id	sid	tid	token	lemma	pos
ejpam-5320	1	1	european	european	PROPN
ejpam-5320	1	2	journal	journal	PROPN
ejpam-5320	1	3	of	of	ADP
ejpam-5320	1	4	pure	pure	ADJ
ejpam-5320	1	5	and	and	CCONJ
ejpam-5320	1	6	applied	apply	VERB
ejpam-5320	1	7	mathematics	mathematic	NOUN
ejpam-5320	1	8	vol	vol	NOUN
ejpam-5320	1	9	.	.	PROPN
ejpam-5320	2	1	17	17	NUM
ejpam-5320	2	2	,	,	PUNCT
ejpam-5320	2	3	no	no	INTJ
ejpam-5320	2	4	.	.	NOUN
ejpam-5320	2	5	3	3	NUM
ejpam-5320	2	6	,	,	PUNCT
ejpam-5320	2	7	2024	2024	NUM
ejpam-5320	2	8	,	,	PUNCT
ejpam-5320	2	9	2288	2288	NUM
ejpam-5320	2	10	-	-	SYM
ejpam-5320	2	11	2298	2298	NUM
ejpam-5320	2	12	issn	issn	VERB
ejpam-5320	2	13	1307	1307	NUM
ejpam-5320	2	14	-	-	SYM
ejpam-5320	2	15	5543	5543	NUM
ejpam-5320	2	16	–	–	PUNCT
ejpam-5320	2	17	ejpam.com	ejpam.com	X
ejpam-5320	2	18	published	publish	VERB
ejpam-5320	2	19	by	by	ADP
ejpam-5320	2	20	new	new	PROPN
ejpam-5320	2	21	york	york	PROPN
ejpam-5320	2	22	business	business	PROPN
ejpam-5320	2	23	global	global	PROPN
ejpam-5320	2	24	c-(τ1	c-(τ1	PROPN
ejpam-5320	2	25	,	,	PUNCT
ejpam-5320	2	26	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5320	2	27	for	for	ADP
ejpam-5320	2	28	multifunctions	multifunction	NOUN
ejpam-5320	2	29	jeeranunt	jeeranunt	PROPN
ejpam-5320	2	30	khampakdee1	khampakdee1	PROPN
ejpam-5320	2	31	,	,	PUNCT
ejpam-5320	2	32	supannee	supannee	PROPN
ejpam-5320	2	33	sompong2	sompong2	PROPN
ejpam-5320	2	34	,	,	PUNCT
ejpam-5320	2	35	chawalit	chawalit	VERB
ejpam-5320	2	36	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5320	2	37	1	1	NUM
ejpam-5320	2	38	mathematics	mathematic	NOUN
ejpam-5320	2	39	and	and	CCONJ
ejpam-5320	2	40	applied	apply	VERB
ejpam-5320	2	41	mathematics	mathematics	PROPN
ejpam-5320	2	42	research	research	NOUN
ejpam-5320	2	43	unit	unit	NOUN
ejpam-5320	2	44	,	,	PUNCT
ejpam-5320	2	45	department	department	NOUN
ejpam-5320	2	46	of	of	ADP
ejpam-5320	2	47	mathematics	mathematic	NOUN
ejpam-5320	2	48	,	,	PUNCT
ejpam-5320	2	49	faculty	faculty	NOUN
ejpam-5320	2	50	of	of	ADP
ejpam-5320	2	51	science	science	NOUN
ejpam-5320	2	52	,	,	PUNCT
ejpam-5320	2	53	mahasarakham	mahasarakham	PROPN
ejpam-5320	2	54	university	university	PROPN
ejpam-5320	2	55	,	,	PUNCT
ejpam-5320	2	56	maha	maha	PROPN
ejpam-5320	2	57	sarakham	sarakham	PROPN
ejpam-5320	2	58	,	,	PUNCT
ejpam-5320	2	59	44150	44150	NUM
ejpam-5320	2	60	,	,	PUNCT
ejpam-5320	2	61	thailand	thailand	PROPN
ejpam-5320	2	62	2	2	NUM
ejpam-5320	2	63	department	department	NOUN
ejpam-5320	2	64	of	of	ADP
ejpam-5320	2	65	mathematics	mathematic	NOUN
ejpam-5320	2	66	and	and	CCONJ
ejpam-5320	2	67	statistics	statistic	NOUN
ejpam-5320	2	68	,	,	PUNCT
ejpam-5320	2	69	faculty	faculty	NOUN
ejpam-5320	2	70	of	of	ADP
ejpam-5320	2	71	science	science	NOUN
ejpam-5320	2	72	and	and	CCONJ
ejpam-5320	2	73	technology	technology	NOUN
ejpam-5320	2	74	,	,	PUNCT
ejpam-5320	2	75	sakon	sakon	PROPN
ejpam-5320	2	76	nakhon	nakhon	PROPN
ejpam-5320	2	77	rajbhat	rajbhat	PROPN
ejpam-5320	2	78	university	university	PROPN
ejpam-5320	2	79	,	,	PUNCT
ejpam-5320	2	80	sakon	sakon	PROPN
ejpam-5320	2	81	nakhon	nakhon	PROPN
ejpam-5320	2	82	,	,	PUNCT
ejpam-5320	2	83	47000	47000	NUM
ejpam-5320	2	84	,	,	PUNCT
ejpam-5320	2	85	thailand	thailand	PROPN
ejpam-5320	2	86	abstract	abstract	NOUN
ejpam-5320	2	87	.	.	PUNCT
ejpam-5320	3	1	this	this	DET
ejpam-5320	3	2	paper	paper	NOUN
ejpam-5320	3	3	is	be	AUX
ejpam-5320	3	4	concerned	concern	VERB
ejpam-5320	3	5	with	with	ADP
ejpam-5320	3	6	the	the	DET
ejpam-5320	3	7	concepts	concept	NOUN
ejpam-5320	3	8	of	of	ADP
ejpam-5320	3	9	upper	upper	ADJ
ejpam-5320	3	10	and	and	CCONJ
ejpam-5320	3	11	lower	low	ADJ
ejpam-5320	3	12	c-(τ1	c-(τ1	PROPN
ejpam-5320	3	13	,	,	PUNCT
ejpam-5320	3	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	3	15	multifunctions	multifunction	NOUN
ejpam-5320	3	16	.	.	PUNCT
ejpam-5320	4	1	moreover	moreover	ADV
ejpam-5320	4	2	,	,	PUNCT
ejpam-5320	4	3	several	several	ADJ
ejpam-5320	4	4	characterizations	characterization	NOUN
ejpam-5320	4	5	of	of	ADP
ejpam-5320	4	6	upper	upper	ADJ
ejpam-5320	4	7	and	and	CCONJ
ejpam-5320	4	8	lower	low	ADJ
ejpam-5320	4	9	c-(τ1	c-(τ1	PROPN
ejpam-5320	4	10	,	,	PUNCT
ejpam-5320	4	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	4	12	multifunctions	multifunction	NOUN
ejpam-5320	4	13	are	be	AUX
ejpam-5320	4	14	investigated	investigate	VERB
ejpam-5320	4	15	.	.	PUNCT
ejpam-5320	5	1	2020	2020	NUM
ejpam-5320	5	2	mathematics	mathematic	NOUN
ejpam-5320	5	3	subject	subject	NOUN
ejpam-5320	5	4	classifications	classification	NOUN
ejpam-5320	5	5	:	:	PUNCT
ejpam-5320	5	6	54c08	54c08	NUM
ejpam-5320	5	7	,	,	PUNCT
ejpam-5320	5	8	54c60	54c60	NUM
ejpam-5320	5	9	,	,	PUNCT
ejpam-5320	5	10	54e55	54e55	NUM
ejpam-5320	5	11	key	key	ADJ
ejpam-5320	5	12	words	word	NOUN
ejpam-5320	5	13	and	and	CCONJ
ejpam-5320	5	14	phrases	phrase	NOUN
ejpam-5320	5	15	:	:	PUNCT
ejpam-5320	5	16	upper	upper	PROPN
ejpam-5320	5	17	c-(τ1	c-(τ1	PROPN
ejpam-5320	5	18	,	,	PUNCT
ejpam-5320	5	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	5	20	multifunction	multifunction	NOUN
ejpam-5320	5	21	,	,	PUNCT
ejpam-5320	5	22	lower	lower	PROPN
ejpam-5320	5	23	c-(τ1	c-(τ1	PROPN
ejpam-5320	5	24	,	,	PUNCT
ejpam-5320	5	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	5	26	multifunction	multifunction	NOUN
ejpam-5320	5	27	1	1	NUM
ejpam-5320	5	28	.	.	PUNCT
ejpam-5320	5	29	introduction	introduction	NOUN
ejpam-5320	5	30	the	the	DET
ejpam-5320	5	31	field	field	NOUN
ejpam-5320	5	32	of	of	ADP
ejpam-5320	5	33	the	the	DET
ejpam-5320	5	34	mathematical	mathematical	ADJ
ejpam-5320	5	35	science	science	NOUN
ejpam-5320	5	36	which	which	PRON
ejpam-5320	5	37	goes	go	VERB
ejpam-5320	5	38	under	under	ADP
ejpam-5320	5	39	the	the	DET
ejpam-5320	5	40	name	name	NOUN
ejpam-5320	5	41	of	of	ADP
ejpam-5320	5	42	topology	topology	NOUN
ejpam-5320	5	43	is	be	AUX
ejpam-5320	5	44	concerned	concern	VERB
ejpam-5320	5	45	with	with	ADP
ejpam-5320	5	46	all	all	DET
ejpam-5320	5	47	questions	question	NOUN
ejpam-5320	5	48	directly	directly	ADV
ejpam-5320	5	49	or	or	CCONJ
ejpam-5320	5	50	indirectly	indirectly	ADV
ejpam-5320	5	51	related	relate	VERB
ejpam-5320	5	52	to	to	ADP
ejpam-5320	5	53	continuity	continuity	NOUN
ejpam-5320	5	54	.	.	PUNCT
ejpam-5320	6	1	semi	semi	ADJ
ejpam-5320	6	2	-	-	ADJ
ejpam-5320	6	3	open	open	ADJ
ejpam-5320	6	4	sets	set	NOUN
ejpam-5320	6	5	,	,	PUNCT
ejpam-5320	6	6	preopen	preopen	ADJ
ejpam-5320	6	7	sets	set	NOUN
ejpam-5320	6	8	,	,	PUNCT
ejpam-5320	6	9	α	α	NOUN
ejpam-5320	6	10	-	-	ADJ
ejpam-5320	6	11	open	open	ADJ
ejpam-5320	6	12	sets	set	NOUN
ejpam-5320	6	13	and	and	CCONJ
ejpam-5320	6	14	β	β	NOUN
ejpam-5320	6	15	-	-	ADJ
ejpam-5320	6	16	open	open	ADJ
ejpam-5320	6	17	sets	set	NOUN
ejpam-5320	6	18	play	play	VERB
ejpam-5320	6	19	an	an	DET
ejpam-5320	6	20	important	important	ADJ
ejpam-5320	6	21	role	role	NOUN
ejpam-5320	6	22	in	in	ADP
ejpam-5320	6	23	topological	topological	ADJ
ejpam-5320	6	24	spaces	space	NOUN
ejpam-5320	6	25	.	.	PUNCT
ejpam-5320	7	1	using	use	VERB
ejpam-5320	7	2	these	these	DET
ejpam-5320	7	3	sets	set	NOUN
ejpam-5320	7	4	,	,	PUNCT
ejpam-5320	7	5	many	many	ADJ
ejpam-5320	7	6	authors	author	NOUN
ejpam-5320	7	7	introduced	introduce	VERB
ejpam-5320	7	8	and	and	CCONJ
ejpam-5320	7	9	studied	study	VERB
ejpam-5320	7	10	various	various	ADJ
ejpam-5320	7	11	types	type	NOUN
ejpam-5320	7	12	of	of	ADP
ejpam-5320	7	13	generalizations	generalization	NOUN
ejpam-5320	7	14	of	of	ADP
ejpam-5320	7	15	continuity	continuity	NOUN
ejpam-5320	7	16	for	for	ADP
ejpam-5320	7	17	functions	function	NOUN
ejpam-5320	7	18	and	and	CCONJ
ejpam-5320	7	19	multifunctions	multifunction	NOUN
ejpam-5320	7	20	.	.	PUNCT
ejpam-5320	8	1	in	in	ADP
ejpam-5320	8	2	1970	1970	NUM
ejpam-5320	8	3	,	,	PUNCT
ejpam-5320	8	4	gentry	gentry	NOUN
ejpam-5320	8	5	and	and	CCONJ
ejpam-5320	8	6	hoyle	hoyle	PROPN
ejpam-5320	8	7	iii	iii	PROPN
ejpam-5320	8	8	[	[	X
ejpam-5320	8	9	23	23	NUM
ejpam-5320	8	10	]	]	PUNCT
ejpam-5320	8	11	introduced	introduce	VERB
ejpam-5320	8	12	and	and	CCONJ
ejpam-5320	8	13	studied	study	VERB
ejpam-5320	8	14	the	the	DET
ejpam-5320	8	15	concept	concept	NOUN
ejpam-5320	8	16	of	of	ADP
ejpam-5320	8	17	c	c	NOUN
ejpam-5320	8	18	-	-	PUNCT
ejpam-5320	8	19	continuous	continuous	ADJ
ejpam-5320	8	20	functions	function	NOUN
ejpam-5320	8	21	.	.	PUNCT
ejpam-5320	9	1	furthermore	furthermore	ADV
ejpam-5320	9	2	,	,	PUNCT
ejpam-5320	9	3	some	some	DET
ejpam-5320	9	4	characterizations	characterization	NOUN
ejpam-5320	9	5	of	of	ADP
ejpam-5320	9	6	c	c	NOUN
ejpam-5320	9	7	-	-	PUNCT
ejpam-5320	9	8	continuous	continuous	ADJ
ejpam-5320	9	9	functions	function	NOUN
ejpam-5320	9	10	were	be	AUX
ejpam-5320	9	11	investigated	investigate	VERB
ejpam-5320	9	12	in	in	ADP
ejpam-5320	9	13	[	[	X
ejpam-5320	9	14	28	28	NUM
ejpam-5320	9	15	]	]	PUNCT
ejpam-5320	9	16	,	,	PUNCT
ejpam-5320	9	17	[	[	X
ejpam-5320	9	18	29	29	NUM
ejpam-5320	9	19	]	]	PUNCT
ejpam-5320	9	20	and	and	CCONJ
ejpam-5320	9	21	[	[	X
ejpam-5320	9	22	32	32	NUM
ejpam-5320	9	23	]	]	PUNCT
ejpam-5320	9	24	,	,	PUNCT
ejpam-5320	9	25	respectively	respectively	ADV
ejpam-5320	9	26	.	.	PUNCT
ejpam-5320	10	1	duangphui	duangphui	NOUN
ejpam-5320	10	2	et	et	PROPN
ejpam-5320	10	3	al	al	PROPN
ejpam-5320	10	4	.	.	PUNCT
ejpam-5320	11	1	[	[	X
ejpam-5320	11	2	22	22	NUM
ejpam-5320	11	3	]	]	PUNCT
ejpam-5320	11	4	introduced	introduce	VERB
ejpam-5320	11	5	and	and	CCONJ
ejpam-5320	11	6	studied	study	VERB
ejpam-5320	11	7	the	the	DET
ejpam-5320	11	8	notion	notion	NOUN
ejpam-5320	11	9	of	of	ADP
ejpam-5320	11	10	(	(	PUNCT
ejpam-5320	11	11	µ	µ	NOUN
ejpam-5320	11	12	,	,	PUNCT
ejpam-5320	11	13	µ′)(m	µ′)(m	VERB
ejpam-5320	11	14	,	,	PUNCT
ejpam-5320	11	15	n)-continuous	n)-continuous	ADJ
ejpam-5320	11	16	functions	function	NOUN
ejpam-5320	11	17	.	.	PUNCT
ejpam-5320	12	1	thongmoon	thongmoon	NOUN
ejpam-5320	12	2	and	and	CCONJ
ejpam-5320	12	3	boonpok	boonpok	VERB
ejpam-5320	13	1	[	[	X
ejpam-5320	13	2	38	38	NUM
ejpam-5320	13	3	]	]	PUNCT
ejpam-5320	13	4	introduced	introduce	VERB
ejpam-5320	13	5	and	and	CCONJ
ejpam-5320	13	6	investigated	investigate	VERB
ejpam-5320	13	7	the	the	DET
ejpam-5320	13	8	notion	notion	NOUN
ejpam-5320	13	9	of	of	ADP
ejpam-5320	13	10	strongly	strongly	ADV
ejpam-5320	13	11	θ(λ	θ(λ	ADJ
ejpam-5320	13	12	,	,	PUNCT
ejpam-5320	13	13	p)continuous	p)continuous	ADJ
ejpam-5320	13	14	functions	function	NOUN
ejpam-5320	13	15	.	.	PUNCT
ejpam-5320	14	1	moreover	moreover	ADV
ejpam-5320	14	2	,	,	PUNCT
ejpam-5320	14	3	several	several	ADJ
ejpam-5320	14	4	characterizations	characterization	NOUN
ejpam-5320	14	5	of	of	ADP
ejpam-5320	14	6	almost	almost	ADV
ejpam-5320	14	7	(	(	PUNCT
ejpam-5320	14	8	λ	λ	PROPN
ejpam-5320	14	9	,	,	PUNCT
ejpam-5320	14	10	p)-continuous	p)-continuous	ADJ
ejpam-5320	14	11	functions	function	NOUN
ejpam-5320	14	12	,	,	PUNCT
ejpam-5320	14	13	almost	almost	ADV
ejpam-5320	14	14	strongly	strongly	ADV
ejpam-5320	14	15	θ(λ	θ(λ	VERB
ejpam-5320	14	16	,	,	PUNCT
ejpam-5320	14	17	p)-continuous	p)-continuous	ADJ
ejpam-5320	14	18	functions	function	NOUN
ejpam-5320	14	19	,	,	PUNCT
ejpam-5320	14	20	θ(λ	θ(λ	PROPN
ejpam-5320	14	21	,	,	PUNCT
ejpam-5320	14	22	p)-continuous	p)-continuous	ADJ
ejpam-5320	14	23	functions	function	NOUN
ejpam-5320	14	24	,	,	PUNCT
ejpam-5320	14	25	weakly	weakly	ADJ
ejpam-5320	14	26	(	(	PUNCT
ejpam-5320	14	27	λ	λ	PROPN
ejpam-5320	14	28	,	,	PUNCT
ejpam-5320	14	29	b)-continuous	b)-continuous	ADJ
ejpam-5320	14	30	functions	function	NOUN
ejpam-5320	14	31	,	,	PUNCT
ejpam-5320	14	32	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5320	14	33	functions	function	NOUN
ejpam-5320	14	34	,	,	PUNCT
ejpam-5320	14	35	⋆-continuous	⋆-continuous	ADJ
ejpam-5320	14	36	functions	function	NOUN
ejpam-5320	14	37	,	,	PUNCT
ejpam-5320	14	38	θ	θ	PROPN
ejpam-5320	14	39	-	-	ADJ
ejpam-5320	14	40	i	i	VERB
ejpam-5320	14	41	continuous	continuous	ADJ
ejpam-5320	14	42	functions	function	NOUN
ejpam-5320	14	43	,	,	PUNCT
ejpam-5320	14	44	almost	almost	ADV
ejpam-5320	14	45	(	(	PUNCT
ejpam-5320	14	46	g	g	NOUN
ejpam-5320	14	47	,	,	PUNCT
ejpam-5320	14	48	m)-continuous	m)-continuous	ADJ
ejpam-5320	14	49	functions	function	NOUN
ejpam-5320	14	50	,	,	PUNCT
ejpam-5320	14	51	(	(	PUNCT
ejpam-5320	14	52	λ	λ	NOUN
ejpam-5320	14	53	,	,	PUNCT
ejpam-5320	14	54	sp)-continuous	sp)-continuous	ADJ
ejpam-5320	14	55	functions	function	NOUN
ejpam-5320	14	56	,	,	PUNCT
ejpam-5320	14	57	δp(λ	δp(λ	NOUN
ejpam-5320	14	58	,	,	PUNCT
ejpam-5320	14	59	s)-continuous	s)-continuous	ADJ
ejpam-5320	14	60	functions	function	NOUN
ejpam-5320	14	61	,	,	PUNCT
ejpam-5320	14	62	(	(	PUNCT
ejpam-5320	14	63	λ	λ	NOUN
ejpam-5320	14	64	,	,	PUNCT
ejpam-5320	14	65	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5320	14	66	functions	function	NOUN
ejpam-5320	14	67	,	,	PUNCT
ejpam-5320	14	68	pairwise	pairwise	NOUN
ejpam-5320	14	69	almostm	almostm	NOUN
ejpam-5320	14	70	-continuous	-continuous	ADJ
ejpam-5320	14	71	functions	function	NOUN
ejpam-5320	14	72	,	,	PUNCT
ejpam-5320	14	73	(	(	PUNCT
ejpam-5320	14	74	τ1	τ1	NOUN
ejpam-5320	14	75	,	,	PUNCT
ejpam-5320	14	76	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	14	77	functions	function	NOUN
ejpam-5320	14	78	,	,	PUNCT
ejpam-5320	14	79	almost	almost	ADV
ejpam-5320	14	80	(	(	PUNCT
ejpam-5320	14	81	τ1	τ1	NOUN
ejpam-5320	14	82	,	,	PUNCT
ejpam-5320	14	83	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	14	84	functions	function	NOUN
ejpam-5320	14	85	and	and	CCONJ
ejpam-5320	14	86	weakly	weakly	ADJ
ejpam-5320	14	87	∗corresponding	∗corresponde	VERB
ejpam-5320	14	88	author	author	NOUN
ejpam-5320	14	89	.	.	PUNCT
ejpam-5320	15	1	doi	doi	NOUN
ejpam-5320	15	2	:	:	PUNCT
ejpam-5320	15	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5320	https://doi.org/10.29020/nybg.ejpam.v17i3.5320	VERB
ejpam-5320	15	4	email	email	NOUN
ejpam-5320	15	5	addresses	address	NOUN
ejpam-5320	15	6	:	:	PUNCT
ejpam-5320	15	7	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-5320	15	8	(	(	PUNCT
ejpam-5320	15	9	j.	j.	PROPN
ejpam-5320	15	10	khampakdee	khampakdee	PROPN
ejpam-5320	15	11	)	)	PUNCT
ejpam-5320	15	12	,	,	PUNCT
ejpam-5320	15	13	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-5320	15	14	(	(	PUNCT
ejpam-5320	15	15	s.	s.	PROPN
ejpam-5320	15	16	sompong	sompong	PROPN
ejpam-5320	15	17	)	)	PUNCT
ejpam-5320	15	18	,	,	PUNCT
ejpam-5320	15	19	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5320	15	20	(	(	PUNCT
ejpam-5320	15	21	c.	c.	PROPN
ejpam-5320	15	22	boonpok	boonpok	PROPN
ejpam-5320	15	23	)	)	PUNCT
ejpam-5320	15	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5320	15	25	2288	2288	NUM
ejpam-5320	16	1	©	©	PROPN
ejpam-5320	16	2	2024	2024	NUM
ejpam-5320	16	3	ejpam	ejpam	NOUN
ejpam-5320	16	4	all	all	DET
ejpam-5320	16	5	rights	right	NOUN
ejpam-5320	16	6	reserved	reserve	VERB
ejpam-5320	16	7	.	.	PUNCT
ejpam-5320	17	1	j.	j.	PROPN
ejpam-5320	17	2	khampakdee	khampakdee	PROPN
ejpam-5320	17	3	,	,	PUNCT
ejpam-5320	17	4	s.	s.	PROPN
ejpam-5320	17	5	sompong	sompong	PROPN
ejpam-5320	17	6	,	,	PUNCT
ejpam-5320	17	7	c.	c.	PROPN
ejpam-5320	17	8	boonpok	boonpok	PROPN
ejpam-5320	17	9	/	/	SYM
ejpam-5320	17	10	eur	eur	PROPN
ejpam-5320	17	11	.	.	PUNCT
ejpam-5320	18	1	j.	j.	PROPN
ejpam-5320	18	2	pure	pure	PROPN
ejpam-5320	18	3	appl	appl	PROPN
ejpam-5320	18	4	.	.	PROPN
ejpam-5320	18	5	math	math	PROPN
ejpam-5320	18	6	,	,	PUNCT
ejpam-5320	18	7	17	17	NUM
ejpam-5320	18	8	(	(	PUNCT
ejpam-5320	18	9	3	3	NUM
ejpam-5320	18	10	)	)	PUNCT
ejpam-5320	18	11	(	(	PUNCT
ejpam-5320	18	12	2024	2024	NUM
ejpam-5320	18	13	)	)	PUNCT
ejpam-5320	18	14	,	,	PUNCT
ejpam-5320	18	15	2288	2288	NUM
ejpam-5320	18	16	-	-	SYM
ejpam-5320	18	17	2298	2298	NUM
ejpam-5320	18	18	2289	2289	NUM
ejpam-5320	18	19	(	(	PUNCT
ejpam-5320	18	20	τ1	τ1	NOUN
ejpam-5320	18	21	,	,	PUNCT
ejpam-5320	18	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	18	23	functions	function	NOUN
ejpam-5320	18	24	were	be	AUX
ejpam-5320	18	25	presented	present	VERB
ejpam-5320	18	26	in	in	ADP
ejpam-5320	18	27	[	[	X
ejpam-5320	18	28	36	36	NUM
ejpam-5320	18	29	]	]	PUNCT
ejpam-5320	18	30	,	,	PUNCT
ejpam-5320	18	31	[	[	X
ejpam-5320	18	32	12	12	NUM
ejpam-5320	18	33	]	]	PUNCT
ejpam-5320	18	34	,	,	PUNCT
ejpam-5320	18	35	[	[	X
ejpam-5320	18	36	34	34	NUM
ejpam-5320	18	37	]	]	PUNCT
ejpam-5320	18	38	,	,	PUNCT
ejpam-5320	18	39	[	[	X
ejpam-5320	18	40	17	17	NUM
ejpam-5320	18	41	]	]	PUNCT
ejpam-5320	18	42	,	,	PUNCT
ejpam-5320	18	43	[	[	X
ejpam-5320	18	44	11	11	NUM
ejpam-5320	18	45	]	]	PUNCT
ejpam-5320	18	46	,	,	PUNCT
ejpam-5320	18	47	[	[	X
ejpam-5320	18	48	10	10	NUM
ejpam-5320	18	49	]	]	PUNCT
ejpam-5320	18	50	,	,	PUNCT
ejpam-5320	18	51	[	[	X
ejpam-5320	18	52	5	5	NUM
ejpam-5320	18	53	]	]	PUNCT
ejpam-5320	18	54	,	,	PUNCT
ejpam-5320	18	55	[	[	X
ejpam-5320	18	56	2	2	NUM
ejpam-5320	18	57	]	]	PUNCT
ejpam-5320	18	58	,	,	PUNCT
ejpam-5320	18	59	[	[	X
ejpam-5320	18	60	40	40	NUM
ejpam-5320	18	61	]	]	PUNCT
ejpam-5320	18	62	,	,	PUNCT
ejpam-5320	18	63	[	[	X
ejpam-5320	18	64	37	37	NUM
ejpam-5320	18	65	]	]	PUNCT
ejpam-5320	18	66	,	,	PUNCT
ejpam-5320	18	67	[	[	X
ejpam-5320	18	68	9	9	NUM
ejpam-5320	18	69	]	]	PUNCT
ejpam-5320	18	70	,	,	PUNCT
ejpam-5320	18	71	[	[	X
ejpam-5320	18	72	3	3	NUM
ejpam-5320	18	73	]	]	PUNCT
ejpam-5320	18	74	,	,	PUNCT
ejpam-5320	18	75	[	[	X
ejpam-5320	18	76	18	18	NUM
ejpam-5320	18	77	]	]	PUNCT
ejpam-5320	18	78	,	,	PUNCT
ejpam-5320	18	79	[	[	X
ejpam-5320	18	80	16	16	NUM
ejpam-5320	18	81	]	]	PUNCT
ejpam-5320	18	82	and	and	CCONJ
ejpam-5320	19	1	[	[	X
ejpam-5320	19	2	13	13	NUM
ejpam-5320	19	3	]	]	PUNCT
ejpam-5320	19	4	,	,	PUNCT
ejpam-5320	19	5	respectively	respectively	ADV
ejpam-5320	19	6	.	.	PUNCT
ejpam-5320	20	1	in	in	ADP
ejpam-5320	20	2	1975	1975	NUM
ejpam-5320	20	3	,	,	PUNCT
ejpam-5320	20	4	popa	popa	NOUN
ejpam-5320	20	5	[	[	X
ejpam-5320	20	6	33	33	NUM
ejpam-5320	20	7	]	]	PUNCT
ejpam-5320	20	8	introduced	introduce	VERB
ejpam-5320	20	9	and	and	CCONJ
ejpam-5320	20	10	studied	study	VERB
ejpam-5320	20	11	the	the	DET
ejpam-5320	20	12	notion	notion	NOUN
ejpam-5320	20	13	of	of	ADP
ejpam-5320	20	14	quasi	quasi	ADJ
ejpam-5320	20	15	-	-	ADJ
ejpam-5320	20	16	continuous	continuous	ADJ
ejpam-5320	20	17	multifunctions	multifunction	NOUN
ejpam-5320	20	18	.	.	PUNCT
ejpam-5320	21	1	neubrunn	neubrunn	NOUN
ejpam-5320	22	1	[	[	X
ejpam-5320	22	2	30	30	NUM
ejpam-5320	22	3	]	]	PUNCT
ejpam-5320	22	4	and	and	CCONJ
ejpam-5320	22	5	holá	holá	NOUN
ejpam-5320	22	6	et	et	PROPN
ejpam-5320	22	7	al	al	PROPN
ejpam-5320	22	8	.	.	PUNCT
ejpam-5320	23	1	[	[	X
ejpam-5320	23	2	24	24	NUM
ejpam-5320	23	3	]	]	PUNCT
ejpam-5320	23	4	extended	extend	VERB
ejpam-5320	23	5	the	the	DET
ejpam-5320	23	6	concept	concept	NOUN
ejpam-5320	23	7	of	of	ADP
ejpam-5320	23	8	c	c	NOUN
ejpam-5320	23	9	-	-	PUNCT
ejpam-5320	23	10	continuous	continuous	ADJ
ejpam-5320	23	11	functions	function	NOUN
ejpam-5320	23	12	to	to	ADP
ejpam-5320	23	13	the	the	DET
ejpam-5320	23	14	setting	setting	NOUN
ejpam-5320	23	15	of	of	ADP
ejpam-5320	23	16	multifunctions	multifunction	NOUN
ejpam-5320	23	17	.	.	PUNCT
ejpam-5320	24	1	lipski	lipski	ADJ
ejpam-5320	25	1	[	[	X
ejpam-5320	25	2	27	27	NUM
ejpam-5320	25	3	]	]	PUNCT
ejpam-5320	25	4	introduced	introduce	VERB
ejpam-5320	25	5	the	the	DET
ejpam-5320	25	6	notion	notion	NOUN
ejpam-5320	25	7	of	of	ADP
ejpam-5320	25	8	c	c	NOUN
ejpam-5320	25	9	-	-	PUNCT
ejpam-5320	25	10	continuous	continuous	ADJ
ejpam-5320	25	11	multifunctions	multifunction	NOUN
ejpam-5320	25	12	as	as	ADP
ejpam-5320	25	13	a	a	DET
ejpam-5320	25	14	generalization	generalization	NOUN
ejpam-5320	25	15	of	of	ADP
ejpam-5320	25	16	c	c	NOUN
ejpam-5320	25	17	-	-	PUNCT
ejpam-5320	25	18	continuous	continuous	ADJ
ejpam-5320	25	19	multifunctions	multifunction	NOUN
ejpam-5320	25	20	[	[	X
ejpam-5320	25	21	30	30	NUM
ejpam-5320	25	22	]	]	PUNCT
ejpam-5320	25	23	and	and	CCONJ
ejpam-5320	25	24	quasi	quasi	ADJ
ejpam-5320	25	25	-	-	ADJ
ejpam-5320	25	26	continuous	continuous	ADJ
ejpam-5320	25	27	multifunctions	multifunction	NOUN
ejpam-5320	25	28	[	[	X
ejpam-5320	25	29	33	33	NUM
ejpam-5320	25	30	]	]	PUNCT
ejpam-5320	25	31	.	.	PUNCT
ejpam-5320	26	1	noiri	noiri	PROPN
ejpam-5320	26	2	and	and	CCONJ
ejpam-5320	26	3	popa	popa	NOUN
ejpam-5320	27	1	[	[	X
ejpam-5320	27	2	31	31	NUM
ejpam-5320	27	3	]	]	PUNCT
ejpam-5320	27	4	introduced	introduce	VERB
ejpam-5320	27	5	and	and	CCONJ
ejpam-5320	27	6	investigated	investigate	VERB
ejpam-5320	27	7	the	the	DET
ejpam-5320	27	8	notion	notion	NOUN
ejpam-5320	27	9	of	of	ADP
ejpam-5320	27	10	cm	cm	NOUN
ejpam-5320	27	11	-	-	PUNCT
ejpam-5320	27	12	continuous	continuous	ADJ
ejpam-5320	27	13	multifunctions	multifunction	NOUN
ejpam-5320	27	14	.	.	PUNCT
ejpam-5320	28	1	viriyapong	viriyapong	PROPN
ejpam-5320	28	2	and	and	CCONJ
ejpam-5320	28	3	boonpok	boonpok	VERB
ejpam-5320	29	1	[	[	X
ejpam-5320	29	2	41	41	NUM
ejpam-5320	29	3	]	]	PUNCT
ejpam-5320	29	4	introduced	introduce	VERB
ejpam-5320	29	5	and	and	CCONJ
ejpam-5320	29	6	studied	study	VERB
ejpam-5320	29	7	the	the	DET
ejpam-5320	29	8	concept	concept	NOUN
ejpam-5320	29	9	of	of	ADP
ejpam-5320	29	10	weakly	weakly	ADJ
ejpam-5320	29	11	quasi	quasi	NOUN
ejpam-5320	29	12	(	(	PUNCT
ejpam-5320	29	13	λ	λ	PROPN
ejpam-5320	29	14	,	,	PUNCT
ejpam-5320	29	15	sp)-continuous	sp)-continuous	ADJ
ejpam-5320	29	16	multifunctions	multifunction	NOUN
ejpam-5320	29	17	.	.	PUNCT
ejpam-5320	30	1	in	in	ADP
ejpam-5320	30	2	[	[	X
ejpam-5320	30	3	7	7	NUM
ejpam-5320	30	4	]	]	PUNCT
ejpam-5320	30	5	,	,	PUNCT
ejpam-5320	30	6	the	the	DET
ejpam-5320	30	7	present	present	ADJ
ejpam-5320	30	8	author	author	NOUN
ejpam-5320	30	9	introduced	introduce	VERB
ejpam-5320	30	10	and	and	CCONJ
ejpam-5320	30	11	investigated	investigate	VERB
ejpam-5320	30	12	the	the	DET
ejpam-5320	30	13	notions	notion	NOUN
ejpam-5320	30	14	of	of	ADP
ejpam-5320	30	15	almost	almost	ADV
ejpam-5320	30	16	quasi	quasi	ADJ
ejpam-5320	30	17	⋆-continuous	⋆-continuous	ADJ
ejpam-5320	30	18	multifunctions	multifunction	NOUN
ejpam-5320	30	19	and	and	CCONJ
ejpam-5320	30	20	weakly	weakly	ADJ
ejpam-5320	30	21	quasi	quasi	ADJ
ejpam-5320	30	22	⋆-continuous	⋆-continuous	ADJ
ejpam-5320	30	23	multifunctions	multifunction	NOUN
ejpam-5320	30	24	.	.	PUNCT
ejpam-5320	31	1	laprom	laprom	ADP
ejpam-5320	31	2	et	et	PROPN
ejpam-5320	31	3	al	al	PROPN
ejpam-5320	31	4	.	.	PUNCT
ejpam-5320	32	1	[	[	X
ejpam-5320	32	2	26	26	NUM
ejpam-5320	32	3	]	]	PUNCT
ejpam-5320	32	4	introduced	introduce	VERB
ejpam-5320	32	5	and	and	CCONJ
ejpam-5320	32	6	studied	study	VERB
ejpam-5320	32	7	the	the	DET
ejpam-5320	32	8	notion	notion	NOUN
ejpam-5320	32	9	of	of	ADP
ejpam-5320	32	10	β(τ1	β(τ1	NOUN
ejpam-5320	32	11	,	,	PUNCT
ejpam-5320	32	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	32	13	multifunctions	multifunction	NOUN
ejpam-5320	32	14	.	.	PUNCT
ejpam-5320	33	1	additionally	additionally	ADV
ejpam-5320	33	2	,	,	PUNCT
ejpam-5320	33	3	some	some	DET
ejpam-5320	33	4	characterizations	characterization	NOUN
ejpam-5320	33	5	of	of	ADP
ejpam-5320	33	6	(	(	PUNCT
ejpam-5320	33	7	τ1	τ1	NOUN
ejpam-5320	33	8	,	,	PUNCT
ejpam-5320	33	9	τ2)δ	τ2)δ	ADJ
ejpam-5320	33	10	-	-	PUNCT
ejpam-5320	33	11	semicontinuous	semicontinuous	ADJ
ejpam-5320	33	12	multifunctions	multifunction	NOUN
ejpam-5320	33	13	,	,	PUNCT
ejpam-5320	33	14	almost	almost	ADV
ejpam-5320	33	15	weakly	weakly	ADJ
ejpam-5320	33	16	⋆-continuous	⋆-continuous	ADJ
ejpam-5320	33	17	multifunctions	multifunction	NOUN
ejpam-5320	33	18	,	,	PUNCT
ejpam-5320	33	19	weakly	weakly	ADJ
ejpam-5320	33	20	⋆-continuous	⋆-continuous	ADJ
ejpam-5320	33	21	multifunctions	multifunction	NOUN
ejpam-5320	33	22	,	,	PUNCT
ejpam-5320	33	23	weakly	weakly	ADJ
ejpam-5320	33	24	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5320	33	25	multifunctions	multifunction	NOUN
ejpam-5320	33	26	,	,	PUNCT
ejpam-5320	33	27	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5320	33	28	multifunctions	multifunction	NOUN
ejpam-5320	33	29	,	,	PUNCT
ejpam-5320	33	30	β(⋆)-continuous	β(⋆)-continuous	ADJ
ejpam-5320	33	31	multifunctions	multifunction	NOUN
ejpam-5320	33	32	,	,	PUNCT
ejpam-5320	33	33	almost	almost	ADV
ejpam-5320	33	34	weakly	weakly	ADJ
ejpam-5320	33	35	(	(	PUNCT
ejpam-5320	33	36	τ1	τ1	NOUN
ejpam-5320	33	37	,	,	PUNCT
ejpam-5320	33	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	33	39	multifunctions	multifunction	NOUN
ejpam-5320	33	40	,	,	PUNCT
ejpam-5320	33	41	almost	almost	ADV
ejpam-5320	33	42	(	(	PUNCT
ejpam-5320	33	43	τ1	τ1	NOUN
ejpam-5320	33	44	,	,	PUNCT
ejpam-5320	33	45	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	33	46	multifunctions	multifunction	NOUN
ejpam-5320	33	47	and	and	CCONJ
ejpam-5320	33	48	(	(	PUNCT
ejpam-5320	33	49	τ1	τ1	NOUN
ejpam-5320	33	50	,	,	PUNCT
ejpam-5320	33	51	τ2)α	τ2)α	ADJ
ejpam-5320	33	52	-	-	PUNCT
ejpam-5320	33	53	continuous	continuous	ADJ
ejpam-5320	33	54	multifunctions	multifunction	NOUN
ejpam-5320	33	55	were	be	AUX
ejpam-5320	33	56	established	establish	VERB
ejpam-5320	33	57	in	in	ADP
ejpam-5320	33	58	[	[	X
ejpam-5320	33	59	6	6	NUM
ejpam-5320	33	60	]	]	PUNCT
ejpam-5320	33	61	,	,	PUNCT
ejpam-5320	33	62	[	[	X
ejpam-5320	33	63	19	19	NUM
ejpam-5320	33	64	]	]	PUNCT
ejpam-5320	33	65	,	,	PUNCT
ejpam-5320	33	66	[	[	X
ejpam-5320	33	67	4	4	NUM
ejpam-5320	33	68	]	]	PUNCT
ejpam-5320	33	69	,	,	PUNCT
ejpam-5320	33	70	[	[	X
ejpam-5320	33	71	15	15	NUM
ejpam-5320	33	72	]	]	PUNCT
ejpam-5320	33	73	,	,	PUNCT
ejpam-5320	33	74	[	[	X
ejpam-5320	33	75	14	14	NUM
ejpam-5320	33	76	]	]	PUNCT
ejpam-5320	33	77	,	,	PUNCT
ejpam-5320	33	78	[	[	X
ejpam-5320	33	79	8	8	NUM
ejpam-5320	33	80	]	]	PUNCT
ejpam-5320	33	81	,	,	PUNCT
ejpam-5320	33	82	[	[	X
ejpam-5320	33	83	20	20	NUM
ejpam-5320	33	84	]	]	PUNCT
ejpam-5320	33	85	,	,	PUNCT
ejpam-5320	33	86	[	[	X
ejpam-5320	33	87	25	25	NUM
ejpam-5320	33	88	]	]	PUNCT
ejpam-5320	33	89	and	and	CCONJ
ejpam-5320	33	90	[	[	X
ejpam-5320	33	91	39	39	NUM
ejpam-5320	33	92	]	]	PUNCT
ejpam-5320	33	93	,	,	PUNCT
ejpam-5320	33	94	respectively	respectively	ADV
ejpam-5320	33	95	.	.	PUNCT
ejpam-5320	34	1	pue	pue	NOUN
ejpam-5320	34	2	-	-	PUNCT
ejpam-5320	34	3	on	on	NOUN
ejpam-5320	34	4	et	et	PROPN
ejpam-5320	34	5	al	al	PROPN
ejpam-5320	34	6	.	.	PUNCT
ejpam-5320	35	1	[	[	X
ejpam-5320	35	2	35	35	NUM
ejpam-5320	35	3	]	]	X
ejpam-5320	35	4	introduce	introduce	NOUN
ejpam-5320	35	5	and	and	CCONJ
ejpam-5320	35	6	investigated	investigate	VERB
ejpam-5320	35	7	the	the	DET
ejpam-5320	35	8	notions	notion	NOUN
ejpam-5320	35	9	of	of	ADP
ejpam-5320	35	10	upper	upper	ADJ
ejpam-5320	35	11	and	and	CCONJ
ejpam-5320	35	12	lower	low	ADJ
ejpam-5320	35	13	(	(	PUNCT
ejpam-5320	35	14	τ1	τ1	NOUN
ejpam-5320	35	15	,	,	PUNCT
ejpam-5320	35	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	35	17	multifunctions	multifunction	NOUN
ejpam-5320	35	18	.	.	PUNCT
ejpam-5320	36	1	in	in	ADP
ejpam-5320	36	2	this	this	DET
ejpam-5320	36	3	paper	paper	NOUN
ejpam-5320	36	4	,	,	PUNCT
ejpam-5320	36	5	we	we	PRON
ejpam-5320	36	6	introduce	introduce	VERB
ejpam-5320	36	7	the	the	DET
ejpam-5320	36	8	concepts	concept	NOUN
ejpam-5320	36	9	of	of	ADP
ejpam-5320	36	10	upper	upper	ADJ
ejpam-5320	36	11	and	and	CCONJ
ejpam-5320	36	12	lower	low	ADJ
ejpam-5320	36	13	c-(τ1	c-(τ1	NOUN
ejpam-5320	36	14	,	,	PUNCT
ejpam-5320	36	15	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	36	16	multifunctions	multifunction	NOUN
ejpam-5320	36	17	.	.	PUNCT
ejpam-5320	37	1	in	in	ADP
ejpam-5320	37	2	particular	particular	ADJ
ejpam-5320	37	3	,	,	PUNCT
ejpam-5320	37	4	several	several	ADJ
ejpam-5320	37	5	characterizations	characterization	NOUN
ejpam-5320	37	6	of	of	ADP
ejpam-5320	37	7	upper	upper	ADJ
ejpam-5320	37	8	and	and	CCONJ
ejpam-5320	37	9	lower	low	ADJ
ejpam-5320	37	10	c-(τ1	c-(τ1	PROPN
ejpam-5320	37	11	,	,	PUNCT
ejpam-5320	37	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	37	13	multifunctions	multifunction	NOUN
ejpam-5320	37	14	are	be	AUX
ejpam-5320	37	15	discussed	discuss	VERB
ejpam-5320	37	16	.	.	PUNCT
ejpam-5320	38	1	2	2	X
ejpam-5320	38	2	.	.	X
ejpam-5320	38	3	preliminaries	preliminary	NOUN
ejpam-5320	38	4	throughout	throughout	ADP
ejpam-5320	38	5	the	the	DET
ejpam-5320	38	6	present	present	ADJ
ejpam-5320	38	7	paper	paper	NOUN
ejpam-5320	38	8	,	,	PUNCT
ejpam-5320	38	9	spaces	space	NOUN
ejpam-5320	38	10	(	(	PUNCT
ejpam-5320	38	11	x	x	NOUN
ejpam-5320	38	12	,	,	PUNCT
ejpam-5320	38	13	τ1	τ1	NOUN
ejpam-5320	38	14	,	,	PUNCT
ejpam-5320	38	15	τ2	τ2	NOUN
ejpam-5320	38	16	)	)	PUNCT
ejpam-5320	38	17	and	and	CCONJ
ejpam-5320	38	18	(	(	PUNCT
ejpam-5320	38	19	y	y	PROPN
ejpam-5320	38	20	,	,	PUNCT
ejpam-5320	38	21	σ1	σ1	PROPN
ejpam-5320	38	22	,	,	PUNCT
ejpam-5320	38	23	σ2	σ2	NOUN
ejpam-5320	38	24	)	)	PUNCT
ejpam-5320	38	25	(	(	PUNCT
ejpam-5320	38	26	or	or	CCONJ
ejpam-5320	38	27	simply	simply	ADV
ejpam-5320	38	28	x	x	X
ejpam-5320	38	29	and	and	CCONJ
ejpam-5320	38	30	y	y	PROPN
ejpam-5320	38	31	)	)	PUNCT
ejpam-5320	38	32	always	always	ADV
ejpam-5320	38	33	mean	mean	VERB
ejpam-5320	38	34	bitopological	bitopological	ADJ
ejpam-5320	38	35	spaces	space	NOUN
ejpam-5320	38	36	on	on	ADP
ejpam-5320	38	37	which	which	PRON
ejpam-5320	38	38	no	no	DET
ejpam-5320	38	39	separation	separation	NOUN
ejpam-5320	38	40	axioms	axiom	NOUN
ejpam-5320	38	41	are	be	AUX
ejpam-5320	38	42	assumed	assume	VERB
ejpam-5320	38	43	unless	unless	SCONJ
ejpam-5320	38	44	explicitly	explicitly	ADV
ejpam-5320	38	45	stated	state	VERB
ejpam-5320	38	46	.	.	PUNCT
ejpam-5320	39	1	let	let	VERB
ejpam-5320	39	2	a	a	DET
ejpam-5320	39	3	be	be	AUX
ejpam-5320	39	4	a	a	DET
ejpam-5320	39	5	subset	subset	NOUN
ejpam-5320	39	6	of	of	ADP
ejpam-5320	39	7	a	a	DET
ejpam-5320	39	8	bitopological	bitopological	ADJ
ejpam-5320	39	9	space	space	NOUN
ejpam-5320	39	10	(	(	PUNCT
ejpam-5320	39	11	x	x	NOUN
ejpam-5320	39	12	,	,	PUNCT
ejpam-5320	39	13	τ1	τ1	NOUN
ejpam-5320	39	14	,	,	PUNCT
ejpam-5320	39	15	τ2	τ2	NOUN
ejpam-5320	39	16	)	)	PUNCT
ejpam-5320	39	17	.	.	PUNCT
ejpam-5320	40	1	the	the	DET
ejpam-5320	40	2	closure	closure	NOUN
ejpam-5320	40	3	of	of	ADP
ejpam-5320	40	4	a	a	PRON
ejpam-5320	40	5	and	and	CCONJ
ejpam-5320	40	6	the	the	DET
ejpam-5320	40	7	interior	interior	NOUN
ejpam-5320	40	8	of	of	ADP
ejpam-5320	40	9	a	a	PRON
ejpam-5320	40	10	with	with	ADP
ejpam-5320	40	11	respect	respect	NOUN
ejpam-5320	40	12	to	to	ADP
ejpam-5320	40	13	τi	τi	PROPN
ejpam-5320	40	14	are	be	AUX
ejpam-5320	40	15	denoted	denote	VERB
ejpam-5320	40	16	by	by	ADP
ejpam-5320	40	17	τi	τi	NOUN
ejpam-5320	40	18	-	-	PUNCT
ejpam-5320	40	19	cl(a	cl(a	NUM
ejpam-5320	40	20	)	)	PUNCT
ejpam-5320	40	21	and	and	CCONJ
ejpam-5320	40	22	τi	τi	NOUN
ejpam-5320	40	23	-	-	PUNCT
ejpam-5320	40	24	int(a	int(a	NOUN
ejpam-5320	40	25	)	)	PUNCT
ejpam-5320	40	26	,	,	PUNCT
ejpam-5320	40	27	respectively	respectively	ADV
ejpam-5320	40	28	,	,	PUNCT
ejpam-5320	40	29	for	for	ADP
ejpam-5320	40	30	i	i	PROPN
ejpam-5320	40	31	=	=	SYM
ejpam-5320	40	32	1	1	NUM
ejpam-5320	40	33	,	,	PUNCT
ejpam-5320	40	34	2	2	NUM
ejpam-5320	40	35	.	.	X
ejpam-5320	40	36	a	a	DET
ejpam-5320	40	37	subset	subset	NOUN
ejpam-5320	40	38	a	a	PRON
ejpam-5320	40	39	of	of	ADP
ejpam-5320	40	40	a	a	DET
ejpam-5320	40	41	bitopological	bitopological	ADJ
ejpam-5320	40	42	space	space	NOUN
ejpam-5320	40	43	(	(	PUNCT
ejpam-5320	40	44	x	x	NOUN
ejpam-5320	40	45	,	,	PUNCT
ejpam-5320	40	46	τ1	τ1	NOUN
ejpam-5320	40	47	,	,	PUNCT
ejpam-5320	40	48	τ2	τ2	NOUN
ejpam-5320	40	49	)	)	PUNCT
ejpam-5320	40	50	is	be	AUX
ejpam-5320	40	51	called	call	VERB
ejpam-5320	40	52	τ1τ2	τ1τ2	VERB
ejpam-5320	40	53	-	-	ADJ
ejpam-5320	40	54	closed	closed	ADJ
ejpam-5320	40	55	[	[	X
ejpam-5320	40	56	21	21	NUM
ejpam-5320	40	57	]	]	X
ejpam-5320	40	58	if	if	SCONJ
ejpam-5320	40	59	a	a	DET
ejpam-5320	40	60	=	=	NOUN
ejpam-5320	40	61	τ1	τ1	NOUN
ejpam-5320	40	62	-	-	PUNCT
ejpam-5320	40	63	cl(τ2	cl(τ2	NOUN
ejpam-5320	40	64	-	-	PUNCT
ejpam-5320	40	65	cl(a	cl(a	NUM
ejpam-5320	40	66	)	)	PUNCT
ejpam-5320	40	67	)	)	PUNCT
ejpam-5320	40	68	.	.	PUNCT
ejpam-5320	41	1	the	the	DET
ejpam-5320	41	2	complement	complement	NOUN
ejpam-5320	41	3	of	of	ADP
ejpam-5320	41	4	a	a	DET
ejpam-5320	41	5	τ1τ2	τ1τ2	ADJ
ejpam-5320	41	6	-	-	ADJ
ejpam-5320	41	7	closed	closed	ADJ
ejpam-5320	41	8	set	set	NOUN
ejpam-5320	41	9	is	be	AUX
ejpam-5320	41	10	called	call	VERB
ejpam-5320	41	11	τ1τ2	τ1τ2	NOUN
ejpam-5320	41	12	-	-	ADJ
ejpam-5320	41	13	open	open	ADJ
ejpam-5320	41	14	.	.	PUNCT
ejpam-5320	42	1	let	let	VERB
ejpam-5320	42	2	a	a	DET
ejpam-5320	42	3	be	be	AUX
ejpam-5320	42	4	a	a	DET
ejpam-5320	42	5	subset	subset	NOUN
ejpam-5320	42	6	of	of	ADP
ejpam-5320	42	7	a	a	DET
ejpam-5320	42	8	bitopological	bitopological	ADJ
ejpam-5320	42	9	space	space	NOUN
ejpam-5320	42	10	(	(	PUNCT
ejpam-5320	42	11	x	x	NOUN
ejpam-5320	42	12	,	,	PUNCT
ejpam-5320	42	13	τ1	τ1	NOUN
ejpam-5320	42	14	,	,	PUNCT
ejpam-5320	42	15	τ2	τ2	NOUN
ejpam-5320	42	16	)	)	PUNCT
ejpam-5320	42	17	.	.	PUNCT
ejpam-5320	43	1	the	the	DET
ejpam-5320	43	2	intersection	intersection	NOUN
ejpam-5320	43	3	of	of	ADP
ejpam-5320	43	4	all	all	DET
ejpam-5320	43	5	τ1τ2	τ1τ2	ADJ
ejpam-5320	43	6	-	-	ADJ
ejpam-5320	43	7	closed	closed	ADJ
ejpam-5320	43	8	sets	set	NOUN
ejpam-5320	43	9	of	of	ADP
ejpam-5320	43	10	x	x	PUNCT
ejpam-5320	43	11	containing	contain	VERB
ejpam-5320	43	12	a	a	PRON
ejpam-5320	43	13	is	be	AUX
ejpam-5320	43	14	called	call	VERB
ejpam-5320	43	15	the	the	DET
ejpam-5320	43	16	τ1τ2	τ1τ2	NOUN
ejpam-5320	43	17	-	-	NOUN
ejpam-5320	43	18	closure	closure	NOUN
ejpam-5320	43	19	[	[	X
ejpam-5320	43	20	21	21	NUM
ejpam-5320	43	21	]	]	PUNCT
ejpam-5320	43	22	of	of	ADP
ejpam-5320	43	23	a	a	PRON
ejpam-5320	43	24	and	and	CCONJ
ejpam-5320	43	25	is	be	AUX
ejpam-5320	43	26	denoted	denote	VERB
ejpam-5320	43	27	by	by	ADP
ejpam-5320	43	28	τ1τ2	τ1τ2	NOUN
ejpam-5320	43	29	-	-	NUM
ejpam-5320	43	30	cl(a	cl(a	NUM
ejpam-5320	43	31	)	)	PUNCT
ejpam-5320	43	32	.	.	PUNCT
ejpam-5320	44	1	the	the	DET
ejpam-5320	44	2	union	union	NOUN
ejpam-5320	44	3	of	of	ADP
ejpam-5320	44	4	all	all	DET
ejpam-5320	44	5	τ1τ2	τ1τ2	ADJ
ejpam-5320	44	6	-	-	ADJ
ejpam-5320	44	7	open	open	ADJ
ejpam-5320	44	8	sets	set	NOUN
ejpam-5320	44	9	of	of	ADP
ejpam-5320	44	10	x	x	PUNCT
ejpam-5320	44	11	contained	contain	VERB
ejpam-5320	44	12	in	in	ADP
ejpam-5320	44	13	a	a	PRON
ejpam-5320	44	14	is	be	AUX
ejpam-5320	44	15	called	call	VERB
ejpam-5320	44	16	the	the	DET
ejpam-5320	44	17	τ1τ2	τ1τ2	NOUN
ejpam-5320	44	18	-	-	ADJ
ejpam-5320	44	19	interior	interior	ADJ
ejpam-5320	44	20	[	[	X
ejpam-5320	44	21	21	21	NUM
ejpam-5320	44	22	]	]	PUNCT
ejpam-5320	44	23	of	of	ADP
ejpam-5320	44	24	a	a	PRON
ejpam-5320	44	25	and	and	CCONJ
ejpam-5320	44	26	is	be	AUX
ejpam-5320	44	27	denoted	denote	VERB
ejpam-5320	44	28	by	by	ADP
ejpam-5320	44	29	τ1τ2	τ1τ2	NOUN
ejpam-5320	44	30	-	-	ADJ
ejpam-5320	44	31	int(a	int(a	NOUN
ejpam-5320	44	32	)	)	PUNCT
ejpam-5320	44	33	.	.	PUNCT
ejpam-5320	45	1	lemma	lemma	PROPN
ejpam-5320	45	2	1	1	NUM
ejpam-5320	45	3	.	.	PUNCT
ejpam-5320	46	1	[	[	X
ejpam-5320	46	2	21	21	NUM
ejpam-5320	46	3	]	]	PUNCT
ejpam-5320	46	4	let	let	VERB
ejpam-5320	46	5	a	a	PRON
ejpam-5320	46	6	and	and	CCONJ
ejpam-5320	46	7	b	b	NOUN
ejpam-5320	46	8	be	be	AUX
ejpam-5320	46	9	subsets	subset	NOUN
ejpam-5320	46	10	of	of	ADP
ejpam-5320	46	11	a	a	DET
ejpam-5320	46	12	bitopological	bitopological	ADJ
ejpam-5320	46	13	space	space	NOUN
ejpam-5320	46	14	(	(	PUNCT
ejpam-5320	46	15	x	x	NOUN
ejpam-5320	46	16	,	,	PUNCT
ejpam-5320	46	17	τ1	τ1	NOUN
ejpam-5320	46	18	,	,	PUNCT
ejpam-5320	46	19	τ2	τ2	NOUN
ejpam-5320	46	20	)	)	PUNCT
ejpam-5320	46	21	.	.	PUNCT
ejpam-5320	47	1	for	for	ADP
ejpam-5320	47	2	the	the	DET
ejpam-5320	47	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5320	47	4	,	,	PUNCT
ejpam-5320	47	5	the	the	DET
ejpam-5320	47	6	following	follow	VERB
ejpam-5320	47	7	properties	property	NOUN
ejpam-5320	47	8	hold	hold	VERB
ejpam-5320	47	9	:	:	PUNCT
ejpam-5320	47	10	(	(	PUNCT
ejpam-5320	47	11	1	1	X
ejpam-5320	47	12	)	)	PUNCT
ejpam-5320	47	13	a	a	DET
ejpam-5320	47	14	⊆	⊆	NUM
ejpam-5320	47	15	τ1τ2	τ1τ2	NOUN
ejpam-5320	47	16	-	-	NUM
ejpam-5320	47	17	cl(a	cl(a	NUM
ejpam-5320	47	18	)	)	PUNCT
ejpam-5320	47	19	and	and	CCONJ
ejpam-5320	47	20	τ1τ2	τ1τ2	NOUN
ejpam-5320	47	21	-	-	ADJ
ejpam-5320	47	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5320	47	23	-	-	PUNCT
ejpam-5320	47	24	cl(a	cl(a	NUM
ejpam-5320	47	25	)	)	PUNCT
ejpam-5320	47	26	)	)	PUNCT
ejpam-5320	48	1	=	=	PUNCT
ejpam-5320	48	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	48	3	-	-	NUM
ejpam-5320	48	4	cl(a	cl(a	NUM
ejpam-5320	48	5	)	)	PUNCT
ejpam-5320	48	6	.	.	PUNCT
ejpam-5320	49	1	(	(	PUNCT
ejpam-5320	49	2	2	2	X
ejpam-5320	49	3	)	)	PUNCT
ejpam-5320	49	4	if	if	SCONJ
ejpam-5320	49	5	a	a	DET
ejpam-5320	49	6	⊆	⊆	NUM
ejpam-5320	49	7	b	b	NOUN
ejpam-5320	49	8	,	,	PUNCT
ejpam-5320	49	9	then	then	ADV
ejpam-5320	49	10	τ1τ2	τ1τ2	NOUN
ejpam-5320	49	11	-	-	NUM
ejpam-5320	49	12	cl(a	cl(a	NUM
ejpam-5320	49	13	)	)	PUNCT
ejpam-5320	49	14	⊆	⊆	NUM
ejpam-5320	49	15	τ1τ2	τ1τ2	NOUN
ejpam-5320	49	16	-	-	NOUN
ejpam-5320	49	17	cl(b	cl(b	NOUN
ejpam-5320	49	18	)	)	PUNCT
ejpam-5320	49	19	.	.	PUNCT
ejpam-5320	50	1	(	(	PUNCT
ejpam-5320	50	2	3	3	X
ejpam-5320	50	3	)	)	PUNCT
ejpam-5320	50	4	τ1τ2	τ1τ2	NOUN
ejpam-5320	50	5	-	-	NUM
ejpam-5320	50	6	cl(a	cl(a	NUM
ejpam-5320	50	7	)	)	PUNCT
ejpam-5320	50	8	is	be	AUX
ejpam-5320	50	9	τ1τ2	τ1τ2	NOUN
ejpam-5320	50	10	-	-	ADJ
ejpam-5320	50	11	closed	closed	ADJ
ejpam-5320	50	12	.	.	PUNCT
ejpam-5320	51	1	(	(	PUNCT
ejpam-5320	51	2	4	4	X
ejpam-5320	51	3	)	)	PUNCT
ejpam-5320	51	4	a	a	PRON
ejpam-5320	51	5	is	be	AUX
ejpam-5320	51	6	τ1τ2	τ1τ2	NOUN
ejpam-5320	51	7	-	-	ADJ
ejpam-5320	51	8	closed	closed	ADJ
ejpam-5320	51	9	if	if	SCONJ
ejpam-5320	51	10	and	and	CCONJ
ejpam-5320	51	11	only	only	ADV
ejpam-5320	51	12	if	if	SCONJ
ejpam-5320	51	13	a	a	DET
ejpam-5320	51	14	=	=	PUNCT
ejpam-5320	51	15	τ1τ2	τ1τ2	NOUN
ejpam-5320	51	16	-	-	NUM
ejpam-5320	51	17	cl(a	cl(a	NUM
ejpam-5320	51	18	)	)	PUNCT
ejpam-5320	51	19	.	.	PUNCT
ejpam-5320	52	1	j.	j.	PROPN
ejpam-5320	52	2	khampakdee	khampakdee	PROPN
ejpam-5320	52	3	,	,	PUNCT
ejpam-5320	52	4	s.	s.	PROPN
ejpam-5320	52	5	sompong	sompong	PROPN
ejpam-5320	52	6	,	,	PUNCT
ejpam-5320	52	7	c.	c.	PROPN
ejpam-5320	52	8	boonpok	boonpok	PROPN
ejpam-5320	52	9	/	/	SYM
ejpam-5320	52	10	eur	eur	PROPN
ejpam-5320	52	11	.	.	PUNCT
ejpam-5320	53	1	j.	j.	PROPN
ejpam-5320	53	2	pure	pure	PROPN
ejpam-5320	53	3	appl	appl	PROPN
ejpam-5320	53	4	.	.	PROPN
ejpam-5320	53	5	math	math	PROPN
ejpam-5320	53	6	,	,	PUNCT
ejpam-5320	53	7	17	17	NUM
ejpam-5320	53	8	(	(	PUNCT
ejpam-5320	53	9	3	3	NUM
ejpam-5320	53	10	)	)	PUNCT
ejpam-5320	53	11	(	(	PUNCT
ejpam-5320	53	12	2024	2024	NUM
ejpam-5320	53	13	)	)	PUNCT
ejpam-5320	53	14	,	,	PUNCT
ejpam-5320	53	15	2288	2288	NUM
ejpam-5320	53	16	-	-	SYM
ejpam-5320	53	17	2298	2298	NUM
ejpam-5320	53	18	2290	2290	NUM
ejpam-5320	53	19	(	(	PUNCT
ejpam-5320	53	20	5	5	NUM
ejpam-5320	53	21	)	)	PUNCT
ejpam-5320	53	22	τ1τ2	τ1τ2	NOUN
ejpam-5320	53	23	-	-	NOUN
ejpam-5320	53	24	cl(x	cl(x	X
ejpam-5320	53	25	−a	−a	NOUN
ejpam-5320	53	26	)	)	PUNCT
ejpam-5320	53	27	=	=	PUNCT
ejpam-5320	54	1	x	x	X
ejpam-5320	54	2	−	−	ADP
ejpam-5320	54	3	τ1τ2	τ1τ2	NOUN
ejpam-5320	54	4	-	-	PUNCT
ejpam-5320	54	5	int(a	int(a	NOUN
ejpam-5320	54	6	)	)	PUNCT
ejpam-5320	54	7	.	.	PUNCT
ejpam-5320	55	1	a	a	DET
ejpam-5320	55	2	bitopological	bitopological	ADJ
ejpam-5320	55	3	space	space	NOUN
ejpam-5320	55	4	(	(	PUNCT
ejpam-5320	55	5	x	x	NOUN
ejpam-5320	55	6	,	,	PUNCT
ejpam-5320	55	7	τ1	τ1	NOUN
ejpam-5320	55	8	,	,	PUNCT
ejpam-5320	55	9	τ2	τ2	NOUN
ejpam-5320	55	10	)	)	PUNCT
ejpam-5320	55	11	is	be	AUX
ejpam-5320	55	12	called	call	VERB
ejpam-5320	55	13	τ1τ2	τ1τ2	ADJ
ejpam-5320	55	14	-	-	ADJ
ejpam-5320	55	15	compact	compact	ADJ
ejpam-5320	55	16	[	[	X
ejpam-5320	55	17	21	21	NUM
ejpam-5320	55	18	]	]	X
ejpam-5320	55	19	if	if	SCONJ
ejpam-5320	55	20	every	every	DET
ejpam-5320	55	21	cover	cover	NOUN
ejpam-5320	55	22	of	of	ADP
ejpam-5320	55	23	x	x	PUNCT
ejpam-5320	55	24	by	by	ADP
ejpam-5320	55	25	τ1τ2	τ1τ2	ADJ
ejpam-5320	55	26	-	-	ADJ
ejpam-5320	55	27	open	open	ADJ
ejpam-5320	55	28	sets	set	NOUN
ejpam-5320	55	29	of	of	ADP
ejpam-5320	55	30	x	x	PUNCT
ejpam-5320	55	31	has	have	VERB
ejpam-5320	55	32	a	a	DET
ejpam-5320	55	33	finite	finite	ADJ
ejpam-5320	55	34	subcover	subcover	PROPN
ejpam-5320	55	35	.	.	PUNCT
ejpam-5320	56	1	a	a	DET
ejpam-5320	56	2	subset	subset	NOUN
ejpam-5320	56	3	a	a	PRON
ejpam-5320	56	4	of	of	ADP
ejpam-5320	56	5	a	a	DET
ejpam-5320	56	6	bitopological	bitopological	ADJ
ejpam-5320	56	7	space	space	NOUN
ejpam-5320	56	8	(	(	PUNCT
ejpam-5320	56	9	x	x	NOUN
ejpam-5320	56	10	,	,	PUNCT
ejpam-5320	56	11	τ1	τ1	NOUN
ejpam-5320	56	12	,	,	PUNCT
ejpam-5320	56	13	τ2	τ2	NOUN
ejpam-5320	56	14	)	)	PUNCT
ejpam-5320	56	15	is	be	AUX
ejpam-5320	56	16	called	call	VERB
ejpam-5320	56	17	(	(	PUNCT
ejpam-5320	56	18	τ1	τ1	NOUN
ejpam-5320	56	19	,	,	PUNCT
ejpam-5320	56	20	τ2)r	τ2)r	NOUN
ejpam-5320	56	21	-	-	PUNCT
ejpam-5320	56	22	open	open	NOUN
ejpam-5320	57	1	[	[	X
ejpam-5320	57	2	39	39	NUM
ejpam-5320	57	3	]	]	PUNCT
ejpam-5320	57	4	(	(	PUNCT
ejpam-5320	57	5	resp	resp	NOUN
ejpam-5320	57	6	.	.	PUNCT
ejpam-5320	58	1	(	(	PUNCT
ejpam-5320	58	2	τ1	τ1	NOUN
ejpam-5320	58	3	,	,	PUNCT
ejpam-5320	58	4	τ2)s	τ2)s	NOUN
ejpam-5320	58	5	-	-	PUNCT
ejpam-5320	58	6	open	open	ADJ
ejpam-5320	58	7	[	[	X
ejpam-5320	58	8	6	6	NUM
ejpam-5320	58	9	]	]	PUNCT
ejpam-5320	58	10	,	,	PUNCT
ejpam-5320	58	11	(	(	PUNCT
ejpam-5320	58	12	τ1	τ1	NOUN
ejpam-5320	58	13	,	,	PUNCT
ejpam-5320	58	14	τ2)p	τ2)p	NOUN
ejpam-5320	58	15	-	-	ADJ
ejpam-5320	58	16	open	open	ADJ
ejpam-5320	58	17	[	[	X
ejpam-5320	58	18	6	6	NUM
ejpam-5320	58	19	]	]	PUNCT
ejpam-5320	58	20	,	,	PUNCT
ejpam-5320	58	21	(	(	PUNCT
ejpam-5320	58	22	τ1	τ1	NOUN
ejpam-5320	58	23	,	,	PUNCT
ejpam-5320	58	24	τ2)β	τ2)β	ADJ
ejpam-5320	58	25	-	-	PUNCT
ejpam-5320	58	26	open	open	NOUN
ejpam-5320	59	1	[	[	X
ejpam-5320	59	2	6	6	NUM
ejpam-5320	59	3	]	]	PUNCT
ejpam-5320	59	4	,	,	PUNCT
ejpam-5320	59	5	α(τ1	α(τ1	NOUN
ejpam-5320	59	6	,	,	PUNCT
ejpam-5320	59	7	τ2)-open	τ2)-open	ADJ
ejpam-5320	59	8	)	)	PUNCT
ejpam-5320	60	1	[	[	X
ejpam-5320	60	2	42	42	NUM
ejpam-5320	60	3	]	]	SYM
ejpam-5320	60	4	)	)	PUNCT
ejpam-5320	60	5	if	if	SCONJ
ejpam-5320	60	6	a	a	DET
ejpam-5320	60	7	=	=	PUNCT
ejpam-5320	60	8	τ1τ2	τ1τ2	NOUN
ejpam-5320	60	9	-	-	NOUN
ejpam-5320	60	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5320	60	11	-	-	PUNCT
ejpam-5320	60	12	cl(a	cl(a	NUM
ejpam-5320	60	13	)	)	PUNCT
ejpam-5320	60	14	)	)	PUNCT
ejpam-5320	60	15	(	(	PUNCT
ejpam-5320	60	16	resp	resp	NOUN
ejpam-5320	60	17	.	.	PUNCT
ejpam-5320	61	1	a	a	DET
ejpam-5320	61	2	⊆	⊆	NUM
ejpam-5320	61	3	τ1τ2	τ1τ2	NOUN
ejpam-5320	61	4	-	-	ADJ
ejpam-5320	61	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5320	61	6	-	-	PUNCT
ejpam-5320	61	7	int(a	int(a	NOUN
ejpam-5320	61	8	)	)	PUNCT
ejpam-5320	61	9	)	)	PUNCT
ejpam-5320	61	10	,	,	PUNCT
ejpam-5320	61	11	a	a	DET
ejpam-5320	61	12	⊆	⊆	NUM
ejpam-5320	61	13	τ1τ2	τ1τ2	NOUN
ejpam-5320	61	14	-	-	NOUN
ejpam-5320	61	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5320	61	16	-	-	PUNCT
ejpam-5320	61	17	cl(a	cl(a	NUM
ejpam-5320	61	18	)	)	PUNCT
ejpam-5320	61	19	)	)	PUNCT
ejpam-5320	61	20	,	,	PUNCT
ejpam-5320	61	21	a	a	DET
ejpam-5320	61	22	⊆	⊆	NUM
ejpam-5320	61	23	τ1τ2	τ1τ2	NOUN
ejpam-5320	61	24	-	-	PUNCT
ejpam-5320	61	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5320	61	26	-	-	PUNCT
ejpam-5320	61	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5320	61	28	-	-	PUNCT
ejpam-5320	61	29	cl(a	cl(a	NUM
ejpam-5320	61	30	)	)	PUNCT
ejpam-5320	61	31	)	)	PUNCT
ejpam-5320	61	32	)	)	PUNCT
ejpam-5320	61	33	,	,	PUNCT
ejpam-5320	61	34	a	a	DET
ejpam-5320	61	35	⊆	⊆	NUM
ejpam-5320	61	36	τ1τ2	τ1τ2	NOUN
ejpam-5320	61	37	-	-	PUNCT
ejpam-5320	61	38	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5320	61	39	-	-	PUNCT
ejpam-5320	61	40	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5320	61	41	-	-	PUNCT
ejpam-5320	61	42	int(a	int(a	NOUN
ejpam-5320	61	43	)	)	PUNCT
ejpam-5320	61	44	)	)	PUNCT
ejpam-5320	61	45	)	)	PUNCT
ejpam-5320	61	46	)	)	PUNCT
ejpam-5320	61	47	.	.	PUNCT
ejpam-5320	62	1	the	the	DET
ejpam-5320	62	2	complement	complement	NOUN
ejpam-5320	62	3	of	of	ADP
ejpam-5320	62	4	a	a	DET
ejpam-5320	62	5	(	(	PUNCT
ejpam-5320	62	6	τ1	τ1	NOUN
ejpam-5320	62	7	,	,	PUNCT
ejpam-5320	62	8	τ2)r	τ2)r	NOUN
ejpam-5320	62	9	-	-	PUNCT
ejpam-5320	62	10	open	open	ADJ
ejpam-5320	62	11	(	(	PUNCT
ejpam-5320	62	12	resp	resp	NOUN
ejpam-5320	62	13	.	.	PUNCT
ejpam-5320	63	1	(	(	PUNCT
ejpam-5320	63	2	τ1	τ1	NOUN
ejpam-5320	63	3	,	,	PUNCT
ejpam-5320	63	4	τ2)s	τ2)s	NOUN
ejpam-5320	63	5	-	-	PUNCT
ejpam-5320	63	6	open	open	ADJ
ejpam-5320	63	7	,	,	PUNCT
ejpam-5320	63	8	(	(	PUNCT
ejpam-5320	63	9	τ1	τ1	NOUN
ejpam-5320	63	10	,	,	PUNCT
ejpam-5320	63	11	τ2)p	τ2)p	NOUN
ejpam-5320	63	12	-	-	ADJ
ejpam-5320	63	13	open	open	ADJ
ejpam-5320	63	14	,	,	PUNCT
ejpam-5320	63	15	(	(	PUNCT
ejpam-5320	63	16	τ1	τ1	NOUN
ejpam-5320	63	17	,	,	PUNCT
ejpam-5320	63	18	τ2)β	τ2)β	ADJ
ejpam-5320	63	19	-	-	PUNCT
ejpam-5320	63	20	open	open	ADJ
ejpam-5320	63	21	,	,	PUNCT
ejpam-5320	63	22	α(τ1	α(τ1	NOUN
ejpam-5320	63	23	,	,	PUNCT
ejpam-5320	63	24	τ2)-open	τ2)-open	ADJ
ejpam-5320	63	25	)	)	PUNCT
ejpam-5320	63	26	set	set	NOUN
ejpam-5320	63	27	is	be	AUX
ejpam-5320	63	28	called	call	VERB
ejpam-5320	63	29	(	(	PUNCT
ejpam-5320	63	30	τ1	τ1	NOUN
ejpam-5320	63	31	,	,	PUNCT
ejpam-5320	63	32	τ2)r	τ2)r	NOUN
ejpam-5320	63	33	-	-	PUNCT
ejpam-5320	63	34	closed	closed	ADJ
ejpam-5320	63	35	(	(	PUNCT
ejpam-5320	63	36	resp	resp	NOUN
ejpam-5320	63	37	.	.	PUNCT
ejpam-5320	64	1	(	(	PUNCT
ejpam-5320	64	2	τ1	τ1	NOUN
ejpam-5320	64	3	,	,	PUNCT
ejpam-5320	64	4	τ2)s	τ2)s	NOUN
ejpam-5320	64	5	-	-	PUNCT
ejpam-5320	64	6	closed	closed	ADJ
ejpam-5320	64	7	,	,	PUNCT
ejpam-5320	64	8	(	(	PUNCT
ejpam-5320	64	9	τ1	τ1	NOUN
ejpam-5320	64	10	,	,	PUNCT
ejpam-5320	64	11	τ2)p	τ2)p	NOUN
ejpam-5320	64	12	-	-	PUNCT
ejpam-5320	64	13	closed	closed	ADJ
ejpam-5320	64	14	,	,	PUNCT
ejpam-5320	64	15	(	(	PUNCT
ejpam-5320	64	16	τ1	τ1	NOUN
ejpam-5320	64	17	,	,	PUNCT
ejpam-5320	64	18	τ2)βclosed	τ2)βclose	VERB
ejpam-5320	64	19	,	,	PUNCT
ejpam-5320	64	20	α(τ1	α(τ1	NOUN
ejpam-5320	64	21	,	,	PUNCT
ejpam-5320	64	22	τ2)-closed	τ2)-closed	ADJ
ejpam-5320	64	23	)	)	PUNCT
ejpam-5320	64	24	.	.	PUNCT
ejpam-5320	65	1	by	by	ADP
ejpam-5320	65	2	a	a	DET
ejpam-5320	65	3	multifunction	multifunction	NOUN
ejpam-5320	65	4	f	f	NOUN
ejpam-5320	65	5	:	:	PUNCT
ejpam-5320	65	6	x	x	X
ejpam-5320	65	7	→	→	SYM
ejpam-5320	65	8	y	y	PROPN
ejpam-5320	65	9	,	,	PUNCT
ejpam-5320	65	10	we	we	PRON
ejpam-5320	65	11	mean	mean	VERB
ejpam-5320	65	12	a	a	DET
ejpam-5320	65	13	point	point	NOUN
ejpam-5320	65	14	-	-	PUNCT
ejpam-5320	65	15	to	to	ADP
ejpam-5320	65	16	-	-	PUNCT
ejpam-5320	65	17	set	set	VERB
ejpam-5320	65	18	correspondence	correspondence	NOUN
ejpam-5320	65	19	from	from	ADP
ejpam-5320	65	20	x	x	PUNCT
ejpam-5320	65	21	into	into	ADP
ejpam-5320	65	22	y	y	PROPN
ejpam-5320	65	23	,	,	PUNCT
ejpam-5320	65	24	and	and	CCONJ
ejpam-5320	65	25	we	we	PRON
ejpam-5320	65	26	always	always	ADV
ejpam-5320	65	27	assume	assume	VERB
ejpam-5320	65	28	that	that	SCONJ
ejpam-5320	65	29	f	f	PROPN
ejpam-5320	65	30	(	(	PUNCT
ejpam-5320	65	31	x	x	X
ejpam-5320	65	32	)	)	PUNCT
ejpam-5320	65	33	̸=	̸=	NOUN
ejpam-5320	65	34	∅	∅	NOUN
ejpam-5320	65	35	for	for	ADP
ejpam-5320	65	36	all	all	PRON
ejpam-5320	65	37	x	x	SYM
ejpam-5320	65	38	∈	∈	ADJ
ejpam-5320	65	39	x.	x.	NOUN
ejpam-5320	65	40	for	for	ADP
ejpam-5320	65	41	a	a	DET
ejpam-5320	65	42	multifunction	multifunction	NOUN
ejpam-5320	65	43	f	f	NOUN
ejpam-5320	66	1	:	:	PUNCT
ejpam-5320	66	2	x	x	X
ejpam-5320	66	3	→	→	SYM
ejpam-5320	66	4	y	y	PROPN
ejpam-5320	66	5	,	,	PUNCT
ejpam-5320	66	6	following	follow	VERB
ejpam-5320	66	7	[	[	X
ejpam-5320	66	8	1	1	X
ejpam-5320	66	9	]	]	PUNCT
ejpam-5320	66	10	we	we	PRON
ejpam-5320	66	11	shall	shall	AUX
ejpam-5320	66	12	denote	denote	VERB
ejpam-5320	66	13	the	the	DET
ejpam-5320	66	14	upper	upper	ADJ
ejpam-5320	66	15	and	and	CCONJ
ejpam-5320	66	16	lower	low	ADJ
ejpam-5320	66	17	inverse	inverse	NOUN
ejpam-5320	66	18	of	of	ADP
ejpam-5320	66	19	a	a	DET
ejpam-5320	66	20	set	set	NOUN
ejpam-5320	66	21	b	b	PROPN
ejpam-5320	66	22	of	of	ADP
ejpam-5320	66	23	y	y	PROPN
ejpam-5320	66	24	by	by	ADP
ejpam-5320	66	25	f+(b	f+(b	NOUN
ejpam-5320	66	26	)	)	PUNCT
ejpam-5320	66	27	and	and	CCONJ
ejpam-5320	66	28	f−(b	f−(b	NOUN
ejpam-5320	66	29	)	)	PUNCT
ejpam-5320	66	30	,	,	PUNCT
ejpam-5320	66	31	respectively	respectively	ADV
ejpam-5320	66	32	,	,	PUNCT
ejpam-5320	66	33	that	that	ADV
ejpam-5320	66	34	is	is	ADV
ejpam-5320	66	35	,	,	PUNCT
ejpam-5320	66	36	f+(b	f+(b	NOUN
ejpam-5320	66	37	)	)	PUNCT
ejpam-5320	66	38	=	=	PRON
ejpam-5320	67	1	{	{	PUNCT
ejpam-5320	67	2	x	x	PUNCT
ejpam-5320	67	3	∈	∈	PROPN
ejpam-5320	67	4	x	x	INTJ
ejpam-5320	68	1	|	|	NOUN
ejpam-5320	68	2	f	f	X
ejpam-5320	68	3	(	(	PUNCT
ejpam-5320	68	4	x	x	NOUN
ejpam-5320	68	5	)	)	PUNCT
ejpam-5320	68	6	⊆	⊆	NUM
ejpam-5320	68	7	b	b	NOUN
ejpam-5320	68	8	}	}	PUNCT
ejpam-5320	68	9	and	and	CCONJ
ejpam-5320	68	10	f−(b	f−(b	PROPN
ejpam-5320	68	11	)	)	PUNCT
ejpam-5320	68	12	=	=	PRON
ejpam-5320	69	1	{	{	PUNCT
ejpam-5320	69	2	x	x	PUNCT
ejpam-5320	69	3	∈	∈	PROPN
ejpam-5320	69	4	x	x	INTJ
ejpam-5320	70	1	|	|	NOUN
ejpam-5320	70	2	f	f	X
ejpam-5320	70	3	(	(	PUNCT
ejpam-5320	70	4	x	x	NOUN
ejpam-5320	70	5	)	)	PUNCT
ejpam-5320	70	6	∩b	∩b	NOUN
ejpam-5320	70	7	̸=	̸=	PROPN
ejpam-5320	70	8	∅	∅	NOUN
ejpam-5320	70	9	}	}	PUNCT
ejpam-5320	70	10	.	.	PUNCT
ejpam-5320	71	1	in	in	ADP
ejpam-5320	71	2	particular	particular	ADJ
ejpam-5320	71	3	,	,	PUNCT
ejpam-5320	71	4	f−(y	f−(y	NOUN
ejpam-5320	71	5	)	)	PUNCT
ejpam-5320	71	6	=	=	SYM
ejpam-5320	72	1	{	{	PUNCT
ejpam-5320	72	2	x	x	PUNCT
ejpam-5320	72	3	∈	∈	PROPN
ejpam-5320	72	4	x	x	INTJ
ejpam-5320	73	1	|	|	ADV
ejpam-5320	73	2	y	y	PROPN
ejpam-5320	73	3	∈	∈	PROPN
ejpam-5320	73	4	f	f	X
ejpam-5320	73	5	(	(	PUNCT
ejpam-5320	73	6	x	x	NOUN
ejpam-5320	73	7	)	)	PUNCT
ejpam-5320	73	8	}	}	PUNCT
ejpam-5320	73	9	for	for	ADP
ejpam-5320	73	10	each	each	DET
ejpam-5320	73	11	point	point	NOUN
ejpam-5320	73	12	y	y	PROPN
ejpam-5320	73	13	∈	∈	PROPN
ejpam-5320	73	14	y	y	PROPN
ejpam-5320	73	15	.	.	PUNCT
ejpam-5320	74	1	for	for	ADP
ejpam-5320	74	2	each	each	DET
ejpam-5320	74	3	a	a	DET
ejpam-5320	74	4	⊆	⊆	NUM
ejpam-5320	74	5	x	x	SYM
ejpam-5320	74	6	,	,	PUNCT
ejpam-5320	74	7	f	f	PROPN
ejpam-5320	74	8	(	(	PUNCT
ejpam-5320	74	9	a	a	NOUN
ejpam-5320	74	10	)	)	PUNCT
ejpam-5320	74	11	=	=	SYM
ejpam-5320	74	12	∪x∈af	∪x∈af	NOUN
ejpam-5320	74	13	(	(	PUNCT
ejpam-5320	74	14	x	x	NOUN
ejpam-5320	74	15	)	)	PUNCT
ejpam-5320	74	16	.	.	PUNCT
ejpam-5320	75	1	3	3	X
ejpam-5320	75	2	.	.	X
ejpam-5320	75	3	upper	upper	ADJ
ejpam-5320	75	4	and	and	CCONJ
ejpam-5320	75	5	lower	low	ADJ
ejpam-5320	75	6	c-(τ1	c-(τ1	PROPN
ejpam-5320	75	7	,	,	PUNCT
ejpam-5320	75	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	75	9	multifunctions	multifunction	NOUN
ejpam-5320	75	10	in	in	ADP
ejpam-5320	75	11	this	this	DET
ejpam-5320	75	12	section	section	NOUN
ejpam-5320	75	13	,	,	PUNCT
ejpam-5320	75	14	we	we	PRON
ejpam-5320	75	15	introduce	introduce	VERB
ejpam-5320	75	16	the	the	DET
ejpam-5320	75	17	notions	notion	NOUN
ejpam-5320	75	18	of	of	ADP
ejpam-5320	75	19	upper	upper	ADJ
ejpam-5320	75	20	and	and	CCONJ
ejpam-5320	75	21	lower	low	ADJ
ejpam-5320	75	22	c-(τ1	c-(τ1	PROPN
ejpam-5320	75	23	,	,	PUNCT
ejpam-5320	75	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	75	25	multifunctions	multifunction	NOUN
ejpam-5320	75	26	.	.	PUNCT
ejpam-5320	76	1	moreover	moreover	ADV
ejpam-5320	76	2	,	,	PUNCT
ejpam-5320	76	3	we	we	PRON
ejpam-5320	76	4	investigate	investigate	VERB
ejpam-5320	76	5	some	some	DET
ejpam-5320	76	6	characterizations	characterization	NOUN
ejpam-5320	76	7	of	of	ADP
ejpam-5320	76	8	upper	upper	ADJ
ejpam-5320	76	9	and	and	CCONJ
ejpam-5320	76	10	lower	low	ADJ
ejpam-5320	76	11	c-(τ1	c-(τ1	NOUN
ejpam-5320	76	12	,	,	PUNCT
ejpam-5320	76	13	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	76	14	multifunctions	multifunction	NOUN
ejpam-5320	76	15	.	.	PUNCT
ejpam-5320	77	1	definition	definition	NOUN
ejpam-5320	77	2	1	1	NUM
ejpam-5320	77	3	.	.	PUNCT
ejpam-5320	78	1	a	a	DET
ejpam-5320	78	2	multifunction	multifunction	NOUN
ejpam-5320	78	3	f	f	NOUN
ejpam-5320	78	4	:	:	PUNCT
ejpam-5320	78	5	(	(	PUNCT
ejpam-5320	78	6	x	x	NOUN
ejpam-5320	78	7	,	,	PUNCT
ejpam-5320	78	8	τ1	τ1	NOUN
ejpam-5320	78	9	,	,	PUNCT
ejpam-5320	78	10	τ2	τ2	NOUN
ejpam-5320	78	11	)	)	PUNCT
ejpam-5320	78	12	→	→	SYM
ejpam-5320	78	13	(	(	PUNCT
ejpam-5320	78	14	y	y	PROPN
ejpam-5320	78	15	,	,	PUNCT
ejpam-5320	78	16	σ1	σ1	PROPN
ejpam-5320	78	17	,	,	PUNCT
ejpam-5320	78	18	σ2	σ2	PROPN
ejpam-5320	78	19	)	)	PUNCT
ejpam-5320	78	20	is	be	AUX
ejpam-5320	78	21	said	say	VERB
ejpam-5320	78	22	to	to	PART
ejpam-5320	78	23	be	be	AUX
ejpam-5320	78	24	upper	upper	ADJ
ejpam-5320	78	25	c-(τ1	c-(τ1	PROPN
ejpam-5320	78	26	,	,	PUNCT
ejpam-5320	78	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	78	28	at	at	ADP
ejpam-5320	78	29	a	a	DET
ejpam-5320	78	30	point	point	NOUN
ejpam-5320	78	31	x	x	SYM
ejpam-5320	78	32	∈	∈	NOUN
ejpam-5320	78	33	x	x	PUNCT
ejpam-5320	78	34	if	if	SCONJ
ejpam-5320	78	35	for	for	ADP
ejpam-5320	78	36	each	each	DET
ejpam-5320	78	37	σ1σ2	σ1σ2	VERB
ejpam-5320	78	38	-	-	ADJ
ejpam-5320	78	39	open	open	ADJ
ejpam-5320	78	40	set	set	NOUN
ejpam-5320	78	41	v	v	NOUN
ejpam-5320	78	42	of	of	ADP
ejpam-5320	78	43	y	y	PROPN
ejpam-5320	78	44	containing	contain	VERB
ejpam-5320	78	45	f	f	PROPN
ejpam-5320	78	46	(	(	PUNCT
ejpam-5320	78	47	x	x	NOUN
ejpam-5320	78	48	)	)	PUNCT
ejpam-5320	78	49	and	and	CCONJ
ejpam-5320	78	50	having	have	VERB
ejpam-5320	78	51	σ1σ2	σ1σ2	NOUN
ejpam-5320	78	52	-	-	ADJ
ejpam-5320	78	53	compact	compact	ADJ
ejpam-5320	78	54	complement	complement	NOUN
ejpam-5320	78	55	,	,	PUNCT
ejpam-5320	78	56	there	there	PRON
ejpam-5320	78	57	exists	exist	VERB
ejpam-5320	78	58	a	a	DET
ejpam-5320	78	59	τ1τ2	τ1τ2	NOUN
ejpam-5320	78	60	-	-	ADJ
ejpam-5320	78	61	open	open	ADJ
ejpam-5320	78	62	set	set	ADJ
ejpam-5320	78	63	u	u	NOUN
ejpam-5320	78	64	of	of	ADP
ejpam-5320	78	65	x	x	PUNCT
ejpam-5320	78	66	containing	contain	VERB
ejpam-5320	78	67	x	x	PUNCT
ejpam-5320	78	68	such	such	ADJ
ejpam-5320	78	69	that	that	SCONJ
ejpam-5320	78	70	f	f	PROPN
ejpam-5320	78	71	(	(	PUNCT
ejpam-5320	78	72	u	u	NOUN
ejpam-5320	78	73	)	)	PUNCT
ejpam-5320	78	74	⊆	⊆	NUM
ejpam-5320	78	75	v	v	NOUN
ejpam-5320	78	76	.	.	PUNCT
ejpam-5320	79	1	a	a	DET
ejpam-5320	79	2	multifunction	multifunction	NOUN
ejpam-5320	79	3	f	f	NOUN
ejpam-5320	79	4	:	:	PUNCT
ejpam-5320	79	5	(	(	PUNCT
ejpam-5320	79	6	x	x	NOUN
ejpam-5320	79	7	,	,	PUNCT
ejpam-5320	79	8	τ1	τ1	NOUN
ejpam-5320	79	9	,	,	PUNCT
ejpam-5320	79	10	τ2	τ2	NOUN
ejpam-5320	79	11	)	)	PUNCT
ejpam-5320	79	12	→	→	SYM
ejpam-5320	79	13	(	(	PUNCT
ejpam-5320	79	14	y	y	PROPN
ejpam-5320	79	15	,	,	PUNCT
ejpam-5320	79	16	σ1	σ1	PROPN
ejpam-5320	79	17	,	,	PUNCT
ejpam-5320	79	18	σ2	σ2	PROPN
ejpam-5320	79	19	)	)	PUNCT
ejpam-5320	79	20	is	be	AUX
ejpam-5320	79	21	said	say	VERB
ejpam-5320	79	22	to	to	PART
ejpam-5320	79	23	be	be	AUX
ejpam-5320	79	24	upper	upper	ADJ
ejpam-5320	79	25	c-(τ1	c-(τ1	NOUN
ejpam-5320	79	26	,	,	PUNCT
ejpam-5320	79	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	79	28	if	if	SCONJ
ejpam-5320	79	29	f	f	PROPN
ejpam-5320	79	30	has	have	VERB
ejpam-5320	79	31	this	this	DET
ejpam-5320	79	32	property	property	NOUN
ejpam-5320	79	33	at	at	ADP
ejpam-5320	79	34	every	every	DET
ejpam-5320	79	35	point	point	NOUN
ejpam-5320	79	36	of	of	ADP
ejpam-5320	79	37	x.	x.	NOUN
ejpam-5320	79	38	theorem	theorem	VERB
ejpam-5320	79	39	1	1	NUM
ejpam-5320	79	40	.	.	X
ejpam-5320	79	41	for	for	ADP
ejpam-5320	79	42	a	a	DET
ejpam-5320	79	43	multifunction	multifunction	NOUN
ejpam-5320	79	44	f	f	NOUN
ejpam-5320	79	45	:	:	PUNCT
ejpam-5320	79	46	(	(	PUNCT
ejpam-5320	79	47	x	x	NOUN
ejpam-5320	79	48	,	,	PUNCT
ejpam-5320	79	49	τ1	τ1	NOUN
ejpam-5320	79	50	,	,	PUNCT
ejpam-5320	79	51	τ2	τ2	NOUN
ejpam-5320	79	52	)	)	PUNCT
ejpam-5320	79	53	→	→	SYM
ejpam-5320	79	54	(	(	PUNCT
ejpam-5320	79	55	y	y	PROPN
ejpam-5320	79	56	,	,	PUNCT
ejpam-5320	79	57	σ1	σ1	PROPN
ejpam-5320	79	58	,	,	PUNCT
ejpam-5320	79	59	σ2	σ2	NOUN
ejpam-5320	79	60	)	)	PUNCT
ejpam-5320	79	61	,	,	PUNCT
ejpam-5320	79	62	the	the	DET
ejpam-5320	79	63	following	follow	VERB
ejpam-5320	79	64	properties	property	NOUN
ejpam-5320	79	65	are	be	AUX
ejpam-5320	79	66	equivalent	equivalent	ADJ
ejpam-5320	79	67	:	:	PUNCT
ejpam-5320	79	68	(	(	PUNCT
ejpam-5320	79	69	1	1	X
ejpam-5320	79	70	)	)	PUNCT
ejpam-5320	79	71	f	f	PROPN
ejpam-5320	79	72	is	be	AUX
ejpam-5320	79	73	upper	upper	ADJ
ejpam-5320	79	74	c-(τ1	c-(τ1	PROPN
ejpam-5320	79	75	,	,	PUNCT
ejpam-5320	79	76	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	79	77	at	at	ADP
ejpam-5320	79	78	x	x	X
ejpam-5320	79	79	∈	∈	PROPN
ejpam-5320	79	80	x	x	X
ejpam-5320	79	81	;	;	PUNCT
ejpam-5320	80	1	(	(	PUNCT
ejpam-5320	80	2	2	2	X
ejpam-5320	80	3	)	)	PUNCT
ejpam-5320	80	4	x	x	SYM
ejpam-5320	80	5	∈	∈	PRON
ejpam-5320	80	6	τ1τ2	τ1τ2	NOUN
ejpam-5320	80	7	-	-	NUM
ejpam-5320	80	8	int(f	int(f	VERB
ejpam-5320	80	9	+	+	ADJ
ejpam-5320	80	10	(	(	PUNCT
ejpam-5320	80	11	v	v	NOUN
ejpam-5320	80	12	)	)	PUNCT
ejpam-5320	80	13	)	)	PUNCT
ejpam-5320	80	14	for	for	ADP
ejpam-5320	80	15	each	each	DET
ejpam-5320	80	16	σ1σ2	σ1σ2	VERB
ejpam-5320	80	17	-	-	ADJ
ejpam-5320	80	18	open	open	ADJ
ejpam-5320	80	19	set	set	NOUN
ejpam-5320	80	20	v	v	NOUN
ejpam-5320	80	21	of	of	ADP
ejpam-5320	80	22	y	y	PROPN
ejpam-5320	80	23	containing	contain	VERB
ejpam-5320	80	24	f	f	PROPN
ejpam-5320	80	25	(	(	PUNCT
ejpam-5320	80	26	x	x	NOUN
ejpam-5320	80	27	)	)	PUNCT
ejpam-5320	80	28	and	and	CCONJ
ejpam-5320	80	29	having	have	VERB
ejpam-5320	80	30	σ1σ2	σ1σ2	NOUN
ejpam-5320	80	31	-	-	ADJ
ejpam-5320	80	32	compact	compact	ADJ
ejpam-5320	80	33	complement	complement	NOUN
ejpam-5320	80	34	;	;	PUNCT
ejpam-5320	80	35	(	(	PUNCT
ejpam-5320	80	36	3	3	X
ejpam-5320	80	37	)	)	PUNCT
ejpam-5320	80	38	x	x	SYM
ejpam-5320	80	39	∈	∈	NOUN
ejpam-5320	80	40	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	80	41	-	-	PUNCT
ejpam-5320	80	42	cl(b	cl(b	NOUN
ejpam-5320	80	43	)	)	PUNCT
ejpam-5320	80	44	)	)	PUNCT
ejpam-5320	80	45	for	for	ADP
ejpam-5320	80	46	each	each	DET
ejpam-5320	80	47	subset	subset	NOUN
ejpam-5320	80	48	b	b	PROPN
ejpam-5320	80	49	of	of	ADP
ejpam-5320	80	50	y	y	PROPN
ejpam-5320	80	51	having	have	VERB
ejpam-5320	80	52	the	the	DET
ejpam-5320	80	53	σ1σ2	σ1σ2	NUM
ejpam-5320	80	54	-	-	ADJ
ejpam-5320	80	55	compact	compact	ADJ
ejpam-5320	80	56	σ1σ2	σ1σ2	NOUN
ejpam-5320	80	57	-	-	NOUN
ejpam-5320	80	58	closure	closure	NOUN
ejpam-5320	80	59	such	such	ADJ
ejpam-5320	80	60	that	that	SCONJ
ejpam-5320	80	61	x	x	PUNCT
ejpam-5320	80	62	∈	∈	PROPN
ejpam-5320	80	63	τ1τ2	τ1τ2	NOUN
ejpam-5320	80	64	-	-	NOUN
ejpam-5320	80	65	cl(f	cl(f	NOUN
ejpam-5320	80	66	−(b	−(b	PROPN
ejpam-5320	80	67	)	)	PUNCT
ejpam-5320	80	68	)	)	PUNCT
ejpam-5320	80	69	;	;	PUNCT
ejpam-5320	80	70	(	(	PUNCT
ejpam-5320	80	71	4	4	X
ejpam-5320	80	72	)	)	PUNCT
ejpam-5320	80	73	x	x	SYM
ejpam-5320	80	74	∈	∈	PRON
ejpam-5320	80	75	τ1τ2	τ1τ2	PUNCT
ejpam-5320	80	76	-	-	NUM
ejpam-5320	80	77	int(f	int(f	VERB
ejpam-5320	80	78	+	+	ADJ
ejpam-5320	80	79	(	(	PUNCT
ejpam-5320	80	80	b	b	NOUN
ejpam-5320	80	81	)	)	PUNCT
ejpam-5320	80	82	)	)	PUNCT
ejpam-5320	80	83	for	for	ADP
ejpam-5320	80	84	each	each	DET
ejpam-5320	80	85	subset	subset	NOUN
ejpam-5320	80	86	b	b	PROPN
ejpam-5320	80	87	of	of	ADP
ejpam-5320	80	88	y	y	PRON
ejpam-5320	80	89	such	such	ADJ
ejpam-5320	80	90	that	that	SCONJ
ejpam-5320	80	91	y	y	PROPN
ejpam-5320	81	1	−	−	ADP
ejpam-5320	81	2	σ1σ2	σ1σ2	NUM
ejpam-5320	81	3	-	-	PUNCT
ejpam-5320	81	4	int(b	int(b	NOUN
ejpam-5320	81	5	)	)	PUNCT
ejpam-5320	81	6	is	be	AUX
ejpam-5320	81	7	σ1σ2compact	σ1σ2compact	PUNCT
ejpam-5320	81	8	and	and	CCONJ
ejpam-5320	81	9	x	x	PUNCT
ejpam-5320	81	10	∈	∈	NOUN
ejpam-5320	81	11	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	81	12	-	-	PUNCT
ejpam-5320	81	13	int(b	int(b	NOUN
ejpam-5320	81	14	)	)	PUNCT
ejpam-5320	81	15	)	)	PUNCT
ejpam-5320	81	16	.	.	PUNCT
ejpam-5320	82	1	j.	j.	PROPN
ejpam-5320	82	2	khampakdee	khampakdee	PROPN
ejpam-5320	82	3	,	,	PUNCT
ejpam-5320	82	4	s.	s.	PROPN
ejpam-5320	82	5	sompong	sompong	PROPN
ejpam-5320	82	6	,	,	PUNCT
ejpam-5320	82	7	c.	c.	PROPN
ejpam-5320	82	8	boonpok	boonpok	PROPN
ejpam-5320	82	9	/	/	SYM
ejpam-5320	82	10	eur	eur	PROPN
ejpam-5320	82	11	.	.	PUNCT
ejpam-5320	83	1	j.	j.	PROPN
ejpam-5320	83	2	pure	pure	PROPN
ejpam-5320	83	3	appl	appl	PROPN
ejpam-5320	83	4	.	.	PROPN
ejpam-5320	83	5	math	math	PROPN
ejpam-5320	83	6	,	,	PUNCT
ejpam-5320	83	7	17	17	NUM
ejpam-5320	83	8	(	(	PUNCT
ejpam-5320	83	9	3	3	NUM
ejpam-5320	83	10	)	)	PUNCT
ejpam-5320	83	11	(	(	PUNCT
ejpam-5320	83	12	2024	2024	NUM
ejpam-5320	83	13	)	)	PUNCT
ejpam-5320	83	14	,	,	PUNCT
ejpam-5320	83	15	2288	2288	NUM
ejpam-5320	83	16	-	-	SYM
ejpam-5320	83	17	2298	2298	NUM
ejpam-5320	83	18	2291	2291	NUM
ejpam-5320	83	19	proof	proof	NOUN
ejpam-5320	83	20	.	.	PUNCT
ejpam-5320	84	1	(	(	PUNCT
ejpam-5320	84	2	1	1	X
ejpam-5320	84	3	)	)	PUNCT
ejpam-5320	84	4	⇒	⇒	NOUN
ejpam-5320	84	5	(	(	PUNCT
ejpam-5320	84	6	2	2	NUM
ejpam-5320	84	7	):	):	PUNCT
ejpam-5320	84	8	let	let	VERB
ejpam-5320	84	9	v	v	PART
ejpam-5320	84	10	be	be	AUX
ejpam-5320	84	11	any	any	DET
ejpam-5320	84	12	σ1σ2	σ1σ2	NOUN
ejpam-5320	84	13	-	-	ADJ
ejpam-5320	84	14	open	open	ADJ
ejpam-5320	84	15	set	set	NOUN
ejpam-5320	84	16	of	of	ADP
ejpam-5320	84	17	y	y	PROPN
ejpam-5320	84	18	containing	contain	VERB
ejpam-5320	84	19	f	f	PROPN
ejpam-5320	84	20	(	(	PUNCT
ejpam-5320	84	21	x	x	NOUN
ejpam-5320	84	22	)	)	PUNCT
ejpam-5320	84	23	and	and	CCONJ
ejpam-5320	84	24	having	have	VERB
ejpam-5320	84	25	σ1σ2	σ1σ2	NOUN
ejpam-5320	84	26	-	-	ADJ
ejpam-5320	84	27	compact	compact	ADJ
ejpam-5320	84	28	complement	complement	NOUN
ejpam-5320	84	29	and	and	CCONJ
ejpam-5320	84	30	x	x	PUNCT
ejpam-5320	84	31	∈	∈	PROPN
ejpam-5320	84	32	f+(v	f+(v	NOUN
ejpam-5320	84	33	)	)	PUNCT
ejpam-5320	84	34	.	.	PUNCT
ejpam-5320	85	1	by	by	ADP
ejpam-5320	85	2	(	(	PUNCT
ejpam-5320	85	3	1	1	NUM
ejpam-5320	85	4	)	)	PUNCT
ejpam-5320	85	5	,	,	PUNCT
ejpam-5320	85	6	there	there	PRON
ejpam-5320	85	7	exists	exist	VERB
ejpam-5320	85	8	a	a	DET
ejpam-5320	85	9	τ1τ2	τ1τ2	NOUN
ejpam-5320	85	10	-	-	ADJ
ejpam-5320	85	11	open	open	ADJ
ejpam-5320	85	12	set	set	ADJ
ejpam-5320	85	13	u	u	NOUN
ejpam-5320	85	14	of	of	ADP
ejpam-5320	85	15	x	x	PUNCT
ejpam-5320	85	16	containing	contain	VERB
ejpam-5320	85	17	x	x	PUNCT
ejpam-5320	85	18	such	such	ADJ
ejpam-5320	85	19	that	that	SCONJ
ejpam-5320	85	20	f	f	PROPN
ejpam-5320	85	21	(	(	PUNCT
ejpam-5320	85	22	u	u	NOUN
ejpam-5320	85	23	)	)	PUNCT
ejpam-5320	85	24	⊆	⊆	NUM
ejpam-5320	85	25	v	v	NOUN
ejpam-5320	85	26	.	.	PUNCT
ejpam-5320	86	1	thus	thus	ADV
ejpam-5320	86	2	,	,	PUNCT
ejpam-5320	86	3	x	x	PUNCT
ejpam-5320	86	4	∈	∈	PROPN
ejpam-5320	86	5	u	u	NOUN
ejpam-5320	86	6	⊆	⊆	NUM
ejpam-5320	86	7	f+(v	f+(v	NOUN
ejpam-5320	86	8	)	)	PUNCT
ejpam-5320	86	9	.	.	PUNCT
ejpam-5320	87	1	since	since	SCONJ
ejpam-5320	87	2	u	u	NOUN
ejpam-5320	87	3	is	be	AUX
ejpam-5320	87	4	τ1τ2	τ1τ2	VERB
ejpam-5320	87	5	-	-	ADJ
ejpam-5320	87	6	open	open	ADJ
ejpam-5320	87	7	,	,	PUNCT
ejpam-5320	87	8	we	we	PRON
ejpam-5320	87	9	have	have	VERB
ejpam-5320	87	10	x	x	PART
ejpam-5320	87	11	∈	∈	PRON
ejpam-5320	87	12	τ1τ2	τ1τ2	NOUN
ejpam-5320	87	13	-	-	NUM
ejpam-5320	87	14	int(f	int(f	VERB
ejpam-5320	87	15	+	+	ADJ
ejpam-5320	87	16	(	(	PUNCT
ejpam-5320	87	17	v	v	NOUN
ejpam-5320	87	18	)	)	PUNCT
ejpam-5320	87	19	)	)	PUNCT
ejpam-5320	87	20	.	.	PUNCT
ejpam-5320	88	1	(	(	PUNCT
ejpam-5320	88	2	2	2	X
ejpam-5320	88	3	)	)	PUNCT
ejpam-5320	88	4	⇒	⇒	NOUN
ejpam-5320	88	5	(	(	PUNCT
ejpam-5320	88	6	3	3	NUM
ejpam-5320	88	7	):	):	PUNCT
ejpam-5320	88	8	suppose	suppose	VERB
ejpam-5320	88	9	that	that	SCONJ
ejpam-5320	88	10	b	b	PROPN
ejpam-5320	88	11	is	be	AUX
ejpam-5320	88	12	any	any	DET
ejpam-5320	88	13	subset	subset	NOUN
ejpam-5320	88	14	of	of	ADP
ejpam-5320	88	15	y	y	PROPN
ejpam-5320	88	16	having	have	VERB
ejpam-5320	88	17	the	the	DET
ejpam-5320	88	18	σ1σ2	σ1σ2	NUM
ejpam-5320	88	19	-	-	ADJ
ejpam-5320	88	20	compact	compact	ADJ
ejpam-5320	88	21	σ1σ2	σ1σ2	NOUN
ejpam-5320	88	22	-	-	NOUN
ejpam-5320	88	23	closure	closure	NOUN
ejpam-5320	88	24	.	.	PUNCT
ejpam-5320	89	1	then	then	ADV
ejpam-5320	89	2	,	,	PUNCT
ejpam-5320	89	3	σ1σ2	σ1σ2	NOUN
ejpam-5320	89	4	-	-	NOUN
ejpam-5320	89	5	cl(b	cl(b	NOUN
ejpam-5320	89	6	)	)	PUNCT
ejpam-5320	89	7	is	be	AUX
ejpam-5320	89	8	σ1σ2	σ1σ2	NOUN
ejpam-5320	89	9	-	-	ADJ
ejpam-5320	89	10	closed	closed	ADJ
ejpam-5320	89	11	and	and	CCONJ
ejpam-5320	89	12	y	y	NOUN
ejpam-5320	89	13	−	−	PROPN
ejpam-5320	89	14	σ1σ2	σ1σ2	NOUN
ejpam-5320	89	15	-	-	PUNCT
ejpam-5320	89	16	cl(b	cl(b	NOUN
ejpam-5320	89	17	)	)	PUNCT
ejpam-5320	89	18	is	be	AUX
ejpam-5320	89	19	a	a	DET
ejpam-5320	89	20	σ1σ2	σ1σ2	NUM
ejpam-5320	89	21	-	-	ADJ
ejpam-5320	89	22	open	open	ADJ
ejpam-5320	89	23	set	set	NOUN
ejpam-5320	89	24	having	have	VERB
ejpam-5320	89	25	σ1σ2compact	σ1σ2compact	PROPN
ejpam-5320	89	26	complement	complement	NOUN
ejpam-5320	89	27	.	.	PUNCT
ejpam-5320	90	1	let	let	VERB
ejpam-5320	90	2	x	x	PUNCT
ejpam-5320	90	3	̸∈	̸∈	PROPN
ejpam-5320	90	4	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	90	5	-	-	PUNCT
ejpam-5320	90	6	cl(b	cl(b	NOUN
ejpam-5320	90	7	)	)	PUNCT
ejpam-5320	90	8	)	)	PUNCT
ejpam-5320	90	9	.	.	PUNCT
ejpam-5320	91	1	thus	thus	ADV
ejpam-5320	91	2	,	,	PUNCT
ejpam-5320	91	3	x	x	PUNCT
ejpam-5320	91	4	∈	∈	NOUN
ejpam-5320	91	5	x	x	PUNCT
ejpam-5320	91	6	−	−	NOUN
ejpam-5320	91	7	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	91	8	-	-	PUNCT
ejpam-5320	91	9	cl(b	cl(b	NOUN
ejpam-5320	91	10	)	)	PUNCT
ejpam-5320	91	11	)	)	PUNCT
ejpam-5320	92	1	=	=	PUNCT
ejpam-5320	93	1	f+(y	f+(y	NOUN
ejpam-5320	93	2	−	−	NUM
ejpam-5320	93	3	σ1σ2	σ1σ2	NUM
ejpam-5320	93	4	-	-	PUNCT
ejpam-5320	93	5	cl(b	cl(b	NOUN
ejpam-5320	93	6	)	)	PUNCT
ejpam-5320	93	7	)	)	PUNCT
ejpam-5320	93	8	.	.	PUNCT
ejpam-5320	94	1	this	this	PRON
ejpam-5320	94	2	implies	imply	VERB
ejpam-5320	94	3	f	f	PROPN
ejpam-5320	94	4	(	(	PUNCT
ejpam-5320	94	5	x	x	NOUN
ejpam-5320	94	6	)	)	PUNCT
ejpam-5320	94	7	⊆	⊆	NUM
ejpam-5320	94	8	y	y	NOUN
ejpam-5320	94	9	−	−	PUNCT
ejpam-5320	94	10	σ1σ2	σ1σ2	NOUN
ejpam-5320	94	11	-	-	NOUN
ejpam-5320	94	12	cl(b	cl(b	NOUN
ejpam-5320	94	13	)	)	PUNCT
ejpam-5320	94	14	.	.	PUNCT
ejpam-5320	95	1	since	since	SCONJ
ejpam-5320	95	2	y	y	PROPN
ejpam-5320	95	3	−	−	PROPN
ejpam-5320	95	4	σ1σ2	σ1σ2	NOUN
ejpam-5320	95	5	-	-	PUNCT
ejpam-5320	95	6	cl(b	cl(b	NOUN
ejpam-5320	95	7	)	)	PUNCT
ejpam-5320	95	8	is	be	AUX
ejpam-5320	95	9	a	a	DET
ejpam-5320	95	10	σ1σ2	σ1σ2	NUM
ejpam-5320	95	11	-	-	ADJ
ejpam-5320	95	12	open	open	ADJ
ejpam-5320	95	13	set	set	NOUN
ejpam-5320	95	14	having	have	VERB
ejpam-5320	95	15	σ1σ2	σ1σ2	ADJ
ejpam-5320	95	16	-	-	ADJ
ejpam-5320	95	17	compact	compact	ADJ
ejpam-5320	95	18	complement	complement	NOUN
ejpam-5320	95	19	,	,	PUNCT
ejpam-5320	95	20	by	by	ADP
ejpam-5320	95	21	(	(	PUNCT
ejpam-5320	95	22	2	2	X
ejpam-5320	95	23	)	)	PUNCT
ejpam-5320	95	24	we	we	PRON
ejpam-5320	95	25	have	have	AUX
ejpam-5320	95	26	x	x	PART
ejpam-5320	95	27	∈	∈	PRON
ejpam-5320	95	28	τ1τ2	τ1τ2	NOUN
ejpam-5320	95	29	-	-	NUM
ejpam-5320	95	30	int(f	int(f	VERB
ejpam-5320	95	31	+	+	ADJ
ejpam-5320	95	32	(	(	PUNCT
ejpam-5320	95	33	y	y	PROPN
ejpam-5320	95	34	−	−	PROPN
ejpam-5320	95	35	σ1σ2	σ1σ2	NOUN
ejpam-5320	95	36	-	-	NOUN
ejpam-5320	95	37	cl(b	cl(b	NOUN
ejpam-5320	95	38	)	)	PUNCT
ejpam-5320	95	39	)	)	PUNCT
ejpam-5320	95	40	)	)	PUNCT
ejpam-5320	96	1	=	=	PUNCT
ejpam-5320	97	1	τ1τ2	τ1τ2	NOUN
ejpam-5320	97	2	-	-	ADJ
ejpam-5320	97	3	int(x	int(x	ADJ
ejpam-5320	97	4	−	−	NOUN
ejpam-5320	97	5	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	97	6	-	-	PUNCT
ejpam-5320	97	7	cl(b	cl(b	NOUN
ejpam-5320	97	8	)	)	PUNCT
ejpam-5320	97	9	)	)	PUNCT
ejpam-5320	97	10	)	)	PUNCT
ejpam-5320	98	1	=	=	PUNCT
ejpam-5320	99	1	x	x	X
ejpam-5320	99	2	−	−	ADP
ejpam-5320	99	3	τ1τ2	τ1τ2	NOUN
ejpam-5320	99	4	-	-	NOUN
ejpam-5320	99	5	cl(f	cl(f	NOUN
ejpam-5320	99	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5320	99	7	-	-	NOUN
ejpam-5320	99	8	cl(b	cl(b	NOUN
ejpam-5320	99	9	)	)	PUNCT
ejpam-5320	99	10	)	)	PUNCT
ejpam-5320	99	11	)	)	PUNCT
ejpam-5320	100	1	⊆	⊆	NUM
ejpam-5320	100	2	x	x	SYM
ejpam-5320	100	3	−	−	PRON
ejpam-5320	100	4	τ1τ2	τ1τ2	NOUN
ejpam-5320	100	5	-	-	NOUN
ejpam-5320	100	6	cl(f	cl(f	NOUN
ejpam-5320	100	7	−(b	−(b	PROPN
ejpam-5320	100	8	)	)	PUNCT
ejpam-5320	100	9	)	)	PUNCT
ejpam-5320	100	10	.	.	PUNCT
ejpam-5320	101	1	therefore	therefore	ADV
ejpam-5320	101	2	,	,	PUNCT
ejpam-5320	101	3	x	x	PROPN
ejpam-5320	101	4	̸∈	̸∈	PROPN
ejpam-5320	101	5	τ1τ2	τ1τ2	PROPN
ejpam-5320	101	6	-	-	PROPN
ejpam-5320	101	7	cl(f	cl(f	NOUN
ejpam-5320	101	8	−(b	−(b	PROPN
ejpam-5320	101	9	)	)	PUNCT
ejpam-5320	101	10	)	)	PUNCT
ejpam-5320	101	11	.	.	PUNCT
ejpam-5320	102	1	(	(	PUNCT
ejpam-5320	102	2	3	3	X
ejpam-5320	102	3	)	)	PUNCT
ejpam-5320	102	4	⇒	⇒	NOUN
ejpam-5320	102	5	(	(	PUNCT
ejpam-5320	102	6	4	4	NUM
ejpam-5320	102	7	):	):	PUNCT
ejpam-5320	102	8	let	let	VERB
ejpam-5320	102	9	b	b	X
ejpam-5320	102	10	be	be	AUX
ejpam-5320	102	11	any	any	DET
ejpam-5320	102	12	subset	subset	NOUN
ejpam-5320	102	13	of	of	ADP
ejpam-5320	102	14	y	y	PRON
ejpam-5320	102	15	such	such	ADJ
ejpam-5320	102	16	that	that	SCONJ
ejpam-5320	102	17	y	y	PROPN
ejpam-5320	102	18	−	−	ADP
ejpam-5320	102	19	σ1σ2	σ1σ2	NUM
ejpam-5320	102	20	-	-	PUNCT
ejpam-5320	102	21	int(b	int(b	NOUN
ejpam-5320	102	22	)	)	PUNCT
ejpam-5320	102	23	is	be	AUX
ejpam-5320	102	24	σ1σ2	σ1σ2	NOUN
ejpam-5320	102	25	-	-	ADJ
ejpam-5320	102	26	compact	compact	ADJ
ejpam-5320	102	27	and	and	CCONJ
ejpam-5320	102	28	let	let	VERB
ejpam-5320	102	29	x	x	SYM
ejpam-5320	102	30	̸∈	̸∈	PROPN
ejpam-5320	102	31	τ1τ2	τ1τ2	PROPN
ejpam-5320	102	32	-	-	NUM
ejpam-5320	102	33	int(f	int(f	VERB
ejpam-5320	102	34	+	+	ADJ
ejpam-5320	102	35	(	(	PUNCT
ejpam-5320	102	36	b	b	NOUN
ejpam-5320	102	37	)	)	PUNCT
ejpam-5320	102	38	)	)	PUNCT
ejpam-5320	102	39	.	.	PUNCT
ejpam-5320	103	1	then	then	ADV
ejpam-5320	103	2	,	,	PUNCT
ejpam-5320	103	3	we	we	PRON
ejpam-5320	103	4	have	have	VERB
ejpam-5320	103	5	x	x	X
ejpam-5320	103	6	∈	∈	NOUN
ejpam-5320	103	7	x	x	INTJ
ejpam-5320	103	8	−	−	PUNCT
ejpam-5320	103	9	τ1τ2	τ1τ2	NOUN
ejpam-5320	103	10	-	-	NUM
ejpam-5320	103	11	int(f	int(f	VERB
ejpam-5320	103	12	+	+	ADJ
ejpam-5320	103	13	(	(	PUNCT
ejpam-5320	103	14	b	b	NOUN
ejpam-5320	103	15	)	)	PUNCT
ejpam-5320	103	16	)	)	PUNCT
ejpam-5320	104	1	=	=	PUNCT
ejpam-5320	104	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	104	3	-	-	NOUN
ejpam-5320	104	4	cl(x	cl(x	SYM
ejpam-5320	104	5	−	−	PROPN
ejpam-5320	104	6	f+(b	f+(b	NOUN
ejpam-5320	104	7	)	)	PUNCT
ejpam-5320	104	8	)	)	PUNCT
ejpam-5320	105	1	=	=	PUNCT
ejpam-5320	105	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	105	3	-	-	PROPN
ejpam-5320	105	4	cl(f	cl(f	NOUN
ejpam-5320	105	5	−(y	−(y	NOUN
ejpam-5320	105	6	−b	−b	NOUN
ejpam-5320	105	7	)	)	PUNCT
ejpam-5320	105	8	)	)	PUNCT
ejpam-5320	105	9	and	and	CCONJ
ejpam-5320	105	10	by	by	ADP
ejpam-5320	105	11	(	(	PUNCT
ejpam-5320	105	12	3	3	NUM
ejpam-5320	105	13	)	)	PUNCT
ejpam-5320	105	14	,	,	PUNCT
ejpam-5320	105	15	x	x	PUNCT
ejpam-5320	105	16	∈	∈	NOUN
ejpam-5320	105	17	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	105	18	-	-	PUNCT
ejpam-5320	105	19	cl(y	cl(y	NOUN
ejpam-5320	105	20	−b	−b	NOUN
ejpam-5320	105	21	)	)	PUNCT
ejpam-5320	105	22	)	)	PUNCT
ejpam-5320	106	1	=	=	PUNCT
ejpam-5320	106	2	f−(y	f−(y	NOUN
ejpam-5320	106	3	−	−	ADP
ejpam-5320	106	4	σ1σ2	σ1σ2	NOUN
ejpam-5320	106	5	-	-	PUNCT
ejpam-5320	106	6	int(b	int(b	NOUN
ejpam-5320	106	7	)	)	PUNCT
ejpam-5320	106	8	)	)	PUNCT
ejpam-5320	107	1	=	=	PUNCT
ejpam-5320	107	2	x	x	X
ejpam-5320	108	1	−	−	ADP
ejpam-5320	108	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	108	3	-	-	PUNCT
ejpam-5320	108	4	int(b	int(b	NOUN
ejpam-5320	108	5	)	)	PUNCT
ejpam-5320	108	6	)	)	PUNCT
ejpam-5320	108	7	.	.	PUNCT
ejpam-5320	109	1	thus	thus	ADV
ejpam-5320	109	2	,	,	PUNCT
ejpam-5320	109	3	x	x	PROPN
ejpam-5320	109	4	̸∈	̸∈	PROPN
ejpam-5320	109	5	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	109	6	-	-	PUNCT
ejpam-5320	109	7	int(b	int(b	NOUN
ejpam-5320	109	8	)	)	PUNCT
ejpam-5320	109	9	)	)	PUNCT
ejpam-5320	109	10	.	.	PUNCT
ejpam-5320	110	1	(	(	PUNCT
ejpam-5320	110	2	4	4	X
ejpam-5320	110	3	)	)	PUNCT
ejpam-5320	110	4	⇒	⇒	NOUN
ejpam-5320	110	5	(	(	PUNCT
ejpam-5320	110	6	1	1	NUM
ejpam-5320	110	7	):	):	PUNCT
ejpam-5320	110	8	let	let	VERB
ejpam-5320	110	9	v	v	PART
ejpam-5320	110	10	be	be	AUX
ejpam-5320	110	11	any	any	DET
ejpam-5320	110	12	σ1σ2	σ1σ2	NOUN
ejpam-5320	110	13	-	-	ADJ
ejpam-5320	110	14	open	open	ADJ
ejpam-5320	110	15	set	set	NOUN
ejpam-5320	110	16	of	of	ADP
ejpam-5320	110	17	y	y	PROPN
ejpam-5320	110	18	containing	contain	VERB
ejpam-5320	110	19	f	f	PROPN
ejpam-5320	110	20	(	(	PUNCT
ejpam-5320	110	21	x	x	NOUN
ejpam-5320	110	22	)	)	PUNCT
ejpam-5320	110	23	and	and	CCONJ
ejpam-5320	110	24	having	have	VERB
ejpam-5320	110	25	σ1σ2	σ1σ2	NOUN
ejpam-5320	110	26	-	-	ADJ
ejpam-5320	110	27	compact	compact	ADJ
ejpam-5320	110	28	complement	complement	NOUN
ejpam-5320	110	29	.	.	PUNCT
ejpam-5320	111	1	we	we	PRON
ejpam-5320	111	2	have	have	VERB
ejpam-5320	111	3	f+(v	f+(v	NOUN
ejpam-5320	111	4	)	)	PUNCT
ejpam-5320	112	1	=	=	PUNCT
ejpam-5320	112	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	112	3	-	-	PUNCT
ejpam-5320	112	4	int(v	int(v	NOUN
ejpam-5320	112	5	)	)	PUNCT
ejpam-5320	112	6	)	)	PUNCT
ejpam-5320	112	7	.	.	PUNCT
ejpam-5320	113	1	then	then	ADV
ejpam-5320	113	2	,	,	PUNCT
ejpam-5320	113	3	y	y	PROPN
ejpam-5320	113	4	−σ1σ2	−σ1σ2	PROPN
ejpam-5320	113	5	-	-	PUNCT
ejpam-5320	113	6	int(v	int(v	NOUN
ejpam-5320	113	7	)	)	PUNCT
ejpam-5320	113	8	=	=	SYM
ejpam-5320	113	9	y	y	PROPN
ejpam-5320	113	10	−v	−v	NOUN
ejpam-5320	113	11	which	which	PRON
ejpam-5320	113	12	is	be	AUX
ejpam-5320	113	13	σ1σ2	σ1σ2	NOUN
ejpam-5320	113	14	-	-	ADJ
ejpam-5320	113	15	compact	compact	ADJ
ejpam-5320	113	16	and	and	CCONJ
ejpam-5320	113	17	by	by	ADP
ejpam-5320	113	18	(	(	PUNCT
ejpam-5320	113	19	4	4	NUM
ejpam-5320	113	20	)	)	PUNCT
ejpam-5320	113	21	,	,	PUNCT
ejpam-5320	113	22	x	x	PUNCT
ejpam-5320	113	23	∈	∈	PROPN
ejpam-5320	113	24	τ1τ2	τ1τ2	PUNCT
ejpam-5320	113	25	-	-	NUM
ejpam-5320	113	26	int(f	int(f	VERB
ejpam-5320	113	27	+	+	ADJ
ejpam-5320	113	28	(	(	PUNCT
ejpam-5320	113	29	v	v	NOUN
ejpam-5320	113	30	)	)	PUNCT
ejpam-5320	113	31	)	)	PUNCT
ejpam-5320	113	32	.	.	PUNCT
ejpam-5320	114	1	therefore	therefore	ADV
ejpam-5320	114	2	,	,	PUNCT
ejpam-5320	114	3	there	there	PRON
ejpam-5320	114	4	exists	exist	VERB
ejpam-5320	114	5	a	a	DET
ejpam-5320	114	6	τ1τ2	τ1τ2	NOUN
ejpam-5320	114	7	-	-	ADJ
ejpam-5320	114	8	open	open	ADJ
ejpam-5320	114	9	set	set	ADJ
ejpam-5320	114	10	u	u	NOUN
ejpam-5320	114	11	of	of	ADP
ejpam-5320	114	12	x	x	PUNCT
ejpam-5320	114	13	containing	contain	VERB
ejpam-5320	114	14	x	x	PUNCT
ejpam-5320	114	15	such	such	ADJ
ejpam-5320	114	16	that	that	SCONJ
ejpam-5320	114	17	x	x	SYM
ejpam-5320	114	18	∈	∈	NUM
ejpam-5320	114	19	u	u	NOUN
ejpam-5320	114	20	⊆	⊆	NUM
ejpam-5320	114	21	f+(v	f+(v	NOUN
ejpam-5320	114	22	)	)	PUNCT
ejpam-5320	114	23	.	.	PUNCT
ejpam-5320	115	1	thus	thus	ADV
ejpam-5320	115	2	,	,	PUNCT
ejpam-5320	115	3	f	f	PROPN
ejpam-5320	115	4	(	(	PUNCT
ejpam-5320	115	5	u	u	NOUN
ejpam-5320	115	6	)	)	PUNCT
ejpam-5320	115	7	⊆	⊆	NUM
ejpam-5320	115	8	v	v	NOUN
ejpam-5320	115	9	.	.	PUNCT
ejpam-5320	116	1	this	this	PRON
ejpam-5320	116	2	shows	show	VERB
ejpam-5320	116	3	that	that	SCONJ
ejpam-5320	116	4	f	f	PROPN
ejpam-5320	116	5	is	be	AUX
ejpam-5320	116	6	upper	upper	ADJ
ejpam-5320	116	7	c-(τ1	c-(τ1	PROPN
ejpam-5320	116	8	,	,	PUNCT
ejpam-5320	116	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	116	10	at	at	ADP
ejpam-5320	116	11	x.	x.	NOUN
ejpam-5320	116	12	definition	definition	NOUN
ejpam-5320	116	13	2	2	NUM
ejpam-5320	116	14	.	.	PUNCT
ejpam-5320	116	15	a	a	DET
ejpam-5320	116	16	multifunction	multifunction	NOUN
ejpam-5320	117	1	f	f	NOUN
ejpam-5320	117	2	:	:	PUNCT
ejpam-5320	117	3	(	(	PUNCT
ejpam-5320	117	4	x	x	NOUN
ejpam-5320	117	5	,	,	PUNCT
ejpam-5320	117	6	τ1	τ1	NOUN
ejpam-5320	117	7	,	,	PUNCT
ejpam-5320	117	8	τ2	τ2	NOUN
ejpam-5320	117	9	)	)	PUNCT
ejpam-5320	117	10	→	→	SYM
ejpam-5320	117	11	(	(	PUNCT
ejpam-5320	117	12	y	y	PROPN
ejpam-5320	117	13	,	,	PUNCT
ejpam-5320	117	14	σ1	σ1	PROPN
ejpam-5320	117	15	,	,	PUNCT
ejpam-5320	117	16	σ2	σ2	PROPN
ejpam-5320	117	17	)	)	PUNCT
ejpam-5320	117	18	is	be	AUX
ejpam-5320	117	19	said	say	VERB
ejpam-5320	117	20	to	to	PART
ejpam-5320	117	21	be	be	AUX
ejpam-5320	117	22	lower	low	ADJ
ejpam-5320	117	23	c-(τ1	c-(τ1	NOUN
ejpam-5320	117	24	,	,	PUNCT
ejpam-5320	117	25	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	117	26	at	at	ADP
ejpam-5320	117	27	a	a	DET
ejpam-5320	117	28	point	point	NOUN
ejpam-5320	117	29	x	x	SYM
ejpam-5320	117	30	∈	∈	NOUN
ejpam-5320	117	31	x	x	PUNCT
ejpam-5320	117	32	if	if	SCONJ
ejpam-5320	117	33	for	for	ADP
ejpam-5320	117	34	each	each	DET
ejpam-5320	117	35	σ1σ2	σ1σ2	VERB
ejpam-5320	117	36	-	-	ADJ
ejpam-5320	117	37	open	open	ADJ
ejpam-5320	117	38	set	set	NOUN
ejpam-5320	117	39	v	v	NOUN
ejpam-5320	117	40	of	of	ADP
ejpam-5320	117	41	y	y	PRON
ejpam-5320	117	42	such	such	ADJ
ejpam-5320	117	43	that	that	SCONJ
ejpam-5320	117	44	f	f	PROPN
ejpam-5320	117	45	(	(	PUNCT
ejpam-5320	117	46	x)∩v	x)∩v	PROPN
ejpam-5320	117	47	̸=	̸=	PROPN
ejpam-5320	117	48	∅	∅	NOUN
ejpam-5320	117	49	and	and	CCONJ
ejpam-5320	117	50	having	have	VERB
ejpam-5320	117	51	σ1σ2	σ1σ2	NOUN
ejpam-5320	117	52	-	-	ADJ
ejpam-5320	117	53	compact	compact	ADJ
ejpam-5320	117	54	complement	complement	NOUN
ejpam-5320	117	55	,	,	PUNCT
ejpam-5320	117	56	there	there	PRON
ejpam-5320	117	57	exists	exist	VERB
ejpam-5320	117	58	a	a	DET
ejpam-5320	117	59	τ1τ2	τ1τ2	NOUN
ejpam-5320	117	60	-	-	ADJ
ejpam-5320	117	61	open	open	ADJ
ejpam-5320	117	62	set	set	ADJ
ejpam-5320	117	63	u	u	NOUN
ejpam-5320	117	64	of	of	ADP
ejpam-5320	117	65	x	x	PUNCT
ejpam-5320	117	66	containing	contain	VERB
ejpam-5320	117	67	x	x	PUNCT
ejpam-5320	117	68	such	such	ADJ
ejpam-5320	117	69	that	that	SCONJ
ejpam-5320	117	70	f	f	PROPN
ejpam-5320	117	71	(	(	PUNCT
ejpam-5320	117	72	z	z	NOUN
ejpam-5320	117	73	)	)	PUNCT
ejpam-5320	117	74	∩	∩	NOUN
ejpam-5320	117	75	v	v	ADP
ejpam-5320	117	76	̸=	̸=	PROPN
ejpam-5320	117	77	∅	∅	NOUN
ejpam-5320	117	78	for	for	ADP
ejpam-5320	117	79	each	each	DET
ejpam-5320	117	80	z	z	NOUN
ejpam-5320	117	81	∈	∈	PROPN
ejpam-5320	117	82	u	u	NOUN
ejpam-5320	117	83	.	.	PUNCT
ejpam-5320	118	1	a	a	DET
ejpam-5320	118	2	multifunction	multifunction	NOUN
ejpam-5320	118	3	f	f	NOUN
ejpam-5320	118	4	:	:	PUNCT
ejpam-5320	118	5	(	(	PUNCT
ejpam-5320	118	6	x	x	NOUN
ejpam-5320	118	7	,	,	PUNCT
ejpam-5320	118	8	τ1	τ1	NOUN
ejpam-5320	118	9	,	,	PUNCT
ejpam-5320	118	10	τ2	τ2	NOUN
ejpam-5320	118	11	)	)	PUNCT
ejpam-5320	118	12	→	→	SYM
ejpam-5320	118	13	(	(	PUNCT
ejpam-5320	118	14	y	y	PROPN
ejpam-5320	118	15	,	,	PUNCT
ejpam-5320	118	16	σ1	σ1	PROPN
ejpam-5320	118	17	,	,	PUNCT
ejpam-5320	118	18	σ2	σ2	PROPN
ejpam-5320	118	19	)	)	PUNCT
ejpam-5320	118	20	is	be	AUX
ejpam-5320	118	21	said	say	VERB
ejpam-5320	118	22	to	to	PART
ejpam-5320	118	23	be	be	AUX
ejpam-5320	118	24	lower	low	ADJ
ejpam-5320	118	25	c-(τ1	c-(τ1	PROPN
ejpam-5320	118	26	,	,	PUNCT
ejpam-5320	118	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	118	28	if	if	SCONJ
ejpam-5320	118	29	f	f	PROPN
ejpam-5320	118	30	has	have	VERB
ejpam-5320	118	31	this	this	DET
ejpam-5320	118	32	property	property	NOUN
ejpam-5320	118	33	at	at	ADP
ejpam-5320	118	34	every	every	DET
ejpam-5320	118	35	point	point	NOUN
ejpam-5320	118	36	of	of	ADP
ejpam-5320	118	37	x.	x.	NOUN
ejpam-5320	118	38	theorem	theorem	VERB
ejpam-5320	118	39	2	2	NUM
ejpam-5320	118	40	.	.	X
ejpam-5320	118	41	for	for	ADP
ejpam-5320	118	42	a	a	DET
ejpam-5320	118	43	multifunction	multifunction	NOUN
ejpam-5320	118	44	f	f	NOUN
ejpam-5320	118	45	:	:	PUNCT
ejpam-5320	118	46	(	(	PUNCT
ejpam-5320	118	47	x	x	NOUN
ejpam-5320	118	48	,	,	PUNCT
ejpam-5320	118	49	τ1	τ1	NOUN
ejpam-5320	118	50	,	,	PUNCT
ejpam-5320	118	51	τ2	τ2	NOUN
ejpam-5320	118	52	)	)	PUNCT
ejpam-5320	118	53	→	→	SYM
ejpam-5320	118	54	(	(	PUNCT
ejpam-5320	118	55	y	y	PROPN
ejpam-5320	118	56	,	,	PUNCT
ejpam-5320	118	57	σ1	σ1	PROPN
ejpam-5320	118	58	,	,	PUNCT
ejpam-5320	118	59	σ2	σ2	NOUN
ejpam-5320	118	60	)	)	PUNCT
ejpam-5320	118	61	,	,	PUNCT
ejpam-5320	118	62	the	the	DET
ejpam-5320	118	63	following	follow	VERB
ejpam-5320	118	64	properties	property	NOUN
ejpam-5320	118	65	are	be	AUX
ejpam-5320	118	66	equivalent	equivalent	ADJ
ejpam-5320	118	67	:	:	PUNCT
ejpam-5320	118	68	j.	j.	PROPN
ejpam-5320	118	69	khampakdee	khampakdee	PROPN
ejpam-5320	118	70	,	,	PUNCT
ejpam-5320	118	71	s.	s.	PROPN
ejpam-5320	118	72	sompong	sompong	PROPN
ejpam-5320	118	73	,	,	PUNCT
ejpam-5320	118	74	c.	c.	PROPN
ejpam-5320	118	75	boonpok	boonpok	PROPN
ejpam-5320	118	76	/	/	SYM
ejpam-5320	118	77	eur	eur	PROPN
ejpam-5320	118	78	.	.	PUNCT
ejpam-5320	119	1	j.	j.	PROPN
ejpam-5320	119	2	pure	pure	PROPN
ejpam-5320	119	3	appl	appl	PROPN
ejpam-5320	119	4	.	.	PROPN
ejpam-5320	119	5	math	math	PROPN
ejpam-5320	119	6	,	,	PUNCT
ejpam-5320	119	7	17	17	NUM
ejpam-5320	119	8	(	(	PUNCT
ejpam-5320	119	9	3	3	NUM
ejpam-5320	119	10	)	)	PUNCT
ejpam-5320	119	11	(	(	PUNCT
ejpam-5320	119	12	2024	2024	NUM
ejpam-5320	119	13	)	)	PUNCT
ejpam-5320	119	14	,	,	PUNCT
ejpam-5320	119	15	2288	2288	NUM
ejpam-5320	119	16	-	-	SYM
ejpam-5320	119	17	2298	2298	NUM
ejpam-5320	119	18	2292	2292	NUM
ejpam-5320	119	19	(	(	PUNCT
ejpam-5320	119	20	1	1	X
ejpam-5320	119	21	)	)	PUNCT
ejpam-5320	119	22	f	f	PROPN
ejpam-5320	119	23	is	be	AUX
ejpam-5320	119	24	lower	low	ADJ
ejpam-5320	119	25	c-(τ1	c-(τ1	PROPN
ejpam-5320	119	26	,	,	PUNCT
ejpam-5320	119	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	119	28	at	at	ADP
ejpam-5320	119	29	x	x	X
ejpam-5320	119	30	∈	∈	PROPN
ejpam-5320	119	31	x	x	X
ejpam-5320	119	32	;	;	PUNCT
ejpam-5320	120	1	(	(	PUNCT
ejpam-5320	120	2	2	2	X
ejpam-5320	120	3	)	)	PUNCT
ejpam-5320	120	4	x	x	SYM
ejpam-5320	120	5	∈	∈	PRON
ejpam-5320	120	6	τ1τ2	τ1τ2	NOUN
ejpam-5320	120	7	-	-	ADJ
ejpam-5320	120	8	int(f	int(f	NUM
ejpam-5320	120	9	−(v	−(v	NOUN
ejpam-5320	120	10	)	)	PUNCT
ejpam-5320	120	11	)	)	PUNCT
ejpam-5320	120	12	for	for	ADP
ejpam-5320	120	13	each	each	DET
ejpam-5320	120	14	σ1σ2	σ1σ2	VERB
ejpam-5320	120	15	-	-	ADJ
ejpam-5320	120	16	open	open	ADJ
ejpam-5320	120	17	set	set	NOUN
ejpam-5320	120	18	v	v	NOUN
ejpam-5320	120	19	of	of	ADP
ejpam-5320	120	20	y	y	PROPN
ejpam-5320	120	21	containing	contain	VERB
ejpam-5320	120	22	f	f	PROPN
ejpam-5320	120	23	(	(	PUNCT
ejpam-5320	120	24	x	x	NOUN
ejpam-5320	120	25	)	)	PUNCT
ejpam-5320	120	26	and	and	CCONJ
ejpam-5320	120	27	having	have	VERB
ejpam-5320	120	28	σ1σ2	σ1σ2	NOUN
ejpam-5320	120	29	-	-	ADJ
ejpam-5320	120	30	compact	compact	ADJ
ejpam-5320	120	31	complement	complement	NOUN
ejpam-5320	120	32	;	;	PUNCT
ejpam-5320	120	33	(	(	PUNCT
ejpam-5320	120	34	3	3	X
ejpam-5320	120	35	)	)	PUNCT
ejpam-5320	120	36	x	x	SYM
ejpam-5320	120	37	∈	∈	VERB
ejpam-5320	120	38	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	120	39	-	-	PUNCT
ejpam-5320	120	40	cl(b	cl(b	NOUN
ejpam-5320	120	41	)	)	PUNCT
ejpam-5320	120	42	)	)	PUNCT
ejpam-5320	120	43	for	for	ADP
ejpam-5320	120	44	each	each	DET
ejpam-5320	120	45	subset	subset	NOUN
ejpam-5320	120	46	b	b	PROPN
ejpam-5320	120	47	of	of	ADP
ejpam-5320	120	48	y	y	PROPN
ejpam-5320	120	49	having	have	VERB
ejpam-5320	120	50	the	the	DET
ejpam-5320	120	51	σ1σ2	σ1σ2	NUM
ejpam-5320	120	52	-	-	ADJ
ejpam-5320	120	53	compact	compact	ADJ
ejpam-5320	120	54	σ1σ2	σ1σ2	NOUN
ejpam-5320	120	55	-	-	NOUN
ejpam-5320	120	56	closure	closure	NOUN
ejpam-5320	120	57	such	such	ADJ
ejpam-5320	120	58	that	that	SCONJ
ejpam-5320	120	59	x	x	PUNCT
ejpam-5320	120	60	∈	∈	PROPN
ejpam-5320	120	61	τ1τ2	τ1τ2	NOUN
ejpam-5320	120	62	-	-	NOUN
ejpam-5320	120	63	cl(f	cl(f	NOUN
ejpam-5320	120	64	+	+	NOUN
ejpam-5320	120	65	(	(	PUNCT
ejpam-5320	120	66	b	b	NOUN
ejpam-5320	120	67	)	)	PUNCT
ejpam-5320	120	68	)	)	PUNCT
ejpam-5320	120	69	;	;	PUNCT
ejpam-5320	120	70	(	(	PUNCT
ejpam-5320	120	71	4	4	X
ejpam-5320	120	72	)	)	PUNCT
ejpam-5320	120	73	x	x	SYM
ejpam-5320	120	74	∈	∈	PRON
ejpam-5320	120	75	τ1τ2	τ1τ2	NOUN
ejpam-5320	120	76	-	-	ADJ
ejpam-5320	120	77	int(f	int(f	VERB
ejpam-5320	120	78	−(b	−(b	NOUN
ejpam-5320	120	79	)	)	PUNCT
ejpam-5320	120	80	)	)	PUNCT
ejpam-5320	120	81	for	for	ADP
ejpam-5320	120	82	each	each	DET
ejpam-5320	120	83	subset	subset	NOUN
ejpam-5320	120	84	b	b	PROPN
ejpam-5320	120	85	of	of	ADP
ejpam-5320	120	86	y	y	PRON
ejpam-5320	120	87	such	such	ADJ
ejpam-5320	120	88	that	that	SCONJ
ejpam-5320	120	89	y	y	PROPN
ejpam-5320	121	1	−	−	ADP
ejpam-5320	121	2	σ1σ2	σ1σ2	NUM
ejpam-5320	121	3	-	-	PUNCT
ejpam-5320	121	4	int(b	int(b	NOUN
ejpam-5320	121	5	)	)	PUNCT
ejpam-5320	121	6	is	be	AUX
ejpam-5320	121	7	σ1σ2compact	σ1σ2compact	PUNCT
ejpam-5320	121	8	and	and	CCONJ
ejpam-5320	121	9	x	x	PUNCT
ejpam-5320	121	10	∈	∈	NOUN
ejpam-5320	121	11	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5320	121	12	-	-	PUNCT
ejpam-5320	121	13	int(b	int(b	NOUN
ejpam-5320	121	14	)	)	PUNCT
ejpam-5320	121	15	)	)	PUNCT
ejpam-5320	121	16	.	.	PUNCT
ejpam-5320	122	1	proof	proof	NOUN
ejpam-5320	122	2	.	.	PUNCT
ejpam-5320	123	1	the	the	DET
ejpam-5320	123	2	proof	proof	NOUN
ejpam-5320	123	3	is	be	AUX
ejpam-5320	123	4	similar	similar	ADJ
ejpam-5320	123	5	to	to	ADP
ejpam-5320	123	6	that	that	PRON
ejpam-5320	123	7	of	of	ADP
ejpam-5320	123	8	theorem	theorem	NOUN
ejpam-5320	123	9	1	1	NUM
ejpam-5320	123	10	.	.	PUNCT
ejpam-5320	123	11	definition	definition	NOUN
ejpam-5320	123	12	3	3	NUM
ejpam-5320	123	13	.	.	PUNCT
ejpam-5320	124	1	a	a	DET
ejpam-5320	124	2	function	function	NOUN
ejpam-5320	124	3	f	f	NOUN
ejpam-5320	124	4	:	:	PUNCT
ejpam-5320	124	5	(	(	PUNCT
ejpam-5320	124	6	x	x	NOUN
ejpam-5320	124	7	,	,	PUNCT
ejpam-5320	124	8	τ1	τ1	NOUN
ejpam-5320	124	9	,	,	PUNCT
ejpam-5320	124	10	τ2	τ2	NOUN
ejpam-5320	124	11	)	)	PUNCT
ejpam-5320	124	12	→	→	SYM
ejpam-5320	124	13	(	(	PUNCT
ejpam-5320	124	14	y	y	PROPN
ejpam-5320	124	15	,	,	PUNCT
ejpam-5320	124	16	σ1	σ1	PROPN
ejpam-5320	124	17	,	,	PUNCT
ejpam-5320	124	18	σ2	σ2	PROPN
ejpam-5320	124	19	)	)	PUNCT
ejpam-5320	124	20	is	be	AUX
ejpam-5320	124	21	said	say	VERB
ejpam-5320	124	22	to	to	PART
ejpam-5320	124	23	be	be	AUX
ejpam-5320	124	24	c-(τ1	c-(τ1	PROPN
ejpam-5320	124	25	,	,	PUNCT
ejpam-5320	124	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	124	27	at	at	ADP
ejpam-5320	124	28	a	a	DET
ejpam-5320	124	29	point	point	NOUN
ejpam-5320	124	30	x	x	SYM
ejpam-5320	124	31	∈	∈	NOUN
ejpam-5320	124	32	x	x	PUNCT
ejpam-5320	124	33	if	if	SCONJ
ejpam-5320	124	34	for	for	ADP
ejpam-5320	124	35	each	each	DET
ejpam-5320	124	36	σ1σ2	σ1σ2	VERB
ejpam-5320	124	37	-	-	ADJ
ejpam-5320	124	38	open	open	ADJ
ejpam-5320	124	39	set	set	NOUN
ejpam-5320	124	40	v	v	NOUN
ejpam-5320	124	41	of	of	ADP
ejpam-5320	124	42	y	y	NOUN
ejpam-5320	124	43	containing	contain	VERB
ejpam-5320	124	44	f(x	f(x	PROPN
ejpam-5320	124	45	)	)	PUNCT
ejpam-5320	124	46	and	and	CCONJ
ejpam-5320	124	47	having	have	VERB
ejpam-5320	124	48	σ1σ2	σ1σ2	NOUN
ejpam-5320	124	49	-	-	ADJ
ejpam-5320	124	50	compact	compact	ADJ
ejpam-5320	124	51	complement	complement	NOUN
ejpam-5320	124	52	,	,	PUNCT
ejpam-5320	124	53	there	there	PRON
ejpam-5320	124	54	exists	exist	VERB
ejpam-5320	124	55	a	a	DET
ejpam-5320	124	56	τ1τ2	τ1τ2	NOUN
ejpam-5320	124	57	-	-	ADJ
ejpam-5320	124	58	open	open	ADJ
ejpam-5320	124	59	set	set	ADJ
ejpam-5320	124	60	u	u	NOUN
ejpam-5320	124	61	of	of	ADP
ejpam-5320	124	62	x	x	PUNCT
ejpam-5320	124	63	containing	contain	VERB
ejpam-5320	124	64	x	x	PUNCT
ejpam-5320	124	65	such	such	ADJ
ejpam-5320	124	66	that	that	DET
ejpam-5320	124	67	f(u	f(u	PROPN
ejpam-5320	124	68	)	)	PUNCT
ejpam-5320	124	69	⊆	⊆	NUM
ejpam-5320	124	70	v	v	NOUN
ejpam-5320	124	71	.	.	PUNCT
ejpam-5320	125	1	a	a	DET
ejpam-5320	125	2	function	function	NOUN
ejpam-5320	125	3	f	f	NOUN
ejpam-5320	125	4	:	:	PUNCT
ejpam-5320	125	5	(	(	PUNCT
ejpam-5320	125	6	x	x	NOUN
ejpam-5320	125	7	,	,	PUNCT
ejpam-5320	125	8	τ1	τ1	NOUN
ejpam-5320	125	9	,	,	PUNCT
ejpam-5320	125	10	τ2	τ2	NOUN
ejpam-5320	125	11	)	)	PUNCT
ejpam-5320	125	12	→	→	SYM
ejpam-5320	125	13	(	(	PUNCT
ejpam-5320	125	14	y	y	PROPN
ejpam-5320	125	15	,	,	PUNCT
ejpam-5320	125	16	σ1	σ1	PROPN
ejpam-5320	125	17	,	,	PUNCT
ejpam-5320	125	18	σ2	σ2	PROPN
ejpam-5320	125	19	)	)	PUNCT
ejpam-5320	125	20	is	be	AUX
ejpam-5320	125	21	said	say	VERB
ejpam-5320	125	22	to	to	PART
ejpam-5320	125	23	be	be	AUX
ejpam-5320	125	24	c-(τ1	c-(τ1	PROPN
ejpam-5320	125	25	,	,	PUNCT
ejpam-5320	125	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	125	27	if	if	SCONJ
ejpam-5320	125	28	f	f	PROPN
ejpam-5320	125	29	has	have	VERB
ejpam-5320	125	30	this	this	DET
ejpam-5320	125	31	property	property	NOUN
ejpam-5320	125	32	at	at	ADP
ejpam-5320	125	33	every	every	DET
ejpam-5320	125	34	point	point	NOUN
ejpam-5320	125	35	of	of	ADP
ejpam-5320	125	36	x.	x.	NOUN
ejpam-5320	125	37	corollary	corollary	NOUN
ejpam-5320	125	38	1	1	NUM
ejpam-5320	125	39	.	.	PUNCT
ejpam-5320	126	1	for	for	ADP
ejpam-5320	126	2	a	a	DET
ejpam-5320	126	3	function	function	NOUN
ejpam-5320	126	4	f	f	NOUN
ejpam-5320	126	5	:	:	PUNCT
ejpam-5320	126	6	(	(	PUNCT
ejpam-5320	126	7	x	x	NOUN
ejpam-5320	126	8	,	,	PUNCT
ejpam-5320	126	9	τ1	τ1	NOUN
ejpam-5320	126	10	,	,	PUNCT
ejpam-5320	126	11	τ2	τ2	NOUN
ejpam-5320	126	12	)	)	PUNCT
ejpam-5320	126	13	→	→	SYM
ejpam-5320	126	14	(	(	PUNCT
ejpam-5320	126	15	y	y	PROPN
ejpam-5320	126	16	,	,	PUNCT
ejpam-5320	126	17	σ1	σ1	PROPN
ejpam-5320	126	18	,	,	PUNCT
ejpam-5320	126	19	σ2	σ2	NOUN
ejpam-5320	126	20	)	)	PUNCT
ejpam-5320	126	21	,	,	PUNCT
ejpam-5320	126	22	the	the	DET
ejpam-5320	126	23	following	follow	VERB
ejpam-5320	126	24	properties	property	NOUN
ejpam-5320	126	25	are	be	AUX
ejpam-5320	126	26	equivalent	equivalent	ADJ
ejpam-5320	126	27	:	:	PUNCT
ejpam-5320	126	28	(	(	PUNCT
ejpam-5320	126	29	1	1	X
ejpam-5320	126	30	)	)	PUNCT
ejpam-5320	126	31	f	f	PROPN
ejpam-5320	126	32	is	be	AUX
ejpam-5320	126	33	c-(τ1	c-(τ1	PROPN
ejpam-5320	126	34	,	,	PUNCT
ejpam-5320	126	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	126	36	at	at	ADP
ejpam-5320	126	37	x	x	X
ejpam-5320	126	38	∈	∈	PROPN
ejpam-5320	126	39	x	x	X
ejpam-5320	126	40	;	;	PUNCT
ejpam-5320	126	41	(	(	PUNCT
ejpam-5320	126	42	2	2	X
ejpam-5320	126	43	)	)	PUNCT
ejpam-5320	126	44	x	x	SYM
ejpam-5320	126	45	∈	∈	PRON
ejpam-5320	126	46	τ1τ2	τ1τ2	NOUN
ejpam-5320	126	47	-	-	NUM
ejpam-5320	126	48	int(f	int(f	X
ejpam-5320	126	49	−1(v	−1(v	NOUN
ejpam-5320	126	50	)	)	PUNCT
ejpam-5320	126	51	)	)	PUNCT
ejpam-5320	126	52	for	for	ADP
ejpam-5320	126	53	each	each	DET
ejpam-5320	126	54	σ1σ2	σ1σ2	VERB
ejpam-5320	126	55	-	-	ADJ
ejpam-5320	126	56	open	open	ADJ
ejpam-5320	126	57	set	set	NOUN
ejpam-5320	126	58	v	v	NOUN
ejpam-5320	126	59	of	of	ADP
ejpam-5320	126	60	y	y	NOUN
ejpam-5320	126	61	containing	contain	VERB
ejpam-5320	126	62	f(x	f(x	PROPN
ejpam-5320	126	63	)	)	PUNCT
ejpam-5320	126	64	and	and	CCONJ
ejpam-5320	126	65	having	have	VERB
ejpam-5320	126	66	σ1σ2	σ1σ2	NOUN
ejpam-5320	126	67	-	-	ADJ
ejpam-5320	126	68	compact	compact	ADJ
ejpam-5320	126	69	complement	complement	NOUN
ejpam-5320	126	70	;	;	PUNCT
ejpam-5320	126	71	(	(	PUNCT
ejpam-5320	126	72	3	3	X
ejpam-5320	126	73	)	)	PUNCT
ejpam-5320	126	74	x	x	SYM
ejpam-5320	126	75	∈	∈	PROPN
ejpam-5320	126	76	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5320	126	77	-	-	PUNCT
ejpam-5320	126	78	cl(b	cl(b	NOUN
ejpam-5320	126	79	)	)	PUNCT
ejpam-5320	126	80	)	)	PUNCT
ejpam-5320	126	81	for	for	ADP
ejpam-5320	126	82	each	each	DET
ejpam-5320	126	83	subset	subset	NOUN
ejpam-5320	126	84	b	b	PROPN
ejpam-5320	126	85	of	of	ADP
ejpam-5320	126	86	y	y	PROPN
ejpam-5320	126	87	having	have	VERB
ejpam-5320	126	88	the	the	DET
ejpam-5320	126	89	σ1σ2	σ1σ2	NUM
ejpam-5320	126	90	-	-	ADJ
ejpam-5320	126	91	compact	compact	ADJ
ejpam-5320	126	92	σ1σ2	σ1σ2	NOUN
ejpam-5320	126	93	-	-	NOUN
ejpam-5320	126	94	closure	closure	NOUN
ejpam-5320	126	95	such	such	ADJ
ejpam-5320	126	96	that	that	SCONJ
ejpam-5320	126	97	x	x	PUNCT
ejpam-5320	126	98	∈	∈	PROPN
ejpam-5320	126	99	τ1τ2	τ1τ2	NOUN
ejpam-5320	126	100	-	-	NOUN
ejpam-5320	126	101	cl(f	cl(f	NOUN
ejpam-5320	126	102	−1(b	−1(b	NOUN
ejpam-5320	126	103	)	)	PUNCT
ejpam-5320	126	104	)	)	PUNCT
ejpam-5320	126	105	;	;	PUNCT
ejpam-5320	126	106	(	(	PUNCT
ejpam-5320	126	107	4	4	X
ejpam-5320	126	108	)	)	PUNCT
ejpam-5320	126	109	x	x	SYM
ejpam-5320	126	110	∈	∈	PRON
ejpam-5320	126	111	τ1τ2	τ1τ2	NOUN
ejpam-5320	126	112	-	-	ADJ
ejpam-5320	126	113	int(f	int(f	NOUN
ejpam-5320	126	114	−1(b	−1(b	NOUN
ejpam-5320	126	115	)	)	PUNCT
ejpam-5320	126	116	)	)	PUNCT
ejpam-5320	126	117	for	for	ADP
ejpam-5320	126	118	each	each	DET
ejpam-5320	126	119	subset	subset	NOUN
ejpam-5320	126	120	b	b	PROPN
ejpam-5320	126	121	of	of	ADP
ejpam-5320	126	122	y	y	PRON
ejpam-5320	126	123	such	such	ADJ
ejpam-5320	126	124	that	that	SCONJ
ejpam-5320	126	125	y	y	PROPN
ejpam-5320	126	126	−	−	ADP
ejpam-5320	126	127	σ1σ2	σ1σ2	NUM
ejpam-5320	126	128	-	-	PUNCT
ejpam-5320	126	129	int(b	int(b	NOUN
ejpam-5320	126	130	)	)	PUNCT
ejpam-5320	126	131	is	be	AUX
ejpam-5320	126	132	σ1σ2compact	σ1σ2compact	PUNCT
ejpam-5320	126	133	and	and	CCONJ
ejpam-5320	126	134	x	x	PUNCT
ejpam-5320	126	135	∈	∈	PROPN
ejpam-5320	126	136	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5320	126	137	-	-	PUNCT
ejpam-5320	126	138	int(b	int(b	NOUN
ejpam-5320	126	139	)	)	PUNCT
ejpam-5320	126	140	)	)	PUNCT
ejpam-5320	126	141	.	.	PUNCT
ejpam-5320	127	1	theorem	theorem	NOUN
ejpam-5320	127	2	3	3	NUM
ejpam-5320	127	3	.	.	X
ejpam-5320	127	4	for	for	ADP
ejpam-5320	127	5	a	a	DET
ejpam-5320	127	6	multifunction	multifunction	NOUN
ejpam-5320	128	1	f	f	NOUN
ejpam-5320	128	2	:	:	PUNCT
ejpam-5320	128	3	(	(	PUNCT
ejpam-5320	128	4	x	x	NOUN
ejpam-5320	128	5	,	,	PUNCT
ejpam-5320	128	6	τ1	τ1	NOUN
ejpam-5320	128	7	,	,	PUNCT
ejpam-5320	128	8	τ2	τ2	NOUN
ejpam-5320	128	9	)	)	PUNCT
ejpam-5320	128	10	→	→	SYM
ejpam-5320	128	11	(	(	PUNCT
ejpam-5320	128	12	y	y	PROPN
ejpam-5320	128	13	,	,	PUNCT
ejpam-5320	128	14	σ1	σ1	PROPN
ejpam-5320	128	15	,	,	PUNCT
ejpam-5320	128	16	σ2	σ2	NOUN
ejpam-5320	128	17	)	)	PUNCT
ejpam-5320	128	18	,	,	PUNCT
ejpam-5320	128	19	the	the	DET
ejpam-5320	128	20	following	follow	VERB
ejpam-5320	128	21	properties	property	NOUN
ejpam-5320	128	22	are	be	AUX
ejpam-5320	128	23	equivalent	equivalent	ADJ
ejpam-5320	128	24	:	:	PUNCT
ejpam-5320	128	25	(	(	PUNCT
ejpam-5320	128	26	1	1	X
ejpam-5320	128	27	)	)	PUNCT
ejpam-5320	128	28	f	f	PROPN
ejpam-5320	128	29	is	be	AUX
ejpam-5320	128	30	upper	upper	ADJ
ejpam-5320	128	31	c-(τ1	c-(τ1	PROPN
ejpam-5320	128	32	,	,	PUNCT
ejpam-5320	128	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	128	34	;	;	PUNCT
ejpam-5320	128	35	(	(	PUNCT
ejpam-5320	128	36	2	2	NUM
ejpam-5320	128	37	)	)	PUNCT
ejpam-5320	128	38	f+(v	f+(v	NOUN
ejpam-5320	128	39	)	)	PUNCT
ejpam-5320	128	40	is	be	AUX
ejpam-5320	128	41	τ1τ2	τ1τ2	NOUN
ejpam-5320	128	42	-	-	ADJ
ejpam-5320	128	43	open	open	ADJ
ejpam-5320	128	44	in	in	ADP
ejpam-5320	128	45	x	x	PUNCT
ejpam-5320	128	46	for	for	ADP
ejpam-5320	128	47	each	each	DET
ejpam-5320	128	48	σ1σ2	σ1σ2	VERB
ejpam-5320	128	49	-	-	ADJ
ejpam-5320	128	50	open	open	ADJ
ejpam-5320	128	51	set	set	NOUN
ejpam-5320	128	52	v	v	NOUN
ejpam-5320	128	53	of	of	ADP
ejpam-5320	128	54	y	y	PROPN
ejpam-5320	128	55	having	have	VERB
ejpam-5320	128	56	σ1σ2	σ1σ2	NOUN
ejpam-5320	128	57	-	-	ADJ
ejpam-5320	128	58	compact	compact	ADJ
ejpam-5320	128	59	complement	complement	NOUN
ejpam-5320	128	60	;	;	PUNCT
ejpam-5320	128	61	(	(	PUNCT
ejpam-5320	128	62	3	3	X
ejpam-5320	128	63	)	)	PUNCT
ejpam-5320	128	64	f−(k	f−(k	PROPN
ejpam-5320	128	65	)	)	PUNCT
ejpam-5320	128	66	is	be	AUX
ejpam-5320	128	67	τ1τ2	τ1τ2	NOUN
ejpam-5320	128	68	-	-	ADJ
ejpam-5320	128	69	closed	closed	ADJ
ejpam-5320	128	70	in	in	ADP
ejpam-5320	128	71	x	x	PUNCT
ejpam-5320	128	72	for	for	ADP
ejpam-5320	128	73	every	every	DET
ejpam-5320	128	74	σ1σ2	σ1σ2	NUM
ejpam-5320	128	75	-	-	ADJ
ejpam-5320	128	76	compact	compact	ADJ
ejpam-5320	128	77	σ1σ2	σ1σ2	VERB
ejpam-5320	128	78	-	-	PUNCT
ejpam-5320	128	79	closed	close	VERB
ejpam-5320	128	80	set	set	NOUN
ejpam-5320	128	81	k	k	PROPN
ejpam-5320	128	82	of	of	ADP
ejpam-5320	128	83	y	y	PROPN
ejpam-5320	128	84	;	;	PUNCT
ejpam-5320	128	85	(	(	PUNCT
ejpam-5320	128	86	4	4	X
ejpam-5320	128	87	)	)	PUNCT
ejpam-5320	128	88	τ1τ2	τ1τ2	NOUN
ejpam-5320	128	89	-	-	NOUN
ejpam-5320	128	90	cl(f	cl(f	NOUN
ejpam-5320	128	91	−(b	−(b	PROPN
ejpam-5320	128	92	)	)	PUNCT
ejpam-5320	128	93	)	)	PUNCT
ejpam-5320	129	1	⊆	⊆	X
ejpam-5320	129	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	129	3	-	-	PUNCT
ejpam-5320	129	4	cl(b	cl(b	NOUN
ejpam-5320	129	5	)	)	PUNCT
ejpam-5320	129	6	)	)	PUNCT
ejpam-5320	130	1	for	for	ADP
ejpam-5320	130	2	every	every	DET
ejpam-5320	130	3	subset	subset	NOUN
ejpam-5320	130	4	b	b	PROPN
ejpam-5320	130	5	of	of	ADP
ejpam-5320	130	6	y	y	PROPN
ejpam-5320	130	7	having	have	VERB
ejpam-5320	130	8	the	the	DET
ejpam-5320	130	9	σ1σ2	σ1σ2	NUM
ejpam-5320	130	10	-	-	ADJ
ejpam-5320	130	11	compact	compact	ADJ
ejpam-5320	130	12	σ1σ2	σ1σ2	NOUN
ejpam-5320	130	13	-	-	NOUN
ejpam-5320	130	14	closure	closure	NOUN
ejpam-5320	130	15	;	;	PUNCT
ejpam-5320	130	16	(	(	PUNCT
ejpam-5320	130	17	5	5	X
ejpam-5320	130	18	)	)	PUNCT
ejpam-5320	130	19	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	130	20	-	-	PUNCT
ejpam-5320	130	21	int(b	int(b	NOUN
ejpam-5320	130	22	)	)	PUNCT
ejpam-5320	130	23	)	)	PUNCT
ejpam-5320	131	1	⊆	⊆	X
ejpam-5320	131	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	131	3	-	-	NUM
ejpam-5320	131	4	int(f	int(f	VERB
ejpam-5320	131	5	+	+	ADJ
ejpam-5320	131	6	(	(	PUNCT
ejpam-5320	131	7	b	b	NOUN
ejpam-5320	131	8	)	)	PUNCT
ejpam-5320	131	9	)	)	PUNCT
ejpam-5320	131	10	for	for	ADP
ejpam-5320	131	11	every	every	DET
ejpam-5320	131	12	subset	subset	NOUN
ejpam-5320	131	13	b	b	PROPN
ejpam-5320	131	14	of	of	ADP
ejpam-5320	131	15	y	y	PRON
ejpam-5320	131	16	such	such	ADJ
ejpam-5320	131	17	that	that	SCONJ
ejpam-5320	131	18	y−σ1σ2	y−σ1σ2	PROPN
ejpam-5320	131	19	-	-	PUNCT
ejpam-5320	131	20	int(b	int(b	NOUN
ejpam-5320	131	21	)	)	PUNCT
ejpam-5320	131	22	is	be	AUX
ejpam-5320	131	23	σ1σ2	σ1σ2	NOUN
ejpam-5320	131	24	-	-	ADJ
ejpam-5320	131	25	compact	compact	ADJ
ejpam-5320	131	26	.	.	PUNCT
ejpam-5320	132	1	j.	j.	PROPN
ejpam-5320	132	2	khampakdee	khampakdee	PROPN
ejpam-5320	132	3	,	,	PUNCT
ejpam-5320	132	4	s.	s.	PROPN
ejpam-5320	132	5	sompong	sompong	PROPN
ejpam-5320	132	6	,	,	PUNCT
ejpam-5320	132	7	c.	c.	PROPN
ejpam-5320	132	8	boonpok	boonpok	PROPN
ejpam-5320	132	9	/	/	SYM
ejpam-5320	132	10	eur	eur	PROPN
ejpam-5320	132	11	.	.	PUNCT
ejpam-5320	133	1	j.	j.	PROPN
ejpam-5320	133	2	pure	pure	PROPN
ejpam-5320	133	3	appl	appl	PROPN
ejpam-5320	133	4	.	.	PROPN
ejpam-5320	133	5	math	math	PROPN
ejpam-5320	133	6	,	,	PUNCT
ejpam-5320	133	7	17	17	NUM
ejpam-5320	133	8	(	(	PUNCT
ejpam-5320	133	9	3	3	NUM
ejpam-5320	133	10	)	)	PUNCT
ejpam-5320	133	11	(	(	PUNCT
ejpam-5320	133	12	2024	2024	NUM
ejpam-5320	133	13	)	)	PUNCT
ejpam-5320	133	14	,	,	PUNCT
ejpam-5320	133	15	2288	2288	NUM
ejpam-5320	133	16	-	-	SYM
ejpam-5320	133	17	2298	2298	NUM
ejpam-5320	133	18	2293	2293	NUM
ejpam-5320	133	19	proof	proof	NOUN
ejpam-5320	133	20	.	.	PUNCT
ejpam-5320	134	1	(	(	PUNCT
ejpam-5320	134	2	1	1	X
ejpam-5320	134	3	)	)	PUNCT
ejpam-5320	134	4	⇒	⇒	NOUN
ejpam-5320	134	5	(	(	PUNCT
ejpam-5320	134	6	2	2	NUM
ejpam-5320	134	7	):	):	PUNCT
ejpam-5320	134	8	let	let	VERB
ejpam-5320	134	9	v	v	PART
ejpam-5320	134	10	be	be	AUX
ejpam-5320	134	11	any	any	DET
ejpam-5320	134	12	σ1σ2	σ1σ2	NOUN
ejpam-5320	134	13	-	-	ADJ
ejpam-5320	134	14	open	open	ADJ
ejpam-5320	134	15	set	set	NOUN
ejpam-5320	134	16	of	of	ADP
ejpam-5320	134	17	y	y	PROPN
ejpam-5320	134	18	containing	contain	VERB
ejpam-5320	134	19	f	f	PROPN
ejpam-5320	134	20	(	(	PUNCT
ejpam-5320	134	21	x	x	NOUN
ejpam-5320	134	22	)	)	PUNCT
ejpam-5320	134	23	and	and	CCONJ
ejpam-5320	134	24	having	have	VERB
ejpam-5320	134	25	σ1σ2	σ1σ2	NOUN
ejpam-5320	134	26	-	-	ADJ
ejpam-5320	134	27	compact	compact	ADJ
ejpam-5320	134	28	complement	complement	NOUN
ejpam-5320	134	29	and	and	CCONJ
ejpam-5320	134	30	x	x	PUNCT
ejpam-5320	134	31	∈	∈	PROPN
ejpam-5320	134	32	f+(v	f+(v	NOUN
ejpam-5320	134	33	)	)	PUNCT
ejpam-5320	134	34	.	.	PUNCT
ejpam-5320	135	1	then	then	ADV
ejpam-5320	135	2	,	,	PUNCT
ejpam-5320	135	3	we	we	PRON
ejpam-5320	135	4	have	have	VERB
ejpam-5320	135	5	f	f	PROPN
ejpam-5320	135	6	(	(	PUNCT
ejpam-5320	135	7	x	x	NOUN
ejpam-5320	135	8	)	)	PUNCT
ejpam-5320	135	9	⊆	⊆	NUM
ejpam-5320	135	10	v	v	NOUN
ejpam-5320	135	11	.	.	PUNCT
ejpam-5320	136	1	by	by	ADP
ejpam-5320	136	2	theorem	theorem	NOUN
ejpam-5320	136	3	1	1	NUM
ejpam-5320	136	4	,	,	PUNCT
ejpam-5320	136	5	x	x	SYM
ejpam-5320	136	6	∈	∈	PRON
ejpam-5320	136	7	τ1τ2	τ1τ2	PUNCT
ejpam-5320	136	8	-	-	NUM
ejpam-5320	136	9	int(f	int(f	VERB
ejpam-5320	136	10	+	+	ADJ
ejpam-5320	136	11	(	(	PUNCT
ejpam-5320	136	12	v	v	NOUN
ejpam-5320	136	13	)	)	PUNCT
ejpam-5320	136	14	)	)	PUNCT
ejpam-5320	136	15	.	.	PUNCT
ejpam-5320	137	1	thus	thus	ADV
ejpam-5320	137	2	,	,	PUNCT
ejpam-5320	137	3	f+(v	f+(v	PROPN
ejpam-5320	137	4	)	)	PUNCT
ejpam-5320	138	1	⊆	⊆	X
ejpam-5320	138	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	138	3	-	-	NUM
ejpam-5320	138	4	int(f	int(f	VERB
ejpam-5320	138	5	+	+	ADJ
ejpam-5320	138	6	(	(	PUNCT
ejpam-5320	138	7	v	v	NOUN
ejpam-5320	138	8	)	)	PUNCT
ejpam-5320	138	9	)	)	PUNCT
ejpam-5320	138	10	and	and	CCONJ
ejpam-5320	138	11	hence	hence	ADV
ejpam-5320	138	12	f+(v	f+(v	PROPN
ejpam-5320	138	13	)	)	PUNCT
ejpam-5320	138	14	is	be	AUX
ejpam-5320	138	15	τ1τ2	τ1τ2	NOUN
ejpam-5320	138	16	-	-	ADJ
ejpam-5320	138	17	open	open	ADJ
ejpam-5320	138	18	in	in	ADP
ejpam-5320	138	19	x.	x.	NOUN
ejpam-5320	138	20	(	(	PUNCT
ejpam-5320	138	21	2	2	NUM
ejpam-5320	138	22	)	)	PUNCT
ejpam-5320	138	23	⇒	⇒	NOUN
ejpam-5320	138	24	(	(	PUNCT
ejpam-5320	138	25	3	3	NUM
ejpam-5320	138	26	):	):	PUNCT
ejpam-5320	138	27	the	the	DET
ejpam-5320	138	28	proof	proof	NOUN
ejpam-5320	138	29	follows	follow	VERB
ejpam-5320	138	30	immediately	immediately	ADV
ejpam-5320	138	31	from	from	ADP
ejpam-5320	138	32	the	the	DET
ejpam-5320	138	33	fact	fact	NOUN
ejpam-5320	138	34	that	that	SCONJ
ejpam-5320	138	35	f+(y	f+(y	PROPN
ejpam-5320	138	36	−b	−b	ADJ
ejpam-5320	138	37	)	)	PUNCT
ejpam-5320	138	38	=	=	SYM
ejpam-5320	138	39	y	y	PROPN
ejpam-5320	138	40	−f−(b	−f−(b	PROPN
ejpam-5320	138	41	)	)	PUNCT
ejpam-5320	138	42	for	for	ADP
ejpam-5320	138	43	every	every	DET
ejpam-5320	138	44	subset	subset	NOUN
ejpam-5320	138	45	b	b	PROPN
ejpam-5320	138	46	of	of	ADP
ejpam-5320	138	47	y	y	PROPN
ejpam-5320	138	48	.	.	PUNCT
ejpam-5320	139	1	(	(	PUNCT
ejpam-5320	139	2	3	3	X
ejpam-5320	139	3	)	)	PUNCT
ejpam-5320	139	4	⇒	⇒	NOUN
ejpam-5320	139	5	(	(	PUNCT
ejpam-5320	139	6	4	4	NUM
ejpam-5320	139	7	):	):	PUNCT
ejpam-5320	139	8	let	let	VERB
ejpam-5320	139	9	b	b	X
ejpam-5320	139	10	be	be	AUX
ejpam-5320	139	11	any	any	DET
ejpam-5320	139	12	subset	subset	NOUN
ejpam-5320	139	13	of	of	ADP
ejpam-5320	139	14	y	y	PROPN
ejpam-5320	139	15	having	have	VERB
ejpam-5320	139	16	the	the	DET
ejpam-5320	139	17	σ1σ2	σ1σ2	NUM
ejpam-5320	139	18	-	-	ADJ
ejpam-5320	139	19	compact	compact	ADJ
ejpam-5320	139	20	σ1σ2	σ1σ2	NOUN
ejpam-5320	139	21	-	-	NOUN
ejpam-5320	139	22	closure	closure	NOUN
ejpam-5320	139	23	.	.	PUNCT
ejpam-5320	140	1	then	then	ADV
ejpam-5320	140	2	,	,	PUNCT
ejpam-5320	140	3	σ1σ2	σ1σ2	NOUN
ejpam-5320	140	4	-	-	NOUN
ejpam-5320	140	5	cl(b	cl(b	NOUN
ejpam-5320	140	6	)	)	PUNCT
ejpam-5320	140	7	is	be	AUX
ejpam-5320	140	8	σ1σ2	σ1σ2	NOUN
ejpam-5320	140	9	-	-	ADJ
ejpam-5320	140	10	closed	closed	ADJ
ejpam-5320	140	11	and	and	CCONJ
ejpam-5320	140	12	by	by	ADP
ejpam-5320	140	13	(	(	PUNCT
ejpam-5320	140	14	3	3	NUM
ejpam-5320	140	15	)	)	PUNCT
ejpam-5320	140	16	,	,	PUNCT
ejpam-5320	140	17	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	140	18	-	-	PUNCT
ejpam-5320	140	19	cl(b	cl(b	NOUN
ejpam-5320	140	20	)	)	PUNCT
ejpam-5320	140	21	)	)	PUNCT
ejpam-5320	141	1	is	be	AUX
ejpam-5320	141	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	141	3	-	-	ADJ
ejpam-5320	141	4	closed	closed	ADJ
ejpam-5320	141	5	in	in	ADP
ejpam-5320	141	6	x.	x.	NOUN
ejpam-5320	141	7	thus	thus	ADV
ejpam-5320	141	8	,	,	PUNCT
ejpam-5320	141	9	f−(b	f−(b	PROPN
ejpam-5320	141	10	)	)	PUNCT
ejpam-5320	141	11	⊆	⊆	NUM
ejpam-5320	141	12	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	141	13	-	-	PUNCT
ejpam-5320	141	14	cl(b	cl(b	NOUN
ejpam-5320	141	15	)	)	PUNCT
ejpam-5320	141	16	)	)	PUNCT
ejpam-5320	142	1	=	=	PUNCT
ejpam-5320	142	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	142	3	-	-	ADJ
ejpam-5320	142	4	cl(f	cl(f	NOUN
ejpam-5320	142	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5320	142	6	-	-	NOUN
ejpam-5320	142	7	cl(b	cl(b	NOUN
ejpam-5320	142	8	)	)	PUNCT
ejpam-5320	142	9	)	)	PUNCT
ejpam-5320	142	10	)	)	PUNCT
ejpam-5320	142	11	and	and	CCONJ
ejpam-5320	142	12	hence	hence	ADV
ejpam-5320	142	13	τ1τ2	τ1τ2	NOUN
ejpam-5320	142	14	-	-	PROPN
ejpam-5320	142	15	cl(f	cl(f	NOUN
ejpam-5320	142	16	−(b	−(b	PROPN
ejpam-5320	142	17	)	)	PUNCT
ejpam-5320	142	18	)	)	PUNCT
ejpam-5320	143	1	⊆	⊆	X
ejpam-5320	143	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5320	143	3	-	-	PUNCT
ejpam-5320	143	4	cl(b	cl(b	NOUN
ejpam-5320	143	5	)	)	PUNCT
ejpam-5320	143	6	)	)	PUNCT
ejpam-5320	143	7	.	.	PUNCT
ejpam-5320	144	1	(	(	PUNCT
ejpam-5320	144	2	4	4	X
ejpam-5320	144	3	)	)	PUNCT
ejpam-5320	144	4	⇒	⇒	NOUN
ejpam-5320	144	5	(	(	PUNCT
ejpam-5320	144	6	5	5	NUM
ejpam-5320	144	7	):	):	PUNCT
ejpam-5320	144	8	let	let	VERB
ejpam-5320	144	9	b	b	X
ejpam-5320	144	10	be	be	AUX
ejpam-5320	144	11	any	any	DET
ejpam-5320	144	12	subset	subset	NOUN
ejpam-5320	144	13	of	of	ADP
ejpam-5320	144	14	y	y	PRON
ejpam-5320	144	15	such	such	ADJ
ejpam-5320	144	16	that	that	SCONJ
ejpam-5320	144	17	y	y	PROPN
ejpam-5320	144	18	−	−	ADP
ejpam-5320	144	19	σ1σ2	σ1σ2	NUM
ejpam-5320	144	20	-	-	PUNCT
ejpam-5320	144	21	int(b	int(b	NOUN
ejpam-5320	144	22	)	)	PUNCT
ejpam-5320	144	23	is	be	AUX
ejpam-5320	144	24	σ1σ2	σ1σ2	NOUN
ejpam-5320	144	25	-	-	ADJ
ejpam-5320	144	26	compact	compact	ADJ
ejpam-5320	144	27	.	.	PUNCT
ejpam-5320	145	1	by	by	ADP
ejpam-5320	145	2	(	(	PUNCT
ejpam-5320	145	3	4	4	NUM
ejpam-5320	145	4	)	)	PUNCT
ejpam-5320	145	5	,	,	PUNCT
ejpam-5320	145	6	we	we	PRON
ejpam-5320	145	7	have	have	VERB
ejpam-5320	145	8	x	x	INTJ
ejpam-5320	145	9	−	−	ADP
ejpam-5320	145	10	τ1τ2	τ1τ2	NOUN
ejpam-5320	145	11	-	-	NUM
ejpam-5320	145	12	int(f	int(f	VERB
ejpam-5320	145	13	+	+	ADJ
ejpam-5320	145	14	(	(	PUNCT
ejpam-5320	145	15	b	b	NOUN
ejpam-5320	145	16	)	)	PUNCT
ejpam-5320	145	17	)	)	PUNCT
ejpam-5320	146	1	=	=	PUNCT
ejpam-5320	146	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	146	3	-	-	NOUN
ejpam-5320	146	4	cl(x	cl(x	SYM
ejpam-5320	146	5	−	−	PROPN
ejpam-5320	146	6	f+(b	f+(b	NOUN
ejpam-5320	146	7	)	)	PUNCT
ejpam-5320	146	8	)	)	PUNCT
ejpam-5320	147	1	=	=	PUNCT
ejpam-5320	148	1	τ1τ2	τ1τ2	NOUN
ejpam-5320	148	2	-	-	PROPN
ejpam-5320	148	3	cl(f	cl(f	NOUN
ejpam-5320	148	4	−(y	−(y	NOUN
ejpam-5320	148	5	−b	−b	NOUN
ejpam-5320	148	6	)	)	PUNCT
ejpam-5320	148	7	)	)	PUNCT
ejpam-5320	149	1	⊆	⊆	X
ejpam-5320	149	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	149	3	-	-	NOUN
ejpam-5320	149	4	cl(f	cl(f	NOUN
ejpam-5320	149	5	−(y	−(y	NOUN
ejpam-5320	149	6	−	−	NOUN
ejpam-5320	149	7	σ1σ2	σ1σ2	SYM
ejpam-5320	149	8	-	-	PUNCT
ejpam-5320	149	9	int(b	int(b	NOUN
ejpam-5320	149	10	)	)	PUNCT
ejpam-5320	149	11	)	)	PUNCT
ejpam-5320	149	12	)	)	PUNCT
ejpam-5320	149	13	⊆	⊆	NUM
ejpam-5320	149	14	f−(y	f−(y	NOUN
ejpam-5320	149	15	−	−	NUM
ejpam-5320	149	16	σ1σ2	σ1σ2	NOUN
ejpam-5320	149	17	-	-	PUNCT
ejpam-5320	149	18	int(b	int(b	NOUN
ejpam-5320	149	19	)	)	PUNCT
ejpam-5320	149	20	)	)	PUNCT
ejpam-5320	149	21	=	=	PUNCT
ejpam-5320	150	1	x	x	X
ejpam-5320	150	2	−	−	ADP
ejpam-5320	150	3	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	150	4	-	-	PUNCT
ejpam-5320	150	5	int(b	int(b	NOUN
ejpam-5320	150	6	)	)	PUNCT
ejpam-5320	150	7	)	)	PUNCT
ejpam-5320	150	8	.	.	PUNCT
ejpam-5320	151	1	thus	thus	ADV
ejpam-5320	151	2	,	,	PUNCT
ejpam-5320	151	3	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	151	4	-	-	PUNCT
ejpam-5320	151	5	int(b	int(b	NOUN
ejpam-5320	151	6	)	)	PUNCT
ejpam-5320	151	7	)	)	PUNCT
ejpam-5320	152	1	⊆	⊆	X
ejpam-5320	152	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	152	3	-	-	NUM
ejpam-5320	152	4	int(f	int(f	VERB
ejpam-5320	152	5	+	+	ADJ
ejpam-5320	152	6	(	(	PUNCT
ejpam-5320	152	7	b	b	NOUN
ejpam-5320	152	8	)	)	PUNCT
ejpam-5320	152	9	)	)	PUNCT
ejpam-5320	152	10	.	.	PUNCT
ejpam-5320	153	1	(	(	PUNCT
ejpam-5320	153	2	5	5	X
ejpam-5320	153	3	)	)	PUNCT
ejpam-5320	153	4	⇒	⇒	NOUN
ejpam-5320	153	5	(	(	PUNCT
ejpam-5320	153	6	1	1	NUM
ejpam-5320	153	7	):	):	PUNCT
ejpam-5320	153	8	let	let	VERB
ejpam-5320	153	9	x	x	PUNCT
ejpam-5320	153	10	∈	∈	PROPN
ejpam-5320	153	11	x	x	X
ejpam-5320	153	12	and	and	CCONJ
ejpam-5320	153	13	v	v	X
ejpam-5320	153	14	be	be	AUX
ejpam-5320	153	15	any	any	DET
ejpam-5320	153	16	σ1σ2	σ1σ2	NOUN
ejpam-5320	153	17	-	-	ADJ
ejpam-5320	153	18	open	open	ADJ
ejpam-5320	153	19	set	set	NOUN
ejpam-5320	153	20	of	of	ADP
ejpam-5320	153	21	y	y	PROPN
ejpam-5320	153	22	containing	contain	VERB
ejpam-5320	153	23	f	f	PROPN
ejpam-5320	153	24	(	(	PUNCT
ejpam-5320	153	25	x	x	NOUN
ejpam-5320	153	26	)	)	PUNCT
ejpam-5320	153	27	and	and	CCONJ
ejpam-5320	153	28	having	have	VERB
ejpam-5320	153	29	σ1σ2	σ1σ2	NOUN
ejpam-5320	153	30	-	-	ADJ
ejpam-5320	153	31	compact	compact	ADJ
ejpam-5320	153	32	complement	complement	NOUN
ejpam-5320	153	33	.	.	PUNCT
ejpam-5320	154	1	then	then	ADV
ejpam-5320	154	2	,	,	PUNCT
ejpam-5320	154	3	x	x	X
ejpam-5320	154	4	∈	∈	NOUN
ejpam-5320	154	5	f+(v	f+(v	NOUN
ejpam-5320	154	6	)	)	PUNCT
ejpam-5320	155	1	=	=	SYM
ejpam-5320	155	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	155	3	-	-	PUNCT
ejpam-5320	155	4	int(v	int(v	NOUN
ejpam-5320	155	5	)	)	PUNCT
ejpam-5320	155	6	)	)	PUNCT
ejpam-5320	156	1	⊆	⊆	X
ejpam-5320	156	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	156	3	-	-	NUM
ejpam-5320	156	4	int(f	int(f	VERB
ejpam-5320	156	5	+	+	ADJ
ejpam-5320	156	6	(	(	PUNCT
ejpam-5320	156	7	v	v	NOUN
ejpam-5320	156	8	)	)	PUNCT
ejpam-5320	156	9	)	)	PUNCT
ejpam-5320	156	10	.	.	PUNCT
ejpam-5320	157	1	by	by	ADP
ejpam-5320	157	2	theorem	theorem	NOUN
ejpam-5320	157	3	1	1	NUM
ejpam-5320	157	4	,	,	PUNCT
ejpam-5320	157	5	f	f	PROPN
ejpam-5320	157	6	is	be	AUX
ejpam-5320	157	7	upper	upper	ADJ
ejpam-5320	157	8	c-(τ1	c-(τ1	PROPN
ejpam-5320	157	9	,	,	PUNCT
ejpam-5320	157	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	157	11	at	at	ADP
ejpam-5320	157	12	x.	x.	NOUN
ejpam-5320	157	13	this	this	PRON
ejpam-5320	157	14	shows	show	VERB
ejpam-5320	157	15	that	that	SCONJ
ejpam-5320	157	16	f	f	PROPN
ejpam-5320	157	17	is	be	AUX
ejpam-5320	157	18	upper	upper	ADJ
ejpam-5320	157	19	c-(τ1	c-(τ1	PROPN
ejpam-5320	157	20	,	,	PUNCT
ejpam-5320	157	21	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	157	22	.	.	PUNCT
ejpam-5320	158	1	theorem	theorem	VERB
ejpam-5320	158	2	4	4	NUM
ejpam-5320	158	3	.	.	X
ejpam-5320	158	4	for	for	ADP
ejpam-5320	158	5	a	a	DET
ejpam-5320	158	6	multifunction	multifunction	NOUN
ejpam-5320	159	1	f	f	NOUN
ejpam-5320	159	2	:	:	PUNCT
ejpam-5320	159	3	(	(	PUNCT
ejpam-5320	159	4	x	x	NOUN
ejpam-5320	159	5	,	,	PUNCT
ejpam-5320	159	6	τ1	τ1	NOUN
ejpam-5320	159	7	,	,	PUNCT
ejpam-5320	159	8	τ2	τ2	NOUN
ejpam-5320	159	9	)	)	PUNCT
ejpam-5320	159	10	→	→	SYM
ejpam-5320	159	11	(	(	PUNCT
ejpam-5320	159	12	y	y	PROPN
ejpam-5320	159	13	,	,	PUNCT
ejpam-5320	159	14	σ1	σ1	PROPN
ejpam-5320	159	15	,	,	PUNCT
ejpam-5320	159	16	σ2	σ2	NOUN
ejpam-5320	159	17	)	)	PUNCT
ejpam-5320	159	18	,	,	PUNCT
ejpam-5320	159	19	the	the	DET
ejpam-5320	159	20	following	follow	VERB
ejpam-5320	159	21	properties	property	NOUN
ejpam-5320	159	22	are	be	AUX
ejpam-5320	159	23	equivalent	equivalent	ADJ
ejpam-5320	159	24	:	:	PUNCT
ejpam-5320	159	25	(	(	PUNCT
ejpam-5320	159	26	1	1	X
ejpam-5320	159	27	)	)	PUNCT
ejpam-5320	159	28	f	f	PROPN
ejpam-5320	159	29	is	be	AUX
ejpam-5320	159	30	lower	low	ADJ
ejpam-5320	159	31	c-(τ1	c-(τ1	NOUN
ejpam-5320	159	32	,	,	PUNCT
ejpam-5320	159	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	159	34	;	;	PUNCT
ejpam-5320	159	35	(	(	PUNCT
ejpam-5320	159	36	2	2	X
ejpam-5320	159	37	)	)	PUNCT
ejpam-5320	159	38	f−(v	f−(v	NOUN
ejpam-5320	159	39	)	)	PUNCT
ejpam-5320	159	40	is	be	AUX
ejpam-5320	159	41	τ1τ2	τ1τ2	NOUN
ejpam-5320	159	42	-	-	ADJ
ejpam-5320	159	43	open	open	ADJ
ejpam-5320	159	44	in	in	ADP
ejpam-5320	159	45	x	x	PUNCT
ejpam-5320	159	46	for	for	ADP
ejpam-5320	159	47	each	each	DET
ejpam-5320	159	48	σ1σ2	σ1σ2	VERB
ejpam-5320	159	49	-	-	ADJ
ejpam-5320	159	50	open	open	ADJ
ejpam-5320	159	51	set	set	NOUN
ejpam-5320	159	52	v	v	NOUN
ejpam-5320	159	53	of	of	ADP
ejpam-5320	159	54	y	y	PROPN
ejpam-5320	159	55	having	have	VERB
ejpam-5320	159	56	σ1σ2	σ1σ2	NOUN
ejpam-5320	159	57	-	-	ADJ
ejpam-5320	159	58	compact	compact	ADJ
ejpam-5320	159	59	complement	complement	NOUN
ejpam-5320	159	60	;	;	PUNCT
ejpam-5320	159	61	(	(	PUNCT
ejpam-5320	159	62	3	3	X
ejpam-5320	159	63	)	)	PUNCT
ejpam-5320	159	64	f+(k	f+(k	NOUN
ejpam-5320	159	65	)	)	PUNCT
ejpam-5320	159	66	is	be	AUX
ejpam-5320	159	67	τ1τ2	τ1τ2	NOUN
ejpam-5320	159	68	-	-	ADJ
ejpam-5320	159	69	open	open	ADJ
ejpam-5320	159	70	in	in	ADP
ejpam-5320	159	71	x	x	PUNCT
ejpam-5320	159	72	for	for	ADP
ejpam-5320	159	73	every	every	DET
ejpam-5320	159	74	σ1σ2	σ1σ2	NUM
ejpam-5320	159	75	-	-	ADJ
ejpam-5320	159	76	compact	compact	ADJ
ejpam-5320	159	77	σ1σ2	σ1σ2	VERB
ejpam-5320	159	78	-	-	PUNCT
ejpam-5320	159	79	closed	close	VERB
ejpam-5320	159	80	set	set	NOUN
ejpam-5320	159	81	k	k	PROPN
ejpam-5320	159	82	of	of	ADP
ejpam-5320	159	83	y	y	PROPN
ejpam-5320	159	84	;	;	PUNCT
ejpam-5320	159	85	(	(	PUNCT
ejpam-5320	159	86	4	4	X
ejpam-5320	159	87	)	)	PUNCT
ejpam-5320	159	88	τ1τ2	τ1τ2	NOUN
ejpam-5320	159	89	-	-	NOUN
ejpam-5320	159	90	cl(f	cl(f	NOUN
ejpam-5320	159	91	+	+	NOUN
ejpam-5320	159	92	(	(	PUNCT
ejpam-5320	159	93	b	b	NOUN
ejpam-5320	159	94	)	)	PUNCT
ejpam-5320	159	95	)	)	PUNCT
ejpam-5320	159	96	⊆	⊆	NUM
ejpam-5320	159	97	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5320	159	98	-	-	PUNCT
ejpam-5320	159	99	cl(b	cl(b	NOUN
ejpam-5320	159	100	)	)	PUNCT
ejpam-5320	159	101	)	)	PUNCT
ejpam-5320	159	102	for	for	ADP
ejpam-5320	159	103	every	every	DET
ejpam-5320	159	104	subset	subset	NOUN
ejpam-5320	159	105	b	b	PROPN
ejpam-5320	159	106	of	of	ADP
ejpam-5320	159	107	y	y	PROPN
ejpam-5320	159	108	having	have	VERB
ejpam-5320	159	109	the	the	DET
ejpam-5320	159	110	σ1σ2	σ1σ2	NUM
ejpam-5320	159	111	-	-	ADJ
ejpam-5320	159	112	compact	compact	ADJ
ejpam-5320	159	113	σ1σ2	σ1σ2	NOUN
ejpam-5320	159	114	-	-	NOUN
ejpam-5320	159	115	closure	closure	NOUN
ejpam-5320	159	116	;	;	PUNCT
ejpam-5320	159	117	(	(	PUNCT
ejpam-5320	159	118	5	5	X
ejpam-5320	159	119	)	)	PUNCT
ejpam-5320	159	120	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5320	159	121	-	-	PUNCT
ejpam-5320	159	122	int(b	int(b	NOUN
ejpam-5320	159	123	)	)	PUNCT
ejpam-5320	159	124	)	)	PUNCT
ejpam-5320	160	1	⊆	⊆	X
ejpam-5320	160	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	160	3	-	-	NUM
ejpam-5320	160	4	int(f	int(f	VERB
ejpam-5320	160	5	−(b	−(b	NOUN
ejpam-5320	160	6	)	)	PUNCT
ejpam-5320	160	7	)	)	PUNCT
ejpam-5320	160	8	for	for	ADP
ejpam-5320	160	9	every	every	DET
ejpam-5320	160	10	subset	subset	NOUN
ejpam-5320	160	11	b	b	PROPN
ejpam-5320	160	12	of	of	ADP
ejpam-5320	160	13	y	y	PRON
ejpam-5320	160	14	such	such	ADJ
ejpam-5320	160	15	that	that	SCONJ
ejpam-5320	160	16	y−σ1σ2	y−σ1σ2	PROPN
ejpam-5320	160	17	-	-	PUNCT
ejpam-5320	160	18	int(b	int(b	NOUN
ejpam-5320	160	19	)	)	PUNCT
ejpam-5320	160	20	is	be	AUX
ejpam-5320	160	21	σ1σ2	σ1σ2	NOUN
ejpam-5320	160	22	-	-	ADJ
ejpam-5320	160	23	compact	compact	ADJ
ejpam-5320	160	24	.	.	PUNCT
ejpam-5320	161	1	proof	proof	NOUN
ejpam-5320	161	2	.	.	PUNCT
ejpam-5320	162	1	the	the	DET
ejpam-5320	162	2	proof	proof	NOUN
ejpam-5320	162	3	is	be	AUX
ejpam-5320	162	4	similar	similar	ADJ
ejpam-5320	162	5	to	to	ADP
ejpam-5320	162	6	that	that	PRON
ejpam-5320	162	7	of	of	ADP
ejpam-5320	162	8	theorem	theorem	NOUN
ejpam-5320	162	9	3	3	NUM
ejpam-5320	162	10	.	.	PUNCT
ejpam-5320	162	11	j.	j.	PROPN
ejpam-5320	162	12	khampakdee	khampakdee	PROPN
ejpam-5320	162	13	,	,	PUNCT
ejpam-5320	162	14	s.	s.	PROPN
ejpam-5320	162	15	sompong	sompong	PROPN
ejpam-5320	162	16	,	,	PUNCT
ejpam-5320	162	17	c.	c.	PROPN
ejpam-5320	162	18	boonpok	boonpok	PROPN
ejpam-5320	162	19	/	/	SYM
ejpam-5320	162	20	eur	eur	PROPN
ejpam-5320	162	21	.	.	PUNCT
ejpam-5320	163	1	j.	j.	PROPN
ejpam-5320	163	2	pure	pure	PROPN
ejpam-5320	163	3	appl	appl	PROPN
ejpam-5320	163	4	.	.	PROPN
ejpam-5320	163	5	math	math	PROPN
ejpam-5320	163	6	,	,	PUNCT
ejpam-5320	163	7	17	17	NUM
ejpam-5320	163	8	(	(	PUNCT
ejpam-5320	163	9	3	3	NUM
ejpam-5320	163	10	)	)	PUNCT
ejpam-5320	163	11	(	(	PUNCT
ejpam-5320	163	12	2024	2024	NUM
ejpam-5320	163	13	)	)	PUNCT
ejpam-5320	163	14	,	,	PUNCT
ejpam-5320	163	15	2288	2288	NUM
ejpam-5320	163	16	-	-	SYM
ejpam-5320	163	17	2298	2298	NUM
ejpam-5320	163	18	2294	2294	NUM
ejpam-5320	163	19	corollary	corollary	NOUN
ejpam-5320	163	20	2	2	NUM
ejpam-5320	163	21	.	.	PUNCT
ejpam-5320	164	1	for	for	ADP
ejpam-5320	164	2	a	a	DET
ejpam-5320	164	3	function	function	NOUN
ejpam-5320	164	4	f	f	NOUN
ejpam-5320	164	5	:	:	PUNCT
ejpam-5320	164	6	(	(	PUNCT
ejpam-5320	164	7	x	x	NOUN
ejpam-5320	164	8	,	,	PUNCT
ejpam-5320	164	9	τ1	τ1	NOUN
ejpam-5320	164	10	,	,	PUNCT
ejpam-5320	164	11	τ2	τ2	NOUN
ejpam-5320	164	12	)	)	PUNCT
ejpam-5320	164	13	→	→	SYM
ejpam-5320	164	14	(	(	PUNCT
ejpam-5320	164	15	y	y	PROPN
ejpam-5320	164	16	,	,	PUNCT
ejpam-5320	164	17	σ1	σ1	PROPN
ejpam-5320	164	18	,	,	PUNCT
ejpam-5320	164	19	σ2	σ2	NOUN
ejpam-5320	164	20	)	)	PUNCT
ejpam-5320	164	21	,	,	PUNCT
ejpam-5320	164	22	the	the	DET
ejpam-5320	164	23	following	follow	VERB
ejpam-5320	164	24	properties	property	NOUN
ejpam-5320	164	25	are	be	AUX
ejpam-5320	164	26	equivalent	equivalent	ADJ
ejpam-5320	164	27	:	:	PUNCT
ejpam-5320	164	28	(	(	PUNCT
ejpam-5320	164	29	1	1	X
ejpam-5320	164	30	)	)	PUNCT
ejpam-5320	164	31	f	f	PROPN
ejpam-5320	164	32	is	be	AUX
ejpam-5320	164	33	c-(τ1	c-(τ1	PROPN
ejpam-5320	164	34	,	,	PUNCT
ejpam-5320	164	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	164	36	;	;	PUNCT
ejpam-5320	164	37	(	(	PUNCT
ejpam-5320	164	38	2	2	X
ejpam-5320	164	39	)	)	PUNCT
ejpam-5320	164	40	f−1(v	f−1(v	NOUN
ejpam-5320	164	41	)	)	PUNCT
ejpam-5320	164	42	is	be	AUX
ejpam-5320	164	43	τ1τ2	τ1τ2	NOUN
ejpam-5320	164	44	-	-	ADJ
ejpam-5320	164	45	open	open	ADJ
ejpam-5320	164	46	in	in	ADP
ejpam-5320	164	47	x	x	PUNCT
ejpam-5320	164	48	for	for	ADP
ejpam-5320	164	49	each	each	DET
ejpam-5320	164	50	σ1σ2	σ1σ2	VERB
ejpam-5320	164	51	-	-	ADJ
ejpam-5320	164	52	open	open	ADJ
ejpam-5320	164	53	set	set	NOUN
ejpam-5320	164	54	v	v	NOUN
ejpam-5320	164	55	of	of	ADP
ejpam-5320	164	56	y	y	PROPN
ejpam-5320	164	57	having	have	VERB
ejpam-5320	164	58	σ1σ2	σ1σ2	NOUN
ejpam-5320	164	59	-	-	ADJ
ejpam-5320	164	60	compact	compact	ADJ
ejpam-5320	164	61	complement	complement	NOUN
ejpam-5320	164	62	;	;	PUNCT
ejpam-5320	164	63	(	(	PUNCT
ejpam-5320	164	64	3	3	X
ejpam-5320	164	65	)	)	PUNCT
ejpam-5320	164	66	f−1(k	f−1(k	PROPN
ejpam-5320	164	67	)	)	PUNCT
ejpam-5320	164	68	is	be	AUX
ejpam-5320	164	69	τ1τ2	τ1τ2	NOUN
ejpam-5320	164	70	-	-	ADJ
ejpam-5320	164	71	open	open	ADJ
ejpam-5320	164	72	in	in	ADP
ejpam-5320	164	73	x	x	PUNCT
ejpam-5320	164	74	for	for	ADP
ejpam-5320	164	75	every	every	DET
ejpam-5320	164	76	σ1σ2	σ1σ2	NUM
ejpam-5320	164	77	-	-	ADJ
ejpam-5320	164	78	compact	compact	ADJ
ejpam-5320	164	79	σ1σ2	σ1σ2	VERB
ejpam-5320	164	80	-	-	PUNCT
ejpam-5320	164	81	closed	close	VERB
ejpam-5320	164	82	set	set	NOUN
ejpam-5320	164	83	k	k	PROPN
ejpam-5320	164	84	of	of	ADP
ejpam-5320	164	85	y	y	PROPN
ejpam-5320	164	86	;	;	PUNCT
ejpam-5320	164	87	(	(	PUNCT
ejpam-5320	164	88	4	4	X
ejpam-5320	164	89	)	)	PUNCT
ejpam-5320	164	90	τ1τ2	τ1τ2	NOUN
ejpam-5320	164	91	-	-	NOUN
ejpam-5320	164	92	cl(f	cl(f	NOUN
ejpam-5320	164	93	−1(b	−1(b	NOUN
ejpam-5320	164	94	)	)	PUNCT
ejpam-5320	164	95	)	)	PUNCT
ejpam-5320	165	1	⊆	⊆	NUM
ejpam-5320	165	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5320	165	3	-	-	PUNCT
ejpam-5320	165	4	cl(b	cl(b	NOUN
ejpam-5320	165	5	)	)	PUNCT
ejpam-5320	165	6	)	)	PUNCT
ejpam-5320	165	7	for	for	ADP
ejpam-5320	165	8	every	every	DET
ejpam-5320	165	9	subset	subset	NOUN
ejpam-5320	165	10	b	b	PROPN
ejpam-5320	165	11	of	of	ADP
ejpam-5320	165	12	y	y	PROPN
ejpam-5320	165	13	having	have	VERB
ejpam-5320	165	14	the	the	DET
ejpam-5320	165	15	σ1σ2	σ1σ2	NUM
ejpam-5320	165	16	-	-	ADJ
ejpam-5320	165	17	compact	compact	ADJ
ejpam-5320	165	18	σ1σ2	σ1σ2	NOUN
ejpam-5320	165	19	-	-	NOUN
ejpam-5320	165	20	closure	closure	NOUN
ejpam-5320	165	21	;	;	PUNCT
ejpam-5320	165	22	(	(	PUNCT
ejpam-5320	165	23	5	5	X
ejpam-5320	165	24	)	)	PUNCT
ejpam-5320	165	25	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5320	165	26	-	-	PUNCT
ejpam-5320	165	27	int(b	int(b	NOUN
ejpam-5320	165	28	)	)	PUNCT
ejpam-5320	165	29	)	)	PUNCT
ejpam-5320	166	1	⊆	⊆	X
ejpam-5320	166	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	166	3	-	-	NUM
ejpam-5320	166	4	int(f	int(f	NOUN
ejpam-5320	166	5	−1(b	−1(b	NOUN
ejpam-5320	166	6	)	)	PUNCT
ejpam-5320	166	7	)	)	PUNCT
ejpam-5320	166	8	for	for	ADP
ejpam-5320	166	9	every	every	DET
ejpam-5320	166	10	subset	subset	NOUN
ejpam-5320	166	11	b	b	PROPN
ejpam-5320	166	12	of	of	ADP
ejpam-5320	166	13	y	y	PRON
ejpam-5320	166	14	such	such	ADJ
ejpam-5320	166	15	that	that	SCONJ
ejpam-5320	166	16	y−σ1σ2	y−σ1σ2	PROPN
ejpam-5320	166	17	-	-	PUNCT
ejpam-5320	166	18	int(b	int(b	NOUN
ejpam-5320	166	19	)	)	PUNCT
ejpam-5320	166	20	is	be	AUX
ejpam-5320	166	21	σ1σ2	σ1σ2	NOUN
ejpam-5320	166	22	-	-	ADJ
ejpam-5320	166	23	compact	compact	ADJ
ejpam-5320	166	24	.	.	PUNCT
ejpam-5320	167	1	4	4	X
ejpam-5320	167	2	.	.	X
ejpam-5320	168	1	some	some	PRON
ejpam-5320	168	2	characterizations	characterization	VERB
ejpam-5320	168	3	the	the	DET
ejpam-5320	168	4	τ1τ2	τ1τ2	NOUN
ejpam-5320	168	5	-	-	NOUN
ejpam-5320	168	6	frontier	frontier	NOUN
ejpam-5320	168	7	[	[	X
ejpam-5320	168	8	21	21	NUM
ejpam-5320	168	9	]	]	PUNCT
ejpam-5320	168	10	of	of	ADP
ejpam-5320	168	11	a	a	DET
ejpam-5320	168	12	subset	subset	NOUN
ejpam-5320	168	13	a	a	PRON
ejpam-5320	168	14	of	of	ADP
ejpam-5320	168	15	a	a	DET
ejpam-5320	168	16	bitopological	bitopological	ADJ
ejpam-5320	168	17	space	space	NOUN
ejpam-5320	168	18	(	(	PUNCT
ejpam-5320	168	19	x	x	NOUN
ejpam-5320	168	20	,	,	PUNCT
ejpam-5320	168	21	τ1	τ1	NOUN
ejpam-5320	168	22	,	,	PUNCT
ejpam-5320	168	23	τ2	τ2	PROPN
ejpam-5320	168	24	)	)	PUNCT
ejpam-5320	168	25	,	,	PUNCT
ejpam-5320	168	26	denoted	denote	VERB
ejpam-5320	168	27	by	by	ADP
ejpam-5320	168	28	τ1τ2	τ1τ2	NOUN
ejpam-5320	168	29	-	-	ADJ
ejpam-5320	168	30	fr(a	fr(a	NUM
ejpam-5320	168	31	)	)	PUNCT
ejpam-5320	168	32	,	,	PUNCT
ejpam-5320	168	33	is	be	AUX
ejpam-5320	168	34	defined	define	VERB
ejpam-5320	168	35	by	by	ADP
ejpam-5320	168	36	τ1τ2	τ1τ2	NOUN
ejpam-5320	168	37	-	-	ADJ
ejpam-5320	168	38	fr(a	fr(a	ADJ
ejpam-5320	168	39	)	)	PUNCT
ejpam-5320	169	1	=	=	PUNCT
ejpam-5320	169	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	169	3	-	-	NUM
ejpam-5320	169	4	cl(a	cl(a	NUM
ejpam-5320	169	5	)	)	PUNCT
ejpam-5320	169	6	∩	∩	NOUN
ejpam-5320	169	7	τ1τ2	τ1τ2	NOUN
ejpam-5320	169	8	-	-	ADJ
ejpam-5320	169	9	cl(x	cl(x	SYM
ejpam-5320	169	10	−a	−a	NOUN
ejpam-5320	169	11	)	)	PUNCT
ejpam-5320	169	12	=	=	PUNCT
ejpam-5320	170	1	τ1τ2	τ1τ2	ADJ
ejpam-5320	170	2	-	-	ADJ
ejpam-5320	170	3	cl(a)−	cl(a)−	ADJ
ejpam-5320	170	4	τ1τ2	τ1τ2	NOUN
ejpam-5320	170	5	-	-	ADJ
ejpam-5320	170	6	int(a	int(a	NOUN
ejpam-5320	170	7	)	)	PUNCT
ejpam-5320	170	8	.	.	PUNCT
ejpam-5320	171	1	theorem	theorem	NOUN
ejpam-5320	171	2	5	5	NUM
ejpam-5320	171	3	.	.	PUNCT
ejpam-5320	172	1	the	the	DET
ejpam-5320	172	2	set	set	NOUN
ejpam-5320	172	3	of	of	ADP
ejpam-5320	172	4	all	all	DET
ejpam-5320	172	5	points	point	NOUN
ejpam-5320	172	6	x	x	X
ejpam-5320	172	7	∈	∈	NOUN
ejpam-5320	172	8	x	x	PUNCT
ejpam-5320	172	9	at	at	ADP
ejpam-5320	172	10	which	which	PRON
ejpam-5320	172	11	a	a	DET
ejpam-5320	172	12	multifunction	multifunction	NOUN
ejpam-5320	172	13	f	f	NOUN
ejpam-5320	172	14	:	:	PUNCT
ejpam-5320	172	15	(	(	PUNCT
ejpam-5320	172	16	x	x	NOUN
ejpam-5320	172	17	,	,	PUNCT
ejpam-5320	172	18	τ1	τ1	NOUN
ejpam-5320	172	19	,	,	PUNCT
ejpam-5320	172	20	τ2	τ2	NOUN
ejpam-5320	172	21	)	)	PUNCT
ejpam-5320	172	22	→	→	SYM
ejpam-5320	172	23	(	(	PUNCT
ejpam-5320	172	24	y	y	PROPN
ejpam-5320	172	25	,	,	PUNCT
ejpam-5320	172	26	σ1	σ1	PROPN
ejpam-5320	172	27	,	,	PUNCT
ejpam-5320	172	28	σ2	σ2	PROPN
ejpam-5320	172	29	)	)	PUNCT
ejpam-5320	172	30	is	be	AUX
ejpam-5320	172	31	not	not	PART
ejpam-5320	172	32	upper	upper	ADJ
ejpam-5320	172	33	c-(τ1	c-(τ1	PROPN
ejpam-5320	172	34	,	,	PUNCT
ejpam-5320	172	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	172	36	is	be	AUX
ejpam-5320	172	37	identical	identical	ADJ
ejpam-5320	172	38	with	with	ADP
ejpam-5320	172	39	the	the	DET
ejpam-5320	172	40	union	union	NOUN
ejpam-5320	172	41	of	of	ADP
ejpam-5320	172	42	the	the	DET
ejpam-5320	172	43	τ1τ2	τ1τ2	NOUN
ejpam-5320	172	44	-	-	NOUN
ejpam-5320	172	45	frontier	frontier	NOUN
ejpam-5320	172	46	of	of	ADP
ejpam-5320	172	47	the	the	DET
ejpam-5320	172	48	upper	upper	ADJ
ejpam-5320	172	49	inverse	inverse	NOUN
ejpam-5320	172	50	images	image	NOUN
ejpam-5320	172	51	of	of	ADP
ejpam-5320	172	52	the	the	DET
ejpam-5320	172	53	σ1σ2	σ1σ2	NOUN
ejpam-5320	172	54	-	-	PUNCT
ejpam-5320	172	55	closures	closure	NOUN
ejpam-5320	172	56	of	of	ADP
ejpam-5320	172	57	σ1σ2	σ1σ2	NOUN
ejpam-5320	172	58	-	-	PUNCT
ejpam-5320	172	59	open	open	ADJ
ejpam-5320	172	60	sets	set	NOUN
ejpam-5320	172	61	containing	contain	VERB
ejpam-5320	172	62	f	f	X
ejpam-5320	172	63	(	(	PUNCT
ejpam-5320	172	64	x	x	NOUN
ejpam-5320	172	65	)	)	PUNCT
ejpam-5320	172	66	and	and	CCONJ
ejpam-5320	172	67	having	have	VERB
ejpam-5320	172	68	σ1σ2	σ1σ2	NOUN
ejpam-5320	172	69	-	-	ADJ
ejpam-5320	172	70	compact	compact	ADJ
ejpam-5320	172	71	complement	complement	NOUN
ejpam-5320	172	72	.	.	PUNCT
ejpam-5320	173	1	proof	proof	NOUN
ejpam-5320	173	2	.	.	PUNCT
ejpam-5320	174	1	suppose	suppose	VERB
ejpam-5320	174	2	that	that	SCONJ
ejpam-5320	174	3	f	f	PROPN
ejpam-5320	174	4	is	be	AUX
ejpam-5320	174	5	not	not	PART
ejpam-5320	174	6	upper	upper	ADJ
ejpam-5320	174	7	c-(τ1	c-(τ1	PROPN
ejpam-5320	174	8	,	,	PUNCT
ejpam-5320	174	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	174	10	at	at	ADP
ejpam-5320	174	11	x	x	SYM
ejpam-5320	174	12	∈	∈	PROPN
ejpam-5320	174	13	x.	x.	NOUN
ejpam-5320	174	14	then	then	ADV
ejpam-5320	174	15	,	,	PUNCT
ejpam-5320	174	16	there	there	PRON
ejpam-5320	174	17	exists	exist	VERB
ejpam-5320	174	18	a	a	DET
ejpam-5320	174	19	σ1σ2	σ1σ2	NUM
ejpam-5320	174	20	-	-	ADJ
ejpam-5320	174	21	open	open	ADJ
ejpam-5320	174	22	set	set	NOUN
ejpam-5320	174	23	v	v	NOUN
ejpam-5320	174	24	of	of	ADP
ejpam-5320	174	25	y	y	PROPN
ejpam-5320	174	26	containing	contain	VERB
ejpam-5320	174	27	f	f	PROPN
ejpam-5320	174	28	(	(	PUNCT
ejpam-5320	174	29	x	x	NOUN
ejpam-5320	174	30	)	)	PUNCT
ejpam-5320	174	31	and	and	CCONJ
ejpam-5320	174	32	having	have	VERB
ejpam-5320	174	33	σ1σ2	σ1σ2	NOUN
ejpam-5320	174	34	-	-	ADJ
ejpam-5320	174	35	compact	compact	ADJ
ejpam-5320	174	36	complement	complement	NOUN
ejpam-5320	174	37	such	such	ADJ
ejpam-5320	174	38	that	that	SCONJ
ejpam-5320	174	39	u	u	PROPN
ejpam-5320	174	40	∩	∩	NOUN
ejpam-5320	174	41	(	(	PUNCT
ejpam-5320	174	42	x	x	NOUN
ejpam-5320	174	43	−	−	PROPN
ejpam-5320	174	44	f+(v	f+(v	NOUN
ejpam-5320	174	45	)	)	PUNCT
ejpam-5320	174	46	)	)	PUNCT
ejpam-5320	175	1	̸=	̸=	NOUN
ejpam-5320	175	2	∅	∅	NOUN
ejpam-5320	175	3	for	for	ADP
ejpam-5320	175	4	every	every	DET
ejpam-5320	175	5	τ1τ2	τ1τ2	ADJ
ejpam-5320	175	6	-	-	ADJ
ejpam-5320	175	7	open	open	ADJ
ejpam-5320	175	8	set	set	ADJ
ejpam-5320	175	9	u	u	NOUN
ejpam-5320	175	10	of	of	ADP
ejpam-5320	175	11	x	x	SYM
ejpam-5320	175	12	containing	contain	VERB
ejpam-5320	175	13	x.	x.	NOUN
ejpam-5320	175	14	then	then	ADV
ejpam-5320	175	15	,	,	PUNCT
ejpam-5320	175	16	we	we	PRON
ejpam-5320	175	17	have	have	VERB
ejpam-5320	175	18	x	x	PART
ejpam-5320	175	19	∈	∈	PROPN
ejpam-5320	175	20	τ1τ2	τ1τ2	NOUN
ejpam-5320	175	21	-	-	NOUN
ejpam-5320	175	22	cl(x	cl(x	NUM
ejpam-5320	175	23	−	−	NOUN
ejpam-5320	175	24	f+(v	f+(v	NOUN
ejpam-5320	175	25	)	)	PUNCT
ejpam-5320	175	26	)	)	PUNCT
ejpam-5320	175	27	.	.	PUNCT
ejpam-5320	176	1	on	on	ADP
ejpam-5320	176	2	the	the	DET
ejpam-5320	176	3	other	other	ADJ
ejpam-5320	176	4	hand	hand	NOUN
ejpam-5320	176	5	,	,	PUNCT
ejpam-5320	176	6	we	we	PRON
ejpam-5320	176	7	have	have	VERB
ejpam-5320	176	8	x	x	X
ejpam-5320	176	9	∈	∈	NOUN
ejpam-5320	176	10	f+(v	f+(v	NOUN
ejpam-5320	176	11	)	)	PUNCT
ejpam-5320	177	1	⊆	⊆	X
ejpam-5320	177	2	τ1τ2	τ1τ2	NOUN
ejpam-5320	177	3	-	-	NOUN
ejpam-5320	177	4	cl(f	cl(f	NOUN
ejpam-5320	177	5	+	+	NOUN
ejpam-5320	177	6	(	(	PUNCT
ejpam-5320	177	7	v	v	NOUN
ejpam-5320	177	8	)	)	PUNCT
ejpam-5320	177	9	)	)	PUNCT
ejpam-5320	177	10	and	and	CCONJ
ejpam-5320	177	11	hence	hence	ADV
ejpam-5320	177	12	x	x	X
ejpam-5320	177	13	∈	∈	PRON
ejpam-5320	177	14	τ1τ2	τ1τ2	NOUN
ejpam-5320	177	15	-	-	ADJ
ejpam-5320	177	16	fr(f	fr(f	PUNCT
ejpam-5320	177	17	+	+	ADJ
ejpam-5320	177	18	(	(	PUNCT
ejpam-5320	177	19	v	v	NOUN
ejpam-5320	177	20	)	)	PUNCT
ejpam-5320	177	21	)	)	PUNCT
ejpam-5320	177	22	.	.	PUNCT
ejpam-5320	178	1	conversely	conversely	ADV
ejpam-5320	178	2	,	,	PUNCT
ejpam-5320	178	3	suppose	suppose	VERB
ejpam-5320	178	4	that	that	SCONJ
ejpam-5320	178	5	v	v	NOUN
ejpam-5320	178	6	is	be	AUX
ejpam-5320	178	7	a	a	DET
ejpam-5320	178	8	σ1σ2	σ1σ2	NOUN
ejpam-5320	178	9	-	-	ADJ
ejpam-5320	178	10	open	open	ADJ
ejpam-5320	178	11	set	set	NOUN
ejpam-5320	178	12	of	of	ADP
ejpam-5320	178	13	y	y	PROPN
ejpam-5320	178	14	containing	contain	VERB
ejpam-5320	178	15	f	f	PROPN
ejpam-5320	178	16	(	(	PUNCT
ejpam-5320	178	17	x	x	NOUN
ejpam-5320	178	18	)	)	PUNCT
ejpam-5320	178	19	and	and	CCONJ
ejpam-5320	178	20	having	have	VERB
ejpam-5320	178	21	σ1σ2compact	σ1σ2compact	NOUN
ejpam-5320	178	22	complement	complement	VERB
ejpam-5320	178	23	such	such	ADJ
ejpam-5320	178	24	that	that	SCONJ
ejpam-5320	178	25	x	x	PUNCT
ejpam-5320	178	26	∈	∈	PRON
ejpam-5320	178	27	τ1τ2	τ1τ2	NOUN
ejpam-5320	178	28	-	-	ADJ
ejpam-5320	178	29	fr(f	fr(f	PUNCT
ejpam-5320	178	30	+	+	ADJ
ejpam-5320	178	31	(	(	PUNCT
ejpam-5320	178	32	v	v	NOUN
ejpam-5320	178	33	)	)	PUNCT
ejpam-5320	178	34	)	)	PUNCT
ejpam-5320	178	35	.	.	PUNCT
ejpam-5320	179	1	if	if	SCONJ
ejpam-5320	179	2	f	f	PROPN
ejpam-5320	179	3	is	be	AUX
ejpam-5320	179	4	upper	upper	ADJ
ejpam-5320	179	5	c-(τ1	c-(τ1	PROPN
ejpam-5320	179	6	,	,	PUNCT
ejpam-5320	179	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	179	8	at	at	ADP
ejpam-5320	179	9	x	x	X
ejpam-5320	179	10	∈	∈	PROPN
ejpam-5320	179	11	x	x	NOUN
ejpam-5320	179	12	,	,	PUNCT
ejpam-5320	179	13	there	there	PRON
ejpam-5320	179	14	exists	exist	VERB
ejpam-5320	179	15	a	a	DET
ejpam-5320	179	16	τ1τ2	τ1τ2	NOUN
ejpam-5320	179	17	-	-	ADJ
ejpam-5320	179	18	open	open	ADJ
ejpam-5320	179	19	set	set	ADJ
ejpam-5320	179	20	u	u	NOUN
ejpam-5320	179	21	of	of	ADP
ejpam-5320	179	22	x	x	PUNCT
ejpam-5320	179	23	containing	contain	VERB
ejpam-5320	179	24	x	x	PUNCT
ejpam-5320	179	25	such	such	ADJ
ejpam-5320	179	26	that	that	SCONJ
ejpam-5320	179	27	u	u	NOUN
ejpam-5320	179	28	⊆	⊆	NUM
ejpam-5320	179	29	f+(v	f+(v	NOUN
ejpam-5320	179	30	)	)	PUNCT
ejpam-5320	179	31	and	and	CCONJ
ejpam-5320	179	32	hence	hence	ADV
ejpam-5320	179	33	x	x	X
ejpam-5320	179	34	∈	∈	PRON
ejpam-5320	179	35	τ1τ2	τ1τ2	NOUN
ejpam-5320	179	36	-	-	NUM
ejpam-5320	179	37	int(f	int(f	VERB
ejpam-5320	179	38	+	+	ADJ
ejpam-5320	179	39	(	(	PUNCT
ejpam-5320	179	40	v	v	NOUN
ejpam-5320	179	41	)	)	PUNCT
ejpam-5320	179	42	)	)	PUNCT
ejpam-5320	179	43	.	.	PUNCT
ejpam-5320	180	1	this	this	PRON
ejpam-5320	180	2	is	be	AUX
ejpam-5320	180	3	a	a	DET
ejpam-5320	180	4	contradiction	contradiction	NOUN
ejpam-5320	181	1	and	and	CCONJ
ejpam-5320	181	2	so	so	ADV
ejpam-5320	181	3	f	f	PROPN
ejpam-5320	181	4	is	be	AUX
ejpam-5320	181	5	not	not	PART
ejpam-5320	181	6	upper	upper	ADJ
ejpam-5320	181	7	c-(τ1	c-(τ1	PROPN
ejpam-5320	181	8	,	,	PUNCT
ejpam-5320	181	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	181	10	at	at	ADP
ejpam-5320	181	11	x.	x.	NOUN
ejpam-5320	181	12	theorem	theorem	VERB
ejpam-5320	181	13	6	6	NUM
ejpam-5320	181	14	.	.	PUNCT
ejpam-5320	182	1	the	the	DET
ejpam-5320	182	2	set	set	NOUN
ejpam-5320	182	3	of	of	ADP
ejpam-5320	182	4	all	all	DET
ejpam-5320	182	5	points	point	NOUN
ejpam-5320	182	6	x	x	X
ejpam-5320	182	7	∈	∈	NOUN
ejpam-5320	182	8	x	x	PUNCT
ejpam-5320	182	9	at	at	ADP
ejpam-5320	182	10	which	which	PRON
ejpam-5320	182	11	a	a	DET
ejpam-5320	182	12	multifunction	multifunction	NOUN
ejpam-5320	182	13	f	f	NOUN
ejpam-5320	182	14	:	:	PUNCT
ejpam-5320	182	15	(	(	PUNCT
ejpam-5320	182	16	x	x	NOUN
ejpam-5320	182	17	,	,	PUNCT
ejpam-5320	182	18	τ1	τ1	NOUN
ejpam-5320	182	19	,	,	PUNCT
ejpam-5320	182	20	τ2	τ2	NOUN
ejpam-5320	182	21	)	)	PUNCT
ejpam-5320	182	22	→	→	SYM
ejpam-5320	182	23	(	(	PUNCT
ejpam-5320	182	24	y	y	PROPN
ejpam-5320	182	25	,	,	PUNCT
ejpam-5320	182	26	σ1	σ1	PROPN
ejpam-5320	182	27	,	,	PUNCT
ejpam-5320	182	28	σ2	σ2	PROPN
ejpam-5320	182	29	)	)	PUNCT
ejpam-5320	182	30	is	be	AUX
ejpam-5320	182	31	not	not	PART
ejpam-5320	182	32	lower	low	ADJ
ejpam-5320	182	33	c-(τ1	c-(τ1	PROPN
ejpam-5320	182	34	,	,	PUNCT
ejpam-5320	182	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	182	36	is	be	AUX
ejpam-5320	182	37	identical	identical	ADJ
ejpam-5320	182	38	with	with	ADP
ejpam-5320	182	39	the	the	DET
ejpam-5320	182	40	union	union	NOUN
ejpam-5320	182	41	of	of	ADP
ejpam-5320	182	42	the	the	DET
ejpam-5320	182	43	τ1τ2	τ1τ2	NOUN
ejpam-5320	182	44	-	-	NOUN
ejpam-5320	182	45	frontier	frontier	NOUN
ejpam-5320	182	46	of	of	ADP
ejpam-5320	182	47	the	the	DET
ejpam-5320	182	48	lower	low	ADJ
ejpam-5320	182	49	inverse	inverse	NOUN
ejpam-5320	182	50	images	image	NOUN
ejpam-5320	182	51	of	of	ADP
ejpam-5320	182	52	the	the	DET
ejpam-5320	182	53	σ1σ2	σ1σ2	NOUN
ejpam-5320	182	54	-	-	PUNCT
ejpam-5320	182	55	closures	closure	NOUN
ejpam-5320	182	56	of	of	ADP
ejpam-5320	182	57	σ1σ2	σ1σ2	NOUN
ejpam-5320	182	58	-	-	PUNCT
ejpam-5320	182	59	open	open	ADJ
ejpam-5320	182	60	sets	set	NOUN
ejpam-5320	182	61	meeting	meet	VERB
ejpam-5320	182	62	f	f	X
ejpam-5320	182	63	(	(	PUNCT
ejpam-5320	182	64	x	x	NOUN
ejpam-5320	182	65	)	)	PUNCT
ejpam-5320	182	66	and	and	CCONJ
ejpam-5320	182	67	having	have	VERB
ejpam-5320	182	68	σ1σ2	σ1σ2	NOUN
ejpam-5320	182	69	-	-	ADJ
ejpam-5320	182	70	compact	compact	ADJ
ejpam-5320	182	71	complement	complement	NOUN
ejpam-5320	182	72	.	.	PUNCT
ejpam-5320	183	1	j.	j.	PROPN
ejpam-5320	183	2	khampakdee	khampakdee	PROPN
ejpam-5320	183	3	,	,	PUNCT
ejpam-5320	183	4	s.	s.	PROPN
ejpam-5320	183	5	sompong	sompong	PROPN
ejpam-5320	183	6	,	,	PUNCT
ejpam-5320	183	7	c.	c.	PROPN
ejpam-5320	183	8	boonpok	boonpok	PROPN
ejpam-5320	183	9	/	/	SYM
ejpam-5320	183	10	eur	eur	PROPN
ejpam-5320	183	11	.	.	PUNCT
ejpam-5320	184	1	j.	j.	PROPN
ejpam-5320	184	2	pure	pure	PROPN
ejpam-5320	184	3	appl	appl	PROPN
ejpam-5320	184	4	.	.	PROPN
ejpam-5320	184	5	math	math	PROPN
ejpam-5320	184	6	,	,	PUNCT
ejpam-5320	184	7	17	17	NUM
ejpam-5320	184	8	(	(	PUNCT
ejpam-5320	184	9	3	3	NUM
ejpam-5320	184	10	)	)	PUNCT
ejpam-5320	184	11	(	(	PUNCT
ejpam-5320	184	12	2024	2024	NUM
ejpam-5320	184	13	)	)	PUNCT
ejpam-5320	184	14	,	,	PUNCT
ejpam-5320	184	15	2288	2288	NUM
ejpam-5320	184	16	-	-	SYM
ejpam-5320	184	17	2298	2298	NUM
ejpam-5320	184	18	2295	2295	NUM
ejpam-5320	184	19	proof	proof	NOUN
ejpam-5320	184	20	.	.	PUNCT
ejpam-5320	185	1	the	the	DET
ejpam-5320	185	2	proof	proof	NOUN
ejpam-5320	185	3	is	be	AUX
ejpam-5320	185	4	similar	similar	ADJ
ejpam-5320	185	5	to	to	ADP
ejpam-5320	185	6	that	that	PRON
ejpam-5320	185	7	of	of	ADP
ejpam-5320	185	8	theorem	theorem	NOUN
ejpam-5320	185	9	5	5	NUM
ejpam-5320	185	10	.	.	X
ejpam-5320	185	11	for	for	ADP
ejpam-5320	185	12	a	a	DET
ejpam-5320	185	13	multifunction	multifunction	NOUN
ejpam-5320	185	14	f	f	NOUN
ejpam-5320	185	15	:	:	PUNCT
ejpam-5320	185	16	(	(	PUNCT
ejpam-5320	185	17	x	x	NOUN
ejpam-5320	185	18	,	,	PUNCT
ejpam-5320	185	19	τ1	τ1	NOUN
ejpam-5320	185	20	,	,	PUNCT
ejpam-5320	185	21	τ2	τ2	NOUN
ejpam-5320	185	22	)	)	PUNCT
ejpam-5320	185	23	→	→	SYM
ejpam-5320	185	24	(	(	PUNCT
ejpam-5320	185	25	y	y	PROPN
ejpam-5320	185	26	,	,	PUNCT
ejpam-5320	185	27	σ1	σ1	PROPN
ejpam-5320	185	28	,	,	PUNCT
ejpam-5320	185	29	σ2	σ2	NOUN
ejpam-5320	185	30	)	)	PUNCT
ejpam-5320	185	31	,	,	PUNCT
ejpam-5320	185	32	by	by	ADP
ejpam-5320	185	33	clf⊛	clf⊛	PROPN
ejpam-5320	185	34	:	:	PUNCT
ejpam-5320	185	35	(	(	PUNCT
ejpam-5320	185	36	x	x	NOUN
ejpam-5320	185	37	,	,	PUNCT
ejpam-5320	185	38	τ1	τ1	NOUN
ejpam-5320	185	39	,	,	PUNCT
ejpam-5320	185	40	τ2	τ2	NOUN
ejpam-5320	185	41	)	)	PUNCT
ejpam-5320	185	42	→	→	SYM
ejpam-5320	185	43	(	(	PUNCT
ejpam-5320	185	44	y	y	PROPN
ejpam-5320	185	45	,	,	PUNCT
ejpam-5320	185	46	σ1	σ1	PROPN
ejpam-5320	185	47	,	,	PUNCT
ejpam-5320	185	48	σ2	σ2	NOUN
ejpam-5320	185	49	)	)	PUNCT
ejpam-5320	186	1	[	[	X
ejpam-5320	186	2	21	21	NUM
ejpam-5320	186	3	]	]	PUNCT
ejpam-5320	186	4	we	we	PRON
ejpam-5320	186	5	denote	denote	VERB
ejpam-5320	186	6	a	a	DET
ejpam-5320	186	7	multifunction	multifunction	NOUN
ejpam-5320	186	8	defined	define	VERB
ejpam-5320	186	9	as	as	SCONJ
ejpam-5320	186	10	follows	follow	VERB
ejpam-5320	186	11	:	:	PUNCT
ejpam-5320	186	12	clf⊛(x	clf⊛(x	PROPN
ejpam-5320	186	13	)	)	PUNCT
ejpam-5320	186	14	=	=	PUNCT
ejpam-5320	187	1	σ1σ2	σ1σ2	X
ejpam-5320	187	2	-	-	NUM
ejpam-5320	187	3	cl(f	cl(f	NOUN
ejpam-5320	187	4	(	(	PUNCT
ejpam-5320	187	5	x	x	NOUN
ejpam-5320	187	6	)	)	PUNCT
ejpam-5320	187	7	)	)	PUNCT
ejpam-5320	187	8	for	for	ADP
ejpam-5320	187	9	each	each	DET
ejpam-5320	187	10	x	x	SYM
ejpam-5320	187	11	∈	∈	PROPN
ejpam-5320	187	12	x.	x.	NOUN
ejpam-5320	187	13	definition	definition	NOUN
ejpam-5320	187	14	4	4	NUM
ejpam-5320	187	15	.	.	PUNCT
ejpam-5320	188	1	[	[	X
ejpam-5320	188	2	21	21	NUM
ejpam-5320	188	3	]	]	X
ejpam-5320	188	4	a	a	DET
ejpam-5320	188	5	subset	subset	NOUN
ejpam-5320	188	6	a	a	PRON
ejpam-5320	188	7	of	of	ADP
ejpam-5320	188	8	a	a	DET
ejpam-5320	188	9	bitopological	bitopological	ADJ
ejpam-5320	188	10	space	space	NOUN
ejpam-5320	188	11	(	(	PUNCT
ejpam-5320	188	12	x	x	NOUN
ejpam-5320	188	13	,	,	PUNCT
ejpam-5320	188	14	τ1	τ1	NOUN
ejpam-5320	188	15	,	,	PUNCT
ejpam-5320	188	16	τ2	τ2	NOUN
ejpam-5320	188	17	)	)	PUNCT
ejpam-5320	188	18	is	be	AUX
ejpam-5320	188	19	said	say	VERB
ejpam-5320	188	20	to	to	PART
ejpam-5320	188	21	be	be	AUX
ejpam-5320	188	22	:	:	PUNCT
ejpam-5320	188	23	(	(	PUNCT
ejpam-5320	188	24	1	1	X
ejpam-5320	188	25	)	)	PUNCT
ejpam-5320	188	26	τ1τ2	τ1τ2	NOUN
ejpam-5320	188	27	-	-	NOUN
ejpam-5320	188	28	paracompact	paracompact	ADJ
ejpam-5320	188	29	if	if	SCONJ
ejpam-5320	188	30	every	every	DET
ejpam-5320	188	31	cover	cover	NOUN
ejpam-5320	188	32	of	of	ADP
ejpam-5320	188	33	a	a	PRON
ejpam-5320	188	34	by	by	ADP
ejpam-5320	188	35	τ1τ2	τ1τ2	ADJ
ejpam-5320	188	36	-	-	ADJ
ejpam-5320	188	37	open	open	ADJ
ejpam-5320	188	38	sets	set	NOUN
ejpam-5320	188	39	of	of	ADP
ejpam-5320	188	40	x	x	VERB
ejpam-5320	188	41	is	be	AUX
ejpam-5320	188	42	refined	refine	VERB
ejpam-5320	188	43	by	by	ADP
ejpam-5320	188	44	a	a	DET
ejpam-5320	188	45	cover	cover	NOUN
ejpam-5320	188	46	of	of	ADP
ejpam-5320	188	47	a	a	PRON
ejpam-5320	188	48	which	which	PRON
ejpam-5320	188	49	consists	consist	VERB
ejpam-5320	188	50	of	of	ADP
ejpam-5320	188	51	τ1τ2	τ1τ2	ADJ
ejpam-5320	188	52	-	-	ADJ
ejpam-5320	188	53	open	open	ADJ
ejpam-5320	188	54	sets	set	NOUN
ejpam-5320	188	55	of	of	ADP
ejpam-5320	188	56	x	x	PUNCT
ejpam-5320	188	57	and	and	CCONJ
ejpam-5320	188	58	is	be	AUX
ejpam-5320	188	59	τ1τ2	τ1τ2	NOUN
ejpam-5320	188	60	-	-	ADJ
ejpam-5320	188	61	locally	locally	ADV
ejpam-5320	188	62	finite	finite	NOUN
ejpam-5320	188	63	in	in	ADP
ejpam-5320	188	64	x	x	PRON
ejpam-5320	188	65	;	;	PUNCT
ejpam-5320	188	66	(	(	PUNCT
ejpam-5320	188	67	2	2	X
ejpam-5320	188	68	)	)	PUNCT
ejpam-5320	188	69	τ1τ2	τ1τ2	NOUN
ejpam-5320	188	70	-	-	NOUN
ejpam-5320	188	71	regular	regular	ADJ
ejpam-5320	188	72	if	if	SCONJ
ejpam-5320	188	73	for	for	ADP
ejpam-5320	188	74	each	each	DET
ejpam-5320	188	75	x	x	SYM
ejpam-5320	188	76	∈	∈	PROPN
ejpam-5320	188	77	a	a	PRON
ejpam-5320	188	78	and	and	CCONJ
ejpam-5320	188	79	each	each	DET
ejpam-5320	188	80	τ1τ2	τ1τ2	ADJ
ejpam-5320	188	81	-	-	ADJ
ejpam-5320	188	82	open	open	ADJ
ejpam-5320	188	83	set	set	ADJ
ejpam-5320	188	84	u	u	NOUN
ejpam-5320	188	85	of	of	ADP
ejpam-5320	188	86	x	x	PUNCT
ejpam-5320	188	87	containing	contain	VERB
ejpam-5320	188	88	x	x	PRON
ejpam-5320	188	89	,	,	PUNCT
ejpam-5320	188	90	there	there	PRON
ejpam-5320	188	91	exists	exist	VERB
ejpam-5320	188	92	a	a	DET
ejpam-5320	188	93	τ1τ2	τ1τ2	NOUN
ejpam-5320	188	94	-	-	ADJ
ejpam-5320	188	95	open	open	ADJ
ejpam-5320	188	96	set	set	NOUN
ejpam-5320	188	97	v	v	NOUN
ejpam-5320	188	98	of	of	ADP
ejpam-5320	188	99	x	x	PUNCT
ejpam-5320	188	100	such	such	ADJ
ejpam-5320	188	101	that	that	SCONJ
ejpam-5320	188	102	x	x	SYM
ejpam-5320	188	103	∈	∈	NOUN
ejpam-5320	188	104	v	v	ADP
ejpam-5320	188	105	⊆	⊆	NUM
ejpam-5320	188	106	τ1τ2	τ1τ2	NOUN
ejpam-5320	188	107	-	-	NOUN
ejpam-5320	188	108	cl(v	cl(v	X
ejpam-5320	188	109	)	)	PUNCT
ejpam-5320	188	110	⊆	⊆	NUM
ejpam-5320	188	111	u	u	NOUN
ejpam-5320	188	112	.	.	PUNCT
ejpam-5320	189	1	lemma	lemma	PROPN
ejpam-5320	189	2	2	2	X
ejpam-5320	189	3	.	.	PUNCT
ejpam-5320	190	1	[	[	X
ejpam-5320	190	2	21	21	NUM
ejpam-5320	190	3	]	]	X
ejpam-5320	190	4	if	if	SCONJ
ejpam-5320	190	5	a	a	PRON
ejpam-5320	190	6	is	be	AUX
ejpam-5320	190	7	a	a	DET
ejpam-5320	190	8	τ1τ2	τ1τ2	ADJ
ejpam-5320	190	9	-	-	ADJ
ejpam-5320	190	10	regular	regular	ADJ
ejpam-5320	190	11	τ1τ2	τ1τ2	NOUN
ejpam-5320	190	12	-	-	ADJ
ejpam-5320	190	13	paracompact	paracompact	ADJ
ejpam-5320	190	14	set	set	NOUN
ejpam-5320	190	15	of	of	ADP
ejpam-5320	190	16	a	a	DET
ejpam-5320	190	17	bitopological	bitopological	ADJ
ejpam-5320	190	18	space	space	NOUN
ejpam-5320	190	19	(	(	PUNCT
ejpam-5320	190	20	x	x	NOUN
ejpam-5320	190	21	,	,	PUNCT
ejpam-5320	190	22	τ1	τ1	NOUN
ejpam-5320	190	23	,	,	PUNCT
ejpam-5320	190	24	τ2	τ2	NOUN
ejpam-5320	190	25	)	)	PUNCT
ejpam-5320	190	26	and	and	CCONJ
ejpam-5320	190	27	u	u	NOUN
ejpam-5320	190	28	is	be	AUX
ejpam-5320	190	29	a	a	DET
ejpam-5320	190	30	τ1τ2	τ1τ2	ADJ
ejpam-5320	190	31	-	-	ADJ
ejpam-5320	190	32	open	open	ADJ
ejpam-5320	190	33	neighbourhood	neighbourhood	NOUN
ejpam-5320	190	34	of	of	ADP
ejpam-5320	190	35	a	a	PRON
ejpam-5320	190	36	,	,	PUNCT
ejpam-5320	190	37	then	then	ADV
ejpam-5320	190	38	there	there	PRON
ejpam-5320	190	39	exists	exist	VERB
ejpam-5320	190	40	a	a	DET
ejpam-5320	190	41	τ1τ2	τ1τ2	NOUN
ejpam-5320	190	42	-	-	ADJ
ejpam-5320	190	43	open	open	ADJ
ejpam-5320	190	44	set	set	NOUN
ejpam-5320	190	45	v	v	NOUN
ejpam-5320	190	46	of	of	ADP
ejpam-5320	190	47	x	x	PUNCT
ejpam-5320	190	48	such	such	ADJ
ejpam-5320	190	49	that	that	SCONJ
ejpam-5320	190	50	a	a	DET
ejpam-5320	190	51	⊆	⊆	NUM
ejpam-5320	190	52	v	v	ADP
ejpam-5320	190	53	⊆	⊆	NUM
ejpam-5320	190	54	τ1τ2	τ1τ2	NOUN
ejpam-5320	190	55	-	-	NOUN
ejpam-5320	190	56	cl(v	cl(v	X
ejpam-5320	190	57	)	)	PUNCT
ejpam-5320	190	58	⊆	⊆	NUM
ejpam-5320	190	59	u	u	NOUN
ejpam-5320	190	60	.	.	PUNCT
ejpam-5320	191	1	lemma	lemma	PROPN
ejpam-5320	191	2	3	3	X
ejpam-5320	191	3	.	.	PUNCT
ejpam-5320	192	1	[	[	X
ejpam-5320	192	2	21	21	NUM
ejpam-5320	192	3	]	]	X
ejpam-5320	192	4	if	if	SCONJ
ejpam-5320	192	5	f	f	PROPN
ejpam-5320	192	6	:	:	PUNCT
ejpam-5320	192	7	(	(	PUNCT
ejpam-5320	192	8	x	x	NOUN
ejpam-5320	192	9	,	,	PUNCT
ejpam-5320	192	10	τ1	τ1	NOUN
ejpam-5320	192	11	,	,	PUNCT
ejpam-5320	192	12	τ2	τ2	NOUN
ejpam-5320	192	13	)	)	PUNCT
ejpam-5320	192	14	→	→	SYM
ejpam-5320	192	15	(	(	PUNCT
ejpam-5320	192	16	y	y	PROPN
ejpam-5320	192	17	,	,	PUNCT
ejpam-5320	192	18	σ1	σ1	PROPN
ejpam-5320	192	19	,	,	PUNCT
ejpam-5320	192	20	σ2	σ2	PROPN
ejpam-5320	192	21	)	)	PUNCT
ejpam-5320	192	22	is	be	AUX
ejpam-5320	192	23	a	a	DET
ejpam-5320	192	24	multifunction	multifunction	NOUN
ejpam-5320	192	25	such	such	ADJ
ejpam-5320	192	26	that	that	SCONJ
ejpam-5320	192	27	f	f	PROPN
ejpam-5320	192	28	(	(	PUNCT
ejpam-5320	192	29	x	x	X
ejpam-5320	192	30	)	)	PUNCT
ejpam-5320	192	31	is	be	AUX
ejpam-5320	192	32	τ1τ2regular	τ1τ2regular	NUM
ejpam-5320	192	33	and	and	CCONJ
ejpam-5320	192	34	τ1τ2	τ1τ2	NOUN
ejpam-5320	192	35	-	-	ADJ
ejpam-5320	192	36	paracompact	paracompact	ADJ
ejpam-5320	192	37	for	for	ADP
ejpam-5320	192	38	each	each	DET
ejpam-5320	192	39	x	x	SYM
ejpam-5320	192	40	∈	∈	PROPN
ejpam-5320	192	41	x	x	NOUN
ejpam-5320	192	42	,	,	PUNCT
ejpam-5320	192	43	then	then	ADV
ejpam-5320	192	44	clf+	clf+	PROPN
ejpam-5320	192	45	⊛	⊛	X
ejpam-5320	192	46	(	(	PUNCT
ejpam-5320	192	47	v	v	NOUN
ejpam-5320	192	48	)	)	PUNCT
ejpam-5320	192	49	=	=	PUNCT
ejpam-5320	192	50	f+(v	f+(v	NOUN
ejpam-5320	192	51	)	)	PUNCT
ejpam-5320	192	52	for	for	ADP
ejpam-5320	192	53	each	each	DET
ejpam-5320	192	54	σ1σ2	σ1σ2	VERB
ejpam-5320	192	55	-	-	ADJ
ejpam-5320	192	56	open	open	ADJ
ejpam-5320	192	57	set	set	NOUN
ejpam-5320	192	58	v	v	NOUN
ejpam-5320	192	59	of	of	ADP
ejpam-5320	192	60	y	y	PROPN
ejpam-5320	192	61	.	.	PUNCT
ejpam-5320	193	1	theorem	theorem	ADJ
ejpam-5320	193	2	7	7	NUM
ejpam-5320	193	3	.	.	PUNCT
ejpam-5320	194	1	let	let	VERB
ejpam-5320	194	2	f	f	NOUN
ejpam-5320	194	3	:	:	PUNCT
ejpam-5320	194	4	(	(	PUNCT
ejpam-5320	194	5	x	x	NOUN
ejpam-5320	194	6	,	,	PUNCT
ejpam-5320	194	7	τ1	τ1	NOUN
ejpam-5320	194	8	,	,	PUNCT
ejpam-5320	194	9	τ2	τ2	NOUN
ejpam-5320	194	10	)	)	PUNCT
ejpam-5320	194	11	→	→	SYM
ejpam-5320	194	12	(	(	PUNCT
ejpam-5320	194	13	y	y	PROPN
ejpam-5320	194	14	,	,	PUNCT
ejpam-5320	194	15	σ1	σ1	PROPN
ejpam-5320	194	16	,	,	PUNCT
ejpam-5320	194	17	σ2	σ2	PROPN
ejpam-5320	194	18	)	)	PUNCT
ejpam-5320	194	19	be	be	VERB
ejpam-5320	194	20	a	a	DET
ejpam-5320	194	21	multifunction	multifunction	NOUN
ejpam-5320	194	22	such	such	ADJ
ejpam-5320	194	23	that	that	SCONJ
ejpam-5320	194	24	f	f	PROPN
ejpam-5320	194	25	(	(	PUNCT
ejpam-5320	194	26	x	x	X
ejpam-5320	194	27	)	)	PUNCT
ejpam-5320	194	28	is	be	AUX
ejpam-5320	194	29	σ1σ2paracompact	σ1σ2paracompact	NUM
ejpam-5320	194	30	and	and	CCONJ
ejpam-5320	194	31	σ1σ2	σ1σ2	NOUN
ejpam-5320	194	32	-	-	ADJ
ejpam-5320	194	33	regular	regular	ADJ
ejpam-5320	194	34	for	for	ADP
ejpam-5320	194	35	each	each	DET
ejpam-5320	194	36	x	x	SYM
ejpam-5320	194	37	∈	∈	PROPN
ejpam-5320	194	38	x.	x.	NOUN
ejpam-5320	194	39	then	then	ADV
ejpam-5320	194	40	,	,	PUNCT
ejpam-5320	194	41	the	the	DET
ejpam-5320	194	42	following	follow	VERB
ejpam-5320	194	43	properties	property	NOUN
ejpam-5320	194	44	are	be	AUX
ejpam-5320	194	45	equivalent	equivalent	ADJ
ejpam-5320	194	46	:	:	PUNCT
ejpam-5320	194	47	(	(	PUNCT
ejpam-5320	194	48	1	1	X
ejpam-5320	194	49	)	)	PUNCT
ejpam-5320	194	50	f	f	PROPN
ejpam-5320	194	51	is	be	AUX
ejpam-5320	194	52	upper	upper	ADJ
ejpam-5320	194	53	c-(τ1	c-(τ1	PROPN
ejpam-5320	194	54	,	,	PUNCT
ejpam-5320	194	55	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	194	56	;	;	PUNCT
ejpam-5320	194	57	(	(	PUNCT
ejpam-5320	194	58	2	2	X
ejpam-5320	194	59	)	)	PUNCT
ejpam-5320	194	60	clf⊛	clf⊛	PROPN
ejpam-5320	194	61	is	be	AUX
ejpam-5320	194	62	upper	upper	ADJ
ejpam-5320	194	63	c-(τ1	c-(τ1	PROPN
ejpam-5320	194	64	,	,	PUNCT
ejpam-5320	194	65	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	194	66	.	.	PUNCT
ejpam-5320	195	1	proof	proof	NOUN
ejpam-5320	195	2	.	.	PUNCT
ejpam-5320	196	1	we	we	PRON
ejpam-5320	196	2	put	put	VERB
ejpam-5320	196	3	g	g	NOUN
ejpam-5320	196	4	=	=	PUNCT
ejpam-5320	196	5	clf⊛.	clf⊛.	NOUN
ejpam-5320	196	6	suppose	suppose	VERB
ejpam-5320	196	7	that	that	SCONJ
ejpam-5320	196	8	f	f	PROPN
ejpam-5320	196	9	is	be	AUX
ejpam-5320	196	10	upper	upper	ADJ
ejpam-5320	196	11	c-(τ1	c-(τ1	PROPN
ejpam-5320	196	12	,	,	PUNCT
ejpam-5320	196	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	196	14	.	.	PUNCT
ejpam-5320	197	1	let	let	VERB
ejpam-5320	197	2	x	x	PUNCT
ejpam-5320	197	3	∈	∈	PROPN
ejpam-5320	197	4	x	x	X
ejpam-5320	197	5	and	and	CCONJ
ejpam-5320	197	6	v	v	X
ejpam-5320	197	7	be	be	AUX
ejpam-5320	197	8	any	any	DET
ejpam-5320	197	9	σ1σ2	σ1σ2	NOUN
ejpam-5320	197	10	-	-	ADJ
ejpam-5320	197	11	open	open	ADJ
ejpam-5320	197	12	set	set	NOUN
ejpam-5320	197	13	of	of	ADP
ejpam-5320	197	14	y	y	NOUN
ejpam-5320	197	15	containing	contain	VERB
ejpam-5320	197	16	g(x	g(x	NOUN
ejpam-5320	197	17	)	)	PUNCT
ejpam-5320	197	18	and	and	CCONJ
ejpam-5320	197	19	having	have	VERB
ejpam-5320	197	20	σ1σ2	σ1σ2	NOUN
ejpam-5320	197	21	-	-	ADJ
ejpam-5320	197	22	compact	compact	ADJ
ejpam-5320	197	23	complement	complement	NOUN
ejpam-5320	197	24	.	.	PUNCT
ejpam-5320	198	1	by	by	ADP
ejpam-5320	198	2	lemma	lemma	PROPN
ejpam-5320	198	3	3	3	NUM
ejpam-5320	198	4	,	,	PUNCT
ejpam-5320	198	5	we	we	PRON
ejpam-5320	198	6	have	have	VERB
ejpam-5320	198	7	x	x	X
ejpam-5320	198	8	∈	∈	PROPN
ejpam-5320	198	9	g+(v	g+(v	PROPN
ejpam-5320	198	10	)	)	PUNCT
ejpam-5320	198	11	=	=	PUNCT
ejpam-5320	199	1	f+(v	f+(v	NOUN
ejpam-5320	199	2	)	)	PUNCT
ejpam-5320	200	1	and	and	CCONJ
ejpam-5320	200	2	hence	hence	ADV
ejpam-5320	200	3	there	there	PRON
ejpam-5320	200	4	exists	exist	VERB
ejpam-5320	200	5	a	a	DET
ejpam-5320	200	6	τ1τ2	τ1τ2	NOUN
ejpam-5320	200	7	-	-	ADJ
ejpam-5320	200	8	open	open	ADJ
ejpam-5320	200	9	set	set	ADJ
ejpam-5320	200	10	u	u	NOUN
ejpam-5320	200	11	of	of	ADP
ejpam-5320	200	12	x	x	PUNCT
ejpam-5320	200	13	containing	contain	VERB
ejpam-5320	200	14	x	x	PUNCT
ejpam-5320	200	15	such	such	ADJ
ejpam-5320	200	16	that	that	SCONJ
ejpam-5320	200	17	f	f	PROPN
ejpam-5320	200	18	(	(	PUNCT
ejpam-5320	200	19	u	u	NOUN
ejpam-5320	200	20	)	)	PUNCT
ejpam-5320	200	21	⊆	⊆	NUM
ejpam-5320	200	22	v	v	NOUN
ejpam-5320	200	23	.	.	PUNCT
ejpam-5320	201	1	since	since	SCONJ
ejpam-5320	201	2	f	f	PROPN
ejpam-5320	201	3	(	(	PUNCT
ejpam-5320	201	4	z	z	NOUN
ejpam-5320	201	5	)	)	PUNCT
ejpam-5320	201	6	is	be	AUX
ejpam-5320	201	7	σ1σ2	σ1σ2	NOUN
ejpam-5320	201	8	-	-	ADJ
ejpam-5320	201	9	paracompact	paracompact	NOUN
ejpam-5320	201	10	and	and	CCONJ
ejpam-5320	201	11	σ1σ2regular	σ1σ2regular	PROPN
ejpam-5320	201	12	for	for	ADP
ejpam-5320	201	13	each	each	DET
ejpam-5320	201	14	z	z	NOUN
ejpam-5320	201	15	∈	∈	PROPN
ejpam-5320	201	16	u	u	NOUN
ejpam-5320	201	17	,	,	PUNCT
ejpam-5320	201	18	by	by	ADP
ejpam-5320	201	19	lemma	lemma	PROPN
ejpam-5320	201	20	2	2	NUM
ejpam-5320	201	21	there	there	PRON
ejpam-5320	201	22	exists	exist	VERB
ejpam-5320	201	23	a	a	DET
ejpam-5320	201	24	τ1τ2	τ1τ2	NOUN
ejpam-5320	201	25	-	-	ADJ
ejpam-5320	201	26	open	open	ADJ
ejpam-5320	201	27	set	set	NOUN
ejpam-5320	201	28	w	w	NOUN
ejpam-5320	201	29	of	of	ADP
ejpam-5320	201	30	x	x	SYM
ejpam-5320	201	31	such	such	ADJ
ejpam-5320	201	32	that	that	SCONJ
ejpam-5320	201	33	f	f	PROPN
ejpam-5320	201	34	(	(	PUNCT
ejpam-5320	201	35	z	z	NOUN
ejpam-5320	201	36	)	)	PUNCT
ejpam-5320	201	37	⊆	⊆	NUM
ejpam-5320	201	38	w	w	ADP
ejpam-5320	201	39	⊆	⊆	NUM
ejpam-5320	201	40	σ1σ2	σ1σ2	NOUN
ejpam-5320	201	41	-	-	PUNCT
ejpam-5320	201	42	cl(w	cl(w	NOUN
ejpam-5320	201	43	)	)	PUNCT
ejpam-5320	201	44	⊆	⊆	NUM
ejpam-5320	201	45	v	v	NOUN
ejpam-5320	201	46	;	;	PUNCT
ejpam-5320	201	47	hence	hence	ADV
ejpam-5320	201	48	g(z	g(z	ADJ
ejpam-5320	201	49	)	)	PUNCT
ejpam-5320	201	50	⊆	⊆	NUM
ejpam-5320	201	51	σ1σ2	σ1σ2	NOUN
ejpam-5320	201	52	-	-	PUNCT
ejpam-5320	201	53	cl(w	cl(w	NOUN
ejpam-5320	201	54	)	)	PUNCT
ejpam-5320	201	55	⊆	⊆	NUM
ejpam-5320	201	56	v	v	NOUN
ejpam-5320	201	57	for	for	ADP
ejpam-5320	201	58	each	each	DET
ejpam-5320	201	59	z	z	NOUN
ejpam-5320	201	60	∈	∈	PROPN
ejpam-5320	201	61	u	u	NOUN
ejpam-5320	201	62	.	.	PUNCT
ejpam-5320	202	1	thus	thus	ADV
ejpam-5320	202	2	,	,	PUNCT
ejpam-5320	202	3	g(u	g(u	PROPN
ejpam-5320	202	4	)	)	PUNCT
ejpam-5320	202	5	⊆	⊆	NUM
ejpam-5320	202	6	v	v	NOUN
ejpam-5320	202	7	and	and	CCONJ
ejpam-5320	202	8	hence	hence	ADV
ejpam-5320	202	9	g	g	PROPN
ejpam-5320	202	10	is	be	AUX
ejpam-5320	202	11	upper	upper	ADJ
ejpam-5320	202	12	c-(τ1	c-(τ1	PROPN
ejpam-5320	202	13	,	,	PUNCT
ejpam-5320	202	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	202	15	.	.	PUNCT
ejpam-5320	203	1	conversely	conversely	ADV
ejpam-5320	203	2	,	,	PUNCT
ejpam-5320	203	3	suppose	suppose	VERB
ejpam-5320	203	4	that	that	SCONJ
ejpam-5320	203	5	g	g	PROPN
ejpam-5320	203	6	is	be	AUX
ejpam-5320	203	7	upper	upper	ADJ
ejpam-5320	203	8	c-(τ1	c-(τ1	PROPN
ejpam-5320	203	9	,	,	PUNCT
ejpam-5320	203	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	203	11	.	.	PUNCT
ejpam-5320	204	1	let	let	VERB
ejpam-5320	204	2	x	x	PUNCT
ejpam-5320	204	3	∈	∈	PROPN
ejpam-5320	204	4	x	x	X
ejpam-5320	204	5	and	and	CCONJ
ejpam-5320	204	6	v	v	X
ejpam-5320	204	7	be	be	AUX
ejpam-5320	204	8	any	any	DET
ejpam-5320	204	9	σ1σ2	σ1σ2	NOUN
ejpam-5320	204	10	-	-	ADJ
ejpam-5320	204	11	open	open	ADJ
ejpam-5320	204	12	set	set	NOUN
ejpam-5320	204	13	of	of	ADP
ejpam-5320	204	14	y	y	PROPN
ejpam-5320	204	15	containing	contain	VERB
ejpam-5320	204	16	f	f	PROPN
ejpam-5320	204	17	(	(	PUNCT
ejpam-5320	204	18	x	x	NOUN
ejpam-5320	204	19	)	)	PUNCT
ejpam-5320	204	20	and	and	CCONJ
ejpam-5320	204	21	having	have	VERB
ejpam-5320	204	22	σ1σ2	σ1σ2	NOUN
ejpam-5320	204	23	-	-	ADJ
ejpam-5320	204	24	compact	compact	ADJ
ejpam-5320	204	25	complement	complement	NOUN
ejpam-5320	204	26	.	.	PUNCT
ejpam-5320	205	1	by	by	ADP
ejpam-5320	205	2	lemma	lemma	PROPN
ejpam-5320	205	3	3	3	NUM
ejpam-5320	205	4	,	,	PUNCT
ejpam-5320	205	5	we	we	PRON
ejpam-5320	205	6	have	have	VERB
ejpam-5320	205	7	x	x	X
ejpam-5320	205	8	∈	∈	NOUN
ejpam-5320	205	9	f+(v	f+(v	NOUN
ejpam-5320	205	10	)	)	PUNCT
ejpam-5320	206	1	=	=	PUNCT
ejpam-5320	206	2	g+(v	g+(v	PROPN
ejpam-5320	206	3	)	)	PUNCT
ejpam-5320	206	4	and	and	CCONJ
ejpam-5320	206	5	hence	hence	ADV
ejpam-5320	206	6	g(x	g(x	NOUN
ejpam-5320	206	7	)	)	PUNCT
ejpam-5320	206	8	⊆	⊆	NUM
ejpam-5320	206	9	v	v	NOUN
ejpam-5320	206	10	.	.	PUNCT
ejpam-5320	207	1	there	there	PRON
ejpam-5320	207	2	exists	exist	VERB
ejpam-5320	207	3	a	a	DET
ejpam-5320	207	4	τ1τ2	τ1τ2	NOUN
ejpam-5320	207	5	-	-	ADJ
ejpam-5320	207	6	open	open	ADJ
ejpam-5320	207	7	set	set	ADJ
ejpam-5320	207	8	u	u	NOUN
ejpam-5320	207	9	of	of	ADP
ejpam-5320	207	10	x	x	PUNCT
ejpam-5320	207	11	containing	contain	VERB
ejpam-5320	207	12	x	x	PUNCT
ejpam-5320	207	13	such	such	ADJ
ejpam-5320	207	14	that	that	SCONJ
ejpam-5320	207	15	g(u	g(u	PROPN
ejpam-5320	207	16	)	)	PUNCT
ejpam-5320	207	17	⊆	⊆	NUM
ejpam-5320	207	18	v	v	NOUN
ejpam-5320	207	19	.	.	PUNCT
ejpam-5320	208	1	thus	thus	ADV
ejpam-5320	208	2	,	,	PUNCT
ejpam-5320	208	3	u	u	PROPN
ejpam-5320	208	4	⊆	⊆	NUM
ejpam-5320	208	5	g+(v	g+(v	PROPN
ejpam-5320	208	6	)	)	PUNCT
ejpam-5320	208	7	=	=	PUNCT
ejpam-5320	209	1	f+(v	f+(v	NOUN
ejpam-5320	209	2	)	)	PUNCT
ejpam-5320	210	1	and	and	CCONJ
ejpam-5320	210	2	so	so	ADV
ejpam-5320	210	3	f	f	PROPN
ejpam-5320	210	4	(	(	PUNCT
ejpam-5320	210	5	u	u	NOUN
ejpam-5320	210	6	)	)	PUNCT
ejpam-5320	210	7	⊆	⊆	NUM
ejpam-5320	210	8	v	v	NOUN
ejpam-5320	210	9	.	.	PUNCT
ejpam-5320	211	1	this	this	PRON
ejpam-5320	211	2	shows	show	VERB
ejpam-5320	211	3	that	that	SCONJ
ejpam-5320	211	4	f	f	PROPN
ejpam-5320	211	5	is	be	AUX
ejpam-5320	211	6	upper	upper	ADJ
ejpam-5320	211	7	c-(τ1	c-(τ1	PROPN
ejpam-5320	211	8	,	,	PUNCT
ejpam-5320	211	9	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5320	211	10	.	.	PUNCT
ejpam-5320	212	1	lemma	lemma	PROPN
ejpam-5320	212	2	4	4	NUM
ejpam-5320	212	3	.	.	PUNCT
ejpam-5320	213	1	[	[	X
ejpam-5320	213	2	21	21	NUM
ejpam-5320	213	3	]	]	PUNCT
ejpam-5320	213	4	for	for	ADP
ejpam-5320	213	5	a	a	DET
ejpam-5320	213	6	multifunction	multifunction	NOUN
ejpam-5320	213	7	f	f	NOUN
ejpam-5320	213	8	:	:	PUNCT
ejpam-5320	213	9	(	(	PUNCT
ejpam-5320	213	10	x	x	NOUN
ejpam-5320	213	11	,	,	PUNCT
ejpam-5320	213	12	τ1	τ1	NOUN
ejpam-5320	213	13	,	,	PUNCT
ejpam-5320	213	14	τ2	τ2	NOUN
ejpam-5320	213	15	)	)	PUNCT
ejpam-5320	213	16	→	→	SYM
ejpam-5320	213	17	(	(	PUNCT
ejpam-5320	213	18	y	y	PROPN
ejpam-5320	213	19	,	,	PUNCT
ejpam-5320	213	20	σ1	σ1	PROPN
ejpam-5320	213	21	,	,	PUNCT
ejpam-5320	213	22	σ2	σ2	NOUN
ejpam-5320	213	23	)	)	PUNCT
ejpam-5320	213	24	,	,	PUNCT
ejpam-5320	213	25	clf	clf	PROPN
ejpam-5320	213	26	−	−	PROPN
ejpam-5320	213	27	⊛	⊛	NUM
ejpam-5320	213	28	(	(	PUNCT
ejpam-5320	213	29	v	v	NOUN
ejpam-5320	213	30	)	)	PUNCT
ejpam-5320	213	31	=	=	SYM
ejpam-5320	213	32	f−(v	f−(v	ADJ
ejpam-5320	213	33	)	)	PUNCT
ejpam-5320	213	34	for	for	ADP
ejpam-5320	213	35	each	each	DET
ejpam-5320	213	36	σ1σ2	σ1σ2	VERB
ejpam-5320	213	37	-	-	ADJ
ejpam-5320	213	38	open	open	ADJ
ejpam-5320	213	39	set	set	NOUN
ejpam-5320	213	40	v	v	NOUN
ejpam-5320	213	41	of	of	ADP
ejpam-5320	213	42	y	y	PROPN
ejpam-5320	213	43	.	.	PUNCT
ejpam-5320	214	1	theorem	theorem	ADJ
ejpam-5320	214	2	8	8	NUM
ejpam-5320	214	3	.	.	PUNCT
ejpam-5320	215	1	for	for	ADP
ejpam-5320	215	2	a	a	DET
ejpam-5320	215	3	multifunction	multifunction	NOUN
ejpam-5320	215	4	f	f	NOUN
ejpam-5320	215	5	:	:	PUNCT
ejpam-5320	215	6	(	(	PUNCT
ejpam-5320	215	7	x	x	NOUN
ejpam-5320	215	8	,	,	PUNCT
ejpam-5320	215	9	τ1	τ1	NOUN
ejpam-5320	215	10	,	,	PUNCT
ejpam-5320	215	11	τ2	τ2	NOUN
ejpam-5320	215	12	)	)	PUNCT
ejpam-5320	215	13	→	→	SYM
ejpam-5320	215	14	(	(	PUNCT
ejpam-5320	215	15	y	y	PROPN
ejpam-5320	215	16	,	,	PUNCT
ejpam-5320	215	17	σ1	σ1	PROPN
ejpam-5320	215	18	,	,	PUNCT
ejpam-5320	215	19	σ2	σ2	NOUN
ejpam-5320	215	20	)	)	PUNCT
ejpam-5320	215	21	,	,	PUNCT
ejpam-5320	215	22	the	the	DET
ejpam-5320	215	23	following	follow	VERB
ejpam-5320	215	24	properties	property	NOUN
ejpam-5320	215	25	are	be	AUX
ejpam-5320	215	26	equivalent	equivalent	ADJ
ejpam-5320	215	27	:	:	PUNCT
ejpam-5320	215	28	references	reference	NOUN
ejpam-5320	215	29	2296	2296	NUM
ejpam-5320	215	30	(	(	PUNCT
ejpam-5320	215	31	1	1	NUM
ejpam-5320	215	32	)	)	PUNCT
ejpam-5320	215	33	f	f	PROPN
ejpam-5320	215	34	is	be	AUX
ejpam-5320	215	35	lower	low	ADJ
ejpam-5320	215	36	c-(τ1	c-(τ1	NOUN
ejpam-5320	215	37	,	,	PUNCT
ejpam-5320	215	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	215	39	;	;	PUNCT
ejpam-5320	215	40	(	(	PUNCT
ejpam-5320	215	41	2	2	X
ejpam-5320	215	42	)	)	PUNCT
ejpam-5320	215	43	clf⊛	clf⊛	PROPN
ejpam-5320	215	44	is	be	AUX
ejpam-5320	215	45	lower	low	ADJ
ejpam-5320	215	46	c-(τ1	c-(τ1	NOUN
ejpam-5320	215	47	,	,	PUNCT
ejpam-5320	215	48	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	215	49	.	.	PUNCT
ejpam-5320	216	1	proof	proof	NOUN
ejpam-5320	216	2	.	.	PUNCT
ejpam-5320	217	1	by	by	ADP
ejpam-5320	217	2	using	use	VERB
ejpam-5320	217	3	lemma	lemma	PROPN
ejpam-5320	217	4	4	4	NUM
ejpam-5320	217	5	this	this	PRON
ejpam-5320	217	6	can	can	AUX
ejpam-5320	217	7	be	be	AUX
ejpam-5320	217	8	shown	show	VERB
ejpam-5320	217	9	similarly	similarly	ADV
ejpam-5320	217	10	to	to	ADP
ejpam-5320	217	11	that	that	PRON
ejpam-5320	217	12	of	of	ADP
ejpam-5320	217	13	theorem	theorem	ADJ
ejpam-5320	217	14	7	7	NUM
ejpam-5320	217	15	.	.	PUNCT
ejpam-5320	217	16	acknowledgements	acknowledgement	NOUN
ejpam-5320	217	17	this	this	DET
ejpam-5320	217	18	research	research	NOUN
ejpam-5320	217	19	project	project	NOUN
ejpam-5320	217	20	was	be	AUX
ejpam-5320	217	21	financially	financially	ADV
ejpam-5320	217	22	supported	support	VERB
ejpam-5320	217	23	by	by	ADP
ejpam-5320	217	24	mahasarakham	mahasarakham	PROPN
ejpam-5320	217	25	university	university	PROPN
ejpam-5320	217	26	.	.	PUNCT
ejpam-5320	218	1	references	reference	NOUN
ejpam-5320	218	2	[	[	X
ejpam-5320	218	3	1	1	NUM
ejpam-5320	218	4	]	]	PUNCT
ejpam-5320	218	5	c.	c.	PROPN
ejpam-5320	218	6	berge	berge	PROPN
ejpam-5320	218	7	.	.	PUNCT
ejpam-5320	219	1	espaces	espace	VERB
ejpam-5320	219	2	topologiques	topologique	NOUN
ejpam-5320	219	3	fonctions	fonction	NOUN
ejpam-5320	219	4	multivoques	multivoque	NOUN
ejpam-5320	219	5	.	.	PUNCT
ejpam-5320	220	1	dunod	dunod	PROPN
ejpam-5320	220	2	,	,	PUNCT
ejpam-5320	220	3	paris	paris	PROPN
ejpam-5320	220	4	,	,	PUNCT
ejpam-5320	220	5	1959	1959	NUM
ejpam-5320	220	6	.	.	PUNCT
ejpam-5320	221	1	[	[	X
ejpam-5320	221	2	2	2	NUM
ejpam-5320	221	3	]	]	PUNCT
ejpam-5320	221	4	c.	c.	PROPN
ejpam-5320	221	5	boonpok	boonpok	PROPN
ejpam-5320	221	6	.	.	PUNCT
ejpam-5320	222	1	almost	almost	ADV
ejpam-5320	222	2	(	(	PUNCT
ejpam-5320	222	3	g	g	NOUN
ejpam-5320	222	4	,	,	PUNCT
ejpam-5320	222	5	m)-continuous	m)-continuous	ADJ
ejpam-5320	222	6	functions	function	NOUN
ejpam-5320	222	7	.	.	PUNCT
ejpam-5320	223	1	international	international	ADJ
ejpam-5320	223	2	journal	journal	PROPN
ejpam-5320	223	3	of	of	ADP
ejpam-5320	223	4	mathematical	mathematical	ADJ
ejpam-5320	223	5	analysis	analysis	NOUN
ejpam-5320	223	6	,	,	PUNCT
ejpam-5320	223	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5320	223	8	,	,	PUNCT
ejpam-5320	223	9	2010	2010	NUM
ejpam-5320	223	10	.	.	PUNCT
ejpam-5320	224	1	[	[	X
ejpam-5320	224	2	3	3	X
ejpam-5320	224	3	]	]	PUNCT
ejpam-5320	224	4	c.	c.	PROPN
ejpam-5320	224	5	boonpok	boonpok	PROPN
ejpam-5320	224	6	.	.	PUNCT
ejpam-5320	225	1	m	m	VERB
ejpam-5320	225	2	-continuous	-continuous	ADJ
ejpam-5320	225	3	functions	function	NOUN
ejpam-5320	225	4	in	in	ADP
ejpam-5320	225	5	biminimal	biminimal	NOUN
ejpam-5320	225	6	structure	structure	NOUN
ejpam-5320	225	7	spaces	space	NOUN
ejpam-5320	225	8	.	.	PUNCT
ejpam-5320	226	1	far	far	PROPN
ejpam-5320	226	2	east	east	PROPN
ejpam-5320	226	3	journal	journal	PROPN
ejpam-5320	226	4	of	of	ADP
ejpam-5320	226	5	mathematical	mathematical	ADJ
ejpam-5320	226	6	sciences	science	NOUN
ejpam-5320	226	7	,	,	PUNCT
ejpam-5320	226	8	43(1):41–58	43(1):41–58	NUM
ejpam-5320	226	9	,	,	PUNCT
ejpam-5320	226	10	2010	2010	NUM
ejpam-5320	226	11	.	.	PUNCT
ejpam-5320	227	1	[	[	X
ejpam-5320	227	2	4	4	NUM
ejpam-5320	227	3	]	]	PUNCT
ejpam-5320	227	4	c.	c.	PROPN
ejpam-5320	227	5	boonpok	boonpok	PROPN
ejpam-5320	227	6	.	.	PUNCT
ejpam-5320	228	1	on	on	ADP
ejpam-5320	228	2	continuous	continuous	ADJ
ejpam-5320	228	3	multifunctions	multifunction	NOUN
ejpam-5320	228	4	in	in	ADP
ejpam-5320	228	5	ideal	ideal	ADJ
ejpam-5320	228	6	topological	topological	ADJ
ejpam-5320	228	7	spaces	space	NOUN
ejpam-5320	228	8	.	.	PUNCT
ejpam-5320	229	1	lobachevskii	lobachevskii	PROPN
ejpam-5320	229	2	journal	journal	PROPN
ejpam-5320	229	3	of	of	ADP
ejpam-5320	229	4	mathematics	mathematic	NOUN
ejpam-5320	229	5	,	,	PUNCT
ejpam-5320	229	6	40(1):24–35	40(1):24–35	NUM
ejpam-5320	229	7	,	,	PUNCT
ejpam-5320	229	8	2019	2019	NUM
ejpam-5320	229	9	.	.	PUNCT
ejpam-5320	230	1	[	[	X
ejpam-5320	230	2	5	5	X
ejpam-5320	230	3	]	]	PUNCT
ejpam-5320	230	4	c.	c.	PROPN
ejpam-5320	230	5	boonpok	boonpok	PROPN
ejpam-5320	230	6	.	.	PUNCT
ejpam-5320	231	1	on	on	ADP
ejpam-5320	231	2	characterizations	characterization	NOUN
ejpam-5320	231	3	of	of	ADP
ejpam-5320	231	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5320	231	5	ideal	ideal	ADJ
ejpam-5320	231	6	topological	topological	ADJ
ejpam-5320	231	7	spaces	space	NOUN
ejpam-5320	231	8	.	.	PUNCT
ejpam-5320	232	1	journal	journal	NOUN
ejpam-5320	232	2	of	of	ADP
ejpam-5320	232	3	mathematics	mathematic	NOUN
ejpam-5320	232	4	,	,	PUNCT
ejpam-5320	232	5	2020:9387601	2020:9387601	NUM
ejpam-5320	232	6	,	,	PUNCT
ejpam-5320	232	7	2020	2020	NUM
ejpam-5320	232	8	.	.	PUNCT
ejpam-5320	233	1	[	[	X
ejpam-5320	233	2	6	6	NUM
ejpam-5320	233	3	]	]	PUNCT
ejpam-5320	233	4	c.	c.	PROPN
ejpam-5320	233	5	boonpok	boonpok	PROPN
ejpam-5320	233	6	.	.	PUNCT
ejpam-5320	234	1	(	(	PUNCT
ejpam-5320	234	2	τ1	τ1	NOUN
ejpam-5320	234	3	,	,	PUNCT
ejpam-5320	234	4	τ2)δ	τ2)δ	ADJ
ejpam-5320	234	5	-	-	PUNCT
ejpam-5320	234	6	semicontinuous	semicontinuous	ADJ
ejpam-5320	234	7	multifunctions	multifunction	NOUN
ejpam-5320	234	8	.	.	PUNCT
ejpam-5320	235	1	heliyon	heliyon	NOUN
ejpam-5320	235	2	,	,	PUNCT
ejpam-5320	235	3	6	6	NUM
ejpam-5320	235	4	:	:	SYM
ejpam-5320	235	5	e05367	e05367	PROPN
ejpam-5320	235	6	,	,	PUNCT
ejpam-5320	235	7	2020	2020	NUM
ejpam-5320	235	8	.	.	PUNCT
ejpam-5320	236	1	[	[	X
ejpam-5320	236	2	7	7	X
ejpam-5320	236	3	]	]	X
ejpam-5320	236	4	c.	c.	PROPN
ejpam-5320	236	5	boonpok	boonpok	PROPN
ejpam-5320	236	6	.	.	PUNCT
ejpam-5320	237	1	weak	weak	ADJ
ejpam-5320	237	2	quasi	quasi	ADJ
ejpam-5320	237	3	continuity	continuity	NOUN
ejpam-5320	237	4	for	for	ADP
ejpam-5320	237	5	multifunctions	multifunction	NOUN
ejpam-5320	237	6	in	in	ADP
ejpam-5320	237	7	ideal	ideal	ADJ
ejpam-5320	237	8	topological	topological	ADJ
ejpam-5320	237	9	spaces	space	NOUN
ejpam-5320	237	10	.	.	PUNCT
ejpam-5320	238	1	advances	advance	NOUN
ejpam-5320	238	2	in	in	ADP
ejpam-5320	238	3	mathematics	mathematic	NOUN
ejpam-5320	238	4	:	:	PUNCT
ejpam-5320	238	5	scientific	scientific	ADJ
ejpam-5320	238	6	journal	journal	NOUN
ejpam-5320	238	7	,	,	PUNCT
ejpam-5320	238	8	9(1):339–355	9(1):339–355	NUM
ejpam-5320	238	9	,	,	PUNCT
ejpam-5320	238	10	2020	2020	NUM
ejpam-5320	238	11	.	.	PUNCT
ejpam-5320	239	1	[	[	X
ejpam-5320	239	2	8	8	NUM
ejpam-5320	239	3	]	]	X
ejpam-5320	239	4	c.	c.	PROPN
ejpam-5320	239	5	boonpok	boonpok	PROPN
ejpam-5320	239	6	.	.	PUNCT
ejpam-5320	240	1	upper	upper	ADJ
ejpam-5320	240	2	and	and	CCONJ
ejpam-5320	240	3	lower	low	ADJ
ejpam-5320	240	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5320	240	5	.	.	PUNCT
ejpam-5320	240	6	heliyon	heliyon	NOUN
ejpam-5320	240	7	,	,	PUNCT
ejpam-5320	240	8	7	7	NUM
ejpam-5320	240	9	:	:	PUNCT
ejpam-5320	240	10	e05986	e05986	PROPN
ejpam-5320	240	11	,	,	PUNCT
ejpam-5320	240	12	2021	2021	NUM
ejpam-5320	240	13	.	.	PUNCT
ejpam-5320	241	1	[	[	X
ejpam-5320	241	2	9	9	NUM
ejpam-5320	241	3	]	]	PUNCT
ejpam-5320	241	4	c.	c.	PROPN
ejpam-5320	241	5	boonpok	boonpok	PROPN
ejpam-5320	241	6	.	.	PUNCT
ejpam-5320	242	1	on	on	ADP
ejpam-5320	242	2	some	some	DET
ejpam-5320	242	3	closed	closed	ADJ
ejpam-5320	242	4	sets	set	NOUN
ejpam-5320	242	5	and	and	CCONJ
ejpam-5320	242	6	low	low	ADJ
ejpam-5320	242	7	separation	separation	NOUN
ejpam-5320	242	8	axioms	axiom	NOUN
ejpam-5320	242	9	via	via	ADP
ejpam-5320	242	10	topological	topological	ADJ
ejpam-5320	242	11	ideals	ideal	NOUN
ejpam-5320	242	12	.	.	PUNCT
ejpam-5320	243	1	european	european	ADJ
ejpam-5320	243	2	journal	journal	PROPN
ejpam-5320	243	3	of	of	ADP
ejpam-5320	243	4	pure	pure	ADJ
ejpam-5320	243	5	and	and	CCONJ
ejpam-5320	243	6	applied	applied	ADJ
ejpam-5320	243	7	mathematics	mathematic	NOUN
ejpam-5320	243	8	,	,	PUNCT
ejpam-5320	243	9	15(3):300–309	15(3):300–309	NOUN
ejpam-5320	243	10	,	,	PUNCT
ejpam-5320	243	11	2022	2022	NUM
ejpam-5320	243	12	.	.	PUNCT
ejpam-5320	244	1	[	[	X
ejpam-5320	244	2	10	10	NUM
ejpam-5320	244	3	]	]	X
ejpam-5320	244	4	c.	c.	PROPN
ejpam-5320	244	5	boonpok	boonpok	PROPN
ejpam-5320	244	6	.	.	PUNCT
ejpam-5320	245	1	on	on	ADP
ejpam-5320	245	2	some	some	DET
ejpam-5320	245	3	spaces	space	NOUN
ejpam-5320	245	4	via	via	ADP
ejpam-5320	245	5	topological	topological	ADJ
ejpam-5320	245	6	ideals	ideal	NOUN
ejpam-5320	245	7	.	.	PUNCT
ejpam-5320	246	1	open	open	ADJ
ejpam-5320	246	2	mathematics	mathematic	NOUN
ejpam-5320	246	3	,	,	PUNCT
ejpam-5320	246	4	21:20230118	21:20230118	NUM
ejpam-5320	246	5	,	,	PUNCT
ejpam-5320	246	6	2023	2023	NUM
ejpam-5320	246	7	.	.	PUNCT
ejpam-5320	247	1	[	[	X
ejpam-5320	247	2	11	11	NUM
ejpam-5320	247	3	]	]	PUNCT
ejpam-5320	247	4	c.	c.	PROPN
ejpam-5320	247	5	boonpok	boonpok	PROPN
ejpam-5320	247	6	.	.	PUNCT
ejpam-5320	248	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5320	248	2	.	.	PUNCT
ejpam-5320	249	1	mathematica	mathematica	PROPN
ejpam-5320	249	2	,	,	PUNCT
ejpam-5320	249	3	65(1):31–42	65(1):31–42	NUM
ejpam-5320	249	4	,	,	PUNCT
ejpam-5320	249	5	2023	2023	NUM
ejpam-5320	249	6	.	.	PUNCT
ejpam-5320	250	1	[	[	X
ejpam-5320	250	2	12	12	NUM
ejpam-5320	250	3	]	]	X
ejpam-5320	250	4	c.	c.	PROPN
ejpam-5320	250	5	boonpok	boonpok	PROPN
ejpam-5320	250	6	and	and	CCONJ
ejpam-5320	250	7	j.	j.	PROPN
ejpam-5320	250	8	khampakdee	khampakdee	PROPN
ejpam-5320	250	9	.	.	PUNCT
ejpam-5320	251	1	almost	almost	ADV
ejpam-5320	251	2	strong	strong	ADJ
ejpam-5320	251	3	θ(λ	θ(λ	PROPN
ejpam-5320	251	4	,	,	PUNCT
ejpam-5320	251	5	p)-continuity	p)-continuity	NOUN
ejpam-5320	251	6	for	for	ADP
ejpam-5320	251	7	functions	function	NOUN
ejpam-5320	251	8	.	.	PUNCT
ejpam-5320	252	1	european	european	ADJ
ejpam-5320	252	2	journal	journal	PROPN
ejpam-5320	252	3	of	of	ADP
ejpam-5320	252	4	pure	pure	ADJ
ejpam-5320	252	5	and	and	CCONJ
ejpam-5320	252	6	applied	applied	ADJ
ejpam-5320	252	7	mathematics	mathematic	NOUN
ejpam-5320	252	8	,	,	PUNCT
ejpam-5320	252	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5320	252	10	,	,	PUNCT
ejpam-5320	252	11	2024	2024	NUM
ejpam-5320	252	12	.	.	PUNCT
ejpam-5320	253	1	[	[	X
ejpam-5320	253	2	13	13	NUM
ejpam-5320	253	3	]	]	PUNCT
ejpam-5320	253	4	c.	c.	PROPN
ejpam-5320	253	5	boonpok	boonpok	PROPN
ejpam-5320	253	6	and	and	CCONJ
ejpam-5320	253	7	c.	c.	PROPN
ejpam-5320	253	8	klanarong	klanarong	PROPN
ejpam-5320	253	9	.	.	PUNCT
ejpam-5320	254	1	on	on	ADP
ejpam-5320	254	2	weakly	weakly	ADJ
ejpam-5320	254	3	(	(	PUNCT
ejpam-5320	254	4	τ1	τ1	NOUN
ejpam-5320	254	5	,	,	PUNCT
ejpam-5320	254	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	254	7	functions	function	NOUN
ejpam-5320	254	8	.	.	PUNCT
ejpam-5320	255	1	european	european	ADJ
ejpam-5320	255	2	journal	journal	PROPN
ejpam-5320	255	3	of	of	ADP
ejpam-5320	255	4	pure	pure	ADJ
ejpam-5320	255	5	and	and	CCONJ
ejpam-5320	255	6	applied	applied	ADJ
ejpam-5320	255	7	mathematics	mathematic	NOUN
ejpam-5320	255	8	,	,	PUNCT
ejpam-5320	255	9	17(1):416–425	17(1):416–425	NUM
ejpam-5320	255	10	,	,	PUNCT
ejpam-5320	255	11	2024	2024	NUM
ejpam-5320	255	12	.	.	PUNCT
ejpam-5320	256	1	references	reference	NOUN
ejpam-5320	256	2	2297	2297	NUM
ejpam-5320	257	1	[	[	X
ejpam-5320	257	2	14	14	NUM
ejpam-5320	257	3	]	]	X
ejpam-5320	257	4	c.	c.	PROPN
ejpam-5320	257	5	boonpok	boonpok	PROPN
ejpam-5320	257	6	and	and	CCONJ
ejpam-5320	257	7	p.	p.	NOUN
ejpam-5320	257	8	pue	pue	NOUN
ejpam-5320	257	9	-	-	PUNCT
ejpam-5320	257	10	on	on	ADP
ejpam-5320	257	11	.	.	PUNCT
ejpam-5320	258	1	continuity	continuity	NOUN
ejpam-5320	258	2	for	for	ADP
ejpam-5320	258	3	multifunctions	multifunction	NOUN
ejpam-5320	258	4	in	in	ADP
ejpam-5320	258	5	ideal	ideal	ADJ
ejpam-5320	258	6	topological	topological	ADJ
ejpam-5320	258	7	spaces	space	NOUN
ejpam-5320	258	8	.	.	PUNCT
ejpam-5320	259	1	wseas	wseas	VERB
ejpam-5320	259	2	transactions	transaction	NOUN
ejpam-5320	259	3	on	on	ADP
ejpam-5320	259	4	mathematics	mathematic	NOUN
ejpam-5320	259	5	,	,	PUNCT
ejpam-5320	259	6	19:624–631	19:624–631	NUM
ejpam-5320	259	7	,	,	PUNCT
ejpam-5320	259	8	2020	2020	NUM
ejpam-5320	259	9	.	.	PUNCT
ejpam-5320	260	1	[	[	X
ejpam-5320	260	2	15	15	NUM
ejpam-5320	260	3	]	]	X
ejpam-5320	260	4	c.	c.	PROPN
ejpam-5320	260	5	boonpok	boonpok	PROPN
ejpam-5320	260	6	and	and	CCONJ
ejpam-5320	260	7	p.	p.	NOUN
ejpam-5320	260	8	pue	pue	NOUN
ejpam-5320	260	9	-	-	PUNCT
ejpam-5320	260	10	on	on	ADP
ejpam-5320	260	11	.	.	PUNCT
ejpam-5320	261	1	upper	upper	ADJ
ejpam-5320	261	2	and	and	CCONJ
ejpam-5320	261	3	lower	low	ADJ
ejpam-5320	261	4	weakly	weakly	ADJ
ejpam-5320	261	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5320	261	6	multifunctions	multifunction	NOUN
ejpam-5320	261	7	.	.	PUNCT
ejpam-5320	262	1	international	international	ADJ
ejpam-5320	262	2	journal	journal	NOUN
ejpam-5320	262	3	of	of	ADP
ejpam-5320	262	4	analysis	analysis	NOUN
ejpam-5320	262	5	and	and	CCONJ
ejpam-5320	262	6	applications	application	NOUN
ejpam-5320	262	7	,	,	PUNCT
ejpam-5320	262	8	21:90	21:90	NUM
ejpam-5320	262	9	,	,	PUNCT
ejpam-5320	262	10	2023	2023	NUM
ejpam-5320	262	11	.	.	PUNCT
ejpam-5320	263	1	[	[	X
ejpam-5320	263	2	16	16	NUM
ejpam-5320	263	3	]	]	X
ejpam-5320	263	4	c.	c.	PROPN
ejpam-5320	263	5	boonpok	boonpok	PROPN
ejpam-5320	263	6	and	and	CCONJ
ejpam-5320	263	7	p.	p.	NOUN
ejpam-5320	263	8	pue	pue	NOUN
ejpam-5320	263	9	-	-	PUNCT
ejpam-5320	263	10	on	on	ADP
ejpam-5320	263	11	.	.	PUNCT
ejpam-5320	264	1	characterizations	characterization	NOUN
ejpam-5320	264	2	of	of	ADP
ejpam-5320	264	3	almost	almost	ADV
ejpam-5320	264	4	(	(	PUNCT
ejpam-5320	264	5	τ1	τ1	NOUN
ejpam-5320	264	6	,	,	PUNCT
ejpam-5320	264	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	264	8	functions	function	NOUN
ejpam-5320	264	9	.	.	PUNCT
ejpam-5320	265	1	international	international	ADJ
ejpam-5320	265	2	journal	journal	NOUN
ejpam-5320	265	3	of	of	ADP
ejpam-5320	265	4	analysis	analysis	NOUN
ejpam-5320	265	5	and	and	CCONJ
ejpam-5320	265	6	applications	application	NOUN
ejpam-5320	265	7	,	,	PUNCT
ejpam-5320	265	8	22:33	22:33	NUM
ejpam-5320	265	9	,	,	PUNCT
ejpam-5320	265	10	2024	2024	NUM
ejpam-5320	265	11	.	.	PUNCT
ejpam-5320	266	1	[	[	X
ejpam-5320	266	2	17	17	NUM
ejpam-5320	266	3	]	]	X
ejpam-5320	266	4	c.	c.	PROPN
ejpam-5320	266	5	boonpok	boonpok	PROPN
ejpam-5320	266	6	and	and	CCONJ
ejpam-5320	266	7	n.	n.	PROPN
ejpam-5320	266	8	srisarakham	srisarakham	PROPN
ejpam-5320	266	9	.	.	PUNCT
ejpam-5320	267	1	weak	weak	ADJ
ejpam-5320	267	2	forms	form	NOUN
ejpam-5320	267	3	of	of	ADP
ejpam-5320	267	4	(	(	PUNCT
ejpam-5320	267	5	λ	λ	PROPN
ejpam-5320	267	6	,	,	PUNCT
ejpam-5320	267	7	b)-open	b)-open	VERB
ejpam-5320	267	8	sets	set	NOUN
ejpam-5320	267	9	and	and	CCONJ
ejpam-5320	267	10	weak	weak	ADJ
ejpam-5320	267	11	(	(	PUNCT
ejpam-5320	267	12	λ	λ	NOUN
ejpam-5320	267	13	,	,	PUNCT
ejpam-5320	267	14	b)continuity	b)continuity	NOUN
ejpam-5320	267	15	.	.	PUNCT
ejpam-5320	268	1	european	european	PROPN
ejpam-5320	268	2	journal	journal	PROPN
ejpam-5320	268	3	of	of	ADP
ejpam-5320	268	4	pure	pure	ADJ
ejpam-5320	268	5	and	and	CCONJ
ejpam-5320	268	6	applied	applied	ADJ
ejpam-5320	268	7	mathematics	mathematic	NOUN
ejpam-5320	268	8	,	,	PUNCT
ejpam-5320	268	9	16(1):29–43	16(1):29–43	NUM
ejpam-5320	268	10	,	,	PUNCT
ejpam-5320	268	11	2023	2023	NUM
ejpam-5320	268	12	.	.	PUNCT
ejpam-5320	269	1	[	[	X
ejpam-5320	269	2	18	18	NUM
ejpam-5320	269	3	]	]	PUNCT
ejpam-5320	269	4	c.	c.	PROPN
ejpam-5320	269	5	boonpok	boonpok	PROPN
ejpam-5320	269	6	and	and	CCONJ
ejpam-5320	269	7	n.	n.	PROPN
ejpam-5320	269	8	srisarakham	srisarakham	PROPN
ejpam-5320	269	9	.	.	PUNCT
ejpam-5320	270	1	(	(	PUNCT
ejpam-5320	270	2	τ1	τ1	NOUN
ejpam-5320	270	3	,	,	PUNCT
ejpam-5320	270	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5320	270	5	for	for	ADP
ejpam-5320	270	6	functions	function	NOUN
ejpam-5320	270	7	.	.	PUNCT
ejpam-5320	271	1	asia	asia	PROPN
ejpam-5320	271	2	pacific	pacific	PROPN
ejpam-5320	271	3	journal	journal	PROPN
ejpam-5320	271	4	of	of	ADP
ejpam-5320	271	5	mathematics	mathematic	NOUN
ejpam-5320	271	6	,	,	PUNCT
ejpam-5320	271	7	11:21	11:21	NUM
ejpam-5320	271	8	,	,	PUNCT
ejpam-5320	271	9	2024	2024	NUM
ejpam-5320	271	10	.	.	PUNCT
ejpam-5320	272	1	[	[	X
ejpam-5320	272	2	19	19	NUM
ejpam-5320	272	3	]	]	X
ejpam-5320	272	4	c.	c.	PROPN
ejpam-5320	272	5	boonpok	boonpok	PROPN
ejpam-5320	272	6	and	and	CCONJ
ejpam-5320	272	7	c.	c.	PROPN
ejpam-5320	272	8	viriyapong	viriyapong	PROPN
ejpam-5320	272	9	.	.	PUNCT
ejpam-5320	273	1	almost	almost	ADV
ejpam-5320	273	2	weak	weak	ADJ
ejpam-5320	273	3	continuity	continuity	NOUN
ejpam-5320	273	4	for	for	ADP
ejpam-5320	273	5	multifunctions	multifunction	NOUN
ejpam-5320	273	6	in	in	ADP
ejpam-5320	273	7	ideal	ideal	ADJ
ejpam-5320	273	8	topological	topological	ADJ
ejpam-5320	273	9	spaces	space	NOUN
ejpam-5320	273	10	.	.	PUNCT
ejpam-5320	274	1	wseas	wseas	VERB
ejpam-5320	274	2	transactions	transaction	NOUN
ejpam-5320	274	3	on	on	ADP
ejpam-5320	274	4	mathematics	mathematic	NOUN
ejpam-5320	274	5	,	,	PUNCT
ejpam-5320	274	6	19:367–372	19:367–372	PROPN
ejpam-5320	274	7	,	,	PUNCT
ejpam-5320	274	8	2020	2020	NUM
ejpam-5320	274	9	.	.	PUNCT
ejpam-5320	275	1	[	[	X
ejpam-5320	275	2	20	20	NUM
ejpam-5320	275	3	]	]	PUNCT
ejpam-5320	275	4	c.	c.	PROPN
ejpam-5320	275	5	boonpok	boonpok	PROPN
ejpam-5320	275	6	and	and	CCONJ
ejpam-5320	275	7	c.	c.	PROPN
ejpam-5320	275	8	viriyapong	viriyapong	PROPN
ejpam-5320	275	9	.	.	PUNCT
ejpam-5320	276	1	upper	upper	ADJ
ejpam-5320	276	2	and	and	CCONJ
ejpam-5320	276	3	lower	low	ADJ
ejpam-5320	276	4	almost	almost	ADV
ejpam-5320	276	5	weak	weak	ADJ
ejpam-5320	276	6	(	(	PUNCT
ejpam-5320	276	7	τ1	τ1	NOUN
ejpam-5320	276	8	,	,	PUNCT
ejpam-5320	276	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5320	276	10	.	.	PUNCT
ejpam-5320	277	1	european	european	PROPN
ejpam-5320	277	2	journal	journal	PROPN
ejpam-5320	277	3	of	of	ADP
ejpam-5320	277	4	pure	pure	ADJ
ejpam-5320	277	5	and	and	CCONJ
ejpam-5320	277	6	applied	applied	ADJ
ejpam-5320	277	7	mathematics	mathematic	NOUN
ejpam-5320	277	8	,	,	PUNCT
ejpam-5320	277	9	14(1):1212–1225	14(1):1212–1225	NUM
ejpam-5320	277	10	,	,	PUNCT
ejpam-5320	277	11	2021	2021	NUM
ejpam-5320	277	12	.	.	PUNCT
ejpam-5320	278	1	[	[	X
ejpam-5320	278	2	21	21	NUM
ejpam-5320	278	3	]	]	X
ejpam-5320	278	4	c.	c.	PROPN
ejpam-5320	278	5	boonpok	boonpok	PROPN
ejpam-5320	278	6	,	,	PUNCT
ejpam-5320	278	7	c.	c.	PROPN
ejpam-5320	278	8	viriyapong	viriyapong	PROPN
ejpam-5320	278	9	,	,	PUNCT
ejpam-5320	278	10	and	and	CCONJ
ejpam-5320	278	11	m.	m.	NOUN
ejpam-5320	278	12	thongmoon	thongmoon	NOUN
ejpam-5320	278	13	.	.	PUNCT
ejpam-5320	279	1	on	on	ADP
ejpam-5320	279	2	upper	upper	ADJ
ejpam-5320	279	3	and	and	CCONJ
ejpam-5320	279	4	lower	low	ADJ
ejpam-5320	279	5	(	(	PUNCT
ejpam-5320	279	6	τ1	τ1	NOUN
ejpam-5320	279	7	,	,	PUNCT
ejpam-5320	279	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5320	279	9	multifunctions	multifunction	NOUN
ejpam-5320	279	10	.	.	PUNCT
ejpam-5320	280	1	journal	journal	PROPN
ejpam-5320	280	2	of	of	ADP
ejpam-5320	280	3	mathematics	mathematics	PROPN
ejpam-5320	280	4	and	and	CCONJ
ejpam-5320	280	5	computer	computer	NOUN
ejpam-5320	280	6	science	science	NOUN
ejpam-5320	280	7	,	,	PUNCT
ejpam-5320	280	8	18:282–293	18:282–293	NUM
ejpam-5320	280	9	,	,	PUNCT
ejpam-5320	280	10	2018	2018	NUM
ejpam-5320	280	11	.	.	PUNCT
ejpam-5320	281	1	[	[	X
ejpam-5320	281	2	22	22	NUM
ejpam-5320	281	3	]	]	PUNCT
ejpam-5320	281	4	t.	t.	PROPN
ejpam-5320	281	5	duangphui	duangphui	PROPN
ejpam-5320	281	6	,	,	PUNCT
ejpam-5320	281	7	c.	c.	PROPN
ejpam-5320	281	8	boonpok	boonpok	PROPN
ejpam-5320	281	9	,	,	PUNCT
ejpam-5320	281	10	and	and	CCONJ
ejpam-5320	281	11	c.	c.	PROPN
ejpam-5320	281	12	viriyapong	viriyapong	PROPN
ejpam-5320	281	13	.	.	PUNCT
ejpam-5320	282	1	continuous	continuous	ADJ
ejpam-5320	282	2	functions	function	NOUN
ejpam-5320	282	3	on	on	ADP
ejpam-5320	282	4	bigeneralized	bigeneralize	VERB
ejpam-5320	282	5	topological	topological	ADJ
ejpam-5320	282	6	spaces	space	NOUN
ejpam-5320	282	7	.	.	PUNCT
ejpam-5320	283	1	international	international	ADJ
ejpam-5320	283	2	journal	journal	PROPN
ejpam-5320	283	3	of	of	ADP
ejpam-5320	283	4	mathematical	mathematical	ADJ
ejpam-5320	283	5	analysis	analysis	NOUN
ejpam-5320	283	6	,	,	PUNCT
ejpam-5320	283	7	5(24):1165	5(24):1165	NUM
ejpam-5320	283	8	–	–	PUNCT
ejpam-5320	283	9	1174	1174	NUM
ejpam-5320	283	10	,	,	PUNCT
ejpam-5320	283	11	2011	2011	NUM
ejpam-5320	283	12	.	.	PUNCT
ejpam-5320	284	1	[	[	X
ejpam-5320	284	2	23	23	NUM
ejpam-5320	284	3	]	]	PUNCT
ejpam-5320	284	4	k.	k.	PROPN
ejpam-5320	284	5	r.	r.	PROPN
ejpam-5320	284	6	gentry	gentry	PROPN
ejpam-5320	284	7	and	and	CCONJ
ejpam-5320	284	8	h.	h.	PROPN
ejpam-5320	284	9	b.	b.	PROPN
ejpam-5320	284	10	hoyle	hoyle	PROPN
ejpam-5320	284	11	iii	iii	PROPN
ejpam-5320	284	12	.	.	PUNCT
ejpam-5320	285	1	c	c	X
ejpam-5320	285	2	-	-	PUNCT
ejpam-5320	285	3	continuous	continuous	ADJ
ejpam-5320	285	4	functions	function	NOUN
ejpam-5320	285	5	.	.	PUNCT
ejpam-5320	286	1	yokohama	yokohama	PROPN
ejpam-5320	286	2	mathematical	mathematical	PROPN
ejpam-5320	286	3	journal	journal	PROPN
ejpam-5320	286	4	,	,	PUNCT
ejpam-5320	286	5	18:71–76	18:71–76	NUM
ejpam-5320	286	6	,	,	PUNCT
ejpam-5320	286	7	1970	1970	NUM
ejpam-5320	286	8	.	.	PUNCT
ejpam-5320	287	1	[	[	X
ejpam-5320	287	2	24	24	NUM
ejpam-5320	287	3	]	]	X
ejpam-5320	287	4	l.	l.	PROPN
ejpam-5320	287	5	holá	holá	PROPN
ejpam-5320	287	6	,	,	PUNCT
ejpam-5320	287	7	v.	v.	ADP
ejpam-5320	287	8	baláz	baláz	NOUN
ejpam-5320	287	9	,	,	PUNCT
ejpam-5320	287	10	and	and	CCONJ
ejpam-5320	287	11	t.	t.	PROPN
ejpam-5320	287	12	neubrunn	neubrunn	PROPN
ejpam-5320	287	13	.	.	PUNCT
ejpam-5320	288	1	remarks	remark	NOUN
ejpam-5320	288	2	on	on	ADP
ejpam-5320	288	3	c	c	NOUN
ejpam-5320	288	4	-	-	PUNCT
ejpam-5320	288	5	continuous	continuous	ADJ
ejpam-5320	288	6	multifunctions	multifunction	NOUN
ejpam-5320	288	7	.	.	PUNCT
ejpam-5320	289	1	acta	acta	PROPN
ejpam-5320	289	2	mathematica	mathematica	PROPN
ejpam-5320	289	3	universitatis	universitatis	PROPN
ejpam-5320	289	4	comenianae	comenianae	PROPN
ejpam-5320	289	5	,	,	PUNCT
ejpam-5320	289	6	50/51:51–59	50/51:51–59	NUM
ejpam-5320	289	7	,	,	PUNCT
ejpam-5320	289	8	1987	1987	NUM
ejpam-5320	289	9	.	.	PUNCT
ejpam-5320	290	1	[	[	X
ejpam-5320	290	2	25	25	NUM
ejpam-5320	290	3	]	]	X
ejpam-5320	290	4	c.	c.	PROPN
ejpam-5320	290	5	klanarong	klanarong	PROPN
ejpam-5320	290	6	,	,	PUNCT
ejpam-5320	290	7	s.	s.	PROPN
ejpam-5320	290	8	sompong	sompong	PROPN
ejpam-5320	290	9	,	,	PUNCT
ejpam-5320	290	10	and	and	CCONJ
ejpam-5320	290	11	c.	c.	PROPN
ejpam-5320	290	12	boonpok	boonpok	PROPN
ejpam-5320	290	13	.	.	PUNCT
ejpam-5320	291	1	upper	upper	ADJ
ejpam-5320	291	2	and	and	CCONJ
ejpam-5320	291	3	lower	low	ADJ
ejpam-5320	291	4	almost	almost	ADV
ejpam-5320	291	5	(	(	PUNCT
ejpam-5320	291	6	τ1	τ1	NOUN
ejpam-5320	291	7	,	,	PUNCT
ejpam-5320	291	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5320	291	9	multifunctions	multifunction	NOUN
ejpam-5320	291	10	.	.	PUNCT
ejpam-5320	292	1	european	european	ADJ
ejpam-5320	292	2	journal	journal	PROPN
ejpam-5320	292	3	of	of	ADP
ejpam-5320	292	4	pure	pure	ADJ
ejpam-5320	292	5	and	and	CCONJ
ejpam-5320	292	6	applied	applied	ADJ
ejpam-5320	292	7	mathematics	mathematic	NOUN
ejpam-5320	292	8	,	,	PUNCT
ejpam-5320	292	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5320	292	10	,	,	PUNCT
ejpam-5320	292	11	2024	2024	NUM
ejpam-5320	292	12	.	.	PUNCT
ejpam-5320	293	1	[	[	X
ejpam-5320	293	2	26	26	NUM
ejpam-5320	293	3	]	]	PUNCT
ejpam-5320	293	4	k.	k.	PROPN
ejpam-5320	293	5	laprom	laprom	PROPN
ejpam-5320	293	6	,	,	PUNCT
ejpam-5320	293	7	c.	c.	PROPN
ejpam-5320	293	8	boonpok	boonpok	PROPN
ejpam-5320	293	9	,	,	PUNCT
ejpam-5320	293	10	and	and	CCONJ
ejpam-5320	293	11	c.	c.	PROPN
ejpam-5320	293	12	viriyapong	viriyapong	PROPN
ejpam-5320	293	13	.	.	PUNCT
ejpam-5320	294	1	β(τ1	β(τ1	PROPN
ejpam-5320	294	2	,	,	PUNCT
ejpam-5320	294	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	294	4	multifunctions	multifunction	NOUN
ejpam-5320	294	5	on	on	ADP
ejpam-5320	294	6	bitopological	bitopological	ADJ
ejpam-5320	294	7	spaces	space	NOUN
ejpam-5320	294	8	.	.	PUNCT
ejpam-5320	295	1	journal	journal	NOUN
ejpam-5320	295	2	of	of	ADP
ejpam-5320	295	3	mathematics	mathematic	NOUN
ejpam-5320	295	4	,	,	PUNCT
ejpam-5320	295	5	2020:4020971	2020:4020971	NUM
ejpam-5320	295	6	,	,	PUNCT
ejpam-5320	295	7	2020	2020	NUM
ejpam-5320	295	8	.	.	PUNCT
ejpam-5320	296	1	[	[	X
ejpam-5320	296	2	27	27	NUM
ejpam-5320	296	3	]	]	PUNCT
ejpam-5320	296	4	t.	t.	NOUN
ejpam-5320	296	5	lipski	lipski	PROPN
ejpam-5320	296	6	.	.	PUNCT
ejpam-5320	297	1	remarks	remark	NOUN
ejpam-5320	297	2	on	on	ADP
ejpam-5320	297	3	limits	limit	NOUN
ejpam-5320	297	4	of	of	ADP
ejpam-5320	297	5	sequences	sequence	NOUN
ejpam-5320	297	6	of	of	ADP
ejpam-5320	297	7	c	c	NOUN
ejpam-5320	297	8	-	-	PUNCT
ejpam-5320	297	9	quasicontinuous	quasicontinuous	ADJ
ejpam-5320	297	10	multivalued	multivalued	ADJ
ejpam-5320	297	11	maps	map	NOUN
ejpam-5320	297	12	.	.	PUNCT
ejpam-5320	298	1	radovi	radovi	PROPN
ejpam-5320	298	2	matematički	matematički	PROPN
ejpam-5320	298	3	,	,	PUNCT
ejpam-5320	298	4	7:17–27	7:17–27	NUM
ejpam-5320	298	5	,	,	PUNCT
ejpam-5320	298	6	1991	1991	NUM
ejpam-5320	298	7	.	.	PUNCT
ejpam-5320	299	1	[	[	X
ejpam-5320	299	2	28	28	NUM
ejpam-5320	299	3	]	]	X
ejpam-5320	300	1	p.	p.	PROPN
ejpam-5320	300	2	e.	e.	PROPN
ejpam-5320	301	1	long	long	PROPN
ejpam-5320	301	2	and	and	CCONJ
ejpam-5320	301	3	michael	michael	PROPN
ejpam-5320	301	4	d.	d.	PROPN
ejpam-5320	301	5	hendrix	hendrix	PROPN
ejpam-5320	301	6	.	.	PUNCT
ejpam-5320	302	1	properties	property	NOUN
ejpam-5320	302	2	of	of	ADP
ejpam-5320	302	3	c	c	NOUN
ejpam-5320	302	4	-	-	PUNCT
ejpam-5320	302	5	continuous	continuous	ADJ
ejpam-5320	302	6	functions	function	NOUN
ejpam-5320	302	7	.	.	PUNCT
ejpam-5320	303	1	yokohama	yokohama	PROPN
ejpam-5320	303	2	mathematical	mathematical	PROPN
ejpam-5320	303	3	journal	journal	PROPN
ejpam-5320	303	4	,	,	PUNCT
ejpam-5320	303	5	22:117–123	22:117–123	NUM
ejpam-5320	303	6	,	,	PUNCT
ejpam-5320	303	7	1974	1974	NUM
ejpam-5320	303	8	.	.	PUNCT
ejpam-5320	304	1	references	reference	NOUN
ejpam-5320	304	2	2298	2298	NUM
ejpam-5320	304	3	[	[	X
ejpam-5320	304	4	29	29	NUM
ejpam-5320	304	5	]	]	PUNCT
ejpam-5320	305	1	p.	p.	PROPN
ejpam-5320	305	2	e.	e.	PROPN
ejpam-5320	306	1	long	long	PROPN
ejpam-5320	306	2	and	and	CCONJ
ejpam-5320	306	3	l.	l.	PROPN
ejpam-5320	306	4	l.	l.	PROPN
ejpam-5320	306	5	herrington	herrington	PROPN
ejpam-5320	306	6	.	.	PUNCT
ejpam-5320	307	1	properties	property	NOUN
ejpam-5320	307	2	of	of	ADP
ejpam-5320	307	3	c	c	NOUN
ejpam-5320	307	4	-	-	PUNCT
ejpam-5320	307	5	continuous	continuous	ADJ
ejpam-5320	307	6	functions	function	NOUN
ejpam-5320	307	7	and	and	CCONJ
ejpam-5320	307	8	c∗continuous	c∗continuous	ADJ
ejpam-5320	307	9	functions	function	NOUN
ejpam-5320	307	10	.	.	PUNCT
ejpam-5320	308	1	kyungpook	kyungpook	PROPN
ejpam-5320	308	2	mathematical	mathematical	PROPN
ejpam-5320	308	3	journal	journal	PROPN
ejpam-5320	308	4	,	,	PUNCT
ejpam-5320	308	5	15:213–221	15:213–221	PROPN
ejpam-5320	308	6	,	,	PUNCT
ejpam-5320	308	7	1975	1975	NUM
ejpam-5320	308	8	.	.	PUNCT
ejpam-5320	309	1	[	[	X
ejpam-5320	309	2	30	30	NUM
ejpam-5320	309	3	]	]	PUNCT
ejpam-5320	309	4	t.	t.	NOUN
ejpam-5320	309	5	neubrunn	neubrunn	PROPN
ejpam-5320	309	6	.	.	PUNCT
ejpam-5320	310	1	c	c	X
ejpam-5320	310	2	-	-	PUNCT
ejpam-5320	310	3	continuity	continuity	NOUN
ejpam-5320	310	4	and	and	CCONJ
ejpam-5320	310	5	closed	closed	ADJ
ejpam-5320	310	6	graphs	graph	NOUN
ejpam-5320	310	7	.	.	PUNCT
ejpam-5320	311	1	časopis	časopis	X
ejpam-5320	311	2	pro	pro	X
ejpam-5320	311	3	pěstováńı	pěstováńı	NOUN
ejpam-5320	311	4	matematiky	matematiky	NOUN
ejpam-5320	311	5	,	,	PUNCT
ejpam-5320	311	6	110:172–178	110:172–178	NUM
ejpam-5320	311	7	,	,	PUNCT
ejpam-5320	311	8	1985	1985	NUM
ejpam-5320	311	9	.	.	PUNCT
ejpam-5320	312	1	[	[	X
ejpam-5320	312	2	31	31	NUM
ejpam-5320	312	3	]	]	PUNCT
ejpam-5320	312	4	t.	t.	PROPN
ejpam-5320	312	5	noiri	noiri	PROPN
ejpam-5320	312	6	and	and	CCONJ
ejpam-5320	312	7	v.	v.	ADP
ejpam-5320	312	8	popa	popa	NOUN
ejpam-5320	312	9	.	.	PUNCT
ejpam-5320	313	1	some	some	DET
ejpam-5320	313	2	forms	form	NOUN
ejpam-5320	313	3	of	of	ADP
ejpam-5320	313	4	c	c	NOUN
ejpam-5320	313	5	-	-	PUNCT
ejpam-5320	313	6	continuity	continuity	NOUN
ejpam-5320	313	7	for	for	ADP
ejpam-5320	313	8	multifunctions	multifunction	NOUN
ejpam-5320	313	9	.	.	PUNCT
ejpam-5320	314	1	european	european	ADJ
ejpam-5320	314	2	journal	journal	PROPN
ejpam-5320	314	3	of	of	ADP
ejpam-5320	314	4	pure	pure	ADJ
ejpam-5320	314	5	and	and	CCONJ
ejpam-5320	314	6	applied	applied	ADJ
ejpam-5320	314	7	mathematics	mathematic	NOUN
ejpam-5320	314	8	,	,	PUNCT
ejpam-5320	314	9	1(1):82–98	1(1):82–98	NUM
ejpam-5320	314	10	,	,	PUNCT
ejpam-5320	314	11	2008	2008	NUM
ejpam-5320	314	12	.	.	PUNCT
ejpam-5320	315	1	[	[	X
ejpam-5320	315	2	32	32	NUM
ejpam-5320	315	3	]	]	PUNCT
ejpam-5320	315	4	ö.	ö.	PROPN
ejpam-5320	315	5	orhan	orhan	PROPN
ejpam-5320	315	6	.	.	PUNCT
ejpam-5320	316	1	properties	property	NOUN
ejpam-5320	316	2	of	of	ADP
ejpam-5320	316	3	c	c	NOUN
ejpam-5320	316	4	-	-	PUNCT
ejpam-5320	316	5	continuous	continuous	ADJ
ejpam-5320	316	6	functions	function	NOUN
ejpam-5320	316	7	.	.	PUNCT
ejpam-5320	317	1	hacettepe	hacettepe	ADJ
ejpam-5320	317	2	bulletin	bulletin	NOUN
ejpam-5320	317	3	of	of	ADP
ejpam-5320	317	4	natural	natural	ADJ
ejpam-5320	317	5	sciences	science	NOUN
ejpam-5320	317	6	and	and	CCONJ
ejpam-5320	317	7	engineering	engineering	NOUN
ejpam-5320	317	8	,	,	PUNCT
ejpam-5320	317	9	7	7	NUM
ejpam-5320	317	10	-	-	SYM
ejpam-5320	317	11	8:77–83	8:77–83	NUM
ejpam-5320	317	12	,	,	PUNCT
ejpam-5320	317	13	1978/79	1978/79	NUM
ejpam-5320	317	14	.	.	PUNCT
ejpam-5320	318	1	[	[	X
ejpam-5320	318	2	33	33	NUM
ejpam-5320	318	3	]	]	X
ejpam-5320	318	4	v.	v.	CCONJ
ejpam-5320	318	5	popa	popa	NOUN
ejpam-5320	318	6	.	.	PUNCT
ejpam-5320	319	1	on	on	ADP
ejpam-5320	319	2	some	some	DET
ejpam-5320	319	3	decomposition	decomposition	NOUN
ejpam-5320	319	4	of	of	ADP
ejpam-5320	319	5	quasi	quasi	NOUN
ejpam-5320	319	6	-	-	NOUN
ejpam-5320	319	7	continuity	continuity	NOUN
ejpam-5320	319	8	of	of	ADP
ejpam-5320	319	9	multifunctions	multifunction	NOUN
ejpam-5320	319	10	(	(	PUNCT
ejpam-5320	319	11	romanian	romanian	ADJ
ejpam-5320	319	12	)	)	PUNCT
ejpam-5320	319	13	.	.	PUNCT
ejpam-5320	320	1	studii	studii	PROPN
ejpam-5320	320	2	şi	şi	PROPN
ejpam-5320	320	3	cercetǎri	cercetǎri	NOUN
ejpam-5320	320	4	de	de	X
ejpam-5320	320	5	matematicǎ	matematicǎ	NOUN
ejpam-5320	320	6	,	,	PUNCT
ejpam-5320	320	7	27:322–328	27:322–328	PROPN
ejpam-5320	320	8	,	,	PUNCT
ejpam-5320	320	9	1975	1975	NUM
ejpam-5320	320	10	.	.	PUNCT
ejpam-5320	321	1	[	[	X
ejpam-5320	321	2	34	34	NUM
ejpam-5320	321	3	]	]	X
ejpam-5320	321	4	p.	p.	NOUN
ejpam-5320	321	5	pue	pue	NOUN
ejpam-5320	321	6	-	-	PUNCT
ejpam-5320	321	7	on	on	ADP
ejpam-5320	321	8	and	and	CCONJ
ejpam-5320	321	9	c.	c.	PROPN
ejpam-5320	321	10	boonpok	boonpok	PROPN
ejpam-5320	321	11	.	.	PUNCT
ejpam-5320	322	1	θ(λ	θ(λ	PROPN
ejpam-5320	322	2	,	,	PUNCT
ejpam-5320	322	3	p)-continuity	p)-continuity	NOUN
ejpam-5320	322	4	for	for	ADP
ejpam-5320	322	5	functions	function	NOUN
ejpam-5320	322	6	.	.	PUNCT
ejpam-5320	323	1	international	international	ADJ
ejpam-5320	323	2	journal	journal	NOUN
ejpam-5320	323	3	of	of	ADP
ejpam-5320	323	4	mathematics	mathematic	NOUN
ejpam-5320	323	5	and	and	CCONJ
ejpam-5320	323	6	computer	computer	NOUN
ejpam-5320	323	7	science	science	NOUN
ejpam-5320	323	8	,	,	PUNCT
ejpam-5320	323	9	19(2):491–495	19(2):491–495	NUM
ejpam-5320	323	10	,	,	PUNCT
ejpam-5320	323	11	2024	2024	NUM
ejpam-5320	323	12	.	.	PUNCT
ejpam-5320	324	1	[	[	X
ejpam-5320	324	2	35	35	NUM
ejpam-5320	324	3	]	]	X
ejpam-5320	324	4	p.	p.	NOUN
ejpam-5320	324	5	pue	pue	NOUN
ejpam-5320	324	6	-	-	PUNCT
ejpam-5320	324	7	on	on	ADP
ejpam-5320	324	8	,	,	PUNCT
ejpam-5320	324	9	s.	s.	PROPN
ejpam-5320	324	10	sompong	sompong	PROPN
ejpam-5320	324	11	,	,	PUNCT
ejpam-5320	324	12	and	and	CCONJ
ejpam-5320	324	13	c.	c.	PROPN
ejpam-5320	324	14	boonpok	boonpok	PROPN
ejpam-5320	324	15	.	.	PUNCT
ejpam-5320	325	1	upper	upper	ADJ
ejpam-5320	325	2	and	and	CCONJ
ejpam-5320	325	3	lower	low	ADJ
ejpam-5320	325	4	(	(	PUNCT
ejpam-5320	325	5	τ1	τ1	NOUN
ejpam-5320	325	6	,	,	PUNCT
ejpam-5320	325	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5320	325	8	multifunctions	multifunction	NOUN
ejpam-5320	325	9	.	.	PUNCT
ejpam-5320	326	1	international	international	ADJ
ejpam-5320	326	2	journal	journal	PROPN
ejpam-5320	326	3	of	of	ADP
ejpam-5320	326	4	mathematics	mathematic	NOUN
ejpam-5320	326	5	and	and	CCONJ
ejpam-5320	326	6	computer	computer	NOUN
ejpam-5320	326	7	science	science	NOUN
ejpam-5320	326	8	,	,	PUNCT
ejpam-5320	326	9	19(4):1305	19(4):1305	NUM
ejpam-5320	326	10	–	–	PUNCT
ejpam-5320	326	11	1310	1310	NUM
ejpam-5320	326	12	,	,	PUNCT
ejpam-5320	326	13	2024	2024	NUM
ejpam-5320	326	14	.	.	PUNCT
ejpam-5320	327	1	[	[	X
ejpam-5320	327	2	36	36	NUM
ejpam-5320	327	3	]	]	X
ejpam-5320	327	4	n.	n.	PROPN
ejpam-5320	327	5	srisarakham	srisarakham	PROPN
ejpam-5320	327	6	and	and	CCONJ
ejpam-5320	327	7	c.	c.	PROPN
ejpam-5320	327	8	boonpok	boonpok	PROPN
ejpam-5320	327	9	.	.	PUNCT
ejpam-5320	328	1	almost	almost	ADV
ejpam-5320	328	2	(	(	PUNCT
ejpam-5320	328	3	λ	λ	NOUN
ejpam-5320	328	4	,	,	PUNCT
ejpam-5320	328	5	p)-continuous	p)-continuous	ADJ
ejpam-5320	328	6	functions	function	NOUN
ejpam-5320	328	7	.	.	PUNCT
ejpam-5320	329	1	international	international	ADJ
ejpam-5320	329	2	journal	journal	PROPN
ejpam-5320	329	3	of	of	ADP
ejpam-5320	329	4	mathematics	mathematic	NOUN
ejpam-5320	329	5	and	and	CCONJ
ejpam-5320	329	6	computer	computer	NOUN
ejpam-5320	329	7	science	science	NOUN
ejpam-5320	329	8	,	,	PUNCT
ejpam-5320	329	9	18(2):255–259	18(2):255–259	NUM
ejpam-5320	329	10	,	,	PUNCT
ejpam-5320	329	11	2023	2023	NUM
ejpam-5320	329	12	.	.	PUNCT
ejpam-5320	330	1	[	[	X
ejpam-5320	330	2	37	37	NUM
ejpam-5320	330	3	]	]	X
ejpam-5320	330	4	n.	n.	NOUN
ejpam-5320	330	5	srisarakham	srisarakham	PROPN
ejpam-5320	330	6	and	and	CCONJ
ejpam-5320	330	7	c.	c.	PROPN
ejpam-5320	330	8	boonpok	boonpok	PROPN
ejpam-5320	330	9	.	.	PUNCT
ejpam-5320	331	1	on	on	ADP
ejpam-5320	331	2	characterizations	characterization	NOUN
ejpam-5320	331	3	of	of	ADP
ejpam-5320	331	4	δp(λ	δp(λ	NOUN
ejpam-5320	331	5	,	,	PUNCT
ejpam-5320	331	6	s)-d1	s)-d1	NOUN
ejpam-5320	331	7	spaces	space	NOUN
ejpam-5320	331	8	.	.	PUNCT
ejpam-5320	332	1	international	international	ADJ
ejpam-5320	332	2	journal	journal	PROPN
ejpam-5320	332	3	of	of	ADP
ejpam-5320	332	4	mathematics	mathematic	NOUN
ejpam-5320	332	5	and	and	CCONJ
ejpam-5320	332	6	computer	computer	NOUN
ejpam-5320	332	7	science	science	NOUN
ejpam-5320	332	8	,	,	PUNCT
ejpam-5320	332	9	18(4):743–747	18(4):743–747	PROPN
ejpam-5320	332	10	,	,	PUNCT
ejpam-5320	332	11	2023	2023	NUM
ejpam-5320	332	12	.	.	PUNCT
ejpam-5320	333	1	[	[	X
ejpam-5320	333	2	38	38	NUM
ejpam-5320	333	3	]	]	PUNCT
ejpam-5320	333	4	m.	m.	NOUN
ejpam-5320	333	5	thongmoon	thongmoon	NOUN
ejpam-5320	333	6	and	and	CCONJ
ejpam-5320	333	7	c.	c.	PROPN
ejpam-5320	333	8	boonpok	boonpok	PROPN
ejpam-5320	333	9	.	.	PUNCT
ejpam-5320	334	1	strongly	strongly	ADV
ejpam-5320	334	2	θ(λ	θ(λ	PROPN
ejpam-5320	334	3	,	,	PUNCT
ejpam-5320	334	4	p)-continuous	p)-continuous	ADJ
ejpam-5320	334	5	functions	function	NOUN
ejpam-5320	334	6	.	.	PUNCT
ejpam-5320	335	1	international	international	ADJ
ejpam-5320	335	2	journal	journal	PROPN
ejpam-5320	335	3	of	of	ADP
ejpam-5320	335	4	mathematics	mathematic	NOUN
ejpam-5320	335	5	and	and	CCONJ
ejpam-5320	335	6	computer	computer	NOUN
ejpam-5320	335	7	science	science	NOUN
ejpam-5320	335	8	,	,	PUNCT
ejpam-5320	335	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5320	335	10	,	,	PUNCT
ejpam-5320	335	11	2024	2024	NUM
ejpam-5320	335	12	.	.	PUNCT
ejpam-5320	336	1	[	[	X
ejpam-5320	336	2	39	39	NUM
ejpam-5320	336	3	]	]	PUNCT
ejpam-5320	336	4	c.	c.	PROPN
ejpam-5320	336	5	viriyapong	viriyapong	PROPN
ejpam-5320	336	6	and	and	CCONJ
ejpam-5320	336	7	c.	c.	PROPN
ejpam-5320	336	8	boonpok	boonpok	PROPN
ejpam-5320	336	9	.	.	PUNCT
ejpam-5320	337	1	(	(	PUNCT
ejpam-5320	337	2	τ1	τ1	NOUN
ejpam-5320	337	3	,	,	PUNCT
ejpam-5320	337	4	τ2)α	τ2)α	NOUN
ejpam-5320	337	5	-	-	PUNCT
ejpam-5320	337	6	continuity	continuity	NOUN
ejpam-5320	337	7	for	for	ADP
ejpam-5320	337	8	multifunctions	multifunction	NOUN
ejpam-5320	337	9	.	.	PUNCT
ejpam-5320	338	1	journal	journal	PROPN
ejpam-5320	338	2	of	of	ADP
ejpam-5320	338	3	mathematics	mathematic	NOUN
ejpam-5320	338	4	,	,	PUNCT
ejpam-5320	338	5	2020:6285763	2020:6285763	NUM
ejpam-5320	338	6	,	,	PUNCT
ejpam-5320	338	7	2020	2020	NUM
ejpam-5320	338	8	.	.	PUNCT
ejpam-5320	339	1	[	[	X
ejpam-5320	339	2	40	40	NUM
ejpam-5320	339	3	]	]	PUNCT
ejpam-5320	339	4	c.	c.	PROPN
ejpam-5320	339	5	viriyapong	viriyapong	PROPN
ejpam-5320	339	6	and	and	CCONJ
ejpam-5320	339	7	c.	c.	PROPN
ejpam-5320	339	8	boonpok	boonpok	PROPN
ejpam-5320	339	9	.	.	PUNCT
ejpam-5320	340	1	(	(	PUNCT
ejpam-5320	340	2	λ	λ	X
ejpam-5320	340	3	,	,	PUNCT
ejpam-5320	340	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5320	340	5	functions	function	NOUN
ejpam-5320	340	6	.	.	PUNCT
ejpam-5320	341	1	wseas	wseas	VERB
ejpam-5320	341	2	transactions	transaction	NOUN
ejpam-5320	341	3	on	on	ADP
ejpam-5320	341	4	mathematics	mathematic	NOUN
ejpam-5320	341	5	,	,	PUNCT
ejpam-5320	341	6	21:380–385	21:380–385	NUM
ejpam-5320	341	7	,	,	PUNCT
ejpam-5320	341	8	2022	2022	NUM
ejpam-5320	341	9	.	.	PUNCT
ejpam-5320	342	1	[	[	X
ejpam-5320	342	2	41	41	NUM
ejpam-5320	342	3	]	]	X
ejpam-5320	342	4	c.	c.	PROPN
ejpam-5320	342	5	viriyapong	viriyapong	PROPN
ejpam-5320	342	6	and	and	CCONJ
ejpam-5320	342	7	c.	c.	PROPN
ejpam-5320	342	8	boonpok	boonpok	PROPN
ejpam-5320	342	9	.	.	PUNCT
ejpam-5320	343	1	weak	weak	ADJ
ejpam-5320	343	2	quasi	quasi	NOUN
ejpam-5320	343	3	(	(	PUNCT
ejpam-5320	343	4	λ	λ	PROPN
ejpam-5320	343	5	,	,	PUNCT
ejpam-5320	343	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5320	343	7	for	for	ADP
ejpam-5320	343	8	multifunctions	multifunction	NOUN
ejpam-5320	343	9	.	.	PUNCT
ejpam-5320	344	1	international	international	ADJ
ejpam-5320	344	2	journal	journal	PROPN
ejpam-5320	344	3	of	of	ADP
ejpam-5320	344	4	mathematics	mathematic	NOUN
ejpam-5320	344	5	and	and	CCONJ
ejpam-5320	344	6	computer	computer	NOUN
ejpam-5320	344	7	science	science	NOUN
ejpam-5320	344	8	,	,	PUNCT
ejpam-5320	344	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5320	344	10	,	,	PUNCT
ejpam-5320	344	11	2022	2022	NUM
ejpam-5320	344	12	.	.	PUNCT
ejpam-5320	345	1	[	[	X
ejpam-5320	345	2	42	42	NUM
ejpam-5320	345	3	]	]	X
ejpam-5320	345	4	n.	n.	PROPN
ejpam-5320	345	5	viriyapong	viriyapong	PROPN
ejpam-5320	345	6	,	,	PUNCT
ejpam-5320	345	7	s.	s.	PROPN
ejpam-5320	345	8	sompong	sompong	PROPN
ejpam-5320	345	9	,	,	PUNCT
ejpam-5320	345	10	and	and	CCONJ
ejpam-5320	345	11	c.	c.	PROPN
ejpam-5320	345	12	boonpok	boonpok	PROPN
ejpam-5320	345	13	.	.	PUNCT
ejpam-5320	346	1	(	(	PUNCT
ejpam-5320	346	2	τ1	τ1	NOUN
ejpam-5320	346	3	,	,	PUNCT
ejpam-5320	346	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5320	346	5	disconnectedness	disconnectedness	NOUN
ejpam-5320	346	6	in	in	ADP
ejpam-5320	346	7	bitopological	bitopological	ADJ
ejpam-5320	346	8	spaces	space	NOUN
ejpam-5320	346	9	.	.	PUNCT
ejpam-5320	347	1	international	international	ADJ
ejpam-5320	347	2	journal	journal	PROPN
ejpam-5320	347	3	of	of	ADP
ejpam-5320	347	4	mathematics	mathematic	NOUN
ejpam-5320	347	5	and	and	CCONJ
ejpam-5320	347	6	computer	computer	NOUN
ejpam-5320	347	7	science	science	NOUN
ejpam-5320	347	8	,	,	PUNCT
ejpam-5320	347	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5320	347	10	,	,	PUNCT
ejpam-5320	347	11	2024	2024	NUM
ejpam-5320	347	12	.	.	PUNCT