id	sid	tid	token	lemma	pos
ejpam-5718	1	1	european	european	PROPN
ejpam-5718	1	2	journal	journal	PROPN
ejpam-5718	1	3	of	of	ADP
ejpam-5718	1	4	pure	pure	ADJ
ejpam-5718	1	5	and	and	CCONJ
ejpam-5718	1	6	applied	applied	ADJ
ejpam-5718	1	7	mathematics	mathematic	NOUN
ejpam-5718	1	8	2025	2025	NUM
ejpam-5718	1	9	,	,	PUNCT
ejpam-5718	1	10	vol	vol	NOUN
ejpam-5718	1	11	.	.	PROPN
ejpam-5718	1	12	18	18	NUM
ejpam-5718	1	13	,	,	PUNCT
ejpam-5718	1	14	issue	issue	NOUN
ejpam-5718	1	15	1	1	NUM
ejpam-5718	1	16	,	,	PUNCT
ejpam-5718	1	17	article	article	NOUN
ejpam-5718	1	18	number	number	NOUN
ejpam-5718	1	19	5718	5718	NUM
ejpam-5718	1	20	issn	issn	PROPN
ejpam-5718	1	21	1307	1307	NUM
ejpam-5718	1	22	-	-	SYM
ejpam-5718	1	23	5543	5543	NUM
ejpam-5718	1	24	–	–	PUNCT
ejpam-5718	1	25	ejpam.com	ejpam.com	X
ejpam-5718	1	26	published	publish	VERB
ejpam-5718	1	27	by	by	ADP
ejpam-5718	1	28	new	new	PROPN
ejpam-5718	1	29	york	york	PROPN
ejpam-5718	1	30	business	business	PROPN
ejpam-5718	1	31	global	global	PROPN
ejpam-5718	1	32	upper	upper	ADJ
ejpam-5718	1	33	and	and	CCONJ
ejpam-5718	1	34	lower	low	ADJ
ejpam-5718	1	35	weakly	weakly	ADJ
ejpam-5718	1	36	s-(τ1	s-(τ1	PROPN
ejpam-5718	1	37	,	,	PUNCT
ejpam-5718	1	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	1	39	multifunctions	multifunction	NOUN
ejpam-5718	1	40	prapart	prapart	VERB
ejpam-5718	1	41	pue	pue	PROPN
ejpam-5718	1	42	-	-	PUNCT
ejpam-5718	1	43	on1	on1	PROPN
ejpam-5718	1	44	,	,	PUNCT
ejpam-5718	1	45	areeyuth	areeyuth	NOUN
ejpam-5718	1	46	sama	sama	NOUN
ejpam-5718	1	47	-	-	PUNCT
ejpam-5718	1	48	ae2	ae2	PROPN
ejpam-5718	1	49	,	,	PUNCT
ejpam-5718	1	50	chawalit	chawalit	VERB
ejpam-5718	1	51	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5718	1	52	1	1	NUM
ejpam-5718	1	53	mathematics	mathematic	NOUN
ejpam-5718	1	54	and	and	CCONJ
ejpam-5718	1	55	applied	apply	VERB
ejpam-5718	1	56	mathematics	mathematics	PROPN
ejpam-5718	1	57	research	research	NOUN
ejpam-5718	1	58	unit	unit	NOUN
ejpam-5718	1	59	,	,	PUNCT
ejpam-5718	1	60	department	department	NOUN
ejpam-5718	1	61	of	of	ADP
ejpam-5718	1	62	mathematics	mathematic	NOUN
ejpam-5718	1	63	,	,	PUNCT
ejpam-5718	1	64	faculty	faculty	NOUN
ejpam-5718	1	65	of	of	ADP
ejpam-5718	1	66	science	science	NOUN
ejpam-5718	1	67	,	,	PUNCT
ejpam-5718	1	68	mahasarakham	mahasarakham	PROPN
ejpam-5718	1	69	university	university	PROPN
ejpam-5718	1	70	,	,	PUNCT
ejpam-5718	1	71	maha	maha	PROPN
ejpam-5718	1	72	sarakham	sarakham	PROPN
ejpam-5718	1	73	,	,	PUNCT
ejpam-5718	1	74	44150	44150	NUM
ejpam-5718	1	75	,	,	PUNCT
ejpam-5718	1	76	thailand	thailand	PROPN
ejpam-5718	1	77	2	2	NUM
ejpam-5718	1	78	department	department	NOUN
ejpam-5718	1	79	of	of	ADP
ejpam-5718	1	80	mathematics	mathematic	NOUN
ejpam-5718	1	81	and	and	CCONJ
ejpam-5718	1	82	computer	computer	NOUN
ejpam-5718	1	83	science	science	NOUN
ejpam-5718	1	84	,	,	PUNCT
ejpam-5718	1	85	faculty	faculty	NOUN
ejpam-5718	1	86	of	of	ADP
ejpam-5718	1	87	science	science	NOUN
ejpam-5718	1	88	and	and	CCONJ
ejpam-5718	1	89	technology	technology	NOUN
ejpam-5718	1	90	,	,	PUNCT
ejpam-5718	1	91	prince	prince	NOUN
ejpam-5718	1	92	of	of	ADP
ejpam-5718	1	93	songkla	songkla	PROPN
ejpam-5718	1	94	university	university	PROPN
ejpam-5718	1	95	,	,	PUNCT
ejpam-5718	1	96	pattani	pattani	NOUN
ejpam-5718	1	97	campus	campus	NOUN
ejpam-5718	1	98	,	,	PUNCT
ejpam-5718	1	99	pattani	pattani	NOUN
ejpam-5718	1	100	,	,	PUNCT
ejpam-5718	1	101	94000	94000	NUM
ejpam-5718	1	102	,	,	PUNCT
ejpam-5718	1	103	thailand	thailand	PROPN
ejpam-5718	1	104	abstract	abstract	PROPN
ejpam-5718	1	105	.	.	PUNCT
ejpam-5718	2	1	this	this	DET
ejpam-5718	2	2	article	article	NOUN
ejpam-5718	2	3	presents	present	VERB
ejpam-5718	2	4	new	new	ADJ
ejpam-5718	2	5	classes	class	NOUN
ejpam-5718	2	6	of	of	ADP
ejpam-5718	2	7	multifunctions	multifunction	NOUN
ejpam-5718	2	8	called	call	VERB
ejpam-5718	2	9	upper	upper	ADJ
ejpam-5718	2	10	weakly	weakly	ADJ
ejpam-5718	2	11	s-(τ1	s-(τ1	PROPN
ejpam-5718	2	12	,	,	PUNCT
ejpam-5718	2	13	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	2	14	multifunctions	multifunction	NOUN
ejpam-5718	2	15	and	and	CCONJ
ejpam-5718	2	16	lower	low	ADJ
ejpam-5718	2	17	weakly	weakly	ADJ
ejpam-5718	2	18	s-(τ1	s-(τ1	PROPN
ejpam-5718	2	19	,	,	PUNCT
ejpam-5718	2	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	2	21	multifunctions	multifunction	NOUN
ejpam-5718	2	22	.	.	PUNCT
ejpam-5718	3	1	furthermore	furthermore	ADV
ejpam-5718	3	2	,	,	PUNCT
ejpam-5718	3	3	several	several	ADJ
ejpam-5718	3	4	characterizations	characterization	NOUN
ejpam-5718	3	5	of	of	ADP
ejpam-5718	3	6	upper	upper	ADJ
ejpam-5718	3	7	weakly	weakly	ADJ
ejpam-5718	3	8	s-(τ1	s-(τ1	PROPN
ejpam-5718	3	9	,	,	PUNCT
ejpam-5718	3	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	3	11	multifunctions	multifunction	NOUN
ejpam-5718	3	12	and	and	CCONJ
ejpam-5718	3	13	lower	low	ADJ
ejpam-5718	3	14	weakly	weakly	ADJ
ejpam-5718	3	15	s-(τ1	s-(τ1	PROPN
ejpam-5718	3	16	,	,	PUNCT
ejpam-5718	3	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	3	18	multifunctions	multifunction	NOUN
ejpam-5718	3	19	are	be	AUX
ejpam-5718	3	20	discussed	discuss	VERB
ejpam-5718	3	21	.	.	PUNCT
ejpam-5718	4	1	2020	2020	NUM
ejpam-5718	4	2	mathematics	mathematic	NOUN
ejpam-5718	4	3	subject	subject	NOUN
ejpam-5718	4	4	classifications	classification	NOUN
ejpam-5718	4	5	:	:	PUNCT
ejpam-5718	4	6	54c08	54c08	NUM
ejpam-5718	4	7	,	,	PUNCT
ejpam-5718	4	8	54c60	54c60	NUM
ejpam-5718	4	9	key	key	ADJ
ejpam-5718	4	10	words	word	NOUN
ejpam-5718	4	11	and	and	CCONJ
ejpam-5718	4	12	phrases	phrase	NOUN
ejpam-5718	4	13	:	:	PUNCT
ejpam-5718	4	14	τ1τ2	τ1τ2	ADJ
ejpam-5718	4	15	-	-	ADJ
ejpam-5718	4	16	open	open	ADJ
ejpam-5718	4	17	set	set	NOUN
ejpam-5718	4	18	,	,	PUNCT
ejpam-5718	4	19	upper	upper	ADJ
ejpam-5718	4	20	weakly	weakly	ADJ
ejpam-5718	4	21	s-(τ1	s-(τ1	PROPN
ejpam-5718	4	22	,	,	PUNCT
ejpam-5718	4	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	4	24	multifunction	multifunction	NOUN
ejpam-5718	4	25	,	,	PUNCT
ejpam-5718	4	26	lower	low	ADJ
ejpam-5718	4	27	weakly	weakly	ADJ
ejpam-5718	4	28	s-(τ1	s-(τ1	PROPN
ejpam-5718	4	29	,	,	PUNCT
ejpam-5718	4	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	4	31	multifunction	multifunction	NOUN
ejpam-5718	4	32	1	1	NUM
ejpam-5718	4	33	.	.	PUNCT
ejpam-5718	5	1	introduction	introduction	NOUN
ejpam-5718	5	2	in	in	ADP
ejpam-5718	5	3	topology	topology	NOUN
ejpam-5718	5	4	,	,	PUNCT
ejpam-5718	5	5	there	there	PRON
ejpam-5718	5	6	has	have	AUX
ejpam-5718	5	7	been	be	AUX
ejpam-5718	5	8	recently	recently	ADV
ejpam-5718	5	9	significant	significant	ADJ
ejpam-5718	5	10	interest	interest	NOUN
ejpam-5718	5	11	in	in	ADP
ejpam-5718	5	12	characterizing	characterize	VERB
ejpam-5718	5	13	and	and	CCONJ
ejpam-5718	5	14	investigating	investigate	VERB
ejpam-5718	5	15	the	the	DET
ejpam-5718	5	16	characterizations	characterization	NOUN
ejpam-5718	5	17	of	of	ADP
ejpam-5718	5	18	some	some	DET
ejpam-5718	5	19	weak	weak	ADJ
ejpam-5718	5	20	forms	form	NOUN
ejpam-5718	5	21	of	of	ADP
ejpam-5718	5	22	continuity	continuity	NOUN
ejpam-5718	5	23	for	for	ADP
ejpam-5718	5	24	functions	function	NOUN
ejpam-5718	5	25	and	and	CCONJ
ejpam-5718	5	26	multifunctions	multifunction	NOUN
ejpam-5718	5	27	.	.	PUNCT
ejpam-5718	6	1	as	as	ADP
ejpam-5718	6	2	weak	weak	ADJ
ejpam-5718	6	3	forms	form	NOUN
ejpam-5718	6	4	of	of	ADP
ejpam-5718	6	5	continuity	continuity	NOUN
ejpam-5718	6	6	in	in	ADP
ejpam-5718	6	7	topological	topological	ADJ
ejpam-5718	6	8	spaces	space	NOUN
ejpam-5718	6	9	,	,	PUNCT
ejpam-5718	6	10	weak	weak	ADJ
ejpam-5718	6	11	continuity	continuity	NOUN
ejpam-5718	6	12	[	[	X
ejpam-5718	6	13	44	44	NUM
ejpam-5718	6	14	]	]	PUNCT
ejpam-5718	6	15	,	,	PUNCT
ejpam-5718	6	16	quasicontinuity	quasicontinuity	NOUN
ejpam-5718	6	17	[	[	X
ejpam-5718	6	18	47	47	NUM
ejpam-5718	6	19	]	]	PUNCT
ejpam-5718	6	20	,	,	PUNCT
ejpam-5718	6	21	semi	semi	ADJ
ejpam-5718	6	22	-	-	NOUN
ejpam-5718	6	23	continuity	continuity	NOUN
ejpam-5718	6	24	[	[	X
ejpam-5718	6	25	45	45	NUM
ejpam-5718	6	26	]	]	PUNCT
ejpam-5718	6	27	and	and	CCONJ
ejpam-5718	6	28	almost	almost	ADV
ejpam-5718	6	29	continuity	continuity	NOUN
ejpam-5718	6	30	in	in	ADP
ejpam-5718	6	31	the	the	DET
ejpam-5718	6	32	sense	sense	NOUN
ejpam-5718	6	33	of	of	ADP
ejpam-5718	6	34	husain	husain	NOUN
ejpam-5718	7	1	[	[	X
ejpam-5718	7	2	36	36	NUM
ejpam-5718	7	3	]	]	PUNCT
ejpam-5718	7	4	are	be	AUX
ejpam-5718	7	5	well	well	ADV
ejpam-5718	7	6	-	-	PUNCT
ejpam-5718	7	7	known	know	VERB
ejpam-5718	7	8	.	.	PUNCT
ejpam-5718	8	1	lee	lee	PROPN
ejpam-5718	9	1	[	[	X
ejpam-5718	9	2	43	43	NUM
ejpam-5718	9	3	]	]	PUNCT
ejpam-5718	9	4	studied	study	VERB
ejpam-5718	9	5	the	the	DET
ejpam-5718	9	6	concept	concept	NOUN
ejpam-5718	9	7	of	of	ADP
ejpam-5718	9	8	semiconnected	semiconnecte	VERB
ejpam-5718	9	9	functions	function	NOUN
ejpam-5718	9	10	.	.	PUNCT
ejpam-5718	10	1	kohli	kohli	PROPN
ejpam-5718	11	1	[	[	X
ejpam-5718	11	2	40	40	NUM
ejpam-5718	11	3	]	]	PUNCT
ejpam-5718	11	4	introduced	introduce	VERB
ejpam-5718	11	5	the	the	DET
ejpam-5718	11	6	notion	notion	NOUN
ejpam-5718	11	7	of	of	ADP
ejpam-5718	11	8	s	s	NOUN
ejpam-5718	11	9	-	-	ADJ
ejpam-5718	11	10	continuous	continuous	ADJ
ejpam-5718	11	11	functions	function	NOUN
ejpam-5718	11	12	and	and	CCONJ
ejpam-5718	11	13	investigated	investigate	VERB
ejpam-5718	11	14	some	some	DET
ejpam-5718	11	15	characterizations	characterization	NOUN
ejpam-5718	11	16	of	of	ADP
ejpam-5718	11	17	semilocally	semilocally	ADV
ejpam-5718	11	18	connected	connect	VERB
ejpam-5718	11	19	spaces	space	NOUN
ejpam-5718	11	20	in	in	ADP
ejpam-5718	11	21	terms	term	NOUN
ejpam-5718	11	22	of	of	ADP
ejpam-5718	11	23	s	s	NOUN
ejpam-5718	11	24	-	-	ADJ
ejpam-5718	11	25	continuous	continuous	ADJ
ejpam-5718	11	26	functions	function	NOUN
ejpam-5718	11	27	.	.	PUNCT
ejpam-5718	12	1	the	the	DET
ejpam-5718	12	2	notion	notion	NOUN
ejpam-5718	12	3	of	of	ADP
ejpam-5718	12	4	s	s	NOUN
ejpam-5718	12	5	-	-	NOUN
ejpam-5718	12	6	continuity	continuity	NOUN
ejpam-5718	12	7	as	as	ADP
ejpam-5718	12	8	a	a	DET
ejpam-5718	12	9	generalization	generalization	NOUN
ejpam-5718	12	10	of	of	ADP
ejpam-5718	12	11	continuity	continuity	NOUN
ejpam-5718	12	12	and	and	CCONJ
ejpam-5718	12	13	semiconnectedness	semiconnectedness	NOUN
ejpam-5718	12	14	.	.	PUNCT
ejpam-5718	13	1	moreover	moreover	ADV
ejpam-5718	13	2	,	,	PUNCT
ejpam-5718	13	3	kohli	kohli	PROPN
ejpam-5718	13	4	[	[	X
ejpam-5718	13	5	41	41	NUM
ejpam-5718	13	6	]	]	PUNCT
ejpam-5718	13	7	introduced	introduce	VERB
ejpam-5718	13	8	the	the	DET
ejpam-5718	13	9	concepts	concept	NOUN
ejpam-5718	13	10	of	of	ADP
ejpam-5718	13	11	s	s	NOUN
ejpam-5718	13	12	-	-	ADJ
ejpam-5718	13	13	regular	regular	ADJ
ejpam-5718	13	14	spaces	space	NOUN
ejpam-5718	13	15	and	and	CCONJ
ejpam-5718	13	16	completely	completely	ADV
ejpam-5718	13	17	s	s	NOUN
ejpam-5718	13	18	-	-	ADJ
ejpam-5718	13	19	regular	regular	ADJ
ejpam-5718	13	20	spaces	space	NOUN
ejpam-5718	13	21	and	and	CCONJ
ejpam-5718	13	22	proved	prove	VERB
ejpam-5718	13	23	that	that	SCONJ
ejpam-5718	13	24	s	s	NOUN
ejpam-5718	13	25	-	-	PUNCT
ejpam-5718	13	26	regularity	regularity	NOUN
ejpam-5718	13	27	and	and	CCONJ
ejpam-5718	13	28	complete	complete	ADJ
ejpam-5718	13	29	s	s	NOUN
ejpam-5718	13	30	-	-	PUNCT
ejpam-5718	13	31	regularity	regularity	NOUN
ejpam-5718	13	32	are	be	AUX
ejpam-5718	13	33	preserved	preserve	VERB
ejpam-5718	13	34	under	under	ADP
ejpam-5718	13	35	certain	certain	ADJ
ejpam-5718	13	36	scontinuous	scontinuous	ADJ
ejpam-5718	13	37	functions	function	NOUN
ejpam-5718	13	38	.	.	PUNCT
ejpam-5718	14	1	viriyapong	viriyapong	PROPN
ejpam-5718	14	2	and	and	CCONJ
ejpam-5718	14	3	boonpok	boonpok	VERB
ejpam-5718	14	4	[	[	X
ejpam-5718	14	5	68	68	NUM
ejpam-5718	14	6	]	]	PUNCT
ejpam-5718	14	7	investigated	investigate	VERB
ejpam-5718	14	8	some	some	DET
ejpam-5718	14	9	characterizations	characterization	NOUN
ejpam-5718	14	10	of	of	ADP
ejpam-5718	14	11	(	(	PUNCT
ejpam-5718	14	12	λ	λ	PROPN
ejpam-5718	14	13	,	,	PUNCT
ejpam-5718	14	14	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	14	15	functions	function	NOUN
ejpam-5718	14	16	by	by	ADP
ejpam-5718	14	17	utilizing	utilize	VERB
ejpam-5718	14	18	the	the	DET
ejpam-5718	14	19	notions	notion	NOUN
ejpam-5718	14	20	of	of	ADP
ejpam-5718	14	21	(	(	PUNCT
ejpam-5718	14	22	λ	λ	PROPN
ejpam-5718	14	23	,	,	PUNCT
ejpam-5718	14	24	sp)-open	sp)-open	ADJ
ejpam-5718	14	25	sets	set	NOUN
ejpam-5718	14	26	and	and	CCONJ
ejpam-5718	14	27	(	(	PUNCT
ejpam-5718	14	28	λ	λ	PROPN
ejpam-5718	14	29	,	,	PUNCT
ejpam-5718	14	30	sp)closed	sp)close	VERB
ejpam-5718	14	31	sets	set	NOUN
ejpam-5718	14	32	due	due	ADP
ejpam-5718	14	33	to	to	ADP
ejpam-5718	14	34	boonpok	boonpok	NOUN
ejpam-5718	14	35	and	and	CCONJ
ejpam-5718	14	36	khampakdee	khampakdee	NOUN
ejpam-5718	15	1	[	[	X
ejpam-5718	15	2	12	12	NUM
ejpam-5718	15	3	]	]	PUNCT
ejpam-5718	15	4	.	.	PUNCT
ejpam-5718	16	1	dungthaisong	dungthaisong	NOUN
ejpam-5718	16	2	et	et	PROPN
ejpam-5718	16	3	al	al	PROPN
ejpam-5718	16	4	.	.	PUNCT
ejpam-5718	17	1	[	[	X
ejpam-5718	17	2	33	33	NUM
ejpam-5718	17	3	]	]	PUNCT
ejpam-5718	17	4	introduced	introduce	VERB
ejpam-5718	17	5	∗corresponding	∗corresponde	VERB
ejpam-5718	17	6	author	author	NOUN
ejpam-5718	17	7	.	.	PUNCT
ejpam-5718	18	1	doi	doi	NOUN
ejpam-5718	18	2	:	:	PUNCT
ejpam-5718	18	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5718	https://doi.org/10.29020/nybg.ejpam.v18i1.5718	PROPN
ejpam-5718	18	4	email	email	NOUN
ejpam-5718	18	5	addresses	address	NOUN
ejpam-5718	18	6	:	:	PUNCT
ejpam-5718	18	7	prapatr.p@msu.ac.th	prapatr.p@msu.ac.th	PROPN
ejpam-5718	18	8	(	(	PUNCT
ejpam-5718	18	9	p.	p.	NOUN
ejpam-5718	18	10	pue	pue	NOUN
ejpam-5718	18	11	-	-	PUNCT
ejpam-5718	18	12	on	on	ADP
ejpam-5718	18	13	)	)	PUNCT
ejpam-5718	18	14	,	,	PUNCT
ejpam-5718	18	15	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-5718	18	16	(	(	PUNCT
ejpam-5718	18	17	a.	a.	PROPN
ejpam-5718	18	18	sama	sama	PROPN
ejpam-5718	18	19	-	-	PUNCT
ejpam-5718	18	20	ae	ae	PROPN
ejpam-5718	18	21	)	)	PUNCT
ejpam-5718	18	22	,	,	PUNCT
ejpam-5718	18	23	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5718	18	24	(	(	PUNCT
ejpam-5718	18	25	c.	c.	PROPN
ejpam-5718	18	26	boonpok	boonpok	PROPN
ejpam-5718	18	27	)	)	PUNCT
ejpam-5718	18	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5718	19	1	1	1	NUM
ejpam-5718	19	2	copyright	copyright	NOUN
ejpam-5718	19	3	:	:	PUNCT
ejpam-5718	19	4	©	©	PROPN
ejpam-5718	19	5	2025	2025	NUM
ejpam-5718	19	6	the	the	DET
ejpam-5718	19	7	author(s	author(s	NOUN
ejpam-5718	19	8	)	)	PUNCT
ejpam-5718	19	9	.	.	PUNCT
ejpam-5718	20	1	(	(	PUNCT
ejpam-5718	20	2	cc	cc	NOUN
ejpam-5718	20	3	by	by	ADP
ejpam-5718	20	4	-	-	PUNCT
ejpam-5718	20	5	nc	nc	PROPN
ejpam-5718	20	6	4.0	4.0	NUM
ejpam-5718	20	7	)	)	PUNCT
ejpam-5718	20	8	p.	p.	NOUN
ejpam-5718	20	9	pue	pue	NOUN
ejpam-5718	20	10	-	-	PUNCT
ejpam-5718	20	11	on	on	ADP
ejpam-5718	20	12	,	,	PUNCT
ejpam-5718	20	13	a.	a.	PROPN
ejpam-5718	20	14	sama	sama	PROPN
ejpam-5718	20	15	-	-	PUNCT
ejpam-5718	20	16	ae	ae	PROPN
ejpam-5718	20	17	,	,	PUNCT
ejpam-5718	20	18	c.	c.	PROPN
ejpam-5718	20	19	boonpok	boonpok	PROPN
ejpam-5718	20	20	/	/	SYM
ejpam-5718	20	21	eur	eur	PROPN
ejpam-5718	20	22	.	.	PUNCT
ejpam-5718	21	1	j.	j.	PROPN
ejpam-5718	21	2	pure	pure	PROPN
ejpam-5718	21	3	appl	appl	PROPN
ejpam-5718	21	4	.	.	PROPN
ejpam-5718	21	5	math	math	PROPN
ejpam-5718	21	6	,	,	PUNCT
ejpam-5718	21	7	18	18	NUM
ejpam-5718	21	8	(	(	PUNCT
ejpam-5718	21	9	1	1	NUM
ejpam-5718	21	10	)	)	PUNCT
ejpam-5718	21	11	(	(	PUNCT
ejpam-5718	21	12	2025	2025	NUM
ejpam-5718	21	13	)	)	PUNCT
ejpam-5718	21	14	,	,	PUNCT
ejpam-5718	21	15	5718	5718	NUM
ejpam-5718	21	16	2	2	NUM
ejpam-5718	21	17	of	of	ADP
ejpam-5718	21	18	16	16	NUM
ejpam-5718	21	19	and	and	CCONJ
ejpam-5718	21	20	studied	study	VERB
ejpam-5718	21	21	the	the	DET
ejpam-5718	21	22	concept	concept	NOUN
ejpam-5718	21	23	of	of	ADP
ejpam-5718	21	24	g(m	g(m	ADJ
ejpam-5718	21	25	,	,	PUNCT
ejpam-5718	21	26	n)-continuous	n)-continuous	ADJ
ejpam-5718	21	27	functions	function	NOUN
ejpam-5718	21	28	.	.	PUNCT
ejpam-5718	22	1	duangphui	duangphui	NOUN
ejpam-5718	22	2	et	et	PROPN
ejpam-5718	22	3	al	al	PROPN
ejpam-5718	22	4	.	.	PUNCT
ejpam-5718	23	1	[	[	X
ejpam-5718	23	2	32	32	NUM
ejpam-5718	23	3	]	]	PUNCT
ejpam-5718	23	4	introduced	introduce	VERB
ejpam-5718	23	5	and	and	CCONJ
ejpam-5718	23	6	investigated	investigate	VERB
ejpam-5718	23	7	the	the	DET
ejpam-5718	23	8	notion	notion	NOUN
ejpam-5718	23	9	of	of	ADP
ejpam-5718	23	10	(	(	PUNCT
ejpam-5718	23	11	µ	µ	NOUN
ejpam-5718	23	12	,	,	PUNCT
ejpam-5718	23	13	µ′)(m	µ′)(m	VERB
ejpam-5718	23	14	,	,	PUNCT
ejpam-5718	23	15	n)-continuous	n)-continuous	ADJ
ejpam-5718	23	16	functions	function	NOUN
ejpam-5718	23	17	.	.	PUNCT
ejpam-5718	24	1	furthermore	furthermore	ADV
ejpam-5718	24	2	,	,	PUNCT
ejpam-5718	24	3	several	several	ADJ
ejpam-5718	24	4	characterizations	characterization	NOUN
ejpam-5718	24	5	of	of	ADP
ejpam-5718	24	6	almost	almost	ADV
ejpam-5718	24	7	(	(	PUNCT
ejpam-5718	24	8	λ	λ	PROPN
ejpam-5718	24	9	,	,	PUNCT
ejpam-5718	24	10	p)-continuous	p)-continuous	ADJ
ejpam-5718	24	11	functions	function	NOUN
ejpam-5718	24	12	,	,	PUNCT
ejpam-5718	24	13	strongly	strongly	ADV
ejpam-5718	24	14	θ(λ	θ(λ	PROPN
ejpam-5718	24	15	,	,	PUNCT
ejpam-5718	24	16	p)-continuous	p)-continuous	ADJ
ejpam-5718	24	17	functions	function	NOUN
ejpam-5718	24	18	,	,	PUNCT
ejpam-5718	24	19	almost	almost	ADV
ejpam-5718	24	20	strongly	strongly	ADV
ejpam-5718	24	21	θ(λ	θ(λ	VERB
ejpam-5718	24	22	,	,	PUNCT
ejpam-5718	24	23	p)-continuous	p)-continuous	ADJ
ejpam-5718	24	24	functions	function	NOUN
ejpam-5718	24	25	,	,	PUNCT
ejpam-5718	24	26	θ(λ	θ(λ	PROPN
ejpam-5718	24	27	,	,	PUNCT
ejpam-5718	24	28	p)-continuous	p)-continuous	ADJ
ejpam-5718	24	29	functions	function	NOUN
ejpam-5718	24	30	,	,	PUNCT
ejpam-5718	24	31	weakly	weakly	ADJ
ejpam-5718	24	32	(	(	PUNCT
ejpam-5718	24	33	λ	λ	PROPN
ejpam-5718	24	34	,	,	PUNCT
ejpam-5718	24	35	b)-continuous	b)-continuous	ADJ
ejpam-5718	24	36	functions	function	NOUN
ejpam-5718	24	37	,	,	PUNCT
ejpam-5718	24	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5718	24	39	functions	function	NOUN
ejpam-5718	24	40	,	,	PUNCT
ejpam-5718	24	41	(	(	PUNCT
ejpam-5718	24	42	λ	λ	NOUN
ejpam-5718	24	43	,	,	PUNCT
ejpam-5718	24	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5718	24	45	functions	function	NOUN
ejpam-5718	24	46	,	,	PUNCT
ejpam-5718	24	47	⋆-continuous	⋆-continuous	ADJ
ejpam-5718	24	48	functions	function	NOUN
ejpam-5718	24	49	,	,	PUNCT
ejpam-5718	24	50	θ	θ	PROPN
ejpam-5718	24	51	-	-	ADJ
ejpam-5718	24	52	i	i	NOUN
ejpam-5718	24	53	-continuous	-continuous	ADJ
ejpam-5718	24	54	functions	function	NOUN
ejpam-5718	24	55	,	,	PUNCT
ejpam-5718	24	56	almost	almost	ADV
ejpam-5718	24	57	(	(	PUNCT
ejpam-5718	24	58	g	g	NOUN
ejpam-5718	24	59	,	,	PUNCT
ejpam-5718	24	60	m)-continuous	m)-continuous	ADJ
ejpam-5718	24	61	functions	function	NOUN
ejpam-5718	24	62	,	,	PUNCT
ejpam-5718	24	63	pairwise	pairwise	NOUN
ejpam-5718	24	64	almost	almost	ADV
ejpam-5718	24	65	m	m	VERB
ejpam-5718	24	66	-continuous	-continuous	ADJ
ejpam-5718	24	67	functions	function	NOUN
ejpam-5718	24	68	,	,	PUNCT
ejpam-5718	24	69	(	(	PUNCT
ejpam-5718	24	70	τ1	τ1	NOUN
ejpam-5718	24	71	,	,	PUNCT
ejpam-5718	24	72	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	24	73	functions	function	NOUN
ejpam-5718	24	74	,	,	PUNCT
ejpam-5718	24	75	almost	almost	ADV
ejpam-5718	24	76	(	(	PUNCT
ejpam-5718	24	77	τ1	τ1	NOUN
ejpam-5718	24	78	,	,	PUNCT
ejpam-5718	24	79	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	24	80	functions	function	NOUN
ejpam-5718	24	81	,	,	PUNCT
ejpam-5718	24	82	weakly	weakly	ADJ
ejpam-5718	24	83	(	(	PUNCT
ejpam-5718	24	84	τ1	τ1	NOUN
ejpam-5718	24	85	,	,	PUNCT
ejpam-5718	24	86	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	24	87	functions	function	NOUN
ejpam-5718	24	88	and	and	CCONJ
ejpam-5718	24	89	slightly	slightly	ADV
ejpam-5718	24	90	(	(	PUNCT
ejpam-5718	24	91	τ1	τ1	NOUN
ejpam-5718	24	92	,	,	PUNCT
ejpam-5718	24	93	τ2)s	τ2)s	ADJ
ejpam-5718	24	94	-	-	PUNCT
ejpam-5718	24	95	continuous	continuous	ADJ
ejpam-5718	24	96	functions	function	NOUN
ejpam-5718	24	97	were	be	AUX
ejpam-5718	24	98	presented	present	VERB
ejpam-5718	24	99	in	in	ADP
ejpam-5718	24	100	[	[	X
ejpam-5718	24	101	60	60	NUM
ejpam-5718	24	102	]	]	PUNCT
ejpam-5718	24	103	,	,	PUNCT
ejpam-5718	24	104	[	[	X
ejpam-5718	24	105	63	63	NUM
ejpam-5718	24	106	]	]	PUNCT
ejpam-5718	24	107	,	,	PUNCT
ejpam-5718	24	108	[	[	X
ejpam-5718	24	109	16	16	NUM
ejpam-5718	24	110	]	]	PUNCT
ejpam-5718	24	111	,	,	PUNCT
ejpam-5718	24	112	[	[	X
ejpam-5718	24	113	54	54	NUM
ejpam-5718	24	114	]	]	PUNCT
ejpam-5718	24	115	,	,	PUNCT
ejpam-5718	24	116	[	[	X
ejpam-5718	24	117	25	25	NUM
ejpam-5718	24	118	]	]	PUNCT
ejpam-5718	24	119	,	,	PUNCT
ejpam-5718	24	120	[	[	X
ejpam-5718	24	121	11	11	NUM
ejpam-5718	24	122	]	]	PUNCT
ejpam-5718	24	123	,	,	PUNCT
ejpam-5718	24	124	[	[	X
ejpam-5718	24	125	8	8	NUM
ejpam-5718	24	126	]	]	PUNCT
ejpam-5718	24	127	,	,	PUNCT
ejpam-5718	24	128	[	[	X
ejpam-5718	24	129	10	10	NUM
ejpam-5718	24	130	]	]	PUNCT
ejpam-5718	24	131	,	,	PUNCT
ejpam-5718	24	132	[	[	X
ejpam-5718	24	133	4	4	NUM
ejpam-5718	24	134	]	]	PUNCT
ejpam-5718	24	135	,	,	PUNCT
ejpam-5718	24	136	[	[	X
ejpam-5718	24	137	1	1	NUM
ejpam-5718	24	138	]	]	PUNCT
ejpam-5718	24	139	,	,	PUNCT
ejpam-5718	24	140	[	[	X
ejpam-5718	24	141	2	2	NUM
ejpam-5718	24	142	]	]	PUNCT
ejpam-5718	24	143	,	,	PUNCT
ejpam-5718	24	144	[	[	X
ejpam-5718	24	145	26	26	NUM
ejpam-5718	24	146	]	]	PUNCT
ejpam-5718	24	147	,	,	PUNCT
ejpam-5718	24	148	[	[	X
ejpam-5718	24	149	23	23	NUM
ejpam-5718	24	150	]	]	PUNCT
ejpam-5718	24	151	,	,	PUNCT
ejpam-5718	24	152	[	[	X
ejpam-5718	24	153	18	18	NUM
ejpam-5718	24	154	]	]	PUNCT
ejpam-5718	24	155	and	and	CCONJ
ejpam-5718	24	156	[	[	X
ejpam-5718	24	157	59	59	NUM
ejpam-5718	24	158	]	]	PUNCT
ejpam-5718	24	159	,	,	PUNCT
ejpam-5718	24	160	respectively	respectively	ADV
ejpam-5718	24	161	.	.	PUNCT
ejpam-5718	25	1	srisarakham	srisarakham	PROPN
ejpam-5718	25	2	et	et	PROPN
ejpam-5718	25	3	al	al	PROPN
ejpam-5718	25	4	.	.	PUNCT
ejpam-5718	26	1	[	[	X
ejpam-5718	26	2	61	61	NUM
ejpam-5718	26	3	]	]	PUNCT
ejpam-5718	26	4	introduced	introduce	VERB
ejpam-5718	26	5	and	and	CCONJ
ejpam-5718	26	6	studied	study	VERB
ejpam-5718	26	7	the	the	DET
ejpam-5718	26	8	concept	concept	NOUN
ejpam-5718	26	9	of	of	ADP
ejpam-5718	26	10	faintly	faintly	ADV
ejpam-5718	26	11	(	(	PUNCT
ejpam-5718	26	12	τ1	τ1	PROPN
ejpam-5718	26	13	,	,	PUNCT
ejpam-5718	26	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	26	15	functions	function	NOUN
ejpam-5718	26	16	.	.	PUNCT
ejpam-5718	27	1	thongmoon	thongmoon	NOUN
ejpam-5718	27	2	et	et	PROPN
ejpam-5718	27	3	al	al	PROPN
ejpam-5718	27	4	.	.	PUNCT
ejpam-5718	28	1	[	[	X
ejpam-5718	28	2	66	66	NUM
ejpam-5718	28	3	]	]	PUNCT
ejpam-5718	28	4	introduced	introduce	VERB
ejpam-5718	28	5	and	and	CCONJ
ejpam-5718	28	6	investigated	investigate	VERB
ejpam-5718	28	7	the	the	DET
ejpam-5718	28	8	notion	notion	NOUN
ejpam-5718	28	9	of	of	ADP
ejpam-5718	28	10	rarely	rarely	ADV
ejpam-5718	28	11	(	(	PUNCT
ejpam-5718	28	12	τ1	τ1	NOUN
ejpam-5718	28	13	,	,	PUNCT
ejpam-5718	28	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	28	15	functions	function	NOUN
ejpam-5718	28	16	.	.	PUNCT
ejpam-5718	29	1	kong	kong	PROPN
ejpam-5718	29	2	-	-	PUNCT
ejpam-5718	29	3	ied	ied	PROPN
ejpam-5718	29	4	at	at	ADP
ejpam-5718	29	5	al	al	PROPN
ejpam-5718	29	6	.	.	PUNCT
ejpam-5718	30	1	[	[	X
ejpam-5718	30	2	42	42	NUM
ejpam-5718	30	3	]	]	PUNCT
ejpam-5718	30	4	introduced	introduce	VERB
ejpam-5718	30	5	and	and	CCONJ
ejpam-5718	30	6	studied	study	VERB
ejpam-5718	30	7	the	the	DET
ejpam-5718	30	8	concept	concept	NOUN
ejpam-5718	30	9	of	of	ADP
ejpam-5718	30	10	almost	almost	ADV
ejpam-5718	30	11	quasi	quasi	X
ejpam-5718	30	12	(	(	PUNCT
ejpam-5718	30	13	τ1	τ1	NOUN
ejpam-5718	30	14	,	,	PUNCT
ejpam-5718	30	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	30	16	functions	function	NOUN
ejpam-5718	30	17	.	.	PUNCT
ejpam-5718	31	1	chiangpradit	chiangpradit	NOUN
ejpam-5718	31	2	et	et	PROPN
ejpam-5718	31	3	al	al	PROPN
ejpam-5718	31	4	.	.	PUNCT
ejpam-5718	32	1	[	[	X
ejpam-5718	32	2	30	30	NUM
ejpam-5718	32	3	]	]	PUNCT
ejpam-5718	32	4	introduced	introduce	VERB
ejpam-5718	32	5	and	and	CCONJ
ejpam-5718	32	6	investigated	investigate	VERB
ejpam-5718	32	7	the	the	DET
ejpam-5718	32	8	notion	notion	NOUN
ejpam-5718	32	9	of	of	ADP
ejpam-5718	32	10	weakly	weakly	ADJ
ejpam-5718	32	11	quasi	quasi	NOUN
ejpam-5718	32	12	(	(	PUNCT
ejpam-5718	32	13	τ1	τ1	PROPN
ejpam-5718	32	14	,	,	PUNCT
ejpam-5718	32	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	32	16	functions	function	NOUN
ejpam-5718	32	17	.	.	PUNCT
ejpam-5718	33	1	prachanpol	prachanpol	NOUN
ejpam-5718	33	2	et	et	PROPN
ejpam-5718	33	3	al	al	PROPN
ejpam-5718	33	4	.	.	PUNCT
ejpam-5718	34	1	[	[	X
ejpam-5718	34	2	53	53	NUM
ejpam-5718	34	3	]	]	PUNCT
ejpam-5718	34	4	introduced	introduce	VERB
ejpam-5718	34	5	and	and	CCONJ
ejpam-5718	34	6	studied	study	VERB
ejpam-5718	34	7	the	the	DET
ejpam-5718	34	8	concept	concept	NOUN
ejpam-5718	34	9	of	of	ADP
ejpam-5718	34	10	weakly	weakly	ADJ
ejpam-5718	34	11	δ(τ1	δ(τ1	NOUN
ejpam-5718	34	12	,	,	PUNCT
ejpam-5718	34	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	34	14	functions	function	NOUN
ejpam-5718	34	15	.	.	PUNCT
ejpam-5718	35	1	in	in	ADP
ejpam-5718	35	2	1989	1989	NUM
ejpam-5718	35	3	,	,	PUNCT
ejpam-5718	35	4	lipski	lipski	NOUN
ejpam-5718	35	5	[	[	X
ejpam-5718	35	6	46	46	NUM
ejpam-5718	35	7	]	]	PUNCT
ejpam-5718	35	8	extended	extend	VERB
ejpam-5718	35	9	the	the	DET
ejpam-5718	35	10	concept	concept	NOUN
ejpam-5718	35	11	of	of	ADP
ejpam-5718	35	12	s	s	NOUN
ejpam-5718	35	13	-	-	ADJ
ejpam-5718	35	14	continuous	continuous	ADJ
ejpam-5718	35	15	functions	function	NOUN
ejpam-5718	35	16	to	to	ADP
ejpam-5718	35	17	the	the	DET
ejpam-5718	35	18	setting	setting	NOUN
ejpam-5718	35	19	of	of	ADP
ejpam-5718	35	20	multifunctions	multifunction	NOUN
ejpam-5718	35	21	.	.	PUNCT
ejpam-5718	36	1	popa	popa	NOUN
ejpam-5718	37	1	[	[	X
ejpam-5718	37	2	49	49	NUM
ejpam-5718	37	3	]	]	PUNCT
ejpam-5718	37	4	introduced	introduce	VERB
ejpam-5718	37	5	the	the	DET
ejpam-5718	37	6	concept	concept	NOUN
ejpam-5718	37	7	of	of	ADP
ejpam-5718	37	8	precontinuous	precontinuous	ADJ
ejpam-5718	37	9	multifunctions	multifunction	NOUN
ejpam-5718	37	10	and	and	CCONJ
ejpam-5718	37	11	showed	show	VERB
ejpam-5718	37	12	that	that	SCONJ
ejpam-5718	37	13	h	h	NOUN
ejpam-5718	37	14	-	-	PUNCT
ejpam-5718	37	15	almost	almost	ADV
ejpam-5718	37	16	continuity	continuity	NOUN
ejpam-5718	37	17	and	and	CCONJ
ejpam-5718	37	18	precontinuity	precontinuity	NOUN
ejpam-5718	37	19	are	be	AUX
ejpam-5718	37	20	equivalent	equivalent	ADJ
ejpam-5718	37	21	for	for	ADP
ejpam-5718	37	22	multifunctions	multifunction	NOUN
ejpam-5718	37	23	.	.	PUNCT
ejpam-5718	38	1	ewert	ewert	PROPN
ejpam-5718	38	2	and	and	CCONJ
ejpam-5718	38	3	lipski	lipski	ADJ
ejpam-5718	38	4	[	[	X
ejpam-5718	38	5	35	35	NUM
ejpam-5718	38	6	]	]	PUNCT
ejpam-5718	38	7	introduced	introduce	VERB
ejpam-5718	38	8	and	and	CCONJ
ejpam-5718	38	9	studied	study	VERB
ejpam-5718	38	10	the	the	DET
ejpam-5718	38	11	concept	concept	NOUN
ejpam-5718	38	12	of	of	ADP
ejpam-5718	38	13	s	s	NOUN
ejpam-5718	38	14	-	-	PUNCT
ejpam-5718	38	15	quasi	quasi	ADJ
ejpam-5718	38	16	-	-	ADJ
ejpam-5718	38	17	continuous	continuous	ADJ
ejpam-5718	38	18	multifunctions	multifunction	NOUN
ejpam-5718	38	19	.	.	PUNCT
ejpam-5718	39	1	popa	popa	NOUN
ejpam-5718	39	2	and	and	CCONJ
ejpam-5718	39	3	noiri	noiri	ADV
ejpam-5718	40	1	[	[	X
ejpam-5718	40	2	52	52	NUM
ejpam-5718	40	3	]	]	PUNCT
ejpam-5718	40	4	introduced	introduce	VERB
ejpam-5718	40	5	and	and	CCONJ
ejpam-5718	40	6	investigated	investigate	VERB
ejpam-5718	40	7	the	the	DET
ejpam-5718	40	8	notion	notion	NOUN
ejpam-5718	40	9	of	of	ADP
ejpam-5718	40	10	s	s	NOUN
ejpam-5718	40	11	-	-	ADJ
ejpam-5718	40	12	precontinuous	precontinuous	ADJ
ejpam-5718	40	13	multifunctions	multifunction	NOUN
ejpam-5718	40	14	as	as	ADP
ejpam-5718	40	15	a	a	DET
ejpam-5718	40	16	generalization	generalization	NOUN
ejpam-5718	40	17	of	of	ADP
ejpam-5718	40	18	s	s	NOUN
ejpam-5718	40	19	-	-	ADJ
ejpam-5718	40	20	continuous	continuous	ADJ
ejpam-5718	40	21	multifunctions	multifunction	NOUN
ejpam-5718	40	22	and	and	CCONJ
ejpam-5718	40	23	precontinuous	precontinuous	ADJ
ejpam-5718	40	24	multifunctions	multifunction	NOUN
ejpam-5718	40	25	.	.	PUNCT
ejpam-5718	41	1	in	in	ADP
ejpam-5718	41	2	particular	particular	ADJ
ejpam-5718	41	3	,	,	PUNCT
ejpam-5718	41	4	popa	popa	NOUN
ejpam-5718	41	5	and	and	CCONJ
ejpam-5718	41	6	noiri	noiri	ADV
ejpam-5718	41	7	[	[	X
ejpam-5718	41	8	51	51	NUM
ejpam-5718	41	9	]	]	PUNCT
ejpam-5718	41	10	introduced	introduce	VERB
ejpam-5718	41	11	and	and	CCONJ
ejpam-5718	41	12	studied	study	VERB
ejpam-5718	41	13	the	the	DET
ejpam-5718	41	14	notion	notion	NOUN
ejpam-5718	41	15	of	of	ADP
ejpam-5718	41	16	sβ	sβ	NOUN
ejpam-5718	41	17	-	-	PUNCT
ejpam-5718	41	18	continuous	continuous	ADJ
ejpam-5718	41	19	multifunctions	multifunction	NOUN
ejpam-5718	41	20	.	.	PUNCT
ejpam-5718	42	1	popa	popa	NOUN
ejpam-5718	42	2	and	and	CCONJ
ejpam-5718	42	3	noiri	noiri	ADV
ejpam-5718	43	1	[	[	X
ejpam-5718	43	2	50	50	NUM
ejpam-5718	43	3	]	]	PUNCT
ejpam-5718	43	4	introduced	introduce	VERB
ejpam-5718	43	5	and	and	CCONJ
ejpam-5718	43	6	investigated	investigate	VERB
ejpam-5718	43	7	the	the	DET
ejpam-5718	43	8	concept	concept	NOUN
ejpam-5718	43	9	of	of	ADP
ejpam-5718	43	10	s	s	NOUN
ejpam-5718	43	11	-	-	PUNCT
ejpam-5718	43	12	m	m	NOUN
ejpam-5718	43	13	-	-	ADJ
ejpam-5718	43	14	continuous	continuous	ADJ
ejpam-5718	43	15	multifunctions	multifunction	NOUN
ejpam-5718	43	16	as	as	ADP
ejpam-5718	43	17	multifunctions	multifunction	NOUN
ejpam-5718	43	18	defined	define	VERB
ejpam-5718	43	19	on	on	ADP
ejpam-5718	43	20	a	a	DET
ejpam-5718	43	21	set	set	NOUN
ejpam-5718	43	22	satisfying	satisfy	VERB
ejpam-5718	43	23	some	some	DET
ejpam-5718	43	24	minimal	minimal	ADJ
ejpam-5718	43	25	conditions	condition	NOUN
ejpam-5718	43	26	.	.	PUNCT
ejpam-5718	44	1	moreover	moreover	ADV
ejpam-5718	44	2	,	,	PUNCT
ejpam-5718	44	3	several	several	ADJ
ejpam-5718	44	4	characterizations	characterization	NOUN
ejpam-5718	44	5	and	and	CCONJ
ejpam-5718	44	6	some	some	DET
ejpam-5718	44	7	properties	property	NOUN
ejpam-5718	44	8	concerning	concern	VERB
ejpam-5718	44	9	(	(	PUNCT
ejpam-5718	44	10	τ1	τ1	NOUN
ejpam-5718	44	11	,	,	PUNCT
ejpam-5718	44	12	τ2)δ	τ2)δ	ADJ
ejpam-5718	44	13	-	-	PUNCT
ejpam-5718	44	14	semicontinuous	semicontinuous	ADJ
ejpam-5718	44	15	multifunctions	multifunction	NOUN
ejpam-5718	44	16	,	,	PUNCT
ejpam-5718	44	17	almost	almost	ADV
ejpam-5718	44	18	weakly	weakly	ADJ
ejpam-5718	44	19	(	(	PUNCT
ejpam-5718	44	20	τ1	τ1	NOUN
ejpam-5718	44	21	,	,	PUNCT
ejpam-5718	44	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	23	multifunctions	multifunction	NOUN
ejpam-5718	44	24	,	,	PUNCT
ejpam-5718	44	25	weakly	weakly	ADJ
ejpam-5718	44	26	quasi	quasi	NOUN
ejpam-5718	44	27	(	(	PUNCT
ejpam-5718	44	28	λ	λ	PROPN
ejpam-5718	44	29	,	,	PUNCT
ejpam-5718	44	30	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	31	multifunctions	multifunction	NOUN
ejpam-5718	44	32	,	,	PUNCT
ejpam-5718	44	33	⋆-continuous	⋆-continuous	ADJ
ejpam-5718	44	34	multifunctions	multifunction	NOUN
ejpam-5718	44	35	,	,	PUNCT
ejpam-5718	44	36	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-5718	44	37	multifunctions	multifunction	NOUN
ejpam-5718	44	38	,	,	PUNCT
ejpam-5718	44	39	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5718	44	40	multifunctions	multifunction	NOUN
ejpam-5718	44	41	,	,	PUNCT
ejpam-5718	44	42	almost	almost	ADV
ejpam-5718	44	43	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5718	44	44	multifunctions	multifunction	NOUN
ejpam-5718	44	45	,	,	PUNCT
ejpam-5718	44	46	almost	almost	ADV
ejpam-5718	44	47	quasi	quasi	VERB
ejpam-5718	44	48	⋆-continuous	⋆-continuous	ADJ
ejpam-5718	44	49	multifunctions	multifunction	NOUN
ejpam-5718	44	50	,	,	PUNCT
ejpam-5718	44	51	weakly	weakly	ADJ
ejpam-5718	44	52	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5718	44	53	multifunctions	multifunction	NOUN
ejpam-5718	44	54	,	,	PUNCT
ejpam-5718	44	55	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5718	44	56	multifunctions	multifunction	NOUN
ejpam-5718	44	57	,	,	PUNCT
ejpam-5718	44	58	weakly	weakly	ADJ
ejpam-5718	44	59	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5718	44	60	multifunctions	multifunction	NOUN
ejpam-5718	44	61	,	,	PUNCT
ejpam-5718	44	62	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-5718	44	63	continuous	continuous	ADJ
ejpam-5718	44	64	multifunctions	multifunction	NOUN
ejpam-5718	44	65	,	,	PUNCT
ejpam-5718	44	66	almost	almost	ADV
ejpam-5718	44	67	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5718	44	68	multifunctions	multifunction	NOUN
ejpam-5718	44	69	,	,	PUNCT
ejpam-5718	44	70	weakly	weakly	ADJ
ejpam-5718	44	71	(	(	PUNCT
ejpam-5718	44	72	λ	λ	NOUN
ejpam-5718	44	73	,	,	PUNCT
ejpam-5718	44	74	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	75	multifunctions	multifunction	NOUN
ejpam-5718	44	76	,	,	PUNCT
ejpam-5718	44	77	α(λ	α(λ	PROPN
ejpam-5718	44	78	,	,	PUNCT
ejpam-5718	44	79	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	80	multifunctions	multifunction	NOUN
ejpam-5718	44	81	,	,	PUNCT
ejpam-5718	44	82	almost	almost	ADV
ejpam-5718	44	83	α(λ	α(λ	PROPN
ejpam-5718	44	84	,	,	PUNCT
ejpam-5718	44	85	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	86	multifunctions	multifunction	NOUN
ejpam-5718	44	87	,	,	PUNCT
ejpam-5718	44	88	weakly	weakly	ADJ
ejpam-5718	44	89	α(λ	α(λ	PROPN
ejpam-5718	44	90	,	,	PUNCT
ejpam-5718	44	91	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	92	multifunctions	multifunction	NOUN
ejpam-5718	44	93	,	,	PUNCT
ejpam-5718	44	94	almost	almost	ADV
ejpam-5718	44	95	β(λ	β(λ	NOUN
ejpam-5718	44	96	,	,	PUNCT
ejpam-5718	44	97	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	98	multifunctions	multifunction	NOUN
ejpam-5718	44	99	,	,	PUNCT
ejpam-5718	44	100	slightly	slightly	ADV
ejpam-5718	44	101	(	(	PUNCT
ejpam-5718	44	102	λ	λ	NOUN
ejpam-5718	44	103	,	,	PUNCT
ejpam-5718	44	104	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	44	105	multifunctions	multifunction	NOUN
ejpam-5718	44	106	,	,	PUNCT
ejpam-5718	44	107	(	(	PUNCT
ejpam-5718	44	108	τ1	τ1	NOUN
ejpam-5718	44	109	,	,	PUNCT
ejpam-5718	44	110	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	111	multifunctions	multifunction	NOUN
ejpam-5718	44	112	,	,	PUNCT
ejpam-5718	44	113	almost	almost	ADV
ejpam-5718	44	114	(	(	PUNCT
ejpam-5718	44	115	τ1	τ1	NOUN
ejpam-5718	44	116	,	,	PUNCT
ejpam-5718	44	117	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	118	multifunctions	multifunction	NOUN
ejpam-5718	44	119	,	,	PUNCT
ejpam-5718	44	120	weakly	weakly	ADJ
ejpam-5718	44	121	(	(	PUNCT
ejpam-5718	44	122	τ1	τ1	NOUN
ejpam-5718	44	123	,	,	PUNCT
ejpam-5718	44	124	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	125	multifunctions	multifunction	NOUN
ejpam-5718	44	126	,	,	PUNCT
ejpam-5718	44	127	weakly	weakly	ADJ
ejpam-5718	44	128	quasi	quasi	NOUN
ejpam-5718	44	129	(	(	PUNCT
ejpam-5718	44	130	τ1	τ1	PROPN
ejpam-5718	44	131	,	,	PUNCT
ejpam-5718	44	132	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	133	multifunctions	multifunction	NOUN
ejpam-5718	44	134	,	,	PUNCT
ejpam-5718	44	135	almost	almost	ADV
ejpam-5718	44	136	quasi	quasi	NOUN
ejpam-5718	44	137	(	(	PUNCT
ejpam-5718	44	138	τ1	τ1	NOUN
ejpam-5718	44	139	,	,	PUNCT
ejpam-5718	44	140	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	141	multifunctions	multifunction	NOUN
ejpam-5718	44	142	,	,	PUNCT
ejpam-5718	44	143	c-(τ1	c-(τ1	PROPN
ejpam-5718	44	144	,	,	PUNCT
ejpam-5718	44	145	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	146	multifunctions	multifunction	NOUN
ejpam-5718	44	147	,	,	PUNCT
ejpam-5718	44	148	c	c	NOUN
ejpam-5718	44	149	-	-	PUNCT
ejpam-5718	44	150	quasi	quasi	NOUN
ejpam-5718	44	151	(	(	PUNCT
ejpam-5718	44	152	τ1	τ1	PROPN
ejpam-5718	44	153	,	,	PUNCT
ejpam-5718	44	154	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	155	multifunctions	multifunction	NOUN
ejpam-5718	44	156	,	,	PUNCT
ejpam-5718	44	157	s-(τ1	s-(τ1	PROPN
ejpam-5718	44	158	,	,	PUNCT
ejpam-5718	44	159	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5718	44	160	multifunctions	multifunction	NOUN
ejpam-5718	44	161	,	,	PUNCT
ejpam-5718	44	162	slightly	slightly	ADV
ejpam-5718	44	163	(	(	PUNCT
ejpam-5718	44	164	τ1	τ1	NOUN
ejpam-5718	44	165	,	,	PUNCT
ejpam-5718	44	166	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	44	167	multifunctions	multifunction	NOUN
ejpam-5718	44	168	and	and	CCONJ
ejpam-5718	44	169	slightly	slightly	ADV
ejpam-5718	44	170	(	(	PUNCT
ejpam-5718	44	171	τ1	τ1	NOUN
ejpam-5718	44	172	,	,	PUNCT
ejpam-5718	44	173	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5718	44	174	multifunctions	multifunction	NOUN
ejpam-5718	44	175	were	be	AUX
ejpam-5718	44	176	established	establish	VERB
ejpam-5718	44	177	in	in	ADP
ejpam-5718	44	178	[	[	X
ejpam-5718	44	179	5	5	NUM
ejpam-5718	44	180	]	]	PUNCT
ejpam-5718	44	181	,	,	PUNCT
ejpam-5718	44	182	[	[	X
ejpam-5718	44	183	28	28	NUM
ejpam-5718	44	184	]	]	PUNCT
ejpam-5718	44	185	,	,	PUNCT
ejpam-5718	44	186	[	[	X
ejpam-5718	44	187	69	69	NUM
ejpam-5718	44	188	]	]	PUNCT
ejpam-5718	44	189	,	,	PUNCT
ejpam-5718	44	190	[	[	X
ejpam-5718	44	191	3	3	NUM
ejpam-5718	44	192	]	]	PUNCT
ejpam-5718	44	193	,	,	PUNCT
ejpam-5718	44	194	[	[	X
ejpam-5718	44	195	7	7	NUM
ejpam-5718	44	196	]	]	PUNCT
ejpam-5718	44	197	,	,	PUNCT
ejpam-5718	44	198	[	[	X
ejpam-5718	44	199	17	17	NUM
ejpam-5718	44	200	]	]	PUNCT
ejpam-5718	44	201	,	,	PUNCT
ejpam-5718	44	202	[	[	X
ejpam-5718	44	203	24	24	NUM
ejpam-5718	44	204	]	]	PUNCT
ejpam-5718	44	205	,	,	PUNCT
ejpam-5718	44	206	[	[	X
ejpam-5718	44	207	6	6	NUM
ejpam-5718	44	208	]	]	PUNCT
ejpam-5718	44	209	,	,	PUNCT
ejpam-5718	44	210	[	[	X
ejpam-5718	44	211	21	21	NUM
ejpam-5718	44	212	]	]	PUNCT
ejpam-5718	44	213	,	,	PUNCT
ejpam-5718	44	214	[	[	X
ejpam-5718	44	215	20	20	NUM
ejpam-5718	44	216	]	]	PUNCT
ejpam-5718	44	217	,	,	PUNCT
ejpam-5718	44	218	[	[	X
ejpam-5718	44	219	15	15	NUM
ejpam-5718	44	220	]	]	PUNCT
ejpam-5718	44	221	,	,	PUNCT
ejpam-5718	44	222	[	[	X
ejpam-5718	44	223	9	9	NUM
ejpam-5718	44	224	]	]	PUNCT
ejpam-5718	44	225	,	,	PUNCT
ejpam-5718	44	226	[	[	X
ejpam-5718	44	227	19	19	NUM
ejpam-5718	44	228	]	]	PUNCT
ejpam-5718	44	229	,	,	PUNCT
ejpam-5718	44	230	[	[	X
ejpam-5718	44	231	22	22	NUM
ejpam-5718	44	232	]	]	PUNCT
ejpam-5718	44	233	,	,	PUNCT
ejpam-5718	44	234	[	[	X
ejpam-5718	44	235	37	37	NUM
ejpam-5718	44	236	]	]	PUNCT
ejpam-5718	44	237	,	,	PUNCT
ejpam-5718	44	238	[	[	X
ejpam-5718	44	239	13	13	NUM
ejpam-5718	44	240	]	]	PUNCT
ejpam-5718	44	241	,	,	PUNCT
ejpam-5718	44	242	[	[	X
ejpam-5718	44	243	27	27	NUM
ejpam-5718	44	244	]	]	PUNCT
ejpam-5718	44	245	,	,	PUNCT
ejpam-5718	44	246	[	[	X
ejpam-5718	44	247	62	62	NUM
ejpam-5718	44	248	]	]	PUNCT
ejpam-5718	44	249	,	,	PUNCT
ejpam-5718	44	250	[	[	X
ejpam-5718	44	251	14	14	NUM
ejpam-5718	44	252	]	]	PUNCT
ejpam-5718	44	253	,	,	PUNCT
ejpam-5718	44	254	[	[	X
ejpam-5718	44	255	57	57	NUM
ejpam-5718	44	256	]	]	PUNCT
ejpam-5718	44	257	,	,	PUNCT
ejpam-5718	44	258	[	[	X
ejpam-5718	44	259	39	39	NUM
ejpam-5718	44	260	]	]	PUNCT
ejpam-5718	44	261	,	,	PUNCT
ejpam-5718	44	262	[	[	X
ejpam-5718	44	263	65	65	NUM
ejpam-5718	44	264	]	]	PUNCT
ejpam-5718	44	265	,	,	PUNCT
ejpam-5718	44	266	[	[	X
ejpam-5718	44	267	58	58	NUM
ejpam-5718	44	268	]	]	PUNCT
ejpam-5718	44	269	,	,	PUNCT
ejpam-5718	44	270	[	[	X
ejpam-5718	44	271	56	56	NUM
ejpam-5718	44	272	]	]	PUNCT
ejpam-5718	44	273	,	,	PUNCT
ejpam-5718	44	274	[	[	X
ejpam-5718	44	275	38	38	NUM
ejpam-5718	44	276	]	]	PUNCT
ejpam-5718	44	277	,	,	PUNCT
ejpam-5718	44	278	[	[	X
ejpam-5718	44	279	55	55	NUM
ejpam-5718	44	280	]	]	PUNCT
ejpam-5718	44	281	,	,	PUNCT
ejpam-5718	44	282	[	[	X
ejpam-5718	44	283	73	73	NUM
ejpam-5718	44	284	]	]	PUNCT
ejpam-5718	44	285	,	,	PUNCT
ejpam-5718	44	286	[	[	X
ejpam-5718	44	287	70	70	NUM
ejpam-5718	44	288	]	]	PUNCT
ejpam-5718	44	289	and	and	CCONJ
ejpam-5718	44	290	[	[	X
ejpam-5718	44	291	71	71	NUM
ejpam-5718	44	292	]	]	PUNCT
ejpam-5718	44	293	,	,	PUNCT
ejpam-5718	44	294	respectively	respectively	ADV
ejpam-5718	44	295	.	.	PUNCT
ejpam-5718	45	1	noiri	noiri	PROPN
ejpam-5718	45	2	and	and	CCONJ
ejpam-5718	45	3	popa	popa	NOUN
ejpam-5718	46	1	[	[	X
ejpam-5718	46	2	48	48	NUM
ejpam-5718	46	3	]	]	PUNCT
ejpam-5718	46	4	introduced	introduce	VERB
ejpam-5718	46	5	and	and	CCONJ
ejpam-5718	46	6	studied	study	VERB
ejpam-5718	46	7	the	the	DET
ejpam-5718	46	8	notion	notion	NOUN
ejpam-5718	46	9	of	of	ADP
ejpam-5718	46	10	weakly	weakly	ADJ
ejpam-5718	46	11	s	s	ADJ
ejpam-5718	46	12	-	-	ADJ
ejpam-5718	46	13	mcontinuous	mcontinuous	ADJ
ejpam-5718	46	14	multifunctions	multifunction	NOUN
ejpam-5718	46	15	as	as	ADP
ejpam-5718	46	16	a	a	DET
ejpam-5718	46	17	generalization	generalization	NOUN
ejpam-5718	46	18	of	of	ADP
ejpam-5718	46	19	both	both	DET
ejpam-5718	46	20	weakly	weakly	ADJ
ejpam-5718	46	21	m	m	ADJ
ejpam-5718	46	22	-	-	ADJ
ejpam-5718	46	23	continuous	continuous	ADJ
ejpam-5718	46	24	multifunctions	multifunction	NOUN
ejpam-5718	46	25	p.	p.	NOUN
ejpam-5718	46	26	pue	pue	NOUN
ejpam-5718	46	27	-	-	PUNCT
ejpam-5718	46	28	on	on	ADP
ejpam-5718	46	29	,	,	PUNCT
ejpam-5718	46	30	a.	a.	PROPN
ejpam-5718	46	31	sama	sama	PROPN
ejpam-5718	46	32	-	-	PUNCT
ejpam-5718	46	33	ae	ae	PROPN
ejpam-5718	46	34	,	,	PUNCT
ejpam-5718	46	35	c.	c.	PROPN
ejpam-5718	46	36	boonpok	boonpok	PROPN
ejpam-5718	46	37	/	/	SYM
ejpam-5718	46	38	eur	eur	PROPN
ejpam-5718	46	39	.	.	PUNCT
ejpam-5718	47	1	j.	j.	PROPN
ejpam-5718	47	2	pure	pure	PROPN
ejpam-5718	47	3	appl	appl	PROPN
ejpam-5718	47	4	.	.	PROPN
ejpam-5718	47	5	math	math	PROPN
ejpam-5718	47	6	,	,	PUNCT
ejpam-5718	47	7	18	18	NUM
ejpam-5718	47	8	(	(	PUNCT
ejpam-5718	47	9	1	1	NUM
ejpam-5718	47	10	)	)	PUNCT
ejpam-5718	47	11	(	(	PUNCT
ejpam-5718	47	12	2025	2025	NUM
ejpam-5718	47	13	)	)	PUNCT
ejpam-5718	47	14	,	,	PUNCT
ejpam-5718	47	15	5718	5718	NUM
ejpam-5718	47	16	3	3	NUM
ejpam-5718	47	17	of	of	ADP
ejpam-5718	47	18	16	16	NUM
ejpam-5718	47	19	and	and	CCONJ
ejpam-5718	47	20	s	s	NOUN
ejpam-5718	47	21	-	-	PUNCT
ejpam-5718	47	22	m	m	NOUN
ejpam-5718	47	23	-	-	ADJ
ejpam-5718	47	24	continuous	continuous	ADJ
ejpam-5718	47	25	multifunctions	multifunction	NOUN
ejpam-5718	47	26	.	.	PUNCT
ejpam-5718	48	1	the	the	DET
ejpam-5718	48	2	class	class	NOUN
ejpam-5718	48	3	of	of	ADP
ejpam-5718	48	4	weakly	weakly	ADJ
ejpam-5718	48	5	s	s	NOUN
ejpam-5718	48	6	-	-	PUNCT
ejpam-5718	48	7	m	m	NOUN
ejpam-5718	48	8	-	-	ADJ
ejpam-5718	48	9	continuous	continuous	ADJ
ejpam-5718	48	10	multifunctions	multifunction	NOUN
ejpam-5718	48	11	contains	contain	VERB
ejpam-5718	48	12	weakly	weakly	ADJ
ejpam-5718	48	13	s	s	NOUN
ejpam-5718	48	14	-	-	ADJ
ejpam-5718	48	15	precontinuous	precontinuous	ADJ
ejpam-5718	48	16	multifunctions	multifunction	NOUN
ejpam-5718	48	17	due	due	ADP
ejpam-5718	48	18	to	to	PART
ejpam-5718	48	19	ekici	ekici	VERB
ejpam-5718	48	20	and	and	CCONJ
ejpam-5718	48	21	park	park	NOUN
ejpam-5718	48	22	[	[	X
ejpam-5718	48	23	34	34	NUM
ejpam-5718	48	24	]	]	PUNCT
ejpam-5718	48	25	.	.	PUNCT
ejpam-5718	49	1	in	in	ADP
ejpam-5718	49	2	this	this	DET
ejpam-5718	49	3	paper	paper	NOUN
ejpam-5718	49	4	,	,	PUNCT
ejpam-5718	49	5	we	we	PRON
ejpam-5718	49	6	introduce	introduce	VERB
ejpam-5718	49	7	the	the	DET
ejpam-5718	49	8	concepts	concept	NOUN
ejpam-5718	49	9	of	of	ADP
ejpam-5718	49	10	upper	upper	ADJ
ejpam-5718	49	11	weakly	weakly	ADJ
ejpam-5718	49	12	s-(τ1	s-(τ1	PROPN
ejpam-5718	49	13	,	,	PUNCT
ejpam-5718	49	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	49	15	multifunctions	multifunction	NOUN
ejpam-5718	49	16	and	and	CCONJ
ejpam-5718	49	17	lower	low	ADJ
ejpam-5718	49	18	weakly	weakly	ADJ
ejpam-5718	49	19	s-(τ1	s-(τ1	PROPN
ejpam-5718	49	20	,	,	PUNCT
ejpam-5718	49	21	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	49	22	multifunctions	multifunction	NOUN
ejpam-5718	49	23	.	.	PUNCT
ejpam-5718	50	1	we	we	PRON
ejpam-5718	50	2	also	also	ADV
ejpam-5718	50	3	investigate	investigate	VERB
ejpam-5718	50	4	several	several	ADJ
ejpam-5718	50	5	characterizations	characterization	NOUN
ejpam-5718	50	6	of	of	ADP
ejpam-5718	50	7	upper	upper	ADJ
ejpam-5718	50	8	weakly	weakly	ADJ
ejpam-5718	50	9	s-(τ1	s-(τ1	PROPN
ejpam-5718	50	10	,	,	PUNCT
ejpam-5718	50	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	50	12	multifunctions	multifunction	NOUN
ejpam-5718	50	13	and	and	CCONJ
ejpam-5718	50	14	lower	low	ADJ
ejpam-5718	50	15	weakly	weakly	ADJ
ejpam-5718	50	16	s-(τ1	s-(τ1	PROPN
ejpam-5718	50	17	,	,	PUNCT
ejpam-5718	50	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	50	19	multifunctions	multifunction	NOUN
ejpam-5718	50	20	.	.	PUNCT
ejpam-5718	51	1	2	2	X
ejpam-5718	51	2	.	.	X
ejpam-5718	51	3	preliminaries	preliminary	NOUN
ejpam-5718	51	4	throughout	throughout	ADP
ejpam-5718	51	5	the	the	DET
ejpam-5718	51	6	present	present	ADJ
ejpam-5718	51	7	paper	paper	NOUN
ejpam-5718	51	8	,	,	PUNCT
ejpam-5718	51	9	spaces	space	NOUN
ejpam-5718	51	10	(	(	PUNCT
ejpam-5718	51	11	x	x	NOUN
ejpam-5718	51	12	,	,	PUNCT
ejpam-5718	51	13	τ1	τ1	NOUN
ejpam-5718	51	14	,	,	PUNCT
ejpam-5718	51	15	τ2	τ2	NOUN
ejpam-5718	51	16	)	)	PUNCT
ejpam-5718	51	17	and	and	CCONJ
ejpam-5718	51	18	(	(	PUNCT
ejpam-5718	51	19	y	y	PROPN
ejpam-5718	51	20	,	,	PUNCT
ejpam-5718	51	21	σ1	σ1	PROPN
ejpam-5718	51	22	,	,	PUNCT
ejpam-5718	51	23	σ2	σ2	NOUN
ejpam-5718	51	24	)	)	PUNCT
ejpam-5718	51	25	(	(	PUNCT
ejpam-5718	51	26	or	or	CCONJ
ejpam-5718	51	27	simply	simply	ADV
ejpam-5718	51	28	x	x	X
ejpam-5718	51	29	and	and	CCONJ
ejpam-5718	51	30	y	y	PROPN
ejpam-5718	51	31	)	)	PUNCT
ejpam-5718	51	32	always	always	ADV
ejpam-5718	51	33	mean	mean	VERB
ejpam-5718	51	34	bitopological	bitopological	ADJ
ejpam-5718	51	35	spaces	space	NOUN
ejpam-5718	51	36	on	on	ADP
ejpam-5718	51	37	which	which	PRON
ejpam-5718	51	38	no	no	DET
ejpam-5718	51	39	separation	separation	NOUN
ejpam-5718	51	40	axioms	axiom	NOUN
ejpam-5718	51	41	are	be	AUX
ejpam-5718	51	42	assumed	assume	VERB
ejpam-5718	51	43	unless	unless	SCONJ
ejpam-5718	51	44	explicitly	explicitly	ADV
ejpam-5718	51	45	stated	state	VERB
ejpam-5718	51	46	.	.	PUNCT
ejpam-5718	52	1	let	let	VERB
ejpam-5718	52	2	a	a	DET
ejpam-5718	52	3	be	be	AUX
ejpam-5718	52	4	a	a	DET
ejpam-5718	52	5	subset	subset	NOUN
ejpam-5718	52	6	of	of	ADP
ejpam-5718	52	7	a	a	DET
ejpam-5718	52	8	bitopological	bitopological	ADJ
ejpam-5718	52	9	space	space	NOUN
ejpam-5718	52	10	(	(	PUNCT
ejpam-5718	52	11	x	x	NOUN
ejpam-5718	52	12	,	,	PUNCT
ejpam-5718	52	13	τ1	τ1	NOUN
ejpam-5718	52	14	,	,	PUNCT
ejpam-5718	52	15	τ2	τ2	NOUN
ejpam-5718	52	16	)	)	PUNCT
ejpam-5718	52	17	.	.	PUNCT
ejpam-5718	53	1	the	the	DET
ejpam-5718	53	2	closure	closure	NOUN
ejpam-5718	53	3	of	of	ADP
ejpam-5718	53	4	a	a	PRON
ejpam-5718	53	5	and	and	CCONJ
ejpam-5718	53	6	the	the	DET
ejpam-5718	53	7	interior	interior	NOUN
ejpam-5718	53	8	of	of	ADP
ejpam-5718	53	9	a	a	PRON
ejpam-5718	53	10	with	with	ADP
ejpam-5718	53	11	respect	respect	NOUN
ejpam-5718	53	12	to	to	ADP
ejpam-5718	53	13	τi	τi	PROPN
ejpam-5718	53	14	are	be	AUX
ejpam-5718	53	15	denoted	denote	VERB
ejpam-5718	53	16	by	by	ADP
ejpam-5718	53	17	τi	τi	NOUN
ejpam-5718	53	18	-	-	PUNCT
ejpam-5718	53	19	cl(a	cl(a	NUM
ejpam-5718	53	20	)	)	PUNCT
ejpam-5718	53	21	and	and	CCONJ
ejpam-5718	53	22	τi	τi	NOUN
ejpam-5718	53	23	-	-	PUNCT
ejpam-5718	53	24	int(a	int(a	NOUN
ejpam-5718	53	25	)	)	PUNCT
ejpam-5718	53	26	,	,	PUNCT
ejpam-5718	53	27	respectively	respectively	ADV
ejpam-5718	53	28	,	,	PUNCT
ejpam-5718	53	29	for	for	ADP
ejpam-5718	53	30	i	i	PROPN
ejpam-5718	53	31	=	=	SYM
ejpam-5718	53	32	1	1	NUM
ejpam-5718	53	33	,	,	PUNCT
ejpam-5718	53	34	2	2	NUM
ejpam-5718	53	35	.	.	X
ejpam-5718	53	36	a	a	DET
ejpam-5718	53	37	subset	subset	NOUN
ejpam-5718	53	38	a	a	PRON
ejpam-5718	53	39	of	of	ADP
ejpam-5718	53	40	a	a	DET
ejpam-5718	53	41	bitopological	bitopological	ADJ
ejpam-5718	53	42	space	space	NOUN
ejpam-5718	53	43	(	(	PUNCT
ejpam-5718	53	44	x	x	NOUN
ejpam-5718	53	45	,	,	PUNCT
ejpam-5718	53	46	τ1	τ1	NOUN
ejpam-5718	53	47	,	,	PUNCT
ejpam-5718	53	48	τ2	τ2	NOUN
ejpam-5718	53	49	)	)	PUNCT
ejpam-5718	53	50	is	be	AUX
ejpam-5718	53	51	called	call	VERB
ejpam-5718	53	52	τ1τ2	τ1τ2	VERB
ejpam-5718	53	53	-	-	ADJ
ejpam-5718	53	54	closed	closed	ADJ
ejpam-5718	53	55	[	[	X
ejpam-5718	53	56	29	29	NUM
ejpam-5718	53	57	]	]	X
ejpam-5718	53	58	if	if	SCONJ
ejpam-5718	53	59	a	a	DET
ejpam-5718	53	60	=	=	NOUN
ejpam-5718	53	61	τ1	τ1	NOUN
ejpam-5718	53	62	-	-	PUNCT
ejpam-5718	53	63	cl(τ2	cl(τ2	NOUN
ejpam-5718	53	64	-	-	PUNCT
ejpam-5718	53	65	cl(a	cl(a	NUM
ejpam-5718	53	66	)	)	PUNCT
ejpam-5718	53	67	)	)	PUNCT
ejpam-5718	53	68	.	.	PUNCT
ejpam-5718	54	1	the	the	DET
ejpam-5718	54	2	complement	complement	NOUN
ejpam-5718	54	3	of	of	ADP
ejpam-5718	54	4	a	a	DET
ejpam-5718	54	5	τ1τ2	τ1τ2	ADJ
ejpam-5718	54	6	-	-	ADJ
ejpam-5718	54	7	closed	closed	ADJ
ejpam-5718	54	8	set	set	NOUN
ejpam-5718	54	9	is	be	AUX
ejpam-5718	54	10	called	call	VERB
ejpam-5718	54	11	τ1τ2	τ1τ2	NOUN
ejpam-5718	54	12	-	-	ADJ
ejpam-5718	54	13	open	open	ADJ
ejpam-5718	54	14	.	.	PUNCT
ejpam-5718	55	1	the	the	DET
ejpam-5718	55	2	intersection	intersection	NOUN
ejpam-5718	55	3	of	of	ADP
ejpam-5718	55	4	all	all	DET
ejpam-5718	55	5	τ1τ2	τ1τ2	ADJ
ejpam-5718	55	6	-	-	ADJ
ejpam-5718	55	7	closed	closed	ADJ
ejpam-5718	55	8	sets	set	NOUN
ejpam-5718	55	9	of	of	ADP
ejpam-5718	55	10	x	x	PUNCT
ejpam-5718	55	11	containing	contain	VERB
ejpam-5718	55	12	a	a	PRON
ejpam-5718	55	13	is	be	AUX
ejpam-5718	55	14	called	call	VERB
ejpam-5718	55	15	the	the	DET
ejpam-5718	55	16	τ1τ2	τ1τ2	NOUN
ejpam-5718	55	17	-	-	NOUN
ejpam-5718	55	18	closure	closure	NOUN
ejpam-5718	55	19	[	[	X
ejpam-5718	55	20	29	29	NUM
ejpam-5718	55	21	]	]	PUNCT
ejpam-5718	55	22	of	of	ADP
ejpam-5718	55	23	a	a	PRON
ejpam-5718	55	24	and	and	CCONJ
ejpam-5718	55	25	is	be	AUX
ejpam-5718	55	26	denoted	denote	VERB
ejpam-5718	55	27	by	by	ADP
ejpam-5718	55	28	τ1τ2	τ1τ2	NOUN
ejpam-5718	55	29	-	-	NUM
ejpam-5718	55	30	cl(a	cl(a	NUM
ejpam-5718	55	31	)	)	PUNCT
ejpam-5718	55	32	.	.	PUNCT
ejpam-5718	56	1	the	the	DET
ejpam-5718	56	2	union	union	NOUN
ejpam-5718	56	3	of	of	ADP
ejpam-5718	56	4	all	all	DET
ejpam-5718	56	5	τ1τ2	τ1τ2	ADJ
ejpam-5718	56	6	-	-	ADJ
ejpam-5718	56	7	open	open	ADJ
ejpam-5718	56	8	sets	set	NOUN
ejpam-5718	56	9	of	of	ADP
ejpam-5718	56	10	x	x	PUNCT
ejpam-5718	56	11	contained	contain	VERB
ejpam-5718	56	12	in	in	ADP
ejpam-5718	56	13	a	a	PRON
ejpam-5718	56	14	is	be	AUX
ejpam-5718	56	15	called	call	VERB
ejpam-5718	56	16	the	the	DET
ejpam-5718	56	17	τ1τ2	τ1τ2	NOUN
ejpam-5718	56	18	-	-	ADJ
ejpam-5718	56	19	interior	interior	ADJ
ejpam-5718	56	20	[	[	X
ejpam-5718	56	21	29	29	NUM
ejpam-5718	56	22	]	]	PUNCT
ejpam-5718	56	23	of	of	ADP
ejpam-5718	56	24	a	a	PRON
ejpam-5718	56	25	and	and	CCONJ
ejpam-5718	56	26	is	be	AUX
ejpam-5718	56	27	denoted	denote	VERB
ejpam-5718	56	28	by	by	ADP
ejpam-5718	56	29	τ1τ2	τ1τ2	NOUN
ejpam-5718	56	30	-	-	ADJ
ejpam-5718	56	31	int(a	int(a	NOUN
ejpam-5718	56	32	)	)	PUNCT
ejpam-5718	56	33	.	.	PUNCT
ejpam-5718	57	1	lemma	lemma	PROPN
ejpam-5718	57	2	1	1	NUM
ejpam-5718	57	3	.	.	PUNCT
ejpam-5718	58	1	[	[	X
ejpam-5718	58	2	29	29	NUM
ejpam-5718	58	3	]	]	PUNCT
ejpam-5718	58	4	let	let	VERB
ejpam-5718	58	5	a	a	PRON
ejpam-5718	58	6	and	and	CCONJ
ejpam-5718	58	7	b	b	NOUN
ejpam-5718	58	8	be	be	AUX
ejpam-5718	58	9	subsets	subset	NOUN
ejpam-5718	58	10	of	of	ADP
ejpam-5718	58	11	a	a	DET
ejpam-5718	58	12	bitopological	bitopological	ADJ
ejpam-5718	58	13	space	space	NOUN
ejpam-5718	58	14	(	(	PUNCT
ejpam-5718	58	15	x	x	NOUN
ejpam-5718	58	16	,	,	PUNCT
ejpam-5718	58	17	τ1	τ1	NOUN
ejpam-5718	58	18	,	,	PUNCT
ejpam-5718	58	19	τ2	τ2	NOUN
ejpam-5718	58	20	)	)	PUNCT
ejpam-5718	58	21	.	.	PUNCT
ejpam-5718	59	1	for	for	ADP
ejpam-5718	59	2	the	the	DET
ejpam-5718	59	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5718	59	4	,	,	PUNCT
ejpam-5718	59	5	the	the	DET
ejpam-5718	59	6	following	follow	VERB
ejpam-5718	59	7	properties	property	NOUN
ejpam-5718	59	8	hold	hold	VERB
ejpam-5718	59	9	:	:	PUNCT
ejpam-5718	59	10	(	(	PUNCT
ejpam-5718	59	11	1	1	X
ejpam-5718	59	12	)	)	PUNCT
ejpam-5718	59	13	a	a	DET
ejpam-5718	59	14	⊆	⊆	NUM
ejpam-5718	59	15	τ1τ2	τ1τ2	NOUN
ejpam-5718	59	16	-	-	NUM
ejpam-5718	59	17	cl(a	cl(a	NUM
ejpam-5718	59	18	)	)	PUNCT
ejpam-5718	59	19	and	and	CCONJ
ejpam-5718	59	20	τ1τ2	τ1τ2	NOUN
ejpam-5718	59	21	-	-	ADJ
ejpam-5718	59	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5718	59	23	-	-	PUNCT
ejpam-5718	59	24	cl(a	cl(a	NUM
ejpam-5718	59	25	)	)	PUNCT
ejpam-5718	59	26	)	)	PUNCT
ejpam-5718	60	1	=	=	PUNCT
ejpam-5718	60	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	60	3	-	-	NUM
ejpam-5718	60	4	cl(a	cl(a	NUM
ejpam-5718	60	5	)	)	PUNCT
ejpam-5718	60	6	.	.	PUNCT
ejpam-5718	61	1	(	(	PUNCT
ejpam-5718	61	2	2	2	X
ejpam-5718	61	3	)	)	PUNCT
ejpam-5718	61	4	if	if	SCONJ
ejpam-5718	61	5	a	a	DET
ejpam-5718	61	6	⊆	⊆	NUM
ejpam-5718	61	7	b	b	NOUN
ejpam-5718	61	8	,	,	PUNCT
ejpam-5718	61	9	then	then	ADV
ejpam-5718	61	10	τ1τ2	τ1τ2	NOUN
ejpam-5718	61	11	-	-	NUM
ejpam-5718	61	12	cl(a	cl(a	NUM
ejpam-5718	61	13	)	)	PUNCT
ejpam-5718	61	14	⊆	⊆	NUM
ejpam-5718	61	15	τ1τ2	τ1τ2	NOUN
ejpam-5718	61	16	-	-	NOUN
ejpam-5718	61	17	cl(b	cl(b	NOUN
ejpam-5718	61	18	)	)	PUNCT
ejpam-5718	61	19	.	.	PUNCT
ejpam-5718	62	1	(	(	PUNCT
ejpam-5718	62	2	3	3	X
ejpam-5718	62	3	)	)	PUNCT
ejpam-5718	62	4	τ1τ2	τ1τ2	NOUN
ejpam-5718	62	5	-	-	NUM
ejpam-5718	62	6	cl(a	cl(a	NUM
ejpam-5718	62	7	)	)	PUNCT
ejpam-5718	62	8	is	be	AUX
ejpam-5718	62	9	τ1τ2	τ1τ2	NOUN
ejpam-5718	62	10	-	-	ADJ
ejpam-5718	62	11	closed	closed	ADJ
ejpam-5718	62	12	.	.	PUNCT
ejpam-5718	63	1	(	(	PUNCT
ejpam-5718	63	2	4	4	X
ejpam-5718	63	3	)	)	PUNCT
ejpam-5718	63	4	a	a	PRON
ejpam-5718	63	5	is	be	AUX
ejpam-5718	63	6	τ1τ2	τ1τ2	NOUN
ejpam-5718	63	7	-	-	ADJ
ejpam-5718	63	8	closed	closed	ADJ
ejpam-5718	63	9	if	if	SCONJ
ejpam-5718	63	10	and	and	CCONJ
ejpam-5718	63	11	only	only	ADV
ejpam-5718	63	12	if	if	SCONJ
ejpam-5718	63	13	a	a	DET
ejpam-5718	63	14	=	=	PUNCT
ejpam-5718	63	15	τ1τ2	τ1τ2	NOUN
ejpam-5718	63	16	-	-	NUM
ejpam-5718	63	17	cl(a	cl(a	NUM
ejpam-5718	63	18	)	)	PUNCT
ejpam-5718	63	19	.	.	PUNCT
ejpam-5718	64	1	(	(	PUNCT
ejpam-5718	64	2	5	5	X
ejpam-5718	64	3	)	)	PUNCT
ejpam-5718	64	4	τ1τ2	τ1τ2	NOUN
ejpam-5718	64	5	-	-	NOUN
ejpam-5718	64	6	cl(x	cl(x	X
ejpam-5718	64	7	−a	−a	NOUN
ejpam-5718	64	8	)	)	PUNCT
ejpam-5718	65	1	=	=	PUNCT
ejpam-5718	65	2	x	x	X
ejpam-5718	66	1	−	−	ADP
ejpam-5718	66	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	66	3	-	-	PUNCT
ejpam-5718	66	4	int(a	int(a	NOUN
ejpam-5718	66	5	)	)	PUNCT
ejpam-5718	66	6	.	.	PUNCT
ejpam-5718	67	1	a	a	DET
ejpam-5718	67	2	subset	subset	NOUN
ejpam-5718	67	3	a	a	PRON
ejpam-5718	67	4	of	of	ADP
ejpam-5718	67	5	a	a	DET
ejpam-5718	67	6	bitopological	bitopological	ADJ
ejpam-5718	67	7	space	space	NOUN
ejpam-5718	67	8	(	(	PUNCT
ejpam-5718	67	9	x	x	NOUN
ejpam-5718	67	10	,	,	PUNCT
ejpam-5718	67	11	τ1	τ1	NOUN
ejpam-5718	67	12	,	,	PUNCT
ejpam-5718	67	13	τ2	τ2	NOUN
ejpam-5718	67	14	)	)	PUNCT
ejpam-5718	67	15	is	be	AUX
ejpam-5718	67	16	called	call	VERB
ejpam-5718	67	17	α(τ1	α(τ1	NOUN
ejpam-5718	67	18	,	,	PUNCT
ejpam-5718	67	19	τ2)-open	τ2)-open	ADJ
ejpam-5718	67	20	[	[	X
ejpam-5718	67	21	72	72	NUM
ejpam-5718	67	22	]	]	X
ejpam-5718	67	23	if	if	SCONJ
ejpam-5718	67	24	a	a	DET
ejpam-5718	67	25	⊆	⊆	NUM
ejpam-5718	67	26	τ1τ2	τ1τ2	NOUN
ejpam-5718	67	27	-	-	PUNCT
ejpam-5718	67	28	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5718	67	29	-	-	PUNCT
ejpam-5718	67	30	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5718	67	31	-	-	PUNCT
ejpam-5718	67	32	int(a	int(a	NOUN
ejpam-5718	67	33	)	)	PUNCT
ejpam-5718	67	34	)	)	PUNCT
ejpam-5718	67	35	)	)	PUNCT
ejpam-5718	67	36	.	.	PUNCT
ejpam-5718	68	1	the	the	DET
ejpam-5718	68	2	complement	complement	NOUN
ejpam-5718	68	3	of	of	ADP
ejpam-5718	68	4	an	an	DET
ejpam-5718	68	5	α(τ1	α(τ1	NOUN
ejpam-5718	68	6	,	,	PUNCT
ejpam-5718	68	7	τ2)-open	τ2)-open	ADJ
ejpam-5718	68	8	set	set	NOUN
ejpam-5718	68	9	is	be	AUX
ejpam-5718	68	10	called	call	VERB
ejpam-5718	68	11	α(τ1	α(τ1	NOUN
ejpam-5718	68	12	,	,	PUNCT
ejpam-5718	68	13	τ2)closed	τ2)close	VERB
ejpam-5718	68	14	.	.	PUNCT
ejpam-5718	69	1	a	a	DET
ejpam-5718	69	2	subset	subset	NOUN
ejpam-5718	69	3	a	a	PRON
ejpam-5718	69	4	of	of	ADP
ejpam-5718	69	5	a	a	DET
ejpam-5718	69	6	bitopological	bitopological	ADJ
ejpam-5718	69	7	space	space	NOUN
ejpam-5718	69	8	(	(	PUNCT
ejpam-5718	69	9	x	x	NOUN
ejpam-5718	69	10	,	,	PUNCT
ejpam-5718	69	11	τ1	τ1	NOUN
ejpam-5718	69	12	,	,	PUNCT
ejpam-5718	69	13	τ2	τ2	NOUN
ejpam-5718	69	14	)	)	PUNCT
ejpam-5718	69	15	is	be	AUX
ejpam-5718	69	16	called	call	VERB
ejpam-5718	69	17	(	(	PUNCT
ejpam-5718	69	18	τ1	τ1	NOUN
ejpam-5718	69	19	,	,	PUNCT
ejpam-5718	69	20	τ2)r	τ2)r	NOUN
ejpam-5718	69	21	-	-	PUNCT
ejpam-5718	69	22	open	open	NOUN
ejpam-5718	70	1	[	[	X
ejpam-5718	70	2	67	67	NUM
ejpam-5718	70	3	]	]	X
ejpam-5718	70	4	(	(	PUNCT
ejpam-5718	70	5	resp	resp	NOUN
ejpam-5718	70	6	.	.	PUNCT
ejpam-5718	71	1	(	(	PUNCT
ejpam-5718	71	2	τ1	τ1	NOUN
ejpam-5718	71	3	,	,	PUNCT
ejpam-5718	71	4	τ2)s	τ2)s	NOUN
ejpam-5718	71	5	-	-	PUNCT
ejpam-5718	71	6	open	open	ADJ
ejpam-5718	71	7	[	[	X
ejpam-5718	71	8	5	5	NUM
ejpam-5718	71	9	]	]	PUNCT
ejpam-5718	71	10	,	,	PUNCT
ejpam-5718	71	11	(	(	PUNCT
ejpam-5718	71	12	τ1	τ1	NOUN
ejpam-5718	71	13	,	,	PUNCT
ejpam-5718	71	14	τ2)p	τ2)p	NOUN
ejpam-5718	71	15	-	-	ADJ
ejpam-5718	71	16	open	open	ADJ
ejpam-5718	71	17	[	[	X
ejpam-5718	71	18	5	5	NUM
ejpam-5718	71	19	]	]	PUNCT
ejpam-5718	71	20	,	,	PUNCT
ejpam-5718	71	21	(	(	PUNCT
ejpam-5718	71	22	τ1	τ1	NOUN
ejpam-5718	71	23	,	,	PUNCT
ejpam-5718	71	24	τ2)β	τ2)β	ADJ
ejpam-5718	71	25	-	-	PUNCT
ejpam-5718	71	26	open	open	ADJ
ejpam-5718	71	27	[	[	X
ejpam-5718	71	28	5	5	NUM
ejpam-5718	71	29	]	]	PUNCT
ejpam-5718	71	30	)	)	PUNCT
ejpam-5718	71	31	if	if	SCONJ
ejpam-5718	71	32	a	a	DET
ejpam-5718	71	33	=	=	PUNCT
ejpam-5718	71	34	τ1τ2	τ1τ2	NOUN
ejpam-5718	71	35	-	-	NOUN
ejpam-5718	71	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5718	71	37	-	-	PUNCT
ejpam-5718	71	38	cl(a	cl(a	NUM
ejpam-5718	71	39	)	)	PUNCT
ejpam-5718	71	40	)	)	PUNCT
ejpam-5718	71	41	(	(	PUNCT
ejpam-5718	71	42	resp	resp	NOUN
ejpam-5718	71	43	.	.	PUNCT
ejpam-5718	72	1	a	a	DET
ejpam-5718	72	2	⊆	⊆	NUM
ejpam-5718	72	3	τ1τ2	τ1τ2	NOUN
ejpam-5718	72	4	-	-	ADJ
ejpam-5718	72	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5718	72	6	-	-	PUNCT
ejpam-5718	72	7	int(a	int(a	NOUN
ejpam-5718	72	8	)	)	PUNCT
ejpam-5718	72	9	)	)	PUNCT
ejpam-5718	72	10	,	,	PUNCT
ejpam-5718	72	11	a	a	DET
ejpam-5718	72	12	⊆	⊆	NUM
ejpam-5718	72	13	τ1τ2	τ1τ2	NOUN
ejpam-5718	72	14	-	-	NOUN
ejpam-5718	72	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5718	72	16	-	-	PUNCT
ejpam-5718	72	17	cl(a	cl(a	NUM
ejpam-5718	72	18	)	)	PUNCT
ejpam-5718	72	19	)	)	PUNCT
ejpam-5718	72	20	,	,	PUNCT
ejpam-5718	72	21	a	a	DET
ejpam-5718	72	22	⊆	⊆	NUM
ejpam-5718	72	23	τ1τ2	τ1τ2	NOUN
ejpam-5718	72	24	-	-	PUNCT
ejpam-5718	72	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5718	72	26	-	-	PUNCT
ejpam-5718	72	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5718	72	28	-	-	PUNCT
ejpam-5718	72	29	cl(a	cl(a	NUM
ejpam-5718	72	30	)	)	PUNCT
ejpam-5718	72	31	)	)	PUNCT
ejpam-5718	72	32	)	)	PUNCT
ejpam-5718	72	33	)	)	PUNCT
ejpam-5718	72	34	.	.	PUNCT
ejpam-5718	73	1	the	the	DET
ejpam-5718	73	2	complement	complement	NOUN
ejpam-5718	73	3	of	of	ADP
ejpam-5718	73	4	a	a	DET
ejpam-5718	73	5	(	(	PUNCT
ejpam-5718	73	6	τ1	τ1	NOUN
ejpam-5718	73	7	,	,	PUNCT
ejpam-5718	73	8	τ2)r	τ2)r	NOUN
ejpam-5718	73	9	-	-	PUNCT
ejpam-5718	73	10	open	open	ADJ
ejpam-5718	73	11	(	(	PUNCT
ejpam-5718	73	12	resp	resp	NOUN
ejpam-5718	73	13	.	.	PUNCT
ejpam-5718	74	1	(	(	PUNCT
ejpam-5718	74	2	τ1	τ1	NOUN
ejpam-5718	74	3	,	,	PUNCT
ejpam-5718	74	4	τ2)s	τ2)s	NOUN
ejpam-5718	74	5	-	-	PUNCT
ejpam-5718	74	6	open	open	ADJ
ejpam-5718	74	7	,	,	PUNCT
ejpam-5718	74	8	(	(	PUNCT
ejpam-5718	74	9	τ1	τ1	NOUN
ejpam-5718	74	10	,	,	PUNCT
ejpam-5718	74	11	τ2)p	τ2)p	NOUN
ejpam-5718	74	12	-	-	ADJ
ejpam-5718	74	13	open	open	ADJ
ejpam-5718	74	14	,	,	PUNCT
ejpam-5718	74	15	(	(	PUNCT
ejpam-5718	74	16	τ1	τ1	NOUN
ejpam-5718	74	17	,	,	PUNCT
ejpam-5718	74	18	τ2)β	τ2)β	ADJ
ejpam-5718	74	19	-	-	PUNCT
ejpam-5718	74	20	open	open	ADJ
ejpam-5718	74	21	,	,	PUNCT
ejpam-5718	74	22	α(τ1	α(τ1	NOUN
ejpam-5718	74	23	,	,	PUNCT
ejpam-5718	74	24	τ2)-open	τ2)-open	ADJ
ejpam-5718	74	25	)	)	PUNCT
ejpam-5718	74	26	set	set	NOUN
ejpam-5718	74	27	is	be	AUX
ejpam-5718	74	28	called	call	VERB
ejpam-5718	74	29	(	(	PUNCT
ejpam-5718	74	30	τ1	τ1	NOUN
ejpam-5718	74	31	,	,	PUNCT
ejpam-5718	74	32	τ2)r	τ2)r	NOUN
ejpam-5718	74	33	-	-	PUNCT
ejpam-5718	74	34	closed	closed	ADJ
ejpam-5718	74	35	(	(	PUNCT
ejpam-5718	74	36	resp	resp	NOUN
ejpam-5718	74	37	.	.	PUNCT
ejpam-5718	75	1	(	(	PUNCT
ejpam-5718	75	2	τ1	τ1	NOUN
ejpam-5718	75	3	,	,	PUNCT
ejpam-5718	75	4	τ2)s	τ2)s	NOUN
ejpam-5718	75	5	-	-	PUNCT
ejpam-5718	75	6	closed	closed	ADJ
ejpam-5718	75	7	,	,	PUNCT
ejpam-5718	75	8	(	(	PUNCT
ejpam-5718	75	9	τ1	τ1	NOUN
ejpam-5718	75	10	,	,	PUNCT
ejpam-5718	75	11	τ2)p	τ2)p	NOUN
ejpam-5718	75	12	-	-	PUNCT
ejpam-5718	75	13	closed	closed	ADJ
ejpam-5718	75	14	)	)	PUNCT
ejpam-5718	75	15	.	.	PUNCT
ejpam-5718	76	1	let	let	VERB
ejpam-5718	76	2	a	a	DET
ejpam-5718	76	3	be	be	AUX
ejpam-5718	76	4	a	a	DET
ejpam-5718	76	5	subset	subset	NOUN
ejpam-5718	76	6	of	of	ADP
ejpam-5718	76	7	a	a	DET
ejpam-5718	76	8	bitopological	bitopological	ADJ
ejpam-5718	76	9	space	space	NOUN
ejpam-5718	76	10	(	(	PUNCT
ejpam-5718	76	11	x	x	NOUN
ejpam-5718	76	12	,	,	PUNCT
ejpam-5718	76	13	τ1	τ1	NOUN
ejpam-5718	76	14	,	,	PUNCT
ejpam-5718	76	15	τ2	τ2	NOUN
ejpam-5718	76	16	)	)	PUNCT
ejpam-5718	76	17	.	.	PUNCT
ejpam-5718	77	1	a	a	DET
ejpam-5718	77	2	point	point	NOUN
ejpam-5718	77	3	x	x	X
ejpam-5718	77	4	∈	∈	NOUN
ejpam-5718	77	5	x	x	PUNCT
ejpam-5718	77	6	is	be	AUX
ejpam-5718	77	7	called	call	VERB
ejpam-5718	77	8	a	a	DET
ejpam-5718	77	9	(	(	PUNCT
ejpam-5718	77	10	τ1	τ1	NOUN
ejpam-5718	77	11	,	,	PUNCT
ejpam-5718	77	12	τ2)θ	τ2)θ	ADJ
ejpam-5718	77	13	-	-	PUNCT
ejpam-5718	77	14	cluster	cluster	NOUN
ejpam-5718	77	15	point	point	NOUN
ejpam-5718	77	16	[	[	X
ejpam-5718	77	17	67	67	NUM
ejpam-5718	77	18	]	]	PUNCT
ejpam-5718	77	19	of	of	ADP
ejpam-5718	77	20	a	a	DET
ejpam-5718	77	21	if	if	SCONJ
ejpam-5718	77	22	τ1τ2	τ1τ2	NOUN
ejpam-5718	77	23	-	-	NOUN
ejpam-5718	77	24	cl(u	cl(u	NOUN
ejpam-5718	77	25	)	)	PUNCT
ejpam-5718	77	26	∩	∩	NOUN
ejpam-5718	77	27	a	a	DET
ejpam-5718	77	28	̸=	̸=	PROPN
ejpam-5718	77	29	∅	∅	NOUN
ejpam-5718	77	30	for	for	ADP
ejpam-5718	77	31	every	every	DET
ejpam-5718	77	32	τ1τ2	τ1τ2	ADJ
ejpam-5718	77	33	-	-	ADJ
ejpam-5718	77	34	open	open	ADJ
ejpam-5718	77	35	set	set	NOUN
ejpam-5718	77	36	u	u	NOUN
ejpam-5718	77	37	containing	contain	VERB
ejpam-5718	77	38	x.	x.	NOUN
ejpam-5718	77	39	the	the	DET
ejpam-5718	77	40	set	set	NOUN
ejpam-5718	77	41	of	of	ADP
ejpam-5718	77	42	all	all	DET
ejpam-5718	77	43	(	(	PUNCT
ejpam-5718	77	44	τ1	τ1	NOUN
ejpam-5718	77	45	,	,	PUNCT
ejpam-5718	77	46	τ2)θ	τ2)θ	ADJ
ejpam-5718	77	47	-	-	PUNCT
ejpam-5718	77	48	cluster	cluster	NOUN
ejpam-5718	77	49	points	point	NOUN
ejpam-5718	77	50	of	of	ADP
ejpam-5718	77	51	a	a	PRON
ejpam-5718	77	52	is	be	AUX
ejpam-5718	77	53	called	call	VERB
ejpam-5718	77	54	the	the	DET
ejpam-5718	77	55	(	(	PUNCT
ejpam-5718	77	56	τ1	τ1	NOUN
ejpam-5718	77	57	,	,	PUNCT
ejpam-5718	77	58	τ2)θ	τ2)θ	ADJ
ejpam-5718	77	59	-	-	PUNCT
ejpam-5718	77	60	closure	closure	NOUN
ejpam-5718	77	61	[	[	X
ejpam-5718	77	62	67	67	NUM
ejpam-5718	77	63	]	]	PUNCT
ejpam-5718	77	64	of	of	ADP
ejpam-5718	77	65	a	a	PRON
ejpam-5718	77	66	and	and	CCONJ
ejpam-5718	77	67	is	be	AUX
ejpam-5718	77	68	denoted	denote	VERB
ejpam-5718	77	69	by	by	ADP
ejpam-5718	77	70	(	(	PUNCT
ejpam-5718	77	71	τ1	τ1	NOUN
ejpam-5718	77	72	,	,	PUNCT
ejpam-5718	77	73	τ2)θ	τ2)θ	NOUN
ejpam-5718	77	74	-	-	PUNCT
ejpam-5718	77	75	cl(a	cl(a	NUM
ejpam-5718	77	76	)	)	PUNCT
ejpam-5718	77	77	.	.	PUNCT
ejpam-5718	78	1	a	a	DET
ejpam-5718	78	2	subset	subset	NOUN
ejpam-5718	78	3	a	a	PRON
ejpam-5718	78	4	of	of	ADP
ejpam-5718	78	5	a	a	DET
ejpam-5718	78	6	bitopological	bitopological	ADJ
ejpam-5718	78	7	space	space	NOUN
ejpam-5718	78	8	(	(	PUNCT
ejpam-5718	78	9	x	x	NOUN
ejpam-5718	78	10	,	,	PUNCT
ejpam-5718	78	11	τ1	τ1	NOUN
ejpam-5718	78	12	,	,	PUNCT
ejpam-5718	78	13	τ2	τ2	NOUN
ejpam-5718	78	14	)	)	PUNCT
ejpam-5718	78	15	is	be	AUX
ejpam-5718	78	16	said	say	VERB
ejpam-5718	78	17	to	to	PART
ejpam-5718	78	18	be	be	AUX
ejpam-5718	78	19	(	(	PUNCT
ejpam-5718	78	20	τ1	τ1	NOUN
ejpam-5718	78	21	,	,	PUNCT
ejpam-5718	78	22	τ2)θ	τ2)θ	NOUN
ejpam-5718	78	23	-	-	PUNCT
ejpam-5718	78	24	closed	closed	ADJ
ejpam-5718	78	25	[	[	X
ejpam-5718	78	26	67	67	NUM
ejpam-5718	78	27	]	]	X
ejpam-5718	78	28	if	if	SCONJ
ejpam-5718	78	29	(	(	PUNCT
ejpam-5718	78	30	τ1	τ1	NOUN
ejpam-5718	78	31	,	,	PUNCT
ejpam-5718	78	32	τ2)θ	τ2)θ	NOUN
ejpam-5718	78	33	-	-	PUNCT
ejpam-5718	78	34	cl(a	cl(a	NUM
ejpam-5718	78	35	)	)	PUNCT
ejpam-5718	79	1	=	=	PUNCT
ejpam-5718	79	2	a.	a.	NOUN
ejpam-5718	79	3	the	the	DET
ejpam-5718	79	4	complement	complement	NOUN
ejpam-5718	79	5	of	of	ADP
ejpam-5718	79	6	a	a	DET
ejpam-5718	79	7	(	(	PUNCT
ejpam-5718	79	8	τ1	τ1	NOUN
ejpam-5718	79	9	,	,	PUNCT
ejpam-5718	79	10	τ2)θ	τ2)θ	ADJ
ejpam-5718	79	11	-	-	PUNCT
ejpam-5718	79	12	closed	close	VERB
ejpam-5718	79	13	set	set	NOUN
ejpam-5718	79	14	is	be	AUX
ejpam-5718	79	15	said	say	VERB
ejpam-5718	79	16	to	to	PART
ejpam-5718	79	17	be	be	AUX
ejpam-5718	79	18	(	(	PUNCT
ejpam-5718	79	19	τ1	τ1	NOUN
ejpam-5718	79	20	,	,	PUNCT
ejpam-5718	79	21	τ2)θopen	τ2)θopen	PROPN
ejpam-5718	79	22	.	.	PUNCT
ejpam-5718	80	1	the	the	DET
ejpam-5718	80	2	union	union	NOUN
ejpam-5718	80	3	of	of	ADP
ejpam-5718	80	4	all	all	DET
ejpam-5718	80	5	(	(	PUNCT
ejpam-5718	80	6	τ1	τ1	NOUN
ejpam-5718	80	7	,	,	PUNCT
ejpam-5718	80	8	τ2)θ	τ2)θ	ADJ
ejpam-5718	80	9	-	-	PUNCT
ejpam-5718	80	10	open	open	ADJ
ejpam-5718	80	11	sets	set	NOUN
ejpam-5718	80	12	of	of	ADP
ejpam-5718	80	13	x	x	PUNCT
ejpam-5718	80	14	contained	contain	VERB
ejpam-5718	80	15	in	in	ADP
ejpam-5718	80	16	a	a	PRON
ejpam-5718	80	17	is	be	AUX
ejpam-5718	80	18	called	call	VERB
ejpam-5718	80	19	the	the	DET
ejpam-5718	80	20	(	(	PUNCT
ejpam-5718	80	21	τ1	τ1	NOUN
ejpam-5718	80	22	,	,	PUNCT
ejpam-5718	80	23	τ2)θ	τ2)θ	ADJ
ejpam-5718	80	24	-	-	PUNCT
ejpam-5718	80	25	interior	interior	NOUN
ejpam-5718	80	26	[	[	X
ejpam-5718	80	27	67	67	NUM
ejpam-5718	80	28	]	]	PUNCT
ejpam-5718	80	29	of	of	ADP
ejpam-5718	80	30	a	a	PRON
ejpam-5718	80	31	and	and	CCONJ
ejpam-5718	80	32	is	be	AUX
ejpam-5718	80	33	denoted	denote	VERB
ejpam-5718	80	34	by	by	ADP
ejpam-5718	80	35	(	(	PUNCT
ejpam-5718	80	36	τ1	τ1	NOUN
ejpam-5718	80	37	,	,	PUNCT
ejpam-5718	80	38	τ2)θ	τ2)θ	NOUN
ejpam-5718	80	39	-	-	PUNCT
ejpam-5718	80	40	int(a	int(a	NOUN
ejpam-5718	80	41	)	)	PUNCT
ejpam-5718	80	42	.	.	PUNCT
ejpam-5718	81	1	p.	p.	NOUN
ejpam-5718	81	2	pue	pue	NOUN
ejpam-5718	81	3	-	-	PUNCT
ejpam-5718	81	4	on	on	ADP
ejpam-5718	81	5	,	,	PUNCT
ejpam-5718	81	6	a.	a.	PROPN
ejpam-5718	81	7	sama	sama	PROPN
ejpam-5718	81	8	-	-	PUNCT
ejpam-5718	81	9	ae	ae	PROPN
ejpam-5718	81	10	,	,	PUNCT
ejpam-5718	81	11	c.	c.	PROPN
ejpam-5718	81	12	boonpok	boonpok	PROPN
ejpam-5718	81	13	/	/	SYM
ejpam-5718	81	14	eur	eur	PROPN
ejpam-5718	81	15	.	.	PUNCT
ejpam-5718	82	1	j.	j.	PROPN
ejpam-5718	82	2	pure	pure	PROPN
ejpam-5718	82	3	appl	appl	PROPN
ejpam-5718	82	4	.	.	PROPN
ejpam-5718	82	5	math	math	PROPN
ejpam-5718	82	6	,	,	PUNCT
ejpam-5718	82	7	18	18	NUM
ejpam-5718	82	8	(	(	PUNCT
ejpam-5718	82	9	1	1	NUM
ejpam-5718	82	10	)	)	PUNCT
ejpam-5718	82	11	(	(	PUNCT
ejpam-5718	82	12	2025	2025	NUM
ejpam-5718	82	13	)	)	PUNCT
ejpam-5718	82	14	,	,	PUNCT
ejpam-5718	82	15	5718	5718	NUM
ejpam-5718	82	16	4	4	NUM
ejpam-5718	82	17	of	of	ADP
ejpam-5718	82	18	16	16	NUM
ejpam-5718	82	19	lemma	lemma	PROPN
ejpam-5718	82	20	2	2	NUM
ejpam-5718	82	21	.	.	PUNCT
ejpam-5718	83	1	[	[	X
ejpam-5718	83	2	67	67	NUM
ejpam-5718	83	3	]	]	PUNCT
ejpam-5718	83	4	for	for	ADP
ejpam-5718	83	5	a	a	DET
ejpam-5718	83	6	subset	subset	NOUN
ejpam-5718	83	7	a	a	PRON
ejpam-5718	83	8	of	of	ADP
ejpam-5718	83	9	a	a	DET
ejpam-5718	83	10	bitopological	bitopological	ADJ
ejpam-5718	83	11	space	space	NOUN
ejpam-5718	83	12	(	(	PUNCT
ejpam-5718	83	13	x	x	NOUN
ejpam-5718	83	14	,	,	PUNCT
ejpam-5718	83	15	τ1	τ1	NOUN
ejpam-5718	83	16	,	,	PUNCT
ejpam-5718	83	17	τ2	τ2	NOUN
ejpam-5718	83	18	)	)	PUNCT
ejpam-5718	83	19	,	,	PUNCT
ejpam-5718	83	20	the	the	DET
ejpam-5718	83	21	following	follow	VERB
ejpam-5718	83	22	properties	property	NOUN
ejpam-5718	83	23	hold	hold	VERB
ejpam-5718	83	24	:	:	PUNCT
ejpam-5718	83	25	(	(	PUNCT
ejpam-5718	83	26	1	1	X
ejpam-5718	83	27	)	)	PUNCT
ejpam-5718	83	28	if	if	SCONJ
ejpam-5718	83	29	a	a	PRON
ejpam-5718	83	30	is	be	AUX
ejpam-5718	83	31	τ1τ2	τ1τ2	NOUN
ejpam-5718	83	32	-	-	ADJ
ejpam-5718	83	33	open	open	ADJ
ejpam-5718	83	34	in	in	ADP
ejpam-5718	83	35	x	x	NOUN
ejpam-5718	83	36	,	,	PUNCT
ejpam-5718	83	37	then	then	ADV
ejpam-5718	83	38	τ1τ2	τ1τ2	NOUN
ejpam-5718	83	39	-	-	NUM
ejpam-5718	83	40	cl(a	cl(a	NUM
ejpam-5718	83	41	)	)	PUNCT
ejpam-5718	83	42	=	=	PUNCT
ejpam-5718	83	43	(	(	PUNCT
ejpam-5718	83	44	τ1	τ1	NOUN
ejpam-5718	83	45	,	,	PUNCT
ejpam-5718	83	46	τ2)θ	τ2)θ	NOUN
ejpam-5718	83	47	-	-	PUNCT
ejpam-5718	83	48	cl(a	cl(a	NUM
ejpam-5718	83	49	)	)	PUNCT
ejpam-5718	83	50	.	.	PUNCT
ejpam-5718	84	1	(	(	PUNCT
ejpam-5718	84	2	2	2	X
ejpam-5718	84	3	)	)	PUNCT
ejpam-5718	84	4	(	(	PUNCT
ejpam-5718	84	5	τ1	τ1	NOUN
ejpam-5718	84	6	,	,	PUNCT
ejpam-5718	84	7	τ2)θ	τ2)θ	NOUN
ejpam-5718	84	8	-	-	PUNCT
ejpam-5718	84	9	cl(a	cl(a	NUM
ejpam-5718	84	10	)	)	PUNCT
ejpam-5718	84	11	is	be	AUX
ejpam-5718	84	12	τ1τ2	τ1τ2	NOUN
ejpam-5718	84	13	-	-	ADJ
ejpam-5718	84	14	closed	closed	ADJ
ejpam-5718	84	15	in	in	ADP
ejpam-5718	84	16	x.	x.	NOUN
ejpam-5718	84	17	by	by	ADP
ejpam-5718	84	18	a	a	DET
ejpam-5718	84	19	multifunction	multifunction	NOUN
ejpam-5718	84	20	f	f	NOUN
ejpam-5718	84	21	:	:	PUNCT
ejpam-5718	84	22	x	x	X
ejpam-5718	84	23	→	→	SYM
ejpam-5718	84	24	y	y	PROPN
ejpam-5718	84	25	,	,	PUNCT
ejpam-5718	84	26	we	we	PRON
ejpam-5718	84	27	mean	mean	VERB
ejpam-5718	84	28	a	a	DET
ejpam-5718	84	29	point	point	NOUN
ejpam-5718	84	30	-	-	PUNCT
ejpam-5718	84	31	to	to	ADP
ejpam-5718	84	32	-	-	PUNCT
ejpam-5718	84	33	set	set	VERB
ejpam-5718	84	34	correspondence	correspondence	NOUN
ejpam-5718	84	35	from	from	ADP
ejpam-5718	84	36	x	x	PUNCT
ejpam-5718	84	37	into	into	ADP
ejpam-5718	84	38	y	y	PROPN
ejpam-5718	84	39	,	,	PUNCT
ejpam-5718	84	40	and	and	CCONJ
ejpam-5718	84	41	we	we	PRON
ejpam-5718	84	42	always	always	ADV
ejpam-5718	84	43	assume	assume	VERB
ejpam-5718	85	1	that	that	SCONJ
ejpam-5718	85	2	f	f	PROPN
ejpam-5718	85	3	(	(	PUNCT
ejpam-5718	85	4	x	x	X
ejpam-5718	85	5	)	)	PUNCT
ejpam-5718	85	6	̸=	̸=	NOUN
ejpam-5718	85	7	∅	∅	NOUN
ejpam-5718	85	8	for	for	ADP
ejpam-5718	85	9	all	all	PRON
ejpam-5718	85	10	x	x	SYM
ejpam-5718	85	11	∈	∈	ADJ
ejpam-5718	85	12	x.	x.	NOUN
ejpam-5718	85	13	for	for	ADP
ejpam-5718	85	14	a	a	DET
ejpam-5718	85	15	multifunction	multifunction	NOUN
ejpam-5718	85	16	f	f	NOUN
ejpam-5718	85	17	:	:	PUNCT
ejpam-5718	85	18	x	x	X
ejpam-5718	85	19	→	→	SYM
ejpam-5718	85	20	y	y	PROPN
ejpam-5718	85	21	,	,	PUNCT
ejpam-5718	85	22	we	we	PRON
ejpam-5718	85	23	shall	shall	AUX
ejpam-5718	85	24	denote	denote	VERB
ejpam-5718	85	25	the	the	DET
ejpam-5718	85	26	upper	upper	ADJ
ejpam-5718	85	27	and	and	CCONJ
ejpam-5718	85	28	lower	low	ADJ
ejpam-5718	85	29	inverse	inverse	NOUN
ejpam-5718	85	30	of	of	ADP
ejpam-5718	85	31	a	a	DET
ejpam-5718	85	32	set	set	NOUN
ejpam-5718	85	33	b	b	PROPN
ejpam-5718	85	34	of	of	ADP
ejpam-5718	85	35	y	y	PROPN
ejpam-5718	85	36	by	by	ADP
ejpam-5718	85	37	f+(b	f+(b	NOUN
ejpam-5718	85	38	)	)	PUNCT
ejpam-5718	85	39	and	and	CCONJ
ejpam-5718	85	40	f−(b	f−(b	NOUN
ejpam-5718	85	41	)	)	PUNCT
ejpam-5718	85	42	,	,	PUNCT
ejpam-5718	85	43	respectively	respectively	ADV
ejpam-5718	85	44	,	,	PUNCT
ejpam-5718	85	45	that	that	ADV
ejpam-5718	85	46	is	is	ADV
ejpam-5718	85	47	,	,	PUNCT
ejpam-5718	85	48	f+(b	f+(b	NOUN
ejpam-5718	85	49	)	)	PUNCT
ejpam-5718	85	50	=	=	PRON
ejpam-5718	86	1	{	{	PUNCT
ejpam-5718	86	2	x	x	PUNCT
ejpam-5718	86	3	∈	∈	PROPN
ejpam-5718	86	4	x	x	INTJ
ejpam-5718	87	1	|	|	NOUN
ejpam-5718	87	2	f	f	X
ejpam-5718	87	3	(	(	PUNCT
ejpam-5718	87	4	x	x	NOUN
ejpam-5718	87	5	)	)	PUNCT
ejpam-5718	87	6	⊆	⊆	NUM
ejpam-5718	87	7	b	b	NOUN
ejpam-5718	87	8	}	}	PUNCT
ejpam-5718	87	9	and	and	CCONJ
ejpam-5718	87	10	f−(b	f−(b	PROPN
ejpam-5718	87	11	)	)	PUNCT
ejpam-5718	87	12	=	=	PRON
ejpam-5718	88	1	{	{	PUNCT
ejpam-5718	88	2	x	x	PUNCT
ejpam-5718	88	3	∈	∈	PROPN
ejpam-5718	88	4	x	x	INTJ
ejpam-5718	89	1	|	|	NOUN
ejpam-5718	89	2	f	f	X
ejpam-5718	89	3	(	(	PUNCT
ejpam-5718	89	4	x	x	NOUN
ejpam-5718	89	5	)	)	PUNCT
ejpam-5718	89	6	∩	∩	NOUN
ejpam-5718	89	7	b	b	PROPN
ejpam-5718	89	8	̸=	̸=	PROPN
ejpam-5718	89	9	∅	∅	NOUN
ejpam-5718	89	10	}	}	PUNCT
ejpam-5718	89	11	.	.	PUNCT
ejpam-5718	90	1	in	in	ADP
ejpam-5718	90	2	particular	particular	ADJ
ejpam-5718	90	3	,	,	PUNCT
ejpam-5718	90	4	f−(y	f−(y	NOUN
ejpam-5718	90	5	)	)	PUNCT
ejpam-5718	90	6	=	=	SYM
ejpam-5718	91	1	{	{	PUNCT
ejpam-5718	91	2	x	x	PUNCT
ejpam-5718	91	3	∈	∈	PROPN
ejpam-5718	91	4	x	x	INTJ
ejpam-5718	92	1	|	|	ADV
ejpam-5718	92	2	y	y	PROPN
ejpam-5718	92	3	∈	∈	PROPN
ejpam-5718	92	4	f	f	X
ejpam-5718	92	5	(	(	PUNCT
ejpam-5718	92	6	x	x	NOUN
ejpam-5718	92	7	)	)	PUNCT
ejpam-5718	92	8	}	}	PUNCT
ejpam-5718	92	9	for	for	ADP
ejpam-5718	92	10	each	each	DET
ejpam-5718	92	11	point	point	NOUN
ejpam-5718	92	12	y	y	PROPN
ejpam-5718	92	13	∈	∈	PROPN
ejpam-5718	92	14	y	y	PROPN
ejpam-5718	92	15	.	.	PUNCT
ejpam-5718	93	1	for	for	ADP
ejpam-5718	93	2	each	each	DET
ejpam-5718	93	3	a	a	DET
ejpam-5718	93	4	⊆	⊆	NUM
ejpam-5718	93	5	x	x	SYM
ejpam-5718	93	6	,	,	PUNCT
ejpam-5718	93	7	f	f	PROPN
ejpam-5718	93	8	(	(	PUNCT
ejpam-5718	93	9	a	a	NOUN
ejpam-5718	93	10	)	)	PUNCT
ejpam-5718	93	11	=	=	SYM
ejpam-5718	93	12	∪x∈af	∪x∈af	NOUN
ejpam-5718	93	13	(	(	PUNCT
ejpam-5718	93	14	x	x	NOUN
ejpam-5718	93	15	)	)	PUNCT
ejpam-5718	93	16	.	.	PUNCT
ejpam-5718	94	1	3	3	X
ejpam-5718	94	2	.	.	X
ejpam-5718	94	3	upper	upper	ADJ
ejpam-5718	94	4	and	and	CCONJ
ejpam-5718	94	5	lower	low	ADJ
ejpam-5718	94	6	wekly	wekly	ADJ
ejpam-5718	94	7	s-(τ1	s-(τ1	PROPN
ejpam-5718	94	8	,	,	PUNCT
ejpam-5718	94	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	94	10	multifunctions	multifunction	NOUN
ejpam-5718	94	11	in	in	ADP
ejpam-5718	94	12	this	this	DET
ejpam-5718	94	13	section	section	NOUN
ejpam-5718	94	14	,	,	PUNCT
ejpam-5718	94	15	we	we	PRON
ejpam-5718	94	16	introduce	introduce	VERB
ejpam-5718	94	17	the	the	DET
ejpam-5718	94	18	notions	notion	NOUN
ejpam-5718	94	19	of	of	ADP
ejpam-5718	94	20	upper	upper	ADJ
ejpam-5718	94	21	weakly	weakly	ADJ
ejpam-5718	94	22	s-(τ1	s-(τ1	PROPN
ejpam-5718	94	23	,	,	PUNCT
ejpam-5718	94	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	94	25	multifunctions	multifunction	NOUN
ejpam-5718	94	26	and	and	CCONJ
ejpam-5718	94	27	lower	low	ADJ
ejpam-5718	94	28	weakly	weakly	ADJ
ejpam-5718	94	29	s-(τ1	s-(τ1	PROPN
ejpam-5718	94	30	,	,	PUNCT
ejpam-5718	94	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	94	32	multifunctions	multifunction	NOUN
ejpam-5718	94	33	.	.	PUNCT
ejpam-5718	95	1	moreover	moreover	ADV
ejpam-5718	95	2	,	,	PUNCT
ejpam-5718	95	3	some	some	DET
ejpam-5718	95	4	characterizations	characterization	NOUN
ejpam-5718	95	5	of	of	ADP
ejpam-5718	95	6	upper	upper	ADJ
ejpam-5718	95	7	weakly	weakly	ADJ
ejpam-5718	95	8	s-(τ1	s-(τ1	PROPN
ejpam-5718	95	9	,	,	PUNCT
ejpam-5718	95	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	95	11	multifunctions	multifunction	NOUN
ejpam-5718	95	12	and	and	CCONJ
ejpam-5718	95	13	lower	low	ADJ
ejpam-5718	95	14	weakly	weakly	ADJ
ejpam-5718	95	15	s-(τ1	s-(τ1	PROPN
ejpam-5718	95	16	,	,	PUNCT
ejpam-5718	95	17	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	95	18	multifunctions	multifunction	NOUN
ejpam-5718	95	19	are	be	AUX
ejpam-5718	95	20	discussed	discuss	VERB
ejpam-5718	95	21	.	.	PUNCT
ejpam-5718	96	1	definition	definition	NOUN
ejpam-5718	96	2	1	1	NUM
ejpam-5718	96	3	.	.	PUNCT
ejpam-5718	97	1	a	a	DET
ejpam-5718	97	2	multifunction	multifunction	NOUN
ejpam-5718	97	3	f	f	NOUN
ejpam-5718	97	4	:	:	PUNCT
ejpam-5718	97	5	(	(	PUNCT
ejpam-5718	97	6	x	x	NOUN
ejpam-5718	97	7	,	,	PUNCT
ejpam-5718	97	8	τ1	τ1	NOUN
ejpam-5718	97	9	,	,	PUNCT
ejpam-5718	97	10	τ2	τ2	NOUN
ejpam-5718	97	11	)	)	PUNCT
ejpam-5718	97	12	→	→	SYM
ejpam-5718	97	13	(	(	PUNCT
ejpam-5718	97	14	y	y	PROPN
ejpam-5718	97	15	,	,	PUNCT
ejpam-5718	97	16	σ1	σ1	PROPN
ejpam-5718	97	17	,	,	PUNCT
ejpam-5718	97	18	σ2	σ2	PROPN
ejpam-5718	97	19	)	)	PUNCT
ejpam-5718	97	20	is	be	AUX
ejpam-5718	97	21	said	say	VERB
ejpam-5718	97	22	to	to	PART
ejpam-5718	97	23	be	be	AUX
ejpam-5718	97	24	upper	upper	ADJ
ejpam-5718	97	25	weakly	weakly	ADJ
ejpam-5718	97	26	s-(τ1	s-(τ1	PROPN
ejpam-5718	97	27	,	,	PUNCT
ejpam-5718	97	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	97	29	at	at	ADP
ejpam-5718	97	30	a	a	DET
ejpam-5718	97	31	point	point	NOUN
ejpam-5718	97	32	x	x	SYM
ejpam-5718	97	33	∈	∈	NOUN
ejpam-5718	97	34	x	x	PUNCT
ejpam-5718	97	35	if	if	SCONJ
ejpam-5718	97	36	for	for	ADP
ejpam-5718	97	37	each	each	DET
ejpam-5718	97	38	σ1σ2	σ1σ2	VERB
ejpam-5718	97	39	-	-	ADJ
ejpam-5718	97	40	open	open	ADJ
ejpam-5718	97	41	set	set	NOUN
ejpam-5718	97	42	v	v	NOUN
ejpam-5718	97	43	of	of	ADP
ejpam-5718	97	44	y	y	PROPN
ejpam-5718	97	45	containing	contain	VERB
ejpam-5718	97	46	f	f	PROPN
ejpam-5718	97	47	(	(	PUNCT
ejpam-5718	97	48	x	x	NOUN
ejpam-5718	97	49	)	)	PUNCT
ejpam-5718	97	50	and	and	CCONJ
ejpam-5718	97	51	having	have	VERB
ejpam-5718	97	52	σ1σ2	σ1σ2	NOUN
ejpam-5718	97	53	-	-	PUNCT
ejpam-5718	97	54	connected	connect	VERB
ejpam-5718	97	55	complement	complement	NOUN
ejpam-5718	97	56	,	,	PUNCT
ejpam-5718	97	57	there	there	PRON
ejpam-5718	97	58	exists	exist	VERB
ejpam-5718	97	59	a	a	DET
ejpam-5718	97	60	τ1τ2	τ1τ2	NOUN
ejpam-5718	97	61	-	-	ADJ
ejpam-5718	97	62	open	open	ADJ
ejpam-5718	97	63	set	set	ADJ
ejpam-5718	97	64	u	u	NOUN
ejpam-5718	97	65	of	of	ADP
ejpam-5718	97	66	x	x	PUNCT
ejpam-5718	97	67	containing	contain	VERB
ejpam-5718	97	68	x	x	PUNCT
ejpam-5718	97	69	such	such	ADJ
ejpam-5718	97	70	that	that	SCONJ
ejpam-5718	97	71	f	f	PROPN
ejpam-5718	97	72	(	(	PUNCT
ejpam-5718	97	73	u	u	NOUN
ejpam-5718	97	74	)	)	PUNCT
ejpam-5718	97	75	⊆	⊆	NUM
ejpam-5718	97	76	σ1σ2	σ1σ2	NOUN
ejpam-5718	97	77	-	-	NUM
ejpam-5718	97	78	cl(v	cl(v	NOUN
ejpam-5718	97	79	)	)	PUNCT
ejpam-5718	97	80	.	.	PUNCT
ejpam-5718	98	1	a	a	DET
ejpam-5718	98	2	multifunction	multifunction	NOUN
ejpam-5718	98	3	f	f	NOUN
ejpam-5718	98	4	:	:	PUNCT
ejpam-5718	98	5	(	(	PUNCT
ejpam-5718	98	6	x	x	NOUN
ejpam-5718	98	7	,	,	PUNCT
ejpam-5718	98	8	τ1	τ1	NOUN
ejpam-5718	98	9	,	,	PUNCT
ejpam-5718	98	10	τ2	τ2	NOUN
ejpam-5718	98	11	)	)	PUNCT
ejpam-5718	98	12	→	→	SYM
ejpam-5718	98	13	(	(	PUNCT
ejpam-5718	98	14	y	y	PROPN
ejpam-5718	98	15	,	,	PUNCT
ejpam-5718	98	16	σ1	σ1	PROPN
ejpam-5718	98	17	,	,	PUNCT
ejpam-5718	98	18	σ2	σ2	PROPN
ejpam-5718	98	19	)	)	PUNCT
ejpam-5718	98	20	is	be	AUX
ejpam-5718	98	21	said	say	VERB
ejpam-5718	98	22	to	to	PART
ejpam-5718	98	23	be	be	AUX
ejpam-5718	98	24	upper	upper	ADJ
ejpam-5718	98	25	weakly	weakly	ADJ
ejpam-5718	98	26	s-(τ1	s-(τ1	PROPN
ejpam-5718	98	27	,	,	PUNCT
ejpam-5718	98	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	98	29	if	if	SCONJ
ejpam-5718	98	30	f	f	PROPN
ejpam-5718	98	31	is	be	AUX
ejpam-5718	98	32	upper	upper	ADJ
ejpam-5718	98	33	weakly	weakly	ADJ
ejpam-5718	98	34	s-(τ1	s-(τ1	PROPN
ejpam-5718	98	35	,	,	PUNCT
ejpam-5718	98	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	98	37	at	at	ADP
ejpam-5718	98	38	each	each	DET
ejpam-5718	98	39	point	point	NOUN
ejpam-5718	98	40	x	x	PUNCT
ejpam-5718	98	41	of	of	ADP
ejpam-5718	98	42	x.	x.	PROPN
ejpam-5718	98	43	theorem	theorem	VERB
ejpam-5718	98	44	1	1	NUM
ejpam-5718	98	45	.	.	X
ejpam-5718	98	46	for	for	ADP
ejpam-5718	98	47	a	a	DET
ejpam-5718	98	48	multifunction	multifunction	NOUN
ejpam-5718	98	49	f	f	NOUN
ejpam-5718	98	50	:	:	PUNCT
ejpam-5718	98	51	(	(	PUNCT
ejpam-5718	98	52	x	x	NOUN
ejpam-5718	98	53	,	,	PUNCT
ejpam-5718	98	54	τ1	τ1	NOUN
ejpam-5718	98	55	,	,	PUNCT
ejpam-5718	98	56	τ2	τ2	NOUN
ejpam-5718	98	57	)	)	PUNCT
ejpam-5718	98	58	→	→	SYM
ejpam-5718	98	59	(	(	PUNCT
ejpam-5718	98	60	y	y	PROPN
ejpam-5718	98	61	,	,	PUNCT
ejpam-5718	98	62	σ1	σ1	PROPN
ejpam-5718	98	63	,	,	PUNCT
ejpam-5718	98	64	σ2	σ2	NOUN
ejpam-5718	98	65	)	)	PUNCT
ejpam-5718	98	66	,	,	PUNCT
ejpam-5718	98	67	the	the	DET
ejpam-5718	98	68	following	follow	VERB
ejpam-5718	98	69	properties	property	NOUN
ejpam-5718	98	70	are	be	AUX
ejpam-5718	98	71	equivalent	equivalent	ADJ
ejpam-5718	98	72	:	:	PUNCT
ejpam-5718	98	73	(	(	PUNCT
ejpam-5718	98	74	1	1	X
ejpam-5718	98	75	)	)	PUNCT
ejpam-5718	98	76	f	f	PROPN
ejpam-5718	98	77	is	be	AUX
ejpam-5718	98	78	upper	upper	ADJ
ejpam-5718	98	79	weakly	weakly	ADJ
ejpam-5718	98	80	s-(τ1	s-(τ1	PROPN
ejpam-5718	98	81	,	,	PUNCT
ejpam-5718	98	82	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	98	83	;	;	PUNCT
ejpam-5718	98	84	(	(	PUNCT
ejpam-5718	98	85	2	2	NUM
ejpam-5718	98	86	)	)	PUNCT
ejpam-5718	98	87	f+(v	f+(v	NOUN
ejpam-5718	98	88	)	)	PUNCT
ejpam-5718	99	1	⊆	⊆	X
ejpam-5718	99	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	99	3	-	-	NUM
ejpam-5718	99	4	int(f	int(f	VERB
ejpam-5718	99	5	+	+	ADJ
ejpam-5718	99	6	(	(	PUNCT
ejpam-5718	99	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	99	8	-	-	NUM
ejpam-5718	99	9	cl(v	cl(v	NOUN
ejpam-5718	99	10	)	)	PUNCT
ejpam-5718	99	11	)	)	PUNCT
ejpam-5718	99	12	)	)	PUNCT
ejpam-5718	99	13	for	for	ADP
ejpam-5718	99	14	every	every	DET
ejpam-5718	99	15	σ1σ2	σ1σ2	NOUN
ejpam-5718	99	16	-	-	ADJ
ejpam-5718	99	17	open	open	ADJ
ejpam-5718	99	18	set	set	NOUN
ejpam-5718	99	19	v	v	NOUN
ejpam-5718	99	20	of	of	ADP
ejpam-5718	99	21	y	y	PROPN
ejpam-5718	99	22	having	have	VERB
ejpam-5718	99	23	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	99	24	complement	complement	NOUN
ejpam-5718	99	25	;	;	PUNCT
ejpam-5718	99	26	(	(	PUNCT
ejpam-5718	99	27	3	3	X
ejpam-5718	99	28	)	)	PUNCT
ejpam-5718	99	29	τ1τ2	τ1τ2	NOUN
ejpam-5718	99	30	-	-	NOUN
ejpam-5718	99	31	cl(f	cl(f	NOUN
ejpam-5718	99	32	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	99	33	-	-	PUNCT
ejpam-5718	99	34	int(k	int(k	NUM
ejpam-5718	99	35	)	)	PUNCT
ejpam-5718	99	36	)	)	PUNCT
ejpam-5718	99	37	)	)	PUNCT
ejpam-5718	100	1	⊆	⊆	X
ejpam-5718	100	2	f−(k	f−(k	PROPN
ejpam-5718	100	3	)	)	PUNCT
ejpam-5718	100	4	for	for	ADP
ejpam-5718	100	5	every	every	DET
ejpam-5718	100	6	σ1σ2	σ1σ2	NOUN
ejpam-5718	100	7	-	-	ADJ
ejpam-5718	100	8	connected	connect	VERB
ejpam-5718	100	9	σ1σ2	σ1σ2	VERB
ejpam-5718	100	10	-	-	PUNCT
ejpam-5718	100	11	closed	closed	ADJ
ejpam-5718	100	12	set	set	NOUN
ejpam-5718	100	13	k	k	PROPN
ejpam-5718	100	14	of	of	ADP
ejpam-5718	100	15	y	y	PROPN
ejpam-5718	100	16	;	;	PUNCT
ejpam-5718	100	17	(	(	PUNCT
ejpam-5718	100	18	4	4	X
ejpam-5718	100	19	)	)	PUNCT
ejpam-5718	100	20	τ1τ2	τ1τ2	NOUN
ejpam-5718	100	21	-	-	NOUN
ejpam-5718	100	22	cl(f	cl(f	NOUN
ejpam-5718	100	23	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	100	24	-	-	PUNCT
ejpam-5718	100	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	100	26	-	-	PUNCT
ejpam-5718	100	27	cl(b	cl(b	NOUN
ejpam-5718	100	28	)	)	PUNCT
ejpam-5718	100	29	)	)	PUNCT
ejpam-5718	100	30	)	)	PUNCT
ejpam-5718	100	31	)	)	PUNCT
ejpam-5718	101	1	⊆	⊆	X
ejpam-5718	101	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5718	101	3	-	-	PUNCT
ejpam-5718	101	4	cl(b	cl(b	NOUN
ejpam-5718	101	5	)	)	PUNCT
ejpam-5718	101	6	)	)	PUNCT
ejpam-5718	102	1	for	for	ADP
ejpam-5718	102	2	every	every	DET
ejpam-5718	102	3	subset	subset	NOUN
ejpam-5718	102	4	b	b	PROPN
ejpam-5718	102	5	of	of	ADP
ejpam-5718	102	6	y	y	PROPN
ejpam-5718	102	7	having	have	VERB
ejpam-5718	102	8	the	the	DET
ejpam-5718	102	9	σ1σ2	σ1σ2	ADV
ejpam-5718	102	10	-	-	PUNCT
ejpam-5718	102	11	connected	connect	VERB
ejpam-5718	102	12	σ1σ2	σ1σ2	NOUN
ejpam-5718	102	13	-	-	NOUN
ejpam-5718	102	14	closure	closure	NOUN
ejpam-5718	102	15	;	;	PUNCT
ejpam-5718	102	16	(	(	PUNCT
ejpam-5718	102	17	5	5	X
ejpam-5718	102	18	)	)	PUNCT
ejpam-5718	102	19	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	102	20	-	-	PUNCT
ejpam-5718	102	21	int(b	int(b	NOUN
ejpam-5718	102	22	)	)	PUNCT
ejpam-5718	102	23	)	)	PUNCT
ejpam-5718	103	1	⊆	⊆	X
ejpam-5718	103	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	103	3	-	-	NUM
ejpam-5718	103	4	int(f	int(f	VERB
ejpam-5718	103	5	+	+	ADJ
ejpam-5718	103	6	(	(	PUNCT
ejpam-5718	103	7	σ1σ2	σ1σ2	NUM
ejpam-5718	103	8	-	-	PUNCT
ejpam-5718	103	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	103	10	-	-	PUNCT
ejpam-5718	103	11	int(b	int(b	NOUN
ejpam-5718	103	12	)	)	PUNCT
ejpam-5718	103	13	)	)	PUNCT
ejpam-5718	103	14	)	)	PUNCT
ejpam-5718	103	15	)	)	PUNCT
ejpam-5718	103	16	for	for	ADP
ejpam-5718	103	17	every	every	DET
ejpam-5718	103	18	subset	subset	NOUN
ejpam-5718	103	19	b	b	PROPN
ejpam-5718	103	20	of	of	ADP
ejpam-5718	103	21	y	y	PRON
ejpam-5718	103	22	such	such	ADJ
ejpam-5718	103	23	that	that	SCONJ
ejpam-5718	103	24	y	y	PROPN
ejpam-5718	104	1	−	−	ADP
ejpam-5718	104	2	σ1σ2	σ1σ2	NUM
ejpam-5718	104	3	-	-	PUNCT
ejpam-5718	104	4	int(b	int(b	NOUN
ejpam-5718	104	5	)	)	PUNCT
ejpam-5718	104	6	is	be	AUX
ejpam-5718	104	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	104	8	-	-	PUNCT
ejpam-5718	104	9	connected	connect	VERB
ejpam-5718	104	10	;	;	PUNCT
ejpam-5718	104	11	(	(	PUNCT
ejpam-5718	104	12	6	6	NUM
ejpam-5718	104	13	)	)	PUNCT
ejpam-5718	104	14	τ1τ2	τ1τ2	NOUN
ejpam-5718	104	15	-	-	NOUN
ejpam-5718	104	16	cl(f	cl(f	NOUN
ejpam-5718	104	17	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	104	18	-	-	PUNCT
ejpam-5718	104	19	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	104	20	-	-	PUNCT
ejpam-5718	104	21	cl(v	cl(v	NOUN
ejpam-5718	104	22	)	)	PUNCT
ejpam-5718	104	23	)	)	PUNCT
ejpam-5718	104	24	)	)	PUNCT
ejpam-5718	104	25	)	)	PUNCT
ejpam-5718	105	1	⊆	⊆	X
ejpam-5718	105	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5718	105	3	-	-	PUNCT
ejpam-5718	105	4	cl(v	cl(v	NOUN
ejpam-5718	105	5	)	)	PUNCT
ejpam-5718	105	6	)	)	PUNCT
ejpam-5718	105	7	for	for	ADP
ejpam-5718	105	8	every	every	DET
ejpam-5718	105	9	σ1σ2	σ1σ2	NOUN
ejpam-5718	105	10	-	-	ADJ
ejpam-5718	105	11	open	open	ADJ
ejpam-5718	105	12	set	set	NOUN
ejpam-5718	105	13	v	v	NOUN
ejpam-5718	105	14	of	of	ADP
ejpam-5718	105	15	y	y	PROPN
ejpam-5718	105	16	having	have	VERB
ejpam-5718	105	17	the	the	DET
ejpam-5718	105	18	σ1σ2	σ1σ2	ADV
ejpam-5718	105	19	-	-	PUNCT
ejpam-5718	105	20	connected	connect	VERB
ejpam-5718	105	21	σ1σ2	σ1σ2	NOUN
ejpam-5718	105	22	-	-	NOUN
ejpam-5718	105	23	closure	closure	NOUN
ejpam-5718	105	24	;	;	PUNCT
ejpam-5718	105	25	p.	p.	NOUN
ejpam-5718	105	26	pue	pue	NOUN
ejpam-5718	105	27	-	-	PUNCT
ejpam-5718	105	28	on	on	ADP
ejpam-5718	105	29	,	,	PUNCT
ejpam-5718	105	30	a.	a.	PROPN
ejpam-5718	105	31	sama	sama	PROPN
ejpam-5718	105	32	-	-	PUNCT
ejpam-5718	105	33	ae	ae	PROPN
ejpam-5718	105	34	,	,	PUNCT
ejpam-5718	105	35	c.	c.	PROPN
ejpam-5718	105	36	boonpok	boonpok	PROPN
ejpam-5718	105	37	/	/	SYM
ejpam-5718	105	38	eur	eur	PROPN
ejpam-5718	105	39	.	.	PUNCT
ejpam-5718	106	1	j.	j.	PROPN
ejpam-5718	106	2	pure	pure	PROPN
ejpam-5718	106	3	appl	appl	PROPN
ejpam-5718	106	4	.	.	PROPN
ejpam-5718	106	5	math	math	PROPN
ejpam-5718	106	6	,	,	PUNCT
ejpam-5718	106	7	18	18	NUM
ejpam-5718	106	8	(	(	PUNCT
ejpam-5718	106	9	1	1	NUM
ejpam-5718	106	10	)	)	PUNCT
ejpam-5718	106	11	(	(	PUNCT
ejpam-5718	106	12	2025	2025	NUM
ejpam-5718	106	13	)	)	PUNCT
ejpam-5718	106	14	,	,	PUNCT
ejpam-5718	106	15	5718	5718	NUM
ejpam-5718	106	16	5	5	NUM
ejpam-5718	106	17	of	of	ADP
ejpam-5718	106	18	16	16	NUM
ejpam-5718	106	19	(	(	PUNCT
ejpam-5718	106	20	7	7	NUM
ejpam-5718	106	21	)	)	PUNCT
ejpam-5718	106	22	τ1τ2	τ1τ2	NOUN
ejpam-5718	106	23	-	-	NOUN
ejpam-5718	106	24	cl(f	cl(f	NUM
ejpam-5718	106	25	−(v	−(v	NOUN
ejpam-5718	106	26	)	)	PUNCT
ejpam-5718	106	27	)	)	PUNCT
ejpam-5718	107	1	⊆	⊆	X
ejpam-5718	107	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5718	107	3	-	-	PUNCT
ejpam-5718	107	4	cl(v	cl(v	NOUN
ejpam-5718	107	5	)	)	PUNCT
ejpam-5718	107	6	)	)	PUNCT
ejpam-5718	107	7	for	for	ADP
ejpam-5718	107	8	every	every	DET
ejpam-5718	107	9	σ1σ2	σ1σ2	NOUN
ejpam-5718	107	10	-	-	ADJ
ejpam-5718	107	11	open	open	ADJ
ejpam-5718	107	12	set	set	NOUN
ejpam-5718	107	13	v	v	NOUN
ejpam-5718	107	14	of	of	ADP
ejpam-5718	107	15	y	y	PROPN
ejpam-5718	107	16	having	have	VERB
ejpam-5718	107	17	the	the	DET
ejpam-5718	107	18	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	107	19	σ1σ2	σ1σ2	NOUN
ejpam-5718	107	20	-	-	NOUN
ejpam-5718	107	21	closure	closure	NOUN
ejpam-5718	107	22	;	;	PUNCT
ejpam-5718	107	23	(	(	PUNCT
ejpam-5718	107	24	8)	8)	NUM
ejpam-5718	107	25	τ1τ2	τ1τ2	NOUN
ejpam-5718	107	26	-	-	NOUN
ejpam-5718	107	27	cl(f	cl(f	NOUN
ejpam-5718	107	28	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	107	29	-	-	PUNCT
ejpam-5718	107	30	int(k	int(k	NUM
ejpam-5718	107	31	)	)	PUNCT
ejpam-5718	107	32	)	)	PUNCT
ejpam-5718	107	33	)	)	PUNCT
ejpam-5718	108	1	⊆	⊆	X
ejpam-5718	108	2	f−(k	f−(k	PROPN
ejpam-5718	108	3	)	)	PUNCT
ejpam-5718	108	4	for	for	ADP
ejpam-5718	108	5	every	every	DET
ejpam-5718	108	6	σ1σ2	σ1σ2	NOUN
ejpam-5718	108	7	-	-	ADJ
ejpam-5718	108	8	connected	connected	ADJ
ejpam-5718	108	9	(	(	PUNCT
ejpam-5718	108	10	σ1	σ1	PROPN
ejpam-5718	108	11	,	,	PUNCT
ejpam-5718	108	12	σ2)r	σ2)r	NOUN
ejpam-5718	108	13	-	-	PUNCT
ejpam-5718	108	14	closed	close	VERB
ejpam-5718	108	15	set	set	ADJ
ejpam-5718	108	16	k	k	PROPN
ejpam-5718	108	17	of	of	ADP
ejpam-5718	108	18	y	y	PROPN
ejpam-5718	108	19	.	.	PUNCT
ejpam-5718	109	1	proof	proof	NOUN
ejpam-5718	109	2	.	.	PUNCT
ejpam-5718	110	1	(	(	PUNCT
ejpam-5718	110	2	1	1	X
ejpam-5718	110	3	)	)	PUNCT
ejpam-5718	110	4	⇒	⇒	NOUN
ejpam-5718	110	5	(	(	PUNCT
ejpam-5718	110	6	2	2	NUM
ejpam-5718	110	7	):	):	PUNCT
ejpam-5718	110	8	let	let	VERB
ejpam-5718	110	9	v	v	PART
ejpam-5718	110	10	be	be	AUX
ejpam-5718	110	11	any	any	DET
ejpam-5718	110	12	σ1σ2	σ1σ2	NOUN
ejpam-5718	110	13	-	-	ADJ
ejpam-5718	110	14	open	open	ADJ
ejpam-5718	110	15	set	set	NOUN
ejpam-5718	110	16	of	of	ADP
ejpam-5718	110	17	y	y	PROPN
ejpam-5718	110	18	having	have	VERB
ejpam-5718	110	19	the	the	DET
ejpam-5718	110	20	σ1σ2	σ1σ2	ADV
ejpam-5718	110	21	-	-	PUNCT
ejpam-5718	110	22	connected	connected	ADJ
ejpam-5718	110	23	complement	complement	NOUN
ejpam-5718	110	24	and	and	CCONJ
ejpam-5718	110	25	x	x	PUNCT
ejpam-5718	110	26	∈	∈	PROPN
ejpam-5718	110	27	f+(v	f+(v	NOUN
ejpam-5718	110	28	)	)	PUNCT
ejpam-5718	110	29	.	.	PUNCT
ejpam-5718	111	1	then	then	ADV
ejpam-5718	111	2	,	,	PUNCT
ejpam-5718	111	3	there	there	PRON
ejpam-5718	111	4	exists	exist	VERB
ejpam-5718	111	5	a	a	DET
ejpam-5718	111	6	τ1τ2	τ1τ2	NOUN
ejpam-5718	111	7	-	-	ADJ
ejpam-5718	111	8	open	open	ADJ
ejpam-5718	111	9	set	set	ADJ
ejpam-5718	111	10	u	u	NOUN
ejpam-5718	111	11	of	of	ADP
ejpam-5718	111	12	x	x	PUNCT
ejpam-5718	111	13	containing	contain	VERB
ejpam-5718	111	14	x	x	PUNCT
ejpam-5718	111	15	such	such	ADJ
ejpam-5718	111	16	that	that	SCONJ
ejpam-5718	111	17	f	f	PROPN
ejpam-5718	111	18	(	(	PUNCT
ejpam-5718	111	19	u	u	NOUN
ejpam-5718	111	20	)	)	PUNCT
ejpam-5718	111	21	⊆	⊆	NUM
ejpam-5718	111	22	σ1σ2	σ1σ2	NOUN
ejpam-5718	111	23	-	-	NUM
ejpam-5718	111	24	cl(v	cl(v	NOUN
ejpam-5718	111	25	)	)	PUNCT
ejpam-5718	111	26	.	.	PUNCT
ejpam-5718	112	1	therefore	therefore	ADV
ejpam-5718	112	2	,	,	PUNCT
ejpam-5718	112	3	we	we	PRON
ejpam-5718	112	4	have	have	VERB
ejpam-5718	112	5	x	x	X
ejpam-5718	112	6	∈	∈	PROPN
ejpam-5718	112	7	u	u	NOUN
ejpam-5718	112	8	⊆	⊆	NUM
ejpam-5718	112	9	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	112	10	-	-	PUNCT
ejpam-5718	112	11	cl(v	cl(v	NOUN
ejpam-5718	112	12	)	)	PUNCT
ejpam-5718	112	13	)	)	PUNCT
ejpam-5718	112	14	.	.	PUNCT
ejpam-5718	113	1	since	since	SCONJ
ejpam-5718	113	2	u	u	NOUN
ejpam-5718	113	3	is	be	AUX
ejpam-5718	113	4	τ1τ2	τ1τ2	VERB
ejpam-5718	113	5	-	-	ADJ
ejpam-5718	113	6	open	open	ADJ
ejpam-5718	113	7	,	,	PUNCT
ejpam-5718	113	8	we	we	PRON
ejpam-5718	113	9	have	have	VERB
ejpam-5718	113	10	x	x	PART
ejpam-5718	113	11	∈	∈	PRON
ejpam-5718	113	12	τ1τ2	τ1τ2	NOUN
ejpam-5718	113	13	-	-	NUM
ejpam-5718	113	14	int(f	int(f	VERB
ejpam-5718	113	15	+	+	ADJ
ejpam-5718	113	16	(	(	PUNCT
ejpam-5718	113	17	σ1σ2	σ1σ2	NOUN
ejpam-5718	113	18	-	-	NUM
ejpam-5718	113	19	cl(v	cl(v	NOUN
ejpam-5718	113	20	)	)	PUNCT
ejpam-5718	113	21	)	)	PUNCT
ejpam-5718	113	22	)	)	PUNCT
ejpam-5718	113	23	and	and	CCONJ
ejpam-5718	113	24	hence	hence	ADV
ejpam-5718	113	25	f+(v	f+(v	NOUN
ejpam-5718	113	26	)	)	PUNCT
ejpam-5718	114	1	⊆	⊆	X
ejpam-5718	114	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	114	3	-	-	NUM
ejpam-5718	114	4	int(f	int(f	VERB
ejpam-5718	114	5	+	+	ADJ
ejpam-5718	114	6	(	(	PUNCT
ejpam-5718	114	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	114	8	-	-	NUM
ejpam-5718	114	9	cl(v	cl(v	NOUN
ejpam-5718	114	10	)	)	PUNCT
ejpam-5718	114	11	)	)	PUNCT
ejpam-5718	114	12	)	)	PUNCT
ejpam-5718	114	13	.	.	PUNCT
ejpam-5718	115	1	(	(	PUNCT
ejpam-5718	115	2	2	2	X
ejpam-5718	115	3	)	)	PUNCT
ejpam-5718	115	4	⇒	⇒	NOUN
ejpam-5718	115	5	(	(	PUNCT
ejpam-5718	115	6	3	3	NUM
ejpam-5718	115	7	):	):	PUNCT
ejpam-5718	115	8	letk	letk	ADJ
ejpam-5718	115	9	be	be	AUX
ejpam-5718	115	10	any	any	DET
ejpam-5718	115	11	σ1σ2	σ1σ2	ADV
ejpam-5718	115	12	-	-	PUNCT
ejpam-5718	115	13	connected	connected	ADJ
ejpam-5718	115	14	σ1σ2closed	σ1σ2close	VERB
ejpam-5718	115	15	set	set	NOUN
ejpam-5718	115	16	of	of	ADP
ejpam-5718	115	17	y	y	PROPN
ejpam-5718	115	18	.	.	PUNCT
ejpam-5718	116	1	then	then	ADV
ejpam-5718	116	2	,	,	PUNCT
ejpam-5718	116	3	y	y	PROPN
ejpam-5718	116	4	−k	−k	PROPN
ejpam-5718	116	5	is	be	AUX
ejpam-5718	116	6	σ1σ2	σ1σ2	NOUN
ejpam-5718	116	7	-	-	ADJ
ejpam-5718	116	8	open	open	ADJ
ejpam-5718	116	9	in	in	ADP
ejpam-5718	116	10	y	y	PROPN
ejpam-5718	116	11	having	have	VERB
ejpam-5718	116	12	σ1σ2	σ1σ2	ADV
ejpam-5718	116	13	-	-	PUNCT
ejpam-5718	116	14	connected	connect	VERB
ejpam-5718	116	15	complement	complement	NOUN
ejpam-5718	116	16	.	.	PUNCT
ejpam-5718	117	1	by	by	ADP
ejpam-5718	117	2	(	(	PUNCT
ejpam-5718	117	3	2	2	NUM
ejpam-5718	117	4	)	)	PUNCT
ejpam-5718	117	5	,	,	PUNCT
ejpam-5718	117	6	we	we	PRON
ejpam-5718	117	7	have	have	VERB
ejpam-5718	117	8	x	x	INTJ
ejpam-5718	117	9	−	−	DET
ejpam-5718	117	10	f−(k	f−(k	PROPN
ejpam-5718	117	11	)	)	PUNCT
ejpam-5718	117	12	=	=	PUNCT
ejpam-5718	118	1	f+(y	f+(y	PROPN
ejpam-5718	118	2	−k	−k	PROPN
ejpam-5718	118	3	)	)	PUNCT
ejpam-5718	118	4	⊆	⊆	NUM
ejpam-5718	118	5	τ1τ2	τ1τ2	NOUN
ejpam-5718	118	6	-	-	NUM
ejpam-5718	118	7	int(f	int(f	VERB
ejpam-5718	118	8	+	+	ADJ
ejpam-5718	118	9	(	(	PUNCT
ejpam-5718	118	10	σ1σ2	σ1σ2	NUM
ejpam-5718	118	11	-	-	PUNCT
ejpam-5718	118	12	cl(y	cl(y	NOUN
ejpam-5718	118	13	−k	−k	NOUN
ejpam-5718	118	14	)	)	PUNCT
ejpam-5718	118	15	)	)	PUNCT
ejpam-5718	118	16	)	)	PUNCT
ejpam-5718	119	1	=	=	PUNCT
ejpam-5718	119	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	119	3	-	-	NUM
ejpam-5718	119	4	int(f	int(f	VERB
ejpam-5718	119	5	+	+	ADJ
ejpam-5718	119	6	(	(	PUNCT
ejpam-5718	119	7	y	y	PROPN
ejpam-5718	119	8	−	−	PROPN
ejpam-5718	119	9	σ1σ2	σ1σ2	NUM
ejpam-5718	119	10	-	-	PUNCT
ejpam-5718	119	11	int(k	int(k	NOUN
ejpam-5718	119	12	)	)	PUNCT
ejpam-5718	119	13	)	)	PUNCT
ejpam-5718	119	14	)	)	PUNCT
ejpam-5718	120	1	=	=	PUNCT
ejpam-5718	120	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	120	3	-	-	ADJ
ejpam-5718	120	4	int(x	int(x	ADJ
ejpam-5718	120	5	−	−	NOUN
ejpam-5718	120	6	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5718	120	7	-	-	PUNCT
ejpam-5718	120	8	int(k	int(k	NOUN
ejpam-5718	120	9	)	)	PUNCT
ejpam-5718	120	10	)	)	PUNCT
ejpam-5718	120	11	)	)	PUNCT
ejpam-5718	121	1	=	=	PUNCT
ejpam-5718	122	1	x	x	X
ejpam-5718	122	2	−	−	ADP
ejpam-5718	122	3	τ1τ2	τ1τ2	NOUN
ejpam-5718	122	4	-	-	NOUN
ejpam-5718	122	5	cl(f	cl(f	NOUN
ejpam-5718	122	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	122	7	-	-	PUNCT
ejpam-5718	122	8	int(k	int(k	NUM
ejpam-5718	122	9	)	)	PUNCT
ejpam-5718	122	10	)	)	PUNCT
ejpam-5718	122	11	)	)	PUNCT
ejpam-5718	123	1	and	and	CCONJ
ejpam-5718	123	2	hence	hence	ADV
ejpam-5718	123	3	τ1τ2	τ1τ2	NOUN
ejpam-5718	123	4	-	-	ADJ
ejpam-5718	123	5	cl(f	cl(f	NOUN
ejpam-5718	123	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	123	7	-	-	PUNCT
ejpam-5718	123	8	int(k	int(k	NUM
ejpam-5718	123	9	)	)	PUNCT
ejpam-5718	123	10	)	)	PUNCT
ejpam-5718	123	11	)	)	PUNCT
ejpam-5718	124	1	⊆	⊆	NUM
ejpam-5718	124	2	f−(k	f−(k	PROPN
ejpam-5718	124	3	)	)	PUNCT
ejpam-5718	124	4	.	.	PUNCT
ejpam-5718	125	1	(	(	PUNCT
ejpam-5718	125	2	3	3	X
ejpam-5718	125	3	)	)	PUNCT
ejpam-5718	125	4	⇒	⇒	NOUN
ejpam-5718	125	5	(	(	PUNCT
ejpam-5718	125	6	4	4	NUM
ejpam-5718	125	7	):	):	PUNCT
ejpam-5718	125	8	let	let	VERB
ejpam-5718	125	9	b	b	X
ejpam-5718	125	10	be	be	AUX
ejpam-5718	125	11	any	any	DET
ejpam-5718	125	12	subset	subset	NOUN
ejpam-5718	125	13	of	of	ADP
ejpam-5718	125	14	y	y	PROPN
ejpam-5718	125	15	having	have	VERB
ejpam-5718	125	16	the	the	DET
ejpam-5718	125	17	σ1σ2	σ1σ2	ADV
ejpam-5718	125	18	-	-	PUNCT
ejpam-5718	125	19	connected	connect	VERB
ejpam-5718	125	20	σ1σ2	σ1σ2	NOUN
ejpam-5718	125	21	-	-	NOUN
ejpam-5718	125	22	closure	closure	NOUN
ejpam-5718	125	23	.	.	PUNCT
ejpam-5718	126	1	then	then	ADV
ejpam-5718	126	2	,	,	PUNCT
ejpam-5718	126	3	σ1σ2	σ1σ2	NOUN
ejpam-5718	126	4	-	-	NOUN
ejpam-5718	126	5	cl(b	cl(b	NOUN
ejpam-5718	126	6	)	)	PUNCT
ejpam-5718	126	7	is	be	AUX
ejpam-5718	126	8	σ1σ2	σ1σ2	NOUN
ejpam-5718	126	9	-	-	ADJ
ejpam-5718	126	10	closed	closed	ADJ
ejpam-5718	126	11	σ1σ2	σ1σ2	NOUN
ejpam-5718	126	12	-	-	PUNCT
ejpam-5718	126	13	connected	connected	ADJ
ejpam-5718	126	14	in	in	ADP
ejpam-5718	126	15	y	y	PROPN
ejpam-5718	126	16	and	and	CCONJ
ejpam-5718	126	17	by	by	ADP
ejpam-5718	126	18	(	(	PUNCT
ejpam-5718	126	19	3	3	NUM
ejpam-5718	126	20	)	)	PUNCT
ejpam-5718	126	21	,	,	PUNCT
ejpam-5718	126	22	we	we	PRON
ejpam-5718	126	23	have	have	VERB
ejpam-5718	126	24	τ1τ2	τ1τ2	NOUN
ejpam-5718	126	25	-	-	ADJ
ejpam-5718	126	26	cl(f	cl(f	NOUN
ejpam-5718	126	27	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	126	28	-	-	PUNCT
ejpam-5718	126	29	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	126	30	-	-	PUNCT
ejpam-5718	126	31	cl(b	cl(b	NOUN
ejpam-5718	126	32	)	)	PUNCT
ejpam-5718	126	33	)	)	PUNCT
ejpam-5718	126	34	)	)	PUNCT
ejpam-5718	126	35	)	)	PUNCT
ejpam-5718	127	1	⊆	⊆	X
ejpam-5718	127	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5718	127	3	-	-	PUNCT
ejpam-5718	127	4	cl(b	cl(b	NOUN
ejpam-5718	127	5	)	)	PUNCT
ejpam-5718	127	6	)	)	PUNCT
ejpam-5718	127	7	.	.	PUNCT
ejpam-5718	128	1	(	(	PUNCT
ejpam-5718	128	2	4	4	X
ejpam-5718	128	3	)	)	PUNCT
ejpam-5718	128	4	⇒	⇒	NOUN
ejpam-5718	128	5	(	(	PUNCT
ejpam-5718	128	6	5	5	NUM
ejpam-5718	128	7	):	):	PUNCT
ejpam-5718	128	8	let	let	VERB
ejpam-5718	128	9	b	b	X
ejpam-5718	128	10	be	be	AUX
ejpam-5718	128	11	any	any	DET
ejpam-5718	128	12	subset	subset	NOUN
ejpam-5718	128	13	of	of	ADP
ejpam-5718	128	14	y	y	PRON
ejpam-5718	128	15	such	such	ADJ
ejpam-5718	128	16	that	that	SCONJ
ejpam-5718	128	17	y	y	PROPN
ejpam-5718	128	18	−	−	ADP
ejpam-5718	128	19	σ1σ2	σ1σ2	NUM
ejpam-5718	128	20	-	-	PUNCT
ejpam-5718	128	21	int(b	int(b	NOUN
ejpam-5718	128	22	)	)	PUNCT
ejpam-5718	128	23	is	be	AUX
ejpam-5718	128	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	128	25	-	-	PUNCT
ejpam-5718	128	26	connected	connect	VERB
ejpam-5718	128	27	.	.	PUNCT
ejpam-5718	129	1	then	then	ADV
ejpam-5718	129	2	by	by	ADP
ejpam-5718	129	3	(	(	PUNCT
ejpam-5718	129	4	4	4	NUM
ejpam-5718	129	5	)	)	PUNCT
ejpam-5718	129	6	,	,	PUNCT
ejpam-5718	129	7	x	x	X
ejpam-5718	129	8	−	−	ADP
ejpam-5718	129	9	τ1τ2	τ1τ2	NOUN
ejpam-5718	129	10	-	-	NUM
ejpam-5718	129	11	int(f	int(f	VERB
ejpam-5718	129	12	+	+	ADJ
ejpam-5718	129	13	(	(	PUNCT
ejpam-5718	129	14	σ1σ2	σ1σ2	NUM
ejpam-5718	129	15	-	-	PUNCT
ejpam-5718	129	16	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	129	17	-	-	PUNCT
ejpam-5718	129	18	int(b	int(b	NOUN
ejpam-5718	129	19	)	)	PUNCT
ejpam-5718	129	20	)	)	PUNCT
ejpam-5718	129	21	)	)	PUNCT
ejpam-5718	129	22	)	)	PUNCT
ejpam-5718	130	1	=	=	PUNCT
ejpam-5718	130	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	130	3	-	-	NOUN
ejpam-5718	130	4	cl(x	cl(x	SYM
ejpam-5718	130	5	−	−	ADP
ejpam-5718	130	6	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5718	130	7	-	-	PUNCT
ejpam-5718	130	8	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	130	9	-	-	PUNCT
ejpam-5718	130	10	int(b	int(b	NOUN
ejpam-5718	130	11	)	)	PUNCT
ejpam-5718	130	12	)	)	PUNCT
ejpam-5718	130	13	)	)	PUNCT
ejpam-5718	130	14	)	)	PUNCT
ejpam-5718	131	1	=	=	PUNCT
ejpam-5718	131	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	131	3	-	-	PROPN
ejpam-5718	131	4	cl(f	cl(f	NOUN
ejpam-5718	131	5	−(y	−(y	NOUN
ejpam-5718	131	6	−	−	PUNCT
ejpam-5718	131	7	σ1σ2	σ1σ2	SYM
ejpam-5718	131	8	-	-	PUNCT
ejpam-5718	131	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	131	10	-	-	PUNCT
ejpam-5718	131	11	int(b	int(b	NOUN
ejpam-5718	131	12	)	)	PUNCT
ejpam-5718	131	13	)	)	PUNCT
ejpam-5718	131	14	)	)	PUNCT
ejpam-5718	131	15	)	)	PUNCT
ejpam-5718	132	1	=	=	PUNCT
ejpam-5718	132	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	132	3	-	-	ADJ
ejpam-5718	132	4	cl(f	cl(f	NOUN
ejpam-5718	132	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	132	6	-	-	PUNCT
ejpam-5718	132	7	int(σ1σ2	int(σ1σ2	VERB
ejpam-5718	132	8	-	-	PUNCT
ejpam-5718	132	9	cl(y	cl(y	NOUN
ejpam-5718	132	10	−b	−b	NOUN
ejpam-5718	132	11	)	)	PUNCT
ejpam-5718	132	12	)	)	PUNCT
ejpam-5718	132	13	)	)	PUNCT
ejpam-5718	132	14	)	)	PUNCT
ejpam-5718	133	1	⊆	⊆	X
ejpam-5718	133	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5718	133	3	-	-	PUNCT
ejpam-5718	133	4	cl(y	cl(y	NOUN
ejpam-5718	133	5	−b	−b	NOUN
ejpam-5718	133	6	)	)	PUNCT
ejpam-5718	133	7	)	)	PUNCT
ejpam-5718	134	1	=	=	PUNCT
ejpam-5718	134	2	x	x	X
ejpam-5718	135	1	−	−	ADP
ejpam-5718	135	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	135	3	-	-	PUNCT
ejpam-5718	135	4	int(b	int(b	NOUN
ejpam-5718	135	5	)	)	PUNCT
ejpam-5718	135	6	)	)	PUNCT
ejpam-5718	135	7	.	.	PUNCT
ejpam-5718	136	1	thus	thus	ADV
ejpam-5718	136	2	,	,	PUNCT
ejpam-5718	136	3	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	136	4	-	-	PUNCT
ejpam-5718	136	5	int(b	int(b	NOUN
ejpam-5718	136	6	)	)	PUNCT
ejpam-5718	136	7	)	)	PUNCT
ejpam-5718	137	1	⊆	⊆	X
ejpam-5718	137	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	137	3	-	-	NUM
ejpam-5718	137	4	int(f	int(f	VERB
ejpam-5718	137	5	+	+	ADJ
ejpam-5718	137	6	(	(	PUNCT
ejpam-5718	137	7	σ1σ2	σ1σ2	NUM
ejpam-5718	137	8	-	-	PUNCT
ejpam-5718	137	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	137	10	-	-	PUNCT
ejpam-5718	137	11	int(b	int(b	NOUN
ejpam-5718	137	12	)	)	PUNCT
ejpam-5718	137	13	)	)	PUNCT
ejpam-5718	137	14	)	)	PUNCT
ejpam-5718	137	15	)	)	PUNCT
ejpam-5718	137	16	.	.	PUNCT
ejpam-5718	138	1	(	(	PUNCT
ejpam-5718	138	2	5	5	X
ejpam-5718	138	3	)	)	PUNCT
ejpam-5718	138	4	⇒	⇒	NOUN
ejpam-5718	138	5	(	(	PUNCT
ejpam-5718	138	6	1	1	NUM
ejpam-5718	138	7	):	):	PUNCT
ejpam-5718	138	8	let	let	VERB
ejpam-5718	138	9	x	x	PUNCT
ejpam-5718	138	10	∈	∈	PROPN
ejpam-5718	138	11	x	x	X
ejpam-5718	138	12	and	and	CCONJ
ejpam-5718	138	13	v	v	X
ejpam-5718	138	14	be	be	AUX
ejpam-5718	138	15	any	any	DET
ejpam-5718	138	16	σ1σ2	σ1σ2	NOUN
ejpam-5718	138	17	-	-	ADJ
ejpam-5718	138	18	open	open	ADJ
ejpam-5718	138	19	set	set	NOUN
ejpam-5718	138	20	of	of	ADP
ejpam-5718	138	21	y	y	PROPN
ejpam-5718	138	22	containing	contain	VERB
ejpam-5718	138	23	f	f	PROPN
ejpam-5718	138	24	(	(	PUNCT
ejpam-5718	138	25	x	x	NOUN
ejpam-5718	138	26	)	)	PUNCT
ejpam-5718	138	27	and	and	CCONJ
ejpam-5718	138	28	having	have	VERB
ejpam-5718	138	29	σ1σ2	σ1σ2	NOUN
ejpam-5718	138	30	-	-	PUNCT
ejpam-5718	138	31	connected	connect	VERB
ejpam-5718	138	32	complement	complement	NOUN
ejpam-5718	138	33	.	.	PUNCT
ejpam-5718	139	1	by	by	ADP
ejpam-5718	139	2	(	(	PUNCT
ejpam-5718	139	3	5	5	NUM
ejpam-5718	139	4	)	)	PUNCT
ejpam-5718	139	5	,	,	PUNCT
ejpam-5718	139	6	we	we	PRON
ejpam-5718	139	7	have	have	VERB
ejpam-5718	139	8	x	x	X
ejpam-5718	139	9	∈	∈	NOUN
ejpam-5718	139	10	f+(v	f+(v	NOUN
ejpam-5718	139	11	)	)	PUNCT
ejpam-5718	140	1	=	=	SYM
ejpam-5718	140	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	140	3	-	-	PUNCT
ejpam-5718	140	4	int(v	int(v	NOUN
ejpam-5718	140	5	)	)	PUNCT
ejpam-5718	140	6	)	)	PUNCT
ejpam-5718	141	1	⊆	⊆	X
ejpam-5718	141	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	141	3	-	-	NUM
ejpam-5718	141	4	int(f	int(f	VERB
ejpam-5718	141	5	+	+	ADJ
ejpam-5718	141	6	(	(	PUNCT
ejpam-5718	141	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	141	8	-	-	NUM
ejpam-5718	141	9	cl(v	cl(v	NOUN
ejpam-5718	141	10	)	)	PUNCT
ejpam-5718	141	11	)	)	PUNCT
ejpam-5718	141	12	)	)	PUNCT
ejpam-5718	141	13	.	.	PUNCT
ejpam-5718	142	1	then	then	ADV
ejpam-5718	142	2	,	,	PUNCT
ejpam-5718	142	3	there	there	PRON
ejpam-5718	142	4	exists	exist	VERB
ejpam-5718	142	5	a	a	DET
ejpam-5718	142	6	τ1τ2	τ1τ2	NOUN
ejpam-5718	142	7	-	-	ADJ
ejpam-5718	142	8	open	open	ADJ
ejpam-5718	142	9	set	set	ADJ
ejpam-5718	142	10	u	u	NOUN
ejpam-5718	142	11	of	of	ADP
ejpam-5718	142	12	x	x	PUNCT
ejpam-5718	142	13	containing	contain	VERB
ejpam-5718	142	14	x	x	PUNCT
ejpam-5718	142	15	such	such	ADJ
ejpam-5718	142	16	that	that	SCONJ
ejpam-5718	142	17	u	u	NOUN
ejpam-5718	142	18	⊆	⊆	NUM
ejpam-5718	142	19	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	142	20	-	-	PUNCT
ejpam-5718	142	21	cl(v	cl(v	NOUN
ejpam-5718	142	22	)	)	PUNCT
ejpam-5718	142	23	)	)	PUNCT
ejpam-5718	142	24	.	.	PUNCT
ejpam-5718	143	1	thus	thus	ADV
ejpam-5718	143	2	,	,	PUNCT
ejpam-5718	143	3	f	f	PROPN
ejpam-5718	143	4	(	(	PUNCT
ejpam-5718	143	5	u	u	NOUN
ejpam-5718	143	6	)	)	PUNCT
ejpam-5718	143	7	⊆	⊆	NUM
ejpam-5718	143	8	σ1σ2	σ1σ2	NOUN
ejpam-5718	143	9	-	-	NUM
ejpam-5718	143	10	cl(v	cl(v	NOUN
ejpam-5718	143	11	)	)	PUNCT
ejpam-5718	143	12	and	and	CCONJ
ejpam-5718	143	13	hence	hence	ADV
ejpam-5718	143	14	f	f	PROPN
ejpam-5718	143	15	is	be	AUX
ejpam-5718	143	16	upper	upper	ADJ
ejpam-5718	143	17	weakly	weakly	ADJ
ejpam-5718	143	18	s-(τ1	s-(τ1	PROPN
ejpam-5718	143	19	,	,	PUNCT
ejpam-5718	143	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	143	21	.	.	PUNCT
ejpam-5718	144	1	(	(	PUNCT
ejpam-5718	144	2	4	4	X
ejpam-5718	144	3	)	)	PUNCT
ejpam-5718	144	4	⇒	⇒	NOUN
ejpam-5718	144	5	(	(	PUNCT
ejpam-5718	144	6	6	6	NUM
ejpam-5718	144	7	)	)	PUNCT
ejpam-5718	144	8	and	and	CCONJ
ejpam-5718	144	9	(	(	PUNCT
ejpam-5718	144	10	6	6	NUM
ejpam-5718	144	11	)	)	PUNCT
ejpam-5718	144	12	⇒	⇒	NOUN
ejpam-5718	144	13	(	(	PUNCT
ejpam-5718	144	14	7	7	NUM
ejpam-5718	144	15	):	):	PUNCT
ejpam-5718	144	16	the	the	DET
ejpam-5718	144	17	proofs	proof	NOUN
ejpam-5718	144	18	are	be	AUX
ejpam-5718	144	19	obvious	obvious	ADJ
ejpam-5718	144	20	.	.	PUNCT
ejpam-5718	145	1	p.	p.	NOUN
ejpam-5718	145	2	pue	pue	NOUN
ejpam-5718	145	3	-	-	PUNCT
ejpam-5718	145	4	on	on	ADP
ejpam-5718	145	5	,	,	PUNCT
ejpam-5718	145	6	a.	a.	PROPN
ejpam-5718	145	7	sama	sama	PROPN
ejpam-5718	145	8	-	-	PUNCT
ejpam-5718	145	9	ae	ae	PROPN
ejpam-5718	145	10	,	,	PUNCT
ejpam-5718	145	11	c.	c.	PROPN
ejpam-5718	145	12	boonpok	boonpok	PROPN
ejpam-5718	145	13	/	/	SYM
ejpam-5718	145	14	eur	eur	PROPN
ejpam-5718	145	15	.	.	PUNCT
ejpam-5718	146	1	j.	j.	PROPN
ejpam-5718	146	2	pure	pure	PROPN
ejpam-5718	146	3	appl	appl	PROPN
ejpam-5718	146	4	.	.	PROPN
ejpam-5718	146	5	math	math	PROPN
ejpam-5718	146	6	,	,	PUNCT
ejpam-5718	146	7	18	18	NUM
ejpam-5718	146	8	(	(	PUNCT
ejpam-5718	146	9	1	1	NUM
ejpam-5718	146	10	)	)	PUNCT
ejpam-5718	146	11	(	(	PUNCT
ejpam-5718	146	12	2025	2025	NUM
ejpam-5718	146	13	)	)	PUNCT
ejpam-5718	146	14	,	,	PUNCT
ejpam-5718	146	15	5718	5718	NUM
ejpam-5718	146	16	6	6	NUM
ejpam-5718	146	17	of	of	ADP
ejpam-5718	146	18	16	16	NUM
ejpam-5718	146	19	(	(	PUNCT
ejpam-5718	146	20	7	7	NUM
ejpam-5718	146	21	)	)	PUNCT
ejpam-5718	146	22	⇒	⇒	NOUN
ejpam-5718	146	23	(	(	PUNCT
ejpam-5718	146	24	8)	8)	NUM
ejpam-5718	146	25	:	:	PUNCT
ejpam-5718	146	26	let	let	VERB
ejpam-5718	146	27	k	k	X
ejpam-5718	146	28	be	be	AUX
ejpam-5718	146	29	any	any	DET
ejpam-5718	146	30	σ1σ2	σ1σ2	NOUN
ejpam-5718	146	31	-	-	ADJ
ejpam-5718	146	32	connected	connected	ADJ
ejpam-5718	146	33	(	(	PUNCT
ejpam-5718	146	34	σ1	σ1	PROPN
ejpam-5718	146	35	,	,	PUNCT
ejpam-5718	146	36	σ2)r	σ2)r	NOUN
ejpam-5718	146	37	-	-	PUNCT
ejpam-5718	146	38	closed	close	VERB
ejpam-5718	146	39	set	set	NOUN
ejpam-5718	146	40	of	of	ADP
ejpam-5718	146	41	y	y	PROPN
ejpam-5718	146	42	.	.	PUNCT
ejpam-5718	147	1	then	then	ADV
ejpam-5718	147	2	,	,	PUNCT
ejpam-5718	147	3	we	we	PRON
ejpam-5718	147	4	have	have	VERB
ejpam-5718	147	5	k	k	NOUN
ejpam-5718	147	6	=	=	SYM
ejpam-5718	147	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	147	8	-	-	PUNCT
ejpam-5718	147	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	147	10	-	-	PUNCT
ejpam-5718	147	11	int(k	int(k	NOUN
ejpam-5718	147	12	)	)	PUNCT
ejpam-5718	147	13	)	)	PUNCT
ejpam-5718	148	1	is	be	AUX
ejpam-5718	148	2	σ1σ2	σ1σ2	NOUN
ejpam-5718	148	3	-	-	PUNCT
ejpam-5718	148	4	connected	connect	VERB
ejpam-5718	148	5	and	and	CCONJ
ejpam-5718	148	6	by	by	ADP
ejpam-5718	148	7	(	(	PUNCT
ejpam-5718	148	8	7	7	NUM
ejpam-5718	148	9	)	)	PUNCT
ejpam-5718	148	10	,	,	PUNCT
ejpam-5718	148	11	τ1τ2	τ1τ2	NOUN
ejpam-5718	148	12	-	-	ADJ
ejpam-5718	148	13	cl(f	cl(f	NOUN
ejpam-5718	148	14	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	148	15	-	-	PUNCT
ejpam-5718	148	16	int(k	int(k	NUM
ejpam-5718	148	17	)	)	PUNCT
ejpam-5718	148	18	)	)	PUNCT
ejpam-5718	148	19	)	)	PUNCT
ejpam-5718	149	1	⊆	⊆	X
ejpam-5718	149	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5718	149	3	-	-	PUNCT
ejpam-5718	149	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	149	5	-	-	PUNCT
ejpam-5718	149	6	int(k	int(k	NOUN
ejpam-5718	149	7	)	)	PUNCT
ejpam-5718	149	8	)	)	PUNCT
ejpam-5718	149	9	)	)	PUNCT
ejpam-5718	150	1	=	=	SYM
ejpam-5718	150	2	f−(k	f−(k	PROPN
ejpam-5718	150	3	)	)	PUNCT
ejpam-5718	150	4	.	.	PUNCT
ejpam-5718	151	1	(	(	PUNCT
ejpam-5718	151	2	8)	8)	NUM
ejpam-5718	151	3	⇒	⇒	NOUN
ejpam-5718	151	4	(	(	PUNCT
ejpam-5718	151	5	3	3	NUM
ejpam-5718	151	6	):	):	PUNCT
ejpam-5718	151	7	let	let	VERB
ejpam-5718	151	8	k	k	PRON
ejpam-5718	151	9	be	be	AUX
ejpam-5718	151	10	any	any	DET
ejpam-5718	151	11	σ1σ2	σ1σ2	NOUN
ejpam-5718	151	12	-	-	ADJ
ejpam-5718	151	13	connected	connect	VERB
ejpam-5718	151	14	σ1σ2	σ1σ2	VERB
ejpam-5718	151	15	-	-	PUNCT
ejpam-5718	151	16	closed	closed	ADJ
ejpam-5718	151	17	set	set	NOUN
ejpam-5718	151	18	of	of	ADP
ejpam-5718	151	19	y	y	PROPN
ejpam-5718	151	20	.	.	PUNCT
ejpam-5718	152	1	since	since	SCONJ
ejpam-5718	152	2	k	k	PROPN
ejpam-5718	152	3	is	be	AUX
ejpam-5718	152	4	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	152	5	,	,	PUNCT
ejpam-5718	152	6	we	we	PRON
ejpam-5718	152	7	have	have	VERB
ejpam-5718	152	8	σ1σ2	σ1σ2	NOUN
ejpam-5718	152	9	-	-	PUNCT
ejpam-5718	152	10	int(k	int(k	NOUN
ejpam-5718	152	11	)	)	PUNCT
ejpam-5718	152	12	is	be	AUX
ejpam-5718	152	13	σ1σ2	σ1σ2	NOUN
ejpam-5718	152	14	-	-	PUNCT
ejpam-5718	152	15	connected	connected	ADJ
ejpam-5718	152	16	and	and	CCONJ
ejpam-5718	152	17	hence	hence	ADV
ejpam-5718	152	18	σ1σ2	σ1σ2	ADV
ejpam-5718	152	19	-	-	PUNCT
ejpam-5718	152	20	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	152	21	-	-	PUNCT
ejpam-5718	152	22	int(k	int(k	NOUN
ejpam-5718	152	23	)	)	PUNCT
ejpam-5718	152	24	)	)	PUNCT
ejpam-5718	153	1	is	be	AUX
ejpam-5718	153	2	σ1σ2	σ1σ2	NOUN
ejpam-5718	153	3	-	-	PUNCT
ejpam-5718	153	4	connected	connect	VERB
ejpam-5718	153	5	.	.	PUNCT
ejpam-5718	154	1	let	let	VERB
ejpam-5718	154	2	h	h	NOUN
ejpam-5718	154	3	=	=	SYM
ejpam-5718	154	4	σ1σ2	σ1σ2	NOUN
ejpam-5718	154	5	-	-	PUNCT
ejpam-5718	154	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	154	7	-	-	PUNCT
ejpam-5718	154	8	int(k	int(k	NOUN
ejpam-5718	154	9	)	)	PUNCT
ejpam-5718	154	10	)	)	PUNCT
ejpam-5718	154	11	.	.	PUNCT
ejpam-5718	155	1	then	then	ADV
ejpam-5718	155	2	,	,	PUNCT
ejpam-5718	155	3	h	h	NOUN
ejpam-5718	155	4	is	be	AUX
ejpam-5718	155	5	a	a	DET
ejpam-5718	155	6	(	(	PUNCT
ejpam-5718	155	7	σ1	σ1	NOUN
ejpam-5718	155	8	,	,	PUNCT
ejpam-5718	155	9	σ2)r	σ2)r	NOUN
ejpam-5718	155	10	-	-	PUNCT
ejpam-5718	155	11	closed	close	VERB
ejpam-5718	155	12	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	155	13	set	set	NOUN
ejpam-5718	155	14	of	of	ADP
ejpam-5718	155	15	y	y	PROPN
ejpam-5718	155	16	and	and	CCONJ
ejpam-5718	155	17	σ1σ2	σ1σ2	NOUN
ejpam-5718	155	18	-	-	PUNCT
ejpam-5718	155	19	int(h	int(h	ADV
ejpam-5718	155	20	)	)	PUNCT
ejpam-5718	155	21	=	=	SYM
ejpam-5718	155	22	σ1σ2	σ1σ2	X
ejpam-5718	155	23	-	-	PUNCT
ejpam-5718	155	24	int(σ1σ2	int(σ1σ2	ADV
ejpam-5718	155	25	-	-	PUNCT
ejpam-5718	155	26	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5718	155	27	-	-	PUNCT
ejpam-5718	155	28	int(k	int(k	NOUN
ejpam-5718	155	29	)	)	PUNCT
ejpam-5718	155	30	)	)	PUNCT
ejpam-5718	155	31	)	)	PUNCT
ejpam-5718	156	1	=	=	PUNCT
ejpam-5718	156	2	σ1σ2	σ1σ2	X
ejpam-5718	156	3	-	-	PUNCT
ejpam-5718	156	4	int(k	int(k	NOUN
ejpam-5718	156	5	)	)	PUNCT
ejpam-5718	156	6	.	.	PUNCT
ejpam-5718	157	1	by	by	ADP
ejpam-5718	157	2	(	(	PUNCT
ejpam-5718	157	3	8)	8)	NUM
ejpam-5718	157	4	,	,	PUNCT
ejpam-5718	157	5	we	we	PRON
ejpam-5718	157	6	have	have	VERB
ejpam-5718	157	7	τ1τ2	τ1τ2	NOUN
ejpam-5718	157	8	-	-	ADJ
ejpam-5718	157	9	cl(f	cl(f	NOUN
ejpam-5718	157	10	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	157	11	-	-	PUNCT
ejpam-5718	157	12	int(k	int(k	NUM
ejpam-5718	157	13	)	)	PUNCT
ejpam-5718	157	14	)	)	PUNCT
ejpam-5718	157	15	)	)	PUNCT
ejpam-5718	158	1	=	=	PUNCT
ejpam-5718	158	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	158	3	-	-	ADJ
ejpam-5718	158	4	cl(f	cl(f	NOUN
ejpam-5718	158	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	158	6	-	-	PUNCT
ejpam-5718	158	7	int(h	int(h	ADJ
ejpam-5718	158	8	)	)	PUNCT
ejpam-5718	158	9	)	)	PUNCT
ejpam-5718	158	10	)	)	PUNCT
ejpam-5718	159	1	⊆	⊆	NUM
ejpam-5718	159	2	f−(h	f−(h	NOUN
ejpam-5718	159	3	)	)	PUNCT
ejpam-5718	159	4	⊆	⊆	NUM
ejpam-5718	159	5	f−(k	f−(k	PROPN
ejpam-5718	159	6	)	)	PUNCT
ejpam-5718	159	7	.	.	PUNCT
ejpam-5718	160	1	definition	definition	NOUN
ejpam-5718	160	2	2	2	NUM
ejpam-5718	160	3	.	.	PUNCT
ejpam-5718	160	4	a	a	DET
ejpam-5718	160	5	multifunction	multifunction	NOUN
ejpam-5718	160	6	f	f	NOUN
ejpam-5718	160	7	:	:	PUNCT
ejpam-5718	160	8	(	(	PUNCT
ejpam-5718	160	9	x	x	NOUN
ejpam-5718	160	10	,	,	PUNCT
ejpam-5718	160	11	τ1	τ1	NOUN
ejpam-5718	160	12	,	,	PUNCT
ejpam-5718	160	13	τ2	τ2	NOUN
ejpam-5718	160	14	)	)	PUNCT
ejpam-5718	160	15	→	→	SYM
ejpam-5718	160	16	(	(	PUNCT
ejpam-5718	160	17	y	y	PROPN
ejpam-5718	160	18	,	,	PUNCT
ejpam-5718	160	19	σ1	σ1	PROPN
ejpam-5718	160	20	,	,	PUNCT
ejpam-5718	160	21	σ2	σ2	PROPN
ejpam-5718	160	22	)	)	PUNCT
ejpam-5718	160	23	is	be	AUX
ejpam-5718	160	24	said	say	VERB
ejpam-5718	160	25	to	to	PART
ejpam-5718	160	26	be	be	AUX
ejpam-5718	160	27	lower	low	ADJ
ejpam-5718	160	28	weakly	weakly	ADJ
ejpam-5718	160	29	s(τ1	s(τ1	NOUN
ejpam-5718	160	30	,	,	PUNCT
ejpam-5718	160	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	160	32	at	at	ADP
ejpam-5718	160	33	a	a	DET
ejpam-5718	160	34	point	point	NOUN
ejpam-5718	160	35	x	x	SYM
ejpam-5718	160	36	∈	∈	NOUN
ejpam-5718	160	37	x	x	PUNCT
ejpam-5718	160	38	if	if	SCONJ
ejpam-5718	160	39	for	for	ADP
ejpam-5718	160	40	each	each	DET
ejpam-5718	160	41	σ1σ2	σ1σ2	VERB
ejpam-5718	160	42	-	-	ADJ
ejpam-5718	160	43	open	open	ADJ
ejpam-5718	160	44	set	set	NOUN
ejpam-5718	160	45	v	v	NOUN
ejpam-5718	160	46	of	of	ADP
ejpam-5718	160	47	y	y	PRON
ejpam-5718	160	48	such	such	ADJ
ejpam-5718	160	49	that	that	SCONJ
ejpam-5718	160	50	f	f	PROPN
ejpam-5718	160	51	(	(	PUNCT
ejpam-5718	160	52	x)∩v	x)∩v	PROPN
ejpam-5718	160	53	̸=	̸=	PROPN
ejpam-5718	160	54	∅	∅	NOUN
ejpam-5718	160	55	and	and	CCONJ
ejpam-5718	160	56	having	have	VERB
ejpam-5718	160	57	σ1σ2	σ1σ2	NOUN
ejpam-5718	160	58	-	-	PUNCT
ejpam-5718	160	59	connected	connect	VERB
ejpam-5718	160	60	complement	complement	NOUN
ejpam-5718	160	61	,	,	PUNCT
ejpam-5718	160	62	there	there	PRON
ejpam-5718	160	63	exists	exist	VERB
ejpam-5718	160	64	a	a	DET
ejpam-5718	160	65	τ1τ2	τ1τ2	NOUN
ejpam-5718	160	66	-	-	ADJ
ejpam-5718	160	67	open	open	ADJ
ejpam-5718	160	68	set	set	ADJ
ejpam-5718	160	69	u	u	NOUN
ejpam-5718	160	70	of	of	ADP
ejpam-5718	160	71	x	x	PUNCT
ejpam-5718	160	72	containing	contain	VERB
ejpam-5718	160	73	x	x	PUNCT
ejpam-5718	160	74	such	such	ADJ
ejpam-5718	160	75	that	that	SCONJ
ejpam-5718	160	76	σ1σ2	σ1σ2	NOUN
ejpam-5718	160	77	-	-	PUNCT
ejpam-5718	160	78	cl(v	cl(v	NOUN
ejpam-5718	160	79	)	)	PUNCT
ejpam-5718	160	80	∩	∩	PROPN
ejpam-5718	160	81	f	f	X
ejpam-5718	160	82	(	(	PUNCT
ejpam-5718	160	83	z	z	NOUN
ejpam-5718	160	84	)	)	PUNCT
ejpam-5718	160	85	̸=	̸=	NOUN
ejpam-5718	160	86	∅	∅	NOUN
ejpam-5718	160	87	for	for	ADP
ejpam-5718	160	88	each	each	DET
ejpam-5718	160	89	z	z	NOUN
ejpam-5718	160	90	∈	∈	PROPN
ejpam-5718	160	91	u	u	NOUN
ejpam-5718	160	92	.	.	PUNCT
ejpam-5718	161	1	a	a	DET
ejpam-5718	161	2	multifunction	multifunction	NOUN
ejpam-5718	161	3	f	f	NOUN
ejpam-5718	161	4	:	:	PUNCT
ejpam-5718	161	5	(	(	PUNCT
ejpam-5718	161	6	x	x	NOUN
ejpam-5718	161	7	,	,	PUNCT
ejpam-5718	161	8	τ1	τ1	NOUN
ejpam-5718	161	9	,	,	PUNCT
ejpam-5718	161	10	τ2	τ2	NOUN
ejpam-5718	161	11	)	)	PUNCT
ejpam-5718	161	12	→	→	SYM
ejpam-5718	161	13	(	(	PUNCT
ejpam-5718	161	14	y	y	PROPN
ejpam-5718	161	15	,	,	PUNCT
ejpam-5718	161	16	σ1	σ1	PROPN
ejpam-5718	161	17	,	,	PUNCT
ejpam-5718	161	18	σ2	σ2	PROPN
ejpam-5718	161	19	)	)	PUNCT
ejpam-5718	161	20	is	be	AUX
ejpam-5718	161	21	said	say	VERB
ejpam-5718	161	22	to	to	PART
ejpam-5718	161	23	be	be	AUX
ejpam-5718	161	24	lower	low	ADJ
ejpam-5718	161	25	weakly	weakly	ADJ
ejpam-5718	161	26	s-(τ1	s-(τ1	PROPN
ejpam-5718	161	27	,	,	PUNCT
ejpam-5718	161	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	161	29	if	if	SCONJ
ejpam-5718	161	30	f	f	PROPN
ejpam-5718	161	31	is	be	AUX
ejpam-5718	161	32	lower	low	ADJ
ejpam-5718	161	33	weakly	weakly	ADJ
ejpam-5718	161	34	s-(τ1	s-(τ1	PROPN
ejpam-5718	161	35	,	,	PUNCT
ejpam-5718	161	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	161	37	at	at	ADP
ejpam-5718	161	38	each	each	DET
ejpam-5718	161	39	point	point	NOUN
ejpam-5718	161	40	x	x	PUNCT
ejpam-5718	161	41	of	of	ADP
ejpam-5718	161	42	x.	x.	PROPN
ejpam-5718	161	43	theorem	theorem	VERB
ejpam-5718	161	44	2	2	NUM
ejpam-5718	161	45	.	.	X
ejpam-5718	161	46	for	for	ADP
ejpam-5718	161	47	a	a	DET
ejpam-5718	161	48	multifunction	multifunction	NOUN
ejpam-5718	161	49	f	f	NOUN
ejpam-5718	161	50	:	:	PUNCT
ejpam-5718	161	51	(	(	PUNCT
ejpam-5718	161	52	x	x	NOUN
ejpam-5718	161	53	,	,	PUNCT
ejpam-5718	161	54	τ1	τ1	NOUN
ejpam-5718	161	55	,	,	PUNCT
ejpam-5718	161	56	τ2	τ2	NOUN
ejpam-5718	161	57	)	)	PUNCT
ejpam-5718	161	58	→	→	SYM
ejpam-5718	161	59	(	(	PUNCT
ejpam-5718	161	60	y	y	PROPN
ejpam-5718	161	61	,	,	PUNCT
ejpam-5718	161	62	σ1	σ1	PROPN
ejpam-5718	161	63	,	,	PUNCT
ejpam-5718	161	64	σ2	σ2	NOUN
ejpam-5718	161	65	)	)	PUNCT
ejpam-5718	161	66	,	,	PUNCT
ejpam-5718	161	67	the	the	DET
ejpam-5718	161	68	following	follow	VERB
ejpam-5718	161	69	properties	property	NOUN
ejpam-5718	161	70	are	be	AUX
ejpam-5718	161	71	equivalent	equivalent	ADJ
ejpam-5718	161	72	:	:	PUNCT
ejpam-5718	161	73	(	(	PUNCT
ejpam-5718	161	74	1	1	X
ejpam-5718	161	75	)	)	PUNCT
ejpam-5718	161	76	f	f	PROPN
ejpam-5718	161	77	is	be	AUX
ejpam-5718	161	78	lower	low	ADJ
ejpam-5718	161	79	weakly	weakly	ADJ
ejpam-5718	161	80	s-(τ1	s-(τ1	PROPN
ejpam-5718	161	81	,	,	PUNCT
ejpam-5718	161	82	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	161	83	;	;	PUNCT
ejpam-5718	161	84	(	(	PUNCT
ejpam-5718	161	85	2	2	X
ejpam-5718	161	86	)	)	PUNCT
ejpam-5718	161	87	f−(v	f−(v	NOUN
ejpam-5718	161	88	)	)	PUNCT
ejpam-5718	162	1	⊆	⊆	NUM
ejpam-5718	162	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	162	3	-	-	NUM
ejpam-5718	162	4	int(f	int(f	PRON
ejpam-5718	162	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	162	6	-	-	NOUN
ejpam-5718	162	7	cl(v	cl(v	NOUN
ejpam-5718	162	8	)	)	PUNCT
ejpam-5718	162	9	)	)	PUNCT
ejpam-5718	162	10	)	)	PUNCT
ejpam-5718	162	11	for	for	ADP
ejpam-5718	162	12	every	every	DET
ejpam-5718	162	13	σ1σ2	σ1σ2	NOUN
ejpam-5718	162	14	-	-	ADJ
ejpam-5718	162	15	open	open	ADJ
ejpam-5718	162	16	set	set	NOUN
ejpam-5718	162	17	v	v	NOUN
ejpam-5718	162	18	of	of	ADP
ejpam-5718	162	19	y	y	PROPN
ejpam-5718	162	20	having	have	VERB
ejpam-5718	162	21	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	162	22	complement	complement	NOUN
ejpam-5718	162	23	;	;	PUNCT
ejpam-5718	162	24	(	(	PUNCT
ejpam-5718	162	25	3	3	X
ejpam-5718	162	26	)	)	PUNCT
ejpam-5718	162	27	τ1τ2	τ1τ2	NOUN
ejpam-5718	162	28	-	-	NOUN
ejpam-5718	162	29	cl(f	cl(f	NOUN
ejpam-5718	162	30	+	+	NOUN
ejpam-5718	162	31	(	(	PUNCT
ejpam-5718	162	32	σ1σ2	σ1σ2	NUM
ejpam-5718	162	33	-	-	PUNCT
ejpam-5718	162	34	int(k	int(k	NUM
ejpam-5718	162	35	)	)	PUNCT
ejpam-5718	162	36	)	)	PUNCT
ejpam-5718	162	37	)	)	PUNCT
ejpam-5718	163	1	⊆	⊆	NUM
ejpam-5718	163	2	f+(k	f+(k	NOUN
ejpam-5718	163	3	)	)	PUNCT
ejpam-5718	163	4	for	for	ADP
ejpam-5718	163	5	every	every	DET
ejpam-5718	163	6	σ1σ2	σ1σ2	NOUN
ejpam-5718	163	7	-	-	ADJ
ejpam-5718	163	8	connected	connect	VERB
ejpam-5718	163	9	σ1σ2	σ1σ2	VERB
ejpam-5718	163	10	-	-	PUNCT
ejpam-5718	163	11	closed	closed	ADJ
ejpam-5718	163	12	set	set	NOUN
ejpam-5718	163	13	k	k	PROPN
ejpam-5718	163	14	of	of	ADP
ejpam-5718	163	15	y	y	PROPN
ejpam-5718	163	16	;	;	PUNCT
ejpam-5718	163	17	(	(	PUNCT
ejpam-5718	163	18	4	4	X
ejpam-5718	163	19	)	)	PUNCT
ejpam-5718	163	20	τ1τ2	τ1τ2	NOUN
ejpam-5718	163	21	-	-	NOUN
ejpam-5718	163	22	cl(f	cl(f	NOUN
ejpam-5718	163	23	+	+	NOUN
ejpam-5718	163	24	(	(	PUNCT
ejpam-5718	163	25	σ1σ2	σ1σ2	NUM
ejpam-5718	163	26	-	-	PUNCT
ejpam-5718	163	27	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	163	28	-	-	PUNCT
ejpam-5718	163	29	cl(b	cl(b	NOUN
ejpam-5718	163	30	)	)	PUNCT
ejpam-5718	163	31	)	)	PUNCT
ejpam-5718	163	32	)	)	PUNCT
ejpam-5718	163	33	)	)	PUNCT
ejpam-5718	164	1	⊆	⊆	X
ejpam-5718	164	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	164	3	-	-	PUNCT
ejpam-5718	164	4	cl(b	cl(b	NOUN
ejpam-5718	164	5	)	)	PUNCT
ejpam-5718	164	6	)	)	PUNCT
ejpam-5718	164	7	for	for	ADP
ejpam-5718	164	8	every	every	DET
ejpam-5718	164	9	subset	subset	NOUN
ejpam-5718	164	10	b	b	PROPN
ejpam-5718	164	11	of	of	ADP
ejpam-5718	164	12	y	y	PROPN
ejpam-5718	164	13	having	have	VERB
ejpam-5718	164	14	the	the	DET
ejpam-5718	164	15	σ1σ2	σ1σ2	ADV
ejpam-5718	164	16	-	-	PUNCT
ejpam-5718	164	17	connected	connect	VERB
ejpam-5718	164	18	σ1σ2	σ1σ2	NOUN
ejpam-5718	164	19	-	-	NOUN
ejpam-5718	164	20	closure	closure	NOUN
ejpam-5718	164	21	;	;	PUNCT
ejpam-5718	164	22	(	(	PUNCT
ejpam-5718	164	23	5	5	X
ejpam-5718	164	24	)	)	PUNCT
ejpam-5718	164	25	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5718	164	26	-	-	PUNCT
ejpam-5718	164	27	int(b	int(b	NOUN
ejpam-5718	164	28	)	)	PUNCT
ejpam-5718	164	29	)	)	PUNCT
ejpam-5718	165	1	⊆	⊆	X
ejpam-5718	165	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	165	3	-	-	NUM
ejpam-5718	165	4	int(f	int(f	PRON
ejpam-5718	165	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	165	6	-	-	PUNCT
ejpam-5718	165	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	165	8	-	-	PUNCT
ejpam-5718	165	9	int(b	int(b	NOUN
ejpam-5718	165	10	)	)	PUNCT
ejpam-5718	165	11	)	)	PUNCT
ejpam-5718	165	12	)	)	PUNCT
ejpam-5718	165	13	)	)	PUNCT
ejpam-5718	165	14	for	for	ADP
ejpam-5718	165	15	every	every	DET
ejpam-5718	165	16	subset	subset	NOUN
ejpam-5718	165	17	b	b	PROPN
ejpam-5718	165	18	of	of	ADP
ejpam-5718	165	19	y	y	PRON
ejpam-5718	165	20	such	such	ADJ
ejpam-5718	165	21	that	that	SCONJ
ejpam-5718	165	22	y	y	PROPN
ejpam-5718	166	1	−	−	ADP
ejpam-5718	166	2	σ1σ2	σ1σ2	NUM
ejpam-5718	166	3	-	-	PUNCT
ejpam-5718	166	4	int(b	int(b	NOUN
ejpam-5718	166	5	)	)	PUNCT
ejpam-5718	166	6	is	be	AUX
ejpam-5718	166	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	166	8	-	-	PUNCT
ejpam-5718	166	9	connected	connect	VERB
ejpam-5718	166	10	;	;	PUNCT
ejpam-5718	166	11	(	(	PUNCT
ejpam-5718	166	12	6	6	NUM
ejpam-5718	166	13	)	)	PUNCT
ejpam-5718	166	14	τ1τ2	τ1τ2	NOUN
ejpam-5718	166	15	-	-	NOUN
ejpam-5718	166	16	cl(f	cl(f	NOUN
ejpam-5718	166	17	+	+	NOUN
ejpam-5718	166	18	(	(	PUNCT
ejpam-5718	166	19	σ1σ2	σ1σ2	NUM
ejpam-5718	166	20	-	-	PUNCT
ejpam-5718	166	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	166	22	-	-	PUNCT
ejpam-5718	166	23	cl(v	cl(v	NOUN
ejpam-5718	166	24	)	)	PUNCT
ejpam-5718	166	25	)	)	PUNCT
ejpam-5718	166	26	)	)	PUNCT
ejpam-5718	166	27	)	)	PUNCT
ejpam-5718	167	1	⊆	⊆	X
ejpam-5718	167	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	167	3	-	-	PUNCT
ejpam-5718	167	4	cl(v	cl(v	NOUN
ejpam-5718	167	5	)	)	PUNCT
ejpam-5718	167	6	)	)	PUNCT
ejpam-5718	167	7	for	for	ADP
ejpam-5718	167	8	every	every	DET
ejpam-5718	167	9	σ1σ2	σ1σ2	NOUN
ejpam-5718	167	10	-	-	ADJ
ejpam-5718	167	11	open	open	ADJ
ejpam-5718	167	12	set	set	NOUN
ejpam-5718	167	13	v	v	NOUN
ejpam-5718	167	14	of	of	ADP
ejpam-5718	167	15	y	y	PROPN
ejpam-5718	167	16	having	have	VERB
ejpam-5718	167	17	the	the	DET
ejpam-5718	167	18	σ1σ2	σ1σ2	ADV
ejpam-5718	167	19	-	-	PUNCT
ejpam-5718	167	20	connected	connect	VERB
ejpam-5718	167	21	σ1σ2	σ1σ2	NOUN
ejpam-5718	167	22	-	-	NOUN
ejpam-5718	167	23	closure	closure	NOUN
ejpam-5718	167	24	;	;	PUNCT
ejpam-5718	167	25	(	(	PUNCT
ejpam-5718	167	26	7	7	X
ejpam-5718	167	27	)	)	PUNCT
ejpam-5718	167	28	τ1τ2	τ1τ2	NOUN
ejpam-5718	167	29	-	-	NOUN
ejpam-5718	167	30	cl(f	cl(f	NOUN
ejpam-5718	167	31	+	+	NOUN
ejpam-5718	167	32	(	(	PUNCT
ejpam-5718	167	33	v	v	NOUN
ejpam-5718	167	34	)	)	PUNCT
ejpam-5718	167	35	)	)	PUNCT
ejpam-5718	167	36	⊆	⊆	NUM
ejpam-5718	167	37	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	167	38	-	-	PUNCT
ejpam-5718	167	39	cl(v	cl(v	NOUN
ejpam-5718	167	40	)	)	PUNCT
ejpam-5718	167	41	)	)	PUNCT
ejpam-5718	167	42	for	for	ADP
ejpam-5718	167	43	every	every	DET
ejpam-5718	167	44	σ1σ2	σ1σ2	NOUN
ejpam-5718	167	45	-	-	ADJ
ejpam-5718	167	46	open	open	ADJ
ejpam-5718	167	47	set	set	NOUN
ejpam-5718	167	48	v	v	NOUN
ejpam-5718	167	49	of	of	ADP
ejpam-5718	167	50	y	y	PROPN
ejpam-5718	167	51	having	have	VERB
ejpam-5718	167	52	the	the	DET
ejpam-5718	167	53	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	167	54	σ1σ2	σ1σ2	NOUN
ejpam-5718	167	55	-	-	NOUN
ejpam-5718	167	56	closure	closure	NOUN
ejpam-5718	167	57	;	;	PUNCT
ejpam-5718	167	58	(	(	PUNCT
ejpam-5718	167	59	8)	8)	NUM
ejpam-5718	167	60	τ1τ2	τ1τ2	NOUN
ejpam-5718	167	61	-	-	NOUN
ejpam-5718	167	62	cl(f	cl(f	NOUN
ejpam-5718	167	63	+	+	NOUN
ejpam-5718	167	64	(	(	PUNCT
ejpam-5718	167	65	σ1σ2	σ1σ2	NUM
ejpam-5718	167	66	-	-	PUNCT
ejpam-5718	167	67	int(k	int(k	NUM
ejpam-5718	167	68	)	)	PUNCT
ejpam-5718	167	69	)	)	PUNCT
ejpam-5718	167	70	)	)	PUNCT
ejpam-5718	167	71	⊆	⊆	NUM
ejpam-5718	167	72	f+(k	f+(k	NOUN
ejpam-5718	167	73	)	)	PUNCT
ejpam-5718	167	74	for	for	ADP
ejpam-5718	167	75	every	every	DET
ejpam-5718	167	76	σ1σ2	σ1σ2	NOUN
ejpam-5718	167	77	-	-	ADJ
ejpam-5718	167	78	connected	connected	ADJ
ejpam-5718	167	79	(	(	PUNCT
ejpam-5718	167	80	σ1	σ1	PROPN
ejpam-5718	167	81	,	,	PUNCT
ejpam-5718	167	82	σ2)r	σ2)r	NOUN
ejpam-5718	167	83	-	-	PUNCT
ejpam-5718	167	84	closed	close	VERB
ejpam-5718	167	85	set	set	ADJ
ejpam-5718	167	86	k	k	PROPN
ejpam-5718	167	87	of	of	ADP
ejpam-5718	167	88	y	y	PROPN
ejpam-5718	167	89	.	.	PUNCT
ejpam-5718	168	1	p.	p.	NOUN
ejpam-5718	168	2	pue	pue	NOUN
ejpam-5718	168	3	-	-	PUNCT
ejpam-5718	168	4	on	on	ADP
ejpam-5718	168	5	,	,	PUNCT
ejpam-5718	168	6	a.	a.	PROPN
ejpam-5718	168	7	sama	sama	PROPN
ejpam-5718	168	8	-	-	PUNCT
ejpam-5718	168	9	ae	ae	PROPN
ejpam-5718	168	10	,	,	PUNCT
ejpam-5718	168	11	c.	c.	PROPN
ejpam-5718	168	12	boonpok	boonpok	PROPN
ejpam-5718	168	13	/	/	SYM
ejpam-5718	168	14	eur	eur	PROPN
ejpam-5718	168	15	.	.	PUNCT
ejpam-5718	169	1	j.	j.	PROPN
ejpam-5718	169	2	pure	pure	PROPN
ejpam-5718	169	3	appl	appl	PROPN
ejpam-5718	169	4	.	.	PROPN
ejpam-5718	169	5	math	math	PROPN
ejpam-5718	169	6	,	,	PUNCT
ejpam-5718	169	7	18	18	NUM
ejpam-5718	169	8	(	(	PUNCT
ejpam-5718	169	9	1	1	NUM
ejpam-5718	169	10	)	)	PUNCT
ejpam-5718	169	11	(	(	PUNCT
ejpam-5718	169	12	2025	2025	NUM
ejpam-5718	169	13	)	)	PUNCT
ejpam-5718	169	14	,	,	PUNCT
ejpam-5718	169	15	5718	5718	NUM
ejpam-5718	169	16	7	7	NUM
ejpam-5718	169	17	of	of	ADP
ejpam-5718	169	18	16	16	NUM
ejpam-5718	169	19	proof	proof	NOUN
ejpam-5718	169	20	.	.	PUNCT
ejpam-5718	170	1	the	the	DET
ejpam-5718	170	2	proof	proof	NOUN
ejpam-5718	170	3	is	be	AUX
ejpam-5718	170	4	similar	similar	ADJ
ejpam-5718	170	5	to	to	ADP
ejpam-5718	170	6	that	that	PRON
ejpam-5718	170	7	of	of	ADP
ejpam-5718	170	8	theorem	theorem	ADJ
ejpam-5718	170	9	1	1	NUM
ejpam-5718	170	10	.	.	PUNCT
ejpam-5718	170	11	theorem	theorem	NOUN
ejpam-5718	170	12	3	3	NUM
ejpam-5718	170	13	.	.	X
ejpam-5718	170	14	for	for	ADP
ejpam-5718	170	15	a	a	DET
ejpam-5718	170	16	multifunction	multifunction	NOUN
ejpam-5718	170	17	f	f	NOUN
ejpam-5718	170	18	:	:	PUNCT
ejpam-5718	170	19	(	(	PUNCT
ejpam-5718	170	20	x	x	NOUN
ejpam-5718	170	21	,	,	PUNCT
ejpam-5718	170	22	τ1	τ1	NOUN
ejpam-5718	170	23	,	,	PUNCT
ejpam-5718	170	24	τ2	τ2	NOUN
ejpam-5718	170	25	)	)	PUNCT
ejpam-5718	170	26	→	→	SYM
ejpam-5718	170	27	(	(	PUNCT
ejpam-5718	170	28	y	y	PROPN
ejpam-5718	170	29	,	,	PUNCT
ejpam-5718	170	30	σ1	σ1	PROPN
ejpam-5718	170	31	,	,	PUNCT
ejpam-5718	170	32	σ2	σ2	NOUN
ejpam-5718	170	33	)	)	PUNCT
ejpam-5718	170	34	,	,	PUNCT
ejpam-5718	170	35	the	the	DET
ejpam-5718	170	36	following	follow	VERB
ejpam-5718	170	37	properties	property	NOUN
ejpam-5718	170	38	are	be	AUX
ejpam-5718	170	39	equivalent	equivalent	ADJ
ejpam-5718	170	40	:	:	PUNCT
ejpam-5718	170	41	(	(	PUNCT
ejpam-5718	170	42	1	1	X
ejpam-5718	170	43	)	)	PUNCT
ejpam-5718	170	44	f	f	PROPN
ejpam-5718	170	45	is	be	AUX
ejpam-5718	170	46	upper	upper	ADJ
ejpam-5718	170	47	weakly	weakly	ADJ
ejpam-5718	170	48	s-(τ1	s-(τ1	PROPN
ejpam-5718	170	49	,	,	PUNCT
ejpam-5718	170	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	170	51	;	;	PUNCT
ejpam-5718	170	52	(	(	PUNCT
ejpam-5718	170	53	2	2	X
ejpam-5718	170	54	)	)	PUNCT
ejpam-5718	170	55	τ1τ2	τ1τ2	NOUN
ejpam-5718	170	56	-	-	NOUN
ejpam-5718	170	57	cl(f	cl(f	NOUN
ejpam-5718	170	58	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	170	59	-	-	PUNCT
ejpam-5718	170	60	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	170	61	-	-	PUNCT
ejpam-5718	170	62	cl(v	cl(v	NOUN
ejpam-5718	170	63	)	)	PUNCT
ejpam-5718	170	64	)	)	PUNCT
ejpam-5718	170	65	)	)	PUNCT
ejpam-5718	170	66	)	)	PUNCT
ejpam-5718	171	1	⊆	⊆	X
ejpam-5718	171	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5718	171	3	-	-	PUNCT
ejpam-5718	171	4	cl(v	cl(v	NOUN
ejpam-5718	171	5	)	)	PUNCT
ejpam-5718	171	6	)	)	PUNCT
ejpam-5718	171	7	for	for	ADP
ejpam-5718	171	8	every	every	DET
ejpam-5718	171	9	(	(	PUNCT
ejpam-5718	171	10	σ1	σ1	PROPN
ejpam-5718	171	11	,	,	PUNCT
ejpam-5718	171	12	σ2)β	σ2)β	NOUN
ejpam-5718	171	13	-	-	PUNCT
ejpam-5718	171	14	open	open	NOUN
ejpam-5718	171	15	set	set	NOUN
ejpam-5718	171	16	v	v	NOUN
ejpam-5718	171	17	of	of	ADP
ejpam-5718	171	18	y	y	PROPN
ejpam-5718	171	19	having	have	VERB
ejpam-5718	171	20	the	the	DET
ejpam-5718	171	21	σ1σ2	σ1σ2	ADV
ejpam-5718	171	22	-	-	PUNCT
ejpam-5718	171	23	connected	connect	VERB
ejpam-5718	171	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	171	25	-	-	NOUN
ejpam-5718	171	26	closure	closure	NOUN
ejpam-5718	171	27	;	;	PUNCT
ejpam-5718	171	28	(	(	PUNCT
ejpam-5718	171	29	3	3	X
ejpam-5718	171	30	)	)	PUNCT
ejpam-5718	171	31	τ1τ2	τ1τ2	NOUN
ejpam-5718	171	32	-	-	NOUN
ejpam-5718	171	33	cl(f	cl(f	NOUN
ejpam-5718	171	34	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	171	35	-	-	PUNCT
ejpam-5718	171	36	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	171	37	-	-	PUNCT
ejpam-5718	171	38	cl(v	cl(v	NOUN
ejpam-5718	171	39	)	)	PUNCT
ejpam-5718	171	40	)	)	PUNCT
ejpam-5718	171	41	)	)	PUNCT
ejpam-5718	171	42	)	)	PUNCT
ejpam-5718	172	1	⊆	⊆	X
ejpam-5718	172	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5718	172	3	-	-	PUNCT
ejpam-5718	172	4	cl(v	cl(v	NOUN
ejpam-5718	172	5	)	)	PUNCT
ejpam-5718	172	6	)	)	PUNCT
ejpam-5718	172	7	for	for	ADP
ejpam-5718	172	8	every	every	DET
ejpam-5718	172	9	(	(	PUNCT
ejpam-5718	172	10	σ1	σ1	PROPN
ejpam-5718	172	11	,	,	PUNCT
ejpam-5718	172	12	σ2)s	σ2)s	NOUN
ejpam-5718	172	13	-	-	PUNCT
ejpam-5718	172	14	open	open	NOUN
ejpam-5718	172	15	set	set	NOUN
ejpam-5718	172	16	v	v	NOUN
ejpam-5718	172	17	of	of	ADP
ejpam-5718	172	18	y	y	PROPN
ejpam-5718	172	19	having	have	VERB
ejpam-5718	172	20	the	the	DET
ejpam-5718	172	21	σ1σ2	σ1σ2	ADV
ejpam-5718	172	22	-	-	PUNCT
ejpam-5718	172	23	connected	connect	VERB
ejpam-5718	172	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	172	25	-	-	NOUN
ejpam-5718	172	26	closure	closure	NOUN
ejpam-5718	172	27	.	.	PUNCT
ejpam-5718	173	1	proof	proof	NOUN
ejpam-5718	173	2	.	.	PUNCT
ejpam-5718	174	1	(	(	PUNCT
ejpam-5718	174	2	1	1	X
ejpam-5718	174	3	)	)	PUNCT
ejpam-5718	174	4	⇒	⇒	NOUN
ejpam-5718	174	5	(	(	PUNCT
ejpam-5718	174	6	2	2	NUM
ejpam-5718	174	7	):	):	PUNCT
ejpam-5718	174	8	this	this	PRON
ejpam-5718	174	9	follows	follow	VERB
ejpam-5718	174	10	from	from	ADP
ejpam-5718	174	11	theorem	theorem	ADJ
ejpam-5718	174	12	1(4	1(4	NUM
ejpam-5718	174	13	)	)	PUNCT
ejpam-5718	174	14	.	.	PUNCT
ejpam-5718	175	1	(	(	PUNCT
ejpam-5718	175	2	2	2	X
ejpam-5718	175	3	)	)	PUNCT
ejpam-5718	175	4	⇒	⇒	NOUN
ejpam-5718	175	5	(	(	PUNCT
ejpam-5718	175	6	3	3	NUM
ejpam-5718	175	7	):	):	PUNCT
ejpam-5718	175	8	the	the	DET
ejpam-5718	175	9	proof	proof	NOUN
ejpam-5718	175	10	is	be	AUX
ejpam-5718	175	11	obvious	obvious	ADJ
ejpam-5718	175	12	since	since	SCONJ
ejpam-5718	175	13	every	every	DET
ejpam-5718	175	14	(	(	PUNCT
ejpam-5718	175	15	σ1	σ1	PROPN
ejpam-5718	175	16	,	,	PUNCT
ejpam-5718	175	17	σ2)s	σ2)s	NOUN
ejpam-5718	175	18	-	-	PUNCT
ejpam-5718	175	19	open	open	ADJ
ejpam-5718	175	20	set	set	NOUN
ejpam-5718	175	21	is	be	AUX
ejpam-5718	175	22	(	(	PUNCT
ejpam-5718	175	23	σ1	σ1	PROPN
ejpam-5718	175	24	,	,	PUNCT
ejpam-5718	175	25	σ2)β	σ2)β	NOUN
ejpam-5718	175	26	-	-	PUNCT
ejpam-5718	175	27	open	open	ADJ
ejpam-5718	175	28	.	.	PUNCT
ejpam-5718	176	1	(	(	PUNCT
ejpam-5718	176	2	3	3	X
ejpam-5718	176	3	)	)	PUNCT
ejpam-5718	176	4	⇒	⇒	NOUN
ejpam-5718	176	5	(	(	PUNCT
ejpam-5718	176	6	1	1	NUM
ejpam-5718	176	7	):	):	PUNCT
ejpam-5718	176	8	since	since	SCONJ
ejpam-5718	176	9	every	every	DET
ejpam-5718	176	10	σ1σ2	σ1σ2	NUM
ejpam-5718	176	11	-	-	ADJ
ejpam-5718	176	12	open	open	ADJ
ejpam-5718	176	13	set	set	NOUN
ejpam-5718	176	14	is	be	AUX
ejpam-5718	176	15	(	(	PUNCT
ejpam-5718	176	16	σ1	σ1	PROPN
ejpam-5718	176	17	,	,	PUNCT
ejpam-5718	176	18	σ2)s	σ2)s	NOUN
ejpam-5718	176	19	-	-	PUNCT
ejpam-5718	176	20	open	open	ADJ
ejpam-5718	176	21	,	,	PUNCT
ejpam-5718	176	22	the	the	DET
ejpam-5718	176	23	proof	proof	NOUN
ejpam-5718	176	24	follows	follow	VERB
ejpam-5718	176	25	from	from	ADP
ejpam-5718	176	26	theorem	theorem	ADJ
ejpam-5718	176	27	1(7	1(7	NUM
ejpam-5718	176	28	)	)	PUNCT
ejpam-5718	176	29	.	.	PUNCT
ejpam-5718	177	1	theorem	theorem	VERB
ejpam-5718	177	2	4	4	NUM
ejpam-5718	177	3	.	.	X
ejpam-5718	177	4	for	for	ADP
ejpam-5718	177	5	a	a	DET
ejpam-5718	177	6	multifunction	multifunction	NOUN
ejpam-5718	178	1	f	f	NOUN
ejpam-5718	178	2	:	:	PUNCT
ejpam-5718	178	3	(	(	PUNCT
ejpam-5718	178	4	x	x	NOUN
ejpam-5718	178	5	,	,	PUNCT
ejpam-5718	178	6	τ1	τ1	NOUN
ejpam-5718	178	7	,	,	PUNCT
ejpam-5718	178	8	τ2	τ2	NOUN
ejpam-5718	178	9	)	)	PUNCT
ejpam-5718	178	10	→	→	SYM
ejpam-5718	178	11	(	(	PUNCT
ejpam-5718	178	12	y	y	PROPN
ejpam-5718	178	13	,	,	PUNCT
ejpam-5718	178	14	σ1	σ1	PROPN
ejpam-5718	178	15	,	,	PUNCT
ejpam-5718	178	16	σ2	σ2	NOUN
ejpam-5718	178	17	)	)	PUNCT
ejpam-5718	178	18	,	,	PUNCT
ejpam-5718	178	19	the	the	DET
ejpam-5718	178	20	following	follow	VERB
ejpam-5718	178	21	properties	property	NOUN
ejpam-5718	178	22	are	be	AUX
ejpam-5718	178	23	equivalent	equivalent	ADJ
ejpam-5718	178	24	:	:	PUNCT
ejpam-5718	178	25	(	(	PUNCT
ejpam-5718	178	26	1	1	X
ejpam-5718	178	27	)	)	PUNCT
ejpam-5718	178	28	f	f	PROPN
ejpam-5718	178	29	is	be	AUX
ejpam-5718	178	30	lower	low	ADJ
ejpam-5718	178	31	weakly	weakly	ADJ
ejpam-5718	178	32	s-(τ1	s-(τ1	PROPN
ejpam-5718	178	33	,	,	PUNCT
ejpam-5718	178	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	178	35	;	;	PUNCT
ejpam-5718	178	36	(	(	PUNCT
ejpam-5718	178	37	2	2	X
ejpam-5718	178	38	)	)	PUNCT
ejpam-5718	178	39	τ1τ2	τ1τ2	NOUN
ejpam-5718	178	40	-	-	NOUN
ejpam-5718	178	41	cl(f	cl(f	NOUN
ejpam-5718	178	42	+	+	NOUN
ejpam-5718	178	43	(	(	PUNCT
ejpam-5718	178	44	σ1σ2	σ1σ2	NUM
ejpam-5718	178	45	-	-	PUNCT
ejpam-5718	178	46	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	178	47	-	-	PUNCT
ejpam-5718	178	48	cl(v	cl(v	NOUN
ejpam-5718	178	49	)	)	PUNCT
ejpam-5718	178	50	)	)	PUNCT
ejpam-5718	178	51	)	)	PUNCT
ejpam-5718	178	52	)	)	PUNCT
ejpam-5718	179	1	⊆	⊆	X
ejpam-5718	179	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	179	3	-	-	PUNCT
ejpam-5718	179	4	cl(v	cl(v	NOUN
ejpam-5718	179	5	)	)	PUNCT
ejpam-5718	179	6	)	)	PUNCT
ejpam-5718	179	7	for	for	ADP
ejpam-5718	179	8	every	every	DET
ejpam-5718	179	9	(	(	PUNCT
ejpam-5718	179	10	σ1	σ1	PROPN
ejpam-5718	179	11	,	,	PUNCT
ejpam-5718	179	12	σ2)β	σ2)β	NOUN
ejpam-5718	179	13	-	-	PUNCT
ejpam-5718	179	14	open	open	NOUN
ejpam-5718	179	15	set	set	NOUN
ejpam-5718	179	16	v	v	NOUN
ejpam-5718	179	17	of	of	ADP
ejpam-5718	179	18	y	y	PROPN
ejpam-5718	179	19	having	have	VERB
ejpam-5718	179	20	the	the	DET
ejpam-5718	179	21	σ1σ2	σ1σ2	ADV
ejpam-5718	179	22	-	-	PUNCT
ejpam-5718	179	23	connected	connect	VERB
ejpam-5718	179	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	179	25	-	-	NOUN
ejpam-5718	179	26	closure	closure	NOUN
ejpam-5718	179	27	;	;	PUNCT
ejpam-5718	179	28	(	(	PUNCT
ejpam-5718	179	29	3	3	X
ejpam-5718	179	30	)	)	PUNCT
ejpam-5718	179	31	τ1τ2	τ1τ2	NOUN
ejpam-5718	179	32	-	-	NOUN
ejpam-5718	179	33	cl(f	cl(f	NOUN
ejpam-5718	179	34	+	+	NOUN
ejpam-5718	179	35	(	(	PUNCT
ejpam-5718	179	36	σ1σ2	σ1σ2	NUM
ejpam-5718	179	37	-	-	PUNCT
ejpam-5718	179	38	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	179	39	-	-	PUNCT
ejpam-5718	179	40	cl(v	cl(v	NOUN
ejpam-5718	179	41	)	)	PUNCT
ejpam-5718	179	42	)	)	PUNCT
ejpam-5718	179	43	)	)	PUNCT
ejpam-5718	179	44	)	)	PUNCT
ejpam-5718	180	1	⊆	⊆	X
ejpam-5718	180	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	180	3	-	-	PUNCT
ejpam-5718	180	4	cl(v	cl(v	NOUN
ejpam-5718	180	5	)	)	PUNCT
ejpam-5718	180	6	)	)	PUNCT
ejpam-5718	180	7	for	for	SCONJ
ejpam-5718	180	8	every	every	DET
ejpam-5718	180	9	(	(	PUNCT
ejpam-5718	180	10	σ1	σ1	PROPN
ejpam-5718	180	11	,	,	PUNCT
ejpam-5718	180	12	σ2)s	σ2)s	NOUN
ejpam-5718	180	13	-	-	PUNCT
ejpam-5718	180	14	open	open	NOUN
ejpam-5718	180	15	set	set	NOUN
ejpam-5718	180	16	v	v	NOUN
ejpam-5718	180	17	of	of	ADP
ejpam-5718	180	18	y	y	PROPN
ejpam-5718	180	19	having	have	VERB
ejpam-5718	180	20	the	the	DET
ejpam-5718	180	21	σ1σ2	σ1σ2	ADV
ejpam-5718	180	22	-	-	PUNCT
ejpam-5718	180	23	connected	connect	VERB
ejpam-5718	180	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	180	25	-	-	NOUN
ejpam-5718	180	26	closure	closure	NOUN
ejpam-5718	180	27	.	.	PUNCT
ejpam-5718	181	1	proof	proof	NOUN
ejpam-5718	181	2	.	.	PUNCT
ejpam-5718	182	1	the	the	DET
ejpam-5718	182	2	proof	proof	NOUN
ejpam-5718	182	3	is	be	AUX
ejpam-5718	182	4	similar	similar	ADJ
ejpam-5718	182	5	to	to	ADP
ejpam-5718	182	6	that	that	PRON
ejpam-5718	182	7	of	of	ADP
ejpam-5718	182	8	theorem	theorem	ADJ
ejpam-5718	182	9	3	3	NUM
ejpam-5718	182	10	.	.	PUNCT
ejpam-5718	182	11	theorem	theorem	NOUN
ejpam-5718	182	12	5	5	NUM
ejpam-5718	182	13	.	.	X
ejpam-5718	182	14	for	for	ADP
ejpam-5718	182	15	a	a	DET
ejpam-5718	182	16	multifunction	multifunction	NOUN
ejpam-5718	182	17	f	f	NOUN
ejpam-5718	182	18	:	:	PUNCT
ejpam-5718	182	19	(	(	PUNCT
ejpam-5718	182	20	x	x	NOUN
ejpam-5718	182	21	,	,	PUNCT
ejpam-5718	182	22	τ1	τ1	NOUN
ejpam-5718	182	23	,	,	PUNCT
ejpam-5718	182	24	τ2	τ2	NOUN
ejpam-5718	182	25	)	)	PUNCT
ejpam-5718	182	26	→	→	SYM
ejpam-5718	182	27	(	(	PUNCT
ejpam-5718	182	28	y	y	PROPN
ejpam-5718	182	29	,	,	PUNCT
ejpam-5718	182	30	σ1	σ1	PROPN
ejpam-5718	182	31	,	,	PUNCT
ejpam-5718	182	32	σ2	σ2	NOUN
ejpam-5718	182	33	)	)	PUNCT
ejpam-5718	182	34	,	,	PUNCT
ejpam-5718	182	35	the	the	DET
ejpam-5718	182	36	following	follow	VERB
ejpam-5718	182	37	properties	property	NOUN
ejpam-5718	182	38	are	be	AUX
ejpam-5718	182	39	equivalent	equivalent	ADJ
ejpam-5718	182	40	:	:	PUNCT
ejpam-5718	182	41	(	(	PUNCT
ejpam-5718	182	42	1	1	X
ejpam-5718	182	43	)	)	PUNCT
ejpam-5718	182	44	f	f	PROPN
ejpam-5718	182	45	is	be	AUX
ejpam-5718	182	46	upper	upper	ADJ
ejpam-5718	182	47	weakly	weakly	ADJ
ejpam-5718	182	48	s-(τ1	s-(τ1	PROPN
ejpam-5718	182	49	,	,	PUNCT
ejpam-5718	182	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	182	51	;	;	PUNCT
ejpam-5718	182	52	(	(	PUNCT
ejpam-5718	182	53	2	2	X
ejpam-5718	182	54	)	)	PUNCT
ejpam-5718	182	55	τ1τ2	τ1τ2	NOUN
ejpam-5718	182	56	-	-	NOUN
ejpam-5718	182	57	cl(f	cl(f	NOUN
ejpam-5718	182	58	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	182	59	-	-	PUNCT
ejpam-5718	182	60	int((σ1	int((σ1	ADJ
ejpam-5718	182	61	,	,	PUNCT
ejpam-5718	182	62	σ2)θ	σ2)θ	ADJ
ejpam-5718	182	63	-	-	PUNCT
ejpam-5718	182	64	cl(b	cl(b	NOUN
ejpam-5718	182	65	)	)	PUNCT
ejpam-5718	182	66	)	)	PUNCT
ejpam-5718	182	67	)	)	PUNCT
ejpam-5718	182	68	)	)	PUNCT
ejpam-5718	183	1	⊆	⊆	NUM
ejpam-5718	183	2	f−((σ1	f−((σ1	NOUN
ejpam-5718	183	3	,	,	PUNCT
ejpam-5718	183	4	σ2)θ	σ2)θ	ADJ
ejpam-5718	183	5	-	-	PUNCT
ejpam-5718	183	6	cl(b	cl(b	NOUN
ejpam-5718	183	7	)	)	PUNCT
ejpam-5718	183	8	)	)	PUNCT
ejpam-5718	183	9	for	for	ADP
ejpam-5718	183	10	every	every	DET
ejpam-5718	183	11	subset	subset	NOUN
ejpam-5718	183	12	b	b	PROPN
ejpam-5718	183	13	of	of	ADP
ejpam-5718	183	14	y	y	PROPN
ejpam-5718	183	15	having	have	VERB
ejpam-5718	183	16	the	the	DET
ejpam-5718	183	17	σ1σ2	σ1σ2	ADV
ejpam-5718	183	18	-	-	PUNCT
ejpam-5718	183	19	connected	connected	ADJ
ejpam-5718	183	20	(	(	PUNCT
ejpam-5718	183	21	σ1	σ1	PROPN
ejpam-5718	183	22	,	,	PUNCT
ejpam-5718	183	23	σ2)θ	σ2)θ	NOUN
ejpam-5718	183	24	-	-	PUNCT
ejpam-5718	183	25	closure	closure	NOUN
ejpam-5718	183	26	;	;	PUNCT
ejpam-5718	183	27	(	(	PUNCT
ejpam-5718	183	28	3	3	X
ejpam-5718	183	29	)	)	PUNCT
ejpam-5718	183	30	τ1τ2	τ1τ2	NOUN
ejpam-5718	183	31	-	-	NOUN
ejpam-5718	183	32	cl(f	cl(f	NOUN
ejpam-5718	183	33	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	183	34	-	-	PUNCT
ejpam-5718	183	35	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	183	36	-	-	PUNCT
ejpam-5718	183	37	cl(b	cl(b	NOUN
ejpam-5718	183	38	)	)	PUNCT
ejpam-5718	183	39	)	)	PUNCT
ejpam-5718	183	40	)	)	PUNCT
ejpam-5718	183	41	)	)	PUNCT
ejpam-5718	184	1	⊆	⊆	NUM
ejpam-5718	184	2	f−((σ1	f−((σ1	NOUN
ejpam-5718	184	3	,	,	PUNCT
ejpam-5718	184	4	σ2)θ	σ2)θ	ADJ
ejpam-5718	184	5	-	-	PUNCT
ejpam-5718	184	6	cl(b	cl(b	NOUN
ejpam-5718	184	7	)	)	PUNCT
ejpam-5718	184	8	)	)	PUNCT
ejpam-5718	184	9	for	for	ADP
ejpam-5718	184	10	every	every	DET
ejpam-5718	184	11	subset	subset	NOUN
ejpam-5718	184	12	b	b	PROPN
ejpam-5718	184	13	of	of	ADP
ejpam-5718	184	14	y	y	PROPN
ejpam-5718	184	15	having	have	VERB
ejpam-5718	184	16	the	the	DET
ejpam-5718	184	17	σ1σ2	σ1σ2	ADV
ejpam-5718	184	18	-	-	PUNCT
ejpam-5718	184	19	connected	connected	ADJ
ejpam-5718	184	20	(	(	PUNCT
ejpam-5718	184	21	σ1	σ1	PROPN
ejpam-5718	184	22	,	,	PUNCT
ejpam-5718	184	23	σ2)θ	σ2)θ	NOUN
ejpam-5718	184	24	-	-	PUNCT
ejpam-5718	184	25	closure	closure	NOUN
ejpam-5718	184	26	.	.	PUNCT
ejpam-5718	185	1	proof	proof	NOUN
ejpam-5718	185	2	.	.	PUNCT
ejpam-5718	186	1	(	(	PUNCT
ejpam-5718	186	2	1	1	X
ejpam-5718	186	3	)	)	PUNCT
ejpam-5718	186	4	⇒	⇒	NOUN
ejpam-5718	186	5	(	(	PUNCT
ejpam-5718	186	6	2	2	NUM
ejpam-5718	186	7	):	):	PUNCT
ejpam-5718	186	8	let	let	VERB
ejpam-5718	186	9	b	b	X
ejpam-5718	186	10	be	be	AUX
ejpam-5718	186	11	any	any	DET
ejpam-5718	186	12	subset	subset	NOUN
ejpam-5718	186	13	of	of	ADP
ejpam-5718	186	14	y	y	PROPN
ejpam-5718	186	15	having	have	VERB
ejpam-5718	186	16	the	the	DET
ejpam-5718	186	17	σ1σ2	σ1σ2	ADV
ejpam-5718	186	18	-	-	PUNCT
ejpam-5718	186	19	connected	connected	ADJ
ejpam-5718	186	20	(	(	PUNCT
ejpam-5718	186	21	σ1	σ1	PROPN
ejpam-5718	186	22	,	,	PUNCT
ejpam-5718	186	23	σ2)θclosure	σ2)θclosure	NOUN
ejpam-5718	186	24	.	.	PUNCT
ejpam-5718	187	1	then	then	ADV
ejpam-5718	187	2	,	,	PUNCT
ejpam-5718	187	3	(	(	PUNCT
ejpam-5718	187	4	σ1	σ1	PROPN
ejpam-5718	187	5	,	,	PUNCT
ejpam-5718	187	6	σ2)θ	σ2)θ	NOUN
ejpam-5718	187	7	-	-	PUNCT
ejpam-5718	187	8	cl(b	cl(b	NOUN
ejpam-5718	187	9	)	)	PUNCT
ejpam-5718	187	10	is	be	AUX
ejpam-5718	187	11	σ1σ2	σ1σ2	NOUN
ejpam-5718	187	12	-	-	ADJ
ejpam-5718	187	13	connected	connect	VERB
ejpam-5718	187	14	σ1σ2	σ1σ2	NOUN
ejpam-5718	187	15	-	-	PUNCT
ejpam-5718	187	16	closed	closed	ADJ
ejpam-5718	187	17	and	and	CCONJ
ejpam-5718	187	18	by	by	ADP
ejpam-5718	187	19	theorem1	theorem1	PROPN
ejpam-5718	187	20	,	,	PUNCT
ejpam-5718	187	21	τ1τ2	τ1τ2	NOUN
ejpam-5718	187	22	-	-	ADJ
ejpam-5718	187	23	cl(f	cl(f	NOUN
ejpam-5718	187	24	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	187	25	-	-	PUNCT
ejpam-5718	187	26	int((σ1	int((σ1	ADJ
ejpam-5718	187	27	,	,	PUNCT
ejpam-5718	187	28	σ2)θ	σ2)θ	ADJ
ejpam-5718	187	29	-	-	PUNCT
ejpam-5718	187	30	cl(b	cl(b	NOUN
ejpam-5718	187	31	)	)	PUNCT
ejpam-5718	187	32	)	)	PUNCT
ejpam-5718	187	33	)	)	PUNCT
ejpam-5718	187	34	)	)	PUNCT
ejpam-5718	188	1	⊆	⊆	NUM
ejpam-5718	188	2	f−((σ1	f−((σ1	NOUN
ejpam-5718	188	3	,	,	PUNCT
ejpam-5718	188	4	σ2)θ	σ2)θ	ADJ
ejpam-5718	188	5	-	-	PUNCT
ejpam-5718	188	6	cl(b	cl(b	NOUN
ejpam-5718	188	7	)	)	PUNCT
ejpam-5718	188	8	)	)	PUNCT
ejpam-5718	188	9	.	.	PUNCT
ejpam-5718	189	1	p.	p.	NOUN
ejpam-5718	189	2	pue	pue	NOUN
ejpam-5718	189	3	-	-	PUNCT
ejpam-5718	189	4	on	on	ADP
ejpam-5718	189	5	,	,	PUNCT
ejpam-5718	189	6	a.	a.	PROPN
ejpam-5718	189	7	sama	sama	PROPN
ejpam-5718	189	8	-	-	PUNCT
ejpam-5718	189	9	ae	ae	PROPN
ejpam-5718	189	10	,	,	PUNCT
ejpam-5718	189	11	c.	c.	PROPN
ejpam-5718	189	12	boonpok	boonpok	PROPN
ejpam-5718	189	13	/	/	SYM
ejpam-5718	189	14	eur	eur	PROPN
ejpam-5718	189	15	.	.	PUNCT
ejpam-5718	190	1	j.	j.	PROPN
ejpam-5718	190	2	pure	pure	PROPN
ejpam-5718	190	3	appl	appl	PROPN
ejpam-5718	190	4	.	.	PROPN
ejpam-5718	190	5	math	math	PROPN
ejpam-5718	190	6	,	,	PUNCT
ejpam-5718	190	7	18	18	NUM
ejpam-5718	190	8	(	(	PUNCT
ejpam-5718	190	9	1	1	NUM
ejpam-5718	190	10	)	)	PUNCT
ejpam-5718	190	11	(	(	PUNCT
ejpam-5718	190	12	2025	2025	NUM
ejpam-5718	190	13	)	)	PUNCT
ejpam-5718	190	14	,	,	PUNCT
ejpam-5718	190	15	5718	5718	NUM
ejpam-5718	190	16	8	8	NUM
ejpam-5718	190	17	of	of	ADP
ejpam-5718	190	18	16	16	NUM
ejpam-5718	190	19	(	(	PUNCT
ejpam-5718	190	20	2	2	NUM
ejpam-5718	190	21	)	)	PUNCT
ejpam-5718	190	22	⇒	⇒	NOUN
ejpam-5718	190	23	(	(	PUNCT
ejpam-5718	190	24	3	3	NUM
ejpam-5718	190	25	):	):	PUNCT
ejpam-5718	190	26	the	the	DET
ejpam-5718	190	27	proof	proof	NOUN
ejpam-5718	190	28	is	be	AUX
ejpam-5718	190	29	obvious	obvious	ADJ
ejpam-5718	190	30	since	since	SCONJ
ejpam-5718	190	31	σ1σ2	σ1σ2	NOUN
ejpam-5718	190	32	-	-	NOUN
ejpam-5718	190	33	cl(b	cl(b	NOUN
ejpam-5718	190	34	)	)	PUNCT
ejpam-5718	190	35	⊆	⊆	NUM
ejpam-5718	190	36	(	(	PUNCT
ejpam-5718	190	37	σ1	σ1	PROPN
ejpam-5718	190	38	,	,	PUNCT
ejpam-5718	190	39	σ2)θ	σ2)θ	NOUN
ejpam-5718	190	40	-	-	PUNCT
ejpam-5718	190	41	cl(b	cl(b	NOUN
ejpam-5718	190	42	)	)	PUNCT
ejpam-5718	190	43	for	for	ADP
ejpam-5718	190	44	every	every	DET
ejpam-5718	190	45	subset	subset	NOUN
ejpam-5718	190	46	b	b	PROPN
ejpam-5718	190	47	of	of	ADP
ejpam-5718	190	48	y	y	PROPN
ejpam-5718	190	49	.	.	PUNCT
ejpam-5718	191	1	(	(	PUNCT
ejpam-5718	191	2	3	3	X
ejpam-5718	191	3	)	)	PUNCT
ejpam-5718	191	4	⇒	⇒	NOUN
ejpam-5718	191	5	(	(	PUNCT
ejpam-5718	191	6	1	1	NUM
ejpam-5718	191	7	):	):	PUNCT
ejpam-5718	191	8	let	let	VERB
ejpam-5718	191	9	k	k	PRON
ejpam-5718	191	10	be	be	AUX
ejpam-5718	191	11	any	any	DET
ejpam-5718	191	12	(	(	PUNCT
ejpam-5718	191	13	σ1	σ1	NOUN
ejpam-5718	191	14	,	,	PUNCT
ejpam-5718	191	15	σ2)r	σ2)r	NOUN
ejpam-5718	191	16	-	-	PUNCT
ejpam-5718	191	17	closed	close	VERB
ejpam-5718	191	18	σ1σ2	σ1σ2	ADV
ejpam-5718	191	19	-	-	PUNCT
ejpam-5718	191	20	connected	connected	ADJ
ejpam-5718	191	21	set	set	NOUN
ejpam-5718	191	22	of	of	ADP
ejpam-5718	191	23	y	y	PROPN
ejpam-5718	191	24	.	.	PUNCT
ejpam-5718	192	1	then	then	ADV
ejpam-5718	192	2	,	,	PUNCT
ejpam-5718	192	3	we	we	PRON
ejpam-5718	192	4	have	have	VERB
ejpam-5718	192	5	(	(	PUNCT
ejpam-5718	192	6	σ1	σ1	PROPN
ejpam-5718	192	7	,	,	PUNCT
ejpam-5718	192	8	σ2)θ	σ2)θ	NOUN
ejpam-5718	192	9	-	-	PUNCT
ejpam-5718	192	10	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	192	11	-	-	PUNCT
ejpam-5718	192	12	int(k	int(k	NOUN
ejpam-5718	192	13	)	)	PUNCT
ejpam-5718	192	14	)	)	PUNCT
ejpam-5718	193	1	=	=	SYM
ejpam-5718	193	2	σ1σ2	σ1σ2	X
ejpam-5718	193	3	-	-	PUNCT
ejpam-5718	193	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	193	5	-	-	PUNCT
ejpam-5718	193	6	int(k	int(k	NOUN
ejpam-5718	193	7	)	)	PUNCT
ejpam-5718	193	8	)	)	PUNCT
ejpam-5718	194	1	=	=	SYM
ejpam-5718	195	1	k	k	PROPN
ejpam-5718	195	2	and	and	CCONJ
ejpam-5718	195	3	by	by	ADP
ejpam-5718	195	4	(	(	PUNCT
ejpam-5718	195	5	3	3	NUM
ejpam-5718	195	6	)	)	PUNCT
ejpam-5718	195	7	,	,	PUNCT
ejpam-5718	195	8	τ1τ2	τ1τ2	NOUN
ejpam-5718	195	9	-	-	ADJ
ejpam-5718	195	10	cl(f	cl(f	NOUN
ejpam-5718	195	11	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	195	12	-	-	PUNCT
ejpam-5718	195	13	int(k	int(k	NUM
ejpam-5718	195	14	)	)	PUNCT
ejpam-5718	195	15	)	)	PUNCT
ejpam-5718	195	16	)	)	PUNCT
ejpam-5718	196	1	=	=	PUNCT
ejpam-5718	196	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	196	3	-	-	ADJ
ejpam-5718	196	4	cl(f	cl(f	NOUN
ejpam-5718	196	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	196	6	-	-	PUNCT
ejpam-5718	196	7	int(σ1σ2	int(σ1σ2	ADV
ejpam-5718	196	8	-	-	PUNCT
ejpam-5718	196	9	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5718	196	10	-	-	PUNCT
ejpam-5718	196	11	int(k	int(k	NOUN
ejpam-5718	196	12	)	)	PUNCT
ejpam-5718	196	13	)	)	PUNCT
ejpam-5718	196	14	)	)	PUNCT
ejpam-5718	196	15	)	)	PUNCT
ejpam-5718	196	16	)	)	PUNCT
ejpam-5718	196	17	⊆	⊆	NUM
ejpam-5718	196	18	f−((σ1	f−((σ1	NOUN
ejpam-5718	196	19	,	,	PUNCT
ejpam-5718	196	20	σ2)θ	σ2)θ	NOUN
ejpam-5718	196	21	-	-	PUNCT
ejpam-5718	196	22	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5718	196	23	-	-	PUNCT
ejpam-5718	196	24	cl(k	cl(k	NOUN
ejpam-5718	196	25	)	)	PUNCT
ejpam-5718	196	26	)	)	PUNCT
ejpam-5718	196	27	)	)	PUNCT
ejpam-5718	197	1	=	=	PUNCT
ejpam-5718	197	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5718	197	3	-	-	PUNCT
ejpam-5718	197	4	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5718	197	5	-	-	PUNCT
ejpam-5718	197	6	cl(k	cl(k	NOUN
ejpam-5718	197	7	)	)	PUNCT
ejpam-5718	197	8	)	)	PUNCT
ejpam-5718	197	9	)	)	PUNCT
ejpam-5718	198	1	=	=	SYM
ejpam-5718	198	2	f−(k	f−(k	PROPN
ejpam-5718	198	3	)	)	PUNCT
ejpam-5718	198	4	.	.	PUNCT
ejpam-5718	199	1	thus	thus	ADV
ejpam-5718	199	2	,	,	PUNCT
ejpam-5718	199	3	τ1τ2	τ1τ2	NOUN
ejpam-5718	199	4	-	-	ADJ
ejpam-5718	199	5	cl(f	cl(f	NOUN
ejpam-5718	199	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5718	199	7	-	-	PUNCT
ejpam-5718	199	8	int(k	int(k	NUM
ejpam-5718	199	9	)	)	PUNCT
ejpam-5718	199	10	)	)	PUNCT
ejpam-5718	199	11	)	)	PUNCT
ejpam-5718	200	1	⊆	⊆	X
ejpam-5718	200	2	f−(k	f−(k	PROPN
ejpam-5718	200	3	)	)	PUNCT
ejpam-5718	200	4	and	and	CCONJ
ejpam-5718	200	5	by	by	ADP
ejpam-5718	200	6	theorem	theorem	NOUN
ejpam-5718	200	7	1(8	1(8	NUM
ejpam-5718	200	8	)	)	PUNCT
ejpam-5718	200	9	,	,	PUNCT
ejpam-5718	200	10	f	f	PROPN
ejpam-5718	200	11	is	be	AUX
ejpam-5718	200	12	upper	upper	ADJ
ejpam-5718	200	13	weakly	weakly	ADJ
ejpam-5718	200	14	s(τ1	s(τ1	NOUN
ejpam-5718	200	15	,	,	PUNCT
ejpam-5718	200	16	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5718	200	17	.	.	PUNCT
ejpam-5718	201	1	theorem	theorem	VERB
ejpam-5718	201	2	6	6	NUM
ejpam-5718	201	3	.	.	PUNCT
ejpam-5718	201	4	for	for	ADP
ejpam-5718	201	5	a	a	DET
ejpam-5718	201	6	multifunction	multifunction	NOUN
ejpam-5718	202	1	f	f	NOUN
ejpam-5718	202	2	:	:	PUNCT
ejpam-5718	202	3	(	(	PUNCT
ejpam-5718	202	4	x	x	NOUN
ejpam-5718	202	5	,	,	PUNCT
ejpam-5718	202	6	τ1	τ1	NOUN
ejpam-5718	202	7	,	,	PUNCT
ejpam-5718	202	8	τ2	τ2	NOUN
ejpam-5718	202	9	)	)	PUNCT
ejpam-5718	202	10	→	→	SYM
ejpam-5718	202	11	(	(	PUNCT
ejpam-5718	202	12	y	y	PROPN
ejpam-5718	202	13	,	,	PUNCT
ejpam-5718	202	14	σ1	σ1	PROPN
ejpam-5718	202	15	,	,	PUNCT
ejpam-5718	202	16	σ2	σ2	NOUN
ejpam-5718	202	17	)	)	PUNCT
ejpam-5718	202	18	,	,	PUNCT
ejpam-5718	202	19	the	the	DET
ejpam-5718	202	20	following	follow	VERB
ejpam-5718	202	21	properties	property	NOUN
ejpam-5718	202	22	are	be	AUX
ejpam-5718	202	23	equivalent	equivalent	ADJ
ejpam-5718	202	24	:	:	PUNCT
ejpam-5718	202	25	(	(	PUNCT
ejpam-5718	202	26	1	1	X
ejpam-5718	202	27	)	)	PUNCT
ejpam-5718	202	28	f	f	PROPN
ejpam-5718	202	29	is	be	AUX
ejpam-5718	202	30	lower	low	ADJ
ejpam-5718	202	31	weakly	weakly	ADJ
ejpam-5718	202	32	s-(τ1	s-(τ1	PROPN
ejpam-5718	202	33	,	,	PUNCT
ejpam-5718	202	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	202	35	;	;	PUNCT
ejpam-5718	202	36	(	(	PUNCT
ejpam-5718	202	37	2	2	X
ejpam-5718	202	38	)	)	PUNCT
ejpam-5718	202	39	τ1τ2	τ1τ2	NOUN
ejpam-5718	202	40	-	-	NOUN
ejpam-5718	202	41	cl(f	cl(f	NOUN
ejpam-5718	202	42	+	+	NOUN
ejpam-5718	202	43	(	(	PUNCT
ejpam-5718	202	44	σ1σ2	σ1σ2	NOUN
ejpam-5718	202	45	-	-	PUNCT
ejpam-5718	202	46	int((σ1	int((σ1	ADJ
ejpam-5718	202	47	,	,	PUNCT
ejpam-5718	202	48	σ2)θ	σ2)θ	ADJ
ejpam-5718	202	49	-	-	PUNCT
ejpam-5718	202	50	cl(b	cl(b	NOUN
ejpam-5718	202	51	)	)	PUNCT
ejpam-5718	202	52	)	)	PUNCT
ejpam-5718	202	53	)	)	PUNCT
ejpam-5718	202	54	)	)	PUNCT
ejpam-5718	203	1	⊆	⊆	NUM
ejpam-5718	203	2	f+((σ1	f+((σ1	NOUN
ejpam-5718	203	3	,	,	PUNCT
ejpam-5718	203	4	σ2)θ	σ2)θ	ADJ
ejpam-5718	203	5	-	-	PUNCT
ejpam-5718	203	6	cl(b	cl(b	NOUN
ejpam-5718	203	7	)	)	PUNCT
ejpam-5718	203	8	)	)	PUNCT
ejpam-5718	203	9	for	for	ADP
ejpam-5718	203	10	every	every	DET
ejpam-5718	203	11	subset	subset	NOUN
ejpam-5718	203	12	b	b	PROPN
ejpam-5718	203	13	of	of	ADP
ejpam-5718	203	14	y	y	PROPN
ejpam-5718	203	15	having	have	VERB
ejpam-5718	203	16	the	the	DET
ejpam-5718	203	17	σ1σ2	σ1σ2	ADV
ejpam-5718	203	18	-	-	PUNCT
ejpam-5718	203	19	connected	connected	ADJ
ejpam-5718	203	20	(	(	PUNCT
ejpam-5718	203	21	σ1	σ1	PROPN
ejpam-5718	203	22	,	,	PUNCT
ejpam-5718	203	23	σ2)θ	σ2)θ	NOUN
ejpam-5718	203	24	-	-	PUNCT
ejpam-5718	203	25	closure	closure	NOUN
ejpam-5718	203	26	;	;	PUNCT
ejpam-5718	203	27	(	(	PUNCT
ejpam-5718	203	28	3	3	X
ejpam-5718	203	29	)	)	PUNCT
ejpam-5718	203	30	τ1τ2	τ1τ2	NOUN
ejpam-5718	203	31	-	-	NOUN
ejpam-5718	203	32	cl(f	cl(f	NOUN
ejpam-5718	203	33	+	+	NOUN
ejpam-5718	203	34	(	(	PUNCT
ejpam-5718	203	35	σ1σ2	σ1σ2	NUM
ejpam-5718	203	36	-	-	PUNCT
ejpam-5718	203	37	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5718	203	38	-	-	PUNCT
ejpam-5718	203	39	cl(b	cl(b	NOUN
ejpam-5718	203	40	)	)	PUNCT
ejpam-5718	203	41	)	)	PUNCT
ejpam-5718	203	42	)	)	PUNCT
ejpam-5718	203	43	)	)	PUNCT
ejpam-5718	204	1	⊆	⊆	NUM
ejpam-5718	204	2	f+((σ1	f+((σ1	NOUN
ejpam-5718	204	3	,	,	PUNCT
ejpam-5718	204	4	σ2)θ	σ2)θ	ADJ
ejpam-5718	204	5	-	-	PUNCT
ejpam-5718	204	6	cl(b	cl(b	NOUN
ejpam-5718	204	7	)	)	PUNCT
ejpam-5718	204	8	)	)	PUNCT
ejpam-5718	204	9	for	for	ADP
ejpam-5718	204	10	every	every	DET
ejpam-5718	204	11	subset	subset	NOUN
ejpam-5718	204	12	b	b	PROPN
ejpam-5718	204	13	of	of	ADP
ejpam-5718	204	14	y	y	PROPN
ejpam-5718	204	15	having	have	VERB
ejpam-5718	204	16	the	the	DET
ejpam-5718	204	17	σ1σ2	σ1σ2	ADV
ejpam-5718	204	18	-	-	PUNCT
ejpam-5718	204	19	connected	connected	ADJ
ejpam-5718	204	20	(	(	PUNCT
ejpam-5718	204	21	σ1	σ1	PROPN
ejpam-5718	204	22	,	,	PUNCT
ejpam-5718	204	23	σ2)θ	σ2)θ	NOUN
ejpam-5718	204	24	-	-	PUNCT
ejpam-5718	204	25	closure	closure	NOUN
ejpam-5718	204	26	.	.	PUNCT
ejpam-5718	205	1	proof	proof	NOUN
ejpam-5718	205	2	.	.	PUNCT
ejpam-5718	206	1	the	the	DET
ejpam-5718	206	2	proof	proof	NOUN
ejpam-5718	206	3	is	be	AUX
ejpam-5718	206	4	similar	similar	ADJ
ejpam-5718	206	5	to	to	ADP
ejpam-5718	206	6	that	that	PRON
ejpam-5718	206	7	of	of	ADP
ejpam-5718	206	8	theorem	theorem	NOUN
ejpam-5718	206	9	5	5	NUM
ejpam-5718	206	10	.	.	X
ejpam-5718	206	11	for	for	ADP
ejpam-5718	206	12	a	a	DET
ejpam-5718	206	13	multifunction	multifunction	NOUN
ejpam-5718	206	14	f	f	NOUN
ejpam-5718	206	15	:	:	PUNCT
ejpam-5718	206	16	(	(	PUNCT
ejpam-5718	206	17	x	x	NOUN
ejpam-5718	206	18	,	,	PUNCT
ejpam-5718	206	19	τ1	τ1	NOUN
ejpam-5718	206	20	,	,	PUNCT
ejpam-5718	206	21	τ2	τ2	NOUN
ejpam-5718	206	22	)	)	PUNCT
ejpam-5718	206	23	→	→	SYM
ejpam-5718	206	24	(	(	PUNCT
ejpam-5718	206	25	y	y	PROPN
ejpam-5718	206	26	,	,	PUNCT
ejpam-5718	206	27	σ1	σ1	PROPN
ejpam-5718	206	28	,	,	PUNCT
ejpam-5718	206	29	σ2	σ2	NOUN
ejpam-5718	206	30	)	)	PUNCT
ejpam-5718	206	31	,	,	PUNCT
ejpam-5718	206	32	by	by	ADP
ejpam-5718	206	33	clf⊛	clf⊛	PROPN
ejpam-5718	206	34	:	:	PUNCT
ejpam-5718	206	35	(	(	PUNCT
ejpam-5718	206	36	x	x	NOUN
ejpam-5718	206	37	,	,	PUNCT
ejpam-5718	206	38	τ1	τ1	NOUN
ejpam-5718	206	39	,	,	PUNCT
ejpam-5718	206	40	τ2	τ2	NOUN
ejpam-5718	206	41	)	)	PUNCT
ejpam-5718	206	42	→	→	SYM
ejpam-5718	206	43	(	(	PUNCT
ejpam-5718	206	44	y	y	PROPN
ejpam-5718	206	45	,	,	PUNCT
ejpam-5718	206	46	σ1	σ1	PROPN
ejpam-5718	206	47	,	,	PUNCT
ejpam-5718	206	48	σ2	σ2	NOUN
ejpam-5718	206	49	)	)	PUNCT
ejpam-5718	207	1	[	[	X
ejpam-5718	207	2	29	29	NUM
ejpam-5718	207	3	]	]	PUNCT
ejpam-5718	207	4	we	we	PRON
ejpam-5718	207	5	denote	denote	VERB
ejpam-5718	207	6	a	a	DET
ejpam-5718	207	7	multifunction	multifunction	NOUN
ejpam-5718	207	8	defined	define	VERB
ejpam-5718	207	9	as	as	SCONJ
ejpam-5718	207	10	follows	follow	VERB
ejpam-5718	207	11	:	:	PUNCT
ejpam-5718	207	12	clf⊛(x	clf⊛(x	PROPN
ejpam-5718	207	13	)	)	PUNCT
ejpam-5718	207	14	=	=	PUNCT
ejpam-5718	208	1	σ1σ2	σ1σ2	X
ejpam-5718	208	2	-	-	NUM
ejpam-5718	208	3	cl(f	cl(f	NOUN
ejpam-5718	208	4	(	(	PUNCT
ejpam-5718	208	5	x	x	NOUN
ejpam-5718	208	6	)	)	PUNCT
ejpam-5718	208	7	)	)	PUNCT
ejpam-5718	208	8	for	for	ADP
ejpam-5718	208	9	each	each	DET
ejpam-5718	208	10	x	x	SYM
ejpam-5718	208	11	∈	∈	PROPN
ejpam-5718	208	12	x.	x.	NOUN
ejpam-5718	208	13	definition	definition	NOUN
ejpam-5718	208	14	3	3	NUM
ejpam-5718	208	15	.	.	PUNCT
ejpam-5718	209	1	[	[	X
ejpam-5718	209	2	29	29	NUM
ejpam-5718	209	3	]	]	PUNCT
ejpam-5718	209	4	a	a	DET
ejpam-5718	209	5	subset	subset	NOUN
ejpam-5718	209	6	a	a	PRON
ejpam-5718	209	7	of	of	ADP
ejpam-5718	209	8	a	a	DET
ejpam-5718	209	9	bitopological	bitopological	ADJ
ejpam-5718	209	10	space	space	NOUN
ejpam-5718	209	11	(	(	PUNCT
ejpam-5718	209	12	x	x	NOUN
ejpam-5718	209	13	,	,	PUNCT
ejpam-5718	209	14	τ1	τ1	NOUN
ejpam-5718	209	15	,	,	PUNCT
ejpam-5718	209	16	τ2	τ2	NOUN
ejpam-5718	209	17	)	)	PUNCT
ejpam-5718	209	18	is	be	AUX
ejpam-5718	209	19	said	say	VERB
ejpam-5718	209	20	to	to	PART
ejpam-5718	209	21	be	be	AUX
ejpam-5718	209	22	:	:	PUNCT
ejpam-5718	209	23	(	(	PUNCT
ejpam-5718	209	24	1	1	X
ejpam-5718	209	25	)	)	PUNCT
ejpam-5718	209	26	τ1τ2	τ1τ2	NOUN
ejpam-5718	209	27	-	-	NOUN
ejpam-5718	209	28	paracompact	paracompact	ADJ
ejpam-5718	209	29	if	if	SCONJ
ejpam-5718	209	30	every	every	DET
ejpam-5718	209	31	cover	cover	NOUN
ejpam-5718	209	32	of	of	ADP
ejpam-5718	209	33	a	a	PRON
ejpam-5718	209	34	by	by	ADP
ejpam-5718	209	35	τ1τ2	τ1τ2	ADJ
ejpam-5718	209	36	-	-	ADJ
ejpam-5718	209	37	open	open	ADJ
ejpam-5718	209	38	sets	set	NOUN
ejpam-5718	209	39	of	of	ADP
ejpam-5718	209	40	x	x	VERB
ejpam-5718	209	41	is	be	AUX
ejpam-5718	209	42	refined	refine	VERB
ejpam-5718	209	43	by	by	ADP
ejpam-5718	209	44	a	a	DET
ejpam-5718	209	45	cover	cover	NOUN
ejpam-5718	209	46	of	of	ADP
ejpam-5718	209	47	a	a	PRON
ejpam-5718	209	48	which	which	PRON
ejpam-5718	209	49	consists	consist	VERB
ejpam-5718	209	50	of	of	ADP
ejpam-5718	209	51	τ1τ2	τ1τ2	ADJ
ejpam-5718	209	52	-	-	ADJ
ejpam-5718	209	53	open	open	ADJ
ejpam-5718	209	54	sets	set	NOUN
ejpam-5718	209	55	of	of	ADP
ejpam-5718	209	56	x	x	PUNCT
ejpam-5718	209	57	and	and	CCONJ
ejpam-5718	209	58	is	be	AUX
ejpam-5718	209	59	τ1τ2	τ1τ2	NOUN
ejpam-5718	209	60	-	-	ADJ
ejpam-5718	209	61	locally	locally	ADV
ejpam-5718	209	62	finite	finite	NOUN
ejpam-5718	209	63	in	in	ADP
ejpam-5718	209	64	x	x	PRON
ejpam-5718	209	65	;	;	PUNCT
ejpam-5718	209	66	(	(	PUNCT
ejpam-5718	209	67	2	2	X
ejpam-5718	209	68	)	)	PUNCT
ejpam-5718	209	69	τ1τ2	τ1τ2	NOUN
ejpam-5718	209	70	-	-	NOUN
ejpam-5718	209	71	regular	regular	ADJ
ejpam-5718	209	72	if	if	SCONJ
ejpam-5718	209	73	for	for	ADP
ejpam-5718	209	74	each	each	DET
ejpam-5718	209	75	x	x	SYM
ejpam-5718	209	76	∈	∈	PROPN
ejpam-5718	209	77	a	a	PRON
ejpam-5718	209	78	and	and	CCONJ
ejpam-5718	209	79	each	each	DET
ejpam-5718	209	80	τ1τ2	τ1τ2	ADJ
ejpam-5718	209	81	-	-	ADJ
ejpam-5718	209	82	open	open	ADJ
ejpam-5718	209	83	set	set	ADJ
ejpam-5718	209	84	u	u	NOUN
ejpam-5718	209	85	of	of	ADP
ejpam-5718	209	86	x	x	PUNCT
ejpam-5718	209	87	containing	contain	VERB
ejpam-5718	209	88	x	x	PRON
ejpam-5718	209	89	,	,	PUNCT
ejpam-5718	209	90	there	there	PRON
ejpam-5718	209	91	exists	exist	VERB
ejpam-5718	209	92	a	a	DET
ejpam-5718	209	93	τ1τ2	τ1τ2	NOUN
ejpam-5718	209	94	-	-	ADJ
ejpam-5718	209	95	open	open	ADJ
ejpam-5718	209	96	set	set	NOUN
ejpam-5718	209	97	v	v	NOUN
ejpam-5718	209	98	of	of	ADP
ejpam-5718	209	99	x	x	PUNCT
ejpam-5718	209	100	such	such	ADJ
ejpam-5718	209	101	that	that	SCONJ
ejpam-5718	209	102	x	x	SYM
ejpam-5718	209	103	∈	∈	NOUN
ejpam-5718	209	104	v	v	ADP
ejpam-5718	209	105	⊆	⊆	NUM
ejpam-5718	209	106	τ1τ2	τ1τ2	NOUN
ejpam-5718	209	107	-	-	NOUN
ejpam-5718	209	108	cl(v	cl(v	X
ejpam-5718	209	109	)	)	PUNCT
ejpam-5718	209	110	⊆	⊆	NUM
ejpam-5718	209	111	u	u	NOUN
ejpam-5718	209	112	.	.	PUNCT
ejpam-5718	210	1	lemma	lemma	PROPN
ejpam-5718	210	2	3	3	X
ejpam-5718	210	3	.	.	PUNCT
ejpam-5718	211	1	[	[	X
ejpam-5718	211	2	29	29	NUM
ejpam-5718	211	3	]	]	X
ejpam-5718	211	4	if	if	SCONJ
ejpam-5718	211	5	f	f	PROPN
ejpam-5718	211	6	:	:	PUNCT
ejpam-5718	211	7	(	(	PUNCT
ejpam-5718	211	8	x	x	NOUN
ejpam-5718	211	9	,	,	PUNCT
ejpam-5718	211	10	τ1	τ1	NOUN
ejpam-5718	211	11	,	,	PUNCT
ejpam-5718	211	12	τ2	τ2	NOUN
ejpam-5718	211	13	)	)	PUNCT
ejpam-5718	211	14	→	→	SYM
ejpam-5718	211	15	(	(	PUNCT
ejpam-5718	211	16	y	y	PROPN
ejpam-5718	211	17	,	,	PUNCT
ejpam-5718	211	18	σ1	σ1	PROPN
ejpam-5718	211	19	,	,	PUNCT
ejpam-5718	211	20	σ2	σ2	PROPN
ejpam-5718	211	21	)	)	PUNCT
ejpam-5718	211	22	is	be	AUX
ejpam-5718	211	23	a	a	DET
ejpam-5718	211	24	multifunction	multifunction	NOUN
ejpam-5718	211	25	such	such	ADJ
ejpam-5718	211	26	that	that	SCONJ
ejpam-5718	211	27	f	f	PROPN
ejpam-5718	211	28	(	(	PUNCT
ejpam-5718	211	29	x	x	X
ejpam-5718	211	30	)	)	PUNCT
ejpam-5718	211	31	is	be	AUX
ejpam-5718	211	32	τ1τ2regular	τ1τ2regular	NUM
ejpam-5718	211	33	and	and	CCONJ
ejpam-5718	211	34	τ1τ2	τ1τ2	NOUN
ejpam-5718	211	35	-	-	ADJ
ejpam-5718	211	36	paracompact	paracompact	ADJ
ejpam-5718	211	37	for	for	ADP
ejpam-5718	211	38	each	each	DET
ejpam-5718	211	39	x	x	SYM
ejpam-5718	211	40	∈	∈	PROPN
ejpam-5718	211	41	x	x	NOUN
ejpam-5718	211	42	,	,	PUNCT
ejpam-5718	211	43	then	then	ADV
ejpam-5718	211	44	clf+	clf+	PROPN
ejpam-5718	211	45	⊛	⊛	X
ejpam-5718	211	46	(	(	PUNCT
ejpam-5718	211	47	v	v	NOUN
ejpam-5718	211	48	)	)	PUNCT
ejpam-5718	211	49	=	=	PUNCT
ejpam-5718	211	50	f+(v	f+(v	NOUN
ejpam-5718	211	51	)	)	PUNCT
ejpam-5718	211	52	for	for	ADP
ejpam-5718	211	53	each	each	DET
ejpam-5718	211	54	σ1σ2	σ1σ2	VERB
ejpam-5718	211	55	-	-	ADJ
ejpam-5718	211	56	open	open	ADJ
ejpam-5718	211	57	set	set	NOUN
ejpam-5718	211	58	v	v	NOUN
ejpam-5718	211	59	of	of	ADP
ejpam-5718	211	60	y	y	PROPN
ejpam-5718	211	61	.	.	PUNCT
ejpam-5718	212	1	lemma	lemma	PROPN
ejpam-5718	212	2	4	4	NUM
ejpam-5718	212	3	.	.	PUNCT
ejpam-5718	213	1	[	[	X
ejpam-5718	213	2	29	29	NUM
ejpam-5718	213	3	]	]	PUNCT
ejpam-5718	213	4	for	for	ADP
ejpam-5718	213	5	a	a	DET
ejpam-5718	213	6	multifunction	multifunction	NOUN
ejpam-5718	213	7	f	f	NOUN
ejpam-5718	213	8	:	:	PUNCT
ejpam-5718	213	9	(	(	PUNCT
ejpam-5718	213	10	x	x	NOUN
ejpam-5718	213	11	,	,	PUNCT
ejpam-5718	213	12	τ1	τ1	NOUN
ejpam-5718	213	13	,	,	PUNCT
ejpam-5718	213	14	τ2	τ2	NOUN
ejpam-5718	213	15	)	)	PUNCT
ejpam-5718	213	16	→	→	SYM
ejpam-5718	213	17	(	(	PUNCT
ejpam-5718	213	18	y	y	PROPN
ejpam-5718	213	19	,	,	PUNCT
ejpam-5718	213	20	σ1	σ1	PROPN
ejpam-5718	213	21	,	,	PUNCT
ejpam-5718	213	22	σ2	σ2	NOUN
ejpam-5718	213	23	)	)	PUNCT
ejpam-5718	213	24	,	,	PUNCT
ejpam-5718	213	25	clf	clf	PROPN
ejpam-5718	213	26	−	−	PROPN
ejpam-5718	213	27	⊛	⊛	NUM
ejpam-5718	213	28	(	(	PUNCT
ejpam-5718	213	29	v	v	NOUN
ejpam-5718	213	30	)	)	PUNCT
ejpam-5718	213	31	=	=	SYM
ejpam-5718	213	32	f−(v	f−(v	ADJ
ejpam-5718	213	33	)	)	PUNCT
ejpam-5718	213	34	for	for	ADP
ejpam-5718	213	35	each	each	DET
ejpam-5718	213	36	σ1σ2	σ1σ2	VERB
ejpam-5718	213	37	-	-	ADJ
ejpam-5718	213	38	open	open	ADJ
ejpam-5718	213	39	set	set	NOUN
ejpam-5718	213	40	v	v	NOUN
ejpam-5718	213	41	of	of	ADP
ejpam-5718	213	42	y	y	PROPN
ejpam-5718	213	43	.	.	PUNCT
ejpam-5718	214	1	theorem	theorem	ADJ
ejpam-5718	214	2	7	7	NUM
ejpam-5718	214	3	.	.	PUNCT
ejpam-5718	215	1	let	let	VERB
ejpam-5718	215	2	f	f	NOUN
ejpam-5718	215	3	:	:	PUNCT
ejpam-5718	215	4	(	(	PUNCT
ejpam-5718	215	5	x	x	NOUN
ejpam-5718	215	6	,	,	PUNCT
ejpam-5718	215	7	τ1	τ1	NOUN
ejpam-5718	215	8	,	,	PUNCT
ejpam-5718	215	9	τ2	τ2	NOUN
ejpam-5718	215	10	)	)	PUNCT
ejpam-5718	215	11	→	→	SYM
ejpam-5718	215	12	(	(	PUNCT
ejpam-5718	215	13	y	y	PROPN
ejpam-5718	215	14	,	,	PUNCT
ejpam-5718	215	15	σ1	σ1	PROPN
ejpam-5718	215	16	,	,	PUNCT
ejpam-5718	215	17	σ2	σ2	PROPN
ejpam-5718	215	18	)	)	PUNCT
ejpam-5718	215	19	be	be	VERB
ejpam-5718	215	20	a	a	DET
ejpam-5718	215	21	multifunction	multifunction	NOUN
ejpam-5718	215	22	such	such	ADJ
ejpam-5718	215	23	that	that	SCONJ
ejpam-5718	215	24	f	f	PROPN
ejpam-5718	215	25	(	(	PUNCT
ejpam-5718	215	26	x	x	X
ejpam-5718	215	27	)	)	PUNCT
ejpam-5718	215	28	is	be	AUX
ejpam-5718	215	29	σ1σ2	σ1σ2	NOUN
ejpam-5718	215	30	-	-	ADJ
ejpam-5718	215	31	paracompact	paracompact	ADJ
ejpam-5718	215	32	and	and	CCONJ
ejpam-5718	215	33	σ1σ2	σ1σ2	NOUN
ejpam-5718	215	34	-	-	ADJ
ejpam-5718	215	35	regular	regular	ADJ
ejpam-5718	215	36	for	for	ADP
ejpam-5718	215	37	each	each	DET
ejpam-5718	215	38	x	x	SYM
ejpam-5718	215	39	∈	∈	PROPN
ejpam-5718	215	40	x.	x.	NOUN
ejpam-5718	215	41	then	then	ADV
ejpam-5718	215	42	,	,	PUNCT
ejpam-5718	215	43	f	f	PROPN
ejpam-5718	215	44	is	be	AUX
ejpam-5718	215	45	upper	upper	ADJ
ejpam-5718	215	46	weakly	weakly	ADJ
ejpam-5718	215	47	s-(τ1	s-(τ1	PROPN
ejpam-5718	215	48	,	,	PUNCT
ejpam-5718	215	49	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	215	50	if	if	SCONJ
ejpam-5718	215	51	and	and	CCONJ
ejpam-5718	215	52	only	only	ADV
ejpam-5718	215	53	if	if	SCONJ
ejpam-5718	215	54	clf⊛	clf⊛	PROPN
ejpam-5718	215	55	:	:	PUNCT
ejpam-5718	215	56	(	(	PUNCT
ejpam-5718	215	57	x	x	NOUN
ejpam-5718	215	58	,	,	PUNCT
ejpam-5718	215	59	τ1	τ1	NOUN
ejpam-5718	215	60	,	,	PUNCT
ejpam-5718	215	61	τ2	τ2	NOUN
ejpam-5718	215	62	)	)	PUNCT
ejpam-5718	215	63	→	→	SYM
ejpam-5718	215	64	(	(	PUNCT
ejpam-5718	215	65	y	y	PROPN
ejpam-5718	215	66	,	,	PUNCT
ejpam-5718	215	67	σ1	σ1	PROPN
ejpam-5718	215	68	,	,	PUNCT
ejpam-5718	215	69	σ2	σ2	PROPN
ejpam-5718	215	70	)	)	PUNCT
ejpam-5718	215	71	is	be	AUX
ejpam-5718	215	72	upper	upper	ADJ
ejpam-5718	215	73	weakly	weakly	ADJ
ejpam-5718	215	74	s-(τ1	s-(τ1	PROPN
ejpam-5718	215	75	,	,	PUNCT
ejpam-5718	215	76	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	215	77	.	.	PUNCT
ejpam-5718	216	1	p.	p.	NOUN
ejpam-5718	216	2	pue	pue	NOUN
ejpam-5718	216	3	-	-	PUNCT
ejpam-5718	216	4	on	on	ADP
ejpam-5718	216	5	,	,	PUNCT
ejpam-5718	216	6	a.	a.	PROPN
ejpam-5718	216	7	sama	sama	PROPN
ejpam-5718	216	8	-	-	PUNCT
ejpam-5718	216	9	ae	ae	PROPN
ejpam-5718	216	10	,	,	PUNCT
ejpam-5718	216	11	c.	c.	PROPN
ejpam-5718	216	12	boonpok	boonpok	PROPN
ejpam-5718	216	13	/	/	SYM
ejpam-5718	216	14	eur	eur	PROPN
ejpam-5718	216	15	.	.	PUNCT
ejpam-5718	217	1	j.	j.	PROPN
ejpam-5718	217	2	pure	pure	PROPN
ejpam-5718	217	3	appl	appl	PROPN
ejpam-5718	217	4	.	.	PROPN
ejpam-5718	217	5	math	math	PROPN
ejpam-5718	217	6	,	,	PUNCT
ejpam-5718	217	7	18	18	NUM
ejpam-5718	217	8	(	(	PUNCT
ejpam-5718	217	9	1	1	NUM
ejpam-5718	217	10	)	)	PUNCT
ejpam-5718	217	11	(	(	PUNCT
ejpam-5718	217	12	2025	2025	NUM
ejpam-5718	217	13	)	)	PUNCT
ejpam-5718	217	14	,	,	PUNCT
ejpam-5718	217	15	5718	5718	NUM
ejpam-5718	217	16	9	9	NUM
ejpam-5718	217	17	of	of	ADP
ejpam-5718	217	18	16	16	NUM
ejpam-5718	217	19	proof	proof	NOUN
ejpam-5718	217	20	.	.	PUNCT
ejpam-5718	217	21	suppose	suppose	VERB
ejpam-5718	217	22	that	that	SCONJ
ejpam-5718	217	23	f	f	PROPN
ejpam-5718	217	24	is	be	AUX
ejpam-5718	217	25	upper	upper	ADJ
ejpam-5718	217	26	weakly	weakly	ADJ
ejpam-5718	217	27	s-(τ1	s-(τ1	PROPN
ejpam-5718	217	28	,	,	PUNCT
ejpam-5718	217	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	217	30	.	.	PUNCT
ejpam-5718	218	1	let	let	VERB
ejpam-5718	218	2	v	v	PART
ejpam-5718	218	3	be	be	AUX
ejpam-5718	218	4	any	any	DET
ejpam-5718	218	5	σ1σ2	σ1σ2	NOUN
ejpam-5718	218	6	-	-	ADJ
ejpam-5718	218	7	open	open	ADJ
ejpam-5718	218	8	set	set	NOUN
ejpam-5718	218	9	of	of	ADP
ejpam-5718	218	10	y	y	PROPN
ejpam-5718	218	11	having	have	VERB
ejpam-5718	218	12	σ1σ2	σ1σ2	ADV
ejpam-5718	218	13	-	-	PUNCT
ejpam-5718	218	14	connected	connect	VERB
ejpam-5718	218	15	complement	complement	NOUN
ejpam-5718	218	16	.	.	PUNCT
ejpam-5718	219	1	by	by	ADP
ejpam-5718	219	2	theorem	theorem	NOUN
ejpam-5718	219	3	1	1	NUM
ejpam-5718	219	4	,	,	PUNCT
ejpam-5718	219	5	lemma	lemma	PROPN
ejpam-5718	219	6	3	3	NUM
ejpam-5718	219	7	and	and	CCONJ
ejpam-5718	219	8	lemma	lemma	PROPN
ejpam-5718	219	9	4	4	NUM
ejpam-5718	219	10	,	,	PUNCT
ejpam-5718	219	11	we	we	PRON
ejpam-5718	219	12	have	have	VERB
ejpam-5718	219	13	clf+	clf+	NOUN
ejpam-5718	219	14	⊛	⊛	ADJ
ejpam-5718	219	15	(	(	PUNCT
ejpam-5718	219	16	v	v	NOUN
ejpam-5718	219	17	)	)	PUNCT
ejpam-5718	219	18	=	=	PUNCT
ejpam-5718	220	1	f+(v	f+(v	NOUN
ejpam-5718	220	2	)	)	PUNCT
ejpam-5718	221	1	⊆	⊆	X
ejpam-5718	221	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	221	3	-	-	NUM
ejpam-5718	221	4	int(f	int(f	VERB
ejpam-5718	221	5	+	+	ADJ
ejpam-5718	221	6	(	(	PUNCT
ejpam-5718	221	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	221	8	-	-	NUM
ejpam-5718	221	9	cl(v	cl(v	NOUN
ejpam-5718	221	10	)	)	PUNCT
ejpam-5718	221	11	)	)	PUNCT
ejpam-5718	221	12	)	)	PUNCT
ejpam-5718	222	1	=	=	PUNCT
ejpam-5718	222	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	222	3	-	-	ADJ
ejpam-5718	222	4	int(clf	int(clf	X
ejpam-5718	222	5	+	+	CCONJ
ejpam-5718	222	6	⊛	⊛	NUM
ejpam-5718	222	7	(	(	PUNCT
ejpam-5718	222	8	σ1σ2	σ1σ2	NOUN
ejpam-5718	222	9	-	-	NUM
ejpam-5718	222	10	cl(v	cl(v	NOUN
ejpam-5718	222	11	)	)	PUNCT
ejpam-5718	222	12	)	)	PUNCT
ejpam-5718	222	13	)	)	PUNCT
ejpam-5718	222	14	.	.	PUNCT
ejpam-5718	223	1	thus	thus	ADV
ejpam-5718	223	2	by	by	ADP
ejpam-5718	223	3	theorem	theorem	NOUN
ejpam-5718	223	4	1	1	NUM
ejpam-5718	223	5	,	,	PUNCT
ejpam-5718	223	6	clf⊛	clf⊛	PROPN
ejpam-5718	223	7	is	be	AUX
ejpam-5718	223	8	upper	upper	ADJ
ejpam-5718	223	9	weakly	weakly	ADJ
ejpam-5718	223	10	s-(τ1	s-(τ1	PROPN
ejpam-5718	223	11	,	,	PUNCT
ejpam-5718	223	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	223	13	.	.	PUNCT
ejpam-5718	224	1	conversely	conversely	ADV
ejpam-5718	224	2	,	,	PUNCT
ejpam-5718	224	3	suppose	suppose	VERB
ejpam-5718	224	4	that	that	SCONJ
ejpam-5718	224	5	clf⊛	clf⊛	PROPN
ejpam-5718	224	6	is	be	AUX
ejpam-5718	224	7	upper	upper	ADJ
ejpam-5718	224	8	weakly	weakly	ADJ
ejpam-5718	224	9	s-(τ1	s-(τ1	PROPN
ejpam-5718	224	10	,	,	PUNCT
ejpam-5718	224	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	224	12	.	.	PUNCT
ejpam-5718	225	1	let	let	VERB
ejpam-5718	225	2	v	v	PART
ejpam-5718	225	3	be	be	AUX
ejpam-5718	225	4	any	any	DET
ejpam-5718	225	5	σ1σ2	σ1σ2	NOUN
ejpam-5718	225	6	-	-	ADJ
ejpam-5718	225	7	open	open	ADJ
ejpam-5718	225	8	set	set	NOUN
ejpam-5718	225	9	of	of	ADP
ejpam-5718	225	10	y	y	PROPN
ejpam-5718	225	11	having	have	VERB
ejpam-5718	225	12	σ1σ2	σ1σ2	ADV
ejpam-5718	225	13	-	-	PUNCT
ejpam-5718	225	14	connected	connect	VERB
ejpam-5718	225	15	complement	complement	NOUN
ejpam-5718	225	16	.	.	PUNCT
ejpam-5718	226	1	by	by	ADP
ejpam-5718	226	2	theorem	theorem	NOUN
ejpam-5718	226	3	1	1	NUM
ejpam-5718	226	4	,	,	PUNCT
ejpam-5718	226	5	lemma	lemma	PROPN
ejpam-5718	226	6	3	3	NUM
ejpam-5718	226	7	and	and	CCONJ
ejpam-5718	226	8	lemma	lemma	PROPN
ejpam-5718	226	9	4	4	NUM
ejpam-5718	226	10	,	,	PUNCT
ejpam-5718	226	11	we	we	PRON
ejpam-5718	226	12	have	have	VERB
ejpam-5718	226	13	f+(v	f+(v	NOUN
ejpam-5718	226	14	)	)	PUNCT
ejpam-5718	227	1	=	=	PUNCT
ejpam-5718	227	2	clf+	clf+	NOUN
ejpam-5718	227	3	⊛	⊛	NUM
ejpam-5718	227	4	(	(	PUNCT
ejpam-5718	227	5	v	v	NOUN
ejpam-5718	227	6	)	)	PUNCT
ejpam-5718	227	7	⊆	⊆	NUM
ejpam-5718	227	8	τ1τ2	τ1τ2	NOUN
ejpam-5718	227	9	-	-	ADJ
ejpam-5718	227	10	int(clf	int(clf	ADJ
ejpam-5718	227	11	+	+	CCONJ
ejpam-5718	227	12	⊛	⊛	NUM
ejpam-5718	227	13	(	(	PUNCT
ejpam-5718	227	14	σ1σ2	σ1σ2	NOUN
ejpam-5718	227	15	-	-	NUM
ejpam-5718	227	16	cl(v	cl(v	NOUN
ejpam-5718	227	17	)	)	PUNCT
ejpam-5718	227	18	)	)	PUNCT
ejpam-5718	227	19	)	)	PUNCT
ejpam-5718	228	1	=	=	PUNCT
ejpam-5718	228	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	228	3	-	-	NUM
ejpam-5718	228	4	int(f	int(f	VERB
ejpam-5718	228	5	+	+	ADJ
ejpam-5718	228	6	(	(	PUNCT
ejpam-5718	228	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	228	8	-	-	NUM
ejpam-5718	228	9	cl(v	cl(v	NOUN
ejpam-5718	228	10	)	)	PUNCT
ejpam-5718	228	11	)	)	PUNCT
ejpam-5718	228	12	)	)	PUNCT
ejpam-5718	228	13	.	.	PUNCT
ejpam-5718	229	1	by	by	ADP
ejpam-5718	229	2	theorem	theorem	NOUN
ejpam-5718	229	3	1	1	NUM
ejpam-5718	229	4	,	,	PUNCT
ejpam-5718	229	5	f	f	PROPN
ejpam-5718	229	6	is	be	AUX
ejpam-5718	229	7	upper	upper	ADJ
ejpam-5718	229	8	weakly	weakly	ADJ
ejpam-5718	229	9	s-(τ1	s-(τ1	PROPN
ejpam-5718	229	10	,	,	PUNCT
ejpam-5718	229	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	229	12	.	.	PUNCT
ejpam-5718	230	1	theorem	theorem	NOUN
ejpam-5718	230	2	8	8	NUM
ejpam-5718	230	3	.	.	PUNCT
ejpam-5718	231	1	let	let	VERB
ejpam-5718	231	2	f	f	NOUN
ejpam-5718	231	3	:	:	PUNCT
ejpam-5718	231	4	(	(	PUNCT
ejpam-5718	231	5	x	x	NOUN
ejpam-5718	231	6	,	,	PUNCT
ejpam-5718	231	7	τ1	τ1	NOUN
ejpam-5718	231	8	,	,	PUNCT
ejpam-5718	231	9	τ2	τ2	NOUN
ejpam-5718	231	10	)	)	PUNCT
ejpam-5718	231	11	→	→	SYM
ejpam-5718	231	12	(	(	PUNCT
ejpam-5718	231	13	y	y	PROPN
ejpam-5718	231	14	,	,	PUNCT
ejpam-5718	231	15	σ1	σ1	PROPN
ejpam-5718	231	16	,	,	PUNCT
ejpam-5718	231	17	σ2	σ2	PROPN
ejpam-5718	231	18	)	)	PUNCT
ejpam-5718	231	19	be	be	VERB
ejpam-5718	231	20	a	a	DET
ejpam-5718	231	21	multifunction	multifunction	NOUN
ejpam-5718	231	22	such	such	ADJ
ejpam-5718	231	23	that	that	SCONJ
ejpam-5718	231	24	f	f	PROPN
ejpam-5718	231	25	(	(	PUNCT
ejpam-5718	231	26	x	x	X
ejpam-5718	231	27	)	)	PUNCT
ejpam-5718	231	28	is	be	AUX
ejpam-5718	231	29	σ1σ2	σ1σ2	NOUN
ejpam-5718	231	30	-	-	ADJ
ejpam-5718	231	31	paracompact	paracompact	ADJ
ejpam-5718	231	32	and	and	CCONJ
ejpam-5718	231	33	σ1σ2	σ1σ2	NOUN
ejpam-5718	231	34	-	-	ADJ
ejpam-5718	231	35	regular	regular	ADJ
ejpam-5718	231	36	for	for	ADP
ejpam-5718	231	37	each	each	DET
ejpam-5718	231	38	x	x	SYM
ejpam-5718	231	39	∈	∈	PROPN
ejpam-5718	231	40	x.	x.	NOUN
ejpam-5718	231	41	then	then	ADV
ejpam-5718	231	42	,	,	PUNCT
ejpam-5718	231	43	f	f	PROPN
ejpam-5718	231	44	is	be	AUX
ejpam-5718	231	45	lower	low	ADJ
ejpam-5718	231	46	weakly	weakly	ADJ
ejpam-5718	231	47	s-(τ1	s-(τ1	NOUN
ejpam-5718	231	48	,	,	PUNCT
ejpam-5718	231	49	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	231	50	if	if	SCONJ
ejpam-5718	231	51	and	and	CCONJ
ejpam-5718	231	52	only	only	ADV
ejpam-5718	231	53	if	if	SCONJ
ejpam-5718	231	54	clf⊛	clf⊛	PROPN
ejpam-5718	231	55	:	:	PUNCT
ejpam-5718	231	56	(	(	PUNCT
ejpam-5718	231	57	x	x	NOUN
ejpam-5718	231	58	,	,	PUNCT
ejpam-5718	231	59	τ1	τ1	NOUN
ejpam-5718	231	60	,	,	PUNCT
ejpam-5718	231	61	τ2	τ2	NOUN
ejpam-5718	231	62	)	)	PUNCT
ejpam-5718	231	63	→	→	SYM
ejpam-5718	231	64	(	(	PUNCT
ejpam-5718	231	65	y	y	PROPN
ejpam-5718	231	66	,	,	PUNCT
ejpam-5718	231	67	σ1	σ1	PROPN
ejpam-5718	231	68	,	,	PUNCT
ejpam-5718	231	69	σ2	σ2	NOUN
ejpam-5718	231	70	)	)	PUNCT
ejpam-5718	231	71	is	be	AUX
ejpam-5718	231	72	lower	low	ADJ
ejpam-5718	231	73	weakly	weakly	ADJ
ejpam-5718	231	74	s-(τ1	s-(τ1	PROPN
ejpam-5718	231	75	,	,	PUNCT
ejpam-5718	231	76	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	231	77	.	.	PUNCT
ejpam-5718	232	1	proof	proof	NOUN
ejpam-5718	232	2	.	.	PUNCT
ejpam-5718	233	1	the	the	DET
ejpam-5718	233	2	proof	proof	NOUN
ejpam-5718	233	3	is	be	AUX
ejpam-5718	233	4	similar	similar	ADJ
ejpam-5718	233	5	to	to	ADP
ejpam-5718	233	6	that	that	PRON
ejpam-5718	233	7	of	of	ADP
ejpam-5718	233	8	theorem	theorem	ADJ
ejpam-5718	233	9	7	7	NUM
ejpam-5718	233	10	.	.	NOUN
ejpam-5718	233	11	4	4	NUM
ejpam-5718	233	12	.	.	X
ejpam-5718	234	1	some	some	DET
ejpam-5718	234	2	results	result	NOUN
ejpam-5718	234	3	on	on	ADP
ejpam-5718	234	4	weak	weak	ADJ
ejpam-5718	234	5	s-(τ1	s-(τ1	NOUN
ejpam-5718	234	6	,	,	PUNCT
ejpam-5718	234	7	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5718	234	8	recall	recall	VERB
ejpam-5718	234	9	that	that	SCONJ
ejpam-5718	234	10	a	a	DET
ejpam-5718	234	11	subset	subset	NOUN
ejpam-5718	234	12	a	a	PRON
ejpam-5718	234	13	of	of	ADP
ejpam-5718	234	14	a	a	DET
ejpam-5718	234	15	bitopological	bitopological	ADJ
ejpam-5718	234	16	space	space	NOUN
ejpam-5718	234	17	(	(	PUNCT
ejpam-5718	234	18	x	x	NOUN
ejpam-5718	234	19	,	,	PUNCT
ejpam-5718	234	20	τ1	τ1	NOUN
ejpam-5718	234	21	,	,	PUNCT
ejpam-5718	234	22	τ2	τ2	NOUN
ejpam-5718	234	23	)	)	PUNCT
ejpam-5718	234	24	is	be	AUX
ejpam-5718	234	25	said	say	VERB
ejpam-5718	234	26	to	to	PART
ejpam-5718	234	27	be	be	AUX
ejpam-5718	234	28	τ1τ2	τ1τ2	NOUN
ejpam-5718	234	29	-	-	ADJ
ejpam-5718	234	30	clopen	clopen	ADJ
ejpam-5718	235	1	[	[	X
ejpam-5718	236	1	29	29	NUM
ejpam-5718	236	2	]	]	X
ejpam-5718	236	3	if	if	SCONJ
ejpam-5718	236	4	a	a	PRON
ejpam-5718	236	5	is	be	AUX
ejpam-5718	236	6	both	both	PRON
ejpam-5718	236	7	τ1τ2	τ1τ2	ADJ
ejpam-5718	236	8	-	-	ADJ
ejpam-5718	236	9	open	open	ADJ
ejpam-5718	236	10	and	and	CCONJ
ejpam-5718	236	11	τ1τ2	τ1τ2	NOUN
ejpam-5718	236	12	-	-	ADJ
ejpam-5718	236	13	closed	closed	ADJ
ejpam-5718	236	14	.	.	PUNCT
ejpam-5718	237	1	definition	definition	NOUN
ejpam-5718	237	2	4	4	NUM
ejpam-5718	237	3	.	.	PUNCT
ejpam-5718	238	1	[	[	X
ejpam-5718	238	2	29	29	NUM
ejpam-5718	238	3	]	]	PUNCT
ejpam-5718	238	4	a	a	DET
ejpam-5718	238	5	bitopological	bitopological	ADJ
ejpam-5718	238	6	space	space	NOUN
ejpam-5718	238	7	(	(	PUNCT
ejpam-5718	238	8	x	x	NOUN
ejpam-5718	238	9	,	,	PUNCT
ejpam-5718	238	10	τ1	τ1	NOUN
ejpam-5718	238	11	,	,	PUNCT
ejpam-5718	238	12	τ2	τ2	NOUN
ejpam-5718	238	13	)	)	PUNCT
ejpam-5718	238	14	is	be	AUX
ejpam-5718	238	15	said	say	VERB
ejpam-5718	238	16	to	to	PART
ejpam-5718	238	17	be	be	AUX
ejpam-5718	238	18	τ1τ2	τ1τ2	NOUN
ejpam-5718	238	19	-	-	ADJ
ejpam-5718	238	20	connected	connected	ADJ
ejpam-5718	238	21	if	if	SCONJ
ejpam-5718	238	22	x	x	PRON
ejpam-5718	238	23	can	can	AUX
ejpam-5718	238	24	not	not	PART
ejpam-5718	238	25	be	be	AUX
ejpam-5718	238	26	written	write	VERB
ejpam-5718	238	27	as	as	ADP
ejpam-5718	238	28	the	the	DET
ejpam-5718	238	29	union	union	NOUN
ejpam-5718	238	30	of	of	ADP
ejpam-5718	238	31	two	two	NUM
ejpam-5718	238	32	disjoint	disjoint	NOUN
ejpam-5718	238	33	nonempty	nonempty	ADJ
ejpam-5718	238	34	τ1τ2	τ1τ2	ADJ
ejpam-5718	238	35	-	-	ADJ
ejpam-5718	238	36	open	open	ADJ
ejpam-5718	238	37	sets	set	NOUN
ejpam-5718	238	38	.	.	PUNCT
ejpam-5718	239	1	definition	definition	NOUN
ejpam-5718	239	2	5	5	NUM
ejpam-5718	239	3	.	.	PUNCT
ejpam-5718	240	1	[	[	X
ejpam-5718	240	2	64	64	NUM
ejpam-5718	240	3	]	]	PUNCT
ejpam-5718	240	4	a	a	DET
ejpam-5718	240	5	bitopological	bitopological	ADJ
ejpam-5718	240	6	space	space	NOUN
ejpam-5718	240	7	(	(	PUNCT
ejpam-5718	240	8	x	x	NOUN
ejpam-5718	240	9	,	,	PUNCT
ejpam-5718	240	10	τ1	τ1	NOUN
ejpam-5718	240	11	,	,	PUNCT
ejpam-5718	240	12	τ2	τ2	NOUN
ejpam-5718	240	13	)	)	PUNCT
ejpam-5718	240	14	is	be	AUX
ejpam-5718	240	15	said	say	VERB
ejpam-5718	240	16	to	to	PART
ejpam-5718	240	17	be	be	AUX
ejpam-5718	240	18	s	s	NOUN
ejpam-5718	240	19	-	-	PUNCT
ejpam-5718	240	20	τ1τ2	τ1τ2	ADJ
ejpam-5718	240	21	-	-	ADJ
ejpam-5718	240	22	connected	connected	ADJ
ejpam-5718	240	23	if	if	SCONJ
ejpam-5718	240	24	x	x	PRON
ejpam-5718	240	25	can	can	AUX
ejpam-5718	240	26	not	not	PART
ejpam-5718	240	27	be	be	AUX
ejpam-5718	240	28	written	write	VERB
ejpam-5718	240	29	as	as	ADP
ejpam-5718	240	30	the	the	DET
ejpam-5718	240	31	union	union	NOUN
ejpam-5718	240	32	of	of	ADP
ejpam-5718	240	33	two	two	NUM
ejpam-5718	240	34	disjoint	disjoint	NOUN
ejpam-5718	240	35	nonempty	nonempty	ADJ
ejpam-5718	240	36	τ1τ2	τ1τ2	ADJ
ejpam-5718	240	37	-	-	ADJ
ejpam-5718	240	38	open	open	ADJ
ejpam-5718	240	39	sets	set	NOUN
ejpam-5718	240	40	having	have	VERB
ejpam-5718	240	41	τ1τ2	τ1τ2	VERB
ejpam-5718	240	42	-	-	ADJ
ejpam-5718	240	43	connected	connected	ADJ
ejpam-5718	240	44	complements	complement	NOUN
ejpam-5718	240	45	.	.	PUNCT
ejpam-5718	241	1	theorem	theorem	VERB
ejpam-5718	241	2	9	9	NUM
ejpam-5718	241	3	.	.	PUNCT
ejpam-5718	242	1	if	if	SCONJ
ejpam-5718	242	2	f	f	PROPN
ejpam-5718	242	3	:	:	PUNCT
ejpam-5718	242	4	(	(	PUNCT
ejpam-5718	242	5	x	x	NOUN
ejpam-5718	242	6	,	,	PUNCT
ejpam-5718	242	7	τ1	τ1	NOUN
ejpam-5718	242	8	,	,	PUNCT
ejpam-5718	242	9	τ2	τ2	NOUN
ejpam-5718	242	10	)	)	PUNCT
ejpam-5718	242	11	→	→	SYM
ejpam-5718	242	12	(	(	PUNCT
ejpam-5718	242	13	y	y	PROPN
ejpam-5718	242	14	,	,	PUNCT
ejpam-5718	242	15	σ1	σ1	PROPN
ejpam-5718	242	16	,	,	PUNCT
ejpam-5718	242	17	σ2	σ2	PROPN
ejpam-5718	242	18	)	)	PUNCT
ejpam-5718	242	19	is	be	AUX
ejpam-5718	242	20	an	an	DET
ejpam-5718	242	21	upper	upper	ADJ
ejpam-5718	242	22	or	or	CCONJ
ejpam-5718	242	23	lower	low	ADJ
ejpam-5718	242	24	weakly	weakly	ADJ
ejpam-5718	242	25	s-(τ1	s-(τ1	NOUN
ejpam-5718	242	26	,	,	PUNCT
ejpam-5718	242	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	242	28	surjective	surjective	ADJ
ejpam-5718	242	29	multifunction	multifunction	NOUN
ejpam-5718	242	30	such	such	ADJ
ejpam-5718	242	31	that	that	SCONJ
ejpam-5718	242	32	f	f	PROPN
ejpam-5718	242	33	(	(	PUNCT
ejpam-5718	242	34	x	x	X
ejpam-5718	242	35	)	)	PUNCT
ejpam-5718	242	36	is	be	AUX
ejpam-5718	242	37	σ1σ2	σ1σ2	NOUN
ejpam-5718	242	38	-	-	PUNCT
ejpam-5718	242	39	connected	connected	ADJ
ejpam-5718	242	40	for	for	ADP
ejpam-5718	242	41	each	each	DET
ejpam-5718	242	42	x	x	SYM
ejpam-5718	242	43	∈	∈	PROPN
ejpam-5718	242	44	x	x	X
ejpam-5718	242	45	and	and	CCONJ
ejpam-5718	242	46	(	(	PUNCT
ejpam-5718	242	47	x	x	NOUN
ejpam-5718	242	48	,	,	PUNCT
ejpam-5718	242	49	τ1	τ1	NOUN
ejpam-5718	242	50	,	,	PUNCT
ejpam-5718	242	51	τ2	τ2	NOUN
ejpam-5718	242	52	)	)	PUNCT
ejpam-5718	242	53	is	be	AUX
ejpam-5718	242	54	τ1τ2	τ1τ2	NOUN
ejpam-5718	242	55	-	-	ADJ
ejpam-5718	242	56	connected	connected	ADJ
ejpam-5718	242	57	,	,	PUNCT
ejpam-5718	242	58	then	then	ADV
ejpam-5718	242	59	(	(	PUNCT
ejpam-5718	242	60	y	y	PROPN
ejpam-5718	242	61	,	,	PUNCT
ejpam-5718	242	62	σ1	σ1	PROPN
ejpam-5718	242	63	,	,	PUNCT
ejpam-5718	242	64	σ2	σ2	PROPN
ejpam-5718	242	65	)	)	PUNCT
ejpam-5718	242	66	is	be	AUX
ejpam-5718	242	67	s	s	NOUN
ejpam-5718	242	68	-	-	PUNCT
ejpam-5718	242	69	σ1σ2	σ1σ2	VERB
ejpam-5718	242	70	-	-	PUNCT
ejpam-5718	242	71	connected	connect	VERB
ejpam-5718	242	72	.	.	PUNCT
ejpam-5718	243	1	proof	proof	NOUN
ejpam-5718	243	2	.	.	PUNCT
ejpam-5718	244	1	suppose	suppose	VERB
ejpam-5718	244	2	that	that	SCONJ
ejpam-5718	244	3	(	(	PUNCT
ejpam-5718	244	4	y	y	PROPN
ejpam-5718	244	5	,	,	PUNCT
ejpam-5718	244	6	σ1	σ1	PROPN
ejpam-5718	244	7	,	,	PUNCT
ejpam-5718	244	8	σ2	σ2	PROPN
ejpam-5718	244	9	)	)	PUNCT
ejpam-5718	244	10	is	be	AUX
ejpam-5718	244	11	not	not	PART
ejpam-5718	244	12	σ1σ2	σ1σ2	VERB
ejpam-5718	244	13	-	-	PUNCT
ejpam-5718	244	14	connected	connect	VERB
ejpam-5718	244	15	.	.	PUNCT
ejpam-5718	245	1	there	there	PRON
ejpam-5718	245	2	exist	exist	VERB
ejpam-5718	245	3	nonempty	nonempty	ADJ
ejpam-5718	245	4	σ1σ2open	σ1σ2open	PUNCT
ejpam-5718	245	5	sets	set	VERB
ejpam-5718	245	6	u	u	NOUN
ejpam-5718	245	7	and	and	CCONJ
ejpam-5718	245	8	v	v	NOUN
ejpam-5718	245	9	of	of	ADP
ejpam-5718	245	10	y	y	PROPN
ejpam-5718	245	11	having	have	VERB
ejpam-5718	245	12	σ1σ2	σ1σ2	ADV
ejpam-5718	245	13	-	-	PUNCT
ejpam-5718	245	14	connected	connected	ADJ
ejpam-5718	245	15	complement	complement	NOUN
ejpam-5718	245	16	such	such	ADJ
ejpam-5718	245	17	that	that	SCONJ
ejpam-5718	245	18	u	u	PROPN
ejpam-5718	245	19	∩	∩	NOUN
ejpam-5718	245	20	v	v	NOUN
ejpam-5718	245	21	=	=	NOUN
ejpam-5718	245	22	∅	∅	NOUN
ejpam-5718	245	23	and	and	CCONJ
ejpam-5718	245	24	u	u	NOUN
ejpam-5718	245	25	∪	∪	NOUN
ejpam-5718	245	26	v	v	ADP
ejpam-5718	245	27	=	=	SYM
ejpam-5718	245	28	y	y	PROPN
ejpam-5718	245	29	.	.	PUNCT
ejpam-5718	246	1	since	since	SCONJ
ejpam-5718	246	2	f	f	PROPN
ejpam-5718	246	3	(	(	PUNCT
ejpam-5718	246	4	x	x	X
ejpam-5718	246	5	)	)	PUNCT
ejpam-5718	246	6	is	be	AUX
ejpam-5718	246	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	246	8	-	-	PUNCT
ejpam-5718	246	9	connected	connected	ADJ
ejpam-5718	246	10	for	for	ADP
ejpam-5718	246	11	each	each	DET
ejpam-5718	246	12	x	x	SYM
ejpam-5718	246	13	∈	∈	PROPN
ejpam-5718	246	14	x	x	NOUN
ejpam-5718	246	15	,	,	PUNCT
ejpam-5718	246	16	either	either	CCONJ
ejpam-5718	246	17	f	f	PROPN
ejpam-5718	246	18	(	(	PUNCT
ejpam-5718	246	19	x	x	X
ejpam-5718	246	20	)	)	PUNCT
ejpam-5718	246	21	⊆	⊆	NUM
ejpam-5718	246	22	u	u	NOUN
ejpam-5718	246	23	or	or	CCONJ
ejpam-5718	246	24	f	f	PROPN
ejpam-5718	246	25	(	(	PUNCT
ejpam-5718	246	26	x	x	NOUN
ejpam-5718	246	27	)	)	PUNCT
ejpam-5718	246	28	⊆	⊆	NUM
ejpam-5718	246	29	v	v	NOUN
ejpam-5718	246	30	.	.	PUNCT
ejpam-5718	247	1	if	if	SCONJ
ejpam-5718	247	2	x	x	SYM
ejpam-5718	247	3	∈	∈	PROPN
ejpam-5718	247	4	f+(u∪v	f+(u∪v	PROPN
ejpam-5718	247	5	)	)	PUNCT
ejpam-5718	247	6	,	,	PUNCT
ejpam-5718	247	7	then	then	ADV
ejpam-5718	247	8	f	f	X
ejpam-5718	247	9	(	(	PUNCT
ejpam-5718	247	10	x	x	X
ejpam-5718	247	11	)	)	PUNCT
ejpam-5718	247	12	⊆	⊆	NUM
ejpam-5718	247	13	u∪v	u∪v	NOUN
ejpam-5718	247	14	and	and	CCONJ
ejpam-5718	247	15	hence	hence	ADV
ejpam-5718	247	16	x	x	PART
ejpam-5718	247	17	∈	∈	NOUN
ejpam-5718	247	18	f+(u)∪f+(v	f+(u)∪f+(v	NOUN
ejpam-5718	247	19	)	)	PUNCT
ejpam-5718	247	20	.	.	PUNCT
ejpam-5718	248	1	moreover	moreover	ADV
ejpam-5718	248	2	,	,	PUNCT
ejpam-5718	248	3	since	since	SCONJ
ejpam-5718	248	4	f	f	PROPN
ejpam-5718	248	5	is	be	AUX
ejpam-5718	248	6	surjective	surjective	ADJ
ejpam-5718	248	7	,	,	PUNCT
ejpam-5718	248	8	there	there	PRON
ejpam-5718	248	9	exist	exist	VERB
ejpam-5718	248	10	x	x	PUNCT
ejpam-5718	248	11	and	and	CCONJ
ejpam-5718	248	12	y	y	PROPN
ejpam-5718	248	13	in	in	ADP
ejpam-5718	248	14	x	x	PUNCT
ejpam-5718	248	15	such	such	ADJ
ejpam-5718	248	16	that	that	SCONJ
ejpam-5718	248	17	f	f	PROPN
ejpam-5718	248	18	(	(	PUNCT
ejpam-5718	248	19	x	x	X
ejpam-5718	248	20	)	)	PUNCT
ejpam-5718	248	21	⊆	⊆	NUM
ejpam-5718	248	22	u	u	NOUN
ejpam-5718	248	23	and	and	CCONJ
ejpam-5718	248	24	f	f	PROPN
ejpam-5718	248	25	(	(	PUNCT
ejpam-5718	248	26	y	y	PROPN
ejpam-5718	248	27	)	)	PUNCT
ejpam-5718	248	28	⊆	⊆	NUM
ejpam-5718	248	29	v	v	NOUN
ejpam-5718	248	30	;	;	PUNCT
ejpam-5718	248	31	hence	hence	ADV
ejpam-5718	248	32	x	x	SYM
ejpam-5718	248	33	∈	∈	PROPN
ejpam-5718	248	34	f+(u	f+(u	NUM
ejpam-5718	248	35	)	)	PUNCT
ejpam-5718	248	36	and	and	CCONJ
ejpam-5718	248	37	y	y	PROPN
ejpam-5718	248	38	∈	∈	PROPN
ejpam-5718	248	39	f+(v	f+(v	PROPN
ejpam-5718	248	40	)	)	PUNCT
ejpam-5718	248	41	.	.	PUNCT
ejpam-5718	249	1	therefore	therefore	ADV
ejpam-5718	249	2	,	,	PUNCT
ejpam-5718	249	3	we	we	PRON
ejpam-5718	249	4	obtain	obtain	VERB
ejpam-5718	249	5	the	the	DET
ejpam-5718	249	6	following	following	NOUN
ejpam-5718	249	7	:	:	PUNCT
ejpam-5718	249	8	(	(	PUNCT
ejpam-5718	249	9	1	1	X
ejpam-5718	249	10	)	)	PUNCT
ejpam-5718	249	11	f+(u	f+(u	NUM
ejpam-5718	249	12	)	)	PUNCT
ejpam-5718	249	13	∪	∪	ADP
ejpam-5718	249	14	f+(v	f+(v	NOUN
ejpam-5718	249	15	)	)	PUNCT
ejpam-5718	250	1	=	=	PUNCT
ejpam-5718	251	1	f+(u	f+(u	PUNCT
ejpam-5718	251	2	∪	∪	ADP
ejpam-5718	251	3	v	v	NOUN
ejpam-5718	251	4	)	)	PUNCT
ejpam-5718	251	5	=	=	SYM
ejpam-5718	252	1	x	x	X
ejpam-5718	252	2	;	;	PUNCT
ejpam-5718	252	3	(	(	PUNCT
ejpam-5718	252	4	2	2	X
ejpam-5718	252	5	)	)	PUNCT
ejpam-5718	252	6	f+(u	f+(u	NUM
ejpam-5718	252	7	)	)	PUNCT
ejpam-5718	252	8	∩	∩	NOUN
ejpam-5718	252	9	f+(v	f+(v	NOUN
ejpam-5718	252	10	)	)	PUNCT
ejpam-5718	252	11	=	=	SYM
ejpam-5718	253	1	f+(u	f+(u	NUM
ejpam-5718	253	2	∩	∩	NOUN
ejpam-5718	253	3	v	v	NOUN
ejpam-5718	253	4	)	)	PUNCT
ejpam-5718	253	5	=	=	NOUN
ejpam-5718	253	6	∅	∅	NOUN
ejpam-5718	253	7	;	;	PUNCT
ejpam-5718	253	8	(	(	PUNCT
ejpam-5718	253	9	3	3	X
ejpam-5718	253	10	)	)	PUNCT
ejpam-5718	253	11	f+(u	f+(u	NUM
ejpam-5718	253	12	)	)	PUNCT
ejpam-5718	253	13	̸=	̸=	PROPN
ejpam-5718	253	14	∅	∅	NOUN
ejpam-5718	253	15	and	and	CCONJ
ejpam-5718	253	16	f+(v	f+(v	NUM
ejpam-5718	253	17	)	)	PUNCT
ejpam-5718	254	1	̸=	̸=	PROPN
ejpam-5718	254	2	∅.	∅.	ADP
ejpam-5718	254	3	p.	p.	NOUN
ejpam-5718	254	4	pue	pue	NOUN
ejpam-5718	254	5	-	-	PUNCT
ejpam-5718	254	6	on	on	ADP
ejpam-5718	254	7	,	,	PUNCT
ejpam-5718	254	8	a.	a.	PROPN
ejpam-5718	254	9	sama	sama	PROPN
ejpam-5718	254	10	-	-	PUNCT
ejpam-5718	254	11	ae	ae	PROPN
ejpam-5718	254	12	,	,	PUNCT
ejpam-5718	254	13	c.	c.	PROPN
ejpam-5718	254	14	boonpok	boonpok	PROPN
ejpam-5718	254	15	/	/	SYM
ejpam-5718	254	16	eur	eur	PROPN
ejpam-5718	254	17	.	.	PUNCT
ejpam-5718	255	1	j.	j.	PROPN
ejpam-5718	255	2	pure	pure	PROPN
ejpam-5718	255	3	appl	appl	PROPN
ejpam-5718	255	4	.	.	PROPN
ejpam-5718	255	5	math	math	PROPN
ejpam-5718	255	6	,	,	PUNCT
ejpam-5718	255	7	18	18	NUM
ejpam-5718	255	8	(	(	PUNCT
ejpam-5718	255	9	1	1	NUM
ejpam-5718	255	10	)	)	PUNCT
ejpam-5718	255	11	(	(	PUNCT
ejpam-5718	255	12	2025	2025	NUM
ejpam-5718	255	13	)	)	PUNCT
ejpam-5718	255	14	,	,	PUNCT
ejpam-5718	255	15	5718	5718	NUM
ejpam-5718	255	16	10	10	NUM
ejpam-5718	255	17	of	of	ADP
ejpam-5718	255	18	16	16	NUM
ejpam-5718	255	19	next	next	ADV
ejpam-5718	256	1	,	,	PUNCT
ejpam-5718	256	2	we	we	PRON
ejpam-5718	256	3	shall	shall	AUX
ejpam-5718	256	4	show	show	VERB
ejpam-5718	256	5	that	that	PRON
ejpam-5718	256	6	f+(u	f+(u	NUM
ejpam-5718	256	7	)	)	PUNCT
ejpam-5718	256	8	and	and	CCONJ
ejpam-5718	256	9	f+(v	f+(v	NUM
ejpam-5718	256	10	)	)	PUNCT
ejpam-5718	256	11	are	be	AUX
ejpam-5718	256	12	τ1τ2	τ1τ2	NOUN
ejpam-5718	256	13	-	-	ADJ
ejpam-5718	256	14	open	open	ADJ
ejpam-5718	256	15	in	in	ADP
ejpam-5718	256	16	x.	x.	PROPN
ejpam-5718	256	17	(	(	PUNCT
ejpam-5718	256	18	i	i	NOUN
ejpam-5718	256	19	)	)	PUNCT
ejpam-5718	256	20	let	let	VERB
ejpam-5718	256	21	f	f	PRON
ejpam-5718	256	22	be	be	AUX
ejpam-5718	256	23	upper	upper	ADJ
ejpam-5718	256	24	weakly	weakly	ADJ
ejpam-5718	256	25	s-(τ1	s-(τ1	PROPN
ejpam-5718	256	26	,	,	PUNCT
ejpam-5718	256	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	256	28	.	.	PUNCT
ejpam-5718	257	1	by	by	ADP
ejpam-5718	257	2	theorem	theorem	NOUN
ejpam-5718	257	3	1	1	NUM
ejpam-5718	257	4	,	,	PUNCT
ejpam-5718	257	5	f+(v	f+(v	PROPN
ejpam-5718	257	6	)	)	PUNCT
ejpam-5718	257	7	⊆	⊆	X
ejpam-5718	257	8	τ1τ2	τ1τ2	NOUN
ejpam-5718	257	9	-	-	NUM
ejpam-5718	257	10	int(f	int(f	VERB
ejpam-5718	257	11	+	+	ADJ
ejpam-5718	257	12	(	(	PUNCT
ejpam-5718	257	13	σ1σ2	σ1σ2	NOUN
ejpam-5718	257	14	-	-	NUM
ejpam-5718	257	15	cl(v	cl(v	NOUN
ejpam-5718	257	16	)	)	PUNCT
ejpam-5718	257	17	)	)	PUNCT
ejpam-5718	257	18	)	)	PUNCT
ejpam-5718	258	1	=	=	PUNCT
ejpam-5718	258	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	258	3	-	-	NUM
ejpam-5718	258	4	int(f	int(f	VERB
ejpam-5718	258	5	+	+	ADJ
ejpam-5718	258	6	(	(	PUNCT
ejpam-5718	258	7	v	v	NOUN
ejpam-5718	258	8	)	)	PUNCT
ejpam-5718	258	9	)	)	PUNCT
ejpam-5718	258	10	since	since	SCONJ
ejpam-5718	258	11	v	v	NUM
ejpam-5718	258	12	is	be	AUX
ejpam-5718	258	13	σ1σ2	σ1σ2	NOUN
ejpam-5718	258	14	-	-	PUNCT
ejpam-5718	258	15	clopen	clopen	ADJ
ejpam-5718	258	16	.	.	PUNCT
ejpam-5718	259	1	thus	thus	ADV
ejpam-5718	259	2	,	,	PUNCT
ejpam-5718	259	3	f+(v	f+(v	PROPN
ejpam-5718	259	4	)	)	PUNCT
ejpam-5718	260	1	=	=	PUNCT
ejpam-5718	260	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	260	3	-	-	NUM
ejpam-5718	260	4	int(f	int(f	VERB
ejpam-5718	260	5	+	+	ADJ
ejpam-5718	260	6	(	(	PUNCT
ejpam-5718	260	7	v	v	NOUN
ejpam-5718	260	8	)	)	PUNCT
ejpam-5718	260	9	)	)	PUNCT
ejpam-5718	260	10	and	and	CCONJ
ejpam-5718	260	11	hence	hence	ADV
ejpam-5718	260	12	f+(v	f+(v	PROPN
ejpam-5718	260	13	)	)	PUNCT
ejpam-5718	260	14	is	be	AUX
ejpam-5718	260	15	τ1τ2	τ1τ2	NOUN
ejpam-5718	260	16	-	-	ADJ
ejpam-5718	260	17	open	open	ADJ
ejpam-5718	260	18	in	in	ADP
ejpam-5718	260	19	x.	x.	NOUN
ejpam-5718	260	20	similarly	similarly	ADV
ejpam-5718	260	21	,	,	PUNCT
ejpam-5718	260	22	we	we	PRON
ejpam-5718	260	23	obtain	obtain	VERB
ejpam-5718	260	24	f+(u	f+(u	PUNCT
ejpam-5718	260	25	)	)	PUNCT
ejpam-5718	260	26	is	be	AUX
ejpam-5718	260	27	τ1τ2	τ1τ2	NOUN
ejpam-5718	260	28	-	-	ADJ
ejpam-5718	260	29	open	open	ADJ
ejpam-5718	260	30	in	in	ADP
ejpam-5718	260	31	x.	x.	NOUN
ejpam-5718	260	32	this	this	PRON
ejpam-5718	260	33	shows	show	VERB
ejpam-5718	260	34	that	that	SCONJ
ejpam-5718	260	35	(	(	PUNCT
ejpam-5718	260	36	x	x	NOUN
ejpam-5718	260	37	,	,	PUNCT
ejpam-5718	260	38	τ1	τ1	NOUN
ejpam-5718	260	39	,	,	PUNCT
ejpam-5718	260	40	τ2	τ2	NOUN
ejpam-5718	260	41	)	)	PUNCT
ejpam-5718	260	42	is	be	AUX
ejpam-5718	260	43	not	not	PART
ejpam-5718	260	44	τ1τ2	τ1τ2	ADJ
ejpam-5718	260	45	-	-	VERB
ejpam-5718	260	46	connected	connected	ADJ
ejpam-5718	260	47	.	.	PUNCT
ejpam-5718	261	1	(	(	PUNCT
ejpam-5718	261	2	ii	ii	NOUN
ejpam-5718	261	3	)	)	PUNCT
ejpam-5718	261	4	let	let	VERB
ejpam-5718	261	5	f	f	PRON
ejpam-5718	261	6	be	be	AUX
ejpam-5718	261	7	lower	low	ADJ
ejpam-5718	261	8	weakly	weakly	ADJ
ejpam-5718	261	9	s-(τ1	s-(τ1	PROPN
ejpam-5718	261	10	,	,	PUNCT
ejpam-5718	261	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	261	12	.	.	PUNCT
ejpam-5718	262	1	since	since	SCONJ
ejpam-5718	262	2	v	v	NOUN
ejpam-5718	262	3	is	be	AUX
ejpam-5718	262	4	a	a	DET
ejpam-5718	262	5	σ1σ2	σ1σ2	NUM
ejpam-5718	262	6	-	-	PUNCT
ejpam-5718	262	7	clopen	clopen	ADJ
ejpam-5718	262	8	set	set	NOUN
ejpam-5718	262	9	with	with	ADP
ejpam-5718	262	10	σ1σ2	σ1σ2	ADV
ejpam-5718	262	11	-	-	PUNCT
ejpam-5718	262	12	connected	connect	VERB
ejpam-5718	262	13	complement	complement	NOUN
ejpam-5718	262	14	,	,	PUNCT
ejpam-5718	262	15	by	by	ADP
ejpam-5718	262	16	theorem	theorem	NOUN
ejpam-5718	262	17	2	2	NUM
ejpam-5718	262	18	τ1τ2	τ1τ2	NOUN
ejpam-5718	262	19	-	-	NOUN
ejpam-5718	262	20	cl(f	cl(f	NOUN
ejpam-5718	262	21	+	+	NOUN
ejpam-5718	262	22	(	(	PUNCT
ejpam-5718	262	23	v	v	NOUN
ejpam-5718	262	24	)	)	PUNCT
ejpam-5718	262	25	)	)	PUNCT
ejpam-5718	263	1	⊆	⊆	NUM
ejpam-5718	263	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	263	3	-	-	PUNCT
ejpam-5718	263	4	cl(v	cl(v	NOUN
ejpam-5718	263	5	)	)	PUNCT
ejpam-5718	263	6	)	)	PUNCT
ejpam-5718	263	7	=	=	PUNCT
ejpam-5718	263	8	f+(v	f+(v	NOUN
ejpam-5718	263	9	)	)	PUNCT
ejpam-5718	263	10	.	.	PUNCT
ejpam-5718	264	1	thus	thus	ADV
ejpam-5718	264	2	,	,	PUNCT
ejpam-5718	264	3	f+(v	f+(v	PROPN
ejpam-5718	264	4	)	)	PUNCT
ejpam-5718	265	1	=	=	PUNCT
ejpam-5718	265	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	265	3	-	-	NOUN
ejpam-5718	265	4	cl(f	cl(f	NOUN
ejpam-5718	265	5	+	+	NOUN
ejpam-5718	265	6	(	(	PUNCT
ejpam-5718	265	7	v	v	NOUN
ejpam-5718	265	8	)	)	PUNCT
ejpam-5718	265	9	)	)	PUNCT
ejpam-5718	265	10	and	and	CCONJ
ejpam-5718	265	11	hence	hence	ADV
ejpam-5718	265	12	f+(v	f+(v	PROPN
ejpam-5718	265	13	)	)	PUNCT
ejpam-5718	265	14	is	be	AUX
ejpam-5718	265	15	τ1τ2	τ1τ2	NOUN
ejpam-5718	265	16	-	-	ADJ
ejpam-5718	265	17	closed	closed	ADJ
ejpam-5718	265	18	in	in	ADP
ejpam-5718	265	19	x.	x.	NOUN
ejpam-5718	265	20	therefore	therefore	ADV
ejpam-5718	265	21	,	,	PUNCT
ejpam-5718	265	22	f+(u	f+(u	NUM
ejpam-5718	265	23	)	)	PUNCT
ejpam-5718	265	24	is	be	AUX
ejpam-5718	265	25	τ1τ2	τ1τ2	NOUN
ejpam-5718	265	26	-	-	ADJ
ejpam-5718	265	27	open	open	ADJ
ejpam-5718	265	28	in	in	ADP
ejpam-5718	265	29	x.	x.	NOUN
ejpam-5718	265	30	similarly	similarly	ADV
ejpam-5718	265	31	,	,	PUNCT
ejpam-5718	265	32	we	we	PRON
ejpam-5718	265	33	obtain	obtain	VERB
ejpam-5718	265	34	f+(v	f+(v	NOUN
ejpam-5718	265	35	)	)	PUNCT
ejpam-5718	265	36	is	be	AUX
ejpam-5718	265	37	τ1τ2	τ1τ2	NOUN
ejpam-5718	265	38	-	-	ADJ
ejpam-5718	265	39	open	open	ADJ
ejpam-5718	265	40	in	in	ADP
ejpam-5718	265	41	x.	x.	NOUN
ejpam-5718	265	42	consequently	consequently	ADV
ejpam-5718	265	43	,	,	PUNCT
ejpam-5718	265	44	this	this	PRON
ejpam-5718	265	45	shows	show	VERB
ejpam-5718	265	46	that	that	SCONJ
ejpam-5718	265	47	(	(	PUNCT
ejpam-5718	265	48	x	x	NOUN
ejpam-5718	265	49	,	,	PUNCT
ejpam-5718	265	50	τ1	τ1	NOUN
ejpam-5718	265	51	,	,	PUNCT
ejpam-5718	265	52	τ2	τ2	NOUN
ejpam-5718	265	53	)	)	PUNCT
ejpam-5718	265	54	is	be	AUX
ejpam-5718	265	55	not	not	PART
ejpam-5718	265	56	τ1τ2	τ1τ2	ADJ
ejpam-5718	265	57	-	-	VERB
ejpam-5718	265	58	connected	connected	ADJ
ejpam-5718	265	59	.	.	PUNCT
ejpam-5718	266	1	this	this	PRON
ejpam-5718	266	2	completes	complete	VERB
ejpam-5718	266	3	the	the	DET
ejpam-5718	266	4	proof	proof	NOUN
ejpam-5718	266	5	.	.	PUNCT
ejpam-5718	267	1	the	the	DET
ejpam-5718	267	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	267	3	-	-	NOUN
ejpam-5718	267	4	frontier	frontier	NOUN
ejpam-5718	267	5	[	[	X
ejpam-5718	267	6	26	26	NUM
ejpam-5718	267	7	]	]	PUNCT
ejpam-5718	267	8	of	of	ADP
ejpam-5718	267	9	a	a	DET
ejpam-5718	267	10	subset	subset	NOUN
ejpam-5718	267	11	a	a	PRON
ejpam-5718	267	12	of	of	ADP
ejpam-5718	267	13	a	a	DET
ejpam-5718	267	14	bitopological	bitopological	ADJ
ejpam-5718	267	15	space	space	NOUN
ejpam-5718	267	16	(	(	PUNCT
ejpam-5718	267	17	x	x	NOUN
ejpam-5718	267	18	,	,	PUNCT
ejpam-5718	267	19	τ1	τ1	NOUN
ejpam-5718	267	20	,	,	PUNCT
ejpam-5718	267	21	τ2	τ2	PROPN
ejpam-5718	267	22	)	)	PUNCT
ejpam-5718	267	23	,	,	PUNCT
ejpam-5718	267	24	denoted	denote	VERB
ejpam-5718	267	25	by	by	ADP
ejpam-5718	267	26	τ1τ2	τ1τ2	NOUN
ejpam-5718	267	27	-	-	ADJ
ejpam-5718	267	28	fr(a	fr(a	NUM
ejpam-5718	267	29	)	)	PUNCT
ejpam-5718	267	30	,	,	PUNCT
ejpam-5718	267	31	is	be	AUX
ejpam-5718	267	32	defined	define	VERB
ejpam-5718	267	33	by	by	ADP
ejpam-5718	267	34	τ1τ2	τ1τ2	NOUN
ejpam-5718	267	35	-	-	ADJ
ejpam-5718	267	36	fr(a	fr(a	ADJ
ejpam-5718	267	37	)	)	PUNCT
ejpam-5718	268	1	=	=	PUNCT
ejpam-5718	268	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	268	3	-	-	ADJ
ejpam-5718	268	4	cl(a)∩τ1τ2	cl(a)∩τ1τ2	NOUN
ejpam-5718	268	5	-	-	PUNCT
ejpam-5718	268	6	cl(x−a	cl(x−a	NOUN
ejpam-5718	268	7	)	)	PUNCT
ejpam-5718	268	8	=	=	PUNCT
ejpam-5718	269	1	τ1τ2	τ1τ2	NOUN
ejpam-5718	269	2	-	-	ADJ
ejpam-5718	269	3	cl(a)−τ1τ2	cl(a)−τ1τ2	ADJ
ejpam-5718	269	4	-	-	PUNCT
ejpam-5718	269	5	int(a	int(a	NOUN
ejpam-5718	269	6	)	)	PUNCT
ejpam-5718	269	7	.	.	PUNCT
ejpam-5718	270	1	theorem	theorem	ADJ
ejpam-5718	270	2	10	10	NUM
ejpam-5718	270	3	.	.	PUNCT
ejpam-5718	271	1	the	the	DET
ejpam-5718	271	2	set	set	NOUN
ejpam-5718	271	3	of	of	ADP
ejpam-5718	271	4	all	all	DET
ejpam-5718	271	5	points	point	NOUN
ejpam-5718	271	6	x	x	X
ejpam-5718	271	7	∈	∈	NOUN
ejpam-5718	271	8	x	x	PUNCT
ejpam-5718	271	9	at	at	ADP
ejpam-5718	271	10	which	which	PRON
ejpam-5718	271	11	a	a	DET
ejpam-5718	271	12	multifunction	multifunction	NOUN
ejpam-5718	271	13	f	f	NOUN
ejpam-5718	271	14	:	:	PUNCT
ejpam-5718	271	15	(	(	PUNCT
ejpam-5718	271	16	x	x	NOUN
ejpam-5718	271	17	,	,	PUNCT
ejpam-5718	271	18	τ1	τ1	NOUN
ejpam-5718	271	19	,	,	PUNCT
ejpam-5718	271	20	τ2	τ2	NOUN
ejpam-5718	271	21	)	)	PUNCT
ejpam-5718	271	22	→	→	SYM
ejpam-5718	271	23	(	(	PUNCT
ejpam-5718	271	24	y	y	PROPN
ejpam-5718	271	25	,	,	PUNCT
ejpam-5718	271	26	σ1	σ1	PROPN
ejpam-5718	271	27	,	,	PUNCT
ejpam-5718	271	28	σ2	σ2	PROPN
ejpam-5718	271	29	)	)	PUNCT
ejpam-5718	271	30	is	be	AUX
ejpam-5718	271	31	not	not	PART
ejpam-5718	271	32	upper	upper	ADJ
ejpam-5718	271	33	weakly	weakly	ADJ
ejpam-5718	271	34	s-(τ1	s-(τ1	PROPN
ejpam-5718	271	35	,	,	PUNCT
ejpam-5718	271	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	271	37	is	be	AUX
ejpam-5718	271	38	identical	identical	ADJ
ejpam-5718	271	39	with	with	ADP
ejpam-5718	271	40	the	the	DET
ejpam-5718	271	41	union	union	NOUN
ejpam-5718	271	42	of	of	ADP
ejpam-5718	271	43	the	the	DET
ejpam-5718	271	44	τ1τ2	τ1τ2	NOUN
ejpam-5718	271	45	-	-	NOUN
ejpam-5718	271	46	frontier	frontier	NOUN
ejpam-5718	271	47	of	of	ADP
ejpam-5718	271	48	the	the	DET
ejpam-5718	271	49	upper	upper	ADJ
ejpam-5718	271	50	inverse	inverse	NOUN
ejpam-5718	271	51	images	image	NOUN
ejpam-5718	271	52	of	of	ADP
ejpam-5718	271	53	the	the	DET
ejpam-5718	271	54	σ1σ2	σ1σ2	NOUN
ejpam-5718	271	55	-	-	NOUN
ejpam-5718	271	56	closure	closure	NOUN
ejpam-5718	271	57	of	of	ADP
ejpam-5718	271	58	σ1σ2	σ1σ2	NOUN
ejpam-5718	271	59	-	-	PUNCT
ejpam-5718	271	60	open	open	ADJ
ejpam-5718	271	61	sets	set	NOUN
ejpam-5718	271	62	containing	contain	VERB
ejpam-5718	271	63	f	f	X
ejpam-5718	271	64	(	(	PUNCT
ejpam-5718	271	65	x	x	NOUN
ejpam-5718	271	66	)	)	PUNCT
ejpam-5718	271	67	and	and	CCONJ
ejpam-5718	271	68	having	have	VERB
ejpam-5718	271	69	σ1σ2	σ1σ2	NOUN
ejpam-5718	271	70	-	-	PUNCT
ejpam-5718	271	71	connected	connect	VERB
ejpam-5718	271	72	complement	complement	NOUN
ejpam-5718	271	73	.	.	PUNCT
ejpam-5718	272	1	proof	proof	NOUN
ejpam-5718	272	2	.	.	PUNCT
ejpam-5718	273	1	let	let	VERB
ejpam-5718	273	2	x	x	PRON
ejpam-5718	273	3	be	be	AUX
ejpam-5718	273	4	a	a	DET
ejpam-5718	273	5	point	point	NOUN
ejpam-5718	273	6	of	of	ADP
ejpam-5718	273	7	x	x	PUNCT
ejpam-5718	273	8	at	at	ADP
ejpam-5718	273	9	which	which	PRON
ejpam-5718	273	10	f	f	NOUN
ejpam-5718	273	11	is	be	AUX
ejpam-5718	273	12	not	not	PART
ejpam-5718	273	13	upper	upper	ADJ
ejpam-5718	273	14	weakly	weakly	ADJ
ejpam-5718	273	15	s-(τ1	s-(τ1	PROPN
ejpam-5718	273	16	,	,	PUNCT
ejpam-5718	273	17	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5718	273	18	.	.	PUNCT
ejpam-5718	274	1	then	then	ADV
ejpam-5718	274	2	,	,	PUNCT
ejpam-5718	274	3	there	there	PRON
ejpam-5718	274	4	exists	exist	VERB
ejpam-5718	274	5	a	a	DET
ejpam-5718	274	6	σ1σ2	σ1σ2	NUM
ejpam-5718	274	7	-	-	ADJ
ejpam-5718	274	8	open	open	ADJ
ejpam-5718	274	9	set	set	NOUN
ejpam-5718	274	10	v	v	NOUN
ejpam-5718	274	11	of	of	ADP
ejpam-5718	274	12	y	y	PROPN
ejpam-5718	274	13	containing	contain	VERB
ejpam-5718	274	14	f	f	PROPN
ejpam-5718	274	15	(	(	PUNCT
ejpam-5718	274	16	x	x	NOUN
ejpam-5718	274	17	)	)	PUNCT
ejpam-5718	274	18	and	and	CCONJ
ejpam-5718	274	19	having	have	VERB
ejpam-5718	274	20	σ1σ2	σ1σ2	NOUN
ejpam-5718	274	21	-	-	PUNCT
ejpam-5718	274	22	connected	connected	ADJ
ejpam-5718	274	23	complement	complement	NOUN
ejpam-5718	274	24	such	such	ADJ
ejpam-5718	274	25	that	that	SCONJ
ejpam-5718	274	26	u	u	PROPN
ejpam-5718	274	27	∩	∩	NOUN
ejpam-5718	274	28	(	(	PUNCT
ejpam-5718	274	29	x	x	SYM
ejpam-5718	274	30	−	−	PRON
ejpam-5718	274	31	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	274	32	-	-	PUNCT
ejpam-5718	274	33	cl(v	cl(v	NOUN
ejpam-5718	274	34	)	)	PUNCT
ejpam-5718	274	35	)	)	PUNCT
ejpam-5718	274	36	)	)	PUNCT
ejpam-5718	275	1	̸=	̸=	NOUN
ejpam-5718	275	2	∅	∅	NOUN
ejpam-5718	275	3	for	for	ADP
ejpam-5718	275	4	every	every	DET
ejpam-5718	275	5	τ1τ2	τ1τ2	ADJ
ejpam-5718	275	6	-	-	ADJ
ejpam-5718	275	7	open	open	ADJ
ejpam-5718	275	8	set	set	ADJ
ejpam-5718	275	9	u	u	NOUN
ejpam-5718	275	10	of	of	ADP
ejpam-5718	275	11	x	x	SYM
ejpam-5718	275	12	containing	contain	VERB
ejpam-5718	275	13	x.	x.	NOUN
ejpam-5718	275	14	then	then	ADV
ejpam-5718	275	15	,	,	PUNCT
ejpam-5718	275	16	we	we	PRON
ejpam-5718	275	17	have	have	VERB
ejpam-5718	275	18	x	x	PART
ejpam-5718	275	19	∈	∈	PROPN
ejpam-5718	275	20	τ1τ2	τ1τ2	NOUN
ejpam-5718	275	21	-	-	NOUN
ejpam-5718	275	22	cl(x	cl(x	SYM
ejpam-5718	275	23	−	−	ADP
ejpam-5718	275	24	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	275	25	-	-	PUNCT
ejpam-5718	275	26	cl(v	cl(v	NOUN
ejpam-5718	275	27	)	)	PUNCT
ejpam-5718	275	28	)	)	PUNCT
ejpam-5718	275	29	)	)	PUNCT
ejpam-5718	276	1	and	and	CCONJ
ejpam-5718	276	2	hence	hence	ADV
ejpam-5718	276	3	x	x	X
ejpam-5718	276	4	∈	∈	PRON
ejpam-5718	276	5	τ1τ2	τ1τ2	NOUN
ejpam-5718	276	6	-	-	ADJ
ejpam-5718	276	7	fr(f	fr(f	PUNCT
ejpam-5718	276	8	+	+	ADJ
ejpam-5718	276	9	(	(	PUNCT
ejpam-5718	276	10	σ1σ2	σ1σ2	NOUN
ejpam-5718	276	11	-	-	NUM
ejpam-5718	276	12	cl(v	cl(v	NOUN
ejpam-5718	276	13	)	)	PUNCT
ejpam-5718	276	14	)	)	PUNCT
ejpam-5718	276	15	)	)	PUNCT
ejpam-5718	277	1	since	since	SCONJ
ejpam-5718	277	2	x	x	PROPN
ejpam-5718	277	3	∈	∈	PROPN
ejpam-5718	277	4	f+(v	f+(v	NOUN
ejpam-5718	277	5	)	)	PUNCT
ejpam-5718	277	6	⊆	⊆	X
ejpam-5718	277	7	τ1τ2	τ1τ2	NOUN
ejpam-5718	277	8	-	-	NOUN
ejpam-5718	277	9	cl(f	cl(f	NOUN
ejpam-5718	277	10	+	+	NOUN
ejpam-5718	277	11	(	(	PUNCT
ejpam-5718	277	12	σ1σ2	σ1σ2	NOUN
ejpam-5718	277	13	-	-	NUM
ejpam-5718	277	14	cl(v	cl(v	NOUN
ejpam-5718	277	15	)	)	PUNCT
ejpam-5718	277	16	)	)	PUNCT
ejpam-5718	277	17	)	)	PUNCT
ejpam-5718	277	18	.	.	PUNCT
ejpam-5718	278	1	conversely	conversely	ADV
ejpam-5718	278	2	,	,	PUNCT
ejpam-5718	278	3	suppose	suppose	VERB
ejpam-5718	278	4	that	that	SCONJ
ejpam-5718	278	5	v	v	NOUN
ejpam-5718	278	6	is	be	AUX
ejpam-5718	278	7	a	a	DET
ejpam-5718	278	8	σ1σ2	σ1σ2	NOUN
ejpam-5718	278	9	-	-	ADJ
ejpam-5718	278	10	open	open	ADJ
ejpam-5718	278	11	set	set	NOUN
ejpam-5718	278	12	of	of	ADP
ejpam-5718	278	13	y	y	PROPN
ejpam-5718	278	14	containing	contain	VERB
ejpam-5718	278	15	f	f	PROPN
ejpam-5718	278	16	(	(	PUNCT
ejpam-5718	278	17	x	x	NOUN
ejpam-5718	278	18	)	)	PUNCT
ejpam-5718	278	19	and	and	CCONJ
ejpam-5718	278	20	having	having	AUX
ejpam-5718	278	21	σ1σ2connected	σ1σ2connecte	VERB
ejpam-5718	278	22	complement	complement	VERB
ejpam-5718	278	23	such	such	ADJ
ejpam-5718	278	24	that	that	SCONJ
ejpam-5718	278	25	x	x	PUNCT
ejpam-5718	278	26	∈	∈	PRON
ejpam-5718	278	27	τ1τ2	τ1τ2	NOUN
ejpam-5718	278	28	-	-	ADJ
ejpam-5718	278	29	fr(f	fr(f	PUNCT
ejpam-5718	278	30	+	+	ADJ
ejpam-5718	278	31	(	(	PUNCT
ejpam-5718	278	32	σ1σ2	σ1σ2	NOUN
ejpam-5718	278	33	-	-	NUM
ejpam-5718	278	34	cl(v	cl(v	NOUN
ejpam-5718	278	35	)	)	PUNCT
ejpam-5718	278	36	)	)	PUNCT
ejpam-5718	278	37	)	)	PUNCT
ejpam-5718	278	38	.	.	PUNCT
ejpam-5718	279	1	if	if	SCONJ
ejpam-5718	279	2	f	f	PROPN
ejpam-5718	279	3	is	be	AUX
ejpam-5718	279	4	upper	upper	ADJ
ejpam-5718	279	5	weakly	weakly	ADJ
ejpam-5718	279	6	s-(τ1	s-(τ1	PROPN
ejpam-5718	279	7	,	,	PUNCT
ejpam-5718	279	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	279	9	at	at	ADP
ejpam-5718	279	10	x	x	X
ejpam-5718	279	11	∈	∈	PROPN
ejpam-5718	279	12	x	x	NOUN
ejpam-5718	279	13	,	,	PUNCT
ejpam-5718	279	14	there	there	PRON
ejpam-5718	279	15	exists	exist	VERB
ejpam-5718	279	16	a	a	DET
ejpam-5718	279	17	τ1τ2	τ1τ2	NOUN
ejpam-5718	279	18	-	-	ADJ
ejpam-5718	279	19	open	open	ADJ
ejpam-5718	279	20	set	set	ADJ
ejpam-5718	279	21	u	u	NOUN
ejpam-5718	279	22	of	of	ADP
ejpam-5718	279	23	x	x	PUNCT
ejpam-5718	279	24	containing	contain	VERB
ejpam-5718	279	25	x	x	PUNCT
ejpam-5718	279	26	such	such	ADJ
ejpam-5718	279	27	that	that	SCONJ
ejpam-5718	279	28	f	f	PROPN
ejpam-5718	279	29	(	(	PUNCT
ejpam-5718	279	30	u	u	NOUN
ejpam-5718	279	31	)	)	PUNCT
ejpam-5718	279	32	⊆	⊆	NUM
ejpam-5718	279	33	σ1σ2	σ1σ2	NOUN
ejpam-5718	279	34	-	-	NUM
ejpam-5718	279	35	cl(v	cl(v	NOUN
ejpam-5718	279	36	)	)	PUNCT
ejpam-5718	279	37	;	;	PUNCT
ejpam-5718	279	38	hence	hence	ADV
ejpam-5718	279	39	u	u	NOUN
ejpam-5718	279	40	⊆	⊆	NUM
ejpam-5718	279	41	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	279	42	-	-	PUNCT
ejpam-5718	279	43	cl(v	cl(v	NOUN
ejpam-5718	279	44	)	)	PUNCT
ejpam-5718	279	45	)	)	PUNCT
ejpam-5718	279	46	.	.	PUNCT
ejpam-5718	280	1	thus	thus	ADV
ejpam-5718	280	2	,	,	PUNCT
ejpam-5718	280	3	x	x	PUNCT
ejpam-5718	280	4	∈	∈	PROPN
ejpam-5718	280	5	u	u	NOUN
ejpam-5718	280	6	⊆	⊆	NUM
ejpam-5718	280	7	τ1τ2	τ1τ2	NOUN
ejpam-5718	280	8	-	-	NUM
ejpam-5718	280	9	int(f	int(f	VERB
ejpam-5718	280	10	+	+	ADJ
ejpam-5718	280	11	(	(	PUNCT
ejpam-5718	280	12	σ1σ2	σ1σ2	NOUN
ejpam-5718	280	13	-	-	NUM
ejpam-5718	280	14	cl(v	cl(v	NOUN
ejpam-5718	280	15	)	)	PUNCT
ejpam-5718	280	16	)	)	PUNCT
ejpam-5718	280	17	)	)	PUNCT
ejpam-5718	280	18	.	.	PUNCT
ejpam-5718	281	1	this	this	PRON
ejpam-5718	281	2	contradicts	contradict	VERB
ejpam-5718	281	3	that	that	SCONJ
ejpam-5718	281	4	x	x	PUNCT
ejpam-5718	281	5	∈	∈	PROPN
ejpam-5718	281	6	τ1τ2	τ1τ2	NOUN
ejpam-5718	281	7	-	-	ADJ
ejpam-5718	281	8	fr(f	fr(f	PUNCT
ejpam-5718	281	9	+	+	ADJ
ejpam-5718	281	10	(	(	PUNCT
ejpam-5718	281	11	σ1σ2	σ1σ2	NOUN
ejpam-5718	281	12	-	-	NUM
ejpam-5718	281	13	cl(v	cl(v	NOUN
ejpam-5718	281	14	)	)	PUNCT
ejpam-5718	281	15	)	)	PUNCT
ejpam-5718	281	16	)	)	PUNCT
ejpam-5718	281	17	.	.	PUNCT
ejpam-5718	282	1	theorem	theorem	VERB
ejpam-5718	282	2	11	11	NUM
ejpam-5718	282	3	.	.	PUNCT
ejpam-5718	283	1	the	the	DET
ejpam-5718	283	2	set	set	NOUN
ejpam-5718	283	3	of	of	ADP
ejpam-5718	283	4	all	all	DET
ejpam-5718	283	5	points	point	NOUN
ejpam-5718	283	6	x	x	X
ejpam-5718	283	7	∈	∈	NOUN
ejpam-5718	283	8	x	x	PUNCT
ejpam-5718	283	9	at	at	ADP
ejpam-5718	283	10	which	which	PRON
ejpam-5718	283	11	a	a	DET
ejpam-5718	283	12	multifunction	multifunction	NOUN
ejpam-5718	283	13	f	f	NOUN
ejpam-5718	283	14	:	:	PUNCT
ejpam-5718	283	15	(	(	PUNCT
ejpam-5718	283	16	x	x	NOUN
ejpam-5718	283	17	,	,	PUNCT
ejpam-5718	283	18	τ1	τ1	NOUN
ejpam-5718	283	19	,	,	PUNCT
ejpam-5718	283	20	τ2	τ2	NOUN
ejpam-5718	283	21	)	)	PUNCT
ejpam-5718	283	22	→	→	SYM
ejpam-5718	283	23	(	(	PUNCT
ejpam-5718	283	24	y	y	PROPN
ejpam-5718	283	25	,	,	PUNCT
ejpam-5718	283	26	σ1	σ1	PROPN
ejpam-5718	283	27	,	,	PUNCT
ejpam-5718	283	28	σ2	σ2	PROPN
ejpam-5718	283	29	)	)	PUNCT
ejpam-5718	283	30	is	be	AUX
ejpam-5718	283	31	not	not	PART
ejpam-5718	283	32	lower	low	ADJ
ejpam-5718	283	33	weakly	weakly	ADJ
ejpam-5718	283	34	s-(τ1	s-(τ1	PROPN
ejpam-5718	283	35	,	,	PUNCT
ejpam-5718	283	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	283	37	is	be	AUX
ejpam-5718	283	38	identical	identical	ADJ
ejpam-5718	283	39	with	with	ADP
ejpam-5718	283	40	the	the	DET
ejpam-5718	283	41	union	union	NOUN
ejpam-5718	283	42	of	of	ADP
ejpam-5718	283	43	the	the	DET
ejpam-5718	283	44	τ1τ2	τ1τ2	NOUN
ejpam-5718	283	45	-	-	NOUN
ejpam-5718	283	46	frontier	frontier	NOUN
ejpam-5718	283	47	of	of	ADP
ejpam-5718	283	48	the	the	DET
ejpam-5718	283	49	lower	low	ADJ
ejpam-5718	283	50	inverse	inverse	NOUN
ejpam-5718	283	51	images	image	NOUN
ejpam-5718	283	52	of	of	ADP
ejpam-5718	283	53	the	the	DET
ejpam-5718	283	54	σ1σ2	σ1σ2	NOUN
ejpam-5718	283	55	-	-	NOUN
ejpam-5718	283	56	closure	closure	NOUN
ejpam-5718	283	57	of	of	ADP
ejpam-5718	283	58	σ1σ2	σ1σ2	NOUN
ejpam-5718	283	59	-	-	PUNCT
ejpam-5718	283	60	open	open	ADJ
ejpam-5718	283	61	sets	set	NOUN
ejpam-5718	283	62	meeting	meet	VERB
ejpam-5718	283	63	f	f	X
ejpam-5718	283	64	(	(	PUNCT
ejpam-5718	283	65	x	x	NOUN
ejpam-5718	283	66	)	)	PUNCT
ejpam-5718	283	67	and	and	CCONJ
ejpam-5718	283	68	having	have	VERB
ejpam-5718	283	69	σ1σ2	σ1σ2	NOUN
ejpam-5718	283	70	-	-	PUNCT
ejpam-5718	283	71	connected	connect	VERB
ejpam-5718	283	72	complement	complement	NOUN
ejpam-5718	283	73	.	.	PUNCT
ejpam-5718	284	1	p.	p.	NOUN
ejpam-5718	284	2	pue	pue	NOUN
ejpam-5718	284	3	-	-	PUNCT
ejpam-5718	284	4	on	on	ADP
ejpam-5718	284	5	,	,	PUNCT
ejpam-5718	284	6	a.	a.	PROPN
ejpam-5718	284	7	sama	sama	PROPN
ejpam-5718	284	8	-	-	PUNCT
ejpam-5718	284	9	ae	ae	PROPN
ejpam-5718	284	10	,	,	PUNCT
ejpam-5718	284	11	c.	c.	PROPN
ejpam-5718	284	12	boonpok	boonpok	PROPN
ejpam-5718	284	13	/	/	SYM
ejpam-5718	284	14	eur	eur	PROPN
ejpam-5718	284	15	.	.	PUNCT
ejpam-5718	285	1	j.	j.	PROPN
ejpam-5718	285	2	pure	pure	PROPN
ejpam-5718	285	3	appl	appl	PROPN
ejpam-5718	285	4	.	.	PROPN
ejpam-5718	285	5	math	math	PROPN
ejpam-5718	285	6	,	,	PUNCT
ejpam-5718	285	7	18	18	NUM
ejpam-5718	285	8	(	(	PUNCT
ejpam-5718	285	9	1	1	NUM
ejpam-5718	285	10	)	)	PUNCT
ejpam-5718	285	11	(	(	PUNCT
ejpam-5718	285	12	2025	2025	NUM
ejpam-5718	285	13	)	)	PUNCT
ejpam-5718	285	14	,	,	PUNCT
ejpam-5718	285	15	5718	5718	NUM
ejpam-5718	285	16	11	11	NUM
ejpam-5718	285	17	of	of	ADP
ejpam-5718	285	18	16	16	NUM
ejpam-5718	285	19	proof	proof	NOUN
ejpam-5718	285	20	.	.	PUNCT
ejpam-5718	286	1	the	the	DET
ejpam-5718	286	2	proof	proof	NOUN
ejpam-5718	286	3	is	be	AUX
ejpam-5718	286	4	similar	similar	ADJ
ejpam-5718	286	5	to	to	ADP
ejpam-5718	286	6	that	that	PRON
ejpam-5718	286	7	of	of	ADP
ejpam-5718	286	8	theorem	theorem	ADJ
ejpam-5718	286	9	10	10	NUM
ejpam-5718	286	10	.	.	PUNCT
ejpam-5718	287	1	a	a	DET
ejpam-5718	287	2	multifunction	multifunction	NOUN
ejpam-5718	287	3	f	f	NOUN
ejpam-5718	287	4	:	:	PUNCT
ejpam-5718	287	5	(	(	PUNCT
ejpam-5718	287	6	x	x	NOUN
ejpam-5718	287	7	,	,	PUNCT
ejpam-5718	287	8	τ1	τ1	NOUN
ejpam-5718	287	9	,	,	PUNCT
ejpam-5718	287	10	τ2	τ2	NOUN
ejpam-5718	287	11	)	)	PUNCT
ejpam-5718	287	12	→	→	SYM
ejpam-5718	287	13	(	(	PUNCT
ejpam-5718	287	14	y	y	PROPN
ejpam-5718	287	15	,	,	PUNCT
ejpam-5718	287	16	σ1	σ1	PROPN
ejpam-5718	287	17	,	,	PUNCT
ejpam-5718	287	18	σ2	σ2	PROPN
ejpam-5718	287	19	)	)	PUNCT
ejpam-5718	287	20	is	be	AUX
ejpam-5718	287	21	said	say	VERB
ejpam-5718	287	22	to	to	PART
ejpam-5718	287	23	be	be	AUX
ejpam-5718	287	24	injective	injective	ADJ
ejpam-5718	287	25	if	if	SCONJ
ejpam-5718	287	26	x	x	PROPN
ejpam-5718	287	27	̸=	̸=	PROPN
ejpam-5718	287	28	y	y	PROPN
ejpam-5718	287	29	implies	imply	VERB
ejpam-5718	287	30	that	that	SCONJ
ejpam-5718	287	31	f	f	PROPN
ejpam-5718	287	32	(	(	PUNCT
ejpam-5718	287	33	x	x	NOUN
ejpam-5718	287	34	)	)	PUNCT
ejpam-5718	287	35	∩	∩	ADJ
ejpam-5718	287	36	f	f	PROPN
ejpam-5718	287	37	(	(	PUNCT
ejpam-5718	287	38	y	y	NOUN
ejpam-5718	287	39	)	)	PUNCT
ejpam-5718	287	40	=	=	PUNCT
ejpam-5718	287	41	∅.	∅.	PRON
ejpam-5718	287	42	definition	definition	NOUN
ejpam-5718	287	43	6	6	NUM
ejpam-5718	287	44	.	.	PUNCT
ejpam-5718	288	1	[	[	X
ejpam-5718	288	2	31	31	NUM
ejpam-5718	288	3	]	]	PUNCT
ejpam-5718	288	4	a	a	DET
ejpam-5718	288	5	bitopological	bitopological	ADJ
ejpam-5718	288	6	space	space	NOUN
ejpam-5718	288	7	(	(	PUNCT
ejpam-5718	288	8	x	x	NOUN
ejpam-5718	288	9	,	,	PUNCT
ejpam-5718	288	10	τ1	τ1	NOUN
ejpam-5718	288	11	,	,	PUNCT
ejpam-5718	288	12	τ2	τ2	NOUN
ejpam-5718	288	13	)	)	PUNCT
ejpam-5718	288	14	is	be	AUX
ejpam-5718	288	15	said	say	VERB
ejpam-5718	288	16	to	to	PART
ejpam-5718	288	17	be	be	AUX
ejpam-5718	288	18	(	(	PUNCT
ejpam-5718	288	19	τ1	τ1	NOUN
ejpam-5718	288	20	,	,	PUNCT
ejpam-5718	288	21	τ2)-t2	τ2)-t2	ADJ
ejpam-5718	288	22	if	if	SCONJ
ejpam-5718	288	23	for	for	ADP
ejpam-5718	288	24	any	any	DET
ejpam-5718	288	25	pair	pair	NOUN
ejpam-5718	288	26	of	of	ADP
ejpam-5718	288	27	distinct	distinct	ADJ
ejpam-5718	288	28	points	point	NOUN
ejpam-5718	288	29	x	x	X
ejpam-5718	288	30	,	,	PUNCT
ejpam-5718	288	31	y	y	PROPN
ejpam-5718	288	32	in	in	ADP
ejpam-5718	288	33	x	x	SYM
ejpam-5718	288	34	,	,	PUNCT
ejpam-5718	288	35	there	there	PRON
ejpam-5718	288	36	exist	exist	VERB
ejpam-5718	288	37	disjoint	disjoint	ADJ
ejpam-5718	288	38	τ1τ2	τ1τ2	ADJ
ejpam-5718	288	39	-	-	ADJ
ejpam-5718	288	40	open	open	ADJ
ejpam-5718	288	41	sets	set	NOUN
ejpam-5718	288	42	u	u	NOUN
ejpam-5718	288	43	and	and	CCONJ
ejpam-5718	288	44	v	v	NOUN
ejpam-5718	288	45	of	of	ADP
ejpam-5718	288	46	x	x	PUNCT
ejpam-5718	288	47	containing	contain	VERB
ejpam-5718	288	48	x	x	PROPN
ejpam-5718	288	49	and	and	CCONJ
ejpam-5718	288	50	y	y	PROPN
ejpam-5718	288	51	,	,	PUNCT
ejpam-5718	288	52	respectively	respectively	ADV
ejpam-5718	288	53	.	.	PUNCT
ejpam-5718	289	1	definition	definition	NOUN
ejpam-5718	289	2	7	7	NUM
ejpam-5718	289	3	.	.	PUNCT
ejpam-5718	290	1	a	a	DET
ejpam-5718	290	2	bitopological	bitopological	ADJ
ejpam-5718	290	3	space	space	NOUN
ejpam-5718	290	4	(	(	PUNCT
ejpam-5718	290	5	x	x	NOUN
ejpam-5718	290	6	,	,	PUNCT
ejpam-5718	290	7	τ1	τ1	NOUN
ejpam-5718	290	8	,	,	PUNCT
ejpam-5718	290	9	τ2	τ2	NOUN
ejpam-5718	290	10	)	)	PUNCT
ejpam-5718	290	11	is	be	AUX
ejpam-5718	290	12	said	say	VERB
ejpam-5718	290	13	to	to	PART
ejpam-5718	290	14	be	be	AUX
ejpam-5718	290	15	strongly	strongly	ADV
ejpam-5718	290	16	s-(τ1	s-(τ1	ADJ
ejpam-5718	290	17	,	,	PUNCT
ejpam-5718	290	18	τ2)-normal	τ2)-normal	ADJ
ejpam-5718	290	19	if	if	SCONJ
ejpam-5718	290	20	for	for	ADP
ejpam-5718	290	21	every	every	DET
ejpam-5718	290	22	disjoint	disjoint	ADJ
ejpam-5718	290	23	τ1τ2	τ1τ2	ADJ
ejpam-5718	290	24	-	-	ADJ
ejpam-5718	290	25	closed	closed	ADJ
ejpam-5718	290	26	sets	set	NOUN
ejpam-5718	290	27	f	f	PROPN
ejpam-5718	290	28	and	and	CCONJ
ejpam-5718	290	29	k	k	PROPN
ejpam-5718	290	30	of	of	ADP
ejpam-5718	290	31	x	x	PRON
ejpam-5718	290	32	,	,	PUNCT
ejpam-5718	290	33	there	there	PRON
ejpam-5718	290	34	exist	exist	VERB
ejpam-5718	290	35	τ1τ2	τ1τ2	ADJ
ejpam-5718	290	36	-	-	ADJ
ejpam-5718	290	37	open	open	ADJ
ejpam-5718	290	38	sets	set	NOUN
ejpam-5718	290	39	u	u	NOUN
ejpam-5718	290	40	and	and	CCONJ
ejpam-5718	290	41	v	v	NOUN
ejpam-5718	290	42	having	have	VERB
ejpam-5718	290	43	τ1τ2	τ1τ2	VERB
ejpam-5718	290	44	-	-	ADJ
ejpam-5718	290	45	connected	connect	VERB
ejpam-5718	290	46	complements	complement	NOUN
ejpam-5718	290	47	such	such	ADJ
ejpam-5718	290	48	that	that	SCONJ
ejpam-5718	290	49	f	f	PROPN
ejpam-5718	290	50	⊆	⊆	NUM
ejpam-5718	290	51	u	u	NOUN
ejpam-5718	290	52	,	,	PUNCT
ejpam-5718	290	53	k	k	PROPN
ejpam-5718	290	54	⊆	⊆	NUM
ejpam-5718	290	55	v	v	ADP
ejpam-5718	290	56	and	and	CCONJ
ejpam-5718	290	57	τ1τ2	τ1τ2	NOUN
ejpam-5718	290	58	-	-	NOUN
ejpam-5718	290	59	cl(u	cl(u	NOUN
ejpam-5718	290	60	)	)	PUNCT
ejpam-5718	290	61	∩	∩	NOUN
ejpam-5718	290	62	τ1τ2	τ1τ2	NOUN
ejpam-5718	290	63	-	-	NOUN
ejpam-5718	290	64	cl(v	cl(v	X
ejpam-5718	290	65	)	)	PUNCT
ejpam-5718	290	66	=	=	PUNCT
ejpam-5718	290	67	∅.	∅.	NOUN
ejpam-5718	290	68	theorem	theorem	VERB
ejpam-5718	290	69	12	12	NUM
ejpam-5718	290	70	.	.	PUNCT
ejpam-5718	291	1	if	if	SCONJ
ejpam-5718	291	2	f	f	PROPN
ejpam-5718	291	3	:	:	PUNCT
ejpam-5718	291	4	(	(	PUNCT
ejpam-5718	291	5	x	x	NOUN
ejpam-5718	291	6	,	,	PUNCT
ejpam-5718	291	7	τ1	τ1	NOUN
ejpam-5718	291	8	,	,	PUNCT
ejpam-5718	291	9	τ2	τ2	NOUN
ejpam-5718	291	10	)	)	PUNCT
ejpam-5718	291	11	→	→	SYM
ejpam-5718	291	12	(	(	PUNCT
ejpam-5718	291	13	y	y	PROPN
ejpam-5718	291	14	,	,	PUNCT
ejpam-5718	291	15	σ1	σ1	PROPN
ejpam-5718	291	16	,	,	PUNCT
ejpam-5718	291	17	σ2	σ2	PROPN
ejpam-5718	291	18	)	)	PUNCT
ejpam-5718	291	19	is	be	AUX
ejpam-5718	291	20	an	an	DET
ejpam-5718	291	21	injective	injective	ADJ
ejpam-5718	291	22	upper	upper	ADJ
ejpam-5718	291	23	weakly	weakly	ADJ
ejpam-5718	291	24	s-(τ1	s-(τ1	PROPN
ejpam-5718	291	25	,	,	PUNCT
ejpam-5718	291	26	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	291	27	multifunction	multifunction	NOUN
ejpam-5718	291	28	into	into	ADP
ejpam-5718	291	29	a	a	DET
ejpam-5718	291	30	strongly	strongly	ADV
ejpam-5718	291	31	s-(τ1	s-(τ1	ADJ
ejpam-5718	291	32	,	,	PUNCT
ejpam-5718	291	33	τ2)-normal	τ2)-normal	ADJ
ejpam-5718	291	34	space	space	NOUN
ejpam-5718	291	35	(	(	PUNCT
ejpam-5718	291	36	y	y	PROPN
ejpam-5718	291	37	,	,	PUNCT
ejpam-5718	291	38	σ1	σ1	PROPN
ejpam-5718	291	39	,	,	PUNCT
ejpam-5718	291	40	σ2	σ2	NOUN
ejpam-5718	291	41	)	)	PUNCT
ejpam-5718	291	42	and	and	CCONJ
ejpam-5718	291	43	f	f	PROPN
ejpam-5718	291	44	(	(	PUNCT
ejpam-5718	291	45	x	x	X
ejpam-5718	291	46	)	)	PUNCT
ejpam-5718	291	47	is	be	AUX
ejpam-5718	291	48	σ1σ2	σ1σ2	NOUN
ejpam-5718	291	49	-	-	ADJ
ejpam-5718	291	50	closed	closed	ADJ
ejpam-5718	291	51	for	for	ADP
ejpam-5718	291	52	each	each	DET
ejpam-5718	291	53	x	x	SYM
ejpam-5718	291	54	∈	∈	PROPN
ejpam-5718	291	55	x	x	NOUN
ejpam-5718	291	56	,	,	PUNCT
ejpam-5718	291	57	then	then	ADV
ejpam-5718	291	58	(	(	PUNCT
ejpam-5718	291	59	x	x	NOUN
ejpam-5718	291	60	,	,	PUNCT
ejpam-5718	291	61	τ1	τ1	NOUN
ejpam-5718	291	62	,	,	PUNCT
ejpam-5718	291	63	τ2	τ2	NOUN
ejpam-5718	291	64	)	)	PUNCT
ejpam-5718	291	65	is	be	AUX
ejpam-5718	291	66	(	(	PUNCT
ejpam-5718	291	67	τ1	τ1	NOUN
ejpam-5718	291	68	,	,	PUNCT
ejpam-5718	291	69	τ2)-t2	τ2)-t2	PROPN
ejpam-5718	291	70	.	.	PUNCT
ejpam-5718	292	1	proof	proof	NOUN
ejpam-5718	292	2	.	.	PUNCT
ejpam-5718	293	1	for	for	ADP
ejpam-5718	293	2	any	any	DET
ejpam-5718	293	3	distinct	distinct	ADJ
ejpam-5718	293	4	points	point	NOUN
ejpam-5718	293	5	x	x	X
ejpam-5718	293	6	,	,	PUNCT
ejpam-5718	293	7	y	y	PROPN
ejpam-5718	293	8	of	of	ADP
ejpam-5718	293	9	x	x	PRON
ejpam-5718	293	10	,	,	PUNCT
ejpam-5718	293	11	we	we	PRON
ejpam-5718	293	12	have	have	VERB
ejpam-5718	293	13	f	f	X
ejpam-5718	293	14	(	(	PUNCT
ejpam-5718	293	15	x)∩f	x)∩f	PROPN
ejpam-5718	293	16	(	(	PUNCT
ejpam-5718	293	17	y	y	NOUN
ejpam-5718	293	18	)	)	PUNCT
ejpam-5718	293	19	=	=	NOUN
ejpam-5718	293	20	∅	∅	NOUN
ejpam-5718	293	21	since	since	SCONJ
ejpam-5718	293	22	f	f	PROPN
ejpam-5718	293	23	is	be	AUX
ejpam-5718	293	24	injective	injective	ADJ
ejpam-5718	293	25	.	.	PUNCT
ejpam-5718	294	1	since	since	SCONJ
ejpam-5718	294	2	f	f	PROPN
ejpam-5718	294	3	(	(	PUNCT
ejpam-5718	294	4	x	x	X
ejpam-5718	294	5	)	)	PUNCT
ejpam-5718	294	6	is	be	AUX
ejpam-5718	294	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	294	8	-	-	ADJ
ejpam-5718	294	9	closed	closed	ADJ
ejpam-5718	294	10	for	for	SCONJ
ejpam-5718	294	11	each	each	DET
ejpam-5718	294	12	x	x	SYM
ejpam-5718	294	13	∈	∈	PROPN
ejpam-5718	294	14	x	x	X
ejpam-5718	294	15	and	and	CCONJ
ejpam-5718	294	16	(	(	PUNCT
ejpam-5718	294	17	y	y	PROPN
ejpam-5718	294	18	,	,	PUNCT
ejpam-5718	294	19	σ1	σ1	PROPN
ejpam-5718	294	20	,	,	PUNCT
ejpam-5718	294	21	σ2	σ2	PROPN
ejpam-5718	294	22	)	)	PUNCT
ejpam-5718	294	23	is	be	AUX
ejpam-5718	294	24	strongly	strongly	ADV
ejpam-5718	294	25	s-(τ1	s-(τ1	ADJ
ejpam-5718	294	26	,	,	PUNCT
ejpam-5718	294	27	τ2)-normal	τ2)-normal	ADJ
ejpam-5718	294	28	,	,	PUNCT
ejpam-5718	294	29	there	there	PRON
ejpam-5718	294	30	exist	exist	VERB
ejpam-5718	294	31	σ1σ2	σ1σ2	NOUN
ejpam-5718	294	32	-	-	ADJ
ejpam-5718	294	33	open	open	ADJ
ejpam-5718	294	34	sets	set	NOUN
ejpam-5718	294	35	v	v	ADP
ejpam-5718	294	36	and	and	CCONJ
ejpam-5718	294	37	w	w	PROPN
ejpam-5718	294	38	of	of	ADP
ejpam-5718	294	39	y	y	PROPN
ejpam-5718	294	40	having	have	VERB
ejpam-5718	294	41	σ1σ2	σ1σ2	ADV
ejpam-5718	294	42	-	-	PUNCT
ejpam-5718	294	43	connected	connect	VERB
ejpam-5718	294	44	complements	complement	NOUN
ejpam-5718	294	45	such	such	ADJ
ejpam-5718	294	46	that	that	SCONJ
ejpam-5718	294	47	f	f	PROPN
ejpam-5718	294	48	(	(	PUNCT
ejpam-5718	294	49	x	x	X
ejpam-5718	294	50	)	)	PUNCT
ejpam-5718	294	51	⊆	⊆	NUM
ejpam-5718	294	52	v	v	NOUN
ejpam-5718	294	53	,	,	PUNCT
ejpam-5718	294	54	f	f	PROPN
ejpam-5718	294	55	(	(	PUNCT
ejpam-5718	294	56	y	y	PROPN
ejpam-5718	294	57	)	)	PUNCT
ejpam-5718	294	58	⊆	⊆	NUM
ejpam-5718	294	59	w	w	NOUN
ejpam-5718	294	60	and	and	CCONJ
ejpam-5718	294	61	σ1σ2	σ1σ2	NOUN
ejpam-5718	294	62	-	-	NUM
ejpam-5718	294	63	cl(v	cl(v	NOUN
ejpam-5718	294	64	)	)	PUNCT
ejpam-5718	294	65	∩	∩	NOUN
ejpam-5718	294	66	σ1σ2	σ1σ2	NOUN
ejpam-5718	294	67	-	-	NUM
ejpam-5718	294	68	cl(w	cl(w	NOUN
ejpam-5718	294	69	)	)	PUNCT
ejpam-5718	294	70	=	=	PUNCT
ejpam-5718	294	71	∅.	∅.	NOUN
ejpam-5718	294	72	since	since	SCONJ
ejpam-5718	294	73	f	f	PROPN
ejpam-5718	294	74	is	be	AUX
ejpam-5718	294	75	upper	upper	ADJ
ejpam-5718	294	76	weakly	weakly	ADJ
ejpam-5718	294	77	s(τ1	s(τ1	NOUN
ejpam-5718	294	78	,	,	PUNCT
ejpam-5718	294	79	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	294	80	,	,	PUNCT
ejpam-5718	294	81	there	there	PRON
ejpam-5718	294	82	exist	exist	VERB
ejpam-5718	294	83	τ1τ2	τ1τ2	ADJ
ejpam-5718	294	84	-	-	ADJ
ejpam-5718	294	85	open	open	ADJ
ejpam-5718	294	86	sets	set	NOUN
ejpam-5718	294	87	g	g	ADP
ejpam-5718	294	88	,	,	PUNCT
ejpam-5718	294	89	u	u	NOUN
ejpam-5718	294	90	of	of	ADP
ejpam-5718	294	91	x	x	PUNCT
ejpam-5718	294	92	containing	contain	VERB
ejpam-5718	294	93	x	x	PROPN
ejpam-5718	294	94	,	,	PUNCT
ejpam-5718	294	95	y	y	PROPN
ejpam-5718	294	96	,	,	PUNCT
ejpam-5718	294	97	respectively	respectively	ADV
ejpam-5718	294	98	,	,	PUNCT
ejpam-5718	294	99	such	such	ADJ
ejpam-5718	294	100	that	that	SCONJ
ejpam-5718	294	101	f	f	PROPN
ejpam-5718	294	102	(	(	PUNCT
ejpam-5718	294	103	g	g	NOUN
ejpam-5718	294	104	)	)	PUNCT
ejpam-5718	294	105	⊆	⊆	NUM
ejpam-5718	294	106	v	v	NOUN
ejpam-5718	294	107	and	and	CCONJ
ejpam-5718	294	108	f	f	PROPN
ejpam-5718	294	109	(	(	PUNCT
ejpam-5718	294	110	u	u	NOUN
ejpam-5718	294	111	)	)	PUNCT
ejpam-5718	294	112	⊆	⊆	NUM
ejpam-5718	294	113	w	w	NOUN
ejpam-5718	294	114	.	.	PUNCT
ejpam-5718	295	1	thus	thus	ADV
ejpam-5718	295	2	,	,	PUNCT
ejpam-5718	295	3	g	g	PROPN
ejpam-5718	295	4	∩	∩	ADJ
ejpam-5718	295	5	u	u	NOUN
ejpam-5718	295	6	=	=	NOUN
ejpam-5718	295	7	∅	∅	NOUN
ejpam-5718	295	8	and	and	CCONJ
ejpam-5718	295	9	hence	hence	ADV
ejpam-5718	295	10	(	(	PUNCT
ejpam-5718	295	11	x	x	NOUN
ejpam-5718	295	12	,	,	PUNCT
ejpam-5718	295	13	τ1	τ1	NOUN
ejpam-5718	295	14	,	,	PUNCT
ejpam-5718	295	15	τ2	τ2	NOUN
ejpam-5718	295	16	)	)	PUNCT
ejpam-5718	295	17	is	be	AUX
ejpam-5718	295	18	(	(	PUNCT
ejpam-5718	295	19	τ1	τ1	NOUN
ejpam-5718	295	20	,	,	PUNCT
ejpam-5718	295	21	τ2)-t2	τ2)-t2	PROPN
ejpam-5718	295	22	.	.	PUNCT
ejpam-5718	296	1	definition	definition	NOUN
ejpam-5718	296	2	8	8	NUM
ejpam-5718	296	3	.	.	PUNCT
ejpam-5718	297	1	[	[	X
ejpam-5718	297	2	64	64	NUM
ejpam-5718	297	3	]	]	PUNCT
ejpam-5718	297	4	a	a	DET
ejpam-5718	297	5	multifunction	multifunction	NOUN
ejpam-5718	297	6	f	f	NOUN
ejpam-5718	297	7	:	:	PUNCT
ejpam-5718	297	8	(	(	PUNCT
ejpam-5718	297	9	x	x	NOUN
ejpam-5718	297	10	,	,	PUNCT
ejpam-5718	297	11	τ1	τ1	NOUN
ejpam-5718	297	12	,	,	PUNCT
ejpam-5718	297	13	τ2	τ2	NOUN
ejpam-5718	297	14	)	)	PUNCT
ejpam-5718	297	15	→	→	SYM
ejpam-5718	297	16	(	(	PUNCT
ejpam-5718	297	17	y	y	PROPN
ejpam-5718	297	18	,	,	PUNCT
ejpam-5718	297	19	σ1	σ1	PROPN
ejpam-5718	297	20	,	,	PUNCT
ejpam-5718	297	21	σ2	σ2	PROPN
ejpam-5718	297	22	)	)	PUNCT
ejpam-5718	297	23	is	be	AUX
ejpam-5718	297	24	said	say	VERB
ejpam-5718	297	25	to	to	PART
ejpam-5718	297	26	be	be	AUX
ejpam-5718	297	27	upper	upper	ADJ
ejpam-5718	297	28	s(τ1	s(τ1	NOUN
ejpam-5718	297	29	,	,	PUNCT
ejpam-5718	297	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	297	31	at	at	ADP
ejpam-5718	297	32	x	x	X
ejpam-5718	297	33	∈	∈	PROPN
ejpam-5718	297	34	x	x	SYM
ejpam-5718	297	35	if	if	SCONJ
ejpam-5718	297	36	for	for	ADP
ejpam-5718	297	37	each	each	DET
ejpam-5718	297	38	σ1σ2	σ1σ2	VERB
ejpam-5718	297	39	-	-	ADJ
ejpam-5718	297	40	open	open	ADJ
ejpam-5718	297	41	set	set	NOUN
ejpam-5718	297	42	v	v	NOUN
ejpam-5718	297	43	of	of	ADP
ejpam-5718	297	44	y	y	PROPN
ejpam-5718	297	45	containing	contain	VERB
ejpam-5718	297	46	f	f	PROPN
ejpam-5718	297	47	(	(	PUNCT
ejpam-5718	297	48	x	x	NOUN
ejpam-5718	297	49	)	)	PUNCT
ejpam-5718	297	50	and	and	CCONJ
ejpam-5718	297	51	having	have	VERB
ejpam-5718	297	52	σ1σ2	σ1σ2	NOUN
ejpam-5718	297	53	-	-	PUNCT
ejpam-5718	297	54	connected	connect	VERB
ejpam-5718	297	55	complement	complement	NOUN
ejpam-5718	297	56	,	,	PUNCT
ejpam-5718	297	57	there	there	PRON
ejpam-5718	297	58	exists	exist	VERB
ejpam-5718	297	59	a	a	DET
ejpam-5718	297	60	τ1τ2	τ1τ2	NOUN
ejpam-5718	297	61	-	-	ADJ
ejpam-5718	297	62	open	open	ADJ
ejpam-5718	297	63	set	set	ADJ
ejpam-5718	297	64	u	u	NOUN
ejpam-5718	297	65	of	of	ADP
ejpam-5718	297	66	x	x	PUNCT
ejpam-5718	297	67	containing	contain	VERB
ejpam-5718	297	68	x	x	PUNCT
ejpam-5718	297	69	such	such	ADJ
ejpam-5718	297	70	that	that	SCONJ
ejpam-5718	297	71	f	f	PROPN
ejpam-5718	297	72	(	(	PUNCT
ejpam-5718	297	73	u	u	NOUN
ejpam-5718	297	74	)	)	PUNCT
ejpam-5718	297	75	⊆	⊆	NUM
ejpam-5718	297	76	v	v	NOUN
ejpam-5718	297	77	.	.	PUNCT
ejpam-5718	298	1	a	a	DET
ejpam-5718	298	2	multifunction	multifunction	NOUN
ejpam-5718	298	3	f	f	NOUN
ejpam-5718	298	4	:	:	PUNCT
ejpam-5718	298	5	(	(	PUNCT
ejpam-5718	298	6	x	x	NOUN
ejpam-5718	298	7	,	,	PUNCT
ejpam-5718	298	8	τ1	τ1	NOUN
ejpam-5718	298	9	,	,	PUNCT
ejpam-5718	298	10	τ2	τ2	NOUN
ejpam-5718	298	11	)	)	PUNCT
ejpam-5718	298	12	→	→	SYM
ejpam-5718	298	13	(	(	PUNCT
ejpam-5718	298	14	y	y	PROPN
ejpam-5718	298	15	,	,	PUNCT
ejpam-5718	298	16	σ1	σ1	PROPN
ejpam-5718	298	17	,	,	PUNCT
ejpam-5718	298	18	σ2	σ2	PROPN
ejpam-5718	298	19	)	)	PUNCT
ejpam-5718	298	20	is	be	AUX
ejpam-5718	298	21	said	say	VERB
ejpam-5718	298	22	to	to	PART
ejpam-5718	298	23	be	be	AUX
ejpam-5718	298	24	upper	upper	ADJ
ejpam-5718	298	25	s-(τ1	s-(τ1	NOUN
ejpam-5718	298	26	,	,	PUNCT
ejpam-5718	298	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	298	28	if	if	SCONJ
ejpam-5718	298	29	f	f	PROPN
ejpam-5718	298	30	has	have	VERB
ejpam-5718	298	31	this	this	DET
ejpam-5718	298	32	property	property	NOUN
ejpam-5718	298	33	at	at	ADP
ejpam-5718	298	34	each	each	DET
ejpam-5718	298	35	point	point	NOUN
ejpam-5718	298	36	x	x	PUNCT
ejpam-5718	298	37	of	of	ADP
ejpam-5718	298	38	x.	x.	PROPN
ejpam-5718	298	39	lemma	lemma	PROPN
ejpam-5718	298	40	5	5	NUM
ejpam-5718	298	41	.	.	PUNCT
ejpam-5718	299	1	[	[	X
ejpam-5718	299	2	64	64	NUM
ejpam-5718	299	3	]	]	PUNCT
ejpam-5718	299	4	for	for	ADP
ejpam-5718	299	5	a	a	DET
ejpam-5718	299	6	multifunction	multifunction	NOUN
ejpam-5718	299	7	f	f	NOUN
ejpam-5718	299	8	:	:	PUNCT
ejpam-5718	299	9	(	(	PUNCT
ejpam-5718	299	10	x	x	NOUN
ejpam-5718	299	11	,	,	PUNCT
ejpam-5718	299	12	τ1	τ1	NOUN
ejpam-5718	299	13	,	,	PUNCT
ejpam-5718	299	14	τ2	τ2	NOUN
ejpam-5718	299	15	)	)	PUNCT
ejpam-5718	299	16	→	→	SYM
ejpam-5718	299	17	(	(	PUNCT
ejpam-5718	299	18	y	y	PROPN
ejpam-5718	299	19	,	,	PUNCT
ejpam-5718	299	20	σ1	σ1	PROPN
ejpam-5718	299	21	,	,	PUNCT
ejpam-5718	299	22	σ2	σ2	NOUN
ejpam-5718	299	23	)	)	PUNCT
ejpam-5718	299	24	,	,	PUNCT
ejpam-5718	299	25	the	the	DET
ejpam-5718	299	26	following	follow	VERB
ejpam-5718	299	27	properties	property	NOUN
ejpam-5718	299	28	are	be	AUX
ejpam-5718	299	29	equivalent	equivalent	ADJ
ejpam-5718	299	30	:	:	PUNCT
ejpam-5718	299	31	(	(	PUNCT
ejpam-5718	299	32	1	1	X
ejpam-5718	299	33	)	)	PUNCT
ejpam-5718	299	34	f	f	PROPN
ejpam-5718	299	35	is	be	AUX
ejpam-5718	299	36	upper	upper	ADJ
ejpam-5718	299	37	s-(τ1	s-(τ1	PROPN
ejpam-5718	299	38	,	,	PUNCT
ejpam-5718	299	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	299	40	;	;	PUNCT
ejpam-5718	299	41	(	(	PUNCT
ejpam-5718	299	42	2	2	NUM
ejpam-5718	299	43	)	)	PUNCT
ejpam-5718	299	44	f+(v	f+(v	NOUN
ejpam-5718	299	45	)	)	PUNCT
ejpam-5718	299	46	is	be	AUX
ejpam-5718	299	47	τ1τ2	τ1τ2	NOUN
ejpam-5718	299	48	-	-	ADJ
ejpam-5718	299	49	open	open	ADJ
ejpam-5718	299	50	in	in	ADP
ejpam-5718	299	51	x	x	PUNCT
ejpam-5718	299	52	for	for	ADP
ejpam-5718	299	53	every	every	DET
ejpam-5718	299	54	σ1σ2	σ1σ2	NOUN
ejpam-5718	299	55	-	-	ADJ
ejpam-5718	299	56	open	open	ADJ
ejpam-5718	299	57	set	set	NOUN
ejpam-5718	299	58	v	v	NOUN
ejpam-5718	299	59	of	of	ADP
ejpam-5718	299	60	y	y	PROPN
ejpam-5718	299	61	having	have	VERB
ejpam-5718	299	62	σ1σ2	σ1σ2	ADV
ejpam-5718	299	63	-	-	PUNCT
ejpam-5718	299	64	connected	connect	VERB
ejpam-5718	299	65	complement	complement	NOUN
ejpam-5718	299	66	;	;	PUNCT
ejpam-5718	299	67	(	(	PUNCT
ejpam-5718	299	68	3	3	X
ejpam-5718	299	69	)	)	PUNCT
ejpam-5718	299	70	f−(k	f−(k	PROPN
ejpam-5718	299	71	)	)	PUNCT
ejpam-5718	299	72	is	be	AUX
ejpam-5718	299	73	τ1τ2	τ1τ2	NOUN
ejpam-5718	299	74	-	-	ADJ
ejpam-5718	299	75	closed	closed	ADJ
ejpam-5718	299	76	in	in	ADP
ejpam-5718	299	77	x	x	PUNCT
ejpam-5718	299	78	for	for	ADP
ejpam-5718	299	79	every	every	DET
ejpam-5718	299	80	σ1σ2	σ1σ2	NOUN
ejpam-5718	299	81	-	-	ADJ
ejpam-5718	299	82	connected	connect	VERB
ejpam-5718	299	83	σ1σ2	σ1σ2	VERB
ejpam-5718	299	84	-	-	PUNCT
ejpam-5718	299	85	closed	closed	ADJ
ejpam-5718	299	86	set	set	NOUN
ejpam-5718	299	87	k	k	PROPN
ejpam-5718	299	88	of	of	ADP
ejpam-5718	299	89	y	y	PROPN
ejpam-5718	299	90	;	;	PUNCT
ejpam-5718	299	91	(	(	PUNCT
ejpam-5718	299	92	4	4	X
ejpam-5718	299	93	)	)	PUNCT
ejpam-5718	299	94	τ1τ2	τ1τ2	NOUN
ejpam-5718	299	95	-	-	NOUN
ejpam-5718	299	96	cl(f	cl(f	NOUN
ejpam-5718	299	97	−(b	−(b	PROPN
ejpam-5718	299	98	)	)	PUNCT
ejpam-5718	299	99	)	)	PUNCT
ejpam-5718	300	1	⊆	⊆	X
ejpam-5718	300	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5718	300	3	-	-	PUNCT
ejpam-5718	300	4	cl(b	cl(b	NOUN
ejpam-5718	300	5	)	)	PUNCT
ejpam-5718	300	6	)	)	PUNCT
ejpam-5718	301	1	for	for	ADP
ejpam-5718	301	2	every	every	DET
ejpam-5718	301	3	subset	subset	NOUN
ejpam-5718	301	4	b	b	PROPN
ejpam-5718	301	5	of	of	ADP
ejpam-5718	301	6	y	y	PROPN
ejpam-5718	301	7	having	have	VERB
ejpam-5718	301	8	the	the	DET
ejpam-5718	301	9	σ1σ2	σ1σ2	ADV
ejpam-5718	301	10	-	-	PUNCT
ejpam-5718	301	11	connected	connect	VERB
ejpam-5718	301	12	σ1σ2	σ1σ2	NOUN
ejpam-5718	301	13	-	-	NOUN
ejpam-5718	301	14	closure	closure	NOUN
ejpam-5718	301	15	;	;	PUNCT
ejpam-5718	301	16	(	(	PUNCT
ejpam-5718	301	17	5	5	X
ejpam-5718	301	18	)	)	PUNCT
ejpam-5718	301	19	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	301	20	-	-	PUNCT
ejpam-5718	301	21	int(b	int(b	NOUN
ejpam-5718	301	22	)	)	PUNCT
ejpam-5718	301	23	)	)	PUNCT
ejpam-5718	302	1	⊆	⊆	X
ejpam-5718	302	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	302	3	-	-	NUM
ejpam-5718	302	4	int(f	int(f	VERB
ejpam-5718	302	5	+	+	ADJ
ejpam-5718	302	6	(	(	PUNCT
ejpam-5718	302	7	b	b	NOUN
ejpam-5718	302	8	)	)	PUNCT
ejpam-5718	302	9	)	)	PUNCT
ejpam-5718	302	10	for	for	ADP
ejpam-5718	302	11	every	every	DET
ejpam-5718	302	12	subset	subset	NOUN
ejpam-5718	302	13	b	b	PROPN
ejpam-5718	302	14	of	of	ADP
ejpam-5718	302	15	y	y	PRON
ejpam-5718	302	16	such	such	ADJ
ejpam-5718	302	17	that	that	SCONJ
ejpam-5718	302	18	y−σ1σ2	y−σ1σ2	PROPN
ejpam-5718	302	19	-	-	PUNCT
ejpam-5718	302	20	int(b	int(b	NOUN
ejpam-5718	302	21	)	)	PUNCT
ejpam-5718	302	22	is	be	AUX
ejpam-5718	302	23	σ1σ2	σ1σ2	NOUN
ejpam-5718	302	24	-	-	PUNCT
ejpam-5718	302	25	connected	connect	VERB
ejpam-5718	302	26	.	.	PUNCT
ejpam-5718	303	1	theorem	theorem	VERB
ejpam-5718	303	2	13	13	NUM
ejpam-5718	303	3	.	.	PUNCT
ejpam-5718	304	1	if	if	SCONJ
ejpam-5718	304	2	f	f	PROPN
ejpam-5718	304	3	:	:	PUNCT
ejpam-5718	304	4	(	(	PUNCT
ejpam-5718	304	5	x	x	NOUN
ejpam-5718	304	6	,	,	PUNCT
ejpam-5718	304	7	τ1	τ1	NOUN
ejpam-5718	304	8	,	,	PUNCT
ejpam-5718	304	9	τ2	τ2	NOUN
ejpam-5718	304	10	)	)	PUNCT
ejpam-5718	304	11	→	→	SYM
ejpam-5718	304	12	(	(	PUNCT
ejpam-5718	304	13	y	y	PROPN
ejpam-5718	304	14	,	,	PUNCT
ejpam-5718	304	15	σ1	σ1	PROPN
ejpam-5718	304	16	,	,	PUNCT
ejpam-5718	304	17	σ2	σ2	PROPN
ejpam-5718	304	18	)	)	PUNCT
ejpam-5718	304	19	is	be	AUX
ejpam-5718	304	20	upper	upper	ADJ
ejpam-5718	304	21	weakly	weakly	ADJ
ejpam-5718	304	22	s-(τ1	s-(τ1	PROPN
ejpam-5718	304	23	,	,	PUNCT
ejpam-5718	304	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	304	25	and	and	CCONJ
ejpam-5718	304	26	satisfies	satisfy	VERB
ejpam-5718	304	27	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5718	304	28	-	-	NOUN
ejpam-5718	304	29	cl(v	cl(v	NOUN
ejpam-5718	304	30	)	)	PUNCT
ejpam-5718	304	31	)	)	PUNCT
ejpam-5718	305	1	⊆	⊆	NUM
ejpam-5718	305	2	f+(v	f+(v	NOUN
ejpam-5718	305	3	)	)	PUNCT
ejpam-5718	305	4	for	for	ADP
ejpam-5718	305	5	every	every	DET
ejpam-5718	305	6	σ1σ2	σ1σ2	NOUN
ejpam-5718	305	7	-	-	ADJ
ejpam-5718	305	8	open	open	ADJ
ejpam-5718	305	9	set	set	NOUN
ejpam-5718	305	10	v	v	NOUN
ejpam-5718	305	11	of	of	ADP
ejpam-5718	305	12	y	y	PROPN
ejpam-5718	305	13	having	have	VERB
ejpam-5718	305	14	σ1σ2	σ1σ2	ADV
ejpam-5718	305	15	-	-	PUNCT
ejpam-5718	305	16	connected	connect	VERB
ejpam-5718	305	17	complement	complement	NOUN
ejpam-5718	305	18	,	,	PUNCT
ejpam-5718	305	19	then	then	ADV
ejpam-5718	305	20	f	f	PROPN
ejpam-5718	305	21	is	be	AUX
ejpam-5718	305	22	upper	upper	ADJ
ejpam-5718	305	23	s-(τ1	s-(τ1	PROPN
ejpam-5718	305	24	,	,	PUNCT
ejpam-5718	305	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	305	26	.	.	PUNCT
ejpam-5718	306	1	p.	p.	NOUN
ejpam-5718	306	2	pue	pue	NOUN
ejpam-5718	306	3	-	-	PUNCT
ejpam-5718	306	4	on	on	ADP
ejpam-5718	306	5	,	,	PUNCT
ejpam-5718	306	6	a.	a.	PROPN
ejpam-5718	306	7	sama	sama	PROPN
ejpam-5718	306	8	-	-	PUNCT
ejpam-5718	306	9	ae	ae	PROPN
ejpam-5718	306	10	,	,	PUNCT
ejpam-5718	306	11	c.	c.	PROPN
ejpam-5718	306	12	boonpok	boonpok	PROPN
ejpam-5718	306	13	/	/	SYM
ejpam-5718	306	14	eur	eur	PROPN
ejpam-5718	306	15	.	.	PUNCT
ejpam-5718	307	1	j.	j.	PROPN
ejpam-5718	307	2	pure	pure	PROPN
ejpam-5718	307	3	appl	appl	PROPN
ejpam-5718	307	4	.	.	PROPN
ejpam-5718	307	5	math	math	PROPN
ejpam-5718	307	6	,	,	PUNCT
ejpam-5718	307	7	18	18	NUM
ejpam-5718	307	8	(	(	PUNCT
ejpam-5718	307	9	1	1	NUM
ejpam-5718	307	10	)	)	PUNCT
ejpam-5718	307	11	(	(	PUNCT
ejpam-5718	307	12	2025	2025	NUM
ejpam-5718	307	13	)	)	PUNCT
ejpam-5718	307	14	,	,	PUNCT
ejpam-5718	307	15	5718	5718	NUM
ejpam-5718	307	16	12	12	NUM
ejpam-5718	307	17	of	of	ADP
ejpam-5718	307	18	16	16	NUM
ejpam-5718	307	19	proof	proof	NOUN
ejpam-5718	307	20	.	.	PUNCT
ejpam-5718	308	1	let	let	VERB
ejpam-5718	308	2	v	v	PART
ejpam-5718	308	3	be	be	AUX
ejpam-5718	308	4	any	any	DET
ejpam-5718	308	5	σ1σ2	σ1σ2	NOUN
ejpam-5718	308	6	-	-	ADJ
ejpam-5718	308	7	open	open	ADJ
ejpam-5718	308	8	set	set	NOUN
ejpam-5718	308	9	of	of	ADP
ejpam-5718	308	10	y	y	PROPN
ejpam-5718	308	11	having	have	VERB
ejpam-5718	308	12	σ1σ2	σ1σ2	ADV
ejpam-5718	308	13	-	-	PUNCT
ejpam-5718	308	14	connected	connect	VERB
ejpam-5718	308	15	complement	complement	NOUN
ejpam-5718	308	16	.	.	PUNCT
ejpam-5718	309	1	since	since	SCONJ
ejpam-5718	309	2	f	f	PROPN
ejpam-5718	309	3	is	be	AUX
ejpam-5718	309	4	upper	upper	ADJ
ejpam-5718	309	5	weakly	weakly	ADJ
ejpam-5718	309	6	s-(τ1	s-(τ1	PROPN
ejpam-5718	309	7	,	,	PUNCT
ejpam-5718	309	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	309	9	,	,	PUNCT
ejpam-5718	309	10	by	by	ADP
ejpam-5718	309	11	theorem	theorem	NOUN
ejpam-5718	309	12	1	1	NUM
ejpam-5718	309	13	we	we	PRON
ejpam-5718	309	14	have	have	VERB
ejpam-5718	309	15	f+(v	f+(v	NOUN
ejpam-5718	309	16	)	)	PUNCT
ejpam-5718	310	1	⊆	⊆	X
ejpam-5718	310	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	310	3	-	-	NUM
ejpam-5718	310	4	int(f	int(f	VERB
ejpam-5718	310	5	+	+	ADJ
ejpam-5718	310	6	(	(	PUNCT
ejpam-5718	310	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	310	8	-	-	NUM
ejpam-5718	310	9	cl(v	cl(v	NOUN
ejpam-5718	310	10	)	)	PUNCT
ejpam-5718	310	11	)	)	PUNCT
ejpam-5718	310	12	)	)	PUNCT
ejpam-5718	311	1	⊆	⊆	X
ejpam-5718	311	2	τ1τ2	τ1τ2	NOUN
ejpam-5718	311	3	-	-	NUM
ejpam-5718	311	4	int(f	int(f	VERB
ejpam-5718	311	5	+	+	ADJ
ejpam-5718	311	6	(	(	PUNCT
ejpam-5718	311	7	v	v	NOUN
ejpam-5718	311	8	)	)	PUNCT
ejpam-5718	311	9	)	)	PUNCT
ejpam-5718	311	10	and	and	CCONJ
ejpam-5718	311	11	hence	hence	ADV
ejpam-5718	311	12	f+(v	f+(v	PROPN
ejpam-5718	311	13	)	)	PUNCT
ejpam-5718	311	14	is	be	AUX
ejpam-5718	311	15	τ1τ2	τ1τ2	NOUN
ejpam-5718	311	16	-	-	ADJ
ejpam-5718	311	17	open	open	ADJ
ejpam-5718	311	18	in	in	ADP
ejpam-5718	311	19	x.	x.	NOUN
ejpam-5718	311	20	by	by	ADP
ejpam-5718	311	21	lemma	lemma	PROPN
ejpam-5718	311	22	5	5	NUM
ejpam-5718	311	23	,	,	PUNCT
ejpam-5718	311	24	f	f	PROPN
ejpam-5718	311	25	is	be	AUX
ejpam-5718	311	26	upper	upper	ADJ
ejpam-5718	311	27	s-(τ1	s-(τ1	PROPN
ejpam-5718	311	28	,	,	PUNCT
ejpam-5718	311	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	311	30	.	.	PUNCT
ejpam-5718	312	1	definition	definition	NOUN
ejpam-5718	312	2	9	9	NUM
ejpam-5718	312	3	.	.	PUNCT
ejpam-5718	313	1	a	a	DET
ejpam-5718	313	2	bitopological	bitopological	ADJ
ejpam-5718	313	3	space	space	NOUN
ejpam-5718	313	4	(	(	PUNCT
ejpam-5718	313	5	x	x	NOUN
ejpam-5718	313	6	,	,	PUNCT
ejpam-5718	313	7	τ1	τ1	NOUN
ejpam-5718	313	8	,	,	PUNCT
ejpam-5718	313	9	τ2	τ2	NOUN
ejpam-5718	313	10	)	)	PUNCT
ejpam-5718	313	11	is	be	AUX
ejpam-5718	313	12	said	say	VERB
ejpam-5718	313	13	to	to	PART
ejpam-5718	313	14	be	be	AUX
ejpam-5718	313	15	s-(τ1	s-(τ1	PROPN
ejpam-5718	313	16	,	,	PUNCT
ejpam-5718	313	17	τ2)-normal	τ2)-normal	ADJ
ejpam-5718	313	18	if	if	SCONJ
ejpam-5718	313	19	for	for	ADP
ejpam-5718	313	20	each	each	DET
ejpam-5718	313	21	disjoint	disjoint	ADJ
ejpam-5718	313	22	τ1τ2	τ1τ2	ADJ
ejpam-5718	313	23	-	-	ADJ
ejpam-5718	313	24	closed	closed	ADJ
ejpam-5718	313	25	sets	set	NOUN
ejpam-5718	313	26	f	f	PROPN
ejpam-5718	313	27	and	and	CCONJ
ejpam-5718	313	28	k	k	PROPN
ejpam-5718	313	29	of	of	ADP
ejpam-5718	313	30	x	x	PRON
ejpam-5718	313	31	,	,	PUNCT
ejpam-5718	313	32	there	there	PRON
ejpam-5718	313	33	exist	exist	VERB
ejpam-5718	313	34	τ1τ2	τ1τ2	ADJ
ejpam-5718	313	35	-	-	ADJ
ejpam-5718	313	36	open	open	ADJ
ejpam-5718	313	37	sets	set	NOUN
ejpam-5718	313	38	u	u	NOUN
ejpam-5718	313	39	and	and	CCONJ
ejpam-5718	313	40	v	v	ADP
ejpam-5718	313	41	having	have	VERB
ejpam-5718	313	42	τ1τ2connected	τ1τ2connecte	VERB
ejpam-5718	313	43	complements	complement	NOUN
ejpam-5718	313	44	such	such	ADJ
ejpam-5718	313	45	that	that	SCONJ
ejpam-5718	313	46	f	f	PROPN
ejpam-5718	313	47	⊆	⊆	NUM
ejpam-5718	313	48	u	u	NOUN
ejpam-5718	313	49	,	,	PUNCT
ejpam-5718	313	50	k	k	PROPN
ejpam-5718	313	51	⊆	⊆	NUM
ejpam-5718	313	52	v	v	NOUN
ejpam-5718	313	53	and	and	CCONJ
ejpam-5718	313	54	u	u	NOUN
ejpam-5718	313	55	∩	∩	NOUN
ejpam-5718	313	56	v	v	NOUN
ejpam-5718	313	57	=	=	PUNCT
ejpam-5718	313	58	∅.	∅.	NOUN
ejpam-5718	313	59	theorem	theorem	VERB
ejpam-5718	313	60	14	14	NUM
ejpam-5718	313	61	.	.	PUNCT
ejpam-5718	314	1	let	let	VERB
ejpam-5718	314	2	f	f	NOUN
ejpam-5718	314	3	:	:	PUNCT
ejpam-5718	314	4	(	(	PUNCT
ejpam-5718	314	5	x	x	NOUN
ejpam-5718	314	6	,	,	PUNCT
ejpam-5718	314	7	τ1	τ1	NOUN
ejpam-5718	314	8	,	,	PUNCT
ejpam-5718	314	9	τ2	τ2	NOUN
ejpam-5718	314	10	)	)	PUNCT
ejpam-5718	314	11	→	→	SYM
ejpam-5718	314	12	(	(	PUNCT
ejpam-5718	314	13	y	y	PROPN
ejpam-5718	314	14	,	,	PUNCT
ejpam-5718	314	15	σ1	σ1	PROPN
ejpam-5718	314	16	,	,	PUNCT
ejpam-5718	314	17	σ2	σ2	PROPN
ejpam-5718	314	18	)	)	PUNCT
ejpam-5718	314	19	be	be	VERB
ejpam-5718	314	20	a	a	DET
ejpam-5718	314	21	multifunction	multifunction	NOUN
ejpam-5718	314	22	such	such	ADJ
ejpam-5718	314	23	that	that	SCONJ
ejpam-5718	314	24	f	f	PROPN
ejpam-5718	314	25	(	(	PUNCT
ejpam-5718	314	26	x	x	X
ejpam-5718	314	27	)	)	PUNCT
ejpam-5718	314	28	is	be	AUX
ejpam-5718	314	29	σ1σ2closed	σ1σ2close	VERB
ejpam-5718	314	30	in	in	ADP
ejpam-5718	314	31	y	y	PROPN
ejpam-5718	314	32	for	for	SCONJ
ejpam-5718	314	33	each	each	DET
ejpam-5718	314	34	x	x	SYM
ejpam-5718	314	35	∈	∈	PROPN
ejpam-5718	314	36	x	x	X
ejpam-5718	314	37	and	and	CCONJ
ejpam-5718	314	38	(	(	PUNCT
ejpam-5718	314	39	y	y	PROPN
ejpam-5718	314	40	,	,	PUNCT
ejpam-5718	314	41	σ1	σ1	PROPN
ejpam-5718	314	42	,	,	PUNCT
ejpam-5718	314	43	σ2	σ2	PROPN
ejpam-5718	314	44	)	)	PUNCT
ejpam-5718	314	45	is	be	AUX
ejpam-5718	314	46	s-(σ1	s-(σ1	NOUN
ejpam-5718	314	47	,	,	PUNCT
ejpam-5718	314	48	σ2)-normal	σ2)-normal	NOUN
ejpam-5718	314	49	.	.	PUNCT
ejpam-5718	315	1	then	then	ADV
ejpam-5718	315	2	,	,	PUNCT
ejpam-5718	315	3	f	f	PROPN
ejpam-5718	315	4	is	be	AUX
ejpam-5718	315	5	upper	upper	ADJ
ejpam-5718	315	6	weakly	weakly	ADJ
ejpam-5718	315	7	s-(τ1	s-(τ1	PROPN
ejpam-5718	315	8	,	,	PUNCT
ejpam-5718	315	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	315	10	if	if	SCONJ
ejpam-5718	315	11	and	and	CCONJ
ejpam-5718	315	12	only	only	ADV
ejpam-5718	315	13	if	if	SCONJ
ejpam-5718	315	14	f	f	PROPN
ejpam-5718	315	15	is	be	AUX
ejpam-5718	315	16	upper	upper	ADJ
ejpam-5718	315	17	s-(τ1	s-(τ1	PROPN
ejpam-5718	315	18	,	,	PUNCT
ejpam-5718	315	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	315	20	.	.	PUNCT
ejpam-5718	316	1	proof	proof	NOUN
ejpam-5718	316	2	.	.	PUNCT
ejpam-5718	317	1	suppose	suppose	VERB
ejpam-5718	317	2	that	that	SCONJ
ejpam-5718	317	3	f	f	PROPN
ejpam-5718	317	4	is	be	AUX
ejpam-5718	317	5	upper	upper	ADJ
ejpam-5718	317	6	weakly	weakly	ADJ
ejpam-5718	317	7	s-(τ1	s-(τ1	PROPN
ejpam-5718	317	8	,	,	PUNCT
ejpam-5718	317	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	317	10	.	.	PUNCT
ejpam-5718	318	1	let	let	VERB
ejpam-5718	318	2	x	x	PUNCT
ejpam-5718	318	3	∈	∈	PROPN
ejpam-5718	318	4	x	x	X
ejpam-5718	318	5	and	and	CCONJ
ejpam-5718	318	6	g	g	PROPN
ejpam-5718	318	7	be	be	VERB
ejpam-5718	318	8	any	any	DET
ejpam-5718	318	9	σ1σ2	σ1σ2	NOUN
ejpam-5718	318	10	-	-	ADJ
ejpam-5718	318	11	open	open	ADJ
ejpam-5718	318	12	set	set	NOUN
ejpam-5718	318	13	of	of	ADP
ejpam-5718	318	14	y	y	PROPN
ejpam-5718	318	15	containing	contain	VERB
ejpam-5718	318	16	f	f	PROPN
ejpam-5718	318	17	(	(	PUNCT
ejpam-5718	318	18	x	x	NOUN
ejpam-5718	318	19	)	)	PUNCT
ejpam-5718	318	20	and	and	CCONJ
ejpam-5718	318	21	having	have	VERB
ejpam-5718	318	22	σ1σ2	σ1σ2	NOUN
ejpam-5718	318	23	-	-	PUNCT
ejpam-5718	318	24	connected	connect	VERB
ejpam-5718	318	25	complement	complement	NOUN
ejpam-5718	318	26	.	.	PUNCT
ejpam-5718	319	1	since	since	SCONJ
ejpam-5718	319	2	f	f	PROPN
ejpam-5718	319	3	(	(	PUNCT
ejpam-5718	319	4	x	x	X
ejpam-5718	319	5	)	)	PUNCT
ejpam-5718	319	6	is	be	AUX
ejpam-5718	319	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	319	8	-	-	ADJ
ejpam-5718	319	9	closed	closed	ADJ
ejpam-5718	319	10	in	in	ADP
ejpam-5718	319	11	y	y	PROPN
ejpam-5718	319	12	,	,	PUNCT
ejpam-5718	319	13	by	by	ADP
ejpam-5718	319	14	the	the	DET
ejpam-5718	319	15	s-(σ1	s-(σ1	NOUN
ejpam-5718	319	16	,	,	PUNCT
ejpam-5718	319	17	σ2)-normality	σ2)-normality	NOUN
ejpam-5718	319	18	of	of	ADP
ejpam-5718	319	19	(	(	PUNCT
ejpam-5718	319	20	y	y	PROPN
ejpam-5718	319	21	,	,	PUNCT
ejpam-5718	319	22	σ1	σ1	PROPN
ejpam-5718	319	23	,	,	PUNCT
ejpam-5718	319	24	σ2	σ2	PROPN
ejpam-5718	319	25	)	)	PUNCT
ejpam-5718	319	26	there	there	PRON
ejpam-5718	319	27	exist	exist	VERB
ejpam-5718	319	28	σ1σ2	σ1σ2	NOUN
ejpam-5718	319	29	-	-	ADJ
ejpam-5718	319	30	open	open	ADJ
ejpam-5718	319	31	sets	set	NOUN
ejpam-5718	319	32	v	v	ADP
ejpam-5718	319	33	and	and	CCONJ
ejpam-5718	319	34	w	w	ADP
ejpam-5718	319	35	having	have	VERB
ejpam-5718	319	36	σ1σ2	σ1σ2	NOUN
ejpam-5718	319	37	-	-	PUNCT
ejpam-5718	319	38	connected	connect	VERB
ejpam-5718	319	39	complements	complement	NOUN
ejpam-5718	319	40	such	such	ADJ
ejpam-5718	319	41	that	that	SCONJ
ejpam-5718	319	42	f	f	PROPN
ejpam-5718	319	43	(	(	PUNCT
ejpam-5718	319	44	x	x	X
ejpam-5718	319	45	)	)	PUNCT
ejpam-5718	319	46	⊆	⊆	NUM
ejpam-5718	319	47	v	v	NOUN
ejpam-5718	319	48	,	,	PUNCT
ejpam-5718	319	49	y	y	PROPN
ejpam-5718	319	50	−g	−g	VERB
ejpam-5718	319	51	⊆	⊆	NUM
ejpam-5718	319	52	w	w	NOUN
ejpam-5718	319	53	and	and	CCONJ
ejpam-5718	319	54	v	v	NOUN
ejpam-5718	319	55	∩w	∩w	NOUN
ejpam-5718	319	56	=	=	PUNCT
ejpam-5718	319	57	∅.	∅.	VERB
ejpam-5718	319	58	thus	thus	ADV
ejpam-5718	319	59	,	,	PUNCT
ejpam-5718	319	60	f	f	PROPN
ejpam-5718	319	61	(	(	PUNCT
ejpam-5718	319	62	x	x	X
ejpam-5718	319	63	)	)	PUNCT
ejpam-5718	319	64	⊆	⊆	NUM
ejpam-5718	319	65	v	v	ADP
ejpam-5718	319	66	⊆	⊆	NUM
ejpam-5718	319	67	σ1σ2	σ1σ2	NOUN
ejpam-5718	319	68	-	-	PUNCT
ejpam-5718	319	69	cl(v	cl(v	NOUN
ejpam-5718	319	70	)	)	PUNCT
ejpam-5718	319	71	⊆	⊆	NUM
ejpam-5718	319	72	σ1σ2	σ1σ2	NUM
ejpam-5718	319	73	-	-	PUNCT
ejpam-5718	319	74	cl(y	cl(y	NOUN
ejpam-5718	319	75	−w	−w	NOUN
ejpam-5718	319	76	)	)	PUNCT
ejpam-5718	320	1	=	=	SYM
ejpam-5718	320	2	y	y	PROPN
ejpam-5718	320	3	−w	−w	ADV
ejpam-5718	320	4	.	.	PUNCT
ejpam-5718	321	1	since	since	SCONJ
ejpam-5718	321	2	f	f	PROPN
ejpam-5718	321	3	is	be	AUX
ejpam-5718	321	4	upper	upper	ADJ
ejpam-5718	321	5	weakly	weakly	ADJ
ejpam-5718	321	6	s-(τ1	s-(τ1	PROPN
ejpam-5718	321	7	,	,	PUNCT
ejpam-5718	321	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	321	9	,	,	PUNCT
ejpam-5718	321	10	there	there	PRON
ejpam-5718	321	11	exists	exist	VERB
ejpam-5718	321	12	a	a	DET
ejpam-5718	321	13	τ1τ2	τ1τ2	NOUN
ejpam-5718	321	14	-	-	ADJ
ejpam-5718	321	15	open	open	ADJ
ejpam-5718	321	16	set	set	ADJ
ejpam-5718	321	17	u	u	NOUN
ejpam-5718	321	18	of	of	ADP
ejpam-5718	321	19	x	x	PUNCT
ejpam-5718	321	20	containing	contain	VERB
ejpam-5718	321	21	x	x	PUNCT
ejpam-5718	321	22	such	such	ADJ
ejpam-5718	321	23	that	that	SCONJ
ejpam-5718	321	24	f	f	PROPN
ejpam-5718	321	25	(	(	PUNCT
ejpam-5718	321	26	u	u	NOUN
ejpam-5718	321	27	)	)	PUNCT
ejpam-5718	321	28	⊆	⊆	NUM
ejpam-5718	321	29	σ1σ2	σ1σ2	NOUN
ejpam-5718	321	30	-	-	NUM
ejpam-5718	321	31	cl(v	cl(v	NOUN
ejpam-5718	321	32	)	)	PUNCT
ejpam-5718	321	33	⊆	⊆	NUM
ejpam-5718	321	34	g.	g.	NOUN
ejpam-5718	321	35	this	this	PRON
ejpam-5718	321	36	shows	show	VERB
ejpam-5718	321	37	that	that	SCONJ
ejpam-5718	321	38	f	f	PROPN
ejpam-5718	321	39	is	be	AUX
ejpam-5718	321	40	upper	upper	ADJ
ejpam-5718	321	41	s-(τ1	s-(τ1	PROPN
ejpam-5718	321	42	,	,	PUNCT
ejpam-5718	321	43	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5718	321	44	.	.	PUNCT
ejpam-5718	322	1	the	the	DET
ejpam-5718	322	2	converse	converse	NOUN
ejpam-5718	322	3	is	be	AUX
ejpam-5718	322	4	obvious	obvious	ADJ
ejpam-5718	322	5	.	.	PUNCT
ejpam-5718	323	1	definition	definition	NOUN
ejpam-5718	323	2	10	10	NUM
ejpam-5718	323	3	.	.	PUNCT
ejpam-5718	324	1	[	[	X
ejpam-5718	324	2	64	64	NUM
ejpam-5718	324	3	]	]	PUNCT
ejpam-5718	324	4	a	a	DET
ejpam-5718	324	5	multifunction	multifunction	NOUN
ejpam-5718	324	6	f	f	NOUN
ejpam-5718	324	7	:	:	PUNCT
ejpam-5718	324	8	(	(	PUNCT
ejpam-5718	324	9	x	x	NOUN
ejpam-5718	324	10	,	,	PUNCT
ejpam-5718	324	11	τ1	τ1	NOUN
ejpam-5718	324	12	,	,	PUNCT
ejpam-5718	324	13	τ2	τ2	NOUN
ejpam-5718	324	14	)	)	PUNCT
ejpam-5718	324	15	→	→	SYM
ejpam-5718	324	16	(	(	PUNCT
ejpam-5718	324	17	y	y	PROPN
ejpam-5718	324	18	,	,	PUNCT
ejpam-5718	324	19	σ1	σ1	PROPN
ejpam-5718	324	20	,	,	PUNCT
ejpam-5718	324	21	σ2	σ2	PROPN
ejpam-5718	324	22	)	)	PUNCT
ejpam-5718	324	23	is	be	AUX
ejpam-5718	324	24	said	say	VERB
ejpam-5718	324	25	to	to	PART
ejpam-5718	324	26	be	be	AUX
ejpam-5718	324	27	lower	low	ADJ
ejpam-5718	324	28	s(τ1	s(τ1	NOUN
ejpam-5718	324	29	,	,	PUNCT
ejpam-5718	324	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	324	31	at	at	ADP
ejpam-5718	324	32	x	x	X
ejpam-5718	324	33	∈	∈	PROPN
ejpam-5718	324	34	x	x	SYM
ejpam-5718	324	35	if	if	SCONJ
ejpam-5718	324	36	for	for	ADP
ejpam-5718	324	37	each	each	DET
ejpam-5718	324	38	σ1σ2	σ1σ2	VERB
ejpam-5718	324	39	-	-	ADJ
ejpam-5718	324	40	open	open	ADJ
ejpam-5718	324	41	set	set	NOUN
ejpam-5718	324	42	v	v	NOUN
ejpam-5718	324	43	of	of	ADP
ejpam-5718	324	44	y	y	PRON
ejpam-5718	324	45	such	such	ADJ
ejpam-5718	324	46	that	that	SCONJ
ejpam-5718	324	47	f	f	PROPN
ejpam-5718	324	48	(	(	PUNCT
ejpam-5718	324	49	x)∩	x)∩	PROPN
ejpam-5718	324	50	v	v	ADP
ejpam-5718	324	51	̸=	̸=	PROPN
ejpam-5718	324	52	∅	∅	NOUN
ejpam-5718	324	53	and	and	CCONJ
ejpam-5718	324	54	having	have	VERB
ejpam-5718	324	55	σ1σ2	σ1σ2	NOUN
ejpam-5718	324	56	-	-	PUNCT
ejpam-5718	324	57	connected	connect	VERB
ejpam-5718	324	58	complement	complement	NOUN
ejpam-5718	324	59	,	,	PUNCT
ejpam-5718	324	60	there	there	PRON
ejpam-5718	324	61	exists	exist	VERB
ejpam-5718	324	62	a	a	DET
ejpam-5718	324	63	τ1τ2	τ1τ2	NOUN
ejpam-5718	324	64	-	-	ADJ
ejpam-5718	324	65	open	open	ADJ
ejpam-5718	324	66	set	set	ADJ
ejpam-5718	324	67	u	u	NOUN
ejpam-5718	324	68	of	of	ADP
ejpam-5718	324	69	x	x	PUNCT
ejpam-5718	324	70	containing	contain	VERB
ejpam-5718	324	71	x	x	PUNCT
ejpam-5718	324	72	such	such	ADJ
ejpam-5718	324	73	that	that	SCONJ
ejpam-5718	324	74	f	f	PROPN
ejpam-5718	324	75	(	(	PUNCT
ejpam-5718	324	76	z	z	NOUN
ejpam-5718	324	77	)	)	PUNCT
ejpam-5718	324	78	∩	∩	NOUN
ejpam-5718	324	79	v	v	ADP
ejpam-5718	324	80	̸=	̸=	PROPN
ejpam-5718	324	81	∅	∅	NOUN
ejpam-5718	324	82	for	for	ADP
ejpam-5718	324	83	each	each	DET
ejpam-5718	324	84	z	z	NOUN
ejpam-5718	324	85	∈	∈	PROPN
ejpam-5718	324	86	u	u	NOUN
ejpam-5718	324	87	.	.	PUNCT
ejpam-5718	325	1	a	a	DET
ejpam-5718	325	2	multifunction	multifunction	NOUN
ejpam-5718	325	3	f	f	NOUN
ejpam-5718	325	4	:	:	PUNCT
ejpam-5718	325	5	(	(	PUNCT
ejpam-5718	325	6	x	x	NOUN
ejpam-5718	325	7	,	,	PUNCT
ejpam-5718	325	8	τ1	τ1	NOUN
ejpam-5718	325	9	,	,	PUNCT
ejpam-5718	325	10	τ2	τ2	NOUN
ejpam-5718	325	11	)	)	PUNCT
ejpam-5718	325	12	→	→	SYM
ejpam-5718	325	13	(	(	PUNCT
ejpam-5718	325	14	y	y	PROPN
ejpam-5718	325	15	,	,	PUNCT
ejpam-5718	325	16	σ1	σ1	PROPN
ejpam-5718	325	17	,	,	PUNCT
ejpam-5718	325	18	σ2	σ2	PROPN
ejpam-5718	325	19	)	)	PUNCT
ejpam-5718	325	20	is	be	AUX
ejpam-5718	325	21	said	say	VERB
ejpam-5718	325	22	to	to	PART
ejpam-5718	325	23	be	be	AUX
ejpam-5718	325	24	lower	low	ADJ
ejpam-5718	325	25	s-(τ1	s-(τ1	NOUN
ejpam-5718	325	26	,	,	PUNCT
ejpam-5718	325	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	325	28	if	if	SCONJ
ejpam-5718	325	29	f	f	PROPN
ejpam-5718	325	30	has	have	VERB
ejpam-5718	325	31	this	this	DET
ejpam-5718	325	32	property	property	NOUN
ejpam-5718	325	33	at	at	ADP
ejpam-5718	325	34	each	each	DET
ejpam-5718	325	35	point	point	NOUN
ejpam-5718	325	36	x	x	PUNCT
ejpam-5718	325	37	of	of	ADP
ejpam-5718	325	38	x.	x.	PROPN
ejpam-5718	325	39	theorem	theorem	VERB
ejpam-5718	325	40	15	15	NUM
ejpam-5718	325	41	.	.	PUNCT
ejpam-5718	326	1	let	let	VERB
ejpam-5718	326	2	f	f	NOUN
ejpam-5718	326	3	:	:	PUNCT
ejpam-5718	326	4	(	(	PUNCT
ejpam-5718	326	5	x	x	NOUN
ejpam-5718	326	6	,	,	PUNCT
ejpam-5718	326	7	τ1	τ1	NOUN
ejpam-5718	326	8	,	,	PUNCT
ejpam-5718	326	9	τ2	τ2	NOUN
ejpam-5718	326	10	)	)	PUNCT
ejpam-5718	326	11	→	→	SYM
ejpam-5718	326	12	(	(	PUNCT
ejpam-5718	326	13	y	y	PROPN
ejpam-5718	326	14	,	,	PUNCT
ejpam-5718	326	15	σ1	σ1	PROPN
ejpam-5718	326	16	,	,	PUNCT
ejpam-5718	326	17	σ2	σ2	PROPN
ejpam-5718	326	18	)	)	PUNCT
ejpam-5718	326	19	be	be	VERB
ejpam-5718	326	20	a	a	DET
ejpam-5718	326	21	multifunction	multifunction	NOUN
ejpam-5718	326	22	such	such	ADJ
ejpam-5718	326	23	that	that	SCONJ
ejpam-5718	326	24	f	f	PROPN
ejpam-5718	326	25	(	(	PUNCT
ejpam-5718	326	26	x	x	X
ejpam-5718	326	27	)	)	PUNCT
ejpam-5718	326	28	is	be	AUX
ejpam-5718	326	29	σ1σ2open	σ1σ2open	VERB
ejpam-5718	326	30	in	in	ADP
ejpam-5718	326	31	y	y	PROPN
ejpam-5718	326	32	for	for	ADP
ejpam-5718	326	33	each	each	DET
ejpam-5718	326	34	x	x	SYM
ejpam-5718	326	35	∈	∈	PROPN
ejpam-5718	326	36	x.	x.	NOUN
ejpam-5718	326	37	then	then	ADV
ejpam-5718	326	38	,	,	PUNCT
ejpam-5718	326	39	f	f	PROPN
ejpam-5718	326	40	is	be	AUX
ejpam-5718	326	41	lower	low	ADJ
ejpam-5718	326	42	weakly	weakly	ADJ
ejpam-5718	326	43	s-(τ1	s-(τ1	PROPN
ejpam-5718	326	44	,	,	PUNCT
ejpam-5718	326	45	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	326	46	if	if	SCONJ
ejpam-5718	326	47	and	and	CCONJ
ejpam-5718	326	48	only	only	ADV
ejpam-5718	326	49	if	if	SCONJ
ejpam-5718	326	50	f	f	PROPN
ejpam-5718	326	51	is	be	AUX
ejpam-5718	326	52	lower	low	ADJ
ejpam-5718	326	53	s-(τ1	s-(τ1	NOUN
ejpam-5718	326	54	,	,	PUNCT
ejpam-5718	326	55	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	326	56	.	.	PUNCT
ejpam-5718	327	1	proof	proof	NOUN
ejpam-5718	327	2	.	.	PUNCT
ejpam-5718	328	1	suppose	suppose	VERB
ejpam-5718	328	2	that	that	SCONJ
ejpam-5718	328	3	f	f	PROPN
ejpam-5718	328	4	is	be	AUX
ejpam-5718	328	5	lower	low	ADJ
ejpam-5718	328	6	weakly	weakly	ADJ
ejpam-5718	328	7	s-(τ1	s-(τ1	PROPN
ejpam-5718	328	8	,	,	PUNCT
ejpam-5718	328	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	328	10	.	.	PUNCT
ejpam-5718	329	1	let	let	VERB
ejpam-5718	329	2	x	x	PUNCT
ejpam-5718	329	3	∈	∈	PROPN
ejpam-5718	329	4	x	x	X
ejpam-5718	329	5	and	and	CCONJ
ejpam-5718	329	6	v	v	X
ejpam-5718	329	7	be	be	AUX
ejpam-5718	329	8	any	any	DET
ejpam-5718	329	9	σ1σ2	σ1σ2	NOUN
ejpam-5718	329	10	-	-	ADJ
ejpam-5718	329	11	open	open	ADJ
ejpam-5718	329	12	set	set	NOUN
ejpam-5718	329	13	of	of	ADP
ejpam-5718	329	14	y	y	PRON
ejpam-5718	329	15	such	such	ADJ
ejpam-5718	329	16	that	that	SCONJ
ejpam-5718	329	17	f	f	PROPN
ejpam-5718	329	18	(	(	PUNCT
ejpam-5718	329	19	x)∩v	x)∩v	PROPN
ejpam-5718	329	20	̸=	̸=	PROPN
ejpam-5718	329	21	∅	∅	NOUN
ejpam-5718	329	22	and	and	CCONJ
ejpam-5718	329	23	having	have	VERB
ejpam-5718	329	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	329	25	-	-	PUNCT
ejpam-5718	329	26	connected	connect	VERB
ejpam-5718	329	27	complement	complement	NOUN
ejpam-5718	329	28	.	.	PUNCT
ejpam-5718	330	1	since	since	SCONJ
ejpam-5718	330	2	f	f	PROPN
ejpam-5718	330	3	is	be	AUX
ejpam-5718	330	4	lower	low	ADJ
ejpam-5718	330	5	weakly	weakly	ADJ
ejpam-5718	330	6	s-(τ1	s-(τ1	PROPN
ejpam-5718	330	7	,	,	PUNCT
ejpam-5718	330	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	330	9	,	,	PUNCT
ejpam-5718	330	10	there	there	PRON
ejpam-5718	330	11	exists	exist	VERB
ejpam-5718	330	12	a	a	DET
ejpam-5718	330	13	τ1τ2	τ1τ2	NOUN
ejpam-5718	330	14	-	-	ADJ
ejpam-5718	330	15	open	open	ADJ
ejpam-5718	330	16	set	set	ADJ
ejpam-5718	330	17	u	u	NOUN
ejpam-5718	330	18	of	of	ADP
ejpam-5718	330	19	x	x	PUNCT
ejpam-5718	330	20	containing	contain	VERB
ejpam-5718	330	21	x	x	PUNCT
ejpam-5718	330	22	such	such	ADJ
ejpam-5718	330	23	that	that	SCONJ
ejpam-5718	330	24	σ1σ2	σ1σ2	NOUN
ejpam-5718	330	25	-	-	PUNCT
ejpam-5718	330	26	cl(v	cl(v	NOUN
ejpam-5718	330	27	)	)	PUNCT
ejpam-5718	330	28	∩	∩	PROPN
ejpam-5718	330	29	f	f	X
ejpam-5718	330	30	(	(	PUNCT
ejpam-5718	330	31	z	z	NOUN
ejpam-5718	330	32	)	)	PUNCT
ejpam-5718	330	33	̸=	̸=	NOUN
ejpam-5718	330	34	∅	∅	NOUN
ejpam-5718	330	35	for	for	ADP
ejpam-5718	330	36	each	each	DET
ejpam-5718	330	37	z	z	NOUN
ejpam-5718	330	38	∈	∈	PROPN
ejpam-5718	330	39	u	u	PROPN
ejpam-5718	330	40	.	.	PUNCT
ejpam-5718	331	1	since	since	SCONJ
ejpam-5718	331	2	f	f	PROPN
ejpam-5718	331	3	(	(	PUNCT
ejpam-5718	331	4	z	z	NOUN
ejpam-5718	331	5	)	)	PUNCT
ejpam-5718	331	6	is	be	AUX
ejpam-5718	331	7	σ1σ2	σ1σ2	NOUN
ejpam-5718	331	8	-	-	ADJ
ejpam-5718	331	9	open	open	ADJ
ejpam-5718	331	10	,	,	PUNCT
ejpam-5718	331	11	f	f	PROPN
ejpam-5718	331	12	(	(	PUNCT
ejpam-5718	331	13	z	z	NOUN
ejpam-5718	331	14	)	)	PUNCT
ejpam-5718	331	15	∩	∩	NOUN
ejpam-5718	331	16	v	v	ADP
ejpam-5718	331	17	̸=	̸=	PROPN
ejpam-5718	331	18	∅	∅	NOUN
ejpam-5718	331	19	for	for	ADP
ejpam-5718	331	20	each	each	DET
ejpam-5718	331	21	z	z	NOUN
ejpam-5718	331	22	∈	∈	PROPN
ejpam-5718	331	23	u	u	NOUN
ejpam-5718	331	24	and	and	CCONJ
ejpam-5718	331	25	hence	hence	ADV
ejpam-5718	331	26	f	f	PROPN
ejpam-5718	331	27	is	be	AUX
ejpam-5718	331	28	lower	low	ADJ
ejpam-5718	331	29	s-(τ1	s-(τ1	NOUN
ejpam-5718	331	30	,	,	PUNCT
ejpam-5718	331	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	331	32	.	.	PUNCT
ejpam-5718	332	1	the	the	DET
ejpam-5718	332	2	converse	converse	NOUN
ejpam-5718	332	3	is	be	AUX
ejpam-5718	332	4	obvious	obvious	ADJ
ejpam-5718	332	5	.	.	PUNCT
ejpam-5718	333	1	acknowledgements	acknowledgement	NOUN
ejpam-5718	333	2	this	this	DET
ejpam-5718	333	3	research	research	NOUN
ejpam-5718	333	4	project	project	NOUN
ejpam-5718	333	5	was	be	AUX
ejpam-5718	333	6	financially	financially	ADV
ejpam-5718	333	7	supported	support	VERB
ejpam-5718	333	8	by	by	ADP
ejpam-5718	333	9	mahasarakham	mahasarakham	PROPN
ejpam-5718	333	10	university	university	PROPN
ejpam-5718	333	11	.	.	PUNCT
ejpam-5718	334	1	p.	p.	NOUN
ejpam-5718	334	2	pue	pue	NOUN
ejpam-5718	334	3	-	-	PUNCT
ejpam-5718	334	4	on	on	ADP
ejpam-5718	334	5	,	,	PUNCT
ejpam-5718	334	6	a.	a.	PROPN
ejpam-5718	334	7	sama	sama	PROPN
ejpam-5718	334	8	-	-	PUNCT
ejpam-5718	334	9	ae	ae	PROPN
ejpam-5718	334	10	,	,	PUNCT
ejpam-5718	334	11	c.	c.	PROPN
ejpam-5718	334	12	boonpok	boonpok	PROPN
ejpam-5718	334	13	/	/	SYM
ejpam-5718	334	14	eur	eur	PROPN
ejpam-5718	334	15	.	.	PUNCT
ejpam-5718	335	1	j.	j.	PROPN
ejpam-5718	335	2	pure	pure	PROPN
ejpam-5718	335	3	appl	appl	PROPN
ejpam-5718	335	4	.	.	PROPN
ejpam-5718	335	5	math	math	PROPN
ejpam-5718	335	6	,	,	PUNCT
ejpam-5718	335	7	18	18	NUM
ejpam-5718	335	8	(	(	PUNCT
ejpam-5718	335	9	1	1	NUM
ejpam-5718	335	10	)	)	PUNCT
ejpam-5718	335	11	(	(	PUNCT
ejpam-5718	335	12	2025	2025	NUM
ejpam-5718	335	13	)	)	PUNCT
ejpam-5718	335	14	,	,	PUNCT
ejpam-5718	335	15	5718	5718	NUM
ejpam-5718	335	16	13	13	NUM
ejpam-5718	335	17	of	of	ADP
ejpam-5718	335	18	16	16	NUM
ejpam-5718	335	19	references	reference	NOUN
ejpam-5718	335	20	[	[	X
ejpam-5718	335	21	1	1	NUM
ejpam-5718	335	22	]	]	PUNCT
ejpam-5718	335	23	c.	c.	PROPN
ejpam-5718	335	24	boonpok	boonpok	PROPN
ejpam-5718	335	25	.	.	PUNCT
ejpam-5718	336	1	almost	almost	ADV
ejpam-5718	336	2	(	(	PUNCT
ejpam-5718	336	3	g	g	NOUN
ejpam-5718	336	4	,	,	PUNCT
ejpam-5718	336	5	m)-continuous	m)-continuous	ADJ
ejpam-5718	336	6	functions	function	NOUN
ejpam-5718	336	7	.	.	PUNCT
ejpam-5718	337	1	international	international	ADJ
ejpam-5718	337	2	journal	journal	PROPN
ejpam-5718	337	3	of	of	ADP
ejpam-5718	337	4	mathematical	mathematical	ADJ
ejpam-5718	337	5	analysis	analysis	NOUN
ejpam-5718	337	6	,	,	PUNCT
ejpam-5718	337	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5718	337	8	,	,	PUNCT
ejpam-5718	337	9	2010	2010	NUM
ejpam-5718	337	10	.	.	PUNCT
ejpam-5718	338	1	[	[	X
ejpam-5718	338	2	2	2	NUM
ejpam-5718	338	3	]	]	PUNCT
ejpam-5718	338	4	c.	c.	PROPN
ejpam-5718	338	5	boonpok	boonpok	PROPN
ejpam-5718	338	6	.	.	PUNCT
ejpam-5718	339	1	m	m	VERB
ejpam-5718	339	2	-continuous	-continuous	ADJ
ejpam-5718	339	3	functions	function	NOUN
ejpam-5718	339	4	in	in	ADP
ejpam-5718	339	5	biminimal	biminimal	NOUN
ejpam-5718	339	6	structure	structure	NOUN
ejpam-5718	339	7	spaces	space	NOUN
ejpam-5718	339	8	.	.	PUNCT
ejpam-5718	340	1	far	far	PROPN
ejpam-5718	340	2	east	east	PROPN
ejpam-5718	340	3	journal	journal	PROPN
ejpam-5718	340	4	of	of	ADP
ejpam-5718	340	5	mathematical	mathematical	ADJ
ejpam-5718	340	6	sciences	science	NOUN
ejpam-5718	340	7	,	,	PUNCT
ejpam-5718	340	8	43(1):41–58	43(1):41–58	NUM
ejpam-5718	340	9	,	,	PUNCT
ejpam-5718	340	10	2010	2010	NUM
ejpam-5718	340	11	.	.	PUNCT
ejpam-5718	341	1	[	[	X
ejpam-5718	341	2	3	3	X
ejpam-5718	341	3	]	]	PUNCT
ejpam-5718	341	4	c.	c.	PROPN
ejpam-5718	341	5	boonpok	boonpok	PROPN
ejpam-5718	341	6	.	.	PUNCT
ejpam-5718	342	1	on	on	ADP
ejpam-5718	342	2	continuous	continuous	ADJ
ejpam-5718	342	3	multifunctions	multifunction	NOUN
ejpam-5718	342	4	in	in	ADP
ejpam-5718	342	5	ideal	ideal	ADJ
ejpam-5718	342	6	topological	topological	ADJ
ejpam-5718	342	7	spaces	space	NOUN
ejpam-5718	342	8	.	.	PUNCT
ejpam-5718	343	1	lobachevskii	lobachevskii	PROPN
ejpam-5718	343	2	journal	journal	PROPN
ejpam-5718	343	3	of	of	ADP
ejpam-5718	343	4	mathematics	mathematic	NOUN
ejpam-5718	343	5	,	,	PUNCT
ejpam-5718	343	6	40(1):24–35	40(1):24–35	NUM
ejpam-5718	343	7	,	,	PUNCT
ejpam-5718	343	8	2019	2019	NUM
ejpam-5718	343	9	.	.	PUNCT
ejpam-5718	344	1	[	[	X
ejpam-5718	344	2	4	4	NUM
ejpam-5718	344	3	]	]	PUNCT
ejpam-5718	344	4	c.	c.	PROPN
ejpam-5718	344	5	boonpok	boonpok	PROPN
ejpam-5718	344	6	.	.	PUNCT
ejpam-5718	345	1	on	on	ADP
ejpam-5718	345	2	characterizations	characterization	NOUN
ejpam-5718	345	3	of	of	ADP
ejpam-5718	345	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5718	345	5	ideal	ideal	ADJ
ejpam-5718	345	6	topological	topological	ADJ
ejpam-5718	345	7	spaces	space	NOUN
ejpam-5718	345	8	.	.	PUNCT
ejpam-5718	346	1	journal	journal	NOUN
ejpam-5718	346	2	of	of	ADP
ejpam-5718	346	3	mathematics	mathematic	NOUN
ejpam-5718	346	4	,	,	PUNCT
ejpam-5718	346	5	2020:9387601	2020:9387601	NUM
ejpam-5718	346	6	,	,	PUNCT
ejpam-5718	346	7	2020	2020	NUM
ejpam-5718	346	8	.	.	PUNCT
ejpam-5718	347	1	[	[	X
ejpam-5718	347	2	5	5	X
ejpam-5718	347	3	]	]	PUNCT
ejpam-5718	347	4	c.	c.	PROPN
ejpam-5718	347	5	boonpok	boonpok	PROPN
ejpam-5718	347	6	.	.	PUNCT
ejpam-5718	348	1	(	(	PUNCT
ejpam-5718	348	2	τ1	τ1	NOUN
ejpam-5718	348	3	,	,	PUNCT
ejpam-5718	348	4	τ2)δ	τ2)δ	ADJ
ejpam-5718	348	5	-	-	PUNCT
ejpam-5718	348	6	semicontinuous	semicontinuous	ADJ
ejpam-5718	348	7	multifunctions	multifunction	NOUN
ejpam-5718	348	8	.	.	PUNCT
ejpam-5718	349	1	heliyon	heliyon	NOUN
ejpam-5718	349	2	,	,	PUNCT
ejpam-5718	349	3	6	6	NUM
ejpam-5718	349	4	:	:	SYM
ejpam-5718	349	5	e05367	e05367	PROPN
ejpam-5718	349	6	,	,	PUNCT
ejpam-5718	349	7	2020	2020	NUM
ejpam-5718	349	8	.	.	PUNCT
ejpam-5718	350	1	[	[	X
ejpam-5718	350	2	6	6	NUM
ejpam-5718	350	3	]	]	PUNCT
ejpam-5718	350	4	c.	c.	PROPN
ejpam-5718	350	5	boonpok	boonpok	PROPN
ejpam-5718	350	6	.	.	PUNCT
ejpam-5718	351	1	weak	weak	ADJ
ejpam-5718	351	2	quasi	quasi	ADJ
ejpam-5718	351	3	continuity	continuity	NOUN
ejpam-5718	351	4	for	for	ADP
ejpam-5718	351	5	multifunctions	multifunction	NOUN
ejpam-5718	351	6	in	in	ADP
ejpam-5718	351	7	ideal	ideal	ADJ
ejpam-5718	351	8	topological	topological	ADJ
ejpam-5718	351	9	spaces	space	NOUN
ejpam-5718	351	10	.	.	PUNCT
ejpam-5718	352	1	advances	advance	NOUN
ejpam-5718	352	2	in	in	ADP
ejpam-5718	352	3	mathematics	mathematic	NOUN
ejpam-5718	352	4	:	:	PUNCT
ejpam-5718	352	5	scientific	scientific	ADJ
ejpam-5718	352	6	journal	journal	NOUN
ejpam-5718	352	7	,	,	PUNCT
ejpam-5718	352	8	9(1):339–355	9(1):339–355	NUM
ejpam-5718	352	9	,	,	PUNCT
ejpam-5718	352	10	2020	2020	NUM
ejpam-5718	352	11	.	.	PUNCT
ejpam-5718	353	1	[	[	X
ejpam-5718	353	2	7	7	X
ejpam-5718	353	3	]	]	X
ejpam-5718	353	4	c.	c.	PROPN
ejpam-5718	353	5	boonpok	boonpok	PROPN
ejpam-5718	353	6	.	.	PUNCT
ejpam-5718	354	1	upper	upper	ADJ
ejpam-5718	354	2	and	and	CCONJ
ejpam-5718	354	3	lower	low	ADJ
ejpam-5718	354	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5718	354	5	.	.	PUNCT
ejpam-5718	354	6	heliyon	heliyon	NOUN
ejpam-5718	354	7	,	,	PUNCT
ejpam-5718	354	8	7	7	NUM
ejpam-5718	354	9	:	:	PUNCT
ejpam-5718	354	10	e05986	e05986	PROPN
ejpam-5718	354	11	,	,	PUNCT
ejpam-5718	354	12	2021	2021	NUM
ejpam-5718	354	13	.	.	PUNCT
ejpam-5718	355	1	[	[	X
ejpam-5718	355	2	8	8	NUM
ejpam-5718	355	3	]	]	X
ejpam-5718	355	4	c.	c.	PROPN
ejpam-5718	355	5	boonpok	boonpok	PROPN
ejpam-5718	355	6	.	.	PUNCT
ejpam-5718	356	1	on	on	ADP
ejpam-5718	356	2	some	some	DET
ejpam-5718	356	3	closed	closed	ADJ
ejpam-5718	356	4	sets	set	NOUN
ejpam-5718	356	5	and	and	CCONJ
ejpam-5718	356	6	low	low	ADJ
ejpam-5718	356	7	separation	separation	NOUN
ejpam-5718	356	8	axioms	axiom	NOUN
ejpam-5718	356	9	via	via	ADP
ejpam-5718	356	10	topological	topological	ADJ
ejpam-5718	356	11	ideals	ideal	NOUN
ejpam-5718	356	12	.	.	PUNCT
ejpam-5718	357	1	european	european	ADJ
ejpam-5718	357	2	journal	journal	PROPN
ejpam-5718	357	3	of	of	ADP
ejpam-5718	357	4	pure	pure	ADJ
ejpam-5718	357	5	and	and	CCONJ
ejpam-5718	357	6	applied	applied	ADJ
ejpam-5718	357	7	mathematics	mathematic	NOUN
ejpam-5718	357	8	,	,	PUNCT
ejpam-5718	357	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5718	357	10	,	,	PUNCT
ejpam-5718	357	11	2022	2022	NUM
ejpam-5718	357	12	.	.	PUNCT
ejpam-5718	358	1	[	[	X
ejpam-5718	358	2	9	9	NUM
ejpam-5718	358	3	]	]	PUNCT
ejpam-5718	358	4	c.	c.	PROPN
ejpam-5718	358	5	boonpok	boonpok	PROPN
ejpam-5718	358	6	.	.	PUNCT
ejpam-5718	359	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-5718	359	2	continuity	continuity	NOUN
ejpam-5718	359	3	for	for	ADP
ejpam-5718	359	4	multifunctions	multifunction	NOUN
ejpam-5718	359	5	.	.	PUNCT
ejpam-5718	360	1	wseas	wseas	PROPN
ejpam-5718	360	2	transactions	transaction	NOUN
ejpam-5718	360	3	on	on	ADP
ejpam-5718	360	4	mathematics	mathematic	NOUN
ejpam-5718	360	5	,	,	PUNCT
ejpam-5718	360	6	21:245–251	21:245–251	NUM
ejpam-5718	360	7	,	,	PUNCT
ejpam-5718	360	8	2022	2022	NUM
ejpam-5718	360	9	.	.	PUNCT
ejpam-5718	361	1	[	[	X
ejpam-5718	361	2	10	10	NUM
ejpam-5718	361	3	]	]	X
ejpam-5718	361	4	c.	c.	PROPN
ejpam-5718	361	5	boonpok	boonpok	PROPN
ejpam-5718	361	6	.	.	PUNCT
ejpam-5718	362	1	on	on	ADP
ejpam-5718	362	2	some	some	DET
ejpam-5718	362	3	spaces	space	NOUN
ejpam-5718	362	4	via	via	ADP
ejpam-5718	362	5	topological	topological	ADJ
ejpam-5718	362	6	ideals	ideal	NOUN
ejpam-5718	362	7	.	.	PUNCT
ejpam-5718	363	1	open	open	ADJ
ejpam-5718	363	2	mathematics	mathematic	NOUN
ejpam-5718	363	3	,	,	PUNCT
ejpam-5718	363	4	21:20230118	21:20230118	NUM
ejpam-5718	363	5	,	,	PUNCT
ejpam-5718	363	6	2023	2023	NUM
ejpam-5718	363	7	.	.	PUNCT
ejpam-5718	364	1	[	[	X
ejpam-5718	364	2	11	11	NUM
ejpam-5718	364	3	]	]	PUNCT
ejpam-5718	364	4	c.	c.	PROPN
ejpam-5718	364	5	boonpok	boonpok	PROPN
ejpam-5718	364	6	.	.	PUNCT
ejpam-5718	365	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5718	365	2	.	.	PUNCT
ejpam-5718	366	1	mathematica	mathematica	PROPN
ejpam-5718	366	2	,	,	PUNCT
ejpam-5718	366	3	65(1):31–42	65(1):31–42	NUM
ejpam-5718	366	4	,	,	PUNCT
ejpam-5718	366	5	2023	2023	NUM
ejpam-5718	366	6	.	.	PUNCT
ejpam-5718	367	1	[	[	X
ejpam-5718	367	2	12	12	NUM
ejpam-5718	367	3	]	]	X
ejpam-5718	367	4	c.	c.	PROPN
ejpam-5718	367	5	boonpok	boonpok	PROPN
ejpam-5718	367	6	and	and	CCONJ
ejpam-5718	367	7	j.	j.	PROPN
ejpam-5718	367	8	khampakdee	khampakdee	PROPN
ejpam-5718	367	9	.	.	PUNCT
ejpam-5718	368	1	(	(	PUNCT
ejpam-5718	368	2	λ	λ	NOUN
ejpam-5718	368	3	,	,	PUNCT
ejpam-5718	368	4	sp)-open	sp)-open	ADJ
ejpam-5718	368	5	sets	set	NOUN
ejpam-5718	368	6	in	in	ADP
ejpam-5718	368	7	topological	topological	ADJ
ejpam-5718	368	8	spaces	space	NOUN
ejpam-5718	368	9	.	.	PUNCT
ejpam-5718	369	1	european	european	ADJ
ejpam-5718	369	2	journal	journal	PROPN
ejpam-5718	369	3	of	of	ADP
ejpam-5718	369	4	pure	pure	ADJ
ejpam-5718	369	5	and	and	CCONJ
ejpam-5718	369	6	applied	applied	ADJ
ejpam-5718	369	7	mathematics	mathematic	NOUN
ejpam-5718	369	8	,	,	PUNCT
ejpam-5718	369	9	15(2):572–588	15(2):572–588	NUM
ejpam-5718	369	10	,	,	PUNCT
ejpam-5718	369	11	2022	2022	NUM
ejpam-5718	369	12	.	.	PUNCT
ejpam-5718	370	1	[	[	X
ejpam-5718	370	2	13	13	NUM
ejpam-5718	370	3	]	]	PUNCT
ejpam-5718	370	4	c.	c.	PROPN
ejpam-5718	370	5	boonpok	boonpok	PROPN
ejpam-5718	370	6	and	and	CCONJ
ejpam-5718	370	7	j.	j.	PROPN
ejpam-5718	370	8	khampakdee	khampakdee	PROPN
ejpam-5718	370	9	.	.	PUNCT
ejpam-5718	371	1	on	on	ADP
ejpam-5718	371	2	almost	almost	ADV
ejpam-5718	371	3	α(λ	α(λ	PROPN
ejpam-5718	371	4	,	,	PUNCT
ejpam-5718	371	5	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	371	6	multifunctions	multifunction	NOUN
ejpam-5718	371	7	.	.	PUNCT
ejpam-5718	372	1	european	european	PROPN
ejpam-5718	372	2	journal	journal	PROPN
ejpam-5718	372	3	of	of	ADP
ejpam-5718	372	4	pure	pure	ADJ
ejpam-5718	372	5	and	and	CCONJ
ejpam-5718	372	6	applied	applied	ADJ
ejpam-5718	372	7	mathematics	mathematic	NOUN
ejpam-5718	372	8	,	,	PUNCT
ejpam-5718	372	9	15(2):626–634	15(2):626–634	PROPN
ejpam-5718	372	10	,	,	PUNCT
ejpam-5718	372	11	2022	2022	NUM
ejpam-5718	372	12	.	.	PUNCT
ejpam-5718	373	1	[	[	X
ejpam-5718	373	2	14	14	NUM
ejpam-5718	373	3	]	]	X
ejpam-5718	373	4	c.	c.	PROPN
ejpam-5718	373	5	boonpok	boonpok	PROPN
ejpam-5718	373	6	and	and	CCONJ
ejpam-5718	373	7	j.	j.	PROPN
ejpam-5718	373	8	khampakdee	khampakdee	PROPN
ejpam-5718	373	9	.	.	PUNCT
ejpam-5718	374	1	slight	slight	PROPN
ejpam-5718	374	2	(	(	PUNCT
ejpam-5718	374	3	λ	λ	NOUN
ejpam-5718	374	4	,	,	PUNCT
ejpam-5718	374	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5718	374	6	and	and	CCONJ
ejpam-5718	374	7	λsp	λsp	NOUN
ejpam-5718	374	8	-	-	PUNCT
ejpam-5718	374	9	extremally	extremally	ADV
ejpam-5718	374	10	disconnectedness	disconnectedness	NOUN
ejpam-5718	374	11	.	.	PUNCT
ejpam-5718	375	1	european	european	ADJ
ejpam-5718	375	2	journal	journal	PROPN
ejpam-5718	375	3	of	of	ADP
ejpam-5718	375	4	pure	pure	ADJ
ejpam-5718	375	5	and	and	CCONJ
ejpam-5718	375	6	applied	applied	ADJ
ejpam-5718	375	7	mathematics	mathematic	NOUN
ejpam-5718	375	8	,	,	PUNCT
ejpam-5718	375	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-5718	375	10	,	,	PUNCT
ejpam-5718	375	11	2022	2022	NUM
ejpam-5718	375	12	.	.	PUNCT
ejpam-5718	376	1	[	[	X
ejpam-5718	376	2	15	15	NUM
ejpam-5718	376	3	]	]	X
ejpam-5718	376	4	c.	c.	PROPN
ejpam-5718	376	5	boonpok	boonpok	PROPN
ejpam-5718	376	6	and	and	CCONJ
ejpam-5718	376	7	j.	j.	PROPN
ejpam-5718	376	8	khampakdee	khampakdee	PROPN
ejpam-5718	376	9	.	.	PUNCT
ejpam-5718	377	1	upper	upper	ADJ
ejpam-5718	377	2	and	and	CCONJ
ejpam-5718	377	3	lower	low	ADJ
ejpam-5718	377	4	weak	weak	ADJ
ejpam-5718	377	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-5718	377	6	.	.	PUNCT
ejpam-5718	378	1	european	european	PROPN
ejpam-5718	378	2	journal	journal	PROPN
ejpam-5718	378	3	of	of	ADP
ejpam-5718	378	4	pure	pure	ADJ
ejpam-5718	378	5	and	and	CCONJ
ejpam-5718	378	6	applied	applied	ADJ
ejpam-5718	378	7	mathematics	mathematic	NOUN
ejpam-5718	378	8	,	,	PUNCT
ejpam-5718	378	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-5718	378	10	,	,	PUNCT
ejpam-5718	378	11	2023	2023	NUM
ejpam-5718	378	12	.	.	PUNCT
ejpam-5718	379	1	[	[	X
ejpam-5718	379	2	16	16	NUM
ejpam-5718	379	3	]	]	X
ejpam-5718	379	4	c.	c.	PROPN
ejpam-5718	379	5	boonpok	boonpok	PROPN
ejpam-5718	379	6	and	and	CCONJ
ejpam-5718	379	7	j.	j.	PROPN
ejpam-5718	379	8	khampakdee	khampakdee	PROPN
ejpam-5718	379	9	.	.	PUNCT
ejpam-5718	380	1	almost	almost	ADV
ejpam-5718	380	2	strong	strong	ADJ
ejpam-5718	380	3	θ(λ	θ(λ	PROPN
ejpam-5718	380	4	,	,	PUNCT
ejpam-5718	380	5	p)-continuity	p)-continuity	NOUN
ejpam-5718	380	6	for	for	ADP
ejpam-5718	380	7	functions	function	NOUN
ejpam-5718	380	8	.	.	PUNCT
ejpam-5718	381	1	european	european	ADJ
ejpam-5718	381	2	journal	journal	PROPN
ejpam-5718	381	3	of	of	ADP
ejpam-5718	381	4	pure	pure	ADJ
ejpam-5718	381	5	and	and	CCONJ
ejpam-5718	381	6	applied	applied	ADJ
ejpam-5718	381	7	mathematics	mathematic	NOUN
ejpam-5718	381	8	,	,	PUNCT
ejpam-5718	381	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5718	381	10	,	,	PUNCT
ejpam-5718	381	11	2024	2024	NUM
ejpam-5718	381	12	.	.	PUNCT
ejpam-5718	382	1	[	[	X
ejpam-5718	382	2	17	17	NUM
ejpam-5718	382	3	]	]	X
ejpam-5718	382	4	c.	c.	PROPN
ejpam-5718	382	5	boonpok	boonpok	PROPN
ejpam-5718	382	6	and	and	CCONJ
ejpam-5718	382	7	j.	j.	PROPN
ejpam-5718	382	8	khampakdee	khampakdee	PROPN
ejpam-5718	382	9	.	.	PUNCT
ejpam-5718	383	1	upper	upper	ADJ
ejpam-5718	383	2	and	and	CCONJ
ejpam-5718	383	3	lower	low	ADJ
ejpam-5718	383	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5718	383	5	.	.	PUNCT
ejpam-5718	383	6	european	european	PROPN
ejpam-5718	383	7	journal	journal	PROPN
ejpam-5718	383	8	of	of	ADP
ejpam-5718	383	9	pure	pure	ADJ
ejpam-5718	383	10	and	and	CCONJ
ejpam-5718	383	11	applied	applied	ADJ
ejpam-5718	383	12	mathematics	mathematic	NOUN
ejpam-5718	383	13	,	,	PUNCT
ejpam-5718	383	14	17(1):201–211	17(1):201–211	NUM
ejpam-5718	383	15	,	,	PUNCT
ejpam-5718	383	16	2024	2024	NUM
ejpam-5718	383	17	.	.	PUNCT
ejpam-5718	384	1	[	[	X
ejpam-5718	384	2	18	18	NUM
ejpam-5718	384	3	]	]	PUNCT
ejpam-5718	384	4	c.	c.	PROPN
ejpam-5718	384	5	boonpok	boonpok	PROPN
ejpam-5718	384	6	and	and	CCONJ
ejpam-5718	384	7	c.	c.	PROPN
ejpam-5718	384	8	klanarong	klanarong	PROPN
ejpam-5718	384	9	.	.	PUNCT
ejpam-5718	385	1	on	on	ADP
ejpam-5718	385	2	weakly	weakly	ADJ
ejpam-5718	385	3	(	(	PUNCT
ejpam-5718	385	4	τ1	τ1	NOUN
ejpam-5718	385	5	,	,	PUNCT
ejpam-5718	385	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	385	7	functions	function	NOUN
ejpam-5718	385	8	.	.	PUNCT
ejpam-5718	386	1	european	european	ADJ
ejpam-5718	386	2	journal	journal	PROPN
ejpam-5718	386	3	of	of	ADP
ejpam-5718	386	4	pure	pure	ADJ
ejpam-5718	386	5	and	and	CCONJ
ejpam-5718	386	6	applied	applied	ADJ
ejpam-5718	386	7	mathematics	mathematic	NOUN
ejpam-5718	386	8	,	,	PUNCT
ejpam-5718	386	9	17(1):416–425	17(1):416–425	NUM
ejpam-5718	386	10	,	,	PUNCT
ejpam-5718	386	11	2024	2024	NUM
ejpam-5718	386	12	.	.	PUNCT
ejpam-5718	387	1	[	[	X
ejpam-5718	387	2	19	19	NUM
ejpam-5718	387	3	]	]	X
ejpam-5718	387	4	c.	c.	PROPN
ejpam-5718	387	5	boonpok	boonpok	PROPN
ejpam-5718	387	6	and	and	CCONJ
ejpam-5718	387	7	p.	p.	NOUN
ejpam-5718	387	8	pue	pue	NOUN
ejpam-5718	387	9	-	-	PUNCT
ejpam-5718	387	10	on	on	ADP
ejpam-5718	387	11	.	.	PUNCT
ejpam-5718	388	1	continuity	continuity	NOUN
ejpam-5718	388	2	for	for	ADP
ejpam-5718	388	3	multifunctions	multifunction	NOUN
ejpam-5718	388	4	in	in	ADP
ejpam-5718	388	5	ideal	ideal	ADJ
ejpam-5718	388	6	topological	topological	ADJ
ejpam-5718	388	7	spaces	space	NOUN
ejpam-5718	388	8	.	.	PUNCT
ejpam-5718	389	1	wseas	wseas	VERB
ejpam-5718	389	2	transactions	transaction	NOUN
ejpam-5718	389	3	on	on	ADP
ejpam-5718	389	4	mathematics	mathematic	NOUN
ejpam-5718	389	5	,	,	PUNCT
ejpam-5718	389	6	19:624–631	19:624–631	NUM
ejpam-5718	389	7	,	,	PUNCT
ejpam-5718	389	8	2020	2020	NUM
ejpam-5718	389	9	.	.	PUNCT
ejpam-5718	390	1	[	[	X
ejpam-5718	390	2	20	20	NUM
ejpam-5718	390	3	]	]	PUNCT
ejpam-5718	390	4	c.	c.	PROPN
ejpam-5718	390	5	boonpok	boonpok	PROPN
ejpam-5718	390	6	and	and	CCONJ
ejpam-5718	390	7	p.	p.	NOUN
ejpam-5718	390	8	pue	pue	NOUN
ejpam-5718	390	9	-	-	PUNCT
ejpam-5718	390	10	on	on	ADP
ejpam-5718	390	11	.	.	PUNCT
ejpam-5718	391	1	upper	upper	ADJ
ejpam-5718	391	2	and	and	CCONJ
ejpam-5718	391	3	lower	low	ADJ
ejpam-5718	391	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5718	391	5	multifunctions	multifunction	NOUN
ejpam-5718	391	6	.	.	PUNCT
ejpam-5718	392	1	european	european	ADJ
ejpam-5718	392	2	journal	journal	PROPN
ejpam-5718	392	3	of	of	ADP
ejpam-5718	392	4	pure	pure	ADJ
ejpam-5718	392	5	and	and	CCONJ
ejpam-5718	392	6	applied	applied	ADJ
ejpam-5718	392	7	mathematics	mathematic	NOUN
ejpam-5718	392	8	,	,	PUNCT
ejpam-5718	392	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-5718	392	10	,	,	PUNCT
ejpam-5718	392	11	2023	2023	NUM
ejpam-5718	392	12	.	.	PUNCT
ejpam-5718	393	1	[	[	X
ejpam-5718	393	2	21	21	NUM
ejpam-5718	393	3	]	]	X
ejpam-5718	393	4	c.	c.	PROPN
ejpam-5718	393	5	boonpok	boonpok	PROPN
ejpam-5718	393	6	and	and	CCONJ
ejpam-5718	393	7	p.	p.	NOUN
ejpam-5718	393	8	pue	pue	NOUN
ejpam-5718	393	9	-	-	PUNCT
ejpam-5718	393	10	on	on	ADP
ejpam-5718	393	11	.	.	PUNCT
ejpam-5718	394	1	upper	upper	ADJ
ejpam-5718	394	2	and	and	CCONJ
ejpam-5718	394	3	lower	low	ADJ
ejpam-5718	394	4	weakly	weakly	ADJ
ejpam-5718	394	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5718	394	6	multifunctions	multifunction	NOUN
ejpam-5718	394	7	.	.	PUNCT
ejpam-5718	395	1	international	international	ADJ
ejpam-5718	395	2	journal	journal	NOUN
ejpam-5718	395	3	of	of	ADP
ejpam-5718	395	4	analysis	analysis	NOUN
ejpam-5718	395	5	and	and	CCONJ
ejpam-5718	395	6	applications	application	NOUN
ejpam-5718	395	7	,	,	PUNCT
ejpam-5718	395	8	21:90	21:90	NUM
ejpam-5718	395	9	,	,	PUNCT
ejpam-5718	395	10	2023	2023	NUM
ejpam-5718	395	11	.	.	PUNCT
ejpam-5718	396	1	[	[	X
ejpam-5718	396	2	22	22	NUM
ejpam-5718	396	3	]	]	PUNCT
ejpam-5718	396	4	c.	c.	PROPN
ejpam-5718	396	5	boonpok	boonpok	PROPN
ejpam-5718	396	6	and	and	CCONJ
ejpam-5718	396	7	p.	p.	NOUN
ejpam-5718	396	8	pue	pue	NOUN
ejpam-5718	396	9	-	-	PUNCT
ejpam-5718	396	10	on	on	ADP
ejpam-5718	396	11	.	.	PUNCT
ejpam-5718	397	1	upper	upper	ADJ
ejpam-5718	397	2	and	and	CCONJ
ejpam-5718	397	3	lower	low	ADJ
ejpam-5718	397	4	weakly	weakly	ADJ
ejpam-5718	397	5	(	(	PUNCT
ejpam-5718	397	6	λ	λ	NOUN
ejpam-5718	397	7	,	,	PUNCT
ejpam-5718	397	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	397	9	multifuncp	multifuncp	NOUN
ejpam-5718	397	10	.	.	PUNCT
ejpam-5718	398	1	pue	pue	NOUN
ejpam-5718	398	2	-	-	PUNCT
ejpam-5718	398	3	on	on	ADP
ejpam-5718	398	4	,	,	PUNCT
ejpam-5718	398	5	a.	a.	PROPN
ejpam-5718	398	6	sama	sama	PROPN
ejpam-5718	398	7	-	-	PUNCT
ejpam-5718	398	8	ae	ae	PROPN
ejpam-5718	398	9	,	,	PUNCT
ejpam-5718	398	10	c.	c.	PROPN
ejpam-5718	398	11	boonpok	boonpok	PROPN
ejpam-5718	398	12	/	/	SYM
ejpam-5718	398	13	eur	eur	PROPN
ejpam-5718	398	14	.	.	PUNCT
ejpam-5718	399	1	j.	j.	PROPN
ejpam-5718	399	2	pure	pure	PROPN
ejpam-5718	399	3	appl	appl	PROPN
ejpam-5718	399	4	.	.	PROPN
ejpam-5718	399	5	math	math	PROPN
ejpam-5718	399	6	,	,	PUNCT
ejpam-5718	399	7	18	18	NUM
ejpam-5718	399	8	(	(	PUNCT
ejpam-5718	399	9	1	1	NUM
ejpam-5718	399	10	)	)	PUNCT
ejpam-5718	399	11	(	(	PUNCT
ejpam-5718	399	12	2025	2025	NUM
ejpam-5718	399	13	)	)	PUNCT
ejpam-5718	399	14	,	,	PUNCT
ejpam-5718	399	15	5718	5718	NUM
ejpam-5718	399	16	14	14	NUM
ejpam-5718	399	17	of	of	ADP
ejpam-5718	399	18	16	16	NUM
ejpam-5718	399	19	tions	tion	NOUN
ejpam-5718	399	20	.	.	PUNCT
ejpam-5718	400	1	european	european	ADJ
ejpam-5718	400	2	journal	journal	PROPN
ejpam-5718	400	3	of	of	ADP
ejpam-5718	400	4	pure	pure	ADJ
ejpam-5718	400	5	and	and	CCONJ
ejpam-5718	400	6	applied	applied	ADJ
ejpam-5718	400	7	mathematics	mathematic	NOUN
ejpam-5718	400	8	,	,	PUNCT
ejpam-5718	400	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5718	400	10	,	,	PUNCT
ejpam-5718	400	11	2023	2023	NUM
ejpam-5718	400	12	.	.	PUNCT
ejpam-5718	401	1	[	[	X
ejpam-5718	401	2	23	23	NUM
ejpam-5718	401	3	]	]	X
ejpam-5718	401	4	c.	c.	PROPN
ejpam-5718	401	5	boonpok	boonpok	PROPN
ejpam-5718	401	6	and	and	CCONJ
ejpam-5718	401	7	p.	p.	NOUN
ejpam-5718	401	8	pue	pue	NOUN
ejpam-5718	401	9	-	-	PUNCT
ejpam-5718	401	10	on	on	ADP
ejpam-5718	401	11	.	.	PUNCT
ejpam-5718	402	1	characterizations	characterization	NOUN
ejpam-5718	402	2	of	of	ADP
ejpam-5718	402	3	almost	almost	ADV
ejpam-5718	402	4	(	(	PUNCT
ejpam-5718	402	5	τ1	τ1	NOUN
ejpam-5718	402	6	,	,	PUNCT
ejpam-5718	402	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	402	8	functions	function	NOUN
ejpam-5718	402	9	.	.	PUNCT
ejpam-5718	403	1	international	international	ADJ
ejpam-5718	403	2	journal	journal	NOUN
ejpam-5718	403	3	of	of	ADP
ejpam-5718	403	4	analysis	analysis	NOUN
ejpam-5718	403	5	and	and	CCONJ
ejpam-5718	403	6	applications	application	NOUN
ejpam-5718	403	7	,	,	PUNCT
ejpam-5718	403	8	22:33	22:33	NUM
ejpam-5718	403	9	,	,	PUNCT
ejpam-5718	403	10	2024	2024	NUM
ejpam-5718	403	11	.	.	PUNCT
ejpam-5718	404	1	[	[	X
ejpam-5718	404	2	24	24	NUM
ejpam-5718	404	3	]	]	PUNCT
ejpam-5718	404	4	c.	c.	PROPN
ejpam-5718	404	5	boonpok	boonpok	PROPN
ejpam-5718	404	6	and	and	CCONJ
ejpam-5718	404	7	n.	n.	PROPN
ejpam-5718	404	8	srisarakham	srisarakham	PROPN
ejpam-5718	404	9	.	.	PUNCT
ejpam-5718	405	1	almost	almost	ADV
ejpam-5718	405	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5718	405	3	for	for	ADP
ejpam-5718	405	4	multifunctions	multifunction	NOUN
ejpam-5718	405	5	.	.	PUNCT
ejpam-5718	406	1	international	international	ADJ
ejpam-5718	406	2	journal	journal	NOUN
ejpam-5718	406	3	of	of	ADP
ejpam-5718	406	4	analysis	analysis	NOUN
ejpam-5718	406	5	and	and	CCONJ
ejpam-5718	406	6	applications	application	NOUN
ejpam-5718	406	7	,	,	PUNCT
ejpam-5718	406	8	21:107	21:107	NUM
ejpam-5718	406	9	,	,	PUNCT
ejpam-5718	406	10	2023	2023	NUM
ejpam-5718	406	11	.	.	PUNCT
ejpam-5718	407	1	[	[	X
ejpam-5718	407	2	25	25	NUM
ejpam-5718	407	3	]	]	PUNCT
ejpam-5718	407	4	c.	c.	PROPN
ejpam-5718	407	5	boonpok	boonpok	PROPN
ejpam-5718	407	6	and	and	CCONJ
ejpam-5718	407	7	n.	n.	PROPN
ejpam-5718	407	8	srisarakham	srisarakham	PROPN
ejpam-5718	407	9	.	.	PUNCT
ejpam-5718	408	1	weak	weak	ADJ
ejpam-5718	408	2	forms	form	NOUN
ejpam-5718	408	3	of	of	ADP
ejpam-5718	408	4	(	(	PUNCT
ejpam-5718	408	5	λ	λ	PROPN
ejpam-5718	408	6	,	,	PUNCT
ejpam-5718	408	7	b)-open	b)-open	VERB
ejpam-5718	408	8	sets	set	NOUN
ejpam-5718	408	9	and	and	CCONJ
ejpam-5718	408	10	weak	weak	ADJ
ejpam-5718	408	11	(	(	PUNCT
ejpam-5718	408	12	λ	λ	NOUN
ejpam-5718	408	13	,	,	PUNCT
ejpam-5718	408	14	b)continuity	b)continuity	NOUN
ejpam-5718	408	15	.	.	PUNCT
ejpam-5718	409	1	european	european	PROPN
ejpam-5718	409	2	journal	journal	PROPN
ejpam-5718	409	3	of	of	ADP
ejpam-5718	409	4	pure	pure	ADJ
ejpam-5718	409	5	and	and	CCONJ
ejpam-5718	409	6	applied	applied	ADJ
ejpam-5718	409	7	mathematics	mathematic	NOUN
ejpam-5718	409	8	,	,	PUNCT
ejpam-5718	409	9	16(1):29–43	16(1):29–43	NUM
ejpam-5718	409	10	,	,	PUNCT
ejpam-5718	409	11	2023	2023	NUM
ejpam-5718	409	12	.	.	PUNCT
ejpam-5718	410	1	[	[	X
ejpam-5718	410	2	26	26	NUM
ejpam-5718	410	3	]	]	X
ejpam-5718	410	4	c.	c.	PROPN
ejpam-5718	410	5	boonpok	boonpok	PROPN
ejpam-5718	410	6	and	and	CCONJ
ejpam-5718	410	7	n.	n.	PROPN
ejpam-5718	410	8	srisarakham	srisarakham	PROPN
ejpam-5718	410	9	.	.	PUNCT
ejpam-5718	411	1	(	(	PUNCT
ejpam-5718	411	2	τ1	τ1	NOUN
ejpam-5718	411	3	,	,	PUNCT
ejpam-5718	411	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5718	411	5	for	for	ADP
ejpam-5718	411	6	functions	function	NOUN
ejpam-5718	411	7	.	.	PUNCT
ejpam-5718	412	1	asia	asia	PROPN
ejpam-5718	412	2	pacific	pacific	PROPN
ejpam-5718	412	3	journal	journal	PROPN
ejpam-5718	412	4	of	of	ADP
ejpam-5718	412	5	mathematics	mathematic	NOUN
ejpam-5718	412	6	,	,	PUNCT
ejpam-5718	412	7	11:21	11:21	NUM
ejpam-5718	412	8	,	,	PUNCT
ejpam-5718	412	9	2024	2024	NUM
ejpam-5718	412	10	.	.	PUNCT
ejpam-5718	413	1	[	[	X
ejpam-5718	413	2	27	27	NUM
ejpam-5718	413	3	]	]	X
ejpam-5718	413	4	c.	c.	PROPN
ejpam-5718	413	5	boonpok	boonpok	PROPN
ejpam-5718	413	6	and	and	CCONJ
ejpam-5718	413	7	m.	m.	NOUN
ejpam-5718	413	8	thongmoon	thongmoon	NOUN
ejpam-5718	413	9	.	.	PUNCT
ejpam-5718	414	1	weak	weak	ADJ
ejpam-5718	414	2	α(λ	α(λ	PROPN
ejpam-5718	414	3	,	,	PUNCT
ejpam-5718	414	4	sp)-continuity	sp)-continuity	NOUN
ejpam-5718	414	5	for	for	ADP
ejpam-5718	414	6	multifunctions	multifunction	NOUN
ejpam-5718	414	7	.	.	PUNCT
ejpam-5718	415	1	european	european	ADJ
ejpam-5718	415	2	journal	journal	PROPN
ejpam-5718	415	3	of	of	ADP
ejpam-5718	415	4	pure	pure	ADJ
ejpam-5718	415	5	and	and	CCONJ
ejpam-5718	415	6	applied	applied	ADJ
ejpam-5718	415	7	mathematics	mathematic	NOUN
ejpam-5718	415	8	,	,	PUNCT
ejpam-5718	415	9	16(1):465–478	16(1):465–478	NUM
ejpam-5718	415	10	,	,	PUNCT
ejpam-5718	415	11	2023	2023	NUM
ejpam-5718	415	12	.	.	PUNCT
ejpam-5718	416	1	[	[	X
ejpam-5718	416	2	28	28	NUM
ejpam-5718	416	3	]	]	X
ejpam-5718	416	4	c.	c.	PROPN
ejpam-5718	416	5	boonpok	boonpok	PROPN
ejpam-5718	416	6	and	and	CCONJ
ejpam-5718	416	7	c.	c.	PROPN
ejpam-5718	416	8	viriyapong	viriyapong	PROPN
ejpam-5718	416	9	.	.	PUNCT
ejpam-5718	417	1	upper	upper	ADJ
ejpam-5718	417	2	and	and	CCONJ
ejpam-5718	417	3	lower	low	ADJ
ejpam-5718	417	4	almost	almost	ADV
ejpam-5718	417	5	weak	weak	ADJ
ejpam-5718	417	6	(	(	PUNCT
ejpam-5718	417	7	τ1	τ1	NOUN
ejpam-5718	417	8	,	,	PUNCT
ejpam-5718	417	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5718	417	10	.	.	PUNCT
ejpam-5718	418	1	european	european	PROPN
ejpam-5718	418	2	journal	journal	PROPN
ejpam-5718	418	3	of	of	ADP
ejpam-5718	418	4	pure	pure	ADJ
ejpam-5718	418	5	and	and	CCONJ
ejpam-5718	418	6	applied	applied	ADJ
ejpam-5718	418	7	mathematics	mathematic	NOUN
ejpam-5718	418	8	,	,	PUNCT
ejpam-5718	418	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5718	418	10	,	,	PUNCT
ejpam-5718	418	11	2021	2021	NUM
ejpam-5718	418	12	.	.	PUNCT
ejpam-5718	419	1	[	[	X
ejpam-5718	419	2	29	29	NUM
ejpam-5718	419	3	]	]	X
ejpam-5718	419	4	c.	c.	PROPN
ejpam-5718	419	5	boonpok	boonpok	PROPN
ejpam-5718	419	6	,	,	PUNCT
ejpam-5718	419	7	c.	c.	PROPN
ejpam-5718	419	8	viriyapong	viriyapong	PROPN
ejpam-5718	419	9	,	,	PUNCT
ejpam-5718	419	10	and	and	CCONJ
ejpam-5718	419	11	m.	m.	NOUN
ejpam-5718	419	12	thongmoon	thongmoon	NOUN
ejpam-5718	419	13	.	.	PUNCT
ejpam-5718	420	1	on	on	ADP
ejpam-5718	420	2	upper	upper	ADJ
ejpam-5718	420	3	and	and	CCONJ
ejpam-5718	420	4	lower	low	ADJ
ejpam-5718	420	5	(	(	PUNCT
ejpam-5718	420	6	τ1	τ1	NOUN
ejpam-5718	420	7	,	,	PUNCT
ejpam-5718	420	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5718	420	9	multifunctions	multifunction	NOUN
ejpam-5718	420	10	.	.	PUNCT
ejpam-5718	421	1	journal	journal	PROPN
ejpam-5718	421	2	of	of	ADP
ejpam-5718	421	3	mathematics	mathematics	PROPN
ejpam-5718	421	4	and	and	CCONJ
ejpam-5718	421	5	computer	computer	NOUN
ejpam-5718	421	6	science	science	NOUN
ejpam-5718	421	7	,	,	PUNCT
ejpam-5718	421	8	18:282–293	18:282–293	NUM
ejpam-5718	421	9	,	,	PUNCT
ejpam-5718	421	10	2018	2018	NUM
ejpam-5718	421	11	.	.	PUNCT
ejpam-5718	422	1	[	[	X
ejpam-5718	422	2	30	30	NUM
ejpam-5718	422	3	]	]	X
ejpam-5718	422	4	m.	m.	NOUN
ejpam-5718	422	5	chiangpradit	chiangpradit	NOUN
ejpam-5718	422	6	,	,	PUNCT
ejpam-5718	422	7	s.	s.	PROPN
ejpam-5718	422	8	sompong	sompong	PROPN
ejpam-5718	422	9	,	,	PUNCT
ejpam-5718	422	10	and	and	CCONJ
ejpam-5718	422	11	c.	c.	PROPN
ejpam-5718	422	12	boonpok	boonpok	PROPN
ejpam-5718	422	13	.	.	PUNCT
ejpam-5718	423	1	weakly	weakly	ADJ
ejpam-5718	423	2	quasi	quasi	NOUN
ejpam-5718	423	3	(	(	PUNCT
ejpam-5718	423	4	τ1	τ1	PROPN
ejpam-5718	423	5	,	,	PUNCT
ejpam-5718	423	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	423	7	functions	function	NOUN
ejpam-5718	423	8	.	.	PUNCT
ejpam-5718	424	1	international	international	ADJ
ejpam-5718	424	2	journal	journal	NOUN
ejpam-5718	424	3	of	of	ADP
ejpam-5718	424	4	analysis	analysis	NOUN
ejpam-5718	424	5	and	and	CCONJ
ejpam-5718	424	6	applications	application	NOUN
ejpam-5718	424	7	,	,	PUNCT
ejpam-5718	424	8	22:125	22:125	NUM
ejpam-5718	424	9	,	,	PUNCT
ejpam-5718	424	10	2024	2024	NUM
ejpam-5718	424	11	.	.	PUNCT
ejpam-5718	425	1	[	[	X
ejpam-5718	425	2	31	31	NUM
ejpam-5718	425	3	]	]	X
ejpam-5718	425	4	n.	n.	NOUN
ejpam-5718	425	5	chutiman	chutiman	NOUN
ejpam-5718	425	6	,	,	PUNCT
ejpam-5718	425	7	s.	s.	PROPN
ejpam-5718	425	8	sompong	sompong	PROPN
ejpam-5718	425	9	,	,	PUNCT
ejpam-5718	425	10	and	and	CCONJ
ejpam-5718	425	11	c.	c.	PROPN
ejpam-5718	425	12	boonpok	boonpok	PROPN
ejpam-5718	425	13	.	.	PUNCT
ejpam-5718	426	1	on	on	ADP
ejpam-5718	426	2	some	some	DET
ejpam-5718	426	3	separation	separation	NOUN
ejpam-5718	426	4	axioms	axiom	NOUN
ejpam-5718	426	5	in	in	ADP
ejpam-5718	426	6	bitopological	bitopological	ADJ
ejpam-5718	426	7	spaces	space	NOUN
ejpam-5718	426	8	.	.	PUNCT
ejpam-5718	427	1	asia	asia	PROPN
ejpam-5718	427	2	pacific	pacific	PROPN
ejpam-5718	427	3	journal	journal	PROPN
ejpam-5718	427	4	of	of	ADP
ejpam-5718	427	5	mathematics	mathematic	NOUN
ejpam-5718	427	6	,	,	PUNCT
ejpam-5718	427	7	11:41	11:41	NUM
ejpam-5718	427	8	,	,	PUNCT
ejpam-5718	427	9	2024	2024	NUM
ejpam-5718	427	10	.	.	PUNCT
ejpam-5718	428	1	[	[	X
ejpam-5718	428	2	32	32	NUM
ejpam-5718	428	3	]	]	PUNCT
ejpam-5718	428	4	t.	t.	PROPN
ejpam-5718	428	5	duangphui	duangphui	PROPN
ejpam-5718	428	6	,	,	PUNCT
ejpam-5718	428	7	c.	c.	PROPN
ejpam-5718	428	8	boonpok	boonpok	PROPN
ejpam-5718	428	9	,	,	PUNCT
ejpam-5718	428	10	and	and	CCONJ
ejpam-5718	428	11	c.	c.	PROPN
ejpam-5718	428	12	viriyapong	viriyapong	PROPN
ejpam-5718	428	13	.	.	PUNCT
ejpam-5718	429	1	continuous	continuous	ADJ
ejpam-5718	429	2	functions	function	NOUN
ejpam-5718	429	3	on	on	ADP
ejpam-5718	429	4	bigeneralized	bigeneralize	VERB
ejpam-5718	429	5	topological	topological	ADJ
ejpam-5718	429	6	spaces	space	NOUN
ejpam-5718	429	7	.	.	PUNCT
ejpam-5718	430	1	international	international	ADJ
ejpam-5718	430	2	journal	journal	PROPN
ejpam-5718	430	3	of	of	ADP
ejpam-5718	430	4	mathematical	mathematical	ADJ
ejpam-5718	430	5	analysis	analysis	NOUN
ejpam-5718	430	6	,	,	PUNCT
ejpam-5718	430	7	5(24):1165	5(24):1165	NUM
ejpam-5718	430	8	–	–	PUNCT
ejpam-5718	430	9	1174	1174	NUM
ejpam-5718	430	10	,	,	PUNCT
ejpam-5718	430	11	2011	2011	NUM
ejpam-5718	430	12	.	.	PUNCT
ejpam-5718	431	1	[	[	X
ejpam-5718	431	2	33	33	NUM
ejpam-5718	431	3	]	]	PUNCT
ejpam-5718	431	4	t.	t.	NOUN
ejpam-5718	431	5	dungthaisong	dungthaisong	PROPN
ejpam-5718	431	6	,	,	PUNCT
ejpam-5718	431	7	c.	c.	PROPN
ejpam-5718	431	8	boonpok	boonpok	PROPN
ejpam-5718	431	9	,	,	PUNCT
ejpam-5718	431	10	and	and	CCONJ
ejpam-5718	431	11	c.	c.	PROPN
ejpam-5718	431	12	viriyapong	viriyapong	PROPN
ejpam-5718	431	13	.	.	PUNCT
ejpam-5718	432	1	generalized	generalize	VERB
ejpam-5718	432	2	closed	close	VERB
ejpam-5718	432	3	sets	set	NOUN
ejpam-5718	432	4	in	in	ADP
ejpam-5718	432	5	bigeneralized	bigeneralize	VERB
ejpam-5718	432	6	topological	topological	ADJ
ejpam-5718	432	7	spaces	space	NOUN
ejpam-5718	432	8	.	.	PUNCT
ejpam-5718	433	1	international	international	ADJ
ejpam-5718	433	2	journal	journal	PROPN
ejpam-5718	433	3	of	of	ADP
ejpam-5718	433	4	mathematical	mathematical	ADJ
ejpam-5718	433	5	analysis	analysis	NOUN
ejpam-5718	433	6	,	,	PUNCT
ejpam-5718	433	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5718	433	8	,	,	PUNCT
ejpam-5718	433	9	2011	2011	NUM
ejpam-5718	433	10	.	.	PUNCT
ejpam-5718	434	1	[	[	X
ejpam-5718	434	2	34	34	NUM
ejpam-5718	434	3	]	]	X
ejpam-5718	434	4	e.	e.	PROPN
ejpam-5718	434	5	ekici	ekici	PROPN
ejpam-5718	434	6	and	and	CCONJ
ejpam-5718	434	7	j.	j.	PROPN
ejpam-5718	434	8	h.	h.	PROPN
ejpam-5718	434	9	park	park	PROPN
ejpam-5718	434	10	.	.	PUNCT
ejpam-5718	435	1	on	on	ADP
ejpam-5718	435	2	weakly	weakly	ADJ
ejpam-5718	435	3	s	s	NOUN
ejpam-5718	435	4	-	-	ADJ
ejpam-5718	435	5	precontinuous	precontinuous	ADJ
ejpam-5718	435	6	multifunctions	multifunction	NOUN
ejpam-5718	435	7	.	.	PUNCT
ejpam-5718	436	1	arabian	arabian	ADJ
ejpam-5718	436	2	journal	journal	PROPN
ejpam-5718	436	3	for	for	ADP
ejpam-5718	436	4	science	science	NOUN
ejpam-5718	436	5	engineering	engineering	NOUN
ejpam-5718	436	6	,	,	PUNCT
ejpam-5718	436	7	32:83–92	32:83–92	PROPN
ejpam-5718	436	8	,	,	PUNCT
ejpam-5718	436	9	2007	2007	NUM
ejpam-5718	436	10	.	.	PUNCT
ejpam-5718	437	1	[	[	X
ejpam-5718	437	2	35	35	NUM
ejpam-5718	437	3	]	]	X
ejpam-5718	437	4	j.	j.	PROPN
ejpam-5718	437	5	ewert	ewert	PROPN
ejpam-5718	437	6	and	and	CCONJ
ejpam-5718	437	7	t.	t.	PROPN
ejpam-5718	437	8	lipski	lipski	PROPN
ejpam-5718	437	9	.	.	PUNCT
ejpam-5718	438	1	on	on	ADP
ejpam-5718	438	2	s	s	NOUN
ejpam-5718	438	3	-	-	PUNCT
ejpam-5718	438	4	quasi	quasi	ADJ
ejpam-5718	438	5	-	-	ADJ
ejpam-5718	438	6	continuous	continuous	ADJ
ejpam-5718	438	7	multivalued	multivalued	ADJ
ejpam-5718	438	8	maps	map	NOUN
ejpam-5718	438	9	.	.	PUNCT
ejpam-5718	439	1	review	review	NOUN
ejpam-5718	439	2	of	of	ADP
ejpam-5718	439	3	research	research	NOUN
ejpam-5718	439	4	faculty	faculty	NOUN
ejpam-5718	439	5	of	of	ADP
ejpam-5718	439	6	science	science	NOUN
ejpam-5718	439	7	mathematics	mathematic	NOUN
ejpam-5718	439	8	series	series	NOUN
ejpam-5718	439	9	,	,	PUNCT
ejpam-5718	439	10	20(1):167–183	20(1):167–183	PROPN
ejpam-5718	439	11	,	,	PUNCT
ejpam-5718	439	12	1990	1990	NUM
ejpam-5718	439	13	.	.	PUNCT
ejpam-5718	440	1	[	[	X
ejpam-5718	440	2	36	36	NUM
ejpam-5718	440	3	]	]	PUNCT
ejpam-5718	440	4	t.	t.	PROPN
ejpam-5718	440	5	husain	husain	PROPN
ejpam-5718	440	6	.	.	PUNCT
ejpam-5718	441	1	almost	almost	ADV
ejpam-5718	441	2	continuous	continuous	ADJ
ejpam-5718	441	3	mappings	mapping	NOUN
ejpam-5718	441	4	.	.	PUNCT
ejpam-5718	442	1	prace	prace	PROPN
ejpam-5718	442	2	matematyczno	matematyczno	PROPN
ejpam-5718	442	3	-	-	PUNCT
ejpam-5718	442	4	fizyczne	fizyczne	NOUN
ejpam-5718	442	5	,	,	PUNCT
ejpam-5718	442	6	10:1–7	10:1–7	NUM
ejpam-5718	442	7	,	,	PUNCT
ejpam-5718	442	8	1966	1966	NUM
ejpam-5718	442	9	.	.	PUNCT
ejpam-5718	443	1	[	[	X
ejpam-5718	443	2	37	37	NUM
ejpam-5718	443	3	]	]	X
ejpam-5718	443	4	j.	j.	PROPN
ejpam-5718	443	5	khampakdee	khampakdee	PROPN
ejpam-5718	443	6	and	and	CCONJ
ejpam-5718	443	7	c.	c.	PROPN
ejpam-5718	443	8	boonpok	boonpok	PROPN
ejpam-5718	443	9	.	.	PUNCT
ejpam-5718	444	1	upper	upper	ADJ
ejpam-5718	444	2	and	and	CCONJ
ejpam-5718	444	3	lower	low	ADJ
ejpam-5718	444	4	α(λ	α(λ	PROPN
ejpam-5718	444	5	,	,	PUNCT
ejpam-5718	444	6	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	444	7	multifunctions	multifunction	NOUN
ejpam-5718	444	8	.	.	PUNCT
ejpam-5718	445	1	wseas	wseas	VERB
ejpam-5718	445	2	transactions	transaction	NOUN
ejpam-5718	445	3	on	on	ADP
ejpam-5718	445	4	mathematics	mathematic	NOUN
ejpam-5718	445	5	,	,	PUNCT
ejpam-5718	445	6	21:684–690	21:684–690	NUM
ejpam-5718	445	7	,	,	PUNCT
ejpam-5718	445	8	2022	2022	NUM
ejpam-5718	445	9	.	.	PUNCT
ejpam-5718	446	1	[	[	X
ejpam-5718	446	2	38	38	NUM
ejpam-5718	446	3	]	]	PUNCT
ejpam-5718	446	4	j.	j.	PROPN
ejpam-5718	446	5	khampakdee	khampakdee	PROPN
ejpam-5718	446	6	,	,	PUNCT
ejpam-5718	446	7	s.	s.	PROPN
ejpam-5718	446	8	sompong	sompong	PROPN
ejpam-5718	446	9	,	,	PUNCT
ejpam-5718	446	10	and	and	CCONJ
ejpam-5718	446	11	c.	c.	PROPN
ejpam-5718	446	12	boonpok	boonpok	PROPN
ejpam-5718	446	13	.	.	PUNCT
ejpam-5718	447	1	c-(τ1	c-(τ1	PROPN
ejpam-5718	447	2	,	,	PUNCT
ejpam-5718	447	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5718	447	4	for	for	ADP
ejpam-5718	447	5	multifunctions	multifunction	NOUN
ejpam-5718	447	6	.	.	PUNCT
ejpam-5718	448	1	european	european	ADJ
ejpam-5718	448	2	journal	journal	PROPN
ejpam-5718	448	3	of	of	ADP
ejpam-5718	448	4	pure	pure	ADJ
ejpam-5718	448	5	and	and	CCONJ
ejpam-5718	448	6	applied	applied	ADJ
ejpam-5718	448	7	mathematics	mathematic	NOUN
ejpam-5718	448	8	,	,	PUNCT
ejpam-5718	448	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-5718	448	10	,	,	PUNCT
ejpam-5718	448	11	2024	2024	NUM
ejpam-5718	448	12	.	.	PUNCT
ejpam-5718	449	1	[	[	X
ejpam-5718	449	2	39	39	NUM
ejpam-5718	449	3	]	]	PUNCT
ejpam-5718	449	4	c.	c.	PROPN
ejpam-5718	449	5	klanarong	klanarong	PROPN
ejpam-5718	449	6	,	,	PUNCT
ejpam-5718	449	7	s.	s.	PROPN
ejpam-5718	449	8	sompong	sompong	PROPN
ejpam-5718	449	9	,	,	PUNCT
ejpam-5718	449	10	and	and	CCONJ
ejpam-5718	449	11	c.	c.	PROPN
ejpam-5718	449	12	boonpok	boonpok	PROPN
ejpam-5718	449	13	.	.	PUNCT
ejpam-5718	450	1	upper	upper	ADJ
ejpam-5718	450	2	and	and	CCONJ
ejpam-5718	450	3	lower	low	ADJ
ejpam-5718	450	4	almost	almost	ADV
ejpam-5718	450	5	(	(	PUNCT
ejpam-5718	450	6	τ1	τ1	NOUN
ejpam-5718	450	7	,	,	PUNCT
ejpam-5718	450	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5718	450	9	multifunctions	multifunction	NOUN
ejpam-5718	450	10	.	.	PUNCT
ejpam-5718	451	1	european	european	ADJ
ejpam-5718	451	2	journal	journal	PROPN
ejpam-5718	451	3	of	of	ADP
ejpam-5718	451	4	pure	pure	ADJ
ejpam-5718	451	5	and	and	CCONJ
ejpam-5718	451	6	applied	applied	ADJ
ejpam-5718	451	7	mathematics	mathematic	NOUN
ejpam-5718	451	8	,	,	PUNCT
ejpam-5718	451	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5718	451	10	,	,	PUNCT
ejpam-5718	451	11	2024	2024	NUM
ejpam-5718	451	12	.	.	PUNCT
ejpam-5718	452	1	[	[	X
ejpam-5718	452	2	40	40	NUM
ejpam-5718	452	3	]	]	PUNCT
ejpam-5718	452	4	j.	j.	PROPN
ejpam-5718	452	5	k.	k.	PROPN
ejpam-5718	452	6	kohli	kohli	PROPN
ejpam-5718	452	7	.	.	PUNCT
ejpam-5718	453	1	a	a	DET
ejpam-5718	453	2	class	class	NOUN
ejpam-5718	453	3	of	of	ADP
ejpam-5718	453	4	mappings	mapping	NOUN
ejpam-5718	453	5	containing	contain	VERB
ejpam-5718	453	6	all	all	PRON
ejpam-5718	453	7	continuous	continuous	ADJ
ejpam-5718	453	8	and	and	CCONJ
ejpam-5718	453	9	all	all	DET
ejpam-5718	453	10	semi	semi	ADJ
ejpam-5718	453	11	-	-	ADJ
ejpam-5718	453	12	connected	connected	ADJ
ejpam-5718	453	13	mappings	mapping	NOUN
ejpam-5718	453	14	.	.	PUNCT
ejpam-5718	454	1	proceedings	proceeding	NOUN
ejpam-5718	454	2	of	of	ADP
ejpam-5718	454	3	the	the	DET
ejpam-5718	454	4	american	american	PROPN
ejpam-5718	454	5	mathematical	mathematical	PROPN
ejpam-5718	454	6	society	society	NOUN
ejpam-5718	454	7	,	,	PUNCT
ejpam-5718	454	8	72:175–181	72:175–181	PROPN
ejpam-5718	454	9	,	,	PUNCT
ejpam-5718	454	10	1978	1978	NUM
ejpam-5718	454	11	.	.	PUNCT
ejpam-5718	455	1	[	[	X
ejpam-5718	455	2	41	41	NUM
ejpam-5718	455	3	]	]	PUNCT
ejpam-5718	455	4	j.	j.	PROPN
ejpam-5718	455	5	k.	k.	PROPN
ejpam-5718	455	6	kohli	kohli	PROPN
ejpam-5718	455	7	.	.	PUNCT
ejpam-5718	456	1	s	s	X
ejpam-5718	456	2	-	-	ADJ
ejpam-5718	456	3	continuous	continuous	ADJ
ejpam-5718	456	4	functions	function	NOUN
ejpam-5718	456	5	and	and	CCONJ
ejpam-5718	456	6	certain	certain	ADJ
ejpam-5718	456	7	weak	weak	ADJ
ejpam-5718	456	8	forms	form	NOUN
ejpam-5718	456	9	of	of	ADP
ejpam-5718	456	10	regularity	regularity	NOUN
ejpam-5718	456	11	and	and	CCONJ
ejpam-5718	456	12	complete	complete	ADJ
ejpam-5718	456	13	regularity	regularity	NOUN
ejpam-5718	456	14	.	.	PUNCT
ejpam-5718	457	1	mathematische	mathematische	PROPN
ejpam-5718	457	2	nachrichten	nachrichten	PROPN
ejpam-5718	457	3	,	,	PUNCT
ejpam-5718	457	4	97:189–196	97:189–196	NUM
ejpam-5718	457	5	,	,	PUNCT
ejpam-5718	457	6	1980	1980	NUM
ejpam-5718	457	7	.	.	PUNCT
ejpam-5718	458	1	p.	p.	NOUN
ejpam-5718	458	2	pue	pue	NOUN
ejpam-5718	458	3	-	-	PUNCT
ejpam-5718	458	4	on	on	ADP
ejpam-5718	458	5	,	,	PUNCT
ejpam-5718	458	6	a.	a.	PROPN
ejpam-5718	458	7	sama	sama	PROPN
ejpam-5718	458	8	-	-	PUNCT
ejpam-5718	458	9	ae	ae	PROPN
ejpam-5718	458	10	,	,	PUNCT
ejpam-5718	458	11	c.	c.	PROPN
ejpam-5718	458	12	boonpok	boonpok	PROPN
ejpam-5718	458	13	/	/	SYM
ejpam-5718	458	14	eur	eur	PROPN
ejpam-5718	458	15	.	.	PUNCT
ejpam-5718	459	1	j.	j.	PROPN
ejpam-5718	459	2	pure	pure	PROPN
ejpam-5718	459	3	appl	appl	PROPN
ejpam-5718	459	4	.	.	PROPN
ejpam-5718	459	5	math	math	PROPN
ejpam-5718	459	6	,	,	PUNCT
ejpam-5718	459	7	18	18	NUM
ejpam-5718	459	8	(	(	PUNCT
ejpam-5718	459	9	1	1	NUM
ejpam-5718	459	10	)	)	PUNCT
ejpam-5718	459	11	(	(	PUNCT
ejpam-5718	459	12	2025	2025	NUM
ejpam-5718	459	13	)	)	PUNCT
ejpam-5718	459	14	,	,	PUNCT
ejpam-5718	459	15	5718	5718	NUM
ejpam-5718	459	16	15	15	NUM
ejpam-5718	459	17	of	of	ADP
ejpam-5718	459	18	16	16	NUM
ejpam-5718	459	19	[	[	X
ejpam-5718	459	20	42	42	NUM
ejpam-5718	459	21	]	]	PUNCT
ejpam-5718	459	22	b.	b.	PROPN
ejpam-5718	459	23	kong	kong	PROPN
ejpam-5718	459	24	-	-	PUNCT
ejpam-5718	459	25	ied	ied	PROPN
ejpam-5718	459	26	,	,	PUNCT
ejpam-5718	459	27	s.	s.	PROPN
ejpam-5718	459	28	sompong	sompong	PROPN
ejpam-5718	459	29	,	,	PUNCT
ejpam-5718	459	30	and	and	CCONJ
ejpam-5718	459	31	c.	c.	PROPN
ejpam-5718	459	32	boonpok	boonpok	PROPN
ejpam-5718	459	33	.	.	PUNCT
ejpam-5718	460	1	almost	almost	ADV
ejpam-5718	460	2	quasi	quasi	X
ejpam-5718	460	3	(	(	PUNCT
ejpam-5718	460	4	τ1	τ1	NOUN
ejpam-5718	460	5	,	,	PUNCT
ejpam-5718	460	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	460	7	functions	function	NOUN
ejpam-5718	460	8	.	.	PUNCT
ejpam-5718	461	1	asia	asia	PROPN
ejpam-5718	461	2	pacific	pacific	PROPN
ejpam-5718	461	3	journal	journal	PROPN
ejpam-5718	461	4	of	of	ADP
ejpam-5718	461	5	mathematics	mathematic	NOUN
ejpam-5718	461	6	,	,	PUNCT
ejpam-5718	461	7	11:64	11:64	NUM
ejpam-5718	461	8	,	,	PUNCT
ejpam-5718	461	9	2024	2024	NUM
ejpam-5718	461	10	.	.	PUNCT
ejpam-5718	462	1	[	[	X
ejpam-5718	462	2	43	43	NUM
ejpam-5718	462	3	]	]	X
ejpam-5718	462	4	y.	y.	PROPN
ejpam-5718	462	5	l.	l.	PROPN
ejpam-5718	462	6	lee	lee	PROPN
ejpam-5718	462	7	.	.	PUNCT
ejpam-5718	463	1	some	some	DET
ejpam-5718	463	2	characterizations	characterization	NOUN
ejpam-5718	463	3	of	of	ADP
ejpam-5718	463	4	semilocally	semilocally	ADV
ejpam-5718	463	5	connected	connected	ADJ
ejpam-5718	463	6	spaces	space	NOUN
ejpam-5718	463	7	.	.	PUNCT
ejpam-5718	464	1	proceedings	proceeding	NOUN
ejpam-5718	464	2	of	of	ADP
ejpam-5718	464	3	the	the	DET
ejpam-5718	464	4	american	american	PROPN
ejpam-5718	464	5	mathematical	mathematical	PROPN
ejpam-5718	464	6	society	society	NOUN
ejpam-5718	464	7	,	,	PUNCT
ejpam-5718	464	8	16:1318–1320	16:1318–1320	NUM
ejpam-5718	464	9	,	,	PUNCT
ejpam-5718	464	10	1965	1965	NUM
ejpam-5718	464	11	.	.	PUNCT
ejpam-5718	465	1	[	[	X
ejpam-5718	465	2	44	44	NUM
ejpam-5718	465	3	]	]	X
ejpam-5718	465	4	n.	n.	PROPN
ejpam-5718	465	5	levine	levine	PROPN
ejpam-5718	465	6	.	.	PUNCT
ejpam-5718	466	1	a	a	DET
ejpam-5718	466	2	decomposition	decomposition	NOUN
ejpam-5718	466	3	of	of	ADP
ejpam-5718	466	4	continuity	continuity	NOUN
ejpam-5718	466	5	in	in	ADP
ejpam-5718	466	6	topological	topological	ADJ
ejpam-5718	466	7	spaces	space	NOUN
ejpam-5718	466	8	.	.	PUNCT
ejpam-5718	467	1	the	the	DET
ejpam-5718	467	2	american	american	PROPN
ejpam-5718	467	3	mathematical	mathematical	PROPN
ejpam-5718	467	4	monthly	monthly	ADV
ejpam-5718	467	5	,	,	PUNCT
ejpam-5718	467	6	68:44–46	68:44–46	NUM
ejpam-5718	467	7	,	,	PUNCT
ejpam-5718	467	8	1961	1961	NUM
ejpam-5718	467	9	.	.	PUNCT
ejpam-5718	468	1	[	[	X
ejpam-5718	468	2	45	45	NUM
ejpam-5718	468	3	]	]	X
ejpam-5718	468	4	n.	n.	PROPN
ejpam-5718	468	5	levine	levine	PROPN
ejpam-5718	468	6	.	.	PUNCT
ejpam-5718	469	1	semi	semi	ADJ
ejpam-5718	469	2	-	-	ADJ
ejpam-5718	469	3	open	open	ADJ
ejpam-5718	469	4	sets	set	NOUN
ejpam-5718	469	5	and	and	CCONJ
ejpam-5718	469	6	semi	semi	ADJ
ejpam-5718	469	7	-	-	NOUN
ejpam-5718	469	8	continuity	continuity	NOUN
ejpam-5718	469	9	in	in	ADP
ejpam-5718	469	10	topological	topological	ADJ
ejpam-5718	469	11	spaces	space	NOUN
ejpam-5718	469	12	.	.	PUNCT
ejpam-5718	470	1	the	the	DET
ejpam-5718	470	2	american	american	PROPN
ejpam-5718	470	3	mathematical	mathematical	PROPN
ejpam-5718	470	4	monthly	monthly	ADV
ejpam-5718	470	5	,	,	PUNCT
ejpam-5718	470	6	70:36–41	70:36–41	NUM
ejpam-5718	470	7	,	,	PUNCT
ejpam-5718	470	8	1963	1963	NUM
ejpam-5718	470	9	.	.	PUNCT
ejpam-5718	471	1	[	[	X
ejpam-5718	471	2	46	46	NUM
ejpam-5718	471	3	]	]	PUNCT
ejpam-5718	471	4	t.	t.	NOUN
ejpam-5718	471	5	lipski	lipski	PROPN
ejpam-5718	471	6	.	.	PUNCT
ejpam-5718	472	1	s	s	X
ejpam-5718	472	2	-	-	ADJ
ejpam-5718	472	3	continuous	continuous	ADJ
ejpam-5718	472	4	multivalued	multivalued	ADJ
ejpam-5718	472	5	maps	map	NOUN
ejpam-5718	472	6	.	.	PUNCT
ejpam-5718	473	1	mathematical	mathematical	ADJ
ejpam-5718	473	2	chronicle	chronicle	PROPN
ejpam-5718	473	3	,	,	PUNCT
ejpam-5718	473	4	18:57–61	18:57–61	PROPN
ejpam-5718	473	5	,	,	PUNCT
ejpam-5718	473	6	1989	1989	NUM
ejpam-5718	473	7	.	.	PUNCT
ejpam-5718	474	1	[	[	X
ejpam-5718	474	2	47	47	NUM
ejpam-5718	474	3	]	]	PUNCT
ejpam-5718	474	4	s.	s.	PROPN
ejpam-5718	474	5	marcus	marcus	PROPN
ejpam-5718	474	6	.	.	PUNCT
ejpam-5718	475	1	sur	sur	PROPN
ejpam-5718	475	2	les	les	PROPN
ejpam-5718	475	3	fonctions	fonctions	PROPN
ejpam-5718	475	4	quasicontinues	quasicontinue	NOUN
ejpam-5718	475	5	au	au	PROPN
ejpam-5718	475	6	sens	sens	X
ejpam-5718	475	7	de	de	PROPN
ejpam-5718	475	8	s.	s.	PROPN
ejpam-5718	475	9	kempisty	kempisty	PROPN
ejpam-5718	475	10	.	.	PUNCT
ejpam-5718	476	1	colloquium	colloquium	NOUN
ejpam-5718	476	2	mathematicum	mathematicum	PROPN
ejpam-5718	476	3	,	,	PUNCT
ejpam-5718	476	4	8:47–53	8:47–53	NUM
ejpam-5718	476	5	,	,	PUNCT
ejpam-5718	476	6	1961	1961	NUM
ejpam-5718	476	7	.	.	PUNCT
ejpam-5718	477	1	[	[	X
ejpam-5718	477	2	48	48	NUM
ejpam-5718	477	3	]	]	PUNCT
ejpam-5718	477	4	t.	t.	PROPN
ejpam-5718	477	5	noiri	noiri	PROPN
ejpam-5718	477	6	and	and	CCONJ
ejpam-5718	477	7	v.	v.	ADP
ejpam-5718	477	8	popa	popa	NOUN
ejpam-5718	477	9	.	.	PUNCT
ejpam-5718	478	1	on	on	ADP
ejpam-5718	478	2	weak	weak	ADJ
ejpam-5718	478	3	s	s	NOUN
ejpam-5718	478	4	-	-	PUNCT
ejpam-5718	478	5	m	m	NOUN
ejpam-5718	478	6	-	-	PUNCT
ejpam-5718	478	7	continuity	continuity	NOUN
ejpam-5718	478	8	for	for	ADP
ejpam-5718	478	9	multifunctions	multifunction	NOUN
ejpam-5718	478	10	.	.	PUNCT
ejpam-5718	479	1	libertas	libertas	PROPN
ejpam-5718	479	2	mathematica	mathematica	PROPN
ejpam-5718	479	3	,	,	PUNCT
ejpam-5718	479	4	29:1–15	29:1–15	NUM
ejpam-5718	479	5	,	,	PUNCT
ejpam-5718	479	6	2009	2009	NUM
ejpam-5718	479	7	.	.	PUNCT
ejpam-5718	480	1	[	[	X
ejpam-5718	480	2	49	49	X
ejpam-5718	480	3	]	]	PUNCT
ejpam-5718	480	4	v.	v.	CCONJ
ejpam-5718	480	5	popa	popa	NOUN
ejpam-5718	480	6	.	.	PUNCT
ejpam-5718	481	1	some	some	DET
ejpam-5718	481	2	properties	property	NOUN
ejpam-5718	481	3	of	of	ADP
ejpam-5718	481	4	h	h	NOUN
ejpam-5718	481	5	-	-	PUNCT
ejpam-5718	481	6	almost	almost	ADV
ejpam-5718	481	7	continuous	continuous	ADJ
ejpam-5718	481	8	multifunctions	multifunction	NOUN
ejpam-5718	481	9	.	.	PUNCT
ejpam-5718	482	1	problemy	problemy	PROPN
ejpam-5718	482	2	matematyczne	matematyczne	PROPN
ejpam-5718	482	3	,	,	PUNCT
ejpam-5718	482	4	10:9–26	10:9–26	NUM
ejpam-5718	482	5	,	,	PUNCT
ejpam-5718	482	6	1988	1988	NUM
ejpam-5718	482	7	.	.	PUNCT
ejpam-5718	483	1	[	[	X
ejpam-5718	483	2	50	50	NUM
ejpam-5718	483	3	]	]	PUNCT
ejpam-5718	483	4	v.	v.	CCONJ
ejpam-5718	483	5	popa	popa	NOUN
ejpam-5718	483	6	and	and	CCONJ
ejpam-5718	483	7	t.	t.	PROPN
ejpam-5718	483	8	noiri	noiri	PROPN
ejpam-5718	483	9	.	.	PUNCT
ejpam-5718	484	1	a	a	DET
ejpam-5718	484	2	unified	unified	ADJ
ejpam-5718	484	3	theory	theory	NOUN
ejpam-5718	484	4	for	for	ADP
ejpam-5718	484	5	s	s	NOUN
ejpam-5718	484	6	-	-	NOUN
ejpam-5718	484	7	continuity	continuity	NOUN
ejpam-5718	484	8	of	of	ADP
ejpam-5718	484	9	multifunctions	multifunction	NOUN
ejpam-5718	484	10	.	.	PUNCT
ejpam-5718	485	1	ístanbul	ístanbul	PROPN
ejpam-5718	485	2	üniversitesi	üniversitesi	PROPN
ejpam-5718	485	3	fen	fen	PROPN
ejpam-5718	485	4	fakültesi	fakültesi	PUNCT
ejpam-5718	485	5	matematik	matematik	PROPN
ejpam-5718	485	6	dergisi	dergisi	PROPN
ejpam-5718	485	7	,	,	PUNCT
ejpam-5718	485	8	59:1–15	59:1–15	NUM
ejpam-5718	485	9	,	,	PUNCT
ejpam-5718	485	10	2000	2000	NUM
ejpam-5718	485	11	.	.	PUNCT
ejpam-5718	486	1	[	[	X
ejpam-5718	486	2	51	51	NUM
ejpam-5718	486	3	]	]	PUNCT
ejpam-5718	486	4	v.	v.	CCONJ
ejpam-5718	486	5	popa	popa	NOUN
ejpam-5718	486	6	and	and	CCONJ
ejpam-5718	486	7	t.	t.	PROPN
ejpam-5718	486	8	noiri	noiri	PROPN
ejpam-5718	486	9	.	.	PUNCT
ejpam-5718	487	1	on	on	ADP
ejpam-5718	487	2	s	s	NOUN
ejpam-5718	487	3	-	-	PUNCT
ejpam-5718	487	4	β	β	NOUN
ejpam-5718	487	5	-	-	ADJ
ejpam-5718	487	6	continuous	continuous	ADJ
ejpam-5718	487	7	multifunctions	multifunction	NOUN
ejpam-5718	487	8	.	.	PUNCT
ejpam-5718	488	1	journal	journal	NOUN
ejpam-5718	488	2	of	of	ADP
ejpam-5718	488	3	the	the	DET
ejpam-5718	488	4	egyptian	egyptian	PROPN
ejpam-5718	488	5	mathematical	mathematical	PROPN
ejpam-5718	488	6	society	society	NOUN
ejpam-5718	488	7	,	,	PUNCT
ejpam-5718	488	8	8:127–137	8:127–137	NUM
ejpam-5718	488	9	,	,	PUNCT
ejpam-5718	488	10	2000	2000	NUM
ejpam-5718	488	11	.	.	PUNCT
ejpam-5718	489	1	[	[	X
ejpam-5718	489	2	52	52	NUM
ejpam-5718	489	3	]	]	PUNCT
ejpam-5718	489	4	v.	v.	CCONJ
ejpam-5718	489	5	popa	popa	NOUN
ejpam-5718	489	6	and	and	CCONJ
ejpam-5718	489	7	t.	t.	PROPN
ejpam-5718	489	8	noiri	noiri	PROPN
ejpam-5718	489	9	.	.	PUNCT
ejpam-5718	490	1	on	on	ADP
ejpam-5718	490	2	s	s	NOUN
ejpam-5718	490	3	-	-	ADJ
ejpam-5718	490	4	precontinuous	precontinuous	ADJ
ejpam-5718	490	5	multifunctions	multifunction	NOUN
ejpam-5718	490	6	.	.	PUNCT
ejpam-5718	491	1	demonstratio	demonstratio	PROPN
ejpam-5718	491	2	mathematica	mathematica	PROPN
ejpam-5718	491	3	,	,	PUNCT
ejpam-5718	491	4	33(3):679–687	33(3):679–687	PROPN
ejpam-5718	491	5	,	,	PUNCT
ejpam-5718	491	6	2000	2000	NUM
ejpam-5718	491	7	.	.	PUNCT
ejpam-5718	492	1	[	[	X
ejpam-5718	492	2	53	53	NUM
ejpam-5718	492	3	]	]	PUNCT
ejpam-5718	492	4	c.	c.	NOUN
ejpam-5718	492	5	prachanpol	prachanpol	NOUN
ejpam-5718	492	6	,	,	PUNCT
ejpam-5718	492	7	c.	c.	PROPN
ejpam-5718	492	8	boonpok	boonpok	PROPN
ejpam-5718	492	9	,	,	PUNCT
ejpam-5718	492	10	and	and	CCONJ
ejpam-5718	492	11	c.	c.	PROPN
ejpam-5718	492	12	viriyapong	viriyapong	PROPN
ejpam-5718	492	13	.	.	PUNCT
ejpam-5718	493	1	δ(τ1	δ(τ1	PROPN
ejpam-5718	493	2	,	,	PUNCT
ejpam-5718	493	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	493	4	functions	function	NOUN
ejpam-5718	493	5	.	.	PUNCT
ejpam-5718	494	1	european	european	ADJ
ejpam-5718	494	2	journal	journal	PROPN
ejpam-5718	494	3	of	of	ADP
ejpam-5718	494	4	pure	pure	ADJ
ejpam-5718	494	5	and	and	CCONJ
ejpam-5718	494	6	applied	applied	ADJ
ejpam-5718	494	7	mathematics	mathematic	NOUN
ejpam-5718	494	8	,	,	PUNCT
ejpam-5718	494	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-5718	494	10	,	,	PUNCT
ejpam-5718	494	11	2024	2024	NUM
ejpam-5718	494	12	.	.	PUNCT
ejpam-5718	495	1	[	[	X
ejpam-5718	495	2	54	54	NUM
ejpam-5718	495	3	]	]	PUNCT
ejpam-5718	495	4	p.	p.	NOUN
ejpam-5718	495	5	pue	pue	NOUN
ejpam-5718	495	6	-	-	PUNCT
ejpam-5718	495	7	on	on	ADP
ejpam-5718	495	8	and	and	CCONJ
ejpam-5718	495	9	c.	c.	PROPN
ejpam-5718	495	10	boonpok	boonpok	PROPN
ejpam-5718	495	11	.	.	PUNCT
ejpam-5718	496	1	θ(λ	θ(λ	PROPN
ejpam-5718	496	2	,	,	PUNCT
ejpam-5718	496	3	p)-continuity	p)-continuity	NOUN
ejpam-5718	496	4	for	for	ADP
ejpam-5718	496	5	functions	function	NOUN
ejpam-5718	496	6	.	.	PUNCT
ejpam-5718	497	1	international	international	ADJ
ejpam-5718	497	2	journal	journal	NOUN
ejpam-5718	497	3	of	of	ADP
ejpam-5718	497	4	mathematics	mathematic	NOUN
ejpam-5718	497	5	and	and	CCONJ
ejpam-5718	497	6	computer	computer	NOUN
ejpam-5718	497	7	science	science	NOUN
ejpam-5718	497	8	,	,	PUNCT
ejpam-5718	497	9	19(2):491–495	19(2):491–495	NUM
ejpam-5718	497	10	,	,	PUNCT
ejpam-5718	497	11	2024	2024	NUM
ejpam-5718	497	12	.	.	PUNCT
ejpam-5718	498	1	[	[	X
ejpam-5718	498	2	55	55	NUM
ejpam-5718	498	3	]	]	X
ejpam-5718	498	4	p.	p.	NOUN
ejpam-5718	498	5	pue	pue	NOUN
ejpam-5718	498	6	-	-	PUNCT
ejpam-5718	498	7	on	on	ADP
ejpam-5718	498	8	,	,	PUNCT
ejpam-5718	498	9	a.	a.	PROPN
ejpam-5718	498	10	sama	sama	PROPN
ejpam-5718	498	11	-	-	PUNCT
ejpam-5718	498	12	ae	ae	PROPN
ejpam-5718	498	13	,	,	PUNCT
ejpam-5718	498	14	and	and	CCONJ
ejpam-5718	498	15	c.	c.	PROPN
ejpam-5718	498	16	boonpok	boonpok	PROPN
ejpam-5718	498	17	.	.	PUNCT
ejpam-5718	499	1	c	c	X
ejpam-5718	499	2	-	-	PUNCT
ejpam-5718	499	3	quasi	quasi	X
ejpam-5718	499	4	(	(	PUNCT
ejpam-5718	499	5	τ1	τ1	PROPN
ejpam-5718	499	6	,	,	PUNCT
ejpam-5718	499	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	499	8	multifunctions	multifunction	NOUN
ejpam-5718	499	9	.	.	PUNCT
ejpam-5718	500	1	european	european	ADJ
ejpam-5718	500	2	journal	journal	PROPN
ejpam-5718	500	3	of	of	ADP
ejpam-5718	500	4	pure	pure	ADJ
ejpam-5718	500	5	and	and	CCONJ
ejpam-5718	500	6	applied	applied	ADJ
ejpam-5718	500	7	mathematics	mathematic	NOUN
ejpam-5718	500	8	,	,	PUNCT
ejpam-5718	500	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-5718	500	10	,	,	PUNCT
ejpam-5718	500	11	2024	2024	NUM
ejpam-5718	500	12	.	.	PUNCT
ejpam-5718	501	1	[	[	X
ejpam-5718	501	2	56	56	NUM
ejpam-5718	501	3	]	]	X
ejpam-5718	501	4	p.	p.	NOUN
ejpam-5718	501	5	pue	pue	NOUN
ejpam-5718	501	6	-	-	PUNCT
ejpam-5718	501	7	on	on	ADP
ejpam-5718	501	8	,	,	PUNCT
ejpam-5718	501	9	s.	s.	PROPN
ejpam-5718	501	10	sompong	sompong	PROPN
ejpam-5718	501	11	,	,	PUNCT
ejpam-5718	501	12	and	and	CCONJ
ejpam-5718	501	13	c.	c.	PROPN
ejpam-5718	501	14	boonpok	boonpok	PROPN
ejpam-5718	501	15	.	.	PUNCT
ejpam-5718	502	1	almost	almost	ADV
ejpam-5718	502	2	quasi	quasi	X
ejpam-5718	502	3	(	(	PUNCT
ejpam-5718	502	4	τ1	τ1	NOUN
ejpam-5718	502	5	,	,	PUNCT
ejpam-5718	502	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5718	502	7	for	for	ADP
ejpam-5718	502	8	multifunctions	multifunction	NOUN
ejpam-5718	502	9	.	.	PUNCT
ejpam-5718	503	1	international	international	ADJ
ejpam-5718	503	2	journal	journal	NOUN
ejpam-5718	503	3	of	of	ADP
ejpam-5718	503	4	analysis	analysis	NOUN
ejpam-5718	503	5	and	and	CCONJ
ejpam-5718	503	6	applications	application	NOUN
ejpam-5718	503	7	,	,	PUNCT
ejpam-5718	503	8	22:97	22:97	NUM
ejpam-5718	503	9	,	,	PUNCT
ejpam-5718	503	10	2024	2024	NUM
ejpam-5718	503	11	.	.	PUNCT
ejpam-5718	504	1	[	[	X
ejpam-5718	504	2	57	57	NUM
ejpam-5718	504	3	]	]	X
ejpam-5718	504	4	p.	p.	NOUN
ejpam-5718	504	5	pue	pue	NOUN
ejpam-5718	504	6	-	-	PUNCT
ejpam-5718	504	7	on	on	ADP
ejpam-5718	504	8	,	,	PUNCT
ejpam-5718	504	9	s.	s.	PROPN
ejpam-5718	504	10	sompong	sompong	PROPN
ejpam-5718	504	11	,	,	PUNCT
ejpam-5718	504	12	and	and	CCONJ
ejpam-5718	504	13	c.	c.	PROPN
ejpam-5718	504	14	boonpok	boonpok	PROPN
ejpam-5718	504	15	.	.	PUNCT
ejpam-5718	505	1	upper	upper	ADJ
ejpam-5718	505	2	and	and	CCONJ
ejpam-5718	505	3	lower	low	ADJ
ejpam-5718	505	4	(	(	PUNCT
ejpam-5718	505	5	τ1	τ1	NOUN
ejpam-5718	505	6	,	,	PUNCT
ejpam-5718	505	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	505	8	mulfunctions	mulfunction	NOUN
ejpam-5718	505	9	.	.	PUNCT
ejpam-5718	506	1	international	international	ADJ
ejpam-5718	506	2	journal	journal	NOUN
ejpam-5718	506	3	of	of	ADP
ejpam-5718	506	4	mathematics	mathematic	NOUN
ejpam-5718	506	5	and	and	CCONJ
ejpam-5718	506	6	computer	computer	NOUN
ejpam-5718	506	7	science	science	NOUN
ejpam-5718	506	8	,	,	PUNCT
ejpam-5718	506	9	19(4):1305	19(4):1305	NUM
ejpam-5718	506	10	–	–	PUNCT
ejpam-5718	506	11	1310	1310	NUM
ejpam-5718	506	12	,	,	PUNCT
ejpam-5718	506	13	2024	2024	NUM
ejpam-5718	506	14	.	.	PUNCT
ejpam-5718	507	1	[	[	X
ejpam-5718	507	2	58	58	NUM
ejpam-5718	507	3	]	]	PUNCT
ejpam-5718	507	4	p.	p.	NOUN
ejpam-5718	507	5	pue	pue	NOUN
ejpam-5718	507	6	-	-	PUNCT
ejpam-5718	507	7	on	on	ADP
ejpam-5718	507	8	,	,	PUNCT
ejpam-5718	507	9	s.	s.	PROPN
ejpam-5718	507	10	sompong	sompong	PROPN
ejpam-5718	507	11	,	,	PUNCT
ejpam-5718	507	12	and	and	CCONJ
ejpam-5718	507	13	c.	c.	PROPN
ejpam-5718	507	14	boonpok	boonpok	PROPN
ejpam-5718	507	15	.	.	PUNCT
ejpam-5718	508	1	weakly	weakly	ADJ
ejpam-5718	508	2	quasi	quasi	NOUN
ejpam-5718	508	3	(	(	PUNCT
ejpam-5718	508	4	τ1	τ1	PROPN
ejpam-5718	508	5	,	,	PUNCT
ejpam-5718	508	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	508	7	multifunctions	multifunction	NOUN
ejpam-5718	508	8	.	.	PUNCT
ejpam-5718	509	1	european	european	ADJ
ejpam-5718	509	2	journal	journal	PROPN
ejpam-5718	509	3	of	of	ADP
ejpam-5718	509	4	pure	pure	ADJ
ejpam-5718	509	5	and	and	CCONJ
ejpam-5718	509	6	applied	applied	ADJ
ejpam-5718	509	7	mathematics	mathematic	NOUN
ejpam-5718	509	8	,	,	PUNCT
ejpam-5718	509	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-5718	509	10	,	,	PUNCT
ejpam-5718	509	11	2024	2024	NUM
ejpam-5718	509	12	.	.	PUNCT
ejpam-5718	510	1	[	[	X
ejpam-5718	510	2	59	59	NUM
ejpam-5718	510	3	]	]	X
ejpam-5718	510	4	p.	p.	NOUN
ejpam-5718	510	5	pue	pue	NOUN
ejpam-5718	510	6	-	-	PUNCT
ejpam-5718	510	7	on	on	ADP
ejpam-5718	510	8	,	,	PUNCT
ejpam-5718	510	9	s.	s.	PROPN
ejpam-5718	510	10	sompong	sompong	PROPN
ejpam-5718	510	11	,	,	PUNCT
ejpam-5718	510	12	and	and	CCONJ
ejpam-5718	510	13	c.	c.	PROPN
ejpam-5718	510	14	boonpok	boonpok	PROPN
ejpam-5718	510	15	.	.	PUNCT
ejpam-5718	511	1	slightly	slightly	ADV
ejpam-5718	511	2	(	(	PUNCT
ejpam-5718	511	3	τ1	τ1	NOUN
ejpam-5718	511	4	,	,	PUNCT
ejpam-5718	511	5	τ2)s	τ2)s	ADJ
ejpam-5718	511	6	-	-	PUNCT
ejpam-5718	511	7	continuous	continuous	ADJ
ejpam-5718	511	8	functions	function	NOUN
ejpam-5718	511	9	.	.	PUNCT
ejpam-5718	512	1	international	international	ADJ
ejpam-5718	512	2	journal	journal	NOUN
ejpam-5718	512	3	of	of	ADP
ejpam-5718	512	4	mathematics	mathematic	NOUN
ejpam-5718	512	5	and	and	CCONJ
ejpam-5718	512	6	computer	computer	NOUN
ejpam-5718	512	7	science	science	NOUN
ejpam-5718	512	8	,	,	PUNCT
ejpam-5718	512	9	20(1):217–221	20(1):217–221	PROPN
ejpam-5718	512	10	,	,	PUNCT
ejpam-5718	512	11	2025	2025	NUM
ejpam-5718	512	12	.	.	PUNCT
ejpam-5718	513	1	[	[	X
ejpam-5718	513	2	60	60	NUM
ejpam-5718	513	3	]	]	X
ejpam-5718	513	4	n.	n.	NOUN
ejpam-5718	513	5	srisarakham	srisarakham	PROPN
ejpam-5718	513	6	and	and	CCONJ
ejpam-5718	513	7	c.	c.	PROPN
ejpam-5718	513	8	boonpok	boonpok	PROPN
ejpam-5718	513	9	.	.	PUNCT
ejpam-5718	514	1	almost	almost	ADV
ejpam-5718	514	2	(	(	PUNCT
ejpam-5718	514	3	λ	λ	NOUN
ejpam-5718	514	4	,	,	PUNCT
ejpam-5718	514	5	p)-continuous	p)-continuous	ADJ
ejpam-5718	514	6	functions	function	NOUN
ejpam-5718	514	7	.	.	PUNCT
ejpam-5718	515	1	international	international	ADJ
ejpam-5718	515	2	journal	journal	PROPN
ejpam-5718	515	3	of	of	ADP
ejpam-5718	515	4	mathematics	mathematic	NOUN
ejpam-5718	515	5	and	and	CCONJ
ejpam-5718	515	6	computer	computer	NOUN
ejpam-5718	515	7	science	science	NOUN
ejpam-5718	515	8	,	,	PUNCT
ejpam-5718	515	9	18(2):255–259	18(2):255–259	NUM
ejpam-5718	515	10	,	,	PUNCT
ejpam-5718	515	11	2023	2023	NUM
ejpam-5718	515	12	.	.	PUNCT
ejpam-5718	516	1	[	[	X
ejpam-5718	516	2	61	61	NUM
ejpam-5718	516	3	]	]	X
ejpam-5718	516	4	n.	n.	NOUN
ejpam-5718	516	5	srisarakham	srisarakham	PROPN
ejpam-5718	516	6	,	,	PUNCT
ejpam-5718	516	7	a.	a.	PROPN
ejpam-5718	516	8	sama	sama	PROPN
ejpam-5718	516	9	-	-	PUNCT
ejpam-5718	516	10	ae	ae	PROPN
ejpam-5718	516	11	,	,	PUNCT
ejpam-5718	516	12	and	and	CCONJ
ejpam-5718	516	13	c.	c.	PROPN
ejpam-5718	516	14	boonpok	boonpok	PROPN
ejpam-5718	516	15	.	.	PUNCT
ejpam-5718	517	1	characterizations	characterization	NOUN
ejpam-5718	517	2	of	of	ADP
ejpam-5718	517	3	faintly	faintly	ADV
ejpam-5718	517	4	(	(	PUNCT
ejpam-5718	517	5	τ1	τ1	PROPN
ejpam-5718	517	6	,	,	PUNCT
ejpam-5718	517	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	517	8	functions	function	NOUN
ejpam-5718	517	9	.	.	PUNCT
ejpam-5718	518	1	european	european	ADJ
ejpam-5718	518	2	journal	journal	PROPN
ejpam-5718	518	3	of	of	ADP
ejpam-5718	518	4	pure	pure	ADJ
ejpam-5718	518	5	and	and	CCONJ
ejpam-5718	518	6	applied	applied	ADJ
ejpam-5718	518	7	mathematics	mathematic	NOUN
ejpam-5718	518	8	,	,	PUNCT
ejpam-5718	518	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-5718	518	10	,	,	PUNCT
ejpam-5718	518	11	2024	2024	NUM
ejpam-5718	518	12	.	.	PUNCT
ejpam-5718	519	1	[	[	X
ejpam-5718	519	2	62	62	NUM
ejpam-5718	519	3	]	]	PUNCT
ejpam-5718	519	4	m.	m.	NOUN
ejpam-5718	519	5	thongmoon	thongmoon	NOUN
ejpam-5718	519	6	and	and	CCONJ
ejpam-5718	519	7	c.	c.	PROPN
ejpam-5718	519	8	boonpok	boonpok	PROPN
ejpam-5718	519	9	.	.	PUNCT
ejpam-5718	520	1	upper	upper	ADJ
ejpam-5718	520	2	and	and	CCONJ
ejpam-5718	520	3	lower	low	ADJ
ejpam-5718	520	4	almost	almost	ADV
ejpam-5718	520	5	β(λ	β(λ	NOUN
ejpam-5718	520	6	,	,	PUNCT
ejpam-5718	520	7	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	520	8	multifunctions	multifunction	NOUN
ejpam-5718	520	9	.	.	PUNCT
ejpam-5718	521	1	wseas	wseas	VERB
ejpam-5718	521	2	transactions	transaction	NOUN
ejpam-5718	521	3	on	on	ADP
ejpam-5718	521	4	mathematics	mathematic	NOUN
ejpam-5718	521	5	,	,	PUNCT
ejpam-5718	521	6	21:844–853	21:844–853	NUM
ejpam-5718	521	7	,	,	PUNCT
ejpam-5718	521	8	2022	2022	NUM
ejpam-5718	521	9	.	.	PUNCT
ejpam-5718	522	1	p.	p.	NOUN
ejpam-5718	522	2	pue	pue	NOUN
ejpam-5718	522	3	-	-	PUNCT
ejpam-5718	522	4	on	on	ADP
ejpam-5718	522	5	,	,	PUNCT
ejpam-5718	522	6	a.	a.	PROPN
ejpam-5718	522	7	sama	sama	PROPN
ejpam-5718	522	8	-	-	PUNCT
ejpam-5718	522	9	ae	ae	PROPN
ejpam-5718	522	10	,	,	PUNCT
ejpam-5718	522	11	c.	c.	PROPN
ejpam-5718	522	12	boonpok	boonpok	PROPN
ejpam-5718	522	13	/	/	SYM
ejpam-5718	522	14	eur	eur	PROPN
ejpam-5718	522	15	.	.	PUNCT
ejpam-5718	523	1	j.	j.	PROPN
ejpam-5718	523	2	pure	pure	PROPN
ejpam-5718	523	3	appl	appl	PROPN
ejpam-5718	523	4	.	.	PROPN
ejpam-5718	523	5	math	math	PROPN
ejpam-5718	523	6	,	,	PUNCT
ejpam-5718	523	7	18	18	NUM
ejpam-5718	523	8	(	(	PUNCT
ejpam-5718	523	9	1	1	NUM
ejpam-5718	523	10	)	)	PUNCT
ejpam-5718	523	11	(	(	PUNCT
ejpam-5718	523	12	2025	2025	NUM
ejpam-5718	523	13	)	)	PUNCT
ejpam-5718	523	14	,	,	PUNCT
ejpam-5718	523	15	5718	5718	NUM
ejpam-5718	523	16	16	16	NUM
ejpam-5718	523	17	of	of	ADP
ejpam-5718	523	18	16	16	NUM
ejpam-5718	523	19	[	[	X
ejpam-5718	523	20	63	63	NUM
ejpam-5718	523	21	]	]	PUNCT
ejpam-5718	523	22	m.	m.	NOUN
ejpam-5718	523	23	thongmoon	thongmoon	NOUN
ejpam-5718	523	24	and	and	CCONJ
ejpam-5718	523	25	c.	c.	PROPN
ejpam-5718	523	26	boonpok	boonpok	PROPN
ejpam-5718	523	27	.	.	PUNCT
ejpam-5718	524	1	strongly	strongly	ADV
ejpam-5718	524	2	θ(λ	θ(λ	PROPN
ejpam-5718	524	3	,	,	PUNCT
ejpam-5718	524	4	p)-continuous	p)-continuous	ADJ
ejpam-5718	524	5	functions	function	NOUN
ejpam-5718	524	6	.	.	PUNCT
ejpam-5718	525	1	international	international	ADJ
ejpam-5718	525	2	journal	journal	PROPN
ejpam-5718	525	3	of	of	ADP
ejpam-5718	525	4	mathematics	mathematic	NOUN
ejpam-5718	525	5	and	and	CCONJ
ejpam-5718	525	6	computer	computer	NOUN
ejpam-5718	525	7	science	science	NOUN
ejpam-5718	525	8	,	,	PUNCT
ejpam-5718	525	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5718	525	10	,	,	PUNCT
ejpam-5718	525	11	2024	2024	NUM
ejpam-5718	525	12	.	.	PUNCT
ejpam-5718	526	1	[	[	X
ejpam-5718	526	2	64	64	NUM
ejpam-5718	526	3	]	]	PUNCT
ejpam-5718	526	4	m.	m.	NOUN
ejpam-5718	526	5	thongmoon	thongmoon	NOUN
ejpam-5718	526	6	,	,	PUNCT
ejpam-5718	526	7	a.	a.	PROPN
ejpam-5718	526	8	sama	sama	PROPN
ejpam-5718	526	9	-	-	PUNCT
ejpam-5718	526	10	ae	ae	PROPN
ejpam-5718	526	11	,	,	PUNCT
ejpam-5718	526	12	and	and	CCONJ
ejpam-5718	526	13	c.	c.	PROPN
ejpam-5718	526	14	boonpok	boonpok	PROPN
ejpam-5718	526	15	.	.	PUNCT
ejpam-5718	527	1	upper	upper	ADJ
ejpam-5718	527	2	and	and	CCONJ
ejpam-5718	527	3	lower	low	ADJ
ejpam-5718	527	4	s-(τ1	s-(τ1	NOUN
ejpam-5718	527	5	,	,	PUNCT
ejpam-5718	527	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5718	527	7	.	.	PUNCT
ejpam-5718	528	1	(	(	PUNCT
ejpam-5718	528	2	accepted	accept	VERB
ejpam-5718	528	3	)	)	PUNCT
ejpam-5718	528	4	.	.	PUNCT
ejpam-5718	529	1	[	[	X
ejpam-5718	529	2	65	65	NUM
ejpam-5718	529	3	]	]	X
ejpam-5718	529	4	m.	m.	NOUN
ejpam-5718	529	5	thongmoon	thongmoon	NOUN
ejpam-5718	529	6	,	,	PUNCT
ejpam-5718	529	7	s.	s.	PROPN
ejpam-5718	529	8	sompong	sompong	PROPN
ejpam-5718	529	9	,	,	PUNCT
ejpam-5718	529	10	and	and	CCONJ
ejpam-5718	529	11	c.	c.	PROPN
ejpam-5718	529	12	boonpok	boonpok	PROPN
ejpam-5718	529	13	.	.	PUNCT
ejpam-5718	530	1	upper	upper	ADJ
ejpam-5718	530	2	and	and	CCONJ
ejpam-5718	530	3	lower	low	ADJ
ejpam-5718	530	4	weak	weak	ADJ
ejpam-5718	530	5	(	(	PUNCT
ejpam-5718	530	6	τ1	τ1	NOUN
ejpam-5718	530	7	,	,	PUNCT
ejpam-5718	530	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5718	530	9	.	.	PUNCT
ejpam-5718	531	1	european	european	PROPN
ejpam-5718	531	2	journal	journal	PROPN
ejpam-5718	531	3	of	of	ADP
ejpam-5718	531	4	pure	pure	ADJ
ejpam-5718	531	5	and	and	CCONJ
ejpam-5718	531	6	applied	applied	ADJ
ejpam-5718	531	7	mathematics	mathematic	NOUN
ejpam-5718	531	8	,	,	PUNCT
ejpam-5718	531	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5718	531	10	,	,	PUNCT
ejpam-5718	531	11	2024	2024	NUM
ejpam-5718	531	12	.	.	PUNCT
ejpam-5718	532	1	[	[	X
ejpam-5718	532	2	66	66	NUM
ejpam-5718	532	3	]	]	PUNCT
ejpam-5718	532	4	m.	m.	NOUN
ejpam-5718	532	5	thongmoon	thongmoon	NOUN
ejpam-5718	532	6	,	,	PUNCT
ejpam-5718	532	7	s.	s.	PROPN
ejpam-5718	532	8	sompong	sompong	PROPN
ejpam-5718	532	9	,	,	PUNCT
ejpam-5718	532	10	and	and	CCONJ
ejpam-5718	532	11	c.	c.	PROPN
ejpam-5718	532	12	boonpok	boonpok	PROPN
ejpam-5718	532	13	.	.	PUNCT
ejpam-5718	533	1	rarely	rarely	ADV
ejpam-5718	533	2	(	(	PUNCT
ejpam-5718	533	3	τ1	τ1	NOUN
ejpam-5718	533	4	,	,	PUNCT
ejpam-5718	533	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5718	533	6	functions	function	NOUN
ejpam-5718	533	7	.	.	PUNCT
ejpam-5718	534	1	international	international	ADJ
ejpam-5718	534	2	journal	journal	NOUN
ejpam-5718	534	3	of	of	ADP
ejpam-5718	534	4	mathematics	mathematic	NOUN
ejpam-5718	534	5	and	and	CCONJ
ejpam-5718	534	6	computer	computer	NOUN
ejpam-5718	534	7	science	science	NOUN
ejpam-5718	534	8	,	,	PUNCT
ejpam-5718	534	9	20(1):423–427	20(1):423–427	NUM
ejpam-5718	534	10	,	,	PUNCT
ejpam-5718	534	11	2025	2025	NUM
ejpam-5718	534	12	.	.	PUNCT
ejpam-5718	535	1	[	[	X
ejpam-5718	535	2	67	67	NUM
ejpam-5718	535	3	]	]	X
ejpam-5718	535	4	c.	c.	PROPN
ejpam-5718	535	5	viriyapong	viriyapong	PROPN
ejpam-5718	535	6	and	and	CCONJ
ejpam-5718	535	7	c.	c.	PROPN
ejpam-5718	535	8	boonpok	boonpok	PROPN
ejpam-5718	535	9	.	.	PUNCT
ejpam-5718	536	1	(	(	PUNCT
ejpam-5718	536	2	τ1	τ1	NOUN
ejpam-5718	536	3	,	,	PUNCT
ejpam-5718	536	4	τ2)α	τ2)α	NOUN
ejpam-5718	536	5	-	-	PUNCT
ejpam-5718	536	6	continuity	continuity	NOUN
ejpam-5718	536	7	for	for	ADP
ejpam-5718	536	8	multifunctions	multifunction	NOUN
ejpam-5718	536	9	.	.	PUNCT
ejpam-5718	537	1	journal	journal	PROPN
ejpam-5718	537	2	of	of	ADP
ejpam-5718	537	3	mathematics	mathematic	NOUN
ejpam-5718	537	4	,	,	PUNCT
ejpam-5718	537	5	2020:6285763	2020:6285763	NUM
ejpam-5718	537	6	,	,	PUNCT
ejpam-5718	537	7	2020	2020	NUM
ejpam-5718	537	8	.	.	PUNCT
ejpam-5718	538	1	[	[	X
ejpam-5718	538	2	68	68	NUM
ejpam-5718	538	3	]	]	X
ejpam-5718	538	4	c.	c.	PROPN
ejpam-5718	538	5	viriyapong	viriyapong	PROPN
ejpam-5718	538	6	and	and	CCONJ
ejpam-5718	538	7	c.	c.	PROPN
ejpam-5718	538	8	boonpok	boonpok	PROPN
ejpam-5718	538	9	.	.	PUNCT
ejpam-5718	539	1	(	(	PUNCT
ejpam-5718	539	2	λ	λ	X
ejpam-5718	539	3	,	,	PUNCT
ejpam-5718	539	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5718	539	5	functions	function	NOUN
ejpam-5718	539	6	.	.	PUNCT
ejpam-5718	540	1	wseas	wseas	VERB
ejpam-5718	540	2	transactions	transaction	NOUN
ejpam-5718	540	3	on	on	ADP
ejpam-5718	540	4	mathematics	mathematic	NOUN
ejpam-5718	540	5	,	,	PUNCT
ejpam-5718	540	6	21:380–385	21:380–385	NUM
ejpam-5718	540	7	,	,	PUNCT
ejpam-5718	540	8	2022	2022	NUM
ejpam-5718	540	9	.	.	PUNCT
ejpam-5718	541	1	[	[	X
ejpam-5718	541	2	69	69	NUM
ejpam-5718	541	3	]	]	X
ejpam-5718	541	4	c.	c.	PROPN
ejpam-5718	541	5	viriyapong	viriyapong	PROPN
ejpam-5718	541	6	and	and	CCONJ
ejpam-5718	541	7	c.	c.	PROPN
ejpam-5718	541	8	boonpok	boonpok	PROPN
ejpam-5718	541	9	.	.	PUNCT
ejpam-5718	542	1	weak	weak	ADJ
ejpam-5718	542	2	quasi	quasi	NOUN
ejpam-5718	542	3	(	(	PUNCT
ejpam-5718	542	4	λ	λ	PROPN
ejpam-5718	542	5	,	,	PUNCT
ejpam-5718	542	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5718	542	7	for	for	ADP
ejpam-5718	542	8	multifunctions	multifunction	NOUN
ejpam-5718	542	9	.	.	PUNCT
ejpam-5718	543	1	international	international	ADJ
ejpam-5718	543	2	journal	journal	PROPN
ejpam-5718	543	3	of	of	ADP
ejpam-5718	543	4	mathematics	mathematic	NOUN
ejpam-5718	543	5	and	and	CCONJ
ejpam-5718	543	6	computer	computer	NOUN
ejpam-5718	543	7	science	science	NOUN
ejpam-5718	543	8	,	,	PUNCT
ejpam-5718	543	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5718	543	10	,	,	PUNCT
ejpam-5718	543	11	2022	2022	NUM
ejpam-5718	543	12	.	.	PUNCT
ejpam-5718	544	1	[	[	X
ejpam-5718	544	2	70	70	NUM
ejpam-5718	544	3	]	]	X
ejpam-5718	544	4	c.	c.	PROPN
ejpam-5718	544	5	viriyapong	viriyapong	PROPN
ejpam-5718	544	6	,	,	PUNCT
ejpam-5718	544	7	s.	s.	PROPN
ejpam-5718	544	8	sompong	sompong	PROPN
ejpam-5718	544	9	,	,	PUNCT
ejpam-5718	544	10	and	and	CCONJ
ejpam-5718	544	11	c.	c.	PROPN
ejpam-5718	544	12	boonpok	boonpok	PROPN
ejpam-5718	544	13	.	.	PUNCT
ejpam-5718	545	1	upper	upper	ADJ
ejpam-5718	545	2	and	and	CCONJ
ejpam-5718	545	3	lower	low	ADJ
ejpam-5718	545	4	slight	slight	ADJ
ejpam-5718	545	5	(	(	PUNCT
ejpam-5718	545	6	τ1	τ1	NOUN
ejpam-5718	545	7	,	,	PUNCT
ejpam-5718	545	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5718	545	9	.	.	PUNCT
ejpam-5718	546	1	european	european	PROPN
ejpam-5718	546	2	journal	journal	PROPN
ejpam-5718	546	3	of	of	ADP
ejpam-5718	546	4	pure	pure	ADJ
ejpam-5718	546	5	and	and	CCONJ
ejpam-5718	546	6	applied	applied	ADJ
ejpam-5718	546	7	mathematics	mathematic	NOUN
ejpam-5718	546	8	,	,	PUNCT
ejpam-5718	546	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-5718	546	10	,	,	PUNCT
ejpam-5718	546	11	2024	2024	NUM
ejpam-5718	546	12	.	.	PUNCT
ejpam-5718	547	1	[	[	X
ejpam-5718	547	2	71	71	NUM
ejpam-5718	547	3	]	]	X
ejpam-5718	547	4	n.	n.	PROPN
ejpam-5718	547	5	viriyapong	viriyapong	PROPN
ejpam-5718	547	6	,	,	PUNCT
ejpam-5718	547	7	s.	s.	PROPN
ejpam-5718	547	8	sompong	sompong	PROPN
ejpam-5718	547	9	,	,	PUNCT
ejpam-5718	547	10	and	and	CCONJ
ejpam-5718	547	11	c.	c.	PROPN
ejpam-5718	547	12	boonpok	boonpok	PROPN
ejpam-5718	547	13	.	.	PUNCT
ejpam-5718	548	1	slightly	slightly	ADV
ejpam-5718	548	2	(	(	PUNCT
ejpam-5718	548	3	τ1	τ1	NOUN
ejpam-5718	548	4	,	,	PUNCT
ejpam-5718	548	5	τ2)p	τ2)p	ADJ
ejpam-5718	548	6	-	-	ADJ
ejpam-5718	548	7	continuous	continuous	ADJ
ejpam-5718	548	8	multifunctions	multifunction	NOUN
ejpam-5718	548	9	.	.	PUNCT
ejpam-5718	549	1	international	international	ADJ
ejpam-5718	549	2	journal	journal	NOUN
ejpam-5718	549	3	of	of	ADP
ejpam-5718	549	4	analysis	analysis	NOUN
ejpam-5718	549	5	and	and	CCONJ
ejpam-5718	549	6	applications	application	NOUN
ejpam-5718	549	7	,	,	PUNCT
ejpam-5718	549	8	22:152	22:152	NUM
ejpam-5718	549	9	,	,	PUNCT
ejpam-5718	549	10	2024	2024	NUM
ejpam-5718	549	11	.	.	PUNCT
ejpam-5718	550	1	[	[	X
ejpam-5718	550	2	72	72	NUM
ejpam-5718	550	3	]	]	X
ejpam-5718	550	4	n.	n.	PROPN
ejpam-5718	550	5	viriyapong	viriyapong	PROPN
ejpam-5718	550	6	,	,	PUNCT
ejpam-5718	550	7	s.	s.	PROPN
ejpam-5718	550	8	sompong	sompong	PROPN
ejpam-5718	550	9	,	,	PUNCT
ejpam-5718	550	10	and	and	CCONJ
ejpam-5718	550	11	c.	c.	PROPN
ejpam-5718	550	12	boonpok	boonpok	PROPN
ejpam-5718	550	13	.	.	PUNCT
ejpam-5718	551	1	(	(	PUNCT
ejpam-5718	551	2	τ1	τ1	NOUN
ejpam-5718	551	3	,	,	PUNCT
ejpam-5718	551	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5718	551	5	disconnectedness	disconnectedness	NOUN
ejpam-5718	551	6	in	in	ADP
ejpam-5718	551	7	bitopological	bitopological	ADJ
ejpam-5718	551	8	spaces	space	NOUN
ejpam-5718	551	9	.	.	PUNCT
ejpam-5718	552	1	international	international	ADJ
ejpam-5718	552	2	journal	journal	PROPN
ejpam-5718	552	3	of	of	ADP
ejpam-5718	552	4	mathematics	mathematic	NOUN
ejpam-5718	552	5	and	and	CCONJ
ejpam-5718	552	6	computer	computer	NOUN
ejpam-5718	552	7	science	science	NOUN
ejpam-5718	552	8	,	,	PUNCT
ejpam-5718	552	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5718	552	10	,	,	PUNCT
ejpam-5718	552	11	2024	2024	NUM
ejpam-5718	552	12	.	.	PUNCT
ejpam-5718	553	1	[	[	X
ejpam-5718	553	2	73	73	NUM
ejpam-5718	553	3	]	]	X
ejpam-5718	553	4	n.	n.	PROPN
ejpam-5718	553	5	viriyapong	viriyapong	PROPN
ejpam-5718	553	6	,	,	PUNCT
ejpam-5718	553	7	s.	s.	PROPN
ejpam-5718	553	8	sompong	sompong	PROPN
ejpam-5718	553	9	,	,	PUNCT
ejpam-5718	553	10	and	and	CCONJ
ejpam-5718	553	11	c.	c.	PROPN
ejpam-5718	553	12	boonpok	boonpok	PROPN
ejpam-5718	553	13	.	.	PUNCT
ejpam-5718	554	1	upper	upper	ADJ
ejpam-5718	554	2	and	and	CCONJ
ejpam-5718	554	3	lower	low	ADJ
ejpam-5718	554	4	s-(τ1	s-(τ1	NOUN
ejpam-5718	554	5	,	,	PUNCT
ejpam-5718	554	6	τ2)p	τ2)p	ADJ
ejpam-5718	554	7	-	-	PUNCT
ejpam-5718	554	8	continuous	continuous	ADJ
ejpam-5718	554	9	multifunctions	multifunction	NOUN
ejpam-5718	554	10	.	.	PUNCT
ejpam-5718	555	1	european	european	ADJ
ejpam-5718	555	2	journal	journal	PROPN
ejpam-5718	555	3	of	of	ADP
ejpam-5718	555	4	pure	pure	ADJ
ejpam-5718	555	5	and	and	CCONJ
ejpam-5718	555	6	applied	applied	ADJ
ejpam-5718	555	7	mathematics	mathematic	NOUN
ejpam-5718	555	8	,	,	PUNCT
ejpam-5718	555	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-5718	555	10	,	,	PUNCT
ejpam-5718	555	11	2024	2024	NUM
ejpam-5718	555	12	.	.	PUNCT