id	sid	tid	token	lemma	pos
ejpam-5633	1	1	european	european	PROPN
ejpam-5633	1	2	journal	journal	PROPN
ejpam-5633	1	3	of	of	ADP
ejpam-5633	1	4	pure	pure	ADJ
ejpam-5633	1	5	and	and	CCONJ
ejpam-5633	1	6	applied	applied	ADJ
ejpam-5633	1	7	mathematics	mathematic	NOUN
ejpam-5633	1	8	2025	2025	NUM
ejpam-5633	1	9	,	,	PUNCT
ejpam-5633	1	10	vol	vol	NOUN
ejpam-5633	1	11	.	.	PROPN
ejpam-5633	1	12	18	18	NUM
ejpam-5633	1	13	,	,	PUNCT
ejpam-5633	1	14	issue	issue	NOUN
ejpam-5633	1	15	1	1	NUM
ejpam-5633	1	16	,	,	PUNCT
ejpam-5633	1	17	article	article	NOUN
ejpam-5633	1	18	number	number	NOUN
ejpam-5633	1	19	5633	5633	NUM
ejpam-5633	1	20	issn	issn	PROPN
ejpam-5633	1	21	1307	1307	NUM
ejpam-5633	1	22	-	-	SYM
ejpam-5633	1	23	5543	5543	NUM
ejpam-5633	1	24	–	–	PUNCT
ejpam-5633	1	25	ejpam.com	ejpam.com	X
ejpam-5633	1	26	published	publish	VERB
ejpam-5633	1	27	by	by	ADP
ejpam-5633	1	28	new	new	PROPN
ejpam-5633	1	29	york	york	PROPN
ejpam-5633	1	30	business	business	PROPN
ejpam-5633	1	31	global	global	PROPN
ejpam-5633	1	32	upper	upper	ADJ
ejpam-5633	1	33	and	and	CCONJ
ejpam-5633	1	34	lower	low	ADJ
ejpam-5633	1	35	near	near	ADV
ejpam-5633	1	36	(	(	PUNCT
ejpam-5633	1	37	τ1	τ1	NOUN
ejpam-5633	1	38	,	,	PUNCT
ejpam-5633	1	39	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5633	1	40	montri	montri	PROPN
ejpam-5633	1	41	thongmoon1	thongmoon1	PROPN
ejpam-5633	1	42	,	,	PUNCT
ejpam-5633	1	43	areeyuth	areeyuth	NOUN
ejpam-5633	1	44	sama	sama	NOUN
ejpam-5633	1	45	-	-	PUNCT
ejpam-5633	1	46	ae2	ae2	PROPN
ejpam-5633	1	47	,	,	PUNCT
ejpam-5633	1	48	chawalit	chawalit	VERB
ejpam-5633	1	49	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5633	1	50	1	1	NUM
ejpam-5633	1	51	mathematics	mathematic	NOUN
ejpam-5633	1	52	and	and	CCONJ
ejpam-5633	1	53	applied	apply	VERB
ejpam-5633	1	54	mathematics	mathematics	PROPN
ejpam-5633	1	55	research	research	NOUN
ejpam-5633	1	56	unit	unit	NOUN
ejpam-5633	1	57	,	,	PUNCT
ejpam-5633	1	58	department	department	NOUN
ejpam-5633	1	59	of	of	ADP
ejpam-5633	1	60	mathematics	mathematic	NOUN
ejpam-5633	1	61	,	,	PUNCT
ejpam-5633	1	62	faculty	faculty	NOUN
ejpam-5633	1	63	of	of	ADP
ejpam-5633	1	64	science	science	NOUN
ejpam-5633	1	65	,	,	PUNCT
ejpam-5633	1	66	mahasarakham	mahasarakham	PROPN
ejpam-5633	1	67	university	university	PROPN
ejpam-5633	1	68	,	,	PUNCT
ejpam-5633	1	69	maha	maha	PROPN
ejpam-5633	1	70	sarakham	sarakham	PROPN
ejpam-5633	1	71	,	,	PUNCT
ejpam-5633	1	72	44150	44150	NUM
ejpam-5633	1	73	,	,	PUNCT
ejpam-5633	1	74	thailand	thailand	PROPN
ejpam-5633	1	75	2	2	NUM
ejpam-5633	1	76	department	department	NOUN
ejpam-5633	1	77	of	of	ADP
ejpam-5633	1	78	mathematics	mathematic	NOUN
ejpam-5633	1	79	and	and	CCONJ
ejpam-5633	1	80	computer	computer	NOUN
ejpam-5633	1	81	science	science	NOUN
ejpam-5633	1	82	,	,	PUNCT
ejpam-5633	1	83	faculty	faculty	NOUN
ejpam-5633	1	84	of	of	ADP
ejpam-5633	1	85	science	science	NOUN
ejpam-5633	1	86	and	and	CCONJ
ejpam-5633	1	87	technology	technology	NOUN
ejpam-5633	1	88	,	,	PUNCT
ejpam-5633	1	89	prince	prince	NOUN
ejpam-5633	1	90	of	of	ADP
ejpam-5633	1	91	songkla	songkla	PROPN
ejpam-5633	1	92	university	university	PROPN
ejpam-5633	1	93	,	,	PUNCT
ejpam-5633	1	94	pattani	pattani	NOUN
ejpam-5633	1	95	campus	campus	NOUN
ejpam-5633	1	96	,	,	PUNCT
ejpam-5633	1	97	pattani	pattani	NOUN
ejpam-5633	1	98	,	,	PUNCT
ejpam-5633	1	99	94000	94000	NUM
ejpam-5633	1	100	,	,	PUNCT
ejpam-5633	1	101	thailand	thailand	PROPN
ejpam-5633	1	102	abstract	abstract	PROPN
ejpam-5633	1	103	.	.	PUNCT
ejpam-5633	2	1	this	this	DET
ejpam-5633	2	2	paper	paper	NOUN
ejpam-5633	2	3	presents	present	VERB
ejpam-5633	2	4	new	new	ADJ
ejpam-5633	2	5	classes	class	NOUN
ejpam-5633	2	6	of	of	ADP
ejpam-5633	2	7	multifunctions	multifunction	NOUN
ejpam-5633	2	8	called	call	VERB
ejpam-5633	2	9	upper	upper	ADV
ejpam-5633	2	10	nearly	nearly	ADV
ejpam-5633	2	11	(	(	PUNCT
ejpam-5633	2	12	τ1	τ1	NOUN
ejpam-5633	2	13	,	,	PUNCT
ejpam-5633	2	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	2	15	multifunctions	multifunction	NOUN
ejpam-5633	2	16	and	and	CCONJ
ejpam-5633	2	17	lower	low	ADJ
ejpam-5633	2	18	nearly	nearly	ADV
ejpam-5633	2	19	(	(	PUNCT
ejpam-5633	2	20	τ1	τ1	NOUN
ejpam-5633	2	21	,	,	PUNCT
ejpam-5633	2	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	2	23	multifunctions	multifunction	NOUN
ejpam-5633	2	24	.	.	PUNCT
ejpam-5633	3	1	furthermore	furthermore	ADV
ejpam-5633	3	2	,	,	PUNCT
ejpam-5633	3	3	some	some	DET
ejpam-5633	3	4	characterizations	characterization	NOUN
ejpam-5633	3	5	of	of	ADP
ejpam-5633	3	6	upper	upper	ADJ
ejpam-5633	3	7	nearly	nearly	ADV
ejpam-5633	3	8	(	(	PUNCT
ejpam-5633	3	9	τ1	τ1	NOUN
ejpam-5633	3	10	,	,	PUNCT
ejpam-5633	3	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	3	12	multifunctions	multifunction	NOUN
ejpam-5633	3	13	and	and	CCONJ
ejpam-5633	3	14	lower	low	ADJ
ejpam-5633	3	15	nearly	nearly	ADV
ejpam-5633	3	16	(	(	PUNCT
ejpam-5633	3	17	τ1	τ1	NOUN
ejpam-5633	3	18	,	,	PUNCT
ejpam-5633	3	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	3	20	multifunctions	multifunction	NOUN
ejpam-5633	3	21	are	be	AUX
ejpam-5633	3	22	established	establish	VERB
ejpam-5633	3	23	.	.	PUNCT
ejpam-5633	4	1	2020	2020	NUM
ejpam-5633	4	2	mathematics	mathematics	PROPN
ejpam-5633	4	3	subject	subject	NOUN
ejpam-5633	4	4	classifications	classification	NOUN
ejpam-5633	4	5	:	:	PUNCT
ejpam-5633	4	6	54c08	54c08	NUM
ejpam-5633	4	7	,	,	PUNCT
ejpam-5633	4	8	54c60	54c60	NUM
ejpam-5633	4	9	key	key	ADJ
ejpam-5633	4	10	words	word	NOUN
ejpam-5633	4	11	and	and	CCONJ
ejpam-5633	4	12	phrases	phrase	NOUN
ejpam-5633	4	13	:	:	PUNCT
ejpam-5633	4	14	upper	upper	ADJ
ejpam-5633	4	15	nearly	nearly	ADV
ejpam-5633	4	16	(	(	PUNCT
ejpam-5633	4	17	τ1	τ1	NOUN
ejpam-5633	4	18	,	,	PUNCT
ejpam-5633	4	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	4	20	multifunction	multifunction	NOUN
ejpam-5633	4	21	,	,	PUNCT
ejpam-5633	4	22	lower	low	ADJ
ejpam-5633	4	23	nearly	nearly	ADV
ejpam-5633	4	24	(	(	PUNCT
ejpam-5633	4	25	τ1	τ1	NOUN
ejpam-5633	4	26	,	,	PUNCT
ejpam-5633	4	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5633	4	28	multifunction	multifunction	NOUN
ejpam-5633	4	29	1	1	NUM
ejpam-5633	4	30	.	.	PUNCT
ejpam-5633	4	31	introduction	introduction	NOUN
ejpam-5633	4	32	the	the	DET
ejpam-5633	4	33	field	field	NOUN
ejpam-5633	4	34	of	of	ADP
ejpam-5633	4	35	the	the	DET
ejpam-5633	4	36	mathematical	mathematical	ADJ
ejpam-5633	4	37	science	science	NOUN
ejpam-5633	4	38	which	which	PRON
ejpam-5633	4	39	goes	go	VERB
ejpam-5633	4	40	under	under	ADP
ejpam-5633	4	41	the	the	DET
ejpam-5633	4	42	name	name	NOUN
ejpam-5633	4	43	of	of	ADP
ejpam-5633	4	44	topology	topology	NOUN
ejpam-5633	4	45	is	be	AUX
ejpam-5633	4	46	concerned	concern	VERB
ejpam-5633	4	47	with	with	ADP
ejpam-5633	4	48	all	all	DET
ejpam-5633	4	49	questions	question	NOUN
ejpam-5633	4	50	directly	directly	ADV
ejpam-5633	4	51	or	or	CCONJ
ejpam-5633	4	52	indirectly	indirectly	ADV
ejpam-5633	4	53	related	relate	VERB
ejpam-5633	4	54	to	to	ADP
ejpam-5633	4	55	continuity	continuity	NOUN
ejpam-5633	4	56	.	.	PUNCT
ejpam-5633	5	1	weaker	weak	ADJ
ejpam-5633	5	2	and	and	CCONJ
ejpam-5633	5	3	stronger	strong	ADJ
ejpam-5633	5	4	forms	form	NOUN
ejpam-5633	5	5	of	of	ADP
ejpam-5633	5	6	open	open	ADJ
ejpam-5633	5	7	sets	set	NOUN
ejpam-5633	5	8	play	play	VERB
ejpam-5633	5	9	an	an	DET
ejpam-5633	5	10	important	important	ADJ
ejpam-5633	5	11	role	role	NOUN
ejpam-5633	5	12	in	in	ADP
ejpam-5633	5	13	the	the	DET
ejpam-5633	5	14	generalization	generalization	NOUN
ejpam-5633	5	15	of	of	ADP
ejpam-5633	5	16	different	different	ADJ
ejpam-5633	5	17	forms	form	NOUN
ejpam-5633	5	18	of	of	ADP
ejpam-5633	5	19	continuity	continuity	NOUN
ejpam-5633	5	20	.	.	PUNCT
ejpam-5633	6	1	using	use	VERB
ejpam-5633	6	2	different	different	ADJ
ejpam-5633	6	3	forms	form	NOUN
ejpam-5633	6	4	of	of	ADP
ejpam-5633	6	5	open	open	ADJ
ejpam-5633	6	6	sets	set	NOUN
ejpam-5633	6	7	,	,	PUNCT
ejpam-5633	6	8	several	several	ADJ
ejpam-5633	6	9	authors	author	NOUN
ejpam-5633	6	10	have	have	AUX
ejpam-5633	6	11	introduced	introduce	VERB
ejpam-5633	6	12	and	and	CCONJ
ejpam-5633	6	13	investigated	investigate	VERB
ejpam-5633	6	14	various	various	ADJ
ejpam-5633	6	15	types	type	NOUN
ejpam-5633	6	16	of	of	ADP
ejpam-5633	6	17	continuity	continuity	NOUN
ejpam-5633	6	18	for	for	ADP
ejpam-5633	6	19	functions	function	NOUN
ejpam-5633	6	20	and	and	CCONJ
ejpam-5633	6	21	multifunctions	multifunction	NOUN
ejpam-5633	6	22	.	.	PUNCT
ejpam-5633	7	1	carnahan	carnahan	PROPN
ejpam-5633	8	1	[	[	X
ejpam-5633	8	2	30	30	NUM
ejpam-5633	8	3	]	]	PUNCT
ejpam-5633	8	4	introduced	introduce	VERB
ejpam-5633	8	5	the	the	DET
ejpam-5633	8	6	notion	notion	NOUN
ejpam-5633	8	7	of	of	ADP
ejpam-5633	8	8	n	n	CCONJ
ejpam-5633	8	9	-	-	PUNCT
ejpam-5633	8	10	closed	closed	ADJ
ejpam-5633	8	11	sets	set	NOUN
ejpam-5633	8	12	in	in	ADP
ejpam-5633	8	13	topological	topological	ADJ
ejpam-5633	8	14	spaces	space	NOUN
ejpam-5633	8	15	.	.	PUNCT
ejpam-5633	9	1	noiri	noiri	PROPN
ejpam-5633	10	1	[	[	X
ejpam-5633	10	2	44	44	NUM
ejpam-5633	10	3	]	]	PUNCT
ejpam-5633	10	4	studied	study	VERB
ejpam-5633	10	5	several	several	ADJ
ejpam-5633	10	6	properties	property	NOUN
ejpam-5633	10	7	of	of	ADP
ejpam-5633	10	8	n	n	CCONJ
ejpam-5633	10	9	-	-	PUNCT
ejpam-5633	10	10	closed	closed	ADJ
ejpam-5633	10	11	sets	set	NOUN
ejpam-5633	10	12	and	and	CCONJ
ejpam-5633	10	13	some	some	DET
ejpam-5633	10	14	separation	separation	NOUN
ejpam-5633	10	15	axioms	axiom	VERB
ejpam-5633	10	16	.	.	PUNCT
ejpam-5633	11	1	the	the	DET
ejpam-5633	11	2	concept	concept	NOUN
ejpam-5633	11	3	of	of	ADP
ejpam-5633	11	4	n	n	CCONJ
ejpam-5633	11	5	-	-	PUNCT
ejpam-5633	11	6	continuous	continuous	ADJ
ejpam-5633	11	7	functions	function	NOUN
ejpam-5633	11	8	was	be	AUX
ejpam-5633	11	9	introduced	introduce	VERB
ejpam-5633	11	10	by	by	ADP
ejpam-5633	11	11	malghan	malghan	PROPN
ejpam-5633	11	12	and	and	CCONJ
ejpam-5633	11	13	hanchinamani	hanchinamani	ADJ
ejpam-5633	11	14	[	[	X
ejpam-5633	11	15	43	43	NUM
ejpam-5633	11	16	]	]	PUNCT
ejpam-5633	11	17	.	.	PUNCT
ejpam-5633	12	1	noiri	noiri	PROPN
ejpam-5633	12	2	and	and	CCONJ
ejpam-5633	12	3	ergun	ergun	NOUN
ejpam-5633	12	4	[	[	X
ejpam-5633	12	5	45	45	NUM
ejpam-5633	12	6	]	]	PUNCT
ejpam-5633	12	7	investigated	investigate	VERB
ejpam-5633	12	8	some	some	DET
ejpam-5633	12	9	characterizations	characterization	NOUN
ejpam-5633	12	10	of	of	ADP
ejpam-5633	12	11	n	n	CCONJ
ejpam-5633	12	12	-	-	PUNCT
ejpam-5633	12	13	continuous	continuous	ADJ
ejpam-5633	12	14	functions	function	NOUN
ejpam-5633	12	15	.	.	PUNCT
ejpam-5633	13	1	viriyapong	viriyapong	PROPN
ejpam-5633	13	2	and	and	CCONJ
ejpam-5633	13	3	boonpok	boonpok	VERB
ejpam-5633	13	4	[	[	X
ejpam-5633	13	5	61	61	NUM
ejpam-5633	13	6	]	]	PUNCT
ejpam-5633	13	7	investigated	investigate	VERB
ejpam-5633	13	8	some	some	DET
ejpam-5633	13	9	characterizations	characterization	NOUN
ejpam-5633	13	10	of	of	ADP
ejpam-5633	13	11	(	(	PUNCT
ejpam-5633	13	12	λ	λ	PROPN
ejpam-5633	13	13	,	,	PUNCT
ejpam-5633	13	14	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	13	15	functions	function	NOUN
ejpam-5633	13	16	by	by	ADP
ejpam-5633	13	17	utilizing	utilize	VERB
ejpam-5633	13	18	the	the	DET
ejpam-5633	13	19	notions	notion	NOUN
ejpam-5633	13	20	of	of	ADP
ejpam-5633	13	21	(	(	PUNCT
ejpam-5633	13	22	λ	λ	PROPN
ejpam-5633	13	23	,	,	PUNCT
ejpam-5633	13	24	sp)-open	sp)-open	ADJ
ejpam-5633	13	25	sets	set	NOUN
ejpam-5633	13	26	and	and	CCONJ
ejpam-5633	13	27	(	(	PUNCT
ejpam-5633	13	28	λ	λ	PROPN
ejpam-5633	13	29	,	,	PUNCT
ejpam-5633	13	30	sp)-closed	sp)-close	VERB
ejpam-5633	13	31	sets	set	NOUN
ejpam-5633	13	32	due	due	ADP
ejpam-5633	13	33	to	to	ADP
ejpam-5633	13	34	boonpok	boonpok	NOUN
ejpam-5633	13	35	and	and	CCONJ
ejpam-5633	13	36	khampakdee	khampakdee	NOUN
ejpam-5633	14	1	[	[	X
ejpam-5633	14	2	12	12	NUM
ejpam-5633	14	3	]	]	PUNCT
ejpam-5633	14	4	.	.	PUNCT
ejpam-5633	15	1	dungthaisong	dungthaisong	NOUN
ejpam-5633	15	2	et	et	PROPN
ejpam-5633	15	3	al	al	PROPN
ejpam-5633	15	4	.	.	PUNCT
ejpam-5633	16	1	[	[	X
ejpam-5633	16	2	36	36	NUM
ejpam-5633	16	3	]	]	PUNCT
ejpam-5633	16	4	introduced	introduce	VERB
ejpam-5633	16	5	and	and	CCONJ
ejpam-5633	16	6	studied	study	VERB
ejpam-5633	16	7	the	the	DET
ejpam-5633	16	8	concept	concept	NOUN
ejpam-5633	16	9	of	of	ADP
ejpam-5633	16	10	g(m	g(m	ADJ
ejpam-5633	16	11	,	,	PUNCT
ejpam-5633	16	12	n)-continuous	n)-continuous	ADJ
ejpam-5633	16	13	functions	function	NOUN
ejpam-5633	16	14	.	.	PUNCT
ejpam-5633	17	1	duangphui	duangphui	NOUN
ejpam-5633	17	2	et	et	PROPN
ejpam-5633	17	3	al	al	PROPN
ejpam-5633	17	4	.	.	PUNCT
ejpam-5633	18	1	[	[	X
ejpam-5633	18	2	35	35	NUM
ejpam-5633	18	3	]	]	PUNCT
ejpam-5633	18	4	introduced	introduce	VERB
ejpam-5633	18	5	and	and	CCONJ
ejpam-5633	18	6	investigated	investigate	VERB
ejpam-5633	18	7	the	the	DET
ejpam-5633	18	8	notion	notion	NOUN
ejpam-5633	18	9	of	of	ADP
ejpam-5633	18	10	(	(	PUNCT
ejpam-5633	18	11	µ	µ	NOUN
ejpam-5633	18	12	,	,	PUNCT
ejpam-5633	18	13	µ′)(m	µ′)(m	VERB
ejpam-5633	18	14	,	,	PUNCT
ejpam-5633	18	15	n)-continuous	n)-continuous	ADJ
ejpam-5633	18	16	functions	function	NOUN
ejpam-5633	18	17	.	.	PUNCT
ejpam-5633	19	1	furthermore	furthermore	ADV
ejpam-5633	19	2	,	,	PUNCT
ejpam-5633	19	3	several	several	ADJ
ejpam-5633	19	4	characterizations	characterization	NOUN
ejpam-5633	19	5	of	of	ADP
ejpam-5633	19	6	almost	almost	ADV
ejpam-5633	19	7	∗corresponding	∗corresponde	VERB
ejpam-5633	19	8	author	author	NOUN
ejpam-5633	19	9	.	.	PUNCT
ejpam-5633	20	1	doi	doi	NOUN
ejpam-5633	20	2	:	:	PUNCT
ejpam-5633	20	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5633	https://doi.org/10.29020/nybg.ejpam.v18i1.5633	PROPN
ejpam-5633	20	4	email	email	NOUN
ejpam-5633	20	5	addresses	address	NOUN
ejpam-5633	20	6	:	:	PUNCT
ejpam-5633	20	7	montri.t@msu.ac.th	montri.t@msu.ac.th	PROPN
ejpam-5633	20	8	(	(	PUNCT
ejpam-5633	20	9	m.	m.	NOUN
ejpam-5633	20	10	thongmoon	thongmoon	PROPN
ejpam-5633	20	11	)	)	PUNCT
ejpam-5633	20	12	,	,	PUNCT
ejpam-5633	20	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-5633	20	14	(	(	PUNCT
ejpam-5633	20	15	a.	a.	PROPN
ejpam-5633	20	16	sama	sama	PROPN
ejpam-5633	20	17	-	-	PUNCT
ejpam-5633	20	18	ae	ae	PROPN
ejpam-5633	20	19	)	)	PUNCT
ejpam-5633	20	20	,	,	PUNCT
ejpam-5633	20	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5633	20	22	(	(	PUNCT
ejpam-5633	20	23	c.	c.	PROPN
ejpam-5633	20	24	boonpok	boonpok	PROPN
ejpam-5633	20	25	)	)	PUNCT
ejpam-5633	20	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5633	20	27	1	1	NUM
ejpam-5633	20	28	copyright	copyright	NOUN
ejpam-5633	20	29	:	:	PUNCT
ejpam-5633	21	1	©	©	PROPN
ejpam-5633	21	2	2025	2025	NUM
ejpam-5633	21	3	the	the	DET
ejpam-5633	21	4	author(s	author(s	NOUN
ejpam-5633	21	5	)	)	PUNCT
ejpam-5633	21	6	.	.	PUNCT
ejpam-5633	22	1	(	(	PUNCT
ejpam-5633	22	2	cc	cc	NOUN
ejpam-5633	22	3	by	by	ADP
ejpam-5633	22	4	-	-	PUNCT
ejpam-5633	22	5	nc	nc	PROPN
ejpam-5633	22	6	4.0	4.0	NUM
ejpam-5633	22	7	)	)	PUNCT
ejpam-5633	22	8	m.	m.	NOUN
ejpam-5633	22	9	thongmoon	thongmoon	NOUN
ejpam-5633	22	10	,	,	PUNCT
ejpam-5633	22	11	a.	a.	PROPN
ejpam-5633	22	12	sama	sama	PROPN
ejpam-5633	22	13	-	-	PUNCT
ejpam-5633	22	14	ae	ae	PROPN
ejpam-5633	22	15	,	,	PUNCT
ejpam-5633	22	16	c.	c.	PROPN
ejpam-5633	22	17	boonpok	boonpok	PROPN
ejpam-5633	22	18	/	/	SYM
ejpam-5633	22	19	eur	eur	PROPN
ejpam-5633	22	20	.	.	PUNCT
ejpam-5633	23	1	j.	j.	PROPN
ejpam-5633	23	2	pure	pure	PROPN
ejpam-5633	23	3	appl	appl	PROPN
ejpam-5633	23	4	.	.	PROPN
ejpam-5633	23	5	math	math	PROPN
ejpam-5633	23	6	,	,	PUNCT
ejpam-5633	23	7	18	18	NUM
ejpam-5633	23	8	(	(	PUNCT
ejpam-5633	23	9	1	1	NUM
ejpam-5633	23	10	)	)	PUNCT
ejpam-5633	23	11	(	(	PUNCT
ejpam-5633	23	12	2025	2025	NUM
ejpam-5633	23	13	)	)	PUNCT
ejpam-5633	23	14	,	,	PUNCT
ejpam-5633	23	15	5633	5633	NUM
ejpam-5633	23	16	2	2	NUM
ejpam-5633	23	17	of	of	ADP
ejpam-5633	23	18	13	13	NUM
ejpam-5633	23	19	(	(	PUNCT
ejpam-5633	23	20	λ	λ	PROPN
ejpam-5633	23	21	,	,	PUNCT
ejpam-5633	23	22	p)-continuous	p)-continuous	ADJ
ejpam-5633	23	23	functions	function	NOUN
ejpam-5633	23	24	,	,	PUNCT
ejpam-5633	23	25	strongly	strongly	ADV
ejpam-5633	23	26	θ(λ	θ(λ	PROPN
ejpam-5633	23	27	,	,	PUNCT
ejpam-5633	23	28	p)-continuous	p)-continuous	ADJ
ejpam-5633	23	29	functions	function	NOUN
ejpam-5633	23	30	,	,	PUNCT
ejpam-5633	23	31	almost	almost	ADV
ejpam-5633	23	32	strongly	strongly	ADV
ejpam-5633	23	33	θ(λ	θ(λ	VERB
ejpam-5633	23	34	,	,	PUNCT
ejpam-5633	23	35	p)continuous	p)continuous	ADJ
ejpam-5633	23	36	functions	function	NOUN
ejpam-5633	23	37	,	,	PUNCT
ejpam-5633	23	38	θ(λ	θ(λ	PROPN
ejpam-5633	23	39	,	,	PUNCT
ejpam-5633	23	40	p)-continuous	p)-continuous	ADJ
ejpam-5633	23	41	functions	function	NOUN
ejpam-5633	23	42	,	,	PUNCT
ejpam-5633	23	43	weakly	weakly	ADJ
ejpam-5633	23	44	(	(	PUNCT
ejpam-5633	23	45	λ	λ	PROPN
ejpam-5633	23	46	,	,	PUNCT
ejpam-5633	23	47	b)-continuous	b)-continuous	ADJ
ejpam-5633	23	48	functions	function	NOUN
ejpam-5633	23	49	,	,	PUNCT
ejpam-5633	23	50	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5633	23	51	functions	function	NOUN
ejpam-5633	23	52	,	,	PUNCT
ejpam-5633	23	53	(	(	PUNCT
ejpam-5633	23	54	λ	λ	NOUN
ejpam-5633	23	55	,	,	PUNCT
ejpam-5633	23	56	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5633	23	57	functions	function	NOUN
ejpam-5633	23	58	,	,	PUNCT
ejpam-5633	23	59	⋆-continuous	⋆-continuous	ADJ
ejpam-5633	23	60	functions	function	NOUN
ejpam-5633	23	61	,	,	PUNCT
ejpam-5633	23	62	θ	θ	PROPN
ejpam-5633	23	63	-	-	ADJ
ejpam-5633	23	64	i	i	VERB
ejpam-5633	23	65	continuous	continuous	ADJ
ejpam-5633	23	66	functions	function	NOUN
ejpam-5633	23	67	,	,	PUNCT
ejpam-5633	23	68	almost	almost	ADV
ejpam-5633	23	69	(	(	PUNCT
ejpam-5633	23	70	g	g	NOUN
ejpam-5633	23	71	,	,	PUNCT
ejpam-5633	23	72	m)-continuous	m)-continuous	ADJ
ejpam-5633	23	73	functions	function	NOUN
ejpam-5633	23	74	,	,	PUNCT
ejpam-5633	23	75	pairwise	pairwise	NOUN
ejpam-5633	23	76	almost	almost	ADV
ejpam-5633	23	77	m	m	VERB
ejpam-5633	23	78	-continuous	-continuous	ADJ
ejpam-5633	23	79	functions	function	NOUN
ejpam-5633	23	80	,	,	PUNCT
ejpam-5633	23	81	(	(	PUNCT
ejpam-5633	23	82	τ1	τ1	NOUN
ejpam-5633	23	83	,	,	PUNCT
ejpam-5633	23	84	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	23	85	functions	function	NOUN
ejpam-5633	23	86	,	,	PUNCT
ejpam-5633	23	87	almost	almost	ADV
ejpam-5633	23	88	(	(	PUNCT
ejpam-5633	23	89	τ1	τ1	NOUN
ejpam-5633	23	90	,	,	PUNCT
ejpam-5633	23	91	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	23	92	functions	function	NOUN
ejpam-5633	23	93	,	,	PUNCT
ejpam-5633	23	94	weakly	weakly	ADJ
ejpam-5633	23	95	(	(	PUNCT
ejpam-5633	23	96	τ1	τ1	NOUN
ejpam-5633	23	97	,	,	PUNCT
ejpam-5633	23	98	τ2)continuous	τ2)continuous	ADJ
ejpam-5633	23	99	functions	function	NOUN
ejpam-5633	23	100	and	and	CCONJ
ejpam-5633	23	101	faintly	faintly	ADV
ejpam-5633	23	102	(	(	PUNCT
ejpam-5633	23	103	τ1	τ1	PROPN
ejpam-5633	23	104	,	,	PUNCT
ejpam-5633	23	105	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	23	106	functions	function	NOUN
ejpam-5633	23	107	were	be	AUX
ejpam-5633	23	108	presented	present	VERB
ejpam-5633	23	109	in	in	ADP
ejpam-5633	23	110	[	[	X
ejpam-5633	23	111	54	54	NUM
ejpam-5633	23	112	]	]	PUNCT
ejpam-5633	23	113	,	,	PUNCT
ejpam-5633	23	114	[	[	X
ejpam-5633	23	115	57	57	NUM
ejpam-5633	23	116	]	]	PUNCT
ejpam-5633	23	117	,	,	PUNCT
ejpam-5633	23	118	[	[	X
ejpam-5633	23	119	16	16	NUM
ejpam-5633	23	120	]	]	PUNCT
ejpam-5633	23	121	,	,	PUNCT
ejpam-5633	23	122	[	[	X
ejpam-5633	23	123	48	48	NUM
ejpam-5633	23	124	]	]	PUNCT
ejpam-5633	23	125	,	,	PUNCT
ejpam-5633	23	126	[	[	X
ejpam-5633	23	127	25	25	NUM
ejpam-5633	23	128	]	]	PUNCT
ejpam-5633	23	129	,	,	PUNCT
ejpam-5633	23	130	[	[	X
ejpam-5633	23	131	11	11	NUM
ejpam-5633	23	132	]	]	PUNCT
ejpam-5633	23	133	,	,	PUNCT
ejpam-5633	23	134	[	[	X
ejpam-5633	23	135	8	8	NUM
ejpam-5633	23	136	]	]	PUNCT
ejpam-5633	23	137	,	,	PUNCT
ejpam-5633	23	138	[	[	X
ejpam-5633	23	139	10	10	NUM
ejpam-5633	23	140	]	]	PUNCT
ejpam-5633	23	141	,	,	PUNCT
ejpam-5633	23	142	[	[	X
ejpam-5633	23	143	4	4	NUM
ejpam-5633	23	144	]	]	PUNCT
ejpam-5633	23	145	,	,	PUNCT
ejpam-5633	23	146	[	[	X
ejpam-5633	23	147	1	1	NUM
ejpam-5633	23	148	]	]	PUNCT
ejpam-5633	23	149	,	,	PUNCT
ejpam-5633	23	150	[	[	X
ejpam-5633	23	151	2	2	NUM
ejpam-5633	23	152	]	]	PUNCT
ejpam-5633	23	153	,	,	PUNCT
ejpam-5633	23	154	[	[	X
ejpam-5633	23	155	26	26	NUM
ejpam-5633	23	156	]	]	PUNCT
ejpam-5633	23	157	,	,	PUNCT
ejpam-5633	23	158	[	[	X
ejpam-5633	23	159	23	23	NUM
ejpam-5633	23	160	]	]	PUNCT
ejpam-5633	23	161	,	,	PUNCT
ejpam-5633	23	162	[	[	X
ejpam-5633	23	163	18	18	NUM
ejpam-5633	23	164	]	]	PUNCT
ejpam-5633	23	165	and	and	CCONJ
ejpam-5633	23	166	[	[	X
ejpam-5633	23	167	55	55	NUM
ejpam-5633	23	168	]	]	PUNCT
ejpam-5633	23	169	,	,	PUNCT
ejpam-5633	23	170	respectively	respectively	ADV
ejpam-5633	23	171	.	.	PUNCT
ejpam-5633	24	1	chiangpradit	chiangpradit	NOUN
ejpam-5633	24	2	et	et	PROPN
ejpam-5633	24	3	al	al	PROPN
ejpam-5633	24	4	.	.	PUNCT
ejpam-5633	25	1	[	[	X
ejpam-5633	25	2	33	33	NUM
ejpam-5633	25	3	]	]	PUNCT
ejpam-5633	25	4	introduced	introduce	VERB
ejpam-5633	25	5	and	and	CCONJ
ejpam-5633	25	6	investigated	investigate	VERB
ejpam-5633	25	7	the	the	DET
ejpam-5633	25	8	notion	notion	NOUN
ejpam-5633	25	9	of	of	ADP
ejpam-5633	25	10	weakly	weakly	ADJ
ejpam-5633	25	11	quasi	quasi	NOUN
ejpam-5633	25	12	(	(	PUNCT
ejpam-5633	25	13	τ1	τ1	PROPN
ejpam-5633	25	14	,	,	PUNCT
ejpam-5633	25	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	25	16	functions	function	NOUN
ejpam-5633	25	17	.	.	PUNCT
ejpam-5633	26	1	kong	kong	PROPN
ejpam-5633	26	2	-	-	PUNCT
ejpam-5633	26	3	ied	ied	PROPN
ejpam-5633	26	4	et	et	PROPN
ejpam-5633	26	5	al	al	PROPN
ejpam-5633	26	6	.	.	PUNCT
ejpam-5633	27	1	[	[	X
ejpam-5633	27	2	42	42	NUM
ejpam-5633	27	3	]	]	PUNCT
ejpam-5633	27	4	introduced	introduce	VERB
ejpam-5633	27	5	and	and	CCONJ
ejpam-5633	27	6	studied	study	VERB
ejpam-5633	27	7	the	the	DET
ejpam-5633	27	8	concept	concept	NOUN
ejpam-5633	27	9	of	of	ADP
ejpam-5633	27	10	almost	almost	ADV
ejpam-5633	27	11	quasi	quasi	X
ejpam-5633	27	12	(	(	PUNCT
ejpam-5633	27	13	τ1	τ1	NOUN
ejpam-5633	27	14	,	,	PUNCT
ejpam-5633	27	15	τ2)continuous	τ2)continuous	ADJ
ejpam-5633	27	16	functions	function	NOUN
ejpam-5633	27	17	.	.	PUNCT
ejpam-5633	28	1	thongmoon	thongmoon	NOUN
ejpam-5633	28	2	et	et	PROPN
ejpam-5633	28	3	al	al	PROPN
ejpam-5633	28	4	.	.	PUNCT
ejpam-5633	29	1	[	[	X
ejpam-5633	29	2	59	59	NUM
ejpam-5633	29	3	]	]	PUNCT
ejpam-5633	29	4	introduced	introduce	VERB
ejpam-5633	29	5	and	and	CCONJ
ejpam-5633	29	6	investigated	investigate	VERB
ejpam-5633	29	7	the	the	DET
ejpam-5633	29	8	notion	notion	NOUN
ejpam-5633	29	9	of	of	ADP
ejpam-5633	29	10	rarely	rarely	ADV
ejpam-5633	29	11	(	(	PUNCT
ejpam-5633	29	12	τ1	τ1	NOUN
ejpam-5633	29	13	,	,	PUNCT
ejpam-5633	29	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	29	15	functions	function	NOUN
ejpam-5633	29	16	.	.	PUNCT
ejpam-5633	30	1	in	in	ADP
ejpam-5633	30	2	2003	2003	NUM
ejpam-5633	30	3	,	,	PUNCT
ejpam-5633	30	4	ekici	ekici	NOUN
ejpam-5633	30	5	[	[	X
ejpam-5633	30	6	37	37	NUM
ejpam-5633	30	7	]	]	PUNCT
ejpam-5633	30	8	introduced	introduce	VERB
ejpam-5633	30	9	and	and	CCONJ
ejpam-5633	30	10	studied	study	VERB
ejpam-5633	30	11	the	the	DET
ejpam-5633	30	12	concept	concept	NOUN
ejpam-5633	30	13	of	of	ADP
ejpam-5633	30	14	nearly	nearly	ADV
ejpam-5633	30	15	continuous	continuous	ADJ
ejpam-5633	30	16	multifunctions	multifunction	NOUN
ejpam-5633	30	17	as	as	ADP
ejpam-5633	30	18	a	a	DET
ejpam-5633	30	19	generalization	generalization	NOUN
ejpam-5633	30	20	of	of	ADP
ejpam-5633	30	21	semi	semi	ADJ
ejpam-5633	30	22	-	-	ADJ
ejpam-5633	30	23	continuous	continuous	ADJ
ejpam-5633	30	24	multifunctions	multifunction	NOUN
ejpam-5633	30	25	and	and	CCONJ
ejpam-5633	30	26	n	n	CCONJ
ejpam-5633	30	27	-	-	PUNCT
ejpam-5633	30	28	continuous	continuous	ADJ
ejpam-5633	30	29	functions	function	NOUN
ejpam-5633	30	30	.	.	PUNCT
ejpam-5633	31	1	moreover	moreover	ADV
ejpam-5633	31	2	,	,	PUNCT
ejpam-5633	31	3	ekici	ekici	NOUN
ejpam-5633	32	1	[	[	X
ejpam-5633	32	2	38	38	NUM
ejpam-5633	32	3	]	]	PUNCT
ejpam-5633	32	4	introduced	introduce	VERB
ejpam-5633	32	5	and	and	CCONJ
ejpam-5633	32	6	investigated	investigate	VERB
ejpam-5633	32	7	the	the	DET
ejpam-5633	32	8	notion	notion	NOUN
ejpam-5633	32	9	of	of	ADP
ejpam-5633	32	10	almost	almost	ADV
ejpam-5633	32	11	nearly	nearly	ADV
ejpam-5633	32	12	continuous	continuous	ADJ
ejpam-5633	32	13	multifunctions	multifunction	NOUN
ejpam-5633	32	14	as	as	ADP
ejpam-5633	32	15	a	a	DET
ejpam-5633	32	16	generalization	generalization	NOUN
ejpam-5633	32	17	of	of	ADP
ejpam-5633	32	18	nearly	nearly	ADV
ejpam-5633	32	19	continuous	continuous	ADJ
ejpam-5633	32	20	multifunctions	multifunction	NOUN
ejpam-5633	32	21	and	and	CCONJ
ejpam-5633	32	22	almost	almost	ADV
ejpam-5633	32	23	continuous	continuous	ADJ
ejpam-5633	32	24	multifunctions	multifunction	NOUN
ejpam-5633	32	25	[	[	X
ejpam-5633	32	26	47	47	NUM
ejpam-5633	32	27	]	]	PUNCT
ejpam-5633	32	28	.	.	PUNCT
ejpam-5633	33	1	furthermore	furthermore	ADV
ejpam-5633	33	2	,	,	PUNCT
ejpam-5633	33	3	several	several	ADJ
ejpam-5633	33	4	characterizations	characterization	NOUN
ejpam-5633	33	5	and	and	CCONJ
ejpam-5633	33	6	some	some	DET
ejpam-5633	33	7	properties	property	NOUN
ejpam-5633	33	8	concerning	concern	VERB
ejpam-5633	33	9	(	(	PUNCT
ejpam-5633	33	10	τ1	τ1	NOUN
ejpam-5633	33	11	,	,	PUNCT
ejpam-5633	33	12	τ2)δ	τ2)δ	ADJ
ejpam-5633	33	13	-	-	PUNCT
ejpam-5633	33	14	semicontinuous	semicontinuous	ADJ
ejpam-5633	33	15	multifunctions	multifunction	NOUN
ejpam-5633	33	16	,	,	PUNCT
ejpam-5633	33	17	almost	almost	ADV
ejpam-5633	33	18	weakly	weakly	ADJ
ejpam-5633	33	19	(	(	PUNCT
ejpam-5633	33	20	τ1	τ1	NOUN
ejpam-5633	33	21	,	,	PUNCT
ejpam-5633	33	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	23	multifunctions	multifunction	NOUN
ejpam-5633	33	24	,	,	PUNCT
ejpam-5633	33	25	weakly	weakly	ADJ
ejpam-5633	33	26	quasi	quasi	NOUN
ejpam-5633	33	27	(	(	PUNCT
ejpam-5633	33	28	λ	λ	PROPN
ejpam-5633	33	29	,	,	PUNCT
ejpam-5633	33	30	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	31	multifunctions	multifunction	NOUN
ejpam-5633	33	32	,	,	PUNCT
ejpam-5633	33	33	⋆-continuous	⋆-continuous	ADJ
ejpam-5633	33	34	multifunctions	multifunction	NOUN
ejpam-5633	33	35	,	,	PUNCT
ejpam-5633	33	36	β(⋆)-continuous	β(⋆)-continuous	ADJ
ejpam-5633	33	37	multifunctions	multifunction	NOUN
ejpam-5633	33	38	,	,	PUNCT
ejpam-5633	33	39	α-⋆-continuous	α-⋆-continuous	PROPN
ejpam-5633	33	40	multifunctions	multifunction	NOUN
ejpam-5633	33	41	,	,	PUNCT
ejpam-5633	33	42	almost	almost	ADV
ejpam-5633	33	43	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5633	33	44	multifunctions	multifunction	NOUN
ejpam-5633	33	45	,	,	PUNCT
ejpam-5633	33	46	almost	almost	ADV
ejpam-5633	33	47	quasi	quasi	VERB
ejpam-5633	33	48	⋆-continuous	⋆-continuous	ADJ
ejpam-5633	33	49	multifunctions	multifunction	NOUN
ejpam-5633	33	50	,	,	PUNCT
ejpam-5633	33	51	weakly	weakly	ADJ
ejpam-5633	33	52	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5633	33	53	multifunctions	multifunction	NOUN
ejpam-5633	33	54	,	,	PUNCT
ejpam-5633	33	55	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5633	33	56	multifunctions	multifunction	NOUN
ejpam-5633	33	57	,	,	PUNCT
ejpam-5633	33	58	weakly	weakly	ADJ
ejpam-5633	33	59	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5633	33	60	multifunctions	multifunction	NOUN
ejpam-5633	33	61	,	,	PUNCT
ejpam-5633	33	62	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-5633	33	63	continuous	continuous	ADJ
ejpam-5633	33	64	multifunctions	multifunction	NOUN
ejpam-5633	33	65	,	,	PUNCT
ejpam-5633	33	66	almost	almost	ADV
ejpam-5633	33	67	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5633	33	68	multifunctions	multifunction	NOUN
ejpam-5633	33	69	,	,	PUNCT
ejpam-5633	33	70	weakly	weakly	ADJ
ejpam-5633	33	71	(	(	PUNCT
ejpam-5633	33	72	λ	λ	NOUN
ejpam-5633	33	73	,	,	PUNCT
ejpam-5633	33	74	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	75	multifunctions	multifunction	NOUN
ejpam-5633	33	76	,	,	PUNCT
ejpam-5633	33	77	α(λ	α(λ	PROPN
ejpam-5633	33	78	,	,	PUNCT
ejpam-5633	33	79	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	80	multifunctions	multifunction	NOUN
ejpam-5633	33	81	,	,	PUNCT
ejpam-5633	33	82	almost	almost	ADV
ejpam-5633	33	83	α(λ	α(λ	PROPN
ejpam-5633	33	84	,	,	PUNCT
ejpam-5633	33	85	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	86	multifunctions	multifunction	NOUN
ejpam-5633	33	87	,	,	PUNCT
ejpam-5633	33	88	weakly	weakly	ADJ
ejpam-5633	33	89	α(λ	α(λ	PROPN
ejpam-5633	33	90	,	,	PUNCT
ejpam-5633	33	91	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	92	multifunctions	multifunction	NOUN
ejpam-5633	33	93	,	,	PUNCT
ejpam-5633	33	94	almost	almost	ADV
ejpam-5633	33	95	β(λ	β(λ	NOUN
ejpam-5633	33	96	,	,	PUNCT
ejpam-5633	33	97	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	98	multifunctions	multifunction	NOUN
ejpam-5633	33	99	,	,	PUNCT
ejpam-5633	33	100	slightly	slightly	ADV
ejpam-5633	33	101	(	(	PUNCT
ejpam-5633	33	102	λ	λ	NOUN
ejpam-5633	33	103	,	,	PUNCT
ejpam-5633	33	104	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	33	105	multifunctions	multifunction	NOUN
ejpam-5633	33	106	,	,	PUNCT
ejpam-5633	33	107	(	(	PUNCT
ejpam-5633	33	108	τ1	τ1	NOUN
ejpam-5633	33	109	,	,	PUNCT
ejpam-5633	33	110	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	111	multifunctions	multifunction	NOUN
ejpam-5633	33	112	,	,	PUNCT
ejpam-5633	33	113	almost	almost	ADV
ejpam-5633	33	114	(	(	PUNCT
ejpam-5633	33	115	τ1	τ1	NOUN
ejpam-5633	33	116	,	,	PUNCT
ejpam-5633	33	117	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	118	multifunctions	multifunction	NOUN
ejpam-5633	33	119	,	,	PUNCT
ejpam-5633	33	120	weakly	weakly	ADJ
ejpam-5633	33	121	(	(	PUNCT
ejpam-5633	33	122	τ1	τ1	NOUN
ejpam-5633	33	123	,	,	PUNCT
ejpam-5633	33	124	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	125	multifunctions	multifunction	NOUN
ejpam-5633	33	126	,	,	PUNCT
ejpam-5633	33	127	weakly	weakly	ADJ
ejpam-5633	33	128	quasi	quasi	NOUN
ejpam-5633	33	129	(	(	PUNCT
ejpam-5633	33	130	τ1	τ1	PROPN
ejpam-5633	33	131	,	,	PUNCT
ejpam-5633	33	132	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	133	multifunctions	multifunction	NOUN
ejpam-5633	33	134	,	,	PUNCT
ejpam-5633	33	135	almost	almost	ADV
ejpam-5633	33	136	quasi	quasi	NOUN
ejpam-5633	33	137	(	(	PUNCT
ejpam-5633	33	138	τ1	τ1	NOUN
ejpam-5633	33	139	,	,	PUNCT
ejpam-5633	33	140	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	141	multifunctions	multifunction	NOUN
ejpam-5633	33	142	,	,	PUNCT
ejpam-5633	33	143	c(τ1	c(τ1	PROPN
ejpam-5633	33	144	,	,	PUNCT
ejpam-5633	33	145	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	146	multifunctions	multifunction	NOUN
ejpam-5633	33	147	,	,	PUNCT
ejpam-5633	33	148	c	c	NOUN
ejpam-5633	33	149	-	-	PUNCT
ejpam-5633	33	150	quasi	quasi	NOUN
ejpam-5633	33	151	(	(	PUNCT
ejpam-5633	33	152	τ1	τ1	PROPN
ejpam-5633	33	153	,	,	PUNCT
ejpam-5633	33	154	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	33	155	multifunctions	multifunction	NOUN
ejpam-5633	33	156	and	and	CCONJ
ejpam-5633	33	157	s-(τ1	s-(τ1	PROPN
ejpam-5633	33	158	,	,	PUNCT
ejpam-5633	33	159	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5633	33	160	multifunctions	multifunction	NOUN
ejpam-5633	33	161	were	be	AUX
ejpam-5633	33	162	established	establish	VERB
ejpam-5633	33	163	in	in	ADP
ejpam-5633	33	164	[	[	X
ejpam-5633	33	165	5	5	NUM
ejpam-5633	33	166	]	]	PUNCT
ejpam-5633	33	167	,	,	PUNCT
ejpam-5633	34	1	[	[	X
ejpam-5633	34	2	28	28	NUM
ejpam-5633	34	3	]	]	PUNCT
ejpam-5633	34	4	,	,	PUNCT
ejpam-5633	35	1	[	[	X
ejpam-5633	35	2	62	62	NUM
ejpam-5633	35	3	]	]	PUNCT
ejpam-5633	35	4	,	,	PUNCT
ejpam-5633	36	1	[	[	X
ejpam-5633	36	2	3	3	NUM
ejpam-5633	36	3	]	]	PUNCT
ejpam-5633	36	4	,	,	PUNCT
ejpam-5633	36	5	[	[	X
ejpam-5633	36	6	7	7	NUM
ejpam-5633	36	7	]	]	PUNCT
ejpam-5633	36	8	,	,	PUNCT
ejpam-5633	36	9	[	[	X
ejpam-5633	36	10	17	17	NUM
ejpam-5633	36	11	]	]	PUNCT
ejpam-5633	36	12	,	,	PUNCT
ejpam-5633	36	13	[	[	X
ejpam-5633	36	14	24	24	NUM
ejpam-5633	36	15	]	]	PUNCT
ejpam-5633	36	16	,	,	PUNCT
ejpam-5633	36	17	[	[	X
ejpam-5633	36	18	6	6	NUM
ejpam-5633	36	19	]	]	PUNCT
ejpam-5633	36	20	,	,	PUNCT
ejpam-5633	36	21	[	[	X
ejpam-5633	36	22	21	21	NUM
ejpam-5633	36	23	]	]	PUNCT
ejpam-5633	36	24	,	,	PUNCT
ejpam-5633	36	25	[	[	X
ejpam-5633	36	26	20	20	NUM
ejpam-5633	36	27	]	]	PUNCT
ejpam-5633	36	28	,	,	PUNCT
ejpam-5633	36	29	[	[	X
ejpam-5633	36	30	15	15	NUM
ejpam-5633	36	31	]	]	PUNCT
ejpam-5633	36	32	,	,	PUNCT
ejpam-5633	36	33	[	[	X
ejpam-5633	36	34	9	9	NUM
ejpam-5633	36	35	]	]	PUNCT
ejpam-5633	36	36	,	,	PUNCT
ejpam-5633	36	37	[	[	X
ejpam-5633	36	38	19	19	NUM
ejpam-5633	36	39	]	]	PUNCT
ejpam-5633	36	40	,	,	PUNCT
ejpam-5633	36	41	[	[	X
ejpam-5633	36	42	22	22	NUM
ejpam-5633	36	43	]	]	PUNCT
ejpam-5633	36	44	,	,	PUNCT
ejpam-5633	36	45	[	[	X
ejpam-5633	36	46	39	39	NUM
ejpam-5633	36	47	]	]	PUNCT
ejpam-5633	36	48	,	,	PUNCT
ejpam-5633	36	49	[	[	X
ejpam-5633	36	50	13	13	NUM
ejpam-5633	36	51	]	]	PUNCT
ejpam-5633	36	52	,	,	PUNCT
ejpam-5633	36	53	[	[	X
ejpam-5633	36	54	27	27	NUM
ejpam-5633	36	55	]	]	PUNCT
ejpam-5633	36	56	,	,	PUNCT
ejpam-5633	36	57	[	[	X
ejpam-5633	36	58	56	56	NUM
ejpam-5633	36	59	]	]	PUNCT
ejpam-5633	36	60	,	,	PUNCT
ejpam-5633	36	61	[	[	X
ejpam-5633	36	62	14	14	NUM
ejpam-5633	36	63	]	]	PUNCT
ejpam-5633	36	64	,	,	PUNCT
ejpam-5633	36	65	[	[	X
ejpam-5633	36	66	51	51	NUM
ejpam-5633	36	67	]	]	PUNCT
ejpam-5633	36	68	,	,	PUNCT
ejpam-5633	36	69	[	[	X
ejpam-5633	36	70	41	41	NUM
ejpam-5633	36	71	]	]	PUNCT
ejpam-5633	36	72	,	,	PUNCT
ejpam-5633	37	1	[	[	X
ejpam-5633	37	2	58	58	NUM
ejpam-5633	37	3	]	]	PUNCT
ejpam-5633	37	4	,	,	PUNCT
ejpam-5633	37	5	[	[	X
ejpam-5633	37	6	52	52	NUM
ejpam-5633	37	7	]	]	PUNCT
ejpam-5633	37	8	,	,	PUNCT
ejpam-5633	37	9	[	[	X
ejpam-5633	37	10	50	50	NUM
ejpam-5633	37	11	]	]	PUNCT
ejpam-5633	37	12	,	,	PUNCT
ejpam-5633	37	13	[	[	X
ejpam-5633	37	14	40	40	NUM
ejpam-5633	37	15	]	]	PUNCT
ejpam-5633	37	16	,	,	PUNCT
ejpam-5633	38	1	[	[	X
ejpam-5633	38	2	49	49	NUM
ejpam-5633	38	3	]	]	PUNCT
ejpam-5633	38	4	and	and	CCONJ
ejpam-5633	38	5	[	[	X
ejpam-5633	38	6	64	64	NUM
ejpam-5633	38	7	]	]	PUNCT
ejpam-5633	38	8	,	,	PUNCT
ejpam-5633	38	9	respectively	respectively	ADV
ejpam-5633	38	10	.	.	PUNCT
ejpam-5633	39	1	noiri	noiri	PROPN
ejpam-5633	39	2	and	and	CCONJ
ejpam-5633	39	3	popa	popa	NOUN
ejpam-5633	39	4	[	[	X
ejpam-5633	39	5	46	46	NUM
ejpam-5633	39	6	]	]	PUNCT
ejpam-5633	39	7	introduced	introduce	VERB
ejpam-5633	39	8	and	and	CCONJ
ejpam-5633	39	9	studied	study	VERB
ejpam-5633	39	10	the	the	DET
ejpam-5633	39	11	notion	notion	NOUN
ejpam-5633	39	12	of	of	ADP
ejpam-5633	39	13	almost	almost	ADV
ejpam-5633	39	14	nearly	nearly	ADV
ejpam-5633	39	15	mcontinuous	mcontinuous	ADJ
ejpam-5633	39	16	multifunctions	multifunction	NOUN
ejpam-5633	39	17	as	as	ADP
ejpam-5633	39	18	multifunctions	multifunction	NOUN
ejpam-5633	39	19	from	from	ADP
ejpam-5633	39	20	a	a	DET
ejpam-5633	39	21	set	set	NOUN
ejpam-5633	39	22	satisfying	satisfy	VERB
ejpam-5633	39	23	some	some	DET
ejpam-5633	39	24	minimal	minimal	ADJ
ejpam-5633	39	25	conditions	condition	NOUN
ejpam-5633	39	26	into	into	ADP
ejpam-5633	39	27	a	a	DET
ejpam-5633	39	28	topological	topological	ADJ
ejpam-5633	39	29	spaces	space	NOUN
ejpam-5633	39	30	.	.	PUNCT
ejpam-5633	40	1	carpintero	carpintero	NOUN
ejpam-5633	40	2	et	et	PROPN
ejpam-5633	40	3	al	al	PROPN
ejpam-5633	40	4	.	.	PUNCT
ejpam-5633	41	1	[	[	X
ejpam-5633	41	2	31	31	NUM
ejpam-5633	41	3	]	]	PUNCT
ejpam-5633	41	4	introduced	introduce	VERB
ejpam-5633	41	5	and	and	CCONJ
ejpam-5633	41	6	studied	study	VERB
ejpam-5633	41	7	the	the	DET
ejpam-5633	41	8	notion	notion	NOUN
ejpam-5633	41	9	of	of	ADP
ejpam-5633	41	10	nearly	nearly	ADV
ejpam-5633	41	11	ω	ω	ADJ
ejpam-5633	41	12	-	-	ADJ
ejpam-5633	41	13	continuous	continuous	ADJ
ejpam-5633	41	14	multifunctions	multifunction	NOUN
ejpam-5633	41	15	as	as	ADP
ejpam-5633	41	16	a	a	DET
ejpam-5633	41	17	weaker	weak	ADJ
ejpam-5633	41	18	form	form	NOUN
ejpam-5633	41	19	of	of	ADP
ejpam-5633	41	20	nearly	nearly	ADV
ejpam-5633	41	21	continuous	continuous	ADJ
ejpam-5633	41	22	multifunctions	multifunction	NOUN
ejpam-5633	41	23	.	.	PUNCT
ejpam-5633	42	1	rosas	rosa	NOUN
ejpam-5633	42	2	et	et	PROPN
ejpam-5633	42	3	al	al	PROPN
ejpam-5633	42	4	.	.	PUNCT
ejpam-5633	43	1	[	[	X
ejpam-5633	43	2	53	53	NUM
ejpam-5633	43	3	]	]	PUNCT
ejpam-5633	43	4	introduced	introduce	VERB
ejpam-5633	43	5	and	and	CCONJ
ejpam-5633	43	6	studied	study	VERB
ejpam-5633	43	7	upper	upper	ADJ
ejpam-5633	43	8	and	and	CCONJ
ejpam-5633	43	9	lower	low	ADJ
ejpam-5633	43	10	almost	almost	ADV
ejpam-5633	43	11	nearly	nearly	ADV
ejpam-5633	43	12	continuous	continuous	ADJ
ejpam-5633	43	13	multifunctions	multifunction	NOUN
ejpam-5633	43	14	using	use	VERB
ejpam-5633	43	15	notions	notion	NOUN
ejpam-5633	43	16	of	of	ADP
ejpam-5633	43	17	topological	topological	ADJ
ejpam-5633	43	18	ideals	ideal	NOUN
ejpam-5633	43	19	.	.	PUNCT
ejpam-5633	44	1	in	in	ADP
ejpam-5633	44	2	this	this	DET
ejpam-5633	44	3	paper	paper	NOUN
ejpam-5633	44	4	,	,	PUNCT
ejpam-5633	44	5	we	we	PRON
ejpam-5633	44	6	introduce	introduce	VERB
ejpam-5633	44	7	the	the	DET
ejpam-5633	44	8	concepts	concept	NOUN
ejpam-5633	44	9	of	of	ADP
ejpam-5633	44	10	upper	upper	ADJ
ejpam-5633	44	11	nearly	nearly	ADV
ejpam-5633	44	12	(	(	PUNCT
ejpam-5633	44	13	τ1	τ1	NOUN
ejpam-5633	44	14	,	,	PUNCT
ejpam-5633	44	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	44	16	multifunctions	multifunction	NOUN
ejpam-5633	44	17	and	and	CCONJ
ejpam-5633	44	18	lower	low	ADJ
ejpam-5633	44	19	nearly	nearly	ADV
ejpam-5633	44	20	(	(	PUNCT
ejpam-5633	44	21	τ1	τ1	NOUN
ejpam-5633	44	22	,	,	PUNCT
ejpam-5633	44	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	44	24	multifunctions	multifunction	NOUN
ejpam-5633	44	25	.	.	PUNCT
ejpam-5633	45	1	we	we	PRON
ejpam-5633	45	2	also	also	ADV
ejpam-5633	45	3	investigate	investigate	VERB
ejpam-5633	45	4	several	several	ADJ
ejpam-5633	45	5	characterizations	characterization	NOUN
ejpam-5633	45	6	of	of	ADP
ejpam-5633	45	7	upper	upper	ADJ
ejpam-5633	45	8	nearly	nearly	ADV
ejpam-5633	45	9	(	(	PUNCT
ejpam-5633	45	10	τ1	τ1	NOUN
ejpam-5633	45	11	,	,	PUNCT
ejpam-5633	45	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	45	13	multifunctions	multifunction	NOUN
ejpam-5633	45	14	and	and	CCONJ
ejpam-5633	45	15	lower	low	ADJ
ejpam-5633	45	16	nearly	nearly	ADV
ejpam-5633	45	17	(	(	PUNCT
ejpam-5633	45	18	τ1	τ1	NOUN
ejpam-5633	45	19	,	,	PUNCT
ejpam-5633	45	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	45	21	multifunctions	multifunction	NOUN
ejpam-5633	45	22	.	.	PUNCT
ejpam-5633	46	1	m.	m.	NOUN
ejpam-5633	46	2	thongmoon	thongmoon	PROPN
ejpam-5633	46	3	,	,	PUNCT
ejpam-5633	46	4	a.	a.	PROPN
ejpam-5633	46	5	sama	sama	PROPN
ejpam-5633	46	6	-	-	PUNCT
ejpam-5633	46	7	ae	ae	PROPN
ejpam-5633	46	8	,	,	PUNCT
ejpam-5633	46	9	c.	c.	PROPN
ejpam-5633	46	10	boonpok	boonpok	PROPN
ejpam-5633	46	11	/	/	SYM
ejpam-5633	46	12	eur	eur	PROPN
ejpam-5633	46	13	.	.	PUNCT
ejpam-5633	47	1	j.	j.	PROPN
ejpam-5633	47	2	pure	pure	PROPN
ejpam-5633	47	3	appl	appl	PROPN
ejpam-5633	47	4	.	.	PROPN
ejpam-5633	47	5	math	math	PROPN
ejpam-5633	47	6	,	,	PUNCT
ejpam-5633	47	7	18	18	NUM
ejpam-5633	47	8	(	(	PUNCT
ejpam-5633	47	9	1	1	NUM
ejpam-5633	47	10	)	)	PUNCT
ejpam-5633	47	11	(	(	PUNCT
ejpam-5633	47	12	2025	2025	NUM
ejpam-5633	47	13	)	)	PUNCT
ejpam-5633	47	14	,	,	PUNCT
ejpam-5633	47	15	5633	5633	NUM
ejpam-5633	47	16	3	3	NUM
ejpam-5633	47	17	of	of	ADP
ejpam-5633	47	18	13	13	NUM
ejpam-5633	47	19	2	2	NUM
ejpam-5633	47	20	.	.	PUNCT
ejpam-5633	47	21	preliminaries	preliminary	NOUN
ejpam-5633	47	22	throughout	throughout	ADP
ejpam-5633	47	23	the	the	DET
ejpam-5633	47	24	present	present	ADJ
ejpam-5633	47	25	paper	paper	NOUN
ejpam-5633	47	26	,	,	PUNCT
ejpam-5633	47	27	spaces	space	NOUN
ejpam-5633	47	28	(	(	PUNCT
ejpam-5633	47	29	x	x	NOUN
ejpam-5633	47	30	,	,	PUNCT
ejpam-5633	47	31	τ1	τ1	NOUN
ejpam-5633	47	32	,	,	PUNCT
ejpam-5633	47	33	τ2	τ2	NOUN
ejpam-5633	47	34	)	)	PUNCT
ejpam-5633	47	35	and	and	CCONJ
ejpam-5633	47	36	(	(	PUNCT
ejpam-5633	47	37	y	y	PROPN
ejpam-5633	47	38	,	,	PUNCT
ejpam-5633	47	39	σ1	σ1	PROPN
ejpam-5633	47	40	,	,	PUNCT
ejpam-5633	47	41	σ2	σ2	NOUN
ejpam-5633	47	42	)	)	PUNCT
ejpam-5633	47	43	(	(	PUNCT
ejpam-5633	47	44	or	or	CCONJ
ejpam-5633	47	45	simply	simply	ADV
ejpam-5633	47	46	x	x	X
ejpam-5633	47	47	and	and	CCONJ
ejpam-5633	47	48	y	y	PROPN
ejpam-5633	47	49	)	)	PUNCT
ejpam-5633	47	50	always	always	ADV
ejpam-5633	47	51	mean	mean	VERB
ejpam-5633	47	52	bitopological	bitopological	ADJ
ejpam-5633	47	53	spaces	space	NOUN
ejpam-5633	47	54	on	on	ADP
ejpam-5633	47	55	which	which	PRON
ejpam-5633	47	56	no	no	DET
ejpam-5633	47	57	separation	separation	NOUN
ejpam-5633	47	58	axioms	axiom	NOUN
ejpam-5633	47	59	are	be	AUX
ejpam-5633	47	60	assumed	assume	VERB
ejpam-5633	47	61	unless	unless	SCONJ
ejpam-5633	47	62	explicitly	explicitly	ADV
ejpam-5633	47	63	stated	state	VERB
ejpam-5633	47	64	.	.	PUNCT
ejpam-5633	48	1	let	let	VERB
ejpam-5633	48	2	a	a	DET
ejpam-5633	48	3	be	be	AUX
ejpam-5633	48	4	a	a	DET
ejpam-5633	48	5	subset	subset	NOUN
ejpam-5633	48	6	of	of	ADP
ejpam-5633	48	7	a	a	DET
ejpam-5633	48	8	bitopological	bitopological	ADJ
ejpam-5633	48	9	space	space	NOUN
ejpam-5633	48	10	(	(	PUNCT
ejpam-5633	48	11	x	x	NOUN
ejpam-5633	48	12	,	,	PUNCT
ejpam-5633	48	13	τ1	τ1	NOUN
ejpam-5633	48	14	,	,	PUNCT
ejpam-5633	48	15	τ2	τ2	NOUN
ejpam-5633	48	16	)	)	PUNCT
ejpam-5633	48	17	.	.	PUNCT
ejpam-5633	49	1	the	the	DET
ejpam-5633	49	2	closure	closure	NOUN
ejpam-5633	49	3	of	of	ADP
ejpam-5633	49	4	a	a	PRON
ejpam-5633	49	5	and	and	CCONJ
ejpam-5633	49	6	the	the	DET
ejpam-5633	49	7	interior	interior	NOUN
ejpam-5633	49	8	of	of	ADP
ejpam-5633	49	9	a	a	PRON
ejpam-5633	49	10	with	with	ADP
ejpam-5633	49	11	respect	respect	NOUN
ejpam-5633	49	12	to	to	ADP
ejpam-5633	49	13	τi	τi	PROPN
ejpam-5633	49	14	are	be	AUX
ejpam-5633	49	15	denoted	denote	VERB
ejpam-5633	49	16	by	by	ADP
ejpam-5633	49	17	τi	τi	NOUN
ejpam-5633	49	18	-	-	PUNCT
ejpam-5633	49	19	cl(a	cl(a	NUM
ejpam-5633	49	20	)	)	PUNCT
ejpam-5633	49	21	and	and	CCONJ
ejpam-5633	49	22	τi	τi	NOUN
ejpam-5633	49	23	-	-	PUNCT
ejpam-5633	49	24	int(a	int(a	NOUN
ejpam-5633	49	25	)	)	PUNCT
ejpam-5633	49	26	,	,	PUNCT
ejpam-5633	49	27	respectively	respectively	ADV
ejpam-5633	49	28	,	,	PUNCT
ejpam-5633	49	29	for	for	ADP
ejpam-5633	49	30	i	i	PROPN
ejpam-5633	49	31	=	=	SYM
ejpam-5633	49	32	1	1	NUM
ejpam-5633	49	33	,	,	PUNCT
ejpam-5633	49	34	2	2	NUM
ejpam-5633	49	35	.	.	X
ejpam-5633	49	36	a	a	DET
ejpam-5633	49	37	subset	subset	NOUN
ejpam-5633	49	38	a	a	PRON
ejpam-5633	49	39	of	of	ADP
ejpam-5633	49	40	a	a	DET
ejpam-5633	49	41	bitopological	bitopological	ADJ
ejpam-5633	49	42	space	space	NOUN
ejpam-5633	49	43	(	(	PUNCT
ejpam-5633	49	44	x	x	NOUN
ejpam-5633	49	45	,	,	PUNCT
ejpam-5633	49	46	τ1	τ1	NOUN
ejpam-5633	49	47	,	,	PUNCT
ejpam-5633	49	48	τ2	τ2	NOUN
ejpam-5633	49	49	)	)	PUNCT
ejpam-5633	49	50	is	be	AUX
ejpam-5633	49	51	called	call	VERB
ejpam-5633	49	52	τ1τ2	τ1τ2	VERB
ejpam-5633	49	53	-	-	ADJ
ejpam-5633	49	54	closed	closed	ADJ
ejpam-5633	49	55	[	[	X
ejpam-5633	49	56	29	29	NUM
ejpam-5633	49	57	]	]	X
ejpam-5633	49	58	if	if	SCONJ
ejpam-5633	49	59	a	a	DET
ejpam-5633	49	60	=	=	NOUN
ejpam-5633	49	61	τ1	τ1	NOUN
ejpam-5633	49	62	-	-	PUNCT
ejpam-5633	49	63	cl(τ2	cl(τ2	NOUN
ejpam-5633	49	64	-	-	PUNCT
ejpam-5633	49	65	cl(a	cl(a	NUM
ejpam-5633	49	66	)	)	PUNCT
ejpam-5633	49	67	)	)	PUNCT
ejpam-5633	49	68	.	.	PUNCT
ejpam-5633	50	1	the	the	DET
ejpam-5633	50	2	complement	complement	NOUN
ejpam-5633	50	3	of	of	ADP
ejpam-5633	50	4	a	a	DET
ejpam-5633	50	5	τ1τ2	τ1τ2	ADJ
ejpam-5633	50	6	-	-	ADJ
ejpam-5633	50	7	closed	closed	ADJ
ejpam-5633	50	8	set	set	NOUN
ejpam-5633	50	9	is	be	AUX
ejpam-5633	50	10	called	call	VERB
ejpam-5633	50	11	τ1τ2	τ1τ2	NOUN
ejpam-5633	50	12	-	-	ADJ
ejpam-5633	50	13	open	open	ADJ
ejpam-5633	50	14	.	.	PUNCT
ejpam-5633	51	1	let	let	VERB
ejpam-5633	51	2	a	a	DET
ejpam-5633	51	3	be	be	AUX
ejpam-5633	51	4	a	a	DET
ejpam-5633	51	5	subset	subset	NOUN
ejpam-5633	51	6	of	of	ADP
ejpam-5633	51	7	a	a	DET
ejpam-5633	51	8	bitopological	bitopological	ADJ
ejpam-5633	51	9	space	space	NOUN
ejpam-5633	51	10	(	(	PUNCT
ejpam-5633	51	11	x	x	NOUN
ejpam-5633	51	12	,	,	PUNCT
ejpam-5633	51	13	τ1	τ1	NOUN
ejpam-5633	51	14	,	,	PUNCT
ejpam-5633	51	15	τ2	τ2	NOUN
ejpam-5633	51	16	)	)	PUNCT
ejpam-5633	51	17	.	.	PUNCT
ejpam-5633	52	1	the	the	DET
ejpam-5633	52	2	intersection	intersection	NOUN
ejpam-5633	52	3	of	of	ADP
ejpam-5633	52	4	all	all	DET
ejpam-5633	52	5	τ1τ2	τ1τ2	ADJ
ejpam-5633	52	6	-	-	ADJ
ejpam-5633	52	7	closed	closed	ADJ
ejpam-5633	52	8	sets	set	NOUN
ejpam-5633	52	9	of	of	ADP
ejpam-5633	52	10	x	x	PUNCT
ejpam-5633	52	11	containing	contain	VERB
ejpam-5633	52	12	a	a	PRON
ejpam-5633	52	13	is	be	AUX
ejpam-5633	52	14	called	call	VERB
ejpam-5633	52	15	the	the	DET
ejpam-5633	52	16	τ1τ2	τ1τ2	NOUN
ejpam-5633	52	17	-	-	NOUN
ejpam-5633	52	18	closure	closure	NOUN
ejpam-5633	52	19	[	[	X
ejpam-5633	52	20	29	29	NUM
ejpam-5633	52	21	]	]	PUNCT
ejpam-5633	52	22	of	of	ADP
ejpam-5633	52	23	a	a	PRON
ejpam-5633	52	24	and	and	CCONJ
ejpam-5633	52	25	is	be	AUX
ejpam-5633	52	26	denoted	denote	VERB
ejpam-5633	52	27	by	by	ADP
ejpam-5633	52	28	τ1τ2	τ1τ2	NOUN
ejpam-5633	52	29	-	-	NUM
ejpam-5633	52	30	cl(a	cl(a	NUM
ejpam-5633	52	31	)	)	PUNCT
ejpam-5633	52	32	.	.	PUNCT
ejpam-5633	53	1	the	the	DET
ejpam-5633	53	2	union	union	NOUN
ejpam-5633	53	3	of	of	ADP
ejpam-5633	53	4	all	all	DET
ejpam-5633	53	5	τ1τ2	τ1τ2	ADJ
ejpam-5633	53	6	-	-	ADJ
ejpam-5633	53	7	open	open	ADJ
ejpam-5633	53	8	sets	set	NOUN
ejpam-5633	53	9	of	of	ADP
ejpam-5633	53	10	x	x	PUNCT
ejpam-5633	53	11	contained	contain	VERB
ejpam-5633	53	12	in	in	ADP
ejpam-5633	53	13	a	a	PRON
ejpam-5633	53	14	is	be	AUX
ejpam-5633	53	15	called	call	VERB
ejpam-5633	53	16	the	the	DET
ejpam-5633	53	17	τ1τ2	τ1τ2	NOUN
ejpam-5633	53	18	-	-	ADJ
ejpam-5633	53	19	interior	interior	ADJ
ejpam-5633	53	20	[	[	X
ejpam-5633	53	21	29	29	NUM
ejpam-5633	53	22	]	]	PUNCT
ejpam-5633	53	23	of	of	ADP
ejpam-5633	53	24	a	a	PRON
ejpam-5633	53	25	and	and	CCONJ
ejpam-5633	53	26	is	be	AUX
ejpam-5633	53	27	denoted	denote	VERB
ejpam-5633	53	28	by	by	ADP
ejpam-5633	53	29	τ1τ2	τ1τ2	NOUN
ejpam-5633	53	30	-	-	ADJ
ejpam-5633	53	31	int(a	int(a	NOUN
ejpam-5633	53	32	)	)	PUNCT
ejpam-5633	53	33	.	.	PUNCT
ejpam-5633	54	1	lemma	lemma	PROPN
ejpam-5633	54	2	1	1	NUM
ejpam-5633	54	3	.	.	PUNCT
ejpam-5633	55	1	[	[	X
ejpam-5633	55	2	29	29	NUM
ejpam-5633	55	3	]	]	PUNCT
ejpam-5633	55	4	let	let	VERB
ejpam-5633	55	5	a	a	PRON
ejpam-5633	55	6	and	and	CCONJ
ejpam-5633	55	7	b	b	NOUN
ejpam-5633	55	8	be	be	AUX
ejpam-5633	55	9	subsets	subset	NOUN
ejpam-5633	55	10	of	of	ADP
ejpam-5633	55	11	a	a	DET
ejpam-5633	55	12	bitopological	bitopological	ADJ
ejpam-5633	55	13	space	space	NOUN
ejpam-5633	55	14	(	(	PUNCT
ejpam-5633	55	15	x	x	NOUN
ejpam-5633	55	16	,	,	PUNCT
ejpam-5633	55	17	τ1	τ1	NOUN
ejpam-5633	55	18	,	,	PUNCT
ejpam-5633	55	19	τ2	τ2	NOUN
ejpam-5633	55	20	)	)	PUNCT
ejpam-5633	55	21	.	.	PUNCT
ejpam-5633	56	1	for	for	ADP
ejpam-5633	56	2	the	the	DET
ejpam-5633	56	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5633	56	4	,	,	PUNCT
ejpam-5633	56	5	the	the	DET
ejpam-5633	56	6	following	follow	VERB
ejpam-5633	56	7	properties	property	NOUN
ejpam-5633	56	8	hold	hold	VERB
ejpam-5633	56	9	:	:	PUNCT
ejpam-5633	56	10	(	(	PUNCT
ejpam-5633	56	11	1	1	X
ejpam-5633	56	12	)	)	PUNCT
ejpam-5633	56	13	a	a	DET
ejpam-5633	56	14	⊆	⊆	NUM
ejpam-5633	56	15	τ1τ2	τ1τ2	NOUN
ejpam-5633	56	16	-	-	NUM
ejpam-5633	56	17	cl(a	cl(a	NUM
ejpam-5633	56	18	)	)	PUNCT
ejpam-5633	56	19	and	and	CCONJ
ejpam-5633	56	20	τ1τ2	τ1τ2	NOUN
ejpam-5633	56	21	-	-	ADJ
ejpam-5633	56	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5633	56	23	-	-	PUNCT
ejpam-5633	56	24	cl(a	cl(a	NUM
ejpam-5633	56	25	)	)	PUNCT
ejpam-5633	56	26	)	)	PUNCT
ejpam-5633	57	1	=	=	PUNCT
ejpam-5633	57	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	57	3	-	-	NUM
ejpam-5633	57	4	cl(a	cl(a	NUM
ejpam-5633	57	5	)	)	PUNCT
ejpam-5633	57	6	.	.	PUNCT
ejpam-5633	58	1	(	(	PUNCT
ejpam-5633	58	2	2	2	X
ejpam-5633	58	3	)	)	PUNCT
ejpam-5633	58	4	if	if	SCONJ
ejpam-5633	58	5	a	a	DET
ejpam-5633	58	6	⊆	⊆	NUM
ejpam-5633	58	7	b	b	NOUN
ejpam-5633	58	8	,	,	PUNCT
ejpam-5633	58	9	then	then	ADV
ejpam-5633	58	10	τ1τ2	τ1τ2	NOUN
ejpam-5633	58	11	-	-	NUM
ejpam-5633	58	12	cl(a	cl(a	NUM
ejpam-5633	58	13	)	)	PUNCT
ejpam-5633	58	14	⊆	⊆	NUM
ejpam-5633	58	15	τ1τ2	τ1τ2	NOUN
ejpam-5633	58	16	-	-	NOUN
ejpam-5633	58	17	cl(b	cl(b	NOUN
ejpam-5633	58	18	)	)	PUNCT
ejpam-5633	58	19	.	.	PUNCT
ejpam-5633	59	1	(	(	PUNCT
ejpam-5633	59	2	3	3	X
ejpam-5633	59	3	)	)	PUNCT
ejpam-5633	59	4	τ1τ2	τ1τ2	NOUN
ejpam-5633	59	5	-	-	NUM
ejpam-5633	59	6	cl(a	cl(a	NUM
ejpam-5633	59	7	)	)	PUNCT
ejpam-5633	59	8	is	be	AUX
ejpam-5633	59	9	τ1τ2	τ1τ2	NOUN
ejpam-5633	59	10	-	-	ADJ
ejpam-5633	59	11	closed	closed	ADJ
ejpam-5633	59	12	.	.	PUNCT
ejpam-5633	60	1	(	(	PUNCT
ejpam-5633	60	2	4	4	X
ejpam-5633	60	3	)	)	PUNCT
ejpam-5633	60	4	a	a	PRON
ejpam-5633	60	5	is	be	AUX
ejpam-5633	60	6	τ1τ2	τ1τ2	NOUN
ejpam-5633	60	7	-	-	ADJ
ejpam-5633	60	8	closed	closed	ADJ
ejpam-5633	60	9	if	if	SCONJ
ejpam-5633	60	10	and	and	CCONJ
ejpam-5633	60	11	only	only	ADV
ejpam-5633	60	12	if	if	SCONJ
ejpam-5633	60	13	a	a	DET
ejpam-5633	60	14	=	=	PUNCT
ejpam-5633	60	15	τ1τ2	τ1τ2	NOUN
ejpam-5633	60	16	-	-	NUM
ejpam-5633	60	17	cl(a	cl(a	NUM
ejpam-5633	60	18	)	)	PUNCT
ejpam-5633	60	19	.	.	PUNCT
ejpam-5633	61	1	(	(	PUNCT
ejpam-5633	61	2	5	5	X
ejpam-5633	61	3	)	)	PUNCT
ejpam-5633	61	4	τ1τ2	τ1τ2	NOUN
ejpam-5633	61	5	-	-	NOUN
ejpam-5633	61	6	cl(x	cl(x	X
ejpam-5633	61	7	−a	−a	NOUN
ejpam-5633	61	8	)	)	PUNCT
ejpam-5633	62	1	=	=	PUNCT
ejpam-5633	62	2	x	x	X
ejpam-5633	63	1	−	−	ADP
ejpam-5633	63	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	63	3	-	-	PUNCT
ejpam-5633	63	4	int(a	int(a	NOUN
ejpam-5633	63	5	)	)	PUNCT
ejpam-5633	63	6	.	.	PUNCT
ejpam-5633	64	1	a	a	DET
ejpam-5633	64	2	subset	subset	NOUN
ejpam-5633	64	3	a	a	PRON
ejpam-5633	64	4	of	of	ADP
ejpam-5633	64	5	a	a	DET
ejpam-5633	64	6	bitopological	bitopological	ADJ
ejpam-5633	64	7	space	space	NOUN
ejpam-5633	64	8	(	(	PUNCT
ejpam-5633	64	9	x	x	NOUN
ejpam-5633	64	10	,	,	PUNCT
ejpam-5633	64	11	τ1	τ1	NOUN
ejpam-5633	64	12	,	,	PUNCT
ejpam-5633	64	13	τ2	τ2	NOUN
ejpam-5633	64	14	)	)	PUNCT
ejpam-5633	64	15	is	be	AUX
ejpam-5633	64	16	said	say	VERB
ejpam-5633	64	17	to	to	PART
ejpam-5633	64	18	be	be	AUX
ejpam-5633	64	19	τ1τ2	τ1τ2	NOUN
ejpam-5633	64	20	-	-	ADJ
ejpam-5633	64	21	clopen	clopen	ADJ
ejpam-5633	64	22	[	[	X
ejpam-5633	64	23	29	29	NUM
ejpam-5633	64	24	]	]	X
ejpam-5633	64	25	if	if	SCONJ
ejpam-5633	64	26	a	a	PRON
ejpam-5633	64	27	is	be	AUX
ejpam-5633	64	28	both	both	PRON
ejpam-5633	64	29	τ1τ2	τ1τ2	ADJ
ejpam-5633	64	30	-	-	ADJ
ejpam-5633	64	31	open	open	ADJ
ejpam-5633	64	32	and	and	CCONJ
ejpam-5633	64	33	τ1τ2	τ1τ2	NOUN
ejpam-5633	64	34	-	-	ADJ
ejpam-5633	64	35	closed	closed	ADJ
ejpam-5633	64	36	.	.	PUNCT
ejpam-5633	65	1	a	a	DET
ejpam-5633	65	2	subset	subset	NOUN
ejpam-5633	65	3	a	a	PRON
ejpam-5633	65	4	of	of	ADP
ejpam-5633	65	5	a	a	DET
ejpam-5633	65	6	bitopological	bitopological	ADJ
ejpam-5633	65	7	space	space	NOUN
ejpam-5633	65	8	(	(	PUNCT
ejpam-5633	65	9	x	x	NOUN
ejpam-5633	65	10	,	,	PUNCT
ejpam-5633	65	11	τ1	τ1	NOUN
ejpam-5633	65	12	,	,	PUNCT
ejpam-5633	65	13	τ2	τ2	NOUN
ejpam-5633	65	14	)	)	PUNCT
ejpam-5633	65	15	is	be	AUX
ejpam-5633	65	16	said	say	VERB
ejpam-5633	65	17	to	to	PART
ejpam-5633	65	18	be	be	AUX
ejpam-5633	65	19	(	(	PUNCT
ejpam-5633	65	20	τ1	τ1	NOUN
ejpam-5633	65	21	,	,	PUNCT
ejpam-5633	65	22	τ2)r	τ2)r	NOUN
ejpam-5633	65	23	-	-	PUNCT
ejpam-5633	65	24	open	open	NOUN
ejpam-5633	65	25	[	[	X
ejpam-5633	65	26	60	60	NUM
ejpam-5633	65	27	]	]	PUNCT
ejpam-5633	65	28	(	(	PUNCT
ejpam-5633	65	29	resp	resp	NOUN
ejpam-5633	65	30	.	.	PUNCT
ejpam-5633	66	1	(	(	PUNCT
ejpam-5633	66	2	τ1	τ1	NOUN
ejpam-5633	66	3	,	,	PUNCT
ejpam-5633	66	4	τ2)s	τ2)s	NOUN
ejpam-5633	66	5	-	-	PUNCT
ejpam-5633	66	6	open	open	ADJ
ejpam-5633	66	7	[	[	X
ejpam-5633	66	8	5	5	NUM
ejpam-5633	66	9	]	]	PUNCT
ejpam-5633	66	10	,	,	PUNCT
ejpam-5633	66	11	(	(	PUNCT
ejpam-5633	66	12	τ1	τ1	NOUN
ejpam-5633	66	13	,	,	PUNCT
ejpam-5633	66	14	τ2)p	τ2)p	NOUN
ejpam-5633	66	15	-	-	ADJ
ejpam-5633	66	16	open	open	ADJ
ejpam-5633	66	17	[	[	X
ejpam-5633	66	18	5	5	NUM
ejpam-5633	66	19	]	]	PUNCT
ejpam-5633	66	20	,	,	PUNCT
ejpam-5633	66	21	(	(	PUNCT
ejpam-5633	66	22	τ1	τ1	NOUN
ejpam-5633	66	23	,	,	PUNCT
ejpam-5633	66	24	τ2)β	τ2)β	ADJ
ejpam-5633	66	25	-	-	PUNCT
ejpam-5633	66	26	open	open	ADJ
ejpam-5633	66	27	[	[	X
ejpam-5633	66	28	5	5	NUM
ejpam-5633	66	29	]	]	PUNCT
ejpam-5633	66	30	)	)	PUNCT
ejpam-5633	66	31	if	if	SCONJ
ejpam-5633	66	32	a	a	DET
ejpam-5633	66	33	=	=	PUNCT
ejpam-5633	66	34	τ1τ2	τ1τ2	NOUN
ejpam-5633	66	35	-	-	NOUN
ejpam-5633	66	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5633	66	37	-	-	PUNCT
ejpam-5633	66	38	cl(a	cl(a	NUM
ejpam-5633	66	39	)	)	PUNCT
ejpam-5633	66	40	)	)	PUNCT
ejpam-5633	66	41	(	(	PUNCT
ejpam-5633	66	42	resp	resp	NOUN
ejpam-5633	66	43	.	.	PUNCT
ejpam-5633	67	1	a	a	DET
ejpam-5633	67	2	⊆	⊆	NUM
ejpam-5633	67	3	τ1τ2	τ1τ2	NOUN
ejpam-5633	67	4	-	-	ADJ
ejpam-5633	67	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5633	67	6	-	-	PUNCT
ejpam-5633	67	7	int(a	int(a	NOUN
ejpam-5633	67	8	)	)	PUNCT
ejpam-5633	67	9	)	)	PUNCT
ejpam-5633	67	10	,	,	PUNCT
ejpam-5633	67	11	a	a	DET
ejpam-5633	67	12	⊆	⊆	NUM
ejpam-5633	67	13	τ1τ2	τ1τ2	NOUN
ejpam-5633	67	14	-	-	NOUN
ejpam-5633	67	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5633	67	16	-	-	PUNCT
ejpam-5633	67	17	cl(a	cl(a	NUM
ejpam-5633	67	18	)	)	PUNCT
ejpam-5633	67	19	)	)	PUNCT
ejpam-5633	67	20	,	,	PUNCT
ejpam-5633	67	21	a	a	DET
ejpam-5633	67	22	⊆	⊆	NUM
ejpam-5633	67	23	τ1τ2	τ1τ2	NOUN
ejpam-5633	67	24	-	-	PUNCT
ejpam-5633	67	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5633	67	26	-	-	PUNCT
ejpam-5633	67	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5633	67	28	-	-	PUNCT
ejpam-5633	67	29	cl(a	cl(a	NUM
ejpam-5633	67	30	)	)	PUNCT
ejpam-5633	67	31	)	)	PUNCT
ejpam-5633	67	32	)	)	PUNCT
ejpam-5633	67	33	)	)	PUNCT
ejpam-5633	67	34	.	.	PUNCT
ejpam-5633	68	1	the	the	DET
ejpam-5633	68	2	complement	complement	NOUN
ejpam-5633	68	3	of	of	ADP
ejpam-5633	68	4	a	a	DET
ejpam-5633	68	5	(	(	PUNCT
ejpam-5633	68	6	τ1	τ1	NOUN
ejpam-5633	68	7	,	,	PUNCT
ejpam-5633	68	8	τ2)r	τ2)r	NOUN
ejpam-5633	68	9	-	-	PUNCT
ejpam-5633	68	10	open	open	ADJ
ejpam-5633	68	11	(	(	PUNCT
ejpam-5633	68	12	resp	resp	NOUN
ejpam-5633	68	13	.	.	PUNCT
ejpam-5633	69	1	(	(	PUNCT
ejpam-5633	69	2	τ1	τ1	NOUN
ejpam-5633	69	3	,	,	PUNCT
ejpam-5633	69	4	τ2)s	τ2)s	NOUN
ejpam-5633	69	5	-	-	PUNCT
ejpam-5633	69	6	open	open	ADJ
ejpam-5633	69	7	,	,	PUNCT
ejpam-5633	69	8	(	(	PUNCT
ejpam-5633	69	9	τ1	τ1	NOUN
ejpam-5633	69	10	,	,	PUNCT
ejpam-5633	69	11	τ2)p	τ2)p	NOUN
ejpam-5633	69	12	-	-	ADJ
ejpam-5633	69	13	open	open	ADJ
ejpam-5633	69	14	,	,	PUNCT
ejpam-5633	69	15	(	(	PUNCT
ejpam-5633	69	16	τ1	τ1	NOUN
ejpam-5633	69	17	,	,	PUNCT
ejpam-5633	69	18	τ2)β	τ2)β	ADJ
ejpam-5633	69	19	-	-	PUNCT
ejpam-5633	69	20	open	open	ADJ
ejpam-5633	69	21	)	)	PUNCT
ejpam-5633	69	22	set	set	NOUN
ejpam-5633	69	23	is	be	AUX
ejpam-5633	69	24	called	call	VERB
ejpam-5633	69	25	(	(	PUNCT
ejpam-5633	69	26	τ1	τ1	NOUN
ejpam-5633	69	27	,	,	PUNCT
ejpam-5633	69	28	τ2)r	τ2)r	NOUN
ejpam-5633	69	29	-	-	PUNCT
ejpam-5633	69	30	closed	closed	ADJ
ejpam-5633	69	31	(	(	PUNCT
ejpam-5633	69	32	resp	resp	NOUN
ejpam-5633	69	33	.	.	PUNCT
ejpam-5633	70	1	(	(	PUNCT
ejpam-5633	70	2	τ1	τ1	NOUN
ejpam-5633	70	3	,	,	PUNCT
ejpam-5633	70	4	τ2)s	τ2)s	NOUN
ejpam-5633	70	5	-	-	PUNCT
ejpam-5633	70	6	closed	closed	ADJ
ejpam-5633	70	7	,	,	PUNCT
ejpam-5633	70	8	(	(	PUNCT
ejpam-5633	70	9	τ1	τ1	NOUN
ejpam-5633	70	10	,	,	PUNCT
ejpam-5633	70	11	τ2)pclosed	τ2)pclose	VERB
ejpam-5633	70	12	,	,	PUNCT
ejpam-5633	70	13	(	(	PUNCT
ejpam-5633	70	14	τ1	τ1	NOUN
ejpam-5633	70	15	,	,	PUNCT
ejpam-5633	70	16	τ2)β	τ2)β	ADJ
ejpam-5633	70	17	-	-	PUNCT
ejpam-5633	70	18	closed	closed	ADJ
ejpam-5633	70	19	)	)	PUNCT
ejpam-5633	70	20	.	.	PUNCT
ejpam-5633	71	1	a	a	DET
ejpam-5633	71	2	subset	subset	NOUN
ejpam-5633	71	3	a	a	PRON
ejpam-5633	71	4	of	of	ADP
ejpam-5633	71	5	a	a	DET
ejpam-5633	71	6	bitopological	bitopological	ADJ
ejpam-5633	71	7	space	space	NOUN
ejpam-5633	71	8	(	(	PUNCT
ejpam-5633	71	9	x	x	NOUN
ejpam-5633	71	10	,	,	PUNCT
ejpam-5633	71	11	τ1	τ1	NOUN
ejpam-5633	71	12	,	,	PUNCT
ejpam-5633	71	13	τ2	τ2	NOUN
ejpam-5633	71	14	)	)	PUNCT
ejpam-5633	71	15	is	be	AUX
ejpam-5633	71	16	said	say	VERB
ejpam-5633	71	17	to	to	PART
ejpam-5633	71	18	be	be	AUX
ejpam-5633	71	19	α(τ1	α(τ1	NOUN
ejpam-5633	71	20	,	,	PUNCT
ejpam-5633	71	21	τ2)-open	τ2)-open	ADJ
ejpam-5633	71	22	[	[	PUNCT
ejpam-5633	71	23	63	63	NUM
ejpam-5633	71	24	]	]	PUNCT
ejpam-5633	71	25	if	if	SCONJ
ejpam-5633	71	26	a	a	DET
ejpam-5633	71	27	⊆	⊆	NUM
ejpam-5633	71	28	τ1τ2	τ1τ2	NOUN
ejpam-5633	71	29	-	-	PUNCT
ejpam-5633	71	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5633	71	31	-	-	PUNCT
ejpam-5633	71	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5633	71	33	-	-	PUNCT
ejpam-5633	71	34	int(a	int(a	NOUN
ejpam-5633	71	35	)	)	PUNCT
ejpam-5633	71	36	)	)	PUNCT
ejpam-5633	71	37	)	)	PUNCT
ejpam-5633	71	38	.	.	PUNCT
ejpam-5633	72	1	the	the	DET
ejpam-5633	72	2	complement	complement	NOUN
ejpam-5633	72	3	of	of	ADP
ejpam-5633	72	4	an	an	DET
ejpam-5633	72	5	α(τ1	α(τ1	NOUN
ejpam-5633	72	6	,	,	PUNCT
ejpam-5633	72	7	τ2)open	τ2)open	PROPN
ejpam-5633	72	8	set	set	NOUN
ejpam-5633	72	9	is	be	AUX
ejpam-5633	72	10	said	say	VERB
ejpam-5633	72	11	to	to	PART
ejpam-5633	72	12	be	be	AUX
ejpam-5633	72	13	α(τ1	α(τ1	NOUN
ejpam-5633	72	14	,	,	PUNCT
ejpam-5633	72	15	τ2)-closed	τ2)-closed	ADJ
ejpam-5633	72	16	.	.	PUNCT
ejpam-5633	73	1	a	a	DET
ejpam-5633	73	2	subset	subset	NOUN
ejpam-5633	73	3	a	a	PRON
ejpam-5633	73	4	of	of	ADP
ejpam-5633	73	5	a	a	DET
ejpam-5633	73	6	bitopological	bitopological	ADJ
ejpam-5633	73	7	space	space	NOUN
ejpam-5633	73	8	(	(	PUNCT
ejpam-5633	73	9	x	x	NOUN
ejpam-5633	73	10	,	,	PUNCT
ejpam-5633	73	11	τ1	τ1	NOUN
ejpam-5633	73	12	,	,	PUNCT
ejpam-5633	73	13	τ2	τ2	NOUN
ejpam-5633	73	14	)	)	PUNCT
ejpam-5633	73	15	is	be	AUX
ejpam-5633	73	16	said	say	VERB
ejpam-5633	73	17	to	to	PART
ejpam-5633	73	18	be	be	AUX
ejpam-5633	73	19	n	n	PRON
ejpam-5633	73	20	(	(	PUNCT
ejpam-5633	73	21	τ1	τ1	NOUN
ejpam-5633	73	22	,	,	PUNCT
ejpam-5633	73	23	τ2)-closed	τ2)-close	VERB
ejpam-5633	73	24	if	if	SCONJ
ejpam-5633	73	25	every	every	DET
ejpam-5633	73	26	cover	cover	NOUN
ejpam-5633	73	27	of	of	ADP
ejpam-5633	73	28	a	a	DET
ejpam-5633	73	29	by	by	ADP
ejpam-5633	73	30	(	(	PUNCT
ejpam-5633	73	31	τ1	τ1	NOUN
ejpam-5633	73	32	,	,	PUNCT
ejpam-5633	73	33	τ2)r	τ2)r	ADJ
ejpam-5633	73	34	-	-	PUNCT
ejpam-5633	73	35	open	open	ADJ
ejpam-5633	73	36	sets	set	NOUN
ejpam-5633	73	37	of	of	ADP
ejpam-5633	73	38	x	x	PUNCT
ejpam-5633	73	39	has	have	VERB
ejpam-5633	73	40	a	a	DET
ejpam-5633	73	41	finite	finite	ADJ
ejpam-5633	73	42	subcover	subcover	PROPN
ejpam-5633	73	43	.	.	PUNCT
ejpam-5633	74	1	let	let	VERB
ejpam-5633	74	2	a	a	DET
ejpam-5633	74	3	be	be	AUX
ejpam-5633	74	4	a	a	DET
ejpam-5633	74	5	subset	subset	NOUN
ejpam-5633	74	6	of	of	ADP
ejpam-5633	74	7	a	a	DET
ejpam-5633	74	8	bitopological	bitopological	ADJ
ejpam-5633	74	9	space	space	NOUN
ejpam-5633	74	10	(	(	PUNCT
ejpam-5633	74	11	x	x	NOUN
ejpam-5633	74	12	,	,	PUNCT
ejpam-5633	74	13	τ1	τ1	NOUN
ejpam-5633	74	14	,	,	PUNCT
ejpam-5633	74	15	τ2	τ2	NOUN
ejpam-5633	74	16	)	)	PUNCT
ejpam-5633	74	17	.	.	PUNCT
ejpam-5633	75	1	a	a	DET
ejpam-5633	75	2	point	point	NOUN
ejpam-5633	75	3	x	x	X
ejpam-5633	75	4	∈	∈	NOUN
ejpam-5633	75	5	x	x	PUNCT
ejpam-5633	75	6	is	be	AUX
ejpam-5633	75	7	called	call	VERB
ejpam-5633	75	8	a	a	DET
ejpam-5633	75	9	(	(	PUNCT
ejpam-5633	75	10	τ1	τ1	NOUN
ejpam-5633	75	11	,	,	PUNCT
ejpam-5633	75	12	τ2)θ	τ2)θ	ADJ
ejpam-5633	75	13	-	-	PUNCT
ejpam-5633	75	14	cluster	cluster	NOUN
ejpam-5633	75	15	point	point	NOUN
ejpam-5633	75	16	[	[	X
ejpam-5633	75	17	60	60	NUM
ejpam-5633	75	18	]	]	PUNCT
ejpam-5633	75	19	of	of	ADP
ejpam-5633	75	20	a	a	DET
ejpam-5633	75	21	if	if	SCONJ
ejpam-5633	75	22	τ1τ2	τ1τ2	ADJ
ejpam-5633	75	23	-	-	ADJ
ejpam-5633	75	24	cl(u)∩a	cl(u)∩a	ADJ
ejpam-5633	75	25	̸=	̸=	PROPN
ejpam-5633	75	26	∅	∅	NOUN
ejpam-5633	75	27	for	for	ADP
ejpam-5633	75	28	every	every	DET
ejpam-5633	75	29	τ1τ2	τ1τ2	ADJ
ejpam-5633	75	30	-	-	ADJ
ejpam-5633	75	31	open	open	ADJ
ejpam-5633	75	32	set	set	NOUN
ejpam-5633	75	33	u	u	NOUN
ejpam-5633	75	34	containing	contain	VERB
ejpam-5633	75	35	x.	x.	NOUN
ejpam-5633	75	36	the	the	DET
ejpam-5633	75	37	set	set	NOUN
ejpam-5633	75	38	of	of	ADP
ejpam-5633	75	39	all	all	DET
ejpam-5633	75	40	(	(	PUNCT
ejpam-5633	75	41	τ1	τ1	NOUN
ejpam-5633	75	42	,	,	PUNCT
ejpam-5633	75	43	τ2)θ	τ2)θ	ADJ
ejpam-5633	75	44	-	-	PUNCT
ejpam-5633	75	45	cluster	cluster	NOUN
ejpam-5633	75	46	points	point	NOUN
ejpam-5633	75	47	of	of	ADP
ejpam-5633	75	48	a	a	PRON
ejpam-5633	75	49	is	be	AUX
ejpam-5633	75	50	called	call	VERB
ejpam-5633	75	51	the	the	DET
ejpam-5633	75	52	(	(	PUNCT
ejpam-5633	75	53	τ1	τ1	NOUN
ejpam-5633	75	54	,	,	PUNCT
ejpam-5633	75	55	τ2)θ	τ2)θ	ADJ
ejpam-5633	75	56	-	-	PUNCT
ejpam-5633	75	57	closure	closure	NOUN
ejpam-5633	75	58	[	[	X
ejpam-5633	75	59	60	60	NUM
ejpam-5633	75	60	]	]	PUNCT
ejpam-5633	75	61	of	of	ADP
ejpam-5633	75	62	a	a	PRON
ejpam-5633	75	63	and	and	CCONJ
ejpam-5633	75	64	is	be	AUX
ejpam-5633	75	65	denoted	denote	VERB
ejpam-5633	75	66	by	by	ADP
ejpam-5633	75	67	(	(	PUNCT
ejpam-5633	75	68	τ1	τ1	NOUN
ejpam-5633	75	69	,	,	PUNCT
ejpam-5633	75	70	τ2)θ	τ2)θ	NOUN
ejpam-5633	75	71	-	-	PUNCT
ejpam-5633	75	72	cl(a	cl(a	NUM
ejpam-5633	75	73	)	)	PUNCT
ejpam-5633	75	74	.	.	PUNCT
ejpam-5633	76	1	a	a	DET
ejpam-5633	76	2	subset	subset	NOUN
ejpam-5633	76	3	a	a	PRON
ejpam-5633	76	4	of	of	ADP
ejpam-5633	76	5	a	a	DET
ejpam-5633	76	6	bitopological	bitopological	ADJ
ejpam-5633	76	7	space	space	NOUN
ejpam-5633	76	8	(	(	PUNCT
ejpam-5633	76	9	x	x	NOUN
ejpam-5633	76	10	,	,	PUNCT
ejpam-5633	76	11	τ1	τ1	NOUN
ejpam-5633	76	12	,	,	PUNCT
ejpam-5633	76	13	τ2	τ2	NOUN
ejpam-5633	76	14	)	)	PUNCT
ejpam-5633	76	15	is	be	AUX
ejpam-5633	76	16	said	say	VERB
ejpam-5633	76	17	to	to	PART
ejpam-5633	76	18	be	be	AUX
ejpam-5633	76	19	(	(	PUNCT
ejpam-5633	76	20	τ1	τ1	NOUN
ejpam-5633	76	21	,	,	PUNCT
ejpam-5633	76	22	τ2)θ	τ2)θ	NOUN
ejpam-5633	76	23	-	-	PUNCT
ejpam-5633	76	24	closed	closed	ADJ
ejpam-5633	76	25	[	[	X
ejpam-5633	76	26	60	60	NUM
ejpam-5633	76	27	]	]	X
ejpam-5633	76	28	if	if	SCONJ
ejpam-5633	76	29	(	(	PUNCT
ejpam-5633	76	30	τ1	τ1	NOUN
ejpam-5633	76	31	,	,	PUNCT
ejpam-5633	76	32	τ2)θ	τ2)θ	NOUN
ejpam-5633	76	33	-	-	PUNCT
ejpam-5633	76	34	cl(a	cl(a	NUM
ejpam-5633	76	35	)	)	PUNCT
ejpam-5633	77	1	=	=	PUNCT
ejpam-5633	77	2	a.	a.	NOUN
ejpam-5633	77	3	the	the	DET
ejpam-5633	77	4	complement	complement	NOUN
ejpam-5633	77	5	of	of	ADP
ejpam-5633	77	6	a	a	DET
ejpam-5633	77	7	(	(	PUNCT
ejpam-5633	77	8	τ1	τ1	NOUN
ejpam-5633	77	9	,	,	PUNCT
ejpam-5633	77	10	τ2)θ	τ2)θ	ADJ
ejpam-5633	77	11	-	-	PUNCT
ejpam-5633	77	12	closed	close	VERB
ejpam-5633	77	13	set	set	NOUN
ejpam-5633	77	14	is	be	AUX
ejpam-5633	77	15	said	say	VERB
ejpam-5633	77	16	to	to	PART
ejpam-5633	77	17	be	be	AUX
ejpam-5633	77	18	(	(	PUNCT
ejpam-5633	77	19	τ1	τ1	NOUN
ejpam-5633	77	20	,	,	PUNCT
ejpam-5633	77	21	τ2)θ	τ2)θ	NOUN
ejpam-5633	77	22	-	-	PUNCT
ejpam-5633	77	23	open	open	ADJ
ejpam-5633	77	24	.	.	PUNCT
ejpam-5633	78	1	the	the	DET
ejpam-5633	78	2	union	union	NOUN
ejpam-5633	78	3	of	of	ADP
ejpam-5633	78	4	all	all	DET
ejpam-5633	78	5	(	(	PUNCT
ejpam-5633	78	6	τ1	τ1	NOUN
ejpam-5633	78	7	,	,	PUNCT
ejpam-5633	78	8	τ2)θ	τ2)θ	ADJ
ejpam-5633	78	9	-	-	PUNCT
ejpam-5633	78	10	open	open	ADJ
ejpam-5633	78	11	sets	set	NOUN
ejpam-5633	78	12	of	of	ADP
ejpam-5633	78	13	x	x	PUNCT
ejpam-5633	78	14	contained	contain	VERB
ejpam-5633	78	15	in	in	ADP
ejpam-5633	78	16	a	a	PRON
ejpam-5633	78	17	is	be	AUX
ejpam-5633	78	18	called	call	VERB
ejpam-5633	78	19	the	the	DET
ejpam-5633	78	20	(	(	PUNCT
ejpam-5633	78	21	τ1	τ1	NOUN
ejpam-5633	78	22	,	,	PUNCT
ejpam-5633	78	23	τ2)θ	τ2)θ	ADJ
ejpam-5633	78	24	-	-	PUNCT
ejpam-5633	78	25	interior	interior	NOUN
ejpam-5633	78	26	[	[	X
ejpam-5633	78	27	60	60	NUM
ejpam-5633	78	28	]	]	PUNCT
ejpam-5633	78	29	of	of	ADP
ejpam-5633	78	30	a	a	PRON
ejpam-5633	78	31	and	and	CCONJ
ejpam-5633	78	32	is	be	AUX
ejpam-5633	78	33	denoted	denote	VERB
ejpam-5633	78	34	by	by	ADP
ejpam-5633	78	35	(	(	PUNCT
ejpam-5633	78	36	τ1	τ1	NOUN
ejpam-5633	78	37	,	,	PUNCT
ejpam-5633	78	38	τ2)θ	τ2)θ	NOUN
ejpam-5633	78	39	-	-	PUNCT
ejpam-5633	78	40	int(a	int(a	NOUN
ejpam-5633	78	41	)	)	PUNCT
ejpam-5633	78	42	.	.	PUNCT
ejpam-5633	79	1	lemma	lemma	PROPN
ejpam-5633	79	2	2	2	NUM
ejpam-5633	79	3	.	.	PUNCT
ejpam-5633	80	1	[	[	X
ejpam-5633	80	2	60	60	NUM
ejpam-5633	80	3	]	]	PUNCT
ejpam-5633	80	4	for	for	ADP
ejpam-5633	80	5	a	a	DET
ejpam-5633	80	6	subset	subset	NOUN
ejpam-5633	80	7	a	a	PRON
ejpam-5633	80	8	of	of	ADP
ejpam-5633	80	9	a	a	DET
ejpam-5633	80	10	bitopological	bitopological	ADJ
ejpam-5633	80	11	space	space	NOUN
ejpam-5633	80	12	(	(	PUNCT
ejpam-5633	80	13	x	x	NOUN
ejpam-5633	80	14	,	,	PUNCT
ejpam-5633	80	15	τ1	τ1	NOUN
ejpam-5633	80	16	,	,	PUNCT
ejpam-5633	80	17	τ2	τ2	NOUN
ejpam-5633	80	18	)	)	PUNCT
ejpam-5633	80	19	,	,	PUNCT
ejpam-5633	80	20	the	the	DET
ejpam-5633	80	21	following	follow	VERB
ejpam-5633	80	22	properties	property	NOUN
ejpam-5633	80	23	hold	hold	VERB
ejpam-5633	80	24	:	:	PUNCT
ejpam-5633	80	25	m.	m.	NOUN
ejpam-5633	80	26	thongmoon	thongmoon	NOUN
ejpam-5633	80	27	,	,	PUNCT
ejpam-5633	80	28	a.	a.	PROPN
ejpam-5633	80	29	sama	sama	PROPN
ejpam-5633	80	30	-	-	PUNCT
ejpam-5633	80	31	ae	ae	PROPN
ejpam-5633	80	32	,	,	PUNCT
ejpam-5633	80	33	c.	c.	PROPN
ejpam-5633	80	34	boonpok	boonpok	PROPN
ejpam-5633	80	35	/	/	SYM
ejpam-5633	80	36	eur	eur	PROPN
ejpam-5633	80	37	.	.	PUNCT
ejpam-5633	81	1	j.	j.	PROPN
ejpam-5633	81	2	pure	pure	PROPN
ejpam-5633	81	3	appl	appl	PROPN
ejpam-5633	81	4	.	.	PROPN
ejpam-5633	81	5	math	math	PROPN
ejpam-5633	81	6	,	,	PUNCT
ejpam-5633	81	7	18	18	NUM
ejpam-5633	81	8	(	(	PUNCT
ejpam-5633	81	9	1	1	NUM
ejpam-5633	81	10	)	)	PUNCT
ejpam-5633	81	11	(	(	PUNCT
ejpam-5633	81	12	2025	2025	NUM
ejpam-5633	81	13	)	)	PUNCT
ejpam-5633	81	14	,	,	PUNCT
ejpam-5633	81	15	5633	5633	NUM
ejpam-5633	81	16	4	4	NUM
ejpam-5633	81	17	of	of	ADP
ejpam-5633	81	18	13	13	NUM
ejpam-5633	81	19	(	(	PUNCT
ejpam-5633	81	20	1	1	NUM
ejpam-5633	81	21	)	)	PUNCT
ejpam-5633	81	22	if	if	SCONJ
ejpam-5633	81	23	a	a	PRON
ejpam-5633	81	24	is	be	AUX
ejpam-5633	81	25	τ1τ2	τ1τ2	NOUN
ejpam-5633	81	26	-	-	ADJ
ejpam-5633	81	27	open	open	ADJ
ejpam-5633	81	28	in	in	ADP
ejpam-5633	81	29	x	x	NOUN
ejpam-5633	81	30	,	,	PUNCT
ejpam-5633	81	31	then	then	ADV
ejpam-5633	81	32	τ1τ2	τ1τ2	NOUN
ejpam-5633	81	33	-	-	NUM
ejpam-5633	81	34	cl(a	cl(a	NUM
ejpam-5633	81	35	)	)	PUNCT
ejpam-5633	81	36	=	=	PUNCT
ejpam-5633	81	37	(	(	PUNCT
ejpam-5633	81	38	τ1	τ1	NOUN
ejpam-5633	81	39	,	,	PUNCT
ejpam-5633	81	40	τ2)θ	τ2)θ	NOUN
ejpam-5633	81	41	-	-	PUNCT
ejpam-5633	81	42	cl(a	cl(a	NUM
ejpam-5633	81	43	)	)	PUNCT
ejpam-5633	81	44	.	.	PUNCT
ejpam-5633	82	1	(	(	PUNCT
ejpam-5633	82	2	2	2	X
ejpam-5633	82	3	)	)	PUNCT
ejpam-5633	82	4	(	(	PUNCT
ejpam-5633	82	5	τ1	τ1	NOUN
ejpam-5633	82	6	,	,	PUNCT
ejpam-5633	82	7	τ2)θ	τ2)θ	NOUN
ejpam-5633	82	8	-	-	PUNCT
ejpam-5633	82	9	cl(a	cl(a	NUM
ejpam-5633	82	10	)	)	PUNCT
ejpam-5633	82	11	is	be	AUX
ejpam-5633	82	12	τ1τ2	τ1τ2	NOUN
ejpam-5633	82	13	-	-	ADJ
ejpam-5633	82	14	closed	closed	ADJ
ejpam-5633	82	15	in	in	ADP
ejpam-5633	82	16	x.	x.	NOUN
ejpam-5633	82	17	by	by	ADP
ejpam-5633	82	18	a	a	DET
ejpam-5633	82	19	multifunction	multifunction	NOUN
ejpam-5633	82	20	f	f	NOUN
ejpam-5633	82	21	:	:	PUNCT
ejpam-5633	82	22	x	x	X
ejpam-5633	82	23	→	→	SYM
ejpam-5633	82	24	y	y	PROPN
ejpam-5633	82	25	,	,	PUNCT
ejpam-5633	82	26	we	we	PRON
ejpam-5633	82	27	mean	mean	VERB
ejpam-5633	82	28	a	a	DET
ejpam-5633	82	29	point	point	NOUN
ejpam-5633	82	30	-	-	PUNCT
ejpam-5633	82	31	to	to	ADP
ejpam-5633	82	32	-	-	PUNCT
ejpam-5633	82	33	set	set	VERB
ejpam-5633	82	34	correspondence	correspondence	NOUN
ejpam-5633	82	35	from	from	ADP
ejpam-5633	82	36	x	x	PUNCT
ejpam-5633	82	37	into	into	ADP
ejpam-5633	82	38	y	y	PROPN
ejpam-5633	82	39	,	,	PUNCT
ejpam-5633	82	40	and	and	CCONJ
ejpam-5633	82	41	we	we	PRON
ejpam-5633	82	42	always	always	ADV
ejpam-5633	82	43	assume	assume	VERB
ejpam-5633	83	1	that	that	SCONJ
ejpam-5633	83	2	f	f	PROPN
ejpam-5633	83	3	(	(	PUNCT
ejpam-5633	83	4	x	x	X
ejpam-5633	83	5	)	)	PUNCT
ejpam-5633	83	6	̸=	̸=	NOUN
ejpam-5633	83	7	∅	∅	NOUN
ejpam-5633	83	8	for	for	ADP
ejpam-5633	83	9	all	all	PRON
ejpam-5633	83	10	x	x	SYM
ejpam-5633	83	11	∈	∈	ADJ
ejpam-5633	83	12	x.	x.	NOUN
ejpam-5633	83	13	for	for	ADP
ejpam-5633	83	14	a	a	DET
ejpam-5633	83	15	multifunction	multifunction	NOUN
ejpam-5633	83	16	f	f	NOUN
ejpam-5633	83	17	:	:	PUNCT
ejpam-5633	83	18	x	x	X
ejpam-5633	83	19	→	→	SYM
ejpam-5633	83	20	y	y	PROPN
ejpam-5633	83	21	,	,	PUNCT
ejpam-5633	83	22	we	we	PRON
ejpam-5633	83	23	shall	shall	AUX
ejpam-5633	83	24	denote	denote	VERB
ejpam-5633	83	25	the	the	DET
ejpam-5633	83	26	upper	upper	ADJ
ejpam-5633	83	27	and	and	CCONJ
ejpam-5633	83	28	lower	low	ADJ
ejpam-5633	83	29	inverse	inverse	NOUN
ejpam-5633	83	30	of	of	ADP
ejpam-5633	83	31	a	a	DET
ejpam-5633	83	32	set	set	NOUN
ejpam-5633	83	33	b	b	PROPN
ejpam-5633	83	34	of	of	ADP
ejpam-5633	83	35	y	y	PROPN
ejpam-5633	83	36	by	by	ADP
ejpam-5633	83	37	f+(b	f+(b	NOUN
ejpam-5633	83	38	)	)	PUNCT
ejpam-5633	83	39	and	and	CCONJ
ejpam-5633	83	40	f−(b	f−(b	NOUN
ejpam-5633	83	41	)	)	PUNCT
ejpam-5633	83	42	,	,	PUNCT
ejpam-5633	83	43	respectively	respectively	ADV
ejpam-5633	83	44	,	,	PUNCT
ejpam-5633	83	45	that	that	ADV
ejpam-5633	83	46	is	is	ADV
ejpam-5633	83	47	,	,	PUNCT
ejpam-5633	83	48	f+(b	f+(b	NOUN
ejpam-5633	83	49	)	)	PUNCT
ejpam-5633	83	50	=	=	PRON
ejpam-5633	84	1	{	{	PUNCT
ejpam-5633	84	2	x	x	PUNCT
ejpam-5633	84	3	∈	∈	PROPN
ejpam-5633	84	4	x	x	INTJ
ejpam-5633	85	1	|	|	NOUN
ejpam-5633	85	2	f	f	X
ejpam-5633	85	3	(	(	PUNCT
ejpam-5633	85	4	x	x	NOUN
ejpam-5633	85	5	)	)	PUNCT
ejpam-5633	85	6	⊆	⊆	NUM
ejpam-5633	85	7	b	b	NOUN
ejpam-5633	85	8	}	}	PUNCT
ejpam-5633	85	9	and	and	CCONJ
ejpam-5633	85	10	f−(b	f−(b	PROPN
ejpam-5633	85	11	)	)	PUNCT
ejpam-5633	85	12	=	=	PRON
ejpam-5633	86	1	{	{	PUNCT
ejpam-5633	86	2	x	x	PUNCT
ejpam-5633	86	3	∈	∈	PROPN
ejpam-5633	86	4	x	x	INTJ
ejpam-5633	87	1	|	|	NOUN
ejpam-5633	87	2	f	f	X
ejpam-5633	87	3	(	(	PUNCT
ejpam-5633	87	4	x	x	NOUN
ejpam-5633	87	5	)	)	PUNCT
ejpam-5633	87	6	∩	∩	NOUN
ejpam-5633	87	7	b	b	PROPN
ejpam-5633	87	8	̸=	̸=	PROPN
ejpam-5633	87	9	∅	∅	NOUN
ejpam-5633	87	10	}	}	PUNCT
ejpam-5633	87	11	.	.	PUNCT
ejpam-5633	88	1	in	in	ADP
ejpam-5633	88	2	particular	particular	ADJ
ejpam-5633	88	3	,	,	PUNCT
ejpam-5633	88	4	f−(y	f−(y	NOUN
ejpam-5633	88	5	)	)	PUNCT
ejpam-5633	88	6	=	=	SYM
ejpam-5633	89	1	{	{	PUNCT
ejpam-5633	89	2	x	x	PUNCT
ejpam-5633	89	3	∈	∈	PROPN
ejpam-5633	89	4	x	x	INTJ
ejpam-5633	90	1	|	|	ADV
ejpam-5633	90	2	y	y	PROPN
ejpam-5633	90	3	∈	∈	PROPN
ejpam-5633	90	4	f	f	X
ejpam-5633	90	5	(	(	PUNCT
ejpam-5633	90	6	x	x	NOUN
ejpam-5633	90	7	)	)	PUNCT
ejpam-5633	90	8	}	}	PUNCT
ejpam-5633	90	9	for	for	ADP
ejpam-5633	90	10	each	each	DET
ejpam-5633	90	11	point	point	NOUN
ejpam-5633	90	12	y	y	PROPN
ejpam-5633	90	13	∈	∈	PROPN
ejpam-5633	90	14	y	y	PROPN
ejpam-5633	90	15	.	.	PUNCT
ejpam-5633	91	1	for	for	ADP
ejpam-5633	91	2	each	each	DET
ejpam-5633	91	3	a	a	DET
ejpam-5633	91	4	⊆	⊆	NUM
ejpam-5633	91	5	x	x	SYM
ejpam-5633	91	6	,	,	PUNCT
ejpam-5633	91	7	f	f	PROPN
ejpam-5633	91	8	(	(	PUNCT
ejpam-5633	91	9	a	a	NOUN
ejpam-5633	91	10	)	)	PUNCT
ejpam-5633	91	11	=	=	SYM
ejpam-5633	91	12	∪x∈af	∪x∈af	NOUN
ejpam-5633	91	13	(	(	PUNCT
ejpam-5633	91	14	x	x	NOUN
ejpam-5633	91	15	)	)	PUNCT
ejpam-5633	91	16	.	.	PUNCT
ejpam-5633	92	1	3	3	X
ejpam-5633	92	2	.	.	X
ejpam-5633	92	3	upper	upper	ADJ
ejpam-5633	92	4	and	and	CCONJ
ejpam-5633	92	5	lower	low	ADJ
ejpam-5633	92	6	nearly	nearly	ADV
ejpam-5633	92	7	(	(	PUNCT
ejpam-5633	92	8	τ1	τ1	NOUN
ejpam-5633	92	9	,	,	PUNCT
ejpam-5633	92	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	92	11	multifunctions	multifunction	NOUN
ejpam-5633	92	12	in	in	ADP
ejpam-5633	92	13	this	this	DET
ejpam-5633	92	14	section	section	NOUN
ejpam-5633	92	15	,	,	PUNCT
ejpam-5633	92	16	we	we	PRON
ejpam-5633	92	17	introduce	introduce	VERB
ejpam-5633	92	18	the	the	DET
ejpam-5633	92	19	notions	notion	NOUN
ejpam-5633	92	20	of	of	ADP
ejpam-5633	92	21	upper	upper	ADJ
ejpam-5633	92	22	nearly	nearly	ADV
ejpam-5633	92	23	(	(	PUNCT
ejpam-5633	92	24	τ1	τ1	NOUN
ejpam-5633	92	25	,	,	PUNCT
ejpam-5633	92	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	92	27	multifunctions	multifunction	NOUN
ejpam-5633	92	28	and	and	CCONJ
ejpam-5633	92	29	lower	low	ADJ
ejpam-5633	92	30	nearly	nearly	ADV
ejpam-5633	92	31	(	(	PUNCT
ejpam-5633	92	32	τ1	τ1	NOUN
ejpam-5633	92	33	,	,	PUNCT
ejpam-5633	92	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	92	35	multifunctions	multifunction	NOUN
ejpam-5633	92	36	.	.	PUNCT
ejpam-5633	93	1	moreover	moreover	ADV
ejpam-5633	93	2	,	,	PUNCT
ejpam-5633	93	3	several	several	ADJ
ejpam-5633	93	4	characterizations	characterization	NOUN
ejpam-5633	93	5	of	of	ADP
ejpam-5633	93	6	upper	upper	ADJ
ejpam-5633	93	7	nearly	nearly	ADV
ejpam-5633	93	8	(	(	PUNCT
ejpam-5633	93	9	τ1	τ1	NOUN
ejpam-5633	93	10	,	,	PUNCT
ejpam-5633	93	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	93	12	multifunctions	multifunction	NOUN
ejpam-5633	93	13	and	and	CCONJ
ejpam-5633	93	14	lower	low	ADJ
ejpam-5633	93	15	nearly	nearly	ADV
ejpam-5633	93	16	(	(	PUNCT
ejpam-5633	93	17	τ1	τ1	NOUN
ejpam-5633	93	18	,	,	PUNCT
ejpam-5633	93	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	93	20	multifunctions	multifunction	NOUN
ejpam-5633	93	21	are	be	AUX
ejpam-5633	93	22	discussed	discuss	VERB
ejpam-5633	93	23	.	.	PUNCT
ejpam-5633	94	1	definition	definition	NOUN
ejpam-5633	94	2	1	1	NUM
ejpam-5633	94	3	.	.	PUNCT
ejpam-5633	95	1	a	a	DET
ejpam-5633	95	2	multifunction	multifunction	NOUN
ejpam-5633	95	3	f	f	NOUN
ejpam-5633	95	4	:	:	PUNCT
ejpam-5633	95	5	(	(	PUNCT
ejpam-5633	95	6	x	x	NOUN
ejpam-5633	95	7	,	,	PUNCT
ejpam-5633	95	8	τ1	τ1	NOUN
ejpam-5633	95	9	,	,	PUNCT
ejpam-5633	95	10	τ2	τ2	NOUN
ejpam-5633	95	11	)	)	PUNCT
ejpam-5633	95	12	→	→	SYM
ejpam-5633	95	13	(	(	PUNCT
ejpam-5633	95	14	y	y	PROPN
ejpam-5633	95	15	,	,	PUNCT
ejpam-5633	95	16	σ1	σ1	PROPN
ejpam-5633	95	17	,	,	PUNCT
ejpam-5633	95	18	σ2	σ2	PROPN
ejpam-5633	95	19	)	)	PUNCT
ejpam-5633	95	20	is	be	AUX
ejpam-5633	95	21	said	say	VERB
ejpam-5633	95	22	to	to	PART
ejpam-5633	95	23	be	be	AUX
ejpam-5633	95	24	upper	upper	ADJ
ejpam-5633	95	25	nearly	nearly	ADV
ejpam-5633	95	26	(	(	PUNCT
ejpam-5633	95	27	τ1	τ1	NOUN
ejpam-5633	95	28	,	,	PUNCT
ejpam-5633	95	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	95	30	at	at	ADP
ejpam-5633	95	31	a	a	DET
ejpam-5633	95	32	point	point	NOUN
ejpam-5633	95	33	x	x	SYM
ejpam-5633	95	34	∈	∈	NOUN
ejpam-5633	95	35	x	x	PUNCT
ejpam-5633	95	36	if	if	SCONJ
ejpam-5633	95	37	for	for	ADP
ejpam-5633	95	38	each	each	DET
ejpam-5633	95	39	σ1σ2	σ1σ2	VERB
ejpam-5633	95	40	-	-	ADJ
ejpam-5633	95	41	open	open	ADJ
ejpam-5633	95	42	set	set	NOUN
ejpam-5633	95	43	v	v	NOUN
ejpam-5633	95	44	of	of	ADP
ejpam-5633	95	45	y	y	PROPN
ejpam-5633	95	46	containing	contain	VERB
ejpam-5633	95	47	f	f	PROPN
ejpam-5633	95	48	(	(	PUNCT
ejpam-5633	95	49	x	x	NOUN
ejpam-5633	95	50	)	)	PUNCT
ejpam-5633	95	51	and	and	CCONJ
ejpam-5633	95	52	having	have	VERB
ejpam-5633	95	53	n	n	PRON
ejpam-5633	95	54	(	(	PUNCT
ejpam-5633	95	55	σ1	σ1	PROPN
ejpam-5633	95	56	,	,	PUNCT
ejpam-5633	95	57	σ2)-closed	σ2)-close	VERB
ejpam-5633	95	58	complement	complement	NOUN
ejpam-5633	95	59	,	,	PUNCT
ejpam-5633	95	60	there	there	PRON
ejpam-5633	95	61	exists	exist	VERB
ejpam-5633	95	62	a	a	DET
ejpam-5633	95	63	τ1τ2	τ1τ2	NOUN
ejpam-5633	95	64	-	-	ADJ
ejpam-5633	95	65	open	open	ADJ
ejpam-5633	95	66	set	set	ADJ
ejpam-5633	95	67	u	u	NOUN
ejpam-5633	95	68	of	of	ADP
ejpam-5633	95	69	x	x	PUNCT
ejpam-5633	95	70	containing	contain	VERB
ejpam-5633	95	71	x	x	PUNCT
ejpam-5633	95	72	such	such	ADJ
ejpam-5633	95	73	that	that	SCONJ
ejpam-5633	95	74	f	f	PROPN
ejpam-5633	95	75	(	(	PUNCT
ejpam-5633	95	76	u	u	NOUN
ejpam-5633	95	77	)	)	PUNCT
ejpam-5633	95	78	⊆	⊆	NUM
ejpam-5633	95	79	v	v	NOUN
ejpam-5633	95	80	.	.	PUNCT
ejpam-5633	96	1	a	a	DET
ejpam-5633	96	2	multifunction	multifunction	NOUN
ejpam-5633	96	3	f	f	NOUN
ejpam-5633	96	4	:	:	PUNCT
ejpam-5633	96	5	(	(	PUNCT
ejpam-5633	96	6	x	x	NOUN
ejpam-5633	96	7	,	,	PUNCT
ejpam-5633	96	8	τ1	τ1	NOUN
ejpam-5633	96	9	,	,	PUNCT
ejpam-5633	96	10	τ2	τ2	NOUN
ejpam-5633	96	11	)	)	PUNCT
ejpam-5633	96	12	→	→	SYM
ejpam-5633	96	13	(	(	PUNCT
ejpam-5633	96	14	y	y	PROPN
ejpam-5633	96	15	,	,	PUNCT
ejpam-5633	96	16	σ1	σ1	PROPN
ejpam-5633	96	17	,	,	PUNCT
ejpam-5633	96	18	σ2	σ2	PROPN
ejpam-5633	96	19	)	)	PUNCT
ejpam-5633	96	20	is	be	AUX
ejpam-5633	96	21	said	say	VERB
ejpam-5633	96	22	to	to	PART
ejpam-5633	96	23	be	be	AUX
ejpam-5633	96	24	upper	upper	ADJ
ejpam-5633	96	25	nearly	nearly	ADV
ejpam-5633	96	26	(	(	PUNCT
ejpam-5633	96	27	τ1	τ1	NOUN
ejpam-5633	96	28	,	,	PUNCT
ejpam-5633	96	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	96	30	if	if	SCONJ
ejpam-5633	96	31	f	f	PROPN
ejpam-5633	96	32	is	be	AUX
ejpam-5633	96	33	upper	upper	ADJ
ejpam-5633	96	34	nearly	nearly	ADV
ejpam-5633	96	35	(	(	PUNCT
ejpam-5633	96	36	τ1	τ1	NOUN
ejpam-5633	96	37	,	,	PUNCT
ejpam-5633	96	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	96	39	at	at	ADP
ejpam-5633	96	40	each	each	DET
ejpam-5633	96	41	point	point	NOUN
ejpam-5633	96	42	x	x	PUNCT
ejpam-5633	96	43	of	of	ADP
ejpam-5633	96	44	x.	x.	PROPN
ejpam-5633	96	45	theorem	theorem	VERB
ejpam-5633	96	46	1	1	NUM
ejpam-5633	96	47	.	.	X
ejpam-5633	96	48	for	for	ADP
ejpam-5633	96	49	a	a	DET
ejpam-5633	96	50	multifunction	multifunction	NOUN
ejpam-5633	96	51	f	f	NOUN
ejpam-5633	96	52	:	:	PUNCT
ejpam-5633	96	53	(	(	PUNCT
ejpam-5633	96	54	x	x	NOUN
ejpam-5633	96	55	,	,	PUNCT
ejpam-5633	96	56	τ1	τ1	NOUN
ejpam-5633	96	57	,	,	PUNCT
ejpam-5633	96	58	τ2	τ2	NOUN
ejpam-5633	96	59	)	)	PUNCT
ejpam-5633	96	60	→	→	SYM
ejpam-5633	96	61	(	(	PUNCT
ejpam-5633	96	62	y	y	PROPN
ejpam-5633	96	63	,	,	PUNCT
ejpam-5633	96	64	σ1	σ1	PROPN
ejpam-5633	96	65	,	,	PUNCT
ejpam-5633	96	66	σ2	σ2	NOUN
ejpam-5633	96	67	)	)	PUNCT
ejpam-5633	96	68	,	,	PUNCT
ejpam-5633	96	69	the	the	DET
ejpam-5633	96	70	following	follow	VERB
ejpam-5633	96	71	properties	property	NOUN
ejpam-5633	96	72	are	be	AUX
ejpam-5633	96	73	equivalent	equivalent	ADJ
ejpam-5633	96	74	:	:	PUNCT
ejpam-5633	96	75	(	(	PUNCT
ejpam-5633	96	76	1	1	X
ejpam-5633	96	77	)	)	PUNCT
ejpam-5633	96	78	f	f	PROPN
ejpam-5633	96	79	is	be	AUX
ejpam-5633	96	80	upper	upper	ADJ
ejpam-5633	96	81	nearly	nearly	ADV
ejpam-5633	96	82	(	(	PUNCT
ejpam-5633	96	83	τ1	τ1	NOUN
ejpam-5633	96	84	,	,	PUNCT
ejpam-5633	96	85	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	96	86	at	at	ADP
ejpam-5633	96	87	x	x	X
ejpam-5633	96	88	∈	∈	PROPN
ejpam-5633	96	89	x	x	X
ejpam-5633	96	90	;	;	PUNCT
ejpam-5633	96	91	(	(	PUNCT
ejpam-5633	96	92	2	2	X
ejpam-5633	96	93	)	)	PUNCT
ejpam-5633	96	94	x	x	SYM
ejpam-5633	96	95	∈	∈	PRON
ejpam-5633	96	96	τ1τ2	τ1τ2	NOUN
ejpam-5633	96	97	-	-	NUM
ejpam-5633	96	98	int(f	int(f	VERB
ejpam-5633	96	99	+	+	ADJ
ejpam-5633	96	100	(	(	PUNCT
ejpam-5633	96	101	v	v	NOUN
ejpam-5633	96	102	)	)	PUNCT
ejpam-5633	96	103	)	)	PUNCT
ejpam-5633	96	104	for	for	ADP
ejpam-5633	96	105	each	each	DET
ejpam-5633	96	106	σ1σ2	σ1σ2	VERB
ejpam-5633	96	107	-	-	ADJ
ejpam-5633	96	108	open	open	ADJ
ejpam-5633	96	109	set	set	NOUN
ejpam-5633	96	110	v	v	NOUN
ejpam-5633	96	111	of	of	ADP
ejpam-5633	96	112	y	y	PROPN
ejpam-5633	96	113	containing	contain	VERB
ejpam-5633	96	114	f	f	PROPN
ejpam-5633	96	115	(	(	PUNCT
ejpam-5633	96	116	x	x	NOUN
ejpam-5633	96	117	)	)	PUNCT
ejpam-5633	96	118	and	and	CCONJ
ejpam-5633	96	119	having	have	VERB
ejpam-5633	96	120	n	n	PRON
ejpam-5633	96	121	(	(	PUNCT
ejpam-5633	96	122	σ1	σ1	PROPN
ejpam-5633	96	123	,	,	PUNCT
ejpam-5633	96	124	σ2)-closed	σ2)-close	VERB
ejpam-5633	96	125	complement	complement	NOUN
ejpam-5633	96	126	;	;	PUNCT
ejpam-5633	96	127	(	(	PUNCT
ejpam-5633	96	128	3	3	X
ejpam-5633	96	129	)	)	PUNCT
ejpam-5633	96	130	x	x	SYM
ejpam-5633	96	131	∈	∈	NOUN
ejpam-5633	96	132	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	96	133	-	-	PUNCT
ejpam-5633	96	134	cl(b	cl(b	NOUN
ejpam-5633	96	135	)	)	PUNCT
ejpam-5633	96	136	)	)	PUNCT
ejpam-5633	96	137	for	for	ADP
ejpam-5633	96	138	each	each	DET
ejpam-5633	96	139	subset	subset	NOUN
ejpam-5633	96	140	b	b	PROPN
ejpam-5633	96	141	of	of	ADP
ejpam-5633	96	142	y	y	PROPN
ejpam-5633	96	143	having	have	VERB
ejpam-5633	96	144	the	the	DET
ejpam-5633	96	145	n	n	PROPN
ejpam-5633	96	146	(	(	PUNCT
ejpam-5633	96	147	σ1	σ1	PROPN
ejpam-5633	96	148	,	,	PUNCT
ejpam-5633	96	149	σ2)-closed	σ2)-close	VERB
ejpam-5633	96	150	σ1σ2closure	σ1σ2closure	NOUN
ejpam-5633	96	151	such	such	ADJ
ejpam-5633	96	152	that	that	SCONJ
ejpam-5633	96	153	x	x	PUNCT
ejpam-5633	96	154	∈	∈	PROPN
ejpam-5633	96	155	τ1τ2	τ1τ2	NOUN
ejpam-5633	96	156	-	-	NOUN
ejpam-5633	96	157	cl(f	cl(f	NOUN
ejpam-5633	96	158	−(b	−(b	PROPN
ejpam-5633	96	159	)	)	PUNCT
ejpam-5633	96	160	)	)	PUNCT
ejpam-5633	96	161	;	;	PUNCT
ejpam-5633	96	162	(	(	PUNCT
ejpam-5633	96	163	4	4	X
ejpam-5633	96	164	)	)	PUNCT
ejpam-5633	96	165	x	x	SYM
ejpam-5633	96	166	∈	∈	PRON
ejpam-5633	96	167	τ1τ2	τ1τ2	PUNCT
ejpam-5633	96	168	-	-	NUM
ejpam-5633	96	169	int(f	int(f	VERB
ejpam-5633	96	170	+	+	ADJ
ejpam-5633	96	171	(	(	PUNCT
ejpam-5633	96	172	b	b	NOUN
ejpam-5633	96	173	)	)	PUNCT
ejpam-5633	96	174	)	)	PUNCT
ejpam-5633	96	175	for	for	ADP
ejpam-5633	96	176	each	each	DET
ejpam-5633	96	177	subset	subset	NOUN
ejpam-5633	96	178	b	b	PROPN
ejpam-5633	96	179	of	of	ADP
ejpam-5633	96	180	y	y	PRON
ejpam-5633	96	181	such	such	ADJ
ejpam-5633	96	182	that	that	SCONJ
ejpam-5633	96	183	y	y	PROPN
ejpam-5633	96	184	−σ1σ2	−σ1σ2	PROPN
ejpam-5633	96	185	-	-	PUNCT
ejpam-5633	96	186	int(b	int(b	NOUN
ejpam-5633	96	187	)	)	PUNCT
ejpam-5633	96	188	is	be	AUX
ejpam-5633	96	189	n	n	PROPN
ejpam-5633	96	190	(	(	PUNCT
ejpam-5633	96	191	σ1	σ1	PROPN
ejpam-5633	96	192	,	,	PUNCT
ejpam-5633	96	193	σ2)closed	σ2)close	VERB
ejpam-5633	96	194	and	and	CCONJ
ejpam-5633	96	195	x	x	PART
ejpam-5633	96	196	∈	∈	NOUN
ejpam-5633	96	197	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	96	198	-	-	PUNCT
ejpam-5633	96	199	int(b	int(b	NOUN
ejpam-5633	96	200	)	)	PUNCT
ejpam-5633	96	201	)	)	PUNCT
ejpam-5633	96	202	.	.	PUNCT
ejpam-5633	97	1	proof	proof	NOUN
ejpam-5633	97	2	.	.	PUNCT
ejpam-5633	98	1	(	(	PUNCT
ejpam-5633	98	2	1	1	X
ejpam-5633	98	3	)	)	PUNCT
ejpam-5633	98	4	⇒	⇒	NOUN
ejpam-5633	98	5	(	(	PUNCT
ejpam-5633	98	6	2	2	NUM
ejpam-5633	98	7	):	):	PUNCT
ejpam-5633	98	8	let	let	VERB
ejpam-5633	98	9	v	v	PART
ejpam-5633	98	10	be	be	AUX
ejpam-5633	98	11	any	any	DET
ejpam-5633	98	12	σ1σ2	σ1σ2	NOUN
ejpam-5633	98	13	-	-	ADJ
ejpam-5633	98	14	open	open	ADJ
ejpam-5633	98	15	set	set	NOUN
ejpam-5633	98	16	of	of	ADP
ejpam-5633	98	17	y	y	PROPN
ejpam-5633	98	18	containing	contain	VERB
ejpam-5633	98	19	f	f	PROPN
ejpam-5633	98	20	(	(	PUNCT
ejpam-5633	98	21	x	x	NOUN
ejpam-5633	98	22	)	)	PUNCT
ejpam-5633	98	23	and	and	CCONJ
ejpam-5633	98	24	having	have	VERB
ejpam-5633	98	25	n	n	PRON
ejpam-5633	98	26	(	(	PUNCT
ejpam-5633	98	27	σ1	σ1	PROPN
ejpam-5633	98	28	,	,	PUNCT
ejpam-5633	98	29	σ2)-closed	σ2)-close	VERB
ejpam-5633	98	30	complement	complement	NOUN
ejpam-5633	98	31	and	and	CCONJ
ejpam-5633	98	32	x	x	NOUN
ejpam-5633	98	33	∈	∈	PROPN
ejpam-5633	98	34	f+(v	f+(v	NOUN
ejpam-5633	98	35	)	)	PUNCT
ejpam-5633	98	36	.	.	PUNCT
ejpam-5633	99	1	by	by	ADP
ejpam-5633	99	2	(	(	PUNCT
ejpam-5633	99	3	1	1	NUM
ejpam-5633	99	4	)	)	PUNCT
ejpam-5633	99	5	,	,	PUNCT
ejpam-5633	99	6	there	there	PRON
ejpam-5633	99	7	exists	exist	VERB
ejpam-5633	99	8	a	a	DET
ejpam-5633	99	9	τ1τ2	τ1τ2	NOUN
ejpam-5633	99	10	-	-	ADJ
ejpam-5633	99	11	open	open	ADJ
ejpam-5633	99	12	set	set	ADJ
ejpam-5633	99	13	u	u	NOUN
ejpam-5633	99	14	of	of	ADP
ejpam-5633	99	15	x	x	PUNCT
ejpam-5633	99	16	containing	contain	VERB
ejpam-5633	99	17	x	x	PUNCT
ejpam-5633	99	18	such	such	ADJ
ejpam-5633	99	19	that	that	SCONJ
ejpam-5633	99	20	f	f	PROPN
ejpam-5633	99	21	(	(	PUNCT
ejpam-5633	99	22	u	u	NOUN
ejpam-5633	99	23	)	)	PUNCT
ejpam-5633	99	24	⊆	⊆	NUM
ejpam-5633	99	25	v	v	NOUN
ejpam-5633	99	26	.	.	PUNCT
ejpam-5633	100	1	thus	thus	ADV
ejpam-5633	100	2	,	,	PUNCT
ejpam-5633	100	3	x	x	PUNCT
ejpam-5633	100	4	∈	∈	PROPN
ejpam-5633	100	5	u	u	NOUN
ejpam-5633	100	6	⊆	⊆	NUM
ejpam-5633	100	7	f+(v	f+(v	NOUN
ejpam-5633	100	8	)	)	PUNCT
ejpam-5633	100	9	.	.	PUNCT
ejpam-5633	101	1	since	since	SCONJ
ejpam-5633	101	2	u	u	NOUN
ejpam-5633	101	3	is	be	AUX
ejpam-5633	101	4	τ1τ2	τ1τ2	VERB
ejpam-5633	101	5	-	-	ADJ
ejpam-5633	101	6	open	open	ADJ
ejpam-5633	101	7	,	,	PUNCT
ejpam-5633	101	8	we	we	PRON
ejpam-5633	101	9	have	have	VERB
ejpam-5633	101	10	x	x	PART
ejpam-5633	101	11	∈	∈	PRON
ejpam-5633	101	12	τ1τ2	τ1τ2	NOUN
ejpam-5633	101	13	-	-	NUM
ejpam-5633	101	14	int(f	int(f	VERB
ejpam-5633	101	15	+	+	ADJ
ejpam-5633	101	16	(	(	PUNCT
ejpam-5633	101	17	v	v	NOUN
ejpam-5633	101	18	)	)	PUNCT
ejpam-5633	101	19	)	)	PUNCT
ejpam-5633	101	20	.	.	PUNCT
ejpam-5633	102	1	(	(	PUNCT
ejpam-5633	102	2	2	2	X
ejpam-5633	102	3	)	)	PUNCT
ejpam-5633	102	4	⇒	⇒	NOUN
ejpam-5633	102	5	(	(	PUNCT
ejpam-5633	102	6	3	3	NUM
ejpam-5633	102	7	):	):	PUNCT
ejpam-5633	102	8	let	let	VERB
ejpam-5633	102	9	b	b	X
ejpam-5633	102	10	be	be	AUX
ejpam-5633	102	11	any	any	DET
ejpam-5633	102	12	subset	subset	NOUN
ejpam-5633	102	13	of	of	ADP
ejpam-5633	102	14	y	y	PROPN
ejpam-5633	102	15	having	have	VERB
ejpam-5633	102	16	the	the	DET
ejpam-5633	102	17	n	n	PROPN
ejpam-5633	102	18	(	(	PUNCT
ejpam-5633	102	19	σ1	σ1	PROPN
ejpam-5633	102	20	,	,	PUNCT
ejpam-5633	102	21	σ2)-closed	σ2)-close	VERB
ejpam-5633	102	22	σ1σ2	σ1σ2	NOUN
ejpam-5633	102	23	-	-	NOUN
ejpam-5633	102	24	closure	closure	NOUN
ejpam-5633	102	25	.	.	PUNCT
ejpam-5633	103	1	then	then	ADV
ejpam-5633	103	2	,	,	PUNCT
ejpam-5633	103	3	σ1σ2	σ1σ2	NOUN
ejpam-5633	103	4	-	-	NOUN
ejpam-5633	103	5	cl(b	cl(b	NOUN
ejpam-5633	103	6	)	)	PUNCT
ejpam-5633	103	7	is	be	AUX
ejpam-5633	103	8	σ1σ2	σ1σ2	NOUN
ejpam-5633	103	9	-	-	ADJ
ejpam-5633	103	10	closed	closed	ADJ
ejpam-5633	103	11	and	and	CCONJ
ejpam-5633	103	12	y	y	PROPN
ejpam-5633	103	13	−σ1σ2	−σ1σ2	NOUN
ejpam-5633	103	14	-	-	PUNCT
ejpam-5633	103	15	cl(b	cl(b	NOUN
ejpam-5633	103	16	)	)	PUNCT
ejpam-5633	103	17	is	be	AUX
ejpam-5633	103	18	a	a	DET
ejpam-5633	103	19	σ1σ2	σ1σ2	NUM
ejpam-5633	103	20	-	-	ADJ
ejpam-5633	103	21	open	open	ADJ
ejpam-5633	103	22	set	set	NOUN
ejpam-5633	103	23	having	have	VERB
ejpam-5633	103	24	n	n	PROPN
ejpam-5633	103	25	(	(	PUNCT
ejpam-5633	103	26	σ1	σ1	PROPN
ejpam-5633	103	27	,	,	PUNCT
ejpam-5633	103	28	σ2)-closed	σ2)-close	VERB
ejpam-5633	103	29	complement	complement	NOUN
ejpam-5633	103	30	.	.	PUNCT
ejpam-5633	104	1	suppose	suppose	VERB
ejpam-5633	104	2	that	that	SCONJ
ejpam-5633	104	3	x	x	PROPN
ejpam-5633	104	4	̸∈	̸∈	PROPN
ejpam-5633	104	5	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	104	6	-	-	PUNCT
ejpam-5633	104	7	cl(b	cl(b	NOUN
ejpam-5633	104	8	)	)	PUNCT
ejpam-5633	104	9	)	)	PUNCT
ejpam-5633	104	10	.	.	PUNCT
ejpam-5633	105	1	then	then	ADV
ejpam-5633	105	2	,	,	PUNCT
ejpam-5633	105	3	we	we	PRON
ejpam-5633	105	4	have	have	VERB
ejpam-5633	105	5	x	x	X
ejpam-5633	105	6	∈	∈	NOUN
ejpam-5633	105	7	x	x	X
ejpam-5633	105	8	−	−	NOUN
ejpam-5633	105	9	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	105	10	-	-	PUNCT
ejpam-5633	105	11	cl(b	cl(b	NOUN
ejpam-5633	105	12	)	)	PUNCT
ejpam-5633	105	13	)	)	PUNCT
ejpam-5633	106	1	=	=	PUNCT
ejpam-5633	107	1	f+(y	f+(y	NOUN
ejpam-5633	107	2	−	−	NUM
ejpam-5633	107	3	σ1σ2	σ1σ2	NUM
ejpam-5633	107	4	-	-	PUNCT
ejpam-5633	107	5	cl(b	cl(b	NOUN
ejpam-5633	107	6	)	)	PUNCT
ejpam-5633	107	7	)	)	PUNCT
ejpam-5633	107	8	m.	m.	NOUN
ejpam-5633	107	9	thongmoon	thongmoon	NOUN
ejpam-5633	107	10	,	,	PUNCT
ejpam-5633	107	11	a.	a.	PROPN
ejpam-5633	107	12	sama	sama	PROPN
ejpam-5633	107	13	-	-	PUNCT
ejpam-5633	107	14	ae	ae	PROPN
ejpam-5633	107	15	,	,	PUNCT
ejpam-5633	107	16	c.	c.	PROPN
ejpam-5633	107	17	boonpok	boonpok	PROPN
ejpam-5633	107	18	/	/	SYM
ejpam-5633	107	19	eur	eur	PROPN
ejpam-5633	107	20	.	.	PUNCT
ejpam-5633	108	1	j.	j.	PROPN
ejpam-5633	108	2	pure	pure	PROPN
ejpam-5633	108	3	appl	appl	PROPN
ejpam-5633	108	4	.	.	PROPN
ejpam-5633	108	5	math	math	PROPN
ejpam-5633	108	6	,	,	PUNCT
ejpam-5633	108	7	18	18	NUM
ejpam-5633	108	8	(	(	PUNCT
ejpam-5633	108	9	1	1	NUM
ejpam-5633	108	10	)	)	PUNCT
ejpam-5633	108	11	(	(	PUNCT
ejpam-5633	108	12	2025	2025	NUM
ejpam-5633	108	13	)	)	PUNCT
ejpam-5633	108	14	,	,	PUNCT
ejpam-5633	108	15	5633	5633	NUM
ejpam-5633	108	16	5	5	NUM
ejpam-5633	108	17	of	of	ADP
ejpam-5633	108	18	13	13	NUM
ejpam-5633	108	19	and	and	CCONJ
ejpam-5633	108	20	hence	hence	ADV
ejpam-5633	108	21	f	f	PROPN
ejpam-5633	108	22	(	(	PUNCT
ejpam-5633	108	23	x	x	X
ejpam-5633	108	24	)	)	PUNCT
ejpam-5633	108	25	⊆	⊆	NUM
ejpam-5633	108	26	y	y	NOUN
ejpam-5633	108	27	−	−	PUNCT
ejpam-5633	108	28	σ1σ2	σ1σ2	NOUN
ejpam-5633	108	29	-	-	NOUN
ejpam-5633	108	30	cl(b	cl(b	NOUN
ejpam-5633	108	31	)	)	PUNCT
ejpam-5633	108	32	.	.	PUNCT
ejpam-5633	109	1	since	since	SCONJ
ejpam-5633	109	2	y	y	PROPN
ejpam-5633	109	3	−	−	PROPN
ejpam-5633	109	4	σ1σ2	σ1σ2	NOUN
ejpam-5633	109	5	-	-	PUNCT
ejpam-5633	109	6	cl(b	cl(b	NOUN
ejpam-5633	109	7	)	)	PUNCT
ejpam-5633	109	8	is	be	AUX
ejpam-5633	109	9	a	a	DET
ejpam-5633	109	10	σ1σ2	σ1σ2	NUM
ejpam-5633	109	11	-	-	ADJ
ejpam-5633	109	12	open	open	ADJ
ejpam-5633	109	13	set	set	NOUN
ejpam-5633	109	14	having	have	VERB
ejpam-5633	109	15	n	n	PROPN
ejpam-5633	109	16	(	(	PUNCT
ejpam-5633	109	17	σ1	σ1	PROPN
ejpam-5633	109	18	,	,	PUNCT
ejpam-5633	109	19	σ2)-closed	σ2)-close	VERB
ejpam-5633	109	20	complement	complement	NOUN
ejpam-5633	109	21	,	,	PUNCT
ejpam-5633	109	22	by	by	ADP
ejpam-5633	109	23	(	(	PUNCT
ejpam-5633	109	24	2	2	X
ejpam-5633	109	25	)	)	PUNCT
ejpam-5633	109	26	we	we	PRON
ejpam-5633	109	27	have	have	AUX
ejpam-5633	109	28	x	x	PART
ejpam-5633	109	29	∈	∈	PRON
ejpam-5633	109	30	τ1τ2	τ1τ2	NOUN
ejpam-5633	109	31	-	-	NUM
ejpam-5633	109	32	int(f	int(f	VERB
ejpam-5633	109	33	+	+	ADJ
ejpam-5633	109	34	(	(	PUNCT
ejpam-5633	109	35	y	y	PROPN
ejpam-5633	109	36	−	−	PROPN
ejpam-5633	109	37	σ1σ2	σ1σ2	NOUN
ejpam-5633	109	38	-	-	NOUN
ejpam-5633	109	39	cl(b	cl(b	NOUN
ejpam-5633	109	40	)	)	PUNCT
ejpam-5633	109	41	)	)	PUNCT
ejpam-5633	109	42	)	)	PUNCT
ejpam-5633	110	1	=	=	PUNCT
ejpam-5633	111	1	τ1τ2	τ1τ2	NOUN
ejpam-5633	111	2	-	-	ADJ
ejpam-5633	111	3	int(x	int(x	ADJ
ejpam-5633	111	4	−	−	NOUN
ejpam-5633	111	5	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	111	6	-	-	PUNCT
ejpam-5633	111	7	cl(b	cl(b	NOUN
ejpam-5633	111	8	)	)	PUNCT
ejpam-5633	111	9	)	)	PUNCT
ejpam-5633	111	10	)	)	PUNCT
ejpam-5633	112	1	=	=	PUNCT
ejpam-5633	113	1	x	x	X
ejpam-5633	113	2	−	−	ADP
ejpam-5633	113	3	τ1τ2	τ1τ2	NOUN
ejpam-5633	113	4	-	-	NOUN
ejpam-5633	113	5	cl(f	cl(f	NOUN
ejpam-5633	113	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5633	113	7	-	-	NOUN
ejpam-5633	113	8	cl(b	cl(b	NOUN
ejpam-5633	113	9	)	)	PUNCT
ejpam-5633	113	10	)	)	PUNCT
ejpam-5633	113	11	)	)	PUNCT
ejpam-5633	114	1	⊆	⊆	NUM
ejpam-5633	114	2	x	x	SYM
ejpam-5633	114	3	−	−	PRON
ejpam-5633	114	4	τ1τ2	τ1τ2	NOUN
ejpam-5633	114	5	-	-	NOUN
ejpam-5633	114	6	cl(f	cl(f	NOUN
ejpam-5633	114	7	−(b	−(b	PROPN
ejpam-5633	114	8	)	)	PUNCT
ejpam-5633	114	9	)	)	PUNCT
ejpam-5633	114	10	.	.	PUNCT
ejpam-5633	115	1	thus	thus	ADV
ejpam-5633	115	2	,	,	PUNCT
ejpam-5633	115	3	x	x	PROPN
ejpam-5633	115	4	̸∈	̸∈	PROPN
ejpam-5633	115	5	τ1τ2	τ1τ2	PROPN
ejpam-5633	115	6	-	-	PROPN
ejpam-5633	115	7	cl(f	cl(f	NOUN
ejpam-5633	115	8	−(b	−(b	PROPN
ejpam-5633	115	9	)	)	PUNCT
ejpam-5633	115	10	)	)	PUNCT
ejpam-5633	115	11	.	.	PUNCT
ejpam-5633	116	1	(	(	PUNCT
ejpam-5633	116	2	3	3	X
ejpam-5633	116	3	)	)	PUNCT
ejpam-5633	116	4	⇒	⇒	NOUN
ejpam-5633	116	5	(	(	PUNCT
ejpam-5633	116	6	4	4	NUM
ejpam-5633	116	7	):	):	PUNCT
ejpam-5633	116	8	let	let	VERB
ejpam-5633	116	9	b	b	X
ejpam-5633	116	10	be	be	AUX
ejpam-5633	116	11	any	any	DET
ejpam-5633	116	12	subset	subset	NOUN
ejpam-5633	116	13	of	of	ADP
ejpam-5633	116	14	y	y	PRON
ejpam-5633	116	15	such	such	ADJ
ejpam-5633	116	16	that	that	SCONJ
ejpam-5633	116	17	y	y	PROPN
ejpam-5633	116	18	−	−	ADP
ejpam-5633	116	19	σ1σ2	σ1σ2	NUM
ejpam-5633	116	20	-	-	PUNCT
ejpam-5633	116	21	int(b	int(b	NOUN
ejpam-5633	116	22	)	)	PUNCT
ejpam-5633	116	23	is	be	AUX
ejpam-5633	116	24	n	n	PROPN
ejpam-5633	116	25	(	(	PUNCT
ejpam-5633	116	26	σ1	σ1	PROPN
ejpam-5633	116	27	,	,	PUNCT
ejpam-5633	116	28	σ2)-closed	σ2)-close	VERB
ejpam-5633	116	29	.	.	PUNCT
ejpam-5633	117	1	suppose	suppose	VERB
ejpam-5633	117	2	that	that	SCONJ
ejpam-5633	117	3	x	x	PROPN
ejpam-5633	117	4	̸∈	̸∈	PROPN
ejpam-5633	117	5	τ1τ2	τ1τ2	PROPN
ejpam-5633	117	6	-	-	NUM
ejpam-5633	117	7	int(f	int(f	VERB
ejpam-5633	117	8	+	+	ADJ
ejpam-5633	117	9	(	(	PUNCT
ejpam-5633	117	10	b	b	NOUN
ejpam-5633	117	11	)	)	PUNCT
ejpam-5633	117	12	)	)	PUNCT
ejpam-5633	117	13	.	.	PUNCT
ejpam-5633	118	1	then	then	ADV
ejpam-5633	118	2	,	,	PUNCT
ejpam-5633	118	3	we	we	PRON
ejpam-5633	118	4	have	have	VERB
ejpam-5633	118	5	x	x	X
ejpam-5633	118	6	∈	∈	NOUN
ejpam-5633	118	7	x	x	INTJ
ejpam-5633	118	8	−	−	PUNCT
ejpam-5633	118	9	τ1τ2	τ1τ2	NOUN
ejpam-5633	118	10	-	-	NUM
ejpam-5633	118	11	int(f	int(f	VERB
ejpam-5633	118	12	+	+	ADJ
ejpam-5633	118	13	(	(	PUNCT
ejpam-5633	118	14	b	b	NOUN
ejpam-5633	118	15	)	)	PUNCT
ejpam-5633	118	16	)	)	PUNCT
ejpam-5633	119	1	=	=	PUNCT
ejpam-5633	119	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	119	3	-	-	NOUN
ejpam-5633	119	4	cl(x	cl(x	SYM
ejpam-5633	119	5	−	−	PROPN
ejpam-5633	119	6	f+(b	f+(b	NOUN
ejpam-5633	119	7	)	)	PUNCT
ejpam-5633	119	8	)	)	PUNCT
ejpam-5633	120	1	=	=	PUNCT
ejpam-5633	120	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	120	3	-	-	PROPN
ejpam-5633	120	4	cl(f	cl(f	NOUN
ejpam-5633	120	5	−(y	−(y	NOUN
ejpam-5633	120	6	−b	−b	NOUN
ejpam-5633	120	7	)	)	PUNCT
ejpam-5633	120	8	)	)	PUNCT
ejpam-5633	120	9	and	and	CCONJ
ejpam-5633	120	10	by	by	ADP
ejpam-5633	120	11	(	(	PUNCT
ejpam-5633	120	12	3	3	NUM
ejpam-5633	120	13	)	)	PUNCT
ejpam-5633	120	14	,	,	PUNCT
ejpam-5633	120	15	x	x	PUNCT
ejpam-5633	120	16	∈	∈	NOUN
ejpam-5633	120	17	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	120	18	-	-	PUNCT
ejpam-5633	120	19	cl(y	cl(y	NOUN
ejpam-5633	120	20	−	−	PROPN
ejpam-5633	120	21	b	b	NOUN
ejpam-5633	120	22	)	)	PUNCT
ejpam-5633	120	23	)	)	PUNCT
ejpam-5633	121	1	=	=	PUNCT
ejpam-5633	121	2	f−(y	f−(y	NOUN
ejpam-5633	122	1	−	−	ADP
ejpam-5633	122	2	σ1σ2	σ1σ2	NOUN
ejpam-5633	122	3	-	-	PUNCT
ejpam-5633	122	4	int(b	int(b	NOUN
ejpam-5633	122	5	)	)	PUNCT
ejpam-5633	122	6	)	)	PUNCT
ejpam-5633	123	1	=	=	PUNCT
ejpam-5633	123	2	x	x	X
ejpam-5633	124	1	−	−	ADP
ejpam-5633	124	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	124	3	-	-	PUNCT
ejpam-5633	124	4	int(b	int(b	NOUN
ejpam-5633	124	5	)	)	PUNCT
ejpam-5633	124	6	)	)	PUNCT
ejpam-5633	124	7	.	.	PUNCT
ejpam-5633	125	1	thus	thus	ADV
ejpam-5633	125	2	,	,	PUNCT
ejpam-5633	125	3	x	x	PROPN
ejpam-5633	125	4	̸∈	̸∈	PROPN
ejpam-5633	125	5	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	125	6	-	-	PUNCT
ejpam-5633	125	7	int(b	int(b	NOUN
ejpam-5633	125	8	)	)	PUNCT
ejpam-5633	125	9	)	)	PUNCT
ejpam-5633	125	10	.	.	PUNCT
ejpam-5633	126	1	(	(	PUNCT
ejpam-5633	126	2	4	4	X
ejpam-5633	126	3	)	)	PUNCT
ejpam-5633	126	4	⇒	⇒	NOUN
ejpam-5633	126	5	(	(	PUNCT
ejpam-5633	126	6	1	1	NUM
ejpam-5633	126	7	):	):	PUNCT
ejpam-5633	126	8	let	let	VERB
ejpam-5633	126	9	v	v	PART
ejpam-5633	126	10	be	be	AUX
ejpam-5633	126	11	any	any	DET
ejpam-5633	126	12	σ1σ2	σ1σ2	NOUN
ejpam-5633	126	13	-	-	ADJ
ejpam-5633	126	14	open	open	ADJ
ejpam-5633	126	15	set	set	NOUN
ejpam-5633	126	16	of	of	ADP
ejpam-5633	126	17	y	y	PROPN
ejpam-5633	126	18	containing	contain	VERB
ejpam-5633	126	19	f	f	PROPN
ejpam-5633	126	20	(	(	PUNCT
ejpam-5633	126	21	x	x	NOUN
ejpam-5633	126	22	)	)	PUNCT
ejpam-5633	126	23	and	and	CCONJ
ejpam-5633	126	24	having	have	VERB
ejpam-5633	126	25	n	n	PRON
ejpam-5633	126	26	(	(	PUNCT
ejpam-5633	126	27	σ1	σ1	PROPN
ejpam-5633	126	28	,	,	PUNCT
ejpam-5633	126	29	σ2)closed	σ2)close	VERB
ejpam-5633	126	30	complement	complement	NOUN
ejpam-5633	126	31	.	.	PUNCT
ejpam-5633	127	1	then	then	ADV
ejpam-5633	127	2	,	,	PUNCT
ejpam-5633	127	3	y	y	PROPN
ejpam-5633	127	4	−	−	PROPN
ejpam-5633	127	5	σ1σ2	σ1σ2	PROPN
ejpam-5633	127	6	-	-	PUNCT
ejpam-5633	127	7	int(v	int(v	NOUN
ejpam-5633	127	8	)	)	PUNCT
ejpam-5633	127	9	=	=	PUNCT
ejpam-5633	127	10	y	y	PROPN
ejpam-5633	127	11	−	−	PROPN
ejpam-5633	127	12	v	v	NUM
ejpam-5633	127	13	which	which	PRON
ejpam-5633	127	14	is	be	AUX
ejpam-5633	127	15	n	n	PROPN
ejpam-5633	127	16	(	(	PUNCT
ejpam-5633	127	17	σ1	σ1	PROPN
ejpam-5633	127	18	,	,	PUNCT
ejpam-5633	127	19	σ2)-closed	σ2)-close	VERB
ejpam-5633	127	20	and	and	CCONJ
ejpam-5633	127	21	x	x	PART
ejpam-5633	127	22	∈	∈	NOUN
ejpam-5633	127	23	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	127	24	-	-	PUNCT
ejpam-5633	127	25	int(v	int(v	NOUN
ejpam-5633	127	26	)	)	PUNCT
ejpam-5633	127	27	)	)	PUNCT
ejpam-5633	127	28	.	.	PUNCT
ejpam-5633	128	1	by	by	ADP
ejpam-5633	128	2	(	(	PUNCT
ejpam-5633	128	3	4	4	NUM
ejpam-5633	128	4	)	)	PUNCT
ejpam-5633	128	5	,	,	PUNCT
ejpam-5633	128	6	we	we	PRON
ejpam-5633	128	7	have	have	VERB
ejpam-5633	128	8	x	x	PART
ejpam-5633	128	9	∈	∈	PRON
ejpam-5633	128	10	τ1τ2	τ1τ2	NOUN
ejpam-5633	128	11	-	-	NUM
ejpam-5633	128	12	int(f	int(f	VERB
ejpam-5633	128	13	+	+	ADJ
ejpam-5633	128	14	(	(	PUNCT
ejpam-5633	128	15	v	v	NOUN
ejpam-5633	128	16	)	)	PUNCT
ejpam-5633	128	17	)	)	PUNCT
ejpam-5633	128	18	.	.	PUNCT
ejpam-5633	129	1	therefore	therefore	ADV
ejpam-5633	129	2	,	,	PUNCT
ejpam-5633	129	3	there	there	PRON
ejpam-5633	129	4	exists	exist	VERB
ejpam-5633	129	5	a	a	DET
ejpam-5633	129	6	τ1τ2	τ1τ2	NOUN
ejpam-5633	129	7	-	-	ADJ
ejpam-5633	129	8	open	open	ADJ
ejpam-5633	129	9	set	set	ADJ
ejpam-5633	129	10	u	u	NOUN
ejpam-5633	129	11	of	of	ADP
ejpam-5633	129	12	x	x	PUNCT
ejpam-5633	129	13	containing	contain	VERB
ejpam-5633	129	14	x	x	PUNCT
ejpam-5633	129	15	such	such	ADJ
ejpam-5633	129	16	that	that	SCONJ
ejpam-5633	129	17	x	x	SYM
ejpam-5633	129	18	∈	∈	NUM
ejpam-5633	129	19	u	u	NOUN
ejpam-5633	129	20	⊆	⊆	NUM
ejpam-5633	129	21	f+(v	f+(v	NOUN
ejpam-5633	129	22	)	)	PUNCT
ejpam-5633	129	23	.	.	PUNCT
ejpam-5633	130	1	thus	thus	ADV
ejpam-5633	130	2	,	,	PUNCT
ejpam-5633	130	3	f	f	PROPN
ejpam-5633	130	4	(	(	PUNCT
ejpam-5633	130	5	u	u	NOUN
ejpam-5633	130	6	)	)	PUNCT
ejpam-5633	130	7	⊆	⊆	NUM
ejpam-5633	130	8	v	v	NOUN
ejpam-5633	130	9	.	.	PUNCT
ejpam-5633	131	1	this	this	PRON
ejpam-5633	131	2	shows	show	VERB
ejpam-5633	131	3	that	that	SCONJ
ejpam-5633	131	4	f	f	PROPN
ejpam-5633	131	5	is	be	AUX
ejpam-5633	131	6	upper	upper	ADJ
ejpam-5633	131	7	nearly	nearly	ADV
ejpam-5633	131	8	(	(	PUNCT
ejpam-5633	131	9	τ1	τ1	NOUN
ejpam-5633	131	10	,	,	PUNCT
ejpam-5633	131	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	131	12	at	at	ADP
ejpam-5633	131	13	x.	x.	NOUN
ejpam-5633	131	14	definition	definition	NOUN
ejpam-5633	131	15	2	2	NUM
ejpam-5633	131	16	.	.	PUNCT
ejpam-5633	131	17	a	a	DET
ejpam-5633	131	18	multifunction	multifunction	NOUN
ejpam-5633	132	1	f	f	NOUN
ejpam-5633	132	2	:	:	PUNCT
ejpam-5633	132	3	(	(	PUNCT
ejpam-5633	132	4	x	x	NOUN
ejpam-5633	132	5	,	,	PUNCT
ejpam-5633	132	6	τ1	τ1	NOUN
ejpam-5633	132	7	,	,	PUNCT
ejpam-5633	132	8	τ2	τ2	NOUN
ejpam-5633	132	9	)	)	PUNCT
ejpam-5633	132	10	→	→	SYM
ejpam-5633	132	11	(	(	PUNCT
ejpam-5633	132	12	y	y	PROPN
ejpam-5633	132	13	,	,	PUNCT
ejpam-5633	132	14	σ1	σ1	PROPN
ejpam-5633	132	15	,	,	PUNCT
ejpam-5633	132	16	σ2	σ2	PROPN
ejpam-5633	132	17	)	)	PUNCT
ejpam-5633	132	18	is	be	AUX
ejpam-5633	132	19	said	say	VERB
ejpam-5633	132	20	to	to	PART
ejpam-5633	132	21	be	be	AUX
ejpam-5633	132	22	lower	low	ADJ
ejpam-5633	132	23	nearly	nearly	ADV
ejpam-5633	132	24	(	(	PUNCT
ejpam-5633	132	25	τ1	τ1	NOUN
ejpam-5633	132	26	,	,	PUNCT
ejpam-5633	132	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	132	28	at	at	ADP
ejpam-5633	132	29	a	a	DET
ejpam-5633	132	30	point	point	NOUN
ejpam-5633	132	31	x	x	SYM
ejpam-5633	132	32	∈	∈	NOUN
ejpam-5633	132	33	x	x	PUNCT
ejpam-5633	132	34	if	if	SCONJ
ejpam-5633	132	35	for	for	ADP
ejpam-5633	132	36	each	each	DET
ejpam-5633	132	37	σ1σ2	σ1σ2	VERB
ejpam-5633	132	38	-	-	ADJ
ejpam-5633	132	39	open	open	ADJ
ejpam-5633	132	40	set	set	NOUN
ejpam-5633	132	41	v	v	NOUN
ejpam-5633	132	42	of	of	ADP
ejpam-5633	132	43	y	y	PRON
ejpam-5633	132	44	such	such	ADJ
ejpam-5633	132	45	that	that	SCONJ
ejpam-5633	132	46	f	f	PROPN
ejpam-5633	132	47	(	(	PUNCT
ejpam-5633	132	48	x)∩v	x)∩v	PROPN
ejpam-5633	132	49	̸=	̸=	PROPN
ejpam-5633	132	50	∅	∅	NOUN
ejpam-5633	132	51	and	and	CCONJ
ejpam-5633	132	52	having	have	VERB
ejpam-5633	132	53	n	n	PROPN
ejpam-5633	132	54	(	(	PUNCT
ejpam-5633	132	55	σ1	σ1	PROPN
ejpam-5633	132	56	,	,	PUNCT
ejpam-5633	132	57	σ2)-closed	σ2)-close	VERB
ejpam-5633	132	58	complement	complement	NOUN
ejpam-5633	132	59	,	,	PUNCT
ejpam-5633	132	60	there	there	PRON
ejpam-5633	132	61	exists	exist	VERB
ejpam-5633	132	62	a	a	DET
ejpam-5633	132	63	τ1τ2	τ1τ2	NOUN
ejpam-5633	132	64	-	-	ADJ
ejpam-5633	132	65	open	open	ADJ
ejpam-5633	132	66	set	set	ADJ
ejpam-5633	132	67	u	u	NOUN
ejpam-5633	132	68	of	of	ADP
ejpam-5633	132	69	x	x	PUNCT
ejpam-5633	132	70	containing	contain	VERB
ejpam-5633	132	71	x	x	PUNCT
ejpam-5633	132	72	such	such	ADJ
ejpam-5633	132	73	that	that	SCONJ
ejpam-5633	132	74	f	f	PROPN
ejpam-5633	132	75	(	(	PUNCT
ejpam-5633	132	76	z	z	NOUN
ejpam-5633	132	77	)	)	PUNCT
ejpam-5633	132	78	∩	∩	NOUN
ejpam-5633	132	79	v	v	ADP
ejpam-5633	132	80	̸=	̸=	PROPN
ejpam-5633	132	81	∅	∅	NOUN
ejpam-5633	132	82	for	for	ADP
ejpam-5633	132	83	each	each	DET
ejpam-5633	132	84	z	z	NOUN
ejpam-5633	132	85	∈	∈	PROPN
ejpam-5633	132	86	u	u	NOUN
ejpam-5633	132	87	.	.	PUNCT
ejpam-5633	133	1	a	a	DET
ejpam-5633	133	2	multifunction	multifunction	NOUN
ejpam-5633	133	3	f	f	NOUN
ejpam-5633	133	4	:	:	PUNCT
ejpam-5633	133	5	(	(	PUNCT
ejpam-5633	133	6	x	x	NOUN
ejpam-5633	133	7	,	,	PUNCT
ejpam-5633	133	8	τ1	τ1	NOUN
ejpam-5633	133	9	,	,	PUNCT
ejpam-5633	133	10	τ2	τ2	NOUN
ejpam-5633	133	11	)	)	PUNCT
ejpam-5633	133	12	→	→	SYM
ejpam-5633	133	13	(	(	PUNCT
ejpam-5633	133	14	y	y	PROPN
ejpam-5633	133	15	,	,	PUNCT
ejpam-5633	133	16	σ1	σ1	PROPN
ejpam-5633	133	17	,	,	PUNCT
ejpam-5633	133	18	σ2	σ2	PROPN
ejpam-5633	133	19	)	)	PUNCT
ejpam-5633	133	20	is	be	AUX
ejpam-5633	133	21	said	say	VERB
ejpam-5633	133	22	to	to	PART
ejpam-5633	133	23	be	be	AUX
ejpam-5633	133	24	lower	low	ADJ
ejpam-5633	133	25	nearly	nearly	ADV
ejpam-5633	133	26	(	(	PUNCT
ejpam-5633	133	27	τ1	τ1	NOUN
ejpam-5633	133	28	,	,	PUNCT
ejpam-5633	133	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	133	30	if	if	SCONJ
ejpam-5633	133	31	f	f	PROPN
ejpam-5633	133	32	is	be	AUX
ejpam-5633	133	33	lower	low	ADJ
ejpam-5633	133	34	nearly	nearly	ADV
ejpam-5633	133	35	(	(	PUNCT
ejpam-5633	133	36	τ1	τ1	NOUN
ejpam-5633	133	37	,	,	PUNCT
ejpam-5633	133	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	133	39	at	at	ADP
ejpam-5633	133	40	each	each	DET
ejpam-5633	133	41	point	point	NOUN
ejpam-5633	133	42	x	x	PUNCT
ejpam-5633	133	43	of	of	ADP
ejpam-5633	133	44	x.	x.	PROPN
ejpam-5633	133	45	theorem	theorem	VERB
ejpam-5633	133	46	2	2	NUM
ejpam-5633	133	47	.	.	X
ejpam-5633	133	48	for	for	ADP
ejpam-5633	133	49	a	a	DET
ejpam-5633	133	50	multifunction	multifunction	NOUN
ejpam-5633	133	51	f	f	NOUN
ejpam-5633	133	52	:	:	PUNCT
ejpam-5633	133	53	(	(	PUNCT
ejpam-5633	133	54	x	x	NOUN
ejpam-5633	133	55	,	,	PUNCT
ejpam-5633	133	56	τ1	τ1	NOUN
ejpam-5633	133	57	,	,	PUNCT
ejpam-5633	133	58	τ2	τ2	NOUN
ejpam-5633	133	59	)	)	PUNCT
ejpam-5633	133	60	→	→	SYM
ejpam-5633	133	61	(	(	PUNCT
ejpam-5633	133	62	y	y	PROPN
ejpam-5633	133	63	,	,	PUNCT
ejpam-5633	133	64	σ1	σ1	PROPN
ejpam-5633	133	65	,	,	PUNCT
ejpam-5633	133	66	σ2	σ2	NOUN
ejpam-5633	133	67	)	)	PUNCT
ejpam-5633	133	68	,	,	PUNCT
ejpam-5633	133	69	the	the	DET
ejpam-5633	133	70	following	follow	VERB
ejpam-5633	133	71	properties	property	NOUN
ejpam-5633	133	72	are	be	AUX
ejpam-5633	133	73	equivalent	equivalent	ADJ
ejpam-5633	133	74	:	:	PUNCT
ejpam-5633	133	75	(	(	PUNCT
ejpam-5633	133	76	1	1	X
ejpam-5633	133	77	)	)	PUNCT
ejpam-5633	133	78	f	f	PROPN
ejpam-5633	133	79	is	be	AUX
ejpam-5633	133	80	lower	low	ADJ
ejpam-5633	133	81	nearly	nearly	ADV
ejpam-5633	133	82	(	(	PUNCT
ejpam-5633	133	83	τ1	τ1	NOUN
ejpam-5633	133	84	,	,	PUNCT
ejpam-5633	133	85	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	133	86	at	at	ADP
ejpam-5633	133	87	x	x	X
ejpam-5633	133	88	∈	∈	PROPN
ejpam-5633	133	89	x	x	X
ejpam-5633	133	90	;	;	PUNCT
ejpam-5633	133	91	(	(	PUNCT
ejpam-5633	133	92	2	2	X
ejpam-5633	133	93	)	)	PUNCT
ejpam-5633	133	94	x	x	SYM
ejpam-5633	133	95	∈	∈	PRON
ejpam-5633	133	96	τ1τ2	τ1τ2	NOUN
ejpam-5633	133	97	-	-	ADJ
ejpam-5633	133	98	int(f	int(f	NUM
ejpam-5633	133	99	−(v	−(v	NOUN
ejpam-5633	133	100	)	)	PUNCT
ejpam-5633	133	101	)	)	PUNCT
ejpam-5633	133	102	for	for	ADP
ejpam-5633	133	103	each	each	DET
ejpam-5633	133	104	σ1σ2	σ1σ2	VERB
ejpam-5633	133	105	-	-	ADJ
ejpam-5633	133	106	open	open	ADJ
ejpam-5633	133	107	set	set	NOUN
ejpam-5633	133	108	v	v	NOUN
ejpam-5633	133	109	of	of	ADP
ejpam-5633	133	110	y	y	PRON
ejpam-5633	133	111	such	such	ADJ
ejpam-5633	133	112	that	that	SCONJ
ejpam-5633	133	113	f	f	PROPN
ejpam-5633	133	114	(	(	PUNCT
ejpam-5633	133	115	x	x	NOUN
ejpam-5633	133	116	)	)	PUNCT
ejpam-5633	133	117	∩	∩	NOUN
ejpam-5633	133	118	v	v	ADP
ejpam-5633	133	119	̸=	̸=	PROPN
ejpam-5633	133	120	∅	∅	NOUN
ejpam-5633	133	121	and	and	CCONJ
ejpam-5633	133	122	having	have	VERB
ejpam-5633	133	123	n	n	PROPN
ejpam-5633	133	124	(	(	PUNCT
ejpam-5633	133	125	σ1	σ1	PROPN
ejpam-5633	133	126	,	,	PUNCT
ejpam-5633	133	127	σ2)-closed	σ2)-close	VERB
ejpam-5633	133	128	complement	complement	NOUN
ejpam-5633	133	129	;	;	PUNCT
ejpam-5633	133	130	(	(	PUNCT
ejpam-5633	133	131	3	3	X
ejpam-5633	133	132	)	)	PUNCT
ejpam-5633	133	133	x	x	SYM
ejpam-5633	133	134	∈	∈	VERB
ejpam-5633	133	135	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	133	136	-	-	PUNCT
ejpam-5633	133	137	cl(b	cl(b	NOUN
ejpam-5633	133	138	)	)	PUNCT
ejpam-5633	133	139	)	)	PUNCT
ejpam-5633	133	140	for	for	ADP
ejpam-5633	133	141	each	each	DET
ejpam-5633	133	142	subset	subset	NOUN
ejpam-5633	133	143	b	b	PROPN
ejpam-5633	133	144	of	of	ADP
ejpam-5633	133	145	y	y	PROPN
ejpam-5633	133	146	having	have	VERB
ejpam-5633	133	147	n	n	PROPN
ejpam-5633	133	148	(	(	PUNCT
ejpam-5633	133	149	σ1	σ1	PROPN
ejpam-5633	133	150	,	,	PUNCT
ejpam-5633	133	151	σ2)-closed	σ2)-close	VERB
ejpam-5633	133	152	σ1σ2	σ1σ2	NOUN
ejpam-5633	133	153	-	-	NOUN
ejpam-5633	133	154	closure	closure	NOUN
ejpam-5633	133	155	such	such	ADJ
ejpam-5633	133	156	that	that	SCONJ
ejpam-5633	133	157	x	x	PUNCT
ejpam-5633	133	158	∈	∈	PROPN
ejpam-5633	133	159	τ1τ2	τ1τ2	NOUN
ejpam-5633	133	160	-	-	NOUN
ejpam-5633	133	161	cl(f	cl(f	NOUN
ejpam-5633	133	162	+	+	NOUN
ejpam-5633	133	163	(	(	PUNCT
ejpam-5633	133	164	b	b	NOUN
ejpam-5633	133	165	)	)	PUNCT
ejpam-5633	133	166	)	)	PUNCT
ejpam-5633	133	167	;	;	PUNCT
ejpam-5633	134	1	(	(	PUNCT
ejpam-5633	134	2	4	4	X
ejpam-5633	134	3	)	)	PUNCT
ejpam-5633	134	4	x	x	SYM
ejpam-5633	134	5	∈	∈	PRON
ejpam-5633	134	6	τ1τ2	τ1τ2	NOUN
ejpam-5633	134	7	-	-	ADJ
ejpam-5633	134	8	int(f	int(f	VERB
ejpam-5633	134	9	−(b	−(b	NOUN
ejpam-5633	134	10	)	)	PUNCT
ejpam-5633	134	11	)	)	PUNCT
ejpam-5633	134	12	for	for	ADP
ejpam-5633	134	13	each	each	DET
ejpam-5633	134	14	subset	subset	NOUN
ejpam-5633	134	15	b	b	PROPN
ejpam-5633	134	16	of	of	ADP
ejpam-5633	134	17	y	y	PRON
ejpam-5633	134	18	such	such	ADJ
ejpam-5633	134	19	that	that	SCONJ
ejpam-5633	134	20	y	y	PROPN
ejpam-5633	134	21	−σ1σ2	−σ1σ2	PROPN
ejpam-5633	134	22	-	-	PUNCT
ejpam-5633	134	23	int(b	int(b	NOUN
ejpam-5633	134	24	)	)	PUNCT
ejpam-5633	134	25	is	be	AUX
ejpam-5633	134	26	n	n	PROPN
ejpam-5633	134	27	(	(	PUNCT
ejpam-5633	134	28	σ1	σ1	PROPN
ejpam-5633	134	29	,	,	PUNCT
ejpam-5633	134	30	σ2)closed	σ2)close	VERB
ejpam-5633	134	31	and	and	CCONJ
ejpam-5633	134	32	x	x	PART
ejpam-5633	134	33	∈	∈	NOUN
ejpam-5633	134	34	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5633	134	35	-	-	PUNCT
ejpam-5633	134	36	int(b	int(b	NOUN
ejpam-5633	134	37	)	)	PUNCT
ejpam-5633	134	38	)	)	PUNCT
ejpam-5633	134	39	.	.	PUNCT
ejpam-5633	135	1	proof	proof	NOUN
ejpam-5633	135	2	.	.	PUNCT
ejpam-5633	136	1	the	the	DET
ejpam-5633	136	2	proof	proof	NOUN
ejpam-5633	136	3	is	be	AUX
ejpam-5633	136	4	similar	similar	ADJ
ejpam-5633	136	5	to	to	ADP
ejpam-5633	136	6	that	that	PRON
ejpam-5633	136	7	of	of	ADP
ejpam-5633	136	8	theorem	theorem	ADJ
ejpam-5633	136	9	1	1	NUM
ejpam-5633	136	10	.	.	PUNCT
ejpam-5633	136	11	theorem	theorem	NOUN
ejpam-5633	136	12	3	3	NUM
ejpam-5633	136	13	.	.	X
ejpam-5633	136	14	for	for	ADP
ejpam-5633	136	15	a	a	DET
ejpam-5633	136	16	multifunction	multifunction	NOUN
ejpam-5633	136	17	f	f	NOUN
ejpam-5633	136	18	:	:	PUNCT
ejpam-5633	136	19	(	(	PUNCT
ejpam-5633	136	20	x	x	NOUN
ejpam-5633	136	21	,	,	PUNCT
ejpam-5633	136	22	τ1	τ1	NOUN
ejpam-5633	136	23	,	,	PUNCT
ejpam-5633	136	24	τ2	τ2	NOUN
ejpam-5633	136	25	)	)	PUNCT
ejpam-5633	136	26	→	→	SYM
ejpam-5633	136	27	(	(	PUNCT
ejpam-5633	136	28	y	y	PROPN
ejpam-5633	136	29	,	,	PUNCT
ejpam-5633	136	30	σ1	σ1	PROPN
ejpam-5633	136	31	,	,	PUNCT
ejpam-5633	136	32	σ2	σ2	NOUN
ejpam-5633	136	33	)	)	PUNCT
ejpam-5633	136	34	,	,	PUNCT
ejpam-5633	136	35	the	the	DET
ejpam-5633	136	36	following	follow	VERB
ejpam-5633	136	37	properties	property	NOUN
ejpam-5633	136	38	are	be	AUX
ejpam-5633	136	39	equivalent	equivalent	ADJ
ejpam-5633	136	40	:	:	PUNCT
ejpam-5633	136	41	m.	m.	NOUN
ejpam-5633	136	42	thongmoon	thongmoon	NOUN
ejpam-5633	136	43	,	,	PUNCT
ejpam-5633	136	44	a.	a.	PROPN
ejpam-5633	136	45	sama	sama	PROPN
ejpam-5633	136	46	-	-	PUNCT
ejpam-5633	136	47	ae	ae	PROPN
ejpam-5633	136	48	,	,	PUNCT
ejpam-5633	136	49	c.	c.	PROPN
ejpam-5633	136	50	boonpok	boonpok	PROPN
ejpam-5633	136	51	/	/	SYM
ejpam-5633	136	52	eur	eur	PROPN
ejpam-5633	136	53	.	.	PUNCT
ejpam-5633	137	1	j.	j.	PROPN
ejpam-5633	137	2	pure	pure	PROPN
ejpam-5633	137	3	appl	appl	PROPN
ejpam-5633	137	4	.	.	PROPN
ejpam-5633	137	5	math	math	PROPN
ejpam-5633	137	6	,	,	PUNCT
ejpam-5633	137	7	18	18	NUM
ejpam-5633	137	8	(	(	PUNCT
ejpam-5633	137	9	1	1	NUM
ejpam-5633	137	10	)	)	PUNCT
ejpam-5633	137	11	(	(	PUNCT
ejpam-5633	137	12	2025	2025	NUM
ejpam-5633	137	13	)	)	PUNCT
ejpam-5633	137	14	,	,	PUNCT
ejpam-5633	137	15	5633	5633	NUM
ejpam-5633	137	16	6	6	NUM
ejpam-5633	137	17	of	of	ADP
ejpam-5633	137	18	13	13	NUM
ejpam-5633	137	19	(	(	PUNCT
ejpam-5633	137	20	1	1	NUM
ejpam-5633	137	21	)	)	PUNCT
ejpam-5633	137	22	f	f	PROPN
ejpam-5633	137	23	is	be	AUX
ejpam-5633	137	24	upper	upper	ADJ
ejpam-5633	137	25	nearly	nearly	ADV
ejpam-5633	137	26	(	(	PUNCT
ejpam-5633	137	27	τ1	τ1	NOUN
ejpam-5633	137	28	,	,	PUNCT
ejpam-5633	137	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	137	30	;	;	PUNCT
ejpam-5633	137	31	(	(	PUNCT
ejpam-5633	137	32	2	2	NUM
ejpam-5633	137	33	)	)	PUNCT
ejpam-5633	137	34	f+(v	f+(v	NOUN
ejpam-5633	137	35	)	)	PUNCT
ejpam-5633	137	36	is	be	AUX
ejpam-5633	137	37	τ1τ2	τ1τ2	NOUN
ejpam-5633	137	38	-	-	ADJ
ejpam-5633	137	39	open	open	ADJ
ejpam-5633	137	40	in	in	ADP
ejpam-5633	137	41	x	x	PUNCT
ejpam-5633	137	42	for	for	ADP
ejpam-5633	137	43	each	each	DET
ejpam-5633	137	44	σ1σ2	σ1σ2	VERB
ejpam-5633	137	45	-	-	ADJ
ejpam-5633	137	46	open	open	ADJ
ejpam-5633	137	47	set	set	NOUN
ejpam-5633	137	48	v	v	NOUN
ejpam-5633	137	49	of	of	ADP
ejpam-5633	137	50	y	y	PROPN
ejpam-5633	137	51	having	have	VERB
ejpam-5633	137	52	n	n	PROPN
ejpam-5633	137	53	(	(	PUNCT
ejpam-5633	137	54	σ1	σ1	PROPN
ejpam-5633	137	55	,	,	PUNCT
ejpam-5633	137	56	σ2)-closed	σ2)-close	VERB
ejpam-5633	137	57	complement	complement	NOUN
ejpam-5633	137	58	;	;	PUNCT
ejpam-5633	137	59	(	(	PUNCT
ejpam-5633	137	60	3	3	X
ejpam-5633	137	61	)	)	PUNCT
ejpam-5633	137	62	f−(k	f−(k	PROPN
ejpam-5633	137	63	)	)	PUNCT
ejpam-5633	137	64	is	be	AUX
ejpam-5633	137	65	τ1τ2	τ1τ2	NOUN
ejpam-5633	137	66	-	-	ADJ
ejpam-5633	137	67	closed	closed	ADJ
ejpam-5633	137	68	in	in	ADP
ejpam-5633	137	69	x	x	PUNCT
ejpam-5633	137	70	for	for	ADP
ejpam-5633	137	71	every	every	DET
ejpam-5633	137	72	n	n	PROPN
ejpam-5633	137	73	(	(	PUNCT
ejpam-5633	137	74	σ1	σ1	PROPN
ejpam-5633	137	75	,	,	PUNCT
ejpam-5633	137	76	σ2)-closed	σ2)-close	VERB
ejpam-5633	137	77	and	and	CCONJ
ejpam-5633	137	78	σ1σ2	σ1σ2	NOUN
ejpam-5633	137	79	-	-	PUNCT
ejpam-5633	137	80	closed	closed	ADJ
ejpam-5633	137	81	set	set	NOUN
ejpam-5633	137	82	k	k	PROPN
ejpam-5633	137	83	of	of	ADP
ejpam-5633	137	84	y	y	PROPN
ejpam-5633	137	85	;	;	PUNCT
ejpam-5633	137	86	(	(	PUNCT
ejpam-5633	137	87	4	4	X
ejpam-5633	137	88	)	)	PUNCT
ejpam-5633	137	89	τ1τ2	τ1τ2	NOUN
ejpam-5633	137	90	-	-	NOUN
ejpam-5633	137	91	cl(f	cl(f	NOUN
ejpam-5633	137	92	−(b	−(b	PROPN
ejpam-5633	137	93	)	)	PUNCT
ejpam-5633	137	94	)	)	PUNCT
ejpam-5633	138	1	⊆	⊆	X
ejpam-5633	138	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	138	3	-	-	PUNCT
ejpam-5633	138	4	cl(b	cl(b	NOUN
ejpam-5633	138	5	)	)	PUNCT
ejpam-5633	138	6	)	)	PUNCT
ejpam-5633	139	1	for	for	ADP
ejpam-5633	139	2	every	every	DET
ejpam-5633	139	3	subset	subset	NOUN
ejpam-5633	139	4	b	b	PROPN
ejpam-5633	139	5	of	of	ADP
ejpam-5633	139	6	y	y	PROPN
ejpam-5633	139	7	having	have	VERB
ejpam-5633	139	8	the	the	DET
ejpam-5633	139	9	n	n	PROPN
ejpam-5633	139	10	(	(	PUNCT
ejpam-5633	139	11	σ1	σ1	PROPN
ejpam-5633	139	12	,	,	PUNCT
ejpam-5633	139	13	σ2)closed	σ2)close	VERB
ejpam-5633	139	14	σ1σ2	σ1σ2	NOUN
ejpam-5633	139	15	-	-	NOUN
ejpam-5633	139	16	closure	closure	NOUN
ejpam-5633	139	17	;	;	PUNCT
ejpam-5633	139	18	(	(	PUNCT
ejpam-5633	139	19	5	5	X
ejpam-5633	139	20	)	)	PUNCT
ejpam-5633	139	21	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	139	22	-	-	PUNCT
ejpam-5633	139	23	int(b	int(b	NOUN
ejpam-5633	139	24	)	)	PUNCT
ejpam-5633	139	25	)	)	PUNCT
ejpam-5633	140	1	⊆	⊆	X
ejpam-5633	140	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	140	3	-	-	NUM
ejpam-5633	140	4	int(f	int(f	VERB
ejpam-5633	140	5	+	+	ADJ
ejpam-5633	140	6	(	(	PUNCT
ejpam-5633	140	7	b	b	NOUN
ejpam-5633	140	8	)	)	PUNCT
ejpam-5633	140	9	)	)	PUNCT
ejpam-5633	140	10	for	for	ADP
ejpam-5633	140	11	every	every	DET
ejpam-5633	140	12	subset	subset	NOUN
ejpam-5633	140	13	b	b	PROPN
ejpam-5633	140	14	of	of	ADP
ejpam-5633	140	15	y	y	PRON
ejpam-5633	140	16	such	such	ADJ
ejpam-5633	140	17	that	that	SCONJ
ejpam-5633	140	18	y−σ1σ2	y−σ1σ2	PROPN
ejpam-5633	140	19	-	-	PUNCT
ejpam-5633	140	20	int(b	int(b	NOUN
ejpam-5633	140	21	)	)	PUNCT
ejpam-5633	140	22	is	be	AUX
ejpam-5633	140	23	n	n	PROPN
ejpam-5633	140	24	(	(	PUNCT
ejpam-5633	140	25	σ1	σ1	PROPN
ejpam-5633	140	26	,	,	PUNCT
ejpam-5633	140	27	σ2)-closed	σ2)-close	VERB
ejpam-5633	140	28	.	.	PUNCT
ejpam-5633	141	1	proof	proof	NOUN
ejpam-5633	141	2	.	.	PUNCT
ejpam-5633	142	1	(	(	PUNCT
ejpam-5633	142	2	1	1	X
ejpam-5633	142	3	)	)	PUNCT
ejpam-5633	142	4	⇒	⇒	NOUN
ejpam-5633	142	5	(	(	PUNCT
ejpam-5633	142	6	2	2	NUM
ejpam-5633	142	7	):	):	PUNCT
ejpam-5633	142	8	let	let	VERB
ejpam-5633	142	9	v	v	PART
ejpam-5633	142	10	be	be	AUX
ejpam-5633	142	11	any	any	DET
ejpam-5633	142	12	σ1σ2	σ1σ2	NOUN
ejpam-5633	142	13	-	-	ADJ
ejpam-5633	142	14	open	open	ADJ
ejpam-5633	142	15	set	set	NOUN
ejpam-5633	142	16	of	of	ADP
ejpam-5633	142	17	y	y	PROPN
ejpam-5633	142	18	containing	contain	VERB
ejpam-5633	142	19	f	f	PROPN
ejpam-5633	142	20	(	(	PUNCT
ejpam-5633	142	21	x	x	NOUN
ejpam-5633	142	22	)	)	PUNCT
ejpam-5633	142	23	and	and	CCONJ
ejpam-5633	142	24	having	have	VERB
ejpam-5633	142	25	n	n	PRON
ejpam-5633	142	26	(	(	PUNCT
ejpam-5633	142	27	σ1	σ1	PROPN
ejpam-5633	142	28	,	,	PUNCT
ejpam-5633	142	29	σ2)-closed	σ2)-close	VERB
ejpam-5633	142	30	complement	complement	NOUN
ejpam-5633	142	31	and	and	CCONJ
ejpam-5633	142	32	x	x	NOUN
ejpam-5633	142	33	∈	∈	PROPN
ejpam-5633	142	34	f+(v	f+(v	NOUN
ejpam-5633	142	35	)	)	PUNCT
ejpam-5633	142	36	.	.	PUNCT
ejpam-5633	143	1	then	then	ADV
ejpam-5633	143	2	,	,	PUNCT
ejpam-5633	143	3	we	we	PRON
ejpam-5633	143	4	have	have	VERB
ejpam-5633	143	5	f	f	PROPN
ejpam-5633	143	6	(	(	PUNCT
ejpam-5633	143	7	x	x	NOUN
ejpam-5633	143	8	)	)	PUNCT
ejpam-5633	143	9	⊆	⊆	NUM
ejpam-5633	143	10	v	v	NOUN
ejpam-5633	143	11	.	.	PUNCT
ejpam-5633	144	1	by	by	ADP
ejpam-5633	144	2	theorem	theorem	NOUN
ejpam-5633	144	3	1	1	NUM
ejpam-5633	144	4	,	,	PUNCT
ejpam-5633	144	5	x	x	SYM
ejpam-5633	144	6	∈	∈	PRON
ejpam-5633	144	7	τ1τ2	τ1τ2	PUNCT
ejpam-5633	144	8	-	-	NUM
ejpam-5633	144	9	int(f	int(f	VERB
ejpam-5633	144	10	+	+	ADJ
ejpam-5633	144	11	(	(	PUNCT
ejpam-5633	144	12	v	v	NOUN
ejpam-5633	144	13	)	)	PUNCT
ejpam-5633	144	14	)	)	PUNCT
ejpam-5633	144	15	.	.	PUNCT
ejpam-5633	145	1	thus	thus	ADV
ejpam-5633	145	2	,	,	PUNCT
ejpam-5633	145	3	f+(v	f+(v	PROPN
ejpam-5633	145	4	)	)	PUNCT
ejpam-5633	146	1	⊆	⊆	X
ejpam-5633	146	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	146	3	-	-	NUM
ejpam-5633	146	4	int(f	int(f	VERB
ejpam-5633	146	5	+	+	ADJ
ejpam-5633	146	6	(	(	PUNCT
ejpam-5633	146	7	v	v	NOUN
ejpam-5633	146	8	)	)	PUNCT
ejpam-5633	146	9	)	)	PUNCT
ejpam-5633	146	10	and	and	CCONJ
ejpam-5633	146	11	hence	hence	ADV
ejpam-5633	146	12	f+(v	f+(v	PROPN
ejpam-5633	146	13	)	)	PUNCT
ejpam-5633	146	14	is	be	AUX
ejpam-5633	146	15	τ1τ2	τ1τ2	NOUN
ejpam-5633	146	16	-	-	ADJ
ejpam-5633	146	17	open	open	ADJ
ejpam-5633	146	18	in	in	ADP
ejpam-5633	146	19	x.	x.	NOUN
ejpam-5633	146	20	(	(	PUNCT
ejpam-5633	146	21	2	2	NUM
ejpam-5633	146	22	)	)	PUNCT
ejpam-5633	146	23	⇒	⇒	NOUN
ejpam-5633	146	24	(	(	PUNCT
ejpam-5633	146	25	3	3	NUM
ejpam-5633	146	26	):	):	PUNCT
ejpam-5633	146	27	the	the	DET
ejpam-5633	146	28	proof	proof	NOUN
ejpam-5633	146	29	follows	follow	VERB
ejpam-5633	146	30	immediately	immediately	ADV
ejpam-5633	146	31	from	from	ADP
ejpam-5633	146	32	the	the	DET
ejpam-5633	146	33	fact	fact	NOUN
ejpam-5633	146	34	that	that	SCONJ
ejpam-5633	146	35	f+(y	f+(y	PROPN
ejpam-5633	146	36	−b	−b	ADJ
ejpam-5633	146	37	)	)	PUNCT
ejpam-5633	146	38	=	=	SYM
ejpam-5633	146	39	y	y	PROPN
ejpam-5633	146	40	−f−(b	−f−(b	PROPN
ejpam-5633	146	41	)	)	PUNCT
ejpam-5633	146	42	for	for	ADP
ejpam-5633	146	43	every	every	DET
ejpam-5633	146	44	subset	subset	NOUN
ejpam-5633	146	45	b	b	PROPN
ejpam-5633	146	46	of	of	ADP
ejpam-5633	146	47	y	y	PROPN
ejpam-5633	146	48	.	.	PUNCT
ejpam-5633	147	1	(	(	PUNCT
ejpam-5633	147	2	3	3	X
ejpam-5633	147	3	)	)	PUNCT
ejpam-5633	147	4	⇒	⇒	NOUN
ejpam-5633	147	5	(	(	PUNCT
ejpam-5633	147	6	4	4	NUM
ejpam-5633	147	7	):	):	PUNCT
ejpam-5633	147	8	let	let	VERB
ejpam-5633	147	9	b	b	X
ejpam-5633	147	10	be	be	AUX
ejpam-5633	147	11	any	any	DET
ejpam-5633	147	12	subset	subset	NOUN
ejpam-5633	147	13	of	of	ADP
ejpam-5633	147	14	y	y	PROPN
ejpam-5633	147	15	having	have	VERB
ejpam-5633	147	16	the	the	DET
ejpam-5633	147	17	n	n	PROPN
ejpam-5633	147	18	(	(	PUNCT
ejpam-5633	147	19	σ1	σ1	PROPN
ejpam-5633	147	20	,	,	PUNCT
ejpam-5633	147	21	σ2)-closed	σ2)-close	VERB
ejpam-5633	147	22	σ1σ2	σ1σ2	NOUN
ejpam-5633	147	23	-	-	NOUN
ejpam-5633	147	24	closure	closure	NOUN
ejpam-5633	147	25	.	.	PUNCT
ejpam-5633	148	1	then	then	ADV
ejpam-5633	148	2	,	,	PUNCT
ejpam-5633	148	3	σ1σ2	σ1σ2	NOUN
ejpam-5633	148	4	-	-	NOUN
ejpam-5633	148	5	cl(b	cl(b	NOUN
ejpam-5633	148	6	)	)	PUNCT
ejpam-5633	148	7	is	be	AUX
ejpam-5633	148	8	σ1σ2	σ1σ2	NOUN
ejpam-5633	148	9	-	-	ADJ
ejpam-5633	148	10	closed	closed	ADJ
ejpam-5633	148	11	and	and	CCONJ
ejpam-5633	148	12	by	by	ADP
ejpam-5633	148	13	(	(	PUNCT
ejpam-5633	148	14	3	3	NUM
ejpam-5633	148	15	)	)	PUNCT
ejpam-5633	148	16	,	,	PUNCT
ejpam-5633	148	17	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	148	18	-	-	PUNCT
ejpam-5633	148	19	cl(b	cl(b	NOUN
ejpam-5633	148	20	)	)	PUNCT
ejpam-5633	148	21	)	)	PUNCT
ejpam-5633	149	1	is	be	AUX
ejpam-5633	149	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	149	3	-	-	ADJ
ejpam-5633	149	4	closed	closed	ADJ
ejpam-5633	149	5	in	in	ADP
ejpam-5633	149	6	x.	x.	NOUN
ejpam-5633	149	7	thus	thus	ADV
ejpam-5633	149	8	,	,	PUNCT
ejpam-5633	149	9	f−(b	f−(b	PROPN
ejpam-5633	149	10	)	)	PUNCT
ejpam-5633	149	11	⊆	⊆	NUM
ejpam-5633	149	12	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	149	13	-	-	PUNCT
ejpam-5633	149	14	cl(b	cl(b	NOUN
ejpam-5633	149	15	)	)	PUNCT
ejpam-5633	149	16	)	)	PUNCT
ejpam-5633	150	1	=	=	PUNCT
ejpam-5633	150	2	τ1τ2	τ1τ2	X
ejpam-5633	150	3	-	-	PUNCT
ejpam-5633	150	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5633	150	5	-	-	PUNCT
ejpam-5633	150	6	cl(b	cl(b	NOUN
ejpam-5633	150	7	)	)	PUNCT
ejpam-5633	150	8	)	)	PUNCT
ejpam-5633	150	9	and	and	CCONJ
ejpam-5633	150	10	hence	hence	ADV
ejpam-5633	150	11	τ1τ2	τ1τ2	NOUN
ejpam-5633	150	12	-	-	PROPN
ejpam-5633	150	13	cl(f	cl(f	NOUN
ejpam-5633	150	14	−(b	−(b	PROPN
ejpam-5633	150	15	)	)	PUNCT
ejpam-5633	150	16	)	)	PUNCT
ejpam-5633	150	17	⊆	⊆	X
ejpam-5633	150	18	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	150	19	-	-	PUNCT
ejpam-5633	150	20	cl(b	cl(b	NOUN
ejpam-5633	150	21	)	)	PUNCT
ejpam-5633	150	22	)	)	PUNCT
ejpam-5633	150	23	.	.	PUNCT
ejpam-5633	151	1	(	(	PUNCT
ejpam-5633	151	2	4	4	X
ejpam-5633	151	3	)	)	PUNCT
ejpam-5633	151	4	⇒	⇒	NOUN
ejpam-5633	151	5	(	(	PUNCT
ejpam-5633	151	6	5	5	NUM
ejpam-5633	151	7	):	):	PUNCT
ejpam-5633	151	8	let	let	VERB
ejpam-5633	151	9	b	b	X
ejpam-5633	151	10	be	be	AUX
ejpam-5633	151	11	any	any	DET
ejpam-5633	151	12	subset	subset	NOUN
ejpam-5633	151	13	of	of	ADP
ejpam-5633	151	14	y	y	PRON
ejpam-5633	151	15	such	such	ADJ
ejpam-5633	151	16	that	that	SCONJ
ejpam-5633	151	17	y	y	PROPN
ejpam-5633	151	18	−	−	ADP
ejpam-5633	151	19	σ1σ2	σ1σ2	NUM
ejpam-5633	151	20	-	-	PUNCT
ejpam-5633	151	21	int(b	int(b	NOUN
ejpam-5633	151	22	)	)	PUNCT
ejpam-5633	151	23	is	be	AUX
ejpam-5633	151	24	n	n	PROPN
ejpam-5633	151	25	(	(	PUNCT
ejpam-5633	151	26	σ1	σ1	PROPN
ejpam-5633	151	27	,	,	PUNCT
ejpam-5633	151	28	σ2)-closed	σ2)-close	VERB
ejpam-5633	151	29	.	.	PUNCT
ejpam-5633	152	1	then	then	ADV
ejpam-5633	152	2	by	by	ADP
ejpam-5633	152	3	(	(	PUNCT
ejpam-5633	152	4	4	4	NUM
ejpam-5633	152	5	)	)	PUNCT
ejpam-5633	152	6	,	,	PUNCT
ejpam-5633	152	7	we	we	PRON
ejpam-5633	152	8	have	have	VERB
ejpam-5633	152	9	x	x	INTJ
ejpam-5633	152	10	−	−	ADP
ejpam-5633	152	11	τ1τ2	τ1τ2	NOUN
ejpam-5633	152	12	-	-	NUM
ejpam-5633	152	13	int(f	int(f	VERB
ejpam-5633	152	14	+	+	ADJ
ejpam-5633	152	15	(	(	PUNCT
ejpam-5633	152	16	b	b	NOUN
ejpam-5633	152	17	)	)	PUNCT
ejpam-5633	152	18	)	)	PUNCT
ejpam-5633	153	1	=	=	PUNCT
ejpam-5633	153	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	153	3	-	-	NOUN
ejpam-5633	153	4	cl(x	cl(x	SYM
ejpam-5633	153	5	−	−	PROPN
ejpam-5633	153	6	f+(b	f+(b	NOUN
ejpam-5633	153	7	)	)	PUNCT
ejpam-5633	153	8	)	)	PUNCT
ejpam-5633	154	1	=	=	PUNCT
ejpam-5633	155	1	τ1τ2	τ1τ2	NOUN
ejpam-5633	155	2	-	-	PROPN
ejpam-5633	155	3	cl(f	cl(f	NOUN
ejpam-5633	155	4	−(y	−(y	NOUN
ejpam-5633	155	5	−b	−b	NOUN
ejpam-5633	155	6	)	)	PUNCT
ejpam-5633	155	7	)	)	PUNCT
ejpam-5633	156	1	⊆	⊆	X
ejpam-5633	156	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	156	3	-	-	NOUN
ejpam-5633	156	4	cl(f	cl(f	NOUN
ejpam-5633	156	5	−(y	−(y	NOUN
ejpam-5633	156	6	−	−	NOUN
ejpam-5633	156	7	σ1σ2	σ1σ2	SYM
ejpam-5633	156	8	-	-	PUNCT
ejpam-5633	156	9	int(b	int(b	NOUN
ejpam-5633	156	10	)	)	PUNCT
ejpam-5633	156	11	)	)	PUNCT
ejpam-5633	156	12	)	)	PUNCT
ejpam-5633	156	13	⊆	⊆	NUM
ejpam-5633	156	14	f−(y	f−(y	NOUN
ejpam-5633	156	15	−	−	NUM
ejpam-5633	156	16	σ1σ2	σ1σ2	NOUN
ejpam-5633	156	17	-	-	PUNCT
ejpam-5633	156	18	int(b	int(b	NOUN
ejpam-5633	156	19	)	)	PUNCT
ejpam-5633	156	20	)	)	PUNCT
ejpam-5633	156	21	=	=	PUNCT
ejpam-5633	157	1	x	x	X
ejpam-5633	157	2	−	−	ADP
ejpam-5633	157	3	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	157	4	-	-	PUNCT
ejpam-5633	157	5	int(b	int(b	NOUN
ejpam-5633	157	6	)	)	PUNCT
ejpam-5633	157	7	)	)	PUNCT
ejpam-5633	157	8	.	.	PUNCT
ejpam-5633	158	1	thus	thus	ADV
ejpam-5633	158	2	,	,	PUNCT
ejpam-5633	158	3	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	158	4	-	-	PUNCT
ejpam-5633	158	5	int(b	int(b	NOUN
ejpam-5633	158	6	)	)	PUNCT
ejpam-5633	158	7	)	)	PUNCT
ejpam-5633	159	1	⊆	⊆	X
ejpam-5633	159	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	159	3	-	-	NUM
ejpam-5633	159	4	int(f	int(f	VERB
ejpam-5633	159	5	+	+	ADJ
ejpam-5633	159	6	(	(	PUNCT
ejpam-5633	159	7	b	b	NOUN
ejpam-5633	159	8	)	)	PUNCT
ejpam-5633	159	9	)	)	PUNCT
ejpam-5633	159	10	.	.	PUNCT
ejpam-5633	160	1	(	(	PUNCT
ejpam-5633	160	2	5	5	X
ejpam-5633	160	3	)	)	PUNCT
ejpam-5633	160	4	⇒	⇒	NOUN
ejpam-5633	160	5	(	(	PUNCT
ejpam-5633	160	6	1	1	NUM
ejpam-5633	160	7	):	):	PUNCT
ejpam-5633	160	8	let	let	VERB
ejpam-5633	160	9	x	x	PUNCT
ejpam-5633	160	10	∈	∈	PROPN
ejpam-5633	160	11	x	x	X
ejpam-5633	160	12	and	and	CCONJ
ejpam-5633	160	13	v	v	X
ejpam-5633	160	14	be	be	AUX
ejpam-5633	160	15	any	any	DET
ejpam-5633	160	16	σ1σ2	σ1σ2	NOUN
ejpam-5633	160	17	-	-	ADJ
ejpam-5633	160	18	open	open	ADJ
ejpam-5633	160	19	set	set	NOUN
ejpam-5633	160	20	of	of	ADP
ejpam-5633	160	21	y	y	PROPN
ejpam-5633	160	22	containing	contain	VERB
ejpam-5633	160	23	f	f	PROPN
ejpam-5633	160	24	(	(	PUNCT
ejpam-5633	160	25	x	x	NOUN
ejpam-5633	160	26	)	)	PUNCT
ejpam-5633	160	27	and	and	CCONJ
ejpam-5633	160	28	having	have	VERB
ejpam-5633	160	29	n	n	PRON
ejpam-5633	160	30	(	(	PUNCT
ejpam-5633	160	31	σ1	σ1	PROPN
ejpam-5633	160	32	,	,	PUNCT
ejpam-5633	160	33	σ2)-closed	σ2)-close	VERB
ejpam-5633	160	34	complement	complement	NOUN
ejpam-5633	160	35	.	.	PUNCT
ejpam-5633	161	1	thus	thus	ADV
ejpam-5633	161	2	by	by	ADP
ejpam-5633	161	3	(	(	PUNCT
ejpam-5633	161	4	5	5	NUM
ejpam-5633	161	5	)	)	PUNCT
ejpam-5633	161	6	,	,	PUNCT
ejpam-5633	161	7	x	x	PUNCT
ejpam-5633	161	8	∈	∈	NOUN
ejpam-5633	161	9	f+(v	f+(v	NOUN
ejpam-5633	161	10	)	)	PUNCT
ejpam-5633	162	1	=	=	SYM
ejpam-5633	162	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	162	3	-	-	PUNCT
ejpam-5633	162	4	int(v	int(v	NOUN
ejpam-5633	162	5	)	)	PUNCT
ejpam-5633	162	6	)	)	PUNCT
ejpam-5633	163	1	⊆	⊆	X
ejpam-5633	163	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	163	3	-	-	NUM
ejpam-5633	163	4	int(f	int(f	VERB
ejpam-5633	163	5	+	+	ADJ
ejpam-5633	163	6	(	(	PUNCT
ejpam-5633	163	7	v	v	NOUN
ejpam-5633	163	8	)	)	PUNCT
ejpam-5633	163	9	)	)	PUNCT
ejpam-5633	163	10	.	.	PUNCT
ejpam-5633	164	1	by	by	ADP
ejpam-5633	164	2	theorem	theorem	NOUN
ejpam-5633	164	3	1	1	NUM
ejpam-5633	164	4	,	,	PUNCT
ejpam-5633	164	5	f	f	PROPN
ejpam-5633	164	6	is	be	AUX
ejpam-5633	164	7	upper	upper	ADJ
ejpam-5633	164	8	nearly	nearly	ADV
ejpam-5633	164	9	(	(	PUNCT
ejpam-5633	164	10	τ1	τ1	NOUN
ejpam-5633	164	11	,	,	PUNCT
ejpam-5633	164	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	164	13	at	at	ADP
ejpam-5633	164	14	x.	x.	NOUN
ejpam-5633	164	15	this	this	PRON
ejpam-5633	164	16	shows	show	VERB
ejpam-5633	164	17	that	that	SCONJ
ejpam-5633	164	18	f	f	PROPN
ejpam-5633	164	19	is	be	AUX
ejpam-5633	164	20	upper	upper	ADJ
ejpam-5633	164	21	nearly	nearly	ADV
ejpam-5633	164	22	(	(	PUNCT
ejpam-5633	164	23	τ1	τ1	NOUN
ejpam-5633	164	24	,	,	PUNCT
ejpam-5633	164	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	164	26	.	.	PUNCT
ejpam-5633	165	1	theorem	theorem	NOUN
ejpam-5633	165	2	4	4	NUM
ejpam-5633	165	3	.	.	X
ejpam-5633	165	4	for	for	ADP
ejpam-5633	165	5	a	a	DET
ejpam-5633	165	6	multifunction	multifunction	NOUN
ejpam-5633	166	1	f	f	NOUN
ejpam-5633	166	2	:	:	PUNCT
ejpam-5633	166	3	(	(	PUNCT
ejpam-5633	166	4	x	x	NOUN
ejpam-5633	166	5	,	,	PUNCT
ejpam-5633	166	6	τ1	τ1	NOUN
ejpam-5633	166	7	,	,	PUNCT
ejpam-5633	166	8	τ2	τ2	NOUN
ejpam-5633	166	9	)	)	PUNCT
ejpam-5633	166	10	→	→	SYM
ejpam-5633	166	11	(	(	PUNCT
ejpam-5633	166	12	y	y	PROPN
ejpam-5633	166	13	,	,	PUNCT
ejpam-5633	166	14	σ1	σ1	PROPN
ejpam-5633	166	15	,	,	PUNCT
ejpam-5633	166	16	σ2	σ2	NOUN
ejpam-5633	166	17	)	)	PUNCT
ejpam-5633	166	18	,	,	PUNCT
ejpam-5633	166	19	the	the	DET
ejpam-5633	166	20	following	follow	VERB
ejpam-5633	166	21	properties	property	NOUN
ejpam-5633	166	22	are	be	AUX
ejpam-5633	166	23	equivalent	equivalent	ADJ
ejpam-5633	166	24	:	:	PUNCT
ejpam-5633	166	25	m.	m.	NOUN
ejpam-5633	166	26	thongmoon	thongmoon	NOUN
ejpam-5633	166	27	,	,	PUNCT
ejpam-5633	166	28	a.	a.	PROPN
ejpam-5633	166	29	sama	sama	PROPN
ejpam-5633	166	30	-	-	PUNCT
ejpam-5633	166	31	ae	ae	PROPN
ejpam-5633	166	32	,	,	PUNCT
ejpam-5633	166	33	c.	c.	PROPN
ejpam-5633	166	34	boonpok	boonpok	PROPN
ejpam-5633	166	35	/	/	SYM
ejpam-5633	166	36	eur	eur	PROPN
ejpam-5633	166	37	.	.	PUNCT
ejpam-5633	167	1	j.	j.	PROPN
ejpam-5633	167	2	pure	pure	PROPN
ejpam-5633	167	3	appl	appl	PROPN
ejpam-5633	167	4	.	.	PROPN
ejpam-5633	167	5	math	math	PROPN
ejpam-5633	167	6	,	,	PUNCT
ejpam-5633	167	7	18	18	NUM
ejpam-5633	167	8	(	(	PUNCT
ejpam-5633	167	9	1	1	NUM
ejpam-5633	167	10	)	)	PUNCT
ejpam-5633	167	11	(	(	PUNCT
ejpam-5633	167	12	2025	2025	NUM
ejpam-5633	167	13	)	)	PUNCT
ejpam-5633	167	14	,	,	PUNCT
ejpam-5633	167	15	5633	5633	NUM
ejpam-5633	167	16	7	7	NUM
ejpam-5633	167	17	of	of	ADP
ejpam-5633	167	18	13	13	NUM
ejpam-5633	167	19	(	(	PUNCT
ejpam-5633	167	20	1	1	NUM
ejpam-5633	167	21	)	)	PUNCT
ejpam-5633	167	22	f	f	PROPN
ejpam-5633	167	23	is	be	AUX
ejpam-5633	167	24	lower	low	ADJ
ejpam-5633	167	25	nearly	nearly	ADV
ejpam-5633	167	26	(	(	PUNCT
ejpam-5633	167	27	τ1	τ1	NOUN
ejpam-5633	167	28	,	,	PUNCT
ejpam-5633	167	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	167	30	;	;	PUNCT
ejpam-5633	167	31	(	(	PUNCT
ejpam-5633	167	32	2	2	X
ejpam-5633	167	33	)	)	PUNCT
ejpam-5633	167	34	f−(v	f−(v	NOUN
ejpam-5633	167	35	)	)	PUNCT
ejpam-5633	167	36	is	be	AUX
ejpam-5633	167	37	τ1τ2	τ1τ2	NOUN
ejpam-5633	167	38	-	-	ADJ
ejpam-5633	167	39	open	open	ADJ
ejpam-5633	167	40	in	in	ADP
ejpam-5633	167	41	x	x	PUNCT
ejpam-5633	167	42	for	for	ADP
ejpam-5633	167	43	each	each	DET
ejpam-5633	167	44	σ1σ2	σ1σ2	VERB
ejpam-5633	167	45	-	-	ADJ
ejpam-5633	167	46	open	open	ADJ
ejpam-5633	167	47	set	set	NOUN
ejpam-5633	167	48	v	v	NOUN
ejpam-5633	167	49	of	of	ADP
ejpam-5633	167	50	y	y	PROPN
ejpam-5633	167	51	having	have	VERB
ejpam-5633	167	52	n	n	PROPN
ejpam-5633	167	53	(	(	PUNCT
ejpam-5633	167	54	σ1	σ1	PROPN
ejpam-5633	167	55	,	,	PUNCT
ejpam-5633	167	56	σ2)-closed	σ2)-close	VERB
ejpam-5633	167	57	complement	complement	NOUN
ejpam-5633	167	58	;	;	PUNCT
ejpam-5633	167	59	(	(	PUNCT
ejpam-5633	167	60	3	3	X
ejpam-5633	167	61	)	)	PUNCT
ejpam-5633	167	62	f+(k	f+(k	NOUN
ejpam-5633	167	63	)	)	PUNCT
ejpam-5633	167	64	is	be	AUX
ejpam-5633	167	65	τ1τ2	τ1τ2	NOUN
ejpam-5633	167	66	-	-	ADJ
ejpam-5633	167	67	open	open	ADJ
ejpam-5633	167	68	in	in	ADP
ejpam-5633	167	69	x	x	PUNCT
ejpam-5633	167	70	for	for	ADP
ejpam-5633	167	71	every	every	DET
ejpam-5633	167	72	n	n	PROPN
ejpam-5633	167	73	(	(	PUNCT
ejpam-5633	167	74	σ1	σ1	PROPN
ejpam-5633	167	75	,	,	PUNCT
ejpam-5633	167	76	σ2)-closed	σ2)-close	VERB
ejpam-5633	167	77	and	and	CCONJ
ejpam-5633	167	78	σ1σ2	σ1σ2	NOUN
ejpam-5633	167	79	-	-	PUNCT
ejpam-5633	167	80	closed	closed	ADJ
ejpam-5633	167	81	set	set	NOUN
ejpam-5633	167	82	k	k	PROPN
ejpam-5633	167	83	of	of	ADP
ejpam-5633	167	84	y	y	PROPN
ejpam-5633	167	85	;	;	PUNCT
ejpam-5633	167	86	(	(	PUNCT
ejpam-5633	167	87	4	4	X
ejpam-5633	167	88	)	)	PUNCT
ejpam-5633	167	89	τ1τ2	τ1τ2	NOUN
ejpam-5633	167	90	-	-	NOUN
ejpam-5633	167	91	cl(f	cl(f	NOUN
ejpam-5633	167	92	+	+	NOUN
ejpam-5633	167	93	(	(	PUNCT
ejpam-5633	167	94	b	b	NOUN
ejpam-5633	167	95	)	)	PUNCT
ejpam-5633	167	96	)	)	PUNCT
ejpam-5633	167	97	⊆	⊆	NUM
ejpam-5633	167	98	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5633	167	99	-	-	PUNCT
ejpam-5633	167	100	cl(b	cl(b	NOUN
ejpam-5633	167	101	)	)	PUNCT
ejpam-5633	167	102	)	)	PUNCT
ejpam-5633	167	103	for	for	ADP
ejpam-5633	167	104	every	every	DET
ejpam-5633	167	105	subset	subset	NOUN
ejpam-5633	167	106	b	b	PROPN
ejpam-5633	167	107	of	of	ADP
ejpam-5633	167	108	y	y	PROPN
ejpam-5633	167	109	having	have	VERB
ejpam-5633	167	110	the	the	DET
ejpam-5633	167	111	n	n	PROPN
ejpam-5633	167	112	(	(	PUNCT
ejpam-5633	167	113	σ1	σ1	PROPN
ejpam-5633	167	114	,	,	PUNCT
ejpam-5633	167	115	σ2)closed	σ2)close	VERB
ejpam-5633	167	116	σ1σ2	σ1σ2	NOUN
ejpam-5633	167	117	-	-	NOUN
ejpam-5633	167	118	closure	closure	NOUN
ejpam-5633	167	119	;	;	PUNCT
ejpam-5633	167	120	(	(	PUNCT
ejpam-5633	167	121	5	5	X
ejpam-5633	167	122	)	)	PUNCT
ejpam-5633	167	123	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5633	167	124	-	-	PUNCT
ejpam-5633	167	125	cl(b	cl(b	NOUN
ejpam-5633	167	126	)	)	PUNCT
ejpam-5633	167	127	)	)	PUNCT
ejpam-5633	168	1	⊆	⊆	X
ejpam-5633	168	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	168	3	-	-	NUM
ejpam-5633	168	4	int(f	int(f	VERB
ejpam-5633	168	5	−(b	−(b	NOUN
ejpam-5633	168	6	)	)	PUNCT
ejpam-5633	168	7	)	)	PUNCT
ejpam-5633	168	8	for	for	ADP
ejpam-5633	168	9	every	every	DET
ejpam-5633	168	10	subset	subset	NOUN
ejpam-5633	168	11	b	b	PROPN
ejpam-5633	168	12	of	of	ADP
ejpam-5633	168	13	y	y	PRON
ejpam-5633	168	14	such	such	ADJ
ejpam-5633	168	15	that	that	SCONJ
ejpam-5633	168	16	y−σ1σ2	y−σ1σ2	PROPN
ejpam-5633	168	17	-	-	PUNCT
ejpam-5633	168	18	int(b	int(b	NOUN
ejpam-5633	168	19	)	)	PUNCT
ejpam-5633	168	20	is	be	AUX
ejpam-5633	168	21	n	n	PROPN
ejpam-5633	168	22	(	(	PUNCT
ejpam-5633	168	23	σ1	σ1	PROPN
ejpam-5633	168	24	,	,	PUNCT
ejpam-5633	168	25	σ2)-closed	σ2)-close	VERB
ejpam-5633	168	26	.	.	PUNCT
ejpam-5633	169	1	proof	proof	NOUN
ejpam-5633	169	2	.	.	PUNCT
ejpam-5633	170	1	the	the	DET
ejpam-5633	170	2	proof	proof	NOUN
ejpam-5633	170	3	is	be	AUX
ejpam-5633	170	4	similar	similar	ADJ
ejpam-5633	170	5	to	to	ADP
ejpam-5633	170	6	that	that	PRON
ejpam-5633	170	7	of	of	ADP
ejpam-5633	170	8	theorem	theorem	ADJ
ejpam-5633	170	9	3	3	NUM
ejpam-5633	170	10	.	.	PUNCT
ejpam-5633	170	11	corollary	corollary	ADJ
ejpam-5633	170	12	1	1	NUM
ejpam-5633	170	13	.	.	PUNCT
ejpam-5633	171	1	a	a	DET
ejpam-5633	171	2	multifunction	multifunction	NOUN
ejpam-5633	171	3	f	f	NOUN
ejpam-5633	171	4	:	:	PUNCT
ejpam-5633	171	5	(	(	PUNCT
ejpam-5633	171	6	x	x	NOUN
ejpam-5633	171	7	,	,	PUNCT
ejpam-5633	171	8	τ1	τ1	NOUN
ejpam-5633	171	9	,	,	PUNCT
ejpam-5633	171	10	τ2	τ2	NOUN
ejpam-5633	171	11	)	)	PUNCT
ejpam-5633	171	12	→	→	SYM
ejpam-5633	171	13	(	(	PUNCT
ejpam-5633	171	14	y	y	PROPN
ejpam-5633	171	15	,	,	PUNCT
ejpam-5633	171	16	σ1	σ1	PROPN
ejpam-5633	171	17	,	,	PUNCT
ejpam-5633	171	18	σ2	σ2	PROPN
ejpam-5633	171	19	)	)	PUNCT
ejpam-5633	171	20	is	be	AUX
ejpam-5633	171	21	upper	upper	ADJ
ejpam-5633	171	22	nearly	nearly	ADV
ejpam-5633	171	23	(	(	PUNCT
ejpam-5633	171	24	τ1	τ1	NOUN
ejpam-5633	171	25	,	,	PUNCT
ejpam-5633	171	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	171	27	if	if	SCONJ
ejpam-5633	171	28	f−(k	f−(k	PROPN
ejpam-5633	171	29	)	)	PUNCT
ejpam-5633	171	30	is	be	AUX
ejpam-5633	171	31	τ1τ2	τ1τ2	NOUN
ejpam-5633	171	32	-	-	ADJ
ejpam-5633	171	33	closed	closed	ADJ
ejpam-5633	171	34	in	in	ADP
ejpam-5633	171	35	x	x	PUNCT
ejpam-5633	171	36	for	for	ADP
ejpam-5633	171	37	every	every	DET
ejpam-5633	171	38	n	n	PROPN
ejpam-5633	171	39	(	(	PUNCT
ejpam-5633	171	40	σ1	σ1	PROPN
ejpam-5633	171	41	,	,	PUNCT
ejpam-5633	171	42	σ2)-closed	σ2)-close	VERB
ejpam-5633	171	43	set	set	VERB
ejpam-5633	171	44	k	k	PROPN
ejpam-5633	171	45	of	of	ADP
ejpam-5633	171	46	y	y	PROPN
ejpam-5633	171	47	.	.	PUNCT
ejpam-5633	172	1	proof	proof	NOUN
ejpam-5633	172	2	.	.	PUNCT
ejpam-5633	173	1	let	let	VERB
ejpam-5633	173	2	v	v	PART
ejpam-5633	173	3	be	be	AUX
ejpam-5633	173	4	any	any	DET
ejpam-5633	173	5	σ1σ2	σ1σ2	NOUN
ejpam-5633	173	6	-	-	ADJ
ejpam-5633	173	7	open	open	ADJ
ejpam-5633	173	8	set	set	NOUN
ejpam-5633	173	9	of	of	ADP
ejpam-5633	173	10	y	y	PROPN
ejpam-5633	173	11	having	have	VERB
ejpam-5633	173	12	n	n	PROPN
ejpam-5633	173	13	(	(	PUNCT
ejpam-5633	173	14	σ1	σ1	PROPN
ejpam-5633	173	15	,	,	PUNCT
ejpam-5633	173	16	σ2)-closed	σ2)-close	VERB
ejpam-5633	173	17	complement	complement	NOUN
ejpam-5633	173	18	.	.	PUNCT
ejpam-5633	174	1	then	then	ADV
ejpam-5633	174	2	,	,	PUNCT
ejpam-5633	174	3	y	y	PROPN
ejpam-5633	174	4	−v	−v	NOUN
ejpam-5633	174	5	is	be	AUX
ejpam-5633	174	6	n	n	PROPN
ejpam-5633	174	7	(	(	PUNCT
ejpam-5633	174	8	σ1	σ1	PROPN
ejpam-5633	174	9	,	,	PUNCT
ejpam-5633	174	10	σ2)-closed	σ2)-close	VERB
ejpam-5633	174	11	.	.	PUNCT
ejpam-5633	175	1	by	by	ADP
ejpam-5633	175	2	the	the	DET
ejpam-5633	175	3	hypothesis	hypothesis	NOUN
ejpam-5633	175	4	,	,	PUNCT
ejpam-5633	175	5	f−(y	f−(y	NOUN
ejpam-5633	175	6	−v	−v	NOUN
ejpam-5633	175	7	)	)	PUNCT
ejpam-5633	176	1	=	=	PUNCT
ejpam-5633	176	2	x	x	PUNCT
ejpam-5633	176	3	−f+(v	−f+(v	NOUN
ejpam-5633	176	4	)	)	PUNCT
ejpam-5633	176	5	is	be	AUX
ejpam-5633	176	6	τ1τ2	τ1τ2	NOUN
ejpam-5633	176	7	-	-	ADJ
ejpam-5633	176	8	closed	closed	ADJ
ejpam-5633	176	9	in	in	ADP
ejpam-5633	176	10	x	x	X
ejpam-5633	176	11	and	and	CCONJ
ejpam-5633	176	12	hence	hence	ADV
ejpam-5633	176	13	f+(v	f+(v	PROPN
ejpam-5633	176	14	)	)	PUNCT
ejpam-5633	177	1	is	be	AUX
ejpam-5633	177	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	177	3	-	-	ADJ
ejpam-5633	177	4	open	open	ADJ
ejpam-5633	177	5	in	in	ADP
ejpam-5633	177	6	x.	x.	NOUN
ejpam-5633	177	7	it	it	PRON
ejpam-5633	177	8	follows	follow	VERB
ejpam-5633	177	9	from	from	ADP
ejpam-5633	177	10	theorem	theorem	ADJ
ejpam-5633	177	11	3	3	NUM
ejpam-5633	177	12	that	that	SCONJ
ejpam-5633	177	13	f	f	PROPN
ejpam-5633	177	14	is	be	AUX
ejpam-5633	177	15	upper	upper	ADJ
ejpam-5633	177	16	nearly	nearly	ADV
ejpam-5633	177	17	(	(	PUNCT
ejpam-5633	177	18	τ1	τ1	NOUN
ejpam-5633	177	19	,	,	PUNCT
ejpam-5633	177	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	177	21	.	.	PUNCT
ejpam-5633	178	1	corollary	corollary	ADJ
ejpam-5633	178	2	2	2	NUM
ejpam-5633	178	3	.	.	PUNCT
ejpam-5633	178	4	a	a	DET
ejpam-5633	178	5	multifunction	multifunction	NOUN
ejpam-5633	179	1	f	f	NOUN
ejpam-5633	179	2	:	:	PUNCT
ejpam-5633	179	3	(	(	PUNCT
ejpam-5633	179	4	x	x	NOUN
ejpam-5633	179	5	,	,	PUNCT
ejpam-5633	179	6	τ1	τ1	NOUN
ejpam-5633	179	7	,	,	PUNCT
ejpam-5633	179	8	τ2	τ2	NOUN
ejpam-5633	179	9	)	)	PUNCT
ejpam-5633	179	10	→	→	SYM
ejpam-5633	179	11	(	(	PUNCT
ejpam-5633	179	12	y	y	PROPN
ejpam-5633	179	13	,	,	PUNCT
ejpam-5633	179	14	σ1	σ1	PROPN
ejpam-5633	179	15	,	,	PUNCT
ejpam-5633	179	16	σ2	σ2	NOUN
ejpam-5633	179	17	)	)	PUNCT
ejpam-5633	179	18	is	be	AUX
ejpam-5633	179	19	lower	low	ADJ
ejpam-5633	179	20	nearly	nearly	ADV
ejpam-5633	179	21	(	(	PUNCT
ejpam-5633	179	22	τ1	τ1	NOUN
ejpam-5633	179	23	,	,	PUNCT
ejpam-5633	179	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	179	25	if	if	SCONJ
ejpam-5633	179	26	f+(k	f+(k	NUM
ejpam-5633	179	27	)	)	PUNCT
ejpam-5633	179	28	is	be	AUX
ejpam-5633	179	29	τ1τ2	τ1τ2	NOUN
ejpam-5633	179	30	-	-	ADJ
ejpam-5633	179	31	closed	closed	ADJ
ejpam-5633	179	32	in	in	ADP
ejpam-5633	179	33	x	x	PUNCT
ejpam-5633	179	34	for	for	SCONJ
ejpam-5633	179	35	every	every	DET
ejpam-5633	179	36	n	n	PROPN
ejpam-5633	179	37	(	(	PUNCT
ejpam-5633	179	38	σ1	σ1	PROPN
ejpam-5633	179	39	,	,	PUNCT
ejpam-5633	179	40	σ2)-closed	σ2)-close	VERB
ejpam-5633	179	41	set	set	VERB
ejpam-5633	179	42	k	k	PROPN
ejpam-5633	179	43	of	of	ADP
ejpam-5633	179	44	y	y	PROPN
ejpam-5633	179	45	.	.	PUNCT
ejpam-5633	180	1	proof	proof	NOUN
ejpam-5633	180	2	.	.	PUNCT
ejpam-5633	181	1	the	the	DET
ejpam-5633	181	2	proof	proof	NOUN
ejpam-5633	181	3	is	be	AUX
ejpam-5633	181	4	similar	similar	ADJ
ejpam-5633	181	5	to	to	ADP
ejpam-5633	181	6	that	that	PRON
ejpam-5633	181	7	of	of	ADP
ejpam-5633	181	8	corollary	corollary	ADJ
ejpam-5633	181	9	1	1	NUM
ejpam-5633	181	10	.	.	PUNCT
ejpam-5633	181	11	recall	recall	VERB
ejpam-5633	181	12	that	that	SCONJ
ejpam-5633	181	13	a	a	DET
ejpam-5633	181	14	bitopological	bitopological	ADJ
ejpam-5633	181	15	space	space	NOUN
ejpam-5633	181	16	(	(	PUNCT
ejpam-5633	181	17	x	x	NOUN
ejpam-5633	181	18	,	,	PUNCT
ejpam-5633	181	19	τ1	τ1	NOUN
ejpam-5633	181	20	,	,	PUNCT
ejpam-5633	181	21	τ2	τ2	NOUN
ejpam-5633	181	22	)	)	PUNCT
ejpam-5633	181	23	is	be	AUX
ejpam-5633	181	24	said	say	VERB
ejpam-5633	181	25	to	to	PART
ejpam-5633	181	26	be	be	AUX
ejpam-5633	181	27	(	(	PUNCT
ejpam-5633	181	28	τ1	τ1	NOUN
ejpam-5633	181	29	,	,	PUNCT
ejpam-5633	181	30	τ2)-regular	τ2)-regular	ADJ
ejpam-5633	181	31	[	[	X
ejpam-5633	181	32	32	32	NUM
ejpam-5633	181	33	]	]	PUNCT
ejpam-5633	181	34	if	if	SCONJ
ejpam-5633	181	35	for	for	ADP
ejpam-5633	181	36	each	each	DET
ejpam-5633	181	37	τ1τ2	τ1τ2	ADJ
ejpam-5633	181	38	-	-	ADJ
ejpam-5633	181	39	closed	closed	ADJ
ejpam-5633	181	40	set	set	VERB
ejpam-5633	181	41	f	f	NOUN
ejpam-5633	181	42	and	and	CCONJ
ejpam-5633	181	43	each	each	DET
ejpam-5633	181	44	point	point	NOUN
ejpam-5633	181	45	x	x	X
ejpam-5633	181	46	∈	∈	NOUN
ejpam-5633	181	47	x	x	X
ejpam-5633	181	48	−	−	PROPN
ejpam-5633	181	49	f	f	NOUN
ejpam-5633	181	50	,	,	PUNCT
ejpam-5633	181	51	there	there	PRON
ejpam-5633	181	52	exist	exist	VERB
ejpam-5633	181	53	disjoint	disjoint	ADJ
ejpam-5633	181	54	τ1τ2	τ1τ2	ADJ
ejpam-5633	181	55	-	-	ADJ
ejpam-5633	181	56	open	open	ADJ
ejpam-5633	181	57	sets	set	NOUN
ejpam-5633	181	58	u	u	NOUN
ejpam-5633	181	59	and	and	CCONJ
ejpam-5633	181	60	v	v	ADP
ejpam-5633	181	61	such	such	ADJ
ejpam-5633	181	62	that	that	SCONJ
ejpam-5633	181	63	x	x	SYM
ejpam-5633	181	64	∈	∈	PROPN
ejpam-5633	181	65	u	u	NOUN
ejpam-5633	181	66	and	and	CCONJ
ejpam-5633	181	67	f	f	PROPN
ejpam-5633	181	68	⊆	⊆	NUM
ejpam-5633	181	69	v	v	NOUN
ejpam-5633	181	70	.	.	PUNCT
ejpam-5633	182	1	theorem	theorem	NOUN
ejpam-5633	182	2	5	5	NUM
ejpam-5633	182	3	.	.	PUNCT
ejpam-5633	183	1	let	let	AUX
ejpam-5633	183	2	(	(	PUNCT
ejpam-5633	183	3	y	y	PROPN
ejpam-5633	183	4	,	,	PUNCT
ejpam-5633	183	5	σ1	σ1	PROPN
ejpam-5633	183	6	,	,	PUNCT
ejpam-5633	183	7	σ2	σ2	PROPN
ejpam-5633	183	8	)	)	PUNCT
ejpam-5633	183	9	be	be	VERB
ejpam-5633	183	10	a	a	DET
ejpam-5633	183	11	(	(	PUNCT
ejpam-5633	183	12	σ1	σ1	NOUN
ejpam-5633	183	13	,	,	PUNCT
ejpam-5633	183	14	σ2)-regular	σ2)-regular	ADJ
ejpam-5633	183	15	space	space	NOUN
ejpam-5633	183	16	.	.	PUNCT
ejpam-5633	184	1	for	for	ADP
ejpam-5633	184	2	a	a	DET
ejpam-5633	184	3	multifunction	multifunction	NOUN
ejpam-5633	184	4	f	f	NOUN
ejpam-5633	184	5	:	:	PUNCT
ejpam-5633	184	6	(	(	PUNCT
ejpam-5633	184	7	x	x	NOUN
ejpam-5633	184	8	,	,	PUNCT
ejpam-5633	184	9	τ1	τ1	NOUN
ejpam-5633	184	10	,	,	PUNCT
ejpam-5633	184	11	τ2	τ2	NOUN
ejpam-5633	184	12	)	)	PUNCT
ejpam-5633	184	13	→	→	SYM
ejpam-5633	184	14	(	(	PUNCT
ejpam-5633	184	15	y	y	PROPN
ejpam-5633	184	16	,	,	PUNCT
ejpam-5633	184	17	σ1	σ1	PROPN
ejpam-5633	184	18	,	,	PUNCT
ejpam-5633	184	19	σ2	σ2	NOUN
ejpam-5633	184	20	)	)	PUNCT
ejpam-5633	184	21	,	,	PUNCT
ejpam-5633	184	22	the	the	DET
ejpam-5633	184	23	following	follow	VERB
ejpam-5633	184	24	properties	property	NOUN
ejpam-5633	184	25	are	be	AUX
ejpam-5633	184	26	equivalent	equivalent	ADJ
ejpam-5633	184	27	:	:	PUNCT
ejpam-5633	184	28	(	(	PUNCT
ejpam-5633	184	29	1	1	X
ejpam-5633	184	30	)	)	PUNCT
ejpam-5633	184	31	f	f	PROPN
ejpam-5633	184	32	is	be	AUX
ejpam-5633	184	33	upper	upper	ADJ
ejpam-5633	184	34	nearly	nearly	ADV
ejpam-5633	184	35	(	(	PUNCT
ejpam-5633	184	36	τ1	τ1	NOUN
ejpam-5633	184	37	,	,	PUNCT
ejpam-5633	184	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	184	39	;	;	PUNCT
ejpam-5633	184	40	(	(	PUNCT
ejpam-5633	184	41	2	2	X
ejpam-5633	184	42	)	)	PUNCT
ejpam-5633	184	43	f−((σ1	f−((σ1	NOUN
ejpam-5633	184	44	,	,	PUNCT
ejpam-5633	184	45	σ2)θ	σ2)θ	ADJ
ejpam-5633	184	46	-	-	PUNCT
ejpam-5633	184	47	cl(b	cl(b	NOUN
ejpam-5633	184	48	)	)	PUNCT
ejpam-5633	184	49	)	)	PUNCT
ejpam-5633	184	50	is	be	AUX
ejpam-5633	184	51	τ1τ2	τ1τ2	NOUN
ejpam-5633	184	52	-	-	ADJ
ejpam-5633	184	53	closed	closed	ADJ
ejpam-5633	184	54	in	in	ADP
ejpam-5633	184	55	x	x	PUNCT
ejpam-5633	184	56	for	for	ADP
ejpam-5633	184	57	every	every	DET
ejpam-5633	184	58	subset	subset	NOUN
ejpam-5633	184	59	b	b	PROPN
ejpam-5633	184	60	of	of	ADP
ejpam-5633	184	61	y	y	PRON
ejpam-5633	184	62	such	such	ADJ
ejpam-5633	184	63	that	that	PRON
ejpam-5633	184	64	(	(	PUNCT
ejpam-5633	184	65	σ1	σ1	PROPN
ejpam-5633	184	66	,	,	PUNCT
ejpam-5633	184	67	σ2)θ	σ2)θ	NOUN
ejpam-5633	184	68	-	-	PUNCT
ejpam-5633	184	69	cl(b	cl(b	NOUN
ejpam-5633	184	70	)	)	PUNCT
ejpam-5633	184	71	is	be	AUX
ejpam-5633	184	72	n	n	PROPN
ejpam-5633	184	73	(	(	PUNCT
ejpam-5633	184	74	σ1	σ1	PROPN
ejpam-5633	184	75	,	,	PUNCT
ejpam-5633	184	76	σ2)-closed	σ2)-close	VERB
ejpam-5633	184	77	;	;	PUNCT
ejpam-5633	184	78	(	(	PUNCT
ejpam-5633	184	79	3	3	X
ejpam-5633	184	80	)	)	PUNCT
ejpam-5633	184	81	f−(k	f−(k	PROPN
ejpam-5633	184	82	)	)	PUNCT
ejpam-5633	184	83	is	be	AUX
ejpam-5633	184	84	τ1τ2	τ1τ2	NOUN
ejpam-5633	184	85	-	-	ADJ
ejpam-5633	184	86	closed	closed	ADJ
ejpam-5633	184	87	in	in	ADP
ejpam-5633	184	88	x	x	PUNCT
ejpam-5633	184	89	for	for	ADP
ejpam-5633	184	90	every	every	DET
ejpam-5633	184	91	n	n	PROPN
ejpam-5633	184	92	(	(	PUNCT
ejpam-5633	184	93	σ1	σ1	PROPN
ejpam-5633	184	94	,	,	PUNCT
ejpam-5633	184	95	σ2)-closed	σ2)-close	VERB
ejpam-5633	184	96	and	and	CCONJ
ejpam-5633	184	97	(	(	PUNCT
ejpam-5633	184	98	σ1	σ1	PROPN
ejpam-5633	184	99	,	,	PUNCT
ejpam-5633	184	100	σ2)θ	σ2)θ	NOUN
ejpam-5633	184	101	-	-	PUNCT
ejpam-5633	184	102	closed	close	VERB
ejpam-5633	184	103	set	set	NOUN
ejpam-5633	184	104	k	k	PROPN
ejpam-5633	184	105	of	of	ADP
ejpam-5633	184	106	y	y	PROPN
ejpam-5633	184	107	;	;	PUNCT
ejpam-5633	184	108	m.	m.	NOUN
ejpam-5633	184	109	thongmoon	thongmoon	NOUN
ejpam-5633	184	110	,	,	PUNCT
ejpam-5633	184	111	a.	a.	PROPN
ejpam-5633	184	112	sama	sama	PROPN
ejpam-5633	184	113	-	-	PUNCT
ejpam-5633	184	114	ae	ae	PROPN
ejpam-5633	184	115	,	,	PUNCT
ejpam-5633	184	116	c.	c.	PROPN
ejpam-5633	184	117	boonpok	boonpok	PROPN
ejpam-5633	184	118	/	/	SYM
ejpam-5633	184	119	eur	eur	PROPN
ejpam-5633	184	120	.	.	PUNCT
ejpam-5633	185	1	j.	j.	PROPN
ejpam-5633	185	2	pure	pure	PROPN
ejpam-5633	185	3	appl	appl	PROPN
ejpam-5633	185	4	.	.	PROPN
ejpam-5633	185	5	math	math	PROPN
ejpam-5633	185	6	,	,	PUNCT
ejpam-5633	185	7	18	18	NUM
ejpam-5633	185	8	(	(	PUNCT
ejpam-5633	185	9	1	1	NUM
ejpam-5633	185	10	)	)	PUNCT
ejpam-5633	185	11	(	(	PUNCT
ejpam-5633	185	12	2025	2025	NUM
ejpam-5633	185	13	)	)	PUNCT
ejpam-5633	185	14	,	,	PUNCT
ejpam-5633	185	15	5633	5633	NUM
ejpam-5633	185	16	8	8	NUM
ejpam-5633	185	17	of	of	ADP
ejpam-5633	185	18	13	13	NUM
ejpam-5633	185	19	(	(	PUNCT
ejpam-5633	185	20	4	4	NUM
ejpam-5633	185	21	)	)	PUNCT
ejpam-5633	185	22	f+(v	f+(v	NOUN
ejpam-5633	185	23	)	)	PUNCT
ejpam-5633	185	24	is	be	AUX
ejpam-5633	185	25	τ1τ2	τ1τ2	NOUN
ejpam-5633	185	26	-	-	ADJ
ejpam-5633	185	27	open	open	ADJ
ejpam-5633	185	28	in	in	ADP
ejpam-5633	185	29	x	x	PUNCT
ejpam-5633	185	30	for	for	SCONJ
ejpam-5633	185	31	each	each	DET
ejpam-5633	185	32	(	(	PUNCT
ejpam-5633	185	33	σ1	σ1	PROPN
ejpam-5633	185	34	,	,	PUNCT
ejpam-5633	185	35	σ2)θ	σ2)θ	NOUN
ejpam-5633	185	36	-	-	PUNCT
ejpam-5633	185	37	open	open	ADJ
ejpam-5633	185	38	set	set	NOUN
ejpam-5633	185	39	v	v	NOUN
ejpam-5633	185	40	of	of	ADP
ejpam-5633	185	41	y	y	PROPN
ejpam-5633	185	42	having	have	VERB
ejpam-5633	185	43	n	n	PROPN
ejpam-5633	185	44	(	(	PUNCT
ejpam-5633	185	45	σ1	σ1	PROPN
ejpam-5633	185	46	,	,	PUNCT
ejpam-5633	185	47	σ2)-closed	σ2)-close	VERB
ejpam-5633	185	48	complement	complement	NOUN
ejpam-5633	185	49	.	.	PUNCT
ejpam-5633	186	1	proof	proof	NOUN
ejpam-5633	186	2	.	.	PUNCT
ejpam-5633	187	1	(	(	PUNCT
ejpam-5633	187	2	1	1	X
ejpam-5633	187	3	)	)	PUNCT
ejpam-5633	187	4	⇒	⇒	NOUN
ejpam-5633	187	5	(	(	PUNCT
ejpam-5633	187	6	2	2	NUM
ejpam-5633	187	7	):	):	PUNCT
ejpam-5633	187	8	let	let	VERB
ejpam-5633	187	9	b	b	X
ejpam-5633	187	10	be	be	AUX
ejpam-5633	187	11	any	any	DET
ejpam-5633	187	12	subset	subset	NOUN
ejpam-5633	187	13	of	of	ADP
ejpam-5633	187	14	y	y	PRON
ejpam-5633	187	15	such	such	ADJ
ejpam-5633	187	16	that	that	PRON
ejpam-5633	187	17	(	(	PUNCT
ejpam-5633	187	18	σ1	σ1	PROPN
ejpam-5633	187	19	,	,	PUNCT
ejpam-5633	187	20	σ2)θ	σ2)θ	NOUN
ejpam-5633	187	21	-	-	PUNCT
ejpam-5633	187	22	cl(b	cl(b	NOUN
ejpam-5633	187	23	)	)	PUNCT
ejpam-5633	187	24	is	be	AUX
ejpam-5633	187	25	n	n	PROPN
ejpam-5633	187	26	(	(	PUNCT
ejpam-5633	187	27	σ1	σ1	PROPN
ejpam-5633	187	28	,	,	PUNCT
ejpam-5633	187	29	σ2)closed	σ2)close	VERB
ejpam-5633	187	30	.	.	PUNCT
ejpam-5633	188	1	then	then	ADV
ejpam-5633	188	2	,	,	PUNCT
ejpam-5633	188	3	(	(	PUNCT
ejpam-5633	188	4	σ1	σ1	PROPN
ejpam-5633	188	5	,	,	PUNCT
ejpam-5633	188	6	σ2)θ	σ2)θ	NOUN
ejpam-5633	188	7	-	-	PUNCT
ejpam-5633	188	8	cl(b	cl(b	NOUN
ejpam-5633	188	9	)	)	PUNCT
ejpam-5633	188	10	is	be	AUX
ejpam-5633	188	11	n	n	PROPN
ejpam-5633	188	12	(	(	PUNCT
ejpam-5633	188	13	σ1	σ1	PROPN
ejpam-5633	188	14	,	,	PUNCT
ejpam-5633	188	15	σ2)-closed	σ2)-close	VERB
ejpam-5633	188	16	and	and	CCONJ
ejpam-5633	188	17	σ1σ2	σ1σ2	NOUN
ejpam-5633	188	18	-	-	PUNCT
ejpam-5633	188	19	closed	closed	ADJ
ejpam-5633	188	20	.	.	PUNCT
ejpam-5633	189	1	thus	thus	ADV
ejpam-5633	189	2	by	by	ADP
ejpam-5633	189	3	theorem	theorem	ADJ
ejpam-5633	189	4	3	3	NUM
ejpam-5633	189	5	,	,	PUNCT
ejpam-5633	189	6	f−((σ1	f−((σ1	NOUN
ejpam-5633	189	7	,	,	PUNCT
ejpam-5633	189	8	σ2)θ	σ2)θ	ADJ
ejpam-5633	189	9	-	-	PUNCT
ejpam-5633	189	10	cl(b	cl(b	NOUN
ejpam-5633	189	11	)	)	PUNCT
ejpam-5633	189	12	)	)	PUNCT
ejpam-5633	189	13	is	be	AUX
ejpam-5633	189	14	τ1τ2	τ1τ2	NOUN
ejpam-5633	189	15	-	-	ADJ
ejpam-5633	189	16	closed	closed	ADJ
ejpam-5633	189	17	in	in	ADP
ejpam-5633	189	18	x	x	X
ejpam-5633	189	19	.	.	PUNCT
ejpam-5633	190	1	(	(	PUNCT
ejpam-5633	190	2	2	2	X
ejpam-5633	190	3	)	)	PUNCT
ejpam-5633	190	4	⇒	⇒	NOUN
ejpam-5633	190	5	(	(	PUNCT
ejpam-5633	190	6	3	3	NUM
ejpam-5633	190	7	):	):	PUNCT
ejpam-5633	190	8	let	let	VERB
ejpam-5633	190	9	k	k	PRON
ejpam-5633	190	10	be	be	AUX
ejpam-5633	190	11	any	any	DET
ejpam-5633	190	12	n	n	PROPN
ejpam-5633	190	13	(	(	PUNCT
ejpam-5633	190	14	σ1	σ1	PROPN
ejpam-5633	190	15	,	,	PUNCT
ejpam-5633	190	16	σ2)-closed	σ2)-close	VERB
ejpam-5633	190	17	and	and	CCONJ
ejpam-5633	190	18	(	(	PUNCT
ejpam-5633	190	19	σ1	σ1	PROPN
ejpam-5633	190	20	,	,	PUNCT
ejpam-5633	190	21	σ2)θ	σ2)θ	NOUN
ejpam-5633	190	22	-	-	PUNCT
ejpam-5633	190	23	closed	close	VERB
ejpam-5633	190	24	set	set	NOUN
ejpam-5633	190	25	of	of	ADP
ejpam-5633	190	26	y	y	PROPN
ejpam-5633	190	27	.	.	PUNCT
ejpam-5633	191	1	then	then	ADV
ejpam-5633	191	2	,	,	PUNCT
ejpam-5633	191	3	we	we	PRON
ejpam-5633	191	4	have	have	VERB
ejpam-5633	191	5	k	k	NOUN
ejpam-5633	191	6	=	=	SYM
ejpam-5633	191	7	(	(	PUNCT
ejpam-5633	191	8	σ1	σ1	PROPN
ejpam-5633	191	9	,	,	PUNCT
ejpam-5633	191	10	σ2)θ	σ2)θ	NOUN
ejpam-5633	191	11	-	-	PUNCT
ejpam-5633	191	12	cl(k	cl(k	NUM
ejpam-5633	191	13	)	)	PUNCT
ejpam-5633	191	14	is	be	AUX
ejpam-5633	191	15	n	n	PROPN
ejpam-5633	191	16	(	(	PUNCT
ejpam-5633	191	17	σ1	σ1	PROPN
ejpam-5633	191	18	,	,	PUNCT
ejpam-5633	191	19	σ2)-closed	σ2)-close	VERB
ejpam-5633	191	20	and	and	CCONJ
ejpam-5633	191	21	by	by	ADP
ejpam-5633	191	22	(	(	PUNCT
ejpam-5633	191	23	2	2	NUM
ejpam-5633	191	24	)	)	PUNCT
ejpam-5633	191	25	,	,	PUNCT
ejpam-5633	191	26	f−(k	f−(k	PROPN
ejpam-5633	191	27	)	)	PUNCT
ejpam-5633	191	28	is	be	AUX
ejpam-5633	191	29	τ1τ2	τ1τ2	NOUN
ejpam-5633	191	30	-	-	ADJ
ejpam-5633	191	31	closed	closed	ADJ
ejpam-5633	191	32	in	in	ADP
ejpam-5633	191	33	x.	x.	NOUN
ejpam-5633	191	34	(	(	PUNCT
ejpam-5633	191	35	3	3	NUM
ejpam-5633	191	36	)	)	PUNCT
ejpam-5633	191	37	⇒	⇒	NOUN
ejpam-5633	191	38	(	(	PUNCT
ejpam-5633	191	39	4	4	NUM
ejpam-5633	191	40	):	):	PUNCT
ejpam-5633	191	41	let	let	VERB
ejpam-5633	191	42	v	v	PART
ejpam-5633	191	43	be	be	AUX
ejpam-5633	191	44	any	any	DET
ejpam-5633	191	45	(	(	PUNCT
ejpam-5633	191	46	σ1	σ1	PROPN
ejpam-5633	191	47	,	,	PUNCT
ejpam-5633	191	48	σ2)θ	σ2)θ	NOUN
ejpam-5633	191	49	-	-	PUNCT
ejpam-5633	191	50	open	open	ADJ
ejpam-5633	191	51	set	set	NOUN
ejpam-5633	191	52	of	of	ADP
ejpam-5633	191	53	y	y	PROPN
ejpam-5633	191	54	having	have	VERB
ejpam-5633	191	55	n	n	PROPN
ejpam-5633	191	56	(	(	PUNCT
ejpam-5633	191	57	σ1	σ1	PROPN
ejpam-5633	191	58	,	,	PUNCT
ejpam-5633	191	59	σ2)-closed	σ2)-close	VERB
ejpam-5633	191	60	complement	complement	NOUN
ejpam-5633	191	61	.	.	PUNCT
ejpam-5633	192	1	then	then	ADV
ejpam-5633	192	2	,	,	PUNCT
ejpam-5633	192	3	y	y	PROPN
ejpam-5633	192	4	−	−	PROPN
ejpam-5633	192	5	v	v	NOUN
ejpam-5633	192	6	is	be	AUX
ejpam-5633	192	7	n	n	PRON
ejpam-5633	192	8	(	(	PUNCT
ejpam-5633	192	9	σ1	σ1	PROPN
ejpam-5633	192	10	,	,	PUNCT
ejpam-5633	192	11	σ2)-closed	σ2)-close	VERB
ejpam-5633	192	12	and	and	CCONJ
ejpam-5633	192	13	(	(	PUNCT
ejpam-5633	192	14	σ1	σ1	PROPN
ejpam-5633	192	15	,	,	PUNCT
ejpam-5633	192	16	σ2)θ	σ2)θ	NOUN
ejpam-5633	192	17	-	-	PUNCT
ejpam-5633	192	18	closed	closed	ADJ
ejpam-5633	192	19	.	.	PUNCT
ejpam-5633	193	1	by	by	ADP
ejpam-5633	193	2	(	(	PUNCT
ejpam-5633	193	3	3	3	NUM
ejpam-5633	193	4	)	)	PUNCT
ejpam-5633	193	5	,	,	PUNCT
ejpam-5633	193	6	f−(y	f−(y	NOUN
ejpam-5633	193	7	−	−	NOUN
ejpam-5633	193	8	v	v	NOUN
ejpam-5633	193	9	)	)	PUNCT
ejpam-5633	193	10	=	=	PUNCT
ejpam-5633	193	11	x	x	SYM
ejpam-5633	193	12	−	−	PROPN
ejpam-5633	193	13	f+(v	f+(v	NOUN
ejpam-5633	193	14	)	)	PUNCT
ejpam-5633	193	15	is	be	AUX
ejpam-5633	193	16	τ1τ2	τ1τ2	NOUN
ejpam-5633	193	17	-	-	ADJ
ejpam-5633	193	18	closed	closed	ADJ
ejpam-5633	193	19	in	in	ADP
ejpam-5633	193	20	x	x	X
ejpam-5633	193	21	and	and	CCONJ
ejpam-5633	193	22	hence	hence	ADV
ejpam-5633	193	23	f+(v	f+(v	PROPN
ejpam-5633	193	24	)	)	PUNCT
ejpam-5633	194	1	is	be	AUX
ejpam-5633	194	2	τ1τ2	τ1τ2	NOUN
ejpam-5633	194	3	-	-	ADJ
ejpam-5633	194	4	open	open	ADJ
ejpam-5633	194	5	in	in	ADP
ejpam-5633	194	6	x.	x.	NOUN
ejpam-5633	194	7	(	(	PUNCT
ejpam-5633	194	8	4	4	NUM
ejpam-5633	194	9	)	)	PUNCT
ejpam-5633	194	10	⇒	⇒	NOUN
ejpam-5633	194	11	(	(	PUNCT
ejpam-5633	194	12	1	1	NUM
ejpam-5633	194	13	):	):	PUNCT
ejpam-5633	194	14	let	let	VERB
ejpam-5633	194	15	v	v	PART
ejpam-5633	194	16	be	be	AUX
ejpam-5633	194	17	any	any	DET
ejpam-5633	194	18	σ1σ2	σ1σ2	NOUN
ejpam-5633	194	19	-	-	ADJ
ejpam-5633	194	20	open	open	ADJ
ejpam-5633	194	21	set	set	NOUN
ejpam-5633	194	22	of	of	ADP
ejpam-5633	194	23	y	y	PROPN
ejpam-5633	194	24	having	have	VERB
ejpam-5633	194	25	n	n	PROPN
ejpam-5633	194	26	(	(	PUNCT
ejpam-5633	194	27	σ1	σ1	PROPN
ejpam-5633	194	28	,	,	PUNCT
ejpam-5633	194	29	σ2)-closed	σ2)-close	VERB
ejpam-5633	194	30	complement	complement	NOUN
ejpam-5633	194	31	.	.	PUNCT
ejpam-5633	195	1	since	since	SCONJ
ejpam-5633	195	2	(	(	PUNCT
ejpam-5633	195	3	y	y	PROPN
ejpam-5633	195	4	,	,	PUNCT
ejpam-5633	195	5	σ1	σ1	PROPN
ejpam-5633	195	6	,	,	PUNCT
ejpam-5633	195	7	σ2	σ2	PROPN
ejpam-5633	195	8	)	)	PUNCT
ejpam-5633	195	9	is	be	AUX
ejpam-5633	195	10	(	(	PUNCT
ejpam-5633	195	11	σ1	σ1	NOUN
ejpam-5633	195	12	,	,	PUNCT
ejpam-5633	195	13	σ2)-regular	σ2)-regular	ADJ
ejpam-5633	195	14	,	,	PUNCT
ejpam-5633	195	15	v	v	NOUN
ejpam-5633	195	16	is	be	AUX
ejpam-5633	195	17	(	(	PUNCT
ejpam-5633	195	18	σ1	σ1	PROPN
ejpam-5633	195	19	,	,	PUNCT
ejpam-5633	195	20	σ2)θ	σ2)θ	NOUN
ejpam-5633	195	21	-	-	PUNCT
ejpam-5633	195	22	open	open	ADJ
ejpam-5633	195	23	in	in	ADP
ejpam-5633	195	24	y	y	PROPN
ejpam-5633	195	25	and	and	CCONJ
ejpam-5633	195	26	having	have	VERB
ejpam-5633	195	27	n	n	PROPN
ejpam-5633	195	28	(	(	PUNCT
ejpam-5633	195	29	σ1	σ1	PROPN
ejpam-5633	195	30	,	,	PUNCT
ejpam-5633	195	31	σ2)-closed	σ2)-close	VERB
ejpam-5633	195	32	complement	complement	NOUN
ejpam-5633	195	33	.	.	PUNCT
ejpam-5633	196	1	by	by	ADP
ejpam-5633	196	2	(	(	PUNCT
ejpam-5633	196	3	4	4	NUM
ejpam-5633	196	4	)	)	PUNCT
ejpam-5633	196	5	,	,	PUNCT
ejpam-5633	196	6	we	we	PRON
ejpam-5633	196	7	have	have	VERB
ejpam-5633	196	8	f+(v	f+(v	NOUN
ejpam-5633	196	9	)	)	PUNCT
ejpam-5633	196	10	is	be	AUX
ejpam-5633	196	11	τ1τ2	τ1τ2	NOUN
ejpam-5633	196	12	-	-	ADJ
ejpam-5633	196	13	open	open	ADJ
ejpam-5633	196	14	in	in	ADP
ejpam-5633	196	15	x	x	X
ejpam-5633	196	16	and	and	CCONJ
ejpam-5633	196	17	by	by	ADP
ejpam-5633	196	18	theorem	theorem	NOUN
ejpam-5633	196	19	3	3	NUM
ejpam-5633	196	20	,	,	PUNCT
ejpam-5633	196	21	f	f	PROPN
ejpam-5633	196	22	is	be	AUX
ejpam-5633	196	23	upper	upper	ADJ
ejpam-5633	196	24	nearly	nearly	ADV
ejpam-5633	196	25	(	(	PUNCT
ejpam-5633	196	26	τ1	τ1	NOUN
ejpam-5633	196	27	,	,	PUNCT
ejpam-5633	196	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	196	29	.	.	PUNCT
ejpam-5633	197	1	theorem	theorem	NOUN
ejpam-5633	197	2	6	6	NUM
ejpam-5633	197	3	.	.	PUNCT
ejpam-5633	198	1	let	let	AUX
ejpam-5633	198	2	(	(	PUNCT
ejpam-5633	198	3	y	y	PROPN
ejpam-5633	198	4	,	,	PUNCT
ejpam-5633	198	5	σ1	σ1	PROPN
ejpam-5633	198	6	,	,	PUNCT
ejpam-5633	198	7	σ2	σ2	PROPN
ejpam-5633	198	8	)	)	PUNCT
ejpam-5633	198	9	be	be	VERB
ejpam-5633	198	10	a	a	DET
ejpam-5633	198	11	(	(	PUNCT
ejpam-5633	198	12	σ1	σ1	NOUN
ejpam-5633	198	13	,	,	PUNCT
ejpam-5633	198	14	σ2)-regular	σ2)-regular	ADJ
ejpam-5633	198	15	space	space	NOUN
ejpam-5633	198	16	.	.	PUNCT
ejpam-5633	199	1	for	for	ADP
ejpam-5633	199	2	a	a	DET
ejpam-5633	199	3	multifunction	multifunction	NOUN
ejpam-5633	199	4	f	f	NOUN
ejpam-5633	199	5	:	:	PUNCT
ejpam-5633	199	6	(	(	PUNCT
ejpam-5633	199	7	x	x	NOUN
ejpam-5633	199	8	,	,	PUNCT
ejpam-5633	199	9	τ1	τ1	NOUN
ejpam-5633	199	10	,	,	PUNCT
ejpam-5633	199	11	τ2	τ2	NOUN
ejpam-5633	199	12	)	)	PUNCT
ejpam-5633	199	13	→	→	SYM
ejpam-5633	199	14	(	(	PUNCT
ejpam-5633	199	15	y	y	PROPN
ejpam-5633	199	16	,	,	PUNCT
ejpam-5633	199	17	σ1	σ1	PROPN
ejpam-5633	199	18	,	,	PUNCT
ejpam-5633	199	19	σ2	σ2	NOUN
ejpam-5633	199	20	)	)	PUNCT
ejpam-5633	199	21	,	,	PUNCT
ejpam-5633	199	22	the	the	DET
ejpam-5633	199	23	following	follow	VERB
ejpam-5633	199	24	properties	property	NOUN
ejpam-5633	199	25	are	be	AUX
ejpam-5633	199	26	equivalent	equivalent	ADJ
ejpam-5633	199	27	:	:	PUNCT
ejpam-5633	199	28	(	(	PUNCT
ejpam-5633	199	29	1	1	X
ejpam-5633	199	30	)	)	PUNCT
ejpam-5633	199	31	f	f	PROPN
ejpam-5633	199	32	is	be	AUX
ejpam-5633	199	33	lower	low	ADJ
ejpam-5633	199	34	nearly	nearly	ADV
ejpam-5633	199	35	(	(	PUNCT
ejpam-5633	199	36	τ1	τ1	NOUN
ejpam-5633	199	37	,	,	PUNCT
ejpam-5633	199	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	199	39	;	;	PUNCT
ejpam-5633	199	40	(	(	PUNCT
ejpam-5633	199	41	2	2	X
ejpam-5633	199	42	)	)	PUNCT
ejpam-5633	199	43	f+((σ1	f+((σ1	NOUN
ejpam-5633	199	44	,	,	PUNCT
ejpam-5633	199	45	σ2)θ	σ2)θ	ADJ
ejpam-5633	199	46	-	-	PUNCT
ejpam-5633	199	47	cl(b	cl(b	NOUN
ejpam-5633	199	48	)	)	PUNCT
ejpam-5633	199	49	)	)	PUNCT
ejpam-5633	199	50	is	be	AUX
ejpam-5633	199	51	τ1τ2	τ1τ2	NOUN
ejpam-5633	199	52	-	-	ADJ
ejpam-5633	199	53	closed	closed	ADJ
ejpam-5633	199	54	in	in	ADP
ejpam-5633	199	55	x	x	PUNCT
ejpam-5633	199	56	for	for	ADP
ejpam-5633	199	57	every	every	DET
ejpam-5633	199	58	subset	subset	NOUN
ejpam-5633	199	59	b	b	PROPN
ejpam-5633	199	60	of	of	ADP
ejpam-5633	199	61	y	y	PRON
ejpam-5633	199	62	such	such	ADJ
ejpam-5633	199	63	that	that	PRON
ejpam-5633	199	64	(	(	PUNCT
ejpam-5633	199	65	σ1	σ1	PROPN
ejpam-5633	199	66	,	,	PUNCT
ejpam-5633	199	67	σ2)θ	σ2)θ	NOUN
ejpam-5633	199	68	-	-	PUNCT
ejpam-5633	199	69	cl(b	cl(b	NOUN
ejpam-5633	199	70	)	)	PUNCT
ejpam-5633	199	71	is	be	AUX
ejpam-5633	199	72	n	n	PROPN
ejpam-5633	199	73	(	(	PUNCT
ejpam-5633	199	74	σ1	σ1	PROPN
ejpam-5633	199	75	,	,	PUNCT
ejpam-5633	199	76	σ2)-closed	σ2)-close	VERB
ejpam-5633	199	77	;	;	PUNCT
ejpam-5633	199	78	(	(	PUNCT
ejpam-5633	199	79	3	3	X
ejpam-5633	199	80	)	)	PUNCT
ejpam-5633	199	81	f+(k	f+(k	NOUN
ejpam-5633	199	82	)	)	PUNCT
ejpam-5633	199	83	is	be	AUX
ejpam-5633	199	84	τ1τ2	τ1τ2	NOUN
ejpam-5633	199	85	-	-	ADJ
ejpam-5633	199	86	closed	closed	ADJ
ejpam-5633	199	87	in	in	ADP
ejpam-5633	199	88	x	x	PUNCT
ejpam-5633	199	89	for	for	ADP
ejpam-5633	199	90	every	every	DET
ejpam-5633	199	91	n	n	PROPN
ejpam-5633	199	92	(	(	PUNCT
ejpam-5633	199	93	σ1	σ1	PROPN
ejpam-5633	199	94	,	,	PUNCT
ejpam-5633	199	95	σ2)-closed	σ2)-close	VERB
ejpam-5633	199	96	(	(	PUNCT
ejpam-5633	199	97	σ1	σ1	NOUN
ejpam-5633	199	98	,	,	PUNCT
ejpam-5633	199	99	σ2)θ	σ2)θ	NOUN
ejpam-5633	199	100	-	-	PUNCT
ejpam-5633	199	101	closed	close	VERB
ejpam-5633	199	102	set	set	NOUN
ejpam-5633	199	103	k	k	PROPN
ejpam-5633	199	104	of	of	ADP
ejpam-5633	199	105	y	y	PROPN
ejpam-5633	199	106	;	;	PUNCT
ejpam-5633	199	107	(	(	PUNCT
ejpam-5633	199	108	4	4	X
ejpam-5633	199	109	)	)	PUNCT
ejpam-5633	199	110	f−(v	f−(v	NOUN
ejpam-5633	199	111	)	)	PUNCT
ejpam-5633	199	112	is	be	AUX
ejpam-5633	199	113	τ1τ2	τ1τ2	NOUN
ejpam-5633	199	114	-	-	ADJ
ejpam-5633	199	115	open	open	ADJ
ejpam-5633	199	116	in	in	ADP
ejpam-5633	199	117	x	x	PUNCT
ejpam-5633	199	118	for	for	ADP
ejpam-5633	199	119	each	each	DET
ejpam-5633	199	120	(	(	PUNCT
ejpam-5633	199	121	σ1	σ1	PROPN
ejpam-5633	199	122	,	,	PUNCT
ejpam-5633	199	123	σ2)θ	σ2)θ	NOUN
ejpam-5633	199	124	-	-	PUNCT
ejpam-5633	199	125	open	open	ADJ
ejpam-5633	199	126	set	set	NOUN
ejpam-5633	199	127	v	v	NOUN
ejpam-5633	199	128	of	of	ADP
ejpam-5633	199	129	y	y	PROPN
ejpam-5633	199	130	having	have	VERB
ejpam-5633	199	131	n	n	PROPN
ejpam-5633	199	132	(	(	PUNCT
ejpam-5633	199	133	σ1	σ1	PROPN
ejpam-5633	199	134	,	,	PUNCT
ejpam-5633	199	135	σ2)-closed	σ2)-close	VERB
ejpam-5633	199	136	complement	complement	NOUN
ejpam-5633	199	137	.	.	PUNCT
ejpam-5633	200	1	proof	proof	NOUN
ejpam-5633	200	2	.	.	PUNCT
ejpam-5633	201	1	the	the	DET
ejpam-5633	201	2	proof	proof	NOUN
ejpam-5633	201	3	is	be	AUX
ejpam-5633	201	4	similar	similar	ADJ
ejpam-5633	201	5	to	to	ADP
ejpam-5633	201	6	that	that	PRON
ejpam-5633	201	7	of	of	ADP
ejpam-5633	201	8	theorem	theorem	NOUN
ejpam-5633	201	9	5	5	NUM
ejpam-5633	201	10	.	.	NOUN
ejpam-5633	201	11	4	4	NUM
ejpam-5633	201	12	.	.	X
ejpam-5633	202	1	some	some	DET
ejpam-5633	202	2	results	result	NOUN
ejpam-5633	202	3	on	on	ADP
ejpam-5633	202	4	near	near	ADJ
ejpam-5633	202	5	(	(	PUNCT
ejpam-5633	202	6	τ1	τ1	NOUN
ejpam-5633	202	7	,	,	PUNCT
ejpam-5633	202	8	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5633	202	9	recall	recall	VERB
ejpam-5633	202	10	that	that	SCONJ
ejpam-5633	202	11	a	a	DET
ejpam-5633	202	12	bitopological	bitopological	ADJ
ejpam-5633	202	13	space	space	NOUN
ejpam-5633	202	14	(	(	PUNCT
ejpam-5633	202	15	x	x	NOUN
ejpam-5633	202	16	,	,	PUNCT
ejpam-5633	202	17	τ1	τ1	NOUN
ejpam-5633	202	18	,	,	PUNCT
ejpam-5633	202	19	τ2	τ2	NOUN
ejpam-5633	202	20	)	)	PUNCT
ejpam-5633	202	21	is	be	AUX
ejpam-5633	202	22	said	say	VERB
ejpam-5633	202	23	to	to	PART
ejpam-5633	202	24	be	be	AUX
ejpam-5633	202	25	(	(	PUNCT
ejpam-5633	202	26	τ1	τ1	NOUN
ejpam-5633	202	27	,	,	PUNCT
ejpam-5633	202	28	τ2)-t2	τ2)-t2	X
ejpam-5633	203	1	[	[	X
ejpam-5633	203	2	34	34	NUM
ejpam-5633	203	3	]	]	X
ejpam-5633	203	4	if	if	SCONJ
ejpam-5633	203	5	for	for	ADP
ejpam-5633	203	6	any	any	DET
ejpam-5633	203	7	pair	pair	NOUN
ejpam-5633	203	8	of	of	ADP
ejpam-5633	203	9	distinct	distinct	ADJ
ejpam-5633	203	10	points	point	NOUN
ejpam-5633	203	11	x	x	X
ejpam-5633	203	12	,	,	PUNCT
ejpam-5633	203	13	y	y	PROPN
ejpam-5633	203	14	in	in	ADP
ejpam-5633	203	15	x	x	SYM
ejpam-5633	203	16	,	,	PUNCT
ejpam-5633	203	17	there	there	PRON
ejpam-5633	203	18	exist	exist	VERB
ejpam-5633	203	19	disjoint	disjoint	ADJ
ejpam-5633	203	20	τ1τ2	τ1τ2	ADJ
ejpam-5633	203	21	-	-	ADJ
ejpam-5633	203	22	open	open	ADJ
ejpam-5633	203	23	sets	set	NOUN
ejpam-5633	203	24	u	u	NOUN
ejpam-5633	203	25	and	and	CCONJ
ejpam-5633	203	26	v	v	NOUN
ejpam-5633	203	27	of	of	ADP
ejpam-5633	203	28	x	x	PUNCT
ejpam-5633	203	29	containing	contain	VERB
ejpam-5633	203	30	x	x	PROPN
ejpam-5633	203	31	and	and	CCONJ
ejpam-5633	203	32	y	y	PROPN
ejpam-5633	203	33	,	,	PUNCT
ejpam-5633	203	34	respectively	respectively	ADV
ejpam-5633	203	35	.	.	PUNCT
ejpam-5633	204	1	definition	definition	NOUN
ejpam-5633	204	2	3	3	NUM
ejpam-5633	204	3	.	.	PUNCT
ejpam-5633	205	1	a	a	DET
ejpam-5633	205	2	bitopological	bitopological	ADJ
ejpam-5633	205	3	space	space	NOUN
ejpam-5633	205	4	(	(	PUNCT
ejpam-5633	205	5	x	x	NOUN
ejpam-5633	205	6	,	,	PUNCT
ejpam-5633	205	7	τ1	τ1	NOUN
ejpam-5633	205	8	,	,	PUNCT
ejpam-5633	205	9	τ2	τ2	NOUN
ejpam-5633	205	10	)	)	PUNCT
ejpam-5633	205	11	is	be	AUX
ejpam-5633	205	12	called	call	VERB
ejpam-5633	205	13	n	n	PROPN
ejpam-5633	205	14	(	(	PUNCT
ejpam-5633	205	15	τ1	τ1	NOUN
ejpam-5633	205	16	,	,	PUNCT
ejpam-5633	205	17	τ2)-normal	τ2)-normal	ADJ
ejpam-5633	205	18	if	if	SCONJ
ejpam-5633	205	19	for	for	ADP
ejpam-5633	205	20	each	each	DET
ejpam-5633	205	21	disjoint	disjoint	ADJ
ejpam-5633	205	22	τ1τ2	τ1τ2	ADJ
ejpam-5633	205	23	-	-	ADJ
ejpam-5633	205	24	closed	closed	ADJ
ejpam-5633	205	25	sets	set	NOUN
ejpam-5633	205	26	k	k	NOUN
ejpam-5633	205	27	and	and	CCONJ
ejpam-5633	205	28	h	h	NOUN
ejpam-5633	205	29	of	of	ADP
ejpam-5633	205	30	x	x	PRON
ejpam-5633	205	31	,	,	PUNCT
ejpam-5633	205	32	there	there	PRON
ejpam-5633	205	33	exist	exist	VERB
ejpam-5633	205	34	τ1τ2	τ1τ2	ADJ
ejpam-5633	205	35	-	-	ADJ
ejpam-5633	205	36	open	open	ADJ
ejpam-5633	205	37	sets	set	NOUN
ejpam-5633	205	38	u	u	NOUN
ejpam-5633	205	39	and	and	CCONJ
ejpam-5633	205	40	v	v	ADP
ejpam-5633	205	41	having	have	VERB
ejpam-5633	205	42	n	n	PROPN
ejpam-5633	205	43	(	(	PUNCT
ejpam-5633	205	44	σ1	σ1	PROPN
ejpam-5633	205	45	,	,	PUNCT
ejpam-5633	205	46	σ2)closed	σ2)close	VERB
ejpam-5633	205	47	complements	complement	NOUN
ejpam-5633	205	48	such	such	ADJ
ejpam-5633	205	49	that	that	SCONJ
ejpam-5633	205	50	k	k	PROPN
ejpam-5633	205	51	⊆	⊆	NUM
ejpam-5633	205	52	u	u	NOUN
ejpam-5633	205	53	,	,	PUNCT
ejpam-5633	205	54	h	h	NOUN
ejpam-5633	205	55	⊆	⊆	NUM
ejpam-5633	205	56	v	v	NOUN
ejpam-5633	205	57	and	and	CCONJ
ejpam-5633	205	58	u	u	NOUN
ejpam-5633	205	59	∩	∩	NOUN
ejpam-5633	205	60	v	v	NOUN
ejpam-5633	205	61	=	=	PUNCT
ejpam-5633	205	62	∅.	∅.	PROPN
ejpam-5633	205	63	m.	m.	NOUN
ejpam-5633	205	64	thongmoon	thongmoon	NOUN
ejpam-5633	205	65	,	,	PUNCT
ejpam-5633	205	66	a.	a.	PROPN
ejpam-5633	205	67	sama	sama	PROPN
ejpam-5633	205	68	-	-	PUNCT
ejpam-5633	205	69	ae	ae	PROPN
ejpam-5633	205	70	,	,	PUNCT
ejpam-5633	205	71	c.	c.	PROPN
ejpam-5633	205	72	boonpok	boonpok	PROPN
ejpam-5633	205	73	/	/	SYM
ejpam-5633	205	74	eur	eur	PROPN
ejpam-5633	205	75	.	.	PUNCT
ejpam-5633	206	1	j.	j.	PROPN
ejpam-5633	206	2	pure	pure	PROPN
ejpam-5633	206	3	appl	appl	PROPN
ejpam-5633	206	4	.	.	PROPN
ejpam-5633	206	5	math	math	PROPN
ejpam-5633	206	6	,	,	PUNCT
ejpam-5633	206	7	18	18	NUM
ejpam-5633	206	8	(	(	PUNCT
ejpam-5633	206	9	1	1	NUM
ejpam-5633	206	10	)	)	PUNCT
ejpam-5633	206	11	(	(	PUNCT
ejpam-5633	206	12	2025	2025	NUM
ejpam-5633	206	13	)	)	PUNCT
ejpam-5633	206	14	,	,	PUNCT
ejpam-5633	206	15	5633	5633	NUM
ejpam-5633	206	16	9	9	NUM
ejpam-5633	206	17	of	of	ADP
ejpam-5633	206	18	13	13	NUM
ejpam-5633	206	19	theorem	theorem	NOUN
ejpam-5633	206	20	7	7	NUM
ejpam-5633	206	21	.	.	PUNCT
ejpam-5633	207	1	if	if	SCONJ
ejpam-5633	207	2	f	f	PROPN
ejpam-5633	207	3	:	:	PUNCT
ejpam-5633	207	4	(	(	PUNCT
ejpam-5633	207	5	x	x	NOUN
ejpam-5633	207	6	,	,	PUNCT
ejpam-5633	207	7	τ1	τ1	NOUN
ejpam-5633	207	8	,	,	PUNCT
ejpam-5633	207	9	τ2	τ2	NOUN
ejpam-5633	207	10	)	)	PUNCT
ejpam-5633	207	11	→	→	SYM
ejpam-5633	207	12	(	(	PUNCT
ejpam-5633	207	13	y	y	PROPN
ejpam-5633	207	14	,	,	PUNCT
ejpam-5633	207	15	σ1	σ1	PROPN
ejpam-5633	207	16	,	,	PUNCT
ejpam-5633	207	17	σ2	σ2	PROPN
ejpam-5633	207	18	)	)	PUNCT
ejpam-5633	207	19	is	be	AUX
ejpam-5633	207	20	an	an	DET
ejpam-5633	207	21	upper	upper	ADJ
ejpam-5633	207	22	nearly	nearly	ADV
ejpam-5633	207	23	(	(	PUNCT
ejpam-5633	207	24	τ1	τ1	NOUN
ejpam-5633	207	25	,	,	PUNCT
ejpam-5633	207	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	207	27	multifunction	multifunction	NOUN
ejpam-5633	207	28	satisfying	satisfy	VERB
ejpam-5633	207	29	the	the	DET
ejpam-5633	207	30	following	follow	VERB
ejpam-5633	207	31	conditions	condition	NOUN
ejpam-5633	207	32	:	:	PUNCT
ejpam-5633	207	33	(	(	PUNCT
ejpam-5633	207	34	1	1	X
ejpam-5633	207	35	)	)	PUNCT
ejpam-5633	207	36	f	f	NOUN
ejpam-5633	207	37	(	(	PUNCT
ejpam-5633	207	38	x	x	X
ejpam-5633	207	39	)	)	PUNCT
ejpam-5633	207	40	is	be	AUX
ejpam-5633	207	41	σ1σ2	σ1σ2	NOUN
ejpam-5633	207	42	-	-	ADJ
ejpam-5633	207	43	closed	closed	ADJ
ejpam-5633	207	44	in	in	ADP
ejpam-5633	207	45	y	y	PROPN
ejpam-5633	207	46	for	for	ADP
ejpam-5633	207	47	each	each	DET
ejpam-5633	207	48	x	x	SYM
ejpam-5633	207	49	∈	∈	PROPN
ejpam-5633	207	50	x	x	X
ejpam-5633	207	51	,	,	PUNCT
ejpam-5633	207	52	(	(	PUNCT
ejpam-5633	207	53	2	2	X
ejpam-5633	207	54	)	)	PUNCT
ejpam-5633	207	55	f	f	NOUN
ejpam-5633	207	56	(	(	PUNCT
ejpam-5633	207	57	x	x	NOUN
ejpam-5633	207	58	)	)	PUNCT
ejpam-5633	207	59	∩	∩	ADJ
ejpam-5633	207	60	f	f	PROPN
ejpam-5633	207	61	(	(	PUNCT
ejpam-5633	207	62	y	y	NOUN
ejpam-5633	207	63	)	)	PUNCT
ejpam-5633	207	64	=	=	NOUN
ejpam-5633	207	65	∅	∅	NOUN
ejpam-5633	207	66	for	for	ADP
ejpam-5633	207	67	each	each	DET
ejpam-5633	207	68	distinct	distinct	ADJ
ejpam-5633	207	69	points	point	NOUN
ejpam-5633	208	1	x	x	NOUN
ejpam-5633	208	2	,	,	PUNCT
ejpam-5633	208	3	y	y	PROPN
ejpam-5633	208	4	∈	∈	PROPN
ejpam-5633	208	5	x	x	X
ejpam-5633	208	6	,	,	PUNCT
ejpam-5633	208	7	and	and	CCONJ
ejpam-5633	208	8	(	(	PUNCT
ejpam-5633	208	9	3	3	X
ejpam-5633	208	10	)	)	PUNCT
ejpam-5633	208	11	(	(	PUNCT
ejpam-5633	208	12	y	y	PROPN
ejpam-5633	208	13	,	,	PUNCT
ejpam-5633	208	14	σ1	σ1	PROPN
ejpam-5633	208	15	,	,	PUNCT
ejpam-5633	208	16	σ2	σ2	PROPN
ejpam-5633	208	17	)	)	PUNCT
ejpam-5633	208	18	is	be	AUX
ejpam-5633	208	19	an	an	DET
ejpam-5633	208	20	n	n	PROPN
ejpam-5633	208	21	(	(	PUNCT
ejpam-5633	208	22	σ1	σ1	PROPN
ejpam-5633	208	23	,	,	PUNCT
ejpam-5633	208	24	σ2)-normal	σ2)-normal	ADJ
ejpam-5633	208	25	space	space	NOUN
ejpam-5633	208	26	,	,	PUNCT
ejpam-5633	208	27	then	then	ADV
ejpam-5633	208	28	(	(	PUNCT
ejpam-5633	208	29	x	x	NOUN
ejpam-5633	208	30	,	,	PUNCT
ejpam-5633	208	31	τ1	τ1	NOUN
ejpam-5633	208	32	,	,	PUNCT
ejpam-5633	208	33	τ2	τ2	NOUN
ejpam-5633	208	34	)	)	PUNCT
ejpam-5633	208	35	is	be	AUX
ejpam-5633	208	36	(	(	PUNCT
ejpam-5633	208	37	τ1	τ1	NOUN
ejpam-5633	208	38	,	,	PUNCT
ejpam-5633	208	39	τ2)-t2	τ2)-t2	PROPN
ejpam-5633	208	40	.	.	PUNCT
ejpam-5633	209	1	proof	proof	NOUN
ejpam-5633	209	2	.	.	PUNCT
ejpam-5633	210	1	let	let	VERB
ejpam-5633	210	2	x	x	PRON
ejpam-5633	210	3	and	and	CCONJ
ejpam-5633	210	4	y	y	PROPN
ejpam-5633	210	5	be	be	AUX
ejpam-5633	210	6	distinct	distinct	ADJ
ejpam-5633	210	7	points	point	NOUN
ejpam-5633	210	8	of	of	ADP
ejpam-5633	210	9	x.	x.	NOUN
ejpam-5633	210	10	then	then	ADV
ejpam-5633	210	11	,	,	PUNCT
ejpam-5633	210	12	we	we	PRON
ejpam-5633	210	13	have	have	AUX
ejpam-5633	210	14	f	f	PROPN
ejpam-5633	210	15	(	(	PUNCT
ejpam-5633	210	16	x	x	NOUN
ejpam-5633	210	17	)	)	PUNCT
ejpam-5633	210	18	∩	∩	ADJ
ejpam-5633	210	19	f	f	PROPN
ejpam-5633	210	20	(	(	PUNCT
ejpam-5633	210	21	y	y	NOUN
ejpam-5633	210	22	)	)	PUNCT
ejpam-5633	210	23	=	=	PUNCT
ejpam-5633	210	24	∅.	∅.	NOUN
ejpam-5633	210	25	since	since	SCONJ
ejpam-5633	210	26	f	f	PROPN
ejpam-5633	210	27	(	(	PUNCT
ejpam-5633	210	28	x	x	NOUN
ejpam-5633	210	29	)	)	PUNCT
ejpam-5633	210	30	and	and	CCONJ
ejpam-5633	210	31	f	f	PROPN
ejpam-5633	210	32	(	(	PUNCT
ejpam-5633	210	33	y	y	NOUN
ejpam-5633	210	34	)	)	PUNCT
ejpam-5633	210	35	are	be	AUX
ejpam-5633	210	36	σ1σ2	σ1σ2	NOUN
ejpam-5633	210	37	-	-	ADJ
ejpam-5633	210	38	closed	closed	ADJ
ejpam-5633	210	39	and	and	CCONJ
ejpam-5633	210	40	(	(	PUNCT
ejpam-5633	210	41	y	y	PROPN
ejpam-5633	210	42	,	,	PUNCT
ejpam-5633	210	43	σ1	σ1	PROPN
ejpam-5633	210	44	,	,	PUNCT
ejpam-5633	210	45	σ2	σ2	PROPN
ejpam-5633	210	46	)	)	PUNCT
ejpam-5633	210	47	is	be	AUX
ejpam-5633	210	48	n	n	PROPN
ejpam-5633	210	49	(	(	PUNCT
ejpam-5633	210	50	σ1	σ1	PROPN
ejpam-5633	210	51	,	,	PUNCT
ejpam-5633	210	52	σ2)-normal	σ2)-normal	PROPN
ejpam-5633	210	53	,	,	PUNCT
ejpam-5633	210	54	there	there	PRON
ejpam-5633	210	55	exist	exist	VERB
ejpam-5633	210	56	disjoint	disjoint	ADJ
ejpam-5633	210	57	σ1σ2	σ1σ2	ADJ
ejpam-5633	210	58	-	-	ADJ
ejpam-5633	210	59	open	open	ADJ
ejpam-5633	210	60	sets	set	NOUN
ejpam-5633	210	61	u	u	NOUN
ejpam-5633	210	62	and	and	CCONJ
ejpam-5633	210	63	v	v	ADP
ejpam-5633	210	64	having	have	VERB
ejpam-5633	210	65	n	n	PRON
ejpam-5633	210	66	(	(	PUNCT
ejpam-5633	210	67	σ1	σ1	PROPN
ejpam-5633	210	68	,	,	PUNCT
ejpam-5633	210	69	σ2)-closed	σ2)-close	VERB
ejpam-5633	210	70	complements	complement	NOUN
ejpam-5633	210	71	such	such	ADJ
ejpam-5633	210	72	that	that	SCONJ
ejpam-5633	210	73	f	f	PROPN
ejpam-5633	210	74	(	(	PUNCT
ejpam-5633	210	75	x	x	X
ejpam-5633	210	76	)	)	PUNCT
ejpam-5633	210	77	⊆	⊆	NUM
ejpam-5633	210	78	u	u	NOUN
ejpam-5633	210	79	and	and	CCONJ
ejpam-5633	210	80	f	f	PROPN
ejpam-5633	210	81	(	(	PUNCT
ejpam-5633	210	82	y	y	PROPN
ejpam-5633	210	83	)	)	PUNCT
ejpam-5633	210	84	⊆	⊆	NUM
ejpam-5633	210	85	v	v	NOUN
ejpam-5633	210	86	.	.	PUNCT
ejpam-5633	211	1	by	by	ADP
ejpam-5633	211	2	theorem	theorem	ADJ
ejpam-5633	211	3	3	3	NUM
ejpam-5633	211	4	,	,	PUNCT
ejpam-5633	211	5	f+(u	f+(u	NUM
ejpam-5633	211	6	)	)	PUNCT
ejpam-5633	211	7	and	and	CCONJ
ejpam-5633	211	8	f+(v	f+(v	NUM
ejpam-5633	211	9	)	)	PUNCT
ejpam-5633	211	10	are	be	AUX
ejpam-5633	211	11	τ1τ2	τ1τ2	NOUN
ejpam-5633	211	12	-	-	ADJ
ejpam-5633	211	13	open	open	ADJ
ejpam-5633	211	14	in	in	ADP
ejpam-5633	211	15	x	x	PUNCT
ejpam-5633	211	16	containing	contain	VERB
ejpam-5633	211	17	x	x	PROPN
ejpam-5633	211	18	and	and	CCONJ
ejpam-5633	211	19	y	y	PROPN
ejpam-5633	211	20	,	,	PUNCT
ejpam-5633	211	21	respectively	respectively	ADV
ejpam-5633	211	22	,	,	PUNCT
ejpam-5633	211	23	such	such	ADJ
ejpam-5633	211	24	that	that	DET
ejpam-5633	211	25	f+(u	f+(u	ADJ
ejpam-5633	211	26	)	)	PUNCT
ejpam-5633	211	27	∩	∩	NOUN
ejpam-5633	211	28	f+(v	f+(v	NOUN
ejpam-5633	211	29	)	)	PUNCT
ejpam-5633	212	1	=	=	PUNCT
ejpam-5633	212	2	∅.	∅.	ADP
ejpam-5633	212	3	this	this	PRON
ejpam-5633	212	4	shows	show	VERB
ejpam-5633	212	5	that	that	SCONJ
ejpam-5633	212	6	(	(	PUNCT
ejpam-5633	212	7	x	x	NOUN
ejpam-5633	212	8	,	,	PUNCT
ejpam-5633	212	9	τ1	τ1	NOUN
ejpam-5633	212	10	,	,	PUNCT
ejpam-5633	212	11	τ2	τ2	NOUN
ejpam-5633	212	12	)	)	PUNCT
ejpam-5633	212	13	is	be	AUX
ejpam-5633	212	14	(	(	PUNCT
ejpam-5633	212	15	τ1	τ1	NOUN
ejpam-5633	212	16	,	,	PUNCT
ejpam-5633	212	17	τ2)-t2	τ2)-t2	PROPN
ejpam-5633	212	18	.	.	PUNCT
ejpam-5633	213	1	theorem	theorem	VERB
ejpam-5633	213	2	8	8	NUM
ejpam-5633	213	3	.	.	PUNCT
ejpam-5633	214	1	let	let	AUX
ejpam-5633	214	2	(	(	PUNCT
ejpam-5633	214	3	x	x	NOUN
ejpam-5633	214	4	,	,	PUNCT
ejpam-5633	214	5	τ1	τ1	NOUN
ejpam-5633	214	6	,	,	PUNCT
ejpam-5633	214	7	τ2	τ2	PROPN
ejpam-5633	214	8	)	)	PUNCT
ejpam-5633	214	9	be	be	VERB
ejpam-5633	214	10	a	a	DET
ejpam-5633	214	11	bitopological	bitopological	ADJ
ejpam-5633	214	12	space	space	NOUN
ejpam-5633	214	13	.	.	PUNCT
ejpam-5633	215	1	if	if	SCONJ
ejpam-5633	215	2	for	for	ADP
ejpam-5633	215	3	each	each	DET
ejpam-5633	215	4	pair	pair	NOUN
ejpam-5633	215	5	of	of	ADP
ejpam-5633	215	6	distinct	distinct	ADJ
ejpam-5633	215	7	points	point	NOUN
ejpam-5633	215	8	x	x	PUNCT
ejpam-5633	215	9	and	and	CCONJ
ejpam-5633	215	10	x′	x′	PROPN
ejpam-5633	215	11	in	in	ADP
ejpam-5633	215	12	x	x	SYM
ejpam-5633	215	13	,	,	PUNCT
ejpam-5633	215	14	there	there	PRON
ejpam-5633	215	15	exists	exist	VERB
ejpam-5633	215	16	a	a	DET
ejpam-5633	215	17	multifunction	multifunction	NOUN
ejpam-5633	215	18	f	f	NOUN
ejpam-5633	215	19	from	from	ADP
ejpam-5633	215	20	(	(	PUNCT
ejpam-5633	215	21	x	x	NOUN
ejpam-5633	215	22	,	,	PUNCT
ejpam-5633	215	23	τ1	τ1	NOUN
ejpam-5633	215	24	,	,	PUNCT
ejpam-5633	215	25	τ2	τ2	NOUN
ejpam-5633	215	26	)	)	PUNCT
ejpam-5633	215	27	into	into	ADP
ejpam-5633	215	28	an	an	DET
ejpam-5633	215	29	n	n	PROPN
ejpam-5633	215	30	(	(	PUNCT
ejpam-5633	215	31	σ1	σ1	PROPN
ejpam-5633	215	32	,	,	PUNCT
ejpam-5633	215	33	σ2)-normal	σ2)-normal	ADJ
ejpam-5633	215	34	space	space	NOUN
ejpam-5633	215	35	(	(	PUNCT
ejpam-5633	215	36	y	y	PROPN
ejpam-5633	215	37	,	,	PUNCT
ejpam-5633	215	38	σ1	σ1	PROPN
ejpam-5633	215	39	,	,	PUNCT
ejpam-5633	215	40	σ2	σ2	NOUN
ejpam-5633	215	41	)	)	PUNCT
ejpam-5633	215	42	satisfying	satisfy	VERB
ejpam-5633	215	43	the	the	DET
ejpam-5633	215	44	following	follow	VERB
ejpam-5633	215	45	conditions	condition	NOUN
ejpam-5633	215	46	:	:	PUNCT
ejpam-5633	215	47	(	(	PUNCT
ejpam-5633	215	48	1	1	X
ejpam-5633	215	49	)	)	PUNCT
ejpam-5633	215	50	f	f	NOUN
ejpam-5633	215	51	(	(	PUNCT
ejpam-5633	215	52	x	x	NOUN
ejpam-5633	215	53	)	)	PUNCT
ejpam-5633	215	54	and	and	CCONJ
ejpam-5633	215	55	f	f	PROPN
ejpam-5633	215	56	(	(	PUNCT
ejpam-5633	215	57	x′	x′	PROPN
ejpam-5633	215	58	)	)	PUNCT
ejpam-5633	215	59	are	be	AUX
ejpam-5633	215	60	σ1σ2	σ1σ2	NOUN
ejpam-5633	215	61	-	-	ADJ
ejpam-5633	215	62	closed	closed	ADJ
ejpam-5633	215	63	in	in	ADP
ejpam-5633	215	64	y	y	PROPN
ejpam-5633	215	65	,	,	PUNCT
ejpam-5633	215	66	(	(	PUNCT
ejpam-5633	215	67	2	2	X
ejpam-5633	215	68	)	)	PUNCT
ejpam-5633	215	69	f	f	PROPN
ejpam-5633	215	70	is	be	AUX
ejpam-5633	215	71	upper	upper	ADJ
ejpam-5633	215	72	nearly	nearly	ADV
ejpam-5633	215	73	(	(	PUNCT
ejpam-5633	215	74	τ1	τ1	NOUN
ejpam-5633	215	75	,	,	PUNCT
ejpam-5633	215	76	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	215	77	at	at	ADP
ejpam-5633	215	78	x	x	PROPN
ejpam-5633	215	79	and	and	CCONJ
ejpam-5633	215	80	x′	x′	NUM
ejpam-5633	215	81	,	,	PUNCT
ejpam-5633	215	82	and	and	CCONJ
ejpam-5633	215	83	(	(	PUNCT
ejpam-5633	215	84	3	3	X
ejpam-5633	215	85	)	)	PUNCT
ejpam-5633	215	86	f	f	NOUN
ejpam-5633	215	87	(	(	PUNCT
ejpam-5633	215	88	x	x	NOUN
ejpam-5633	215	89	)	)	PUNCT
ejpam-5633	215	90	∩	∩	ADJ
ejpam-5633	215	91	f	f	X
ejpam-5633	215	92	(	(	PUNCT
ejpam-5633	215	93	x′	x′	NUM
ejpam-5633	215	94	)	)	PUNCT
ejpam-5633	216	1	=	=	NOUN
ejpam-5633	216	2	∅	∅	NOUN
ejpam-5633	216	3	,	,	PUNCT
ejpam-5633	216	4	then	then	ADV
ejpam-5633	216	5	(	(	PUNCT
ejpam-5633	216	6	x	x	NOUN
ejpam-5633	216	7	,	,	PUNCT
ejpam-5633	216	8	τ1	τ1	NOUN
ejpam-5633	216	9	,	,	PUNCT
ejpam-5633	216	10	τ2	τ2	NOUN
ejpam-5633	216	11	)	)	PUNCT
ejpam-5633	216	12	is	be	AUX
ejpam-5633	216	13	(	(	PUNCT
ejpam-5633	216	14	τ1	τ1	NOUN
ejpam-5633	216	15	,	,	PUNCT
ejpam-5633	216	16	τ2)-t2	τ2)-t2	PROPN
ejpam-5633	216	17	.	.	PUNCT
ejpam-5633	217	1	proof	proof	NOUN
ejpam-5633	217	2	.	.	PUNCT
ejpam-5633	218	1	let	let	VERB
ejpam-5633	218	2	x	x	PRON
ejpam-5633	218	3	and	and	CCONJ
ejpam-5633	218	4	x′	x′	PROPN
ejpam-5633	218	5	be	be	AUX
ejpam-5633	218	6	distinct	distinct	ADJ
ejpam-5633	218	7	points	point	NOUN
ejpam-5633	218	8	of	of	ADP
ejpam-5633	218	9	x.	x.	NOUN
ejpam-5633	218	10	then	then	ADV
ejpam-5633	218	11	,	,	PUNCT
ejpam-5633	218	12	we	we	PRON
ejpam-5633	218	13	have	have	VERB
ejpam-5633	218	14	f	f	PROPN
ejpam-5633	218	15	(	(	PUNCT
ejpam-5633	218	16	x	x	NOUN
ejpam-5633	218	17	)	)	PUNCT
ejpam-5633	218	18	∩	∩	ADJ
ejpam-5633	218	19	f	f	X
ejpam-5633	218	20	(	(	PUNCT
ejpam-5633	218	21	x′	x′	NUM
ejpam-5633	218	22	)	)	PUNCT
ejpam-5633	219	1	=	=	PUNCT
ejpam-5633	219	2	∅.	∅.	NOUN
ejpam-5633	219	3	since	since	SCONJ
ejpam-5633	219	4	f	f	PROPN
ejpam-5633	219	5	(	(	PUNCT
ejpam-5633	219	6	x	x	NOUN
ejpam-5633	219	7	)	)	PUNCT
ejpam-5633	219	8	and	and	CCONJ
ejpam-5633	219	9	f	f	PROPN
ejpam-5633	219	10	(	(	PUNCT
ejpam-5633	219	11	x′	x′	PROPN
ejpam-5633	219	12	)	)	PUNCT
ejpam-5633	219	13	are	be	AUX
ejpam-5633	219	14	σ1σ2	σ1σ2	NOUN
ejpam-5633	219	15	-	-	ADJ
ejpam-5633	219	16	closed	closed	ADJ
ejpam-5633	219	17	and	and	CCONJ
ejpam-5633	219	18	(	(	PUNCT
ejpam-5633	219	19	y	y	PROPN
ejpam-5633	219	20	,	,	PUNCT
ejpam-5633	219	21	σ1	σ1	PROPN
ejpam-5633	219	22	,	,	PUNCT
ejpam-5633	219	23	σ2	σ2	PROPN
ejpam-5633	219	24	)	)	PUNCT
ejpam-5633	219	25	is	be	AUX
ejpam-5633	219	26	n	n	PROPN
ejpam-5633	219	27	(	(	PUNCT
ejpam-5633	219	28	σ1	σ1	PROPN
ejpam-5633	219	29	,	,	PUNCT
ejpam-5633	219	30	σ2)-normal	σ2)-normal	PROPN
ejpam-5633	219	31	,	,	PUNCT
ejpam-5633	219	32	there	there	PRON
ejpam-5633	219	33	exist	exist	VERB
ejpam-5633	219	34	disjoint	disjoint	ADJ
ejpam-5633	219	35	σ1σ2	σ1σ2	ADJ
ejpam-5633	219	36	-	-	ADJ
ejpam-5633	219	37	open	open	ADJ
ejpam-5633	219	38	sets	set	NOUN
ejpam-5633	219	39	v	v	ADP
ejpam-5633	219	40	and	and	CCONJ
ejpam-5633	219	41	v	v	NOUN
ejpam-5633	219	42	′	′	NOUN
ejpam-5633	219	43	having	have	VERB
ejpam-5633	219	44	n	n	PROPN
ejpam-5633	219	45	(	(	PUNCT
ejpam-5633	219	46	σ1	σ1	PROPN
ejpam-5633	219	47	,	,	PUNCT
ejpam-5633	219	48	σ2)-closed	σ2)-close	VERB
ejpam-5633	219	49	complements	complement	NOUN
ejpam-5633	219	50	such	such	ADJ
ejpam-5633	219	51	that	that	SCONJ
ejpam-5633	219	52	f	f	PROPN
ejpam-5633	219	53	(	(	PUNCT
ejpam-5633	219	54	x	x	X
ejpam-5633	219	55	)	)	PUNCT
ejpam-5633	219	56	⊆	⊆	NUM
ejpam-5633	219	57	v	v	NOUN
ejpam-5633	219	58	and	and	CCONJ
ejpam-5633	219	59	f	f	PROPN
ejpam-5633	219	60	(	(	PUNCT
ejpam-5633	219	61	x′	x′	NUM
ejpam-5633	219	62	)	)	PUNCT
ejpam-5633	219	63	⊆	⊆	NUM
ejpam-5633	219	64	v	v	ADP
ejpam-5633	219	65	′.	′.	NOUN
ejpam-5633	219	66	since	since	SCONJ
ejpam-5633	219	67	f	f	PROPN
ejpam-5633	219	68	is	be	AUX
ejpam-5633	219	69	upper	upper	ADJ
ejpam-5633	219	70	nearly	nearly	ADV
ejpam-5633	219	71	(	(	PUNCT
ejpam-5633	219	72	τ1	τ1	NOUN
ejpam-5633	219	73	,	,	PUNCT
ejpam-5633	219	74	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	219	75	at	at	ADP
ejpam-5633	219	76	x	x	PROPN
ejpam-5633	219	77	and	and	CCONJ
ejpam-5633	219	78	x′	x′	NUM
ejpam-5633	219	79	,	,	PUNCT
ejpam-5633	219	80	there	there	PRON
ejpam-5633	219	81	exist	exist	VERB
ejpam-5633	219	82	τ1τ2	τ1τ2	ADJ
ejpam-5633	219	83	-	-	ADJ
ejpam-5633	219	84	open	open	ADJ
ejpam-5633	219	85	sets	set	NOUN
ejpam-5633	219	86	u	u	NOUN
ejpam-5633	219	87	and	and	CCONJ
ejpam-5633	219	88	u	u	NOUN
ejpam-5633	219	89	′	′	NOUN
ejpam-5633	219	90	of	of	ADP
ejpam-5633	219	91	x	x	PUNCT
ejpam-5633	219	92	containing	contain	VERB
ejpam-5633	219	93	x	x	PROPN
ejpam-5633	219	94	and	and	CCONJ
ejpam-5633	219	95	x′	x′	NUM
ejpam-5633	219	96	,	,	PUNCT
ejpam-5633	219	97	respectively	respectively	ADV
ejpam-5633	219	98	,	,	PUNCT
ejpam-5633	219	99	such	such	ADJ
ejpam-5633	219	100	that	that	SCONJ
ejpam-5633	219	101	f	f	PROPN
ejpam-5633	219	102	(	(	PUNCT
ejpam-5633	219	103	u	u	NOUN
ejpam-5633	219	104	)	)	PUNCT
ejpam-5633	219	105	⊆	⊆	NUM
ejpam-5633	219	106	v	v	NOUN
ejpam-5633	219	107	and	and	CCONJ
ejpam-5633	219	108	f	f	PROPN
ejpam-5633	219	109	(	(	PUNCT
ejpam-5633	219	110	u	u	NOUN
ejpam-5633	219	111	′	′	NOUN
ejpam-5633	219	112	)	)	PUNCT
ejpam-5633	219	113	⊆	⊆	NUM
ejpam-5633	219	114	v	v	ADP
ejpam-5633	219	115	′.	′.	NOUN
ejpam-5633	219	116	this	this	PRON
ejpam-5633	219	117	implies	imply	VERB
ejpam-5633	219	118	that	that	SCONJ
ejpam-5633	219	119	u	u	PROPN
ejpam-5633	219	120	∩	∩	NOUN
ejpam-5633	219	121	u	u	NOUN
ejpam-5633	219	122	′	′	NOUN
ejpam-5633	219	123	=	=	PUNCT
ejpam-5633	219	124	∅.	∅.	VERB
ejpam-5633	219	125	thus	thus	ADV
ejpam-5633	219	126	,	,	PUNCT
ejpam-5633	219	127	(	(	PUNCT
ejpam-5633	219	128	x	x	NOUN
ejpam-5633	219	129	,	,	PUNCT
ejpam-5633	219	130	τ1	τ1	NOUN
ejpam-5633	219	131	,	,	PUNCT
ejpam-5633	219	132	τ2	τ2	NOUN
ejpam-5633	219	133	)	)	PUNCT
ejpam-5633	219	134	is	be	AUX
ejpam-5633	219	135	(	(	PUNCT
ejpam-5633	219	136	τ1	τ1	NOUN
ejpam-5633	219	137	,	,	PUNCT
ejpam-5633	219	138	τ2)-t2	τ2)-t2	PROPN
ejpam-5633	219	139	.	.	PUNCT
ejpam-5633	220	1	definition	definition	NOUN
ejpam-5633	220	2	4	4	NUM
ejpam-5633	220	3	.	.	PUNCT
ejpam-5633	221	1	a	a	DET
ejpam-5633	221	2	subset	subset	NOUN
ejpam-5633	221	3	a	a	PRON
ejpam-5633	221	4	of	of	ADP
ejpam-5633	221	5	a	a	DET
ejpam-5633	221	6	bitopological	bitopological	ADJ
ejpam-5633	221	7	space	space	NOUN
ejpam-5633	221	8	(	(	PUNCT
ejpam-5633	221	9	x	x	NOUN
ejpam-5633	221	10	,	,	PUNCT
ejpam-5633	221	11	τ1	τ1	NOUN
ejpam-5633	221	12	,	,	PUNCT
ejpam-5633	221	13	τ2	τ2	NOUN
ejpam-5633	221	14	)	)	PUNCT
ejpam-5633	221	15	is	be	AUX
ejpam-5633	221	16	said	say	VERB
ejpam-5633	221	17	to	to	PART
ejpam-5633	221	18	be	be	AUX
ejpam-5633	221	19	τ1τ2	τ1τ2	NOUN
ejpam-5633	221	20	-	-	ADJ
ejpam-5633	221	21	dense	dense	ADJ
ejpam-5633	221	22	on	on	ADP
ejpam-5633	221	23	x	x	SYM
ejpam-5633	221	24	if	if	SCONJ
ejpam-5633	221	25	τ1τ2	τ1τ2	NOUN
ejpam-5633	221	26	-	-	NUM
ejpam-5633	221	27	cl(a	cl(a	NUM
ejpam-5633	221	28	)	)	PUNCT
ejpam-5633	221	29	=	=	SYM
ejpam-5633	221	30	x.	x.	NOUN
ejpam-5633	221	31	theorem	theorem	VERB
ejpam-5633	221	32	9	9	NUM
ejpam-5633	221	33	.	.	PUNCT
ejpam-5633	222	1	let	let	AUX
ejpam-5633	222	2	(	(	PUNCT
ejpam-5633	222	3	x	x	NOUN
ejpam-5633	222	4	,	,	PUNCT
ejpam-5633	222	5	τ1	τ1	NOUN
ejpam-5633	222	6	,	,	PUNCT
ejpam-5633	222	7	τ2	τ2	PROPN
ejpam-5633	222	8	)	)	PUNCT
ejpam-5633	222	9	be	be	VERB
ejpam-5633	222	10	a	a	DET
ejpam-5633	222	11	bitopological	bitopological	ADJ
ejpam-5633	222	12	space	space	NOUN
ejpam-5633	222	13	and	and	CCONJ
ejpam-5633	222	14	(	(	PUNCT
ejpam-5633	222	15	y	y	PROPN
ejpam-5633	222	16	,	,	PUNCT
ejpam-5633	222	17	σ1	σ1	PROPN
ejpam-5633	222	18	,	,	PUNCT
ejpam-5633	222	19	σ2	σ2	PROPN
ejpam-5633	222	20	)	)	PUNCT
ejpam-5633	222	21	be	be	VERB
ejpam-5633	222	22	an	an	DET
ejpam-5633	222	23	n	n	PROPN
ejpam-5633	222	24	(	(	PUNCT
ejpam-5633	222	25	σ1	σ1	PROPN
ejpam-5633	222	26	,	,	PUNCT
ejpam-5633	222	27	σ2)-normal	σ2)-normal	ADJ
ejpam-5633	222	28	space	space	NOUN
ejpam-5633	222	29	.	.	PUNCT
ejpam-5633	223	1	if	if	SCONJ
ejpam-5633	223	2	the	the	DET
ejpam-5633	223	3	following	follow	VERB
ejpam-5633	223	4	four	four	NUM
ejpam-5633	223	5	conditions	condition	NOUN
ejpam-5633	223	6	are	be	AUX
ejpam-5633	223	7	satisfied	satisfied	ADJ
ejpam-5633	223	8	:	:	PUNCT
ejpam-5633	223	9	(	(	PUNCT
ejpam-5633	223	10	1	1	X
ejpam-5633	223	11	)	)	PUNCT
ejpam-5633	223	12	f	f	NOUN
ejpam-5633	223	13	:	:	PUNCT
ejpam-5633	223	14	(	(	PUNCT
ejpam-5633	223	15	x	x	NOUN
ejpam-5633	223	16	,	,	PUNCT
ejpam-5633	223	17	τ1	τ1	NOUN
ejpam-5633	223	18	,	,	PUNCT
ejpam-5633	223	19	τ2	τ2	NOUN
ejpam-5633	223	20	)	)	PUNCT
ejpam-5633	223	21	→	→	SYM
ejpam-5633	223	22	(	(	PUNCT
ejpam-5633	223	23	y	y	PROPN
ejpam-5633	223	24	,	,	PUNCT
ejpam-5633	223	25	σ1	σ1	PROPN
ejpam-5633	223	26	,	,	PUNCT
ejpam-5633	223	27	σ2	σ2	PROPN
ejpam-5633	223	28	)	)	PUNCT
ejpam-5633	223	29	is	be	AUX
ejpam-5633	223	30	upper	upper	ADJ
ejpam-5633	223	31	nearly	nearly	ADV
ejpam-5633	223	32	(	(	PUNCT
ejpam-5633	223	33	τ1	τ1	NOUN
ejpam-5633	223	34	,	,	PUNCT
ejpam-5633	223	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	223	36	,	,	PUNCT
ejpam-5633	223	37	(	(	PUNCT
ejpam-5633	223	38	2	2	X
ejpam-5633	223	39	)	)	PUNCT
ejpam-5633	223	40	g	g	NOUN
ejpam-5633	223	41	:	:	PUNCT
ejpam-5633	223	42	(	(	PUNCT
ejpam-5633	223	43	x	x	NOUN
ejpam-5633	223	44	,	,	PUNCT
ejpam-5633	223	45	τ1	τ1	NOUN
ejpam-5633	223	46	,	,	PUNCT
ejpam-5633	223	47	τ2	τ2	NOUN
ejpam-5633	223	48	)	)	PUNCT
ejpam-5633	223	49	→	→	SYM
ejpam-5633	223	50	(	(	PUNCT
ejpam-5633	223	51	y	y	PROPN
ejpam-5633	223	52	,	,	PUNCT
ejpam-5633	223	53	σ1	σ1	PROPN
ejpam-5633	223	54	,	,	PUNCT
ejpam-5633	223	55	σ2	σ2	PROPN
ejpam-5633	223	56	)	)	PUNCT
ejpam-5633	223	57	is	be	AUX
ejpam-5633	223	58	upper	upper	ADJ
ejpam-5633	223	59	nearly	nearly	ADV
ejpam-5633	223	60	(	(	PUNCT
ejpam-5633	223	61	τ1	τ1	NOUN
ejpam-5633	223	62	,	,	PUNCT
ejpam-5633	223	63	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	223	64	,	,	PUNCT
ejpam-5633	223	65	(	(	PUNCT
ejpam-5633	223	66	3	3	X
ejpam-5633	223	67	)	)	PUNCT
ejpam-5633	223	68	f	f	NOUN
ejpam-5633	223	69	(	(	PUNCT
ejpam-5633	223	70	x	x	NOUN
ejpam-5633	223	71	)	)	PUNCT
ejpam-5633	223	72	and	and	CCONJ
ejpam-5633	223	73	g(x	g(x	NOUN
ejpam-5633	223	74	)	)	PUNCT
ejpam-5633	223	75	are	be	AUX
ejpam-5633	223	76	σ1σ2	σ1σ2	NOUN
ejpam-5633	223	77	-	-	ADJ
ejpam-5633	223	78	closed	closed	ADJ
ejpam-5633	223	79	in	in	ADP
ejpam-5633	223	80	y	y	PROPN
ejpam-5633	223	81	for	for	ADP
ejpam-5633	223	82	each	each	DET
ejpam-5633	223	83	x	x	SYM
ejpam-5633	223	84	∈	∈	PROPN
ejpam-5633	223	85	x	x	NOUN
ejpam-5633	223	86	,	,	PUNCT
ejpam-5633	223	87	and	and	CCONJ
ejpam-5633	223	88	(	(	PUNCT
ejpam-5633	223	89	4	4	X
ejpam-5633	223	90	)	)	PUNCT
ejpam-5633	223	91	a	a	DET
ejpam-5633	223	92	=	=	SYM
ejpam-5633	223	93	{	{	PUNCT
ejpam-5633	223	94	x	x	SYM
ejpam-5633	223	95	∈	∈	PROPN
ejpam-5633	223	96	x	x	INTJ
ejpam-5633	224	1	|	|	NOUN
ejpam-5633	224	2	f	f	X
ejpam-5633	224	3	(	(	PUNCT
ejpam-5633	224	4	x	x	X
ejpam-5633	224	5	)	)	PUNCT
ejpam-5633	224	6	∩g(x	∩g(x	ADJ
ejpam-5633	224	7	)	)	PUNCT
ejpam-5633	224	8	̸=	̸=	PROPN
ejpam-5633	224	9	∅	∅	NOUN
ejpam-5633	224	10	}	}	PUNCT
ejpam-5633	224	11	,	,	PUNCT
ejpam-5633	224	12	m.	m.	NOUN
ejpam-5633	224	13	thongmoon	thongmoon	NOUN
ejpam-5633	224	14	,	,	PUNCT
ejpam-5633	224	15	a.	a.	PROPN
ejpam-5633	224	16	sama	sama	PROPN
ejpam-5633	224	17	-	-	PUNCT
ejpam-5633	224	18	ae	ae	PROPN
ejpam-5633	224	19	,	,	PUNCT
ejpam-5633	224	20	c.	c.	PROPN
ejpam-5633	224	21	boonpok	boonpok	PROPN
ejpam-5633	224	22	/	/	SYM
ejpam-5633	224	23	eur	eur	PROPN
ejpam-5633	224	24	.	.	PUNCT
ejpam-5633	225	1	j.	j.	PROPN
ejpam-5633	225	2	pure	pure	PROPN
ejpam-5633	225	3	appl	appl	PROPN
ejpam-5633	225	4	.	.	PROPN
ejpam-5633	225	5	math	math	PROPN
ejpam-5633	225	6	,	,	PUNCT
ejpam-5633	225	7	18	18	NUM
ejpam-5633	225	8	(	(	PUNCT
ejpam-5633	225	9	1	1	NUM
ejpam-5633	225	10	)	)	PUNCT
ejpam-5633	225	11	(	(	PUNCT
ejpam-5633	225	12	2025	2025	NUM
ejpam-5633	225	13	)	)	PUNCT
ejpam-5633	225	14	,	,	PUNCT
ejpam-5633	225	15	5633	5633	NUM
ejpam-5633	225	16	10	10	NUM
ejpam-5633	225	17	of	of	ADP
ejpam-5633	225	18	13	13	NUM
ejpam-5633	225	19	then	then	ADV
ejpam-5633	225	20	a	a	PRON
ejpam-5633	225	21	is	be	AUX
ejpam-5633	225	22	τ1τ2	τ1τ2	NOUN
ejpam-5633	225	23	-	-	ADJ
ejpam-5633	225	24	closed	closed	ADJ
ejpam-5633	225	25	.	.	PUNCT
ejpam-5633	226	1	if	if	SCONJ
ejpam-5633	226	2	f	f	PROPN
ejpam-5633	226	3	(	(	PUNCT
ejpam-5633	226	4	x	x	NOUN
ejpam-5633	226	5	)	)	PUNCT
ejpam-5633	226	6	∩	∩	ADJ
ejpam-5633	226	7	g(x	g(x	NOUN
ejpam-5633	226	8	)	)	PUNCT
ejpam-5633	226	9	̸=	̸=	NOUN
ejpam-5633	226	10	∅	∅	NOUN
ejpam-5633	226	11	for	for	ADP
ejpam-5633	226	12	each	each	DET
ejpam-5633	226	13	point	point	NOUN
ejpam-5633	226	14	x	x	X
ejpam-5633	226	15	in	in	ADP
ejpam-5633	226	16	a	a	DET
ejpam-5633	226	17	τ1τ2	τ1τ2	ADJ
ejpam-5633	226	18	-	-	ADJ
ejpam-5633	226	19	dense	dense	ADJ
ejpam-5633	226	20	set	set	NOUN
ejpam-5633	226	21	d	d	PROPN
ejpam-5633	226	22	of	of	ADP
ejpam-5633	226	23	x	x	PROPN
ejpam-5633	226	24	,	,	PUNCT
ejpam-5633	226	25	then	then	ADV
ejpam-5633	226	26	f	f	PROPN
ejpam-5633	226	27	(	(	PUNCT
ejpam-5633	226	28	x	x	X
ejpam-5633	226	29	)	)	PUNCT
ejpam-5633	226	30	∩g(x	∩g(x	ADJ
ejpam-5633	226	31	)	)	PUNCT
ejpam-5633	226	32	̸=	̸=	NOUN
ejpam-5633	226	33	∅	∅	NOUN
ejpam-5633	226	34	for	for	ADP
ejpam-5633	226	35	each	each	DET
ejpam-5633	226	36	point	point	NOUN
ejpam-5633	226	37	x	x	X
ejpam-5633	226	38	∈	∈	NOUN
ejpam-5633	226	39	x.	x.	NOUN
ejpam-5633	226	40	proof	proof	NOUN
ejpam-5633	226	41	.	.	PUNCT
ejpam-5633	226	42	suppose	suppose	VERB
ejpam-5633	226	43	that	that	SCONJ
ejpam-5633	226	44	x	x	PROPN
ejpam-5633	226	45	̸∈	̸∈	PROPN
ejpam-5633	226	46	a.	a.	NOUN
ejpam-5633	226	47	then	then	ADV
ejpam-5633	226	48	,	,	PUNCT
ejpam-5633	226	49	f	f	PROPN
ejpam-5633	226	50	(	(	PUNCT
ejpam-5633	226	51	x	x	NOUN
ejpam-5633	226	52	)	)	PUNCT
ejpam-5633	226	53	∩	∩	ADJ
ejpam-5633	226	54	g(x	g(x	NOUN
ejpam-5633	226	55	)	)	PUNCT
ejpam-5633	226	56	=	=	PUNCT
ejpam-5633	226	57	∅.	∅.	NOUN
ejpam-5633	226	58	since	since	SCONJ
ejpam-5633	226	59	f	f	PROPN
ejpam-5633	226	60	(	(	PUNCT
ejpam-5633	226	61	x	x	NOUN
ejpam-5633	226	62	)	)	PUNCT
ejpam-5633	226	63	and	and	CCONJ
ejpam-5633	226	64	g(x	g(x	NOUN
ejpam-5633	226	65	)	)	PUNCT
ejpam-5633	226	66	are	be	AUX
ejpam-5633	226	67	σ1σ2	σ1σ2	NOUN
ejpam-5633	226	68	-	-	ADJ
ejpam-5633	226	69	closed	closed	ADJ
ejpam-5633	226	70	and	and	CCONJ
ejpam-5633	226	71	(	(	PUNCT
ejpam-5633	226	72	y	y	PROPN
ejpam-5633	226	73	,	,	PUNCT
ejpam-5633	226	74	σ1	σ1	PROPN
ejpam-5633	226	75	,	,	PUNCT
ejpam-5633	226	76	σ2	σ2	PROPN
ejpam-5633	226	77	)	)	PUNCT
ejpam-5633	226	78	is	be	AUX
ejpam-5633	226	79	n	n	PROPN
ejpam-5633	226	80	(	(	PUNCT
ejpam-5633	226	81	σ1	σ1	PROPN
ejpam-5633	226	82	,	,	PUNCT
ejpam-5633	226	83	σ2)-normal	σ2)-normal	PROPN
ejpam-5633	226	84	,	,	PUNCT
ejpam-5633	226	85	there	there	PRON
ejpam-5633	226	86	exist	exist	VERB
ejpam-5633	226	87	σ1σ2	σ1σ2	NOUN
ejpam-5633	226	88	-	-	ADJ
ejpam-5633	226	89	open	open	ADJ
ejpam-5633	226	90	sets	set	NOUN
ejpam-5633	226	91	v	v	ADP
ejpam-5633	226	92	and	and	CCONJ
ejpam-5633	226	93	w	w	NOUN
ejpam-5633	226	94	in	in	ADP
ejpam-5633	226	95	y	y	PROPN
ejpam-5633	226	96	having	have	VERB
ejpam-5633	226	97	n	n	PROPN
ejpam-5633	226	98	(	(	PUNCT
ejpam-5633	226	99	σ1	σ1	PROPN
ejpam-5633	226	100	,	,	PUNCT
ejpam-5633	226	101	σ2)-closed	σ2)-close	VERB
ejpam-5633	226	102	complements	complement	NOUN
ejpam-5633	226	103	such	such	ADJ
ejpam-5633	226	104	that	that	SCONJ
ejpam-5633	226	105	f	f	PROPN
ejpam-5633	226	106	(	(	PUNCT
ejpam-5633	226	107	x	x	X
ejpam-5633	226	108	)	)	PUNCT
ejpam-5633	226	109	⊆	⊆	NUM
ejpam-5633	226	110	v	v	NOUN
ejpam-5633	226	111	,	,	PUNCT
ejpam-5633	226	112	g(x	g(x	NOUN
ejpam-5633	226	113	)	)	PUNCT
ejpam-5633	226	114	⊆	⊆	NUM
ejpam-5633	226	115	w	w	NOUN
ejpam-5633	226	116	and	and	CCONJ
ejpam-5633	226	117	v	v	NOUN
ejpam-5633	226	118	∩w	∩w	NOUN
ejpam-5633	226	119	=	=	PUNCT
ejpam-5633	226	120	∅.	∅.	NOUN
ejpam-5633	226	121	since	since	SCONJ
ejpam-5633	226	122	f	f	PROPN
ejpam-5633	226	123	is	be	AUX
ejpam-5633	226	124	upper	upper	ADJ
ejpam-5633	226	125	nearly	nearly	ADV
ejpam-5633	226	126	(	(	PUNCT
ejpam-5633	226	127	τ1	τ1	NOUN
ejpam-5633	226	128	,	,	PUNCT
ejpam-5633	226	129	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	226	130	at	at	ADP
ejpam-5633	226	131	x	x	X
ejpam-5633	226	132	,	,	PUNCT
ejpam-5633	226	133	there	there	PRON
ejpam-5633	226	134	exists	exist	VERB
ejpam-5633	226	135	a	a	DET
ejpam-5633	226	136	τ1τ2	τ1τ2	NOUN
ejpam-5633	226	137	-	-	ADJ
ejpam-5633	226	138	open	open	ADJ
ejpam-5633	226	139	set	set	ADJ
ejpam-5633	226	140	u	u	NOUN
ejpam-5633	226	141	′	′	NOUN
ejpam-5633	226	142	of	of	ADP
ejpam-5633	226	143	x	x	PUNCT
ejpam-5633	226	144	containing	contain	VERB
ejpam-5633	226	145	x	x	PUNCT
ejpam-5633	226	146	such	such	ADJ
ejpam-5633	226	147	that	that	SCONJ
ejpam-5633	226	148	f	f	PROPN
ejpam-5633	226	149	(	(	PUNCT
ejpam-5633	226	150	u	u	NOUN
ejpam-5633	226	151	′	′	NOUN
ejpam-5633	226	152	)	)	PUNCT
ejpam-5633	226	153	⊆	⊆	NUM
ejpam-5633	226	154	v	v	NOUN
ejpam-5633	226	155	.	.	PUNCT
ejpam-5633	227	1	since	since	SCONJ
ejpam-5633	227	2	g	g	PROPN
ejpam-5633	227	3	is	be	AUX
ejpam-5633	227	4	upper	upper	ADJ
ejpam-5633	227	5	nearly	nearly	ADV
ejpam-5633	227	6	(	(	PUNCT
ejpam-5633	227	7	τ1	τ1	NOUN
ejpam-5633	227	8	,	,	PUNCT
ejpam-5633	227	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	227	10	at	at	ADP
ejpam-5633	227	11	x	x	X
ejpam-5633	227	12	,	,	PUNCT
ejpam-5633	227	13	there	there	PRON
ejpam-5633	227	14	exists	exist	VERB
ejpam-5633	227	15	a	a	DET
ejpam-5633	227	16	τ1τ2	τ1τ2	NOUN
ejpam-5633	227	17	-	-	ADJ
ejpam-5633	227	18	open	open	ADJ
ejpam-5633	227	19	set	set	NOUN
ejpam-5633	227	20	u	u	PROPN
ejpam-5633	227	21	′′	′′	PROPN
ejpam-5633	227	22	of	of	ADP
ejpam-5633	227	23	x	x	SYM
ejpam-5633	227	24	containing	contain	VERB
ejpam-5633	227	25	x	x	PUNCT
ejpam-5633	227	26	such	such	ADJ
ejpam-5633	227	27	that	that	SCONJ
ejpam-5633	227	28	f	f	PROPN
ejpam-5633	227	29	(	(	PUNCT
ejpam-5633	227	30	u	u	PROPN
ejpam-5633	227	31	′′	′′	PROPN
ejpam-5633	227	32	)	)	PUNCT
ejpam-5633	227	33	⊆	⊆	NUM
ejpam-5633	227	34	w	w	NOUN
ejpam-5633	227	35	.	.	PUNCT
ejpam-5633	228	1	now	now	ADV
ejpam-5633	228	2	set	set	VERB
ejpam-5633	228	3	u	u	NOUN
ejpam-5633	228	4	=	=	PUNCT
ejpam-5633	228	5	u	u	NOUN
ejpam-5633	228	6	′	′	NOUN
ejpam-5633	228	7	∩u	∩u	NOUN
ejpam-5633	229	1	′′	′′	PROPN
ejpam-5633	229	2	,	,	PUNCT
ejpam-5633	229	3	then	then	ADV
ejpam-5633	229	4	u	u	NOUN
ejpam-5633	229	5	is	be	AUX
ejpam-5633	229	6	τ1τ2	τ1τ2	NOUN
ejpam-5633	229	7	-	-	ADJ
ejpam-5633	229	8	open	open	ADJ
ejpam-5633	229	9	in	in	ADP
ejpam-5633	229	10	x	x	X
ejpam-5633	229	11	and	and	CCONJ
ejpam-5633	229	12	u	u	NOUN
ejpam-5633	229	13	∩a	∩a	NOUN
ejpam-5633	229	14	=	=	PUNCT
ejpam-5633	229	15	∅.	∅.	VERB
ejpam-5633	229	16	thus	thus	ADV
ejpam-5633	229	17	,	,	PUNCT
ejpam-5633	229	18	x	x	PROPN
ejpam-5633	229	19	̸∈	̸∈	PROPN
ejpam-5633	229	20	τ1τ2	τ1τ2	PROPN
ejpam-5633	229	21	-	-	NUM
ejpam-5633	229	22	cl(a	cl(a	NUM
ejpam-5633	229	23	)	)	PUNCT
ejpam-5633	229	24	and	and	CCONJ
ejpam-5633	229	25	hence	hence	ADV
ejpam-5633	229	26	a	a	DET
ejpam-5633	229	27	=	=	PUNCT
ejpam-5633	229	28	τ1τ2	τ1τ2	NOUN
ejpam-5633	229	29	-	-	NUM
ejpam-5633	229	30	cl(a	cl(a	NUM
ejpam-5633	229	31	)	)	PUNCT
ejpam-5633	229	32	.	.	PUNCT
ejpam-5633	230	1	this	this	PRON
ejpam-5633	230	2	shows	show	VERB
ejpam-5633	230	3	that	that	SCONJ
ejpam-5633	230	4	a	a	PRON
ejpam-5633	230	5	is	be	AUX
ejpam-5633	230	6	τ1τ2	τ1τ2	NOUN
ejpam-5633	230	7	-	-	ADJ
ejpam-5633	230	8	closed	closed	ADJ
ejpam-5633	230	9	.	.	PUNCT
ejpam-5633	231	1	on	on	ADP
ejpam-5633	231	2	the	the	DET
ejpam-5633	231	3	other	other	ADJ
ejpam-5633	231	4	hand	hand	NOUN
ejpam-5633	231	5	,	,	PUNCT
ejpam-5633	231	6	if	if	SCONJ
ejpam-5633	231	7	f	f	PROPN
ejpam-5633	231	8	(	(	PUNCT
ejpam-5633	231	9	x	x	X
ejpam-5633	231	10	)	)	PUNCT
ejpam-5633	231	11	∩g(x	∩g(x	ADJ
ejpam-5633	231	12	)	)	PUNCT
ejpam-5633	231	13	̸=	̸=	NOUN
ejpam-5633	231	14	∅	∅	NOUN
ejpam-5633	231	15	on	on	ADP
ejpam-5633	231	16	a	a	DET
ejpam-5633	231	17	τ1τ2	τ1τ2	ADJ
ejpam-5633	231	18	-	-	ADJ
ejpam-5633	231	19	dense	dense	ADJ
ejpam-5633	231	20	set	set	NOUN
ejpam-5633	231	21	d	d	PROPN
ejpam-5633	231	22	of	of	ADP
ejpam-5633	231	23	x	x	PRON
ejpam-5633	231	24	,	,	PUNCT
ejpam-5633	231	25	then	then	ADV
ejpam-5633	231	26	we	we	PRON
ejpam-5633	231	27	have	have	VERB
ejpam-5633	231	28	x	x	NOUN
ejpam-5633	231	29	=	=	SYM
ejpam-5633	231	30	τ1τ2	τ1τ2	NOUN
ejpam-5633	231	31	-	-	PUNCT
ejpam-5633	231	32	cl(d	cl(d	NUM
ejpam-5633	231	33	)	)	PUNCT
ejpam-5633	231	34	⊆	⊆	NUM
ejpam-5633	231	35	τ1τ2	τ1τ2	NOUN
ejpam-5633	231	36	-	-	NUM
ejpam-5633	231	37	cl(a	cl(a	NUM
ejpam-5633	231	38	)	)	PUNCT
ejpam-5633	231	39	=	=	SYM
ejpam-5633	231	40	a.	a.	NOUN
ejpam-5633	231	41	thus	thus	ADV
ejpam-5633	231	42	,	,	PUNCT
ejpam-5633	231	43	f	f	PROPN
ejpam-5633	231	44	(	(	PUNCT
ejpam-5633	231	45	x	x	X
ejpam-5633	231	46	)	)	PUNCT
ejpam-5633	231	47	∩g(x	∩g(x	ADJ
ejpam-5633	231	48	)	)	PUNCT
ejpam-5633	231	49	̸=	̸=	NOUN
ejpam-5633	231	50	∅	∅	NOUN
ejpam-5633	231	51	for	for	ADP
ejpam-5633	231	52	each	each	DET
ejpam-5633	231	53	x	x	SYM
ejpam-5633	231	54	∈	∈	PROPN
ejpam-5633	231	55	x.	x.	NOUN
ejpam-5633	231	56	acknowledgements	acknowledgement	VERB
ejpam-5633	231	57	this	this	DET
ejpam-5633	231	58	research	research	NOUN
ejpam-5633	231	59	project	project	NOUN
ejpam-5633	231	60	was	be	AUX
ejpam-5633	231	61	financially	financially	ADV
ejpam-5633	231	62	supported	support	VERB
ejpam-5633	231	63	by	by	ADP
ejpam-5633	231	64	mahasarakham	mahasarakham	PROPN
ejpam-5633	231	65	university	university	PROPN
ejpam-5633	231	66	.	.	PUNCT
ejpam-5633	232	1	references	reference	NOUN
ejpam-5633	232	2	[	[	X
ejpam-5633	232	3	1	1	NUM
ejpam-5633	232	4	]	]	PUNCT
ejpam-5633	232	5	c.	c.	PROPN
ejpam-5633	232	6	boonpok	boonpok	PROPN
ejpam-5633	232	7	.	.	PUNCT
ejpam-5633	233	1	almost	almost	ADV
ejpam-5633	233	2	(	(	PUNCT
ejpam-5633	233	3	g	g	NOUN
ejpam-5633	233	4	,	,	PUNCT
ejpam-5633	233	5	m)-continuous	m)-continuous	ADJ
ejpam-5633	233	6	functions	function	NOUN
ejpam-5633	233	7	.	.	PUNCT
ejpam-5633	234	1	international	international	ADJ
ejpam-5633	234	2	journal	journal	PROPN
ejpam-5633	234	3	of	of	ADP
ejpam-5633	234	4	mathematical	mathematical	ADJ
ejpam-5633	234	5	analysis	analysis	NOUN
ejpam-5633	234	6	,	,	PUNCT
ejpam-5633	234	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5633	234	8	,	,	PUNCT
ejpam-5633	234	9	2010	2010	NUM
ejpam-5633	234	10	.	.	PUNCT
ejpam-5633	235	1	[	[	X
ejpam-5633	235	2	2	2	NUM
ejpam-5633	235	3	]	]	PUNCT
ejpam-5633	235	4	c.	c.	PROPN
ejpam-5633	235	5	boonpok	boonpok	PROPN
ejpam-5633	235	6	.	.	PUNCT
ejpam-5633	236	1	m	m	VERB
ejpam-5633	236	2	-continuous	-continuous	ADJ
ejpam-5633	236	3	functions	function	NOUN
ejpam-5633	236	4	in	in	ADP
ejpam-5633	236	5	biminimal	biminimal	NOUN
ejpam-5633	236	6	structure	structure	NOUN
ejpam-5633	236	7	spaces	space	NOUN
ejpam-5633	236	8	.	.	PUNCT
ejpam-5633	237	1	far	far	PROPN
ejpam-5633	237	2	east	east	PROPN
ejpam-5633	237	3	journal	journal	PROPN
ejpam-5633	237	4	of	of	ADP
ejpam-5633	237	5	mathematical	mathematical	ADJ
ejpam-5633	237	6	sciences	science	NOUN
ejpam-5633	237	7	,	,	PUNCT
ejpam-5633	237	8	43(1):41–58	43(1):41–58	NUM
ejpam-5633	237	9	,	,	PUNCT
ejpam-5633	237	10	2010	2010	NUM
ejpam-5633	237	11	.	.	PUNCT
ejpam-5633	238	1	[	[	X
ejpam-5633	238	2	3	3	X
ejpam-5633	238	3	]	]	PUNCT
ejpam-5633	238	4	c.	c.	PROPN
ejpam-5633	238	5	boonpok	boonpok	PROPN
ejpam-5633	238	6	.	.	PUNCT
ejpam-5633	239	1	on	on	ADP
ejpam-5633	239	2	continuous	continuous	ADJ
ejpam-5633	239	3	multifunctions	multifunction	NOUN
ejpam-5633	239	4	in	in	ADP
ejpam-5633	239	5	ideal	ideal	ADJ
ejpam-5633	239	6	topological	topological	ADJ
ejpam-5633	239	7	spaces	space	NOUN
ejpam-5633	239	8	.	.	PUNCT
ejpam-5633	240	1	lobachevskii	lobachevskii	PROPN
ejpam-5633	240	2	journal	journal	PROPN
ejpam-5633	240	3	of	of	ADP
ejpam-5633	240	4	mathematics	mathematic	NOUN
ejpam-5633	240	5	,	,	PUNCT
ejpam-5633	240	6	40(1):24–35	40(1):24–35	NUM
ejpam-5633	240	7	,	,	PUNCT
ejpam-5633	240	8	2019	2019	NUM
ejpam-5633	240	9	.	.	PUNCT
ejpam-5633	241	1	[	[	X
ejpam-5633	241	2	4	4	NUM
ejpam-5633	241	3	]	]	PUNCT
ejpam-5633	241	4	c.	c.	PROPN
ejpam-5633	241	5	boonpok	boonpok	PROPN
ejpam-5633	241	6	.	.	PUNCT
ejpam-5633	242	1	on	on	ADP
ejpam-5633	242	2	characterizations	characterization	NOUN
ejpam-5633	242	3	of	of	ADP
ejpam-5633	242	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5633	242	5	ideal	ideal	ADJ
ejpam-5633	242	6	topological	topological	ADJ
ejpam-5633	242	7	spaces	space	NOUN
ejpam-5633	242	8	.	.	PUNCT
ejpam-5633	243	1	journal	journal	NOUN
ejpam-5633	243	2	of	of	ADP
ejpam-5633	243	3	mathematics	mathematic	NOUN
ejpam-5633	243	4	,	,	PUNCT
ejpam-5633	243	5	2020:9387601	2020:9387601	NUM
ejpam-5633	243	6	,	,	PUNCT
ejpam-5633	243	7	2020	2020	NUM
ejpam-5633	243	8	.	.	PUNCT
ejpam-5633	244	1	[	[	X
ejpam-5633	244	2	5	5	X
ejpam-5633	244	3	]	]	PUNCT
ejpam-5633	244	4	c.	c.	PROPN
ejpam-5633	244	5	boonpok	boonpok	PROPN
ejpam-5633	244	6	.	.	PUNCT
ejpam-5633	245	1	(	(	PUNCT
ejpam-5633	245	2	τ1	τ1	NOUN
ejpam-5633	245	3	,	,	PUNCT
ejpam-5633	245	4	τ2)δ	τ2)δ	ADJ
ejpam-5633	245	5	-	-	PUNCT
ejpam-5633	245	6	semicontinuous	semicontinuous	ADJ
ejpam-5633	245	7	multifunctions	multifunction	NOUN
ejpam-5633	245	8	.	.	PUNCT
ejpam-5633	246	1	heliyon	heliyon	NOUN
ejpam-5633	246	2	,	,	PUNCT
ejpam-5633	246	3	6	6	NUM
ejpam-5633	246	4	:	:	SYM
ejpam-5633	246	5	e05367	e05367	PROPN
ejpam-5633	246	6	,	,	PUNCT
ejpam-5633	246	7	2020	2020	NUM
ejpam-5633	246	8	.	.	PUNCT
ejpam-5633	247	1	[	[	X
ejpam-5633	247	2	6	6	NUM
ejpam-5633	247	3	]	]	PUNCT
ejpam-5633	247	4	c.	c.	PROPN
ejpam-5633	247	5	boonpok	boonpok	PROPN
ejpam-5633	247	6	.	.	PUNCT
ejpam-5633	248	1	weak	weak	ADJ
ejpam-5633	248	2	quasi	quasi	ADJ
ejpam-5633	248	3	continuity	continuity	NOUN
ejpam-5633	248	4	for	for	ADP
ejpam-5633	248	5	multifunctions	multifunction	NOUN
ejpam-5633	248	6	in	in	ADP
ejpam-5633	248	7	ideal	ideal	ADJ
ejpam-5633	248	8	topological	topological	ADJ
ejpam-5633	248	9	spaces	space	NOUN
ejpam-5633	248	10	.	.	PUNCT
ejpam-5633	249	1	advances	advance	NOUN
ejpam-5633	249	2	in	in	ADP
ejpam-5633	249	3	mathematics	mathematic	NOUN
ejpam-5633	249	4	:	:	PUNCT
ejpam-5633	249	5	scientific	scientific	ADJ
ejpam-5633	249	6	journal	journal	NOUN
ejpam-5633	249	7	,	,	PUNCT
ejpam-5633	249	8	9(1):339–355	9(1):339–355	NUM
ejpam-5633	249	9	,	,	PUNCT
ejpam-5633	249	10	2020	2020	NUM
ejpam-5633	249	11	.	.	PUNCT
ejpam-5633	250	1	[	[	X
ejpam-5633	250	2	7	7	X
ejpam-5633	250	3	]	]	X
ejpam-5633	250	4	c.	c.	PROPN
ejpam-5633	250	5	boonpok	boonpok	PROPN
ejpam-5633	250	6	.	.	PUNCT
ejpam-5633	251	1	upper	upper	ADJ
ejpam-5633	251	2	and	and	CCONJ
ejpam-5633	251	3	lower	low	ADJ
ejpam-5633	251	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5633	251	5	.	.	PUNCT
ejpam-5633	251	6	heliyon	heliyon	NOUN
ejpam-5633	251	7	,	,	PUNCT
ejpam-5633	251	8	7	7	NUM
ejpam-5633	251	9	:	:	PUNCT
ejpam-5633	251	10	e05986	e05986	PROPN
ejpam-5633	251	11	,	,	PUNCT
ejpam-5633	251	12	2021	2021	NUM
ejpam-5633	251	13	.	.	PUNCT
ejpam-5633	252	1	[	[	X
ejpam-5633	252	2	8	8	NUM
ejpam-5633	252	3	]	]	X
ejpam-5633	252	4	c.	c.	PROPN
ejpam-5633	252	5	boonpok	boonpok	PROPN
ejpam-5633	252	6	.	.	PUNCT
ejpam-5633	253	1	on	on	ADP
ejpam-5633	253	2	some	some	DET
ejpam-5633	253	3	closed	closed	ADJ
ejpam-5633	253	4	sets	set	NOUN
ejpam-5633	253	5	and	and	CCONJ
ejpam-5633	253	6	low	low	ADJ
ejpam-5633	253	7	separation	separation	NOUN
ejpam-5633	253	8	axioms	axiom	NOUN
ejpam-5633	253	9	via	via	ADP
ejpam-5633	253	10	topological	topological	ADJ
ejpam-5633	253	11	ideals	ideal	NOUN
ejpam-5633	253	12	.	.	PUNCT
ejpam-5633	254	1	european	european	ADJ
ejpam-5633	254	2	journal	journal	PROPN
ejpam-5633	254	3	of	of	ADP
ejpam-5633	254	4	pure	pure	ADJ
ejpam-5633	254	5	and	and	CCONJ
ejpam-5633	254	6	applied	applied	ADJ
ejpam-5633	254	7	mathematics	mathematic	NOUN
ejpam-5633	254	8	,	,	PUNCT
ejpam-5633	254	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5633	254	10	,	,	PUNCT
ejpam-5633	254	11	2022	2022	NUM
ejpam-5633	254	12	.	.	PUNCT
ejpam-5633	255	1	[	[	X
ejpam-5633	255	2	9	9	NUM
ejpam-5633	255	3	]	]	PUNCT
ejpam-5633	255	4	c.	c.	PROPN
ejpam-5633	255	5	boonpok	boonpok	PROPN
ejpam-5633	255	6	.	.	PUNCT
ejpam-5633	256	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-5633	256	2	continuity	continuity	NOUN
ejpam-5633	256	3	for	for	ADP
ejpam-5633	256	4	multifunctions	multifunction	NOUN
ejpam-5633	256	5	.	.	PUNCT
ejpam-5633	257	1	wseas	wseas	PROPN
ejpam-5633	257	2	transactions	transaction	NOUN
ejpam-5633	257	3	on	on	ADP
ejpam-5633	257	4	mathematics	mathematic	NOUN
ejpam-5633	257	5	,	,	PUNCT
ejpam-5633	257	6	21:245–251	21:245–251	NUM
ejpam-5633	257	7	,	,	PUNCT
ejpam-5633	257	8	2022	2022	NUM
ejpam-5633	257	9	.	.	PUNCT
ejpam-5633	258	1	[	[	X
ejpam-5633	258	2	10	10	NUM
ejpam-5633	258	3	]	]	X
ejpam-5633	258	4	c.	c.	PROPN
ejpam-5633	258	5	boonpok	boonpok	PROPN
ejpam-5633	258	6	.	.	PUNCT
ejpam-5633	259	1	on	on	ADP
ejpam-5633	259	2	some	some	DET
ejpam-5633	259	3	spaces	space	NOUN
ejpam-5633	259	4	via	via	ADP
ejpam-5633	259	5	topological	topological	ADJ
ejpam-5633	259	6	ideals	ideal	NOUN
ejpam-5633	259	7	.	.	PUNCT
ejpam-5633	260	1	open	open	ADJ
ejpam-5633	260	2	mathematics	mathematic	NOUN
ejpam-5633	260	3	,	,	PUNCT
ejpam-5633	260	4	21:20230118	21:20230118	NUM
ejpam-5633	260	5	,	,	PUNCT
ejpam-5633	260	6	2023	2023	NUM
ejpam-5633	260	7	.	.	PUNCT
ejpam-5633	261	1	[	[	X
ejpam-5633	261	2	11	11	NUM
ejpam-5633	261	3	]	]	PUNCT
ejpam-5633	261	4	c.	c.	PROPN
ejpam-5633	261	5	boonpok	boonpok	PROPN
ejpam-5633	261	6	.	.	PUNCT
ejpam-5633	262	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5633	262	2	.	.	PUNCT
ejpam-5633	263	1	mathematica	mathematica	PROPN
ejpam-5633	263	2	,	,	PUNCT
ejpam-5633	263	3	65(1):31–42	65(1):31–42	NUM
ejpam-5633	263	4	,	,	PUNCT
ejpam-5633	263	5	2023	2023	NUM
ejpam-5633	263	6	.	.	PUNCT
ejpam-5633	264	1	[	[	X
ejpam-5633	264	2	12	12	NUM
ejpam-5633	264	3	]	]	X
ejpam-5633	264	4	c.	c.	PROPN
ejpam-5633	264	5	boonpok	boonpok	PROPN
ejpam-5633	264	6	and	and	CCONJ
ejpam-5633	264	7	j.	j.	PROPN
ejpam-5633	264	8	khampakdee	khampakdee	PROPN
ejpam-5633	264	9	.	.	PUNCT
ejpam-5633	265	1	(	(	PUNCT
ejpam-5633	265	2	λ	λ	NOUN
ejpam-5633	265	3	,	,	PUNCT
ejpam-5633	265	4	sp)-open	sp)-open	ADJ
ejpam-5633	265	5	sets	set	NOUN
ejpam-5633	265	6	in	in	ADP
ejpam-5633	265	7	topological	topological	ADJ
ejpam-5633	265	8	spaces	space	NOUN
ejpam-5633	265	9	.	.	PUNCT
ejpam-5633	266	1	european	european	ADJ
ejpam-5633	266	2	journal	journal	PROPN
ejpam-5633	266	3	of	of	ADP
ejpam-5633	266	4	pure	pure	ADJ
ejpam-5633	266	5	and	and	CCONJ
ejpam-5633	266	6	applied	applied	ADJ
ejpam-5633	266	7	mathematics	mathematic	NOUN
ejpam-5633	266	8	,	,	PUNCT
ejpam-5633	266	9	15(2):572–588	15(2):572–588	NUM
ejpam-5633	266	10	,	,	PUNCT
ejpam-5633	266	11	2022	2022	NUM
ejpam-5633	266	12	.	.	PUNCT
ejpam-5633	267	1	[	[	X
ejpam-5633	267	2	13	13	NUM
ejpam-5633	267	3	]	]	PUNCT
ejpam-5633	267	4	c.	c.	PROPN
ejpam-5633	267	5	boonpok	boonpok	PROPN
ejpam-5633	267	6	and	and	CCONJ
ejpam-5633	267	7	j.	j.	PROPN
ejpam-5633	267	8	khampakdee	khampakdee	PROPN
ejpam-5633	267	9	.	.	PUNCT
ejpam-5633	268	1	on	on	ADP
ejpam-5633	268	2	almost	almost	ADV
ejpam-5633	268	3	α(λ	α(λ	PROPN
ejpam-5633	268	4	,	,	PUNCT
ejpam-5633	268	5	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	268	6	multifunctions	multifunction	NOUN
ejpam-5633	268	7	.	.	PUNCT
ejpam-5633	269	1	european	european	PROPN
ejpam-5633	269	2	journal	journal	PROPN
ejpam-5633	269	3	of	of	ADP
ejpam-5633	269	4	pure	pure	ADJ
ejpam-5633	269	5	and	and	CCONJ
ejpam-5633	269	6	applied	applied	ADJ
ejpam-5633	269	7	mathematics	mathematic	NOUN
ejpam-5633	269	8	,	,	PUNCT
ejpam-5633	269	9	15(2):626–634	15(2):626–634	PROPN
ejpam-5633	269	10	,	,	PUNCT
ejpam-5633	269	11	2022	2022	NUM
ejpam-5633	269	12	.	.	PUNCT
ejpam-5633	270	1	m.	m.	NOUN
ejpam-5633	270	2	thongmoon	thongmoon	PROPN
ejpam-5633	270	3	,	,	PUNCT
ejpam-5633	270	4	a.	a.	PROPN
ejpam-5633	270	5	sama	sama	PROPN
ejpam-5633	270	6	-	-	PUNCT
ejpam-5633	270	7	ae	ae	PROPN
ejpam-5633	270	8	,	,	PUNCT
ejpam-5633	270	9	c.	c.	PROPN
ejpam-5633	270	10	boonpok	boonpok	PROPN
ejpam-5633	270	11	/	/	SYM
ejpam-5633	270	12	eur	eur	PROPN
ejpam-5633	270	13	.	.	PUNCT
ejpam-5633	271	1	j.	j.	PROPN
ejpam-5633	271	2	pure	pure	PROPN
ejpam-5633	271	3	appl	appl	PROPN
ejpam-5633	271	4	.	.	PROPN
ejpam-5633	271	5	math	math	PROPN
ejpam-5633	271	6	,	,	PUNCT
ejpam-5633	271	7	18	18	NUM
ejpam-5633	271	8	(	(	PUNCT
ejpam-5633	271	9	1	1	NUM
ejpam-5633	271	10	)	)	PUNCT
ejpam-5633	271	11	(	(	PUNCT
ejpam-5633	271	12	2025	2025	NUM
ejpam-5633	271	13	)	)	PUNCT
ejpam-5633	271	14	,	,	PUNCT
ejpam-5633	271	15	5633	5633	NUM
ejpam-5633	271	16	11	11	NUM
ejpam-5633	271	17	of	of	ADP
ejpam-5633	271	18	13	13	NUM
ejpam-5633	271	19	[	[	SYM
ejpam-5633	271	20	14	14	NUM
ejpam-5633	271	21	]	]	PUNCT
ejpam-5633	271	22	c.	c.	PROPN
ejpam-5633	271	23	boonpok	boonpok	PROPN
ejpam-5633	271	24	and	and	CCONJ
ejpam-5633	271	25	j.	j.	PROPN
ejpam-5633	271	26	khampakdee	khampakdee	PROPN
ejpam-5633	271	27	.	.	PUNCT
ejpam-5633	272	1	slight	slight	PROPN
ejpam-5633	272	2	(	(	PUNCT
ejpam-5633	272	3	λ	λ	NOUN
ejpam-5633	272	4	,	,	PUNCT
ejpam-5633	272	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5633	272	6	and	and	CCONJ
ejpam-5633	272	7	λsp	λsp	NOUN
ejpam-5633	272	8	-	-	PUNCT
ejpam-5633	272	9	extremally	extremally	ADV
ejpam-5633	272	10	disconnectedness	disconnectedness	NOUN
ejpam-5633	272	11	.	.	PUNCT
ejpam-5633	273	1	european	european	ADJ
ejpam-5633	273	2	journal	journal	PROPN
ejpam-5633	273	3	of	of	ADP
ejpam-5633	273	4	pure	pure	ADJ
ejpam-5633	273	5	and	and	CCONJ
ejpam-5633	273	6	applied	applied	ADJ
ejpam-5633	273	7	mathematics	mathematic	NOUN
ejpam-5633	273	8	,	,	PUNCT
ejpam-5633	273	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-5633	273	10	,	,	PUNCT
ejpam-5633	273	11	2022	2022	NUM
ejpam-5633	273	12	.	.	PUNCT
ejpam-5633	274	1	[	[	X
ejpam-5633	274	2	15	15	NUM
ejpam-5633	274	3	]	]	X
ejpam-5633	274	4	c.	c.	PROPN
ejpam-5633	274	5	boonpok	boonpok	PROPN
ejpam-5633	274	6	and	and	CCONJ
ejpam-5633	274	7	j.	j.	PROPN
ejpam-5633	274	8	khampakdee	khampakdee	PROPN
ejpam-5633	274	9	.	.	PUNCT
ejpam-5633	275	1	upper	upper	ADJ
ejpam-5633	275	2	and	and	CCONJ
ejpam-5633	275	3	lower	low	ADJ
ejpam-5633	275	4	weak	weak	ADJ
ejpam-5633	275	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-5633	275	6	.	.	PUNCT
ejpam-5633	276	1	european	european	PROPN
ejpam-5633	276	2	journal	journal	PROPN
ejpam-5633	276	3	of	of	ADP
ejpam-5633	276	4	pure	pure	ADJ
ejpam-5633	276	5	and	and	CCONJ
ejpam-5633	276	6	applied	applied	ADJ
ejpam-5633	276	7	mathematics	mathematic	NOUN
ejpam-5633	276	8	,	,	PUNCT
ejpam-5633	276	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-5633	276	10	,	,	PUNCT
ejpam-5633	276	11	2023	2023	NUM
ejpam-5633	276	12	.	.	PUNCT
ejpam-5633	277	1	[	[	X
ejpam-5633	277	2	16	16	NUM
ejpam-5633	277	3	]	]	X
ejpam-5633	277	4	c.	c.	PROPN
ejpam-5633	277	5	boonpok	boonpok	PROPN
ejpam-5633	277	6	and	and	CCONJ
ejpam-5633	277	7	j.	j.	PROPN
ejpam-5633	277	8	khampakdee	khampakdee	PROPN
ejpam-5633	277	9	.	.	PUNCT
ejpam-5633	278	1	almost	almost	ADV
ejpam-5633	278	2	strong	strong	ADJ
ejpam-5633	278	3	θ(λ	θ(λ	PROPN
ejpam-5633	278	4	,	,	PUNCT
ejpam-5633	278	5	p)-continuity	p)-continuity	NOUN
ejpam-5633	278	6	for	for	ADP
ejpam-5633	278	7	functions	function	NOUN
ejpam-5633	278	8	.	.	PUNCT
ejpam-5633	279	1	european	european	ADJ
ejpam-5633	279	2	journal	journal	PROPN
ejpam-5633	279	3	of	of	ADP
ejpam-5633	279	4	pure	pure	ADJ
ejpam-5633	279	5	and	and	CCONJ
ejpam-5633	279	6	applied	applied	ADJ
ejpam-5633	279	7	mathematics	mathematic	NOUN
ejpam-5633	279	8	,	,	PUNCT
ejpam-5633	279	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5633	279	10	,	,	PUNCT
ejpam-5633	279	11	2024	2024	NUM
ejpam-5633	279	12	.	.	PUNCT
ejpam-5633	280	1	[	[	X
ejpam-5633	280	2	17	17	NUM
ejpam-5633	280	3	]	]	X
ejpam-5633	280	4	c.	c.	PROPN
ejpam-5633	280	5	boonpok	boonpok	PROPN
ejpam-5633	280	6	and	and	CCONJ
ejpam-5633	280	7	j.	j.	PROPN
ejpam-5633	280	8	khampakdee	khampakdee	PROPN
ejpam-5633	280	9	.	.	PUNCT
ejpam-5633	281	1	upper	upper	ADJ
ejpam-5633	281	2	and	and	CCONJ
ejpam-5633	281	3	lower	low	ADJ
ejpam-5633	281	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5633	281	5	.	.	PUNCT
ejpam-5633	281	6	european	european	PROPN
ejpam-5633	281	7	journal	journal	PROPN
ejpam-5633	281	8	of	of	ADP
ejpam-5633	281	9	pure	pure	ADJ
ejpam-5633	281	10	and	and	CCONJ
ejpam-5633	281	11	applied	applied	ADJ
ejpam-5633	281	12	mathematics	mathematic	NOUN
ejpam-5633	281	13	,	,	PUNCT
ejpam-5633	281	14	17(1):201–211	17(1):201–211	NUM
ejpam-5633	281	15	,	,	PUNCT
ejpam-5633	281	16	2024	2024	NUM
ejpam-5633	281	17	.	.	PUNCT
ejpam-5633	282	1	[	[	X
ejpam-5633	282	2	18	18	NUM
ejpam-5633	282	3	]	]	PUNCT
ejpam-5633	282	4	c.	c.	PROPN
ejpam-5633	282	5	boonpok	boonpok	PROPN
ejpam-5633	282	6	and	and	CCONJ
ejpam-5633	282	7	c.	c.	PROPN
ejpam-5633	282	8	klanarong	klanarong	PROPN
ejpam-5633	282	9	.	.	PUNCT
ejpam-5633	283	1	on	on	ADP
ejpam-5633	283	2	weakly	weakly	ADJ
ejpam-5633	283	3	(	(	PUNCT
ejpam-5633	283	4	τ1	τ1	NOUN
ejpam-5633	283	5	,	,	PUNCT
ejpam-5633	283	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	283	7	functions	function	NOUN
ejpam-5633	283	8	.	.	PUNCT
ejpam-5633	284	1	european	european	ADJ
ejpam-5633	284	2	journal	journal	PROPN
ejpam-5633	284	3	of	of	ADP
ejpam-5633	284	4	pure	pure	ADJ
ejpam-5633	284	5	and	and	CCONJ
ejpam-5633	284	6	applied	applied	ADJ
ejpam-5633	284	7	mathematics	mathematic	NOUN
ejpam-5633	284	8	,	,	PUNCT
ejpam-5633	284	9	17(1):416–425	17(1):416–425	NUM
ejpam-5633	284	10	,	,	PUNCT
ejpam-5633	284	11	2024	2024	NUM
ejpam-5633	284	12	.	.	PUNCT
ejpam-5633	285	1	[	[	X
ejpam-5633	285	2	19	19	NUM
ejpam-5633	285	3	]	]	X
ejpam-5633	285	4	c.	c.	PROPN
ejpam-5633	285	5	boonpok	boonpok	PROPN
ejpam-5633	285	6	and	and	CCONJ
ejpam-5633	285	7	p.	p.	NOUN
ejpam-5633	285	8	pue	pue	NOUN
ejpam-5633	285	9	-	-	PUNCT
ejpam-5633	285	10	on	on	ADP
ejpam-5633	285	11	.	.	PUNCT
ejpam-5633	286	1	continuity	continuity	NOUN
ejpam-5633	286	2	for	for	ADP
ejpam-5633	286	3	multifunctions	multifunction	NOUN
ejpam-5633	286	4	in	in	ADP
ejpam-5633	286	5	ideal	ideal	ADJ
ejpam-5633	286	6	topological	topological	ADJ
ejpam-5633	286	7	spaces	space	NOUN
ejpam-5633	286	8	.	.	PUNCT
ejpam-5633	287	1	wseas	wseas	VERB
ejpam-5633	287	2	transactions	transaction	NOUN
ejpam-5633	287	3	on	on	ADP
ejpam-5633	287	4	mathematics	mathematic	NOUN
ejpam-5633	287	5	,	,	PUNCT
ejpam-5633	287	6	19:624–631	19:624–631	NUM
ejpam-5633	287	7	,	,	PUNCT
ejpam-5633	287	8	2020	2020	NUM
ejpam-5633	287	9	.	.	PUNCT
ejpam-5633	288	1	[	[	X
ejpam-5633	288	2	20	20	NUM
ejpam-5633	288	3	]	]	PUNCT
ejpam-5633	288	4	c.	c.	PROPN
ejpam-5633	288	5	boonpok	boonpok	PROPN
ejpam-5633	288	6	and	and	CCONJ
ejpam-5633	288	7	p.	p.	NOUN
ejpam-5633	288	8	pue	pue	NOUN
ejpam-5633	288	9	-	-	PUNCT
ejpam-5633	288	10	on	on	ADP
ejpam-5633	288	11	.	.	PUNCT
ejpam-5633	289	1	upper	upper	ADJ
ejpam-5633	289	2	and	and	CCONJ
ejpam-5633	289	3	lower	low	ADJ
ejpam-5633	289	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5633	289	5	multifunctions	multifunction	NOUN
ejpam-5633	289	6	.	.	PUNCT
ejpam-5633	290	1	european	european	ADJ
ejpam-5633	290	2	journal	journal	PROPN
ejpam-5633	290	3	of	of	ADP
ejpam-5633	290	4	pure	pure	ADJ
ejpam-5633	290	5	and	and	CCONJ
ejpam-5633	290	6	applied	applied	ADJ
ejpam-5633	290	7	mathematics	mathematic	NOUN
ejpam-5633	290	8	,	,	PUNCT
ejpam-5633	290	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-5633	290	10	,	,	PUNCT
ejpam-5633	290	11	2023	2023	NUM
ejpam-5633	290	12	.	.	PUNCT
ejpam-5633	291	1	[	[	X
ejpam-5633	291	2	21	21	NUM
ejpam-5633	291	3	]	]	X
ejpam-5633	291	4	c.	c.	PROPN
ejpam-5633	291	5	boonpok	boonpok	PROPN
ejpam-5633	291	6	and	and	CCONJ
ejpam-5633	291	7	p.	p.	NOUN
ejpam-5633	291	8	pue	pue	NOUN
ejpam-5633	291	9	-	-	PUNCT
ejpam-5633	291	10	on	on	ADP
ejpam-5633	291	11	.	.	PUNCT
ejpam-5633	292	1	upper	upper	ADJ
ejpam-5633	292	2	and	and	CCONJ
ejpam-5633	292	3	lower	low	ADJ
ejpam-5633	292	4	weakly	weakly	ADJ
ejpam-5633	292	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5633	292	6	multifunctions	multifunction	NOUN
ejpam-5633	292	7	.	.	PUNCT
ejpam-5633	293	1	international	international	ADJ
ejpam-5633	293	2	journal	journal	NOUN
ejpam-5633	293	3	of	of	ADP
ejpam-5633	293	4	analysis	analysis	NOUN
ejpam-5633	293	5	and	and	CCONJ
ejpam-5633	293	6	applications	application	NOUN
ejpam-5633	293	7	,	,	PUNCT
ejpam-5633	293	8	21:90	21:90	NUM
ejpam-5633	293	9	,	,	PUNCT
ejpam-5633	293	10	2023	2023	NUM
ejpam-5633	293	11	.	.	PUNCT
ejpam-5633	294	1	[	[	X
ejpam-5633	294	2	22	22	NUM
ejpam-5633	294	3	]	]	PUNCT
ejpam-5633	294	4	c.	c.	PROPN
ejpam-5633	294	5	boonpok	boonpok	PROPN
ejpam-5633	294	6	and	and	CCONJ
ejpam-5633	294	7	p.	p.	NOUN
ejpam-5633	294	8	pue	pue	NOUN
ejpam-5633	294	9	-	-	PUNCT
ejpam-5633	294	10	on	on	ADP
ejpam-5633	294	11	.	.	PUNCT
ejpam-5633	295	1	upper	upper	ADJ
ejpam-5633	295	2	and	and	CCONJ
ejpam-5633	295	3	lower	low	ADJ
ejpam-5633	295	4	weakly	weakly	ADJ
ejpam-5633	295	5	(	(	PUNCT
ejpam-5633	295	6	λ	λ	NOUN
ejpam-5633	295	7	,	,	PUNCT
ejpam-5633	295	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	295	9	multifunctions	multifunction	NOUN
ejpam-5633	295	10	.	.	PUNCT
ejpam-5633	296	1	european	european	PROPN
ejpam-5633	296	2	journal	journal	PROPN
ejpam-5633	296	3	of	of	ADP
ejpam-5633	296	4	pure	pure	ADJ
ejpam-5633	296	5	and	and	CCONJ
ejpam-5633	296	6	applied	applied	ADJ
ejpam-5633	296	7	mathematics	mathematic	NOUN
ejpam-5633	296	8	,	,	PUNCT
ejpam-5633	296	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5633	296	10	,	,	PUNCT
ejpam-5633	296	11	2023	2023	NUM
ejpam-5633	296	12	.	.	PUNCT
ejpam-5633	297	1	[	[	X
ejpam-5633	297	2	23	23	NUM
ejpam-5633	297	3	]	]	X
ejpam-5633	297	4	c.	c.	PROPN
ejpam-5633	297	5	boonpok	boonpok	PROPN
ejpam-5633	297	6	and	and	CCONJ
ejpam-5633	297	7	p.	p.	NOUN
ejpam-5633	297	8	pue	pue	NOUN
ejpam-5633	297	9	-	-	PUNCT
ejpam-5633	297	10	on	on	ADP
ejpam-5633	297	11	.	.	PUNCT
ejpam-5633	298	1	characterizations	characterization	NOUN
ejpam-5633	298	2	of	of	ADP
ejpam-5633	298	3	almost	almost	ADV
ejpam-5633	298	4	(	(	PUNCT
ejpam-5633	298	5	τ1	τ1	NOUN
ejpam-5633	298	6	,	,	PUNCT
ejpam-5633	298	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	298	8	functions	function	NOUN
ejpam-5633	298	9	.	.	PUNCT
ejpam-5633	299	1	international	international	ADJ
ejpam-5633	299	2	journal	journal	NOUN
ejpam-5633	299	3	of	of	ADP
ejpam-5633	299	4	analysis	analysis	NOUN
ejpam-5633	299	5	and	and	CCONJ
ejpam-5633	299	6	applications	application	NOUN
ejpam-5633	299	7	,	,	PUNCT
ejpam-5633	299	8	22:33	22:33	NUM
ejpam-5633	299	9	,	,	PUNCT
ejpam-5633	299	10	2024	2024	NUM
ejpam-5633	299	11	.	.	PUNCT
ejpam-5633	300	1	[	[	X
ejpam-5633	300	2	24	24	NUM
ejpam-5633	300	3	]	]	PUNCT
ejpam-5633	300	4	c.	c.	PROPN
ejpam-5633	300	5	boonpok	boonpok	PROPN
ejpam-5633	300	6	and	and	CCONJ
ejpam-5633	300	7	n.	n.	PROPN
ejpam-5633	300	8	srisarakham	srisarakham	PROPN
ejpam-5633	300	9	.	.	PUNCT
ejpam-5633	301	1	almost	almost	ADV
ejpam-5633	301	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5633	301	3	for	for	ADP
ejpam-5633	301	4	multifunctions	multifunction	NOUN
ejpam-5633	301	5	.	.	PUNCT
ejpam-5633	302	1	international	international	ADJ
ejpam-5633	302	2	journal	journal	NOUN
ejpam-5633	302	3	of	of	ADP
ejpam-5633	302	4	analysis	analysis	NOUN
ejpam-5633	302	5	and	and	CCONJ
ejpam-5633	302	6	applications	application	NOUN
ejpam-5633	302	7	,	,	PUNCT
ejpam-5633	302	8	21:107	21:107	NUM
ejpam-5633	302	9	,	,	PUNCT
ejpam-5633	302	10	2023	2023	NUM
ejpam-5633	302	11	.	.	PUNCT
ejpam-5633	303	1	[	[	X
ejpam-5633	303	2	25	25	NUM
ejpam-5633	303	3	]	]	PUNCT
ejpam-5633	303	4	c.	c.	PROPN
ejpam-5633	303	5	boonpok	boonpok	PROPN
ejpam-5633	303	6	and	and	CCONJ
ejpam-5633	303	7	n.	n.	PROPN
ejpam-5633	303	8	srisarakham	srisarakham	PROPN
ejpam-5633	303	9	.	.	PUNCT
ejpam-5633	304	1	weak	weak	ADJ
ejpam-5633	304	2	forms	form	NOUN
ejpam-5633	304	3	of	of	ADP
ejpam-5633	304	4	(	(	PUNCT
ejpam-5633	304	5	λ	λ	PROPN
ejpam-5633	304	6	,	,	PUNCT
ejpam-5633	304	7	b)-open	b)-open	VERB
ejpam-5633	304	8	sets	set	NOUN
ejpam-5633	304	9	and	and	CCONJ
ejpam-5633	304	10	weak	weak	ADJ
ejpam-5633	304	11	(	(	PUNCT
ejpam-5633	304	12	λ	λ	NOUN
ejpam-5633	304	13	,	,	PUNCT
ejpam-5633	304	14	b)continuity	b)continuity	NOUN
ejpam-5633	304	15	.	.	PUNCT
ejpam-5633	305	1	european	european	PROPN
ejpam-5633	305	2	journal	journal	PROPN
ejpam-5633	305	3	of	of	ADP
ejpam-5633	305	4	pure	pure	ADJ
ejpam-5633	305	5	and	and	CCONJ
ejpam-5633	305	6	applied	applied	ADJ
ejpam-5633	305	7	mathematics	mathematic	NOUN
ejpam-5633	305	8	,	,	PUNCT
ejpam-5633	305	9	16(1):29–43	16(1):29–43	NUM
ejpam-5633	305	10	,	,	PUNCT
ejpam-5633	305	11	2023	2023	NUM
ejpam-5633	305	12	.	.	PUNCT
ejpam-5633	306	1	[	[	X
ejpam-5633	306	2	26	26	NUM
ejpam-5633	306	3	]	]	X
ejpam-5633	306	4	c.	c.	PROPN
ejpam-5633	306	5	boonpok	boonpok	PROPN
ejpam-5633	306	6	and	and	CCONJ
ejpam-5633	306	7	n.	n.	PROPN
ejpam-5633	306	8	srisarakham	srisarakham	PROPN
ejpam-5633	306	9	.	.	PUNCT
ejpam-5633	307	1	(	(	PUNCT
ejpam-5633	307	2	τ1	τ1	NOUN
ejpam-5633	307	3	,	,	PUNCT
ejpam-5633	307	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5633	307	5	for	for	ADP
ejpam-5633	307	6	functions	function	NOUN
ejpam-5633	307	7	.	.	PUNCT
ejpam-5633	308	1	asia	asia	PROPN
ejpam-5633	308	2	pacific	pacific	PROPN
ejpam-5633	308	3	journal	journal	PROPN
ejpam-5633	308	4	of	of	ADP
ejpam-5633	308	5	mathematics	mathematic	NOUN
ejpam-5633	308	6	,	,	PUNCT
ejpam-5633	308	7	11:21	11:21	NUM
ejpam-5633	308	8	,	,	PUNCT
ejpam-5633	308	9	2024	2024	NUM
ejpam-5633	308	10	.	.	PUNCT
ejpam-5633	309	1	[	[	X
ejpam-5633	309	2	27	27	NUM
ejpam-5633	309	3	]	]	X
ejpam-5633	309	4	c.	c.	PROPN
ejpam-5633	309	5	boonpok	boonpok	PROPN
ejpam-5633	309	6	and	and	CCONJ
ejpam-5633	309	7	m.	m.	NOUN
ejpam-5633	309	8	thongmoon	thongmoon	NOUN
ejpam-5633	309	9	.	.	PUNCT
ejpam-5633	310	1	weak	weak	ADJ
ejpam-5633	310	2	α(λ	α(λ	PROPN
ejpam-5633	310	3	,	,	PUNCT
ejpam-5633	310	4	sp)-continuity	sp)-continuity	NOUN
ejpam-5633	310	5	for	for	ADP
ejpam-5633	310	6	multifunctions	multifunction	NOUN
ejpam-5633	310	7	.	.	PUNCT
ejpam-5633	311	1	european	european	ADJ
ejpam-5633	311	2	journal	journal	PROPN
ejpam-5633	311	3	of	of	ADP
ejpam-5633	311	4	pure	pure	ADJ
ejpam-5633	311	5	and	and	CCONJ
ejpam-5633	311	6	applied	applied	ADJ
ejpam-5633	311	7	mathematics	mathematic	NOUN
ejpam-5633	311	8	,	,	PUNCT
ejpam-5633	311	9	16(1):465–478	16(1):465–478	NUM
ejpam-5633	311	10	,	,	PUNCT
ejpam-5633	311	11	2023	2023	NUM
ejpam-5633	311	12	.	.	PUNCT
ejpam-5633	312	1	[	[	X
ejpam-5633	312	2	28	28	NUM
ejpam-5633	312	3	]	]	X
ejpam-5633	312	4	c.	c.	PROPN
ejpam-5633	312	5	boonpok	boonpok	PROPN
ejpam-5633	312	6	and	and	CCONJ
ejpam-5633	312	7	c.	c.	PROPN
ejpam-5633	312	8	viriyapong	viriyapong	PROPN
ejpam-5633	312	9	.	.	PUNCT
ejpam-5633	313	1	upper	upper	ADJ
ejpam-5633	313	2	and	and	CCONJ
ejpam-5633	313	3	lower	low	ADJ
ejpam-5633	313	4	almost	almost	ADV
ejpam-5633	313	5	weak	weak	ADJ
ejpam-5633	313	6	(	(	PUNCT
ejpam-5633	313	7	τ1	τ1	NOUN
ejpam-5633	313	8	,	,	PUNCT
ejpam-5633	313	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5633	313	10	.	.	PUNCT
ejpam-5633	314	1	european	european	PROPN
ejpam-5633	314	2	journal	journal	PROPN
ejpam-5633	314	3	of	of	ADP
ejpam-5633	314	4	pure	pure	ADJ
ejpam-5633	314	5	and	and	CCONJ
ejpam-5633	314	6	applied	applied	ADJ
ejpam-5633	314	7	mathematics	mathematic	NOUN
ejpam-5633	314	8	,	,	PUNCT
ejpam-5633	314	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5633	314	10	,	,	PUNCT
ejpam-5633	314	11	2021	2021	NUM
ejpam-5633	314	12	.	.	PUNCT
ejpam-5633	315	1	[	[	X
ejpam-5633	315	2	29	29	NUM
ejpam-5633	315	3	]	]	X
ejpam-5633	315	4	c.	c.	PROPN
ejpam-5633	315	5	boonpok	boonpok	PROPN
ejpam-5633	315	6	,	,	PUNCT
ejpam-5633	315	7	c.	c.	PROPN
ejpam-5633	315	8	viriyapong	viriyapong	PROPN
ejpam-5633	315	9	,	,	PUNCT
ejpam-5633	315	10	and	and	CCONJ
ejpam-5633	315	11	m.	m.	NOUN
ejpam-5633	315	12	thongmoon	thongmoon	NOUN
ejpam-5633	315	13	.	.	PUNCT
ejpam-5633	316	1	on	on	ADP
ejpam-5633	316	2	upper	upper	ADJ
ejpam-5633	316	3	and	and	CCONJ
ejpam-5633	316	4	lower	low	ADJ
ejpam-5633	316	5	(	(	PUNCT
ejpam-5633	316	6	τ1	τ1	NOUN
ejpam-5633	316	7	,	,	PUNCT
ejpam-5633	316	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5633	316	9	multifunctions	multifunction	NOUN
ejpam-5633	316	10	.	.	PUNCT
ejpam-5633	317	1	journal	journal	PROPN
ejpam-5633	317	2	of	of	ADP
ejpam-5633	317	3	mathematics	mathematics	PROPN
ejpam-5633	317	4	and	and	CCONJ
ejpam-5633	317	5	computer	computer	NOUN
ejpam-5633	317	6	science	science	NOUN
ejpam-5633	317	7	,	,	PUNCT
ejpam-5633	317	8	18:282–293	18:282–293	NUM
ejpam-5633	317	9	,	,	PUNCT
ejpam-5633	317	10	2018	2018	NUM
ejpam-5633	317	11	.	.	PUNCT
ejpam-5633	318	1	[	[	X
ejpam-5633	318	2	30	30	NUM
ejpam-5633	318	3	]	]	X
ejpam-5633	318	4	d.	d.	PROPN
ejpam-5633	318	5	carnahan	carnahan	PROPN
ejpam-5633	318	6	.	.	PUNCT
ejpam-5633	319	1	locally	locally	ADV
ejpam-5633	319	2	nearly	nearly	ADV
ejpam-5633	319	3	compact	compact	ADJ
ejpam-5633	319	4	spaces	space	NOUN
ejpam-5633	319	5	.	.	PUNCT
ejpam-5633	320	1	bollettino	bollettino	PROPN
ejpam-5633	320	2	dell	dell	PROPN
ejpam-5633	320	3	’	'	PUNCT
ejpam-5633	320	4	unione	unione	PROPN
ejpam-5633	320	5	matematica	matematica	PROPN
ejpam-5633	320	6	italiana	italiana	PROPN
ejpam-5633	320	7	,	,	PUNCT
ejpam-5633	320	8	6:143–153	6:143–153	NUM
ejpam-5633	320	9	,	,	PUNCT
ejpam-5633	320	10	1972	1972	NUM
ejpam-5633	320	11	.	.	PUNCT
ejpam-5633	321	1	[	[	X
ejpam-5633	321	2	31	31	NUM
ejpam-5633	321	3	]	]	X
ejpam-5633	321	4	c.	c.	PROPN
ejpam-5633	321	5	carpintero	carpintero	PROPN
ejpam-5633	321	6	,	,	PUNCT
ejpam-5633	321	7	j.	j.	PROPN
ejpam-5633	321	8	pacheco	pacheco	PROPN
ejpam-5633	321	9	,	,	PUNCT
ejpam-5633	321	10	n.	n.	PROPN
ejpam-5633	321	11	rajesh	rajesh	PROPN
ejpam-5633	321	12	,	,	PUNCT
ejpam-5633	321	13	e.	e.	PROPN
ejpam-5633	321	14	rosas	rosas	PROPN
ejpam-5633	321	15	,	,	PUNCT
ejpam-5633	321	16	and	and	CCONJ
ejpam-5633	321	17	s.	s.	PROPN
ejpam-5633	321	18	saranyasri	saranyasri	PROPN
ejpam-5633	321	19	.	.	PUNCT
ejpam-5633	322	1	properties	property	NOUN
ejpam-5633	322	2	of	of	ADP
ejpam-5633	322	3	nearly	nearly	ADV
ejpam-5633	322	4	ω	ω	ADJ
ejpam-5633	322	5	-	-	ADJ
ejpam-5633	322	6	continuous	continuous	ADJ
ejpam-5633	322	7	multifunctions	multifunction	NOUN
ejpam-5633	322	8	.	.	PUNCT
ejpam-5633	323	1	acta	acta	PROPN
ejpam-5633	323	2	universitatis	universitatis	PROPN
ejpam-5633	323	3	sapientiae	sapientiae	PROPN
ejpam-5633	323	4	,	,	PUNCT
ejpam-5633	323	5	mathematica	mathematica	PROPN
ejpam-5633	323	6	,	,	PUNCT
ejpam-5633	323	7	9(1):13–25	9(1):13–25	NUM
ejpam-5633	323	8	,	,	PUNCT
ejpam-5633	323	9	2017	2017	NUM
ejpam-5633	323	10	.	.	PUNCT
ejpam-5633	324	1	[	[	X
ejpam-5633	324	2	32	32	NUM
ejpam-5633	324	3	]	]	PUNCT
ejpam-5633	324	4	m.	m.	NOUN
ejpam-5633	324	5	chiangpradit	chiangpradit	NOUN
ejpam-5633	324	6	,	,	PUNCT
ejpam-5633	324	7	s.	s.	PROPN
ejpam-5633	324	8	sompong	sompong	PROPN
ejpam-5633	324	9	,	,	PUNCT
ejpam-5633	324	10	and	and	CCONJ
ejpam-5633	324	11	c.	c.	PROPN
ejpam-5633	324	12	boonpok	boonpok	PROPN
ejpam-5633	324	13	.	.	PUNCT
ejpam-5633	325	1	on	on	ADP
ejpam-5633	325	2	characterizations	characterization	NOUN
ejpam-5633	325	3	of	of	ADP
ejpam-5633	325	4	(	(	PUNCT
ejpam-5633	325	5	τ1	τ1	NOUN
ejpam-5633	325	6	,	,	PUNCT
ejpam-5633	325	7	τ2)regular	τ2)regular	ADJ
ejpam-5633	325	8	spaces	space	NOUN
ejpam-5633	325	9	.	.	PUNCT
ejpam-5633	326	1	international	international	ADJ
ejpam-5633	326	2	journal	journal	PROPN
ejpam-5633	326	3	of	of	ADP
ejpam-5633	326	4	mathematics	mathematic	NOUN
ejpam-5633	326	5	and	and	CCONJ
ejpam-5633	326	6	computer	computer	NOUN
ejpam-5633	326	7	science	science	NOUN
ejpam-5633	326	8	,	,	PUNCT
ejpam-5633	326	9	19(4):1329–1334	19(4):1329–1334	NUM
ejpam-5633	326	10	,	,	PUNCT
ejpam-5633	326	11	2024	2024	NUM
ejpam-5633	326	12	.	.	PUNCT
ejpam-5633	327	1	[	[	X
ejpam-5633	327	2	33	33	NUM
ejpam-5633	327	3	]	]	PUNCT
ejpam-5633	327	4	m.	m.	NOUN
ejpam-5633	327	5	chiangpradit	chiangpradit	NOUN
ejpam-5633	327	6	,	,	PUNCT
ejpam-5633	327	7	s.	s.	PROPN
ejpam-5633	327	8	sompong	sompong	PROPN
ejpam-5633	327	9	,	,	PUNCT
ejpam-5633	327	10	and	and	CCONJ
ejpam-5633	327	11	c.	c.	PROPN
ejpam-5633	327	12	boonpok	boonpok	PROPN
ejpam-5633	327	13	.	.	PUNCT
ejpam-5633	328	1	weakly	weakly	ADJ
ejpam-5633	328	2	quasi	quasi	NOUN
ejpam-5633	328	3	(	(	PUNCT
ejpam-5633	328	4	τ1	τ1	PROPN
ejpam-5633	328	5	,	,	PUNCT
ejpam-5633	328	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	328	7	m.	m.	NOUN
ejpam-5633	328	8	thongmoon	thongmoon	NOUN
ejpam-5633	328	9	,	,	PUNCT
ejpam-5633	328	10	a.	a.	PROPN
ejpam-5633	328	11	sama	sama	PROPN
ejpam-5633	328	12	-	-	PUNCT
ejpam-5633	328	13	ae	ae	PROPN
ejpam-5633	328	14	,	,	PUNCT
ejpam-5633	328	15	c.	c.	PROPN
ejpam-5633	328	16	boonpok	boonpok	PROPN
ejpam-5633	328	17	/	/	SYM
ejpam-5633	328	18	eur	eur	PROPN
ejpam-5633	328	19	.	.	PUNCT
ejpam-5633	329	1	j.	j.	PROPN
ejpam-5633	329	2	pure	pure	PROPN
ejpam-5633	329	3	appl	appl	PROPN
ejpam-5633	329	4	.	.	PROPN
ejpam-5633	329	5	math	math	PROPN
ejpam-5633	329	6	,	,	PUNCT
ejpam-5633	329	7	18	18	NUM
ejpam-5633	329	8	(	(	PUNCT
ejpam-5633	329	9	1	1	NUM
ejpam-5633	329	10	)	)	PUNCT
ejpam-5633	329	11	(	(	PUNCT
ejpam-5633	329	12	2025	2025	NUM
ejpam-5633	329	13	)	)	PUNCT
ejpam-5633	329	14	,	,	PUNCT
ejpam-5633	329	15	5633	5633	NUM
ejpam-5633	329	16	12	12	NUM
ejpam-5633	329	17	of	of	ADP
ejpam-5633	329	18	13	13	NUM
ejpam-5633	329	19	functions	function	NOUN
ejpam-5633	329	20	.	.	PUNCT
ejpam-5633	330	1	international	international	ADJ
ejpam-5633	330	2	journal	journal	NOUN
ejpam-5633	330	3	of	of	ADP
ejpam-5633	330	4	analysis	analysis	NOUN
ejpam-5633	330	5	and	and	CCONJ
ejpam-5633	330	6	applications	application	NOUN
ejpam-5633	330	7	,	,	PUNCT
ejpam-5633	330	8	22:125	22:125	NUM
ejpam-5633	330	9	,	,	PUNCT
ejpam-5633	330	10	2024	2024	NUM
ejpam-5633	330	11	.	.	PUNCT
ejpam-5633	331	1	[	[	X
ejpam-5633	331	2	34	34	NUM
ejpam-5633	331	3	]	]	X
ejpam-5633	331	4	n.	n.	NOUN
ejpam-5633	331	5	chutiman	chutiman	NOUN
ejpam-5633	331	6	,	,	PUNCT
ejpam-5633	331	7	s.	s.	PROPN
ejpam-5633	331	8	sompong	sompong	PROPN
ejpam-5633	331	9	,	,	PUNCT
ejpam-5633	331	10	and	and	CCONJ
ejpam-5633	331	11	c.	c.	PROPN
ejpam-5633	331	12	boonpok	boonpok	PROPN
ejpam-5633	331	13	.	.	PUNCT
ejpam-5633	332	1	on	on	ADP
ejpam-5633	332	2	some	some	DET
ejpam-5633	332	3	separation	separation	NOUN
ejpam-5633	332	4	axioms	axiom	NOUN
ejpam-5633	332	5	in	in	ADP
ejpam-5633	332	6	bitopological	bitopological	ADJ
ejpam-5633	332	7	spaces	space	NOUN
ejpam-5633	332	8	.	.	PUNCT
ejpam-5633	333	1	asia	asia	PROPN
ejpam-5633	333	2	pacific	pacific	PROPN
ejpam-5633	333	3	journal	journal	PROPN
ejpam-5633	333	4	of	of	ADP
ejpam-5633	333	5	mathematics	mathematic	NOUN
ejpam-5633	333	6	,	,	PUNCT
ejpam-5633	333	7	11:41	11:41	NUM
ejpam-5633	333	8	,	,	PUNCT
ejpam-5633	333	9	2024	2024	NUM
ejpam-5633	333	10	.	.	PUNCT
ejpam-5633	334	1	[	[	X
ejpam-5633	334	2	35	35	NUM
ejpam-5633	334	3	]	]	X
ejpam-5633	334	4	t.	t.	PROPN
ejpam-5633	334	5	duangphui	duangphui	PROPN
ejpam-5633	334	6	,	,	PUNCT
ejpam-5633	334	7	c.	c.	PROPN
ejpam-5633	334	8	boonpok	boonpok	PROPN
ejpam-5633	334	9	,	,	PUNCT
ejpam-5633	334	10	and	and	CCONJ
ejpam-5633	334	11	c.	c.	PROPN
ejpam-5633	334	12	viriyapong	viriyapong	PROPN
ejpam-5633	334	13	.	.	PUNCT
ejpam-5633	335	1	continuous	continuous	ADJ
ejpam-5633	335	2	functions	function	NOUN
ejpam-5633	335	3	on	on	ADP
ejpam-5633	335	4	bigeneralized	bigeneralize	VERB
ejpam-5633	335	5	topological	topological	ADJ
ejpam-5633	335	6	spaces	space	NOUN
ejpam-5633	335	7	.	.	PUNCT
ejpam-5633	336	1	international	international	ADJ
ejpam-5633	336	2	journal	journal	PROPN
ejpam-5633	336	3	of	of	ADP
ejpam-5633	336	4	mathematical	mathematical	ADJ
ejpam-5633	336	5	analysis	analysis	NOUN
ejpam-5633	336	6	,	,	PUNCT
ejpam-5633	336	7	5(24):1165	5(24):1165	NUM
ejpam-5633	336	8	–	–	PUNCT
ejpam-5633	336	9	1174	1174	NUM
ejpam-5633	336	10	,	,	PUNCT
ejpam-5633	336	11	2011	2011	NUM
ejpam-5633	336	12	.	.	PUNCT
ejpam-5633	337	1	[	[	X
ejpam-5633	337	2	36	36	NUM
ejpam-5633	337	3	]	]	PUNCT
ejpam-5633	337	4	t.	t.	NOUN
ejpam-5633	337	5	dungthaisong	dungthaisong	PROPN
ejpam-5633	337	6	,	,	PUNCT
ejpam-5633	337	7	c.	c.	PROPN
ejpam-5633	337	8	boonpok	boonpok	PROPN
ejpam-5633	337	9	,	,	PUNCT
ejpam-5633	337	10	and	and	CCONJ
ejpam-5633	337	11	c.	c.	PROPN
ejpam-5633	337	12	viriyapong	viriyapong	PROPN
ejpam-5633	337	13	.	.	PUNCT
ejpam-5633	338	1	generalized	generalize	VERB
ejpam-5633	338	2	closed	close	VERB
ejpam-5633	338	3	sets	set	NOUN
ejpam-5633	338	4	in	in	ADP
ejpam-5633	338	5	bigeneralized	bigeneralize	VERB
ejpam-5633	338	6	topological	topological	ADJ
ejpam-5633	338	7	spaces	space	NOUN
ejpam-5633	338	8	.	.	PUNCT
ejpam-5633	339	1	international	international	ADJ
ejpam-5633	339	2	journal	journal	PROPN
ejpam-5633	339	3	of	of	ADP
ejpam-5633	339	4	mathematical	mathematical	ADJ
ejpam-5633	339	5	analysis	analysis	NOUN
ejpam-5633	339	6	,	,	PUNCT
ejpam-5633	339	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5633	339	8	,	,	PUNCT
ejpam-5633	339	9	2011	2011	NUM
ejpam-5633	339	10	.	.	PUNCT
ejpam-5633	340	1	[	[	X
ejpam-5633	340	2	37	37	NUM
ejpam-5633	340	3	]	]	PUNCT
ejpam-5633	340	4	e.	e.	PROPN
ejpam-5633	340	5	ekici	ekici	PROPN
ejpam-5633	340	6	.	.	PUNCT
ejpam-5633	341	1	nearly	nearly	ADV
ejpam-5633	341	2	continuous	continuous	ADJ
ejpam-5633	341	3	multifunctions	multifunction	NOUN
ejpam-5633	341	4	.	.	PUNCT
ejpam-5633	342	1	acta	acta	PROPN
ejpam-5633	342	2	mathematica	mathematica	PROPN
ejpam-5633	342	3	universitatis	universitatis	PROPN
ejpam-5633	342	4	comenianae	comenianae	PROPN
ejpam-5633	342	5	,	,	PUNCT
ejpam-5633	342	6	72:229–235	72:229–235	PROPN
ejpam-5633	342	7	,	,	PUNCT
ejpam-5633	342	8	2003	2003	NUM
ejpam-5633	342	9	.	.	PUNCT
ejpam-5633	343	1	[	[	X
ejpam-5633	343	2	38	38	NUM
ejpam-5633	343	3	]	]	PUNCT
ejpam-5633	343	4	e.	e.	PROPN
ejpam-5633	343	5	ekici	ekici	PROPN
ejpam-5633	343	6	.	.	PUNCT
ejpam-5633	344	1	almost	almost	ADV
ejpam-5633	344	2	nearly	nearly	ADV
ejpam-5633	344	3	continuous	continuous	ADJ
ejpam-5633	344	4	multifunctions	multifunction	NOUN
ejpam-5633	344	5	.	.	PUNCT
ejpam-5633	345	1	acta	acta	PROPN
ejpam-5633	345	2	mathematica	mathematica	PROPN
ejpam-5633	345	3	universitatis	universitatis	PROPN
ejpam-5633	345	4	comenianae	comenianae	PROPN
ejpam-5633	345	5	,	,	PUNCT
ejpam-5633	345	6	73:175–186	73:175–186	PROPN
ejpam-5633	345	7	,	,	PUNCT
ejpam-5633	345	8	2004	2004	NUM
ejpam-5633	345	9	.	.	PUNCT
ejpam-5633	346	1	[	[	X
ejpam-5633	346	2	39	39	NUM
ejpam-5633	346	3	]	]	PUNCT
ejpam-5633	346	4	j.	j.	PROPN
ejpam-5633	346	5	khampakdee	khampakdee	PROPN
ejpam-5633	346	6	and	and	CCONJ
ejpam-5633	346	7	c.	c.	PROPN
ejpam-5633	346	8	boonpok	boonpok	PROPN
ejpam-5633	346	9	.	.	PUNCT
ejpam-5633	347	1	upper	upper	ADJ
ejpam-5633	347	2	and	and	CCONJ
ejpam-5633	347	3	lower	low	ADJ
ejpam-5633	347	4	α(λ	α(λ	PROPN
ejpam-5633	347	5	,	,	PUNCT
ejpam-5633	347	6	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	347	7	multifunctions	multifunction	NOUN
ejpam-5633	347	8	.	.	PUNCT
ejpam-5633	348	1	wseas	wseas	VERB
ejpam-5633	348	2	transactions	transaction	NOUN
ejpam-5633	348	3	on	on	ADP
ejpam-5633	348	4	mathematics	mathematic	NOUN
ejpam-5633	348	5	,	,	PUNCT
ejpam-5633	348	6	21:684–690	21:684–690	NUM
ejpam-5633	348	7	,	,	PUNCT
ejpam-5633	348	8	2022	2022	NUM
ejpam-5633	348	9	.	.	PUNCT
ejpam-5633	349	1	[	[	X
ejpam-5633	349	2	40	40	NUM
ejpam-5633	349	3	]	]	PUNCT
ejpam-5633	349	4	j.	j.	PROPN
ejpam-5633	349	5	khampakdee	khampakdee	PROPN
ejpam-5633	349	6	,	,	PUNCT
ejpam-5633	349	7	s.	s.	PROPN
ejpam-5633	349	8	sompong	sompong	PROPN
ejpam-5633	349	9	,	,	PUNCT
ejpam-5633	349	10	and	and	CCONJ
ejpam-5633	349	11	c.	c.	PROPN
ejpam-5633	349	12	boonpok	boonpok	PROPN
ejpam-5633	349	13	.	.	PUNCT
ejpam-5633	350	1	c-(τ1	c-(τ1	PROPN
ejpam-5633	350	2	,	,	PUNCT
ejpam-5633	350	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5633	350	4	for	for	ADP
ejpam-5633	350	5	multifunctions	multifunction	NOUN
ejpam-5633	350	6	.	.	PUNCT
ejpam-5633	351	1	european	european	ADJ
ejpam-5633	351	2	journal	journal	PROPN
ejpam-5633	351	3	of	of	ADP
ejpam-5633	351	4	pure	pure	ADJ
ejpam-5633	351	5	and	and	CCONJ
ejpam-5633	351	6	applied	applied	ADJ
ejpam-5633	351	7	mathematics	mathematic	NOUN
ejpam-5633	351	8	,	,	PUNCT
ejpam-5633	351	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-5633	351	10	,	,	PUNCT
ejpam-5633	351	11	2024	2024	NUM
ejpam-5633	351	12	.	.	PUNCT
ejpam-5633	352	1	[	[	X
ejpam-5633	352	2	41	41	NUM
ejpam-5633	352	3	]	]	X
ejpam-5633	352	4	c.	c.	PROPN
ejpam-5633	352	5	klanarong	klanarong	PROPN
ejpam-5633	352	6	,	,	PUNCT
ejpam-5633	352	7	s.	s.	PROPN
ejpam-5633	352	8	sompong	sompong	PROPN
ejpam-5633	352	9	,	,	PUNCT
ejpam-5633	352	10	and	and	CCONJ
ejpam-5633	352	11	c.	c.	PROPN
ejpam-5633	352	12	boonpok	boonpok	PROPN
ejpam-5633	352	13	.	.	PUNCT
ejpam-5633	353	1	upper	upper	ADJ
ejpam-5633	353	2	and	and	CCONJ
ejpam-5633	353	3	lower	low	ADJ
ejpam-5633	353	4	almost	almost	ADV
ejpam-5633	353	5	(	(	PUNCT
ejpam-5633	353	6	τ1	τ1	NOUN
ejpam-5633	353	7	,	,	PUNCT
ejpam-5633	353	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5633	353	9	multifunctions	multifunction	NOUN
ejpam-5633	353	10	.	.	PUNCT
ejpam-5633	354	1	european	european	ADJ
ejpam-5633	354	2	journal	journal	PROPN
ejpam-5633	354	3	of	of	ADP
ejpam-5633	354	4	pure	pure	ADJ
ejpam-5633	354	5	and	and	CCONJ
ejpam-5633	354	6	applied	applied	ADJ
ejpam-5633	354	7	mathematics	mathematic	NOUN
ejpam-5633	354	8	,	,	PUNCT
ejpam-5633	354	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5633	354	10	,	,	PUNCT
ejpam-5633	354	11	2024	2024	NUM
ejpam-5633	354	12	.	.	PUNCT
ejpam-5633	355	1	[	[	X
ejpam-5633	355	2	42	42	NUM
ejpam-5633	355	3	]	]	X
ejpam-5633	355	4	b.	b.	PROPN
ejpam-5633	355	5	kong	kong	PROPN
ejpam-5633	355	6	-	-	PUNCT
ejpam-5633	355	7	ied	ied	PROPN
ejpam-5633	355	8	,	,	PUNCT
ejpam-5633	355	9	s.	s.	PROPN
ejpam-5633	355	10	sompong	sompong	PROPN
ejpam-5633	355	11	,	,	PUNCT
ejpam-5633	355	12	and	and	CCONJ
ejpam-5633	355	13	c.	c.	PROPN
ejpam-5633	355	14	boonpok	boonpok	PROPN
ejpam-5633	355	15	.	.	PUNCT
ejpam-5633	356	1	almost	almost	ADV
ejpam-5633	356	2	quasi	quasi	X
ejpam-5633	356	3	(	(	PUNCT
ejpam-5633	356	4	τ1	τ1	NOUN
ejpam-5633	356	5	,	,	PUNCT
ejpam-5633	356	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	356	7	functions	function	NOUN
ejpam-5633	356	8	.	.	PUNCT
ejpam-5633	357	1	asia	asia	PROPN
ejpam-5633	357	2	pacific	pacific	PROPN
ejpam-5633	357	3	journal	journal	PROPN
ejpam-5633	357	4	of	of	ADP
ejpam-5633	357	5	mathematics	mathematic	NOUN
ejpam-5633	357	6	,	,	PUNCT
ejpam-5633	357	7	11:64	11:64	NUM
ejpam-5633	357	8	,	,	PUNCT
ejpam-5633	357	9	2024	2024	NUM
ejpam-5633	357	10	.	.	PUNCT
ejpam-5633	358	1	[	[	X
ejpam-5633	358	2	43	43	NUM
ejpam-5633	358	3	]	]	X
ejpam-5633	358	4	s.	s.	PROPN
ejpam-5633	358	5	r.	r.	PROPN
ejpam-5633	358	6	malghan	malghan	PROPN
ejpam-5633	358	7	and	and	CCONJ
ejpam-5633	358	8	v.	v.	ADP
ejpam-5633	358	9	v.	v.	CCONJ
ejpam-5633	358	10	hanchinamani	hanchinamani	PROPN
ejpam-5633	358	11	.	.	PUNCT
ejpam-5633	359	1	n	n	CCONJ
ejpam-5633	359	2	-	-	PUNCT
ejpam-5633	359	3	continuous	continuous	ADJ
ejpam-5633	359	4	functions	function	NOUN
ejpam-5633	359	5	.	.	PUNCT
ejpam-5633	360	1	annales	annales	PROPN
ejpam-5633	360	2	de	de	ADP
ejpam-5633	360	3	la	la	PROPN
ejpam-5633	360	4	société	société	PROPN
ejpam-5633	360	5	scientifique	scientifique	PROPN
ejpam-5633	360	6	de	de	X
ejpam-5633	360	7	bruxelles	bruxelle	NOUN
ejpam-5633	360	8	,	,	PUNCT
ejpam-5633	360	9	98:69–79	98:69–79	ADV
ejpam-5633	360	10	,	,	PUNCT
ejpam-5633	360	11	1984	1984	NUM
ejpam-5633	360	12	.	.	PUNCT
ejpam-5633	361	1	[	[	X
ejpam-5633	361	2	44	44	NUM
ejpam-5633	361	3	]	]	PUNCT
ejpam-5633	361	4	t.	t.	PROPN
ejpam-5633	361	5	noiri	noiri	PROPN
ejpam-5633	361	6	.	.	PUNCT
ejpam-5633	362	1	n	n	CCONJ
ejpam-5633	362	2	-	-	PUNCT
ejpam-5633	362	3	closed	close	VERB
ejpam-5633	362	4	sets	set	NOUN
ejpam-5633	362	5	and	and	CCONJ
ejpam-5633	362	6	some	some	DET
ejpam-5633	362	7	separation	separation	NOUN
ejpam-5633	362	8	axioms	axiom	VERB
ejpam-5633	362	9	.	.	PUNCT
ejpam-5633	363	1	annales	annales	PROPN
ejpam-5633	363	2	de	de	ADP
ejpam-5633	363	3	la	la	PROPN
ejpam-5633	363	4	société	société	PROPN
ejpam-5633	363	5	scientifique	scientifique	PROPN
ejpam-5633	363	6	de	de	X
ejpam-5633	363	7	bruxelles	bruxelle	NOUN
ejpam-5633	363	8	,	,	PUNCT
ejpam-5633	363	9	88:195–199	88:195–199	PROPN
ejpam-5633	363	10	,	,	PUNCT
ejpam-5633	363	11	1974	1974	NUM
ejpam-5633	363	12	.	.	PUNCT
ejpam-5633	364	1	[	[	X
ejpam-5633	364	2	45	45	NUM
ejpam-5633	364	3	]	]	PUNCT
ejpam-5633	364	4	t.	t.	PROPN
ejpam-5633	364	5	noiri	noiri	PROPN
ejpam-5633	364	6	and	and	CCONJ
ejpam-5633	364	7	n.	n.	PROPN
ejpam-5633	364	8	ergun	ergun	PROPN
ejpam-5633	364	9	.	.	PUNCT
ejpam-5633	365	1	notes	note	NOUN
ejpam-5633	365	2	on	on	ADP
ejpam-5633	365	3	n	n	CCONJ
ejpam-5633	365	4	-	-	PUNCT
ejpam-5633	365	5	continuous	continuous	ADJ
ejpam-5633	365	6	functions	function	NOUN
ejpam-5633	365	7	.	.	PUNCT
ejpam-5633	366	1	research	research	NOUN
ejpam-5633	366	2	reports	report	NOUN
ejpam-5633	366	3	of	of	ADP
ejpam-5633	366	4	yatsushiro	yatsushiro	PROPN
ejpam-5633	366	5	national	national	PROPN
ejpam-5633	366	6	college	college	PROPN
ejpam-5633	366	7	of	of	ADP
ejpam-5633	366	8	technology	technology	NOUN
ejpam-5633	366	9	,	,	PUNCT
ejpam-5633	366	10	11:65–68	11:65–68	NUM
ejpam-5633	366	11	,	,	PUNCT
ejpam-5633	366	12	1989	1989	NUM
ejpam-5633	366	13	.	.	PUNCT
ejpam-5633	367	1	[	[	X
ejpam-5633	367	2	46	46	NUM
ejpam-5633	367	3	]	]	PUNCT
ejpam-5633	367	4	t.	t.	PROPN
ejpam-5633	367	5	noiri	noiri	PROPN
ejpam-5633	367	6	and	and	CCONJ
ejpam-5633	367	7	v.	v.	ADP
ejpam-5633	367	8	popa	popa	NOUN
ejpam-5633	367	9	.	.	PUNCT
ejpam-5633	368	1	a	a	DET
ejpam-5633	368	2	unified	unified	ADJ
ejpam-5633	368	3	theory	theory	NOUN
ejpam-5633	368	4	of	of	ADP
ejpam-5633	368	5	upper	upper	ADJ
ejpam-5633	368	6	and	and	CCONJ
ejpam-5633	368	7	lower	low	ADJ
ejpam-5633	368	8	almost	almost	ADV
ejpam-5633	368	9	nearly	nearly	ADV
ejpam-5633	368	10	continuous	continuous	ADJ
ejpam-5633	368	11	multifunctions	multifunction	NOUN
ejpam-5633	368	12	.	.	PUNCT
ejpam-5633	369	1	mathematica	mathematica	PROPN
ejpam-5633	369	2	balkanica	balkanica	PROPN
ejpam-5633	369	3	,	,	PUNCT
ejpam-5633	369	4	23:51–72	23:51–72	PROPN
ejpam-5633	369	5	,	,	PUNCT
ejpam-5633	369	6	2009	2009	NUM
ejpam-5633	369	7	.	.	PUNCT
ejpam-5633	370	1	[	[	X
ejpam-5633	370	2	47	47	NUM
ejpam-5633	370	3	]	]	PUNCT
ejpam-5633	370	4	v.	v.	CCONJ
ejpam-5633	370	5	popa	popa	NOUN
ejpam-5633	370	6	.	.	PUNCT
ejpam-5633	371	1	almost	almost	ADV
ejpam-5633	371	2	continuous	continuous	ADJ
ejpam-5633	371	3	multifunctions	multifunction	NOUN
ejpam-5633	371	4	.	.	PUNCT
ejpam-5633	372	1	matematički	matematički	PROPN
ejpam-5633	372	2	vesnik	vesnik	PROPN
ejpam-5633	372	3	,	,	PUNCT
ejpam-5633	372	4	34:75–84	34:75–84	NUM
ejpam-5633	372	5	,	,	PUNCT
ejpam-5633	372	6	1982	1982	NUM
ejpam-5633	372	7	.	.	PUNCT
ejpam-5633	373	1	[	[	X
ejpam-5633	373	2	48	48	NUM
ejpam-5633	373	3	]	]	PUNCT
ejpam-5633	373	4	p.	p.	NOUN
ejpam-5633	373	5	pue	pue	NOUN
ejpam-5633	373	6	-	-	PUNCT
ejpam-5633	373	7	on	on	ADP
ejpam-5633	373	8	and	and	CCONJ
ejpam-5633	373	9	c.	c.	PROPN
ejpam-5633	373	10	boonpok	boonpok	PROPN
ejpam-5633	373	11	.	.	PUNCT
ejpam-5633	374	1	θ(λ	θ(λ	PROPN
ejpam-5633	374	2	,	,	PUNCT
ejpam-5633	374	3	p)-continuity	p)-continuity	NOUN
ejpam-5633	374	4	for	for	ADP
ejpam-5633	374	5	functions	function	NOUN
ejpam-5633	374	6	.	.	PUNCT
ejpam-5633	375	1	international	international	ADJ
ejpam-5633	375	2	journal	journal	NOUN
ejpam-5633	375	3	of	of	ADP
ejpam-5633	375	4	mathematics	mathematic	NOUN
ejpam-5633	375	5	and	and	CCONJ
ejpam-5633	375	6	computer	computer	NOUN
ejpam-5633	375	7	science	science	NOUN
ejpam-5633	375	8	,	,	PUNCT
ejpam-5633	375	9	19(2):491–495	19(2):491–495	NUM
ejpam-5633	375	10	,	,	PUNCT
ejpam-5633	375	11	2024	2024	NUM
ejpam-5633	375	12	.	.	PUNCT
ejpam-5633	376	1	[	[	X
ejpam-5633	376	2	49	49	NUM
ejpam-5633	376	3	]	]	PUNCT
ejpam-5633	376	4	p.	p.	NOUN
ejpam-5633	376	5	pue	pue	NOUN
ejpam-5633	376	6	-	-	PUNCT
ejpam-5633	376	7	on	on	ADP
ejpam-5633	376	8	,	,	PUNCT
ejpam-5633	376	9	a.	a.	PROPN
ejpam-5633	376	10	sama	sama	PROPN
ejpam-5633	376	11	-	-	PUNCT
ejpam-5633	376	12	ae	ae	PROPN
ejpam-5633	376	13	,	,	PUNCT
ejpam-5633	376	14	and	and	CCONJ
ejpam-5633	376	15	c.	c.	PROPN
ejpam-5633	376	16	boonpok	boonpok	PROPN
ejpam-5633	376	17	.	.	PUNCT
ejpam-5633	377	1	c	c	X
ejpam-5633	377	2	-	-	PUNCT
ejpam-5633	377	3	quasi	quasi	X
ejpam-5633	377	4	(	(	PUNCT
ejpam-5633	377	5	τ1	τ1	PROPN
ejpam-5633	377	6	,	,	PUNCT
ejpam-5633	377	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	377	8	multifunctions	multifunction	NOUN
ejpam-5633	377	9	.	.	PUNCT
ejpam-5633	378	1	european	european	ADJ
ejpam-5633	378	2	journal	journal	PROPN
ejpam-5633	378	3	of	of	ADP
ejpam-5633	378	4	pure	pure	ADJ
ejpam-5633	378	5	and	and	CCONJ
ejpam-5633	378	6	applied	applied	ADJ
ejpam-5633	378	7	mathematics	mathematic	NOUN
ejpam-5633	378	8	,	,	PUNCT
ejpam-5633	378	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-5633	378	10	,	,	PUNCT
ejpam-5633	378	11	2024	2024	NUM
ejpam-5633	378	12	.	.	PUNCT
ejpam-5633	379	1	[	[	X
ejpam-5633	379	2	50	50	NUM
ejpam-5633	379	3	]	]	PUNCT
ejpam-5633	379	4	p.	p.	NOUN
ejpam-5633	379	5	pue	pue	NOUN
ejpam-5633	379	6	-	-	PUNCT
ejpam-5633	379	7	on	on	ADP
ejpam-5633	379	8	,	,	PUNCT
ejpam-5633	379	9	s.	s.	PROPN
ejpam-5633	379	10	sompong	sompong	PROPN
ejpam-5633	379	11	,	,	PUNCT
ejpam-5633	379	12	and	and	CCONJ
ejpam-5633	379	13	c.	c.	PROPN
ejpam-5633	379	14	boonpok	boonpok	PROPN
ejpam-5633	379	15	.	.	PUNCT
ejpam-5633	380	1	almost	almost	ADV
ejpam-5633	380	2	quasi	quasi	X
ejpam-5633	380	3	(	(	PUNCT
ejpam-5633	380	4	τ1	τ1	NOUN
ejpam-5633	380	5	,	,	PUNCT
ejpam-5633	380	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5633	380	7	for	for	ADP
ejpam-5633	380	8	multifunctions	multifunction	NOUN
ejpam-5633	380	9	.	.	PUNCT
ejpam-5633	381	1	international	international	ADJ
ejpam-5633	381	2	journal	journal	NOUN
ejpam-5633	381	3	of	of	ADP
ejpam-5633	381	4	analysis	analysis	NOUN
ejpam-5633	381	5	and	and	CCONJ
ejpam-5633	381	6	applications	application	NOUN
ejpam-5633	381	7	,	,	PUNCT
ejpam-5633	381	8	22:97	22:97	NUM
ejpam-5633	381	9	,	,	PUNCT
ejpam-5633	381	10	2024	2024	NUM
ejpam-5633	381	11	.	.	PUNCT
ejpam-5633	382	1	[	[	X
ejpam-5633	382	2	51	51	NUM
ejpam-5633	382	3	]	]	X
ejpam-5633	382	4	p.	p.	NOUN
ejpam-5633	382	5	pue	pue	NOUN
ejpam-5633	382	6	-	-	PUNCT
ejpam-5633	382	7	on	on	ADP
ejpam-5633	382	8	,	,	PUNCT
ejpam-5633	382	9	s.	s.	PROPN
ejpam-5633	382	10	sompong	sompong	PROPN
ejpam-5633	382	11	,	,	PUNCT
ejpam-5633	382	12	and	and	CCONJ
ejpam-5633	382	13	c.	c.	PROPN
ejpam-5633	382	14	boonpok	boonpok	PROPN
ejpam-5633	382	15	.	.	PUNCT
ejpam-5633	383	1	upper	upper	ADJ
ejpam-5633	383	2	and	and	CCONJ
ejpam-5633	383	3	lower	low	ADJ
ejpam-5633	383	4	(	(	PUNCT
ejpam-5633	383	5	τ1	τ1	NOUN
ejpam-5633	383	6	,	,	PUNCT
ejpam-5633	383	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	383	8	mulfunctions	mulfunction	NOUN
ejpam-5633	383	9	.	.	PUNCT
ejpam-5633	384	1	international	international	ADJ
ejpam-5633	384	2	journal	journal	NOUN
ejpam-5633	384	3	of	of	ADP
ejpam-5633	384	4	mathematics	mathematic	NOUN
ejpam-5633	384	5	and	and	CCONJ
ejpam-5633	384	6	computer	computer	NOUN
ejpam-5633	384	7	science	science	NOUN
ejpam-5633	384	8	,	,	PUNCT
ejpam-5633	384	9	19(4):1305	19(4):1305	NUM
ejpam-5633	384	10	–	–	PUNCT
ejpam-5633	384	11	1310	1310	NUM
ejpam-5633	384	12	,	,	PUNCT
ejpam-5633	384	13	2024	2024	NUM
ejpam-5633	384	14	.	.	PUNCT
ejpam-5633	385	1	[	[	X
ejpam-5633	385	2	52	52	NUM
ejpam-5633	385	3	]	]	PUNCT
ejpam-5633	385	4	p.	p.	NOUN
ejpam-5633	385	5	pue	pue	NOUN
ejpam-5633	385	6	-	-	PUNCT
ejpam-5633	385	7	on	on	ADP
ejpam-5633	385	8	,	,	PUNCT
ejpam-5633	385	9	s.	s.	PROPN
ejpam-5633	385	10	sompong	sompong	PROPN
ejpam-5633	385	11	,	,	PUNCT
ejpam-5633	385	12	and	and	CCONJ
ejpam-5633	385	13	c.	c.	PROPN
ejpam-5633	385	14	boonpok	boonpok	PROPN
ejpam-5633	385	15	.	.	PUNCT
ejpam-5633	386	1	weakly	weakly	ADJ
ejpam-5633	386	2	quasi	quasi	NOUN
ejpam-5633	386	3	(	(	PUNCT
ejpam-5633	386	4	τ1	τ1	PROPN
ejpam-5633	386	5	,	,	PUNCT
ejpam-5633	386	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	386	7	multifunctions	multifunction	NOUN
ejpam-5633	386	8	.	.	PUNCT
ejpam-5633	387	1	european	european	ADJ
ejpam-5633	387	2	journal	journal	PROPN
ejpam-5633	387	3	of	of	ADP
ejpam-5633	387	4	pure	pure	ADJ
ejpam-5633	387	5	and	and	CCONJ
ejpam-5633	387	6	applied	applied	ADJ
ejpam-5633	387	7	mathematics	mathematic	NOUN
ejpam-5633	387	8	,	,	PUNCT
ejpam-5633	387	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-5633	387	10	,	,	PUNCT
ejpam-5633	387	11	2024	2024	NUM
ejpam-5633	387	12	.	.	PUNCT
ejpam-5633	388	1	[	[	X
ejpam-5633	388	2	53	53	NUM
ejpam-5633	388	3	]	]	PUNCT
ejpam-5633	388	4	e.	e.	PROPN
ejpam-5633	388	5	rosas	rosas	PROPN
ejpam-5633	388	6	,	,	PUNCT
ejpam-5633	388	7	c.	c.	PROPN
ejpam-5633	388	8	carpintero	carpintero	PROPN
ejpam-5633	388	9	,	,	PUNCT
ejpam-5633	388	10	and	and	CCONJ
ejpam-5633	388	11	j.	j.	PROPN
ejpam-5633	388	12	moreno	moreno	PROPN
ejpam-5633	388	13	.	.	PUNCT
ejpam-5633	389	1	more	more	ADV
ejpam-5633	389	2	on	on	ADP
ejpam-5633	389	3	upper	upper	ADJ
ejpam-5633	389	4	and	and	CCONJ
ejpam-5633	389	5	lower	low	ADJ
ejpam-5633	389	6	almost	almost	ADV
ejpam-5633	389	7	nearly	nearly	ADV
ejpam-5633	389	8	i	i	PRON
ejpam-5633	389	9	m.	m.	NOUN
ejpam-5633	389	10	thongmoon	thongmoon	NOUN
ejpam-5633	389	11	,	,	PUNCT
ejpam-5633	389	12	a.	a.	PROPN
ejpam-5633	389	13	sama	sama	PROPN
ejpam-5633	389	14	-	-	PUNCT
ejpam-5633	389	15	ae	ae	PROPN
ejpam-5633	389	16	,	,	PUNCT
ejpam-5633	389	17	c.	c.	PROPN
ejpam-5633	389	18	boonpok	boonpok	PROPN
ejpam-5633	389	19	/	/	SYM
ejpam-5633	389	20	eur	eur	PROPN
ejpam-5633	389	21	.	.	PUNCT
ejpam-5633	390	1	j.	j.	PROPN
ejpam-5633	390	2	pure	pure	PROPN
ejpam-5633	390	3	appl	appl	PROPN
ejpam-5633	390	4	.	.	PROPN
ejpam-5633	390	5	math	math	PROPN
ejpam-5633	390	6	,	,	PUNCT
ejpam-5633	390	7	18	18	NUM
ejpam-5633	390	8	(	(	PUNCT
ejpam-5633	390	9	1	1	NUM
ejpam-5633	390	10	)	)	PUNCT
ejpam-5633	390	11	(	(	PUNCT
ejpam-5633	390	12	2025	2025	NUM
ejpam-5633	390	13	)	)	PUNCT
ejpam-5633	390	14	,	,	PUNCT
ejpam-5633	390	15	5633	5633	NUM
ejpam-5633	390	16	13	13	NUM
ejpam-5633	390	17	of	of	ADP
ejpam-5633	390	18	13	13	NUM
ejpam-5633	390	19	continuous	continuous	ADJ
ejpam-5633	390	20	multifunctions	multifunction	NOUN
ejpam-5633	390	21	.	.	PUNCT
ejpam-5633	391	1	international	international	ADJ
ejpam-5633	391	2	journal	journal	NOUN
ejpam-5633	391	3	of	of	ADP
ejpam-5633	391	4	pure	pure	ADJ
ejpam-5633	391	5	and	and	CCONJ
ejpam-5633	391	6	applied	applied	ADJ
ejpam-5633	391	7	mathematics	mathematic	NOUN
ejpam-5633	391	8	,	,	PUNCT
ejpam-5633	391	9	117(3):521–537	117(3):521–537	NUM
ejpam-5633	391	10	,	,	PUNCT
ejpam-5633	391	11	2017	2017	NUM
ejpam-5633	391	12	.	.	PUNCT
ejpam-5633	392	1	[	[	X
ejpam-5633	392	2	54	54	NUM
ejpam-5633	392	3	]	]	X
ejpam-5633	392	4	n.	n.	PROPN
ejpam-5633	392	5	srisarakham	srisarakham	PROPN
ejpam-5633	392	6	and	and	CCONJ
ejpam-5633	392	7	c.	c.	PROPN
ejpam-5633	392	8	boonpok	boonpok	PROPN
ejpam-5633	392	9	.	.	PUNCT
ejpam-5633	393	1	almost	almost	ADV
ejpam-5633	393	2	(	(	PUNCT
ejpam-5633	393	3	λ	λ	NOUN
ejpam-5633	393	4	,	,	PUNCT
ejpam-5633	393	5	p)-continuous	p)-continuous	ADJ
ejpam-5633	393	6	functions	function	NOUN
ejpam-5633	393	7	.	.	PUNCT
ejpam-5633	394	1	international	international	ADJ
ejpam-5633	394	2	journal	journal	PROPN
ejpam-5633	394	3	of	of	ADP
ejpam-5633	394	4	mathematics	mathematic	NOUN
ejpam-5633	394	5	and	and	CCONJ
ejpam-5633	394	6	computer	computer	NOUN
ejpam-5633	394	7	science	science	NOUN
ejpam-5633	394	8	,	,	PUNCT
ejpam-5633	394	9	18(2):255–259	18(2):255–259	NUM
ejpam-5633	394	10	,	,	PUNCT
ejpam-5633	394	11	2023	2023	NUM
ejpam-5633	394	12	.	.	PUNCT
ejpam-5633	395	1	[	[	X
ejpam-5633	395	2	55	55	NUM
ejpam-5633	395	3	]	]	X
ejpam-5633	395	4	n.	n.	PROPN
ejpam-5633	395	5	srisarakham	srisarakham	PROPN
ejpam-5633	395	6	,	,	PUNCT
ejpam-5633	395	7	a.	a.	PROPN
ejpam-5633	395	8	sama	sama	PROPN
ejpam-5633	395	9	-	-	PUNCT
ejpam-5633	395	10	ae	ae	PROPN
ejpam-5633	395	11	,	,	PUNCT
ejpam-5633	395	12	and	and	CCONJ
ejpam-5633	395	13	c.	c.	PROPN
ejpam-5633	395	14	boonpok	boonpok	PROPN
ejpam-5633	395	15	.	.	PUNCT
ejpam-5633	396	1	characterizations	characterization	NOUN
ejpam-5633	396	2	of	of	ADP
ejpam-5633	396	3	faintly	faintly	ADV
ejpam-5633	396	4	(	(	PUNCT
ejpam-5633	396	5	τ1	τ1	PROPN
ejpam-5633	396	6	,	,	PUNCT
ejpam-5633	396	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	396	8	functions	function	NOUN
ejpam-5633	396	9	.	.	PUNCT
ejpam-5633	397	1	european	european	ADJ
ejpam-5633	397	2	journal	journal	PROPN
ejpam-5633	397	3	of	of	ADP
ejpam-5633	397	4	pure	pure	ADJ
ejpam-5633	397	5	and	and	CCONJ
ejpam-5633	397	6	applied	applied	ADJ
ejpam-5633	397	7	mathematics	mathematic	NOUN
ejpam-5633	397	8	,	,	PUNCT
ejpam-5633	397	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-5633	397	10	,	,	PUNCT
ejpam-5633	397	11	2024	2024	NUM
ejpam-5633	397	12	.	.	PUNCT
ejpam-5633	398	1	[	[	X
ejpam-5633	398	2	56	56	NUM
ejpam-5633	398	3	]	]	PUNCT
ejpam-5633	398	4	m.	m.	NOUN
ejpam-5633	398	5	thongmoon	thongmoon	NOUN
ejpam-5633	398	6	and	and	CCONJ
ejpam-5633	398	7	c.	c.	PROPN
ejpam-5633	398	8	boonpok	boonpok	PROPN
ejpam-5633	398	9	.	.	PUNCT
ejpam-5633	399	1	upper	upper	ADJ
ejpam-5633	399	2	and	and	CCONJ
ejpam-5633	399	3	lower	low	ADJ
ejpam-5633	399	4	almost	almost	ADV
ejpam-5633	399	5	β(λ	β(λ	NOUN
ejpam-5633	399	6	,	,	PUNCT
ejpam-5633	399	7	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	399	8	multifunctions	multifunction	NOUN
ejpam-5633	399	9	.	.	PUNCT
ejpam-5633	400	1	wseas	wseas	VERB
ejpam-5633	400	2	transactions	transaction	NOUN
ejpam-5633	400	3	on	on	ADP
ejpam-5633	400	4	mathematics	mathematic	NOUN
ejpam-5633	400	5	,	,	PUNCT
ejpam-5633	400	6	21:844–853	21:844–853	NUM
ejpam-5633	400	7	,	,	PUNCT
ejpam-5633	400	8	2022	2022	NUM
ejpam-5633	400	9	.	.	PUNCT
ejpam-5633	401	1	[	[	X
ejpam-5633	401	2	57	57	NUM
ejpam-5633	401	3	]	]	PUNCT
ejpam-5633	401	4	m.	m.	NOUN
ejpam-5633	401	5	thongmoon	thongmoon	NOUN
ejpam-5633	401	6	and	and	CCONJ
ejpam-5633	401	7	c.	c.	PROPN
ejpam-5633	401	8	boonpok	boonpok	PROPN
ejpam-5633	401	9	.	.	PUNCT
ejpam-5633	402	1	strongly	strongly	ADV
ejpam-5633	402	2	θ(λ	θ(λ	PROPN
ejpam-5633	402	3	,	,	PUNCT
ejpam-5633	402	4	p)-continuous	p)-continuous	ADJ
ejpam-5633	402	5	functions	function	NOUN
ejpam-5633	402	6	.	.	PUNCT
ejpam-5633	403	1	international	international	ADJ
ejpam-5633	403	2	journal	journal	PROPN
ejpam-5633	403	3	of	of	ADP
ejpam-5633	403	4	mathematics	mathematic	NOUN
ejpam-5633	403	5	and	and	CCONJ
ejpam-5633	403	6	computer	computer	NOUN
ejpam-5633	403	7	science	science	NOUN
ejpam-5633	403	8	,	,	PUNCT
ejpam-5633	403	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5633	403	10	,	,	PUNCT
ejpam-5633	403	11	2024	2024	NUM
ejpam-5633	403	12	.	.	PUNCT
ejpam-5633	404	1	[	[	X
ejpam-5633	404	2	58	58	NUM
ejpam-5633	404	3	]	]	PUNCT
ejpam-5633	404	4	m.	m.	NOUN
ejpam-5633	404	5	thongmoon	thongmoon	NOUN
ejpam-5633	404	6	,	,	PUNCT
ejpam-5633	404	7	s.	s.	PROPN
ejpam-5633	404	8	sompong	sompong	PROPN
ejpam-5633	404	9	,	,	PUNCT
ejpam-5633	404	10	and	and	CCONJ
ejpam-5633	404	11	c.	c.	PROPN
ejpam-5633	404	12	boonpok	boonpok	PROPN
ejpam-5633	404	13	.	.	PUNCT
ejpam-5633	405	1	upper	upper	ADJ
ejpam-5633	405	2	and	and	CCONJ
ejpam-5633	405	3	lower	low	ADJ
ejpam-5633	405	4	weak	weak	ADJ
ejpam-5633	405	5	(	(	PUNCT
ejpam-5633	405	6	τ1	τ1	NOUN
ejpam-5633	405	7	,	,	PUNCT
ejpam-5633	405	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5633	405	9	.	.	PUNCT
ejpam-5633	406	1	european	european	PROPN
ejpam-5633	406	2	journal	journal	PROPN
ejpam-5633	406	3	of	of	ADP
ejpam-5633	406	4	pure	pure	ADJ
ejpam-5633	406	5	and	and	CCONJ
ejpam-5633	406	6	applied	applied	ADJ
ejpam-5633	406	7	mathematics	mathematic	NOUN
ejpam-5633	406	8	,	,	PUNCT
ejpam-5633	406	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5633	406	10	,	,	PUNCT
ejpam-5633	406	11	2024	2024	NUM
ejpam-5633	406	12	.	.	PUNCT
ejpam-5633	407	1	[	[	X
ejpam-5633	407	2	59	59	NUM
ejpam-5633	407	3	]	]	PUNCT
ejpam-5633	407	4	m.	m.	NOUN
ejpam-5633	407	5	thongmoon	thongmoon	NOUN
ejpam-5633	407	6	,	,	PUNCT
ejpam-5633	407	7	s.	s.	PROPN
ejpam-5633	407	8	sompong	sompong	PROPN
ejpam-5633	407	9	,	,	PUNCT
ejpam-5633	407	10	and	and	CCONJ
ejpam-5633	407	11	c.	c.	PROPN
ejpam-5633	407	12	boonpok	boonpok	PROPN
ejpam-5633	407	13	.	.	PUNCT
ejpam-5633	408	1	rarely	rarely	ADV
ejpam-5633	408	2	(	(	PUNCT
ejpam-5633	408	3	τ1	τ1	NOUN
ejpam-5633	408	4	,	,	PUNCT
ejpam-5633	408	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5633	408	6	functions	function	NOUN
ejpam-5633	408	7	.	.	PUNCT
ejpam-5633	409	1	international	international	ADJ
ejpam-5633	409	2	journal	journal	NOUN
ejpam-5633	409	3	of	of	ADP
ejpam-5633	409	4	mathematics	mathematic	NOUN
ejpam-5633	409	5	and	and	CCONJ
ejpam-5633	409	6	computer	computer	NOUN
ejpam-5633	409	7	science	science	NOUN
ejpam-5633	409	8	,	,	PUNCT
ejpam-5633	409	9	20(1):423–427	20(1):423–427	NUM
ejpam-5633	409	10	,	,	PUNCT
ejpam-5633	409	11	2025	2025	NUM
ejpam-5633	409	12	.	.	PUNCT
ejpam-5633	410	1	[	[	X
ejpam-5633	410	2	60	60	NUM
ejpam-5633	410	3	]	]	X
ejpam-5633	410	4	c.	c.	PROPN
ejpam-5633	410	5	viriyapong	viriyapong	PROPN
ejpam-5633	410	6	and	and	CCONJ
ejpam-5633	410	7	c.	c.	PROPN
ejpam-5633	410	8	boonpok	boonpok	PROPN
ejpam-5633	410	9	.	.	PUNCT
ejpam-5633	411	1	(	(	PUNCT
ejpam-5633	411	2	τ1	τ1	NOUN
ejpam-5633	411	3	,	,	PUNCT
ejpam-5633	411	4	τ2)α	τ2)α	NOUN
ejpam-5633	411	5	-	-	PUNCT
ejpam-5633	411	6	continuity	continuity	NOUN
ejpam-5633	411	7	for	for	ADP
ejpam-5633	411	8	multifunctions	multifunction	NOUN
ejpam-5633	411	9	.	.	PUNCT
ejpam-5633	412	1	journal	journal	PROPN
ejpam-5633	412	2	of	of	ADP
ejpam-5633	412	3	mathematics	mathematic	NOUN
ejpam-5633	412	4	,	,	PUNCT
ejpam-5633	412	5	2020:6285763	2020:6285763	NUM
ejpam-5633	412	6	,	,	PUNCT
ejpam-5633	412	7	2020	2020	NUM
ejpam-5633	412	8	.	.	PUNCT
ejpam-5633	413	1	[	[	X
ejpam-5633	413	2	61	61	NUM
ejpam-5633	413	3	]	]	X
ejpam-5633	413	4	c.	c.	PROPN
ejpam-5633	413	5	viriyapong	viriyapong	PROPN
ejpam-5633	413	6	and	and	CCONJ
ejpam-5633	413	7	c.	c.	PROPN
ejpam-5633	413	8	boonpok	boonpok	PROPN
ejpam-5633	413	9	.	.	PUNCT
ejpam-5633	414	1	(	(	PUNCT
ejpam-5633	414	2	λ	λ	X
ejpam-5633	414	3	,	,	PUNCT
ejpam-5633	414	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5633	414	5	functions	function	NOUN
ejpam-5633	414	6	.	.	PUNCT
ejpam-5633	415	1	wseas	wseas	VERB
ejpam-5633	415	2	transactions	transaction	NOUN
ejpam-5633	415	3	on	on	ADP
ejpam-5633	415	4	mathematics	mathematic	NOUN
ejpam-5633	415	5	,	,	PUNCT
ejpam-5633	415	6	21:380–385	21:380–385	NUM
ejpam-5633	415	7	,	,	PUNCT
ejpam-5633	415	8	2022	2022	NUM
ejpam-5633	415	9	.	.	PUNCT
ejpam-5633	416	1	[	[	X
ejpam-5633	416	2	62	62	NUM
ejpam-5633	416	3	]	]	PUNCT
ejpam-5633	416	4	c.	c.	PROPN
ejpam-5633	416	5	viriyapong	viriyapong	PROPN
ejpam-5633	416	6	and	and	CCONJ
ejpam-5633	416	7	c.	c.	PROPN
ejpam-5633	416	8	boonpok	boonpok	PROPN
ejpam-5633	416	9	.	.	PUNCT
ejpam-5633	417	1	weak	weak	ADJ
ejpam-5633	417	2	quasi	quasi	NOUN
ejpam-5633	417	3	(	(	PUNCT
ejpam-5633	417	4	λ	λ	PROPN
ejpam-5633	417	5	,	,	PUNCT
ejpam-5633	417	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5633	417	7	for	for	ADP
ejpam-5633	417	8	multifunctions	multifunction	NOUN
ejpam-5633	417	9	.	.	PUNCT
ejpam-5633	418	1	international	international	ADJ
ejpam-5633	418	2	journal	journal	PROPN
ejpam-5633	418	3	of	of	ADP
ejpam-5633	418	4	mathematics	mathematic	NOUN
ejpam-5633	418	5	and	and	CCONJ
ejpam-5633	418	6	computer	computer	NOUN
ejpam-5633	418	7	science	science	NOUN
ejpam-5633	418	8	,	,	PUNCT
ejpam-5633	418	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5633	418	10	,	,	PUNCT
ejpam-5633	418	11	2022	2022	NUM
ejpam-5633	418	12	.	.	PUNCT
ejpam-5633	419	1	[	[	X
ejpam-5633	419	2	63	63	NUM
ejpam-5633	419	3	]	]	PUNCT
ejpam-5633	419	4	n.	n.	PROPN
ejpam-5633	419	5	viriyapong	viriyapong	PROPN
ejpam-5633	419	6	,	,	PUNCT
ejpam-5633	419	7	s.	s.	PROPN
ejpam-5633	419	8	sompong	sompong	PROPN
ejpam-5633	419	9	,	,	PUNCT
ejpam-5633	419	10	and	and	CCONJ
ejpam-5633	419	11	c.	c.	PROPN
ejpam-5633	419	12	boonpok	boonpok	PROPN
ejpam-5633	419	13	.	.	PUNCT
ejpam-5633	420	1	(	(	PUNCT
ejpam-5633	420	2	τ1	τ1	NOUN
ejpam-5633	420	3	,	,	PUNCT
ejpam-5633	420	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5633	420	5	disconnectedness	disconnectedness	NOUN
ejpam-5633	420	6	in	in	ADP
ejpam-5633	420	7	bitopological	bitopological	ADJ
ejpam-5633	420	8	spaces	space	NOUN
ejpam-5633	420	9	.	.	PUNCT
ejpam-5633	421	1	international	international	ADJ
ejpam-5633	421	2	journal	journal	PROPN
ejpam-5633	421	3	of	of	ADP
ejpam-5633	421	4	mathematics	mathematic	NOUN
ejpam-5633	421	5	and	and	CCONJ
ejpam-5633	421	6	computer	computer	NOUN
ejpam-5633	421	7	science	science	NOUN
ejpam-5633	421	8	,	,	PUNCT
ejpam-5633	421	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5633	421	10	,	,	PUNCT
ejpam-5633	421	11	2024	2024	NUM
ejpam-5633	421	12	.	.	PUNCT
ejpam-5633	422	1	[	[	X
ejpam-5633	422	2	64	64	NUM
ejpam-5633	422	3	]	]	X
ejpam-5633	422	4	n.	n.	PROPN
ejpam-5633	422	5	viriyapong	viriyapong	PROPN
ejpam-5633	422	6	,	,	PUNCT
ejpam-5633	422	7	s.	s.	PROPN
ejpam-5633	422	8	sompong	sompong	PROPN
ejpam-5633	422	9	,	,	PUNCT
ejpam-5633	422	10	and	and	CCONJ
ejpam-5633	422	11	c.	c.	PROPN
ejpam-5633	422	12	boonpok	boonpok	PROPN
ejpam-5633	422	13	.	.	PUNCT
ejpam-5633	423	1	upper	upper	ADJ
ejpam-5633	423	2	and	and	CCONJ
ejpam-5633	423	3	lower	low	ADJ
ejpam-5633	423	4	s-(τ1	s-(τ1	NOUN
ejpam-5633	423	5	,	,	PUNCT
ejpam-5633	423	6	τ2)p	τ2)p	ADJ
ejpam-5633	423	7	-	-	PUNCT
ejpam-5633	423	8	continuous	continuous	ADJ
ejpam-5633	423	9	multifunctions	multifunction	NOUN
ejpam-5633	423	10	.	.	PUNCT
ejpam-5633	424	1	european	european	ADJ
ejpam-5633	424	2	journal	journal	PROPN
ejpam-5633	424	3	of	of	ADP
ejpam-5633	424	4	pure	pure	ADJ
ejpam-5633	424	5	and	and	CCONJ
ejpam-5633	424	6	applied	applied	ADJ
ejpam-5633	424	7	mathematics	mathematic	NOUN
ejpam-5633	424	8	,	,	PUNCT
ejpam-5633	424	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-5633	424	10	,	,	PUNCT
ejpam-5633	424	11	2024	2024	NUM
ejpam-5633	424	12	.	.	PUNCT