCT
ejpam-6010	363	37	of	of	ADP
ejpam-6010	363	38	x.	x.	PROPN
ejpam-6010	363	39	theorem	theorem	VERB
ejpam-6010	363	40	16	16	NUM
ejpam-6010	363	41	.	.	PUNCT
ejpam-6010	364	1	if	if	SCONJ
ejpam-6010	364	2	f	f	PROPN
ejpam-6010	364	3	:	:	PUNCT
ejpam-6010	364	4	(	(	PUNCT
ejpam-6010	364	5	x	x	NOUN
ejpam-6010	364	6	,	,	PUNCT
ejpam-6010	364	7	τ1	τ1	NOUN
ejpam-6010	364	8	,	,	PUNCT
ejpam-6010	364	9	τ2	τ2	NOUN
ejpam-6010	364	10	)	)	PUNCT
ejpam-6010	364	11	→	→	SYM
ejpam-6010	364	12	(	(	PUNCT
ejpam-6010	364	13	y	y	PROPN
ejpam-6010	364	14	,	,	PUNCT
ejpam-6010	364	15	σ1	σ1	PROPN
ejpam-6010	364	16	,	,	PUNCT
ejpam-6010	364	17	σ2	σ2	PROPN
ejpam-6010	364	18	)	)	PUNCT
ejpam-6010	364	19	is	be	AUX
ejpam-6010	364	20	a	a	DET
ejpam-6010	364	21	lower	low	ADJ
ejpam-6010	364	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	364	23	,	,	PUNCT
ejpam-6010	364	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	364	25	multifunction	multifunction	NOUN
ejpam-6010	364	26	,	,	PUNCT
ejpam-6010	364	27	then	then	ADV
ejpam-6010	364	28	f	f	PROPN
ejpam-6010	364	29	is	be	AUX
ejpam-6010	364	30	lower	low	ADJ
ejpam-6010	364	31	almost	almost	ADV
ejpam-6010	364	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	364	33	,	,	PUNCT
ejpam-6010	364	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	364	35	.	.	PUNCT
ejpam-6010	365	1	proof	proof	NOUN
ejpam-6010	365	2	.	.	PUNCT
ejpam-6010	366	1	it	it	PRON
ejpam-6010	366	2	is	be	AUX
ejpam-6010	366	3	similar	similar	ADJ
ejpam-6010	366	4	to	to	ADP
ejpam-6010	366	5	that	that	PRON
ejpam-6010	366	6	of	of	ADP
ejpam-6010	366	7	theorem	theorem	NOUN
ejpam-6010	366	8	15	15	NUM
ejpam-6010	366	9	.	.	PUNCT
ejpam-6010	367	1	definition	definition	NOUN
ejpam-6010	367	2	7	7	NUM
ejpam-6010	367	3	.	.	PUNCT
ejpam-6010	368	1	[	[	X
ejpam-6010	368	2	58	58	NUM
ejpam-6010	368	3	]	]	PUNCT
ejpam-6010	368	4	a	a	DET
ejpam-6010	368	5	multifunction	multifunction	NOUN
ejpam-6010	368	6	f	f	NOUN
ejpam-6010	368	7	:	:	PUNCT
ejpam-6010	368	8	(	(	PUNCT
ejpam-6010	368	9	x	x	NOUN
ejpam-6010	368	10	,	,	PUNCT
ejpam-6010	368	11	τ1	τ1	NOUN
ejpam-6010	368	12	,	,	PUNCT
ejpam-6010	368	13	τ2	τ2	NOUN
ejpam-6010	368	14	)	)	PUNCT
ejpam-6010	368	15	→	→	SYM
ejpam-6010	368	16	(	(	PUNCT
ejpam-6010	368	17	y	y	PROPN
ejpam-6010	368	18	,	,	PUNCT
ejpam-6010	368	19	σ1	σ1	PROPN
ejpam-6010	368	20	,	,	PUNCT
ejpam-6010	368	21	σ2	σ2	PROPN
ejpam-6010	368	22	)	)	PUNCT
ejpam-6010	368	23	is	be	AUX
ejpam-6010	368	24	said	say	VERB
ejpam-6010	368	25	to	to	PART
ejpam-6010	368	26	be	be	AUX
ejpam-6010	368	27	:	:	PUNCT
ejpam-6010	368	28	(	(	PUNCT
ejpam-6010	368	29	1	1	X
ejpam-6010	368	30	)	)	PUNCT
ejpam-6010	368	31	upper	upper	ADJ
ejpam-6010	368	32	(	(	PUNCT
ejpam-6010	368	33	τ1	τ1	NOUN
ejpam-6010	368	34	,	,	PUNCT
ejpam-6010	368	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	368	36	if	if	SCONJ
ejpam-6010	368	37	for	for	ADP
ejpam-6010	368	38	each	each	DET
ejpam-6010	368	39	x	x	SYM
ejpam-6010	368	40	∈	∈	PROPN
ejpam-6010	368	41	x	x	X
ejpam-6010	368	42	and	and	CCONJ
ejpam-6010	368	43	each	each	DET
ejpam-6010	368	44	σ1σ2	σ1σ2	VERB
ejpam-6010	368	45	-	-	ADJ
ejpam-6010	368	46	open	open	ADJ
ejpam-6010	368	47	set	set	NOUN
ejpam-6010	368	48	v	v	NOUN
ejpam-6010	368	49	of	of	ADP
ejpam-6010	368	50	y	y	PRON
ejpam-6010	368	51	such	such	ADJ
ejpam-6010	368	52	that	that	SCONJ
ejpam-6010	368	53	f	f	PROPN
ejpam-6010	368	54	(	(	PUNCT
ejpam-6010	368	55	x	x	X
ejpam-6010	368	56	)	)	PUNCT
ejpam-6010	368	57	⊆	⊆	NUM
ejpam-6010	368	58	v	v	NOUN
ejpam-6010	368	59	,	,	PUNCT
ejpam-6010	368	60	there	there	PRON
ejpam-6010	368	61	exists	exist	VERB
ejpam-6010	368	62	a	a	DET
ejpam-6010	368	63	τ1τ2	τ1τ2	NOUN
ejpam-6010	368	64	-	-	ADJ
ejpam-6010	368	65	open	open	ADJ
ejpam-6010	368	66	set	set	ADJ
ejpam-6010	368	67	u	u	NOUN
ejpam-6010	368	68	of	of	ADP
ejpam-6010	368	69	x	x	PUNCT
ejpam-6010	368	70	containing	contain	VERB
ejpam-6010	368	71	x	x	PUNCT
ejpam-6010	369	1	such	such	ADJ
ejpam-6010	369	2	that	that	SCONJ
ejpam-6010	369	3	f	f	PROPN
ejpam-6010	369	4	(	(	PUNCT
ejpam-6010	369	5	u	u	NOUN
ejpam-6010	369	6	)	)	PUNCT
ejpam-6010	369	7	⊆	⊆	NUM
ejpam-6010	369	8	v	v	NOUN
ejpam-6010	369	9	;	;	PUNCT
ejpam-6010	369	10	(	(	PUNCT
ejpam-6010	369	11	2	2	X
ejpam-6010	369	12	)	)	PUNCT
ejpam-6010	369	13	lower	low	ADJ
ejpam-6010	369	14	(	(	PUNCT
ejpam-6010	369	15	τ1	τ1	NOUN
ejpam-6010	369	16	,	,	PUNCT
ejpam-6010	369	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	369	18	if	if	SCONJ
ejpam-6010	369	19	for	for	ADP
ejpam-6010	369	20	each	each	DET
ejpam-6010	369	21	x	x	SYM
ejpam-6010	369	22	∈	∈	PROPN
ejpam-6010	369	23	x	x	X
ejpam-6010	369	24	and	and	CCONJ
ejpam-6010	369	25	each	each	DET
ejpam-6010	369	26	σ1σ2	σ1σ2	VERB
ejpam-6010	369	27	-	-	ADJ
ejpam-6010	369	28	open	open	ADJ
ejpam-6010	369	29	set	set	NOUN
ejpam-6010	369	30	v	v	NOUN
ejpam-6010	369	31	of	of	ADP
ejpam-6010	369	32	y	y	PRON
ejpam-6010	369	33	such	such	ADJ
ejpam-6010	369	34	that	that	SCONJ
ejpam-6010	369	35	f	f	PROPN
ejpam-6010	369	36	(	(	PUNCT
ejpam-6010	369	37	x)∩v	x)∩v	PROPN
ejpam-6010	369	38	̸=	̸=	PROPN
ejpam-6010	369	39	∅	∅	NOUN
ejpam-6010	369	40	,	,	PUNCT
ejpam-6010	369	41	there	there	PRON
ejpam-6010	369	42	exists	exist	VERB
ejpam-6010	369	43	a	a	DET
ejpam-6010	369	44	τ1τ2	τ1τ2	NOUN
ejpam-6010	369	45	-	-	ADJ
ejpam-6010	369	46	open	open	ADJ
ejpam-6010	369	47	set	set	ADJ
ejpam-6010	369	48	u	u	NOUN
ejpam-6010	369	49	of	of	ADP
ejpam-6010	369	50	x	x	PUNCT
ejpam-6010	369	51	containing	contain	VERB
ejpam-6010	369	52	x	x	PUNCT
ejpam-6010	369	53	such	such	ADJ
ejpam-6010	369	54	that	that	SCONJ
ejpam-6010	369	55	f	f	PROPN
ejpam-6010	369	56	(	(	PUNCT
ejpam-6010	369	57	z)∩v	z)∩v	PROPN
ejpam-6010	369	58	̸=	̸=	PROPN
ejpam-6010	369	59	∅	∅	NOUN
ejpam-6010	369	60	for	for	ADP
ejpam-6010	369	61	each	each	DET
ejpam-6010	369	62	z	z	NOUN
ejpam-6010	369	63	∈	∈	PROPN
ejpam-6010	369	64	u	u	PROPN
ejpam-6010	369	65	.	.	PUNCT
ejpam-6010	370	1	lemma	lemma	PROPN
ejpam-6010	370	2	5	5	NUM
ejpam-6010	370	3	.	.	PUNCT
ejpam-6010	371	1	[	[	X
ejpam-6010	371	2	58	58	NUM
ejpam-6010	371	3	]	]	PUNCT
ejpam-6010	371	4	for	for	ADP
ejpam-6010	371	5	a	a	DET
ejpam-6010	371	6	multifunction	multifunction	NOUN
ejpam-6010	371	7	f	f	NOUN
ejpam-6010	371	8	:	:	PUNCT
ejpam-6010	371	9	(	(	PUNCT
ejpam-6010	371	10	x	x	NOUN
ejpam-6010	371	11	,	,	PUNCT
ejpam-6010	371	12	τ1	τ1	NOUN
ejpam-6010	371	13	,	,	PUNCT
ejpam-6010	371	14	τ2	τ2	NOUN
ejpam-6010	371	15	)	)	PUNCT
ejpam-6010	371	16	→	→	SYM
ejpam-6010	371	17	(	(	PUNCT
ejpam-6010	371	18	y	y	PROPN
ejpam-6010	371	19	,	,	PUNCT
ejpam-6010	371	20	σ1	σ1	PROPN
ejpam-6010	371	21	,	,	PUNCT
ejpam-6010	371	22	σ2	σ2	NOUN
ejpam-6010	371	23	)	)	PUNCT
ejpam-6010	371	24	,	,	PUNCT
ejpam-6010	371	25	the	the	DET
ejpam-6010	371	26	following	follow	VERB
ejpam-6010	371	27	properties	property	NOUN
ejpam-6010	371	28	are	be	AUX
ejpam-6010	371	29	equivalent	equivalent	ADJ
ejpam-6010	371	30	:	:	PUNCT
ejpam-6010	371	31	(	(	PUNCT
ejpam-6010	371	32	1	1	X
ejpam-6010	371	33	)	)	PUNCT
ejpam-6010	371	34	f	f	PROPN
ejpam-6010	371	35	is	be	AUX
ejpam-6010	371	36	upper	upper	ADJ
ejpam-6010	371	37	(	(	PUNCT
ejpam-6010	371	38	τ1	τ1	NOUN
ejpam-6010	371	39	,	,	PUNCT
ejpam-6010	371	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	371	41	;	;	PUNCT
ejpam-6010	371	42	(	(	PUNCT
ejpam-6010	371	43	2	2	NUM
ejpam-6010	371	44	)	)	PUNCT
ejpam-6010	371	45	f+(v	f+(v	NOUN
ejpam-6010	371	46	)	)	PUNCT
ejpam-6010	371	47	is	be	AUX
ejpam-6010	371	48	τ1τ2	τ1τ2	NOUN
ejpam-6010	371	49	-	-	ADJ
ejpam-6010	371	50	open	open	ADJ
ejpam-6010	371	51	in	in	ADP
ejpam-6010	371	52	x	x	PUNCT
ejpam-6010	371	53	for	for	ADP
ejpam-6010	371	54	every	every	DET
ejpam-6010	371	55	σ1σ2	σ1σ2	NOUN
ejpam-6010	371	56	-	-	ADJ
ejpam-6010	371	57	open	open	ADJ
ejpam-6010	371	58	set	set	NOUN
ejpam-6010	371	59	v	v	NOUN
ejpam-6010	371	60	of	of	ADP
ejpam-6010	371	61	y	y	PROPN
ejpam-6010	371	62	;	;	PUNCT
ejpam-6010	371	63	(	(	PUNCT
ejpam-6010	371	64	3	3	X
ejpam-6010	371	65	)	)	PUNCT
ejpam-6010	371	66	f−(k	f−(k	PROPN
ejpam-6010	371	67	)	)	PUNCT
ejpam-6010	371	68	is	be	AUX
ejpam-6010	371	69	τ1τ2	τ1τ2	NOUN
ejpam-6010	371	70	-	-	ADJ
ejpam-6010	371	71	closed	closed	ADJ
ejpam-6010	371	72	in	in	ADP
ejpam-6010	371	73	x	x	PUNCT
ejpam-6010	371	74	for	for	ADP
ejpam-6010	371	75	every	every	DET
ejpam-6010	371	76	σ1σ2	σ1σ2	NUM
ejpam-6010	371	77	-	-	PUNCT
ejpam-6010	371	78	closed	closed	ADJ
ejpam-6010	371	79	set	set	NOUN
ejpam-6010	371	80	k	k	PROPN
ejpam-6010	371	81	of	of	ADP
ejpam-6010	371	82	y	y	PROPN
ejpam-6010	371	83	;	;	PUNCT
ejpam-6010	371	84	(	(	PUNCT
ejpam-6010	371	85	4	4	X
ejpam-6010	371	86	)	)	PUNCT
ejpam-6010	371	87	τ1τ2	τ1τ2	NOUN
ejpam-6010	371	88	-	-	NOUN
ejpam-6010	371	89	cl(f	cl(f	NOUN
ejpam-6010	371	90	−(b	−(b	PROPN
ejpam-6010	371	91	)	)	PUNCT
ejpam-6010	371	92	)	)	PUNCT
ejpam-6010	372	1	⊆	⊆	X
ejpam-6010	372	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6010	372	3	-	-	PUNCT
ejpam-6010	372	4	cl(b	cl(b	NOUN
ejpam-6010	372	5	)	)	PUNCT
ejpam-6010	372	6	)	)	PUNCT
ejpam-6010	373	1	for	for	ADP
ejpam-6010	373	2	every	every	DET
ejpam-6010	373	3	subset	subset	NOUN
ejpam-6010	373	4	b	b	PROPN
ejpam-6010	373	5	of	of	ADP
ejpam-6010	373	6	y	y	PROPN
ejpam-6010	373	7	;	;	PUNCT
ejpam-6010	373	8	(	(	PUNCT
ejpam-6010	373	9	5	5	X
ejpam-6010	373	10	)	)	PUNCT
ejpam-6010	373	11	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	373	12	-	-	PUNCT
ejpam-6010	373	13	int(b	int(b	NOUN
ejpam-6010	373	14	)	)	PUNCT
ejpam-6010	373	15	)	)	PUNCT
ejpam-6010	374	1	⊆	⊆	X
ejpam-6010	374	2	τ1τ2	τ1τ2	NOUN
ejpam-6010	374	3	-	-	NUM
ejpam-6010	374	4	int(f	int(f	VERB
ejpam-6010	374	5	+	+	ADJ
ejpam-6010	374	6	(	(	PUNCT
ejpam-6010	374	7	b	b	NOUN
ejpam-6010	374	8	)	)	PUNCT
ejpam-6010	374	9	)	)	PUNCT
ejpam-6010	374	10	for	for	ADP
ejpam-6010	374	11	every	every	DET
ejpam-6010	374	12	subset	subset	NOUN
ejpam-6010	374	13	b	b	PROPN
ejpam-6010	374	14	of	of	ADP
ejpam-6010	374	15	y	y	PROPN
ejpam-6010	374	16	.	.	PUNCT
ejpam-6010	375	1	lemma	lemma	PROPN
ejpam-6010	375	2	6	6	NUM
ejpam-6010	375	3	.	.	PUNCT
ejpam-6010	376	1	[	[	X
ejpam-6010	376	2	58	58	NUM
ejpam-6010	376	3	]	]	PUNCT
ejpam-6010	376	4	for	for	ADP
ejpam-6010	376	5	a	a	DET
ejpam-6010	376	6	multifunction	multifunction	NOUN
ejpam-6010	376	7	f	f	NOUN
ejpam-6010	376	8	:	:	PUNCT
ejpam-6010	376	9	(	(	PUNCT
ejpam-6010	376	10	x	x	NOUN
ejpam-6010	376	11	,	,	PUNCT
ejpam-6010	376	12	τ1	τ1	NOUN
ejpam-6010	376	13	,	,	PUNCT
ejpam-6010	376	14	τ2	τ2	NOUN
ejpam-6010	376	15	)	)	PUNCT
ejpam-6010	376	16	→	→	SYM
ejpam-6010	376	17	(	(	PUNCT
ejpam-6010	376	18	y	y	PROPN
ejpam-6010	376	19	,	,	PUNCT
ejpam-6010	376	20	σ1	σ1	PROPN
ejpam-6010	376	21	,	,	PUNCT
ejpam-6010	376	22	σ2	σ2	NOUN
ejpam-6010	376	23	)	)	PUNCT
ejpam-6010	376	24	,	,	PUNCT
ejpam-6010	376	25	the	the	DET
ejpam-6010	376	26	following	follow	VERB
ejpam-6010	376	27	properties	property	NOUN
ejpam-6010	376	28	are	be	AUX
ejpam-6010	376	29	equivalent	equivalent	ADJ
ejpam-6010	376	30	:	:	PUNCT
ejpam-6010	376	31	j.	j.	PROPN
ejpam-6010	376	32	khampakdee	khampakdee	PROPN
ejpam-6010	376	33	,	,	PUNCT
ejpam-6010	376	34	a.	a.	PROPN
ejpam-6010	376	35	sama	sama	PROPN
ejpam-6010	376	36	-	-	PUNCT
ejpam-6010	376	37	ae	ae	PROPN
ejpam-6010	376	38	,	,	PUNCT
ejpam-6010	376	39	c.	c.	PROPN
ejpam-6010	376	40	boonpok	boonpok	PROPN
ejpam-6010	376	41	/	/	SYM
ejpam-6010	376	42	eur	eur	PROPN
ejpam-6010	376	43	.	.	PUNCT
ejpam-6010	377	1	j.	j.	PROPN
ejpam-6010	377	2	pure	pure	PROPN
ejpam-6010	377	3	appl	appl	PROPN
ejpam-6010	377	4	.	.	PROPN
ejpam-6010	377	5	math	math	PROPN
ejpam-6010	377	6	,	,	PUNCT
ejpam-6010	377	7	18	18	NUM
ejpam-6010	377	8	(	(	PUNCT
ejpam-6010	377	9	2	2	NUM
ejpam-6010	377	10	)	)	PUNCT
ejpam-6010	377	11	(	(	PUNCT
ejpam-6010	377	12	2025	2025	NUM
ejpam-6010	377	13	)	)	PUNCT
ejpam-6010	377	14	,	,	PUNCT
ejpam-6010	377	15	6010	6010	NUM
ejpam-6010	377	16	14	14	NUM
ejpam-6010	377	17	of	of	ADP
ejpam-6010	377	18	19	19	NUM
ejpam-6010	377	19	(	(	PUNCT
ejpam-6010	377	20	1	1	NUM
ejpam-6010	377	21	)	)	PUNCT
ejpam-6010	377	22	f	f	PROPN
ejpam-6010	377	23	is	be	AUX
ejpam-6010	377	24	lower	low	ADJ
ejpam-6010	377	25	(	(	PUNCT
ejpam-6010	377	26	τ1	τ1	NOUN
ejpam-6010	377	27	,	,	PUNCT
ejpam-6010	377	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	377	29	;	;	PUNCT
ejpam-6010	377	30	(	(	PUNCT
ejpam-6010	377	31	2	2	X
ejpam-6010	377	32	)	)	PUNCT
ejpam-6010	377	33	f−(v	f−(v	NOUN
ejpam-6010	377	34	)	)	PUNCT
ejpam-6010	377	35	is	be	AUX
ejpam-6010	377	36	τ1τ2	τ1τ2	NOUN
ejpam-6010	377	37	-	-	ADJ
ejpam-6010	377	38	open	open	ADJ
ejpam-6010	377	39	in	in	ADP
ejpam-6010	377	40	x	x	PUNCT
ejpam-6010	377	41	for	for	ADP
ejpam-6010	377	42	every	every	DET
ejpam-6010	377	43	σ1σ2	σ1σ2	NOUN
ejpam-6010	377	44	-	-	ADJ
ejpam-6010	377	45	open	open	ADJ
ejpam-6010	377	46	set	set	NOUN
ejpam-6010	377	47	v	v	NOUN
ejpam-6010	377	48	of	of	ADP
ejpam-6010	377	49	y	y	PROPN
ejpam-6010	377	50	;	;	PUNCT
ejpam-6010	377	51	(	(	PUNCT
ejpam-6010	377	52	3	3	X
ejpam-6010	377	53	)	)	PUNCT
ejpam-6010	377	54	f+(k	f+(k	NOUN
ejpam-6010	377	55	)	)	PUNCT
ejpam-6010	377	56	is	be	AUX
ejpam-6010	377	57	τ1τ2	τ1τ2	NOUN
ejpam-6010	377	58	-	-	ADJ
ejpam-6010	377	59	closed	closed	ADJ
ejpam-6010	377	60	in	in	ADP
ejpam-6010	377	61	x	x	PUNCT
ejpam-6010	377	62	for	for	ADP
ejpam-6010	377	63	every	every	DET
ejpam-6010	377	64	σ1σ2	σ1σ2	NUM
ejpam-6010	377	65	-	-	PUNCT
ejpam-6010	377	66	closed	closed	ADJ
ejpam-6010	377	67	set	set	NOUN
ejpam-6010	377	68	k	k	PROPN
ejpam-6010	377	69	of	of	ADP
ejpam-6010	377	70	y	y	PROPN
ejpam-6010	377	71	;	;	PUNCT
ejpam-6010	377	72	(	(	PUNCT
ejpam-6010	377	73	4	4	X
ejpam-6010	377	74	)	)	PUNCT
ejpam-6010	377	75	τ1τ2	τ1τ2	NOUN
ejpam-6010	377	76	-	-	NOUN
ejpam-6010	377	77	cl(f	cl(f	NOUN
ejpam-6010	377	78	+	+	NOUN
ejpam-6010	377	79	(	(	PUNCT
ejpam-6010	377	80	b	b	NOUN
ejpam-6010	377	81	)	)	PUNCT
ejpam-6010	377	82	)	)	PUNCT
ejpam-6010	377	83	⊆	⊆	NUM
ejpam-6010	377	84	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6010	377	85	-	-	PUNCT
ejpam-6010	377	86	cl(b	cl(b	NOUN
ejpam-6010	377	87	)	)	PUNCT
ejpam-6010	377	88	)	)	PUNCT
ejpam-6010	377	89	for	for	ADP
ejpam-6010	377	90	every	every	DET
ejpam-6010	377	91	subset	subset	NOUN
ejpam-6010	377	92	b	b	PROPN
ejpam-6010	377	93	of	of	ADP
ejpam-6010	377	94	y	y	PROPN
ejpam-6010	377	95	;	;	PUNCT
ejpam-6010	377	96	(	(	PUNCT
ejpam-6010	377	97	5	5	X
ejpam-6010	377	98	)	)	PUNCT
ejpam-6010	377	99	f	f	NOUN
ejpam-6010	377	100	(	(	PUNCT
ejpam-6010	377	101	τ1τ2	τ1τ2	NOUN
ejpam-6010	377	102	-	-	NUM
ejpam-6010	377	103	cl(a	cl(a	NUM
ejpam-6010	377	104	)	)	PUNCT
ejpam-6010	377	105	)	)	PUNCT
ejpam-6010	378	1	⊆	⊆	X
ejpam-6010	378	2	σ1σ2	σ1σ2	X
ejpam-6010	378	3	-	-	NUM
ejpam-6010	378	4	cl(f	cl(f	NOUN
ejpam-6010	378	5	(	(	PUNCT
ejpam-6010	378	6	a	a	NOUN
ejpam-6010	378	7	)	)	PUNCT
ejpam-6010	378	8	)	)	PUNCT
ejpam-6010	378	9	for	for	ADP
ejpam-6010	378	10	every	every	DET
ejpam-6010	378	11	subset	subset	NOUN
ejpam-6010	378	12	a	a	PRON
ejpam-6010	378	13	of	of	ADP
ejpam-6010	378	14	x	x	PRON
ejpam-6010	378	15	;	;	PUNCT
ejpam-6010	378	16	(	(	PUNCT
ejpam-6010	378	17	6	6	X
ejpam-6010	378	18	)	)	PUNCT
ejpam-6010	378	19	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6010	378	20	-	-	PUNCT
ejpam-6010	378	21	int(b	int(b	NOUN
ejpam-6010	378	22	)	)	PUNCT
ejpam-6010	378	23	)	)	PUNCT
ejpam-6010	378	24	⊆	⊆	X
ejpam-6010	378	25	τ1τ2	τ1τ2	NOUN
ejpam-6010	378	26	-	-	NUM
ejpam-6010	378	27	int(f	int(f	VERB
ejpam-6010	378	28	−(b	−(b	NOUN
ejpam-6010	378	29	)	)	PUNCT
ejpam-6010	378	30	)	)	PUNCT
ejpam-6010	378	31	for	for	ADP
ejpam-6010	378	32	every	every	DET
ejpam-6010	378	33	subset	subset	NOUN
ejpam-6010	378	34	b	b	PROPN
ejpam-6010	378	35	of	of	ADP
ejpam-6010	378	36	y	y	PROPN
ejpam-6010	378	37	.	.	PUNCT
ejpam-6010	379	1	theorem	theorem	VERB
ejpam-6010	379	2	17	17	NUM
ejpam-6010	379	3	.	.	PUNCT
ejpam-6010	380	1	if	if	SCONJ
ejpam-6010	380	2	f	f	PROPN
ejpam-6010	380	3	:	:	PUNCT
ejpam-6010	380	4	(	(	PUNCT
ejpam-6010	380	5	x	x	NOUN
ejpam-6010	380	6	,	,	PUNCT
ejpam-6010	380	7	τ1	τ1	NOUN
ejpam-6010	380	8	,	,	PUNCT
ejpam-6010	380	9	τ2	τ2	NOUN
ejpam-6010	380	10	)	)	PUNCT
ejpam-6010	380	11	→	→	SYM
ejpam-6010	380	12	(	(	PUNCT
ejpam-6010	380	13	y	y	PROPN
ejpam-6010	380	14	,	,	PUNCT
ejpam-6010	380	15	σ1	σ1	PROPN
ejpam-6010	380	16	,	,	PUNCT
ejpam-6010	380	17	σ2	σ2	PROPN
ejpam-6010	380	18	)	)	PUNCT
ejpam-6010	380	19	is	be	AUX
ejpam-6010	380	20	an	an	DET
ejpam-6010	380	21	upper	upper	ADJ
ejpam-6010	380	22	(	(	PUNCT
ejpam-6010	380	23	τ1	τ1	NOUN
ejpam-6010	380	24	,	,	PUNCT
ejpam-6010	380	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	380	26	multifunction	multifunction	NOUN
ejpam-6010	380	27	and	and	CCONJ
ejpam-6010	380	28	g	g	NOUN
ejpam-6010	380	29	:	:	PUNCT
ejpam-6010	380	30	(	(	PUNCT
ejpam-6010	380	31	y	y	PROPN
ejpam-6010	380	32	,	,	PUNCT
ejpam-6010	380	33	σ1	σ1	PROPN
ejpam-6010	380	34	,	,	PUNCT
ejpam-6010	380	35	σ2	σ2	NOUN
ejpam-6010	380	36	)	)	PUNCT
ejpam-6010	380	37	→	→	SYM
ejpam-6010	380	38	(	(	PUNCT
ejpam-6010	380	39	z	z	NOUN
ejpam-6010	380	40	,	,	PUNCT
ejpam-6010	380	41	ρ1	ρ1	NOUN
ejpam-6010	380	42	,	,	PUNCT
ejpam-6010	380	43	ρ2	ρ2	NOUN
ejpam-6010	380	44	)	)	PUNCT
ejpam-6010	380	45	is	be	AUX
ejpam-6010	380	46	an	an	DET
ejpam-6010	380	47	upper	upper	ADJ
ejpam-6010	380	48	almost	almost	ADV
ejpam-6010	380	49	contra-(σ1	contra-(σ1	ADJ
ejpam-6010	380	50	,	,	PUNCT
ejpam-6010	380	51	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6010	380	52	multifunction	multifunction	NOUN
ejpam-6010	380	53	,	,	PUNCT
ejpam-6010	380	54	then	then	ADV
ejpam-6010	380	55	g	g	PROPN
ejpam-6010	380	56	◦	◦	NOUN
ejpam-6010	380	57	f	f	X
ejpam-6010	380	58	:	:	PUNCT
ejpam-6010	380	59	(	(	PUNCT
ejpam-6010	380	60	x	x	NOUN
ejpam-6010	380	61	,	,	PUNCT
ejpam-6010	380	62	τ1	τ1	NOUN
ejpam-6010	380	63	,	,	PUNCT
ejpam-6010	380	64	τ2	τ2	NOUN
ejpam-6010	380	65	)	)	PUNCT
ejpam-6010	380	66	→	→	SYM
ejpam-6010	380	67	(	(	PUNCT
ejpam-6010	380	68	z	z	NOUN
ejpam-6010	380	69	,	,	PUNCT
ejpam-6010	380	70	ρ1	ρ1	NOUN
ejpam-6010	380	71	,	,	PUNCT
ejpam-6010	380	72	ρ2	ρ2	NOUN
ejpam-6010	380	73	)	)	PUNCT
ejpam-6010	380	74	is	be	AUX
ejpam-6010	380	75	upper	upper	ADJ
ejpam-6010	380	76	almost	almost	ADV
ejpam-6010	380	77	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	380	78	,	,	PUNCT
ejpam-6010	380	79	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	380	80	.	.	PUNCT
ejpam-6010	381	1	proof	proof	NOUN
ejpam-6010	381	2	.	.	PUNCT
ejpam-6010	382	1	let	let	VERB
ejpam-6010	382	2	k	k	PRON
ejpam-6010	382	3	be	be	AUX
ejpam-6010	382	4	any	any	DET
ejpam-6010	382	5	(	(	PUNCT
ejpam-6010	382	6	ρ1	ρ1	NOUN
ejpam-6010	382	7	,	,	PUNCT
ejpam-6010	382	8	ρ2)r	ρ2)r	NOUN
ejpam-6010	382	9	-	-	PUNCT
ejpam-6010	382	10	closed	close	VERB
ejpam-6010	382	11	set	set	NOUN
ejpam-6010	382	12	of	of	ADP
ejpam-6010	382	13	z.	z.	PROPN
ejpam-6010	382	14	since	since	SCONJ
ejpam-6010	382	15	g	g	PROPN
ejpam-6010	382	16	is	be	AUX
ejpam-6010	382	17	upper	upper	ADJ
ejpam-6010	382	18	almost	almost	ADV
ejpam-6010	382	19	contra-(σ1	contra-(σ1	ADJ
ejpam-6010	382	20	,	,	PUNCT
ejpam-6010	382	21	σ2)continuous	σ2)continuous	ADJ
ejpam-6010	382	22	,	,	PUNCT
ejpam-6010	382	23	by	by	ADP
ejpam-6010	382	24	theorem	theorem	NOUN
ejpam-6010	382	25	1	1	NUM
ejpam-6010	382	26	we	we	PRON
ejpam-6010	382	27	have	have	VERB
ejpam-6010	382	28	f+(k	f+(k	NOUN
ejpam-6010	382	29	)	)	PUNCT
ejpam-6010	382	30	is	be	AUX
ejpam-6010	382	31	σ1σ2	σ1σ2	NOUN
ejpam-6010	382	32	-	-	ADJ
ejpam-6010	382	33	open	open	ADJ
ejpam-6010	382	34	in	in	ADP
ejpam-6010	382	35	y	y	PROPN
ejpam-6010	382	36	.	.	PUNCT
ejpam-6010	383	1	since	since	SCONJ
ejpam-6010	383	2	f	f	PROPN
ejpam-6010	383	3	is	be	AUX
ejpam-6010	383	4	upper	upper	ADJ
ejpam-6010	383	5	(	(	PUNCT
ejpam-6010	383	6	τ1	τ1	NOUN
ejpam-6010	383	7	,	,	PUNCT
ejpam-6010	383	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	383	9	,	,	PUNCT
ejpam-6010	383	10	by	by	ADP
ejpam-6010	383	11	lemma	lemma	PROPN
ejpam-6010	383	12	5	5	NUM
ejpam-6010	383	13	we	we	PRON
ejpam-6010	383	14	have	have	VERB
ejpam-6010	383	15	(	(	PUNCT
ejpam-6010	383	16	g	g	PROPN
ejpam-6010	383	17	◦	◦	NOUN
ejpam-6010	383	18	f	f	NOUN
ejpam-6010	383	19	)	)	PUNCT
ejpam-6010	384	1	+	+	PROPN
ejpam-6010	384	2	(	(	PUNCT
ejpam-6010	384	3	k	k	NOUN
ejpam-6010	384	4	)	)	PUNCT
ejpam-6010	384	5	=	=	SYM
ejpam-6010	384	6	f+(g+(k	f+(g+(k	NOUN
ejpam-6010	384	7	)	)	PUNCT
ejpam-6010	384	8	)	)	PUNCT
ejpam-6010	384	9	is	be	AUX
ejpam-6010	384	10	τ1τ2	τ1τ2	NOUN
ejpam-6010	384	11	-	-	ADJ
ejpam-6010	384	12	open	open	ADJ
ejpam-6010	384	13	in	in	ADP
ejpam-6010	384	14	x.	x.	NOUN
ejpam-6010	384	15	thus	thus	ADV
ejpam-6010	384	16	by	by	ADP
ejpam-6010	384	17	theorem	theorem	NOUN
ejpam-6010	384	18	1	1	NUM
ejpam-6010	384	19	,	,	PUNCT
ejpam-6010	384	20	g	g	NOUN
ejpam-6010	384	21	◦	◦	NOUN
ejpam-6010	384	22	f	f	PROPN
ejpam-6010	384	23	is	be	AUX
ejpam-6010	384	24	upper	upper	ADJ
ejpam-6010	384	25	almost	almost	ADV
ejpam-6010	384	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	384	27	,	,	PUNCT
ejpam-6010	384	28	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	384	29	.	.	PUNCT
ejpam-6010	385	1	theorem	theorem	VERB
ejpam-6010	385	2	18	18	NUM
ejpam-6010	385	3	.	.	PUNCT
ejpam-6010	386	1	if	if	SCONJ
ejpam-6010	386	2	f	f	PROPN
ejpam-6010	386	3	:	:	PUNCT
ejpam-6010	386	4	(	(	PUNCT
ejpam-6010	386	5	x	x	NOUN
ejpam-6010	386	6	,	,	PUNCT
ejpam-6010	386	7	τ1	τ1	NOUN
ejpam-6010	386	8	,	,	PUNCT
ejpam-6010	386	9	τ2	τ2	NOUN
ejpam-6010	386	10	)	)	PUNCT
ejpam-6010	386	11	→	→	SYM
ejpam-6010	386	12	(	(	PUNCT
ejpam-6010	386	13	y	y	PROPN
ejpam-6010	386	14	,	,	PUNCT
ejpam-6010	386	15	σ1	σ1	PROPN
ejpam-6010	386	16	,	,	PUNCT
ejpam-6010	386	17	σ2	σ2	PROPN
ejpam-6010	386	18	)	)	PUNCT
ejpam-6010	386	19	is	be	AUX
ejpam-6010	386	20	an	an	DET
ejpam-6010	386	21	lower	low	ADJ
ejpam-6010	386	22	(	(	PUNCT
ejpam-6010	386	23	τ1	τ1	NOUN
ejpam-6010	386	24	,	,	PUNCT
ejpam-6010	386	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	386	26	multifunction	multifunction	NOUN
ejpam-6010	386	27	and	and	CCONJ
ejpam-6010	386	28	g	g	NOUN
ejpam-6010	386	29	:	:	PUNCT
ejpam-6010	386	30	(	(	PUNCT
ejpam-6010	386	31	y	y	PROPN
ejpam-6010	386	32	,	,	PUNCT
ejpam-6010	386	33	σ1	σ1	PROPN
ejpam-6010	386	34	,	,	PUNCT
ejpam-6010	386	35	σ2	σ2	NOUN
ejpam-6010	386	36	)	)	PUNCT
ejpam-6010	386	37	→	→	SYM
ejpam-6010	386	38	(	(	PUNCT
ejpam-6010	386	39	z	z	NOUN
ejpam-6010	386	40	,	,	PUNCT
ejpam-6010	386	41	ρ1	ρ1	NOUN
ejpam-6010	386	42	,	,	PUNCT
ejpam-6010	386	43	ρ2	ρ2	NOUN
ejpam-6010	386	44	)	)	PUNCT
ejpam-6010	386	45	is	be	AUX
ejpam-6010	386	46	an	an	DET
ejpam-6010	386	47	lower	low	ADJ
ejpam-6010	386	48	almost	almost	ADV
ejpam-6010	386	49	contra-(σ1	contra-(σ1	ADJ
ejpam-6010	386	50	,	,	PUNCT
ejpam-6010	386	51	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6010	386	52	multifunction	multifunction	NOUN
ejpam-6010	386	53	,	,	PUNCT
ejpam-6010	386	54	then	then	ADV
ejpam-6010	386	55	g	g	PROPN
ejpam-6010	386	56	◦	◦	NOUN
ejpam-6010	386	57	f	f	X
ejpam-6010	386	58	:	:	PUNCT
ejpam-6010	386	59	(	(	PUNCT
ejpam-6010	386	60	x	x	NOUN
ejpam-6010	386	61	,	,	PUNCT
ejpam-6010	386	62	τ1	τ1	NOUN
ejpam-6010	386	63	,	,	PUNCT
ejpam-6010	386	64	τ2	τ2	NOUN
ejpam-6010	386	65	)	)	PUNCT
ejpam-6010	386	66	→	→	SYM
ejpam-6010	386	67	(	(	PUNCT
ejpam-6010	386	68	z	z	NOUN
ejpam-6010	386	69	,	,	PUNCT
ejpam-6010	386	70	ρ1	ρ1	NOUN
ejpam-6010	386	71	,	,	PUNCT
ejpam-6010	386	72	ρ2	ρ2	NOUN
ejpam-6010	386	73	)	)	PUNCT
ejpam-6010	386	74	is	be	AUX
ejpam-6010	386	75	lower	low	ADJ
ejpam-6010	386	76	almost	almost	ADV
ejpam-6010	386	77	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	386	78	,	,	PUNCT
ejpam-6010	386	79	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	386	80	.	.	PUNCT
ejpam-6010	387	1	proof	proof	NOUN
ejpam-6010	387	2	.	.	PUNCT
ejpam-6010	388	1	it	it	PRON
ejpam-6010	388	2	is	be	AUX
ejpam-6010	388	3	similar	similar	ADJ
ejpam-6010	388	4	to	to	ADP
ejpam-6010	388	5	that	that	PRON
ejpam-6010	388	6	of	of	ADP
ejpam-6010	388	7	theorem	theorem	NOUN
ejpam-6010	388	8	17	17	NUM
ejpam-6010	388	9	.	.	PUNCT
ejpam-6010	389	1	for	for	ADP
ejpam-6010	389	2	a	a	DET
ejpam-6010	389	3	multifunction	multifunction	NOUN
ejpam-6010	389	4	f	f	NOUN
ejpam-6010	389	5	:	:	PUNCT
ejpam-6010	389	6	(	(	PUNCT
ejpam-6010	389	7	x	x	NOUN
ejpam-6010	389	8	,	,	PUNCT
ejpam-6010	389	9	τ1	τ1	NOUN
ejpam-6010	389	10	,	,	PUNCT
ejpam-6010	389	11	τ2	τ2	NOUN
ejpam-6010	389	12	)	)	PUNCT
ejpam-6010	389	13	→	→	SYM
ejpam-6010	389	14	(	(	PUNCT
ejpam-6010	389	15	y	y	PROPN
ejpam-6010	389	16	,	,	PUNCT
ejpam-6010	389	17	σ1	σ1	PROPN
ejpam-6010	389	18	,	,	PUNCT
ejpam-6010	389	19	σ2	σ2	PROPN
ejpam-6010	389	20	)	)	PUNCT
ejpam-6010	389	21	,	,	PUNCT
ejpam-6010	389	22	a	a	DET
ejpam-6010	389	23	multifunction	multifunction	NOUN
ejpam-6010	389	24	clf⊛	clf⊛	NOUN
ejpam-6010	389	25	:	:	PUNCT
ejpam-6010	389	26	(	(	PUNCT
ejpam-6010	389	27	x	x	NOUN
ejpam-6010	389	28	,	,	PUNCT
ejpam-6010	389	29	τ1	τ1	NOUN
ejpam-6010	389	30	,	,	PUNCT
ejpam-6010	389	31	τ2	τ2	NOUN
ejpam-6010	389	32	)	)	PUNCT
ejpam-6010	389	33	→	→	SYM
ejpam-6010	389	34	(	(	PUNCT
ejpam-6010	389	35	y	y	PROPN
ejpam-6010	389	36	,	,	PUNCT
ejpam-6010	389	37	σ1	σ1	PROPN
ejpam-6010	389	38	,	,	PUNCT
ejpam-6010	389	39	σ2	σ2	PROPN
ejpam-6010	389	40	)	)	PUNCT
ejpam-6010	389	41	is	be	AUX
ejpam-6010	389	42	defined	define	VERB
ejpam-6010	389	43	in	in	ADP
ejpam-6010	389	44	[	[	X
ejpam-6010	389	45	78	78	NUM
ejpam-6010	389	46	]	]	PUNCT
ejpam-6010	389	47	as	as	SCONJ
ejpam-6010	389	48	follows	follow	VERB
ejpam-6010	389	49	:	:	PUNCT
ejpam-6010	389	50	clf⊛(x	clf⊛(x	PROPN
ejpam-6010	389	51	)	)	PUNCT
ejpam-6010	389	52	=	=	PUNCT
ejpam-6010	390	1	σ1σ2	σ1σ2	X
ejpam-6010	390	2	-	-	NUM
ejpam-6010	390	3	cl(f	cl(f	NOUN
ejpam-6010	390	4	(	(	PUNCT
ejpam-6010	390	5	x	x	NOUN
ejpam-6010	390	6	)	)	PUNCT
ejpam-6010	390	7	)	)	PUNCT
ejpam-6010	390	8	for	for	ADP
ejpam-6010	390	9	each	each	DET
ejpam-6010	390	10	x	x	SYM
ejpam-6010	390	11	∈	∈	PROPN
ejpam-6010	390	12	x.	x.	NOUN
ejpam-6010	390	13	definition	definition	NOUN
ejpam-6010	390	14	8	8	NUM
ejpam-6010	390	15	.	.	PUNCT
ejpam-6010	391	1	[	[	X
ejpam-6010	391	2	78	78	NUM
ejpam-6010	391	3	]	]	PUNCT
ejpam-6010	391	4	a	a	DET
ejpam-6010	391	5	subset	subset	NOUN
ejpam-6010	391	6	a	a	PRON
ejpam-6010	391	7	of	of	ADP
ejpam-6010	391	8	a	a	DET
ejpam-6010	391	9	bitopological	bitopological	ADJ
ejpam-6010	391	10	space	space	NOUN
ejpam-6010	391	11	(	(	PUNCT
ejpam-6010	391	12	x	x	NOUN
ejpam-6010	391	13	,	,	PUNCT
ejpam-6010	391	14	τ1	τ1	NOUN
ejpam-6010	391	15	,	,	PUNCT
ejpam-6010	391	16	τ2	τ2	NOUN
ejpam-6010	391	17	)	)	PUNCT
ejpam-6010	391	18	is	be	AUX
ejpam-6010	391	19	said	say	VERB
ejpam-6010	391	20	to	to	PART
ejpam-6010	391	21	be	be	AUX
ejpam-6010	391	22	:	:	PUNCT
ejpam-6010	391	23	(	(	PUNCT
ejpam-6010	391	24	1	1	X
ejpam-6010	391	25	)	)	PUNCT
ejpam-6010	391	26	τ1τ2	τ1τ2	NOUN
ejpam-6010	391	27	-	-	NOUN
ejpam-6010	391	28	paracompact	paracompact	ADJ
ejpam-6010	391	29	if	if	SCONJ
ejpam-6010	391	30	every	every	DET
ejpam-6010	391	31	cover	cover	NOUN
ejpam-6010	391	32	of	of	ADP
ejpam-6010	391	33	a	a	PRON
ejpam-6010	391	34	by	by	ADP
ejpam-6010	391	35	τ1τ2	τ1τ2	ADJ
ejpam-6010	391	36	-	-	ADJ
ejpam-6010	391	37	open	open	ADJ
ejpam-6010	391	38	sets	set	NOUN
ejpam-6010	391	39	of	of	ADP
ejpam-6010	391	40	x	x	VERB
ejpam-6010	391	41	is	be	AUX
ejpam-6010	391	42	refined	refine	VERB
ejpam-6010	391	43	by	by	ADP
ejpam-6010	391	44	a	a	DET
ejpam-6010	391	45	cover	cover	NOUN
ejpam-6010	391	46	of	of	ADP
ejpam-6010	391	47	a	a	PRON
ejpam-6010	391	48	which	which	PRON
ejpam-6010	391	49	consists	consist	VERB
ejpam-6010	391	50	of	of	ADP
ejpam-6010	391	51	τ1τ2	τ1τ2	ADJ
ejpam-6010	391	52	-	-	ADJ
ejpam-6010	391	53	open	open	ADJ
ejpam-6010	391	54	sets	set	NOUN
ejpam-6010	391	55	of	of	ADP
ejpam-6010	391	56	x	x	PUNCT
ejpam-6010	391	57	and	and	CCONJ
ejpam-6010	391	58	is	be	AUX
ejpam-6010	391	59	τ1τ2	τ1τ2	NOUN
ejpam-6010	391	60	-	-	ADJ
ejpam-6010	391	61	locally	locally	ADV
ejpam-6010	391	62	finite	finite	NOUN
ejpam-6010	391	63	in	in	ADP
ejpam-6010	391	64	x	x	PRON
ejpam-6010	391	65	;	;	PUNCT
ejpam-6010	391	66	(	(	PUNCT
ejpam-6010	391	67	2	2	X
ejpam-6010	391	68	)	)	PUNCT
ejpam-6010	391	69	τ1τ2	τ1τ2	NOUN
ejpam-6010	391	70	-	-	NOUN
ejpam-6010	391	71	regular	regular	ADJ
ejpam-6010	391	72	if	if	SCONJ
ejpam-6010	391	73	for	for	ADP
ejpam-6010	391	74	each	each	DET
ejpam-6010	391	75	x	x	SYM
ejpam-6010	391	76	∈	∈	PROPN
ejpam-6010	391	77	a	a	PRON
ejpam-6010	391	78	and	and	CCONJ
ejpam-6010	391	79	each	each	DET
ejpam-6010	391	80	τ1τ2	τ1τ2	ADJ
ejpam-6010	391	81	-	-	ADJ
ejpam-6010	391	82	open	open	ADJ
ejpam-6010	391	83	set	set	ADJ
ejpam-6010	391	84	u	u	NOUN
ejpam-6010	391	85	of	of	ADP
ejpam-6010	391	86	x	x	PUNCT
ejpam-6010	391	87	containing	contain	VERB
ejpam-6010	391	88	x	x	PRON
ejpam-6010	391	89	,	,	PUNCT
ejpam-6010	391	90	there	there	PRON
ejpam-6010	391	91	exists	exist	VERB
ejpam-6010	391	92	a	a	DET
ejpam-6010	391	93	τ1τ2	τ1τ2	NOUN
ejpam-6010	391	94	-	-	ADJ
ejpam-6010	391	95	open	open	ADJ
ejpam-6010	391	96	set	set	NOUN
ejpam-6010	391	97	v	v	NOUN
ejpam-6010	391	98	of	of	ADP
ejpam-6010	391	99	x	x	PUNCT
ejpam-6010	391	100	such	such	ADJ
ejpam-6010	391	101	that	that	SCONJ
ejpam-6010	391	102	x	x	SYM
ejpam-6010	391	103	∈	∈	NOUN
ejpam-6010	391	104	v	v	ADP
ejpam-6010	391	105	⊆	⊆	NUM
ejpam-6010	391	106	τ1τ2	τ1τ2	NOUN
ejpam-6010	391	107	-	-	NOUN
ejpam-6010	391	108	cl(v	cl(v	X
ejpam-6010	391	109	)	)	PUNCT
ejpam-6010	391	110	⊆	⊆	NUM
ejpam-6010	391	111	u	u	NOUN
ejpam-6010	391	112	.	.	PUNCT
ejpam-6010	392	1	lemma	lemma	PROPN
ejpam-6010	392	2	7	7	NUM
ejpam-6010	392	3	.	.	PUNCT
ejpam-6010	393	1	[	[	X
ejpam-6010	393	2	78	78	NUM
ejpam-6010	393	3	]	]	PUNCT
ejpam-6010	393	4	if	if	SCONJ
ejpam-6010	393	5	f	f	PROPN
ejpam-6010	393	6	:	:	PUNCT
ejpam-6010	393	7	(	(	PUNCT
ejpam-6010	393	8	x	x	NOUN
ejpam-6010	393	9	,	,	PUNCT
ejpam-6010	393	10	τ1	τ1	NOUN
ejpam-6010	393	11	,	,	PUNCT
ejpam-6010	393	12	τ2	τ2	NOUN
ejpam-6010	393	13	)	)	PUNCT
ejpam-6010	393	14	→	→	SYM
ejpam-6010	393	15	(	(	PUNCT
ejpam-6010	393	16	y	y	PROPN
ejpam-6010	393	17	,	,	PUNCT
ejpam-6010	393	18	σ1	σ1	PROPN
ejpam-6010	393	19	,	,	PUNCT
ejpam-6010	393	20	σ2	σ2	PROPN
ejpam-6010	393	21	)	)	PUNCT
ejpam-6010	393	22	is	be	AUX
ejpam-6010	393	23	a	a	DET
ejpam-6010	393	24	multifunction	multifunction	NOUN
ejpam-6010	393	25	such	such	ADJ
ejpam-6010	393	26	that	that	SCONJ
ejpam-6010	393	27	f	f	PROPN
ejpam-6010	393	28	(	(	PUNCT
ejpam-6010	393	29	x	x	X
ejpam-6010	393	30	)	)	PUNCT
ejpam-6010	393	31	is	be	AUX
ejpam-6010	393	32	σ1σ2regular	σ1σ2regular	PROPN
ejpam-6010	393	33	and	and	CCONJ
ejpam-6010	393	34	σ1σ2	σ1σ2	NOUN
ejpam-6010	393	35	-	-	ADJ
ejpam-6010	393	36	paracompact	paracompact	NOUN
ejpam-6010	393	37	for	for	ADP
ejpam-6010	393	38	each	each	DET
ejpam-6010	393	39	x	x	SYM
ejpam-6010	393	40	∈	∈	PROPN
ejpam-6010	393	41	x	x	NOUN
ejpam-6010	393	42	,	,	PUNCT
ejpam-6010	393	43	then	then	ADV
ejpam-6010	393	44	clf+	clf+	PROPN
ejpam-6010	393	45	⊛	⊛	X
ejpam-6010	393	46	(	(	PUNCT
ejpam-6010	393	47	v	v	NOUN
ejpam-6010	393	48	)	)	PUNCT
ejpam-6010	393	49	=	=	PUNCT
ejpam-6010	393	50	f+(v	f+(v	NOUN
ejpam-6010	393	51	)	)	PUNCT
ejpam-6010	393	52	for	for	ADP
ejpam-6010	393	53	each	each	DET
ejpam-6010	393	54	σ1σ2	σ1σ2	VERB
ejpam-6010	393	55	-	-	ADJ
ejpam-6010	393	56	open	open	ADJ
ejpam-6010	393	57	set	set	NOUN
ejpam-6010	393	58	v	v	NOUN
ejpam-6010	393	59	of	of	ADP
ejpam-6010	393	60	y	y	PROPN
ejpam-6010	393	61	.	.	PUNCT
ejpam-6010	394	1	lemma	lemma	PROPN
ejpam-6010	394	2	8	8	NUM
ejpam-6010	394	3	.	.	PUNCT
ejpam-6010	395	1	[	[	X
ejpam-6010	395	2	82	82	X
ejpam-6010	395	3	]	]	X
ejpam-6010	395	4	if	if	SCONJ
ejpam-6010	395	5	f	f	PROPN
ejpam-6010	395	6	:	:	PUNCT
ejpam-6010	395	7	(	(	PUNCT
ejpam-6010	395	8	x	x	NOUN
ejpam-6010	395	9	,	,	PUNCT
ejpam-6010	395	10	τ1	τ1	NOUN
ejpam-6010	395	11	,	,	PUNCT
ejpam-6010	395	12	τ2	τ2	NOUN
ejpam-6010	395	13	)	)	PUNCT
ejpam-6010	395	14	→	→	SYM
ejpam-6010	395	15	(	(	PUNCT
ejpam-6010	395	16	y	y	PROPN
ejpam-6010	395	17	,	,	PUNCT
ejpam-6010	395	18	σ1	σ1	PROPN
ejpam-6010	395	19	,	,	PUNCT
ejpam-6010	395	20	σ2	σ2	PROPN
ejpam-6010	395	21	)	)	PUNCT
ejpam-6010	395	22	is	be	AUX
ejpam-6010	395	23	a	a	DET
ejpam-6010	395	24	multifunction	multifunction	NOUN
ejpam-6010	395	25	such	such	ADJ
ejpam-6010	395	26	that	that	SCONJ
ejpam-6010	395	27	f	f	PROPN
ejpam-6010	395	28	(	(	PUNCT
ejpam-6010	395	29	x	x	X
ejpam-6010	395	30	)	)	PUNCT
ejpam-6010	395	31	is	be	AUX
ejpam-6010	395	32	σ1σ2regular	σ1σ2regular	PROPN
ejpam-6010	395	33	and	and	CCONJ
ejpam-6010	395	34	σ1σ2	σ1σ2	NOUN
ejpam-6010	395	35	-	-	ADJ
ejpam-6010	395	36	paracompact	paracompact	NOUN
ejpam-6010	395	37	for	for	ADP
ejpam-6010	395	38	each	each	DET
ejpam-6010	395	39	x	x	SYM
ejpam-6010	395	40	∈	∈	PROPN
ejpam-6010	395	41	x	x	NOUN
ejpam-6010	395	42	,	,	PUNCT
ejpam-6010	395	43	then	then	ADV
ejpam-6010	395	44	clf−	clf−	PROPN
ejpam-6010	395	45	⊛	⊛	ADJ
ejpam-6010	395	46	(	(	PUNCT
ejpam-6010	395	47	k	k	X
ejpam-6010	395	48	)	)	PUNCT
ejpam-6010	395	49	=	=	SYM
ejpam-6010	395	50	f−(k	f−(k	PROPN
ejpam-6010	395	51	)	)	PUNCT
ejpam-6010	395	52	for	for	ADP
ejpam-6010	395	53	each	each	DET
ejpam-6010	395	54	σ1σ2closed	σ1σ2close	VERB
ejpam-6010	395	55	set	set	NOUN
ejpam-6010	395	56	k	k	PROPN
ejpam-6010	395	57	of	of	ADP
ejpam-6010	395	58	y	y	PROPN
ejpam-6010	395	59	.	.	PUNCT
ejpam-6010	396	1	j.	j.	PROPN
ejpam-6010	396	2	khampakdee	khampakdee	PROPN
ejpam-6010	396	3	,	,	PUNCT
ejpam-6010	396	4	a.	a.	PROPN
ejpam-6010	396	5	sama	sama	PROPN
ejpam-6010	396	6	-	-	PUNCT
ejpam-6010	396	7	ae	ae	PROPN
ejpam-6010	396	8	,	,	PUNCT
ejpam-6010	396	9	c.	c.	PROPN
ejpam-6010	396	10	boonpok	boonpok	PROPN
ejpam-6010	396	11	/	/	SYM
ejpam-6010	396	12	eur	eur	PROPN
ejpam-6010	396	13	.	.	PUNCT
ejpam-6010	397	1	j.	j.	PROPN
ejpam-6010	397	2	pure	pure	PROPN
ejpam-6010	397	3	appl	appl	PROPN
ejpam-6010	397	4	.	.	PROPN
ejpam-6010	397	5	math	math	PROPN
ejpam-6010	397	6	,	,	PUNCT
ejpam-6010	397	7	18	18	NUM
ejpam-6010	397	8	(	(	PUNCT
ejpam-6010	397	9	2	2	NUM
ejpam-6010	397	10	)	)	PUNCT
ejpam-6010	397	11	(	(	PUNCT
ejpam-6010	397	12	2025	2025	NUM
ejpam-6010	397	13	)	)	PUNCT
ejpam-6010	397	14	,	,	PUNCT
ejpam-6010	397	15	6010	6010	NUM
ejpam-6010	397	16	15	15	NUM
ejpam-6010	397	17	of	of	ADP
ejpam-6010	397	18	19	19	NUM
ejpam-6010	397	19	lemma	lemma	PROPN
ejpam-6010	397	20	9	9	NUM
ejpam-6010	397	21	.	.	PUNCT
ejpam-6010	398	1	[	[	X
ejpam-6010	398	2	78	78	NUM
ejpam-6010	398	3	]	]	PUNCT
ejpam-6010	398	4	for	for	ADP
ejpam-6010	398	5	a	a	DET
ejpam-6010	398	6	multifunction	multifunction	NOUN
ejpam-6010	398	7	f	f	NOUN
ejpam-6010	398	8	:	:	PUNCT
ejpam-6010	398	9	(	(	PUNCT
ejpam-6010	398	10	x	x	NOUN
ejpam-6010	398	11	,	,	PUNCT
ejpam-6010	398	12	τ1	τ1	NOUN
ejpam-6010	398	13	,	,	PUNCT
ejpam-6010	398	14	τ2	τ2	NOUN
ejpam-6010	398	15	)	)	PUNCT
ejpam-6010	398	16	→	→	SYM
ejpam-6010	398	17	(	(	PUNCT
ejpam-6010	398	18	y	y	PROPN
ejpam-6010	398	19	,	,	PUNCT
ejpam-6010	398	20	σ1	σ1	PROPN
ejpam-6010	398	21	,	,	PUNCT
ejpam-6010	398	22	σ2	σ2	NOUN
ejpam-6010	398	23	)	)	PUNCT
ejpam-6010	398	24	,	,	PUNCT
ejpam-6010	398	25	clf	clf	PROPN
ejpam-6010	398	26	−	−	PROPN
ejpam-6010	398	27	⊛	⊛	NUM
ejpam-6010	398	28	(	(	PUNCT
ejpam-6010	398	29	v	v	NOUN
ejpam-6010	398	30	)	)	PUNCT
ejpam-6010	398	31	=	=	SYM
ejpam-6010	398	32	f−(v	f−(v	ADJ
ejpam-6010	398	33	)	)	PUNCT
ejpam-6010	398	34	for	for	ADP
ejpam-6010	398	35	each	each	DET
ejpam-6010	398	36	σ1σ2	σ1σ2	VERB
ejpam-6010	398	37	-	-	ADJ
ejpam-6010	398	38	open	open	ADJ
ejpam-6010	398	39	set	set	NOUN
ejpam-6010	398	40	v	v	NOUN
ejpam-6010	398	41	of	of	ADP
ejpam-6010	398	42	y	y	PROPN
ejpam-6010	398	43	.	.	PUNCT
ejpam-6010	399	1	lemma	lemma	PROPN
ejpam-6010	399	2	10	10	NUM
ejpam-6010	399	3	.	.	PUNCT
ejpam-6010	400	1	[	[	X
ejpam-6010	400	2	82	82	NUM
ejpam-6010	400	3	]	]	X
ejpam-6010	400	4	for	for	ADP
ejpam-6010	400	5	a	a	DET
ejpam-6010	400	6	multifunction	multifunction	NOUN
ejpam-6010	400	7	f	f	NOUN
ejpam-6010	400	8	:	:	PUNCT
ejpam-6010	400	9	(	(	PUNCT
ejpam-6010	400	10	x	x	NOUN
ejpam-6010	400	11	,	,	PUNCT
ejpam-6010	400	12	τ1	τ1	NOUN
ejpam-6010	400	13	,	,	PUNCT
ejpam-6010	400	14	τ2	τ2	NOUN
ejpam-6010	400	15	)	)	PUNCT
ejpam-6010	400	16	→	→	SYM
ejpam-6010	400	17	(	(	PUNCT
ejpam-6010	400	18	y	y	PROPN
ejpam-6010	400	19	,	,	PUNCT
ejpam-6010	400	20	σ1	σ1	PROPN
ejpam-6010	400	21	,	,	PUNCT
ejpam-6010	400	22	σ2	σ2	NOUN
ejpam-6010	400	23	)	)	PUNCT
ejpam-6010	400	24	,	,	PUNCT
ejpam-6010	400	25	clf	clf	PROPN
ejpam-6010	400	26	+	+	PROPN
ejpam-6010	400	27	⊛	⊛	PROPN
ejpam-6010	400	28	(	(	PUNCT
ejpam-6010	400	29	k	k	NOUN
ejpam-6010	400	30	)	)	PUNCT
ejpam-6010	400	31	=	=	SYM
ejpam-6010	400	32	f+(k	f+(k	X
ejpam-6010	400	33	)	)	PUNCT
ejpam-6010	400	34	for	for	ADP
ejpam-6010	400	35	each	each	DET
ejpam-6010	400	36	σ1σ2	σ1σ2	NUM
ejpam-6010	400	37	-	-	PUNCT
ejpam-6010	400	38	closed	closed	ADJ
ejpam-6010	400	39	set	set	NOUN
ejpam-6010	400	40	k	k	PROPN
ejpam-6010	400	41	of	of	ADP
ejpam-6010	400	42	y	y	PROPN
ejpam-6010	400	43	.	.	PUNCT
ejpam-6010	401	1	theorem	theorem	PROPN
ejpam-6010	401	2	19	19	NUM
ejpam-6010	401	3	.	.	PUNCT
ejpam-6010	402	1	a	a	DET
ejpam-6010	402	2	multifunction	multifunction	NOUN
ejpam-6010	402	3	f	f	NOUN
ejpam-6010	402	4	:	:	PUNCT
ejpam-6010	402	5	(	(	PUNCT
ejpam-6010	402	6	x	x	NOUN
ejpam-6010	402	7	,	,	PUNCT
ejpam-6010	402	8	τ1	τ1	NOUN
ejpam-6010	402	9	,	,	PUNCT
ejpam-6010	402	10	τ2	τ2	NOUN
ejpam-6010	402	11	)	)	PUNCT
ejpam-6010	402	12	→	→	SYM
ejpam-6010	402	13	(	(	PUNCT
ejpam-6010	402	14	y	y	PROPN
ejpam-6010	402	15	,	,	PUNCT
ejpam-6010	402	16	σ1	σ1	PROPN
ejpam-6010	402	17	,	,	PUNCT
ejpam-6010	402	18	σ2	σ2	PROPN
ejpam-6010	402	19	)	)	PUNCT
ejpam-6010	402	20	is	be	AUX
ejpam-6010	402	21	upper	upper	ADJ
ejpam-6010	402	22	almost	almost	ADV
ejpam-6010	402	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	402	24	,	,	PUNCT
ejpam-6010	402	25	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	402	26	if	if	SCONJ
ejpam-6010	402	27	and	and	CCONJ
ejpam-6010	402	28	only	only	ADV
ejpam-6010	402	29	if	if	SCONJ
ejpam-6010	402	30	clf⊛	clf⊛	PROPN
ejpam-6010	402	31	:	:	PUNCT
ejpam-6010	402	32	(	(	PUNCT
ejpam-6010	402	33	x	x	NOUN
ejpam-6010	402	34	,	,	PUNCT
ejpam-6010	402	35	τ1	τ1	NOUN
ejpam-6010	402	36	,	,	PUNCT
ejpam-6010	402	37	τ2	τ2	NOUN
ejpam-6010	402	38	)	)	PUNCT
ejpam-6010	402	39	→	→	SYM
ejpam-6010	402	40	(	(	PUNCT
ejpam-6010	402	41	y	y	PROPN
ejpam-6010	402	42	,	,	PUNCT
ejpam-6010	402	43	σ1	σ1	PROPN
ejpam-6010	402	44	,	,	PUNCT
ejpam-6010	402	45	σ2	σ2	PROPN
ejpam-6010	402	46	)	)	PUNCT
ejpam-6010	402	47	is	be	AUX
ejpam-6010	402	48	upper	upper	ADJ
ejpam-6010	402	49	almost	almost	ADV
ejpam-6010	402	50	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	402	51	,	,	PUNCT
ejpam-6010	402	52	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	402	53	.	.	PUNCT
ejpam-6010	403	1	proof	proof	NOUN
ejpam-6010	403	2	.	.	PUNCT
ejpam-6010	404	1	suppose	suppose	VERB
ejpam-6010	404	2	that	that	SCONJ
ejpam-6010	404	3	f	f	PROPN
ejpam-6010	404	4	is	be	AUX
ejpam-6010	404	5	upper	upper	ADJ
ejpam-6010	404	6	almost	almost	ADV
ejpam-6010	404	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	404	8	,	,	PUNCT
ejpam-6010	404	9	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	404	10	.	.	PUNCT
ejpam-6010	405	1	let	let	VERB
ejpam-6010	405	2	k	k	PRON
ejpam-6010	405	3	be	be	AUX
ejpam-6010	405	4	any	any	DET
ejpam-6010	405	5	(	(	PUNCT
ejpam-6010	405	6	σ1	σ1	NOUN
ejpam-6010	405	7	,	,	PUNCT
ejpam-6010	405	8	σ2)r	σ2)r	NOUN
ejpam-6010	405	9	-	-	PUNCT
ejpam-6010	405	10	closed	close	VERB
ejpam-6010	405	11	set	set	NOUN
ejpam-6010	405	12	of	of	ADP
ejpam-6010	405	13	y	y	PROPN
ejpam-6010	405	14	.	.	PUNCT
ejpam-6010	406	1	it	it	PRON
ejpam-6010	406	2	follows	follow	VERB
ejpam-6010	406	3	from	from	ADP
ejpam-6010	406	4	lemma	lemma	PROPN
ejpam-6010	406	5	9	9	NUM
ejpam-6010	406	6	,	,	PUNCT
ejpam-6010	406	7	lemma	lemma	PROPN
ejpam-6010	406	8	10	10	NUM
ejpam-6010	406	9	and	and	CCONJ
ejpam-6010	406	10	theorem	theorem	VERB
ejpam-6010	406	11	1	1	NUM
ejpam-6010	406	12	,	,	PUNCT
ejpam-6010	406	13	clf+	clf+	NOUN
ejpam-6010	406	14	⊛	⊛	X
ejpam-6010	406	15	(	(	PUNCT
ejpam-6010	406	16	k	k	X
ejpam-6010	406	17	)	)	PUNCT
ejpam-6010	406	18	=	=	SYM
ejpam-6010	406	19	f+(k	f+(k	X
ejpam-6010	406	20	)	)	PUNCT
ejpam-6010	406	21	is	be	AUX
ejpam-6010	406	22	τ1τ2	τ1τ2	NOUN
ejpam-6010	406	23	-	-	ADJ
ejpam-6010	406	24	open	open	ADJ
ejpam-6010	406	25	in	in	ADP
ejpam-6010	406	26	x.	x.	PROPN
ejpam-6010	406	27	thus	thus	ADV
ejpam-6010	406	28	,	,	PUNCT
ejpam-6010	406	29	clf⊛	clf⊛	PROPN
ejpam-6010	406	30	is	be	AUX
ejpam-6010	406	31	upper	upper	ADJ
ejpam-6010	406	32	almost	almost	ADV
ejpam-6010	406	33	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	406	34	,	,	PUNCT
ejpam-6010	406	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	406	36	.	.	PUNCT
ejpam-6010	407	1	conversely	conversely	ADV
ejpam-6010	407	2	,	,	PUNCT
ejpam-6010	407	3	suppose	suppose	VERB
ejpam-6010	407	4	that	that	SCONJ
ejpam-6010	407	5	clf⊛	clf⊛	PROPN
ejpam-6010	407	6	is	be	AUX
ejpam-6010	407	7	upper	upper	ADJ
ejpam-6010	407	8	almost	almost	ADV
ejpam-6010	407	9	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	407	10	,	,	PUNCT
ejpam-6010	407	11	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	407	12	.	.	PUNCT
ejpam-6010	408	1	let	let	VERB
ejpam-6010	408	2	k	k	PRON
ejpam-6010	408	3	be	be	AUX
ejpam-6010	408	4	any	any	DET
ejpam-6010	408	5	(	(	PUNCT
ejpam-6010	408	6	σ1	σ1	NOUN
ejpam-6010	408	7	,	,	PUNCT
ejpam-6010	408	8	σ2)r	σ2)r	NOUN
ejpam-6010	408	9	-	-	PUNCT
ejpam-6010	408	10	closed	close	VERB
ejpam-6010	408	11	set	set	NOUN
ejpam-6010	408	12	of	of	ADP
ejpam-6010	408	13	y	y	PROPN
ejpam-6010	408	14	.	.	PUNCT
ejpam-6010	409	1	by	by	ADP
ejpam-6010	409	2	lemma	lemma	PROPN
ejpam-6010	409	3	9	9	NUM
ejpam-6010	409	4	,	,	PUNCT
ejpam-6010	409	5	lemma	lemma	PROPN
ejpam-6010	409	6	10	10	NUM
ejpam-6010	409	7	and	and	CCONJ
ejpam-6010	409	8	theorem	theorem	VERB
ejpam-6010	409	9	1	1	NUM
ejpam-6010	409	10	,	,	PUNCT
ejpam-6010	409	11	f+(k	f+(k	NUM
ejpam-6010	409	12	)	)	PUNCT
ejpam-6010	409	13	=	=	PUNCT
ejpam-6010	409	14	clf+	clf+	NOUN
ejpam-6010	409	15	⊛	⊛	NUM
ejpam-6010	409	16	(	(	PUNCT
ejpam-6010	409	17	k	k	X
ejpam-6010	409	18	)	)	PUNCT
ejpam-6010	409	19	is	be	AUX
ejpam-6010	409	20	τ1τ2	τ1τ2	NOUN
ejpam-6010	409	21	-	-	ADJ
ejpam-6010	409	22	open	open	ADJ
ejpam-6010	409	23	in	in	ADP
ejpam-6010	409	24	x.	x.	PROPN
ejpam-6010	409	25	thus	thus	ADV
ejpam-6010	409	26	,	,	PUNCT
ejpam-6010	409	27	f	f	PROPN
ejpam-6010	409	28	is	be	AUX
ejpam-6010	409	29	upper	upper	ADJ
ejpam-6010	409	30	almost	almost	ADV
ejpam-6010	409	31	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	409	32	,	,	PUNCT
ejpam-6010	409	33	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	409	34	.	.	PUNCT
ejpam-6010	410	1	theorem	theorem	NOUN
ejpam-6010	410	2	20	20	NUM
ejpam-6010	410	3	.	.	PUNCT
ejpam-6010	411	1	let	let	VERB
ejpam-6010	411	2	f	f	NOUN
ejpam-6010	411	3	:	:	PUNCT
ejpam-6010	411	4	(	(	PUNCT
ejpam-6010	411	5	x	x	NOUN
ejpam-6010	411	6	,	,	PUNCT
ejpam-6010	411	7	τ1	τ1	NOUN
ejpam-6010	411	8	,	,	PUNCT
ejpam-6010	411	9	τ2	τ2	NOUN
ejpam-6010	411	10	)	)	PUNCT
ejpam-6010	411	11	→	→	SYM
ejpam-6010	411	12	(	(	PUNCT
ejpam-6010	411	13	y	y	PROPN
ejpam-6010	411	14	,	,	PUNCT
ejpam-6010	411	15	σ1	σ1	PROPN
ejpam-6010	411	16	,	,	PUNCT
ejpam-6010	411	17	σ2	σ2	PROPN
ejpam-6010	411	18	)	)	PUNCT
ejpam-6010	411	19	be	be	VERB
ejpam-6010	411	20	a	a	DET
ejpam-6010	411	21	multifunction	multifunction	NOUN
ejpam-6010	411	22	such	such	ADJ
ejpam-6010	411	23	that	that	SCONJ
ejpam-6010	411	24	f	f	PROPN
ejpam-6010	411	25	(	(	PUNCT
ejpam-6010	411	26	x	x	X
ejpam-6010	411	27	)	)	PUNCT
ejpam-6010	411	28	is	be	AUX
ejpam-6010	411	29	σ1σ2	σ1σ2	NOUN
ejpam-6010	411	30	-	-	ADJ
ejpam-6010	411	31	paracompact	paracompact	ADJ
ejpam-6010	411	32	and	and	CCONJ
ejpam-6010	411	33	σ1σ2	σ1σ2	NOUN
ejpam-6010	411	34	-	-	ADJ
ejpam-6010	411	35	regular	regular	ADJ
ejpam-6010	411	36	for	for	ADP
ejpam-6010	411	37	each	each	DET
ejpam-6010	411	38	x	x	SYM
ejpam-6010	411	39	∈	∈	PROPN
ejpam-6010	411	40	x.	x.	NOUN
ejpam-6010	411	41	then	then	ADV
ejpam-6010	411	42	,	,	PUNCT
ejpam-6010	411	43	f	f	PROPN
ejpam-6010	411	44	is	be	AUX
ejpam-6010	411	45	lower	low	ADJ
ejpam-6010	411	46	almost	almost	ADV
ejpam-6010	411	47	contra(τ1	contra(τ1	NOUN
ejpam-6010	411	48	,	,	PUNCT
ejpam-6010	411	49	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	412	1	if	if	SCONJ
ejpam-6010	412	2	and	and	CCONJ
ejpam-6010	412	3	only	only	ADV
ejpam-6010	412	4	if	if	SCONJ
ejpam-6010	412	5	clf⊛	clf⊛	PROPN
ejpam-6010	412	6	:	:	PUNCT
ejpam-6010	412	7	(	(	PUNCT
ejpam-6010	412	8	x	x	NOUN
ejpam-6010	412	9	,	,	PUNCT
ejpam-6010	412	10	τ1	τ1	NOUN
ejpam-6010	412	11	,	,	PUNCT
ejpam-6010	412	12	τ2	τ2	NOUN
ejpam-6010	412	13	)	)	PUNCT
ejpam-6010	412	14	→	→	SYM
ejpam-6010	412	15	(	(	PUNCT
ejpam-6010	412	16	y	y	PROPN
ejpam-6010	412	17	,	,	PUNCT
ejpam-6010	412	18	σ1	σ1	PROPN
ejpam-6010	412	19	,	,	PUNCT
ejpam-6010	412	20	σ2	σ2	NOUN
ejpam-6010	412	21	)	)	PUNCT
ejpam-6010	412	22	is	be	AUX
ejpam-6010	412	23	lower	low	ADJ
ejpam-6010	412	24	almost	almost	ADV
ejpam-6010	412	25	contra(τ1	contra(τ1	NOUN
ejpam-6010	412	26	,	,	PUNCT
ejpam-6010	412	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	412	28	.	.	PUNCT
ejpam-6010	413	1	proof	proof	NOUN
ejpam-6010	413	2	.	.	PUNCT
ejpam-6010	414	1	suppose	suppose	VERB
ejpam-6010	414	2	that	that	SCONJ
ejpam-6010	414	3	f	f	PROPN
ejpam-6010	414	4	is	be	AUX
ejpam-6010	414	5	lower	low	ADJ
ejpam-6010	414	6	almost	almost	ADV
ejpam-6010	414	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	414	8	,	,	PUNCT
ejpam-6010	414	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	414	10	.	.	PUNCT
ejpam-6010	415	1	let	let	VERB
ejpam-6010	415	2	k	k	PRON
ejpam-6010	415	3	be	be	AUX
ejpam-6010	415	4	any	any	DET
ejpam-6010	415	5	(	(	PUNCT
ejpam-6010	415	6	σ1	σ1	NOUN
ejpam-6010	415	7	,	,	PUNCT
ejpam-6010	415	8	σ2)r	σ2)r	NOUN
ejpam-6010	415	9	-	-	PUNCT
ejpam-6010	415	10	closed	close	VERB
ejpam-6010	415	11	set	set	NOUN
ejpam-6010	415	12	of	of	ADP
ejpam-6010	415	13	y	y	PROPN
ejpam-6010	415	14	.	.	PUNCT
ejpam-6010	416	1	by	by	ADP
ejpam-6010	416	2	lemma	lemma	PROPN
ejpam-6010	416	3	7	7	NUM
ejpam-6010	416	4	,	,	PUNCT
ejpam-6010	416	5	lemma	lemma	X
ejpam-6010	416	6	8	8	NUM
ejpam-6010	416	7	and	and	CCONJ
ejpam-6010	416	8	theorem	theorem	VERB
ejpam-6010	416	9	2	2	NUM
ejpam-6010	416	10	,	,	PUNCT
ejpam-6010	416	11	clf−	clf−	PROPN
ejpam-6010	416	12	⊛	⊛	X
ejpam-6010	416	13	(	(	PUNCT
ejpam-6010	416	14	k	k	X
ejpam-6010	416	15	)	)	PUNCT
ejpam-6010	416	16	=	=	SYM
ejpam-6010	416	17	f−(k	f−(k	PROPN
ejpam-6010	416	18	)	)	PUNCT
ejpam-6010	416	19	is	be	AUX
ejpam-6010	416	20	τ1τ2	τ1τ2	NOUN
ejpam-6010	416	21	-	-	ADJ
ejpam-6010	416	22	open	open	ADJ
ejpam-6010	416	23	in	in	ADP
ejpam-6010	416	24	x.	x.	NOUN
ejpam-6010	416	25	this	this	PRON
ejpam-6010	416	26	shows	show	VERB
ejpam-6010	416	27	that	that	SCONJ
ejpam-6010	416	28	clf⊛	clf⊛	PROPN
ejpam-6010	416	29	is	be	AUX
ejpam-6010	416	30	lower	low	ADJ
ejpam-6010	416	31	almost	almost	ADV
ejpam-6010	416	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	416	33	,	,	PUNCT
ejpam-6010	416	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	416	35	.	.	PUNCT
ejpam-6010	417	1	conversely	conversely	ADV
ejpam-6010	417	2	,	,	PUNCT
ejpam-6010	417	3	suppose	suppose	VERB
ejpam-6010	417	4	that	that	SCONJ
ejpam-6010	417	5	clf⊛	clf⊛	PROPN
ejpam-6010	417	6	is	be	AUX
ejpam-6010	417	7	lower	low	ADJ
ejpam-6010	417	8	almost	almost	ADV
ejpam-6010	417	9	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	417	10	,	,	PUNCT
ejpam-6010	417	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	417	12	.	.	PUNCT
ejpam-6010	418	1	let	let	VERB
ejpam-6010	418	2	k	k	PRON
ejpam-6010	418	3	be	be	AUX
ejpam-6010	418	4	any	any	DET
ejpam-6010	418	5	(	(	PUNCT
ejpam-6010	418	6	σ1	σ1	NOUN
ejpam-6010	418	7	,	,	PUNCT
ejpam-6010	418	8	σ2)r	σ2)r	NOUN
ejpam-6010	418	9	-	-	PUNCT
ejpam-6010	418	10	closed	close	VERB
ejpam-6010	418	11	set	set	NOUN
ejpam-6010	418	12	of	of	ADP
ejpam-6010	418	13	y	y	PROPN
ejpam-6010	418	14	.	.	PUNCT
ejpam-6010	419	1	by	by	ADP
ejpam-6010	419	2	lemma	lemma	PROPN
ejpam-6010	419	3	7	7	NUM
ejpam-6010	419	4	,	,	PUNCT
ejpam-6010	419	5	lemma	lemma	X
ejpam-6010	419	6	8	8	NUM
ejpam-6010	419	7	and	and	CCONJ
ejpam-6010	419	8	theorem	theorem	VERB
ejpam-6010	419	9	2	2	NUM
ejpam-6010	419	10	,	,	PUNCT
ejpam-6010	419	11	f−(k	f−(k	PROPN
ejpam-6010	419	12	)	)	PUNCT
ejpam-6010	419	13	=	=	SYM
ejpam-6010	419	14	clf−	clf−	PROPN
ejpam-6010	419	15	⊛	⊛	X
ejpam-6010	419	16	(	(	PUNCT
ejpam-6010	419	17	k	k	X
ejpam-6010	419	18	)	)	PUNCT
ejpam-6010	419	19	is	be	AUX
ejpam-6010	419	20	τ1τ2	τ1τ2	NOUN
ejpam-6010	419	21	-	-	ADJ
ejpam-6010	419	22	open	open	ADJ
ejpam-6010	419	23	in	in	ADP
ejpam-6010	419	24	x.	x.	NOUN
ejpam-6010	419	25	this	this	PRON
ejpam-6010	419	26	shows	show	VERB
ejpam-6010	419	27	that	that	SCONJ
ejpam-6010	419	28	f	f	PROPN
ejpam-6010	419	29	is	be	AUX
ejpam-6010	419	30	lower	low	ADJ
ejpam-6010	419	31	almost	almost	ADV
ejpam-6010	419	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	419	33	,	,	PUNCT
ejpam-6010	419	34	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6010	419	35	.	.	PUNCT
ejpam-6010	420	1	acknowledgements	acknowledgement	NOUN
ejpam-6010	420	2	this	this	DET
ejpam-6010	420	3	research	research	NOUN
ejpam-6010	420	4	project	project	NOUN
ejpam-6010	420	5	was	be	AUX
ejpam-6010	420	6	financially	financially	ADV
ejpam-6010	420	7	supported	support	VERB
ejpam-6010	420	8	by	by	ADP
ejpam-6010	420	9	mahasarakham	mahasarakham	PROPN
ejpam-6010	420	10	university	university	PROPN
ejpam-6010	420	11	.	.	PUNCT
ejpam-6010	421	1	references	reference	NOUN
ejpam-6010	421	2	[	[	X
ejpam-6010	421	3	1	1	NUM
ejpam-6010	421	4	]	]	PUNCT
ejpam-6010	421	5	c.	c.	PROPN
ejpam-6010	421	6	boonpok	boonpok	PROPN
ejpam-6010	421	7	and	and	CCONJ
ejpam-6010	421	8	j.	j.	PROPN
ejpam-6010	421	9	khampakdee	khampakdee	PROPN
ejpam-6010	421	10	.	.	PUNCT
ejpam-6010	422	1	(	(	PUNCT
ejpam-6010	422	2	λ	λ	NOUN
ejpam-6010	422	3	,	,	PUNCT
ejpam-6010	422	4	sp)-open	sp)-open	ADJ
ejpam-6010	422	5	sets	set	NOUN
ejpam-6010	422	6	in	in	ADP
ejpam-6010	422	7	topological	topological	ADJ
ejpam-6010	422	8	spaces	space	NOUN
ejpam-6010	422	9	.	.	PUNCT
ejpam-6010	423	1	european	european	ADJ
ejpam-6010	423	2	journal	journal	PROPN
ejpam-6010	423	3	of	of	ADP
ejpam-6010	423	4	pure	pure	ADJ
ejpam-6010	423	5	and	and	CCONJ
ejpam-6010	423	6	applied	applied	ADJ
ejpam-6010	423	7	mathematics	mathematic	NOUN
ejpam-6010	423	8	,	,	PUNCT
ejpam-6010	423	9	15(2):572–588	15(2):572–588	NUM
ejpam-6010	423	10	,	,	PUNCT
ejpam-6010	423	11	2022	2022	NUM
ejpam-6010	423	12	.	.	PUNCT
ejpam-6010	424	1	[	[	X
ejpam-6010	424	2	2	2	NUM
ejpam-6010	424	3	]	]	PUNCT
ejpam-6010	424	4	c.	c.	PROPN
ejpam-6010	424	5	viriyapong	viriyapong	PROPN
ejpam-6010	424	6	and	and	CCONJ
ejpam-6010	424	7	c.	c.	PROPN
ejpam-6010	424	8	boonpok	boonpok	PROPN
ejpam-6010	424	9	.	.	PUNCT
ejpam-6010	425	1	(	(	PUNCT
ejpam-6010	425	2	λ	λ	X
ejpam-6010	425	3	,	,	PUNCT
ejpam-6010	425	4	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	425	5	functions	function	NOUN
ejpam-6010	425	6	.	.	PUNCT
ejpam-6010	426	1	wseas	wseas	VERB
ejpam-6010	426	2	transactions	transaction	NOUN
ejpam-6010	426	3	on	on	ADP
ejpam-6010	426	4	mathematics	mathematic	NOUN
ejpam-6010	426	5	,	,	PUNCT
ejpam-6010	426	6	21:380–385	21:380–385	NUM
ejpam-6010	426	7	,	,	PUNCT
ejpam-6010	426	8	2022	2022	NUM
ejpam-6010	426	9	.	.	PUNCT
ejpam-6010	427	1	[	[	X
ejpam-6010	427	2	3	3	X
ejpam-6010	427	3	]	]	PUNCT
ejpam-6010	427	4	t.	t.	NOUN
ejpam-6010	427	5	dungthaisong	dungthaisong	PROPN
ejpam-6010	427	6	,	,	PUNCT
ejpam-6010	427	7	c.	c.	PROPN
ejpam-6010	427	8	boonpok	boonpok	PROPN
ejpam-6010	427	9	,	,	PUNCT
ejpam-6010	427	10	and	and	CCONJ
ejpam-6010	427	11	c.	c.	PROPN
ejpam-6010	427	12	viriyapong	viriyapong	PROPN
ejpam-6010	427	13	.	.	PUNCT
ejpam-6010	428	1	generalized	generalize	VERB
ejpam-6010	428	2	closed	close	VERB
ejpam-6010	428	3	sets	set	NOUN
ejpam-6010	428	4	in	in	ADP
ejpam-6010	428	5	bigeneralized	bigeneralize	VERB
ejpam-6010	428	6	topological	topological	ADJ
ejpam-6010	428	7	spaces	space	NOUN
ejpam-6010	428	8	.	.	PUNCT
ejpam-6010	429	1	international	international	ADJ
ejpam-6010	429	2	journal	journal	PROPN
ejpam-6010	429	3	of	of	ADP
ejpam-6010	429	4	mathematical	mathematical	ADJ
ejpam-6010	429	5	analysis	analysis	NOUN
ejpam-6010	429	6	,	,	PUNCT
ejpam-6010	429	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-6010	429	8	,	,	PUNCT
ejpam-6010	429	9	2011	2011	NUM
ejpam-6010	429	10	.	.	PUNCT
ejpam-6010	430	1	[	[	X
ejpam-6010	430	2	4	4	X
ejpam-6010	430	3	]	]	PUNCT
ejpam-6010	430	4	t.	t.	PROPN
ejpam-6010	430	5	duangphui	duangphui	PROPN
ejpam-6010	430	6	,	,	PUNCT
ejpam-6010	430	7	c.	c.	PROPN
ejpam-6010	430	8	boonpok	boonpok	PROPN
ejpam-6010	430	9	,	,	PUNCT
ejpam-6010	430	10	and	and	CCONJ
ejpam-6010	430	11	c.	c.	PROPN
ejpam-6010	430	12	viriyapong	viriyapong	PROPN
ejpam-6010	430	13	.	.	PUNCT
ejpam-6010	431	1	continuous	continuous	ADJ
ejpam-6010	431	2	functions	function	NOUN
ejpam-6010	431	3	on	on	ADP
ejpam-6010	431	4	bigeneralized	bigeneralize	VERB
ejpam-6010	431	5	topological	topological	ADJ
ejpam-6010	431	6	spaces	space	NOUN
ejpam-6010	431	7	.	.	PUNCT
ejpam-6010	432	1	international	international	ADJ
ejpam-6010	432	2	journal	journal	PROPN
ejpam-6010	432	3	of	of	ADP
ejpam-6010	432	4	mathematical	mathematical	ADJ
ejpam-6010	432	5	analysis	analysis	NOUN
ejpam-6010	432	6	,	,	PUNCT
ejpam-6010	432	7	5(24):1165	5(24):1165	NUM
ejpam-6010	432	8	–	–	PUNCT
ejpam-6010	432	9	1174	1174	NUM
ejpam-6010	432	10	,	,	PUNCT
ejpam-6010	432	11	2011	2011	NUM
ejpam-6010	432	12	.	.	PUNCT
ejpam-6010	433	1	j.	j.	PROPN
ejpam-6010	433	2	khampakdee	khampakdee	PROPN
ejpam-6010	433	3	,	,	PUNCT
ejpam-6010	433	4	a.	a.	PROPN
ejpam-6010	433	5	sama	sama	PROPN
ejpam-6010	433	6	-	-	PUNCT
ejpam-6010	433	7	ae	ae	PROPN
ejpam-6010	433	8	,	,	PUNCT
ejpam-6010	433	9	c.	c.	PROPN
ejpam-6010	433	10	boonpok	boonpok	PROPN
ejpam-6010	433	11	/	/	SYM
ejpam-6010	433	12	eur	eur	PROPN
ejpam-6010	433	13	.	.	PUNCT
ejpam-6010	434	1	j.	j.	PROPN
ejpam-6010	434	2	pure	pure	PROPN
ejpam-6010	434	3	appl	appl	PROPN
ejpam-6010	434	4	.	.	PROPN
ejpam-6010	434	5	math	math	PROPN
ejpam-6010	434	6	,	,	PUNCT
ejpam-6010	434	7	18	18	NUM
ejpam-6010	434	8	(	(	PUNCT
ejpam-6010	434	9	2	2	NUM
ejpam-6010	434	10	)	)	PUNCT
ejpam-6010	434	11	(	(	PUNCT
ejpam-6010	434	12	2025	2025	NUM
ejpam-6010	434	13	)	)	PUNCT
ejpam-6010	434	14	,	,	PUNCT
ejpam-6010	434	15	6010	6010	NUM
ejpam-6010	434	16	16	16	NUM
ejpam-6010	434	17	of	of	ADP
ejpam-6010	434	18	19	19	NUM
ejpam-6010	434	19	[	[	SYM
ejpam-6010	434	20	5	5	NUM
ejpam-6010	434	21	]	]	X
ejpam-6010	434	22	n.	n.	NOUN
ejpam-6010	434	23	srisarakham	srisarakham	PROPN
ejpam-6010	434	24	and	and	CCONJ
ejpam-6010	434	25	c.	c.	PROPN
ejpam-6010	434	26	boonpok	boonpok	PROPN
ejpam-6010	434	27	.	.	PUNCT
ejpam-6010	435	1	almost	almost	ADV
ejpam-6010	435	2	(	(	PUNCT
ejpam-6010	435	3	λ	λ	NOUN
ejpam-6010	435	4	,	,	PUNCT
ejpam-6010	435	5	p)-continuous	p)-continuous	ADJ
ejpam-6010	435	6	functions	function	NOUN
ejpam-6010	435	7	.	.	PUNCT
ejpam-6010	436	1	international	international	ADJ
ejpam-6010	436	2	journal	journal	PROPN
ejpam-6010	436	3	of	of	ADP
ejpam-6010	436	4	mathematics	mathematic	NOUN
ejpam-6010	436	5	and	and	CCONJ
ejpam-6010	436	6	computer	computer	NOUN
ejpam-6010	436	7	science	science	NOUN
ejpam-6010	436	8	,	,	PUNCT
ejpam-6010	436	9	18(2):255–259	18(2):255–259	NUM
ejpam-6010	436	10	,	,	PUNCT
ejpam-6010	436	11	2023	2023	NUM
ejpam-6010	436	12	.	.	PUNCT
ejpam-6010	437	1	[	[	X
ejpam-6010	437	2	6	6	NUM
ejpam-6010	437	3	]	]	PUNCT
ejpam-6010	437	4	m.	m.	NOUN
ejpam-6010	437	5	thongmoon	thongmoon	NOUN
ejpam-6010	437	6	and	and	CCONJ
ejpam-6010	437	7	c.	c.	PROPN
ejpam-6010	437	8	boonpok	boonpok	PROPN
ejpam-6010	437	9	.	.	PUNCT
ejpam-6010	438	1	strongly	strongly	ADV
ejpam-6010	438	2	θ(λ	θ(λ	PROPN
ejpam-6010	438	3	,	,	PUNCT
ejpam-6010	438	4	p)-continuous	p)-continuous	ADJ
ejpam-6010	438	5	functions	function	NOUN
ejpam-6010	438	6	.	.	PUNCT
ejpam-6010	439	1	international	international	ADJ
ejpam-6010	439	2	journal	journal	PROPN
ejpam-6010	439	3	of	of	ADP
ejpam-6010	439	4	mathematics	mathematic	NOUN
ejpam-6010	439	5	and	and	CCONJ
ejpam-6010	439	6	computer	computer	NOUN
ejpam-6010	439	7	science	science	NOUN
ejpam-6010	439	8	,	,	PUNCT
ejpam-6010	439	9	19(2):475–479	19(2):475–479	PROPN
ejpam-6010	439	10	,	,	PUNCT
ejpam-6010	439	11	2024	2024	NUM
ejpam-6010	439	12	.	.	PUNCT
ejpam-6010	440	1	[	[	X
ejpam-6010	440	2	7	7	X
ejpam-6010	440	3	]	]	X
ejpam-6010	440	4	c.	c.	PROPN
ejpam-6010	440	5	boonpok	boonpok	PROPN
ejpam-6010	440	6	and	and	CCONJ
ejpam-6010	440	7	j.	j.	PROPN
ejpam-6010	440	8	khampakdee	khampakdee	PROPN
ejpam-6010	440	9	.	.	PUNCT
ejpam-6010	441	1	almost	almost	ADV
ejpam-6010	441	2	strong	strong	ADJ
ejpam-6010	441	3	θ(λ	θ(λ	PROPN
ejpam-6010	441	4	,	,	PUNCT
ejpam-6010	441	5	p)-continuity	p)-continuity	NOUN
ejpam-6010	441	6	for	for	ADP
ejpam-6010	441	7	functions	function	NOUN
ejpam-6010	441	8	.	.	PUNCT
ejpam-6010	442	1	european	european	ADJ
ejpam-6010	442	2	journal	journal	PROPN
ejpam-6010	442	3	of	of	ADP
ejpam-6010	442	4	pure	pure	ADJ
ejpam-6010	442	5	and	and	CCONJ
ejpam-6010	442	6	applied	applied	ADJ
ejpam-6010	442	7	mathematics	mathematic	NOUN
ejpam-6010	442	8	,	,	PUNCT
ejpam-6010	442	9	17(1):300–309	17(1):300–309	PROPN
ejpam-6010	442	10	,	,	PUNCT
ejpam-6010	442	11	2024	2024	NUM
ejpam-6010	442	12	.	.	PUNCT
ejpam-6010	443	1	[	[	X
ejpam-6010	443	2	8	8	NUM
ejpam-6010	443	3	]	]	X
ejpam-6010	443	4	p.	p.	NOUN
ejpam-6010	443	5	pue	pue	NOUN
ejpam-6010	443	6	-	-	PUNCT
ejpam-6010	443	7	on	on	ADP
ejpam-6010	443	8	and	and	CCONJ
ejpam-6010	443	9	c.	c.	PROPN
ejpam-6010	443	10	boonpok	boonpok	PROPN
ejpam-6010	443	11	.	.	PUNCT
ejpam-6010	444	1	θ(λ	θ(λ	PROPN
ejpam-6010	444	2	,	,	PUNCT
ejpam-6010	444	3	p)-continuity	p)-continuity	NOUN
ejpam-6010	444	4	for	for	ADP
ejpam-6010	444	5	functions	function	NOUN
ejpam-6010	444	6	.	.	PUNCT
ejpam-6010	445	1	international	international	ADJ
ejpam-6010	445	2	journal	journal	NOUN
ejpam-6010	445	3	of	of	ADP
ejpam-6010	445	4	mathematics	mathematic	NOUN
ejpam-6010	445	5	and	and	CCONJ
ejpam-6010	445	6	computer	computer	NOUN
ejpam-6010	445	7	science	science	NOUN
ejpam-6010	445	8	,	,	PUNCT
ejpam-6010	445	9	19(2):491–495	19(2):491–495	NUM
ejpam-6010	445	10	,	,	PUNCT
ejpam-6010	445	11	2024	2024	NUM
ejpam-6010	445	12	.	.	PUNCT
ejpam-6010	446	1	[	[	X
ejpam-6010	446	2	9	9	NUM
ejpam-6010	446	3	]	]	PUNCT
ejpam-6010	446	4	c.	c.	NOUN
ejpam-6010	446	5	boonpok	boonpok	PROPN
ejpam-6010	446	6	and	and	CCONJ
ejpam-6010	446	7	n.	n.	PROPN
ejpam-6010	446	8	srisarakham	srisarakham	PROPN
ejpam-6010	446	9	.	.	PUNCT
ejpam-6010	447	1	weak	weak	ADJ
ejpam-6010	447	2	forms	form	NOUN
ejpam-6010	447	3	of	of	ADP
ejpam-6010	447	4	(	(	PUNCT
ejpam-6010	447	5	λ	λ	PROPN
ejpam-6010	447	6	,	,	PUNCT
ejpam-6010	447	7	b)-open	b)-open	VERB
ejpam-6010	447	8	sets	set	NOUN
ejpam-6010	447	9	and	and	CCONJ
ejpam-6010	447	10	weak	weak	ADJ
ejpam-6010	447	11	(	(	PUNCT
ejpam-6010	447	12	λ	λ	NOUN
ejpam-6010	447	13	,	,	PUNCT
ejpam-6010	447	14	b)continuity	b)continuity	NOUN
ejpam-6010	447	15	.	.	PUNCT
ejpam-6010	448	1	european	european	PROPN
ejpam-6010	448	2	journal	journal	PROPN
ejpam-6010	448	3	of	of	ADP
ejpam-6010	448	4	pure	pure	ADJ
ejpam-6010	448	5	and	and	CCONJ
ejpam-6010	448	6	applied	applied	ADJ
ejpam-6010	448	7	mathematics	mathematic	NOUN
ejpam-6010	448	8	,	,	PUNCT
ejpam-6010	448	9	16(1):29–43	16(1):29–43	NUM
ejpam-6010	448	10	,	,	PUNCT
ejpam-6010	448	11	2023	2023	NUM
ejpam-6010	448	12	.	.	PUNCT
ejpam-6010	449	1	[	[	X
ejpam-6010	449	2	10	10	NUM
ejpam-6010	449	3	]	]	X
ejpam-6010	449	4	c.	c.	PROPN
ejpam-6010	449	5	boonpok	boonpok	PROPN
ejpam-6010	449	6	.	.	PUNCT
ejpam-6010	450	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-6010	450	2	.	.	PUNCT
ejpam-6010	451	1	mathematica	mathematica	PROPN
ejpam-6010	451	2	,	,	PUNCT
ejpam-6010	451	3	65(1):31–42	65(1):31–42	NUM
ejpam-6010	451	4	,	,	PUNCT
ejpam-6010	451	5	2023	2023	NUM
ejpam-6010	451	6	.	.	PUNCT
ejpam-6010	452	1	[	[	X
ejpam-6010	452	2	11	11	NUM
ejpam-6010	452	3	]	]	PUNCT
ejpam-6010	452	4	c.	c.	PROPN
ejpam-6010	452	5	boonpok	boonpok	PROPN
ejpam-6010	452	6	.	.	PUNCT
ejpam-6010	453	1	on	on	ADP
ejpam-6010	453	2	some	some	DET
ejpam-6010	453	3	closed	closed	ADJ
ejpam-6010	453	4	sets	set	NOUN
ejpam-6010	453	5	and	and	CCONJ
ejpam-6010	453	6	low	low	ADJ
ejpam-6010	453	7	separation	separation	NOUN
ejpam-6010	453	8	axioms	axiom	NOUN
ejpam-6010	453	9	via	via	ADP
ejpam-6010	453	10	topological	topological	ADJ
ejpam-6010	453	11	ideals	ideal	NOUN
ejpam-6010	453	12	.	.	PUNCT
ejpam-6010	454	1	european	european	ADJ
ejpam-6010	454	2	journal	journal	PROPN
ejpam-6010	454	3	of	of	ADP
ejpam-6010	454	4	pure	pure	ADJ
ejpam-6010	454	5	and	and	CCONJ
ejpam-6010	454	6	applied	applied	ADJ
ejpam-6010	454	7	mathematics	mathematic	NOUN
ejpam-6010	454	8	,	,	PUNCT
ejpam-6010	454	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-6010	454	10	,	,	PUNCT
ejpam-6010	454	11	2022	2022	NUM
ejpam-6010	454	12	.	.	PUNCT
ejpam-6010	455	1	[	[	X
ejpam-6010	455	2	12	12	NUM
ejpam-6010	455	3	]	]	PUNCT
ejpam-6010	455	4	c.	c.	PROPN
ejpam-6010	455	5	boonpok	boonpok	PROPN
ejpam-6010	455	6	.	.	PUNCT
ejpam-6010	456	1	on	on	ADP
ejpam-6010	456	2	some	some	DET
ejpam-6010	456	3	spaces	space	NOUN
ejpam-6010	456	4	via	via	ADP
ejpam-6010	456	5	topological	topological	ADJ
ejpam-6010	456	6	ideals	ideal	NOUN
ejpam-6010	456	7	.	.	PUNCT
ejpam-6010	457	1	open	open	ADJ
ejpam-6010	457	2	mathematics	mathematic	NOUN
ejpam-6010	457	3	,	,	PUNCT
ejpam-6010	457	4	21:20230118	21:20230118	NUM
ejpam-6010	457	5	,	,	PUNCT
ejpam-6010	457	6	2023	2023	NUM
ejpam-6010	457	7	.	.	PUNCT
ejpam-6010	458	1	[	[	X
ejpam-6010	458	2	13	13	NUM
ejpam-6010	458	3	]	]	PUNCT
ejpam-6010	458	4	c.	c.	PROPN
ejpam-6010	458	5	boonpok	boonpok	PROPN
ejpam-6010	458	6	.	.	PUNCT
ejpam-6010	459	1	on	on	ADP
ejpam-6010	459	2	characterizations	characterization	NOUN
ejpam-6010	459	3	of	of	ADP
ejpam-6010	459	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-6010	459	5	ideal	ideal	ADJ
ejpam-6010	459	6	topological	topological	ADJ
ejpam-6010	459	7	spaces	space	NOUN
ejpam-6010	459	8	.	.	PUNCT
ejpam-6010	460	1	journal	journal	NOUN
ejpam-6010	460	2	of	of	ADP
ejpam-6010	460	3	mathematics	mathematic	NOUN
ejpam-6010	460	4	,	,	PUNCT
ejpam-6010	460	5	2020:9387601	2020:9387601	NUM
ejpam-6010	460	6	,	,	PUNCT
ejpam-6010	460	7	2020	2020	NUM
ejpam-6010	460	8	.	.	PUNCT
ejpam-6010	461	1	[	[	X
ejpam-6010	461	2	14	14	NUM
ejpam-6010	461	3	]	]	X
ejpam-6010	461	4	c.	c.	PROPN
ejpam-6010	461	5	boonpok	boonpok	PROPN
ejpam-6010	461	6	.	.	PUNCT
ejpam-6010	462	1	almost	almost	ADV
ejpam-6010	462	2	(	(	PUNCT
ejpam-6010	462	3	g	g	NOUN
ejpam-6010	462	4	,	,	PUNCT
ejpam-6010	462	5	m)-continuous	m)-continuous	ADJ
ejpam-6010	462	6	functions	function	NOUN
ejpam-6010	462	7	.	.	PUNCT
ejpam-6010	463	1	international	international	ADJ
ejpam-6010	463	2	journal	journal	PROPN
ejpam-6010	463	3	of	of	ADP
ejpam-6010	463	4	mathematical	mathematical	ADJ
ejpam-6010	463	5	analysis	analysis	NOUN
ejpam-6010	463	6	,	,	PUNCT
ejpam-6010	463	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-6010	463	8	,	,	PUNCT
ejpam-6010	463	9	2010	2010	NUM
ejpam-6010	463	10	.	.	PUNCT
ejpam-6010	464	1	[	[	X
ejpam-6010	464	2	15	15	NUM
ejpam-6010	464	3	]	]	X
ejpam-6010	464	4	c.	c.	PROPN
ejpam-6010	464	5	boonpok	boonpok	PROPN
ejpam-6010	464	6	.	.	PUNCT
ejpam-6010	465	1	m	m	VERB
ejpam-6010	465	2	-continuous	-continuous	ADJ
ejpam-6010	465	3	functions	function	NOUN
ejpam-6010	465	4	in	in	ADP
ejpam-6010	465	5	biminimal	biminimal	NOUN
ejpam-6010	465	6	structure	structure	NOUN
ejpam-6010	465	7	spaces	space	NOUN
ejpam-6010	465	8	.	.	PUNCT
ejpam-6010	466	1	far	far	PROPN
ejpam-6010	466	2	east	east	PROPN
ejpam-6010	466	3	journal	journal	PROPN
ejpam-6010	466	4	of	of	ADP
ejpam-6010	466	5	mathematical	mathematical	ADJ
ejpam-6010	466	6	sciences	science	NOUN
ejpam-6010	466	7	,	,	PUNCT
ejpam-6010	466	8	43(1):41–58	43(1):41–58	NUM
ejpam-6010	466	9	,	,	PUNCT
ejpam-6010	466	10	2010	2010	NUM
ejpam-6010	466	11	.	.	PUNCT
ejpam-6010	467	1	[	[	X
ejpam-6010	467	2	16	16	NUM
ejpam-6010	467	3	]	]	X
ejpam-6010	467	4	c.	c.	PROPN
ejpam-6010	467	5	boonpok	boonpok	PROPN
ejpam-6010	467	6	and	and	CCONJ
ejpam-6010	467	7	n.	n.	PROPN
ejpam-6010	467	8	srisarakham	srisarakham	PROPN
ejpam-6010	467	9	.	.	PUNCT
ejpam-6010	468	1	(	(	PUNCT
ejpam-6010	468	2	τ1	τ1	NOUN
ejpam-6010	468	3	,	,	PUNCT
ejpam-6010	468	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	468	5	for	for	ADP
ejpam-6010	468	6	functions	function	NOUN
ejpam-6010	468	7	.	.	PUNCT
ejpam-6010	469	1	asia	asia	PROPN
ejpam-6010	469	2	pacific	pacific	PROPN
ejpam-6010	469	3	journal	journal	PROPN
ejpam-6010	469	4	of	of	ADP
ejpam-6010	469	5	mathematics	mathematic	NOUN
ejpam-6010	469	6	,	,	PUNCT
ejpam-6010	469	7	11:21	11:21	NUM
ejpam-6010	469	8	,	,	PUNCT
ejpam-6010	469	9	2024	2024	NUM
ejpam-6010	469	10	.	.	PUNCT
ejpam-6010	470	1	[	[	X
ejpam-6010	470	2	17	17	NUM
ejpam-6010	470	3	]	]	X
ejpam-6010	470	4	c.	c.	PROPN
ejpam-6010	470	5	boonpok	boonpok	PROPN
ejpam-6010	470	6	and	and	CCONJ
ejpam-6010	470	7	p.	p.	NOUN
ejpam-6010	470	8	pue	pue	NOUN
ejpam-6010	470	9	-	-	PUNCT
ejpam-6010	470	10	on	on	ADP
ejpam-6010	470	11	.	.	PUNCT
ejpam-6010	471	1	characterizations	characterization	NOUN
ejpam-6010	471	2	of	of	ADP
ejpam-6010	471	3	almost	almost	ADV
ejpam-6010	471	4	(	(	PUNCT
ejpam-6010	471	5	τ1	τ1	NOUN
ejpam-6010	471	6	,	,	PUNCT
ejpam-6010	471	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	471	8	functions	function	NOUN
ejpam-6010	471	9	.	.	PUNCT
ejpam-6010	472	1	international	international	ADJ
ejpam-6010	472	2	journal	journal	NOUN
ejpam-6010	472	3	of	of	ADP
ejpam-6010	472	4	analysis	analysis	NOUN
ejpam-6010	472	5	and	and	CCONJ
ejpam-6010	472	6	applications	application	NOUN
ejpam-6010	472	7	,	,	PUNCT
ejpam-6010	472	8	22:33	22:33	NUM
ejpam-6010	472	9	,	,	PUNCT
ejpam-6010	472	10	2024	2024	NUM
ejpam-6010	472	11	.	.	PUNCT
ejpam-6010	473	1	[	[	X
ejpam-6010	473	2	18	18	NUM
ejpam-6010	473	3	]	]	PUNCT
ejpam-6010	473	4	c.	c.	PROPN
ejpam-6010	473	5	boonpok	boonpok	PROPN
ejpam-6010	473	6	and	and	CCONJ
ejpam-6010	473	7	c.	c.	PROPN
ejpam-6010	473	8	klanarong	klanarong	PROPN
ejpam-6010	473	9	.	.	PUNCT
ejpam-6010	474	1	on	on	ADP
ejpam-6010	474	2	weakly	weakly	ADJ
ejpam-6010	474	3	(	(	PUNCT
ejpam-6010	474	4	τ1	τ1	NOUN
ejpam-6010	474	5	,	,	PUNCT
ejpam-6010	474	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	474	7	functions	function	NOUN
ejpam-6010	474	8	.	.	PUNCT
ejpam-6010	475	1	european	european	ADJ
ejpam-6010	475	2	journal	journal	PROPN
ejpam-6010	475	3	of	of	ADP
ejpam-6010	475	4	pure	pure	ADJ
ejpam-6010	475	5	and	and	CCONJ
ejpam-6010	475	6	applied	applied	ADJ
ejpam-6010	475	7	mathematics	mathematic	NOUN
ejpam-6010	475	8	,	,	PUNCT
ejpam-6010	475	9	17(1):416–425	17(1):416–425	NUM
ejpam-6010	475	10	,	,	PUNCT
ejpam-6010	475	11	2024	2024	NUM
ejpam-6010	475	12	.	.	PUNCT
ejpam-6010	476	1	[	[	X
ejpam-6010	476	2	19	19	NUM
ejpam-6010	476	3	]	]	X
ejpam-6010	476	4	p.	p.	NOUN
ejpam-6010	476	5	pue	pue	NOUN
ejpam-6010	476	6	-	-	PUNCT
ejpam-6010	476	7	on	on	ADP
ejpam-6010	476	8	,	,	PUNCT
ejpam-6010	476	9	s.	s.	PROPN
ejpam-6010	476	10	sompong	sompong	PROPN
ejpam-6010	476	11	,	,	PUNCT
ejpam-6010	476	12	and	and	CCONJ
ejpam-6010	476	13	c.	c.	PROPN
ejpam-6010	476	14	boonpok	boonpok	PROPN
ejpam-6010	476	15	.	.	PUNCT
ejpam-6010	477	1	slightly	slightly	ADV
ejpam-6010	477	2	(	(	PUNCT
ejpam-6010	477	3	τ1	τ1	NOUN
ejpam-6010	477	4	,	,	PUNCT
ejpam-6010	477	5	τ2)s	τ2)s	ADJ
ejpam-6010	477	6	-	-	PUNCT
ejpam-6010	477	7	continuous	continuous	ADJ
ejpam-6010	477	8	functions	function	NOUN
ejpam-6010	477	9	.	.	PUNCT
ejpam-6010	478	1	international	international	ADJ
ejpam-6010	478	2	journal	journal	NOUN
ejpam-6010	478	3	of	of	ADP
ejpam-6010	478	4	mathematics	mathematic	NOUN
ejpam-6010	478	5	and	and	CCONJ
ejpam-6010	478	6	computer	computer	NOUN
ejpam-6010	478	7	science	science	NOUN
ejpam-6010	478	8	,	,	PUNCT
ejpam-6010	478	9	20(1):217–221	20(1):217–221	PROPN
ejpam-6010	478	10	,	,	PUNCT
ejpam-6010	478	11	2025	2025	NUM
ejpam-6010	478	12	.	.	PUNCT
ejpam-6010	479	1	[	[	X
ejpam-6010	479	2	20	20	NUM
ejpam-6010	479	3	]	]	PUNCT
ejpam-6010	479	4	b.	b.	PROPN
ejpam-6010	479	5	kong	kong	PROPN
ejpam-6010	479	6	-	-	PUNCT
ejpam-6010	479	7	ied	ied	PROPN
ejpam-6010	479	8	,	,	PUNCT
ejpam-6010	479	9	s.	s.	PROPN
ejpam-6010	479	10	sompong	sompong	PROPN
ejpam-6010	479	11	,	,	PUNCT
ejpam-6010	479	12	and	and	CCONJ
ejpam-6010	479	13	c.	c.	PROPN
ejpam-6010	479	14	boonpok	boonpok	PROPN
ejpam-6010	479	15	.	.	PUNCT
ejpam-6010	480	1	almost	almost	ADV
ejpam-6010	480	2	quasi	quasi	X
ejpam-6010	480	3	(	(	PUNCT
ejpam-6010	480	4	τ1	τ1	NOUN
ejpam-6010	480	5	,	,	PUNCT
ejpam-6010	480	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	480	7	functions	function	NOUN
ejpam-6010	480	8	.	.	PUNCT
ejpam-6010	481	1	asia	asia	PROPN
ejpam-6010	481	2	pacific	pacific	PROPN
ejpam-6010	481	3	journal	journal	PROPN
ejpam-6010	481	4	of	of	ADP
ejpam-6010	481	5	mathematics	mathematic	NOUN
ejpam-6010	481	6	,	,	PUNCT
ejpam-6010	481	7	11:64	11:64	NUM
ejpam-6010	481	8	,	,	PUNCT
ejpam-6010	481	9	2024	2024	NUM
ejpam-6010	481	10	.	.	PUNCT
ejpam-6010	482	1	[	[	X
ejpam-6010	482	2	21	21	NUM
ejpam-6010	482	3	]	]	PUNCT
ejpam-6010	482	4	m.	m.	NOUN
ejpam-6010	482	5	chiangpradit	chiangpradit	NOUN
ejpam-6010	482	6	,	,	PUNCT
ejpam-6010	482	7	s.	s.	PROPN
ejpam-6010	482	8	sompong	sompong	PROPN
ejpam-6010	482	9	,	,	PUNCT
ejpam-6010	482	10	and	and	CCONJ
ejpam-6010	482	11	c.	c.	PROPN
ejpam-6010	482	12	boonpok	boonpok	PROPN
ejpam-6010	482	13	.	.	PUNCT
ejpam-6010	483	1	weakly	weakly	ADJ
ejpam-6010	483	2	quasi	quasi	NOUN
ejpam-6010	483	3	(	(	PUNCT
ejpam-6010	483	4	τ1	τ1	PROPN
ejpam-6010	483	5	,	,	PUNCT
ejpam-6010	483	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	483	7	functions	function	NOUN
ejpam-6010	483	8	.	.	PUNCT
ejpam-6010	484	1	international	international	ADJ
ejpam-6010	484	2	journal	journal	NOUN
ejpam-6010	484	3	of	of	ADP
ejpam-6010	484	4	analysis	analysis	NOUN
ejpam-6010	484	5	and	and	CCONJ
ejpam-6010	484	6	applications	application	NOUN
ejpam-6010	484	7	,	,	PUNCT
ejpam-6010	484	8	22:125	22:125	NUM
ejpam-6010	484	9	,	,	PUNCT
ejpam-6010	484	10	2024	2024	NUM
ejpam-6010	484	11	.	.	PUNCT
ejpam-6010	485	1	[	[	X
ejpam-6010	485	2	22	22	NUM
ejpam-6010	485	3	]	]	PUNCT
ejpam-6010	485	4	m.	m.	NOUN
ejpam-6010	485	5	thongmoon	thongmoon	NOUN
ejpam-6010	485	6	,	,	PUNCT
ejpam-6010	485	7	s.	s.	PROPN
ejpam-6010	485	8	sompong	sompong	PROPN
ejpam-6010	485	9	,	,	PUNCT
ejpam-6010	485	10	and	and	CCONJ
ejpam-6010	485	11	c.	c.	PROPN
ejpam-6010	485	12	boonpok	boonpok	PROPN
ejpam-6010	485	13	.	.	PUNCT
ejpam-6010	486	1	rarely	rarely	ADV
ejpam-6010	486	2	(	(	PUNCT
ejpam-6010	486	3	τ1	τ1	NOUN
ejpam-6010	486	4	,	,	PUNCT
ejpam-6010	486	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	486	6	functions	function	NOUN
ejpam-6010	486	7	.	.	PUNCT
ejpam-6010	487	1	international	international	ADJ
ejpam-6010	487	2	journal	journal	NOUN
ejpam-6010	487	3	of	of	ADP
ejpam-6010	487	4	mathematics	mathematic	NOUN
ejpam-6010	487	5	and	and	CCONJ
ejpam-6010	487	6	computer	computer	NOUN
ejpam-6010	487	7	science	science	NOUN
ejpam-6010	487	8	,	,	PUNCT
ejpam-6010	487	9	20(1):423–427	20(1):423–427	NUM
ejpam-6010	487	10	,	,	PUNCT
ejpam-6010	487	11	2025	2025	NUM
ejpam-6010	487	12	.	.	PUNCT
ejpam-6010	488	1	[	[	X
ejpam-6010	488	2	23	23	NUM
ejpam-6010	488	3	]	]	X
ejpam-6010	488	4	n.	n.	PROPN
ejpam-6010	488	5	srisarakham	srisarakham	PROPN
ejpam-6010	488	6	,	,	PUNCT
ejpam-6010	488	7	a.	a.	PROPN
ejpam-6010	488	8	sama	sama	PROPN
ejpam-6010	488	9	-	-	PUNCT
ejpam-6010	488	10	ae	ae	PROPN
ejpam-6010	488	11	,	,	PUNCT
ejpam-6010	488	12	and	and	CCONJ
ejpam-6010	488	13	c.	c.	PROPN
ejpam-6010	488	14	boonpok	boonpok	PROPN
ejpam-6010	488	15	.	.	PUNCT
ejpam-6010	489	1	characterizations	characterization	NOUN
ejpam-6010	489	2	of	of	ADP
ejpam-6010	489	3	faintly	faintly	ADV
ejpam-6010	489	4	(	(	PUNCT
ejpam-6010	489	5	τ1	τ1	PROPN
ejpam-6010	489	6	,	,	PUNCT
ejpam-6010	489	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	489	8	functions	function	NOUN
ejpam-6010	489	9	.	.	PUNCT
ejpam-6010	490	1	european	european	ADJ
ejpam-6010	490	2	journal	journal	PROPN
ejpam-6010	490	3	of	of	ADP
ejpam-6010	490	4	pure	pure	ADJ
ejpam-6010	490	5	and	and	CCONJ
ejpam-6010	490	6	applied	applied	ADJ
ejpam-6010	490	7	mathematics	mathematic	NOUN
ejpam-6010	490	8	,	,	PUNCT
ejpam-6010	490	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-6010	490	10	,	,	PUNCT
ejpam-6010	490	11	2024	2024	NUM
ejpam-6010	490	12	.	.	PUNCT
ejpam-6010	491	1	[	[	X
ejpam-6010	491	2	24	24	NUM
ejpam-6010	491	3	]	]	PUNCT
ejpam-6010	491	4	c.	c.	NOUN
ejpam-6010	491	5	prachanpol	prachanpol	NOUN
ejpam-6010	491	6	,	,	PUNCT
ejpam-6010	491	7	c.	c.	PROPN
ejpam-6010	491	8	boonpok	boonpok	PROPN
ejpam-6010	491	9	,	,	PUNCT
ejpam-6010	491	10	and	and	CCONJ
ejpam-6010	491	11	c.	c.	PROPN
ejpam-6010	491	12	viriyapong	viriyapong	PROPN
ejpam-6010	491	13	.	.	PUNCT
ejpam-6010	492	1	δ(τ1	δ(τ1	PROPN
ejpam-6010	492	2	,	,	PUNCT
ejpam-6010	492	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	492	4	functions	function	NOUN
ejpam-6010	492	5	.	.	PUNCT
ejpam-6010	493	1	european	european	ADJ
ejpam-6010	493	2	journal	journal	PROPN
ejpam-6010	493	3	of	of	ADP
ejpam-6010	493	4	pure	pure	ADJ
ejpam-6010	493	5	and	and	CCONJ
ejpam-6010	493	6	applied	applied	ADJ
ejpam-6010	493	7	mathematics	mathematic	NOUN
ejpam-6010	493	8	,	,	PUNCT
ejpam-6010	493	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-6010	493	10	,	,	PUNCT
ejpam-6010	493	11	2024	2024	NUM
ejpam-6010	493	12	.	.	PUNCT
ejpam-6010	494	1	[	[	X
ejpam-6010	494	2	25	25	NUM
ejpam-6010	494	3	]	]	X
ejpam-6010	494	4	n.	n.	NOUN
ejpam-6010	494	5	srisarakham	srisarakham	PROPN
ejpam-6010	494	6	,	,	PUNCT
ejpam-6010	494	7	s.	s.	PROPN
ejpam-6010	494	8	sompong	sompong	PROPN
ejpam-6010	494	9	,	,	PUNCT
ejpam-6010	494	10	and	and	CCONJ
ejpam-6010	494	11	c.	c.	PROPN
ejpam-6010	494	12	boonpok	boonpok	PROPN
ejpam-6010	494	13	.	.	PUNCT
ejpam-6010	495	1	quasi	quasi	PROPN
ejpam-6010	495	2	θ(τ1	θ(τ1	PROPN
ejpam-6010	495	3	,	,	PUNCT
ejpam-6010	495	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	495	5	functions	function	NOUN
ejpam-6010	495	6	.	.	PUNCT
ejpam-6010	496	1	european	european	ADJ
ejpam-6010	496	2	journal	journal	PROPN
ejpam-6010	496	3	of	of	ADP
ejpam-6010	496	4	pure	pure	ADJ
ejpam-6010	496	5	and	and	CCONJ
ejpam-6010	496	6	applied	applied	ADJ
ejpam-6010	496	7	mathematics	mathematic	NOUN
ejpam-6010	496	8	,	,	PUNCT
ejpam-6010	496	9	18(1):5722	18(1):5722	NUM
ejpam-6010	496	10	,	,	PUNCT
ejpam-6010	496	11	2025	2025	NUM
ejpam-6010	496	12	.	.	PUNCT
ejpam-6010	497	1	[	[	X
ejpam-6010	497	2	26	26	NUM
ejpam-6010	497	3	]	]	X
ejpam-6010	497	4	j.	j.	PROPN
ejpam-6010	497	5	khampakdee	khampakdee	PROPN
ejpam-6010	497	6	,	,	PUNCT
ejpam-6010	497	7	s.	s.	PROPN
ejpam-6010	497	8	sompong	sompong	PROPN
ejpam-6010	497	9	,	,	PUNCT
ejpam-6010	497	10	and	and	CCONJ
ejpam-6010	497	11	c.	c.	PROPN
ejpam-6010	497	12	boonpok	boonpok	PROPN
ejpam-6010	497	13	.	.	PUNCT
ejpam-6010	498	1	almost	almost	ADV
ejpam-6010	498	2	weakly	weakly	ADJ
ejpam-6010	498	3	(	(	PUNCT
ejpam-6010	498	4	τ1	τ1	NOUN
ejpam-6010	498	5	,	,	PUNCT
ejpam-6010	498	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	498	7	j.	j.	PROPN
ejpam-6010	498	8	khampakdee	khampakdee	PROPN
ejpam-6010	498	9	,	,	PUNCT
ejpam-6010	498	10	a.	a.	PROPN
ejpam-6010	498	11	sama	sama	PROPN
ejpam-6010	498	12	-	-	PUNCT
ejpam-6010	498	13	ae	ae	PROPN
ejpam-6010	498	14	,	,	PUNCT
ejpam-6010	498	15	c.	c.	PROPN
ejpam-6010	498	16	boonpok	boonpok	PROPN
ejpam-6010	498	17	/	/	SYM
ejpam-6010	498	18	eur	eur	PROPN
ejpam-6010	498	19	.	.	PUNCT
ejpam-6010	499	1	j.	j.	PROPN
ejpam-6010	499	2	pure	pure	PROPN
ejpam-6010	499	3	appl	appl	PROPN
ejpam-6010	499	4	.	.	PROPN
ejpam-6010	499	5	math	math	PROPN
ejpam-6010	499	6	,	,	PUNCT
ejpam-6010	499	7	18	18	NUM
ejpam-6010	499	8	(	(	PUNCT
ejpam-6010	499	9	2	2	NUM
ejpam-6010	499	10	)	)	PUNCT
ejpam-6010	499	11	(	(	PUNCT
ejpam-6010	499	12	2025	2025	NUM
ejpam-6010	499	13	)	)	PUNCT
ejpam-6010	499	14	,	,	PUNCT
ejpam-6010	499	15	6010	6010	NUM
ejpam-6010	499	16	17	17	NUM
ejpam-6010	499	17	of	of	ADP
ejpam-6010	499	18	19	19	NUM
ejpam-6010	499	19	functions	function	NOUN
ejpam-6010	499	20	.	.	PUNCT
ejpam-6010	500	1	european	european	ADJ
ejpam-6010	500	2	journal	journal	PROPN
ejpam-6010	500	3	of	of	ADP
ejpam-6010	500	4	pure	pure	ADJ
ejpam-6010	500	5	and	and	CCONJ
ejpam-6010	500	6	applied	applied	ADJ
ejpam-6010	500	7	mathematics	mathematic	NOUN
ejpam-6010	500	8	,	,	PUNCT
ejpam-6010	500	9	18(1):5721	18(1):5721	NUM
ejpam-6010	500	10	,	,	PUNCT
ejpam-6010	500	11	2025	2025	NUM
ejpam-6010	500	12	.	.	PUNCT
ejpam-6010	501	1	[	[	X
ejpam-6010	501	2	27	27	NUM
ejpam-6010	501	3	]	]	X
ejpam-6010	501	4	b.	b.	PROPN
ejpam-6010	501	5	kong	kong	PROPN
ejpam-6010	501	6	-	-	PUNCT
ejpam-6010	501	7	ied	ied	PROPN
ejpam-6010	501	8	,	,	PUNCT
ejpam-6010	501	9	a.	a.	PROPN
ejpam-6010	501	10	sama	sama	PROPN
ejpam-6010	501	11	-	-	PUNCT
ejpam-6010	501	12	ae	ae	PROPN
ejpam-6010	501	13	,	,	PUNCT
ejpam-6010	501	14	and	and	CCONJ
ejpam-6010	501	15	c.	c.	PROPN
ejpam-6010	501	16	boonpok	boonpok	PROPN
ejpam-6010	501	17	.	.	PUNCT
ejpam-6010	502	1	almost	almost	ADV
ejpam-6010	502	2	nearly	nearly	ADV
ejpam-6010	502	3	(	(	PUNCT
ejpam-6010	502	4	τ1	τ1	NOUN
ejpam-6010	502	5	,	,	PUNCT
ejpam-6010	502	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	502	7	functions	function	NOUN
ejpam-6010	502	8	.	.	PUNCT
ejpam-6010	503	1	international	international	ADJ
ejpam-6010	503	2	journal	journal	NOUN
ejpam-6010	503	3	of	of	ADP
ejpam-6010	503	4	analysis	analysis	NOUN
ejpam-6010	503	5	and	and	CCONJ
ejpam-6010	503	6	applications	application	NOUN
ejpam-6010	503	7	,	,	PUNCT
ejpam-6010	503	8	23:14	23:14	NUM
ejpam-6010	503	9	,	,	PUNCT
ejpam-6010	503	10	2025	2025	NUM
ejpam-6010	503	11	.	.	PUNCT
ejpam-6010	504	1	[	[	X
ejpam-6010	504	2	28	28	NUM
ejpam-6010	504	3	]	]	X
ejpam-6010	504	4	j.	j.	PROPN
ejpam-6010	504	5	dontchev	dontchev	PROPN
ejpam-6010	504	6	.	.	PUNCT
ejpam-6010	505	1	contra	contra	ADJ
ejpam-6010	505	2	-	-	ADJ
ejpam-6010	505	3	continuous	continuous	ADJ
ejpam-6010	505	4	functions	function	NOUN
ejpam-6010	505	5	and	and	CCONJ
ejpam-6010	505	6	strongly	strongly	ADV
ejpam-6010	505	7	s	s	NOUN
ejpam-6010	505	8	-	-	PUNCT
ejpam-6010	505	9	closed	closed	ADJ
ejpam-6010	505	10	spaces	space	NOUN
ejpam-6010	505	11	.	.	PUNCT
ejpam-6010	506	1	international	international	ADJ
ejpam-6010	506	2	journal	journal	PROPN
ejpam-6010	506	3	of	of	ADP
ejpam-6010	506	4	mathematics	mathematics	PROPN
ejpam-6010	506	5	and	and	CCONJ
ejpam-6010	506	6	mathematical	mathematical	ADJ
ejpam-6010	506	7	sciences	science	NOUN
ejpam-6010	506	8	,	,	PUNCT
ejpam-6010	506	9	19:303–310	19:303–310	PROPN
ejpam-6010	506	10	,	,	PUNCT
ejpam-6010	506	11	1966	1966	NUM
ejpam-6010	506	12	.	.	PUNCT
ejpam-6010	507	1	[	[	X
ejpam-6010	507	2	29	29	NUM
ejpam-6010	507	3	]	]	X
ejpam-6010	507	4	j.	j.	PROPN
ejpam-6010	507	5	dontchev	dontchev	PROPN
ejpam-6010	507	6	and	and	CCONJ
ejpam-6010	507	7	t.	t.	PROPN
ejpam-6010	507	8	noiri	noiri	PROPN
ejpam-6010	507	9	.	.	PUNCT
ejpam-6010	508	1	contra	contra	ADJ
ejpam-6010	508	2	-	-	ADJ
ejpam-6010	508	3	semicontinuous	semicontinuous	ADJ
ejpam-6010	508	4	functions	function	NOUN
ejpam-6010	508	5	.	.	PUNCT
ejpam-6010	509	1	mathematica	mathematica	PROPN
ejpam-6010	509	2	pannonica	pannonica	PROPN
ejpam-6010	509	3	,	,	PUNCT
ejpam-6010	509	4	10:159–168	10:159–168	NOUN
ejpam-6010	509	5	,	,	PUNCT
ejpam-6010	509	6	1999	1999	NUM
ejpam-6010	509	7	.	.	PUNCT
ejpam-6010	510	1	[	[	X
ejpam-6010	510	2	30	30	NUM
ejpam-6010	510	3	]	]	X
ejpam-6010	510	4	s.	s.	PROPN
ejpam-6010	510	5	jafari	jafari	PROPN
ejpam-6010	510	6	and	and	CCONJ
ejpam-6010	510	7	t.	t.	PROPN
ejpam-6010	510	8	noiri	noiri	PROPN
ejpam-6010	510	9	.	.	PUNCT
ejpam-6010	511	1	on	on	ADP
ejpam-6010	511	2	contra	contra	ADJ
ejpam-6010	511	3	-	-	ADJ
ejpam-6010	511	4	precontinuous	precontinuous	ADJ
ejpam-6010	511	5	functions	function	NOUN
ejpam-6010	511	6	.	.	PUNCT
ejpam-6010	512	1	bulletin	bulletin	NOUN
ejpam-6010	512	2	of	of	ADP
ejpam-6010	512	3	the	the	DET
ejpam-6010	512	4	malaysian	malaysian	PROPN
ejpam-6010	512	5	mathematical	mathematical	PROPN
ejpam-6010	512	6	sciences	sciences	PROPN
ejpam-6010	512	7	society	society	NOUN
ejpam-6010	512	8	,	,	PUNCT
ejpam-6010	512	9	25:115–128	25:115–128	PROPN
ejpam-6010	512	10	,	,	PUNCT
ejpam-6010	512	11	2002	2002	NUM
ejpam-6010	512	12	.	.	PUNCT
ejpam-6010	513	1	[	[	X
ejpam-6010	513	2	31	31	NUM
ejpam-6010	513	3	]	]	PUNCT
ejpam-6010	513	4	e.	e.	PROPN
ejpam-6010	513	5	ekici	ekici	PROPN
ejpam-6010	513	6	.	.	PUNCT
ejpam-6010	514	1	almost	almost	ADV
ejpam-6010	514	2	contra	contra	ADJ
ejpam-6010	514	3	-	-	ADJ
ejpam-6010	514	4	precontinuous	precontinuous	ADJ
ejpam-6010	514	5	functions	function	NOUN
ejpam-6010	514	6	.	.	PUNCT
ejpam-6010	515	1	bulletin	bulletin	NOUN
ejpam-6010	515	2	of	of	ADP
ejpam-6010	515	3	the	the	DET
ejpam-6010	515	4	malaysian	malaysian	PROPN
ejpam-6010	515	5	mathematical	mathematical	PROPN
ejpam-6010	515	6	sciences	sciences	PROPN
ejpam-6010	515	7	society	society	NOUN
ejpam-6010	515	8	,	,	PUNCT
ejpam-6010	515	9	27:53–65	27:53–65	NUM
ejpam-6010	515	10	,	,	PUNCT
ejpam-6010	515	11	2004	2004	NUM
ejpam-6010	515	12	.	.	PUNCT
ejpam-6010	516	1	[	[	X
ejpam-6010	516	2	32	32	NUM
ejpam-6010	516	3	]	]	PUNCT
ejpam-6010	516	4	j.	j.	PROPN
ejpam-6010	516	5	dontchev	dontchev	PROPN
ejpam-6010	516	6	,	,	PUNCT
ejpam-6010	516	7	m.	m.	NOUN
ejpam-6010	516	8	ganster	ganster	NOUN
ejpam-6010	516	9	,	,	PUNCT
ejpam-6010	516	10	and	and	CCONJ
ejpam-6010	516	11	i.	i.	PROPN
ejpam-6010	516	12	reilly	reilly	PROPN
ejpam-6010	516	13	.	.	PUNCT
ejpam-6010	517	1	more	more	ADV
ejpam-6010	517	2	on	on	ADP
ejpam-6010	517	3	almost	almost	ADV
ejpam-6010	517	4	s	s	NOUN
ejpam-6010	517	5	-	-	NOUN
ejpam-6010	517	6	continuity	continuity	NOUN
ejpam-6010	517	7	.	.	PUNCT
ejpam-6010	518	1	indian	indian	ADJ
ejpam-6010	518	2	journal	journal	PROPN
ejpam-6010	518	3	of	of	ADP
ejpam-6010	518	4	mathematics	mathematics	PROPN
ejpam-6010	518	5	,	,	PUNCT
ejpam-6010	518	6	41:139–146	41:139–146	PROPN
ejpam-6010	518	7	,	,	PUNCT
ejpam-6010	518	8	1999	1999	NUM
ejpam-6010	518	9	.	.	PUNCT
ejpam-6010	519	1	[	[	X
ejpam-6010	519	2	33	33	NUM
ejpam-6010	519	3	]	]	PUNCT
ejpam-6010	519	4	t.	t.	PROPN
ejpam-6010	519	5	noiri	noiri	PROPN
ejpam-6010	519	6	,	,	PUNCT
ejpam-6010	519	7	b.	b.	PROPN
ejpam-6010	519	8	ahmad	ahmad	PROPN
ejpam-6010	519	9	,	,	PUNCT
ejpam-6010	519	10	and	and	CCONJ
ejpam-6010	519	11	m.	m.	PROPN
ejpam-6010	519	12	khan	khan	PROPN
ejpam-6010	519	13	.	.	PUNCT
ejpam-6010	520	1	almost	almost	ADV
ejpam-6010	520	2	s	s	NOUN
ejpam-6010	520	3	-	-	PUNCT
ejpam-6010	520	4	continuous	continuous	ADJ
ejpam-6010	520	5	functions	function	NOUN
ejpam-6010	520	6	.	.	PUNCT
ejpam-6010	521	1	kyungpook	kyungpook	PROPN
ejpam-6010	521	2	mathematical	mathematical	PROPN
ejpam-6010	521	3	journal	journal	PROPN
ejpam-6010	521	4	,	,	PUNCT
ejpam-6010	521	5	35:311–322	35:311–322	PROPN
ejpam-6010	521	6	,	,	PUNCT
ejpam-6010	521	7	1995	1995	NUM
ejpam-6010	521	8	.	.	PUNCT
ejpam-6010	522	1	[	[	X
ejpam-6010	522	2	34	34	NUM
ejpam-6010	522	3	]	]	PUNCT
ejpam-6010	522	4	t.	t.	PROPN
ejpam-6010	522	5	noiri	noiri	PROPN
ejpam-6010	522	6	.	.	PUNCT
ejpam-6010	523	1	super	super	ADJ
ejpam-6010	523	2	-	-	NOUN
ejpam-6010	523	3	continuity	continuity	NOUN
ejpam-6010	523	4	and	and	CCONJ
ejpam-6010	523	5	some	some	DET
ejpam-6010	523	6	strong	strong	ADJ
ejpam-6010	523	7	forms	form	NOUN
ejpam-6010	523	8	of	of	ADP
ejpam-6010	523	9	continuity	continuity	NOUN
ejpam-6010	523	10	.	.	PUNCT
ejpam-6010	524	1	indian	indian	ADJ
ejpam-6010	524	2	journal	journal	PROPN
ejpam-6010	524	3	of	of	ADP
ejpam-6010	524	4	pure	pure	ADJ
ejpam-6010	524	5	and	and	CCONJ
ejpam-6010	524	6	applied	applied	ADJ
ejpam-6010	524	7	mathematics	mathematic	NOUN
ejpam-6010	524	8	,	,	PUNCT
ejpam-6010	524	9	15:241–250	15:241–250	NUM
ejpam-6010	524	10	,	,	PUNCT
ejpam-6010	524	11	1984	1984	NUM
ejpam-6010	524	12	.	.	PUNCT
ejpam-6010	525	1	[	[	X
ejpam-6010	525	2	35	35	NUM
ejpam-6010	525	3	]	]	X
ejpam-6010	525	4	e.	e.	PROPN
ejpam-6010	525	5	ekici	ekici	PROPN
ejpam-6010	525	6	,	,	PUNCT
ejpam-6010	525	7	s.	s.	PROPN
ejpam-6010	525	8	jafari	jafari	PROPN
ejpam-6010	525	9	,	,	PUNCT
ejpam-6010	525	10	and	and	CCONJ
ejpam-6010	525	11	t.	t.	PROPN
ejpam-6010	525	12	noiri	noiri	PROPN
ejpam-6010	525	13	.	.	PUNCT
ejpam-6010	526	1	on	on	ADP
ejpam-6010	526	2	upper	upper	ADJ
ejpam-6010	526	3	and	and	CCONJ
ejpam-6010	526	4	lower	low	ADJ
ejpam-6010	526	5	contra	contra	ADJ
ejpam-6010	526	6	-	-	ADJ
ejpam-6010	526	7	continuous	continuous	ADJ
ejpam-6010	526	8	multifunctions	multifunction	NOUN
ejpam-6010	526	9	.	.	PUNCT
ejpam-6010	527	1	analele	analele	ADP
ejpam-6010	527	2	ştiinţifice	ştiinţifice	PROPN
ejpam-6010	527	3	ale	ale	NOUN
ejpam-6010	527	4	universităţii	universităţii	AUX
ejpam-6010	527	5	al	al	PROPN
ejpam-6010	527	6	.	.	PROPN
ejpam-6010	527	7	i.	i.	PROPN
ejpam-6010	527	8	cuza	cuza	AUX
ejpam-6010	527	9	din	din	PROPN
ejpam-6010	527	10	iaşi	iaşi	VERB
ejpam-6010	527	11	matematică	matematică	NOUN
ejpam-6010	527	12	,	,	PUNCT
ejpam-6010	527	13	54(1):75	54(1):75	NUM
ejpam-6010	527	14	–	–	PUNCT
ejpam-6010	527	15	85	85	NUM
ejpam-6010	527	16	,	,	PUNCT
ejpam-6010	527	17	2008	2008	NUM
ejpam-6010	527	18	.	.	PUNCT
ejpam-6010	528	1	[	[	X
ejpam-6010	528	2	36	36	NUM
ejpam-6010	528	3	]	]	PUNCT
ejpam-6010	528	4	t.	t.	PROPN
ejpam-6010	528	5	noiri	noiri	PROPN
ejpam-6010	528	6	and	and	CCONJ
ejpam-6010	528	7	v.	v.	ADP
ejpam-6010	528	8	popa	popa	NOUN
ejpam-6010	528	9	.	.	PUNCT
ejpam-6010	529	1	almost	almost	ADV
ejpam-6010	529	2	weakly	weakly	ADJ
ejpam-6010	529	3	continuous	continuous	ADJ
ejpam-6010	529	4	multifunctions	multifunction	NOUN
ejpam-6010	529	5	.	.	PUNCT
ejpam-6010	530	1	demonstratio	demonstratio	PROPN
ejpam-6010	530	2	mathematica	mathematica	PROPN
ejpam-6010	530	3	,	,	PUNCT
ejpam-6010	530	4	26:363–380	26:363–380	PROPN
ejpam-6010	530	5	,	,	PUNCT
ejpam-6010	530	6	1993	1993	NUM
ejpam-6010	530	7	.	.	PUNCT
ejpam-6010	531	1	[	[	X
ejpam-6010	531	2	37	37	NUM
ejpam-6010	531	3	]	]	PUNCT
ejpam-6010	531	4	e.	e.	PROPN
ejpam-6010	531	5	ekici	ekici	PROPN
ejpam-6010	531	6	,	,	PUNCT
ejpam-6010	531	7	s.	s.	PROPN
ejpam-6010	531	8	jafari	jafari	PROPN
ejpam-6010	531	9	,	,	PUNCT
ejpam-6010	531	10	and	and	CCONJ
ejpam-6010	531	11	v.	v.	ADP
ejpam-6010	531	12	popa	popa	NOUN
ejpam-6010	531	13	.	.	PUNCT
ejpam-6010	532	1	on	on	ADP
ejpam-6010	532	2	contra	contra	PROPN
ejpam-6010	532	3	-	-	ADJ
ejpam-6010	532	4	precontinuous	precontinuous	ADJ
ejpam-6010	532	5	and	and	CCONJ
ejpam-6010	532	6	almost	almost	ADV
ejpam-6010	532	7	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6010	532	8	multifunctions	multifunction	NOUN
ejpam-6010	532	9	.	.	PUNCT
ejpam-6010	533	1	journal	journal	PROPN
ejpam-6010	533	2	of	of	ADP
ejpam-6010	533	3	advanced	advanced	ADJ
ejpam-6010	533	4	research	research	NOUN
ejpam-6010	533	5	in	in	ADP
ejpam-6010	533	6	pure	pure	ADJ
ejpam-6010	533	7	mathematics	mathematic	NOUN
ejpam-6010	533	8	,	,	PUNCT
ejpam-6010	533	9	2(1):11–25	2(1):11–25	NUM
ejpam-6010	533	10	,	,	PUNCT
ejpam-6010	533	11	2010	2010	NUM
ejpam-6010	533	12	.	.	PUNCT
ejpam-6010	534	1	[	[	X
ejpam-6010	534	2	38	38	NUM
ejpam-6010	534	3	]	]	PUNCT
ejpam-6010	534	4	k.	k.	PROPN
ejpam-6010	535	1	laprom	laprom	PROPN
ejpam-6010	535	2	,	,	PUNCT
ejpam-6010	535	3	c.	c.	PROPN
ejpam-6010	535	4	boonpok	boonpok	PROPN
ejpam-6010	535	5	,	,	PUNCT
ejpam-6010	535	6	and	and	CCONJ
ejpam-6010	535	7	c.	c.	PROPN
ejpam-6010	535	8	viriyapong	viriyapong	PROPN
ejpam-6010	535	9	.	.	PUNCT
ejpam-6010	536	1	β(τ1	β(τ1	PROPN
ejpam-6010	536	2	,	,	PUNCT
ejpam-6010	536	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	536	4	multifunctions	multifunction	NOUN
ejpam-6010	536	5	on	on	ADP
ejpam-6010	536	6	bitopological	bitopological	ADJ
ejpam-6010	536	7	spaces	space	NOUN
ejpam-6010	536	8	.	.	PUNCT
ejpam-6010	537	1	journal	journal	NOUN
ejpam-6010	537	2	of	of	ADP
ejpam-6010	537	3	mathematics	mathematic	NOUN
ejpam-6010	537	4	,	,	PUNCT
ejpam-6010	537	5	2020:4020971	2020:4020971	NUM
ejpam-6010	537	6	,	,	PUNCT
ejpam-6010	537	7	2020	2020	NUM
ejpam-6010	537	8	.	.	PUNCT
ejpam-6010	538	1	[	[	X
ejpam-6010	538	2	39	39	NUM
ejpam-6010	538	3	]	]	PUNCT
ejpam-6010	538	4	c.	c.	PROPN
ejpam-6010	538	5	boonpok	boonpok	PROPN
ejpam-6010	538	6	.	.	PUNCT
ejpam-6010	539	1	(	(	PUNCT
ejpam-6010	539	2	τ1	τ1	NOUN
ejpam-6010	539	3	,	,	PUNCT
ejpam-6010	539	4	τ2)δ	τ2)δ	ADJ
ejpam-6010	539	5	-	-	PUNCT
ejpam-6010	539	6	semicontinuous	semicontinuous	ADJ
ejpam-6010	539	7	multifunctions	multifunction	NOUN
ejpam-6010	539	8	.	.	PUNCT
ejpam-6010	540	1	heliyon	heliyon	NOUN
ejpam-6010	540	2	,	,	PUNCT
ejpam-6010	540	3	6	6	NUM
ejpam-6010	540	4	:	:	SYM
ejpam-6010	540	5	e05367	e05367	PROPN
ejpam-6010	540	6	,	,	PUNCT
ejpam-6010	540	7	2020	2020	NUM
ejpam-6010	540	8	.	.	PUNCT
ejpam-6010	541	1	[	[	X
ejpam-6010	541	2	40	40	NUM
ejpam-6010	541	3	]	]	PUNCT
ejpam-6010	541	4	c.	c.	PROPN
ejpam-6010	541	5	boonpok	boonpok	PROPN
ejpam-6010	541	6	and	and	CCONJ
ejpam-6010	541	7	c.	c.	PROPN
ejpam-6010	541	8	viriyapong	viriyapong	PROPN
ejpam-6010	541	9	.	.	PUNCT
ejpam-6010	542	1	upper	upper	ADJ
ejpam-6010	542	2	and	and	CCONJ
ejpam-6010	542	3	lower	low	ADJ
ejpam-6010	542	4	almost	almost	ADV
ejpam-6010	542	5	weak	weak	ADJ
ejpam-6010	542	6	(	(	PUNCT
ejpam-6010	542	7	τ1	τ1	NOUN
ejpam-6010	542	8	,	,	PUNCT
ejpam-6010	542	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	542	10	.	.	PUNCT
ejpam-6010	543	1	european	european	PROPN
ejpam-6010	543	2	journal	journal	PROPN
ejpam-6010	543	3	of	of	ADP
ejpam-6010	543	4	pure	pure	ADJ
ejpam-6010	543	5	and	and	CCONJ
ejpam-6010	543	6	applied	applied	ADJ
ejpam-6010	543	7	mathematics	mathematic	NOUN
ejpam-6010	543	8	,	,	PUNCT
ejpam-6010	543	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-6010	543	10	,	,	PUNCT
ejpam-6010	543	11	2021	2021	NUM
ejpam-6010	543	12	.	.	PUNCT
ejpam-6010	544	1	[	[	X
ejpam-6010	544	2	41	41	NUM
ejpam-6010	544	3	]	]	X
ejpam-6010	544	4	c.	c.	PROPN
ejpam-6010	544	5	viriyapong	viriyapong	PROPN
ejpam-6010	544	6	and	and	CCONJ
ejpam-6010	544	7	c.	c.	PROPN
ejpam-6010	544	8	boonpok	boonpok	PROPN
ejpam-6010	544	9	.	.	PUNCT
ejpam-6010	545	1	weak	weak	ADJ
ejpam-6010	545	2	quasi	quasi	NOUN
ejpam-6010	545	3	(	(	PUNCT
ejpam-6010	545	4	λ	λ	PROPN
ejpam-6010	545	5	,	,	PUNCT
ejpam-6010	545	6	sp)-continuity	sp)-continuity	NOUN
ejpam-6010	545	7	for	for	ADP
ejpam-6010	545	8	multifunctions	multifunction	NOUN
ejpam-6010	545	9	.	.	PUNCT
ejpam-6010	546	1	international	international	ADJ
ejpam-6010	546	2	journal	journal	PROPN
ejpam-6010	546	3	of	of	ADP
ejpam-6010	546	4	mathematics	mathematic	NOUN
ejpam-6010	546	5	and	and	CCONJ
ejpam-6010	546	6	computer	computer	NOUN
ejpam-6010	546	7	science	science	NOUN
ejpam-6010	546	8	,	,	PUNCT
ejpam-6010	546	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-6010	546	10	,	,	PUNCT
ejpam-6010	546	11	2022	2022	NUM
ejpam-6010	546	12	.	.	PUNCT
ejpam-6010	547	1	[	[	X
ejpam-6010	547	2	42	42	NUM
ejpam-6010	547	3	]	]	PUNCT
ejpam-6010	547	4	c.	c.	PROPN
ejpam-6010	547	5	boonpok	boonpok	PROPN
ejpam-6010	547	6	.	.	PUNCT
ejpam-6010	548	1	on	on	ADP
ejpam-6010	548	2	continuous	continuous	ADJ
ejpam-6010	548	3	multifunctions	multifunction	NOUN
ejpam-6010	548	4	in	in	ADP
ejpam-6010	548	5	ideal	ideal	ADJ
ejpam-6010	548	6	topological	topological	ADJ
ejpam-6010	548	7	spaces	space	NOUN
ejpam-6010	548	8	.	.	PUNCT
ejpam-6010	549	1	lobachevskii	lobachevskii	PROPN
ejpam-6010	549	2	journal	journal	PROPN
ejpam-6010	549	3	of	of	ADP
ejpam-6010	549	4	mathematics	mathematic	NOUN
ejpam-6010	549	5	,	,	PUNCT
ejpam-6010	549	6	40(1):24–35	40(1):24–35	NUM
ejpam-6010	549	7	,	,	PUNCT
ejpam-6010	549	8	2019	2019	NUM
ejpam-6010	549	9	.	.	PUNCT
ejpam-6010	550	1	[	[	X
ejpam-6010	550	2	43	43	NUM
ejpam-6010	550	3	]	]	X
ejpam-6010	550	4	c.	c.	PROPN
ejpam-6010	550	5	boonpok	boonpok	PROPN
ejpam-6010	550	6	.	.	PUNCT
ejpam-6010	551	1	upper	upper	ADJ
ejpam-6010	551	2	and	and	CCONJ
ejpam-6010	551	3	lower	low	ADJ
ejpam-6010	551	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-6010	551	5	.	.	PUNCT
ejpam-6010	551	6	heliyon	heliyon	NOUN
ejpam-6010	551	7	,	,	PUNCT
ejpam-6010	551	8	7	7	NUM
ejpam-6010	551	9	:	:	PUNCT
ejpam-6010	551	10	e05986	e05986	PROPN
ejpam-6010	551	11	,	,	PUNCT
ejpam-6010	551	12	2021	2021	NUM
ejpam-6010	551	13	.	.	PUNCT
ejpam-6010	552	1	[	[	X
ejpam-6010	552	2	44	44	NUM
ejpam-6010	552	3	]	]	PUNCT
ejpam-6010	552	4	c.	c.	PROPN
ejpam-6010	552	5	boonpok	boonpok	PROPN
ejpam-6010	552	6	and	and	CCONJ
ejpam-6010	552	7	j.	j.	PROPN
ejpam-6010	552	8	khampakdee	khampakdee	PROPN
ejpam-6010	552	9	.	.	PUNCT
ejpam-6010	553	1	upper	upper	ADJ
ejpam-6010	553	2	and	and	CCONJ
ejpam-6010	553	3	lower	low	ADJ
ejpam-6010	553	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-6010	553	5	.	.	PUNCT
ejpam-6010	553	6	european	european	PROPN
ejpam-6010	553	7	journal	journal	PROPN
ejpam-6010	553	8	of	of	ADP
ejpam-6010	553	9	pure	pure	ADJ
ejpam-6010	553	10	and	and	CCONJ
ejpam-6010	553	11	applied	applied	ADJ
ejpam-6010	553	12	mathematics	mathematic	NOUN
ejpam-6010	553	13	,	,	PUNCT
ejpam-6010	553	14	17(1):201–211	17(1):201–211	NUM
ejpam-6010	553	15	,	,	PUNCT
ejpam-6010	553	16	2024	2024	NUM
ejpam-6010	553	17	.	.	PUNCT
ejpam-6010	554	1	[	[	X
ejpam-6010	554	2	45	45	NUM
ejpam-6010	554	3	]	]	PUNCT
ejpam-6010	554	4	c.	c.	PROPN
ejpam-6010	554	5	boonpok	boonpok	PROPN
ejpam-6010	554	6	and	and	CCONJ
ejpam-6010	554	7	n.	n.	PROPN
ejpam-6010	554	8	srisarakham	srisarakham	PROPN
ejpam-6010	554	9	.	.	PUNCT
ejpam-6010	555	1	almost	almost	ADV
ejpam-6010	555	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-6010	555	3	for	for	ADP
ejpam-6010	555	4	multifunctions	multifunction	NOUN
ejpam-6010	555	5	.	.	PUNCT
ejpam-6010	556	1	international	international	ADJ
ejpam-6010	556	2	journal	journal	NOUN
ejpam-6010	556	3	of	of	ADP
ejpam-6010	556	4	analysis	analysis	NOUN
ejpam-6010	556	5	and	and	CCONJ
ejpam-6010	556	6	applications	application	NOUN
ejpam-6010	556	7	,	,	PUNCT
ejpam-6010	556	8	21:107	21:107	NUM
ejpam-6010	556	9	,	,	PUNCT
ejpam-6010	556	10	2023	2023	NUM
ejpam-6010	556	11	.	.	PUNCT
ejpam-6010	557	1	[	[	X
ejpam-6010	557	2	46	46	NUM
ejpam-6010	557	3	]	]	X
ejpam-6010	557	4	c.	c.	PROPN
ejpam-6010	557	5	boonpok	boonpok	PROPN
ejpam-6010	557	6	.	.	PUNCT
ejpam-6010	558	1	weak	weak	ADJ
ejpam-6010	558	2	quasi	quasi	ADJ
ejpam-6010	558	3	continuity	continuity	NOUN
ejpam-6010	558	4	for	for	ADP
ejpam-6010	558	5	multifunctions	multifunction	NOUN
ejpam-6010	558	6	in	in	ADP
ejpam-6010	558	7	ideal	ideal	ADJ
ejpam-6010	558	8	topological	topological	ADJ
ejpam-6010	558	9	spaces	space	NOUN
ejpam-6010	558	10	.	.	PUNCT
ejpam-6010	559	1	advances	advance	NOUN
ejpam-6010	559	2	in	in	ADP
ejpam-6010	559	3	mathematics	mathematic	NOUN
ejpam-6010	559	4	:	:	PUNCT
ejpam-6010	559	5	scientific	scientific	ADJ
ejpam-6010	559	6	journal	journal	NOUN
ejpam-6010	559	7	,	,	PUNCT
ejpam-6010	559	8	9(1):339–355	9(1):339–355	NUM
ejpam-6010	559	9	,	,	PUNCT
ejpam-6010	559	10	2020	2020	NUM
ejpam-6010	559	11	.	.	PUNCT
ejpam-6010	560	1	[	[	X
ejpam-6010	560	2	47	47	NUM
ejpam-6010	560	3	]	]	X
ejpam-6010	560	4	c.	c.	PROPN
ejpam-6010	560	5	boonpok	boonpok	PROPN
ejpam-6010	560	6	and	and	CCONJ
ejpam-6010	560	7	p.	p.	NOUN
ejpam-6010	560	8	pue	pue	NOUN
ejpam-6010	560	9	-	-	PUNCT
ejpam-6010	560	10	on	on	ADP
ejpam-6010	560	11	.	.	PUNCT
ejpam-6010	561	1	upper	upper	ADJ
ejpam-6010	561	2	and	and	CCONJ
ejpam-6010	561	3	lower	low	ADJ
ejpam-6010	561	4	weakly	weakly	ADJ
ejpam-6010	561	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6010	561	6	multifunctions	multifunction	NOUN
ejpam-6010	561	7	.	.	PUNCT
ejpam-6010	562	1	international	international	ADJ
ejpam-6010	562	2	journal	journal	NOUN
ejpam-6010	562	3	of	of	ADP
ejpam-6010	562	4	analysis	analysis	NOUN
ejpam-6010	562	5	and	and	CCONJ
ejpam-6010	562	6	applications	application	NOUN
ejpam-6010	562	7	,	,	PUNCT
ejpam-6010	562	8	21:90	21:90	NUM
ejpam-6010	562	9	,	,	PUNCT
ejpam-6010	562	10	2023	2023	NUM
ejpam-6010	562	11	.	.	PUNCT
ejpam-6010	563	1	j.	j.	PROPN
ejpam-6010	563	2	khampakdee	khampakdee	PROPN
ejpam-6010	563	3	,	,	PUNCT
ejpam-6010	563	4	a.	a.	PROPN
ejpam-6010	563	5	sama	sama	PROPN
ejpam-6010	563	6	-	-	PUNCT
ejpam-6010	563	7	ae	ae	PROPN
ejpam-6010	563	8	,	,	PUNCT
ejpam-6010	563	9	c.	c.	PROPN
ejpam-6010	563	10	boonpok	boonpok	PROPN
ejpam-6010	563	11	/	/	SYM
ejpam-6010	563	12	eur	eur	PROPN
ejpam-6010	563	13	.	.	PUNCT
ejpam-6010	564	1	j.	j.	PROPN
ejpam-6010	564	2	pure	pure	PROPN
ejpam-6010	564	3	appl	appl	PROPN
ejpam-6010	564	4	.	.	PROPN
ejpam-6010	564	5	math	math	PROPN
ejpam-6010	564	6	,	,	PUNCT
ejpam-6010	564	7	18	18	NUM
ejpam-6010	564	8	(	(	PUNCT
ejpam-6010	564	9	2	2	NUM
ejpam-6010	564	10	)	)	PUNCT
ejpam-6010	564	11	(	(	PUNCT
ejpam-6010	564	12	2025	2025	NUM
ejpam-6010	564	13	)	)	PUNCT
ejpam-6010	564	14	,	,	PUNCT
ejpam-6010	564	15	6010	6010	NUM
ejpam-6010	564	16	18	18	NUM
ejpam-6010	564	17	of	of	ADP
ejpam-6010	564	18	19	19	NUM
ejpam-6010	564	19	[	[	SYM
ejpam-6010	564	20	48	48	NUM
ejpam-6010	564	21	]	]	PUNCT
ejpam-6010	564	22	c.	c.	PROPN
ejpam-6010	564	23	boonpok	boonpok	PROPN
ejpam-6010	564	24	and	and	CCONJ
ejpam-6010	564	25	p.	p.	NOUN
ejpam-6010	564	26	pue	pue	NOUN
ejpam-6010	564	27	-	-	PUNCT
ejpam-6010	564	28	on	on	ADP
ejpam-6010	564	29	.	.	PUNCT
ejpam-6010	565	1	upper	upper	ADJ
ejpam-6010	565	2	and	and	CCONJ
ejpam-6010	565	3	lower	low	ADJ
ejpam-6010	565	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6010	565	5	multifunctions	multifunction	NOUN
ejpam-6010	565	6	.	.	PUNCT
ejpam-6010	566	1	european	european	ADJ
ejpam-6010	566	2	journal	journal	PROPN
ejpam-6010	566	3	of	of	ADP
ejpam-6010	566	4	pure	pure	ADJ
ejpam-6010	566	5	and	and	CCONJ
ejpam-6010	566	6	applied	applied	ADJ
ejpam-6010	566	7	mathematics	mathematic	NOUN
ejpam-6010	566	8	,	,	PUNCT
ejpam-6010	566	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-6010	566	10	,	,	PUNCT
ejpam-6010	566	11	2023	2023	NUM
ejpam-6010	566	12	.	.	PUNCT
ejpam-6010	567	1	[	[	X
ejpam-6010	567	2	49	49	NUM
ejpam-6010	567	3	]	]	PUNCT
ejpam-6010	567	4	c.	c.	PROPN
ejpam-6010	567	5	boonpok	boonpok	PROPN
ejpam-6010	567	6	and	and	CCONJ
ejpam-6010	567	7	j.	j.	PROPN
ejpam-6010	567	8	khampakdee	khampakdee	PROPN
ejpam-6010	567	9	.	.	PUNCT
ejpam-6010	568	1	upper	upper	ADJ
ejpam-6010	568	2	and	and	CCONJ
ejpam-6010	568	3	lower	low	ADJ
ejpam-6010	568	4	weak	weak	ADJ
ejpam-6010	568	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-6010	568	6	.	.	PUNCT
ejpam-6010	569	1	european	european	PROPN
ejpam-6010	569	2	journal	journal	PROPN
ejpam-6010	569	3	of	of	ADP
ejpam-6010	569	4	pure	pure	ADJ
ejpam-6010	569	5	and	and	CCONJ
ejpam-6010	569	6	applied	applied	ADJ
ejpam-6010	569	7	mathematics	mathematic	NOUN
ejpam-6010	569	8	,	,	PUNCT
ejpam-6010	569	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-6010	569	10	,	,	PUNCT
ejpam-6010	569	11	2023	2023	NUM
ejpam-6010	569	12	.	.	PUNCT
ejpam-6010	570	1	[	[	X
ejpam-6010	570	2	50	50	NUM
ejpam-6010	570	3	]	]	PUNCT
ejpam-6010	570	4	c.	c.	PROPN
ejpam-6010	570	5	boonpok	boonpok	PROPN
ejpam-6010	570	6	.	.	PUNCT
ejpam-6010	571	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-6010	571	2	continuity	continuity	NOUN
ejpam-6010	571	3	for	for	ADP
ejpam-6010	571	4	multifunctions	multifunction	NOUN
ejpam-6010	571	5	.	.	PUNCT
ejpam-6010	572	1	wseas	wseas	PROPN
ejpam-6010	572	2	transactions	transaction	NOUN
ejpam-6010	572	3	on	on	ADP
ejpam-6010	572	4	mathematics	mathematic	NOUN
ejpam-6010	572	5	,	,	PUNCT
ejpam-6010	572	6	21:245–251	21:245–251	NUM
ejpam-6010	572	7	,	,	PUNCT
ejpam-6010	572	8	2022	2022	NUM
ejpam-6010	572	9	.	.	PUNCT
ejpam-6010	573	1	[	[	X
ejpam-6010	573	2	51	51	NUM
ejpam-6010	573	3	]	]	PUNCT
ejpam-6010	573	4	c.	c.	PROPN
ejpam-6010	573	5	boonpok	boonpok	PROPN
ejpam-6010	573	6	and	and	CCONJ
ejpam-6010	573	7	p.	p.	NOUN
ejpam-6010	573	8	pue	pue	NOUN
ejpam-6010	573	9	-	-	PUNCT
ejpam-6010	573	10	on	on	ADP
ejpam-6010	573	11	.	.	PUNCT
ejpam-6010	574	1	continuity	continuity	NOUN
ejpam-6010	574	2	for	for	ADP
ejpam-6010	574	3	multifunctions	multifunction	NOUN
ejpam-6010	574	4	in	in	ADP
ejpam-6010	574	5	ideal	ideal	ADJ
ejpam-6010	574	6	topological	topological	ADJ
ejpam-6010	574	7	spaces	space	NOUN
ejpam-6010	574	8	.	.	PUNCT
ejpam-6010	575	1	wseas	wseas	VERB
ejpam-6010	575	2	transactions	transaction	NOUN
ejpam-6010	575	3	on	on	ADP
ejpam-6010	575	4	mathematics	mathematic	NOUN
ejpam-6010	575	5	,	,	PUNCT
ejpam-6010	575	6	19:624–631	19:624–631	NUM
ejpam-6010	575	7	,	,	PUNCT
ejpam-6010	575	8	2020	2020	NUM
ejpam-6010	575	9	.	.	PUNCT
ejpam-6010	576	1	[	[	X
ejpam-6010	576	2	52	52	NUM
ejpam-6010	576	3	]	]	PUNCT
ejpam-6010	576	4	c.	c.	PROPN
ejpam-6010	576	5	boonpok	boonpok	PROPN
ejpam-6010	576	6	and	and	CCONJ
ejpam-6010	576	7	p.	p.	NOUN
ejpam-6010	576	8	pue	pue	NOUN
ejpam-6010	576	9	-	-	PUNCT
ejpam-6010	576	10	on	on	ADP
ejpam-6010	576	11	.	.	PUNCT
ejpam-6010	577	1	upper	upper	ADJ
ejpam-6010	577	2	and	and	CCONJ
ejpam-6010	577	3	lower	low	ADJ
ejpam-6010	577	4	weakly	weakly	ADJ
ejpam-6010	577	5	(	(	PUNCT
ejpam-6010	577	6	λ	λ	NOUN
ejpam-6010	577	7	,	,	PUNCT
ejpam-6010	577	8	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	577	9	multifunctions	multifunction	NOUN
ejpam-6010	577	10	.	.	PUNCT
ejpam-6010	578	1	european	european	PROPN
ejpam-6010	578	2	journal	journal	PROPN
ejpam-6010	578	3	of	of	ADP
ejpam-6010	578	4	pure	pure	ADJ
ejpam-6010	578	5	and	and	CCONJ
ejpam-6010	578	6	applied	applied	ADJ
ejpam-6010	578	7	mathematics	mathematic	NOUN
ejpam-6010	578	8	,	,	PUNCT
ejpam-6010	578	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-6010	578	10	,	,	PUNCT
ejpam-6010	578	11	2023	2023	NUM
ejpam-6010	578	12	.	.	PUNCT
ejpam-6010	579	1	[	[	X
ejpam-6010	579	2	53	53	NUM
ejpam-6010	579	3	]	]	PUNCT
ejpam-6010	579	4	j.	j.	PROPN
ejpam-6010	579	5	khampakdee	khampakdee	PROPN
ejpam-6010	579	6	and	and	CCONJ
ejpam-6010	579	7	c.	c.	PROPN
ejpam-6010	579	8	boonpok	boonpok	PROPN
ejpam-6010	579	9	.	.	PUNCT
ejpam-6010	580	1	upper	upper	ADJ
ejpam-6010	580	2	and	and	CCONJ
ejpam-6010	580	3	lower	low	ADJ
ejpam-6010	580	4	α(λ	α(λ	PROPN
ejpam-6010	580	5	,	,	PUNCT
ejpam-6010	580	6	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	580	7	multifunctions	multifunction	NOUN
ejpam-6010	580	8	.	.	PUNCT
ejpam-6010	581	1	wseas	wseas	VERB
ejpam-6010	581	2	transactions	transaction	NOUN
ejpam-6010	581	3	on	on	ADP
ejpam-6010	581	4	mathematics	mathematic	NOUN
ejpam-6010	581	5	,	,	PUNCT
ejpam-6010	581	6	21:684–690	21:684–690	NUM
ejpam-6010	581	7	,	,	PUNCT
ejpam-6010	581	8	2022	2022	NUM
ejpam-6010	581	9	.	.	PUNCT
ejpam-6010	582	1	[	[	X
ejpam-6010	582	2	54	54	NUM
ejpam-6010	582	3	]	]	PUNCT
ejpam-6010	582	4	c.	c.	PROPN
ejpam-6010	582	5	boonpok	boonpok	PROPN
ejpam-6010	582	6	and	and	CCONJ
ejpam-6010	582	7	j.	j.	PROPN
ejpam-6010	582	8	khampakdee	khampakdee	PROPN
ejpam-6010	582	9	.	.	PUNCT
ejpam-6010	583	1	on	on	ADP
ejpam-6010	583	2	almost	almost	ADV
ejpam-6010	583	3	α(λ	α(λ	PROPN
ejpam-6010	583	4	,	,	PUNCT
ejpam-6010	583	5	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	583	6	multifunctions	multifunction	NOUN
ejpam-6010	583	7	.	.	PUNCT
ejpam-6010	584	1	european	european	PROPN
ejpam-6010	584	2	journal	journal	PROPN
ejpam-6010	584	3	of	of	ADP
ejpam-6010	584	4	pure	pure	ADJ
ejpam-6010	584	5	and	and	CCONJ
ejpam-6010	584	6	applied	applied	ADJ
ejpam-6010	584	7	mathematics	mathematic	NOUN
ejpam-6010	584	8	,	,	PUNCT
ejpam-6010	584	9	15(2):626–634	15(2):626–634	PROPN
ejpam-6010	584	10	,	,	PUNCT
ejpam-6010	584	11	2022	2022	NUM
ejpam-6010	584	12	.	.	PUNCT
ejpam-6010	585	1	[	[	X
ejpam-6010	585	2	55	55	NUM
ejpam-6010	585	3	]	]	PUNCT
ejpam-6010	585	4	c.	c.	PROPN
ejpam-6010	585	5	boonpok	boonpok	PROPN
ejpam-6010	585	6	and	and	CCONJ
ejpam-6010	585	7	m.	m.	NOUN
ejpam-6010	585	8	thongmoon	thongmoon	NOUN
ejpam-6010	585	9	.	.	PUNCT
ejpam-6010	586	1	weak	weak	ADJ
ejpam-6010	586	2	α(λ	α(λ	PROPN
ejpam-6010	586	3	,	,	PUNCT
ejpam-6010	586	4	sp)-continuity	sp)-continuity	NOUN
ejpam-6010	586	5	for	for	ADP
ejpam-6010	586	6	multifunctions	multifunction	NOUN
ejpam-6010	586	7	.	.	PUNCT
ejpam-6010	587	1	european	european	ADJ
ejpam-6010	587	2	journal	journal	PROPN
ejpam-6010	587	3	of	of	ADP
ejpam-6010	587	4	pure	pure	ADJ
ejpam-6010	587	5	and	and	CCONJ
ejpam-6010	587	6	applied	applied	ADJ
ejpam-6010	587	7	mathematics	mathematic	NOUN
ejpam-6010	587	8	,	,	PUNCT
ejpam-6010	587	9	16(1):465–478	16(1):465–478	NUM
ejpam-6010	587	10	,	,	PUNCT
ejpam-6010	587	11	2023	2023	NUM
ejpam-6010	587	12	.	.	PUNCT
ejpam-6010	588	1	[	[	X
ejpam-6010	588	2	56	56	NUM
ejpam-6010	588	3	]	]	PUNCT
ejpam-6010	588	4	m.	m.	NOUN
ejpam-6010	588	5	thongmoon	thongmoon	NOUN
ejpam-6010	588	6	and	and	CCONJ
ejpam-6010	588	7	c.	c.	PROPN
ejpam-6010	588	8	boonpok	boonpok	PROPN
ejpam-6010	588	9	.	.	PUNCT
ejpam-6010	589	1	upper	upper	ADJ
ejpam-6010	589	2	and	and	CCONJ
ejpam-6010	589	3	lower	low	ADJ
ejpam-6010	589	4	almost	almost	ADV
ejpam-6010	589	5	β(λ	β(λ	NOUN
ejpam-6010	589	6	,	,	PUNCT
ejpam-6010	589	7	sp)-continuous	sp)-continuous	ADJ
ejpam-6010	589	8	multifunctions	multifunction	NOUN
ejpam-6010	589	9	.	.	PUNCT
ejpam-6010	590	1	wseas	wseas	VERB
ejpam-6010	590	2	transactions	transaction	NOUN
ejpam-6010	590	3	on	on	ADP
ejpam-6010	590	4	mathematics	mathematic	NOUN
ejpam-6010	590	5	,	,	PUNCT
ejpam-6010	590	6	21:844–853	21:844–853	NUM
ejpam-6010	590	7	,	,	PUNCT
ejpam-6010	590	8	2022	2022	NUM
ejpam-6010	590	9	.	.	PUNCT
ejpam-6010	591	1	[	[	X
ejpam-6010	591	2	57	57	NUM
ejpam-6010	591	3	]	]	PUNCT
ejpam-6010	591	4	c.	c.	PROPN
ejpam-6010	591	5	boonpok	boonpok	PROPN
ejpam-6010	591	6	and	and	CCONJ
ejpam-6010	591	7	j.	j.	PROPN
ejpam-6010	591	8	khampakdee	khampakdee	PROPN
ejpam-6010	591	9	.	.	PUNCT
ejpam-6010	592	1	slight	slight	PROPN
ejpam-6010	592	2	(	(	PUNCT
ejpam-6010	592	3	λ	λ	NOUN
ejpam-6010	592	4	,	,	PUNCT
ejpam-6010	592	5	sp)-continuity	sp)-continuity	NOUN
ejpam-6010	592	6	and	and	CCONJ
ejpam-6010	592	7	λsp	λsp	NOUN
ejpam-6010	592	8	-	-	PUNCT
ejpam-6010	592	9	extremally	extremally	ADV
ejpam-6010	592	10	disconnectedness	disconnectedness	NOUN
ejpam-6010	592	11	.	.	PUNCT
ejpam-6010	593	1	european	european	ADJ
ejpam-6010	593	2	journal	journal	PROPN
ejpam-6010	593	3	of	of	ADP
ejpam-6010	593	4	pure	pure	ADJ
ejpam-6010	593	5	and	and	CCONJ
ejpam-6010	593	6	applied	applied	ADJ
ejpam-6010	593	7	mathematics	mathematic	NOUN
ejpam-6010	593	8	,	,	PUNCT
ejpam-6010	593	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-6010	593	10	,	,	PUNCT
ejpam-6010	593	11	2022	2022	NUM
ejpam-6010	593	12	.	.	PUNCT
ejpam-6010	594	1	[	[	X
ejpam-6010	594	2	58	58	NUM
ejpam-6010	594	3	]	]	PUNCT
ejpam-6010	594	4	p.	p.	NOUN
ejpam-6010	594	5	pue	pue	NOUN
ejpam-6010	594	6	-	-	PUNCT
ejpam-6010	594	7	on	on	ADP
ejpam-6010	594	8	,	,	PUNCT
ejpam-6010	594	9	s.	s.	PROPN
ejpam-6010	594	10	sompong	sompong	PROPN
ejpam-6010	594	11	,	,	PUNCT
ejpam-6010	594	12	and	and	CCONJ
ejpam-6010	594	13	c.	c.	PROPN
ejpam-6010	594	14	boonpok	boonpok	PROPN
ejpam-6010	594	15	.	.	PUNCT
ejpam-6010	595	1	upper	upper	ADJ
ejpam-6010	595	2	and	and	CCONJ
ejpam-6010	595	3	lower	low	ADJ
ejpam-6010	595	4	(	(	PUNCT
ejpam-6010	595	5	τ1	τ1	NOUN
ejpam-6010	595	6	,	,	PUNCT
ejpam-6010	595	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	595	8	mulfunctions	mulfunction	NOUN
ejpam-6010	595	9	.	.	PUNCT
ejpam-6010	596	1	international	international	ADJ
ejpam-6010	596	2	journal	journal	NOUN
ejpam-6010	596	3	of	of	ADP
ejpam-6010	596	4	mathematics	mathematic	NOUN
ejpam-6010	596	5	and	and	CCONJ
ejpam-6010	596	6	computer	computer	NOUN
ejpam-6010	596	7	science	science	NOUN
ejpam-6010	596	8	,	,	PUNCT
ejpam-6010	596	9	19(4):1305	19(4):1305	NUM
ejpam-6010	596	10	–	–	PUNCT
ejpam-6010	596	11	1310	1310	NUM
ejpam-6010	596	12	,	,	PUNCT
ejpam-6010	596	13	2024	2024	NUM
ejpam-6010	596	14	.	.	PUNCT
ejpam-6010	597	1	[	[	X
ejpam-6010	597	2	59	59	NUM
ejpam-6010	597	3	]	]	PUNCT
ejpam-6010	597	4	c.	c.	PROPN
ejpam-6010	597	5	klanarong	klanarong	PROPN
ejpam-6010	597	6	,	,	PUNCT
ejpam-6010	597	7	s.	s.	PROPN
ejpam-6010	597	8	sompong	sompong	PROPN
ejpam-6010	597	9	,	,	PUNCT
ejpam-6010	597	10	and	and	CCONJ
ejpam-6010	597	11	c.	c.	PROPN
ejpam-6010	597	12	boonpok	boonpok	PROPN
ejpam-6010	597	13	.	.	PUNCT
ejpam-6010	598	1	upper	upper	ADJ
ejpam-6010	598	2	and	and	CCONJ
ejpam-6010	598	3	lower	low	ADJ
ejpam-6010	598	4	almost	almost	ADV
ejpam-6010	598	5	(	(	PUNCT
ejpam-6010	598	6	τ1	τ1	NOUN
ejpam-6010	598	7	,	,	PUNCT
ejpam-6010	598	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	598	9	multifunctions	multifunction	NOUN
ejpam-6010	598	10	.	.	PUNCT
ejpam-6010	599	1	european	european	ADJ
ejpam-6010	599	2	journal	journal	PROPN
ejpam-6010	599	3	of	of	ADP
ejpam-6010	599	4	pure	pure	ADJ
ejpam-6010	599	5	and	and	CCONJ
ejpam-6010	599	6	applied	applied	ADJ
ejpam-6010	599	7	mathematics	mathematic	NOUN
ejpam-6010	599	8	,	,	PUNCT
ejpam-6010	599	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-6010	599	10	,	,	PUNCT
ejpam-6010	599	11	2024	2024	NUM
ejpam-6010	599	12	.	.	PUNCT
ejpam-6010	600	1	[	[	X
ejpam-6010	600	2	60	60	NUM
ejpam-6010	600	3	]	]	PUNCT
ejpam-6010	600	4	m.	m.	NOUN
ejpam-6010	600	5	thongmoon	thongmoon	NOUN
ejpam-6010	600	6	,	,	PUNCT
ejpam-6010	600	7	s.	s.	PROPN
ejpam-6010	600	8	sompong	sompong	PROPN
ejpam-6010	600	9	,	,	PUNCT
ejpam-6010	600	10	and	and	CCONJ
ejpam-6010	600	11	c.	c.	PROPN
ejpam-6010	600	12	boonpok	boonpok	PROPN
ejpam-6010	600	13	.	.	PUNCT
ejpam-6010	601	1	upper	upper	ADJ
ejpam-6010	601	2	and	and	CCONJ
ejpam-6010	601	3	lower	low	ADJ
ejpam-6010	601	4	weak	weak	ADJ
ejpam-6010	601	5	(	(	PUNCT
ejpam-6010	601	6	τ1	τ1	NOUN
ejpam-6010	601	7	,	,	PUNCT
ejpam-6010	601	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6010	601	9	.	.	PUNCT
ejpam-6010	602	1	european	european	PROPN
ejpam-6010	602	2	journal	journal	PROPN
ejpam-6010	602	3	of	of	ADP
ejpam-6010	602	4	pure	pure	ADJ
ejpam-6010	602	5	and	and	CCONJ
ejpam-6010	602	6	applied	applied	ADJ
ejpam-6010	602	7	mathematics	mathematic	NOUN
ejpam-6010	602	8	,	,	PUNCT
ejpam-6010	602	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-6010	602	10	,	,	PUNCT
ejpam-6010	602	11	2024	2024	NUM
ejpam-6010	602	12	.	.	PUNCT
ejpam-6010	603	1	[	[	X
ejpam-6010	603	2	61	61	NUM
ejpam-6010	603	3	]	]	X
ejpam-6010	603	4	p.	p.	NOUN
ejpam-6010	603	5	pue	pue	NOUN
ejpam-6010	603	6	-	-	PUNCT
ejpam-6010	603	7	on	on	ADP
ejpam-6010	603	8	,	,	PUNCT
ejpam-6010	603	9	s.	s.	PROPN
ejpam-6010	603	10	sompong	sompong	PROPN
ejpam-6010	603	11	,	,	PUNCT
ejpam-6010	603	12	and	and	CCONJ
ejpam-6010	603	13	c.	c.	PROPN
ejpam-6010	603	14	boonpok	boonpok	PROPN
ejpam-6010	603	15	.	.	PUNCT
ejpam-6010	604	1	weakly	weakly	ADJ
ejpam-6010	604	2	quasi	quasi	NOUN
ejpam-6010	604	3	(	(	PUNCT
ejpam-6010	604	4	τ1	τ1	PROPN
ejpam-6010	604	5	,	,	PUNCT
ejpam-6010	604	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	604	7	multifunctions	multifunction	NOUN
ejpam-6010	604	8	.	.	PUNCT
ejpam-6010	605	1	european	european	ADJ
ejpam-6010	605	2	journal	journal	PROPN
ejpam-6010	605	3	of	of	ADP
ejpam-6010	605	4	pure	pure	ADJ
ejpam-6010	605	5	and	and	CCONJ
ejpam-6010	605	6	applied	applied	ADJ
ejpam-6010	605	7	mathematics	mathematic	NOUN
ejpam-6010	605	8	,	,	PUNCT
ejpam-6010	605	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-6010	605	10	,	,	PUNCT
ejpam-6010	605	11	2024	2024	NUM
ejpam-6010	605	12	.	.	PUNCT
ejpam-6010	606	1	[	[	X
ejpam-6010	606	2	62	62	NUM
ejpam-6010	606	3	]	]	PUNCT
ejpam-6010	606	4	p.	p.	NOUN
ejpam-6010	606	5	pue	pue	NOUN
ejpam-6010	606	6	-	-	PUNCT
ejpam-6010	606	7	on	on	ADP
ejpam-6010	606	8	,	,	PUNCT
ejpam-6010	606	9	s.	s.	PROPN
ejpam-6010	606	10	sompong	sompong	PROPN
ejpam-6010	606	11	,	,	PUNCT
ejpam-6010	606	12	and	and	CCONJ
ejpam-6010	606	13	c.	c.	PROPN
ejpam-6010	606	14	boonpok	boonpok	PROPN
ejpam-6010	606	15	.	.	PUNCT
ejpam-6010	607	1	almost	almost	ADV
ejpam-6010	607	2	quasi	quasi	X
ejpam-6010	607	3	(	(	PUNCT
ejpam-6010	607	4	τ1	τ1	NOUN
ejpam-6010	607	5	,	,	PUNCT
ejpam-6010	607	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	607	7	for	for	ADP
ejpam-6010	607	8	multifunctions	multifunction	NOUN
ejpam-6010	607	9	.	.	PUNCT
ejpam-6010	608	1	international	international	ADJ
ejpam-6010	608	2	journal	journal	NOUN
ejpam-6010	608	3	of	of	ADP
ejpam-6010	608	4	analysis	analysis	NOUN
ejpam-6010	608	5	and	and	CCONJ
ejpam-6010	608	6	applications	application	NOUN
ejpam-6010	608	7	,	,	PUNCT
ejpam-6010	608	8	22:97	22:97	NUM
ejpam-6010	608	9	,	,	PUNCT
ejpam-6010	608	10	2024	2024	NUM
ejpam-6010	608	11	.	.	PUNCT
ejpam-6010	609	1	[	[	X
ejpam-6010	609	2	63	63	NUM
ejpam-6010	609	3	]	]	PUNCT
ejpam-6010	609	4	j.	j.	PROPN
ejpam-6010	609	5	khampakdee	khampakdee	PROPN
ejpam-6010	609	6	,	,	PUNCT
ejpam-6010	609	7	s.	s.	PROPN
ejpam-6010	609	8	sompong	sompong	PROPN
ejpam-6010	609	9	,	,	PUNCT
ejpam-6010	609	10	and	and	CCONJ
ejpam-6010	609	11	c.	c.	PROPN
ejpam-6010	609	12	boonpok	boonpok	PROPN
ejpam-6010	609	13	.	.	PUNCT
ejpam-6010	610	1	c-(τ1	c-(τ1	PROPN
ejpam-6010	610	2	,	,	PUNCT
ejpam-6010	610	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	610	4	for	for	ADP
ejpam-6010	610	5	multifunctions	multifunction	NOUN
ejpam-6010	610	6	.	.	PUNCT
ejpam-6010	611	1	european	european	ADJ
ejpam-6010	611	2	journal	journal	PROPN
ejpam-6010	611	3	of	of	ADP
ejpam-6010	611	4	pure	pure	ADJ
ejpam-6010	611	5	and	and	CCONJ
ejpam-6010	611	6	applied	applied	ADJ
ejpam-6010	611	7	mathematics	mathematic	NOUN
ejpam-6010	611	8	,	,	PUNCT
ejpam-6010	611	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-6010	611	10	,	,	PUNCT
ejpam-6010	611	11	2024	2024	NUM
ejpam-6010	611	12	.	.	PUNCT
ejpam-6010	612	1	[	[	X
ejpam-6010	612	2	64	64	NUM
ejpam-6010	612	3	]	]	PUNCT
ejpam-6010	612	4	p.	p.	NOUN
ejpam-6010	612	5	pue	pue	NOUN
ejpam-6010	612	6	-	-	PUNCT
ejpam-6010	612	7	on	on	ADP
ejpam-6010	612	8	,	,	PUNCT
ejpam-6010	612	9	a.	a.	PROPN
ejpam-6010	612	10	sama	sama	PROPN
ejpam-6010	612	11	-	-	PUNCT
ejpam-6010	612	12	ae	ae	PROPN
ejpam-6010	612	13	,	,	PUNCT
ejpam-6010	612	14	and	and	CCONJ
ejpam-6010	612	15	c.	c.	PROPN
ejpam-6010	612	16	boonpok	boonpok	PROPN
ejpam-6010	612	17	.	.	PUNCT
ejpam-6010	613	1	c	c	X
ejpam-6010	613	2	-	-	PUNCT
ejpam-6010	613	3	quasi	quasi	X
ejpam-6010	613	4	(	(	PUNCT
ejpam-6010	613	5	τ1	τ1	PROPN
ejpam-6010	613	6	,	,	PUNCT
ejpam-6010	613	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6010	613	8	multifunctions	multifunction	NOUN
ejpam-6010	613	9	.	.	PUNCT
ejpam-6010	614	1	european	european	ADJ
ejpam-6010	614	2	journal	journal	PROPN
ejpam-6010	614	3	of	of	ADP
ejpam-6010	614	4	pure	pure	ADJ
ejpam-6010	614	5	and	and	CCONJ
ejpam-6010	614	6	applied	applied	ADJ
ejpam-6010	614	7	mathematics	mathematic	NOUN
ejpam-6010	614	8	,	,	PUNCT
ejpam-6010	614	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-6010	614	10	,	,	PUNCT
ejpam-6010	614	11	2024	2024	NUM
ejpam-6010	614	12	.	.	PUNCT
ejpam-6010	615	1	[	[	X
ejpam-6010	615	2	65	65	NUM
ejpam-6010	615	3	]	]	X
ejpam-6010	615	4	n.	n.	PROPN
ejpam-6010	615	5	viriyapong	viriyapong	PROPN
ejpam-6010	615	6	,	,	PUNCT
ejpam-6010	615	7	s.	s.	PROPN
ejpam-6010	615	8	sompong	sompong	PROPN
ejpam-6010	615	9	,	,	PUNCT
ejpam-6010	615	10	and	and	CCONJ
ejpam-6010	615	11	c.	c.	PROPN
ejpam-6010	615	12	boonpok	boonpok	PROPN
ejpam-6010	615	13	.	.	PUNCT
ejpam-6010	616	1	upper	upper	ADJ
ejpam-6010	616	2	and	and	CCONJ
ejpam-6010	616	3	lower	low	ADJ
ejpam-6010	616	4	s-(τ1	s-(τ1	NOUN
ejpam-6010	616	5	,	,	PUNCT
ejpam-6010	616	6	τ2)p	τ2)p	ADJ
ejpam-6010	616	7	-	-	PUNCT
ejpam-6010	616	8	continuous	continuous	ADJ
ejpam-6010	616	9	multifunctions	multifunction	NOUN
ejpam-6010	616	10	.	.	PUNCT
ejpam-6010	617	1	european	european	ADJ
ejpam-6010	617	2	journal	journal	PROPN
ejpam-6010	617	3	of	of	ADP
ejpam-6010	617	4	pure	pure	ADJ
ejpam-6010	617	5	and	and	CCONJ
ejpam-6010	617	6	applied	applied	ADJ
ejpam-6010	617	7	mathematics	mathematic	NOUN
ejpam-6010	617	8	,	,	PUNCT
ejpam-6010	617	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-6010	617	10	,	,	PUNCT
ejpam-6010	617	11	2024	2024	NUM
ejpam-6010	617	12	.	.	PUNCT
ejpam-6010	618	1	[	[	X
ejpam-6010	618	2	66	66	NUM
ejpam-6010	618	3	]	]	PUNCT
ejpam-6010	618	4	c.	c.	PROPN
ejpam-6010	618	5	viriyapong	viriyapong	PROPN
ejpam-6010	618	6	,	,	PUNCT
ejpam-6010	618	7	s.	s.	PROPN
ejpam-6010	618	8	sompong	sompong	PROPN
ejpam-6010	618	9	,	,	PUNCT
ejpam-6010	618	10	and	and	CCONJ
ejpam-6010	618	11	c.	c.	PROPN
ejpam-6010	618	12	boonpok	boonpok	PROPN
ejpam-6010	618	13	.	.	PUNCT
ejpam-6010	619	1	upper	upper	ADJ
ejpam-6010	619	2	and	and	CCONJ
ejpam-6010	619	3	lower	low	ADJ
ejpam-6010	619	4	slight	slight	ADJ
ejpam-6010	619	5	α(τ1	α(τ1	NOUN
ejpam-6010	619	6	,	,	PUNCT
ejpam-6010	619	7	τ2)continuity	τ2)continuity	PROPN
ejpam-6010	619	8	.	.	PUNCT
ejpam-6010	620	1	european	european	PROPN
ejpam-6010	620	2	journal	journal	PROPN
ejpam-6010	620	3	of	of	ADP
ejpam-6010	620	4	pure	pure	ADJ
ejpam-6010	620	5	and	and	CCONJ
ejpam-6010	620	6	applied	applied	ADJ
ejpam-6010	620	7	mathematics	mathematic	NOUN
ejpam-6010	620	8	,	,	PUNCT
ejpam-6010	620	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-6010	620	10	,	,	PUNCT
ejpam-6010	620	11	j.	j.	PROPN
ejpam-6010	620	12	khampakdee	khampakdee	PROPN
ejpam-6010	620	13	,	,	PUNCT
ejpam-6010	620	14	a.	a.	PROPN
ejpam-6010	620	15	sama	sama	PROPN
ejpam-6010	620	16	-	-	PUNCT
ejpam-6010	620	17	ae	ae	PROPN
ejpam-6010	620	18	,	,	PUNCT
ejpam-6010	620	19	c.	c.	PROPN
ejpam-6010	620	20	boonpok	boonpok	PROPN
ejpam-6010	620	21	/	/	SYM
ejpam-6010	620	22	eur	eur	PROPN
ejpam-6010	620	23	.	.	PUNCT
ejpam-6010	621	1	j.	j.	PROPN
ejpam-6010	621	2	pure	pure	PROPN
ejpam-6010	621	3	appl	appl	PROPN
ejpam-6010	621	4	.	.	PROPN
ejpam-6010	621	5	math	math	PROPN
ejpam-6010	621	6	,	,	PUNCT
ejpam-6010	621	7	18	18	NUM
ejpam-6010	621	8	(	(	PUNCT
ejpam-6010	621	9	2	2	NUM
ejpam-6010	621	10	)	)	PUNCT
ejpam-6010	621	11	(	(	PUNCT
ejpam-6010	621	12	2025	2025	NUM
ejpam-6010	621	13	)	)	PUNCT
ejpam-6010	621	14	,	,	PUNCT
ejpam-6010	621	15	6010	6010	NUM
ejpam-6010	621	16	19	19	NUM
ejpam-6010	621	17	of	of	ADP
ejpam-6010	621	18	19	19	NUM
ejpam-6010	621	19	2024	2024	NUM
ejpam-6010	621	20	.	.	PUNCT
ejpam-6010	622	1	[	[	X
ejpam-6010	622	2	67	67	NUM
ejpam-6010	622	3	]	]	X
ejpam-6010	622	4	n.	n.	PROPN
ejpam-6010	622	5	viriyapong	viriyapong	PROPN
ejpam-6010	622	6	,	,	PUNCT
ejpam-6010	622	7	s.	s.	PROPN
ejpam-6010	622	8	sompong	sompong	PROPN
ejpam-6010	622	9	,	,	PUNCT
ejpam-6010	622	10	and	and	CCONJ
ejpam-6010	622	11	c.	c.	PROPN
ejpam-6010	622	12	boonpok	boonpok	PROPN
ejpam-6010	622	13	.	.	PUNCT
ejpam-6010	623	1	slightly	slightly	ADV
ejpam-6010	623	2	(	(	PUNCT
ejpam-6010	623	3	τ1	τ1	NOUN
ejpam-6010	623	4	,	,	PUNCT
ejpam-6010	623	5	τ2)p	τ2)p	ADJ
ejpam-6010	623	6	-	-	ADJ
ejpam-6010	623	7	continuous	continuous	ADJ
ejpam-6010	623	8	multifunctions	multifunction	NOUN
ejpam-6010	623	9	.	.	PUNCT
ejpam-6010	624	1	international	international	ADJ
ejpam-6010	624	2	journal	journal	NOUN
ejpam-6010	624	3	of	of	ADP
ejpam-6010	624	4	analysis	analysis	NOUN
ejpam-6010	624	5	and	and	CCONJ
ejpam-6010	624	6	applications	application	NOUN
ejpam-6010	624	7	,	,	PUNCT
ejpam-6010	624	8	22:152	22:152	NUM
ejpam-6010	624	9	,	,	PUNCT
ejpam-6010	624	10	2024	2024	NUM
ejpam-6010	624	11	.	.	PUNCT
ejpam-6010	625	1	[	[	X
ejpam-6010	625	2	68	68	NUM
ejpam-6010	625	3	]	]	X
ejpam-6010	625	4	b.	b.	PROPN
ejpam-6010	625	5	kong	kong	PROPN
ejpam-6010	625	6	-	-	PUNCT
ejpam-6010	625	7	ied	ied	PROPN
ejpam-6010	625	8	,	,	PUNCT
ejpam-6010	625	9	s.	s.	PROPN
ejpam-6010	625	10	sompong	sompong	PROPN
ejpam-6010	625	11	,	,	PUNCT
ejpam-6010	625	12	and	and	CCONJ
ejpam-6010	625	13	c.	c.	PROPN
ejpam-6010	625	14	boonpok	boonpok	PROPN
ejpam-6010	625	15	.	.	PUNCT
ejpam-6010	626	1	rarely	rarely	ADV
ejpam-6010	626	2	s-(τ1	s-(τ1	VERB
ejpam-6010	626	3	,	,	PUNCT
ejpam-6010	626	4	τ2)p	τ2)p	ADJ
ejpam-6010	626	5	-	-	PUNCT
ejpam-6010	626	6	continuous	continuous	ADJ
ejpam-6010	626	7	multifunctions	multifunction	NOUN
ejpam-6010	626	8	.	.	PUNCT
ejpam-6010	627	1	european	european	ADJ
ejpam-6010	627	2	journal	journal	PROPN
ejpam-6010	627	3	of	of	ADP
ejpam-6010	627	4	pure	pure	ADJ
ejpam-6010	627	5	and	and	CCONJ
ejpam-6010	627	6	applied	applied	ADJ
ejpam-6010	627	7	mathematics	mathematic	NOUN
ejpam-6010	627	8	,	,	PUNCT
ejpam-6010	627	9	18(1):5649	18(1):5649	NUM
ejpam-6010	627	10	,	,	PUNCT
ejpam-6010	627	11	2025	2025	NUM
ejpam-6010	627	12	.	.	PUNCT
ejpam-6010	628	1	[	[	X
ejpam-6010	628	2	69	69	NUM
ejpam-6010	628	3	]	]	X
ejpam-6010	628	4	n.	n.	NOUN
ejpam-6010	628	5	chutiman	chutiman	NOUN
ejpam-6010	628	6	,	,	PUNCT
ejpam-6010	628	7	a.	a.	PROPN
ejpam-6010	628	8	sama	sama	PROPN
ejpam-6010	628	9	-	-	PUNCT
ejpam-6010	628	10	ae	ae	PROPN
ejpam-6010	628	11	,	,	PUNCT
ejpam-6010	628	12	and	and	CCONJ
ejpam-6010	628	13	c.	c.	PROPN
ejpam-6010	628	14	boonpok	boonpok	PROPN
ejpam-6010	628	15	.	.	PUNCT
ejpam-6010	629	1	almost	almost	ADV
ejpam-6010	629	2	near	near	ADV
ejpam-6010	629	3	(	(	PUNCT
ejpam-6010	629	4	τ1	τ1	NOUN
ejpam-6010	629	5	,	,	PUNCT
ejpam-6010	629	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	629	7	for	for	ADP
ejpam-6010	629	8	multifunctions	multifunction	NOUN
ejpam-6010	629	9	.	.	PUNCT
ejpam-6010	630	1	european	european	ADJ
ejpam-6010	630	2	journal	journal	PROPN
ejpam-6010	630	3	of	of	ADP
ejpam-6010	630	4	pure	pure	ADJ
ejpam-6010	630	5	and	and	CCONJ
ejpam-6010	630	6	applied	applied	ADJ
ejpam-6010	630	7	mathematics	mathematic	NOUN
ejpam-6010	630	8	,	,	PUNCT
ejpam-6010	630	9	18(1):5650	18(1):5650	NUM
ejpam-6010	630	10	,	,	PUNCT
ejpam-6010	630	11	2025	2025	NUM
ejpam-6010	630	12	.	.	PUNCT
ejpam-6010	631	1	[	[	X
ejpam-6010	631	2	70	70	NUM
ejpam-6010	631	3	]	]	X
ejpam-6010	631	4	m.	m.	NOUN
ejpam-6010	631	5	chiangpradit	chiangpradit	NOUN
ejpam-6010	631	6	,	,	PUNCT
ejpam-6010	631	7	a.	a.	PROPN
ejpam-6010	631	8	sama	sama	PROPN
ejpam-6010	631	9	-	-	PUNCT
ejpam-6010	631	10	ae	ae	PROPN
ejpam-6010	631	11	,	,	PUNCT
ejpam-6010	631	12	and	and	CCONJ
ejpam-6010	631	13	c.	c.	PROPN
ejpam-6010	631	14	boonpok	boonpok	PROPN
ejpam-6010	631	15	.	.	PUNCT
ejpam-6010	632	1	s-(τ1	s-(τ1	PROPN
ejpam-6010	632	2	,	,	PUNCT
ejpam-6010	632	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	632	4	for	for	ADP
ejpam-6010	632	5	multifunctions	multifunction	NOUN
ejpam-6010	632	6	.	.	PUNCT
ejpam-6010	633	1	european	european	ADJ
ejpam-6010	633	2	journal	journal	PROPN
ejpam-6010	633	3	of	of	ADP
ejpam-6010	633	4	pure	pure	ADJ
ejpam-6010	633	5	and	and	CCONJ
ejpam-6010	633	6	applied	applied	ADJ
ejpam-6010	633	7	mathematics	mathematic	NOUN
ejpam-6010	633	8	,	,	PUNCT
ejpam-6010	633	9	18(1):5634	18(1):5634	NUM
ejpam-6010	633	10	,	,	PUNCT
ejpam-6010	633	11	2025	2025	NUM
ejpam-6010	633	12	.	.	PUNCT
ejpam-6010	634	1	[	[	X
ejpam-6010	634	2	71	71	NUM
ejpam-6010	634	3	]	]	X
ejpam-6010	634	4	p.	p.	NOUN
ejpam-6010	634	5	pue	pue	NOUN
ejpam-6010	634	6	-	-	PUNCT
ejpam-6010	634	7	on	on	ADP
ejpam-6010	634	8	,	,	PUNCT
ejpam-6010	634	9	a.	a.	PROPN
ejpam-6010	634	10	sama	sama	PROPN
ejpam-6010	634	11	-	-	PUNCT
ejpam-6010	634	12	ae	ae	PROPN
ejpam-6010	634	13	,	,	PUNCT
ejpam-6010	634	14	and	and	CCONJ
ejpam-6010	634	15	c.	c.	PROPN
ejpam-6010	634	16	boonpok	boonpok	PROPN
ejpam-6010	634	17	.	.	PUNCT
ejpam-6010	635	1	quasi	quasi	PROPN
ejpam-6010	635	2	θ(τ1	θ(τ1	PROPN
ejpam-6010	635	3	,	,	PUNCT
ejpam-6010	635	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	635	5	for	for	ADP
ejpam-6010	635	6	multifunctions	multifunction	NOUN
ejpam-6010	635	7	.	.	PUNCT
ejpam-6010	636	1	european	european	ADJ
ejpam-6010	636	2	journal	journal	PROPN
ejpam-6010	636	3	of	of	ADP
ejpam-6010	636	4	pure	pure	ADJ
ejpam-6010	636	5	and	and	CCONJ
ejpam-6010	636	6	applied	applied	ADJ
ejpam-6010	636	7	mathematics	mathematic	NOUN
ejpam-6010	636	8	,	,	PUNCT
ejpam-6010	636	9	18(1):5717	18(1):5717	NUM
ejpam-6010	636	10	,	,	PUNCT
ejpam-6010	636	11	2025	2025	NUM
ejpam-6010	636	12	.	.	PUNCT
ejpam-6010	637	1	[	[	X
ejpam-6010	637	2	72	72	NUM
ejpam-6010	637	3	]	]	X
ejpam-6010	637	4	j.	j.	PROPN
ejpam-6010	637	5	khampakdee	khampakdee	PROPN
ejpam-6010	637	6	,	,	PUNCT
ejpam-6010	637	7	a.	a.	PROPN
ejpam-6010	637	8	sama	sama	PROPN
ejpam-6010	637	9	-	-	PUNCT
ejpam-6010	637	10	ae	ae	PROPN
ejpam-6010	637	11	,	,	PUNCT
ejpam-6010	637	12	and	and	CCONJ
ejpam-6010	637	13	c.	c.	PROPN
ejpam-6010	637	14	boonpok	boonpok	PROPN
ejpam-6010	637	15	.	.	PUNCT
ejpam-6010	638	1	almost	almost	ADV
ejpam-6010	638	2	nearly	nearly	ADV
ejpam-6010	638	3	quasi	quasi	NOUN
ejpam-6010	638	4	(	(	PUNCT
ejpam-6010	638	5	τ1	τ1	NOUN
ejpam-6010	638	6	,	,	PUNCT
ejpam-6010	638	7	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	638	8	multifunctions	multifunction	NOUN
ejpam-6010	638	9	.	.	PUNCT
ejpam-6010	639	1	european	european	ADJ
ejpam-6010	639	2	journal	journal	PROPN
ejpam-6010	639	3	of	of	ADP
ejpam-6010	639	4	pure	pure	ADJ
ejpam-6010	639	5	and	and	CCONJ
ejpam-6010	639	6	applied	applied	ADJ
ejpam-6010	639	7	mathematics	mathematic	NOUN
ejpam-6010	639	8	,	,	PUNCT
ejpam-6010	639	9	18(1):5720	18(1):5720	NUM
ejpam-6010	639	10	,	,	PUNCT
ejpam-6010	639	11	2025	2025	NUM
ejpam-6010	639	12	.	.	PUNCT
ejpam-6010	640	1	[	[	X
ejpam-6010	640	2	73	73	NUM
ejpam-6010	640	3	]	]	X
ejpam-6010	640	4	p.	p.	NOUN
ejpam-6010	640	5	pue	pue	NOUN
ejpam-6010	640	6	-	-	PUNCT
ejpam-6010	640	7	on	on	ADP
ejpam-6010	640	8	,	,	PUNCT
ejpam-6010	640	9	a.	a.	PROPN
ejpam-6010	640	10	sama	sama	PROPN
ejpam-6010	640	11	-	-	PUNCT
ejpam-6010	640	12	ae	ae	PROPN
ejpam-6010	640	13	,	,	PUNCT
ejpam-6010	640	14	and	and	CCONJ
ejpam-6010	640	15	c.	c.	PROPN
ejpam-6010	640	16	boonpok	boonpok	PROPN
ejpam-6010	640	17	.	.	PUNCT
ejpam-6010	641	1	upper	upper	ADJ
ejpam-6010	641	2	and	and	CCONJ
ejpam-6010	641	3	lower	low	ADJ
ejpam-6010	641	4	weakly	weakly	ADJ
ejpam-6010	641	5	s-(τ1	s-(τ1	PROPN
ejpam-6010	641	6	,	,	PUNCT
ejpam-6010	641	7	τ2)continuous	τ2)continuous	ADJ
ejpam-6010	641	8	multifunctions	multifunction	NOUN
ejpam-6010	641	9	.	.	PUNCT
ejpam-6010	642	1	european	european	ADJ
ejpam-6010	642	2	journal	journal	PROPN
ejpam-6010	642	3	of	of	ADP
ejpam-6010	642	4	pure	pure	ADJ
ejpam-6010	642	5	and	and	CCONJ
ejpam-6010	642	6	applied	applied	ADJ
ejpam-6010	642	7	mathematics	mathematic	NOUN
ejpam-6010	642	8	,	,	PUNCT
ejpam-6010	642	9	18(1):5718	18(1):5718	NUM
ejpam-6010	642	10	,	,	PUNCT
ejpam-6010	642	11	2025	2025	NUM
ejpam-6010	642	12	.	.	PUNCT
ejpam-6010	643	1	[	[	X
ejpam-6010	643	2	74	74	NUM
ejpam-6010	643	3	]	]	PUNCT
ejpam-6010	643	4	m.	m.	NOUN
ejpam-6010	643	5	thongmoon	thongmoon	NOUN
ejpam-6010	643	6	,	,	PUNCT
ejpam-6010	643	7	a.	a.	PROPN
ejpam-6010	643	8	sama	sama	PROPN
ejpam-6010	643	9	-	-	PUNCT
ejpam-6010	643	10	ae	ae	PROPN
ejpam-6010	643	11	,	,	PUNCT
ejpam-6010	643	12	and	and	CCONJ
ejpam-6010	643	13	c.	c.	PROPN
ejpam-6010	643	14	boonpok	boonpok	PROPN
ejpam-6010	643	15	.	.	PUNCT
ejpam-6010	644	1	upper	upper	ADJ
ejpam-6010	644	2	and	and	CCONJ
ejpam-6010	644	3	lower	low	ADJ
ejpam-6010	644	4	near	near	ADV
ejpam-6010	644	5	(	(	PUNCT
ejpam-6010	644	6	τ1	τ1	NOUN
ejpam-6010	644	7	,	,	PUNCT
ejpam-6010	644	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6010	644	9	.	.	PUNCT
ejpam-6010	645	1	european	european	PROPN
ejpam-6010	645	2	journal	journal	PROPN
ejpam-6010	645	3	of	of	ADP
ejpam-6010	645	4	pure	pure	ADJ
ejpam-6010	645	5	and	and	CCONJ
ejpam-6010	645	6	applied	applied	ADJ
ejpam-6010	645	7	mathematics	mathematic	NOUN
ejpam-6010	645	8	,	,	PUNCT
ejpam-6010	645	9	18(1):5633	18(1):5633	NUM
ejpam-6010	645	10	,	,	PUNCT
ejpam-6010	645	11	2025	2025	NUM
ejpam-6010	645	12	.	.	PUNCT
ejpam-6010	646	1	[	[	X
ejpam-6010	646	2	75	75	NUM
ejpam-6010	646	3	]	]	PUNCT
ejpam-6010	646	4	m.	m.	NOUN
ejpam-6010	646	5	chiangpradit	chiangpradit	NOUN
ejpam-6010	646	6	,	,	PUNCT
ejpam-6010	646	7	s.	s.	PROPN
ejpam-6010	646	8	sompong	sompong	PROPN
ejpam-6010	646	9	,	,	PUNCT
ejpam-6010	646	10	and	and	CCONJ
ejpam-6010	646	11	c.	c.	PROPN
ejpam-6010	646	12	boonpok	boonpok	PROPN
ejpam-6010	646	13	.	.	PUNCT
ejpam-6010	647	1	upper	upper	ADJ
ejpam-6010	647	2	and	and	CCONJ
ejpam-6010	647	3	lower	low	ADJ
ejpam-6010	647	4	almost	almost	ADV
ejpam-6010	647	5	quasi	quasi	NOUN
ejpam-6010	647	6	(	(	PUNCT
ejpam-6010	647	7	τ1	τ1	NOUN
ejpam-6010	647	8	,	,	PUNCT
ejpam-6010	647	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6010	647	10	.	.	PUNCT
ejpam-6010	647	11	asia	asia	PROPN
ejpam-6010	647	12	pacific	pacific	PROPN
ejpam-6010	647	13	journal	journal	PROPN
ejpam-6010	647	14	of	of	ADP
ejpam-6010	647	15	mathematics	mathematic	NOUN
ejpam-6010	647	16	,	,	PUNCT
ejpam-6010	647	17	12:12	12:12	NUM
ejpam-6010	647	18	,	,	PUNCT
ejpam-6010	647	19	2025	2025	NUM
ejpam-6010	647	20	.	.	PUNCT
ejpam-6010	648	1	[	[	X
ejpam-6010	648	2	76	76	NUM
ejpam-6010	648	3	]	]	X
ejpam-6010	648	4	e.	e.	PROPN
ejpam-6010	648	5	ekici	ekici	PROPN
ejpam-6010	648	6	,	,	PUNCT
ejpam-6010	648	7	s.	s.	PROPN
ejpam-6010	648	8	jafari	jafari	PROPN
ejpam-6010	648	9	,	,	PUNCT
ejpam-6010	648	10	and	and	CCONJ
ejpam-6010	648	11	v.	v.	ADP
ejpam-6010	648	12	popa	popa	NOUN
ejpam-6010	648	13	.	.	PUNCT
ejpam-6010	649	1	on	on	ADP
ejpam-6010	649	2	almost	almost	ADV
ejpam-6010	649	3	contra	contra	ADJ
ejpam-6010	649	4	-	-	ADJ
ejpam-6010	649	5	continuous	continuous	ADJ
ejpam-6010	649	6	multifunctions	multifunction	NOUN
ejpam-6010	649	7	.	.	PUNCT
ejpam-6010	650	1	lobachevskii	lobachevskii	PROPN
ejpam-6010	650	2	journal	journal	PROPN
ejpam-6010	650	3	of	of	ADP
ejpam-6010	650	4	mathematics	mathematic	NOUN
ejpam-6010	650	5	,	,	PUNCT
ejpam-6010	650	6	30(2):124–131	30(2):124–131	PROPN
ejpam-6010	650	7	,	,	PUNCT
ejpam-6010	650	8	2009	2009	NUM
ejpam-6010	650	9	.	.	PUNCT
ejpam-6010	651	1	[	[	X
ejpam-6010	651	2	77	77	NUM
ejpam-6010	651	3	]	]	X
ejpam-6010	651	4	c.	c.	PROPN
ejpam-6010	651	5	boonpok	boonpok	PROPN
ejpam-6010	651	6	and	and	CCONJ
ejpam-6010	651	7	j.	j.	PROPN
ejpam-6010	651	8	khampakdee	khampakdee	PROPN
ejpam-6010	651	9	.	.	PUNCT
ejpam-6010	652	1	upper	upper	ADJ
ejpam-6010	652	2	and	and	CCONJ
ejpam-6010	652	3	lower	low	ADJ
ejpam-6010	652	4	almost	almost	ADV
ejpam-6010	652	5	contra-(λ	contra-(λ	PROPN
ejpam-6010	652	6	,	,	PUNCT
ejpam-6010	652	7	sp)-continuity	sp)-continuity	NOUN
ejpam-6010	652	8	.	.	PUNCT
ejpam-6010	653	1	european	european	PROPN
ejpam-6010	653	2	journal	journal	PROPN
ejpam-6010	653	3	of	of	ADP
ejpam-6010	653	4	pure	pure	ADJ
ejpam-6010	653	5	and	and	CCONJ
ejpam-6010	653	6	applied	applied	ADJ
ejpam-6010	653	7	mathematics	mathematic	NOUN
ejpam-6010	653	8	,	,	PUNCT
ejpam-6010	653	9	16(1):156–168	16(1):156–168	PROPN
ejpam-6010	653	10	,	,	PUNCT
ejpam-6010	653	11	2023	2023	NUM
ejpam-6010	653	12	.	.	PUNCT
ejpam-6010	654	1	[	[	X
ejpam-6010	654	2	78	78	NUM
ejpam-6010	654	3	]	]	PUNCT
ejpam-6010	654	4	c.	c.	PROPN
ejpam-6010	654	5	boonpok	boonpok	PROPN
ejpam-6010	654	6	,	,	PUNCT
ejpam-6010	654	7	c.	c.	PROPN
ejpam-6010	654	8	viriyapong	viriyapong	PROPN
ejpam-6010	654	9	,	,	PUNCT
ejpam-6010	654	10	and	and	CCONJ
ejpam-6010	654	11	m.	m.	NOUN
ejpam-6010	654	12	thongmoon	thongmoon	NOUN
ejpam-6010	654	13	.	.	PUNCT
ejpam-6010	655	1	on	on	ADP
ejpam-6010	655	2	upper	upper	ADJ
ejpam-6010	655	3	and	and	CCONJ
ejpam-6010	655	4	lower	low	ADJ
ejpam-6010	655	5	(	(	PUNCT
ejpam-6010	655	6	τ1	τ1	NOUN
ejpam-6010	655	7	,	,	PUNCT
ejpam-6010	655	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6010	655	9	multifunctions	multifunction	NOUN
ejpam-6010	655	10	.	.	PUNCT
ejpam-6010	656	1	journal	journal	PROPN
ejpam-6010	656	2	of	of	ADP
ejpam-6010	656	3	mathematics	mathematics	PROPN
ejpam-6010	656	4	and	and	CCONJ
ejpam-6010	656	5	computer	computer	NOUN
ejpam-6010	656	6	science	science	NOUN
ejpam-6010	656	7	,	,	PUNCT
ejpam-6010	656	8	18:282–293	18:282–293	NUM
ejpam-6010	656	9	,	,	PUNCT
ejpam-6010	656	10	2018	2018	NUM
ejpam-6010	656	11	.	.	PUNCT
ejpam-6010	657	1	[	[	X
ejpam-6010	657	2	79	79	NUM
ejpam-6010	657	3	]	]	X
ejpam-6010	657	4	c.	c.	PROPN
ejpam-6010	657	5	viriyapong	viriyapong	PROPN
ejpam-6010	657	6	and	and	CCONJ
ejpam-6010	657	7	c.	c.	PROPN
ejpam-6010	657	8	boonpok	boonpok	PROPN
ejpam-6010	657	9	.	.	PUNCT
ejpam-6010	658	1	(	(	PUNCT
ejpam-6010	658	2	τ1	τ1	NOUN
ejpam-6010	658	3	,	,	PUNCT
ejpam-6010	658	4	τ2)α	τ2)α	NOUN
ejpam-6010	658	5	-	-	PUNCT
ejpam-6010	658	6	continuity	continuity	NOUN
ejpam-6010	658	7	for	for	ADP
ejpam-6010	658	8	multifunctions	multifunction	NOUN
ejpam-6010	658	9	.	.	PUNCT
ejpam-6010	659	1	journal	journal	PROPN
ejpam-6010	659	2	of	of	ADP
ejpam-6010	659	3	mathematics	mathematic	NOUN
ejpam-6010	659	4	,	,	PUNCT
ejpam-6010	659	5	2020:6285763	2020:6285763	NUM
ejpam-6010	659	6	,	,	PUNCT
ejpam-6010	659	7	2020	2020	NUM
ejpam-6010	659	8	.	.	PUNCT
ejpam-6010	660	1	[	[	X
ejpam-6010	660	2	80	80	NUM
ejpam-6010	660	3	]	]	X
ejpam-6010	660	4	n.	n.	PROPN
ejpam-6010	660	5	viriyapong	viriyapong	PROPN
ejpam-6010	660	6	,	,	PUNCT
ejpam-6010	660	7	s.	s.	PROPN
ejpam-6010	660	8	sompong	sompong	PROPN
ejpam-6010	660	9	,	,	PUNCT
ejpam-6010	660	10	and	and	CCONJ
ejpam-6010	660	11	c.	c.	PROPN
ejpam-6010	660	12	boonpok	boonpok	PROPN
ejpam-6010	660	13	.	.	PUNCT
ejpam-6010	661	1	(	(	PUNCT
ejpam-6010	661	2	τ1	τ1	NOUN
ejpam-6010	661	3	,	,	PUNCT
ejpam-6010	661	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6010	661	5	disconnectedness	disconnectedness	NOUN
ejpam-6010	661	6	in	in	ADP
ejpam-6010	661	7	bitopological	bitopological	ADJ
ejpam-6010	661	8	spaces	space	NOUN
ejpam-6010	661	9	.	.	PUNCT
ejpam-6010	662	1	international	international	ADJ
ejpam-6010	662	2	journal	journal	PROPN
ejpam-6010	662	3	of	of	ADP
ejpam-6010	662	4	mathematics	mathematic	NOUN
ejpam-6010	662	5	and	and	CCONJ
ejpam-6010	662	6	computer	computer	NOUN
ejpam-6010	662	7	science	science	NOUN
ejpam-6010	662	8	,	,	PUNCT
ejpam-6010	662	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6010	662	10	,	,	PUNCT
ejpam-6010	662	11	2024	2024	NUM
ejpam-6010	662	12	.	.	PUNCT
ejpam-6010	663	1	[	[	X
ejpam-6010	663	2	81	81	NUM
ejpam-6010	663	3	]	]	PUNCT
ejpam-6010	663	4	p.	p.	NOUN
ejpam-6010	663	5	pue	pue	NOUN
ejpam-6010	663	6	-	-	PUNCT
ejpam-6010	663	7	on	on	ADP
ejpam-6010	663	8	,	,	PUNCT
ejpam-6010	663	9	s.	s.	PROPN
ejpam-6010	663	10	sompong	sompong	PROPN
ejpam-6010	663	11	,	,	PUNCT
ejpam-6010	663	12	and	and	CCONJ
ejpam-6010	663	13	c.	c.	PROPN
ejpam-6010	663	14	boonpok	boonpok	PROPN
ejpam-6010	663	15	.	.	PUNCT
ejpam-6010	664	1	almost	almost	ADV
ejpam-6010	664	2	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	664	3	,	,	PUNCT
ejpam-6010	664	4	τ2)p	τ2)p	NOUN
ejpam-6010	664	5	-	-	PUNCT
ejpam-6010	664	6	continuity	continuity	NOUN
ejpam-6010	664	7	for	for	ADP
ejpam-6010	664	8	functions	function	NOUN
ejpam-6010	664	9	.	.	PUNCT
ejpam-6010	665	1	(	(	PUNCT
ejpam-6010	665	2	accepted	accept	VERB
ejpam-6010	665	3	)	)	PUNCT
ejpam-6010	665	4	.	.	PUNCT
ejpam-6010	666	1	[	[	X
ejpam-6010	666	2	82	82	NUM
ejpam-6010	666	3	]	]	X
ejpam-6010	666	4	n.	n.	PROPN
ejpam-6010	666	5	viriyapong	viriyapong	PROPN
ejpam-6010	666	6	,	,	PUNCT
ejpam-6010	666	7	a.	a.	PROPN
ejpam-6010	666	8	sama	sama	PROPN
ejpam-6010	666	9	-	-	PUNCT
ejpam-6010	666	10	ae	ae	PROPN
ejpam-6010	666	11	,	,	PUNCT
ejpam-6010	666	12	and	and	CCONJ
ejpam-6010	666	13	c.	c.	PROPN
ejpam-6010	666	14	boonpok	boonpok	PROPN
ejpam-6010	666	15	.	.	PUNCT
ejpam-6010	667	1	upper	upper	ADJ
ejpam-6010	667	2	and	and	CCONJ
ejpam-6010	667	3	lower	low	ADJ
ejpam-6010	667	4	contra-(τ1	contra-(τ1	NOUN
ejpam-6010	667	5	,	,	PUNCT
ejpam-6010	667	6	τ2)continuity	τ2)continuity	PROPN
ejpam-6010	667	7	.	.	PUNCT
ejpam-6010	668	1	(	(	PUNCT
ejpam-6010	668	2	accepted	accept	VERB
ejpam-6010	668	3	)	)	PUNCT
ejpam-6010	668	4	.	.	PUNCT