id	sid	tid	token	lemma	pos
ejpam-6009	1	1	european	european	PROPN
ejpam-6009	1	2	journal	journal	PROPN
ejpam-6009	1	3	of	of	ADP
ejpam-6009	1	4	pure	pure	ADJ
ejpam-6009	1	5	and	and	CCONJ
ejpam-6009	1	6	applied	applied	ADJ
ejpam-6009	1	7	mathematics	mathematic	NOUN
ejpam-6009	1	8	2025	2025	NUM
ejpam-6009	1	9	,	,	PUNCT
ejpam-6009	1	10	vol	vol	NOUN
ejpam-6009	1	11	.	.	PROPN
ejpam-6009	1	12	18	18	NUM
ejpam-6009	1	13	,	,	PUNCT
ejpam-6009	1	14	issue	issue	NOUN
ejpam-6009	1	15	2	2	NUM
ejpam-6009	1	16	,	,	PUNCT
ejpam-6009	1	17	article	article	NOUN
ejpam-6009	1	18	number	number	NOUN
ejpam-6009	1	19	6009	6009	NUM
ejpam-6009	1	20	issn	issn	PROPN
ejpam-6009	1	21	1307	1307	NUM
ejpam-6009	1	22	-	-	SYM
ejpam-6009	1	23	5543	5543	NUM
ejpam-6009	1	24	–	–	PUNCT
ejpam-6009	1	25	ejpam.com	ejpam.com	X
ejpam-6009	1	26	published	publish	VERB
ejpam-6009	1	27	by	by	ADP
ejpam-6009	1	28	new	new	PROPN
ejpam-6009	1	29	york	york	PROPN
ejpam-6009	1	30	business	business	PROPN
ejpam-6009	1	31	global	global	PROPN
ejpam-6009	1	32	on	on	ADP
ejpam-6009	1	33	contra-(τ1	contra-(τ1	PROPN
ejpam-6009	1	34	,	,	PUNCT
ejpam-6009	1	35	τ2)p	τ2)p	NOUN
ejpam-6009	1	36	-	-	PUNCT
ejpam-6009	1	37	continuity	continuity	NOUN
ejpam-6009	1	38	and	and	CCONJ
ejpam-6009	1	39	almost	almost	ADV
ejpam-6009	1	40	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	1	41	,	,	PUNCT
ejpam-6009	1	42	τ2)p	τ2)p	NOUN
ejpam-6009	1	43	-	-	PUNCT
ejpam-6009	1	44	continuity	continuity	NOUN
ejpam-6009	1	45	for	for	ADP
ejpam-6009	1	46	multifunctions	multifunction	NOUN
ejpam-6009	1	47	chokchai	chokchai	ADJ
ejpam-6009	1	48	viriyapong1	viriyapong1	PROPN
ejpam-6009	1	49	,	,	PUNCT
ejpam-6009	1	50	areeyuth	areeyuth	NOUN
ejpam-6009	1	51	sama	sama	NOUN
ejpam-6009	1	52	-	-	PUNCT
ejpam-6009	1	53	ae2	ae2	PROPN
ejpam-6009	1	54	,	,	PUNCT
ejpam-6009	1	55	chawalit	chawalit	VERB
ejpam-6009	1	56	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6009	1	57	1	1	NUM
ejpam-6009	1	58	mathematics	mathematic	NOUN
ejpam-6009	1	59	and	and	CCONJ
ejpam-6009	1	60	applied	apply	VERB
ejpam-6009	1	61	mathematics	mathematics	PROPN
ejpam-6009	1	62	research	research	NOUN
ejpam-6009	1	63	unit	unit	NOUN
ejpam-6009	1	64	,	,	PUNCT
ejpam-6009	1	65	department	department	NOUN
ejpam-6009	1	66	of	of	ADP
ejpam-6009	1	67	mathematics	mathematic	NOUN
ejpam-6009	1	68	,	,	PUNCT
ejpam-6009	1	69	faculty	faculty	NOUN
ejpam-6009	1	70	of	of	ADP
ejpam-6009	1	71	science	science	NOUN
ejpam-6009	1	72	,	,	PUNCT
ejpam-6009	1	73	mahasarakham	mahasarakham	PROPN
ejpam-6009	1	74	university	university	PROPN
ejpam-6009	1	75	,	,	PUNCT
ejpam-6009	1	76	maha	maha	PROPN
ejpam-6009	1	77	sarakham	sarakham	PROPN
ejpam-6009	1	78	,	,	PUNCT
ejpam-6009	1	79	44150	44150	NUM
ejpam-6009	1	80	,	,	PUNCT
ejpam-6009	1	81	thailand	thailand	PROPN
ejpam-6009	1	82	2	2	NUM
ejpam-6009	1	83	department	department	NOUN
ejpam-6009	1	84	of	of	ADP
ejpam-6009	1	85	mathematics	mathematic	NOUN
ejpam-6009	1	86	and	and	CCONJ
ejpam-6009	1	87	computer	computer	NOUN
ejpam-6009	1	88	science	science	NOUN
ejpam-6009	1	89	,	,	PUNCT
ejpam-6009	1	90	faculty	faculty	NOUN
ejpam-6009	1	91	of	of	ADP
ejpam-6009	1	92	science	science	NOUN
ejpam-6009	1	93	and	and	CCONJ
ejpam-6009	1	94	technology	technology	NOUN
ejpam-6009	1	95	,	,	PUNCT
ejpam-6009	1	96	prince	prince	NOUN
ejpam-6009	1	97	of	of	ADP
ejpam-6009	1	98	songkla	songkla	PROPN
ejpam-6009	1	99	university	university	PROPN
ejpam-6009	1	100	,	,	PUNCT
ejpam-6009	1	101	pattani	pattani	NOUN
ejpam-6009	1	102	campus	campus	NOUN
ejpam-6009	1	103	,	,	PUNCT
ejpam-6009	1	104	pattani	pattani	NOUN
ejpam-6009	1	105	,	,	PUNCT
ejpam-6009	1	106	94000	94000	NUM
ejpam-6009	1	107	,	,	PUNCT
ejpam-6009	1	108	thailand	thailand	PROPN
ejpam-6009	1	109	abstract	abstract	PROPN
ejpam-6009	1	110	.	.	PUNCT
ejpam-6009	2	1	this	this	DET
ejpam-6009	2	2	paper	paper	NOUN
ejpam-6009	2	3	presents	present	VERB
ejpam-6009	2	4	four	four	NUM
ejpam-6009	2	5	new	new	ADJ
ejpam-6009	2	6	classes	class	NOUN
ejpam-6009	2	7	of	of	ADP
ejpam-6009	2	8	multifunctions	multifunction	NOUN
ejpam-6009	2	9	called	call	VERB
ejpam-6009	2	10	upper	upper	ADJ
ejpam-6009	2	11	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	2	12	,	,	PUNCT
ejpam-6009	2	13	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	2	14	multifunctions	multifunction	NOUN
ejpam-6009	2	15	,	,	PUNCT
ejpam-6009	2	16	lower	low	ADJ
ejpam-6009	2	17	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	2	18	,	,	PUNCT
ejpam-6009	2	19	τ2)p	τ2)p	ADJ
ejpam-6009	2	20	-	-	PUNCT
ejpam-6009	2	21	continuous	continuous	ADJ
ejpam-6009	2	22	multifunctions	multifunction	NOUN
ejpam-6009	2	23	,	,	PUNCT
ejpam-6009	2	24	upper	upper	ADJ
ejpam-6009	2	25	almost	almost	ADV
ejpam-6009	2	26	contra(τ1	contra(τ1	NOUN
ejpam-6009	2	27	,	,	PUNCT
ejpam-6009	2	28	τ2)p	τ2)p	ADJ
ejpam-6009	2	29	-	-	ADJ
ejpam-6009	2	30	continuous	continuous	ADJ
ejpam-6009	2	31	multifunctions	multifunction	NOUN
ejpam-6009	2	32	and	and	CCONJ
ejpam-6009	2	33	lower	low	ADJ
ejpam-6009	2	34	almost	almost	ADV
ejpam-6009	2	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	2	36	,	,	PUNCT
ejpam-6009	2	37	τ2)p	τ2)p	ADJ
ejpam-6009	2	38	-	-	PUNCT
ejpam-6009	2	39	continuous	continuous	ADJ
ejpam-6009	2	40	multifunctions	multifunction	NOUN
ejpam-6009	2	41	.	.	PUNCT
ejpam-6009	3	1	furthermore	furthermore	ADV
ejpam-6009	3	2	,	,	PUNCT
ejpam-6009	3	3	several	several	ADJ
ejpam-6009	3	4	characterizations	characterization	NOUN
ejpam-6009	3	5	and	and	CCONJ
ejpam-6009	3	6	some	some	DET
ejpam-6009	3	7	properties	property	NOUN
ejpam-6009	3	8	concerning	concern	VERB
ejpam-6009	3	9	upper	upper	ADJ
ejpam-6009	3	10	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	3	11	,	,	PUNCT
ejpam-6009	3	12	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	3	13	multifunctions	multifunction	NOUN
ejpam-6009	3	14	,	,	PUNCT
ejpam-6009	3	15	lower	low	ADJ
ejpam-6009	3	16	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	3	17	,	,	PUNCT
ejpam-6009	3	18	τ2)p	τ2)p	ADJ
ejpam-6009	3	19	-	-	PUNCT
ejpam-6009	3	20	continuous	continuous	ADJ
ejpam-6009	3	21	multifunctions	multifunction	NOUN
ejpam-6009	3	22	,	,	PUNCT
ejpam-6009	3	23	upper	upper	ADJ
ejpam-6009	3	24	almost	almost	ADV
ejpam-6009	3	25	contra(τ1	contra(τ1	NOUN
ejpam-6009	3	26	,	,	PUNCT
ejpam-6009	3	27	τ2)p	τ2)p	ADJ
ejpam-6009	3	28	-	-	ADJ
ejpam-6009	3	29	continuous	continuous	ADJ
ejpam-6009	3	30	multifunctions	multifunction	NOUN
ejpam-6009	3	31	and	and	CCONJ
ejpam-6009	3	32	lower	low	ADJ
ejpam-6009	3	33	almost	almost	ADV
ejpam-6009	3	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	3	35	,	,	PUNCT
ejpam-6009	3	36	τ2)p	τ2)p	ADJ
ejpam-6009	3	37	-	-	PUNCT
ejpam-6009	3	38	continuous	continuous	ADJ
ejpam-6009	3	39	multifunctions	multifunction	NOUN
ejpam-6009	3	40	are	be	AUX
ejpam-6009	3	41	established	establish	VERB
ejpam-6009	3	42	.	.	PUNCT
ejpam-6009	4	1	2020	2020	NUM
ejpam-6009	4	2	mathematics	mathematics	PROPN
ejpam-6009	4	3	subject	subject	NOUN
ejpam-6009	4	4	classifications	classification	NOUN
ejpam-6009	4	5	:	:	PUNCT
ejpam-6009	4	6	54c08	54c08	NUM
ejpam-6009	4	7	,	,	PUNCT
ejpam-6009	4	8	54c60	54c60	NUM
ejpam-6009	4	9	key	key	ADJ
ejpam-6009	4	10	words	word	NOUN
ejpam-6009	4	11	and	and	CCONJ
ejpam-6009	4	12	phrases	phrase	NOUN
ejpam-6009	4	13	:	:	PUNCT
ejpam-6009	4	14	upper	upper	ADJ
ejpam-6009	4	15	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	4	16	,	,	PUNCT
ejpam-6009	4	17	τ2)p	τ2)p	ADJ
ejpam-6009	4	18	-	-	PUNCT
ejpam-6009	4	19	continuous	continuous	ADJ
ejpam-6009	4	20	multifunction	multifunction	NOUN
ejpam-6009	4	21	,	,	PUNCT
ejpam-6009	4	22	lower	low	ADJ
ejpam-6009	4	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	4	24	,	,	PUNCT
ejpam-6009	4	25	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	4	26	multifunction	multifunction	NOUN
ejpam-6009	4	27	,	,	PUNCT
ejpam-6009	4	28	upper	upper	ADJ
ejpam-6009	4	29	almost	almost	ADV
ejpam-6009	4	30	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	4	31	,	,	PUNCT
ejpam-6009	4	32	τ2)p	τ2)p	ADJ
ejpam-6009	4	33	-	-	PUNCT
ejpam-6009	4	34	continuous	continuous	ADJ
ejpam-6009	4	35	multifunction	multifunction	NOUN
ejpam-6009	4	36	,	,	PUNCT
ejpam-6009	4	37	lower	low	ADJ
ejpam-6009	4	38	almost	almost	ADV
ejpam-6009	4	39	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	4	40	,	,	PUNCT
ejpam-6009	4	41	τ2)p	τ2)p	ADJ
ejpam-6009	4	42	-	-	PUNCT
ejpam-6009	4	43	continuous	continuous	ADJ
ejpam-6009	4	44	multifunction	multifunction	NOUN
ejpam-6009	4	45	1	1	NUM
ejpam-6009	4	46	.	.	PUNCT
ejpam-6009	4	47	introduction	introduction	NOUN
ejpam-6009	4	48	the	the	DET
ejpam-6009	4	49	field	field	NOUN
ejpam-6009	4	50	of	of	ADP
ejpam-6009	4	51	the	the	DET
ejpam-6009	4	52	mathematical	mathematical	ADJ
ejpam-6009	4	53	science	science	NOUN
ejpam-6009	4	54	which	which	PRON
ejpam-6009	4	55	goes	go	VERB
ejpam-6009	4	56	under	under	ADP
ejpam-6009	4	57	the	the	DET
ejpam-6009	4	58	name	name	NOUN
ejpam-6009	4	59	of	of	ADP
ejpam-6009	4	60	topology	topology	NOUN
ejpam-6009	4	61	is	be	AUX
ejpam-6009	4	62	concerned	concern	VERB
ejpam-6009	4	63	with	with	ADP
ejpam-6009	4	64	all	all	DET
ejpam-6009	4	65	questions	question	NOUN
ejpam-6009	4	66	directly	directly	ADV
ejpam-6009	4	67	or	or	CCONJ
ejpam-6009	4	68	indirectly	indirectly	ADV
ejpam-6009	4	69	related	relate	VERB
ejpam-6009	4	70	to	to	ADP
ejpam-6009	4	71	continuity	continuity	NOUN
ejpam-6009	4	72	.	.	PUNCT
ejpam-6009	5	1	in	in	ADP
ejpam-6009	5	2	topology	topology	NOUN
ejpam-6009	5	3	,	,	PUNCT
ejpam-6009	5	4	there	there	PRON
ejpam-6009	5	5	has	have	AUX
ejpam-6009	5	6	been	be	AUX
ejpam-6009	5	7	recently	recently	ADV
ejpam-6009	5	8	significant	significant	ADJ
ejpam-6009	5	9	interest	interest	NOUN
ejpam-6009	5	10	in	in	ADP
ejpam-6009	5	11	characterizing	characterize	VERB
ejpam-6009	5	12	and	and	CCONJ
ejpam-6009	5	13	investigating	investigate	VERB
ejpam-6009	5	14	the	the	DET
ejpam-6009	5	15	characterizations	characterization	NOUN
ejpam-6009	5	16	of	of	ADP
ejpam-6009	5	17	some	some	DET
ejpam-6009	5	18	weak	weak	ADJ
ejpam-6009	5	19	forms	form	NOUN
ejpam-6009	5	20	of	of	ADP
ejpam-6009	5	21	continuity	continuity	NOUN
ejpam-6009	5	22	for	for	ADP
ejpam-6009	5	23	functions	function	NOUN
ejpam-6009	5	24	and	and	CCONJ
ejpam-6009	5	25	multifunctions	multifunction	NOUN
ejpam-6009	5	26	.	.	PUNCT
ejpam-6009	6	1	weaker	weak	ADJ
ejpam-6009	6	2	and	and	CCONJ
ejpam-6009	6	3	stronger	strong	ADJ
ejpam-6009	6	4	forms	form	NOUN
ejpam-6009	6	5	of	of	ADP
ejpam-6009	6	6	open	open	ADJ
ejpam-6009	6	7	sets	set	NOUN
ejpam-6009	6	8	play	play	VERB
ejpam-6009	6	9	an	an	DET
ejpam-6009	6	10	important	important	ADJ
ejpam-6009	6	11	role	role	NOUN
ejpam-6009	6	12	in	in	ADP
ejpam-6009	6	13	the	the	DET
ejpam-6009	6	14	generalization	generalization	NOUN
ejpam-6009	6	15	of	of	ADP
ejpam-6009	6	16	different	different	ADJ
ejpam-6009	6	17	forms	form	NOUN
ejpam-6009	6	18	of	of	ADP
ejpam-6009	6	19	continuity	continuity	NOUN
ejpam-6009	6	20	.	.	PUNCT
ejpam-6009	7	1	using	use	VERB
ejpam-6009	7	2	different	different	ADJ
ejpam-6009	7	3	forms	form	NOUN
ejpam-6009	7	4	of	of	ADP
ejpam-6009	7	5	open	open	ADJ
ejpam-6009	7	6	sets	set	NOUN
ejpam-6009	7	7	,	,	PUNCT
ejpam-6009	7	8	several	several	ADJ
ejpam-6009	7	9	authors	author	NOUN
ejpam-6009	7	10	have	have	AUX
ejpam-6009	7	11	introduced	introduce	VERB
ejpam-6009	7	12	and	and	CCONJ
ejpam-6009	7	13	studied	study	VERB
ejpam-6009	7	14	various	various	ADJ
ejpam-6009	7	15	types	type	NOUN
ejpam-6009	7	16	of	of	ADP
ejpam-6009	7	17	continuity	continuity	NOUN
ejpam-6009	7	18	.	.	PUNCT
ejpam-6009	8	1	the	the	DET
ejpam-6009	8	2	concepts	concept	NOUN
ejpam-6009	8	3	of	of	ADP
ejpam-6009	8	4	(	(	PUNCT
ejpam-6009	8	5	λ	λ	PROPN
ejpam-6009	8	6	,	,	PUNCT
ejpam-6009	8	7	sp)-open	sp)-open	ADJ
ejpam-6009	8	8	sets	set	NOUN
ejpam-6009	8	9	,	,	PUNCT
ejpam-6009	8	10	s(λ	s(λ	PROPN
ejpam-6009	8	11	,	,	PUNCT
ejpam-6009	8	12	sp)-open	sp)-open	ADJ
ejpam-6009	8	13	sets	set	NOUN
ejpam-6009	8	14	,	,	PUNCT
ejpam-6009	8	15	p(λ	p(λ	NOUN
ejpam-6009	8	16	,	,	PUNCT
ejpam-6009	8	17	sp)-open	sp)-open	ADJ
ejpam-6009	8	18	sets	set	NOUN
ejpam-6009	8	19	,	,	PUNCT
ejpam-6009	8	20	α(λ	α(λ	PROPN
ejpam-6009	8	21	,	,	PUNCT
ejpam-6009	8	22	sp)-open	sp)-open	ADJ
ejpam-6009	8	23	sets	set	NOUN
ejpam-6009	8	24	and	and	CCONJ
ejpam-6009	8	25	β(λ	β(λ	NOUN
ejpam-6009	8	26	,	,	PUNCT
ejpam-6009	8	27	sp)-open	sp)-open	ADJ
ejpam-6009	8	28	sets	set	NOUN
ejpam-6009	8	29	were	be	AUX
ejpam-6009	8	30	studied	study	VERB
ejpam-6009	8	31	in	in	ADP
ejpam-6009	8	32	[	[	X
ejpam-6009	8	33	1	1	NUM
ejpam-6009	8	34	]	]	PUNCT
ejpam-6009	8	35	.	.	PUNCT
ejpam-6009	9	1	viriyapong	viriyapong	PROPN
ejpam-6009	9	2	and	and	CCONJ
ejpam-6009	9	3	boonpok	boonpok	VERB
ejpam-6009	9	4	[	[	X
ejpam-6009	9	5	2	2	NUM
ejpam-6009	9	6	]	]	PUNCT
ejpam-6009	9	7	investigated	investigate	VERB
ejpam-6009	9	8	several	several	ADJ
ejpam-6009	9	9	characterizations	characterization	NOUN
ejpam-6009	9	10	of	of	ADP
ejpam-6009	9	11	(	(	PUNCT
ejpam-6009	9	12	λ	λ	PROPN
ejpam-6009	9	13	,	,	PUNCT
ejpam-6009	9	14	sp)continuous	sp)continuous	ADJ
ejpam-6009	9	15	functions	function	NOUN
ejpam-6009	9	16	by	by	ADP
ejpam-6009	9	17	utilizing	utilize	VERB
ejpam-6009	9	18	the	the	DET
ejpam-6009	9	19	notions	notion	NOUN
ejpam-6009	9	20	of	of	ADP
ejpam-6009	9	21	(	(	PUNCT
ejpam-6009	9	22	λ	λ	PROPN
ejpam-6009	9	23	,	,	PUNCT
ejpam-6009	9	24	sp)-open	sp)-open	ADJ
ejpam-6009	9	25	sets	set	NOUN
ejpam-6009	9	26	and	and	CCONJ
ejpam-6009	9	27	(	(	PUNCT
ejpam-6009	9	28	λ	λ	PROPN
ejpam-6009	9	29	,	,	PUNCT
ejpam-6009	9	30	sp)-closed	sp)-close	VERB
ejpam-6009	9	31	sets	set	NOUN
ejpam-6009	9	32	.	.	PUNCT
ejpam-6009	10	1	∗corresponding	∗corresponde	VERB
ejpam-6009	10	2	author	author	NOUN
ejpam-6009	10	3	.	.	PUNCT
ejpam-6009	11	1	doi	doi	NOUN
ejpam-6009	11	2	:	:	PUNCT
ejpam-6009	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6009	https://doi.org/10.29020/nybg.ejpam.v18i2.6009	X
ejpam-6009	11	4	email	email	NOUN
ejpam-6009	11	5	addresses	address	VERB
ejpam-6009	11	6	:	:	PUNCT
ejpam-6009	11	7	chokchai.v@msu.ac.th	chokchai.v@msu.ac.th	PROPN
ejpam-6009	11	8	(	(	PUNCT
ejpam-6009	11	9	c.	c.	PROPN
ejpam-6009	11	10	viriyapong	viriyapong	PROPN
ejpam-6009	11	11	)	)	PUNCT
ejpam-6009	11	12	,	,	PUNCT
ejpam-6009	11	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-6009	11	14	(	(	PUNCT
ejpam-6009	11	15	a.	a.	PROPN
ejpam-6009	11	16	sama	sama	PROPN
ejpam-6009	11	17	-	-	PUNCT
ejpam-6009	11	18	ae	ae	PROPN
ejpam-6009	11	19	)	)	PUNCT
ejpam-6009	11	20	,	,	PUNCT
ejpam-6009	11	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6009	11	22	(	(	PUNCT
ejpam-6009	11	23	c.	c.	PROPN
ejpam-6009	11	24	boonpok	boonpok	PROPN
ejpam-6009	11	25	)	)	PUNCT
ejpam-6009	11	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6009	12	1	1	1	NUM
ejpam-6009	12	2	copyright	copyright	NOUN
ejpam-6009	12	3	:	:	PUNCT
ejpam-6009	12	4	©	©	PROPN
ejpam-6009	12	5	2025	2025	NUM
ejpam-6009	12	6	the	the	DET
ejpam-6009	12	7	author(s	author(s	NOUN
ejpam-6009	12	8	)	)	PUNCT
ejpam-6009	12	9	.	.	PUNCT
ejpam-6009	13	1	(	(	PUNCT
ejpam-6009	13	2	cc	cc	NOUN
ejpam-6009	13	3	by	by	ADP
ejpam-6009	13	4	-	-	PUNCT
ejpam-6009	13	5	nc	nc	PROPN
ejpam-6009	13	6	4.0	4.0	NUM
ejpam-6009	13	7	)	)	PUNCT
ejpam-6009	13	8	c.	c.	PROPN
ejpam-6009	13	9	viriyapong	viriyapong	PROPN
ejpam-6009	13	10	,	,	PUNCT
ejpam-6009	13	11	a.	a.	PROPN
ejpam-6009	13	12	sama	sama	PROPN
ejpam-6009	13	13	-	-	PUNCT
ejpam-6009	13	14	ae	ae	PROPN
ejpam-6009	13	15	,	,	PUNCT
ejpam-6009	13	16	c.	c.	PROPN
ejpam-6009	13	17	boonpok	boonpok	PROPN
ejpam-6009	13	18	/	/	SYM
ejpam-6009	13	19	eur	eur	PROPN
ejpam-6009	13	20	.	.	PUNCT
ejpam-6009	14	1	j.	j.	PROPN
ejpam-6009	14	2	pure	pure	PROPN
ejpam-6009	14	3	appl	appl	PROPN
ejpam-6009	14	4	.	.	PROPN
ejpam-6009	14	5	math	math	PROPN
ejpam-6009	14	6	,	,	PUNCT
ejpam-6009	14	7	18	18	NUM
ejpam-6009	14	8	(	(	PUNCT
ejpam-6009	14	9	2	2	NUM
ejpam-6009	14	10	)	)	PUNCT
ejpam-6009	14	11	(	(	PUNCT
ejpam-6009	14	12	2025	2025	NUM
ejpam-6009	14	13	)	)	PUNCT
ejpam-6009	14	14	,	,	PUNCT
ejpam-6009	14	15	6009	6009	NUM
ejpam-6009	14	16	2	2	NUM
ejpam-6009	14	17	of	of	ADP
ejpam-6009	14	18	18	18	NUM
ejpam-6009	14	19	dungthaisong	dungthaisong	NOUN
ejpam-6009	14	20	et	et	PROPN
ejpam-6009	14	21	al	al	PROPN
ejpam-6009	14	22	.	.	PUNCT
ejpam-6009	15	1	[	[	X
ejpam-6009	15	2	3	3	NUM
ejpam-6009	15	3	]	]	PUNCT
ejpam-6009	15	4	introduced	introduce	VERB
ejpam-6009	15	5	and	and	CCONJ
ejpam-6009	15	6	studied	study	VERB
ejpam-6009	15	7	the	the	DET
ejpam-6009	15	8	concept	concept	NOUN
ejpam-6009	15	9	of	of	ADP
ejpam-6009	15	10	g(m	g(m	ADJ
ejpam-6009	15	11	,	,	PUNCT
ejpam-6009	15	12	n)-continuous	n)-continuous	ADJ
ejpam-6009	15	13	functions	function	NOUN
ejpam-6009	15	14	.	.	PUNCT
ejpam-6009	16	1	duangphui	duangphui	NOUN
ejpam-6009	16	2	et	et	PROPN
ejpam-6009	16	3	al	al	PROPN
ejpam-6009	16	4	.	.	PUNCT
ejpam-6009	17	1	[	[	X
ejpam-6009	17	2	4	4	X
ejpam-6009	17	3	]	]	PUNCT
ejpam-6009	17	4	introduced	introduce	VERB
ejpam-6009	17	5	and	and	CCONJ
ejpam-6009	17	6	investigated	investigate	VERB
ejpam-6009	17	7	the	the	DET
ejpam-6009	17	8	notion	notion	NOUN
ejpam-6009	17	9	of	of	ADP
ejpam-6009	17	10	almost	almost	ADV
ejpam-6009	17	11	(	(	PUNCT
ejpam-6009	17	12	µ	µ	NUM
ejpam-6009	17	13	,	,	PUNCT
ejpam-6009	17	14	µ′)(m	µ′)(m	VERB
ejpam-6009	17	15	,	,	PUNCT
ejpam-6009	17	16	n)continuous	n)continuous	ADJ
ejpam-6009	17	17	functions	function	NOUN
ejpam-6009	17	18	.	.	PUNCT
ejpam-6009	18	1	furthermore	furthermore	ADV
ejpam-6009	18	2	,	,	PUNCT
ejpam-6009	18	3	several	several	ADJ
ejpam-6009	18	4	characterizations	characterization	NOUN
ejpam-6009	18	5	of	of	ADP
ejpam-6009	18	6	almost	almost	ADV
ejpam-6009	18	7	(	(	PUNCT
ejpam-6009	18	8	λ	λ	PROPN
ejpam-6009	18	9	,	,	PUNCT
ejpam-6009	18	10	p)-continuous	p)-continuous	ADJ
ejpam-6009	18	11	functions	function	NOUN
ejpam-6009	18	12	,	,	PUNCT
ejpam-6009	18	13	strongly	strongly	ADV
ejpam-6009	18	14	θ(λ	θ(λ	PROPN
ejpam-6009	18	15	,	,	PUNCT
ejpam-6009	18	16	p)-continuous	p)-continuous	ADJ
ejpam-6009	18	17	functions	function	NOUN
ejpam-6009	18	18	,	,	PUNCT
ejpam-6009	18	19	almost	almost	ADV
ejpam-6009	18	20	strongly	strongly	ADV
ejpam-6009	18	21	θ(λ	θ(λ	VERB
ejpam-6009	18	22	,	,	PUNCT
ejpam-6009	18	23	p)-continuous	p)-continuous	ADJ
ejpam-6009	18	24	functions	function	NOUN
ejpam-6009	18	25	,	,	PUNCT
ejpam-6009	18	26	θ(λ	θ(λ	PROPN
ejpam-6009	18	27	,	,	PUNCT
ejpam-6009	18	28	p)-continuous	p)-continuous	ADJ
ejpam-6009	18	29	functions	function	NOUN
ejpam-6009	18	30	,	,	PUNCT
ejpam-6009	18	31	weakly	weakly	ADJ
ejpam-6009	18	32	(	(	PUNCT
ejpam-6009	18	33	λ	λ	PROPN
ejpam-6009	18	34	,	,	PUNCT
ejpam-6009	18	35	b)-continuous	b)-continuous	ADJ
ejpam-6009	18	36	functions	function	NOUN
ejpam-6009	18	37	,	,	PUNCT
ejpam-6009	18	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-6009	18	39	functions	function	NOUN
ejpam-6009	18	40	,	,	PUNCT
ejpam-6009	18	41	(	(	PUNCT
ejpam-6009	18	42	λ	λ	NOUN
ejpam-6009	18	43	,	,	PUNCT
ejpam-6009	18	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-6009	18	45	functions	function	NOUN
ejpam-6009	18	46	,	,	PUNCT
ejpam-6009	18	47	⋆-continuous	⋆-continuous	ADJ
ejpam-6009	18	48	functions	function	NOUN
ejpam-6009	18	49	,	,	PUNCT
ejpam-6009	18	50	θ	θ	PROPN
ejpam-6009	18	51	-	-	ADJ
ejpam-6009	18	52	i	i	NOUN
ejpam-6009	18	53	-continuous	-continuous	ADJ
ejpam-6009	18	54	functions	function	NOUN
ejpam-6009	18	55	,	,	PUNCT
ejpam-6009	18	56	almost	almost	ADV
ejpam-6009	18	57	(	(	PUNCT
ejpam-6009	18	58	g	g	NOUN
ejpam-6009	18	59	,	,	PUNCT
ejpam-6009	18	60	m)-continuous	m)-continuous	ADJ
ejpam-6009	18	61	functions	function	NOUN
ejpam-6009	18	62	,	,	PUNCT
ejpam-6009	18	63	pairwise	pairwise	NOUN
ejpam-6009	18	64	almostm	almostm	NOUN
ejpam-6009	18	65	-continuous	-continuous	ADJ
ejpam-6009	18	66	functions	function	NOUN
ejpam-6009	18	67	,	,	PUNCT
ejpam-6009	18	68	(	(	PUNCT
ejpam-6009	18	69	τ1	τ1	NOUN
ejpam-6009	18	70	,	,	PUNCT
ejpam-6009	18	71	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	18	72	functions	function	NOUN
ejpam-6009	18	73	,	,	PUNCT
ejpam-6009	18	74	almost	almost	ADV
ejpam-6009	18	75	(	(	PUNCT
ejpam-6009	18	76	τ1	τ1	NOUN
ejpam-6009	18	77	,	,	PUNCT
ejpam-6009	18	78	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	18	79	functions	function	NOUN
ejpam-6009	18	80	,	,	PUNCT
ejpam-6009	18	81	weakly	weakly	ADJ
ejpam-6009	18	82	(	(	PUNCT
ejpam-6009	18	83	τ1	τ1	NOUN
ejpam-6009	18	84	,	,	PUNCT
ejpam-6009	18	85	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	18	86	functions	function	NOUN
ejpam-6009	18	87	and	and	CCONJ
ejpam-6009	18	88	slightly	slightly	ADV
ejpam-6009	18	89	(	(	PUNCT
ejpam-6009	18	90	τ1	τ1	NOUN
ejpam-6009	18	91	,	,	PUNCT
ejpam-6009	18	92	τ2)s	τ2)s	ADJ
ejpam-6009	18	93	-	-	PUNCT
ejpam-6009	18	94	continuous	continuous	ADJ
ejpam-6009	18	95	functions	function	NOUN
ejpam-6009	18	96	were	be	AUX
ejpam-6009	18	97	presented	present	VERB
ejpam-6009	18	98	in	in	ADP
ejpam-6009	18	99	[	[	X
ejpam-6009	18	100	5	5	NUM
ejpam-6009	18	101	]	]	PUNCT
ejpam-6009	18	102	,	,	PUNCT
ejpam-6009	18	103	[	[	X
ejpam-6009	18	104	6	6	NUM
ejpam-6009	18	105	]	]	PUNCT
ejpam-6009	18	106	,	,	PUNCT
ejpam-6009	18	107	[	[	X
ejpam-6009	18	108	7	7	NUM
ejpam-6009	18	109	]	]	PUNCT
ejpam-6009	18	110	,	,	PUNCT
ejpam-6009	18	111	[	[	X
ejpam-6009	18	112	8	8	NUM
ejpam-6009	18	113	]	]	PUNCT
ejpam-6009	18	114	,	,	PUNCT
ejpam-6009	19	1	[	[	X
ejpam-6009	19	2	9	9	NUM
ejpam-6009	19	3	]	]	PUNCT
ejpam-6009	19	4	,	,	PUNCT
ejpam-6009	19	5	[	[	X
ejpam-6009	19	6	10	10	NUM
ejpam-6009	19	7	]	]	PUNCT
ejpam-6009	19	8	,	,	PUNCT
ejpam-6009	20	1	[	[	X
ejpam-6009	20	2	11	11	NUM
ejpam-6009	20	3	]	]	PUNCT
ejpam-6009	20	4	,	,	PUNCT
ejpam-6009	20	5	[	[	X
ejpam-6009	20	6	12	12	NUM
ejpam-6009	20	7	]	]	PUNCT
ejpam-6009	20	8	,	,	PUNCT
ejpam-6009	20	9	[	[	X
ejpam-6009	20	10	13	13	NUM
ejpam-6009	20	11	]	]	PUNCT
ejpam-6009	20	12	,	,	PUNCT
ejpam-6009	20	13	[	[	X
ejpam-6009	20	14	14	14	NUM
ejpam-6009	20	15	]	]	PUNCT
ejpam-6009	20	16	,	,	PUNCT
ejpam-6009	20	17	[	[	X
ejpam-6009	20	18	15	15	NUM
ejpam-6009	20	19	]	]	PUNCT
ejpam-6009	20	20	,	,	PUNCT
ejpam-6009	20	21	[	[	X
ejpam-6009	20	22	16	16	NUM
ejpam-6009	20	23	]	]	PUNCT
ejpam-6009	20	24	,	,	PUNCT
ejpam-6009	21	1	[	[	X
ejpam-6009	21	2	17	17	NUM
ejpam-6009	21	3	]	]	PUNCT
ejpam-6009	21	4	,	,	PUNCT
ejpam-6009	21	5	[	[	X
ejpam-6009	21	6	18	18	NUM
ejpam-6009	21	7	]	]	PUNCT
ejpam-6009	21	8	and	and	CCONJ
ejpam-6009	21	9	[	[	X
ejpam-6009	21	10	19	19	NUM
ejpam-6009	21	11	]	]	PUNCT
ejpam-6009	21	12	,	,	PUNCT
ejpam-6009	21	13	respectively	respectively	ADV
ejpam-6009	21	14	.	.	PUNCT
ejpam-6009	22	1	kong	kong	PROPN
ejpam-6009	22	2	-	-	PUNCT
ejpam-6009	22	3	ied	ied	PROPN
ejpam-6009	22	4	at	at	ADP
ejpam-6009	22	5	al	al	PROPN
ejpam-6009	22	6	.	.	PUNCT
ejpam-6009	23	1	[	[	X
ejpam-6009	23	2	20	20	NUM
ejpam-6009	23	3	]	]	PUNCT
ejpam-6009	23	4	introduced	introduce	VERB
ejpam-6009	23	5	and	and	CCONJ
ejpam-6009	23	6	studied	study	VERB
ejpam-6009	23	7	the	the	DET
ejpam-6009	23	8	concept	concept	NOUN
ejpam-6009	23	9	of	of	ADP
ejpam-6009	23	10	almost	almost	ADV
ejpam-6009	23	11	quasi	quasi	X
ejpam-6009	23	12	(	(	PUNCT
ejpam-6009	23	13	τ1	τ1	NOUN
ejpam-6009	23	14	,	,	PUNCT
ejpam-6009	23	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	23	16	functions	function	NOUN
ejpam-6009	23	17	.	.	PUNCT
ejpam-6009	24	1	chiangpradit	chiangpradit	NOUN
ejpam-6009	24	2	et	et	PROPN
ejpam-6009	24	3	al	al	PROPN
ejpam-6009	24	4	.	.	PUNCT
ejpam-6009	25	1	[	[	X
ejpam-6009	25	2	21	21	NUM
ejpam-6009	25	3	]	]	PUNCT
ejpam-6009	25	4	introduced	introduce	VERB
ejpam-6009	25	5	and	and	CCONJ
ejpam-6009	25	6	investigated	investigate	VERB
ejpam-6009	25	7	the	the	DET
ejpam-6009	25	8	notion	notion	NOUN
ejpam-6009	25	9	of	of	ADP
ejpam-6009	25	10	weakly	weakly	ADJ
ejpam-6009	25	11	quasi	quasi	NOUN
ejpam-6009	25	12	(	(	PUNCT
ejpam-6009	25	13	τ1	τ1	PROPN
ejpam-6009	25	14	,	,	PUNCT
ejpam-6009	25	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	25	16	functions	function	NOUN
ejpam-6009	25	17	.	.	PUNCT
ejpam-6009	26	1	thongmoon	thongmoon	NOUN
ejpam-6009	26	2	et	et	PROPN
ejpam-6009	26	3	al	al	PROPN
ejpam-6009	26	4	.	.	PUNCT
ejpam-6009	27	1	[	[	X
ejpam-6009	27	2	22	22	NUM
ejpam-6009	27	3	]	]	PUNCT
ejpam-6009	27	4	introduced	introduce	VERB
ejpam-6009	27	5	and	and	CCONJ
ejpam-6009	27	6	studied	study	VERB
ejpam-6009	27	7	the	the	DET
ejpam-6009	27	8	notion	notion	NOUN
ejpam-6009	27	9	of	of	ADP
ejpam-6009	27	10	rarely	rarely	ADV
ejpam-6009	27	11	(	(	PUNCT
ejpam-6009	27	12	τ1	τ1	NOUN
ejpam-6009	27	13	,	,	PUNCT
ejpam-6009	27	14	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	27	15	functions	function	NOUN
ejpam-6009	27	16	.	.	PUNCT
ejpam-6009	28	1	srisarakham	srisarakham	PROPN
ejpam-6009	28	2	et	et	PROPN
ejpam-6009	28	3	al	al	PROPN
ejpam-6009	28	4	.	.	PUNCT
ejpam-6009	29	1	[	[	X
ejpam-6009	29	2	23	23	NUM
ejpam-6009	29	3	]	]	PUNCT
ejpam-6009	29	4	introduced	introduce	VERB
ejpam-6009	29	5	and	and	CCONJ
ejpam-6009	29	6	investigated	investigate	VERB
ejpam-6009	29	7	the	the	DET
ejpam-6009	29	8	concept	concept	NOUN
ejpam-6009	29	9	of	of	ADP
ejpam-6009	29	10	faintly	faintly	ADV
ejpam-6009	29	11	(	(	PUNCT
ejpam-6009	29	12	τ1	τ1	PROPN
ejpam-6009	29	13	,	,	PUNCT
ejpam-6009	29	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	29	15	functions	function	NOUN
ejpam-6009	29	16	.	.	PUNCT
ejpam-6009	30	1	on	on	ADP
ejpam-6009	30	2	the	the	DET
ejpam-6009	30	3	other	other	ADJ
ejpam-6009	30	4	hand	hand	NOUN
ejpam-6009	30	5	,	,	PUNCT
ejpam-6009	30	6	the	the	DET
ejpam-6009	30	7	present	present	ADJ
ejpam-6009	30	8	authors	author	NOUN
ejpam-6009	30	9	introduced	introduce	VERB
ejpam-6009	30	10	and	and	CCONJ
ejpam-6009	30	11	studied	study	VERB
ejpam-6009	30	12	the	the	DET
ejpam-6009	30	13	notions	notion	NOUN
ejpam-6009	30	14	of	of	ADP
ejpam-6009	30	15	δ(τ1	δ(τ1	NOUN
ejpam-6009	30	16	,	,	PUNCT
ejpam-6009	30	17	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	30	18	functions	function	NOUN
ejpam-6009	30	19	[	[	X
ejpam-6009	30	20	24	24	NUM
ejpam-6009	30	21	]	]	PUNCT
ejpam-6009	30	22	,	,	PUNCT
ejpam-6009	30	23	quasi	quasi	NOUN
ejpam-6009	30	24	θ(τ1	θ(τ1	PROPN
ejpam-6009	30	25	,	,	PUNCT
ejpam-6009	30	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	30	27	functions	function	NOUN
ejpam-6009	30	28	[	[	X
ejpam-6009	30	29	25	25	NUM
ejpam-6009	30	30	]	]	PUNCT
ejpam-6009	30	31	,	,	PUNCT
ejpam-6009	30	32	almost	almost	ADV
ejpam-6009	30	33	weakly	weakly	ADJ
ejpam-6009	30	34	(	(	PUNCT
ejpam-6009	30	35	τ1	τ1	NOUN
ejpam-6009	30	36	,	,	PUNCT
ejpam-6009	30	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	30	38	functions	function	NOUN
ejpam-6009	30	39	[	[	X
ejpam-6009	30	40	26	26	NUM
ejpam-6009	30	41	]	]	PUNCT
ejpam-6009	30	42	and	and	CCONJ
ejpam-6009	30	43	almost	almost	ADV
ejpam-6009	30	44	nearly	nearly	ADV
ejpam-6009	30	45	(	(	PUNCT
ejpam-6009	30	46	τ1	τ1	NOUN
ejpam-6009	30	47	,	,	PUNCT
ejpam-6009	30	48	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	30	49	functions	function	NOUN
ejpam-6009	30	50	[	[	X
ejpam-6009	30	51	27	27	NUM
ejpam-6009	30	52	]	]	PUNCT
ejpam-6009	30	53	.	.	PUNCT
ejpam-6009	31	1	in	in	ADP
ejpam-6009	31	2	1966	1966	NUM
ejpam-6009	31	3	,	,	PUNCT
ejpam-6009	31	4	dontchev	dontchev	ADJ
ejpam-6009	31	5	[	[	X
ejpam-6009	31	6	28	28	NUM
ejpam-6009	31	7	]	]	PUNCT
ejpam-6009	31	8	introduced	introduce	VERB
ejpam-6009	31	9	the	the	DET
ejpam-6009	31	10	concepts	concept	NOUN
ejpam-6009	31	11	of	of	ADP
ejpam-6009	31	12	contracontinuity	contracontinuity	NOUN
ejpam-6009	31	13	and	and	CCONJ
ejpam-6009	31	14	strong	strong	ADJ
ejpam-6009	31	15	s	s	NOUN
ejpam-6009	31	16	-	-	NOUN
ejpam-6009	31	17	closedness	closedness	ADJ
ejpam-6009	31	18	in	in	ADP
ejpam-6009	31	19	topological	topological	ADJ
ejpam-6009	31	20	spaces	space	NOUN
ejpam-6009	31	21	.	.	PUNCT
ejpam-6009	32	1	moreover	moreover	ADV
ejpam-6009	32	2	,	,	PUNCT
ejpam-6009	32	3	dontchev	dontchev	ADJ
ejpam-6009	32	4	[	[	X
ejpam-6009	32	5	28	28	NUM
ejpam-6009	32	6	]	]	PUNCT
ejpam-6009	32	7	obtained	obtain	VERB
ejpam-6009	32	8	very	very	ADV
ejpam-6009	32	9	interesting	interesting	ADJ
ejpam-6009	32	10	and	and	CCONJ
ejpam-6009	32	11	important	important	ADJ
ejpam-6009	32	12	results	result	NOUN
ejpam-6009	32	13	concerning	concern	VERB
ejpam-6009	32	14	contra	contra	NOUN
ejpam-6009	32	15	-	-	ADJ
ejpam-6009	32	16	continuity	continuity	NOUN
ejpam-6009	32	17	,	,	PUNCT
ejpam-6009	32	18	compactness	compactness	NOUN
ejpam-6009	32	19	,	,	PUNCT
ejpam-6009	32	20	s	s	NOUN
ejpam-6009	32	21	-	-	PUNCT
ejpam-6009	32	22	closedness	closedness	ADJ
ejpam-6009	32	23	and	and	CCONJ
ejpam-6009	32	24	strong	strong	ADJ
ejpam-6009	32	25	s	s	NOUN
ejpam-6009	32	26	-	-	PUNCT
ejpam-6009	32	27	closedness	closedness	NOUN
ejpam-6009	32	28	.	.	PUNCT
ejpam-6009	33	1	dontchev	dontchev	NOUN
ejpam-6009	33	2	et	et	PROPN
ejpam-6009	33	3	al	al	PROPN
ejpam-6009	33	4	.	.	PUNCT
ejpam-6009	34	1	[	[	X
ejpam-6009	34	2	29	29	NUM
ejpam-6009	34	3	]	]	PUNCT
ejpam-6009	34	4	defined	define	VERB
ejpam-6009	34	5	a	a	DET
ejpam-6009	34	6	new	new	ADJ
ejpam-6009	34	7	class	class	NOUN
ejpam-6009	34	8	of	of	ADP
ejpam-6009	34	9	functions	function	NOUN
ejpam-6009	34	10	called	call	VERB
ejpam-6009	34	11	regular	regular	ADJ
ejpam-6009	34	12	set	set	NOUN
ejpam-6009	34	13	-	-	PUNCT
ejpam-6009	34	14	connected	connect	VERB
ejpam-6009	34	15	functions	function	NOUN
ejpam-6009	34	16	.	.	PUNCT
ejpam-6009	35	1	dontchev	dontchev	NOUN
ejpam-6009	35	2	and	and	CCONJ
ejpam-6009	35	3	noiri	noiri	ADV
ejpam-6009	36	1	[	[	X
ejpam-6009	36	2	30	30	NUM
ejpam-6009	36	3	]	]	PUNCT
ejpam-6009	36	4	introduced	introduce	VERB
ejpam-6009	36	5	and	and	CCONJ
ejpam-6009	36	6	studied	study	VERB
ejpam-6009	36	7	the	the	DET
ejpam-6009	36	8	concept	concept	NOUN
ejpam-6009	36	9	of	of	ADP
ejpam-6009	36	10	rc	rc	NOUN
ejpam-6009	36	11	-	-	NOUN
ejpam-6009	36	12	continuity	continuity	NOUN
ejpam-6009	36	13	between	between	ADP
ejpam-6009	36	14	topological	topological	ADJ
ejpam-6009	36	15	spaces	space	NOUN
ejpam-6009	36	16	which	which	PRON
ejpam-6009	36	17	is	be	AUX
ejpam-6009	36	18	weaker	weak	ADJ
ejpam-6009	36	19	than	than	ADP
ejpam-6009	36	20	contra	contra	NOUN
ejpam-6009	36	21	-	-	NOUN
ejpam-6009	36	22	continuity	continuity	NOUN
ejpam-6009	36	23	.	.	PUNCT
ejpam-6009	37	1	jafari	jafari	PROPN
ejpam-6009	37	2	and	and	CCONJ
ejpam-6009	37	3	noiri	noiri	ADV
ejpam-6009	37	4	[	[	X
ejpam-6009	37	5	31	31	NUM
ejpam-6009	37	6	]	]	PUNCT
ejpam-6009	37	7	introduced	introduce	VERB
ejpam-6009	37	8	a	a	DET
ejpam-6009	37	9	new	new	ADJ
ejpam-6009	37	10	class	class	NOUN
ejpam-6009	37	11	of	of	ADP
ejpam-6009	37	12	functions	function	NOUN
ejpam-6009	37	13	called	call	VERB
ejpam-6009	37	14	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6009	37	15	functions	function	NOUN
ejpam-6009	37	16	which	which	PRON
ejpam-6009	37	17	is	be	AUX
ejpam-6009	37	18	weaker	weak	ADJ
ejpam-6009	37	19	than	than	ADP
ejpam-6009	37	20	contra	contra	ADJ
ejpam-6009	37	21	-	-	ADJ
ejpam-6009	37	22	continuous	continuous	ADJ
ejpam-6009	37	23	functions	function	NOUN
ejpam-6009	37	24	and	and	CCONJ
ejpam-6009	37	25	studied	study	VERB
ejpam-6009	37	26	several	several	ADJ
ejpam-6009	37	27	basic	basic	ADJ
ejpam-6009	37	28	properties	property	NOUN
ejpam-6009	37	29	of	of	ADP
ejpam-6009	37	30	contra	contra	ADJ
ejpam-6009	37	31	-	-	ADJ
ejpam-6009	37	32	precontinuous	precontinuous	ADJ
ejpam-6009	37	33	functions	function	NOUN
ejpam-6009	37	34	.	.	PUNCT
ejpam-6009	38	1	in	in	ADP
ejpam-6009	38	2	2004	2004	NUM
ejpam-6009	38	3	,	,	PUNCT
ejpam-6009	38	4	ekici	ekici	NOUN
ejpam-6009	38	5	[	[	X
ejpam-6009	38	6	32	32	NUM
ejpam-6009	38	7	]	]	PUNCT
ejpam-6009	38	8	introduced	introduce	VERB
ejpam-6009	38	9	and	and	CCONJ
ejpam-6009	38	10	studied	study	VERB
ejpam-6009	38	11	a	a	DET
ejpam-6009	38	12	new	new	ADJ
ejpam-6009	38	13	class	class	NOUN
ejpam-6009	38	14	of	of	ADP
ejpam-6009	38	15	functions	function	NOUN
ejpam-6009	38	16	called	call	VERB
ejpam-6009	38	17	almost	almost	ADV
ejpam-6009	38	18	contra	contra	ADJ
ejpam-6009	38	19	-	-	ADJ
ejpam-6009	38	20	precontinuous	precontinuous	ADJ
ejpam-6009	38	21	functions	function	NOUN
ejpam-6009	38	22	which	which	PRON
ejpam-6009	38	23	generalize	generalize	VERB
ejpam-6009	38	24	classes	class	NOUN
ejpam-6009	38	25	of	of	ADP
ejpam-6009	38	26	regular	regular	ADJ
ejpam-6009	38	27	set	set	NOUN
ejpam-6009	38	28	-	-	PUNCT
ejpam-6009	38	29	connected	connect	VERB
ejpam-6009	38	30	functions	function	NOUN
ejpam-6009	38	31	[	[	X
ejpam-6009	38	32	29	29	NUM
ejpam-6009	38	33	]	]	PUNCT
ejpam-6009	38	34	,	,	PUNCT
ejpam-6009	38	35	contra	contra	ADJ
ejpam-6009	38	36	-	-	ADJ
ejpam-6009	38	37	precontinuous	precontinuous	ADJ
ejpam-6009	38	38	functions	function	NOUN
ejpam-6009	38	39	[	[	X
ejpam-6009	38	40	31	31	NUM
ejpam-6009	38	41	]	]	PUNCT
ejpam-6009	38	42	,	,	PUNCT
ejpam-6009	38	43	contra	contra	ADJ
ejpam-6009	38	44	-	-	ADJ
ejpam-6009	38	45	continuous	continuous	ADJ
ejpam-6009	38	46	functions	function	NOUN
ejpam-6009	38	47	[	[	X
ejpam-6009	38	48	28	28	NUM
ejpam-6009	38	49	]	]	X
ejpam-6009	38	50	,	,	PUNCT
ejpam-6009	38	51	almost	almost	ADV
ejpam-6009	38	52	s	s	NOUN
ejpam-6009	38	53	-	-	PUNCT
ejpam-6009	38	54	continuous	continuous	ADJ
ejpam-6009	38	55	functions	function	NOUN
ejpam-6009	38	56	[	[	X
ejpam-6009	38	57	33	33	NUM
ejpam-6009	38	58	]	]	PUNCT
ejpam-6009	38	59	and	and	CCONJ
ejpam-6009	38	60	perfectly	perfectly	ADV
ejpam-6009	38	61	continuous	continuous	ADJ
ejpam-6009	38	62	functions	function	NOUN
ejpam-6009	38	63	[	[	X
ejpam-6009	38	64	34	34	NUM
ejpam-6009	38	65	]	]	PUNCT
ejpam-6009	38	66	.	.	PUNCT
ejpam-6009	39	1	in	in	ADP
ejpam-6009	39	2	2008	2008	NUM
ejpam-6009	39	3	,	,	PUNCT
ejpam-6009	39	4	ekici	ekici	NOUN
ejpam-6009	39	5	et	et	PROPN
ejpam-6009	39	6	al	al	PROPN
ejpam-6009	39	7	.	.	PUNCT
ejpam-6009	40	1	[	[	X
ejpam-6009	40	2	35	35	NUM
ejpam-6009	40	3	]	]	PUNCT
ejpam-6009	40	4	extended	extend	VERB
ejpam-6009	40	5	the	the	DET
ejpam-6009	40	6	notion	notion	NOUN
ejpam-6009	40	7	of	of	ADP
ejpam-6009	40	8	contra	contra	ADJ
ejpam-6009	40	9	-	-	ADJ
ejpam-6009	40	10	continuous	continuous	ADJ
ejpam-6009	40	11	functions	function	NOUN
ejpam-6009	40	12	to	to	ADP
ejpam-6009	40	13	the	the	DET
ejpam-6009	40	14	setting	setting	NOUN
ejpam-6009	40	15	of	of	ADP
ejpam-6009	40	16	multifunctions	multifunction	NOUN
ejpam-6009	40	17	.	.	PUNCT
ejpam-6009	41	1	noiri	noiri	PROPN
ejpam-6009	41	2	and	and	CCONJ
ejpam-6009	41	3	popa	popa	NOUN
ejpam-6009	41	4	[	[	X
ejpam-6009	41	5	36	36	NUM
ejpam-6009	41	6	]	]	PUNCT
ejpam-6009	41	7	introduced	introduce	VERB
ejpam-6009	41	8	the	the	DET
ejpam-6009	41	9	notion	notion	NOUN
ejpam-6009	41	10	of	of	ADP
ejpam-6009	41	11	weakly	weakly	ADJ
ejpam-6009	41	12	precontinuous	precontinuous	ADJ
ejpam-6009	41	13	multifunctions	multifunction	NOUN
ejpam-6009	41	14	.	.	PUNCT
ejpam-6009	42	1	ekici	ekici	NOUN
ejpam-6009	42	2	et	et	PROPN
ejpam-6009	42	3	al	al	PROPN
ejpam-6009	42	4	.	.	PUNCT
ejpam-6009	43	1	[	[	X
ejpam-6009	43	2	37	37	NUM
ejpam-6009	43	3	]	]	PUNCT
ejpam-6009	43	4	introduced	introduce	VERB
ejpam-6009	43	5	and	and	CCONJ
ejpam-6009	43	6	studied	study	VERB
ejpam-6009	43	7	two	two	NUM
ejpam-6009	43	8	new	new	ADJ
ejpam-6009	43	9	concepts	concept	NOUN
ejpam-6009	43	10	namely	namely	ADV
ejpam-6009	43	11	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6009	43	12	multifunctions	multifunction	NOUN
ejpam-6009	43	13	and	and	CCONJ
ejpam-6009	43	14	almost	almost	ADV
ejpam-6009	43	15	contra	contra	ADJ
ejpam-6009	43	16	-	-	ADJ
ejpam-6009	43	17	precontinuous	precontinuous	ADJ
ejpam-6009	43	18	multifunctions	multifunction	NOUN
ejpam-6009	43	19	which	which	PRON
ejpam-6009	43	20	are	be	AUX
ejpam-6009	43	21	containing	contain	VERB
ejpam-6009	43	22	the	the	DET
ejpam-6009	43	23	class	class	NOUN
ejpam-6009	43	24	of	of	ADP
ejpam-6009	43	25	contra	contra	ADJ
ejpam-6009	43	26	-	-	ADJ
ejpam-6009	43	27	continuous	continuous	ADJ
ejpam-6009	43	28	multifunctions	multifunction	NOUN
ejpam-6009	43	29	[	[	X
ejpam-6009	43	30	35	35	NUM
ejpam-6009	43	31	]	]	PUNCT
ejpam-6009	43	32	and	and	CCONJ
ejpam-6009	43	33	contained	contain	VERB
ejpam-6009	43	34	in	in	ADP
ejpam-6009	43	35	the	the	DET
ejpam-6009	43	36	class	class	NOUN
ejpam-6009	43	37	of	of	ADP
ejpam-6009	43	38	weakly	weakly	ADJ
ejpam-6009	43	39	precontinuous	precontinuous	ADJ
ejpam-6009	43	40	multifunctions	multifunction	NOUN
ejpam-6009	43	41	.	.	PUNCT
ejpam-6009	44	1	laprom	laprom	ADP
ejpam-6009	44	2	et	et	PROPN
ejpam-6009	44	3	al	al	PROPN
ejpam-6009	44	4	.	.	PUNCT
ejpam-6009	45	1	[	[	X
ejpam-6009	45	2	38	38	NUM
ejpam-6009	45	3	]	]	PUNCT
ejpam-6009	45	4	introduced	introduce	VERB
ejpam-6009	45	5	and	and	CCONJ
ejpam-6009	45	6	investigated	investigate	VERB
ejpam-6009	45	7	the	the	DET
ejpam-6009	45	8	notion	notion	NOUN
ejpam-6009	45	9	of	of	ADP
ejpam-6009	45	10	almost	almost	ADV
ejpam-6009	45	11	β(τ1	β(τ1	NOUN
ejpam-6009	45	12	,	,	PUNCT
ejpam-6009	45	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	45	14	multifunctions	multifunction	NOUN
ejpam-6009	45	15	.	.	PUNCT
ejpam-6009	46	1	moreover	moreover	ADV
ejpam-6009	46	2	,	,	PUNCT
ejpam-6009	46	3	some	some	DET
ejpam-6009	46	4	characterizations	characterization	NOUN
ejpam-6009	46	5	of	of	ADP
ejpam-6009	46	6	(	(	PUNCT
ejpam-6009	46	7	τ1	τ1	NOUN
ejpam-6009	46	8	,	,	PUNCT
ejpam-6009	46	9	τ2)δ	τ2)δ	ADJ
ejpam-6009	46	10	-	-	PUNCT
ejpam-6009	46	11	semicontinuous	semicontinuous	ADJ
ejpam-6009	46	12	multifunctions	multifunction	NOUN
ejpam-6009	46	13	,	,	PUNCT
ejpam-6009	46	14	almost	almost	ADV
ejpam-6009	46	15	weakly	weakly	ADJ
ejpam-6009	46	16	(	(	PUNCT
ejpam-6009	46	17	τ1	τ1	NOUN
ejpam-6009	46	18	,	,	PUNCT
ejpam-6009	46	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	46	20	multifunctions	multifunction	NOUN
ejpam-6009	46	21	,	,	PUNCT
ejpam-6009	46	22	weakly	weakly	ADJ
ejpam-6009	46	23	quasi	quasi	NOUN
ejpam-6009	46	24	(	(	PUNCT
ejpam-6009	46	25	λ	λ	PROPN
ejpam-6009	46	26	,	,	PUNCT
ejpam-6009	46	27	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	46	28	multifunctions	multifunction	NOUN
ejpam-6009	46	29	,	,	PUNCT
ejpam-6009	46	30	⋆-continuous	⋆-continuous	ADJ
ejpam-6009	46	31	multifunctions	multifunction	NOUN
ejpam-6009	46	32	,	,	PUNCT
ejpam-6009	46	33	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-6009	46	34	multifunctions	multifunction	NOUN
ejpam-6009	46	35	,	,	PUNCT
ejpam-6009	46	36	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6009	46	37	multifunctions	multifunction	NOUN
ejpam-6009	46	38	,	,	PUNCT
ejpam-6009	46	39	almost	almost	ADV
ejpam-6009	46	40	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6009	46	41	multifunctions	multifunction	NOUN
ejpam-6009	46	42	,	,	PUNCT
ejpam-6009	46	43	almost	almost	ADV
ejpam-6009	46	44	quasi	quasi	VERB
ejpam-6009	46	45	⋆-continuous	⋆-continuous	ADJ
ejpam-6009	46	46	multifunctions	multifunction	NOUN
ejpam-6009	46	47	,	,	PUNCT
ejpam-6009	46	48	weakly	weakly	ADJ
ejpam-6009	46	49	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6009	46	50	multifunctions	multifunction	NOUN
ejpam-6009	46	51	,	,	PUNCT
ejpam-6009	46	52	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6009	46	53	multifunctions	multifunction	NOUN
ejpam-6009	46	54	,	,	PUNCT
ejpam-6009	46	55	weakly	weakly	ADJ
ejpam-6009	46	56	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6009	46	57	multifunctions	multifunction	NOUN
ejpam-6009	46	58	,	,	PUNCT
ejpam-6009	46	59	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-6009	46	60	continuous	continuous	ADJ
ejpam-6009	46	61	multifunctions	multifunction	NOUN
ejpam-6009	46	62	,	,	PUNCT
ejpam-6009	46	63	almost	almost	ADV
ejpam-6009	46	64	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-6009	46	65	multifunctions	multifunction	NOUN
ejpam-6009	46	66	,	,	PUNCT
ejpam-6009	46	67	weakly	weakly	ADJ
ejpam-6009	46	68	(	(	PUNCT
ejpam-6009	46	69	λ	λ	NOUN
ejpam-6009	46	70	,	,	PUNCT
ejpam-6009	46	71	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	46	72	c.	c.	PROPN
ejpam-6009	46	73	viriyapong	viriyapong	PROPN
ejpam-6009	46	74	,	,	PUNCT
ejpam-6009	46	75	a.	a.	PROPN
ejpam-6009	46	76	sama	sama	PROPN
ejpam-6009	46	77	-	-	PUNCT
ejpam-6009	46	78	ae	ae	PROPN
ejpam-6009	46	79	,	,	PUNCT
ejpam-6009	46	80	c.	c.	PROPN
ejpam-6009	46	81	boonpok	boonpok	PROPN
ejpam-6009	46	82	/	/	SYM
ejpam-6009	46	83	eur	eur	PROPN
ejpam-6009	46	84	.	.	PUNCT
ejpam-6009	47	1	j.	j.	PROPN
ejpam-6009	47	2	pure	pure	PROPN
ejpam-6009	47	3	appl	appl	PROPN
ejpam-6009	47	4	.	.	PROPN
ejpam-6009	47	5	math	math	PROPN
ejpam-6009	47	6	,	,	PUNCT
ejpam-6009	47	7	18	18	NUM
ejpam-6009	47	8	(	(	PUNCT
ejpam-6009	47	9	2	2	NUM
ejpam-6009	47	10	)	)	PUNCT
ejpam-6009	47	11	(	(	PUNCT
ejpam-6009	47	12	2025	2025	NUM
ejpam-6009	47	13	)	)	PUNCT
ejpam-6009	47	14	,	,	PUNCT
ejpam-6009	47	15	6009	6009	NUM
ejpam-6009	47	16	3	3	NUM
ejpam-6009	47	17	of	of	ADP
ejpam-6009	47	18	18	18	NUM
ejpam-6009	47	19	multifunctions	multifunction	NOUN
ejpam-6009	47	20	,	,	PUNCT
ejpam-6009	47	21	α(λ	α(λ	PROPN
ejpam-6009	47	22	,	,	PUNCT
ejpam-6009	47	23	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	47	24	multifunctions	multifunction	NOUN
ejpam-6009	47	25	,	,	PUNCT
ejpam-6009	47	26	almost	almost	ADV
ejpam-6009	47	27	α(λ	α(λ	PROPN
ejpam-6009	47	28	,	,	PUNCT
ejpam-6009	47	29	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	47	30	multifunctions	multifunction	NOUN
ejpam-6009	47	31	,	,	PUNCT
ejpam-6009	47	32	weakly	weakly	ADJ
ejpam-6009	47	33	α(λ	α(λ	PROPN
ejpam-6009	47	34	,	,	PUNCT
ejpam-6009	47	35	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	47	36	multifunctions	multifunction	NOUN
ejpam-6009	47	37	,	,	PUNCT
ejpam-6009	47	38	almost	almost	ADV
ejpam-6009	47	39	β(λ	β(λ	NOUN
ejpam-6009	47	40	,	,	PUNCT
ejpam-6009	47	41	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	47	42	multifunctions	multifunction	NOUN
ejpam-6009	47	43	,	,	PUNCT
ejpam-6009	47	44	slightly	slightly	ADV
ejpam-6009	47	45	(	(	PUNCT
ejpam-6009	47	46	λ	λ	NOUN
ejpam-6009	47	47	,	,	PUNCT
ejpam-6009	47	48	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	47	49	multifunctions	multifunction	NOUN
ejpam-6009	47	50	,	,	PUNCT
ejpam-6009	47	51	weakly	weakly	ADJ
ejpam-6009	47	52	quasi	quasi	NOUN
ejpam-6009	47	53	(	(	PUNCT
ejpam-6009	47	54	τ1	τ1	PROPN
ejpam-6009	47	55	,	,	PUNCT
ejpam-6009	47	56	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	47	57	multifunctions	multifunction	NOUN
ejpam-6009	47	58	,	,	PUNCT
ejpam-6009	47	59	almost	almost	ADV
ejpam-6009	47	60	quasi	quasi	NOUN
ejpam-6009	47	61	(	(	PUNCT
ejpam-6009	47	62	τ1	τ1	NOUN
ejpam-6009	47	63	,	,	PUNCT
ejpam-6009	47	64	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	47	65	multifunctions	multifunction	NOUN
ejpam-6009	47	66	,	,	PUNCT
ejpam-6009	47	67	c-(τ1	c-(τ1	PROPN
ejpam-6009	47	68	,	,	PUNCT
ejpam-6009	47	69	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	47	70	multifunctions	multifunction	NOUN
ejpam-6009	47	71	,	,	PUNCT
ejpam-6009	47	72	c	c	NOUN
ejpam-6009	47	73	-	-	PUNCT
ejpam-6009	47	74	quasi	quasi	NOUN
ejpam-6009	47	75	(	(	PUNCT
ejpam-6009	47	76	τ1	τ1	PROPN
ejpam-6009	47	77	,	,	PUNCT
ejpam-6009	47	78	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	47	79	multifunctions	multifunction	NOUN
ejpam-6009	47	80	,	,	PUNCT
ejpam-6009	47	81	s-(τ1	s-(τ1	PROPN
ejpam-6009	47	82	,	,	PUNCT
ejpam-6009	47	83	τ2)p	τ2)p	ADJ
ejpam-6009	47	84	-	-	PUNCT
ejpam-6009	47	85	continuous	continuous	ADJ
ejpam-6009	47	86	multifunctions	multifunction	NOUN
ejpam-6009	47	87	,	,	PUNCT
ejpam-6009	47	88	slightly	slightly	ADV
ejpam-6009	47	89	α(τ1	α(τ1	NOUN
ejpam-6009	47	90	,	,	PUNCT
ejpam-6009	47	91	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	47	92	multifunctions	multifunction	NOUN
ejpam-6009	47	93	and	and	CCONJ
ejpam-6009	47	94	slightly	slightly	ADV
ejpam-6009	47	95	(	(	PUNCT
ejpam-6009	47	96	τ1	τ1	NOUN
ejpam-6009	47	97	,	,	PUNCT
ejpam-6009	47	98	τ2)p	τ2)p	ADJ
ejpam-6009	47	99	-	-	PUNCT
ejpam-6009	47	100	continuous	continuous	ADJ
ejpam-6009	47	101	multifunctions	multifunction	NOUN
ejpam-6009	47	102	were	be	AUX
ejpam-6009	47	103	established	establish	VERB
ejpam-6009	47	104	in	in	ADP
ejpam-6009	47	105	[	[	X
ejpam-6009	47	106	39	39	NUM
ejpam-6009	47	107	]	]	PUNCT
ejpam-6009	47	108	,	,	PUNCT
ejpam-6009	47	109	[	[	X
ejpam-6009	47	110	40	40	NUM
ejpam-6009	47	111	]	]	PUNCT
ejpam-6009	47	112	,	,	PUNCT
ejpam-6009	47	113	[	[	X
ejpam-6009	47	114	41	41	NUM
ejpam-6009	47	115	]	]	PUNCT
ejpam-6009	47	116	,	,	PUNCT
ejpam-6009	47	117	[	[	X
ejpam-6009	47	118	42	42	NUM
ejpam-6009	47	119	]	]	PUNCT
ejpam-6009	47	120	,	,	PUNCT
ejpam-6009	47	121	[	[	X
ejpam-6009	47	122	43	43	NUM
ejpam-6009	47	123	]	]	PUNCT
ejpam-6009	47	124	,	,	PUNCT
ejpam-6009	47	125	[	[	X
ejpam-6009	47	126	44	44	NUM
ejpam-6009	47	127	]	]	PUNCT
ejpam-6009	47	128	,	,	PUNCT
ejpam-6009	47	129	[	[	X
ejpam-6009	47	130	45	45	NUM
ejpam-6009	47	131	]	]	PUNCT
ejpam-6009	47	132	,	,	PUNCT
ejpam-6009	47	133	[	[	X
ejpam-6009	47	134	46	46	NUM
ejpam-6009	47	135	]	]	PUNCT
ejpam-6009	47	136	,	,	PUNCT
ejpam-6009	47	137	[	[	X
ejpam-6009	47	138	47	47	NUM
ejpam-6009	47	139	]	]	PUNCT
ejpam-6009	47	140	,	,	PUNCT
ejpam-6009	47	141	[	[	X
ejpam-6009	47	142	48	48	NUM
ejpam-6009	47	143	]	]	PUNCT
ejpam-6009	47	144	,	,	PUNCT
ejpam-6009	47	145	[	[	X
ejpam-6009	47	146	49	49	NUM
ejpam-6009	47	147	]	]	PUNCT
ejpam-6009	47	148	,	,	PUNCT
ejpam-6009	47	149	[	[	X
ejpam-6009	47	150	50	50	NUM
ejpam-6009	47	151	]	]	PUNCT
ejpam-6009	47	152	,	,	PUNCT
ejpam-6009	47	153	[	[	X
ejpam-6009	47	154	51	51	NUM
ejpam-6009	47	155	]	]	PUNCT
ejpam-6009	47	156	,	,	PUNCT
ejpam-6009	47	157	[	[	X
ejpam-6009	47	158	52	52	NUM
ejpam-6009	47	159	]	]	PUNCT
ejpam-6009	47	160	,	,	PUNCT
ejpam-6009	47	161	[	[	X
ejpam-6009	47	162	53	53	NUM
ejpam-6009	47	163	]	]	PUNCT
ejpam-6009	47	164	,	,	PUNCT
ejpam-6009	47	165	[	[	X
ejpam-6009	47	166	54	54	NUM
ejpam-6009	47	167	]	]	PUNCT
ejpam-6009	47	168	,	,	PUNCT
ejpam-6009	47	169	[	[	X
ejpam-6009	47	170	55	55	NUM
ejpam-6009	47	171	]	]	PUNCT
ejpam-6009	47	172	,	,	PUNCT
ejpam-6009	47	173	[	[	X
ejpam-6009	47	174	56	56	NUM
ejpam-6009	47	175	]	]	PUNCT
ejpam-6009	47	176	,	,	PUNCT
ejpam-6009	47	177	[	[	X
ejpam-6009	47	178	57	57	NUM
ejpam-6009	47	179	]	]	PUNCT
ejpam-6009	47	180	,	,	PUNCT
ejpam-6009	47	181	[	[	X
ejpam-6009	47	182	58	58	NUM
ejpam-6009	47	183	]	]	PUNCT
ejpam-6009	47	184	,	,	PUNCT
ejpam-6009	47	185	[	[	X
ejpam-6009	47	186	59	59	NUM
ejpam-6009	47	187	]	]	PUNCT
ejpam-6009	47	188	,	,	PUNCT
ejpam-6009	47	189	[	[	X
ejpam-6009	47	190	60	60	NUM
ejpam-6009	47	191	]	]	PUNCT
ejpam-6009	47	192	,	,	PUNCT
ejpam-6009	47	193	[	[	X
ejpam-6009	47	194	61	61	NUM
ejpam-6009	47	195	]	]	PUNCT
ejpam-6009	47	196	,	,	PUNCT
ejpam-6009	47	197	[	[	X
ejpam-6009	47	198	62	62	NUM
ejpam-6009	47	199	]	]	PUNCT
ejpam-6009	47	200	,	,	PUNCT
ejpam-6009	47	201	[	[	X
ejpam-6009	47	202	63	63	NUM
ejpam-6009	47	203	]	]	PUNCT
ejpam-6009	47	204	and	and	CCONJ
ejpam-6009	47	205	[	[	X
ejpam-6009	47	206	64	64	NUM
ejpam-6009	47	207	]	]	PUNCT
ejpam-6009	47	208	,	,	PUNCT
ejpam-6009	47	209	respectively	respectively	ADV
ejpam-6009	47	210	.	.	PUNCT
ejpam-6009	48	1	on	on	ADP
ejpam-6009	48	2	the	the	DET
ejpam-6009	48	3	other	other	ADJ
ejpam-6009	48	4	hand	hand	NOUN
ejpam-6009	48	5	,	,	PUNCT
ejpam-6009	48	6	the	the	DET
ejpam-6009	48	7	present	present	ADJ
ejpam-6009	48	8	authors	author	NOUN
ejpam-6009	48	9	introduced	introduce	VERB
ejpam-6009	48	10	and	and	CCONJ
ejpam-6009	48	11	investigated	investigate	VERB
ejpam-6009	48	12	the	the	DET
ejpam-6009	48	13	notions	notion	NOUN
ejpam-6009	48	14	of	of	ADP
ejpam-6009	48	15	rarely	rarely	ADV
ejpam-6009	48	16	s-(τ1	s-(τ1	NOUN
ejpam-6009	48	17	,	,	PUNCT
ejpam-6009	48	18	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	48	19	multifunctions	multifunction	NOUN
ejpam-6009	49	1	[	[	X
ejpam-6009	49	2	65	65	NUM
ejpam-6009	49	3	]	]	X
ejpam-6009	49	4	,	,	PUNCT
ejpam-6009	49	5	almost	almost	ADV
ejpam-6009	49	6	nearly	nearly	ADV
ejpam-6009	49	7	(	(	PUNCT
ejpam-6009	49	8	τ1	τ1	NOUN
ejpam-6009	49	9	,	,	PUNCT
ejpam-6009	49	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	49	11	multifunctions	multifunction	NOUN
ejpam-6009	50	1	[	[	X
ejpam-6009	50	2	66	66	NUM
ejpam-6009	50	3	]	]	PUNCT
ejpam-6009	50	4	,	,	PUNCT
ejpam-6009	50	5	s(τ1	s(τ1	PROPN
ejpam-6009	50	6	,	,	PUNCT
ejpam-6009	50	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	50	8	multifunctions	multifunction	NOUN
ejpam-6009	51	1	[	[	X
ejpam-6009	51	2	67	67	NUM
ejpam-6009	51	3	]	]	PUNCT
ejpam-6009	51	4	,	,	PUNCT
ejpam-6009	51	5	quasi	quasi	NOUN
ejpam-6009	51	6	θ(τ1	θ(τ1	NOUN
ejpam-6009	51	7	,	,	PUNCT
ejpam-6009	51	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	51	9	multifunctions	multifunction	NOUN
ejpam-6009	52	1	[	[	X
ejpam-6009	52	2	68	68	NUM
ejpam-6009	52	3	]	]	X
ejpam-6009	52	4	,	,	PUNCT
ejpam-6009	52	5	almost	almost	ADV
ejpam-6009	52	6	nearly	nearly	ADV
ejpam-6009	52	7	quasi	quasi	NOUN
ejpam-6009	52	8	(	(	PUNCT
ejpam-6009	52	9	τ1	τ1	NOUN
ejpam-6009	52	10	,	,	PUNCT
ejpam-6009	52	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	52	12	multifunctions	multifunction	NOUN
ejpam-6009	52	13	[	[	X
ejpam-6009	52	14	69	69	NUM
ejpam-6009	52	15	]	]	PUNCT
ejpam-6009	52	16	,	,	PUNCT
ejpam-6009	52	17	weakly	weakly	ADJ
ejpam-6009	52	18	s-(τ1	s-(τ1	PROPN
ejpam-6009	52	19	,	,	PUNCT
ejpam-6009	52	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	52	21	multifunctions	multifunction	NOUN
ejpam-6009	53	1	[	[	X
ejpam-6009	53	2	70	70	NUM
ejpam-6009	53	3	]	]	PUNCT
ejpam-6009	53	4	,	,	PUNCT
ejpam-6009	53	5	nearly	nearly	ADV
ejpam-6009	53	6	(	(	PUNCT
ejpam-6009	53	7	τ1	τ1	NOUN
ejpam-6009	53	8	,	,	PUNCT
ejpam-6009	53	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	53	10	multifunctions	multifunction	NOUN
ejpam-6009	54	1	[	[	X
ejpam-6009	54	2	71	71	NUM
ejpam-6009	54	3	]	]	PUNCT
ejpam-6009	54	4	and	and	CCONJ
ejpam-6009	54	5	almost	almost	ADV
ejpam-6009	54	6	quasi	quasi	X
ejpam-6009	54	7	(	(	PUNCT
ejpam-6009	54	8	τ1	τ1	NOUN
ejpam-6009	54	9	,	,	PUNCT
ejpam-6009	54	10	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	54	11	multifunctions	multifunction	NOUN
ejpam-6009	55	1	[	[	X
ejpam-6009	55	2	72	72	NUM
ejpam-6009	55	3	]	]	PUNCT
ejpam-6009	55	4	.	.	PUNCT
ejpam-6009	56	1	in	in	ADP
ejpam-6009	56	2	2023	2023	NUM
ejpam-6009	56	3	,	,	PUNCT
ejpam-6009	56	4	the	the	DET
ejpam-6009	56	5	present	present	ADJ
ejpam-6009	56	6	authors	author	NOUN
ejpam-6009	56	7	[	[	X
ejpam-6009	56	8	73	73	NUM
ejpam-6009	56	9	]	]	PUNCT
ejpam-6009	56	10	introduced	introduce	VERB
ejpam-6009	56	11	and	and	CCONJ
ejpam-6009	56	12	investigated	investigate	VERB
ejpam-6009	56	13	the	the	DET
ejpam-6009	56	14	notion	notion	NOUN
ejpam-6009	56	15	of	of	ADP
ejpam-6009	56	16	almost	almost	ADV
ejpam-6009	56	17	contra-(λ	contra-(λ	PROPN
ejpam-6009	56	18	,	,	PUNCT
ejpam-6009	56	19	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	56	20	multifunctions	multifunction	NOUN
ejpam-6009	56	21	.	.	PUNCT
ejpam-6009	57	1	pue	pue	NOUN
ejpam-6009	57	2	-	-	PUNCT
ejpam-6009	57	3	on	on	NOUN
ejpam-6009	57	4	et	et	PROPN
ejpam-6009	57	5	al	al	PROPN
ejpam-6009	57	6	.	.	PUNCT
ejpam-6009	58	1	[	[	X
ejpam-6009	58	2	74	74	NUM
ejpam-6009	58	3	]	]	PUNCT
ejpam-6009	58	4	introduced	introduce	VERB
ejpam-6009	58	5	and	and	CCONJ
ejpam-6009	58	6	studied	study	VERB
ejpam-6009	58	7	the	the	DET
ejpam-6009	58	8	notions	notion	NOUN
ejpam-6009	58	9	of	of	ADP
ejpam-6009	58	10	upper	upper	ADJ
ejpam-6009	58	11	(	(	PUNCT
ejpam-6009	58	12	τ1	τ1	NOUN
ejpam-6009	58	13	,	,	PUNCT
ejpam-6009	58	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	58	15	multifunctions	multifunction	NOUN
ejpam-6009	58	16	and	and	CCONJ
ejpam-6009	58	17	lower	low	ADJ
ejpam-6009	58	18	(	(	PUNCT
ejpam-6009	58	19	τ1	τ1	NOUN
ejpam-6009	58	20	,	,	PUNCT
ejpam-6009	58	21	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	58	22	multifunctions	multifunction	NOUN
ejpam-6009	58	23	.	.	PUNCT
ejpam-6009	59	1	klanarong	klanarong	NOUN
ejpam-6009	59	2	et	et	PROPN
ejpam-6009	59	3	al	al	PROPN
ejpam-6009	59	4	.	.	PUNCT
ejpam-6009	60	1	[	[	X
ejpam-6009	60	2	75	75	NUM
ejpam-6009	60	3	]	]	PUNCT
ejpam-6009	60	4	introduced	introduce	VERB
ejpam-6009	60	5	and	and	CCONJ
ejpam-6009	60	6	investigated	investigate	VERB
ejpam-6009	60	7	the	the	DET
ejpam-6009	60	8	concepts	concept	NOUN
ejpam-6009	60	9	of	of	ADP
ejpam-6009	60	10	upper	upper	ADJ
ejpam-6009	60	11	almost	almost	ADV
ejpam-6009	60	12	(	(	PUNCT
ejpam-6009	60	13	τ1	τ1	NOUN
ejpam-6009	60	14	,	,	PUNCT
ejpam-6009	60	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	60	16	multifunctions	multifunction	NOUN
ejpam-6009	60	17	and	and	CCONJ
ejpam-6009	60	18	lower	low	ADJ
ejpam-6009	60	19	almost	almost	ADV
ejpam-6009	60	20	(	(	PUNCT
ejpam-6009	60	21	τ1	τ1	NOUN
ejpam-6009	60	22	,	,	PUNCT
ejpam-6009	60	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	60	24	multifunctions	multifunction	NOUN
ejpam-6009	60	25	.	.	PUNCT
ejpam-6009	61	1	thongmoon	thongmoon	NOUN
ejpam-6009	61	2	et	et	PROPN
ejpam-6009	61	3	al	al	PROPN
ejpam-6009	61	4	.	.	PUNCT
ejpam-6009	62	1	[	[	X
ejpam-6009	62	2	76	76	NUM
ejpam-6009	62	3	]	]	PUNCT
ejpam-6009	62	4	introduced	introduce	VERB
ejpam-6009	62	5	and	and	CCONJ
ejpam-6009	62	6	studied	study	VERB
ejpam-6009	62	7	the	the	DET
ejpam-6009	62	8	notions	notion	NOUN
ejpam-6009	62	9	of	of	ADP
ejpam-6009	62	10	upper	upper	ADJ
ejpam-6009	62	11	weakly	weakly	ADJ
ejpam-6009	62	12	(	(	PUNCT
ejpam-6009	62	13	τ1	τ1	NOUN
ejpam-6009	62	14	,	,	PUNCT
ejpam-6009	62	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	62	16	multifunctions	multifunction	NOUN
ejpam-6009	62	17	and	and	CCONJ
ejpam-6009	62	18	lower	low	ADJ
ejpam-6009	62	19	weakly	weakly	ADJ
ejpam-6009	62	20	(	(	PUNCT
ejpam-6009	62	21	τ1	τ1	NOUN
ejpam-6009	62	22	,	,	PUNCT
ejpam-6009	62	23	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	62	24	multifunctions	multifunction	NOUN
ejpam-6009	62	25	.	.	PUNCT
ejpam-6009	63	1	in	in	ADP
ejpam-6009	63	2	this	this	DET
ejpam-6009	63	3	paper	paper	NOUN
ejpam-6009	63	4	,	,	PUNCT
ejpam-6009	63	5	we	we	PRON
ejpam-6009	63	6	introduce	introduce	VERB
ejpam-6009	63	7	the	the	DET
ejpam-6009	63	8	concepts	concept	NOUN
ejpam-6009	63	9	of	of	ADP
ejpam-6009	63	10	upper	upper	ADJ
ejpam-6009	63	11	contra(τ1	contra(τ1	NOUN
ejpam-6009	63	12	,	,	PUNCT
ejpam-6009	63	13	τ2)p	τ2)p	ADJ
ejpam-6009	63	14	-	-	PUNCT
ejpam-6009	63	15	continuous	continuous	ADJ
ejpam-6009	63	16	multifunctions	multifunction	NOUN
ejpam-6009	63	17	,	,	PUNCT
ejpam-6009	63	18	lower	low	ADJ
ejpam-6009	63	19	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	63	20	,	,	PUNCT
ejpam-6009	63	21	τ2)p	τ2)p	ADJ
ejpam-6009	63	22	-	-	PUNCT
ejpam-6009	63	23	continuous	continuous	ADJ
ejpam-6009	63	24	multifunctions	multifunction	NOUN
ejpam-6009	63	25	,	,	PUNCT
ejpam-6009	63	26	upper	upper	ADJ
ejpam-6009	63	27	almost	almost	ADV
ejpam-6009	63	28	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	63	29	,	,	PUNCT
ejpam-6009	63	30	τ2)p	τ2)p	ADJ
ejpam-6009	63	31	-	-	ADJ
ejpam-6009	63	32	continuous	continuous	ADJ
ejpam-6009	63	33	multifunctions	multifunction	NOUN
ejpam-6009	63	34	and	and	CCONJ
ejpam-6009	63	35	lower	low	ADJ
ejpam-6009	63	36	almost	almost	ADV
ejpam-6009	63	37	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	63	38	,	,	PUNCT
ejpam-6009	63	39	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	63	40	multifunctions	multifunction	NOUN
ejpam-6009	63	41	.	.	PUNCT
ejpam-6009	64	1	we	we	PRON
ejpam-6009	64	2	also	also	ADV
ejpam-6009	64	3	investigate	investigate	VERB
ejpam-6009	64	4	several	several	ADJ
ejpam-6009	64	5	characterizations	characterization	NOUN
ejpam-6009	64	6	of	of	ADP
ejpam-6009	64	7	upper	upper	ADJ
ejpam-6009	64	8	contra(τ1	contra(τ1	NOUN
ejpam-6009	64	9	,	,	PUNCT
ejpam-6009	64	10	τ2)p	τ2)p	ADJ
ejpam-6009	64	11	-	-	PUNCT
ejpam-6009	64	12	continuous	continuous	ADJ
ejpam-6009	64	13	multifunctions	multifunction	NOUN
ejpam-6009	64	14	,	,	PUNCT
ejpam-6009	64	15	lower	low	ADJ
ejpam-6009	64	16	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	64	17	,	,	PUNCT
ejpam-6009	64	18	τ2)p	τ2)p	ADJ
ejpam-6009	64	19	-	-	PUNCT
ejpam-6009	64	20	continuous	continuous	ADJ
ejpam-6009	64	21	multifunctions	multifunction	NOUN
ejpam-6009	64	22	,	,	PUNCT
ejpam-6009	64	23	upper	upper	ADJ
ejpam-6009	64	24	almost	almost	ADV
ejpam-6009	64	25	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	64	26	,	,	PUNCT
ejpam-6009	64	27	τ2)p	τ2)p	ADJ
ejpam-6009	64	28	-	-	ADJ
ejpam-6009	64	29	continuous	continuous	ADJ
ejpam-6009	64	30	multifunctions	multifunction	NOUN
ejpam-6009	64	31	and	and	CCONJ
ejpam-6009	64	32	lower	low	ADJ
ejpam-6009	64	33	almost	almost	ADV
ejpam-6009	64	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	64	35	,	,	PUNCT
ejpam-6009	64	36	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	64	37	multifunctions	multifunction	NOUN
ejpam-6009	64	38	.	.	PUNCT
ejpam-6009	65	1	2	2	X
ejpam-6009	65	2	.	.	X
ejpam-6009	65	3	preliminaries	preliminary	NOUN
ejpam-6009	65	4	throughout	throughout	ADP
ejpam-6009	65	5	the	the	DET
ejpam-6009	65	6	present	present	ADJ
ejpam-6009	65	7	paper	paper	NOUN
ejpam-6009	65	8	,	,	PUNCT
ejpam-6009	65	9	spaces	space	NOUN
ejpam-6009	65	10	(	(	PUNCT
ejpam-6009	65	11	x	x	NOUN
ejpam-6009	65	12	,	,	PUNCT
ejpam-6009	65	13	τ1	τ1	NOUN
ejpam-6009	65	14	,	,	PUNCT
ejpam-6009	65	15	τ2	τ2	NOUN
ejpam-6009	65	16	)	)	PUNCT
ejpam-6009	65	17	and	and	CCONJ
ejpam-6009	65	18	(	(	PUNCT
ejpam-6009	65	19	y	y	PROPN
ejpam-6009	65	20	,	,	PUNCT
ejpam-6009	65	21	σ1	σ1	PROPN
ejpam-6009	65	22	,	,	PUNCT
ejpam-6009	65	23	σ2	σ2	NOUN
ejpam-6009	65	24	)	)	PUNCT
ejpam-6009	65	25	(	(	PUNCT
ejpam-6009	65	26	or	or	CCONJ
ejpam-6009	65	27	simply	simply	ADV
ejpam-6009	65	28	x	x	X
ejpam-6009	65	29	and	and	CCONJ
ejpam-6009	65	30	y	y	PROPN
ejpam-6009	65	31	)	)	PUNCT
ejpam-6009	65	32	always	always	ADV
ejpam-6009	65	33	mean	mean	VERB
ejpam-6009	65	34	bitopological	bitopological	ADJ
ejpam-6009	65	35	spaces	space	NOUN
ejpam-6009	65	36	on	on	ADP
ejpam-6009	65	37	which	which	PRON
ejpam-6009	65	38	no	no	DET
ejpam-6009	65	39	separation	separation	NOUN
ejpam-6009	65	40	axioms	axiom	NOUN
ejpam-6009	65	41	are	be	AUX
ejpam-6009	65	42	assumed	assume	VERB
ejpam-6009	65	43	unless	unless	SCONJ
ejpam-6009	65	44	explicitly	explicitly	ADV
ejpam-6009	65	45	stated	state	VERB
ejpam-6009	65	46	.	.	PUNCT
ejpam-6009	66	1	let	let	VERB
ejpam-6009	66	2	a	a	DET
ejpam-6009	66	3	be	be	AUX
ejpam-6009	66	4	a	a	DET
ejpam-6009	66	5	subset	subset	NOUN
ejpam-6009	66	6	of	of	ADP
ejpam-6009	66	7	a	a	DET
ejpam-6009	66	8	bitopological	bitopological	ADJ
ejpam-6009	66	9	space	space	NOUN
ejpam-6009	66	10	(	(	PUNCT
ejpam-6009	66	11	x	x	NOUN
ejpam-6009	66	12	,	,	PUNCT
ejpam-6009	66	13	τ1	τ1	NOUN
ejpam-6009	66	14	,	,	PUNCT
ejpam-6009	66	15	τ2	τ2	NOUN
ejpam-6009	66	16	)	)	PUNCT
ejpam-6009	66	17	.	.	PUNCT
ejpam-6009	67	1	the	the	DET
ejpam-6009	67	2	closure	closure	NOUN
ejpam-6009	67	3	of	of	ADP
ejpam-6009	67	4	a	a	PRON
ejpam-6009	67	5	and	and	CCONJ
ejpam-6009	67	6	the	the	DET
ejpam-6009	67	7	interior	interior	NOUN
ejpam-6009	67	8	of	of	ADP
ejpam-6009	67	9	a	a	PRON
ejpam-6009	67	10	with	with	ADP
ejpam-6009	67	11	respect	respect	NOUN
ejpam-6009	67	12	to	to	ADP
ejpam-6009	67	13	τi	τi	PROPN
ejpam-6009	67	14	are	be	AUX
ejpam-6009	67	15	denoted	denote	VERB
ejpam-6009	67	16	by	by	ADP
ejpam-6009	67	17	τi	τi	NOUN
ejpam-6009	67	18	-	-	PUNCT
ejpam-6009	67	19	cl(a	cl(a	NUM
ejpam-6009	67	20	)	)	PUNCT
ejpam-6009	67	21	and	and	CCONJ
ejpam-6009	67	22	τi	τi	NOUN
ejpam-6009	67	23	-	-	PUNCT
ejpam-6009	67	24	int(a	int(a	NOUN
ejpam-6009	67	25	)	)	PUNCT
ejpam-6009	67	26	,	,	PUNCT
ejpam-6009	67	27	respectively	respectively	ADV
ejpam-6009	67	28	,	,	PUNCT
ejpam-6009	67	29	for	for	ADP
ejpam-6009	67	30	i	i	PROPN
ejpam-6009	67	31	=	=	SYM
ejpam-6009	67	32	1	1	NUM
ejpam-6009	67	33	,	,	PUNCT
ejpam-6009	67	34	2	2	NUM
ejpam-6009	67	35	.	.	X
ejpam-6009	67	36	a	a	DET
ejpam-6009	67	37	subset	subset	NOUN
ejpam-6009	67	38	a	a	PRON
ejpam-6009	67	39	of	of	ADP
ejpam-6009	67	40	a	a	DET
ejpam-6009	67	41	bitopological	bitopological	ADJ
ejpam-6009	67	42	space	space	NOUN
ejpam-6009	67	43	(	(	PUNCT
ejpam-6009	67	44	x	x	NOUN
ejpam-6009	67	45	,	,	PUNCT
ejpam-6009	67	46	τ1	τ1	NOUN
ejpam-6009	67	47	,	,	PUNCT
ejpam-6009	67	48	τ2	τ2	NOUN
ejpam-6009	67	49	)	)	PUNCT
ejpam-6009	67	50	is	be	AUX
ejpam-6009	67	51	called	call	VERB
ejpam-6009	67	52	τ1τ2	τ1τ2	VERB
ejpam-6009	67	53	-	-	ADJ
ejpam-6009	67	54	closed	closed	ADJ
ejpam-6009	67	55	[	[	X
ejpam-6009	67	56	77	77	NUM
ejpam-6009	67	57	]	]	X
ejpam-6009	67	58	if	if	SCONJ
ejpam-6009	67	59	a	a	DET
ejpam-6009	67	60	=	=	NOUN
ejpam-6009	67	61	τ1	τ1	NOUN
ejpam-6009	67	62	-	-	PUNCT
ejpam-6009	67	63	cl(τ2	cl(τ2	NOUN
ejpam-6009	67	64	-	-	PUNCT
ejpam-6009	67	65	cl(a	cl(a	NUM
ejpam-6009	67	66	)	)	PUNCT
ejpam-6009	67	67	)	)	PUNCT
ejpam-6009	67	68	.	.	PUNCT
ejpam-6009	68	1	the	the	DET
ejpam-6009	68	2	complement	complement	NOUN
ejpam-6009	68	3	of	of	ADP
ejpam-6009	68	4	a	a	DET
ejpam-6009	68	5	τ1τ2	τ1τ2	ADJ
ejpam-6009	68	6	-	-	ADJ
ejpam-6009	68	7	closed	closed	ADJ
ejpam-6009	68	8	set	set	NOUN
ejpam-6009	68	9	is	be	AUX
ejpam-6009	68	10	called	call	VERB
ejpam-6009	68	11	τ1τ2	τ1τ2	NOUN
ejpam-6009	68	12	-	-	ADJ
ejpam-6009	68	13	open	open	ADJ
ejpam-6009	68	14	.	.	PUNCT
ejpam-6009	69	1	the	the	DET
ejpam-6009	69	2	intersection	intersection	NOUN
ejpam-6009	69	3	of	of	ADP
ejpam-6009	69	4	all	all	DET
ejpam-6009	69	5	τ1τ2	τ1τ2	ADJ
ejpam-6009	69	6	-	-	ADJ
ejpam-6009	69	7	closed	closed	ADJ
ejpam-6009	69	8	sets	set	NOUN
ejpam-6009	69	9	of	of	ADP
ejpam-6009	69	10	x	x	PUNCT
ejpam-6009	69	11	containing	contain	VERB
ejpam-6009	69	12	a	a	PRON
ejpam-6009	69	13	is	be	AUX
ejpam-6009	69	14	called	call	VERB
ejpam-6009	69	15	the	the	DET
ejpam-6009	69	16	τ1τ2	τ1τ2	NOUN
ejpam-6009	69	17	-	-	NOUN
ejpam-6009	69	18	closure	closure	NOUN
ejpam-6009	69	19	[	[	X
ejpam-6009	69	20	77	77	NUM
ejpam-6009	69	21	]	]	PUNCT
ejpam-6009	69	22	of	of	ADP
ejpam-6009	69	23	a	a	PRON
ejpam-6009	69	24	and	and	CCONJ
ejpam-6009	69	25	is	be	AUX
ejpam-6009	69	26	denoted	denote	VERB
ejpam-6009	69	27	by	by	ADP
ejpam-6009	69	28	τ1τ2	τ1τ2	NOUN
ejpam-6009	69	29	-	-	NUM
ejpam-6009	69	30	cl(a	cl(a	NUM
ejpam-6009	69	31	)	)	PUNCT
ejpam-6009	69	32	.	.	PUNCT
ejpam-6009	70	1	the	the	DET
ejpam-6009	70	2	union	union	NOUN
ejpam-6009	70	3	of	of	ADP
ejpam-6009	70	4	all	all	DET
ejpam-6009	70	5	τ1τ2	τ1τ2	ADJ
ejpam-6009	70	6	-	-	ADJ
ejpam-6009	70	7	open	open	ADJ
ejpam-6009	70	8	sets	set	NOUN
ejpam-6009	70	9	of	of	ADP
ejpam-6009	70	10	x	x	PUNCT
ejpam-6009	70	11	contained	contain	VERB
ejpam-6009	70	12	in	in	ADP
ejpam-6009	70	13	a	a	PRON
ejpam-6009	70	14	is	be	AUX
ejpam-6009	70	15	called	call	VERB
ejpam-6009	70	16	the	the	DET
ejpam-6009	70	17	τ1τ2	τ1τ2	NOUN
ejpam-6009	70	18	-	-	ADJ
ejpam-6009	70	19	interior	interior	ADJ
ejpam-6009	70	20	[	[	X
ejpam-6009	70	21	77	77	NUM
ejpam-6009	70	22	]	]	PUNCT
ejpam-6009	70	23	of	of	ADP
ejpam-6009	70	24	a	a	PRON
ejpam-6009	70	25	and	and	CCONJ
ejpam-6009	70	26	is	be	AUX
ejpam-6009	70	27	denoted	denote	VERB
ejpam-6009	70	28	by	by	ADP
ejpam-6009	70	29	τ1τ2	τ1τ2	NOUN
ejpam-6009	70	30	-	-	ADJ
ejpam-6009	70	31	int(a	int(a	NOUN
ejpam-6009	70	32	)	)	PUNCT
ejpam-6009	70	33	.	.	PUNCT
ejpam-6009	71	1	let	let	VERB
ejpam-6009	71	2	a	a	DET
ejpam-6009	71	3	be	be	AUX
ejpam-6009	71	4	a	a	DET
ejpam-6009	71	5	subset	subset	NOUN
ejpam-6009	71	6	of	of	ADP
ejpam-6009	71	7	a	a	DET
ejpam-6009	71	8	bitopological	bitopological	ADJ
ejpam-6009	71	9	space	space	NOUN
ejpam-6009	71	10	(	(	PUNCT
ejpam-6009	71	11	x	x	NOUN
ejpam-6009	71	12	,	,	PUNCT
ejpam-6009	71	13	τ1	τ1	NOUN
ejpam-6009	71	14	,	,	PUNCT
ejpam-6009	71	15	τ2	τ2	NOUN
ejpam-6009	71	16	)	)	PUNCT
ejpam-6009	71	17	.	.	PUNCT
ejpam-6009	72	1	the	the	DET
ejpam-6009	72	2	set	set	NOUN
ejpam-6009	72	3	∩{g	∩{g	INTJ
ejpam-6009	72	4	|	|	ADV
ejpam-6009	72	5	a	a	DET
ejpam-6009	72	6	⊆	⊆	NUM
ejpam-6009	72	7	g	g	NOUN
ejpam-6009	72	8	and	and	CCONJ
ejpam-6009	72	9	g	g	PROPN
ejpam-6009	72	10	is	be	AUX
ejpam-6009	72	11	τ1τ2	τ1τ2	VERB
ejpam-6009	72	12	-	-	ADJ
ejpam-6009	72	13	open	open	ADJ
ejpam-6009	72	14	}	}	PUNCT
ejpam-6009	72	15	is	be	AUX
ejpam-6009	72	16	called	call	VERB
ejpam-6009	72	17	the	the	DET
ejpam-6009	72	18	τ1τ2	τ1τ2	NOUN
ejpam-6009	72	19	-	-	NOUN
ejpam-6009	72	20	kernel	kernel	NOUN
ejpam-6009	73	1	[	[	X
ejpam-6009	73	2	77	77	NUM
ejpam-6009	73	3	]	]	PUNCT
ejpam-6009	73	4	of	of	ADP
ejpam-6009	73	5	a	a	PRON
ejpam-6009	73	6	and	and	CCONJ
ejpam-6009	73	7	is	be	AUX
ejpam-6009	73	8	denoted	denote	VERB
ejpam-6009	73	9	by	by	ADP
ejpam-6009	73	10	τ1τ2	τ1τ2	NOUN
ejpam-6009	73	11	-	-	ADJ
ejpam-6009	73	12	ker(a	ker(a	ADJ
ejpam-6009	73	13	)	)	PUNCT
ejpam-6009	73	14	.	.	PUNCT
ejpam-6009	74	1	lemma	lemma	PROPN
ejpam-6009	74	2	1	1	NUM
ejpam-6009	74	3	.	.	PUNCT
ejpam-6009	75	1	[	[	X
ejpam-6009	75	2	77	77	NUM
ejpam-6009	75	3	]	]	PUNCT
ejpam-6009	75	4	for	for	ADP
ejpam-6009	75	5	subsets	subset	NOUN
ejpam-6009	75	6	a	a	DET
ejpam-6009	75	7	,	,	PUNCT
ejpam-6009	75	8	b	b	NOUN
ejpam-6009	75	9	of	of	ADP
ejpam-6009	75	10	a	a	DET
ejpam-6009	75	11	bitopological	bitopological	ADJ
ejpam-6009	75	12	space	space	NOUN
ejpam-6009	75	13	(	(	PUNCT
ejpam-6009	75	14	x	x	NOUN
ejpam-6009	75	15	,	,	PUNCT
ejpam-6009	75	16	τ1	τ1	NOUN
ejpam-6009	75	17	,	,	PUNCT
ejpam-6009	75	18	τ2	τ2	NOUN
ejpam-6009	75	19	)	)	PUNCT
ejpam-6009	75	20	,	,	PUNCT
ejpam-6009	75	21	the	the	DET
ejpam-6009	75	22	following	follow	VERB
ejpam-6009	75	23	properties	property	NOUN
ejpam-6009	75	24	hold	hold	VERB
ejpam-6009	75	25	:	:	PUNCT
ejpam-6009	75	26	c.	c.	PROPN
ejpam-6009	75	27	viriyapong	viriyapong	PROPN
ejpam-6009	75	28	,	,	PUNCT
ejpam-6009	75	29	a.	a.	PROPN
ejpam-6009	75	30	sama	sama	PROPN
ejpam-6009	75	31	-	-	PUNCT
ejpam-6009	75	32	ae	ae	PROPN
ejpam-6009	75	33	,	,	PUNCT
ejpam-6009	75	34	c.	c.	PROPN
ejpam-6009	75	35	boonpok	boonpok	PROPN
ejpam-6009	75	36	/	/	SYM
ejpam-6009	75	37	eur	eur	PROPN
ejpam-6009	75	38	.	.	PUNCT
ejpam-6009	76	1	j.	j.	PROPN
ejpam-6009	76	2	pure	pure	PROPN
ejpam-6009	76	3	appl	appl	PROPN
ejpam-6009	76	4	.	.	PROPN
ejpam-6009	76	5	math	math	PROPN
ejpam-6009	76	6	,	,	PUNCT
ejpam-6009	76	7	18	18	NUM
ejpam-6009	76	8	(	(	PUNCT
ejpam-6009	76	9	2	2	NUM
ejpam-6009	76	10	)	)	PUNCT
ejpam-6009	76	11	(	(	PUNCT
ejpam-6009	76	12	2025	2025	NUM
ejpam-6009	76	13	)	)	PUNCT
ejpam-6009	76	14	,	,	PUNCT
ejpam-6009	76	15	6009	6009	NUM
ejpam-6009	76	16	4	4	NUM
ejpam-6009	76	17	of	of	ADP
ejpam-6009	76	18	18	18	NUM
ejpam-6009	76	19	(	(	PUNCT
ejpam-6009	76	20	1	1	NUM
ejpam-6009	76	21	)	)	PUNCT
ejpam-6009	76	22	a	a	DET
ejpam-6009	76	23	⊆	⊆	NUM
ejpam-6009	76	24	τ1τ2	τ1τ2	NOUN
ejpam-6009	76	25	-	-	ADJ
ejpam-6009	76	26	ker(a	ker(a	ADJ
ejpam-6009	76	27	)	)	PUNCT
ejpam-6009	76	28	.	.	PUNCT
ejpam-6009	77	1	(	(	PUNCT
ejpam-6009	77	2	2	2	X
ejpam-6009	77	3	)	)	PUNCT
ejpam-6009	77	4	if	if	SCONJ
ejpam-6009	77	5	a	a	DET
ejpam-6009	77	6	⊆	⊆	NUM
ejpam-6009	77	7	b	b	NOUN
ejpam-6009	77	8	,	,	PUNCT
ejpam-6009	77	9	then	then	ADV
ejpam-6009	77	10	τ1τ2	τ1τ2	NOUN
ejpam-6009	77	11	-	-	ADJ
ejpam-6009	77	12	ker(a	ker(a	ADJ
ejpam-6009	77	13	)	)	PUNCT
ejpam-6009	77	14	⊆	⊆	NUM
ejpam-6009	77	15	τ1τ2	τ1τ2	PROPN
ejpam-6009	77	16	-	-	ADJ
ejpam-6009	77	17	ker(b	ker(b	PROPN
ejpam-6009	77	18	)	)	PUNCT
ejpam-6009	77	19	.	.	PUNCT
ejpam-6009	78	1	(	(	PUNCT
ejpam-6009	78	2	3	3	X
ejpam-6009	78	3	)	)	PUNCT
ejpam-6009	78	4	if	if	SCONJ
ejpam-6009	78	5	a	a	PRON
ejpam-6009	78	6	is	be	AUX
ejpam-6009	78	7	τ1τ2	τ1τ2	NOUN
ejpam-6009	78	8	-	-	ADJ
ejpam-6009	78	9	open	open	ADJ
ejpam-6009	78	10	,	,	PUNCT
ejpam-6009	78	11	then	then	ADV
ejpam-6009	78	12	τ1τ2	τ1τ2	NOUN
ejpam-6009	78	13	-	-	ADJ
ejpam-6009	78	14	ker(a	ker(a	ADJ
ejpam-6009	78	15	)	)	PUNCT
ejpam-6009	78	16	=	=	SYM
ejpam-6009	78	17	a.	a.	NOUN
ejpam-6009	78	18	(	(	PUNCT
ejpam-6009	78	19	4	4	NUM
ejpam-6009	78	20	)	)	PUNCT
ejpam-6009	78	21	x	x	SYM
ejpam-6009	78	22	∈	∈	PROPN
ejpam-6009	78	23	τ1τ2	τ1τ2	NOUN
ejpam-6009	78	24	-	-	ADJ
ejpam-6009	78	25	ker(a	ker(a	ADJ
ejpam-6009	78	26	)	)	PUNCT
ejpam-6009	78	27	if	if	SCONJ
ejpam-6009	78	28	and	and	CCONJ
ejpam-6009	78	29	only	only	ADV
ejpam-6009	78	30	if	if	SCONJ
ejpam-6009	78	31	a	a	DET
ejpam-6009	78	32	∩h	∩h	ADJ
ejpam-6009	78	33	̸=	̸=	PROPN
ejpam-6009	78	34	∅	∅	NOUN
ejpam-6009	78	35	for	for	ADP
ejpam-6009	78	36	every	every	DET
ejpam-6009	78	37	τ1τ2	τ1τ2	ADJ
ejpam-6009	78	38	-	-	ADJ
ejpam-6009	78	39	closed	closed	ADJ
ejpam-6009	78	40	set	set	ADJ
ejpam-6009	78	41	h	h	NOUN
ejpam-6009	78	42	containing	contain	VERB
ejpam-6009	78	43	x.	x.	NOUN
ejpam-6009	78	44	lemma	lemma	PROPN
ejpam-6009	78	45	2	2	NUM
ejpam-6009	78	46	.	.	PUNCT
ejpam-6009	79	1	[	[	X
ejpam-6009	79	2	77	77	NUM
ejpam-6009	79	3	]	]	PUNCT
ejpam-6009	79	4	let	let	VERB
ejpam-6009	79	5	a	a	PRON
ejpam-6009	79	6	and	and	CCONJ
ejpam-6009	79	7	b	b	NOUN
ejpam-6009	79	8	be	be	AUX
ejpam-6009	79	9	subsets	subset	NOUN
ejpam-6009	79	10	of	of	ADP
ejpam-6009	79	11	a	a	DET
ejpam-6009	79	12	bitopological	bitopological	ADJ
ejpam-6009	79	13	space	space	NOUN
ejpam-6009	79	14	(	(	PUNCT
ejpam-6009	79	15	x	x	NOUN
ejpam-6009	79	16	,	,	PUNCT
ejpam-6009	79	17	τ1	τ1	NOUN
ejpam-6009	79	18	,	,	PUNCT
ejpam-6009	79	19	τ2	τ2	NOUN
ejpam-6009	79	20	)	)	PUNCT
ejpam-6009	79	21	.	.	PUNCT
ejpam-6009	80	1	for	for	ADP
ejpam-6009	80	2	the	the	DET
ejpam-6009	80	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-6009	80	4	,	,	PUNCT
ejpam-6009	80	5	the	the	DET
ejpam-6009	80	6	following	follow	VERB
ejpam-6009	80	7	properties	property	NOUN
ejpam-6009	80	8	hold	hold	VERB
ejpam-6009	80	9	:	:	PUNCT
ejpam-6009	80	10	(	(	PUNCT
ejpam-6009	80	11	1	1	X
ejpam-6009	80	12	)	)	PUNCT
ejpam-6009	80	13	a	a	DET
ejpam-6009	80	14	⊆	⊆	NUM
ejpam-6009	80	15	τ1τ2	τ1τ2	NOUN
ejpam-6009	80	16	-	-	NUM
ejpam-6009	80	17	cl(a	cl(a	NUM
ejpam-6009	80	18	)	)	PUNCT
ejpam-6009	80	19	and	and	CCONJ
ejpam-6009	80	20	τ1τ2	τ1τ2	NOUN
ejpam-6009	80	21	-	-	ADJ
ejpam-6009	80	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6009	80	23	-	-	PUNCT
ejpam-6009	80	24	cl(a	cl(a	NUM
ejpam-6009	80	25	)	)	PUNCT
ejpam-6009	80	26	)	)	PUNCT
ejpam-6009	81	1	=	=	PUNCT
ejpam-6009	81	2	τ1τ2	τ1τ2	NOUN
ejpam-6009	81	3	-	-	NUM
ejpam-6009	81	4	cl(a	cl(a	NUM
ejpam-6009	81	5	)	)	PUNCT
ejpam-6009	81	6	.	.	PUNCT
ejpam-6009	82	1	(	(	PUNCT
ejpam-6009	82	2	2	2	X
ejpam-6009	82	3	)	)	PUNCT
ejpam-6009	82	4	if	if	SCONJ
ejpam-6009	82	5	a	a	DET
ejpam-6009	82	6	⊆	⊆	NUM
ejpam-6009	82	7	b	b	NOUN
ejpam-6009	82	8	,	,	PUNCT
ejpam-6009	82	9	then	then	ADV
ejpam-6009	82	10	τ1τ2	τ1τ2	NOUN
ejpam-6009	82	11	-	-	NUM
ejpam-6009	82	12	cl(a	cl(a	NUM
ejpam-6009	82	13	)	)	PUNCT
ejpam-6009	82	14	⊆	⊆	NUM
ejpam-6009	82	15	τ1τ2	τ1τ2	NOUN
ejpam-6009	82	16	-	-	NOUN
ejpam-6009	82	17	cl(b	cl(b	NOUN
ejpam-6009	82	18	)	)	PUNCT
ejpam-6009	82	19	.	.	PUNCT
ejpam-6009	83	1	(	(	PUNCT
ejpam-6009	83	2	3	3	X
ejpam-6009	83	3	)	)	PUNCT
ejpam-6009	83	4	τ1τ2	τ1τ2	NOUN
ejpam-6009	83	5	-	-	NUM
ejpam-6009	83	6	cl(a	cl(a	NUM
ejpam-6009	83	7	)	)	PUNCT
ejpam-6009	83	8	is	be	AUX
ejpam-6009	83	9	τ1τ2	τ1τ2	NOUN
ejpam-6009	83	10	-	-	ADJ
ejpam-6009	83	11	closed	closed	ADJ
ejpam-6009	83	12	.	.	PUNCT
ejpam-6009	84	1	(	(	PUNCT
ejpam-6009	84	2	4	4	X
ejpam-6009	84	3	)	)	PUNCT
ejpam-6009	84	4	a	a	PRON
ejpam-6009	84	5	is	be	AUX
ejpam-6009	84	6	τ1τ2	τ1τ2	NOUN
ejpam-6009	84	7	-	-	ADJ
ejpam-6009	84	8	closed	closed	ADJ
ejpam-6009	84	9	if	if	SCONJ
ejpam-6009	84	10	and	and	CCONJ
ejpam-6009	84	11	only	only	ADV
ejpam-6009	84	12	if	if	SCONJ
ejpam-6009	84	13	a	a	DET
ejpam-6009	84	14	=	=	PUNCT
ejpam-6009	84	15	τ1τ2	τ1τ2	NOUN
ejpam-6009	84	16	-	-	NUM
ejpam-6009	84	17	cl(a	cl(a	NUM
ejpam-6009	84	18	)	)	PUNCT
ejpam-6009	84	19	.	.	PUNCT
ejpam-6009	85	1	(	(	PUNCT
ejpam-6009	85	2	5	5	X
ejpam-6009	85	3	)	)	PUNCT
ejpam-6009	85	4	τ1τ2	τ1τ2	NOUN
ejpam-6009	85	5	-	-	NOUN
ejpam-6009	85	6	cl(x	cl(x	X
ejpam-6009	85	7	−a	−a	NOUN
ejpam-6009	85	8	)	)	PUNCT
ejpam-6009	86	1	=	=	PUNCT
ejpam-6009	86	2	x	x	X
ejpam-6009	87	1	−	−	ADP
ejpam-6009	87	2	τ1τ2	τ1τ2	NOUN
ejpam-6009	87	3	-	-	PUNCT
ejpam-6009	87	4	int(a	int(a	NOUN
ejpam-6009	87	5	)	)	PUNCT
ejpam-6009	87	6	.	.	PUNCT
ejpam-6009	88	1	a	a	DET
ejpam-6009	88	2	subset	subset	NOUN
ejpam-6009	88	3	a	a	PRON
ejpam-6009	88	4	of	of	ADP
ejpam-6009	88	5	a	a	DET
ejpam-6009	88	6	bitopological	bitopological	ADJ
ejpam-6009	88	7	space	space	NOUN
ejpam-6009	88	8	(	(	PUNCT
ejpam-6009	88	9	x	x	NOUN
ejpam-6009	88	10	,	,	PUNCT
ejpam-6009	88	11	τ1	τ1	NOUN
ejpam-6009	88	12	,	,	PUNCT
ejpam-6009	88	13	τ2	τ2	NOUN
ejpam-6009	88	14	)	)	PUNCT
ejpam-6009	88	15	is	be	AUX
ejpam-6009	88	16	said	say	VERB
ejpam-6009	88	17	to	to	PART
ejpam-6009	88	18	be	be	AUX
ejpam-6009	88	19	(	(	PUNCT
ejpam-6009	88	20	τ1	τ1	NOUN
ejpam-6009	88	21	,	,	PUNCT
ejpam-6009	88	22	τ2)r	τ2)r	NOUN
ejpam-6009	88	23	-	-	PUNCT
ejpam-6009	88	24	open	open	ADJ
ejpam-6009	89	1	[	[	X
ejpam-6009	89	2	78	78	NUM
ejpam-6009	89	3	]	]	PUNCT
ejpam-6009	89	4	(	(	PUNCT
ejpam-6009	89	5	resp	resp	NOUN
ejpam-6009	89	6	.	.	PUNCT
ejpam-6009	90	1	(	(	PUNCT
ejpam-6009	90	2	τ1	τ1	NOUN
ejpam-6009	90	3	,	,	PUNCT
ejpam-6009	90	4	τ2)s	τ2)s	NOUN
ejpam-6009	90	5	-	-	PUNCT
ejpam-6009	90	6	open	open	ADJ
ejpam-6009	90	7	[	[	X
ejpam-6009	90	8	39	39	NUM
ejpam-6009	90	9	]	]	PUNCT
ejpam-6009	90	10	,	,	PUNCT
ejpam-6009	90	11	(	(	PUNCT
ejpam-6009	90	12	τ1	τ1	NOUN
ejpam-6009	90	13	,	,	PUNCT
ejpam-6009	90	14	τ2)p	τ2)p	NOUN
ejpam-6009	90	15	-	-	ADJ
ejpam-6009	90	16	open	open	ADJ
ejpam-6009	91	1	[	[	X
ejpam-6009	91	2	39	39	NUM
ejpam-6009	91	3	]	]	PUNCT
ejpam-6009	91	4	,	,	PUNCT
ejpam-6009	91	5	(	(	PUNCT
ejpam-6009	91	6	τ1	τ1	NOUN
ejpam-6009	91	7	,	,	PUNCT
ejpam-6009	91	8	τ2)β	τ2)β	ADJ
ejpam-6009	91	9	-	-	PUNCT
ejpam-6009	91	10	open	open	NOUN
ejpam-6009	92	1	[	[	X
ejpam-6009	92	2	39	39	NUM
ejpam-6009	92	3	]	]	PUNCT
ejpam-6009	92	4	)	)	PUNCT
ejpam-6009	92	5	if	if	SCONJ
ejpam-6009	92	6	a	a	DET
ejpam-6009	92	7	=	=	PUNCT
ejpam-6009	92	8	τ1τ2	τ1τ2	NOUN
ejpam-6009	92	9	-	-	NOUN
ejpam-6009	92	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	92	11	-	-	PUNCT
ejpam-6009	92	12	cl(a	cl(a	NUM
ejpam-6009	92	13	)	)	PUNCT
ejpam-6009	92	14	)	)	PUNCT
ejpam-6009	92	15	(	(	PUNCT
ejpam-6009	92	16	resp	resp	NOUN
ejpam-6009	92	17	.	.	PUNCT
ejpam-6009	93	1	a	a	DET
ejpam-6009	93	2	⊆	⊆	NUM
ejpam-6009	93	3	τ1τ2	τ1τ2	NOUN
ejpam-6009	93	4	-	-	ADJ
ejpam-6009	93	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6009	93	6	-	-	PUNCT
ejpam-6009	93	7	int(a	int(a	NOUN
ejpam-6009	93	8	)	)	PUNCT
ejpam-6009	93	9	)	)	PUNCT
ejpam-6009	93	10	,	,	PUNCT
ejpam-6009	93	11	a	a	DET
ejpam-6009	93	12	⊆	⊆	NUM
ejpam-6009	93	13	τ1τ2	τ1τ2	NOUN
ejpam-6009	93	14	-	-	NOUN
ejpam-6009	93	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	93	16	-	-	PUNCT
ejpam-6009	93	17	cl(a	cl(a	NUM
ejpam-6009	93	18	)	)	PUNCT
ejpam-6009	93	19	)	)	PUNCT
ejpam-6009	93	20	,	,	PUNCT
ejpam-6009	93	21	a	a	DET
ejpam-6009	93	22	⊆	⊆	NUM
ejpam-6009	93	23	τ1τ2	τ1τ2	NOUN
ejpam-6009	93	24	-	-	PUNCT
ejpam-6009	93	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6009	93	26	-	-	PUNCT
ejpam-6009	93	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	93	28	-	-	PUNCT
ejpam-6009	93	29	cl(a	cl(a	NUM
ejpam-6009	93	30	)	)	PUNCT
ejpam-6009	93	31	)	)	PUNCT
ejpam-6009	93	32	)	)	PUNCT
ejpam-6009	93	33	)	)	PUNCT
ejpam-6009	93	34	.	.	PUNCT
ejpam-6009	94	1	the	the	DET
ejpam-6009	94	2	complement	complement	NOUN
ejpam-6009	94	3	of	of	ADP
ejpam-6009	94	4	a	a	DET
ejpam-6009	94	5	(	(	PUNCT
ejpam-6009	94	6	τ1	τ1	NOUN
ejpam-6009	94	7	,	,	PUNCT
ejpam-6009	94	8	τ2)r	τ2)r	NOUN
ejpam-6009	94	9	-	-	PUNCT
ejpam-6009	94	10	open	open	ADJ
ejpam-6009	94	11	(	(	PUNCT
ejpam-6009	94	12	resp	resp	NOUN
ejpam-6009	94	13	.	.	PUNCT
ejpam-6009	95	1	(	(	PUNCT
ejpam-6009	95	2	τ1	τ1	NOUN
ejpam-6009	95	3	,	,	PUNCT
ejpam-6009	95	4	τ2)s	τ2)s	NOUN
ejpam-6009	95	5	-	-	PUNCT
ejpam-6009	95	6	open	open	ADJ
ejpam-6009	95	7	,	,	PUNCT
ejpam-6009	95	8	(	(	PUNCT
ejpam-6009	95	9	τ1	τ1	NOUN
ejpam-6009	95	10	,	,	PUNCT
ejpam-6009	95	11	τ2)p	τ2)p	NOUN
ejpam-6009	95	12	-	-	ADJ
ejpam-6009	95	13	open	open	ADJ
ejpam-6009	95	14	,	,	PUNCT
ejpam-6009	95	15	(	(	PUNCT
ejpam-6009	95	16	τ1	τ1	NOUN
ejpam-6009	95	17	,	,	PUNCT
ejpam-6009	95	18	τ2)β	τ2)β	ADJ
ejpam-6009	95	19	-	-	PUNCT
ejpam-6009	95	20	open	open	ADJ
ejpam-6009	95	21	)	)	PUNCT
ejpam-6009	95	22	set	set	NOUN
ejpam-6009	95	23	is	be	AUX
ejpam-6009	95	24	said	say	VERB
ejpam-6009	95	25	to	to	PART
ejpam-6009	95	26	be	be	AUX
ejpam-6009	95	27	(	(	PUNCT
ejpam-6009	95	28	τ1	τ1	NOUN
ejpam-6009	95	29	,	,	PUNCT
ejpam-6009	95	30	τ2)r	τ2)r	NOUN
ejpam-6009	95	31	-	-	PUNCT
ejpam-6009	95	32	closed	closed	ADJ
ejpam-6009	95	33	(	(	PUNCT
ejpam-6009	95	34	resp	resp	NOUN
ejpam-6009	95	35	.	.	PUNCT
ejpam-6009	96	1	(	(	PUNCT
ejpam-6009	96	2	τ1	τ1	NOUN
ejpam-6009	96	3	,	,	PUNCT
ejpam-6009	96	4	τ2)s	τ2)s	NOUN
ejpam-6009	96	5	-	-	PUNCT
ejpam-6009	96	6	closed	closed	ADJ
ejpam-6009	96	7	,	,	PUNCT
ejpam-6009	96	8	(	(	PUNCT
ejpam-6009	96	9	τ1	τ1	NOUN
ejpam-6009	96	10	,	,	PUNCT
ejpam-6009	96	11	τ2)p	τ2)p	NOUN
ejpam-6009	96	12	-	-	PUNCT
ejpam-6009	96	13	closed	closed	ADJ
ejpam-6009	96	14	,	,	PUNCT
ejpam-6009	96	15	(	(	PUNCT
ejpam-6009	96	16	τ1	τ1	NOUN
ejpam-6009	96	17	,	,	PUNCT
ejpam-6009	96	18	τ2)β	τ2)β	ADJ
ejpam-6009	96	19	-	-	PUNCT
ejpam-6009	96	20	closed	closed	ADJ
ejpam-6009	96	21	)	)	PUNCT
ejpam-6009	96	22	.	.	PUNCT
ejpam-6009	97	1	a	a	DET
ejpam-6009	97	2	subset	subset	NOUN
ejpam-6009	97	3	a	a	PRON
ejpam-6009	97	4	of	of	ADP
ejpam-6009	97	5	a	a	DET
ejpam-6009	97	6	bitopological	bitopological	ADJ
ejpam-6009	97	7	space	space	NOUN
ejpam-6009	97	8	(	(	PUNCT
ejpam-6009	97	9	x	x	NOUN
ejpam-6009	97	10	,	,	PUNCT
ejpam-6009	97	11	τ1	τ1	NOUN
ejpam-6009	97	12	,	,	PUNCT
ejpam-6009	97	13	τ2	τ2	NOUN
ejpam-6009	97	14	)	)	PUNCT
ejpam-6009	97	15	is	be	AUX
ejpam-6009	97	16	said	say	VERB
ejpam-6009	97	17	to	to	PART
ejpam-6009	97	18	be	be	AUX
ejpam-6009	97	19	α(τ1	α(τ1	NOUN
ejpam-6009	97	20	,	,	PUNCT
ejpam-6009	97	21	τ2)-open	τ2)-open	ADJ
ejpam-6009	97	22	[	[	X
ejpam-6009	97	23	79	79	NUM
ejpam-6009	97	24	]	]	X
ejpam-6009	97	25	if	if	SCONJ
ejpam-6009	97	26	a	a	DET
ejpam-6009	97	27	⊆	⊆	NUM
ejpam-6009	97	28	τ1τ2	τ1τ2	NOUN
ejpam-6009	97	29	-	-	PUNCT
ejpam-6009	97	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	97	31	-	-	PUNCT
ejpam-6009	97	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6009	97	33	-	-	PUNCT
ejpam-6009	97	34	int(a	int(a	NOUN
ejpam-6009	97	35	)	)	PUNCT
ejpam-6009	97	36	)	)	PUNCT
ejpam-6009	97	37	)	)	PUNCT
ejpam-6009	97	38	.	.	PUNCT
ejpam-6009	98	1	the	the	DET
ejpam-6009	98	2	complement	complement	NOUN
ejpam-6009	98	3	of	of	ADP
ejpam-6009	98	4	an	an	DET
ejpam-6009	98	5	α(τ1	α(τ1	NOUN
ejpam-6009	98	6	,	,	PUNCT
ejpam-6009	98	7	τ2)-open	τ2)-open	ADJ
ejpam-6009	98	8	set	set	NOUN
ejpam-6009	98	9	is	be	AUX
ejpam-6009	98	10	called	call	VERB
ejpam-6009	98	11	α(τ1	α(τ1	NOUN
ejpam-6009	98	12	,	,	PUNCT
ejpam-6009	98	13	τ2)closed	τ2)close	VERB
ejpam-6009	98	14	.	.	PUNCT
ejpam-6009	99	1	a	a	DET
ejpam-6009	99	2	subset	subset	NOUN
ejpam-6009	99	3	a	a	PRON
ejpam-6009	99	4	of	of	ADP
ejpam-6009	99	5	a	a	DET
ejpam-6009	99	6	bitopological	bitopological	ADJ
ejpam-6009	99	7	space	space	NOUN
ejpam-6009	99	8	(	(	PUNCT
ejpam-6009	99	9	x	x	NOUN
ejpam-6009	99	10	,	,	PUNCT
ejpam-6009	99	11	τ1	τ1	NOUN
ejpam-6009	99	12	,	,	PUNCT
ejpam-6009	99	13	τ2	τ2	NOUN
ejpam-6009	99	14	)	)	PUNCT
ejpam-6009	99	15	is	be	AUX
ejpam-6009	99	16	said	say	VERB
ejpam-6009	99	17	to	to	PART
ejpam-6009	99	18	be	be	AUX
ejpam-6009	99	19	τ1τ2	τ1τ2	NOUN
ejpam-6009	99	20	-	-	ADJ
ejpam-6009	99	21	δ	δ	NOUN
ejpam-6009	99	22	-	-	NOUN
ejpam-6009	99	23	open	open	ADJ
ejpam-6009	99	24	[	[	X
ejpam-6009	99	25	17	17	NUM
ejpam-6009	99	26	]	]	X
ejpam-6009	99	27	if	if	SCONJ
ejpam-6009	99	28	a	a	PRON
ejpam-6009	99	29	is	be	AUX
ejpam-6009	99	30	the	the	DET
ejpam-6009	99	31	union	union	NOUN
ejpam-6009	99	32	of	of	ADP
ejpam-6009	99	33	(	(	PUNCT
ejpam-6009	99	34	τ1	τ1	NOUN
ejpam-6009	99	35	,	,	PUNCT
ejpam-6009	99	36	τ2)r	τ2)r	ADJ
ejpam-6009	99	37	-	-	PUNCT
ejpam-6009	99	38	open	open	ADJ
ejpam-6009	99	39	sets	set	NOUN
ejpam-6009	99	40	of	of	ADP
ejpam-6009	99	41	x.	x.	NOUN
ejpam-6009	99	42	the	the	DET
ejpam-6009	99	43	complement	complement	NOUN
ejpam-6009	99	44	of	of	ADP
ejpam-6009	99	45	a	a	DET
ejpam-6009	99	46	τ1τ2	τ1τ2	ADJ
ejpam-6009	99	47	-	-	ADJ
ejpam-6009	99	48	δ	δ	NOUN
ejpam-6009	99	49	-	-	ADJ
ejpam-6009	99	50	open	open	ADJ
ejpam-6009	99	51	set	set	NOUN
ejpam-6009	99	52	is	be	AUX
ejpam-6009	99	53	called	call	VERB
ejpam-6009	99	54	τ1τ2	τ1τ2	NOUN
ejpam-6009	99	55	-	-	ADJ
ejpam-6009	99	56	δ	δ	NOUN
ejpam-6009	99	57	-	-	PUNCT
ejpam-6009	99	58	closed	closed	ADJ
ejpam-6009	99	59	[	[	X
ejpam-6009	99	60	17	17	NUM
ejpam-6009	99	61	]	]	PUNCT
ejpam-6009	99	62	.	.	PUNCT
ejpam-6009	100	1	let	let	VERB
ejpam-6009	100	2	a	a	DET
ejpam-6009	100	3	be	be	AUX
ejpam-6009	100	4	a	a	DET
ejpam-6009	100	5	subset	subset	NOUN
ejpam-6009	100	6	of	of	ADP
ejpam-6009	100	7	a	a	DET
ejpam-6009	100	8	bitopological	bitopological	ADJ
ejpam-6009	100	9	space	space	NOUN
ejpam-6009	100	10	(	(	PUNCT
ejpam-6009	100	11	x	x	NOUN
ejpam-6009	100	12	,	,	PUNCT
ejpam-6009	100	13	τ1	τ1	NOUN
ejpam-6009	100	14	,	,	PUNCT
ejpam-6009	100	15	τ2	τ2	NOUN
ejpam-6009	100	16	)	)	PUNCT
ejpam-6009	100	17	.	.	PUNCT
ejpam-6009	101	1	the	the	DET
ejpam-6009	101	2	union	union	NOUN
ejpam-6009	101	3	of	of	ADP
ejpam-6009	101	4	all	all	DET
ejpam-6009	101	5	τ1τ2	τ1τ2	NOUN
ejpam-6009	101	6	-	-	ADJ
ejpam-6009	101	7	δ	δ	NOUN
ejpam-6009	101	8	-	-	ADJ
ejpam-6009	101	9	open	open	ADJ
ejpam-6009	101	10	sets	set	NOUN
ejpam-6009	101	11	of	of	ADP
ejpam-6009	101	12	x	x	PUNCT
ejpam-6009	101	13	contained	contain	VERB
ejpam-6009	101	14	in	in	ADP
ejpam-6009	101	15	a	a	PRON
ejpam-6009	101	16	is	be	AUX
ejpam-6009	101	17	called	call	VERB
ejpam-6009	101	18	the	the	DET
ejpam-6009	101	19	τ1τ2	τ1τ2	ADJ
ejpam-6009	101	20	-	-	ADJ
ejpam-6009	101	21	δ	δ	NOUN
ejpam-6009	101	22	-	-	NOUN
ejpam-6009	101	23	interior	interior	NOUN
ejpam-6009	101	24	[	[	X
ejpam-6009	101	25	17	17	NUM
ejpam-6009	101	26	]	]	PUNCT
ejpam-6009	101	27	of	of	ADP
ejpam-6009	101	28	a	a	PRON
ejpam-6009	101	29	and	and	CCONJ
ejpam-6009	101	30	is	be	AUX
ejpam-6009	101	31	denoted	denote	VERB
ejpam-6009	101	32	by	by	ADP
ejpam-6009	101	33	τ1τ2	τ1τ2	ADJ
ejpam-6009	101	34	-	-	ADJ
ejpam-6009	101	35	δ	δ	NOUN
ejpam-6009	101	36	-	-	PUNCT
ejpam-6009	101	37	int(a	int(a	PROPN
ejpam-6009	101	38	)	)	PUNCT
ejpam-6009	101	39	.	.	PUNCT
ejpam-6009	102	1	the	the	DET
ejpam-6009	102	2	intersection	intersection	NOUN
ejpam-6009	102	3	of	of	ADP
ejpam-6009	102	4	all	all	DET
ejpam-6009	102	5	τ1τ2	τ1τ2	NOUN
ejpam-6009	102	6	-	-	ADJ
ejpam-6009	102	7	δ	δ	NOUN
ejpam-6009	102	8	-	-	PUNCT
ejpam-6009	102	9	closed	close	VERB
ejpam-6009	102	10	sets	set	NOUN
ejpam-6009	102	11	of	of	ADP
ejpam-6009	102	12	x	x	PUNCT
ejpam-6009	102	13	containing	contain	VERB
ejpam-6009	102	14	a	a	PRON
ejpam-6009	102	15	is	be	AUX
ejpam-6009	102	16	called	call	VERB
ejpam-6009	102	17	the	the	DET
ejpam-6009	102	18	τ1τ2	τ1τ2	ADJ
ejpam-6009	102	19	-	-	ADJ
ejpam-6009	102	20	δ	δ	NOUN
ejpam-6009	102	21	-	-	NOUN
ejpam-6009	102	22	closure	closure	NOUN
ejpam-6009	102	23	[	[	X
ejpam-6009	102	24	17	17	NUM
ejpam-6009	102	25	]	]	PUNCT
ejpam-6009	102	26	of	of	ADP
ejpam-6009	102	27	a	a	PRON
ejpam-6009	102	28	and	and	CCONJ
ejpam-6009	102	29	is	be	AUX
ejpam-6009	102	30	denoted	denote	VERB
ejpam-6009	102	31	by	by	ADP
ejpam-6009	102	32	τ1τ2	τ1τ2	ADJ
ejpam-6009	102	33	-	-	ADJ
ejpam-6009	102	34	δ	δ	NOUN
ejpam-6009	102	35	-	-	PUNCT
ejpam-6009	102	36	cl(a	cl(a	NUM
ejpam-6009	102	37	)	)	PUNCT
ejpam-6009	102	38	.	.	PUNCT
ejpam-6009	103	1	the	the	DET
ejpam-6009	103	2	intersection	intersection	NOUN
ejpam-6009	103	3	of	of	ADP
ejpam-6009	103	4	all	all	DET
ejpam-6009	103	5	(	(	PUNCT
ejpam-6009	103	6	τ1	τ1	NOUN
ejpam-6009	103	7	,	,	PUNCT
ejpam-6009	103	8	τ2)p	τ2)p	NOUN
ejpam-6009	103	9	-	-	PUNCT
ejpam-6009	103	10	closed	closed	ADJ
ejpam-6009	103	11	(	(	PUNCT
ejpam-6009	103	12	resp	resp	NOUN
ejpam-6009	103	13	.	.	PUNCT
ejpam-6009	104	1	(	(	PUNCT
ejpam-6009	104	2	τ1	τ1	NOUN
ejpam-6009	104	3	,	,	PUNCT
ejpam-6009	104	4	τ2)s	τ2)s	NOUN
ejpam-6009	104	5	-	-	PUNCT
ejpam-6009	104	6	closed	closed	ADJ
ejpam-6009	104	7	,	,	PUNCT
ejpam-6009	104	8	α(τ1	α(τ1	NOUN
ejpam-6009	104	9	,	,	PUNCT
ejpam-6009	104	10	τ2)-closed	τ2)-closed	ADJ
ejpam-6009	104	11	)	)	PUNCT
ejpam-6009	104	12	sets	set	NOUN
ejpam-6009	104	13	of	of	ADP
ejpam-6009	104	14	x	x	PUNCT
ejpam-6009	104	15	containing	contain	VERB
ejpam-6009	104	16	a	a	PRON
ejpam-6009	104	17	is	be	AUX
ejpam-6009	104	18	called	call	VERB
ejpam-6009	104	19	the	the	DET
ejpam-6009	104	20	(	(	PUNCT
ejpam-6009	104	21	τ1	τ1	NOUN
ejpam-6009	104	22	,	,	PUNCT
ejpam-6009	104	23	τ2)p	τ2)p	NOUN
ejpam-6009	104	24	-	-	NOUN
ejpam-6009	104	25	closure	closure	NOUN
ejpam-6009	104	26	[	[	X
ejpam-6009	104	27	62	62	NUM
ejpam-6009	104	28	]	]	PUNCT
ejpam-6009	104	29	(	(	PUNCT
ejpam-6009	104	30	resp	resp	NOUN
ejpam-6009	104	31	.	.	PUNCT
ejpam-6009	105	1	(	(	PUNCT
ejpam-6009	105	2	τ1	τ1	NOUN
ejpam-6009	105	3	,	,	PUNCT
ejpam-6009	105	4	τ2)s	τ2)s	NOUN
ejpam-6009	105	5	-	-	PUNCT
ejpam-6009	105	6	closure	closure	NOUN
ejpam-6009	105	7	[	[	X
ejpam-6009	105	8	39	39	NUM
ejpam-6009	105	9	]	]	PUNCT
ejpam-6009	105	10	,	,	PUNCT
ejpam-6009	105	11	α(τ1	α(τ1	NOUN
ejpam-6009	105	12	,	,	PUNCT
ejpam-6009	105	13	τ2)-closure	τ2)-closure	NOUN
ejpam-6009	105	14	[	[	X
ejpam-6009	105	15	63	63	NUM
ejpam-6009	105	16	]	]	PUNCT
ejpam-6009	105	17	)	)	PUNCT
ejpam-6009	105	18	of	of	ADP
ejpam-6009	105	19	a	a	PRON
ejpam-6009	105	20	and	and	CCONJ
ejpam-6009	105	21	is	be	AUX
ejpam-6009	105	22	denoted	denote	VERB
ejpam-6009	105	23	by	by	ADP
ejpam-6009	105	24	(	(	PUNCT
ejpam-6009	105	25	τ1	τ1	NOUN
ejpam-6009	105	26	,	,	PUNCT
ejpam-6009	105	27	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6009	105	28	)	)	PUNCT
ejpam-6009	105	29	(	(	PUNCT
ejpam-6009	105	30	resp	resp	NOUN
ejpam-6009	105	31	.	.	PUNCT
ejpam-6009	106	1	(	(	PUNCT
ejpam-6009	106	2	τ1	τ1	NOUN
ejpam-6009	106	3	,	,	PUNCT
ejpam-6009	106	4	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6009	106	5	)	)	PUNCT
ejpam-6009	106	6	,	,	PUNCT
ejpam-6009	106	7	α(τ1	α(τ1	NOUN
ejpam-6009	106	8	,	,	PUNCT
ejpam-6009	106	9	τ2)-cl(a	τ2)-cl(a	NUM
ejpam-6009	106	10	)	)	PUNCT
ejpam-6009	106	11	)	)	PUNCT
ejpam-6009	106	12	.	.	PUNCT
ejpam-6009	107	1	the	the	DET
ejpam-6009	107	2	union	union	NOUN
ejpam-6009	107	3	of	of	ADP
ejpam-6009	107	4	all	all	DET
ejpam-6009	107	5	(	(	PUNCT
ejpam-6009	107	6	τ1	τ1	NOUN
ejpam-6009	107	7	,	,	PUNCT
ejpam-6009	107	8	τ2)p	τ2)p	NOUN
ejpam-6009	107	9	-	-	ADJ
ejpam-6009	107	10	open	open	ADJ
ejpam-6009	107	11	(	(	PUNCT
ejpam-6009	107	12	resp	resp	NOUN
ejpam-6009	107	13	.	.	PUNCT
ejpam-6009	108	1	(	(	PUNCT
ejpam-6009	108	2	τ1	τ1	NOUN
ejpam-6009	108	3	,	,	PUNCT
ejpam-6009	108	4	τ2)s	τ2)s	NOUN
ejpam-6009	108	5	-	-	PUNCT
ejpam-6009	108	6	open	open	ADJ
ejpam-6009	108	7	,	,	PUNCT
ejpam-6009	108	8	α(τ1	α(τ1	NOUN
ejpam-6009	108	9	,	,	PUNCT
ejpam-6009	108	10	τ2)-open	τ2)-open	ADJ
ejpam-6009	108	11	)	)	PUNCT
ejpam-6009	108	12	sets	set	NOUN
ejpam-6009	108	13	of	of	ADP
ejpam-6009	108	14	x	x	PUNCT
ejpam-6009	108	15	contained	contain	VERB
ejpam-6009	108	16	in	in	ADP
ejpam-6009	108	17	a	a	PRON
ejpam-6009	108	18	is	be	AUX
ejpam-6009	108	19	called	call	VERB
ejpam-6009	108	20	the	the	DET
ejpam-6009	108	21	(	(	PUNCT
ejpam-6009	108	22	τ1	τ1	NOUN
ejpam-6009	108	23	,	,	PUNCT
ejpam-6009	108	24	τ2)p	τ2)p	ADJ
ejpam-6009	108	25	-	-	NOUN
ejpam-6009	108	26	interior	interior	ADJ
ejpam-6009	108	27	[	[	X
ejpam-6009	108	28	62	62	NUM
ejpam-6009	108	29	]	]	PUNCT
ejpam-6009	108	30	(	(	PUNCT
ejpam-6009	108	31	resp	resp	NOUN
ejpam-6009	108	32	.	.	PUNCT
ejpam-6009	109	1	(	(	PUNCT
ejpam-6009	109	2	τ1	τ1	NOUN
ejpam-6009	109	3	,	,	PUNCT
ejpam-6009	109	4	τ2)s	τ2)s	NOUN
ejpam-6009	109	5	-	-	NOUN
ejpam-6009	109	6	interior	interior	NOUN
ejpam-6009	109	7	[	[	X
ejpam-6009	109	8	39	39	NUM
ejpam-6009	109	9	]	]	PUNCT
ejpam-6009	109	10	,	,	PUNCT
ejpam-6009	109	11	α(τ1	α(τ1	NOUN
ejpam-6009	109	12	,	,	PUNCT
ejpam-6009	109	13	τ2)-interior	τ2)-interior	PROPN
ejpam-6009	109	14	[	[	X
ejpam-6009	109	15	63	63	NUM
ejpam-6009	109	16	]	]	PUNCT
ejpam-6009	109	17	)	)	PUNCT
ejpam-6009	109	18	of	of	ADP
ejpam-6009	109	19	a	a	PRON
ejpam-6009	109	20	and	and	CCONJ
ejpam-6009	109	21	is	be	AUX
ejpam-6009	109	22	denoted	denote	VERB
ejpam-6009	109	23	by	by	ADP
ejpam-6009	109	24	(	(	PUNCT
ejpam-6009	109	25	τ1	τ1	NOUN
ejpam-6009	109	26	,	,	PUNCT
ejpam-6009	109	27	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6009	109	28	)	)	PUNCT
ejpam-6009	109	29	(	(	PUNCT
ejpam-6009	109	30	resp	resp	NOUN
ejpam-6009	109	31	.	.	PUNCT
ejpam-6009	110	1	(	(	PUNCT
ejpam-6009	110	2	τ1	τ1	NOUN
ejpam-6009	110	3	,	,	PUNCT
ejpam-6009	110	4	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6009	110	5	)	)	PUNCT
ejpam-6009	110	6	,	,	PUNCT
ejpam-6009	110	7	α(τ1	α(τ1	NOUN
ejpam-6009	110	8	,	,	PUNCT
ejpam-6009	110	9	τ2)-int(a	τ2)-int(a	NOUN
ejpam-6009	110	10	)	)	PUNCT
ejpam-6009	110	11	)	)	PUNCT
ejpam-6009	110	12	.	.	PUNCT
ejpam-6009	111	1	lemma	lemma	PROPN
ejpam-6009	111	2	3	3	X
ejpam-6009	111	3	.	.	X
ejpam-6009	112	1	for	for	ADP
ejpam-6009	112	2	a	a	DET
ejpam-6009	112	3	subset	subset	NOUN
ejpam-6009	112	4	a	a	PRON
ejpam-6009	112	5	of	of	ADP
ejpam-6009	112	6	a	a	DET
ejpam-6009	112	7	bitopological	bitopological	ADJ
ejpam-6009	112	8	space	space	NOUN
ejpam-6009	112	9	(	(	PUNCT
ejpam-6009	112	10	x	x	NOUN
ejpam-6009	112	11	,	,	PUNCT
ejpam-6009	112	12	τ1	τ1	NOUN
ejpam-6009	112	13	,	,	PUNCT
ejpam-6009	112	14	τ2	τ2	NOUN
ejpam-6009	112	15	)	)	PUNCT
ejpam-6009	112	16	,	,	PUNCT
ejpam-6009	112	17	the	the	DET
ejpam-6009	112	18	following	follow	VERB
ejpam-6009	112	19	properties	property	NOUN
ejpam-6009	112	20	hold	hold	VERB
ejpam-6009	112	21	:	:	PUNCT
ejpam-6009	112	22	(	(	PUNCT
ejpam-6009	112	23	1	1	X
ejpam-6009	112	24	)	)	PUNCT
ejpam-6009	112	25	(	(	PUNCT
ejpam-6009	112	26	τ1	τ1	NOUN
ejpam-6009	112	27	,	,	PUNCT
ejpam-6009	112	28	τ2)-pcl(a	τ2)-pcl(a	ADJ
ejpam-6009	112	29	)	)	PUNCT
ejpam-6009	112	30	=	=	PUNCT
ejpam-6009	113	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	113	2	-	-	ADJ
ejpam-6009	113	3	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6009	113	4	-	-	PUNCT
ejpam-6009	113	5	int(a	int(a	NOUN
ejpam-6009	113	6	)	)	PUNCT
ejpam-6009	113	7	)	)	PUNCT
ejpam-6009	113	8	∪a	∪a	X
ejpam-6009	114	1	[	[	X
ejpam-6009	114	2	62	62	NUM
ejpam-6009	114	3	]	]	PUNCT
ejpam-6009	114	4	;	;	PUNCT
ejpam-6009	114	5	(	(	PUNCT
ejpam-6009	114	6	2	2	X
ejpam-6009	114	7	)	)	PUNCT
ejpam-6009	114	8	(	(	PUNCT
ejpam-6009	114	9	τ1	τ1	NOUN
ejpam-6009	114	10	,	,	PUNCT
ejpam-6009	114	11	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6009	114	12	)	)	PUNCT
ejpam-6009	114	13	=	=	PUNCT
ejpam-6009	115	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	115	2	-	-	NOUN
ejpam-6009	115	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	115	4	-	-	PUNCT
ejpam-6009	115	5	cl(a	cl(a	NUM
ejpam-6009	115	6	)	)	PUNCT
ejpam-6009	115	7	)	)	PUNCT
ejpam-6009	116	1	∩a	∩a	PROPN
ejpam-6009	117	1	[	[	X
ejpam-6009	117	2	26	26	NUM
ejpam-6009	117	3	]	]	X
ejpam-6009	117	4	;	;	PUNCT
ejpam-6009	117	5	c.	c.	PROPN
ejpam-6009	117	6	viriyapong	viriyapong	PROPN
ejpam-6009	117	7	,	,	PUNCT
ejpam-6009	117	8	a.	a.	PROPN
ejpam-6009	117	9	sama	sama	PROPN
ejpam-6009	117	10	-	-	PUNCT
ejpam-6009	117	11	ae	ae	PROPN
ejpam-6009	117	12	,	,	PUNCT
ejpam-6009	117	13	c.	c.	PROPN
ejpam-6009	117	14	boonpok	boonpok	PROPN
ejpam-6009	117	15	/	/	SYM
ejpam-6009	117	16	eur	eur	PROPN
ejpam-6009	117	17	.	.	PUNCT
ejpam-6009	118	1	j.	j.	PROPN
ejpam-6009	118	2	pure	pure	PROPN
ejpam-6009	118	3	appl	appl	PROPN
ejpam-6009	118	4	.	.	PROPN
ejpam-6009	118	5	math	math	PROPN
ejpam-6009	118	6	,	,	PUNCT
ejpam-6009	118	7	18	18	NUM
ejpam-6009	118	8	(	(	PUNCT
ejpam-6009	118	9	2	2	NUM
ejpam-6009	118	10	)	)	PUNCT
ejpam-6009	118	11	(	(	PUNCT
ejpam-6009	118	12	2025	2025	NUM
ejpam-6009	118	13	)	)	PUNCT
ejpam-6009	118	14	,	,	PUNCT
ejpam-6009	118	15	6009	6009	NUM
ejpam-6009	118	16	5	5	NUM
ejpam-6009	118	17	of	of	ADP
ejpam-6009	118	18	18	18	NUM
ejpam-6009	118	19	(	(	PUNCT
ejpam-6009	118	20	3	3	NUM
ejpam-6009	118	21	)	)	PUNCT
ejpam-6009	118	22	(	(	PUNCT
ejpam-6009	118	23	τ1	τ1	NOUN
ejpam-6009	118	24	,	,	PUNCT
ejpam-6009	118	25	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6009	118	26	)	)	PUNCT
ejpam-6009	118	27	=	=	PUNCT
ejpam-6009	119	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	119	2	-	-	NOUN
ejpam-6009	119	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	119	4	-	-	PUNCT
ejpam-6009	119	5	cl(a	cl(a	NUM
ejpam-6009	119	6	)	)	PUNCT
ejpam-6009	119	7	)	)	PUNCT
ejpam-6009	120	1	∪a	∪a	X
ejpam-6009	121	1	[	[	X
ejpam-6009	121	2	39	39	NUM
ejpam-6009	121	3	]	]	PUNCT
ejpam-6009	121	4	;	;	PUNCT
ejpam-6009	121	5	(	(	PUNCT
ejpam-6009	121	6	4	4	NUM
ejpam-6009	121	7	)	)	PUNCT
ejpam-6009	121	8	(	(	PUNCT
ejpam-6009	121	9	τ1	τ1	NOUN
ejpam-6009	121	10	,	,	PUNCT
ejpam-6009	121	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6009	121	12	)	)	PUNCT
ejpam-6009	121	13	=	=	PUNCT
ejpam-6009	122	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	122	2	-	-	ADJ
ejpam-6009	122	3	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6009	122	4	-	-	PUNCT
ejpam-6009	122	5	int(a	int(a	NOUN
ejpam-6009	122	6	)	)	PUNCT
ejpam-6009	122	7	)	)	PUNCT
ejpam-6009	123	1	∩a	∩a	PROPN
ejpam-6009	124	1	[	[	X
ejpam-6009	124	2	59	59	NUM
ejpam-6009	124	3	]	]	PUNCT
ejpam-6009	124	4	.	.	PUNCT
ejpam-6009	125	1	let	let	VERB
ejpam-6009	125	2	a	a	DET
ejpam-6009	125	3	be	be	AUX
ejpam-6009	125	4	a	a	DET
ejpam-6009	125	5	subset	subset	NOUN
ejpam-6009	125	6	of	of	ADP
ejpam-6009	125	7	a	a	DET
ejpam-6009	125	8	bitopological	bitopological	ADJ
ejpam-6009	125	9	space	space	NOUN
ejpam-6009	125	10	(	(	PUNCT
ejpam-6009	125	11	x	x	NOUN
ejpam-6009	125	12	,	,	PUNCT
ejpam-6009	125	13	τ1	τ1	NOUN
ejpam-6009	125	14	,	,	PUNCT
ejpam-6009	125	15	τ2	τ2	NOUN
ejpam-6009	125	16	)	)	PUNCT
ejpam-6009	125	17	.	.	PUNCT
ejpam-6009	126	1	a	a	DET
ejpam-6009	126	2	point	point	NOUN
ejpam-6009	126	3	x	x	X
ejpam-6009	126	4	∈	∈	NOUN
ejpam-6009	126	5	x	x	PUNCT
ejpam-6009	126	6	is	be	AUX
ejpam-6009	126	7	called	call	VERB
ejpam-6009	126	8	a	a	DET
ejpam-6009	126	9	s(τ1	s(τ1	NOUN
ejpam-6009	126	10	,	,	PUNCT
ejpam-6009	126	11	τ2)θ	τ2)θ	ADJ
ejpam-6009	126	12	-	-	PUNCT
ejpam-6009	126	13	cluster	cluster	NOUN
ejpam-6009	126	14	point	point	NOUN
ejpam-6009	126	15	[	[	X
ejpam-6009	126	16	80	80	NUM
ejpam-6009	126	17	]	]	PUNCT
ejpam-6009	126	18	of	of	ADP
ejpam-6009	126	19	a	a	DET
ejpam-6009	126	20	if	if	SCONJ
ejpam-6009	126	21	τ1τ2	τ1τ2	NOUN
ejpam-6009	126	22	-	-	NOUN
ejpam-6009	126	23	cl(u	cl(u	NOUN
ejpam-6009	126	24	)	)	PUNCT
ejpam-6009	126	25	∩	∩	NOUN
ejpam-6009	126	26	a	a	DET
ejpam-6009	126	27	̸=	̸=	PROPN
ejpam-6009	126	28	∅	∅	NOUN
ejpam-6009	126	29	for	for	ADP
ejpam-6009	126	30	every	every	DET
ejpam-6009	126	31	(	(	PUNCT
ejpam-6009	126	32	τ1	τ1	NOUN
ejpam-6009	126	33	,	,	PUNCT
ejpam-6009	126	34	τ2)s	τ2)s	NOUN
ejpam-6009	126	35	-	-	PUNCT
ejpam-6009	126	36	open	open	ADJ
ejpam-6009	126	37	set	set	NOUN
ejpam-6009	126	38	u	u	NOUN
ejpam-6009	126	39	containing	contain	VERB
ejpam-6009	126	40	x.	x.	NOUN
ejpam-6009	126	41	the	the	DET
ejpam-6009	126	42	set	set	NOUN
ejpam-6009	126	43	of	of	ADP
ejpam-6009	126	44	all	all	DET
ejpam-6009	126	45	s(τ1	s(τ1	NOUN
ejpam-6009	126	46	,	,	PUNCT
ejpam-6009	126	47	τ2)θ	τ2)θ	ADJ
ejpam-6009	126	48	-	-	PUNCT
ejpam-6009	126	49	cluster	cluster	NOUN
ejpam-6009	126	50	points	point	NOUN
ejpam-6009	126	51	of	of	ADP
ejpam-6009	126	52	a	a	PRON
ejpam-6009	126	53	is	be	AUX
ejpam-6009	126	54	called	call	VERB
ejpam-6009	126	55	the	the	DET
ejpam-6009	126	56	s(τ1	s(τ1	NOUN
ejpam-6009	126	57	,	,	PUNCT
ejpam-6009	126	58	τ2)θ	τ2)θ	NOUN
ejpam-6009	126	59	-	-	PUNCT
ejpam-6009	126	60	closure	closure	NOUN
ejpam-6009	126	61	[	[	X
ejpam-6009	126	62	80	80	NUM
ejpam-6009	126	63	]	]	PUNCT
ejpam-6009	126	64	of	of	ADP
ejpam-6009	126	65	a	a	PRON
ejpam-6009	126	66	and	and	CCONJ
ejpam-6009	126	67	is	be	AUX
ejpam-6009	126	68	denoted	denote	VERB
ejpam-6009	126	69	by	by	ADP
ejpam-6009	126	70	s(τ1	s(τ1	NOUN
ejpam-6009	126	71	,	,	PUNCT
ejpam-6009	126	72	τ2)θ	τ2)θ	NOUN
ejpam-6009	126	73	-	-	PUNCT
ejpam-6009	126	74	cl(a	cl(a	NUM
ejpam-6009	126	75	)	)	PUNCT
ejpam-6009	126	76	.	.	PUNCT
ejpam-6009	127	1	a	a	DET
ejpam-6009	127	2	subset	subset	NOUN
ejpam-6009	127	3	a	a	PRON
ejpam-6009	127	4	of	of	ADP
ejpam-6009	127	5	a	a	DET
ejpam-6009	127	6	bitopological	bitopological	ADJ
ejpam-6009	127	7	space	space	NOUN
ejpam-6009	127	8	(	(	PUNCT
ejpam-6009	127	9	x	x	NOUN
ejpam-6009	127	10	,	,	PUNCT
ejpam-6009	127	11	τ1	τ1	NOUN
ejpam-6009	127	12	,	,	PUNCT
ejpam-6009	127	13	τ2	τ2	NOUN
ejpam-6009	127	14	)	)	PUNCT
ejpam-6009	127	15	is	be	AUX
ejpam-6009	127	16	called	call	VERB
ejpam-6009	127	17	s(τ1	s(τ1	NOUN
ejpam-6009	127	18	,	,	PUNCT
ejpam-6009	127	19	τ2)θ	τ2)θ	NOUN
ejpam-6009	127	20	-	-	PUNCT
ejpam-6009	127	21	closed	closed	ADJ
ejpam-6009	127	22	[	[	X
ejpam-6009	127	23	80	80	NUM
ejpam-6009	127	24	]	]	X
ejpam-6009	127	25	if	if	SCONJ
ejpam-6009	127	26	s(τ1	s(τ1	NOUN
ejpam-6009	127	27	,	,	PUNCT
ejpam-6009	127	28	τ2)θ	τ2)θ	NOUN
ejpam-6009	127	29	-	-	PUNCT
ejpam-6009	127	30	cl(a	cl(a	NUM
ejpam-6009	127	31	)	)	PUNCT
ejpam-6009	127	32	=	=	PUNCT
ejpam-6009	128	1	a.	a.	NOUN
ejpam-6009	128	2	the	the	DET
ejpam-6009	128	3	complement	complement	NOUN
ejpam-6009	128	4	of	of	ADP
ejpam-6009	128	5	a	a	DET
ejpam-6009	128	6	s(τ1	s(τ1	NOUN
ejpam-6009	128	7	,	,	PUNCT
ejpam-6009	128	8	τ2)θ	τ2)θ	ADJ
ejpam-6009	128	9	-	-	PUNCT
ejpam-6009	128	10	closed	close	VERB
ejpam-6009	128	11	set	set	NOUN
ejpam-6009	128	12	is	be	AUX
ejpam-6009	128	13	said	say	VERB
ejpam-6009	128	14	to	to	PART
ejpam-6009	128	15	be	be	AUX
ejpam-6009	128	16	s(τ1	s(τ1	NOUN
ejpam-6009	128	17	,	,	PUNCT
ejpam-6009	128	18	τ2)θ	τ2)θ	ADJ
ejpam-6009	128	19	-	-	PUNCT
ejpam-6009	128	20	open	open	NOUN
ejpam-6009	129	1	[	[	X
ejpam-6009	129	2	80	80	NUM
ejpam-6009	129	3	]	]	PUNCT
ejpam-6009	129	4	.	.	PUNCT
ejpam-6009	130	1	the	the	DET
ejpam-6009	130	2	union	union	NOUN
ejpam-6009	130	3	of	of	ADP
ejpam-6009	130	4	all	all	DET
ejpam-6009	130	5	s(τ1	s(τ1	NOUN
ejpam-6009	130	6	,	,	PUNCT
ejpam-6009	130	7	τ2)θ	τ2)θ	ADJ
ejpam-6009	130	8	-	-	PUNCT
ejpam-6009	130	9	open	open	ADJ
ejpam-6009	130	10	sets	set	NOUN
ejpam-6009	130	11	of	of	ADP
ejpam-6009	130	12	x	x	PUNCT
ejpam-6009	130	13	contained	contain	VERB
ejpam-6009	130	14	in	in	ADP
ejpam-6009	130	15	a	a	PRON
ejpam-6009	130	16	is	be	AUX
ejpam-6009	130	17	called	call	VERB
ejpam-6009	130	18	the	the	DET
ejpam-6009	130	19	s(τ1	s(τ1	NOUN
ejpam-6009	130	20	,	,	PUNCT
ejpam-6009	130	21	τ2)θ	τ2)θ	ADJ
ejpam-6009	130	22	-	-	PUNCT
ejpam-6009	130	23	interior	interior	NOUN
ejpam-6009	130	24	[	[	X
ejpam-6009	130	25	80	80	NUM
ejpam-6009	130	26	]	]	PUNCT
ejpam-6009	130	27	of	of	ADP
ejpam-6009	130	28	a	a	PRON
ejpam-6009	130	29	and	and	CCONJ
ejpam-6009	130	30	is	be	AUX
ejpam-6009	130	31	denoted	denote	VERB
ejpam-6009	130	32	by	by	ADP
ejpam-6009	130	33	s(τ1	s(τ1	NOUN
ejpam-6009	130	34	,	,	PUNCT
ejpam-6009	130	35	τ2)θ	τ2)θ	NOUN
ejpam-6009	130	36	-	-	PUNCT
ejpam-6009	130	37	int(a	int(a	NOUN
ejpam-6009	130	38	)	)	PUNCT
ejpam-6009	130	39	.	.	PUNCT
ejpam-6009	131	1	by	by	ADP
ejpam-6009	131	2	a	a	DET
ejpam-6009	131	3	multifunction	multifunction	NOUN
ejpam-6009	131	4	f	f	NOUN
ejpam-6009	131	5	:	:	PUNCT
ejpam-6009	131	6	x	x	X
ejpam-6009	131	7	→	→	SYM
ejpam-6009	131	8	y	y	PROPN
ejpam-6009	131	9	,	,	PUNCT
ejpam-6009	131	10	we	we	PRON
ejpam-6009	131	11	mean	mean	VERB
ejpam-6009	131	12	a	a	DET
ejpam-6009	131	13	point	point	NOUN
ejpam-6009	131	14	-	-	PUNCT
ejpam-6009	131	15	to	to	ADP
ejpam-6009	131	16	-	-	PUNCT
ejpam-6009	131	17	set	set	VERB
ejpam-6009	131	18	correspondence	correspondence	NOUN
ejpam-6009	131	19	from	from	ADP
ejpam-6009	131	20	x	x	PUNCT
ejpam-6009	131	21	into	into	ADP
ejpam-6009	131	22	y	y	PROPN
ejpam-6009	131	23	,	,	PUNCT
ejpam-6009	131	24	and	and	CCONJ
ejpam-6009	131	25	we	we	PRON
ejpam-6009	131	26	always	always	ADV
ejpam-6009	131	27	assume	assume	VERB
ejpam-6009	131	28	that	that	SCONJ
ejpam-6009	131	29	f	f	PROPN
ejpam-6009	131	30	(	(	PUNCT
ejpam-6009	131	31	x	x	X
ejpam-6009	131	32	)	)	PUNCT
ejpam-6009	131	33	̸=	̸=	NOUN
ejpam-6009	131	34	∅	∅	NOUN
ejpam-6009	131	35	for	for	ADP
ejpam-6009	131	36	all	all	PRON
ejpam-6009	131	37	x	x	SYM
ejpam-6009	131	38	∈	∈	ADJ
ejpam-6009	131	39	x.	x.	NOUN
ejpam-6009	131	40	for	for	ADP
ejpam-6009	131	41	a	a	DET
ejpam-6009	131	42	multifunction	multifunction	NOUN
ejpam-6009	131	43	f	f	NOUN
ejpam-6009	131	44	:	:	PUNCT
ejpam-6009	131	45	x	x	X
ejpam-6009	131	46	→	→	SYM
ejpam-6009	131	47	y	y	PROPN
ejpam-6009	131	48	,	,	PUNCT
ejpam-6009	131	49	we	we	PRON
ejpam-6009	131	50	shall	shall	AUX
ejpam-6009	131	51	denote	denote	VERB
ejpam-6009	131	52	the	the	DET
ejpam-6009	131	53	upper	upper	ADJ
ejpam-6009	131	54	and	and	CCONJ
ejpam-6009	131	55	lower	low	ADJ
ejpam-6009	131	56	inverse	inverse	NOUN
ejpam-6009	131	57	of	of	ADP
ejpam-6009	131	58	a	a	DET
ejpam-6009	131	59	set	set	NOUN
ejpam-6009	131	60	b	b	PROPN
ejpam-6009	131	61	of	of	ADP
ejpam-6009	131	62	y	y	PROPN
ejpam-6009	131	63	by	by	ADP
ejpam-6009	131	64	f+(b	f+(b	NOUN
ejpam-6009	131	65	)	)	PUNCT
ejpam-6009	131	66	and	and	CCONJ
ejpam-6009	131	67	f−(b	f−(b	NOUN
ejpam-6009	131	68	)	)	PUNCT
ejpam-6009	131	69	,	,	PUNCT
ejpam-6009	131	70	respectively	respectively	ADV
ejpam-6009	131	71	,	,	PUNCT
ejpam-6009	131	72	that	that	ADV
ejpam-6009	131	73	is	is	ADV
ejpam-6009	131	74	,	,	PUNCT
ejpam-6009	131	75	f+(b	f+(b	NOUN
ejpam-6009	131	76	)	)	PUNCT
ejpam-6009	131	77	=	=	PRON
ejpam-6009	132	1	{	{	PUNCT
ejpam-6009	132	2	x	x	PUNCT
ejpam-6009	132	3	∈	∈	PROPN
ejpam-6009	132	4	x	x	INTJ
ejpam-6009	133	1	|	|	NOUN
ejpam-6009	133	2	f	f	X
ejpam-6009	133	3	(	(	PUNCT
ejpam-6009	133	4	x	x	NOUN
ejpam-6009	133	5	)	)	PUNCT
ejpam-6009	133	6	⊆	⊆	NUM
ejpam-6009	133	7	b	b	NOUN
ejpam-6009	133	8	}	}	PUNCT
ejpam-6009	133	9	and	and	CCONJ
ejpam-6009	133	10	f−(b	f−(b	PROPN
ejpam-6009	133	11	)	)	PUNCT
ejpam-6009	133	12	=	=	PRON
ejpam-6009	134	1	{	{	PUNCT
ejpam-6009	134	2	x	x	PUNCT
ejpam-6009	134	3	∈	∈	PROPN
ejpam-6009	134	4	x	x	INTJ
ejpam-6009	135	1	|	|	NOUN
ejpam-6009	135	2	f	f	X
ejpam-6009	135	3	(	(	PUNCT
ejpam-6009	135	4	x	x	NOUN
ejpam-6009	135	5	)	)	PUNCT
ejpam-6009	135	6	∩	∩	NOUN
ejpam-6009	135	7	b	b	PROPN
ejpam-6009	135	8	̸=	̸=	PROPN
ejpam-6009	135	9	∅	∅	NOUN
ejpam-6009	135	10	}	}	PUNCT
ejpam-6009	135	11	.	.	PUNCT
ejpam-6009	136	1	in	in	ADP
ejpam-6009	136	2	particular	particular	ADJ
ejpam-6009	136	3	,	,	PUNCT
ejpam-6009	136	4	f−(y	f−(y	NOUN
ejpam-6009	136	5	)	)	PUNCT
ejpam-6009	136	6	=	=	SYM
ejpam-6009	137	1	{	{	PUNCT
ejpam-6009	137	2	x	x	PUNCT
ejpam-6009	137	3	∈	∈	PROPN
ejpam-6009	137	4	x	x	INTJ
ejpam-6009	138	1	|	|	ADV
ejpam-6009	138	2	y	y	PROPN
ejpam-6009	138	3	∈	∈	PROPN
ejpam-6009	138	4	f	f	X
ejpam-6009	138	5	(	(	PUNCT
ejpam-6009	138	6	x	x	NOUN
ejpam-6009	138	7	)	)	PUNCT
ejpam-6009	138	8	}	}	PUNCT
ejpam-6009	138	9	for	for	ADP
ejpam-6009	138	10	each	each	DET
ejpam-6009	138	11	point	point	NOUN
ejpam-6009	138	12	y	y	PROPN
ejpam-6009	138	13	∈	∈	PROPN
ejpam-6009	138	14	y	y	PROPN
ejpam-6009	138	15	.	.	PUNCT
ejpam-6009	139	1	for	for	ADP
ejpam-6009	139	2	each	each	DET
ejpam-6009	139	3	a	a	DET
ejpam-6009	139	4	⊆	⊆	NUM
ejpam-6009	139	5	x	x	SYM
ejpam-6009	139	6	,	,	PUNCT
ejpam-6009	139	7	f	f	PROPN
ejpam-6009	139	8	(	(	PUNCT
ejpam-6009	139	9	a	a	NOUN
ejpam-6009	139	10	)	)	PUNCT
ejpam-6009	139	11	=	=	SYM
ejpam-6009	139	12	∪x∈af	∪x∈af	NOUN
ejpam-6009	139	13	(	(	PUNCT
ejpam-6009	139	14	x	x	NOUN
ejpam-6009	139	15	)	)	PUNCT
ejpam-6009	139	16	.	.	PUNCT
ejpam-6009	140	1	3	3	X
ejpam-6009	140	2	.	.	X
ejpam-6009	140	3	upper	upper	ADJ
ejpam-6009	140	4	and	and	CCONJ
ejpam-6009	140	5	lower	low	ADJ
ejpam-6009	140	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	140	7	,	,	PUNCT
ejpam-6009	140	8	τ2)p	τ2)p	ADJ
ejpam-6009	140	9	-	-	ADJ
ejpam-6009	140	10	continuous	continuous	ADJ
ejpam-6009	140	11	multifunctions	multifunction	NOUN
ejpam-6009	140	12	in	in	ADP
ejpam-6009	140	13	this	this	DET
ejpam-6009	140	14	section	section	NOUN
ejpam-6009	140	15	,	,	PUNCT
ejpam-6009	140	16	we	we	PRON
ejpam-6009	140	17	introduce	introduce	VERB
ejpam-6009	140	18	the	the	DET
ejpam-6009	140	19	concepts	concept	NOUN
ejpam-6009	140	20	of	of	ADP
ejpam-6009	140	21	upper	upper	ADJ
ejpam-6009	140	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	140	23	,	,	PUNCT
ejpam-6009	140	24	τ2)p	τ2)p	ADJ
ejpam-6009	140	25	-	-	ADJ
ejpam-6009	140	26	continuous	continuous	ADJ
ejpam-6009	140	27	multifunctions	multifunction	NOUN
ejpam-6009	140	28	and	and	CCONJ
ejpam-6009	140	29	lower	low	ADJ
ejpam-6009	140	30	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	140	31	,	,	PUNCT
ejpam-6009	140	32	τ2)p	τ2)p	ADJ
ejpam-6009	140	33	-	-	PUNCT
ejpam-6009	140	34	continuous	continuous	ADJ
ejpam-6009	140	35	multifunctions	multifunction	NOUN
ejpam-6009	140	36	.	.	PUNCT
ejpam-6009	141	1	furthermore	furthermore	ADV
ejpam-6009	141	2	,	,	PUNCT
ejpam-6009	141	3	several	several	ADJ
ejpam-6009	141	4	characterizations	characterization	NOUN
ejpam-6009	141	5	of	of	ADP
ejpam-6009	141	6	upper	upper	ADJ
ejpam-6009	141	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	141	8	,	,	PUNCT
ejpam-6009	141	9	τ2)p	τ2)p	ADJ
ejpam-6009	141	10	-	-	ADJ
ejpam-6009	141	11	continuous	continuous	ADJ
ejpam-6009	141	12	multifunctions	multifunction	NOUN
ejpam-6009	141	13	and	and	CCONJ
ejpam-6009	141	14	lower	low	ADJ
ejpam-6009	141	15	contra(τ1	contra(τ1	NOUN
ejpam-6009	141	16	,	,	PUNCT
ejpam-6009	141	17	τ2)p	τ2)p	ADJ
ejpam-6009	141	18	-	-	PUNCT
ejpam-6009	141	19	continuous	continuous	ADJ
ejpam-6009	141	20	multifunctions	multifunction	NOUN
ejpam-6009	141	21	are	be	AUX
ejpam-6009	141	22	discussed	discuss	VERB
ejpam-6009	141	23	.	.	PUNCT
ejpam-6009	142	1	definition	definition	NOUN
ejpam-6009	142	2	1	1	NUM
ejpam-6009	142	3	.	.	PUNCT
ejpam-6009	143	1	a	a	DET
ejpam-6009	143	2	multifunction	multifunction	NOUN
ejpam-6009	143	3	f	f	NOUN
ejpam-6009	143	4	:	:	PUNCT
ejpam-6009	143	5	(	(	PUNCT
ejpam-6009	143	6	x	x	NOUN
ejpam-6009	143	7	,	,	PUNCT
ejpam-6009	143	8	τ1	τ1	NOUN
ejpam-6009	143	9	,	,	PUNCT
ejpam-6009	143	10	τ2	τ2	NOUN
ejpam-6009	143	11	)	)	PUNCT
ejpam-6009	143	12	→	→	SYM
ejpam-6009	143	13	(	(	PUNCT
ejpam-6009	143	14	y	y	PROPN
ejpam-6009	143	15	,	,	PUNCT
ejpam-6009	143	16	σ1	σ1	PROPN
ejpam-6009	143	17	,	,	PUNCT
ejpam-6009	143	18	σ2	σ2	PROPN
ejpam-6009	143	19	)	)	PUNCT
ejpam-6009	143	20	is	be	AUX
ejpam-6009	143	21	called	call	VERB
ejpam-6009	143	22	upper	upper	ADJ
ejpam-6009	143	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	143	24	,	,	PUNCT
ejpam-6009	143	25	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	143	26	at	at	ADP
ejpam-6009	143	27	a	a	DET
ejpam-6009	143	28	point	point	NOUN
ejpam-6009	143	29	x	x	SYM
ejpam-6009	143	30	∈	∈	NOUN
ejpam-6009	143	31	x	x	PUNCT
ejpam-6009	143	32	if	if	SCONJ
ejpam-6009	143	33	for	for	ADP
ejpam-6009	143	34	each	each	DET
ejpam-6009	143	35	σ1σ2	σ1σ2	NUM
ejpam-6009	143	36	-	-	PUNCT
ejpam-6009	143	37	closed	closed	ADJ
ejpam-6009	143	38	set	set	NOUN
ejpam-6009	143	39	k	k	PROPN
ejpam-6009	143	40	of	of	ADP
ejpam-6009	143	41	y	y	PROPN
ejpam-6009	143	42	with	with	ADP
ejpam-6009	143	43	x	x	PROPN
ejpam-6009	143	44	∈	∈	PROPN
ejpam-6009	143	45	f+(k	f+(k	PROPN
ejpam-6009	143	46	)	)	PUNCT
ejpam-6009	143	47	,	,	PUNCT
ejpam-6009	143	48	there	there	PRON
ejpam-6009	143	49	exists	exist	VERB
ejpam-6009	143	50	a	a	DET
ejpam-6009	143	51	(	(	PUNCT
ejpam-6009	143	52	τ1	τ1	NOUN
ejpam-6009	143	53	,	,	PUNCT
ejpam-6009	143	54	τ2)p	τ2)p	ADJ
ejpam-6009	143	55	-	-	PUNCT
ejpam-6009	143	56	open	open	ADJ
ejpam-6009	143	57	set	set	NOUN
ejpam-6009	143	58	u	u	NOUN
ejpam-6009	143	59	of	of	ADP
ejpam-6009	143	60	x	x	PUNCT
ejpam-6009	143	61	containing	contain	VERB
ejpam-6009	143	62	x	x	PUNCT
ejpam-6009	143	63	such	such	ADJ
ejpam-6009	143	64	that	that	SCONJ
ejpam-6009	143	65	u	u	PROPN
ejpam-6009	143	66	⊆	⊆	NUM
ejpam-6009	143	67	f+(k	f+(k	NUM
ejpam-6009	143	68	)	)	PUNCT
ejpam-6009	143	69	.	.	PUNCT
ejpam-6009	144	1	a	a	DET
ejpam-6009	144	2	multifunction	multifunction	NOUN
ejpam-6009	144	3	f	f	NOUN
ejpam-6009	144	4	:	:	PUNCT
ejpam-6009	144	5	(	(	PUNCT
ejpam-6009	144	6	x	x	NOUN
ejpam-6009	144	7	,	,	PUNCT
ejpam-6009	144	8	τ1	τ1	NOUN
ejpam-6009	144	9	,	,	PUNCT
ejpam-6009	144	10	τ2	τ2	NOUN
ejpam-6009	144	11	)	)	PUNCT
ejpam-6009	144	12	→	→	SYM
ejpam-6009	144	13	(	(	PUNCT
ejpam-6009	144	14	y	y	PROPN
ejpam-6009	144	15	,	,	PUNCT
ejpam-6009	144	16	σ1	σ1	PROPN
ejpam-6009	144	17	,	,	PUNCT
ejpam-6009	144	18	σ2	σ2	PROPN
ejpam-6009	144	19	)	)	PUNCT
ejpam-6009	144	20	is	be	AUX
ejpam-6009	144	21	called	call	VERB
ejpam-6009	144	22	upper	upper	ADJ
ejpam-6009	144	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	144	24	,	,	PUNCT
ejpam-6009	144	25	τ2)p	τ2)p	ADJ
ejpam-6009	144	26	-	-	ADJ
ejpam-6009	144	27	continuous	continuous	ADJ
ejpam-6009	144	28	if	if	SCONJ
ejpam-6009	144	29	f	f	PROPN
ejpam-6009	144	30	is	be	AUX
ejpam-6009	144	31	upper	upper	ADJ
ejpam-6009	144	32	contra(τ1	contra(τ1	NOUN
ejpam-6009	144	33	,	,	PUNCT
ejpam-6009	144	34	τ2)p	τ2)p	ADJ
ejpam-6009	144	35	-	-	ADJ
ejpam-6009	144	36	continuous	continuous	ADJ
ejpam-6009	144	37	at	at	ADP
ejpam-6009	144	38	each	each	DET
ejpam-6009	144	39	point	point	NOUN
ejpam-6009	144	40	x	x	PUNCT
ejpam-6009	144	41	of	of	ADP
ejpam-6009	144	42	x.	x.	PROPN
ejpam-6009	144	43	theorem	theorem	VERB
ejpam-6009	144	44	1	1	NUM
ejpam-6009	144	45	.	.	X
ejpam-6009	144	46	for	for	ADP
ejpam-6009	144	47	a	a	DET
ejpam-6009	144	48	multifunction	multifunction	NOUN
ejpam-6009	144	49	f	f	NOUN
ejpam-6009	144	50	:	:	PUNCT
ejpam-6009	144	51	(	(	PUNCT
ejpam-6009	144	52	x	x	NOUN
ejpam-6009	144	53	,	,	PUNCT
ejpam-6009	144	54	τ1	τ1	NOUN
ejpam-6009	144	55	,	,	PUNCT
ejpam-6009	144	56	τ2	τ2	NOUN
ejpam-6009	144	57	)	)	PUNCT
ejpam-6009	144	58	→	→	SYM
ejpam-6009	144	59	(	(	PUNCT
ejpam-6009	144	60	y	y	PROPN
ejpam-6009	144	61	,	,	PUNCT
ejpam-6009	144	62	σ1	σ1	PROPN
ejpam-6009	144	63	,	,	PUNCT
ejpam-6009	144	64	σ2	σ2	NOUN
ejpam-6009	144	65	)	)	PUNCT
ejpam-6009	144	66	,	,	PUNCT
ejpam-6009	144	67	the	the	DET
ejpam-6009	144	68	following	follow	VERB
ejpam-6009	144	69	properties	property	NOUN
ejpam-6009	144	70	are	be	AUX
ejpam-6009	144	71	equivalent	equivalent	ADJ
ejpam-6009	144	72	:	:	PUNCT
ejpam-6009	144	73	(	(	PUNCT
ejpam-6009	144	74	1	1	X
ejpam-6009	144	75	)	)	PUNCT
ejpam-6009	144	76	f	f	PROPN
ejpam-6009	144	77	is	be	AUX
ejpam-6009	144	78	upper	upper	ADJ
ejpam-6009	144	79	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	144	80	,	,	PUNCT
ejpam-6009	144	81	τ2)p	τ2)p	ADJ
ejpam-6009	144	82	-	-	NOUN
ejpam-6009	144	83	continuous	continuous	ADJ
ejpam-6009	144	84	;	;	PUNCT
ejpam-6009	144	85	(	(	PUNCT
ejpam-6009	144	86	2	2	X
ejpam-6009	144	87	)	)	PUNCT
ejpam-6009	144	88	f+(k	f+(k	NOUN
ejpam-6009	144	89	)	)	PUNCT
ejpam-6009	144	90	is	be	AUX
ejpam-6009	144	91	(	(	PUNCT
ejpam-6009	144	92	τ1	τ1	NOUN
ejpam-6009	144	93	,	,	PUNCT
ejpam-6009	144	94	τ2)p	τ2)p	NOUN
ejpam-6009	144	95	-	-	PUNCT
ejpam-6009	144	96	open	open	ADJ
ejpam-6009	144	97	in	in	ADP
ejpam-6009	144	98	x	x	PUNCT
ejpam-6009	144	99	for	for	ADP
ejpam-6009	144	100	every	every	DET
ejpam-6009	144	101	σ1σ2	σ1σ2	NUM
ejpam-6009	144	102	-	-	PUNCT
ejpam-6009	144	103	closed	closed	ADJ
ejpam-6009	144	104	set	set	NOUN
ejpam-6009	144	105	k	k	PROPN
ejpam-6009	144	106	of	of	ADP
ejpam-6009	144	107	y	y	PROPN
ejpam-6009	144	108	;	;	PUNCT
ejpam-6009	144	109	(	(	PUNCT
ejpam-6009	144	110	3	3	X
ejpam-6009	144	111	)	)	PUNCT
ejpam-6009	144	112	f−(v	f−(v	NOUN
ejpam-6009	144	113	)	)	PUNCT
ejpam-6009	144	114	is	be	AUX
ejpam-6009	144	115	(	(	PUNCT
ejpam-6009	144	116	τ1	τ1	NOUN
ejpam-6009	144	117	,	,	PUNCT
ejpam-6009	144	118	τ2)p	τ2)p	NOUN
ejpam-6009	144	119	-	-	PUNCT
ejpam-6009	144	120	closed	closed	ADJ
ejpam-6009	144	121	in	in	ADP
ejpam-6009	144	122	x	x	PUNCT
ejpam-6009	144	123	for	for	ADP
ejpam-6009	144	124	every	every	DET
ejpam-6009	144	125	σ1σ2	σ1σ2	NOUN
ejpam-6009	144	126	-	-	ADJ
ejpam-6009	144	127	open	open	ADJ
ejpam-6009	144	128	set	set	NOUN
ejpam-6009	144	129	v	v	NOUN
ejpam-6009	144	130	of	of	ADP
ejpam-6009	144	131	y	y	PROPN
ejpam-6009	144	132	;	;	PUNCT
ejpam-6009	144	133	(	(	PUNCT
ejpam-6009	144	134	4	4	X
ejpam-6009	144	135	)	)	PUNCT
ejpam-6009	144	136	for	for	ADP
ejpam-6009	144	137	each	each	DET
ejpam-6009	144	138	x	x	SYM
ejpam-6009	144	139	∈	∈	PROPN
ejpam-6009	144	140	x	x	X
ejpam-6009	144	141	and	and	CCONJ
ejpam-6009	144	142	each	each	PRON
ejpam-6009	144	143	σ1σ2	σ1σ2	VERB
ejpam-6009	144	144	-	-	PUNCT
ejpam-6009	144	145	closed	closed	ADJ
ejpam-6009	144	146	set	set	NOUN
ejpam-6009	144	147	k	k	PROPN
ejpam-6009	144	148	of	of	ADP
ejpam-6009	144	149	y	y	PROPN
ejpam-6009	144	150	containing	contain	VERB
ejpam-6009	144	151	f	f	PROPN
ejpam-6009	144	152	(	(	PUNCT
ejpam-6009	144	153	x	x	NOUN
ejpam-6009	144	154	)	)	PUNCT
ejpam-6009	144	155	,	,	PUNCT
ejpam-6009	144	156	there	there	PRON
ejpam-6009	144	157	exists	exist	VERB
ejpam-6009	144	158	a	a	DET
ejpam-6009	144	159	(	(	PUNCT
ejpam-6009	144	160	τ1	τ1	NOUN
ejpam-6009	144	161	,	,	PUNCT
ejpam-6009	144	162	τ2)p	τ2)p	ADJ
ejpam-6009	144	163	-	-	PUNCT
ejpam-6009	144	164	open	open	ADJ
ejpam-6009	144	165	set	set	NOUN
ejpam-6009	144	166	u	u	NOUN
ejpam-6009	144	167	of	of	ADP
ejpam-6009	144	168	x	x	PUNCT
ejpam-6009	144	169	containing	contain	VERB
ejpam-6009	144	170	x	x	PUNCT
ejpam-6009	144	171	such	such	ADJ
ejpam-6009	144	172	that	that	SCONJ
ejpam-6009	144	173	if	if	SCONJ
ejpam-6009	144	174	y	y	PROPN
ejpam-6009	144	175	∈	∈	PROPN
ejpam-6009	144	176	u	u	PROPN
ejpam-6009	144	177	,	,	PUNCT
ejpam-6009	144	178	then	then	ADV
ejpam-6009	144	179	f	f	PROPN
ejpam-6009	144	180	(	(	PUNCT
ejpam-6009	144	181	y	y	PROPN
ejpam-6009	144	182	)	)	PUNCT
ejpam-6009	144	183	⊆	⊆	NUM
ejpam-6009	144	184	k.	k.	NOUN
ejpam-6009	144	185	proof	proof	NOUN
ejpam-6009	144	186	.	.	PUNCT
ejpam-6009	145	1	(	(	PUNCT
ejpam-6009	145	2	1	1	X
ejpam-6009	145	3	)	)	PUNCT
ejpam-6009	145	4	⇔	⇔	X
ejpam-6009	145	5	(	(	PUNCT
ejpam-6009	145	6	2	2	NUM
ejpam-6009	145	7	):	):	PUNCT
ejpam-6009	145	8	let	let	VERB
ejpam-6009	145	9	k	k	PRON
ejpam-6009	145	10	be	be	AUX
ejpam-6009	145	11	any	any	DET
ejpam-6009	145	12	σ1σ2	σ1σ2	NUM
ejpam-6009	145	13	-	-	PUNCT
ejpam-6009	145	14	closed	closed	ADJ
ejpam-6009	145	15	set	set	NOUN
ejpam-6009	145	16	of	of	ADP
ejpam-6009	145	17	y	y	PROPN
ejpam-6009	145	18	and	and	CCONJ
ejpam-6009	145	19	x	x	PUNCT
ejpam-6009	145	20	∈	∈	PROPN
ejpam-6009	145	21	f+(k	f+(k	PROPN
ejpam-6009	145	22	)	)	PUNCT
ejpam-6009	145	23	.	.	PUNCT
ejpam-6009	146	1	since	since	SCONJ
ejpam-6009	146	2	f	f	PROPN
ejpam-6009	146	3	is	be	AUX
ejpam-6009	146	4	upper	upper	ADJ
ejpam-6009	146	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	146	6	,	,	PUNCT
ejpam-6009	146	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	146	8	,	,	PUNCT
ejpam-6009	146	9	there	there	PRON
ejpam-6009	146	10	exists	exist	VERB
ejpam-6009	146	11	a	a	DET
ejpam-6009	146	12	(	(	PUNCT
ejpam-6009	146	13	τ1	τ1	NOUN
ejpam-6009	146	14	,	,	PUNCT
ejpam-6009	146	15	τ2)p	τ2)p	ADJ
ejpam-6009	146	16	-	-	PUNCT
ejpam-6009	146	17	open	open	ADJ
ejpam-6009	146	18	set	set	NOUN
ejpam-6009	146	19	u	u	NOUN
ejpam-6009	146	20	of	of	ADP
ejpam-6009	146	21	x	x	PUNCT
ejpam-6009	146	22	containing	contain	VERB
ejpam-6009	146	23	x	x	PUNCT
ejpam-6009	146	24	such	such	ADJ
ejpam-6009	146	25	that	that	SCONJ
ejpam-6009	146	26	u	u	PROPN
ejpam-6009	146	27	⊆	⊆	NUM
ejpam-6009	146	28	f+(k	f+(k	NUM
ejpam-6009	146	29	)	)	PUNCT
ejpam-6009	146	30	.	.	PUNCT
ejpam-6009	147	1	thus	thus	ADV
ejpam-6009	147	2	,	,	PUNCT
ejpam-6009	147	3	f+(k	f+(k	X
ejpam-6009	147	4	)	)	PUNCT
ejpam-6009	147	5	is	be	AUX
ejpam-6009	147	6	(	(	PUNCT
ejpam-6009	147	7	τ1	τ1	NOUN
ejpam-6009	147	8	,	,	PUNCT
ejpam-6009	147	9	τ2)p	τ2)p	NOUN
ejpam-6009	147	10	-	-	PUNCT
ejpam-6009	147	11	open	open	ADJ
ejpam-6009	147	12	in	in	ADP
ejpam-6009	147	13	x.	x.	NOUN
ejpam-6009	147	14	the	the	DET
ejpam-6009	147	15	converse	converse	NOUN
ejpam-6009	147	16	of	of	ADP
ejpam-6009	147	17	the	the	DET
ejpam-6009	147	18	proof	proof	NOUN
ejpam-6009	147	19	is	be	AUX
ejpam-6009	147	20	similar	similar	ADJ
ejpam-6009	147	21	.	.	PUNCT
ejpam-6009	148	1	c.	c.	PROPN
ejpam-6009	148	2	viriyapong	viriyapong	PROPN
ejpam-6009	148	3	,	,	PUNCT
ejpam-6009	148	4	a.	a.	PROPN
ejpam-6009	148	5	sama	sama	PROPN
ejpam-6009	148	6	-	-	PUNCT
ejpam-6009	148	7	ae	ae	PROPN
ejpam-6009	148	8	,	,	PUNCT
ejpam-6009	148	9	c.	c.	PROPN
ejpam-6009	148	10	boonpok	boonpok	PROPN
ejpam-6009	148	11	/	/	SYM
ejpam-6009	148	12	eur	eur	PROPN
ejpam-6009	148	13	.	.	PUNCT
ejpam-6009	149	1	j.	j.	PROPN
ejpam-6009	149	2	pure	pure	PROPN
ejpam-6009	149	3	appl	appl	PROPN
ejpam-6009	149	4	.	.	PROPN
ejpam-6009	149	5	math	math	PROPN
ejpam-6009	149	6	,	,	PUNCT
ejpam-6009	149	7	18	18	NUM
ejpam-6009	149	8	(	(	PUNCT
ejpam-6009	149	9	2	2	NUM
ejpam-6009	149	10	)	)	PUNCT
ejpam-6009	149	11	(	(	PUNCT
ejpam-6009	149	12	2025	2025	NUM
ejpam-6009	149	13	)	)	PUNCT
ejpam-6009	149	14	,	,	PUNCT
ejpam-6009	149	15	6009	6009	NUM
ejpam-6009	149	16	6	6	NUM
ejpam-6009	149	17	of	of	ADP
ejpam-6009	149	18	18	18	NUM
ejpam-6009	149	19	(	(	PUNCT
ejpam-6009	149	20	2	2	NUM
ejpam-6009	149	21	)	)	PUNCT
ejpam-6009	149	22	⇔	⇔	NOUN
ejpam-6009	149	23	(	(	PUNCT
ejpam-6009	149	24	3	3	NUM
ejpam-6009	149	25	):	):	PUNCT
ejpam-6009	149	26	this	this	PRON
ejpam-6009	149	27	follows	follow	VERB
ejpam-6009	149	28	from	from	ADP
ejpam-6009	149	29	the	the	DET
ejpam-6009	149	30	fact	fact	NOUN
ejpam-6009	149	31	that	that	SCONJ
ejpam-6009	149	32	f+(y	f+(y	PROPN
ejpam-6009	149	33	−b	−b	ADV
ejpam-6009	149	34	)	)	PUNCT
ejpam-6009	149	35	=	=	PUNCT
ejpam-6009	150	1	x	x	X
ejpam-6009	150	2	−	−	PROPN
ejpam-6009	150	3	f−(b	f−(b	PROPN
ejpam-6009	150	4	)	)	PUNCT
ejpam-6009	150	5	for	for	ADP
ejpam-6009	150	6	every	every	DET
ejpam-6009	150	7	subset	subset	NOUN
ejpam-6009	150	8	b	b	PROPN
ejpam-6009	150	9	of	of	ADP
ejpam-6009	150	10	y	y	PROPN
ejpam-6009	150	11	.	.	PUNCT
ejpam-6009	151	1	(	(	PUNCT
ejpam-6009	151	2	1	1	X
ejpam-6009	151	3	)	)	PUNCT
ejpam-6009	151	4	⇔	⇔	X
ejpam-6009	151	5	(	(	PUNCT
ejpam-6009	151	6	4	4	NUM
ejpam-6009	151	7	):	):	PUNCT
ejpam-6009	151	8	obvious	obvious	ADJ
ejpam-6009	151	9	.	.	PUNCT
ejpam-6009	152	1	definition	definition	NOUN
ejpam-6009	152	2	2	2	NUM
ejpam-6009	152	3	.	.	PUNCT
ejpam-6009	152	4	a	a	DET
ejpam-6009	152	5	multifunction	multifunction	NOUN
ejpam-6009	152	6	f	f	NOUN
ejpam-6009	152	7	:	:	PUNCT
ejpam-6009	152	8	(	(	PUNCT
ejpam-6009	152	9	x	x	NOUN
ejpam-6009	152	10	,	,	PUNCT
ejpam-6009	152	11	τ1	τ1	NOUN
ejpam-6009	152	12	,	,	PUNCT
ejpam-6009	152	13	τ2	τ2	NOUN
ejpam-6009	152	14	)	)	PUNCT
ejpam-6009	152	15	→	→	SYM
ejpam-6009	152	16	(	(	PUNCT
ejpam-6009	152	17	y	y	PROPN
ejpam-6009	152	18	,	,	PUNCT
ejpam-6009	152	19	σ1	σ1	PROPN
ejpam-6009	152	20	,	,	PUNCT
ejpam-6009	152	21	σ2	σ2	PROPN
ejpam-6009	152	22	)	)	PUNCT
ejpam-6009	152	23	is	be	AUX
ejpam-6009	152	24	called	call	VERB
ejpam-6009	152	25	lower	low	ADJ
ejpam-6009	152	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	152	27	,	,	PUNCT
ejpam-6009	152	28	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	152	29	at	at	ADP
ejpam-6009	152	30	a	a	DET
ejpam-6009	152	31	point	point	NOUN
ejpam-6009	152	32	x	x	SYM
ejpam-6009	152	33	∈	∈	NOUN
ejpam-6009	152	34	x	x	PUNCT
ejpam-6009	152	35	if	if	SCONJ
ejpam-6009	152	36	for	for	ADP
ejpam-6009	152	37	each	each	DET
ejpam-6009	152	38	σ1σ2	σ1σ2	NUM
ejpam-6009	152	39	-	-	PUNCT
ejpam-6009	152	40	closed	closed	ADJ
ejpam-6009	152	41	set	set	NOUN
ejpam-6009	152	42	k	k	PROPN
ejpam-6009	152	43	of	of	ADP
ejpam-6009	152	44	y	y	PROPN
ejpam-6009	152	45	with	with	ADP
ejpam-6009	152	46	x	x	PROPN
ejpam-6009	152	47	∈	∈	PROPN
ejpam-6009	152	48	f−(k	f−(k	PROPN
ejpam-6009	152	49	)	)	PUNCT
ejpam-6009	152	50	,	,	PUNCT
ejpam-6009	152	51	there	there	PRON
ejpam-6009	152	52	exists	exist	VERB
ejpam-6009	152	53	a	a	DET
ejpam-6009	152	54	(	(	PUNCT
ejpam-6009	152	55	τ1	τ1	NOUN
ejpam-6009	152	56	,	,	PUNCT
ejpam-6009	152	57	τ2)p	τ2)p	ADJ
ejpam-6009	152	58	-	-	PUNCT
ejpam-6009	152	59	open	open	ADJ
ejpam-6009	152	60	set	set	NOUN
ejpam-6009	152	61	u	u	NOUN
ejpam-6009	152	62	of	of	ADP
ejpam-6009	152	63	x	x	PUNCT
ejpam-6009	152	64	containing	contain	VERB
ejpam-6009	152	65	x	x	PUNCT
ejpam-6009	152	66	such	such	ADJ
ejpam-6009	152	67	that	that	SCONJ
ejpam-6009	152	68	u	u	PROPN
ejpam-6009	152	69	⊆	⊆	NUM
ejpam-6009	152	70	f−(k	f−(k	PROPN
ejpam-6009	152	71	)	)	PUNCT
ejpam-6009	152	72	.	.	PUNCT
ejpam-6009	153	1	a	a	DET
ejpam-6009	153	2	multifunction	multifunction	NOUN
ejpam-6009	153	3	f	f	NOUN
ejpam-6009	153	4	:	:	PUNCT
ejpam-6009	153	5	(	(	PUNCT
ejpam-6009	153	6	x	x	NOUN
ejpam-6009	153	7	,	,	PUNCT
ejpam-6009	153	8	τ1	τ1	NOUN
ejpam-6009	153	9	,	,	PUNCT
ejpam-6009	153	10	τ2	τ2	NOUN
ejpam-6009	153	11	)	)	PUNCT
ejpam-6009	153	12	→	→	SYM
ejpam-6009	153	13	(	(	PUNCT
ejpam-6009	153	14	y	y	PROPN
ejpam-6009	153	15	,	,	PUNCT
ejpam-6009	153	16	σ1	σ1	PROPN
ejpam-6009	153	17	,	,	PUNCT
ejpam-6009	153	18	σ2	σ2	PROPN
ejpam-6009	153	19	)	)	PUNCT
ejpam-6009	153	20	is	be	AUX
ejpam-6009	153	21	called	call	VERB
ejpam-6009	153	22	lower	low	ADJ
ejpam-6009	153	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	153	24	,	,	PUNCT
ejpam-6009	153	25	τ2)p	τ2)p	ADJ
ejpam-6009	153	26	-	-	ADJ
ejpam-6009	153	27	continuous	continuous	ADJ
ejpam-6009	153	28	if	if	SCONJ
ejpam-6009	153	29	f	f	PROPN
ejpam-6009	153	30	is	be	AUX
ejpam-6009	153	31	lower	low	ADJ
ejpam-6009	153	32	contra(τ1	contra(τ1	NOUN
ejpam-6009	153	33	,	,	PUNCT
ejpam-6009	153	34	τ2)p	τ2)p	ADJ
ejpam-6009	153	35	-	-	ADJ
ejpam-6009	153	36	continuous	continuous	ADJ
ejpam-6009	153	37	at	at	ADP
ejpam-6009	153	38	each	each	DET
ejpam-6009	153	39	point	point	NOUN
ejpam-6009	153	40	x	x	PUNCT
ejpam-6009	153	41	of	of	ADP
ejpam-6009	153	42	x.	x.	PROPN
ejpam-6009	153	43	theorem	theorem	VERB
ejpam-6009	153	44	2	2	NUM
ejpam-6009	153	45	.	.	X
ejpam-6009	153	46	for	for	ADP
ejpam-6009	153	47	a	a	DET
ejpam-6009	153	48	multifunction	multifunction	NOUN
ejpam-6009	153	49	f	f	NOUN
ejpam-6009	153	50	:	:	PUNCT
ejpam-6009	153	51	(	(	PUNCT
ejpam-6009	153	52	x	x	NOUN
ejpam-6009	153	53	,	,	PUNCT
ejpam-6009	153	54	τ1	τ1	NOUN
ejpam-6009	153	55	,	,	PUNCT
ejpam-6009	153	56	τ2	τ2	NOUN
ejpam-6009	153	57	)	)	PUNCT
ejpam-6009	153	58	→	→	SYM
ejpam-6009	153	59	(	(	PUNCT
ejpam-6009	153	60	y	y	PROPN
ejpam-6009	153	61	,	,	PUNCT
ejpam-6009	153	62	σ1	σ1	PROPN
ejpam-6009	153	63	,	,	PUNCT
ejpam-6009	153	64	σ2	σ2	NOUN
ejpam-6009	153	65	)	)	PUNCT
ejpam-6009	153	66	,	,	PUNCT
ejpam-6009	153	67	the	the	DET
ejpam-6009	153	68	following	follow	VERB
ejpam-6009	153	69	properties	property	NOUN
ejpam-6009	153	70	are	be	AUX
ejpam-6009	153	71	equivalent	equivalent	ADJ
ejpam-6009	153	72	:	:	PUNCT
ejpam-6009	153	73	(	(	PUNCT
ejpam-6009	153	74	1	1	X
ejpam-6009	153	75	)	)	PUNCT
ejpam-6009	153	76	f	f	PROPN
ejpam-6009	153	77	is	be	AUX
ejpam-6009	153	78	lower	low	ADJ
ejpam-6009	153	79	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	153	80	,	,	PUNCT
ejpam-6009	153	81	τ2)p	τ2)p	ADJ
ejpam-6009	153	82	-	-	NOUN
ejpam-6009	153	83	continuous	continuous	ADJ
ejpam-6009	153	84	;	;	PUNCT
ejpam-6009	153	85	(	(	PUNCT
ejpam-6009	153	86	2	2	X
ejpam-6009	153	87	)	)	PUNCT
ejpam-6009	153	88	f−(k	f−(k	PROPN
ejpam-6009	153	89	)	)	PUNCT
ejpam-6009	153	90	is	be	AUX
ejpam-6009	153	91	(	(	PUNCT
ejpam-6009	153	92	τ1	τ1	NOUN
ejpam-6009	153	93	,	,	PUNCT
ejpam-6009	153	94	τ2)p	τ2)p	NOUN
ejpam-6009	153	95	-	-	PUNCT
ejpam-6009	153	96	open	open	ADJ
ejpam-6009	153	97	in	in	ADP
ejpam-6009	153	98	x	x	PUNCT
ejpam-6009	153	99	for	for	ADP
ejpam-6009	153	100	every	every	DET
ejpam-6009	153	101	σ1σ2	σ1σ2	NUM
ejpam-6009	153	102	-	-	PUNCT
ejpam-6009	153	103	closed	closed	ADJ
ejpam-6009	153	104	set	set	NOUN
ejpam-6009	153	105	k	k	PROPN
ejpam-6009	153	106	of	of	ADP
ejpam-6009	153	107	y	y	PROPN
ejpam-6009	153	108	;	;	PUNCT
ejpam-6009	153	109	(	(	PUNCT
ejpam-6009	153	110	3	3	X
ejpam-6009	153	111	)	)	PUNCT
ejpam-6009	153	112	f+(v	f+(v	NOUN
ejpam-6009	153	113	)	)	PUNCT
ejpam-6009	154	1	is	be	AUX
ejpam-6009	154	2	(	(	PUNCT
ejpam-6009	154	3	τ1	τ1	NOUN
ejpam-6009	154	4	,	,	PUNCT
ejpam-6009	154	5	τ2)p	τ2)p	NOUN
ejpam-6009	154	6	-	-	PUNCT
ejpam-6009	154	7	closed	closed	ADJ
ejpam-6009	154	8	in	in	ADP
ejpam-6009	154	9	x	x	PUNCT
ejpam-6009	154	10	for	for	ADP
ejpam-6009	154	11	every	every	DET
ejpam-6009	154	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	154	13	-	-	ADJ
ejpam-6009	154	14	open	open	ADJ
ejpam-6009	154	15	set	set	NOUN
ejpam-6009	154	16	v	v	NOUN
ejpam-6009	154	17	of	of	ADP
ejpam-6009	154	18	y	y	PROPN
ejpam-6009	154	19	;	;	PUNCT
ejpam-6009	154	20	(	(	PUNCT
ejpam-6009	154	21	4	4	X
ejpam-6009	154	22	)	)	PUNCT
ejpam-6009	154	23	for	for	ADP
ejpam-6009	154	24	each	each	DET
ejpam-6009	154	25	x	x	SYM
ejpam-6009	154	26	∈	∈	PROPN
ejpam-6009	154	27	x	x	X
ejpam-6009	154	28	and	and	CCONJ
ejpam-6009	154	29	each	each	DET
ejpam-6009	154	30	σ1σ2	σ1σ2	VERB
ejpam-6009	154	31	-	-	PUNCT
ejpam-6009	154	32	closed	closed	ADJ
ejpam-6009	154	33	set	set	NOUN
ejpam-6009	154	34	k	k	PROPN
ejpam-6009	154	35	of	of	ADP
ejpam-6009	154	36	y	y	PRON
ejpam-6009	154	37	such	such	ADJ
ejpam-6009	154	38	that	that	SCONJ
ejpam-6009	154	39	f	f	PROPN
ejpam-6009	154	40	(	(	PUNCT
ejpam-6009	154	41	x)∩k	x)∩k	PROPN
ejpam-6009	154	42	̸=	̸=	PROPN
ejpam-6009	154	43	∅	∅	NOUN
ejpam-6009	154	44	,	,	PUNCT
ejpam-6009	154	45	there	there	PRON
ejpam-6009	154	46	exists	exist	VERB
ejpam-6009	154	47	a	a	DET
ejpam-6009	154	48	(	(	PUNCT
ejpam-6009	154	49	τ1	τ1	NOUN
ejpam-6009	154	50	,	,	PUNCT
ejpam-6009	154	51	τ2)p	τ2)p	ADJ
ejpam-6009	154	52	-	-	PUNCT
ejpam-6009	154	53	open	open	ADJ
ejpam-6009	154	54	set	set	NOUN
ejpam-6009	154	55	u	u	NOUN
ejpam-6009	154	56	of	of	ADP
ejpam-6009	154	57	x	x	PUNCT
ejpam-6009	154	58	containing	contain	VERB
ejpam-6009	154	59	x	x	PUNCT
ejpam-6009	154	60	such	such	ADJ
ejpam-6009	154	61	that	that	SCONJ
ejpam-6009	154	62	if	if	SCONJ
ejpam-6009	154	63	y	y	PROPN
ejpam-6009	154	64	∈	∈	PROPN
ejpam-6009	154	65	u	u	PROPN
ejpam-6009	154	66	,	,	PUNCT
ejpam-6009	154	67	then	then	ADV
ejpam-6009	154	68	f	f	PROPN
ejpam-6009	154	69	(	(	PUNCT
ejpam-6009	154	70	y	y	NOUN
ejpam-6009	154	71	)	)	PUNCT
ejpam-6009	154	72	∩k	∩k	NOUN
ejpam-6009	154	73	̸=	̸=	PROPN
ejpam-6009	154	74	∅.	∅.	ADP
ejpam-6009	154	75	proof	proof	NOUN
ejpam-6009	154	76	.	.	PUNCT
ejpam-6009	155	1	the	the	DET
ejpam-6009	155	2	proof	proof	NOUN
ejpam-6009	155	3	is	be	AUX
ejpam-6009	155	4	similar	similar	ADJ
ejpam-6009	155	5	to	to	ADP
ejpam-6009	155	6	that	that	PRON
ejpam-6009	155	7	of	of	ADP
ejpam-6009	155	8	theorem	theorem	NOUN
ejpam-6009	155	9	1	1	NUM
ejpam-6009	155	10	.	.	X
ejpam-6009	155	11	recall	recall	VERB
ejpam-6009	155	12	that	that	SCONJ
ejpam-6009	155	13	a	a	DET
ejpam-6009	155	14	bitopological	bitopological	ADJ
ejpam-6009	155	15	space	space	NOUN
ejpam-6009	155	16	(	(	PUNCT
ejpam-6009	155	17	x	x	NOUN
ejpam-6009	155	18	,	,	PUNCT
ejpam-6009	155	19	τ1	τ1	NOUN
ejpam-6009	155	20	,	,	PUNCT
ejpam-6009	155	21	τ2	τ2	NOUN
ejpam-6009	155	22	)	)	PUNCT
ejpam-6009	155	23	is	be	AUX
ejpam-6009	155	24	said	say	VERB
ejpam-6009	155	25	to	to	PART
ejpam-6009	155	26	be	be	AUX
ejpam-6009	155	27	(	(	PUNCT
ejpam-6009	155	28	τ1	τ1	NOUN
ejpam-6009	155	29	,	,	PUNCT
ejpam-6009	155	30	τ2)s	τ2)s	NOUN
ejpam-6009	155	31	-	-	PUNCT
ejpam-6009	155	32	regular	regular	ADJ
ejpam-6009	155	33	[	[	X
ejpam-6009	155	34	6	6	NUM
ejpam-6009	155	35	]	]	X
ejpam-6009	155	36	if	if	SCONJ
ejpam-6009	155	37	for	for	ADP
ejpam-6009	155	38	each	each	DET
ejpam-6009	155	39	(	(	PUNCT
ejpam-6009	155	40	τ1	τ1	NOUN
ejpam-6009	155	41	,	,	PUNCT
ejpam-6009	155	42	τ2)s	τ2)s	NOUN
ejpam-6009	155	43	-	-	PUNCT
ejpam-6009	155	44	closed	close	VERB
ejpam-6009	155	45	set	set	VERB
ejpam-6009	155	46	f	f	NOUN
ejpam-6009	155	47	and	and	CCONJ
ejpam-6009	155	48	each	each	DET
ejpam-6009	155	49	x	x	PROPN
ejpam-6009	155	50	̸∈	̸∈	PROPN
ejpam-6009	155	51	f	f	PROPN
ejpam-6009	155	52	,	,	PUNCT
ejpam-6009	155	53	there	there	PRON
ejpam-6009	155	54	exist	exist	VERB
ejpam-6009	155	55	disjoint	disjoint	NOUN
ejpam-6009	155	56	(	(	PUNCT
ejpam-6009	155	57	τ1	τ1	NOUN
ejpam-6009	155	58	,	,	PUNCT
ejpam-6009	155	59	τ2)s	τ2)s	NOUN
ejpam-6009	155	60	-	-	PUNCT
ejpam-6009	155	61	open	open	ADJ
ejpam-6009	155	62	sets	set	VERB
ejpam-6009	155	63	u	u	NOUN
ejpam-6009	155	64	and	and	CCONJ
ejpam-6009	155	65	v	v	ADP
ejpam-6009	155	66	such	such	ADJ
ejpam-6009	155	67	that	that	SCONJ
ejpam-6009	155	68	x	x	SYM
ejpam-6009	155	69	∈	∈	PROPN
ejpam-6009	155	70	u	u	NOUN
ejpam-6009	155	71	and	and	CCONJ
ejpam-6009	155	72	f	f	PROPN
ejpam-6009	155	73	⊆	⊆	NUM
ejpam-6009	155	74	v	v	NOUN
ejpam-6009	155	75	.	.	PUNCT
ejpam-6009	156	1	lemma	lemma	PROPN
ejpam-6009	156	2	4	4	NUM
ejpam-6009	156	3	.	.	PUNCT
ejpam-6009	157	1	[	[	X
ejpam-6009	157	2	81	81	NUM
ejpam-6009	157	3	]	]	PUNCT
ejpam-6009	157	4	let	let	VERB
ejpam-6009	157	5	(	(	PUNCT
ejpam-6009	157	6	x	x	NOUN
ejpam-6009	157	7	,	,	PUNCT
ejpam-6009	157	8	τ1	τ1	NOUN
ejpam-6009	157	9	,	,	PUNCT
ejpam-6009	157	10	τ2	τ2	PROPN
ejpam-6009	157	11	)	)	PUNCT
ejpam-6009	157	12	be	be	VERB
ejpam-6009	157	13	a	a	DET
ejpam-6009	157	14	(	(	PUNCT
ejpam-6009	157	15	τ1	τ1	NOUN
ejpam-6009	157	16	,	,	PUNCT
ejpam-6009	157	17	τ2)s	τ2)s	NOUN
ejpam-6009	157	18	-	-	PUNCT
ejpam-6009	157	19	regular	regular	ADJ
ejpam-6009	157	20	space	space	NOUN
ejpam-6009	157	21	.	.	PUNCT
ejpam-6009	158	1	then	then	ADV
ejpam-6009	158	2	,	,	PUNCT
ejpam-6009	158	3	the	the	DET
ejpam-6009	158	4	following	follow	VERB
ejpam-6009	158	5	properties	property	NOUN
ejpam-6009	158	6	hold	hold	VERB
ejpam-6009	158	7	:	:	PUNCT
ejpam-6009	158	8	(	(	PUNCT
ejpam-6009	158	9	1	1	X
ejpam-6009	158	10	)	)	PUNCT
ejpam-6009	158	11	τ1τ2	τ1τ2	NOUN
ejpam-6009	158	12	-	-	NUM
ejpam-6009	158	13	cl(a	cl(a	NUM
ejpam-6009	158	14	)	)	PUNCT
ejpam-6009	158	15	=	=	PUNCT
ejpam-6009	159	1	τ1τ2	τ1τ2	PROPN
ejpam-6009	159	2	-	-	ADJ
ejpam-6009	159	3	δ	δ	NOUN
ejpam-6009	159	4	-	-	PUNCT
ejpam-6009	159	5	cl(a	cl(a	NUM
ejpam-6009	159	6	)	)	PUNCT
ejpam-6009	159	7	for	for	ADP
ejpam-6009	159	8	every	every	DET
ejpam-6009	159	9	subset	subset	NOUN
ejpam-6009	159	10	a	a	PRON
ejpam-6009	159	11	of	of	ADP
ejpam-6009	159	12	x	x	PRON
ejpam-6009	159	13	;	;	PUNCT
ejpam-6009	159	14	(	(	PUNCT
ejpam-6009	159	15	2	2	X
ejpam-6009	159	16	)	)	PUNCT
ejpam-6009	159	17	every	every	DET
ejpam-6009	159	18	τ1τ2	τ1τ2	NOUN
ejpam-6009	159	19	-	-	ADJ
ejpam-6009	159	20	open	open	ADJ
ejpam-6009	159	21	set	set	NOUN
ejpam-6009	159	22	is	be	AUX
ejpam-6009	159	23	τ1τ2	τ1τ2	ADJ
ejpam-6009	159	24	-	-	ADJ
ejpam-6009	159	25	δ	δ	NOUN
ejpam-6009	159	26	-	-	ADJ
ejpam-6009	159	27	open	open	ADJ
ejpam-6009	159	28	.	.	PUNCT
ejpam-6009	160	1	theorem	theorem	NOUN
ejpam-6009	160	2	3	3	NUM
ejpam-6009	160	3	.	.	X
ejpam-6009	160	4	for	for	ADP
ejpam-6009	160	5	a	a	DET
ejpam-6009	160	6	multifunction	multifunction	NOUN
ejpam-6009	161	1	f	f	NOUN
ejpam-6009	161	2	:	:	PUNCT
ejpam-6009	161	3	(	(	PUNCT
ejpam-6009	161	4	x	x	NOUN
ejpam-6009	161	5	,	,	PUNCT
ejpam-6009	161	6	τ1	τ1	NOUN
ejpam-6009	161	7	,	,	PUNCT
ejpam-6009	161	8	τ2	τ2	NOUN
ejpam-6009	161	9	)	)	PUNCT
ejpam-6009	161	10	→	→	SYM
ejpam-6009	161	11	(	(	PUNCT
ejpam-6009	161	12	y	y	PROPN
ejpam-6009	161	13	,	,	PUNCT
ejpam-6009	161	14	σ1	σ1	PROPN
ejpam-6009	161	15	,	,	PUNCT
ejpam-6009	161	16	σ2	σ2	NOUN
ejpam-6009	161	17	)	)	PUNCT
ejpam-6009	161	18	,	,	PUNCT
ejpam-6009	161	19	where	where	SCONJ
ejpam-6009	161	20	(	(	PUNCT
ejpam-6009	161	21	y	y	PROPN
ejpam-6009	161	22	,	,	PUNCT
ejpam-6009	161	23	σ1	σ1	PROPN
ejpam-6009	161	24	,	,	PUNCT
ejpam-6009	161	25	σ2	σ2	PROPN
ejpam-6009	161	26	)	)	PUNCT
ejpam-6009	161	27	is	be	AUX
ejpam-6009	161	28	(	(	PUNCT
ejpam-6009	161	29	σ1	σ1	PROPN
ejpam-6009	161	30	,	,	PUNCT
ejpam-6009	161	31	σ2)sregular	σ2)sregular	PROPN
ejpam-6009	161	32	,	,	PUNCT
ejpam-6009	161	33	the	the	DET
ejpam-6009	161	34	following	follow	VERB
ejpam-6009	161	35	properties	property	NOUN
ejpam-6009	161	36	are	be	AUX
ejpam-6009	161	37	equivalent	equivalent	ADJ
ejpam-6009	161	38	:	:	PUNCT
ejpam-6009	161	39	(	(	PUNCT
ejpam-6009	161	40	1	1	X
ejpam-6009	161	41	)	)	PUNCT
ejpam-6009	161	42	f	f	PROPN
ejpam-6009	161	43	is	be	AUX
ejpam-6009	161	44	upper	upper	ADJ
ejpam-6009	161	45	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	161	46	,	,	PUNCT
ejpam-6009	161	47	τ2)p	τ2)p	ADJ
ejpam-6009	161	48	-	-	NOUN
ejpam-6009	161	49	continuous	continuous	ADJ
ejpam-6009	161	50	;	;	PUNCT
ejpam-6009	161	51	(	(	PUNCT
ejpam-6009	161	52	2	2	X
ejpam-6009	161	53	)	)	PUNCT
ejpam-6009	161	54	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	161	55	-	-	PUNCT
ejpam-6009	161	56	δ	δ	NOUN
ejpam-6009	161	57	-	-	NOUN
ejpam-6009	161	58	cl(b	cl(b	NOUN
ejpam-6009	161	59	)	)	PUNCT
ejpam-6009	161	60	)	)	PUNCT
ejpam-6009	162	1	is	be	AUX
ejpam-6009	162	2	(	(	PUNCT
ejpam-6009	162	3	τ1	τ1	NOUN
ejpam-6009	162	4	,	,	PUNCT
ejpam-6009	162	5	τ2)p	τ2)p	NOUN
ejpam-6009	162	6	-	-	PUNCT
ejpam-6009	162	7	open	open	ADJ
ejpam-6009	162	8	in	in	ADP
ejpam-6009	162	9	x	x	PUNCT
ejpam-6009	162	10	for	for	ADP
ejpam-6009	162	11	every	every	DET
ejpam-6009	162	12	subset	subset	NOUN
ejpam-6009	162	13	b	b	PROPN
ejpam-6009	162	14	of	of	ADP
ejpam-6009	162	15	y	y	PROPN
ejpam-6009	162	16	;	;	PUNCT
ejpam-6009	162	17	(	(	PUNCT
ejpam-6009	162	18	3	3	X
ejpam-6009	162	19	)	)	PUNCT
ejpam-6009	162	20	f+(k	f+(k	NUM
ejpam-6009	162	21	)	)	PUNCT
ejpam-6009	162	22	is	be	AUX
ejpam-6009	162	23	(	(	PUNCT
ejpam-6009	162	24	τ1	τ1	NOUN
ejpam-6009	162	25	,	,	PUNCT
ejpam-6009	162	26	τ2)p	τ2)p	NOUN
ejpam-6009	162	27	-	-	PUNCT
ejpam-6009	162	28	open	open	ADJ
ejpam-6009	162	29	in	in	ADP
ejpam-6009	162	30	x	x	PUNCT
ejpam-6009	162	31	for	for	ADP
ejpam-6009	162	32	every	every	DET
ejpam-6009	162	33	σ1σ2	σ1σ2	NUM
ejpam-6009	162	34	-	-	PUNCT
ejpam-6009	162	35	δ	δ	NOUN
ejpam-6009	162	36	-	-	PUNCT
ejpam-6009	162	37	closed	close	VERB
ejpam-6009	162	38	set	set	ADJ
ejpam-6009	162	39	k	k	PROPN
ejpam-6009	162	40	of	of	ADP
ejpam-6009	162	41	y	y	PROPN
ejpam-6009	162	42	;	;	PUNCT
ejpam-6009	162	43	(	(	PUNCT
ejpam-6009	162	44	4	4	X
ejpam-6009	162	45	)	)	PUNCT
ejpam-6009	162	46	f−(v	f−(v	NOUN
ejpam-6009	162	47	)	)	PUNCT
ejpam-6009	162	48	is	be	AUX
ejpam-6009	162	49	(	(	PUNCT
ejpam-6009	162	50	τ1	τ1	NOUN
ejpam-6009	162	51	,	,	PUNCT
ejpam-6009	162	52	τ2)p	τ2)p	NOUN
ejpam-6009	162	53	-	-	PUNCT
ejpam-6009	162	54	closed	closed	ADJ
ejpam-6009	162	55	in	in	ADP
ejpam-6009	162	56	x	x	PUNCT
ejpam-6009	162	57	for	for	ADP
ejpam-6009	162	58	every	every	DET
ejpam-6009	162	59	σ1σ2	σ1σ2	NUM
ejpam-6009	162	60	-	-	PUNCT
ejpam-6009	162	61	δ	δ	NOUN
ejpam-6009	162	62	-	-	ADJ
ejpam-6009	162	63	open	open	ADJ
ejpam-6009	162	64	set	set	VERB
ejpam-6009	162	65	v	v	NOUN
ejpam-6009	162	66	of	of	ADP
ejpam-6009	162	67	y	y	PROPN
ejpam-6009	162	68	.	.	PUNCT
ejpam-6009	163	1	c.	c.	PROPN
ejpam-6009	163	2	viriyapong	viriyapong	PROPN
ejpam-6009	163	3	,	,	PUNCT
ejpam-6009	163	4	a.	a.	PROPN
ejpam-6009	163	5	sama	sama	PROPN
ejpam-6009	163	6	-	-	PUNCT
ejpam-6009	163	7	ae	ae	PROPN
ejpam-6009	163	8	,	,	PUNCT
ejpam-6009	163	9	c.	c.	PROPN
ejpam-6009	163	10	boonpok	boonpok	PROPN
ejpam-6009	163	11	/	/	SYM
ejpam-6009	163	12	eur	eur	PROPN
ejpam-6009	163	13	.	.	PUNCT
ejpam-6009	164	1	j.	j.	PROPN
ejpam-6009	164	2	pure	pure	PROPN
ejpam-6009	164	3	appl	appl	PROPN
ejpam-6009	164	4	.	.	PROPN
ejpam-6009	164	5	math	math	PROPN
ejpam-6009	164	6	,	,	PUNCT
ejpam-6009	164	7	18	18	NUM
ejpam-6009	164	8	(	(	PUNCT
ejpam-6009	164	9	2	2	NUM
ejpam-6009	164	10	)	)	PUNCT
ejpam-6009	164	11	(	(	PUNCT
ejpam-6009	164	12	2025	2025	NUM
ejpam-6009	164	13	)	)	PUNCT
ejpam-6009	164	14	,	,	PUNCT
ejpam-6009	164	15	6009	6009	NUM
ejpam-6009	164	16	7	7	NUM
ejpam-6009	164	17	of	of	ADP
ejpam-6009	164	18	18	18	NUM
ejpam-6009	164	19	proof	proof	NOUN
ejpam-6009	164	20	.	.	PUNCT
ejpam-6009	165	1	(	(	PUNCT
ejpam-6009	165	2	1	1	X
ejpam-6009	165	3	)	)	PUNCT
ejpam-6009	165	4	⇒	⇒	NOUN
ejpam-6009	165	5	(	(	PUNCT
ejpam-6009	165	6	2	2	NUM
ejpam-6009	165	7	):	):	PUNCT
ejpam-6009	165	8	let	let	VERB
ejpam-6009	165	9	b	b	X
ejpam-6009	165	10	be	be	AUX
ejpam-6009	165	11	any	any	DET
ejpam-6009	165	12	subset	subset	NOUN
ejpam-6009	165	13	of	of	ADP
ejpam-6009	165	14	y	y	PROPN
ejpam-6009	165	15	.	.	PUNCT
ejpam-6009	166	1	then	then	ADV
ejpam-6009	166	2	,	,	PUNCT
ejpam-6009	166	3	σ1σ2	σ1σ2	PROPN
ejpam-6009	166	4	-	-	PUNCT
ejpam-6009	166	5	δ	δ	NOUN
ejpam-6009	166	6	-	-	NOUN
ejpam-6009	166	7	cl(b	cl(b	NOUN
ejpam-6009	166	8	)	)	PUNCT
ejpam-6009	166	9	is	be	AUX
ejpam-6009	166	10	a	a	DET
ejpam-6009	166	11	σ1σ2	σ1σ2	NUM
ejpam-6009	166	12	-	-	PUNCT
ejpam-6009	166	13	closed	closed	ADJ
ejpam-6009	166	14	set	set	NOUN
ejpam-6009	166	15	of	of	ADP
ejpam-6009	166	16	y	y	PROPN
ejpam-6009	166	17	and	and	CCONJ
ejpam-6009	166	18	by	by	ADP
ejpam-6009	166	19	theorem	theorem	ADJ
ejpam-6009	166	20	1	1	NUM
ejpam-6009	166	21	,	,	PUNCT
ejpam-6009	166	22	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-6009	166	23	-	-	PUNCT
ejpam-6009	166	24	δ	δ	NOUN
ejpam-6009	166	25	-	-	NOUN
ejpam-6009	166	26	cl(b	cl(b	NOUN
ejpam-6009	166	27	)	)	PUNCT
ejpam-6009	166	28	)	)	PUNCT
ejpam-6009	167	1	is	be	AUX
ejpam-6009	167	2	(	(	PUNCT
ejpam-6009	167	3	τ1	τ1	NOUN
ejpam-6009	167	4	,	,	PUNCT
ejpam-6009	167	5	τ2)p	τ2)p	NOUN
ejpam-6009	167	6	-	-	PUNCT
ejpam-6009	167	7	open	open	ADJ
ejpam-6009	167	8	in	in	ADP
ejpam-6009	167	9	x.	x.	NOUN
ejpam-6009	167	10	(	(	PUNCT
ejpam-6009	167	11	2	2	NUM
ejpam-6009	167	12	)	)	PUNCT
ejpam-6009	167	13	⇒	⇒	NOUN
ejpam-6009	167	14	(	(	PUNCT
ejpam-6009	167	15	3	3	NUM
ejpam-6009	167	16	):	):	PUNCT
ejpam-6009	167	17	let	let	VERB
ejpam-6009	167	18	k	k	PRON
ejpam-6009	167	19	be	be	AUX
ejpam-6009	167	20	any	any	DET
ejpam-6009	167	21	σ1σ2	σ1σ2	NUM
ejpam-6009	167	22	-	-	PUNCT
ejpam-6009	167	23	δ	δ	NOUN
ejpam-6009	167	24	-	-	PUNCT
ejpam-6009	167	25	closed	closed	ADJ
ejpam-6009	167	26	set	set	NOUN
ejpam-6009	167	27	of	of	ADP
ejpam-6009	167	28	y	y	PROPN
ejpam-6009	167	29	.	.	PUNCT
ejpam-6009	168	1	then	then	ADV
ejpam-6009	168	2	,	,	PUNCT
ejpam-6009	168	3	σ1σ2	σ1σ2	PROPN
ejpam-6009	168	4	-	-	PUNCT
ejpam-6009	168	5	δ	δ	NOUN
ejpam-6009	168	6	-	-	NOUN
ejpam-6009	168	7	cl(k	cl(k	NOUN
ejpam-6009	168	8	)	)	PUNCT
ejpam-6009	169	1	=	=	VERB
ejpam-6009	169	2	k.	k.	PROPN
ejpam-6009	169	3	by	by	ADP
ejpam-6009	169	4	(	(	PUNCT
ejpam-6009	169	5	2	2	NUM
ejpam-6009	169	6	)	)	PUNCT
ejpam-6009	169	7	,	,	PUNCT
ejpam-6009	169	8	f+(k	f+(k	X
ejpam-6009	169	9	)	)	PUNCT
ejpam-6009	169	10	is	be	AUX
ejpam-6009	169	11	(	(	PUNCT
ejpam-6009	169	12	τ1	τ1	NOUN
ejpam-6009	169	13	,	,	PUNCT
ejpam-6009	169	14	τ2)p	τ2)p	NOUN
ejpam-6009	169	15	-	-	PUNCT
ejpam-6009	169	16	open	open	ADJ
ejpam-6009	169	17	in	in	ADP
ejpam-6009	169	18	x.	x.	NOUN
ejpam-6009	169	19	(	(	PUNCT
ejpam-6009	169	20	3	3	NUM
ejpam-6009	169	21	)	)	PUNCT
ejpam-6009	169	22	⇒	⇒	NOUN
ejpam-6009	169	23	(	(	PUNCT
ejpam-6009	169	24	4	4	NUM
ejpam-6009	169	25	):	):	PUNCT
ejpam-6009	169	26	let	let	VERB
ejpam-6009	169	27	v	v	PART
ejpam-6009	169	28	be	be	AUX
ejpam-6009	169	29	any	any	DET
ejpam-6009	169	30	σ1σ2	σ1σ2	NOUN
ejpam-6009	169	31	-	-	PUNCT
ejpam-6009	169	32	δ	δ	NOUN
ejpam-6009	169	33	-	-	ADJ
ejpam-6009	169	34	open	open	ADJ
ejpam-6009	169	35	set	set	NOUN
ejpam-6009	169	36	of	of	ADP
ejpam-6009	169	37	y	y	PROPN
ejpam-6009	169	38	.	.	PUNCT
ejpam-6009	170	1	then	then	ADV
ejpam-6009	170	2	,	,	PUNCT
ejpam-6009	170	3	y	y	PROPN
ejpam-6009	170	4	−v	−v	NOUN
ejpam-6009	170	5	is	be	AUX
ejpam-6009	170	6	σ1σ2	σ1σ2	NOUN
ejpam-6009	170	7	-	-	PUNCT
ejpam-6009	170	8	δ	δ	NOUN
ejpam-6009	170	9	-	-	PUNCT
ejpam-6009	170	10	closed	closed	ADJ
ejpam-6009	170	11	in	in	ADP
ejpam-6009	170	12	y	y	PROPN
ejpam-6009	170	13	.	.	PUNCT
ejpam-6009	171	1	by	by	ADP
ejpam-6009	171	2	(	(	PUNCT
ejpam-6009	171	3	3	3	NUM
ejpam-6009	171	4	)	)	PUNCT
ejpam-6009	171	5	,	,	PUNCT
ejpam-6009	171	6	f+(y	f+(y	PROPN
ejpam-6009	171	7	−	−	PROPN
ejpam-6009	171	8	v	v	NOUN
ejpam-6009	171	9	)	)	PUNCT
ejpam-6009	171	10	=	=	PUNCT
ejpam-6009	171	11	x	x	SYM
ejpam-6009	171	12	−	−	PROPN
ejpam-6009	171	13	f−(v	f−(v	PROPN
ejpam-6009	171	14	)	)	PUNCT
ejpam-6009	171	15	is	be	AUX
ejpam-6009	171	16	(	(	PUNCT
ejpam-6009	171	17	τ1	τ1	NOUN
ejpam-6009	171	18	,	,	PUNCT
ejpam-6009	171	19	τ2)p	τ2)p	NOUN
ejpam-6009	171	20	-	-	PUNCT
ejpam-6009	171	21	open	open	ADJ
ejpam-6009	171	22	in	in	ADP
ejpam-6009	171	23	x.	x.	PROPN
ejpam-6009	171	24	thus	thus	ADV
ejpam-6009	171	25	,	,	PUNCT
ejpam-6009	171	26	f−(v	f−(v	ADJ
ejpam-6009	171	27	)	)	PUNCT
ejpam-6009	171	28	is	be	AUX
ejpam-6009	171	29	(	(	PUNCT
ejpam-6009	171	30	τ1	τ1	NOUN
ejpam-6009	171	31	,	,	PUNCT
ejpam-6009	171	32	τ2)p	τ2)p	NOUN
ejpam-6009	171	33	-	-	PUNCT
ejpam-6009	171	34	closed	closed	ADJ
ejpam-6009	171	35	in	in	ADP
ejpam-6009	171	36	x.	x.	NOUN
ejpam-6009	171	37	(	(	PUNCT
ejpam-6009	171	38	4	4	NUM
ejpam-6009	171	39	)	)	PUNCT
ejpam-6009	171	40	⇒	⇒	NOUN
ejpam-6009	171	41	(	(	PUNCT
ejpam-6009	171	42	1	1	NUM
ejpam-6009	171	43	):	):	PUNCT
ejpam-6009	171	44	let	let	VERB
ejpam-6009	171	45	v	v	PART
ejpam-6009	171	46	be	be	AUX
ejpam-6009	171	47	any	any	DET
ejpam-6009	171	48	σ1σ2	σ1σ2	NOUN
ejpam-6009	171	49	-	-	ADJ
ejpam-6009	171	50	open	open	ADJ
ejpam-6009	171	51	set	set	NOUN
ejpam-6009	171	52	of	of	ADP
ejpam-6009	171	53	y	y	PROPN
ejpam-6009	171	54	.	.	PUNCT
ejpam-6009	172	1	since	since	SCONJ
ejpam-6009	172	2	(	(	PUNCT
ejpam-6009	172	3	y	y	PROPN
ejpam-6009	172	4	,	,	PUNCT
ejpam-6009	172	5	σ1	σ1	PROPN
ejpam-6009	172	6	,	,	PUNCT
ejpam-6009	172	7	σ2	σ2	PROPN
ejpam-6009	172	8	)	)	PUNCT
ejpam-6009	172	9	is	be	AUX
ejpam-6009	172	10	(	(	PUNCT
ejpam-6009	172	11	σ1	σ1	PROPN
ejpam-6009	172	12	,	,	PUNCT
ejpam-6009	172	13	σ2)s	σ2)s	NOUN
ejpam-6009	172	14	-	-	PUNCT
ejpam-6009	172	15	regular	regular	ADJ
ejpam-6009	172	16	,	,	PUNCT
ejpam-6009	172	17	by	by	ADP
ejpam-6009	172	18	lemma	lemma	PROPN
ejpam-6009	172	19	4	4	NUM
ejpam-6009	172	20	we	we	PRON
ejpam-6009	172	21	have	have	VERB
ejpam-6009	172	22	v	v	NOUN
ejpam-6009	172	23	is	be	AUX
ejpam-6009	172	24	σ1σ2	σ1σ2	NOUN
ejpam-6009	172	25	-	-	PUNCT
ejpam-6009	172	26	δ	δ	NOUN
ejpam-6009	172	27	-	-	NOUN
ejpam-6009	172	28	open	open	ADJ
ejpam-6009	172	29	in	in	ADP
ejpam-6009	172	30	y	y	PROPN
ejpam-6009	172	31	.	.	PUNCT
ejpam-6009	173	1	by	by	ADP
ejpam-6009	173	2	(	(	PUNCT
ejpam-6009	173	3	4	4	NUM
ejpam-6009	173	4	)	)	PUNCT
ejpam-6009	173	5	,	,	PUNCT
ejpam-6009	173	6	f−(v	f−(v	ADJ
ejpam-6009	173	7	)	)	PUNCT
ejpam-6009	173	8	is	be	AUX
ejpam-6009	173	9	(	(	PUNCT
ejpam-6009	173	10	τ1	τ1	NOUN
ejpam-6009	173	11	,	,	PUNCT
ejpam-6009	173	12	τ2)p	τ2)p	NOUN
ejpam-6009	173	13	-	-	PUNCT
ejpam-6009	173	14	closed	closed	ADJ
ejpam-6009	173	15	in	in	ADP
ejpam-6009	173	16	x	x	X
ejpam-6009	173	17	and	and	CCONJ
ejpam-6009	173	18	by	by	ADP
ejpam-6009	173	19	theorem	theorem	NOUN
ejpam-6009	173	20	1	1	NUM
ejpam-6009	173	21	,	,	PUNCT
ejpam-6009	173	22	f	f	PROPN
ejpam-6009	173	23	is	be	AUX
ejpam-6009	173	24	upper	upper	ADJ
ejpam-6009	173	25	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	173	26	,	,	PUNCT
ejpam-6009	173	27	τ2)p	τ2)p	ADJ
ejpam-6009	173	28	-	-	ADJ
ejpam-6009	173	29	continuous	continuous	ADJ
ejpam-6009	173	30	.	.	PUNCT
ejpam-6009	174	1	theorem	theorem	ADJ
ejpam-6009	174	2	4	4	NUM
ejpam-6009	174	3	.	.	X
ejpam-6009	174	4	for	for	ADP
ejpam-6009	174	5	a	a	DET
ejpam-6009	174	6	multifunction	multifunction	NOUN
ejpam-6009	175	1	f	f	NOUN
ejpam-6009	175	2	:	:	PUNCT
ejpam-6009	175	3	(	(	PUNCT
ejpam-6009	175	4	x	x	NOUN
ejpam-6009	175	5	,	,	PUNCT
ejpam-6009	175	6	τ1	τ1	NOUN
ejpam-6009	175	7	,	,	PUNCT
ejpam-6009	175	8	τ2	τ2	NOUN
ejpam-6009	175	9	)	)	PUNCT
ejpam-6009	175	10	→	→	SYM
ejpam-6009	175	11	(	(	PUNCT
ejpam-6009	175	12	y	y	PROPN
ejpam-6009	175	13	,	,	PUNCT
ejpam-6009	175	14	σ1	σ1	PROPN
ejpam-6009	175	15	,	,	PUNCT
ejpam-6009	175	16	σ2	σ2	NOUN
ejpam-6009	175	17	)	)	PUNCT
ejpam-6009	175	18	,	,	PUNCT
ejpam-6009	175	19	where	where	SCONJ
ejpam-6009	175	20	(	(	PUNCT
ejpam-6009	175	21	y	y	PROPN
ejpam-6009	175	22	,	,	PUNCT
ejpam-6009	175	23	σ1	σ1	PROPN
ejpam-6009	175	24	,	,	PUNCT
ejpam-6009	175	25	σ2	σ2	PROPN
ejpam-6009	175	26	)	)	PUNCT
ejpam-6009	175	27	is	be	AUX
ejpam-6009	175	28	(	(	PUNCT
ejpam-6009	175	29	σ1	σ1	PROPN
ejpam-6009	175	30	,	,	PUNCT
ejpam-6009	175	31	σ2)sregular	σ2)sregular	PROPN
ejpam-6009	175	32	,	,	PUNCT
ejpam-6009	175	33	the	the	DET
ejpam-6009	175	34	following	follow	VERB
ejpam-6009	175	35	properties	property	NOUN
ejpam-6009	175	36	are	be	AUX
ejpam-6009	175	37	equivalent	equivalent	ADJ
ejpam-6009	175	38	:	:	PUNCT
ejpam-6009	175	39	(	(	PUNCT
ejpam-6009	175	40	1	1	X
ejpam-6009	175	41	)	)	PUNCT
ejpam-6009	175	42	f	f	PROPN
ejpam-6009	175	43	is	be	AUX
ejpam-6009	175	44	lower	low	ADJ
ejpam-6009	175	45	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	175	46	,	,	PUNCT
ejpam-6009	175	47	τ2)p	τ2)p	ADJ
ejpam-6009	175	48	-	-	NOUN
ejpam-6009	175	49	continuous	continuous	ADJ
ejpam-6009	175	50	;	;	PUNCT
ejpam-6009	175	51	(	(	PUNCT
ejpam-6009	175	52	2	2	X
ejpam-6009	175	53	)	)	PUNCT
ejpam-6009	175	54	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6009	175	55	-	-	PUNCT
ejpam-6009	175	56	δ	δ	NOUN
ejpam-6009	175	57	-	-	NOUN
ejpam-6009	175	58	cl(b	cl(b	NOUN
ejpam-6009	175	59	)	)	PUNCT
ejpam-6009	175	60	)	)	PUNCT
ejpam-6009	176	1	is	be	AUX
ejpam-6009	176	2	(	(	PUNCT
ejpam-6009	176	3	τ1	τ1	NOUN
ejpam-6009	176	4	,	,	PUNCT
ejpam-6009	176	5	τ2)p	τ2)p	NOUN
ejpam-6009	176	6	-	-	PUNCT
ejpam-6009	176	7	open	open	ADJ
ejpam-6009	176	8	in	in	ADP
ejpam-6009	176	9	x	x	PUNCT
ejpam-6009	176	10	for	for	ADP
ejpam-6009	176	11	every	every	DET
ejpam-6009	176	12	subset	subset	NOUN
ejpam-6009	176	13	b	b	PROPN
ejpam-6009	176	14	of	of	ADP
ejpam-6009	176	15	y	y	PROPN
ejpam-6009	176	16	;	;	PUNCT
ejpam-6009	176	17	(	(	PUNCT
ejpam-6009	176	18	3	3	X
ejpam-6009	176	19	)	)	PUNCT
ejpam-6009	176	20	f−(k	f−(k	PROPN
ejpam-6009	176	21	)	)	PUNCT
ejpam-6009	176	22	is	be	AUX
ejpam-6009	176	23	(	(	PUNCT
ejpam-6009	176	24	τ1	τ1	NOUN
ejpam-6009	176	25	,	,	PUNCT
ejpam-6009	176	26	τ2)p	τ2)p	NOUN
ejpam-6009	176	27	-	-	PUNCT
ejpam-6009	176	28	open	open	ADJ
ejpam-6009	176	29	in	in	ADP
ejpam-6009	176	30	x	x	PUNCT
ejpam-6009	176	31	for	for	ADP
ejpam-6009	176	32	every	every	DET
ejpam-6009	176	33	σ1σ2	σ1σ2	NUM
ejpam-6009	176	34	-	-	PUNCT
ejpam-6009	176	35	δ	δ	NOUN
ejpam-6009	176	36	-	-	PUNCT
ejpam-6009	176	37	closed	close	VERB
ejpam-6009	176	38	set	set	ADJ
ejpam-6009	176	39	k	k	PROPN
ejpam-6009	176	40	of	of	ADP
ejpam-6009	176	41	y	y	PROPN
ejpam-6009	176	42	;	;	PUNCT
ejpam-6009	176	43	(	(	PUNCT
ejpam-6009	176	44	4	4	X
ejpam-6009	176	45	)	)	PUNCT
ejpam-6009	176	46	f+(v	f+(v	NOUN
ejpam-6009	176	47	)	)	PUNCT
ejpam-6009	177	1	is	be	AUX
ejpam-6009	177	2	(	(	PUNCT
ejpam-6009	177	3	τ1	τ1	NOUN
ejpam-6009	177	4	,	,	PUNCT
ejpam-6009	177	5	τ2)p	τ2)p	NOUN
ejpam-6009	177	6	-	-	PUNCT
ejpam-6009	177	7	closed	closed	ADJ
ejpam-6009	177	8	in	in	ADP
ejpam-6009	177	9	x	x	PUNCT
ejpam-6009	177	10	for	for	ADP
ejpam-6009	177	11	every	every	DET
ejpam-6009	177	12	σ1σ2	σ1σ2	NUM
ejpam-6009	177	13	-	-	PUNCT
ejpam-6009	177	14	δ	δ	NOUN
ejpam-6009	177	15	-	-	ADJ
ejpam-6009	177	16	open	open	ADJ
ejpam-6009	177	17	set	set	VERB
ejpam-6009	177	18	v	v	NOUN
ejpam-6009	177	19	of	of	ADP
ejpam-6009	177	20	y	y	PROPN
ejpam-6009	177	21	.	.	PUNCT
ejpam-6009	178	1	proof	proof	NOUN
ejpam-6009	178	2	.	.	PUNCT
ejpam-6009	179	1	the	the	DET
ejpam-6009	179	2	proof	proof	NOUN
ejpam-6009	179	3	is	be	AUX
ejpam-6009	179	4	similar	similar	ADJ
ejpam-6009	179	5	to	to	ADP
ejpam-6009	179	6	that	that	PRON
ejpam-6009	179	7	of	of	ADP
ejpam-6009	179	8	theorem	theorem	NOUN
ejpam-6009	179	9	3	3	NUM
ejpam-6009	179	10	.	.	NOUN
ejpam-6009	179	11	4	4	NUM
ejpam-6009	179	12	.	.	NOUN
ejpam-6009	179	13	upper	upper	ADJ
ejpam-6009	179	14	and	and	CCONJ
ejpam-6009	179	15	lower	low	ADJ
ejpam-6009	179	16	almost	almost	ADV
ejpam-6009	179	17	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	179	18	,	,	PUNCT
ejpam-6009	179	19	τ2)p	τ2)p	ADJ
ejpam-6009	179	20	-	-	ADJ
ejpam-6009	179	21	continuous	continuous	ADJ
ejpam-6009	179	22	multifunctions	multifunction	NOUN
ejpam-6009	179	23	in	in	ADP
ejpam-6009	179	24	this	this	DET
ejpam-6009	179	25	section	section	NOUN
ejpam-6009	179	26	,	,	PUNCT
ejpam-6009	179	27	we	we	PRON
ejpam-6009	179	28	introduce	introduce	VERB
ejpam-6009	179	29	the	the	DET
ejpam-6009	179	30	concepts	concept	NOUN
ejpam-6009	179	31	of	of	ADP
ejpam-6009	179	32	upper	upper	ADJ
ejpam-6009	179	33	almost	almost	ADV
ejpam-6009	179	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	179	35	,	,	PUNCT
ejpam-6009	179	36	τ2)p	τ2)p	ADJ
ejpam-6009	179	37	-	-	ADJ
ejpam-6009	179	38	continuous	continuous	ADJ
ejpam-6009	179	39	multifunctions	multifunction	NOUN
ejpam-6009	179	40	and	and	CCONJ
ejpam-6009	179	41	lower	low	ADJ
ejpam-6009	179	42	almost	almost	ADV
ejpam-6009	179	43	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	179	44	,	,	PUNCT
ejpam-6009	179	45	τ2)p	τ2)p	ADJ
ejpam-6009	179	46	-	-	PUNCT
ejpam-6009	179	47	continuous	continuous	ADJ
ejpam-6009	179	48	multifunctions	multifunction	NOUN
ejpam-6009	179	49	.	.	PUNCT
ejpam-6009	180	1	moreover	moreover	ADV
ejpam-6009	180	2	,	,	PUNCT
ejpam-6009	180	3	some	some	DET
ejpam-6009	180	4	characterizations	characterization	NOUN
ejpam-6009	180	5	of	of	ADP
ejpam-6009	180	6	upper	upper	ADJ
ejpam-6009	180	7	almost	almost	ADV
ejpam-6009	180	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	180	9	,	,	PUNCT
ejpam-6009	180	10	τ2)p	τ2)p	ADJ
ejpam-6009	180	11	-	-	ADJ
ejpam-6009	180	12	continuous	continuous	ADJ
ejpam-6009	180	13	multifunctions	multifunction	NOUN
ejpam-6009	180	14	and	and	CCONJ
ejpam-6009	180	15	lower	low	ADJ
ejpam-6009	180	16	almost	almost	ADV
ejpam-6009	180	17	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	180	18	,	,	PUNCT
ejpam-6009	180	19	τ2)p	τ2)p	ADJ
ejpam-6009	180	20	-	-	PUNCT
ejpam-6009	180	21	continuous	continuous	ADJ
ejpam-6009	180	22	multifunctions	multifunction	NOUN
ejpam-6009	180	23	are	be	AUX
ejpam-6009	180	24	considered	consider	VERB
ejpam-6009	180	25	.	.	PUNCT
ejpam-6009	181	1	definition	definition	NOUN
ejpam-6009	181	2	3	3	NUM
ejpam-6009	181	3	.	.	PUNCT
ejpam-6009	182	1	a	a	DET
ejpam-6009	182	2	multifunction	multifunction	NOUN
ejpam-6009	182	3	f	f	NOUN
ejpam-6009	182	4	:	:	PUNCT
ejpam-6009	182	5	(	(	PUNCT
ejpam-6009	182	6	x	x	NOUN
ejpam-6009	182	7	,	,	PUNCT
ejpam-6009	182	8	τ1	τ1	NOUN
ejpam-6009	182	9	,	,	PUNCT
ejpam-6009	182	10	τ2	τ2	NOUN
ejpam-6009	182	11	)	)	PUNCT
ejpam-6009	182	12	→	→	SYM
ejpam-6009	182	13	(	(	PUNCT
ejpam-6009	182	14	y	y	PROPN
ejpam-6009	182	15	,	,	PUNCT
ejpam-6009	182	16	σ1	σ1	PROPN
ejpam-6009	182	17	,	,	PUNCT
ejpam-6009	182	18	σ2	σ2	PROPN
ejpam-6009	182	19	)	)	PUNCT
ejpam-6009	182	20	is	be	AUX
ejpam-6009	182	21	said	say	VERB
ejpam-6009	182	22	to	to	PART
ejpam-6009	182	23	be	be	AUX
ejpam-6009	182	24	upper	upper	ADJ
ejpam-6009	182	25	almost	almost	ADV
ejpam-6009	182	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	182	27	,	,	PUNCT
ejpam-6009	182	28	τ2)p	τ2)p	ADJ
ejpam-6009	182	29	-	-	ADJ
ejpam-6009	182	30	continuous	continuous	ADJ
ejpam-6009	182	31	at	at	ADP
ejpam-6009	182	32	a	a	DET
ejpam-6009	182	33	point	point	NOUN
ejpam-6009	182	34	x	x	SYM
ejpam-6009	182	35	∈	∈	NOUN
ejpam-6009	182	36	x	x	INTJ
ejpam-6009	182	37	if	if	SCONJ
ejpam-6009	182	38	for	for	ADP
ejpam-6009	182	39	each	each	DET
ejpam-6009	182	40	(	(	PUNCT
ejpam-6009	182	41	σ1	σ1	PROPN
ejpam-6009	182	42	,	,	PUNCT
ejpam-6009	182	43	σ2)r	σ2)r	NOUN
ejpam-6009	182	44	-	-	PUNCT
ejpam-6009	182	45	closed	close	VERB
ejpam-6009	182	46	set	set	ADJ
ejpam-6009	182	47	k	k	PROPN
ejpam-6009	182	48	of	of	ADP
ejpam-6009	182	49	y	y	PROPN
ejpam-6009	182	50	with	with	ADP
ejpam-6009	182	51	x	x	PROPN
ejpam-6009	182	52	∈	∈	PROPN
ejpam-6009	182	53	f+(k	f+(k	PROPN
ejpam-6009	182	54	)	)	PUNCT
ejpam-6009	182	55	,	,	PUNCT
ejpam-6009	182	56	there	there	PRON
ejpam-6009	182	57	exists	exist	VERB
ejpam-6009	182	58	a	a	DET
ejpam-6009	182	59	(	(	PUNCT
ejpam-6009	182	60	τ1	τ1	NOUN
ejpam-6009	182	61	,	,	PUNCT
ejpam-6009	182	62	τ2)p	τ2)p	ADJ
ejpam-6009	182	63	-	-	PUNCT
ejpam-6009	182	64	open	open	ADJ
ejpam-6009	182	65	set	set	NOUN
ejpam-6009	182	66	u	u	NOUN
ejpam-6009	182	67	of	of	ADP
ejpam-6009	182	68	x	x	PUNCT
ejpam-6009	182	69	containing	contain	VERB
ejpam-6009	182	70	x	x	PUNCT
ejpam-6009	182	71	such	such	ADJ
ejpam-6009	182	72	that	that	SCONJ
ejpam-6009	182	73	u	u	PROPN
ejpam-6009	182	74	⊆	⊆	NUM
ejpam-6009	182	75	f+(k	f+(k	NUM
ejpam-6009	182	76	)	)	PUNCT
ejpam-6009	182	77	.	.	PUNCT
ejpam-6009	183	1	a	a	DET
ejpam-6009	183	2	multifunction	multifunction	NOUN
ejpam-6009	183	3	f	f	NOUN
ejpam-6009	183	4	:	:	PUNCT
ejpam-6009	183	5	(	(	PUNCT
ejpam-6009	183	6	x	x	NOUN
ejpam-6009	183	7	,	,	PUNCT
ejpam-6009	183	8	τ1	τ1	NOUN
ejpam-6009	183	9	,	,	PUNCT
ejpam-6009	183	10	τ2	τ2	NOUN
ejpam-6009	183	11	)	)	PUNCT
ejpam-6009	183	12	→	→	SYM
ejpam-6009	183	13	(	(	PUNCT
ejpam-6009	183	14	y	y	PROPN
ejpam-6009	183	15	,	,	PUNCT
ejpam-6009	183	16	σ1	σ1	PROPN
ejpam-6009	183	17	,	,	PUNCT
ejpam-6009	183	18	σ2	σ2	PROPN
ejpam-6009	183	19	)	)	PUNCT
ejpam-6009	183	20	is	be	AUX
ejpam-6009	183	21	said	say	VERB
ejpam-6009	183	22	to	to	PART
ejpam-6009	183	23	be	be	AUX
ejpam-6009	183	24	upper	upper	ADJ
ejpam-6009	183	25	almost	almost	ADV
ejpam-6009	183	26	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	183	27	,	,	PUNCT
ejpam-6009	183	28	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	183	29	if	if	SCONJ
ejpam-6009	183	30	f	f	PROPN
ejpam-6009	183	31	is	be	AUX
ejpam-6009	183	32	upper	upper	ADJ
ejpam-6009	183	33	almost	almost	ADV
ejpam-6009	183	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	183	35	,	,	PUNCT
ejpam-6009	183	36	τ2)p	τ2)p	ADJ
ejpam-6009	183	37	-	-	ADJ
ejpam-6009	183	38	continuous	continuous	ADJ
ejpam-6009	183	39	at	at	ADP
ejpam-6009	183	40	each	each	DET
ejpam-6009	183	41	point	point	NOUN
ejpam-6009	183	42	x	x	PUNCT
ejpam-6009	183	43	of	of	ADP
ejpam-6009	183	44	x.	x.	NOUN
ejpam-6009	183	45	remark	remark	PROPN
ejpam-6009	183	46	1	1	NUM
ejpam-6009	183	47	.	.	PUNCT
ejpam-6009	183	48	for	for	ADP
ejpam-6009	183	49	a	a	DET
ejpam-6009	183	50	multifunction	multifunction	NOUN
ejpam-6009	183	51	f	f	NOUN
ejpam-6009	183	52	:	:	PUNCT
ejpam-6009	183	53	(	(	PUNCT
ejpam-6009	183	54	x	x	NOUN
ejpam-6009	183	55	,	,	PUNCT
ejpam-6009	183	56	τ1	τ1	NOUN
ejpam-6009	183	57	,	,	PUNCT
ejpam-6009	183	58	τ2	τ2	NOUN
ejpam-6009	183	59	)	)	PUNCT
ejpam-6009	183	60	→	→	SYM
ejpam-6009	183	61	(	(	PUNCT
ejpam-6009	183	62	y	y	PROPN
ejpam-6009	183	63	,	,	PUNCT
ejpam-6009	183	64	σ1	σ1	PROPN
ejpam-6009	183	65	,	,	PUNCT
ejpam-6009	183	66	σ2	σ2	NOUN
ejpam-6009	183	67	)	)	PUNCT
ejpam-6009	183	68	,	,	PUNCT
ejpam-6009	183	69	the	the	DET
ejpam-6009	183	70	following	follow	VERB
ejpam-6009	183	71	implication	implication	NOUN
ejpam-6009	183	72	holds	hold	VERB
ejpam-6009	183	73	:	:	PUNCT
ejpam-6009	183	74	upper	upper	ADJ
ejpam-6009	183	75	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	183	76	,	,	PUNCT
ejpam-6009	183	77	τ2)p	τ2)p	ADJ
ejpam-6009	183	78	-	-	PUNCT
ejpam-6009	183	79	continuity	continuity	NOUN
ejpam-6009	183	80	⇒	⇒	NOUN
ejpam-6009	183	81	upper	upper	ADJ
ejpam-6009	183	82	almost	almost	ADV
ejpam-6009	183	83	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	183	84	,	,	PUNCT
ejpam-6009	183	85	τ2)p	τ2)p	NOUN
ejpam-6009	183	86	-	-	PUNCT
ejpam-6009	183	87	continuity	continuity	NOUN
ejpam-6009	183	88	.	.	PUNCT
ejpam-6009	184	1	the	the	DET
ejpam-6009	184	2	converse	converse	NOUN
ejpam-6009	184	3	of	of	ADP
ejpam-6009	184	4	the	the	DET
ejpam-6009	184	5	implication	implication	NOUN
ejpam-6009	184	6	is	be	AUX
ejpam-6009	184	7	not	not	PART
ejpam-6009	184	8	true	true	ADJ
ejpam-6009	184	9	in	in	ADP
ejpam-6009	184	10	general	general	ADJ
ejpam-6009	184	11	.	.	PUNCT
ejpam-6009	185	1	we	we	PRON
ejpam-6009	185	2	give	give	VERB
ejpam-6009	185	3	an	an	DET
ejpam-6009	185	4	example	example	NOUN
ejpam-6009	185	5	for	for	ADP
ejpam-6009	185	6	the	the	DET
ejpam-6009	185	7	implication	implication	NOUN
ejpam-6009	185	8	as	as	SCONJ
ejpam-6009	185	9	follows	follow	VERB
ejpam-6009	185	10	.	.	PUNCT
ejpam-6009	186	1	c.	c.	PROPN
ejpam-6009	186	2	viriyapong	viriyapong	PROPN
ejpam-6009	186	3	,	,	PUNCT
ejpam-6009	186	4	a.	a.	PROPN
ejpam-6009	186	5	sama	sama	PROPN
ejpam-6009	186	6	-	-	PUNCT
ejpam-6009	186	7	ae	ae	PROPN
ejpam-6009	186	8	,	,	PUNCT
ejpam-6009	186	9	c.	c.	PROPN
ejpam-6009	186	10	boonpok	boonpok	PROPN
ejpam-6009	186	11	/	/	SYM
ejpam-6009	186	12	eur	eur	PROPN
ejpam-6009	186	13	.	.	PUNCT
ejpam-6009	187	1	j.	j.	PROPN
ejpam-6009	187	2	pure	pure	PROPN
ejpam-6009	187	3	appl	appl	PROPN
ejpam-6009	187	4	.	.	PROPN
ejpam-6009	187	5	math	math	PROPN
ejpam-6009	187	6	,	,	PUNCT
ejpam-6009	187	7	18	18	NUM
ejpam-6009	187	8	(	(	PUNCT
ejpam-6009	187	9	2	2	NUM
ejpam-6009	187	10	)	)	PUNCT
ejpam-6009	187	11	(	(	PUNCT
ejpam-6009	187	12	2025	2025	NUM
ejpam-6009	187	13	)	)	PUNCT
ejpam-6009	187	14	,	,	PUNCT
ejpam-6009	187	15	6009	6009	NUM
ejpam-6009	187	16	8	8	NUM
ejpam-6009	187	17	of	of	ADP
ejpam-6009	187	18	18	18	NUM
ejpam-6009	187	19	example	example	NOUN
ejpam-6009	187	20	1	1	NUM
ejpam-6009	187	21	.	.	PUNCT
ejpam-6009	188	1	let	let	VERB
ejpam-6009	188	2	x	x	PUNCT
ejpam-6009	188	3	=	=	PRON
ejpam-6009	188	4	{	{	PUNCT
ejpam-6009	188	5	a	a	PRON
ejpam-6009	188	6	,	,	PUNCT
ejpam-6009	188	7	b	b	NOUN
ejpam-6009	188	8	,	,	PUNCT
ejpam-6009	188	9	c	c	NOUN
ejpam-6009	188	10	,	,	PUNCT
ejpam-6009	188	11	d	d	NOUN
ejpam-6009	188	12	}	}	PUNCT
ejpam-6009	188	13	with	with	ADP
ejpam-6009	188	14	topologies	topology	NOUN
ejpam-6009	188	15	τ1	τ1	NOUN
ejpam-6009	188	16	=	=	SYM
ejpam-6009	188	17	{	{	PUNCT
ejpam-6009	188	18	∅	∅	NOUN
ejpam-6009	188	19	,	,	PUNCT
ejpam-6009	188	20	{	{	PUNCT
ejpam-6009	188	21	a	a	X
ejpam-6009	188	22	}	}	PUNCT
ejpam-6009	188	23	,	,	PUNCT
ejpam-6009	188	24	{	{	PUNCT
ejpam-6009	188	25	c	c	X
ejpam-6009	188	26	}	}	PUNCT
ejpam-6009	188	27	,	,	PUNCT
ejpam-6009	188	28	{	{	PUNCT
ejpam-6009	188	29	a	a	DET
ejpam-6009	188	30	,	,	PUNCT
ejpam-6009	188	31	b	b	NOUN
ejpam-6009	188	32	}	}	PUNCT
ejpam-6009	188	33	,	,	PUNCT
ejpam-6009	188	34	{	{	PUNCT
ejpam-6009	188	35	a	a	X
ejpam-6009	188	36	,	,	PUNCT
ejpam-6009	188	37	c	c	NOUN
ejpam-6009	188	38	}	}	PUNCT
ejpam-6009	188	39	,	,	PUNCT
ejpam-6009	188	40	{	{	PUNCT
ejpam-6009	188	41	a	a	DET
ejpam-6009	188	42	,	,	PUNCT
ejpam-6009	188	43	d	d	NOUN
ejpam-6009	188	44	}	}	PUNCT
ejpam-6009	188	45	,	,	PUNCT
ejpam-6009	188	46	{	{	PUNCT
ejpam-6009	188	47	a	a	DET
ejpam-6009	188	48	,	,	PUNCT
ejpam-6009	188	49	b	b	NOUN
ejpam-6009	188	50	,	,	PUNCT
ejpam-6009	188	51	c	c	NOUN
ejpam-6009	188	52	}	}	PUNCT
ejpam-6009	188	53	,	,	PUNCT
ejpam-6009	188	54	{	{	PUNCT
ejpam-6009	188	55	a	a	DET
ejpam-6009	188	56	,	,	PUNCT
ejpam-6009	188	57	b	b	NOUN
ejpam-6009	188	58	,	,	PUNCT
ejpam-6009	188	59	d	d	NOUN
ejpam-6009	188	60	}	}	PUNCT
ejpam-6009	188	61	,	,	PUNCT
ejpam-6009	188	62	{	{	PUNCT
ejpam-6009	188	63	a	a	PRON
ejpam-6009	188	64	,	,	PUNCT
ejpam-6009	188	65	c	c	NOUN
ejpam-6009	188	66	,	,	PUNCT
ejpam-6009	188	67	d	d	NOUN
ejpam-6009	188	68	}	}	PUNCT
ejpam-6009	188	69	,	,	PUNCT
ejpam-6009	188	70	x	x	NOUN
ejpam-6009	188	71	}	}	PUNCT
ejpam-6009	188	72	and	and	CCONJ
ejpam-6009	188	73	τ2	τ2	NOUN
ejpam-6009	188	74	=	=	SYM
ejpam-6009	188	75	{	{	PUNCT
ejpam-6009	188	76	∅	∅	NOUN
ejpam-6009	188	77	,	,	PUNCT
ejpam-6009	188	78	{	{	PUNCT
ejpam-6009	188	79	a	a	X
ejpam-6009	188	80	}	}	PUNCT
ejpam-6009	188	81	,	,	PUNCT
ejpam-6009	188	82	{	{	PUNCT
ejpam-6009	188	83	c	c	X
ejpam-6009	188	84	}	}	PUNCT
ejpam-6009	188	85	,	,	PUNCT
ejpam-6009	188	86	{	{	PUNCT
ejpam-6009	188	87	a	a	DET
ejpam-6009	188	88	,	,	PUNCT
ejpam-6009	188	89	b	b	NOUN
ejpam-6009	188	90	}	}	PUNCT
ejpam-6009	188	91	,	,	PUNCT
ejpam-6009	188	92	{	{	PUNCT
ejpam-6009	188	93	a	a	X
ejpam-6009	188	94	,	,	PUNCT
ejpam-6009	188	95	c	c	NOUN
ejpam-6009	188	96	}	}	PUNCT
ejpam-6009	188	97	,	,	PUNCT
ejpam-6009	188	98	{	{	PUNCT
ejpam-6009	188	99	a	a	DET
ejpam-6009	188	100	,	,	PUNCT
ejpam-6009	188	101	b	b	NOUN
ejpam-6009	188	102	,	,	PUNCT
ejpam-6009	188	103	c	c	NOUN
ejpam-6009	188	104	}	}	PUNCT
ejpam-6009	188	105	,	,	PUNCT
ejpam-6009	188	106	{	{	PUNCT
ejpam-6009	188	107	a	a	DET
ejpam-6009	188	108	,	,	PUNCT
ejpam-6009	188	109	b	b	NOUN
ejpam-6009	188	110	,	,	PUNCT
ejpam-6009	188	111	d	d	NOUN
ejpam-6009	188	112	}	}	PUNCT
ejpam-6009	188	113	,	,	PUNCT
ejpam-6009	188	114	x	x	NOUN
ejpam-6009	188	115	}	}	PUNCT
ejpam-6009	188	116	.	.	PUNCT
ejpam-6009	189	1	let	let	VERB
ejpam-6009	189	2	y	y	PROPN
ejpam-6009	189	3	=	=	PUNCT
ejpam-6009	189	4	{	{	PUNCT
ejpam-6009	189	5	1	1	NUM
ejpam-6009	189	6	,	,	PUNCT
ejpam-6009	189	7	2	2	NUM
ejpam-6009	189	8	,	,	PUNCT
ejpam-6009	189	9	3	3	NUM
ejpam-6009	189	10	,	,	PUNCT
ejpam-6009	189	11	4	4	NUM
ejpam-6009	189	12	}	}	PUNCT
ejpam-6009	189	13	with	with	ADP
ejpam-6009	189	14	topologies	topology	NOUN
ejpam-6009	189	15	σ1	σ1	NOUN
ejpam-6009	189	16	=	=	SYM
ejpam-6009	189	17	{	{	PUNCT
ejpam-6009	189	18	∅	∅	NOUN
ejpam-6009	189	19	,	,	PUNCT
ejpam-6009	189	20	{	{	PUNCT
ejpam-6009	189	21	1	1	NUM
ejpam-6009	189	22	}	}	PUNCT
ejpam-6009	189	23	,	,	PUNCT
ejpam-6009	189	24	{	{	PUNCT
ejpam-6009	189	25	3	3	NUM
ejpam-6009	189	26	}	}	PUNCT
ejpam-6009	189	27	,	,	PUNCT
ejpam-6009	189	28	{	{	PUNCT
ejpam-6009	189	29	1	1	NUM
ejpam-6009	189	30	,	,	PUNCT
ejpam-6009	189	31	2	2	NUM
ejpam-6009	189	32	}	}	PUNCT
ejpam-6009	189	33	,	,	PUNCT
ejpam-6009	189	34	{	{	PUNCT
ejpam-6009	189	35	1	1	NUM
ejpam-6009	189	36	,	,	PUNCT
ejpam-6009	189	37	3	3	NUM
ejpam-6009	189	38	}	}	PUNCT
ejpam-6009	189	39	,	,	PUNCT
ejpam-6009	189	40	{	{	PUNCT
ejpam-6009	189	41	1	1	NUM
ejpam-6009	189	42	,	,	PUNCT
ejpam-6009	189	43	2	2	NUM
ejpam-6009	189	44	,	,	PUNCT
ejpam-6009	189	45	3	3	NUM
ejpam-6009	189	46	}	}	PUNCT
ejpam-6009	189	47	,	,	PUNCT
ejpam-6009	189	48	{	{	PUNCT
ejpam-6009	189	49	1	1	NUM
ejpam-6009	189	50	,	,	PUNCT
ejpam-6009	189	51	2	2	NUM
ejpam-6009	189	52	,	,	PUNCT
ejpam-6009	189	53	4	4	NUM
ejpam-6009	189	54	}	}	PUNCT
ejpam-6009	189	55	,	,	PUNCT
ejpam-6009	189	56	y	y	PROPN
ejpam-6009	189	57	}	}	PUNCT
ejpam-6009	189	58	and	and	CCONJ
ejpam-6009	189	59	σ2	σ2	PROPN
ejpam-6009	189	60	=	=	SYM
ejpam-6009	189	61	{	{	PUNCT
ejpam-6009	189	62	∅	∅	NOUN
ejpam-6009	189	63	,	,	PUNCT
ejpam-6009	189	64	{	{	PUNCT
ejpam-6009	189	65	1	1	NUM
ejpam-6009	189	66	}	}	PUNCT
ejpam-6009	189	67	,	,	PUNCT
ejpam-6009	189	68	{	{	PUNCT
ejpam-6009	189	69	3	3	NUM
ejpam-6009	189	70	}	}	PUNCT
ejpam-6009	189	71	,	,	PUNCT
ejpam-6009	189	72	{	{	PUNCT
ejpam-6009	189	73	1	1	NUM
ejpam-6009	189	74	,	,	PUNCT
ejpam-6009	189	75	2	2	NUM
ejpam-6009	189	76	}	}	PUNCT
ejpam-6009	189	77	,	,	PUNCT
ejpam-6009	189	78	{	{	PUNCT
ejpam-6009	189	79	1	1	NUM
ejpam-6009	189	80	,	,	PUNCT
ejpam-6009	189	81	3	3	NUM
ejpam-6009	189	82	}	}	PUNCT
ejpam-6009	189	83	,	,	PUNCT
ejpam-6009	189	84	{	{	PUNCT
ejpam-6009	189	85	1	1	NUM
ejpam-6009	189	86	,	,	PUNCT
ejpam-6009	189	87	4	4	NUM
ejpam-6009	189	88	}	}	PUNCT
ejpam-6009	189	89	,	,	PUNCT
ejpam-6009	189	90	{	{	PUNCT
ejpam-6009	189	91	1	1	NUM
ejpam-6009	189	92	,	,	PUNCT
ejpam-6009	189	93	2	2	NUM
ejpam-6009	189	94	,	,	PUNCT
ejpam-6009	189	95	3	3	NUM
ejpam-6009	189	96	}	}	PUNCT
ejpam-6009	189	97	,	,	PUNCT
ejpam-6009	189	98	{	{	PUNCT
ejpam-6009	189	99	1	1	NUM
ejpam-6009	189	100	,	,	PUNCT
ejpam-6009	189	101	2	2	NUM
ejpam-6009	189	102	,	,	PUNCT
ejpam-6009	189	103	4	4	NUM
ejpam-6009	189	104	}	}	PUNCT
ejpam-6009	189	105	,	,	PUNCT
ejpam-6009	189	106	{	{	PUNCT
ejpam-6009	189	107	1	1	NUM
ejpam-6009	189	108	,	,	PUNCT
ejpam-6009	189	109	3	3	NUM
ejpam-6009	189	110	,	,	PUNCT
ejpam-6009	189	111	4	4	NUM
ejpam-6009	189	112	}	}	PUNCT
ejpam-6009	189	113	,	,	PUNCT
ejpam-6009	189	114	y	y	PROPN
ejpam-6009	189	115	}	}	PUNCT
ejpam-6009	189	116	.	.	PUNCT
ejpam-6009	190	1	a	a	DET
ejpam-6009	190	2	multifunction	multifunction	NOUN
ejpam-6009	190	3	f	f	NOUN
ejpam-6009	190	4	:	:	PUNCT
ejpam-6009	190	5	(	(	PUNCT
ejpam-6009	190	6	x	x	NOUN
ejpam-6009	190	7	,	,	PUNCT
ejpam-6009	190	8	τ1	τ1	NOUN
ejpam-6009	190	9	,	,	PUNCT
ejpam-6009	190	10	τ2	τ2	NOUN
ejpam-6009	190	11	)	)	PUNCT
ejpam-6009	190	12	→	→	SYM
ejpam-6009	190	13	(	(	PUNCT
ejpam-6009	190	14	y	y	PROPN
ejpam-6009	190	15	,	,	PUNCT
ejpam-6009	190	16	σ1	σ1	PROPN
ejpam-6009	190	17	,	,	PUNCT
ejpam-6009	190	18	σ2	σ2	PROPN
ejpam-6009	190	19	)	)	PUNCT
ejpam-6009	190	20	is	be	AUX
ejpam-6009	190	21	defined	define	VERB
ejpam-6009	190	22	as	as	SCONJ
ejpam-6009	190	23	follows	follow	VERB
ejpam-6009	190	24	:	:	PUNCT
ejpam-6009	190	25	f	f	X
ejpam-6009	190	26	(	(	PUNCT
ejpam-6009	190	27	a	a	X
ejpam-6009	190	28	)	)	PUNCT
ejpam-6009	190	29	=	=	PUNCT
ejpam-6009	190	30	{	{	PUNCT
ejpam-6009	190	31	4	4	NUM
ejpam-6009	190	32	}	}	PUNCT
ejpam-6009	190	33	,	,	PUNCT
ejpam-6009	190	34	f	f	PROPN
ejpam-6009	190	35	(	(	PUNCT
ejpam-6009	190	36	b	b	X
ejpam-6009	190	37	)	)	PUNCT
ejpam-6009	190	38	=	=	PUNCT
ejpam-6009	190	39	{	{	PUNCT
ejpam-6009	190	40	3	3	NUM
ejpam-6009	190	41	}	}	PUNCT
ejpam-6009	190	42	,	,	PUNCT
ejpam-6009	190	43	f	f	PROPN
ejpam-6009	190	44	(	(	PUNCT
ejpam-6009	190	45	c	c	X
ejpam-6009	190	46	)	)	PUNCT
ejpam-6009	190	47	=	=	PRON
ejpam-6009	190	48	{	{	PUNCT
ejpam-6009	190	49	1	1	NUM
ejpam-6009	190	50	}	}	PUNCT
ejpam-6009	190	51	and	and	CCONJ
ejpam-6009	190	52	f	f	PROPN
ejpam-6009	190	53	(	(	PUNCT
ejpam-6009	190	54	d	d	X
ejpam-6009	190	55	)	)	PUNCT
ejpam-6009	190	56	=	=	SYM
ejpam-6009	190	57	{	{	PUNCT
ejpam-6009	190	58	2	2	NUM
ejpam-6009	190	59	}	}	PUNCT
ejpam-6009	190	60	.	.	PUNCT
ejpam-6009	191	1	then	then	ADV
ejpam-6009	191	2	,	,	PUNCT
ejpam-6009	191	3	f	f	PROPN
ejpam-6009	191	4	is	be	AUX
ejpam-6009	191	5	upper	upper	ADJ
ejpam-6009	191	6	almost	almost	ADV
ejpam-6009	191	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	191	8	,	,	PUNCT
ejpam-6009	191	9	τ2)p	τ2)p	ADJ
ejpam-6009	191	10	-	-	ADJ
ejpam-6009	191	11	continuous	continuous	ADJ
ejpam-6009	191	12	but	but	CCONJ
ejpam-6009	191	13	f	f	PROPN
ejpam-6009	191	14	is	be	AUX
ejpam-6009	191	15	not	not	PART
ejpam-6009	191	16	upper	upper	ADJ
ejpam-6009	191	17	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	191	18	,	,	PUNCT
ejpam-6009	191	19	τ2)p	τ2)p	ADJ
ejpam-6009	191	20	-	-	ADJ
ejpam-6009	191	21	continuous	continuous	ADJ
ejpam-6009	191	22	.	.	PUNCT
ejpam-6009	192	1	theorem	theorem	NOUN
ejpam-6009	192	2	5	5	NUM
ejpam-6009	192	3	.	.	X
ejpam-6009	192	4	for	for	ADP
ejpam-6009	192	5	a	a	DET
ejpam-6009	192	6	multifunction	multifunction	NOUN
ejpam-6009	193	1	f	f	NOUN
ejpam-6009	193	2	:	:	PUNCT
ejpam-6009	193	3	(	(	PUNCT
ejpam-6009	193	4	x	x	NOUN
ejpam-6009	193	5	,	,	PUNCT
ejpam-6009	193	6	τ1	τ1	NOUN
ejpam-6009	193	7	,	,	PUNCT
ejpam-6009	193	8	τ2	τ2	NOUN
ejpam-6009	193	9	)	)	PUNCT
ejpam-6009	193	10	→	→	SYM
ejpam-6009	193	11	(	(	PUNCT
ejpam-6009	193	12	y	y	PROPN
ejpam-6009	193	13	,	,	PUNCT
ejpam-6009	193	14	σ1	σ1	PROPN
ejpam-6009	193	15	,	,	PUNCT
ejpam-6009	193	16	σ2	σ2	NOUN
ejpam-6009	193	17	)	)	PUNCT
ejpam-6009	193	18	,	,	PUNCT
ejpam-6009	193	19	the	the	DET
ejpam-6009	193	20	following	follow	VERB
ejpam-6009	193	21	properties	property	NOUN
ejpam-6009	193	22	are	be	AUX
ejpam-6009	193	23	equivalent	equivalent	ADJ
ejpam-6009	193	24	:	:	PUNCT
ejpam-6009	193	25	(	(	PUNCT
ejpam-6009	193	26	1	1	X
ejpam-6009	193	27	)	)	PUNCT
ejpam-6009	193	28	f	f	PROPN
ejpam-6009	193	29	is	be	AUX
ejpam-6009	193	30	upper	upper	ADJ
ejpam-6009	193	31	almost	almost	ADV
ejpam-6009	193	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	193	33	,	,	PUNCT
ejpam-6009	193	34	τ2)p	τ2)p	ADJ
ejpam-6009	193	35	-	-	NOUN
ejpam-6009	193	36	continuous	continuous	ADJ
ejpam-6009	193	37	;	;	PUNCT
ejpam-6009	193	38	(	(	PUNCT
ejpam-6009	193	39	2	2	X
ejpam-6009	193	40	)	)	PUNCT
ejpam-6009	193	41	f+(k	f+(k	NOUN
ejpam-6009	193	42	)	)	PUNCT
ejpam-6009	193	43	is	be	AUX
ejpam-6009	193	44	(	(	PUNCT
ejpam-6009	193	45	τ1	τ1	NOUN
ejpam-6009	193	46	,	,	PUNCT
ejpam-6009	193	47	τ2)p	τ2)p	NOUN
ejpam-6009	193	48	-	-	PUNCT
ejpam-6009	193	49	open	open	ADJ
ejpam-6009	193	50	in	in	ADP
ejpam-6009	193	51	x	x	PUNCT
ejpam-6009	193	52	for	for	ADP
ejpam-6009	193	53	every	every	DET
ejpam-6009	193	54	(	(	PUNCT
ejpam-6009	193	55	σ1	σ1	PROPN
ejpam-6009	193	56	,	,	PUNCT
ejpam-6009	194	1	σ2)r	σ2)r	NOUN
ejpam-6009	194	2	-	-	PUNCT
ejpam-6009	194	3	closed	close	VERB
ejpam-6009	194	4	set	set	ADJ
ejpam-6009	194	5	k	k	PROPN
ejpam-6009	194	6	of	of	ADP
ejpam-6009	194	7	y	y	PROPN
ejpam-6009	194	8	;	;	PUNCT
ejpam-6009	194	9	(	(	PUNCT
ejpam-6009	194	10	3	3	X
ejpam-6009	194	11	)	)	PUNCT
ejpam-6009	194	12	f−(v	f−(v	NOUN
ejpam-6009	194	13	)	)	PUNCT
ejpam-6009	194	14	is	be	AUX
ejpam-6009	194	15	(	(	PUNCT
ejpam-6009	194	16	τ1	τ1	NOUN
ejpam-6009	194	17	,	,	PUNCT
ejpam-6009	194	18	τ2)p	τ2)p	NOUN
ejpam-6009	194	19	-	-	PUNCT
ejpam-6009	194	20	closed	closed	ADJ
ejpam-6009	194	21	in	in	ADP
ejpam-6009	194	22	x	x	PUNCT
ejpam-6009	194	23	for	for	ADP
ejpam-6009	194	24	every	every	DET
ejpam-6009	194	25	(	(	PUNCT
ejpam-6009	194	26	σ1	σ1	PROPN
ejpam-6009	194	27	,	,	PUNCT
ejpam-6009	194	28	σ2)r	σ2)r	NOUN
ejpam-6009	194	29	-	-	PUNCT
ejpam-6009	194	30	open	open	ADJ
ejpam-6009	194	31	set	set	VERB
ejpam-6009	194	32	v	v	NOUN
ejpam-6009	194	33	of	of	ADP
ejpam-6009	194	34	y	y	PROPN
ejpam-6009	194	35	;	;	PUNCT
ejpam-6009	194	36	(	(	PUNCT
ejpam-6009	194	37	4	4	X
ejpam-6009	194	38	)	)	PUNCT
ejpam-6009	194	39	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6009	194	40	-	-	PUNCT
ejpam-6009	194	41	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	194	42	-	-	PUNCT
ejpam-6009	194	43	cl(v	cl(v	NOUN
ejpam-6009	194	44	)	)	PUNCT
ejpam-6009	194	45	)	)	PUNCT
ejpam-6009	194	46	)	)	PUNCT
ejpam-6009	195	1	is	be	AUX
ejpam-6009	195	2	(	(	PUNCT
ejpam-6009	195	3	τ1	τ1	NOUN
ejpam-6009	195	4	,	,	PUNCT
ejpam-6009	195	5	τ2)p	τ2)p	NOUN
ejpam-6009	195	6	-	-	PUNCT
ejpam-6009	195	7	closed	closed	ADJ
ejpam-6009	195	8	in	in	ADP
ejpam-6009	195	9	x	x	PUNCT
ejpam-6009	195	10	for	for	ADP
ejpam-6009	195	11	every	every	DET
ejpam-6009	195	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	195	13	-	-	ADJ
ejpam-6009	195	14	open	open	ADJ
ejpam-6009	195	15	set	set	NOUN
ejpam-6009	195	16	v	v	NOUN
ejpam-6009	195	17	of	of	ADP
ejpam-6009	195	18	y	y	PROPN
ejpam-6009	195	19	;	;	PUNCT
ejpam-6009	195	20	(	(	PUNCT
ejpam-6009	195	21	5	5	X
ejpam-6009	195	22	)	)	PUNCT
ejpam-6009	195	23	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	195	24	-	-	PUNCT
ejpam-6009	195	25	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6009	195	26	-	-	PUNCT
ejpam-6009	195	27	int(k	int(k	NOUN
ejpam-6009	195	28	)	)	PUNCT
ejpam-6009	195	29	)	)	PUNCT
ejpam-6009	195	30	)	)	PUNCT
ejpam-6009	196	1	is	be	AUX
ejpam-6009	196	2	(	(	PUNCT
ejpam-6009	196	3	τ1	τ1	NOUN
ejpam-6009	196	4	,	,	PUNCT
ejpam-6009	196	5	τ2)p	τ2)p	NOUN
ejpam-6009	196	6	-	-	PUNCT
ejpam-6009	196	7	open	open	ADJ
ejpam-6009	196	8	in	in	ADP
ejpam-6009	196	9	x	x	PUNCT
ejpam-6009	196	10	for	for	ADP
ejpam-6009	196	11	every	every	DET
ejpam-6009	196	12	σ1σ2	σ1σ2	NUM
ejpam-6009	196	13	-	-	PUNCT
ejpam-6009	196	14	closed	closed	ADJ
ejpam-6009	196	15	set	set	NOUN
ejpam-6009	196	16	k	k	PROPN
ejpam-6009	196	17	of	of	ADP
ejpam-6009	196	18	y	y	PROPN
ejpam-6009	196	19	;	;	PUNCT
ejpam-6009	196	20	(	(	PUNCT
ejpam-6009	196	21	6	6	NUM
ejpam-6009	196	22	)	)	PUNCT
ejpam-6009	196	23	for	for	ADP
ejpam-6009	196	24	each	each	DET
ejpam-6009	196	25	x	x	SYM
ejpam-6009	196	26	∈	∈	PROPN
ejpam-6009	196	27	x	x	X
ejpam-6009	196	28	and	and	CCONJ
ejpam-6009	196	29	each	each	DET
ejpam-6009	196	30	(	(	PUNCT
ejpam-6009	196	31	σ1	σ1	PROPN
ejpam-6009	196	32	,	,	PUNCT
ejpam-6009	196	33	σ2)s	σ2)s	NOUN
ejpam-6009	196	34	-	-	PUNCT
ejpam-6009	196	35	open	open	NOUN
ejpam-6009	196	36	set	set	NOUN
ejpam-6009	196	37	v	v	NOUN
ejpam-6009	196	38	of	of	ADP
ejpam-6009	196	39	y	y	PROPN
ejpam-6009	196	40	containing	contain	VERB
ejpam-6009	196	41	f	f	PROPN
ejpam-6009	196	42	(	(	PUNCT
ejpam-6009	196	43	x	x	NOUN
ejpam-6009	196	44	)	)	PUNCT
ejpam-6009	196	45	,	,	PUNCT
ejpam-6009	196	46	there	there	PRON
ejpam-6009	196	47	exists	exist	VERB
ejpam-6009	196	48	a	a	DET
ejpam-6009	196	49	(	(	PUNCT
ejpam-6009	196	50	τ1	τ1	NOUN
ejpam-6009	196	51	,	,	PUNCT
ejpam-6009	196	52	τ2)p	τ2)p	ADJ
ejpam-6009	196	53	-	-	PUNCT
ejpam-6009	196	54	open	open	ADJ
ejpam-6009	196	55	set	set	NOUN
ejpam-6009	196	56	u	u	NOUN
ejpam-6009	196	57	of	of	ADP
ejpam-6009	196	58	x	x	PUNCT
ejpam-6009	196	59	containing	contain	VERB
ejpam-6009	196	60	x	x	PUNCT
ejpam-6009	196	61	such	such	ADJ
ejpam-6009	196	62	that	that	SCONJ
ejpam-6009	196	63	f	f	PROPN
ejpam-6009	196	64	(	(	PUNCT
ejpam-6009	196	65	u	u	NOUN
ejpam-6009	196	66	)	)	PUNCT
ejpam-6009	196	67	⊆	⊆	NUM
ejpam-6009	196	68	σ1σ2	σ1σ2	NOUN
ejpam-6009	196	69	-	-	NUM
ejpam-6009	196	70	cl(v	cl(v	NOUN
ejpam-6009	196	71	)	)	PUNCT
ejpam-6009	196	72	;	;	PUNCT
ejpam-6009	196	73	(	(	PUNCT
ejpam-6009	196	74	7	7	X
ejpam-6009	196	75	)	)	PUNCT
ejpam-6009	196	76	f+(v	f+(v	NOUN
ejpam-6009	196	77	)	)	PUNCT
ejpam-6009	197	1	⊆	⊆	NUM
ejpam-6009	197	2	(	(	PUNCT
ejpam-6009	197	3	τ1	τ1	NOUN
ejpam-6009	197	4	,	,	PUNCT
ejpam-6009	197	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	198	1	+	+	ADJ
ejpam-6009	198	2	(	(	PUNCT
ejpam-6009	198	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	198	4	-	-	NUM
ejpam-6009	198	5	cl(v	cl(v	NOUN
ejpam-6009	198	6	)	)	PUNCT
ejpam-6009	198	7	)	)	PUNCT
ejpam-6009	198	8	)	)	PUNCT
ejpam-6009	199	1	for	for	ADP
ejpam-6009	199	2	every	every	DET
ejpam-6009	199	3	(	(	PUNCT
ejpam-6009	199	4	σ1	σ1	PROPN
ejpam-6009	199	5	,	,	PUNCT
ejpam-6009	199	6	σ2)s	σ2)s	NOUN
ejpam-6009	199	7	-	-	PUNCT
ejpam-6009	199	8	open	open	NOUN
ejpam-6009	199	9	set	set	NOUN
ejpam-6009	199	10	v	v	NOUN
ejpam-6009	199	11	of	of	ADP
ejpam-6009	199	12	y	y	PROPN
ejpam-6009	199	13	.	.	PUNCT
ejpam-6009	200	1	proof	proof	NOUN
ejpam-6009	200	2	.	.	PUNCT
ejpam-6009	201	1	(	(	PUNCT
ejpam-6009	201	2	1	1	X
ejpam-6009	201	3	)	)	PUNCT
ejpam-6009	201	4	⇒	⇒	NOUN
ejpam-6009	201	5	(	(	PUNCT
ejpam-6009	201	6	2	2	NUM
ejpam-6009	201	7	):	):	PUNCT
ejpam-6009	201	8	let	let	VERB
ejpam-6009	201	9	k	k	PRON
ejpam-6009	201	10	be	be	AUX
ejpam-6009	201	11	any	any	DET
ejpam-6009	201	12	(	(	PUNCT
ejpam-6009	201	13	σ1	σ1	NOUN
ejpam-6009	201	14	,	,	PUNCT
ejpam-6009	201	15	σ2)r	σ2)r	NOUN
ejpam-6009	201	16	-	-	PUNCT
ejpam-6009	201	17	closed	close	VERB
ejpam-6009	201	18	set	set	NOUN
ejpam-6009	201	19	of	of	ADP
ejpam-6009	201	20	y	y	PROPN
ejpam-6009	201	21	and	and	CCONJ
ejpam-6009	201	22	x	x	PUNCT
ejpam-6009	201	23	∈	∈	PROPN
ejpam-6009	201	24	f+(k	f+(k	PROPN
ejpam-6009	201	25	)	)	PUNCT
ejpam-6009	201	26	.	.	PUNCT
ejpam-6009	202	1	since	since	SCONJ
ejpam-6009	202	2	f	f	PROPN
ejpam-6009	202	3	is	be	AUX
ejpam-6009	202	4	upper	upper	ADJ
ejpam-6009	202	5	almost	almost	ADV
ejpam-6009	202	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	202	7	,	,	PUNCT
ejpam-6009	202	8	τ2)p	τ2)p	ADJ
ejpam-6009	202	9	-	-	ADJ
ejpam-6009	202	10	continuous	continuous	ADJ
ejpam-6009	202	11	,	,	PUNCT
ejpam-6009	202	12	there	there	PRON
ejpam-6009	202	13	exists	exist	VERB
ejpam-6009	202	14	a	a	DET
ejpam-6009	202	15	(	(	PUNCT
ejpam-6009	202	16	τ1	τ1	NOUN
ejpam-6009	202	17	,	,	PUNCT
ejpam-6009	202	18	τ2)p	τ2)p	ADJ
ejpam-6009	202	19	-	-	PUNCT
ejpam-6009	202	20	open	open	ADJ
ejpam-6009	202	21	set	set	NOUN
ejpam-6009	202	22	u	u	NOUN
ejpam-6009	202	23	of	of	ADP
ejpam-6009	202	24	x	x	PUNCT
ejpam-6009	202	25	containing	contain	VERB
ejpam-6009	202	26	x	x	PUNCT
ejpam-6009	202	27	such	such	ADJ
ejpam-6009	202	28	that	that	SCONJ
ejpam-6009	202	29	u	u	PROPN
ejpam-6009	202	30	⊆	⊆	NUM
ejpam-6009	202	31	f+(k	f+(k	NUM
ejpam-6009	202	32	)	)	PUNCT
ejpam-6009	202	33	.	.	PUNCT
ejpam-6009	203	1	thus	thus	ADV
ejpam-6009	203	2	,	,	PUNCT
ejpam-6009	203	3	f+(k	f+(k	X
ejpam-6009	203	4	)	)	PUNCT
ejpam-6009	203	5	is	be	AUX
ejpam-6009	203	6	(	(	PUNCT
ejpam-6009	203	7	τ1	τ1	NOUN
ejpam-6009	203	8	,	,	PUNCT
ejpam-6009	203	9	τ2)p	τ2)p	NOUN
ejpam-6009	203	10	-	-	PUNCT
ejpam-6009	203	11	open	open	ADJ
ejpam-6009	203	12	in	in	ADP
ejpam-6009	203	13	x.	x.	NOUN
ejpam-6009	203	14	(	(	PUNCT
ejpam-6009	203	15	2	2	NUM
ejpam-6009	203	16	)	)	PUNCT
ejpam-6009	203	17	⇒	⇒	NOUN
ejpam-6009	203	18	(	(	PUNCT
ejpam-6009	203	19	1	1	NUM
ejpam-6009	203	20	):	):	PUNCT
ejpam-6009	203	21	the	the	DET
ejpam-6009	203	22	proof	proof	NOUN
ejpam-6009	203	23	is	be	AUX
ejpam-6009	203	24	obvious	obvious	ADJ
ejpam-6009	203	25	.	.	PUNCT
ejpam-6009	204	1	(	(	PUNCT
ejpam-6009	204	2	2	2	X
ejpam-6009	204	3	)	)	PUNCT
ejpam-6009	204	4	⇔	⇔	X
ejpam-6009	204	5	(	(	PUNCT
ejpam-6009	204	6	3	3	NUM
ejpam-6009	204	7	)	)	PUNCT
ejpam-6009	204	8	and	and	CCONJ
ejpam-6009	204	9	(	(	PUNCT
ejpam-6009	204	10	4	4	X
ejpam-6009	204	11	)	)	PUNCT
ejpam-6009	204	12	⇔	⇔	X
ejpam-6009	204	13	(	(	PUNCT
ejpam-6009	204	14	5	5	NUM
ejpam-6009	204	15	):	):	PUNCT
ejpam-6009	204	16	it	it	PRON
ejpam-6009	204	17	follows	follow	VERB
ejpam-6009	204	18	from	from	ADP
ejpam-6009	204	19	the	the	DET
ejpam-6009	204	20	fact	fact	NOUN
ejpam-6009	204	21	that	that	SCONJ
ejpam-6009	204	22	f+(y	f+(y	PROPN
ejpam-6009	204	23	−	−	PROPN
ejpam-6009	204	24	b	b	NOUN
ejpam-6009	204	25	)	)	PUNCT
ejpam-6009	204	26	=	=	PUNCT
ejpam-6009	205	1	x	x	SYM
ejpam-6009	205	2	−	−	PROPN
ejpam-6009	205	3	f−(b	f−(b	PROPN
ejpam-6009	205	4	)	)	PUNCT
ejpam-6009	205	5	for	for	ADP
ejpam-6009	205	6	every	every	DET
ejpam-6009	205	7	subset	subset	NOUN
ejpam-6009	205	8	b	b	PROPN
ejpam-6009	205	9	of	of	ADP
ejpam-6009	205	10	y	y	PROPN
ejpam-6009	205	11	.	.	PUNCT
ejpam-6009	206	1	(	(	PUNCT
ejpam-6009	206	2	3	3	X
ejpam-6009	206	3	)	)	PUNCT
ejpam-6009	206	4	⇔	⇔	X
ejpam-6009	206	5	(	(	PUNCT
ejpam-6009	206	6	4	4	NUM
ejpam-6009	206	7	):	):	PUNCT
ejpam-6009	206	8	let	let	VERB
ejpam-6009	206	9	v	v	PART
ejpam-6009	206	10	be	be	AUX
ejpam-6009	206	11	any	any	DET
ejpam-6009	206	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	206	13	-	-	ADJ
ejpam-6009	206	14	open	open	ADJ
ejpam-6009	206	15	set	set	NOUN
ejpam-6009	206	16	of	of	ADP
ejpam-6009	206	17	y	y	PROPN
ejpam-6009	206	18	.	.	PUNCT
ejpam-6009	207	1	since	since	SCONJ
ejpam-6009	207	2	σ1σ2	σ1σ2	ADV
ejpam-6009	207	3	-	-	PUNCT
ejpam-6009	207	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	207	5	-	-	PUNCT
ejpam-6009	207	6	cl(v	cl(v	NOUN
ejpam-6009	207	7	)	)	PUNCT
ejpam-6009	207	8	)	)	PUNCT
ejpam-6009	207	9	is	be	AUX
ejpam-6009	207	10	(	(	PUNCT
ejpam-6009	207	11	σ1	σ1	PROPN
ejpam-6009	207	12	,	,	PUNCT
ejpam-6009	207	13	σ2)ropen	σ2)ropen	NOUN
ejpam-6009	207	14	in	in	ADP
ejpam-6009	207	15	y	y	PROPN
ejpam-6009	207	16	,	,	PUNCT
ejpam-6009	207	17	by	by	ADP
ejpam-6009	207	18	(	(	PUNCT
ejpam-6009	207	19	3	3	X
ejpam-6009	207	20	)	)	PUNCT
ejpam-6009	207	21	we	we	PRON
ejpam-6009	207	22	have	have	VERB
ejpam-6009	207	23	f−(σ1σ2	f−(σ1σ2	VERB
ejpam-6009	207	24	-	-	PUNCT
ejpam-6009	207	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	207	26	-	-	PUNCT
ejpam-6009	207	27	cl(v	cl(v	NOUN
ejpam-6009	207	28	)	)	PUNCT
ejpam-6009	207	29	)	)	PUNCT
ejpam-6009	207	30	)	)	PUNCT
ejpam-6009	208	1	is	be	AUX
ejpam-6009	208	2	(	(	PUNCT
ejpam-6009	208	3	τ1	τ1	NOUN
ejpam-6009	208	4	,	,	PUNCT
ejpam-6009	208	5	τ2)p	τ2)p	NOUN
ejpam-6009	208	6	-	-	PUNCT
ejpam-6009	208	7	closed	closed	ADJ
ejpam-6009	208	8	in	in	ADP
ejpam-6009	208	9	x.	x.	NOUN
ejpam-6009	208	10	the	the	DET
ejpam-6009	208	11	converse	converse	NOUN
ejpam-6009	208	12	is	be	AUX
ejpam-6009	208	13	obvious	obvious	ADJ
ejpam-6009	208	14	.	.	PUNCT
ejpam-6009	209	1	(	(	PUNCT
ejpam-6009	209	2	5	5	X
ejpam-6009	209	3	)	)	PUNCT
ejpam-6009	209	4	⇔	⇔	X
ejpam-6009	209	5	(	(	PUNCT
ejpam-6009	209	6	2	2	NUM
ejpam-6009	209	7	):	):	PUNCT
ejpam-6009	209	8	it	it	PRON
ejpam-6009	209	9	is	be	AUX
ejpam-6009	209	10	similar	similar	ADJ
ejpam-6009	209	11	to	to	ADP
ejpam-6009	209	12	that	that	PRON
ejpam-6009	209	13	of	of	ADP
ejpam-6009	209	14	(	(	PUNCT
ejpam-6009	209	15	3	3	X
ejpam-6009	209	16	)	)	PUNCT
ejpam-6009	209	17	⇔	⇔	X
ejpam-6009	209	18	(	(	PUNCT
ejpam-6009	209	19	4	4	NUM
ejpam-6009	209	20	)	)	PUNCT
ejpam-6009	209	21	.	.	PUNCT
ejpam-6009	210	1	(	(	PUNCT
ejpam-6009	210	2	6	6	X
ejpam-6009	210	3	)	)	PUNCT
ejpam-6009	210	4	⇒	⇒	NOUN
ejpam-6009	210	5	(	(	PUNCT
ejpam-6009	210	6	7	7	NUM
ejpam-6009	210	7	):	):	PUNCT
ejpam-6009	210	8	let	let	VERB
ejpam-6009	210	9	v	v	PART
ejpam-6009	210	10	be	be	AUX
ejpam-6009	210	11	any	any	DET
ejpam-6009	210	12	(	(	PUNCT
ejpam-6009	210	13	σ1	σ1	NOUN
ejpam-6009	210	14	,	,	PUNCT
ejpam-6009	210	15	σ2)s	σ2)s	NOUN
ejpam-6009	210	16	-	-	PUNCT
ejpam-6009	210	17	open	open	ADJ
ejpam-6009	210	18	set	set	NOUN
ejpam-6009	210	19	of	of	ADP
ejpam-6009	210	20	y	y	PROPN
ejpam-6009	210	21	and	and	CCONJ
ejpam-6009	210	22	x	x	PROPN
ejpam-6009	210	23	∈	∈	PROPN
ejpam-6009	210	24	f+(v	f+(v	NOUN
ejpam-6009	210	25	)	)	PUNCT
ejpam-6009	210	26	.	.	PUNCT
ejpam-6009	211	1	then	then	ADV
ejpam-6009	211	2	,	,	PUNCT
ejpam-6009	211	3	f	f	PROPN
ejpam-6009	211	4	(	(	PUNCT
ejpam-6009	211	5	x	x	X
ejpam-6009	211	6	)	)	PUNCT
ejpam-6009	211	7	⊆	⊆	NUM
ejpam-6009	211	8	v	v	NOUN
ejpam-6009	211	9	.	.	PUNCT
ejpam-6009	212	1	by	by	ADP
ejpam-6009	212	2	(	(	PUNCT
ejpam-6009	212	3	6	6	NUM
ejpam-6009	212	4	)	)	PUNCT
ejpam-6009	212	5	,	,	PUNCT
ejpam-6009	212	6	there	there	PRON
ejpam-6009	212	7	exists	exist	VERB
ejpam-6009	212	8	a	a	DET
ejpam-6009	212	9	(	(	PUNCT
ejpam-6009	212	10	τ1	τ1	NOUN
ejpam-6009	212	11	,	,	PUNCT
ejpam-6009	212	12	τ2)p	τ2)p	ADJ
ejpam-6009	212	13	-	-	PUNCT
ejpam-6009	212	14	open	open	ADJ
ejpam-6009	212	15	set	set	NOUN
ejpam-6009	212	16	u	u	NOUN
ejpam-6009	212	17	of	of	ADP
ejpam-6009	212	18	x	x	PUNCT
ejpam-6009	212	19	containing	contain	VERB
ejpam-6009	212	20	x	x	PUNCT
ejpam-6009	212	21	such	such	ADJ
ejpam-6009	212	22	that	that	SCONJ
ejpam-6009	212	23	f	f	PROPN
ejpam-6009	212	24	(	(	PUNCT
ejpam-6009	212	25	u	u	NOUN
ejpam-6009	212	26	)	)	PUNCT
ejpam-6009	212	27	⊆	⊆	NUM
ejpam-6009	212	28	σ1σ2	σ1σ2	NOUN
ejpam-6009	212	29	-	-	NUM
ejpam-6009	212	30	cl(v	cl(v	NOUN
ejpam-6009	212	31	)	)	PUNCT
ejpam-6009	212	32	.	.	PUNCT
ejpam-6009	213	1	this	this	PRON
ejpam-6009	213	2	implies	imply	VERB
ejpam-6009	213	3	that	that	SCONJ
ejpam-6009	213	4	x	x	PUNCT
ejpam-6009	213	5	∈	∈	PROPN
ejpam-6009	213	6	u	u	NOUN
ejpam-6009	213	7	⊆	⊆	NUM
ejpam-6009	213	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	213	9	-	-	PUNCT
ejpam-6009	213	10	cl(v	cl(v	NOUN
ejpam-6009	213	11	)	)	PUNCT
ejpam-6009	213	12	)	)	PUNCT
ejpam-6009	213	13	.	.	PUNCT
ejpam-6009	214	1	thus	thus	ADV
ejpam-6009	214	2	,	,	PUNCT
ejpam-6009	214	3	x	x	SYM
ejpam-6009	214	4	∈	∈	PROPN
ejpam-6009	214	5	(	(	PUNCT
ejpam-6009	214	6	τ1	τ1	NOUN
ejpam-6009	214	7	,	,	PUNCT
ejpam-6009	214	8	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	214	9	+	+	ADJ
ejpam-6009	214	10	(	(	PUNCT
ejpam-6009	214	11	σ1σ2	σ1σ2	NOUN
ejpam-6009	214	12	-	-	NUM
ejpam-6009	214	13	cl(v	cl(v	NOUN
ejpam-6009	214	14	)	)	PUNCT
ejpam-6009	214	15	)	)	PUNCT
ejpam-6009	214	16	)	)	PUNCT
ejpam-6009	214	17	and	and	CCONJ
ejpam-6009	214	18	hence	hence	ADV
ejpam-6009	214	19	f+(v	f+(v	NOUN
ejpam-6009	214	20	)	)	PUNCT
ejpam-6009	215	1	⊆	⊆	NUM
ejpam-6009	215	2	(	(	PUNCT
ejpam-6009	215	3	τ1	τ1	NOUN
ejpam-6009	215	4	,	,	PUNCT
ejpam-6009	215	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	216	1	+	+	ADJ
ejpam-6009	216	2	(	(	PUNCT
ejpam-6009	216	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	216	4	-	-	NUM
ejpam-6009	216	5	cl(v	cl(v	NOUN
ejpam-6009	216	6	)	)	PUNCT
ejpam-6009	216	7	)	)	PUNCT
ejpam-6009	216	8	)	)	PUNCT
ejpam-6009	216	9	.	.	PUNCT
ejpam-6009	217	1	(	(	PUNCT
ejpam-6009	217	2	7	7	X
ejpam-6009	217	3	)	)	PUNCT
ejpam-6009	217	4	⇒	⇒	NOUN
ejpam-6009	217	5	(	(	PUNCT
ejpam-6009	217	6	2	2	NUM
ejpam-6009	217	7	):	):	PUNCT
ejpam-6009	217	8	let	let	VERB
ejpam-6009	217	9	k	k	PRON
ejpam-6009	217	10	be	be	AUX
ejpam-6009	217	11	any	any	DET
ejpam-6009	217	12	(	(	PUNCT
ejpam-6009	217	13	σ1	σ1	NOUN
ejpam-6009	217	14	,	,	PUNCT
ejpam-6009	217	15	σ2)r	σ2)r	NOUN
ejpam-6009	217	16	-	-	PUNCT
ejpam-6009	217	17	closed	close	VERB
ejpam-6009	217	18	set	set	NOUN
ejpam-6009	217	19	of	of	ADP
ejpam-6009	217	20	y	y	PROPN
ejpam-6009	217	21	.	.	PUNCT
ejpam-6009	218	1	then	then	ADV
ejpam-6009	218	2	,	,	PUNCT
ejpam-6009	218	3	k	k	X
ejpam-6009	218	4	is	be	AUX
ejpam-6009	218	5	(	(	PUNCT
ejpam-6009	218	6	σ1	σ1	PROPN
ejpam-6009	218	7	,	,	PUNCT
ejpam-6009	218	8	σ2)s	σ2)s	NOUN
ejpam-6009	218	9	-	-	PUNCT
ejpam-6009	218	10	open	open	ADJ
ejpam-6009	218	11	in	in	ADP
ejpam-6009	218	12	y	y	PROPN
ejpam-6009	218	13	.	.	PUNCT
ejpam-6009	219	1	by	by	ADP
ejpam-6009	219	2	(	(	PUNCT
ejpam-6009	219	3	7	7	NUM
ejpam-6009	219	4	)	)	PUNCT
ejpam-6009	219	5	,	,	PUNCT
ejpam-6009	219	6	we	we	PRON
ejpam-6009	219	7	have	have	VERB
ejpam-6009	219	8	f+(k	f+(k	NUM
ejpam-6009	219	9	)	)	PUNCT
ejpam-6009	220	1	⊆	⊆	NUM
ejpam-6009	220	2	(	(	PUNCT
ejpam-6009	220	3	τ1	τ1	NOUN
ejpam-6009	220	4	,	,	PUNCT
ejpam-6009	220	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	221	1	+	+	ADJ
ejpam-6009	221	2	(	(	PUNCT
ejpam-6009	221	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	221	4	-	-	NUM
ejpam-6009	221	5	cl(k	cl(k	NUM
ejpam-6009	221	6	)	)	PUNCT
ejpam-6009	221	7	)	)	PUNCT
ejpam-6009	221	8	)	)	PUNCT
ejpam-6009	222	1	and	and	CCONJ
ejpam-6009	222	2	hence	hence	ADV
ejpam-6009	222	3	f+(k	f+(k	NUM
ejpam-6009	222	4	)	)	PUNCT
ejpam-6009	222	5	is	be	AUX
ejpam-6009	222	6	(	(	PUNCT
ejpam-6009	222	7	τ1	τ1	NOUN
ejpam-6009	222	8	,	,	PUNCT
ejpam-6009	222	9	τ2)p	τ2)p	NOUN
ejpam-6009	222	10	-	-	PUNCT
ejpam-6009	222	11	open	open	ADJ
ejpam-6009	222	12	in	in	ADP
ejpam-6009	222	13	x.	x.	PROPN
ejpam-6009	222	14	c.	c.	PROPN
ejpam-6009	222	15	viriyapong	viriyapong	PROPN
ejpam-6009	222	16	,	,	PUNCT
ejpam-6009	222	17	a.	a.	PROPN
ejpam-6009	222	18	sama	sama	PROPN
ejpam-6009	222	19	-	-	PUNCT
ejpam-6009	222	20	ae	ae	PROPN
ejpam-6009	222	21	,	,	PUNCT
ejpam-6009	222	22	c.	c.	PROPN
ejpam-6009	222	23	boonpok	boonpok	PROPN
ejpam-6009	222	24	/	/	SYM
ejpam-6009	222	25	eur	eur	PROPN
ejpam-6009	222	26	.	.	PUNCT
ejpam-6009	223	1	j.	j.	PROPN
ejpam-6009	223	2	pure	pure	PROPN
ejpam-6009	223	3	appl	appl	PROPN
ejpam-6009	223	4	.	.	PROPN
ejpam-6009	223	5	math	math	PROPN
ejpam-6009	223	6	,	,	PUNCT
ejpam-6009	223	7	18	18	NUM
ejpam-6009	223	8	(	(	PUNCT
ejpam-6009	223	9	2	2	NUM
ejpam-6009	223	10	)	)	PUNCT
ejpam-6009	223	11	(	(	PUNCT
ejpam-6009	223	12	2025	2025	NUM
ejpam-6009	223	13	)	)	PUNCT
ejpam-6009	223	14	,	,	PUNCT
ejpam-6009	223	15	6009	6009	NUM
ejpam-6009	223	16	9	9	NUM
ejpam-6009	223	17	of	of	ADP
ejpam-6009	223	18	18	18	NUM
ejpam-6009	223	19	(	(	PUNCT
ejpam-6009	223	20	2	2	NUM
ejpam-6009	223	21	)	)	PUNCT
ejpam-6009	223	22	⇒	⇒	NOUN
ejpam-6009	223	23	(	(	PUNCT
ejpam-6009	223	24	6	6	NUM
ejpam-6009	223	25	):	):	PUNCT
ejpam-6009	223	26	let	let	VERB
ejpam-6009	223	27	x	x	PUNCT
ejpam-6009	223	28	∈	∈	PROPN
ejpam-6009	223	29	x	x	X
ejpam-6009	223	30	and	and	CCONJ
ejpam-6009	223	31	v	v	AUX
ejpam-6009	223	32	be	be	AUX
ejpam-6009	223	33	any	any	DET
ejpam-6009	223	34	(	(	PUNCT
ejpam-6009	223	35	σ1	σ1	NOUN
ejpam-6009	223	36	,	,	PUNCT
ejpam-6009	223	37	σ2)s	σ2)s	NOUN
ejpam-6009	223	38	-	-	PUNCT
ejpam-6009	223	39	open	open	ADJ
ejpam-6009	223	40	set	set	NOUN
ejpam-6009	223	41	of	of	ADP
ejpam-6009	223	42	y	y	PROPN
ejpam-6009	223	43	with	with	ADP
ejpam-6009	223	44	f	f	PROPN
ejpam-6009	223	45	(	(	PUNCT
ejpam-6009	223	46	x	x	NOUN
ejpam-6009	223	47	)	)	PUNCT
ejpam-6009	223	48	⊆	⊆	NUM
ejpam-6009	223	49	v	v	NOUN
ejpam-6009	223	50	.	.	PUNCT
ejpam-6009	224	1	since	since	SCONJ
ejpam-6009	224	2	σ1σ2	σ1σ2	NOUN
ejpam-6009	224	3	-	-	NOUN
ejpam-6009	224	4	cl(v	cl(v	NOUN
ejpam-6009	224	5	)	)	PUNCT
ejpam-6009	224	6	is	be	AUX
ejpam-6009	224	7	(	(	PUNCT
ejpam-6009	224	8	σ1	σ1	NOUN
ejpam-6009	224	9	,	,	PUNCT
ejpam-6009	224	10	σ2)r	σ2)r	NOUN
ejpam-6009	224	11	-	-	PUNCT
ejpam-6009	224	12	closed	closed	ADJ
ejpam-6009	224	13	,	,	PUNCT
ejpam-6009	224	14	by	by	ADP
ejpam-6009	224	15	(	(	PUNCT
ejpam-6009	224	16	2	2	X
ejpam-6009	224	17	)	)	PUNCT
ejpam-6009	224	18	we	we	PRON
ejpam-6009	224	19	have	have	AUX
ejpam-6009	224	20	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	224	21	-	-	NOUN
ejpam-6009	224	22	cl(v	cl(v	NOUN
ejpam-6009	224	23	)	)	PUNCT
ejpam-6009	224	24	)	)	PUNCT
ejpam-6009	225	1	is	be	AUX
ejpam-6009	225	2	(	(	PUNCT
ejpam-6009	225	3	τ1	τ1	NOUN
ejpam-6009	225	4	,	,	PUNCT
ejpam-6009	225	5	τ2)p	τ2)p	NOUN
ejpam-6009	225	6	-	-	PUNCT
ejpam-6009	225	7	open	open	ADJ
ejpam-6009	225	8	in	in	ADP
ejpam-6009	225	9	x.	x.	NOUN
ejpam-6009	225	10	then	then	ADV
ejpam-6009	225	11	,	,	PUNCT
ejpam-6009	225	12	there	there	PRON
ejpam-6009	225	13	exists	exist	VERB
ejpam-6009	225	14	a	a	DET
ejpam-6009	225	15	(	(	PUNCT
ejpam-6009	225	16	τ1	τ1	NOUN
ejpam-6009	225	17	,	,	PUNCT
ejpam-6009	225	18	τ2)p	τ2)p	ADJ
ejpam-6009	225	19	-	-	PUNCT
ejpam-6009	225	20	open	open	ADJ
ejpam-6009	225	21	set	set	NOUN
ejpam-6009	225	22	u	u	NOUN
ejpam-6009	225	23	of	of	ADP
ejpam-6009	225	24	x	x	PUNCT
ejpam-6009	225	25	containing	contain	VERB
ejpam-6009	225	26	x	x	PUNCT
ejpam-6009	225	27	such	such	ADJ
ejpam-6009	225	28	that	that	SCONJ
ejpam-6009	225	29	u	u	NOUN
ejpam-6009	225	30	⊆	⊆	NUM
ejpam-6009	225	31	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	225	32	-	-	PUNCT
ejpam-6009	225	33	cl(v	cl(v	NOUN
ejpam-6009	225	34	)	)	PUNCT
ejpam-6009	225	35	)	)	PUNCT
ejpam-6009	225	36	.	.	PUNCT
ejpam-6009	226	1	thus	thus	ADV
ejpam-6009	226	2	,	,	PUNCT
ejpam-6009	226	3	f	f	PROPN
ejpam-6009	226	4	(	(	PUNCT
ejpam-6009	226	5	u	u	NOUN
ejpam-6009	226	6	)	)	PUNCT
ejpam-6009	226	7	⊆	⊆	NUM
ejpam-6009	226	8	σ1σ2	σ1σ2	NOUN
ejpam-6009	226	9	-	-	NUM
ejpam-6009	226	10	cl(v	cl(v	NOUN
ejpam-6009	226	11	)	)	PUNCT
ejpam-6009	226	12	.	.	PUNCT
ejpam-6009	227	1	theorem	theorem	ADJ
ejpam-6009	227	2	6	6	NUM
ejpam-6009	227	3	.	.	PUNCT
ejpam-6009	227	4	for	for	ADP
ejpam-6009	227	5	a	a	DET
ejpam-6009	227	6	multifunction	multifunction	NOUN
ejpam-6009	228	1	f	f	NOUN
ejpam-6009	228	2	:	:	PUNCT
ejpam-6009	228	3	(	(	PUNCT
ejpam-6009	228	4	x	x	NOUN
ejpam-6009	228	5	,	,	PUNCT
ejpam-6009	228	6	τ1	τ1	NOUN
ejpam-6009	228	7	,	,	PUNCT
ejpam-6009	228	8	τ2	τ2	NOUN
ejpam-6009	228	9	)	)	PUNCT
ejpam-6009	228	10	→	→	SYM
ejpam-6009	228	11	(	(	PUNCT
ejpam-6009	228	12	y	y	PROPN
ejpam-6009	228	13	,	,	PUNCT
ejpam-6009	228	14	σ1	σ1	PROPN
ejpam-6009	228	15	,	,	PUNCT
ejpam-6009	228	16	σ2	σ2	NOUN
ejpam-6009	228	17	)	)	PUNCT
ejpam-6009	228	18	,	,	PUNCT
ejpam-6009	228	19	the	the	DET
ejpam-6009	228	20	following	follow	VERB
ejpam-6009	228	21	properties	property	NOUN
ejpam-6009	228	22	are	be	AUX
ejpam-6009	228	23	equivalent	equivalent	ADJ
ejpam-6009	228	24	:	:	PUNCT
ejpam-6009	228	25	(	(	PUNCT
ejpam-6009	228	26	1	1	X
ejpam-6009	228	27	)	)	PUNCT
ejpam-6009	228	28	f	f	PROPN
ejpam-6009	228	29	is	be	AUX
ejpam-6009	228	30	lower	low	ADJ
ejpam-6009	228	31	almost	almost	ADV
ejpam-6009	228	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	228	33	,	,	PUNCT
ejpam-6009	228	34	τ2)p	τ2)p	ADJ
ejpam-6009	228	35	-	-	NOUN
ejpam-6009	228	36	continuous	continuous	ADJ
ejpam-6009	228	37	;	;	PUNCT
ejpam-6009	228	38	(	(	PUNCT
ejpam-6009	228	39	2	2	X
ejpam-6009	228	40	)	)	PUNCT
ejpam-6009	228	41	f−(k	f−(k	PROPN
ejpam-6009	228	42	)	)	PUNCT
ejpam-6009	228	43	is	be	AUX
ejpam-6009	228	44	(	(	PUNCT
ejpam-6009	228	45	τ1	τ1	NOUN
ejpam-6009	228	46	,	,	PUNCT
ejpam-6009	228	47	τ2)p	τ2)p	NOUN
ejpam-6009	228	48	-	-	PUNCT
ejpam-6009	228	49	open	open	ADJ
ejpam-6009	228	50	in	in	ADP
ejpam-6009	228	51	x	x	PUNCT
ejpam-6009	228	52	for	for	ADP
ejpam-6009	228	53	every	every	DET
ejpam-6009	228	54	(	(	PUNCT
ejpam-6009	228	55	σ1	σ1	PROPN
ejpam-6009	228	56	,	,	PUNCT
ejpam-6009	229	1	σ2)r	σ2)r	NOUN
ejpam-6009	229	2	-	-	PUNCT
ejpam-6009	229	3	closed	close	VERB
ejpam-6009	229	4	set	set	ADJ
ejpam-6009	229	5	k	k	PROPN
ejpam-6009	229	6	of	of	ADP
ejpam-6009	229	7	y	y	PROPN
ejpam-6009	229	8	;	;	PUNCT
ejpam-6009	229	9	(	(	PUNCT
ejpam-6009	229	10	3	3	X
ejpam-6009	229	11	)	)	PUNCT
ejpam-6009	229	12	f+(v	f+(v	NOUN
ejpam-6009	229	13	)	)	PUNCT
ejpam-6009	229	14	is	be	AUX
ejpam-6009	229	15	(	(	PUNCT
ejpam-6009	229	16	τ1	τ1	NOUN
ejpam-6009	229	17	,	,	PUNCT
ejpam-6009	229	18	τ2)p	τ2)p	NOUN
ejpam-6009	229	19	-	-	PUNCT
ejpam-6009	229	20	closed	closed	ADJ
ejpam-6009	229	21	in	in	ADP
ejpam-6009	229	22	x	x	PUNCT
ejpam-6009	229	23	for	for	ADP
ejpam-6009	229	24	every	every	DET
ejpam-6009	229	25	(	(	PUNCT
ejpam-6009	229	26	σ1	σ1	PROPN
ejpam-6009	229	27	,	,	PUNCT
ejpam-6009	229	28	σ2)r	σ2)r	NOUN
ejpam-6009	229	29	-	-	PUNCT
ejpam-6009	229	30	open	open	ADJ
ejpam-6009	229	31	set	set	VERB
ejpam-6009	229	32	v	v	NOUN
ejpam-6009	229	33	of	of	ADP
ejpam-6009	229	34	y	y	PROPN
ejpam-6009	229	35	;	;	PUNCT
ejpam-6009	229	36	(	(	PUNCT
ejpam-6009	229	37	4	4	X
ejpam-6009	229	38	)	)	PUNCT
ejpam-6009	229	39	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	229	40	-	-	PUNCT
ejpam-6009	229	41	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	229	42	-	-	PUNCT
ejpam-6009	229	43	cl(v	cl(v	NOUN
ejpam-6009	229	44	)	)	PUNCT
ejpam-6009	229	45	)	)	PUNCT
ejpam-6009	229	46	)	)	PUNCT
ejpam-6009	230	1	is	be	AUX
ejpam-6009	230	2	(	(	PUNCT
ejpam-6009	230	3	τ1	τ1	NOUN
ejpam-6009	230	4	,	,	PUNCT
ejpam-6009	230	5	τ2)p	τ2)p	NOUN
ejpam-6009	230	6	-	-	PUNCT
ejpam-6009	230	7	closed	closed	ADJ
ejpam-6009	230	8	in	in	ADP
ejpam-6009	230	9	x	x	PUNCT
ejpam-6009	230	10	for	for	ADP
ejpam-6009	230	11	every	every	DET
ejpam-6009	230	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	230	13	-	-	ADJ
ejpam-6009	230	14	open	open	ADJ
ejpam-6009	230	15	set	set	NOUN
ejpam-6009	230	16	v	v	NOUN
ejpam-6009	230	17	of	of	ADP
ejpam-6009	230	18	y	y	PROPN
ejpam-6009	230	19	;	;	PUNCT
ejpam-6009	230	20	(	(	PUNCT
ejpam-6009	230	21	5	5	X
ejpam-6009	230	22	)	)	PUNCT
ejpam-6009	230	23	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	230	24	-	-	PUNCT
ejpam-6009	230	25	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6009	230	26	-	-	PUNCT
ejpam-6009	230	27	int(k	int(k	NOUN
ejpam-6009	230	28	)	)	PUNCT
ejpam-6009	230	29	)	)	PUNCT
ejpam-6009	230	30	)	)	PUNCT
ejpam-6009	231	1	is	be	AUX
ejpam-6009	231	2	(	(	PUNCT
ejpam-6009	231	3	τ1	τ1	NOUN
ejpam-6009	231	4	,	,	PUNCT
ejpam-6009	231	5	τ2)p	τ2)p	NOUN
ejpam-6009	231	6	-	-	PUNCT
ejpam-6009	231	7	open	open	ADJ
ejpam-6009	231	8	in	in	ADP
ejpam-6009	231	9	x	x	PUNCT
ejpam-6009	231	10	for	for	ADP
ejpam-6009	231	11	every	every	DET
ejpam-6009	231	12	σ1σ2	σ1σ2	NUM
ejpam-6009	231	13	-	-	PUNCT
ejpam-6009	231	14	closed	closed	ADJ
ejpam-6009	231	15	set	set	NOUN
ejpam-6009	231	16	k	k	PROPN
ejpam-6009	231	17	of	of	ADP
ejpam-6009	231	18	y	y	PROPN
ejpam-6009	231	19	;	;	PUNCT
ejpam-6009	231	20	(	(	PUNCT
ejpam-6009	231	21	6	6	NUM
ejpam-6009	231	22	)	)	PUNCT
ejpam-6009	231	23	for	for	ADP
ejpam-6009	231	24	each	each	DET
ejpam-6009	231	25	x	x	SYM
ejpam-6009	231	26	∈	∈	PROPN
ejpam-6009	231	27	x	x	X
ejpam-6009	231	28	and	and	CCONJ
ejpam-6009	231	29	each	each	DET
ejpam-6009	231	30	(	(	PUNCT
ejpam-6009	231	31	σ1	σ1	PROPN
ejpam-6009	231	32	,	,	PUNCT
ejpam-6009	231	33	σ2)s	σ2)s	NOUN
ejpam-6009	231	34	-	-	PUNCT
ejpam-6009	231	35	open	open	NOUN
ejpam-6009	231	36	set	set	NOUN
ejpam-6009	231	37	v	v	NOUN
ejpam-6009	231	38	of	of	ADP
ejpam-6009	231	39	y	y	PRON
ejpam-6009	231	40	such	such	ADJ
ejpam-6009	231	41	that	that	SCONJ
ejpam-6009	231	42	f	f	PROPN
ejpam-6009	231	43	(	(	PUNCT
ejpam-6009	231	44	x	x	NOUN
ejpam-6009	231	45	)	)	PUNCT
ejpam-6009	231	46	∩	∩	NOUN
ejpam-6009	231	47	v	v	ADP
ejpam-6009	231	48	̸=	̸=	PROPN
ejpam-6009	231	49	∅	∅	NOUN
ejpam-6009	231	50	,	,	PUNCT
ejpam-6009	231	51	there	there	PRON
ejpam-6009	231	52	exists	exist	VERB
ejpam-6009	231	53	a	a	DET
ejpam-6009	231	54	(	(	PUNCT
ejpam-6009	231	55	τ1	τ1	NOUN
ejpam-6009	231	56	,	,	PUNCT
ejpam-6009	231	57	τ2)p	τ2)p	ADJ
ejpam-6009	231	58	-	-	PUNCT
ejpam-6009	231	59	open	open	ADJ
ejpam-6009	231	60	set	set	NOUN
ejpam-6009	231	61	u	u	NOUN
ejpam-6009	231	62	of	of	ADP
ejpam-6009	231	63	x	x	PUNCT
ejpam-6009	231	64	containing	contain	VERB
ejpam-6009	231	65	x	x	PUNCT
ejpam-6009	231	66	such	such	ADJ
ejpam-6009	231	67	that	that	SCONJ
ejpam-6009	231	68	f	f	PROPN
ejpam-6009	231	69	(	(	PUNCT
ejpam-6009	231	70	z	z	NOUN
ejpam-6009	231	71	)	)	PUNCT
ejpam-6009	231	72	∩	∩	NOUN
ejpam-6009	231	73	σ1σ2	σ1σ2	NOUN
ejpam-6009	231	74	-	-	NUM
ejpam-6009	231	75	cl(v	cl(v	NOUN
ejpam-6009	231	76	)	)	PUNCT
ejpam-6009	231	77	̸=	̸=	NOUN
ejpam-6009	231	78	∅	∅	NOUN
ejpam-6009	231	79	for	for	ADP
ejpam-6009	231	80	each	each	DET
ejpam-6009	231	81	z	z	NOUN
ejpam-6009	231	82	∈	∈	PROPN
ejpam-6009	231	83	u	u	NOUN
ejpam-6009	231	84	;	;	PUNCT
ejpam-6009	231	85	(	(	PUNCT
ejpam-6009	231	86	7	7	X
ejpam-6009	231	87	)	)	PUNCT
ejpam-6009	231	88	f−(v	f−(v	NOUN
ejpam-6009	231	89	)	)	PUNCT
ejpam-6009	231	90	⊆	⊆	NUM
ejpam-6009	231	91	(	(	PUNCT
ejpam-6009	231	92	τ1	τ1	NOUN
ejpam-6009	231	93	,	,	PUNCT
ejpam-6009	231	94	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	231	95	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	231	96	-	-	NOUN
ejpam-6009	231	97	cl(v	cl(v	NOUN
ejpam-6009	231	98	)	)	PUNCT
ejpam-6009	231	99	)	)	PUNCT
ejpam-6009	231	100	)	)	PUNCT
ejpam-6009	231	101	for	for	ADP
ejpam-6009	231	102	every	every	DET
ejpam-6009	231	103	(	(	PUNCT
ejpam-6009	231	104	σ1	σ1	PROPN
ejpam-6009	231	105	,	,	PUNCT
ejpam-6009	231	106	σ2)s	σ2)s	NOUN
ejpam-6009	231	107	-	-	PUNCT
ejpam-6009	231	108	open	open	NOUN
ejpam-6009	231	109	set	set	NOUN
ejpam-6009	231	110	v	v	NOUN
ejpam-6009	231	111	of	of	ADP
ejpam-6009	231	112	y	y	PROPN
ejpam-6009	231	113	.	.	PUNCT
ejpam-6009	232	1	proof	proof	NOUN
ejpam-6009	232	2	.	.	PUNCT
ejpam-6009	233	1	the	the	DET
ejpam-6009	233	2	proof	proof	NOUN
ejpam-6009	233	3	is	be	AUX
ejpam-6009	233	4	similar	similar	ADJ
ejpam-6009	233	5	to	to	ADP
ejpam-6009	233	6	that	that	PRON
ejpam-6009	233	7	of	of	ADP
ejpam-6009	233	8	theorem	theorem	ADJ
ejpam-6009	233	9	5	5	NUM
ejpam-6009	233	10	.	.	PUNCT
ejpam-6009	233	11	theorem	theorem	VERB
ejpam-6009	233	12	7	7	NUM
ejpam-6009	233	13	.	.	X
ejpam-6009	233	14	for	for	ADP
ejpam-6009	233	15	a	a	DET
ejpam-6009	233	16	multifunction	multifunction	NOUN
ejpam-6009	233	17	f	f	NOUN
ejpam-6009	233	18	:	:	PUNCT
ejpam-6009	233	19	(	(	PUNCT
ejpam-6009	233	20	x	x	NOUN
ejpam-6009	233	21	,	,	PUNCT
ejpam-6009	233	22	τ1	τ1	NOUN
ejpam-6009	233	23	,	,	PUNCT
ejpam-6009	233	24	τ2	τ2	NOUN
ejpam-6009	233	25	)	)	PUNCT
ejpam-6009	233	26	→	→	SYM
ejpam-6009	233	27	(	(	PUNCT
ejpam-6009	233	28	y	y	PROPN
ejpam-6009	233	29	,	,	PUNCT
ejpam-6009	233	30	σ1	σ1	PROPN
ejpam-6009	233	31	,	,	PUNCT
ejpam-6009	233	32	σ2	σ2	NOUN
ejpam-6009	233	33	)	)	PUNCT
ejpam-6009	233	34	,	,	PUNCT
ejpam-6009	233	35	the	the	DET
ejpam-6009	233	36	following	follow	VERB
ejpam-6009	233	37	properties	property	NOUN
ejpam-6009	233	38	are	be	AUX
ejpam-6009	233	39	equivalent	equivalent	ADJ
ejpam-6009	233	40	:	:	PUNCT
ejpam-6009	233	41	(	(	PUNCT
ejpam-6009	233	42	1	1	X
ejpam-6009	233	43	)	)	PUNCT
ejpam-6009	233	44	f	f	PROPN
ejpam-6009	233	45	is	be	AUX
ejpam-6009	233	46	upper	upper	ADJ
ejpam-6009	233	47	almost	almost	ADV
ejpam-6009	233	48	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	233	49	,	,	PUNCT
ejpam-6009	233	50	τ2)p	τ2)p	ADJ
ejpam-6009	233	51	-	-	NOUN
ejpam-6009	233	52	continuous	continuous	ADJ
ejpam-6009	233	53	;	;	PUNCT
ejpam-6009	233	54	(	(	PUNCT
ejpam-6009	233	55	2	2	X
ejpam-6009	233	56	)	)	PUNCT
ejpam-6009	233	57	(	(	PUNCT
ejpam-6009	233	58	τ1	τ1	NOUN
ejpam-6009	233	59	,	,	PUNCT
ejpam-6009	233	60	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	233	61	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	233	62	-	-	SYM
ejpam-6009	233	63	int(k	int(k	NUM
ejpam-6009	233	64	)	)	PUNCT
ejpam-6009	233	65	)	)	PUNCT
ejpam-6009	233	66	)	)	PUNCT
ejpam-6009	234	1	⊆	⊆	X
ejpam-6009	234	2	f−(k	f−(k	PROPN
ejpam-6009	234	3	)	)	PUNCT
ejpam-6009	234	4	for	for	ADP
ejpam-6009	234	5	every	every	DET
ejpam-6009	234	6	(	(	PUNCT
ejpam-6009	234	7	σ1	σ1	PROPN
ejpam-6009	234	8	,	,	PUNCT
ejpam-6009	234	9	σ2)s	σ2)s	NOUN
ejpam-6009	234	10	-	-	PUNCT
ejpam-6009	234	11	closed	close	VERB
ejpam-6009	234	12	set	set	NOUN
ejpam-6009	234	13	k	k	PROPN
ejpam-6009	234	14	of	of	ADP
ejpam-6009	234	15	y	y	PROPN
ejpam-6009	234	16	;	;	PUNCT
ejpam-6009	234	17	(	(	PUNCT
ejpam-6009	234	18	3	3	X
ejpam-6009	234	19	)	)	PUNCT
ejpam-6009	234	20	(	(	PUNCT
ejpam-6009	234	21	τ1	τ1	NOUN
ejpam-6009	234	22	,	,	PUNCT
ejpam-6009	234	23	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	234	24	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	234	25	-	-	PUNCT
ejpam-6009	234	26	int((σ1	int((σ1	ADJ
ejpam-6009	234	27	,	,	PUNCT
ejpam-6009	234	28	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	234	29	)	)	PUNCT
ejpam-6009	234	30	)	)	PUNCT
ejpam-6009	234	31	)	)	PUNCT
ejpam-6009	234	32	)	)	PUNCT
ejpam-6009	235	1	⊆	⊆	NUM
ejpam-6009	235	2	f−((σ1	f−((σ1	NOUN
ejpam-6009	235	3	,	,	PUNCT
ejpam-6009	235	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	235	5	)	)	PUNCT
ejpam-6009	235	6	)	)	PUNCT
ejpam-6009	235	7	for	for	ADP
ejpam-6009	235	8	every	every	DET
ejpam-6009	235	9	subset	subset	NOUN
ejpam-6009	235	10	b	b	PROPN
ejpam-6009	235	11	of	of	ADP
ejpam-6009	235	12	y	y	PROPN
ejpam-6009	235	13	;	;	PUNCT
ejpam-6009	235	14	(	(	PUNCT
ejpam-6009	235	15	4	4	X
ejpam-6009	235	16	)	)	PUNCT
ejpam-6009	235	17	f+((σ1	f+((σ1	NOUN
ejpam-6009	235	18	,	,	PUNCT
ejpam-6009	235	19	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	235	20	)	)	PUNCT
ejpam-6009	235	21	)	)	PUNCT
ejpam-6009	235	22	⊆	⊆	NUM
ejpam-6009	235	23	(	(	PUNCT
ejpam-6009	235	24	τ1	τ1	NOUN
ejpam-6009	235	25	,	,	PUNCT
ejpam-6009	235	26	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	236	1	+	+	ADJ
ejpam-6009	236	2	(	(	PUNCT
ejpam-6009	236	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	236	4	-	-	PUNCT
ejpam-6009	236	5	cl((σ1	cl((σ1	NOUN
ejpam-6009	236	6	,	,	PUNCT
ejpam-6009	236	7	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	236	8	)	)	PUNCT
ejpam-6009	236	9	)	)	PUNCT
ejpam-6009	236	10	)	)	PUNCT
ejpam-6009	236	11	)	)	PUNCT
ejpam-6009	236	12	for	for	ADP
ejpam-6009	236	13	every	every	DET
ejpam-6009	236	14	subset	subset	NOUN
ejpam-6009	236	15	b	b	PROPN
ejpam-6009	236	16	of	of	ADP
ejpam-6009	236	17	y	y	PROPN
ejpam-6009	236	18	.	.	PUNCT
ejpam-6009	237	1	proof	proof	NOUN
ejpam-6009	237	2	.	.	PUNCT
ejpam-6009	238	1	(	(	PUNCT
ejpam-6009	238	2	1	1	X
ejpam-6009	238	3	)	)	PUNCT
ejpam-6009	238	4	⇒	⇒	NOUN
ejpam-6009	238	5	(	(	PUNCT
ejpam-6009	238	6	2	2	NUM
ejpam-6009	238	7	):	):	PUNCT
ejpam-6009	238	8	letk	letk	ADJ
ejpam-6009	238	9	be	be	VERB
ejpam-6009	238	10	any	any	DET
ejpam-6009	238	11	(	(	PUNCT
ejpam-6009	238	12	σ1	σ1	NOUN
ejpam-6009	238	13	,	,	PUNCT
ejpam-6009	238	14	σ2)s	σ2)s	NOUN
ejpam-6009	238	15	-	-	PUNCT
ejpam-6009	238	16	closed	close	VERB
ejpam-6009	238	17	set	set	NOUN
ejpam-6009	238	18	of	of	ADP
ejpam-6009	238	19	y	y	PROPN
ejpam-6009	238	20	.	.	PUNCT
ejpam-6009	239	1	then	then	ADV
ejpam-6009	239	2	,	,	PUNCT
ejpam-6009	239	3	y	y	PROPN
ejpam-6009	239	4	−k	−k	PROPN
ejpam-6009	239	5	is	be	AUX
ejpam-6009	239	6	(	(	PUNCT
ejpam-6009	239	7	σ1	σ1	PROPN
ejpam-6009	239	8	,	,	PUNCT
ejpam-6009	239	9	σ2)s	σ2)s	NOUN
ejpam-6009	239	10	-	-	PUNCT
ejpam-6009	239	11	open	open	ADJ
ejpam-6009	239	12	in	in	ADP
ejpam-6009	239	13	y	y	PROPN
ejpam-6009	239	14	.	.	PUNCT
ejpam-6009	240	1	by	by	ADP
ejpam-6009	240	2	theorem	theorem	NOUN
ejpam-6009	240	3	5	5	NUM
ejpam-6009	240	4	,	,	PUNCT
ejpam-6009	240	5	f+(y	f+(y	PROPN
ejpam-6009	240	6	−k	−k	PROPN
ejpam-6009	240	7	)	)	PUNCT
ejpam-6009	240	8	⊆	⊆	NUM
ejpam-6009	240	9	(	(	PUNCT
ejpam-6009	240	10	τ1	τ1	NOUN
ejpam-6009	240	11	,	,	PUNCT
ejpam-6009	240	12	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	240	13	+	+	ADJ
ejpam-6009	240	14	(	(	PUNCT
ejpam-6009	240	15	y	y	PROPN
ejpam-6009	240	16	−	−	PROPN
ejpam-6009	240	17	σ1σ2	σ1σ2	NUM
ejpam-6009	240	18	-	-	PUNCT
ejpam-6009	240	19	int(k	int(k	NOUN
ejpam-6009	240	20	)	)	PUNCT
ejpam-6009	240	21	)	)	PUNCT
ejpam-6009	240	22	)	)	PUNCT
ejpam-6009	240	23	.	.	PUNCT
ejpam-6009	241	1	thus	thus	ADV
ejpam-6009	241	2	,	,	PUNCT
ejpam-6009	241	3	x	x	PUNCT
ejpam-6009	241	4	−	−	PRON
ejpam-6009	241	5	f−(k	f−(k	PROPN
ejpam-6009	241	6	)	)	PUNCT
ejpam-6009	241	7	⊆	⊆	NUM
ejpam-6009	241	8	(	(	PUNCT
ejpam-6009	241	9	τ1	τ1	NOUN
ejpam-6009	241	10	,	,	PUNCT
ejpam-6009	241	11	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	241	12	+	+	ADJ
ejpam-6009	241	13	(	(	PUNCT
ejpam-6009	241	14	y	y	PROPN
ejpam-6009	241	15	−	−	PROPN
ejpam-6009	241	16	σ1σ2	σ1σ2	NUM
ejpam-6009	241	17	-	-	PUNCT
ejpam-6009	241	18	int(k	int(k	NOUN
ejpam-6009	241	19	)	)	PUNCT
ejpam-6009	241	20	)	)	PUNCT
ejpam-6009	241	21	)	)	PUNCT
ejpam-6009	242	1	=	=	PRON
ejpam-6009	242	2	(	(	PUNCT
ejpam-6009	242	3	τ1	τ1	NOUN
ejpam-6009	242	4	,	,	PUNCT
ejpam-6009	242	5	τ2)-pint(x	τ2)-pint(x	PUNCT
ejpam-6009	242	6	−	−	ADP
ejpam-6009	242	7	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	242	8	-	-	PUNCT
ejpam-6009	242	9	int(k	int(k	NOUN
ejpam-6009	242	10	)	)	PUNCT
ejpam-6009	242	11	)	)	PUNCT
ejpam-6009	242	12	)	)	PUNCT
ejpam-6009	243	1	=	=	PUNCT
ejpam-6009	243	2	x	x	X
ejpam-6009	243	3	−	−	PROPN
ejpam-6009	243	4	(	(	PUNCT
ejpam-6009	243	5	τ1	τ1	PROPN
ejpam-6009	243	6	,	,	PUNCT
ejpam-6009	243	7	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	243	8	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	243	9	-	-	SYM
ejpam-6009	243	10	int(k	int(k	NUM
ejpam-6009	243	11	)	)	PUNCT
ejpam-6009	243	12	)	)	PUNCT
ejpam-6009	243	13	)	)	PUNCT
ejpam-6009	243	14	and	and	CCONJ
ejpam-6009	243	15	hence	hence	ADV
ejpam-6009	243	16	(	(	PUNCT
ejpam-6009	243	17	τ1	τ1	NOUN
ejpam-6009	243	18	,	,	PUNCT
ejpam-6009	243	19	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	243	20	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	243	21	-	-	SYM
ejpam-6009	243	22	int(k	int(k	NUM
ejpam-6009	243	23	)	)	PUNCT
ejpam-6009	243	24	)	)	PUNCT
ejpam-6009	243	25	)	)	PUNCT
ejpam-6009	244	1	⊆	⊆	NUM
ejpam-6009	244	2	f−(k	f−(k	PROPN
ejpam-6009	244	3	)	)	PUNCT
ejpam-6009	244	4	.	.	PUNCT
ejpam-6009	245	1	c.	c.	PROPN
ejpam-6009	245	2	viriyapong	viriyapong	PROPN
ejpam-6009	245	3	,	,	PUNCT
ejpam-6009	245	4	a.	a.	PROPN
ejpam-6009	245	5	sama	sama	PROPN
ejpam-6009	245	6	-	-	PUNCT
ejpam-6009	245	7	ae	ae	PROPN
ejpam-6009	245	8	,	,	PUNCT
ejpam-6009	245	9	c.	c.	PROPN
ejpam-6009	245	10	boonpok	boonpok	PROPN
ejpam-6009	245	11	/	/	SYM
ejpam-6009	245	12	eur	eur	PROPN
ejpam-6009	245	13	.	.	PUNCT
ejpam-6009	246	1	j.	j.	PROPN
ejpam-6009	246	2	pure	pure	PROPN
ejpam-6009	246	3	appl	appl	PROPN
ejpam-6009	246	4	.	.	PROPN
ejpam-6009	246	5	math	math	PROPN
ejpam-6009	246	6	,	,	PUNCT
ejpam-6009	246	7	18	18	NUM
ejpam-6009	246	8	(	(	PUNCT
ejpam-6009	246	9	2	2	NUM
ejpam-6009	246	10	)	)	PUNCT
ejpam-6009	246	11	(	(	PUNCT
ejpam-6009	246	12	2025	2025	NUM
ejpam-6009	246	13	)	)	PUNCT
ejpam-6009	246	14	,	,	PUNCT
ejpam-6009	246	15	6009	6009	NUM
ejpam-6009	246	16	10	10	NUM
ejpam-6009	246	17	of	of	ADP
ejpam-6009	246	18	18	18	NUM
ejpam-6009	246	19	(	(	PUNCT
ejpam-6009	246	20	2	2	NUM
ejpam-6009	246	21	)	)	PUNCT
ejpam-6009	246	22	⇒	⇒	NOUN
ejpam-6009	246	23	(	(	PUNCT
ejpam-6009	246	24	3	3	NUM
ejpam-6009	246	25	):	):	PUNCT
ejpam-6009	246	26	let	let	VERB
ejpam-6009	246	27	b	b	X
ejpam-6009	246	28	be	be	AUX
ejpam-6009	246	29	any	any	DET
ejpam-6009	246	30	subset	subset	NOUN
ejpam-6009	246	31	of	of	ADP
ejpam-6009	246	32	y	y	PROPN
ejpam-6009	246	33	.	.	PUNCT
ejpam-6009	247	1	then	then	ADV
ejpam-6009	247	2	,	,	PUNCT
ejpam-6009	247	3	(	(	PUNCT
ejpam-6009	247	4	σ1	σ1	PROPN
ejpam-6009	247	5	,	,	PUNCT
ejpam-6009	247	6	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	247	7	)	)	PUNCT
ejpam-6009	247	8	)	)	PUNCT
ejpam-6009	247	9	is	be	AUX
ejpam-6009	247	10	(	(	PUNCT
ejpam-6009	247	11	σ1	σ1	PROPN
ejpam-6009	247	12	,	,	PUNCT
ejpam-6009	247	13	σ2)s	σ2)s	NOUN
ejpam-6009	247	14	-	-	PUNCT
ejpam-6009	247	15	closed	close	VERB
ejpam-6009	247	16	in	in	ADP
ejpam-6009	247	17	y	y	PROPN
ejpam-6009	247	18	,	,	PUNCT
ejpam-6009	247	19	by	by	ADP
ejpam-6009	247	20	(	(	PUNCT
ejpam-6009	247	21	2	2	X
ejpam-6009	247	22	)	)	PUNCT
ejpam-6009	247	23	we	we	PRON
ejpam-6009	247	24	have	have	AUX
ejpam-6009	247	25	(	(	PUNCT
ejpam-6009	247	26	τ1	τ1	NOUN
ejpam-6009	247	27	,	,	PUNCT
ejpam-6009	247	28	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	247	29	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	247	30	-	-	PUNCT
ejpam-6009	247	31	int((σ1	int((σ1	ADJ
ejpam-6009	247	32	,	,	PUNCT
ejpam-6009	247	33	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	247	34	)	)	PUNCT
ejpam-6009	247	35	)	)	PUNCT
ejpam-6009	247	36	)	)	PUNCT
ejpam-6009	247	37	)	)	PUNCT
ejpam-6009	248	1	⊆	⊆	NUM
ejpam-6009	248	2	f−((σ1	f−((σ1	NOUN
ejpam-6009	248	3	,	,	PUNCT
ejpam-6009	248	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	248	5	)	)	PUNCT
ejpam-6009	248	6	)	)	PUNCT
ejpam-6009	248	7	.	.	PUNCT
ejpam-6009	249	1	(	(	PUNCT
ejpam-6009	249	2	3	3	X
ejpam-6009	249	3	)	)	PUNCT
ejpam-6009	249	4	⇒	⇒	NOUN
ejpam-6009	249	5	(	(	PUNCT
ejpam-6009	249	6	4	4	NUM
ejpam-6009	249	7	):	):	PUNCT
ejpam-6009	249	8	let	let	VERB
ejpam-6009	249	9	b	b	X
ejpam-6009	249	10	be	be	AUX
ejpam-6009	249	11	any	any	DET
ejpam-6009	249	12	subset	subset	NOUN
ejpam-6009	249	13	of	of	ADP
ejpam-6009	249	14	y	y	PROPN
ejpam-6009	249	15	.	.	PUNCT
ejpam-6009	250	1	by	by	ADP
ejpam-6009	250	2	(	(	PUNCT
ejpam-6009	250	3	3	3	NUM
ejpam-6009	250	4	)	)	PUNCT
ejpam-6009	250	5	,	,	PUNCT
ejpam-6009	250	6	we	we	PRON
ejpam-6009	250	7	have	have	VERB
ejpam-6009	250	8	x	x	X
ejpam-6009	250	9	−	−	NOUN
ejpam-6009	250	10	f+((σ1	f+((σ1	NOUN
ejpam-6009	250	11	,	,	PUNCT
ejpam-6009	250	12	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	250	13	)	)	PUNCT
ejpam-6009	250	14	)	)	PUNCT
ejpam-6009	251	1	=	=	SYM
ejpam-6009	251	2	f−((σ1	f−((σ1	NOUN
ejpam-6009	251	3	,	,	PUNCT
ejpam-6009	251	4	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6009	251	5	−b	−b	ADJ
ejpam-6009	251	6	)	)	PUNCT
ejpam-6009	251	7	)	)	PUNCT
ejpam-6009	251	8	⊇	⊇	NOUN
ejpam-6009	251	9	(	(	PUNCT
ejpam-6009	251	10	τ1	τ1	PROPN
ejpam-6009	251	11	,	,	PUNCT
ejpam-6009	251	12	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	251	13	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	251	14	-	-	PUNCT
ejpam-6009	251	15	int((σ1	int((σ1	ADJ
ejpam-6009	251	16	,	,	PUNCT
ejpam-6009	251	17	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6009	251	18	−b	−b	NOUN
ejpam-6009	251	19	)	)	PUNCT
ejpam-6009	251	20	)	)	PUNCT
ejpam-6009	251	21	)	)	PUNCT
ejpam-6009	251	22	)	)	PUNCT
ejpam-6009	252	1	=	=	PRON
ejpam-6009	252	2	(	(	PUNCT
ejpam-6009	252	3	τ1	τ1	PROPN
ejpam-6009	252	4	,	,	PUNCT
ejpam-6009	252	5	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6009	252	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	252	7	-	-	PUNCT
ejpam-6009	252	8	int(y	int(y	ADJ
ejpam-6009	252	9	−	−	PROPN
ejpam-6009	252	10	(	(	PUNCT
ejpam-6009	252	11	σ1	σ1	PROPN
ejpam-6009	252	12	,	,	PUNCT
ejpam-6009	252	13	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	252	14	)	)	PUNCT
ejpam-6009	252	15	)	)	PUNCT
ejpam-6009	252	16	)	)	PUNCT
ejpam-6009	252	17	)	)	PUNCT
ejpam-6009	253	1	=	=	PRON
ejpam-6009	253	2	(	(	PUNCT
ejpam-6009	253	3	τ1	τ1	PROPN
ejpam-6009	253	4	,	,	PUNCT
ejpam-6009	253	5	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	253	6	−(y	−(y	NOUN
ejpam-6009	253	7	−	−	NOUN
ejpam-6009	253	8	σ1σ2	σ1σ2	NOUN
ejpam-6009	253	9	-	-	PUNCT
ejpam-6009	253	10	cl((σ1	cl((σ1	NOUN
ejpam-6009	253	11	,	,	PUNCT
ejpam-6009	253	12	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	253	13	)	)	PUNCT
ejpam-6009	253	14	)	)	PUNCT
ejpam-6009	253	15	)	)	PUNCT
ejpam-6009	253	16	)	)	PUNCT
ejpam-6009	254	1	=	=	PRON
ejpam-6009	254	2	(	(	PUNCT
ejpam-6009	254	3	τ1	τ1	PROPN
ejpam-6009	254	4	,	,	PUNCT
ejpam-6009	254	5	τ2)-pcl(x	τ2)-pcl(x	PUNCT
ejpam-6009	255	1	−	−	VERB
ejpam-6009	255	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	255	3	-	-	PUNCT
ejpam-6009	255	4	cl((σ1	cl((σ1	NOUN
ejpam-6009	255	5	,	,	PUNCT
ejpam-6009	255	6	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	255	7	)	)	PUNCT
ejpam-6009	255	8	)	)	PUNCT
ejpam-6009	255	9	)	)	PUNCT
ejpam-6009	255	10	)	)	PUNCT
ejpam-6009	256	1	=	=	PUNCT
ejpam-6009	256	2	x	x	X
ejpam-6009	257	1	−	−	PROPN
ejpam-6009	257	2	(	(	PUNCT
ejpam-6009	257	3	τ1	τ1	NOUN
ejpam-6009	257	4	,	,	PUNCT
ejpam-6009	257	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	258	1	+	+	ADJ
ejpam-6009	258	2	(	(	PUNCT
ejpam-6009	258	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	258	4	-	-	PUNCT
ejpam-6009	258	5	cl((σ1	cl((σ1	NOUN
ejpam-6009	258	6	,	,	PUNCT
ejpam-6009	258	7	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	258	8	)	)	PUNCT
ejpam-6009	258	9	)	)	PUNCT
ejpam-6009	258	10	)	)	PUNCT
ejpam-6009	258	11	)	)	PUNCT
ejpam-6009	258	12	and	and	CCONJ
ejpam-6009	258	13	hence	hence	ADV
ejpam-6009	258	14	f+((σ1	f+((σ1	ADV
ejpam-6009	258	15	,	,	PUNCT
ejpam-6009	258	16	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	258	17	)	)	PUNCT
ejpam-6009	258	18	)	)	PUNCT
ejpam-6009	259	1	⊆	⊆	NUM
ejpam-6009	259	2	(	(	PUNCT
ejpam-6009	259	3	τ1	τ1	NOUN
ejpam-6009	259	4	,	,	PUNCT
ejpam-6009	259	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	259	6	+	+	ADJ
ejpam-6009	259	7	(	(	PUNCT
ejpam-6009	259	8	σ1σ2	σ1σ2	NOUN
ejpam-6009	259	9	-	-	PUNCT
ejpam-6009	259	10	cl((σ1	cl((σ1	NOUN
ejpam-6009	259	11	,	,	PUNCT
ejpam-6009	259	12	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	259	13	)	)	PUNCT
ejpam-6009	259	14	)	)	PUNCT
ejpam-6009	259	15	)	)	PUNCT
ejpam-6009	259	16	)	)	PUNCT
ejpam-6009	259	17	.	.	PUNCT
ejpam-6009	260	1	(	(	PUNCT
ejpam-6009	260	2	4	4	X
ejpam-6009	260	3	)	)	PUNCT
ejpam-6009	260	4	⇒	⇒	NOUN
ejpam-6009	260	5	(	(	PUNCT
ejpam-6009	260	6	1	1	NUM
ejpam-6009	260	7	):	):	PUNCT
ejpam-6009	260	8	let	let	VERB
ejpam-6009	260	9	v	v	PART
ejpam-6009	260	10	be	be	AUX
ejpam-6009	260	11	any	any	DET
ejpam-6009	260	12	(	(	PUNCT
ejpam-6009	260	13	σ1	σ1	NOUN
ejpam-6009	260	14	,	,	PUNCT
ejpam-6009	260	15	σ2)s	σ2)s	NOUN
ejpam-6009	260	16	-	-	PUNCT
ejpam-6009	260	17	open	open	ADJ
ejpam-6009	260	18	set	set	NOUN
ejpam-6009	260	19	of	of	ADP
ejpam-6009	260	20	y	y	PROPN
ejpam-6009	260	21	.	.	PUNCT
ejpam-6009	261	1	then	then	ADV
ejpam-6009	261	2	,	,	PUNCT
ejpam-6009	261	3	v	v	NOUN
ejpam-6009	261	4	=	=	SYM
ejpam-6009	261	5	(	(	PUNCT
ejpam-6009	261	6	σ1	σ1	PROPN
ejpam-6009	261	7	,	,	PUNCT
ejpam-6009	261	8	σ2)-sint(v	σ2)-sint(v	PROPN
ejpam-6009	261	9	)	)	PUNCT
ejpam-6009	261	10	and	and	CCONJ
ejpam-6009	261	11	by	by	ADP
ejpam-6009	261	12	(	(	PUNCT
ejpam-6009	261	13	4	4	NUM
ejpam-6009	261	14	)	)	PUNCT
ejpam-6009	261	15	,	,	PUNCT
ejpam-6009	261	16	f+(v	f+(v	PROPN
ejpam-6009	261	17	)	)	PUNCT
ejpam-6009	262	1	⊆	⊆	NUM
ejpam-6009	262	2	(	(	PUNCT
ejpam-6009	262	3	τ1	τ1	NOUN
ejpam-6009	262	4	,	,	PUNCT
ejpam-6009	262	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	263	1	+	+	ADJ
ejpam-6009	263	2	(	(	PUNCT
ejpam-6009	263	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	263	4	-	-	NUM
ejpam-6009	263	5	cl(v	cl(v	NOUN
ejpam-6009	263	6	)	)	PUNCT
ejpam-6009	263	7	)	)	PUNCT
ejpam-6009	263	8	)	)	PUNCT
ejpam-6009	263	9	.	.	PUNCT
ejpam-6009	264	1	by	by	ADP
ejpam-6009	264	2	theorem	theorem	NOUN
ejpam-6009	264	3	5	5	NUM
ejpam-6009	264	4	,	,	PUNCT
ejpam-6009	264	5	f	f	PROPN
ejpam-6009	264	6	is	be	AUX
ejpam-6009	264	7	upper	upper	ADJ
ejpam-6009	264	8	almost	almost	ADV
ejpam-6009	264	9	contra(τ1	contra(τ1	NOUN
ejpam-6009	264	10	,	,	PUNCT
ejpam-6009	264	11	τ2)p	τ2)p	ADJ
ejpam-6009	264	12	-	-	ADJ
ejpam-6009	264	13	continuous	continuous	ADJ
ejpam-6009	264	14	.	.	PUNCT
ejpam-6009	265	1	theorem	theorem	ADJ
ejpam-6009	265	2	8	8	NUM
ejpam-6009	265	3	.	.	PUNCT
ejpam-6009	266	1	for	for	ADP
ejpam-6009	266	2	a	a	DET
ejpam-6009	266	3	multifunction	multifunction	NOUN
ejpam-6009	266	4	f	f	NOUN
ejpam-6009	266	5	:	:	PUNCT
ejpam-6009	266	6	(	(	PUNCT
ejpam-6009	266	7	x	x	NOUN
ejpam-6009	266	8	,	,	PUNCT
ejpam-6009	266	9	τ1	τ1	NOUN
ejpam-6009	266	10	,	,	PUNCT
ejpam-6009	266	11	τ2	τ2	NOUN
ejpam-6009	266	12	)	)	PUNCT
ejpam-6009	266	13	→	→	SYM
ejpam-6009	266	14	(	(	PUNCT
ejpam-6009	266	15	y	y	PROPN
ejpam-6009	266	16	,	,	PUNCT
ejpam-6009	266	17	σ1	σ1	PROPN
ejpam-6009	266	18	,	,	PUNCT
ejpam-6009	266	19	σ2	σ2	NOUN
ejpam-6009	266	20	)	)	PUNCT
ejpam-6009	266	21	,	,	PUNCT
ejpam-6009	266	22	the	the	DET
ejpam-6009	266	23	following	follow	VERB
ejpam-6009	266	24	properties	property	NOUN
ejpam-6009	266	25	are	be	AUX
ejpam-6009	266	26	equivalent	equivalent	ADJ
ejpam-6009	266	27	:	:	PUNCT
ejpam-6009	266	28	(	(	PUNCT
ejpam-6009	266	29	1	1	X
ejpam-6009	266	30	)	)	PUNCT
ejpam-6009	266	31	f	f	PROPN
ejpam-6009	266	32	is	be	AUX
ejpam-6009	266	33	lower	low	ADJ
ejpam-6009	266	34	almost	almost	ADV
ejpam-6009	266	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	266	36	,	,	PUNCT
ejpam-6009	266	37	τ2)p	τ2)p	ADJ
ejpam-6009	266	38	-	-	NOUN
ejpam-6009	266	39	continuous	continuous	ADJ
ejpam-6009	266	40	;	;	PUNCT
ejpam-6009	266	41	(	(	PUNCT
ejpam-6009	266	42	2	2	X
ejpam-6009	266	43	)	)	PUNCT
ejpam-6009	266	44	(	(	PUNCT
ejpam-6009	266	45	τ1	τ1	NOUN
ejpam-6009	266	46	,	,	PUNCT
ejpam-6009	266	47	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	267	1	+	+	PROPN
ejpam-6009	267	2	(	(	PUNCT
ejpam-6009	267	3	σ1σ2	σ1σ2	NUM
ejpam-6009	267	4	-	-	PUNCT
ejpam-6009	267	5	int(k	int(k	NUM
ejpam-6009	267	6	)	)	PUNCT
ejpam-6009	267	7	)	)	PUNCT
ejpam-6009	267	8	)	)	PUNCT
ejpam-6009	268	1	⊆	⊆	NUM
ejpam-6009	268	2	f+(k	f+(k	NOUN
ejpam-6009	268	3	)	)	PUNCT
ejpam-6009	268	4	for	for	ADP
ejpam-6009	268	5	every	every	DET
ejpam-6009	268	6	(	(	PUNCT
ejpam-6009	268	7	σ1	σ1	PROPN
ejpam-6009	268	8	,	,	PUNCT
ejpam-6009	268	9	σ2)s	σ2)s	NOUN
ejpam-6009	268	10	-	-	PUNCT
ejpam-6009	268	11	closed	close	VERB
ejpam-6009	268	12	set	set	NOUN
ejpam-6009	268	13	k	k	PROPN
ejpam-6009	268	14	of	of	ADP
ejpam-6009	268	15	y	y	PROPN
ejpam-6009	268	16	;	;	PUNCT
ejpam-6009	268	17	(	(	PUNCT
ejpam-6009	268	18	3	3	X
ejpam-6009	268	19	)	)	PUNCT
ejpam-6009	268	20	(	(	PUNCT
ejpam-6009	268	21	τ1	τ1	NOUN
ejpam-6009	268	22	,	,	PUNCT
ejpam-6009	268	23	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	269	1	+	+	PROPN
ejpam-6009	269	2	(	(	PUNCT
ejpam-6009	269	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	269	4	-	-	PUNCT
ejpam-6009	269	5	int((σ1	int((σ1	ADJ
ejpam-6009	269	6	,	,	PUNCT
ejpam-6009	269	7	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	269	8	)	)	PUNCT
ejpam-6009	269	9	)	)	PUNCT
ejpam-6009	269	10	)	)	PUNCT
ejpam-6009	269	11	)	)	PUNCT
ejpam-6009	270	1	⊆	⊆	NUM
ejpam-6009	270	2	f+((σ1	f+((σ1	NOUN
ejpam-6009	270	3	,	,	PUNCT
ejpam-6009	270	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	270	5	)	)	PUNCT
ejpam-6009	270	6	)	)	PUNCT
ejpam-6009	270	7	for	for	ADP
ejpam-6009	270	8	every	every	DET
ejpam-6009	270	9	subset	subset	NOUN
ejpam-6009	270	10	b	b	PROPN
ejpam-6009	270	11	of	of	ADP
ejpam-6009	270	12	y	y	PROPN
ejpam-6009	270	13	;	;	PUNCT
ejpam-6009	270	14	(	(	PUNCT
ejpam-6009	270	15	4	4	X
ejpam-6009	270	16	)	)	PUNCT
ejpam-6009	270	17	f−((σ1	f−((σ1	NOUN
ejpam-6009	270	18	,	,	PUNCT
ejpam-6009	270	19	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	270	20	)	)	PUNCT
ejpam-6009	270	21	)	)	PUNCT
ejpam-6009	271	1	⊆	⊆	NUM
ejpam-6009	271	2	(	(	PUNCT
ejpam-6009	271	3	τ1	τ1	NOUN
ejpam-6009	271	4	,	,	PUNCT
ejpam-6009	271	5	τ2)-pint(f	τ2)-pint(f	NUM
ejpam-6009	271	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	271	7	-	-	PUNCT
ejpam-6009	271	8	cl((σ1	cl((σ1	NOUN
ejpam-6009	271	9	,	,	PUNCT
ejpam-6009	271	10	σ2)-sint(b	σ2)-sint(b	NOUN
ejpam-6009	271	11	)	)	PUNCT
ejpam-6009	271	12	)	)	PUNCT
ejpam-6009	271	13	)	)	PUNCT
ejpam-6009	271	14	)	)	PUNCT
ejpam-6009	271	15	for	for	ADP
ejpam-6009	271	16	every	every	DET
ejpam-6009	271	17	subset	subset	NOUN
ejpam-6009	271	18	b	b	PROPN
ejpam-6009	271	19	of	of	ADP
ejpam-6009	271	20	y	y	PROPN
ejpam-6009	271	21	.	.	PUNCT
ejpam-6009	272	1	proof	proof	NOUN
ejpam-6009	272	2	.	.	PUNCT
ejpam-6009	273	1	the	the	DET
ejpam-6009	273	2	proof	proof	NOUN
ejpam-6009	273	3	is	be	AUX
ejpam-6009	273	4	similar	similar	ADJ
ejpam-6009	273	5	to	to	ADP
ejpam-6009	273	6	that	that	PRON
ejpam-6009	273	7	of	of	ADP
ejpam-6009	273	8	theorem	theorem	NOUN
ejpam-6009	273	9	7	7	NUM
ejpam-6009	273	10	.	.	PUNCT
ejpam-6009	273	11	lemma	lemma	PROPN
ejpam-6009	273	12	5	5	NUM
ejpam-6009	273	13	.	.	PUNCT
ejpam-6009	274	1	[	[	X
ejpam-6009	274	2	80	80	NUM
ejpam-6009	274	3	]	]	PUNCT
ejpam-6009	274	4	for	for	ADP
ejpam-6009	274	5	a	a	DET
ejpam-6009	274	6	bitopological	bitopological	ADJ
ejpam-6009	274	7	space	space	NOUN
ejpam-6009	274	8	(	(	PUNCT
ejpam-6009	274	9	x	x	NOUN
ejpam-6009	274	10	,	,	PUNCT
ejpam-6009	274	11	τ1	τ1	NOUN
ejpam-6009	274	12	,	,	PUNCT
ejpam-6009	274	13	τ2	τ2	NOUN
ejpam-6009	274	14	)	)	PUNCT
ejpam-6009	274	15	,	,	PUNCT
ejpam-6009	274	16	the	the	DET
ejpam-6009	274	17	following	follow	VERB
ejpam-6009	274	18	properties	property	NOUN
ejpam-6009	274	19	hold	hold	VERB
ejpam-6009	274	20	:	:	PUNCT
ejpam-6009	274	21	(	(	PUNCT
ejpam-6009	274	22	1	1	X
ejpam-6009	274	23	)	)	PUNCT
ejpam-6009	274	24	α(τ1	α(τ1	NOUN
ejpam-6009	274	25	,	,	PUNCT
ejpam-6009	274	26	τ2)-cl(v	τ2)-cl(v	NOUN
ejpam-6009	274	27	)	)	PUNCT
ejpam-6009	274	28	=	=	PUNCT
ejpam-6009	275	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	275	2	-	-	NOUN
ejpam-6009	275	3	cl(v	cl(v	X
ejpam-6009	275	4	)	)	PUNCT
ejpam-6009	275	5	for	for	ADP
ejpam-6009	275	6	every	every	DET
ejpam-6009	275	7	(	(	PUNCT
ejpam-6009	275	8	τ1	τ1	NOUN
ejpam-6009	275	9	,	,	PUNCT
ejpam-6009	275	10	τ2)β	τ2)β	ADJ
ejpam-6009	275	11	-	-	PUNCT
ejpam-6009	275	12	open	open	NOUN
ejpam-6009	275	13	set	set	NOUN
ejpam-6009	275	14	v	v	NOUN
ejpam-6009	275	15	of	of	ADP
ejpam-6009	275	16	x	x	PRON
ejpam-6009	275	17	;	;	PUNCT
ejpam-6009	275	18	(	(	PUNCT
ejpam-6009	275	19	2	2	X
ejpam-6009	275	20	)	)	PUNCT
ejpam-6009	275	21	(	(	PUNCT
ejpam-6009	275	22	τ1	τ1	NOUN
ejpam-6009	275	23	,	,	PUNCT
ejpam-6009	275	24	τ2)-pcl(v	τ2)-pcl(v	NOUN
ejpam-6009	275	25	)	)	PUNCT
ejpam-6009	275	26	=	=	PUNCT
ejpam-6009	276	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	276	2	-	-	NOUN
ejpam-6009	276	3	cl(v	cl(v	X
ejpam-6009	276	4	)	)	PUNCT
ejpam-6009	276	5	for	for	ADP
ejpam-6009	276	6	every	every	DET
ejpam-6009	276	7	(	(	PUNCT
ejpam-6009	276	8	τ1	τ1	NOUN
ejpam-6009	276	9	,	,	PUNCT
ejpam-6009	276	10	τ2)s	τ2)s	NOUN
ejpam-6009	276	11	-	-	PUNCT
ejpam-6009	276	12	open	open	ADJ
ejpam-6009	276	13	set	set	NOUN
ejpam-6009	276	14	v	v	NOUN
ejpam-6009	276	15	of	of	ADP
ejpam-6009	276	16	x	x	PRON
ejpam-6009	276	17	;	;	PUNCT
ejpam-6009	276	18	(	(	PUNCT
ejpam-6009	276	19	3	3	X
ejpam-6009	276	20	)	)	PUNCT
ejpam-6009	276	21	(	(	PUNCT
ejpam-6009	276	22	τ1	τ1	NOUN
ejpam-6009	276	23	,	,	PUNCT
ejpam-6009	276	24	τ2)-scl(v	τ2)-scl(v	NOUN
ejpam-6009	276	25	)	)	PUNCT
ejpam-6009	277	1	=	=	PUNCT
ejpam-6009	278	1	τ1τ2	τ1τ2	NOUN
ejpam-6009	278	2	-	-	NOUN
ejpam-6009	278	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6009	278	4	-	-	PUNCT
ejpam-6009	278	5	cl(v	cl(v	NOUN
ejpam-6009	278	6	)	)	PUNCT
ejpam-6009	278	7	)	)	PUNCT
ejpam-6009	278	8	for	for	ADP
ejpam-6009	278	9	every	every	DET
ejpam-6009	278	10	(	(	PUNCT
ejpam-6009	278	11	τ1	τ1	NOUN
ejpam-6009	278	12	,	,	PUNCT
ejpam-6009	278	13	τ2)p	τ2)p	ADJ
ejpam-6009	278	14	-	-	PUNCT
ejpam-6009	278	15	open	open	ADJ
ejpam-6009	278	16	set	set	NOUN
ejpam-6009	278	17	v	v	NOUN
ejpam-6009	278	18	of	of	ADP
ejpam-6009	278	19	x.	x.	NOUN
ejpam-6009	278	20	theorem	theorem	VERB
ejpam-6009	278	21	9	9	NUM
ejpam-6009	278	22	.	.	PUNCT
ejpam-6009	278	23	for	for	ADP
ejpam-6009	278	24	a	a	DET
ejpam-6009	278	25	multifunction	multifunction	NOUN
ejpam-6009	278	26	f	f	NOUN
ejpam-6009	278	27	:	:	PUNCT
ejpam-6009	278	28	(	(	PUNCT
ejpam-6009	278	29	x	x	NOUN
ejpam-6009	278	30	,	,	PUNCT
ejpam-6009	278	31	τ1	τ1	NOUN
ejpam-6009	278	32	,	,	PUNCT
ejpam-6009	278	33	τ2	τ2	NOUN
ejpam-6009	278	34	)	)	PUNCT
ejpam-6009	278	35	→	→	SYM
ejpam-6009	278	36	(	(	PUNCT
ejpam-6009	278	37	y	y	PROPN
ejpam-6009	278	38	,	,	PUNCT
ejpam-6009	278	39	σ1	σ1	PROPN
ejpam-6009	278	40	,	,	PUNCT
ejpam-6009	278	41	σ2	σ2	NOUN
ejpam-6009	278	42	)	)	PUNCT
ejpam-6009	278	43	,	,	PUNCT
ejpam-6009	278	44	the	the	DET
ejpam-6009	278	45	following	follow	VERB
ejpam-6009	278	46	properties	property	NOUN
ejpam-6009	278	47	are	be	AUX
ejpam-6009	278	48	equivalent	equivalent	ADJ
ejpam-6009	278	49	:	:	PUNCT
ejpam-6009	278	50	(	(	PUNCT
ejpam-6009	278	51	1	1	X
ejpam-6009	278	52	)	)	PUNCT
ejpam-6009	278	53	f	f	PROPN
ejpam-6009	278	54	is	be	AUX
ejpam-6009	278	55	lower	low	ADJ
ejpam-6009	278	56	almost	almost	ADV
ejpam-6009	278	57	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	278	58	,	,	PUNCT
ejpam-6009	278	59	τ2)p	τ2)p	ADJ
ejpam-6009	278	60	-	-	NOUN
ejpam-6009	278	61	continuous	continuous	ADJ
ejpam-6009	278	62	;	;	PUNCT
ejpam-6009	278	63	(	(	PUNCT
ejpam-6009	278	64	2	2	X
ejpam-6009	278	65	)	)	PUNCT
ejpam-6009	278	66	f−(v	f−(v	NOUN
ejpam-6009	278	67	)	)	PUNCT
ejpam-6009	278	68	is	be	AUX
ejpam-6009	278	69	(	(	PUNCT
ejpam-6009	278	70	τ1	τ1	NOUN
ejpam-6009	278	71	,	,	PUNCT
ejpam-6009	278	72	τ2)p	τ2)p	NOUN
ejpam-6009	278	73	-	-	PUNCT
ejpam-6009	278	74	open	open	ADJ
ejpam-6009	278	75	in	in	ADP
ejpam-6009	278	76	x	x	PUNCT
ejpam-6009	278	77	for	for	ADP
ejpam-6009	278	78	every	every	DET
ejpam-6009	278	79	s(σ1	s(σ1	NOUN
ejpam-6009	278	80	,	,	PUNCT
ejpam-6009	278	81	σ2)θ	σ2)θ	NOUN
ejpam-6009	278	82	-	-	PUNCT
ejpam-6009	278	83	open	open	ADJ
ejpam-6009	278	84	set	set	NOUN
ejpam-6009	278	85	v	v	NOUN
ejpam-6009	278	86	of	of	ADP
ejpam-6009	278	87	y	y	PROPN
ejpam-6009	278	88	;	;	PUNCT
ejpam-6009	278	89	(	(	PUNCT
ejpam-6009	278	90	3	3	X
ejpam-6009	278	91	)	)	PUNCT
ejpam-6009	278	92	f+(k	f+(k	NUM
ejpam-6009	278	93	)	)	PUNCT
ejpam-6009	279	1	is	be	AUX
ejpam-6009	279	2	(	(	PUNCT
ejpam-6009	279	3	τ1	τ1	NOUN
ejpam-6009	279	4	,	,	PUNCT
ejpam-6009	279	5	τ2)p	τ2)p	NOUN
ejpam-6009	279	6	-	-	PUNCT
ejpam-6009	279	7	closed	closed	ADJ
ejpam-6009	279	8	in	in	ADP
ejpam-6009	279	9	x	x	PUNCT
ejpam-6009	279	10	for	for	ADP
ejpam-6009	279	11	every	every	DET
ejpam-6009	279	12	s(σ1	s(σ1	NOUN
ejpam-6009	279	13	,	,	PUNCT
ejpam-6009	279	14	σ2)θ	σ2)θ	NOUN
ejpam-6009	279	15	-	-	PUNCT
ejpam-6009	279	16	closed	close	VERB
ejpam-6009	279	17	set	set	NOUN
ejpam-6009	279	18	k	k	PROPN
ejpam-6009	279	19	of	of	ADP
ejpam-6009	279	20	y	y	PROPN
ejpam-6009	279	21	;	;	PUNCT
ejpam-6009	279	22	c.	c.	PROPN
ejpam-6009	279	23	viriyapong	viriyapong	PROPN
ejpam-6009	279	24	,	,	PUNCT
ejpam-6009	279	25	a.	a.	PROPN
ejpam-6009	279	26	sama	sama	PROPN
ejpam-6009	279	27	-	-	PUNCT
ejpam-6009	279	28	ae	ae	PROPN
ejpam-6009	279	29	,	,	PUNCT
ejpam-6009	279	30	c.	c.	PROPN
ejpam-6009	279	31	boonpok	boonpok	PROPN
ejpam-6009	279	32	/	/	SYM
ejpam-6009	279	33	eur	eur	PROPN
ejpam-6009	279	34	.	.	PUNCT
ejpam-6009	280	1	j.	j.	PROPN
ejpam-6009	280	2	pure	pure	PROPN
ejpam-6009	280	3	appl	appl	PROPN
ejpam-6009	280	4	.	.	PROPN
ejpam-6009	280	5	math	math	PROPN
ejpam-6009	280	6	,	,	PUNCT
ejpam-6009	280	7	18	18	NUM
ejpam-6009	280	8	(	(	PUNCT
ejpam-6009	280	9	2	2	NUM
ejpam-6009	280	10	)	)	PUNCT
ejpam-6009	280	11	(	(	PUNCT
ejpam-6009	280	12	2025	2025	NUM
ejpam-6009	280	13	)	)	PUNCT
ejpam-6009	280	14	,	,	PUNCT
ejpam-6009	280	15	6009	6009	NUM
ejpam-6009	280	16	11	11	NUM
ejpam-6009	280	17	of	of	ADP
ejpam-6009	280	18	18	18	NUM
ejpam-6009	280	19	(	(	PUNCT
ejpam-6009	280	20	4	4	NUM
ejpam-6009	280	21	)	)	PUNCT
ejpam-6009	280	22	(	(	PUNCT
ejpam-6009	280	23	τ1	τ1	NOUN
ejpam-6009	280	24	,	,	PUNCT
ejpam-6009	280	25	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	281	1	+	+	PROPN
ejpam-6009	281	2	(	(	PUNCT
ejpam-6009	281	3	σ1σ2	σ1σ2	NUM
ejpam-6009	281	4	-	-	PUNCT
ejpam-6009	281	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	281	6	-	-	PUNCT
ejpam-6009	281	7	cl(b	cl(b	NOUN
ejpam-6009	281	8	)	)	PUNCT
ejpam-6009	281	9	)	)	PUNCT
ejpam-6009	281	10	)	)	PUNCT
ejpam-6009	281	11	)	)	PUNCT
ejpam-6009	282	1	⊆	⊆	NUM
ejpam-6009	282	2	f+((σ1	f+((σ1	NOUN
ejpam-6009	282	3	,	,	PUNCT
ejpam-6009	282	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	282	5	)	)	PUNCT
ejpam-6009	282	6	)	)	PUNCT
ejpam-6009	282	7	for	for	ADP
ejpam-6009	282	8	every	every	DET
ejpam-6009	282	9	subset	subset	NOUN
ejpam-6009	282	10	b	b	PROPN
ejpam-6009	282	11	of	of	ADP
ejpam-6009	282	12	y	y	PROPN
ejpam-6009	282	13	;	;	PUNCT
ejpam-6009	282	14	(	(	PUNCT
ejpam-6009	282	15	5	5	X
ejpam-6009	282	16	)	)	PUNCT
ejpam-6009	282	17	(	(	PUNCT
ejpam-6009	282	18	τ1	τ1	NOUN
ejpam-6009	282	19	,	,	PUNCT
ejpam-6009	282	20	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	282	21	+	+	PROPN
ejpam-6009	282	22	(	(	PUNCT
ejpam-6009	282	23	b	b	NOUN
ejpam-6009	282	24	)	)	PUNCT
ejpam-6009	282	25	)	)	PUNCT
ejpam-6009	282	26	⊆	⊆	NUM
ejpam-6009	282	27	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6009	282	28	,	,	PUNCT
ejpam-6009	282	29	σ2)θ	σ2)θ	NOUN
ejpam-6009	282	30	-	-	PUNCT
ejpam-6009	282	31	cl(b	cl(b	NOUN
ejpam-6009	282	32	)	)	PUNCT
ejpam-6009	282	33	)	)	PUNCT
ejpam-6009	282	34	for	for	ADP
ejpam-6009	282	35	every	every	DET
ejpam-6009	282	36	subset	subset	NOUN
ejpam-6009	282	37	b	b	PROPN
ejpam-6009	282	38	of	of	ADP
ejpam-6009	282	39	y	y	PROPN
ejpam-6009	282	40	;	;	PUNCT
ejpam-6009	282	41	(	(	PUNCT
ejpam-6009	282	42	6	6	X
ejpam-6009	282	43	)	)	PUNCT
ejpam-6009	282	44	f	f	NOUN
ejpam-6009	282	45	(	(	PUNCT
ejpam-6009	282	46	(	(	PUNCT
ejpam-6009	282	47	τ1	τ1	PROPN
ejpam-6009	282	48	,	,	PUNCT
ejpam-6009	282	49	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6009	282	50	)	)	PUNCT
ejpam-6009	282	51	)	)	PUNCT
ejpam-6009	282	52	⊆	⊆	NUM
ejpam-6009	282	53	s(σ1	s(σ1	NOUN
ejpam-6009	282	54	,	,	PUNCT
ejpam-6009	282	55	σ2)θ	σ2)θ	NOUN
ejpam-6009	282	56	-	-	PUNCT
ejpam-6009	282	57	cl(f	cl(f	PROPN
ejpam-6009	282	58	(	(	PUNCT
ejpam-6009	282	59	a	a	NOUN
ejpam-6009	282	60	)	)	PUNCT
ejpam-6009	282	61	)	)	PUNCT
ejpam-6009	282	62	for	for	ADP
ejpam-6009	282	63	every	every	DET
ejpam-6009	282	64	subset	subset	NOUN
ejpam-6009	282	65	a	a	PRON
ejpam-6009	282	66	of	of	ADP
ejpam-6009	282	67	x.	x.	NOUN
ejpam-6009	282	68	proof	proof	NOUN
ejpam-6009	282	69	.	.	PUNCT
ejpam-6009	283	1	(	(	PUNCT
ejpam-6009	283	2	1	1	X
ejpam-6009	283	3	)	)	PUNCT
ejpam-6009	283	4	⇒	⇒	NOUN
ejpam-6009	283	5	(	(	PUNCT
ejpam-6009	283	6	2	2	NUM
ejpam-6009	283	7	):	):	PUNCT
ejpam-6009	283	8	let	let	VERB
ejpam-6009	283	9	v	v	PART
ejpam-6009	283	10	be	be	AUX
ejpam-6009	283	11	any	any	DET
ejpam-6009	283	12	s(σ1	s(σ1	NOUN
ejpam-6009	283	13	,	,	PUNCT
ejpam-6009	283	14	σ2)θ	σ2)θ	ADJ
ejpam-6009	283	15	-	-	PUNCT
ejpam-6009	283	16	open	open	ADJ
ejpam-6009	283	17	set	set	NOUN
ejpam-6009	283	18	of	of	ADP
ejpam-6009	283	19	y	y	PROPN
ejpam-6009	283	20	.	.	PUNCT
ejpam-6009	284	1	there	there	PRON
ejpam-6009	284	2	exists	exist	VERB
ejpam-6009	284	3	a	a	DET
ejpam-6009	284	4	family	family	NOUN
ejpam-6009	284	5	of	of	ADP
ejpam-6009	284	6	(	(	PUNCT
ejpam-6009	284	7	σ1	σ1	PROPN
ejpam-6009	284	8	,	,	PUNCT
ejpam-6009	284	9	σ2)r	σ2)r	NOUN
ejpam-6009	284	10	-	-	PUNCT
ejpam-6009	284	11	closed	close	VERB
ejpam-6009	284	12	sets	set	NOUN
ejpam-6009	284	13	{	{	PUNCT
ejpam-6009	284	14	kγ	kγ	NOUN
ejpam-6009	284	15	|	|	ADV
ejpam-6009	284	16	γ	γ	PROPN
ejpam-6009	284	17	∈	∈	PROPN
ejpam-6009	284	18	∇	∇	X
ejpam-6009	284	19	}	}	PUNCT
ejpam-6009	285	1	such	such	ADJ
ejpam-6009	285	2	that	that	PRON
ejpam-6009	285	3	v	v	NOUN
ejpam-6009	285	4	=	=	SYM
ejpam-6009	285	5	∪{kγ	∪{kγ	PROPN
ejpam-6009	285	6	|	|	ADV
ejpam-6009	285	7	γ	γ	X
ejpam-6009	285	8	∈	∈	NOUN
ejpam-6009	285	9	∇	∇	X
ejpam-6009	285	10	}	}	PUNCT
ejpam-6009	285	11	.	.	PUNCT
ejpam-6009	286	1	it	it	PRON
ejpam-6009	286	2	follows	follow	VERB
ejpam-6009	286	3	from	from	ADP
ejpam-6009	286	4	theorem	theorem	ADJ
ejpam-6009	286	5	5	5	NUM
ejpam-6009	286	6	that	that	DET
ejpam-6009	286	7	f−(v	f−(v	ADJ
ejpam-6009	286	8	)	)	PUNCT
ejpam-6009	287	1	=	=	SYM
ejpam-6009	287	2	∪{f−(kγ	∪{f−(kγ	PROPN
ejpam-6009	287	3	)	)	PUNCT
ejpam-6009	287	4	|	|	ADV
ejpam-6009	287	5	γ	γ	PROPN
ejpam-6009	287	6	∈	∈	PROPN
ejpam-6009	287	7	∇	∇	X
ejpam-6009	287	8	}	}	PUNCT
ejpam-6009	287	9	is	be	AUX
ejpam-6009	287	10	(	(	PUNCT
ejpam-6009	287	11	τ1	τ1	NOUN
ejpam-6009	287	12	,	,	PUNCT
ejpam-6009	287	13	τ2)p	τ2)p	NOUN
ejpam-6009	287	14	-	-	PUNCT
ejpam-6009	287	15	open	open	ADJ
ejpam-6009	287	16	in	in	ADP
ejpam-6009	287	17	x.	x.	NOUN
ejpam-6009	287	18	(	(	PUNCT
ejpam-6009	287	19	2	2	NUM
ejpam-6009	287	20	)	)	PUNCT
ejpam-6009	287	21	⇒	⇒	NOUN
ejpam-6009	287	22	(	(	PUNCT
ejpam-6009	287	23	3	3	NUM
ejpam-6009	287	24	):	):	PUNCT
ejpam-6009	287	25	the	the	DET
ejpam-6009	287	26	proof	proof	NOUN
ejpam-6009	287	27	is	be	AUX
ejpam-6009	287	28	obvious	obvious	ADJ
ejpam-6009	287	29	.	.	PUNCT
ejpam-6009	288	1	(	(	PUNCT
ejpam-6009	288	2	3	3	X
ejpam-6009	288	3	)	)	PUNCT
ejpam-6009	288	4	⇒	⇒	NOUN
ejpam-6009	288	5	(	(	PUNCT
ejpam-6009	288	6	4	4	NUM
ejpam-6009	288	7	):	):	PUNCT
ejpam-6009	288	8	let	let	VERB
ejpam-6009	288	9	b	b	X
ejpam-6009	288	10	be	be	AUX
ejpam-6009	288	11	any	any	DET
ejpam-6009	288	12	subset	subset	NOUN
ejpam-6009	288	13	of	of	ADP
ejpam-6009	288	14	y	y	PROPN
ejpam-6009	288	15	.	.	PUNCT
ejpam-6009	289	1	then	then	ADV
ejpam-6009	289	2	,	,	PUNCT
ejpam-6009	289	3	σ1σ2	σ1σ2	X
ejpam-6009	289	4	-	-	PUNCT
ejpam-6009	289	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	289	6	-	-	PUNCT
ejpam-6009	289	7	cl(b	cl(b	NOUN
ejpam-6009	289	8	)	)	PUNCT
ejpam-6009	289	9	)	)	PUNCT
ejpam-6009	289	10	is	be	AUX
ejpam-6009	289	11	(	(	PUNCT
ejpam-6009	289	12	σ1	σ1	NOUN
ejpam-6009	289	13	,	,	PUNCT
ejpam-6009	289	14	σ2)r	σ2)r	NOUN
ejpam-6009	289	15	-	-	PUNCT
ejpam-6009	289	16	open	open	ADJ
ejpam-6009	289	17	and	and	CCONJ
ejpam-6009	289	18	hence	hence	ADV
ejpam-6009	289	19	σ1σ2	σ1σ2	ADV
ejpam-6009	289	20	-	-	PUNCT
ejpam-6009	289	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	289	22	-	-	PUNCT
ejpam-6009	289	23	cl(b	cl(b	NOUN
ejpam-6009	289	24	)	)	PUNCT
ejpam-6009	289	25	)	)	PUNCT
ejpam-6009	290	1	is	be	AUX
ejpam-6009	290	2	s(σ1	s(σ1	ADV
ejpam-6009	290	3	,	,	PUNCT
ejpam-6009	290	4	σ2)θ	σ2)θ	NOUN
ejpam-6009	290	5	-	-	PUNCT
ejpam-6009	290	6	closed	closed	ADJ
ejpam-6009	290	7	in	in	ADP
ejpam-6009	290	8	y	y	PROPN
ejpam-6009	290	9	.	.	PUNCT
ejpam-6009	291	1	by	by	ADP
ejpam-6009	291	2	(	(	PUNCT
ejpam-6009	291	3	3	3	NUM
ejpam-6009	291	4	)	)	PUNCT
ejpam-6009	291	5	,	,	PUNCT
ejpam-6009	291	6	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	291	7	-	-	PUNCT
ejpam-6009	291	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	291	9	-	-	PUNCT
ejpam-6009	291	10	cl(b	cl(b	NOUN
ejpam-6009	291	11	)	)	PUNCT
ejpam-6009	291	12	)	)	PUNCT
ejpam-6009	291	13	)	)	PUNCT
ejpam-6009	291	14	is	be	AUX
ejpam-6009	291	15	(	(	PUNCT
ejpam-6009	291	16	τ1	τ1	NOUN
ejpam-6009	291	17	,	,	PUNCT
ejpam-6009	291	18	τ2)p	τ2)p	NOUN
ejpam-6009	291	19	-	-	PUNCT
ejpam-6009	291	20	closed	closed	ADJ
ejpam-6009	291	21	in	in	ADP
ejpam-6009	291	22	x.	x.	NOUN
ejpam-6009	291	23	thus	thus	ADV
ejpam-6009	291	24	,	,	PUNCT
ejpam-6009	291	25	(	(	PUNCT
ejpam-6009	291	26	τ1	τ1	NOUN
ejpam-6009	291	27	,	,	PUNCT
ejpam-6009	291	28	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	292	1	+	+	PROPN
ejpam-6009	292	2	(	(	PUNCT
ejpam-6009	292	3	σ1σ2	σ1σ2	NUM
ejpam-6009	292	4	-	-	PUNCT
ejpam-6009	292	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	292	6	-	-	PUNCT
ejpam-6009	292	7	cl(b	cl(b	NOUN
ejpam-6009	292	8	)	)	PUNCT
ejpam-6009	292	9	)	)	PUNCT
ejpam-6009	292	10	)	)	PUNCT
ejpam-6009	292	11	)	)	PUNCT
ejpam-6009	293	1	=	=	SYM
ejpam-6009	293	2	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-6009	293	3	-	-	PUNCT
ejpam-6009	293	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	293	5	-	-	PUNCT
ejpam-6009	293	6	cl(b	cl(b	NOUN
ejpam-6009	293	7	)	)	PUNCT
ejpam-6009	293	8	)	)	PUNCT
ejpam-6009	293	9	)	)	PUNCT
ejpam-6009	294	1	⊆	⊆	NUM
ejpam-6009	294	2	f+((σ1	f+((σ1	NOUN
ejpam-6009	294	3	,	,	PUNCT
ejpam-6009	294	4	σ2)-scl(b	σ2)-scl(b	NOUN
ejpam-6009	294	5	)	)	PUNCT
ejpam-6009	294	6	)	)	PUNCT
ejpam-6009	294	7	.	.	PUNCT
ejpam-6009	295	1	(	(	PUNCT
ejpam-6009	295	2	4	4	X
ejpam-6009	295	3	)	)	PUNCT
ejpam-6009	295	4	⇒	⇒	NOUN
ejpam-6009	295	5	(	(	PUNCT
ejpam-6009	295	6	5	5	NUM
ejpam-6009	295	7	):	):	PUNCT
ejpam-6009	295	8	let	let	VERB
ejpam-6009	295	9	b	b	X
ejpam-6009	295	10	be	be	AUX
ejpam-6009	295	11	any	any	DET
ejpam-6009	295	12	subset	subset	NOUN
ejpam-6009	295	13	of	of	ADP
ejpam-6009	295	14	y	y	PROPN
ejpam-6009	295	15	.	.	PUNCT
ejpam-6009	296	1	for	for	ADP
ejpam-6009	296	2	any	any	DET
ejpam-6009	296	3	(	(	PUNCT
ejpam-6009	296	4	σ1	σ1	NOUN
ejpam-6009	296	5	,	,	PUNCT
ejpam-6009	296	6	σ2)r	σ2)r	NOUN
ejpam-6009	296	7	-	-	PUNCT
ejpam-6009	296	8	open	open	ADJ
ejpam-6009	296	9	set	set	VERB
ejpam-6009	296	10	v	v	NOUN
ejpam-6009	296	11	of	of	ADP
ejpam-6009	296	12	y	y	PROPN
ejpam-6009	296	13	with	with	ADP
ejpam-6009	296	14	b	b	PROPN
ejpam-6009	296	15	⊆	⊆	NUM
ejpam-6009	296	16	v	v	NOUN
ejpam-6009	296	17	,	,	PUNCT
ejpam-6009	296	18	by	by	ADP
ejpam-6009	296	19	(	(	PUNCT
ejpam-6009	296	20	4	4	NUM
ejpam-6009	296	21	)	)	PUNCT
ejpam-6009	296	22	and	and	CCONJ
ejpam-6009	296	23	lemma	lemma	PROPN
ejpam-6009	296	24	5	5	NUM
ejpam-6009	296	25	we	we	PRON
ejpam-6009	296	26	have	have	AUX
ejpam-6009	296	27	(	(	PUNCT
ejpam-6009	296	28	τ1	τ1	NOUN
ejpam-6009	296	29	,	,	PUNCT
ejpam-6009	296	30	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	297	1	+	+	PROPN
ejpam-6009	297	2	(	(	PUNCT
ejpam-6009	297	3	b	b	NOUN
ejpam-6009	297	4	)	)	PUNCT
ejpam-6009	297	5	)	)	PUNCT
ejpam-6009	298	1	⊆	⊆	NUM
ejpam-6009	298	2	(	(	PUNCT
ejpam-6009	298	3	τ1	τ1	NOUN
ejpam-6009	298	4	,	,	PUNCT
ejpam-6009	298	5	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	298	6	+	+	PROPN
ejpam-6009	298	7	(	(	PUNCT
ejpam-6009	298	8	v	v	NOUN
ejpam-6009	298	9	)	)	PUNCT
ejpam-6009	298	10	)	)	PUNCT
ejpam-6009	299	1	=	=	PRON
ejpam-6009	299	2	(	(	PUNCT
ejpam-6009	299	3	τ1	τ1	PROPN
ejpam-6009	299	4	,	,	PUNCT
ejpam-6009	299	5	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	299	6	+	+	PROPN
ejpam-6009	299	7	(	(	PUNCT
ejpam-6009	299	8	σ1σ2	σ1σ2	ADJ
ejpam-6009	299	9	-	-	PUNCT
ejpam-6009	299	10	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	299	11	-	-	PUNCT
ejpam-6009	299	12	cl(v	cl(v	NOUN
ejpam-6009	299	13	)	)	PUNCT
ejpam-6009	299	14	)	)	PUNCT
ejpam-6009	299	15	)	)	PUNCT
ejpam-6009	299	16	)	)	PUNCT
ejpam-6009	300	1	⊆	⊆	NUM
ejpam-6009	300	2	f+((σ1	f+((σ1	NOUN
ejpam-6009	300	3	,	,	PUNCT
ejpam-6009	300	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6009	300	5	)	)	PUNCT
ejpam-6009	300	6	)	)	PUNCT
ejpam-6009	301	1	=	=	PUNCT
ejpam-6009	301	2	f+(v	f+(v	NOUN
ejpam-6009	301	3	)	)	PUNCT
ejpam-6009	301	4	.	.	PUNCT
ejpam-6009	302	1	thus	thus	ADV
ejpam-6009	302	2	,	,	PUNCT
ejpam-6009	302	3	(	(	PUNCT
ejpam-6009	302	4	τ1	τ1	NOUN
ejpam-6009	302	5	,	,	PUNCT
ejpam-6009	302	6	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	303	1	+	+	PROPN
ejpam-6009	303	2	(	(	PUNCT
ejpam-6009	303	3	b	b	NOUN
ejpam-6009	303	4	)	)	PUNCT
ejpam-6009	303	5	)	)	PUNCT
ejpam-6009	304	1	⊆	⊆	NUM
ejpam-6009	304	2	f+(∩{v	f+(∩{v	NOUN
ejpam-6009	304	3	|	|	ADV
ejpam-6009	304	4	v	v	NOUN
ejpam-6009	304	5	is	be	AUX
ejpam-6009	304	6	(	(	PUNCT
ejpam-6009	304	7	σ1	σ1	NOUN
ejpam-6009	304	8	,	,	PUNCT
ejpam-6009	304	9	σ2)r	σ2)r	NOUN
ejpam-6009	304	10	-	-	PUNCT
ejpam-6009	304	11	open	open	ADJ
ejpam-6009	304	12	in	in	ADP
ejpam-6009	304	13	y	y	PROPN
ejpam-6009	304	14	and	and	CCONJ
ejpam-6009	304	15	b	b	PROPN
ejpam-6009	304	16	⊆	⊆	NUM
ejpam-6009	304	17	v	v	NOUN
ejpam-6009	304	18	}	}	PUNCT
ejpam-6009	304	19	)	)	PUNCT
ejpam-6009	304	20	=	=	SYM
ejpam-6009	304	21	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6009	304	22	,	,	PUNCT
ejpam-6009	304	23	σ2)θ	σ2)θ	NOUN
ejpam-6009	304	24	-	-	PUNCT
ejpam-6009	304	25	cl(b	cl(b	NOUN
ejpam-6009	304	26	)	)	PUNCT
ejpam-6009	304	27	)	)	PUNCT
ejpam-6009	304	28	.	.	PUNCT
ejpam-6009	305	1	(	(	PUNCT
ejpam-6009	305	2	5	5	X
ejpam-6009	305	3	)	)	PUNCT
ejpam-6009	305	4	⇒	⇒	NOUN
ejpam-6009	305	5	(	(	PUNCT
ejpam-6009	305	6	1	1	NUM
ejpam-6009	305	7	):	):	PUNCT
ejpam-6009	305	8	let	let	VERB
ejpam-6009	305	9	v	v	PART
ejpam-6009	305	10	be	be	AUX
ejpam-6009	305	11	any	any	DET
ejpam-6009	305	12	(	(	PUNCT
ejpam-6009	305	13	σ1	σ1	NOUN
ejpam-6009	305	14	,	,	PUNCT
ejpam-6009	305	15	σ2)s	σ2)s	NOUN
ejpam-6009	305	16	-	-	PUNCT
ejpam-6009	305	17	open	open	ADJ
ejpam-6009	305	18	set	set	NOUN
ejpam-6009	305	19	of	of	ADP
ejpam-6009	305	20	y	y	PROPN
ejpam-6009	305	21	.	.	PUNCT
ejpam-6009	306	1	by	by	ADP
ejpam-6009	306	2	(	(	PUNCT
ejpam-6009	306	3	5	5	NUM
ejpam-6009	306	4	)	)	PUNCT
ejpam-6009	306	5	,	,	PUNCT
ejpam-6009	306	6	we	we	PRON
ejpam-6009	306	7	have	have	VERB
ejpam-6009	306	8	x	x	X
ejpam-6009	306	9	−	−	PROPN
ejpam-6009	306	10	(	(	PUNCT
ejpam-6009	306	11	τ1	τ1	NOUN
ejpam-6009	306	12	,	,	PUNCT
ejpam-6009	306	13	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	306	14	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	306	15	-	-	NOUN
ejpam-6009	306	16	cl(v	cl(v	NOUN
ejpam-6009	306	17	)	)	PUNCT
ejpam-6009	306	18	)	)	PUNCT
ejpam-6009	306	19	)	)	PUNCT
ejpam-6009	307	1	=	=	PRON
ejpam-6009	307	2	(	(	PUNCT
ejpam-6009	307	3	τ1	τ1	PROPN
ejpam-6009	307	4	,	,	PUNCT
ejpam-6009	307	5	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	307	6	+	+	PROPN
ejpam-6009	307	7	(	(	PUNCT
ejpam-6009	307	8	y	y	PROPN
ejpam-6009	307	9	−	−	PROPN
ejpam-6009	307	10	σ1σ2	σ1σ2	NOUN
ejpam-6009	307	11	-	-	NUM
ejpam-6009	307	12	cl(v	cl(v	NOUN
ejpam-6009	307	13	)	)	PUNCT
ejpam-6009	307	14	)	)	PUNCT
ejpam-6009	307	15	)	)	PUNCT
ejpam-6009	308	1	⊆	⊆	NUM
ejpam-6009	308	2	f+((σ1	f+((σ1	NOUN
ejpam-6009	308	3	,	,	PUNCT
ejpam-6009	308	4	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6009	308	5	−	−	NOUN
ejpam-6009	308	6	σ1σ2	σ1σ2	NOUN
ejpam-6009	308	7	-	-	NUM
ejpam-6009	308	8	cl(v	cl(v	NOUN
ejpam-6009	308	9	)	)	PUNCT
ejpam-6009	308	10	)	)	PUNCT
ejpam-6009	308	11	)	)	PUNCT
ejpam-6009	309	1	=	=	PUNCT
ejpam-6009	310	1	f+(y	f+(y	NOUN
ejpam-6009	310	2	−	−	NUM
ejpam-6009	310	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	310	4	-	-	NUM
ejpam-6009	310	5	cl(v	cl(v	NOUN
ejpam-6009	310	6	)	)	PUNCT
ejpam-6009	310	7	)	)	PUNCT
ejpam-6009	311	1	=	=	PUNCT
ejpam-6009	311	2	x	x	PUNCT
ejpam-6009	311	3	−	−	NOUN
ejpam-6009	311	4	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	311	5	-	-	PUNCT
ejpam-6009	311	6	cl(v	cl(v	NOUN
ejpam-6009	311	7	)	)	PUNCT
ejpam-6009	311	8	)	)	PUNCT
ejpam-6009	311	9	and	and	CCONJ
ejpam-6009	311	10	hence	hence	ADV
ejpam-6009	311	11	f−(v	f−(v	ADJ
ejpam-6009	311	12	)	)	PUNCT
ejpam-6009	311	13	⊆	⊆	NUM
ejpam-6009	311	14	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	311	15	-	-	PUNCT
ejpam-6009	311	16	cl(v	cl(v	NOUN
ejpam-6009	311	17	)	)	PUNCT
ejpam-6009	311	18	)	)	PUNCT
ejpam-6009	312	1	⊆	⊆	NUM
ejpam-6009	312	2	(	(	PUNCT
ejpam-6009	312	3	τ1	τ1	NOUN
ejpam-6009	312	4	,	,	PUNCT
ejpam-6009	312	5	τ2)-pint(f	τ2)-pint(f	PUNCT
ejpam-6009	312	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-6009	312	7	-	-	NOUN
ejpam-6009	312	8	cl(v	cl(v	NOUN
ejpam-6009	312	9	)	)	PUNCT
ejpam-6009	312	10	)	)	PUNCT
ejpam-6009	312	11	)	)	PUNCT
ejpam-6009	312	12	.	.	PUNCT
ejpam-6009	313	1	by	by	ADP
ejpam-6009	313	2	theorem	theorem	NOUN
ejpam-6009	313	3	6	6	NUM
ejpam-6009	313	4	,	,	PUNCT
ejpam-6009	313	5	f	f	PROPN
ejpam-6009	313	6	is	be	AUX
ejpam-6009	313	7	lower	low	ADJ
ejpam-6009	313	8	almost	almost	ADV
ejpam-6009	313	9	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	313	10	,	,	PUNCT
ejpam-6009	313	11	τ2)p	τ2)p	ADJ
ejpam-6009	313	12	-	-	NOUN
ejpam-6009	313	13	continuous	continuous	ADJ
ejpam-6009	313	14	.	.	PUNCT
ejpam-6009	314	1	(	(	PUNCT
ejpam-6009	314	2	5	5	X
ejpam-6009	314	3	)	)	PUNCT
ejpam-6009	314	4	⇒	⇒	NOUN
ejpam-6009	314	5	(	(	PUNCT
ejpam-6009	314	6	6	6	NUM
ejpam-6009	314	7	):	):	PUNCT
ejpam-6009	314	8	let	let	VERB
ejpam-6009	314	9	a	a	PRON
ejpam-6009	314	10	be	be	AUX
ejpam-6009	314	11	any	any	DET
ejpam-6009	314	12	subset	subset	NOUN
ejpam-6009	314	13	of	of	ADP
ejpam-6009	314	14	x	x	PROPN
ejpam-6009	314	15	and	and	CCONJ
ejpam-6009	314	16	b	b	X
ejpam-6009	314	17	=	=	SYM
ejpam-6009	314	18	f	f	PROPN
ejpam-6009	314	19	(	(	PUNCT
ejpam-6009	314	20	a	a	NOUN
ejpam-6009	314	21	)	)	PUNCT
ejpam-6009	314	22	.	.	PUNCT
ejpam-6009	315	1	then	then	ADV
ejpam-6009	315	2	,	,	PUNCT
ejpam-6009	315	3	a	a	DET
ejpam-6009	315	4	⊆	⊆	NUM
ejpam-6009	315	5	f+(b	f+(b	NOUN
ejpam-6009	315	6	)	)	PUNCT
ejpam-6009	315	7	and	and	CCONJ
ejpam-6009	315	8	by	by	ADP
ejpam-6009	315	9	(	(	PUNCT
ejpam-6009	315	10	5	5	NUM
ejpam-6009	315	11	)	)	PUNCT
ejpam-6009	315	12	,	,	PUNCT
ejpam-6009	315	13	(	(	PUNCT
ejpam-6009	315	14	τ1	τ1	NOUN
ejpam-6009	315	15	,	,	PUNCT
ejpam-6009	315	16	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6009	315	17	)	)	PUNCT
ejpam-6009	315	18	⊆	⊆	NUM
ejpam-6009	315	19	(	(	PUNCT
ejpam-6009	315	20	τ1	τ1	NOUN
ejpam-6009	315	21	,	,	PUNCT
ejpam-6009	315	22	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	315	23	+	+	PROPN
ejpam-6009	315	24	(	(	PUNCT
ejpam-6009	315	25	b	b	NOUN
ejpam-6009	315	26	)	)	PUNCT
ejpam-6009	315	27	)	)	PUNCT
ejpam-6009	316	1	⊆	⊆	NUM
ejpam-6009	316	2	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6009	316	3	,	,	PUNCT
ejpam-6009	316	4	σ2)θ	σ2)θ	NOUN
ejpam-6009	316	5	-	-	PUNCT
ejpam-6009	316	6	cl(b	cl(b	NOUN
ejpam-6009	316	7	)	)	PUNCT
ejpam-6009	316	8	)	)	PUNCT
ejpam-6009	316	9	.	.	PUNCT
ejpam-6009	317	1	thus	thus	ADV
ejpam-6009	317	2	,	,	PUNCT
ejpam-6009	317	3	f	f	PROPN
ejpam-6009	317	4	(	(	PUNCT
ejpam-6009	317	5	(	(	PUNCT
ejpam-6009	317	6	τ1	τ1	PROPN
ejpam-6009	317	7	,	,	PUNCT
ejpam-6009	317	8	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6009	317	9	)	)	PUNCT
ejpam-6009	317	10	)	)	PUNCT
ejpam-6009	318	1	⊆	⊆	NUM
ejpam-6009	318	2	f	f	X
ejpam-6009	318	3	(	(	PUNCT
ejpam-6009	318	4	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6009	318	5	,	,	PUNCT
ejpam-6009	318	6	σ2)θ	σ2)θ	NOUN
ejpam-6009	318	7	-	-	PUNCT
ejpam-6009	318	8	cl(b	cl(b	NOUN
ejpam-6009	318	9	)	)	PUNCT
ejpam-6009	318	10	)	)	PUNCT
ejpam-6009	318	11	)	)	PUNCT
ejpam-6009	319	1	c.	c.	PROPN
ejpam-6009	319	2	viriyapong	viriyapong	PROPN
ejpam-6009	319	3	,	,	PUNCT
ejpam-6009	319	4	a.	a.	PROPN
ejpam-6009	319	5	sama	sama	PROPN
ejpam-6009	319	6	-	-	PUNCT
ejpam-6009	319	7	ae	ae	PROPN
ejpam-6009	319	8	,	,	PUNCT
ejpam-6009	319	9	c.	c.	PROPN
ejpam-6009	319	10	boonpok	boonpok	PROPN
ejpam-6009	319	11	/	/	SYM
ejpam-6009	319	12	eur	eur	PROPN
ejpam-6009	319	13	.	.	PUNCT
ejpam-6009	320	1	j.	j.	PROPN
ejpam-6009	320	2	pure	pure	PROPN
ejpam-6009	320	3	appl	appl	PROPN
ejpam-6009	320	4	.	.	PROPN
ejpam-6009	320	5	math	math	PROPN
ejpam-6009	320	6	,	,	PUNCT
ejpam-6009	320	7	18	18	NUM
ejpam-6009	320	8	(	(	PUNCT
ejpam-6009	320	9	2	2	NUM
ejpam-6009	320	10	)	)	PUNCT
ejpam-6009	320	11	(	(	PUNCT
ejpam-6009	320	12	2025	2025	NUM
ejpam-6009	320	13	)	)	PUNCT
ejpam-6009	320	14	,	,	PUNCT
ejpam-6009	320	15	6009	6009	NUM
ejpam-6009	320	16	12	12	NUM
ejpam-6009	320	17	of	of	ADP
ejpam-6009	320	18	18	18	NUM
ejpam-6009	320	19	⊆	⊆	NUM
ejpam-6009	320	20	s(σ1	s(σ1	NOUN
ejpam-6009	320	21	,	,	PUNCT
ejpam-6009	320	22	σ2)θ	σ2)θ	NOUN
ejpam-6009	320	23	-	-	PUNCT
ejpam-6009	320	24	cl(b	cl(b	NOUN
ejpam-6009	320	25	)	)	PUNCT
ejpam-6009	320	26	=	=	PUNCT
ejpam-6009	320	27	s(σ1	s(σ1	ADV
ejpam-6009	320	28	,	,	PUNCT
ejpam-6009	320	29	σ2)θ	σ2)θ	NOUN
ejpam-6009	320	30	-	-	PUNCT
ejpam-6009	320	31	cl(f	cl(f	PROPN
ejpam-6009	320	32	(	(	PUNCT
ejpam-6009	320	33	a	a	NOUN
ejpam-6009	320	34	)	)	PUNCT
ejpam-6009	320	35	)	)	PUNCT
ejpam-6009	320	36	.	.	PUNCT
ejpam-6009	321	1	(	(	PUNCT
ejpam-6009	321	2	6	6	X
ejpam-6009	321	3	)	)	PUNCT
ejpam-6009	321	4	⇒	⇒	NOUN
ejpam-6009	321	5	(	(	PUNCT
ejpam-6009	321	6	5	5	NUM
ejpam-6009	321	7	):	):	PUNCT
ejpam-6009	321	8	let	let	VERB
ejpam-6009	321	9	b	b	X
ejpam-6009	321	10	be	be	AUX
ejpam-6009	321	11	any	any	DET
ejpam-6009	321	12	subset	subset	NOUN
ejpam-6009	321	13	of	of	ADP
ejpam-6009	321	14	y	y	PROPN
ejpam-6009	321	15	.	.	PUNCT
ejpam-6009	322	1	by	by	ADP
ejpam-6009	322	2	(	(	PUNCT
ejpam-6009	322	3	6	6	NUM
ejpam-6009	322	4	)	)	PUNCT
ejpam-6009	322	5	,	,	PUNCT
ejpam-6009	322	6	we	we	PRON
ejpam-6009	322	7	have	have	VERB
ejpam-6009	322	8	f	f	X
ejpam-6009	322	9	(	(	PUNCT
ejpam-6009	322	10	(	(	PUNCT
ejpam-6009	322	11	τ1	τ1	NOUN
ejpam-6009	322	12	,	,	PUNCT
ejpam-6009	322	13	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	323	1	+	+	PROPN
ejpam-6009	323	2	(	(	PUNCT
ejpam-6009	323	3	b	b	NOUN
ejpam-6009	323	4	)	)	PUNCT
ejpam-6009	323	5	)	)	PUNCT
ejpam-6009	323	6	)	)	PUNCT
ejpam-6009	324	1	⊆	⊆	NUM
ejpam-6009	324	2	s(σ1	s(σ1	NOUN
ejpam-6009	324	3	,	,	PUNCT
ejpam-6009	324	4	σ2)θ	σ2)θ	NOUN
ejpam-6009	324	5	-	-	PUNCT
ejpam-6009	324	6	cl(f	cl(f	PROPN
ejpam-6009	324	7	(	(	PUNCT
ejpam-6009	324	8	f+(b	f+(b	PROPN
ejpam-6009	324	9	)	)	PUNCT
ejpam-6009	324	10	)	)	PUNCT
ejpam-6009	324	11	)	)	PUNCT
ejpam-6009	324	12	⊆	⊆	NUM
ejpam-6009	324	13	s(σ1	s(σ1	NOUN
ejpam-6009	324	14	,	,	PUNCT
ejpam-6009	324	15	σ2)θ	σ2)θ	NOUN
ejpam-6009	324	16	-	-	PUNCT
ejpam-6009	324	17	cl(b	cl(b	NOUN
ejpam-6009	324	18	)	)	PUNCT
ejpam-6009	324	19	and	and	CCONJ
ejpam-6009	324	20	hence	hence	ADV
ejpam-6009	324	21	(	(	PUNCT
ejpam-6009	324	22	τ1	τ1	NOUN
ejpam-6009	324	23	,	,	PUNCT
ejpam-6009	324	24	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	324	25	+	+	PROPN
ejpam-6009	324	26	(	(	PUNCT
ejpam-6009	324	27	b	b	NOUN
ejpam-6009	324	28	)	)	PUNCT
ejpam-6009	324	29	)	)	PUNCT
ejpam-6009	324	30	⊆	⊆	NUM
ejpam-6009	324	31	f+(s(σ1	f+(s(σ1	NOUN
ejpam-6009	324	32	,	,	PUNCT
ejpam-6009	324	33	σ2)θ	σ2)θ	NOUN
ejpam-6009	324	34	-	-	PUNCT
ejpam-6009	324	35	cl(b	cl(b	NOUN
ejpam-6009	324	36	)	)	PUNCT
ejpam-6009	324	37	)	)	PUNCT
ejpam-6009	324	38	.	.	PUNCT
ejpam-6009	325	1	theorem	theorem	ADJ
ejpam-6009	325	2	10	10	NUM
ejpam-6009	325	3	.	.	PUNCT
ejpam-6009	326	1	for	for	ADP
ejpam-6009	326	2	a	a	DET
ejpam-6009	326	3	multifunction	multifunction	NOUN
ejpam-6009	326	4	f	f	NOUN
ejpam-6009	326	5	:	:	PUNCT
ejpam-6009	326	6	(	(	PUNCT
ejpam-6009	326	7	x	x	NOUN
ejpam-6009	326	8	,	,	PUNCT
ejpam-6009	326	9	τ1	τ1	NOUN
ejpam-6009	326	10	,	,	PUNCT
ejpam-6009	326	11	τ2	τ2	NOUN
ejpam-6009	326	12	)	)	PUNCT
ejpam-6009	326	13	→	→	SYM
ejpam-6009	326	14	(	(	PUNCT
ejpam-6009	326	15	y	y	PROPN
ejpam-6009	326	16	,	,	PUNCT
ejpam-6009	326	17	σ1	σ1	PROPN
ejpam-6009	326	18	,	,	PUNCT
ejpam-6009	326	19	σ2	σ2	NOUN
ejpam-6009	326	20	)	)	PUNCT
ejpam-6009	326	21	,	,	PUNCT
ejpam-6009	326	22	the	the	DET
ejpam-6009	326	23	following	follow	VERB
ejpam-6009	326	24	properties	property	NOUN
ejpam-6009	326	25	are	be	AUX
ejpam-6009	326	26	equivalent	equivalent	ADJ
ejpam-6009	326	27	:	:	PUNCT
ejpam-6009	326	28	(	(	PUNCT
ejpam-6009	326	29	1	1	X
ejpam-6009	326	30	)	)	PUNCT
ejpam-6009	326	31	f	f	PROPN
ejpam-6009	326	32	is	be	AUX
ejpam-6009	326	33	upper	upper	ADJ
ejpam-6009	326	34	almost	almost	ADV
ejpam-6009	326	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	326	36	,	,	PUNCT
ejpam-6009	326	37	τ2)p	τ2)p	ADJ
ejpam-6009	326	38	-	-	NOUN
ejpam-6009	326	39	continuous	continuous	ADJ
ejpam-6009	326	40	;	;	PUNCT
ejpam-6009	326	41	(	(	PUNCT
ejpam-6009	326	42	2	2	X
ejpam-6009	326	43	)	)	PUNCT
ejpam-6009	326	44	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	326	45	-	-	PUNCT
ejpam-6009	326	46	cl(v	cl(v	NOUN
ejpam-6009	326	47	)	)	PUNCT
ejpam-6009	326	48	)	)	PUNCT
ejpam-6009	327	1	is	be	AUX
ejpam-6009	327	2	(	(	PUNCT
ejpam-6009	327	3	τ1	τ1	NOUN
ejpam-6009	327	4	,	,	PUNCT
ejpam-6009	327	5	τ2)p	τ2)p	NOUN
ejpam-6009	327	6	-	-	PUNCT
ejpam-6009	327	7	open	open	ADJ
ejpam-6009	327	8	in	in	ADP
ejpam-6009	327	9	x	x	PUNCT
ejpam-6009	327	10	for	for	ADP
ejpam-6009	327	11	every	every	DET
ejpam-6009	327	12	(	(	PUNCT
ejpam-6009	327	13	σ1	σ1	PROPN
ejpam-6009	327	14	,	,	PUNCT
ejpam-6009	327	15	σ2)β	σ2)β	NOUN
ejpam-6009	327	16	-	-	PUNCT
ejpam-6009	327	17	open	open	NOUN
ejpam-6009	327	18	set	set	NOUN
ejpam-6009	327	19	v	v	NOUN
ejpam-6009	327	20	of	of	ADP
ejpam-6009	327	21	y	y	PROPN
ejpam-6009	327	22	;	;	PUNCT
ejpam-6009	327	23	(	(	PUNCT
ejpam-6009	327	24	3	3	X
ejpam-6009	327	25	)	)	PUNCT
ejpam-6009	327	26	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	327	27	-	-	PUNCT
ejpam-6009	327	28	cl(v	cl(v	NOUN
ejpam-6009	327	29	)	)	PUNCT
ejpam-6009	327	30	)	)	PUNCT
ejpam-6009	328	1	is	be	AUX
ejpam-6009	328	2	(	(	PUNCT
ejpam-6009	328	3	τ1	τ1	NOUN
ejpam-6009	328	4	,	,	PUNCT
ejpam-6009	328	5	τ2)p	τ2)p	NOUN
ejpam-6009	328	6	-	-	PUNCT
ejpam-6009	328	7	open	open	ADJ
ejpam-6009	328	8	in	in	ADP
ejpam-6009	328	9	x	x	PUNCT
ejpam-6009	328	10	for	for	ADP
ejpam-6009	328	11	every	every	DET
ejpam-6009	328	12	(	(	PUNCT
ejpam-6009	328	13	σ1	σ1	PROPN
ejpam-6009	328	14	,	,	PUNCT
ejpam-6009	328	15	σ2)s	σ2)s	NOUN
ejpam-6009	328	16	-	-	PUNCT
ejpam-6009	328	17	open	open	NOUN
ejpam-6009	328	18	set	set	NOUN
ejpam-6009	328	19	v	v	NOUN
ejpam-6009	328	20	of	of	ADP
ejpam-6009	328	21	y	y	PROPN
ejpam-6009	328	22	;	;	PUNCT
ejpam-6009	328	23	(	(	PUNCT
ejpam-6009	328	24	4	4	X
ejpam-6009	328	25	)	)	PUNCT
ejpam-6009	328	26	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6009	328	27	-	-	PUNCT
ejpam-6009	328	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	328	29	-	-	PUNCT
ejpam-6009	328	30	cl(v	cl(v	NOUN
ejpam-6009	328	31	)	)	PUNCT
ejpam-6009	328	32	)	)	PUNCT
ejpam-6009	328	33	)	)	PUNCT
ejpam-6009	329	1	is	be	AUX
ejpam-6009	329	2	(	(	PUNCT
ejpam-6009	329	3	τ1	τ1	NOUN
ejpam-6009	329	4	,	,	PUNCT
ejpam-6009	329	5	τ2)p	τ2)p	NOUN
ejpam-6009	329	6	-	-	PUNCT
ejpam-6009	329	7	closed	closed	ADJ
ejpam-6009	329	8	in	in	ADP
ejpam-6009	329	9	x	x	PUNCT
ejpam-6009	329	10	for	for	ADP
ejpam-6009	329	11	every	every	DET
ejpam-6009	329	12	(	(	PUNCT
ejpam-6009	329	13	σ1	σ1	PROPN
ejpam-6009	329	14	,	,	PUNCT
ejpam-6009	329	15	σ2)p	σ2)p	NOUN
ejpam-6009	329	16	-	-	PUNCT
ejpam-6009	329	17	open	open	NOUN
ejpam-6009	329	18	set	set	NOUN
ejpam-6009	329	19	v	v	NOUN
ejpam-6009	329	20	of	of	ADP
ejpam-6009	329	21	y	y	PROPN
ejpam-6009	329	22	.	.	PUNCT
ejpam-6009	330	1	proof	proof	NOUN
ejpam-6009	330	2	.	.	PUNCT
ejpam-6009	331	1	(	(	PUNCT
ejpam-6009	331	2	1	1	X
ejpam-6009	331	3	)	)	PUNCT
ejpam-6009	331	4	⇒	⇒	NOUN
ejpam-6009	331	5	(	(	PUNCT
ejpam-6009	331	6	2	2	NUM
ejpam-6009	331	7	):	):	PUNCT
ejpam-6009	331	8	let	let	VERB
ejpam-6009	331	9	v	v	PART
ejpam-6009	331	10	be	be	AUX
ejpam-6009	331	11	any	any	DET
ejpam-6009	331	12	(	(	PUNCT
ejpam-6009	331	13	σ1	σ1	PROPN
ejpam-6009	331	14	,	,	PUNCT
ejpam-6009	331	15	σ2)β	σ2)β	NOUN
ejpam-6009	331	16	-	-	PUNCT
ejpam-6009	331	17	open	open	ADJ
ejpam-6009	331	18	set	set	NOUN
ejpam-6009	331	19	of	of	ADP
ejpam-6009	331	20	y	y	PROPN
ejpam-6009	331	21	.	.	PUNCT
ejpam-6009	332	1	then	then	ADV
ejpam-6009	332	2	,	,	PUNCT
ejpam-6009	332	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	332	4	-	-	NUM
ejpam-6009	332	5	cl(v	cl(v	NOUN
ejpam-6009	332	6	)	)	PUNCT
ejpam-6009	332	7	is	be	AUX
ejpam-6009	332	8	(	(	PUNCT
ejpam-6009	332	9	σ1	σ1	PROPN
ejpam-6009	332	10	,	,	PUNCT
ejpam-6009	332	11	σ2)rclosed	σ2)rclose	VERB
ejpam-6009	332	12	in	in	ADP
ejpam-6009	332	13	y	y	PROPN
ejpam-6009	332	14	,	,	PUNCT
ejpam-6009	332	15	by	by	ADP
ejpam-6009	332	16	theorem	theorem	NOUN
ejpam-6009	332	17	5	5	NUM
ejpam-6009	332	18	we	we	PRON
ejpam-6009	332	19	have	have	VERB
ejpam-6009	332	20	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	332	21	-	-	NOUN
ejpam-6009	332	22	cl(v	cl(v	NOUN
ejpam-6009	332	23	)	)	PUNCT
ejpam-6009	332	24	)	)	PUNCT
ejpam-6009	333	1	is	be	AUX
ejpam-6009	333	2	(	(	PUNCT
ejpam-6009	333	3	τ1	τ1	NOUN
ejpam-6009	333	4	,	,	PUNCT
ejpam-6009	333	5	τ2)p	τ2)p	NOUN
ejpam-6009	333	6	-	-	PUNCT
ejpam-6009	333	7	open	open	ADJ
ejpam-6009	333	8	in	in	ADP
ejpam-6009	333	9	x.	x.	NOUN
ejpam-6009	333	10	(	(	PUNCT
ejpam-6009	333	11	2	2	NUM
ejpam-6009	333	12	)	)	PUNCT
ejpam-6009	333	13	⇒	⇒	NOUN
ejpam-6009	333	14	(	(	PUNCT
ejpam-6009	333	15	3	3	NUM
ejpam-6009	333	16	):	):	PUNCT
ejpam-6009	333	17	this	this	PRON
ejpam-6009	333	18	is	be	AUX
ejpam-6009	333	19	obvious	obvious	ADJ
ejpam-6009	333	20	since	since	SCONJ
ejpam-6009	333	21	every	every	DET
ejpam-6009	333	22	(	(	PUNCT
ejpam-6009	333	23	σ1	σ1	PROPN
ejpam-6009	333	24	,	,	PUNCT
ejpam-6009	333	25	σ2)s	σ2)s	NOUN
ejpam-6009	333	26	-	-	PUNCT
ejpam-6009	333	27	open	open	ADJ
ejpam-6009	333	28	set	set	NOUN
ejpam-6009	333	29	is	be	AUX
ejpam-6009	333	30	(	(	PUNCT
ejpam-6009	333	31	σ1	σ1	PROPN
ejpam-6009	333	32	,	,	PUNCT
ejpam-6009	333	33	σ2)β	σ2)β	NOUN
ejpam-6009	333	34	-	-	PUNCT
ejpam-6009	333	35	open	open	ADJ
ejpam-6009	333	36	.	.	PUNCT
ejpam-6009	334	1	(	(	PUNCT
ejpam-6009	334	2	3	3	X
ejpam-6009	334	3	)	)	PUNCT
ejpam-6009	334	4	⇒	⇒	NOUN
ejpam-6009	334	5	(	(	PUNCT
ejpam-6009	334	6	4	4	NUM
ejpam-6009	334	7	):	):	PUNCT
ejpam-6009	334	8	let	let	VERB
ejpam-6009	334	9	v	v	PART
ejpam-6009	334	10	be	be	AUX
ejpam-6009	334	11	any	any	DET
ejpam-6009	334	12	(	(	PUNCT
ejpam-6009	334	13	σ1	σ1	PROPN
ejpam-6009	334	14	,	,	PUNCT
ejpam-6009	334	15	σ2)p	σ2)p	NOUN
ejpam-6009	334	16	-	-	PUNCT
ejpam-6009	334	17	open	open	ADJ
ejpam-6009	334	18	set	set	NOUN
ejpam-6009	334	19	of	of	ADP
ejpam-6009	334	20	y	y	PROPN
ejpam-6009	334	21	.	.	PUNCT
ejpam-6009	335	1	this	this	PRON
ejpam-6009	335	2	implies	imply	VERB
ejpam-6009	335	3	that	that	SCONJ
ejpam-6009	335	4	y	y	PROPN
ejpam-6009	335	5	−	−	PUNCT
ejpam-6009	335	6	σ1σ2	σ1σ2	NUM
ejpam-6009	335	7	-	-	PUNCT
ejpam-6009	335	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	335	9	-	-	PUNCT
ejpam-6009	335	10	cl(v	cl(v	NOUN
ejpam-6009	335	11	)	)	PUNCT
ejpam-6009	335	12	)	)	PUNCT
ejpam-6009	335	13	is	be	AUX
ejpam-6009	335	14	(	(	PUNCT
ejpam-6009	335	15	σ1	σ1	NOUN
ejpam-6009	335	16	,	,	PUNCT
ejpam-6009	335	17	σ2)r	σ2)r	NOUN
ejpam-6009	335	18	-	-	PUNCT
ejpam-6009	335	19	closed	close	VERB
ejpam-6009	335	20	and	and	CCONJ
ejpam-6009	335	21	(	(	PUNCT
ejpam-6009	335	22	σ1	σ1	PROPN
ejpam-6009	335	23	,	,	PUNCT
ejpam-6009	335	24	σ2)s	σ2)s	NOUN
ejpam-6009	335	25	-	-	PUNCT
ejpam-6009	335	26	open	open	ADJ
ejpam-6009	335	27	in	in	ADP
ejpam-6009	335	28	y	y	PROPN
ejpam-6009	335	29	.	.	PUNCT
ejpam-6009	336	1	by	by	ADP
ejpam-6009	336	2	(	(	PUNCT
ejpam-6009	336	3	3	3	NUM
ejpam-6009	336	4	)	)	PUNCT
ejpam-6009	336	5	,	,	PUNCT
ejpam-6009	336	6	we	we	PRON
ejpam-6009	336	7	have	have	VERB
ejpam-6009	336	8	x	x	NOUN
ejpam-6009	336	9	−	−	PUNCT
ejpam-6009	336	10	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6009	336	11	-	-	PUNCT
ejpam-6009	336	12	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	336	13	-	-	PUNCT
ejpam-6009	336	14	cl(v	cl(v	NOUN
ejpam-6009	336	15	)	)	PUNCT
ejpam-6009	336	16	)	)	PUNCT
ejpam-6009	336	17	)	)	PUNCT
ejpam-6009	337	1	=	=	PUNCT
ejpam-6009	338	1	f+(y	f+(y	NOUN
ejpam-6009	338	2	−	−	NUM
ejpam-6009	338	3	σ1σ2	σ1σ2	X
ejpam-6009	338	4	-	-	PUNCT
ejpam-6009	338	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	338	6	-	-	PUNCT
ejpam-6009	338	7	cl(v	cl(v	NOUN
ejpam-6009	338	8	)	)	PUNCT
ejpam-6009	338	9	)	)	PUNCT
ejpam-6009	338	10	)	)	PUNCT
ejpam-6009	339	1	=	=	SYM
ejpam-6009	339	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	339	3	-	-	PUNCT
ejpam-6009	339	4	cl(y	cl(y	NOUN
ejpam-6009	339	5	−	−	NOUN
ejpam-6009	339	6	σ1σ2	σ1σ2	NUM
ejpam-6009	339	7	-	-	PUNCT
ejpam-6009	339	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	339	9	-	-	PUNCT
ejpam-6009	339	10	cl(v	cl(v	NOUN
ejpam-6009	339	11	)	)	PUNCT
ejpam-6009	339	12	)	)	PUNCT
ejpam-6009	339	13	)	)	PUNCT
ejpam-6009	339	14	)	)	PUNCT
ejpam-6009	339	15	is	be	AUX
ejpam-6009	339	16	(	(	PUNCT
ejpam-6009	339	17	τ1	τ1	NOUN
ejpam-6009	339	18	,	,	PUNCT
ejpam-6009	339	19	τ2)p	τ2)p	NOUN
ejpam-6009	339	20	-	-	PUNCT
ejpam-6009	339	21	open	open	ADJ
ejpam-6009	339	22	in	in	ADP
ejpam-6009	339	23	x.	x.	PROPN
ejpam-6009	339	24	thus	thus	ADV
ejpam-6009	339	25	,	,	PUNCT
ejpam-6009	339	26	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	339	27	-	-	PUNCT
ejpam-6009	339	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	339	29	-	-	PUNCT
ejpam-6009	339	30	cl(v	cl(v	NOUN
ejpam-6009	339	31	)	)	PUNCT
ejpam-6009	339	32	)	)	PUNCT
ejpam-6009	339	33	)	)	PUNCT
ejpam-6009	340	1	is	be	AUX
ejpam-6009	340	2	(	(	PUNCT
ejpam-6009	340	3	τ1	τ1	NOUN
ejpam-6009	340	4	,	,	PUNCT
ejpam-6009	340	5	τ2)p	τ2)p	NOUN
ejpam-6009	340	6	-	-	PUNCT
ejpam-6009	340	7	closed	closed	ADJ
ejpam-6009	340	8	in	in	ADP
ejpam-6009	340	9	x.	x.	NOUN
ejpam-6009	340	10	(	(	PUNCT
ejpam-6009	340	11	4	4	NUM
ejpam-6009	340	12	)	)	PUNCT
ejpam-6009	340	13	⇒	⇒	NOUN
ejpam-6009	340	14	(	(	PUNCT
ejpam-6009	340	15	1	1	NUM
ejpam-6009	340	16	):	):	PUNCT
ejpam-6009	340	17	let	let	VERB
ejpam-6009	340	18	v	v	PART
ejpam-6009	340	19	be	be	AUX
ejpam-6009	340	20	any	any	DET
ejpam-6009	340	21	(	(	PUNCT
ejpam-6009	340	22	σ1	σ1	NOUN
ejpam-6009	340	23	,	,	PUNCT
ejpam-6009	340	24	σ2)r	σ2)r	NOUN
ejpam-6009	340	25	-	-	PUNCT
ejpam-6009	340	26	open	open	ADJ
ejpam-6009	340	27	set	set	NOUN
ejpam-6009	340	28	of	of	ADP
ejpam-6009	340	29	y	y	PROPN
ejpam-6009	340	30	.	.	PUNCT
ejpam-6009	341	1	then	then	ADV
ejpam-6009	341	2	,	,	PUNCT
ejpam-6009	341	3	v	v	NOUN
ejpam-6009	341	4	is	be	AUX
ejpam-6009	341	5	(	(	PUNCT
ejpam-6009	341	6	σ1	σ1	PROPN
ejpam-6009	341	7	,	,	PUNCT
ejpam-6009	341	8	σ2)p	σ2)p	NOUN
ejpam-6009	341	9	-	-	PUNCT
ejpam-6009	341	10	open	open	ADJ
ejpam-6009	341	11	in	in	ADP
ejpam-6009	341	12	y	y	PROPN
ejpam-6009	341	13	and	and	CCONJ
ejpam-6009	341	14	by	by	ADP
ejpam-6009	341	15	(	(	PUNCT
ejpam-6009	341	16	4	4	NUM
ejpam-6009	341	17	)	)	PUNCT
ejpam-6009	341	18	,	,	PUNCT
ejpam-6009	341	19	f−(v	f−(v	ADJ
ejpam-6009	341	20	)	)	PUNCT
ejpam-6009	341	21	=	=	SYM
ejpam-6009	341	22	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6009	341	23	-	-	PUNCT
ejpam-6009	341	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	341	25	-	-	PUNCT
ejpam-6009	341	26	cl(v	cl(v	NOUN
ejpam-6009	341	27	)	)	PUNCT
ejpam-6009	341	28	)	)	PUNCT
ejpam-6009	341	29	)	)	PUNCT
ejpam-6009	342	1	is	be	AUX
ejpam-6009	342	2	(	(	PUNCT
ejpam-6009	342	3	τ1	τ1	NOUN
ejpam-6009	342	4	,	,	PUNCT
ejpam-6009	342	5	τ2)p	τ2)p	NOUN
ejpam-6009	342	6	-	-	PUNCT
ejpam-6009	342	7	closed	closed	ADJ
ejpam-6009	342	8	in	in	ADP
ejpam-6009	342	9	x.	x.	NOUN
ejpam-6009	342	10	thus	thus	ADV
ejpam-6009	342	11	by	by	ADP
ejpam-6009	342	12	theorem	theorem	NOUN
ejpam-6009	342	13	5	5	NUM
ejpam-6009	342	14	,	,	PUNCT
ejpam-6009	342	15	f	f	PROPN
ejpam-6009	342	16	is	be	AUX
ejpam-6009	342	17	upper	upper	ADJ
ejpam-6009	342	18	almost	almost	ADV
ejpam-6009	342	19	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	342	20	,	,	PUNCT
ejpam-6009	342	21	τ2)p	τ2)p	ADJ
ejpam-6009	342	22	-	-	ADJ
ejpam-6009	342	23	continuous	continuous	ADJ
ejpam-6009	342	24	.	.	PUNCT
ejpam-6009	343	1	theorem	theorem	VERB
ejpam-6009	343	2	11	11	NUM
ejpam-6009	343	3	.	.	PUNCT
ejpam-6009	344	1	for	for	ADP
ejpam-6009	344	2	a	a	DET
ejpam-6009	344	3	multifunction	multifunction	NOUN
ejpam-6009	344	4	f	f	NOUN
ejpam-6009	344	5	:	:	PUNCT
ejpam-6009	344	6	(	(	PUNCT
ejpam-6009	344	7	x	x	NOUN
ejpam-6009	344	8	,	,	PUNCT
ejpam-6009	344	9	τ1	τ1	NOUN
ejpam-6009	344	10	,	,	PUNCT
ejpam-6009	344	11	τ2	τ2	NOUN
ejpam-6009	344	12	)	)	PUNCT
ejpam-6009	344	13	→	→	SYM
ejpam-6009	344	14	(	(	PUNCT
ejpam-6009	344	15	y	y	PROPN
ejpam-6009	344	16	,	,	PUNCT
ejpam-6009	344	17	σ1	σ1	PROPN
ejpam-6009	344	18	,	,	PUNCT
ejpam-6009	344	19	σ2	σ2	NOUN
ejpam-6009	344	20	)	)	PUNCT
ejpam-6009	344	21	,	,	PUNCT
ejpam-6009	344	22	the	the	DET
ejpam-6009	344	23	following	follow	VERB
ejpam-6009	344	24	properties	property	NOUN
ejpam-6009	344	25	are	be	AUX
ejpam-6009	344	26	equivalent	equivalent	ADJ
ejpam-6009	344	27	:	:	PUNCT
ejpam-6009	344	28	(	(	PUNCT
ejpam-6009	344	29	1	1	X
ejpam-6009	344	30	)	)	PUNCT
ejpam-6009	344	31	f	f	PROPN
ejpam-6009	344	32	is	be	AUX
ejpam-6009	344	33	lower	low	ADJ
ejpam-6009	344	34	almost	almost	ADV
ejpam-6009	344	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	344	36	,	,	PUNCT
ejpam-6009	344	37	τ2)p	τ2)p	ADJ
ejpam-6009	344	38	-	-	NOUN
ejpam-6009	344	39	continuous	continuous	ADJ
ejpam-6009	344	40	;	;	PUNCT
ejpam-6009	344	41	(	(	PUNCT
ejpam-6009	344	42	2	2	X
ejpam-6009	344	43	)	)	PUNCT
ejpam-6009	344	44	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	344	45	-	-	PUNCT
ejpam-6009	344	46	cl(v	cl(v	NOUN
ejpam-6009	344	47	)	)	PUNCT
ejpam-6009	344	48	)	)	PUNCT
ejpam-6009	345	1	is	be	AUX
ejpam-6009	345	2	(	(	PUNCT
ejpam-6009	345	3	τ1	τ1	NOUN
ejpam-6009	345	4	,	,	PUNCT
ejpam-6009	345	5	τ2)p	τ2)p	NOUN
ejpam-6009	345	6	-	-	PUNCT
ejpam-6009	345	7	open	open	ADJ
ejpam-6009	345	8	in	in	ADP
ejpam-6009	345	9	x	x	PUNCT
ejpam-6009	345	10	for	for	ADP
ejpam-6009	345	11	every	every	DET
ejpam-6009	345	12	(	(	PUNCT
ejpam-6009	345	13	σ1	σ1	PROPN
ejpam-6009	345	14	,	,	PUNCT
ejpam-6009	345	15	σ2)β	σ2)β	NOUN
ejpam-6009	345	16	-	-	PUNCT
ejpam-6009	345	17	open	open	NOUN
ejpam-6009	345	18	set	set	NOUN
ejpam-6009	345	19	v	v	NOUN
ejpam-6009	345	20	of	of	ADP
ejpam-6009	345	21	y	y	PROPN
ejpam-6009	345	22	;	;	PUNCT
ejpam-6009	345	23	(	(	PUNCT
ejpam-6009	345	24	3	3	X
ejpam-6009	345	25	)	)	PUNCT
ejpam-6009	345	26	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	345	27	-	-	PUNCT
ejpam-6009	345	28	cl(v	cl(v	NOUN
ejpam-6009	345	29	)	)	PUNCT
ejpam-6009	345	30	)	)	PUNCT
ejpam-6009	346	1	is	be	AUX
ejpam-6009	346	2	(	(	PUNCT
ejpam-6009	346	3	τ1	τ1	NOUN
ejpam-6009	346	4	,	,	PUNCT
ejpam-6009	346	5	τ2)p	τ2)p	NOUN
ejpam-6009	346	6	-	-	PUNCT
ejpam-6009	346	7	open	open	ADJ
ejpam-6009	346	8	in	in	ADP
ejpam-6009	346	9	x	x	PUNCT
ejpam-6009	346	10	for	for	ADP
ejpam-6009	346	11	every	every	DET
ejpam-6009	346	12	(	(	PUNCT
ejpam-6009	346	13	σ1	σ1	PROPN
ejpam-6009	346	14	,	,	PUNCT
ejpam-6009	346	15	σ2)s	σ2)s	NOUN
ejpam-6009	346	16	-	-	PUNCT
ejpam-6009	346	17	open	open	NOUN
ejpam-6009	346	18	set	set	NOUN
ejpam-6009	346	19	v	v	NOUN
ejpam-6009	346	20	of	of	ADP
ejpam-6009	346	21	y	y	PROPN
ejpam-6009	346	22	;	;	PUNCT
ejpam-6009	346	23	c.	c.	PROPN
ejpam-6009	346	24	viriyapong	viriyapong	PROPN
ejpam-6009	346	25	,	,	PUNCT
ejpam-6009	346	26	a.	a.	PROPN
ejpam-6009	346	27	sama	sama	PROPN
ejpam-6009	346	28	-	-	PUNCT
ejpam-6009	346	29	ae	ae	PROPN
ejpam-6009	346	30	,	,	PUNCT
ejpam-6009	346	31	c.	c.	PROPN
ejpam-6009	346	32	boonpok	boonpok	PROPN
ejpam-6009	346	33	/	/	SYM
ejpam-6009	346	34	eur	eur	PROPN
ejpam-6009	346	35	.	.	PUNCT
ejpam-6009	347	1	j.	j.	PROPN
ejpam-6009	347	2	pure	pure	PROPN
ejpam-6009	347	3	appl	appl	PROPN
ejpam-6009	347	4	.	.	PROPN
ejpam-6009	347	5	math	math	PROPN
ejpam-6009	347	6	,	,	PUNCT
ejpam-6009	347	7	18	18	NUM
ejpam-6009	347	8	(	(	PUNCT
ejpam-6009	347	9	2	2	NUM
ejpam-6009	347	10	)	)	PUNCT
ejpam-6009	347	11	(	(	PUNCT
ejpam-6009	347	12	2025	2025	NUM
ejpam-6009	347	13	)	)	PUNCT
ejpam-6009	347	14	,	,	PUNCT
ejpam-6009	347	15	6009	6009	NUM
ejpam-6009	347	16	13	13	NUM
ejpam-6009	347	17	of	of	ADP
ejpam-6009	347	18	18	18	NUM
ejpam-6009	347	19	(	(	PUNCT
ejpam-6009	347	20	4	4	NUM
ejpam-6009	347	21	)	)	PUNCT
ejpam-6009	347	22	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	347	23	-	-	PUNCT
ejpam-6009	347	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	347	25	-	-	PUNCT
ejpam-6009	347	26	cl(v	cl(v	NOUN
ejpam-6009	347	27	)	)	PUNCT
ejpam-6009	347	28	)	)	PUNCT
ejpam-6009	347	29	)	)	PUNCT
ejpam-6009	347	30	is	be	AUX
ejpam-6009	347	31	(	(	PUNCT
ejpam-6009	347	32	τ1	τ1	NOUN
ejpam-6009	347	33	,	,	PUNCT
ejpam-6009	347	34	τ2)p	τ2)p	NOUN
ejpam-6009	347	35	-	-	PUNCT
ejpam-6009	347	36	closed	closed	ADJ
ejpam-6009	347	37	in	in	ADP
ejpam-6009	347	38	x	x	PUNCT
ejpam-6009	347	39	for	for	ADP
ejpam-6009	347	40	every	every	DET
ejpam-6009	347	41	(	(	PUNCT
ejpam-6009	347	42	σ1	σ1	PROPN
ejpam-6009	347	43	,	,	PUNCT
ejpam-6009	347	44	σ2)p	σ2)p	NOUN
ejpam-6009	347	45	-	-	PUNCT
ejpam-6009	347	46	open	open	NOUN
ejpam-6009	347	47	set	set	NOUN
ejpam-6009	347	48	v	v	NOUN
ejpam-6009	347	49	of	of	ADP
ejpam-6009	347	50	y	y	PROPN
ejpam-6009	347	51	.	.	PUNCT
ejpam-6009	348	1	proof	proof	NOUN
ejpam-6009	348	2	.	.	PUNCT
ejpam-6009	349	1	the	the	DET
ejpam-6009	349	2	proof	proof	NOUN
ejpam-6009	349	3	is	be	AUX
ejpam-6009	349	4	similar	similar	ADJ
ejpam-6009	349	5	to	to	ADP
ejpam-6009	349	6	that	that	PRON
ejpam-6009	349	7	of	of	ADP
ejpam-6009	349	8	theorem	theorem	ADJ
ejpam-6009	349	9	10	10	NUM
ejpam-6009	349	10	.	.	PUNCT
ejpam-6009	349	11	corollary	corollary	ADJ
ejpam-6009	349	12	1	1	NUM
ejpam-6009	349	13	.	.	PUNCT
ejpam-6009	349	14	for	for	ADP
ejpam-6009	349	15	a	a	DET
ejpam-6009	349	16	multifunction	multifunction	NOUN
ejpam-6009	349	17	f	f	NOUN
ejpam-6009	349	18	:	:	PUNCT
ejpam-6009	349	19	(	(	PUNCT
ejpam-6009	349	20	x	x	NOUN
ejpam-6009	349	21	,	,	PUNCT
ejpam-6009	349	22	τ1	τ1	NOUN
ejpam-6009	349	23	,	,	PUNCT
ejpam-6009	349	24	τ2	τ2	NOUN
ejpam-6009	349	25	)	)	PUNCT
ejpam-6009	349	26	→	→	SYM
ejpam-6009	349	27	(	(	PUNCT
ejpam-6009	349	28	y	y	PROPN
ejpam-6009	349	29	,	,	PUNCT
ejpam-6009	349	30	σ1	σ1	PROPN
ejpam-6009	349	31	,	,	PUNCT
ejpam-6009	349	32	σ2	σ2	NOUN
ejpam-6009	349	33	)	)	PUNCT
ejpam-6009	349	34	,	,	PUNCT
ejpam-6009	349	35	the	the	DET
ejpam-6009	349	36	following	follow	VERB
ejpam-6009	349	37	properties	property	NOUN
ejpam-6009	349	38	are	be	AUX
ejpam-6009	349	39	equivalent	equivalent	ADJ
ejpam-6009	349	40	:	:	PUNCT
ejpam-6009	349	41	(	(	PUNCT
ejpam-6009	349	42	1	1	X
ejpam-6009	349	43	)	)	PUNCT
ejpam-6009	349	44	f	f	PROPN
ejpam-6009	349	45	is	be	AUX
ejpam-6009	349	46	upper	upper	ADJ
ejpam-6009	349	47	almost	almost	ADV
ejpam-6009	349	48	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	349	49	,	,	PUNCT
ejpam-6009	349	50	τ2)p	τ2)p	ADJ
ejpam-6009	349	51	-	-	NOUN
ejpam-6009	349	52	continuous	continuous	ADJ
ejpam-6009	349	53	;	;	PUNCT
ejpam-6009	349	54	(	(	PUNCT
ejpam-6009	349	55	2	2	X
ejpam-6009	349	56	)	)	PUNCT
ejpam-6009	349	57	f+(α(σ1	f+(α(σ1	NOUN
ejpam-6009	349	58	,	,	PUNCT
ejpam-6009	349	59	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-6009	349	60	)	)	PUNCT
ejpam-6009	349	61	)	)	PUNCT
ejpam-6009	349	62	is	be	AUX
ejpam-6009	349	63	(	(	PUNCT
ejpam-6009	349	64	τ1	τ1	NOUN
ejpam-6009	349	65	,	,	PUNCT
ejpam-6009	349	66	τ2)p	τ2)p	NOUN
ejpam-6009	349	67	-	-	PUNCT
ejpam-6009	349	68	open	open	ADJ
ejpam-6009	349	69	in	in	ADP
ejpam-6009	349	70	x	x	PUNCT
ejpam-6009	349	71	for	for	ADP
ejpam-6009	349	72	every	every	DET
ejpam-6009	349	73	(	(	PUNCT
ejpam-6009	349	74	σ1	σ1	PROPN
ejpam-6009	349	75	,	,	PUNCT
ejpam-6009	349	76	σ2)β	σ2)β	NOUN
ejpam-6009	349	77	-	-	PUNCT
ejpam-6009	349	78	open	open	NOUN
ejpam-6009	349	79	set	set	NOUN
ejpam-6009	349	80	v	v	NOUN
ejpam-6009	349	81	of	of	ADP
ejpam-6009	349	82	y	y	PROPN
ejpam-6009	349	83	;	;	PUNCT
ejpam-6009	349	84	(	(	PUNCT
ejpam-6009	349	85	3	3	X
ejpam-6009	349	86	)	)	PUNCT
ejpam-6009	349	87	f+((σ1	f+((σ1	NOUN
ejpam-6009	349	88	,	,	PUNCT
ejpam-6009	349	89	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-6009	349	90	)	)	PUNCT
ejpam-6009	349	91	)	)	PUNCT
ejpam-6009	350	1	is	be	AUX
ejpam-6009	350	2	(	(	PUNCT
ejpam-6009	350	3	τ1	τ1	NOUN
ejpam-6009	350	4	,	,	PUNCT
ejpam-6009	350	5	τ2)p	τ2)p	NOUN
ejpam-6009	350	6	-	-	PUNCT
ejpam-6009	350	7	open	open	ADJ
ejpam-6009	350	8	in	in	ADP
ejpam-6009	350	9	x	x	PUNCT
ejpam-6009	350	10	for	for	ADP
ejpam-6009	350	11	every	every	DET
ejpam-6009	350	12	(	(	PUNCT
ejpam-6009	350	13	σ1	σ1	PROPN
ejpam-6009	350	14	,	,	PUNCT
ejpam-6009	350	15	σ2)s	σ2)s	NOUN
ejpam-6009	350	16	-	-	PUNCT
ejpam-6009	350	17	open	open	NOUN
ejpam-6009	350	18	set	set	NOUN
ejpam-6009	350	19	v	v	NOUN
ejpam-6009	350	20	of	of	ADP
ejpam-6009	350	21	y	y	PROPN
ejpam-6009	350	22	;	;	PUNCT
ejpam-6009	350	23	(	(	PUNCT
ejpam-6009	350	24	4	4	X
ejpam-6009	350	25	)	)	PUNCT
ejpam-6009	350	26	f−((σ1	f−((σ1	NOUN
ejpam-6009	350	27	,	,	PUNCT
ejpam-6009	350	28	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6009	350	29	)	)	PUNCT
ejpam-6009	350	30	)	)	PUNCT
ejpam-6009	351	1	is	be	AUX
ejpam-6009	351	2	(	(	PUNCT
ejpam-6009	351	3	τ1	τ1	NOUN
ejpam-6009	351	4	,	,	PUNCT
ejpam-6009	351	5	τ2)p	τ2)p	NOUN
ejpam-6009	351	6	-	-	PUNCT
ejpam-6009	351	7	closed	closed	ADJ
ejpam-6009	351	8	in	in	ADP
ejpam-6009	351	9	x	x	PUNCT
ejpam-6009	351	10	for	for	ADP
ejpam-6009	351	11	every	every	DET
ejpam-6009	351	12	(	(	PUNCT
ejpam-6009	351	13	σ1	σ1	PROPN
ejpam-6009	351	14	,	,	PUNCT
ejpam-6009	351	15	σ2)p	σ2)p	NOUN
ejpam-6009	351	16	-	-	PUNCT
ejpam-6009	351	17	open	open	NOUN
ejpam-6009	351	18	set	set	NOUN
ejpam-6009	351	19	v	v	NOUN
ejpam-6009	351	20	of	of	ADP
ejpam-6009	351	21	y	y	PROPN
ejpam-6009	351	22	.	.	PUNCT
ejpam-6009	352	1	corollary	corollary	ADJ
ejpam-6009	352	2	2	2	NUM
ejpam-6009	352	3	.	.	PUNCT
ejpam-6009	352	4	for	for	ADP
ejpam-6009	352	5	a	a	DET
ejpam-6009	352	6	multifunction	multifunction	NOUN
ejpam-6009	353	1	f	f	NOUN
ejpam-6009	353	2	:	:	PUNCT
ejpam-6009	353	3	(	(	PUNCT
ejpam-6009	353	4	x	x	NOUN
ejpam-6009	353	5	,	,	PUNCT
ejpam-6009	353	6	τ1	τ1	NOUN
ejpam-6009	353	7	,	,	PUNCT
ejpam-6009	353	8	τ2	τ2	NOUN
ejpam-6009	353	9	)	)	PUNCT
ejpam-6009	353	10	→	→	SYM
ejpam-6009	353	11	(	(	PUNCT
ejpam-6009	353	12	y	y	PROPN
ejpam-6009	353	13	,	,	PUNCT
ejpam-6009	353	14	σ1	σ1	PROPN
ejpam-6009	353	15	,	,	PUNCT
ejpam-6009	353	16	σ2	σ2	NOUN
ejpam-6009	353	17	)	)	PUNCT
ejpam-6009	353	18	,	,	PUNCT
ejpam-6009	353	19	the	the	DET
ejpam-6009	353	20	following	follow	VERB
ejpam-6009	353	21	properties	property	NOUN
ejpam-6009	353	22	are	be	AUX
ejpam-6009	353	23	equivalent	equivalent	ADJ
ejpam-6009	353	24	:	:	PUNCT
ejpam-6009	353	25	(	(	PUNCT
ejpam-6009	353	26	1	1	X
ejpam-6009	353	27	)	)	PUNCT
ejpam-6009	353	28	f	f	PROPN
ejpam-6009	353	29	is	be	AUX
ejpam-6009	353	30	lower	low	ADJ
ejpam-6009	353	31	almost	almost	ADV
ejpam-6009	353	32	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	353	33	,	,	PUNCT
ejpam-6009	353	34	τ2)p	τ2)p	ADJ
ejpam-6009	353	35	-	-	NOUN
ejpam-6009	353	36	continuous	continuous	ADJ
ejpam-6009	353	37	;	;	PUNCT
ejpam-6009	353	38	(	(	PUNCT
ejpam-6009	353	39	2	2	X
ejpam-6009	353	40	)	)	PUNCT
ejpam-6009	353	41	f−(α(σ1	f−(α(σ1	NOUN
ejpam-6009	353	42	,	,	PUNCT
ejpam-6009	353	43	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-6009	353	44	)	)	PUNCT
ejpam-6009	353	45	)	)	PUNCT
ejpam-6009	353	46	is	be	AUX
ejpam-6009	353	47	(	(	PUNCT
ejpam-6009	353	48	τ1	τ1	NOUN
ejpam-6009	353	49	,	,	PUNCT
ejpam-6009	353	50	τ2)p	τ2)p	NOUN
ejpam-6009	353	51	-	-	PUNCT
ejpam-6009	353	52	open	open	ADJ
ejpam-6009	353	53	in	in	ADP
ejpam-6009	353	54	x	x	PUNCT
ejpam-6009	353	55	for	for	ADP
ejpam-6009	353	56	every	every	DET
ejpam-6009	353	57	(	(	PUNCT
ejpam-6009	353	58	σ1	σ1	PROPN
ejpam-6009	353	59	,	,	PUNCT
ejpam-6009	353	60	σ2)β	σ2)β	NOUN
ejpam-6009	353	61	-	-	PUNCT
ejpam-6009	353	62	open	open	NOUN
ejpam-6009	353	63	set	set	NOUN
ejpam-6009	353	64	v	v	NOUN
ejpam-6009	353	65	of	of	ADP
ejpam-6009	353	66	y	y	PROPN
ejpam-6009	353	67	;	;	PUNCT
ejpam-6009	353	68	(	(	PUNCT
ejpam-6009	353	69	3	3	X
ejpam-6009	353	70	)	)	PUNCT
ejpam-6009	353	71	f−((σ1	f−((σ1	NOUN
ejpam-6009	353	72	,	,	PUNCT
ejpam-6009	353	73	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-6009	353	74	)	)	PUNCT
ejpam-6009	353	75	)	)	PUNCT
ejpam-6009	354	1	is	be	AUX
ejpam-6009	354	2	(	(	PUNCT
ejpam-6009	354	3	τ1	τ1	NOUN
ejpam-6009	354	4	,	,	PUNCT
ejpam-6009	354	5	τ2)p	τ2)p	NOUN
ejpam-6009	354	6	-	-	PUNCT
ejpam-6009	354	7	open	open	ADJ
ejpam-6009	354	8	in	in	ADP
ejpam-6009	354	9	x	x	PUNCT
ejpam-6009	354	10	for	for	ADP
ejpam-6009	354	11	every	every	DET
ejpam-6009	354	12	(	(	PUNCT
ejpam-6009	354	13	σ1	σ1	PROPN
ejpam-6009	354	14	,	,	PUNCT
ejpam-6009	354	15	σ2)s	σ2)s	NOUN
ejpam-6009	354	16	-	-	PUNCT
ejpam-6009	354	17	open	open	NOUN
ejpam-6009	354	18	set	set	NOUN
ejpam-6009	354	19	v	v	NOUN
ejpam-6009	354	20	of	of	ADP
ejpam-6009	354	21	y	y	PROPN
ejpam-6009	354	22	;	;	PUNCT
ejpam-6009	354	23	(	(	PUNCT
ejpam-6009	354	24	4	4	X
ejpam-6009	354	25	)	)	PUNCT
ejpam-6009	354	26	f+((σ1	f+((σ1	NOUN
ejpam-6009	354	27	,	,	PUNCT
ejpam-6009	354	28	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6009	354	29	)	)	PUNCT
ejpam-6009	354	30	)	)	PUNCT
ejpam-6009	355	1	is	be	AUX
ejpam-6009	355	2	(	(	PUNCT
ejpam-6009	355	3	τ1	τ1	NOUN
ejpam-6009	355	4	,	,	PUNCT
ejpam-6009	355	5	τ2)p	τ2)p	NOUN
ejpam-6009	355	6	-	-	PUNCT
ejpam-6009	355	7	closed	closed	ADJ
ejpam-6009	355	8	in	in	ADP
ejpam-6009	355	9	x	x	PUNCT
ejpam-6009	355	10	for	for	ADP
ejpam-6009	355	11	every	every	DET
ejpam-6009	355	12	(	(	PUNCT
ejpam-6009	355	13	σ1	σ1	PROPN
ejpam-6009	355	14	,	,	PUNCT
ejpam-6009	355	15	σ2)p	σ2)p	NOUN
ejpam-6009	355	16	-	-	PUNCT
ejpam-6009	355	17	open	open	NOUN
ejpam-6009	355	18	set	set	NOUN
ejpam-6009	355	19	v	v	NOUN
ejpam-6009	355	20	of	of	ADP
ejpam-6009	355	21	y	y	PROPN
ejpam-6009	355	22	.	.	PUNCT
ejpam-6009	356	1	theorem	theorem	PROPN
ejpam-6009	356	2	12	12	NUM
ejpam-6009	356	3	.	.	PUNCT
ejpam-6009	357	1	for	for	ADP
ejpam-6009	357	2	a	a	DET
ejpam-6009	357	3	multifunction	multifunction	NOUN
ejpam-6009	357	4	f	f	NOUN
ejpam-6009	357	5	:	:	PUNCT
ejpam-6009	357	6	(	(	PUNCT
ejpam-6009	357	7	x	x	NOUN
ejpam-6009	357	8	,	,	PUNCT
ejpam-6009	357	9	τ1	τ1	NOUN
ejpam-6009	357	10	,	,	PUNCT
ejpam-6009	357	11	τ2	τ2	NOUN
ejpam-6009	357	12	)	)	PUNCT
ejpam-6009	357	13	→	→	SYM
ejpam-6009	357	14	(	(	PUNCT
ejpam-6009	357	15	y	y	PROPN
ejpam-6009	357	16	,	,	PUNCT
ejpam-6009	357	17	σ1	σ1	PROPN
ejpam-6009	357	18	,	,	PUNCT
ejpam-6009	357	19	σ2	σ2	NOUN
ejpam-6009	357	20	)	)	PUNCT
ejpam-6009	357	21	,	,	PUNCT
ejpam-6009	357	22	the	the	DET
ejpam-6009	357	23	following	follow	VERB
ejpam-6009	357	24	properties	property	NOUN
ejpam-6009	357	25	are	be	AUX
ejpam-6009	357	26	equivalent	equivalent	ADJ
ejpam-6009	357	27	:	:	PUNCT
ejpam-6009	357	28	(	(	PUNCT
ejpam-6009	357	29	1	1	X
ejpam-6009	357	30	)	)	PUNCT
ejpam-6009	357	31	f	f	PROPN
ejpam-6009	357	32	is	be	AUX
ejpam-6009	357	33	upper	upper	ADJ
ejpam-6009	357	34	almost	almost	ADV
ejpam-6009	357	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	357	36	,	,	PUNCT
ejpam-6009	357	37	τ2)p	τ2)p	ADJ
ejpam-6009	357	38	-	-	NOUN
ejpam-6009	357	39	continuous	continuous	ADJ
ejpam-6009	357	40	;	;	PUNCT
ejpam-6009	357	41	(	(	PUNCT
ejpam-6009	357	42	2	2	X
ejpam-6009	357	43	)	)	PUNCT
ejpam-6009	357	44	(	(	PUNCT
ejpam-6009	357	45	τ1	τ1	NOUN
ejpam-6009	357	46	,	,	PUNCT
ejpam-6009	357	47	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	357	48	−(v	−(v	NOUN
ejpam-6009	357	49	)	)	PUNCT
ejpam-6009	357	50	)	)	PUNCT
ejpam-6009	358	1	⊆	⊆	X
ejpam-6009	358	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6009	358	3	-	-	PUNCT
ejpam-6009	358	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	358	5	-	-	PUNCT
ejpam-6009	358	6	cl(v	cl(v	NOUN
ejpam-6009	358	7	)	)	PUNCT
ejpam-6009	358	8	)	)	PUNCT
ejpam-6009	358	9	)	)	PUNCT
ejpam-6009	358	10	for	for	ADP
ejpam-6009	358	11	every	every	DET
ejpam-6009	358	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	358	13	-	-	ADJ
ejpam-6009	358	14	open	open	ADJ
ejpam-6009	358	15	set	set	NOUN
ejpam-6009	358	16	v	v	NOUN
ejpam-6009	358	17	of	of	ADP
ejpam-6009	358	18	y	y	PROPN
ejpam-6009	358	19	;	;	PUNCT
ejpam-6009	358	20	(	(	PUNCT
ejpam-6009	358	21	3	3	X
ejpam-6009	358	22	)	)	PUNCT
ejpam-6009	358	23	(	(	PUNCT
ejpam-6009	358	24	τ1	τ1	PROPN
ejpam-6009	358	25	,	,	PUNCT
ejpam-6009	358	26	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	358	27	−(v	−(v	NOUN
ejpam-6009	358	28	)	)	PUNCT
ejpam-6009	358	29	)	)	PUNCT
ejpam-6009	359	1	⊆	⊆	NUM
ejpam-6009	359	2	f−((σ1	f−((σ1	NOUN
ejpam-6009	359	3	,	,	PUNCT
ejpam-6009	359	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6009	359	5	)	)	PUNCT
ejpam-6009	359	6	)	)	PUNCT
ejpam-6009	359	7	for	for	ADP
ejpam-6009	359	8	every	every	DET
ejpam-6009	359	9	σ1σ2	σ1σ2	NOUN
ejpam-6009	359	10	-	-	ADJ
ejpam-6009	359	11	open	open	ADJ
ejpam-6009	359	12	set	set	NOUN
ejpam-6009	359	13	v	v	NOUN
ejpam-6009	359	14	of	of	ADP
ejpam-6009	359	15	y	y	PROPN
ejpam-6009	359	16	.	.	PUNCT
ejpam-6009	360	1	proof	proof	NOUN
ejpam-6009	360	2	.	.	PUNCT
ejpam-6009	361	1	(	(	PUNCT
ejpam-6009	361	2	1	1	X
ejpam-6009	361	3	)	)	PUNCT
ejpam-6009	361	4	⇒	⇒	NOUN
ejpam-6009	361	5	(	(	PUNCT
ejpam-6009	361	6	2	2	NUM
ejpam-6009	361	7	):	):	PUNCT
ejpam-6009	361	8	let	let	VERB
ejpam-6009	361	9	v	v	PART
ejpam-6009	361	10	be	be	AUX
ejpam-6009	361	11	any	any	DET
ejpam-6009	361	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	361	13	-	-	ADJ
ejpam-6009	361	14	open	open	ADJ
ejpam-6009	361	15	set	set	NOUN
ejpam-6009	361	16	of	of	ADP
ejpam-6009	361	17	y	y	PROPN
ejpam-6009	361	18	.	.	PUNCT
ejpam-6009	362	1	then	then	ADV
ejpam-6009	362	2	,	,	PUNCT
ejpam-6009	362	3	σ1σ2	σ1σ2	X
ejpam-6009	362	4	-	-	PUNCT
ejpam-6009	362	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	362	6	-	-	PUNCT
ejpam-6009	362	7	cl(v	cl(v	NOUN
ejpam-6009	362	8	)	)	PUNCT
ejpam-6009	362	9	)	)	PUNCT
ejpam-6009	362	10	is	be	AUX
ejpam-6009	362	11	(	(	PUNCT
ejpam-6009	362	12	σ1	σ1	NOUN
ejpam-6009	362	13	,	,	PUNCT
ejpam-6009	362	14	σ2)r	σ2)r	NOUN
ejpam-6009	362	15	-	-	PUNCT
ejpam-6009	362	16	open	open	ADJ
ejpam-6009	362	17	in	in	ADP
ejpam-6009	362	18	y	y	PROPN
ejpam-6009	362	19	.	.	PUNCT
ejpam-6009	363	1	thus	thus	ADV
ejpam-6009	363	2	by	by	ADP
ejpam-6009	363	3	(	(	PUNCT
ejpam-6009	363	4	1	1	NUM
ejpam-6009	363	5	)	)	PUNCT
ejpam-6009	363	6	,	,	PUNCT
ejpam-6009	363	7	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	363	8	-	-	PUNCT
ejpam-6009	363	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	363	10	-	-	PUNCT
ejpam-6009	363	11	cl(v	cl(v	NOUN
ejpam-6009	363	12	)	)	PUNCT
ejpam-6009	363	13	)	)	PUNCT
ejpam-6009	363	14	)	)	PUNCT
ejpam-6009	363	15	is	be	AUX
ejpam-6009	363	16	(	(	PUNCT
ejpam-6009	363	17	τ1	τ1	NOUN
ejpam-6009	363	18	,	,	PUNCT
ejpam-6009	363	19	τ2)p	τ2)p	NOUN
ejpam-6009	363	20	-	-	PUNCT
ejpam-6009	363	21	closed	closed	ADJ
ejpam-6009	363	22	in	in	ADP
ejpam-6009	363	23	x.	x.	NOUN
ejpam-6009	363	24	since	since	SCONJ
ejpam-6009	363	25	v	v	NUM
ejpam-6009	363	26	⊆	⊆	NUM
ejpam-6009	363	27	σ1σ2	σ1σ2	NOUN
ejpam-6009	363	28	-	-	PUNCT
ejpam-6009	363	29	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	363	30	-	-	PUNCT
ejpam-6009	363	31	cl(v	cl(v	NOUN
ejpam-6009	363	32	)	)	PUNCT
ejpam-6009	363	33	)	)	PUNCT
ejpam-6009	363	34	,	,	PUNCT
ejpam-6009	363	35	we	we	PRON
ejpam-6009	363	36	have	have	VERB
ejpam-6009	363	37	f−(v	f−(v	NOUN
ejpam-6009	363	38	)	)	PUNCT
ejpam-6009	363	39	⊆	⊆	NUM
ejpam-6009	363	40	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6009	363	41	-	-	PUNCT
ejpam-6009	363	42	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	363	43	-	-	PUNCT
ejpam-6009	363	44	cl(v	cl(v	NOUN
ejpam-6009	363	45	)	)	PUNCT
ejpam-6009	363	46	)	)	PUNCT
ejpam-6009	363	47	)	)	PUNCT
ejpam-6009	364	1	and	and	CCONJ
ejpam-6009	364	2	hence	hence	ADV
ejpam-6009	364	3	(	(	PUNCT
ejpam-6009	364	4	τ1	τ1	PROPN
ejpam-6009	364	5	,	,	PUNCT
ejpam-6009	364	6	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	364	7	−(v	−(v	NOUN
ejpam-6009	364	8	)	)	PUNCT
ejpam-6009	364	9	)	)	PUNCT
ejpam-6009	365	1	⊆	⊆	X
ejpam-6009	365	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6009	365	3	-	-	PUNCT
ejpam-6009	365	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	365	5	-	-	PUNCT
ejpam-6009	365	6	cl(v	cl(v	NOUN
ejpam-6009	365	7	)	)	PUNCT
ejpam-6009	365	8	)	)	PUNCT
ejpam-6009	365	9	)	)	PUNCT
ejpam-6009	365	10	.	.	PUNCT
ejpam-6009	366	1	(	(	PUNCT
ejpam-6009	366	2	2	2	X
ejpam-6009	366	3	)	)	PUNCT
ejpam-6009	366	4	⇒	⇒	NOUN
ejpam-6009	366	5	(	(	PUNCT
ejpam-6009	366	6	1	1	NUM
ejpam-6009	366	7	):	):	PUNCT
ejpam-6009	366	8	let	let	VERB
ejpam-6009	366	9	v	v	PART
ejpam-6009	366	10	be	be	AUX
ejpam-6009	366	11	any	any	DET
ejpam-6009	366	12	(	(	PUNCT
ejpam-6009	366	13	σ1	σ1	NOUN
ejpam-6009	366	14	,	,	PUNCT
ejpam-6009	366	15	σ2)r	σ2)r	NOUN
ejpam-6009	366	16	-	-	PUNCT
ejpam-6009	366	17	open	open	ADJ
ejpam-6009	366	18	set	set	NOUN
ejpam-6009	366	19	of	of	ADP
ejpam-6009	366	20	y	y	PROPN
ejpam-6009	366	21	.	.	PUNCT
ejpam-6009	367	1	by	by	ADP
ejpam-6009	367	2	(	(	PUNCT
ejpam-6009	367	3	2	2	NUM
ejpam-6009	367	4	)	)	PUNCT
ejpam-6009	367	5	,	,	PUNCT
ejpam-6009	367	6	we	we	PRON
ejpam-6009	367	7	have	have	VERB
ejpam-6009	367	8	(	(	PUNCT
ejpam-6009	367	9	τ1	τ1	NOUN
ejpam-6009	367	10	,	,	PUNCT
ejpam-6009	367	11	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	367	12	−(v	−(v	NOUN
ejpam-6009	367	13	)	)	PUNCT
ejpam-6009	367	14	)	)	PUNCT
ejpam-6009	368	1	⊆	⊆	X
ejpam-6009	368	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6009	368	3	-	-	PUNCT
ejpam-6009	368	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	368	5	-	-	PUNCT
ejpam-6009	368	6	cl(v	cl(v	NOUN
ejpam-6009	368	7	)	)	PUNCT
ejpam-6009	368	8	)	)	PUNCT
ejpam-6009	368	9	)	)	PUNCT
ejpam-6009	369	1	=	=	SYM
ejpam-6009	369	2	f−(v	f−(v	ADJ
ejpam-6009	369	3	)	)	PUNCT
ejpam-6009	369	4	and	and	CCONJ
ejpam-6009	369	5	hence	hence	ADV
ejpam-6009	369	6	f−(v	f−(v	ADJ
ejpam-6009	369	7	)	)	PUNCT
ejpam-6009	369	8	is	be	AUX
ejpam-6009	369	9	(	(	PUNCT
ejpam-6009	369	10	τ1	τ1	NOUN
ejpam-6009	369	11	,	,	PUNCT
ejpam-6009	369	12	τ2)p	τ2)p	NOUN
ejpam-6009	369	13	-	-	PUNCT
ejpam-6009	369	14	closed	closed	ADJ
ejpam-6009	369	15	in	in	ADP
ejpam-6009	369	16	x	x	X
ejpam-6009	369	17	,	,	PUNCT
ejpam-6009	369	18	by	by	ADP
ejpam-6009	369	19	theorem	theorem	NOUN
ejpam-6009	369	20	5	5	NUM
ejpam-6009	369	21	we	we	PRON
ejpam-6009	369	22	have	have	VERB
ejpam-6009	369	23	f	f	PROPN
ejpam-6009	369	24	is	be	AUX
ejpam-6009	369	25	upper	upper	ADJ
ejpam-6009	369	26	almost	almost	ADV
ejpam-6009	369	27	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	369	28	,	,	PUNCT
ejpam-6009	369	29	τ2)p	τ2)p	ADJ
ejpam-6009	369	30	-	-	NOUN
ejpam-6009	369	31	continuous	continuous	ADJ
ejpam-6009	369	32	.	.	PUNCT
ejpam-6009	370	1	(	(	PUNCT
ejpam-6009	370	2	2	2	X
ejpam-6009	370	3	)	)	PUNCT
ejpam-6009	370	4	⇔	⇔	X
ejpam-6009	370	5	(	(	PUNCT
ejpam-6009	370	6	3	3	NUM
ejpam-6009	370	7	):	):	PUNCT
ejpam-6009	370	8	it	it	PRON
ejpam-6009	370	9	follows	follow	VERB
ejpam-6009	370	10	from	from	ADP
ejpam-6009	370	11	lemma	lemma	PROPN
ejpam-6009	370	12	5	5	NUM
ejpam-6009	370	13	.	.	PUNCT
ejpam-6009	370	14	c.	c.	PROPN
ejpam-6009	370	15	viriyapong	viriyapong	PROPN
ejpam-6009	370	16	,	,	PUNCT
ejpam-6009	370	17	a.	a.	PROPN
ejpam-6009	370	18	sama	sama	PROPN
ejpam-6009	370	19	-	-	PUNCT
ejpam-6009	370	20	ae	ae	PROPN
ejpam-6009	370	21	,	,	PUNCT
ejpam-6009	370	22	c.	c.	PROPN
ejpam-6009	370	23	boonpok	boonpok	PROPN
ejpam-6009	370	24	/	/	SYM
ejpam-6009	370	25	eur	eur	PROPN
ejpam-6009	370	26	.	.	PUNCT
ejpam-6009	371	1	j.	j.	PROPN
ejpam-6009	371	2	pure	pure	PROPN
ejpam-6009	371	3	appl	appl	PROPN
ejpam-6009	371	4	.	.	PROPN
ejpam-6009	371	5	math	math	PROPN
ejpam-6009	371	6	,	,	PUNCT
ejpam-6009	371	7	18	18	NUM
ejpam-6009	371	8	(	(	PUNCT
ejpam-6009	371	9	2	2	NUM
ejpam-6009	371	10	)	)	PUNCT
ejpam-6009	371	11	(	(	PUNCT
ejpam-6009	371	12	2025	2025	NUM
ejpam-6009	371	13	)	)	PUNCT
ejpam-6009	371	14	,	,	PUNCT
ejpam-6009	371	15	6009	6009	NUM
ejpam-6009	371	16	14	14	NUM
ejpam-6009	371	17	of	of	ADP
ejpam-6009	371	18	18	18	NUM
ejpam-6009	371	19	theorem	theorem	VERB
ejpam-6009	371	20	13	13	NUM
ejpam-6009	371	21	.	.	PUNCT
ejpam-6009	372	1	for	for	ADP
ejpam-6009	372	2	a	a	DET
ejpam-6009	372	3	multifunction	multifunction	NOUN
ejpam-6009	372	4	f	f	NOUN
ejpam-6009	372	5	:	:	PUNCT
ejpam-6009	372	6	(	(	PUNCT
ejpam-6009	372	7	x	x	NOUN
ejpam-6009	372	8	,	,	PUNCT
ejpam-6009	372	9	τ1	τ1	NOUN
ejpam-6009	372	10	,	,	PUNCT
ejpam-6009	372	11	τ2	τ2	NOUN
ejpam-6009	372	12	)	)	PUNCT
ejpam-6009	372	13	→	→	SYM
ejpam-6009	372	14	(	(	PUNCT
ejpam-6009	372	15	y	y	PROPN
ejpam-6009	372	16	,	,	PUNCT
ejpam-6009	372	17	σ1	σ1	PROPN
ejpam-6009	372	18	,	,	PUNCT
ejpam-6009	372	19	σ2	σ2	NOUN
ejpam-6009	372	20	)	)	PUNCT
ejpam-6009	372	21	,	,	PUNCT
ejpam-6009	372	22	the	the	DET
ejpam-6009	372	23	following	follow	VERB
ejpam-6009	372	24	properties	property	NOUN
ejpam-6009	372	25	are	be	AUX
ejpam-6009	372	26	equivalent	equivalent	ADJ
ejpam-6009	372	27	:	:	PUNCT
ejpam-6009	372	28	(	(	PUNCT
ejpam-6009	372	29	1	1	X
ejpam-6009	372	30	)	)	PUNCT
ejpam-6009	372	31	f	f	PROPN
ejpam-6009	372	32	is	be	AUX
ejpam-6009	372	33	lower	low	ADJ
ejpam-6009	372	34	almost	almost	ADV
ejpam-6009	372	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	372	36	,	,	PUNCT
ejpam-6009	372	37	τ2)p	τ2)p	ADJ
ejpam-6009	372	38	-	-	NOUN
ejpam-6009	372	39	continuous	continuous	ADJ
ejpam-6009	372	40	;	;	PUNCT
ejpam-6009	372	41	(	(	PUNCT
ejpam-6009	372	42	2	2	X
ejpam-6009	372	43	)	)	PUNCT
ejpam-6009	372	44	(	(	PUNCT
ejpam-6009	372	45	τ1	τ1	NOUN
ejpam-6009	372	46	,	,	PUNCT
ejpam-6009	372	47	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	373	1	+	+	PROPN
ejpam-6009	373	2	(	(	PUNCT
ejpam-6009	373	3	v	v	NOUN
ejpam-6009	373	4	)	)	PUNCT
ejpam-6009	373	5	)	)	PUNCT
ejpam-6009	374	1	⊆	⊆	X
ejpam-6009	374	2	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-6009	374	3	-	-	PUNCT
ejpam-6009	374	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6009	374	5	-	-	PUNCT
ejpam-6009	374	6	cl(v	cl(v	NOUN
ejpam-6009	374	7	)	)	PUNCT
ejpam-6009	374	8	)	)	PUNCT
ejpam-6009	374	9	)	)	PUNCT
ejpam-6009	374	10	for	for	ADP
ejpam-6009	374	11	every	every	DET
ejpam-6009	374	12	σ1σ2	σ1σ2	NOUN
ejpam-6009	374	13	-	-	ADJ
ejpam-6009	374	14	open	open	ADJ
ejpam-6009	374	15	set	set	NOUN
ejpam-6009	374	16	v	v	NOUN
ejpam-6009	374	17	of	of	ADP
ejpam-6009	374	18	y	y	PROPN
ejpam-6009	374	19	;	;	PUNCT
ejpam-6009	374	20	(	(	PUNCT
ejpam-6009	374	21	3	3	X
ejpam-6009	374	22	)	)	PUNCT
ejpam-6009	374	23	(	(	PUNCT
ejpam-6009	374	24	τ1	τ1	NOUN
ejpam-6009	374	25	,	,	PUNCT
ejpam-6009	374	26	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	374	27	+	+	PROPN
ejpam-6009	374	28	(	(	PUNCT
ejpam-6009	374	29	v	v	NOUN
ejpam-6009	374	30	)	)	PUNCT
ejpam-6009	374	31	)	)	PUNCT
ejpam-6009	375	1	⊆	⊆	NUM
ejpam-6009	375	2	f+((σ1	f+((σ1	NOUN
ejpam-6009	375	3	,	,	PUNCT
ejpam-6009	375	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6009	375	5	)	)	PUNCT
ejpam-6009	375	6	)	)	PUNCT
ejpam-6009	376	1	for	for	ADP
ejpam-6009	376	2	every	every	DET
ejpam-6009	376	3	σ1σ2	σ1σ2	NOUN
ejpam-6009	376	4	-	-	ADJ
ejpam-6009	376	5	open	open	ADJ
ejpam-6009	376	6	set	set	NOUN
ejpam-6009	376	7	v	v	NOUN
ejpam-6009	376	8	of	of	ADP
ejpam-6009	376	9	y	y	PROPN
ejpam-6009	376	10	.	.	PUNCT
ejpam-6009	377	1	proof	proof	NOUN
ejpam-6009	377	2	.	.	PUNCT
ejpam-6009	378	1	the	the	DET
ejpam-6009	378	2	proof	proof	NOUN
ejpam-6009	378	3	is	be	AUX
ejpam-6009	378	4	similar	similar	ADJ
ejpam-6009	378	5	to	to	ADP
ejpam-6009	378	6	that	that	PRON
ejpam-6009	378	7	of	of	ADP
ejpam-6009	378	8	theorem	theorem	ADJ
ejpam-6009	378	9	12	12	NUM
ejpam-6009	378	10	.	.	PUNCT
ejpam-6009	379	1	theorem	theorem	NOUN
ejpam-6009	379	2	14	14	NUM
ejpam-6009	379	3	.	.	PUNCT
ejpam-6009	380	1	let	let	VERB
ejpam-6009	380	2	f	f	NOUN
ejpam-6009	380	3	:	:	PUNCT
ejpam-6009	380	4	(	(	PUNCT
ejpam-6009	380	5	x	x	NOUN
ejpam-6009	380	6	,	,	PUNCT
ejpam-6009	380	7	τ1	τ1	NOUN
ejpam-6009	380	8	,	,	PUNCT
ejpam-6009	380	9	τ2	τ2	NOUN
ejpam-6009	380	10	)	)	PUNCT
ejpam-6009	380	11	→	→	SYM
ejpam-6009	380	12	(	(	PUNCT
ejpam-6009	380	13	y	y	PROPN
ejpam-6009	380	14	,	,	PUNCT
ejpam-6009	380	15	σ1	σ1	PROPN
ejpam-6009	380	16	,	,	PUNCT
ejpam-6009	380	17	σ2	σ2	PROPN
ejpam-6009	380	18	)	)	PUNCT
ejpam-6009	380	19	be	be	AUX
ejpam-6009	380	20	a	a	DET
ejpam-6009	380	21	multifunction	multifunction	NOUN
ejpam-6009	380	22	.	.	PUNCT
ejpam-6009	381	1	if	if	SCONJ
ejpam-6009	381	2	(	(	PUNCT
ejpam-6009	381	3	τ1	τ1	NOUN
ejpam-6009	381	4	,	,	PUNCT
ejpam-6009	381	5	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	381	6	−(b	−(b	PROPN
ejpam-6009	381	7	)	)	PUNCT
ejpam-6009	381	8	)	)	PUNCT
ejpam-6009	381	9	⊆	⊆	X
ejpam-6009	381	10	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	381	11	-	-	PUNCT
ejpam-6009	381	12	ker(b	ker(b	PROPN
ejpam-6009	381	13	)	)	PUNCT
ejpam-6009	381	14	)	)	PUNCT
ejpam-6009	381	15	for	for	ADP
ejpam-6009	381	16	every	every	DET
ejpam-6009	381	17	subset	subset	NOUN
ejpam-6009	381	18	b	b	PROPN
ejpam-6009	381	19	of	of	ADP
ejpam-6009	381	20	y	y	PROPN
ejpam-6009	381	21	,	,	PUNCT
ejpam-6009	381	22	then	then	ADV
ejpam-6009	381	23	f	f	PROPN
ejpam-6009	381	24	is	be	AUX
ejpam-6009	381	25	upper	upper	ADJ
ejpam-6009	381	26	almost	almost	ADV
ejpam-6009	381	27	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	381	28	,	,	PUNCT
ejpam-6009	381	29	τ2)p	τ2)p	ADJ
ejpam-6009	381	30	-	-	ADJ
ejpam-6009	381	31	continuous	continuous	ADJ
ejpam-6009	381	32	.	.	PUNCT
ejpam-6009	382	1	proof	proof	NOUN
ejpam-6009	382	2	.	.	PUNCT
ejpam-6009	383	1	let	let	VERB
ejpam-6009	383	2	v	v	PART
ejpam-6009	383	3	be	be	AUX
ejpam-6009	383	4	any	any	DET
ejpam-6009	383	5	(	(	PUNCT
ejpam-6009	383	6	σ1	σ1	NOUN
ejpam-6009	383	7	,	,	PUNCT
ejpam-6009	383	8	σ2)r	σ2)r	NOUN
ejpam-6009	383	9	-	-	PUNCT
ejpam-6009	383	10	open	open	ADJ
ejpam-6009	383	11	set	set	NOUN
ejpam-6009	383	12	of	of	ADP
ejpam-6009	383	13	y	y	PROPN
ejpam-6009	383	14	.	.	PUNCT
ejpam-6009	384	1	by	by	ADP
ejpam-6009	384	2	lemma	lemma	PROPN
ejpam-6009	384	3	1	1	NUM
ejpam-6009	384	4	,	,	PUNCT
ejpam-6009	384	5	we	we	PRON
ejpam-6009	384	6	have	have	VERB
ejpam-6009	384	7	(	(	PUNCT
ejpam-6009	384	8	τ1	τ1	NOUN
ejpam-6009	384	9	,	,	PUNCT
ejpam-6009	384	10	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	384	11	−(v	−(v	NOUN
ejpam-6009	384	12	)	)	PUNCT
ejpam-6009	384	13	)	)	PUNCT
ejpam-6009	385	1	⊆	⊆	X
ejpam-6009	385	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6009	385	3	-	-	PUNCT
ejpam-6009	385	4	ker(v	ker(v	NOUN
ejpam-6009	385	5	)	)	PUNCT
ejpam-6009	385	6	)	)	PUNCT
ejpam-6009	386	1	=	=	SYM
ejpam-6009	386	2	f−(v	f−(v	ADJ
ejpam-6009	386	3	)	)	PUNCT
ejpam-6009	386	4	and	and	CCONJ
ejpam-6009	386	5	hence	hence	ADV
ejpam-6009	386	6	f−(v	f−(v	ADJ
ejpam-6009	386	7	)	)	PUNCT
ejpam-6009	386	8	is	be	AUX
ejpam-6009	386	9	(	(	PUNCT
ejpam-6009	386	10	τ1	τ1	NOUN
ejpam-6009	386	11	,	,	PUNCT
ejpam-6009	386	12	τ2)p	τ2)p	NOUN
ejpam-6009	386	13	-	-	PUNCT
ejpam-6009	386	14	closed	closed	ADJ
ejpam-6009	386	15	in	in	ADP
ejpam-6009	386	16	x.	x.	NOUN
ejpam-6009	386	17	thus	thus	ADV
ejpam-6009	386	18	by	by	ADP
ejpam-6009	386	19	theorem	theorem	NOUN
ejpam-6009	386	20	5	5	NUM
ejpam-6009	386	21	,	,	PUNCT
ejpam-6009	386	22	f	f	PROPN
ejpam-6009	386	23	is	be	AUX
ejpam-6009	386	24	upper	upper	ADJ
ejpam-6009	386	25	almost	almost	ADV
ejpam-6009	386	26	contra(τ1	contra(τ1	NOUN
ejpam-6009	386	27	,	,	PUNCT
ejpam-6009	386	28	τ2)p	τ2)p	ADJ
ejpam-6009	386	29	-	-	ADJ
ejpam-6009	386	30	continuous	continuous	ADJ
ejpam-6009	386	31	.	.	PUNCT
ejpam-6009	387	1	theorem	theorem	NOUN
ejpam-6009	387	2	15	15	NUM
ejpam-6009	387	3	.	.	PUNCT
ejpam-6009	388	1	let	let	VERB
ejpam-6009	388	2	f	f	NOUN
ejpam-6009	388	3	:	:	PUNCT
ejpam-6009	388	4	(	(	PUNCT
ejpam-6009	388	5	x	x	NOUN
ejpam-6009	388	6	,	,	PUNCT
ejpam-6009	388	7	τ1	τ1	NOUN
ejpam-6009	388	8	,	,	PUNCT
ejpam-6009	388	9	τ2	τ2	NOUN
ejpam-6009	388	10	)	)	PUNCT
ejpam-6009	388	11	→	→	SYM
ejpam-6009	388	12	(	(	PUNCT
ejpam-6009	388	13	y	y	PROPN
ejpam-6009	388	14	,	,	PUNCT
ejpam-6009	388	15	σ1	σ1	PROPN
ejpam-6009	388	16	,	,	PUNCT
ejpam-6009	388	17	σ2	σ2	PROPN
ejpam-6009	388	18	)	)	PUNCT
ejpam-6009	388	19	be	be	AUX
ejpam-6009	388	20	a	a	DET
ejpam-6009	388	21	multifunction	multifunction	NOUN
ejpam-6009	388	22	.	.	PUNCT
ejpam-6009	389	1	if	if	SCONJ
ejpam-6009	389	2	f	f	PROPN
ejpam-6009	389	3	(	(	PUNCT
ejpam-6009	389	4	(	(	PUNCT
ejpam-6009	389	5	τ1	τ1	PROPN
ejpam-6009	389	6	,	,	PUNCT
ejpam-6009	389	7	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6009	389	8	)	)	PUNCT
ejpam-6009	389	9	)	)	PUNCT
ejpam-6009	390	1	⊆	⊆	X
ejpam-6009	390	2	σ1σ2	σ1σ2	NUM
ejpam-6009	390	3	-	-	PUNCT
ejpam-6009	390	4	ker(f	ker(f	PROPN
ejpam-6009	390	5	(	(	PUNCT
ejpam-6009	390	6	a	a	NOUN
ejpam-6009	390	7	)	)	PUNCT
ejpam-6009	390	8	)	)	PUNCT
ejpam-6009	390	9	for	for	ADP
ejpam-6009	390	10	every	every	DET
ejpam-6009	390	11	subset	subset	NOUN
ejpam-6009	390	12	a	a	PRON
ejpam-6009	390	13	of	of	ADP
ejpam-6009	390	14	x	x	PRON
ejpam-6009	390	15	,	,	PUNCT
ejpam-6009	390	16	then	then	ADV
ejpam-6009	390	17	f	f	PROPN
ejpam-6009	390	18	is	be	AUX
ejpam-6009	390	19	lower	low	ADJ
ejpam-6009	390	20	almost	almost	ADV
ejpam-6009	390	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	390	22	,	,	PUNCT
ejpam-6009	390	23	τ2)p	τ2)p	ADJ
ejpam-6009	390	24	-	-	ADJ
ejpam-6009	390	25	continuous	continuous	ADJ
ejpam-6009	390	26	.	.	PUNCT
ejpam-6009	391	1	proof	proof	NOUN
ejpam-6009	391	2	.	.	PUNCT
ejpam-6009	392	1	let	let	VERB
ejpam-6009	392	2	v	v	PART
ejpam-6009	392	3	be	be	AUX
ejpam-6009	392	4	any	any	DET
ejpam-6009	392	5	(	(	PUNCT
ejpam-6009	392	6	σ1	σ1	NOUN
ejpam-6009	392	7	,	,	PUNCT
ejpam-6009	392	8	σ2)r	σ2)r	NOUN
ejpam-6009	392	9	-	-	PUNCT
ejpam-6009	392	10	open	open	ADJ
ejpam-6009	392	11	set	set	NOUN
ejpam-6009	392	12	of	of	ADP
ejpam-6009	392	13	y	y	PROPN
ejpam-6009	392	14	.	.	PUNCT
ejpam-6009	393	1	this	this	PRON
ejpam-6009	393	2	implies	imply	VERB
ejpam-6009	393	3	that	that	SCONJ
ejpam-6009	393	4	f	f	PROPN
ejpam-6009	393	5	(	(	PUNCT
ejpam-6009	393	6	(	(	PUNCT
ejpam-6009	393	7	τ1	τ1	PROPN
ejpam-6009	393	8	,	,	PUNCT
ejpam-6009	393	9	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	393	10	+	+	PROPN
ejpam-6009	393	11	(	(	PUNCT
ejpam-6009	393	12	v	v	NOUN
ejpam-6009	393	13	)	)	PUNCT
ejpam-6009	393	14	)	)	PUNCT
ejpam-6009	393	15	)	)	PUNCT
ejpam-6009	394	1	⊆	⊆	X
ejpam-6009	394	2	σ1σ2	σ1σ2	X
ejpam-6009	394	3	-	-	PUNCT
ejpam-6009	394	4	ker(v	ker(v	NOUN
ejpam-6009	394	5	)	)	PUNCT
ejpam-6009	394	6	and	and	CCONJ
ejpam-6009	394	7	hence	hence	ADV
ejpam-6009	394	8	(	(	PUNCT
ejpam-6009	394	9	τ1	τ1	NOUN
ejpam-6009	394	10	,	,	PUNCT
ejpam-6009	394	11	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	394	12	+	+	PROPN
ejpam-6009	394	13	(	(	PUNCT
ejpam-6009	394	14	v	v	NOUN
ejpam-6009	394	15	)	)	PUNCT
ejpam-6009	394	16	)	)	PUNCT
ejpam-6009	395	1	⊆	⊆	NUM
ejpam-6009	395	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	395	3	-	-	PUNCT
ejpam-6009	395	4	ker(v	ker(v	NOUN
ejpam-6009	395	5	)	)	PUNCT
ejpam-6009	395	6	)	)	PUNCT
ejpam-6009	395	7	.	.	PUNCT
ejpam-6009	396	1	by	by	ADP
ejpam-6009	396	2	lemma	lemma	PROPN
ejpam-6009	396	3	1	1	NUM
ejpam-6009	396	4	,	,	PUNCT
ejpam-6009	396	5	we	we	PRON
ejpam-6009	396	6	have	have	VERB
ejpam-6009	396	7	(	(	PUNCT
ejpam-6009	396	8	τ1	τ1	NOUN
ejpam-6009	396	9	,	,	PUNCT
ejpam-6009	396	10	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6009	397	1	+	+	PROPN
ejpam-6009	397	2	(	(	PUNCT
ejpam-6009	397	3	v	v	NOUN
ejpam-6009	397	4	)	)	PUNCT
ejpam-6009	397	5	)	)	PUNCT
ejpam-6009	398	1	⊆	⊆	NUM
ejpam-6009	398	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6009	398	3	-	-	PUNCT
ejpam-6009	398	4	ker(v	ker(v	NOUN
ejpam-6009	398	5	)	)	PUNCT
ejpam-6009	398	6	)	)	PUNCT
ejpam-6009	398	7	=	=	PUNCT
ejpam-6009	399	1	f+(v	f+(v	NOUN
ejpam-6009	399	2	)	)	PUNCT
ejpam-6009	400	1	and	and	CCONJ
ejpam-6009	400	2	so	so	ADV
ejpam-6009	400	3	f+(v	f+(v	PROPN
ejpam-6009	400	4	)	)	PUNCT
ejpam-6009	400	5	is	be	AUX
ejpam-6009	400	6	τ1τ2	τ1τ2	NOUN
ejpam-6009	400	7	-	-	ADJ
ejpam-6009	400	8	closed	closed	ADJ
ejpam-6009	400	9	in	in	ADP
ejpam-6009	400	10	x.	x.	NOUN
ejpam-6009	400	11	by	by	ADP
ejpam-6009	400	12	theorem	theorem	NOUN
ejpam-6009	400	13	6	6	NUM
ejpam-6009	400	14	,	,	PUNCT
ejpam-6009	400	15	f	f	PROPN
ejpam-6009	400	16	is	be	AUX
ejpam-6009	400	17	lower	low	ADJ
ejpam-6009	400	18	almost	almost	ADV
ejpam-6009	400	19	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	400	20	,	,	PUNCT
ejpam-6009	400	21	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6009	400	22	.	.	PUNCT
ejpam-6009	401	1	acknowledgements	acknowledgement	NOUN
ejpam-6009	401	2	this	this	DET
ejpam-6009	401	3	research	research	NOUN
ejpam-6009	401	4	project	project	NOUN
ejpam-6009	401	5	was	be	AUX
ejpam-6009	401	6	financially	financially	ADV
ejpam-6009	401	7	supported	support	VERB
ejpam-6009	401	8	by	by	ADP
ejpam-6009	401	9	mahasarakham	mahasarakham	PROPN
ejpam-6009	401	10	university	university	PROPN
ejpam-6009	401	11	.	.	PUNCT
ejpam-6009	402	1	references	reference	NOUN
ejpam-6009	402	2	[	[	X
ejpam-6009	402	3	1	1	NUM
ejpam-6009	402	4	]	]	PUNCT
ejpam-6009	402	5	c.	c.	PROPN
ejpam-6009	402	6	boonpok	boonpok	PROPN
ejpam-6009	402	7	and	and	CCONJ
ejpam-6009	402	8	j.	j.	PROPN
ejpam-6009	402	9	khampakdee	khampakdee	PROPN
ejpam-6009	402	10	.	.	PUNCT
ejpam-6009	403	1	(	(	PUNCT
ejpam-6009	403	2	λ	λ	NOUN
ejpam-6009	403	3	,	,	PUNCT
ejpam-6009	403	4	sp)-open	sp)-open	ADJ
ejpam-6009	403	5	sets	set	NOUN
ejpam-6009	403	6	in	in	ADP
ejpam-6009	403	7	topological	topological	ADJ
ejpam-6009	403	8	spaces	space	NOUN
ejpam-6009	403	9	.	.	PUNCT
ejpam-6009	404	1	european	european	ADJ
ejpam-6009	404	2	journal	journal	PROPN
ejpam-6009	404	3	of	of	ADP
ejpam-6009	404	4	pure	pure	ADJ
ejpam-6009	404	5	and	and	CCONJ
ejpam-6009	404	6	applied	applied	ADJ
ejpam-6009	404	7	mathematics	mathematic	NOUN
ejpam-6009	404	8	,	,	PUNCT
ejpam-6009	404	9	15(2):572–588	15(2):572–588	NUM
ejpam-6009	404	10	,	,	PUNCT
ejpam-6009	404	11	2022	2022	NUM
ejpam-6009	404	12	.	.	PUNCT
ejpam-6009	405	1	[	[	X
ejpam-6009	405	2	2	2	NUM
ejpam-6009	405	3	]	]	PUNCT
ejpam-6009	405	4	c.	c.	PROPN
ejpam-6009	405	5	viriyapong	viriyapong	PROPN
ejpam-6009	405	6	and	and	CCONJ
ejpam-6009	405	7	c.	c.	PROPN
ejpam-6009	405	8	boonpok	boonpok	PROPN
ejpam-6009	405	9	.	.	PUNCT
ejpam-6009	406	1	(	(	PUNCT
ejpam-6009	406	2	λ	λ	X
ejpam-6009	406	3	,	,	PUNCT
ejpam-6009	406	4	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	406	5	functions	function	NOUN
ejpam-6009	406	6	.	.	PUNCT
ejpam-6009	407	1	wseas	wseas	VERB
ejpam-6009	407	2	transactions	transaction	NOUN
ejpam-6009	407	3	on	on	ADP
ejpam-6009	407	4	mathematics	mathematic	NOUN
ejpam-6009	407	5	,	,	PUNCT
ejpam-6009	407	6	21:380–385	21:380–385	NUM
ejpam-6009	407	7	,	,	PUNCT
ejpam-6009	407	8	2022	2022	NUM
ejpam-6009	407	9	.	.	PUNCT
ejpam-6009	408	1	c.	c.	PROPN
ejpam-6009	408	2	viriyapong	viriyapong	PROPN
ejpam-6009	408	3	,	,	PUNCT
ejpam-6009	408	4	a.	a.	PROPN
ejpam-6009	408	5	sama	sama	PROPN
ejpam-6009	408	6	-	-	PUNCT
ejpam-6009	408	7	ae	ae	PROPN
ejpam-6009	408	8	,	,	PUNCT
ejpam-6009	408	9	c.	c.	PROPN
ejpam-6009	408	10	boonpok	boonpok	PROPN
ejpam-6009	408	11	/	/	SYM
ejpam-6009	408	12	eur	eur	PROPN
ejpam-6009	408	13	.	.	PUNCT
ejpam-6009	409	1	j.	j.	PROPN
ejpam-6009	409	2	pure	pure	PROPN
ejpam-6009	409	3	appl	appl	PROPN
ejpam-6009	409	4	.	.	PROPN
ejpam-6009	409	5	math	math	PROPN
ejpam-6009	409	6	,	,	PUNCT
ejpam-6009	409	7	18	18	NUM
ejpam-6009	409	8	(	(	PUNCT
ejpam-6009	409	9	2	2	NUM
ejpam-6009	409	10	)	)	PUNCT
ejpam-6009	409	11	(	(	PUNCT
ejpam-6009	409	12	2025	2025	NUM
ejpam-6009	409	13	)	)	PUNCT
ejpam-6009	409	14	,	,	PUNCT
ejpam-6009	409	15	6009	6009	NUM
ejpam-6009	409	16	15	15	NUM
ejpam-6009	409	17	of	of	ADP
ejpam-6009	409	18	18	18	NUM
ejpam-6009	409	19	[	[	SYM
ejpam-6009	409	20	3	3	NUM
ejpam-6009	409	21	]	]	PUNCT
ejpam-6009	409	22	t.	t.	NOUN
ejpam-6009	409	23	dungthaisong	dungthaisong	PROPN
ejpam-6009	409	24	,	,	PUNCT
ejpam-6009	409	25	c.	c.	PROPN
ejpam-6009	409	26	boonpok	boonpok	PROPN
ejpam-6009	409	27	,	,	PUNCT
ejpam-6009	409	28	and	and	CCONJ
ejpam-6009	409	29	c.	c.	PROPN
ejpam-6009	409	30	viriyapong	viriyapong	PROPN
ejpam-6009	409	31	.	.	PUNCT
ejpam-6009	410	1	generalized	generalize	VERB
ejpam-6009	410	2	closed	close	VERB
ejpam-6009	410	3	sets	set	NOUN
ejpam-6009	410	4	in	in	ADP
ejpam-6009	410	5	bigeneralized	bigeneralize	VERB
ejpam-6009	410	6	topological	topological	ADJ
ejpam-6009	410	7	spaces	space	NOUN
ejpam-6009	410	8	.	.	PUNCT
ejpam-6009	411	1	international	international	ADJ
ejpam-6009	411	2	journal	journal	PROPN
ejpam-6009	411	3	of	of	ADP
ejpam-6009	411	4	mathematical	mathematical	ADJ
ejpam-6009	411	5	analysis	analysis	NOUN
ejpam-6009	411	6	,	,	PUNCT
ejpam-6009	411	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-6009	411	8	,	,	PUNCT
ejpam-6009	411	9	2011	2011	NUM
ejpam-6009	411	10	.	.	PUNCT
ejpam-6009	412	1	[	[	X
ejpam-6009	412	2	4	4	X
ejpam-6009	412	3	]	]	PUNCT
ejpam-6009	412	4	t.	t.	PROPN
ejpam-6009	412	5	duangphui	duangphui	PROPN
ejpam-6009	412	6	,	,	PUNCT
ejpam-6009	412	7	c.	c.	PROPN
ejpam-6009	412	8	boonpok	boonpok	PROPN
ejpam-6009	412	9	,	,	PUNCT
ejpam-6009	412	10	and	and	CCONJ
ejpam-6009	412	11	c.	c.	PROPN
ejpam-6009	412	12	viriyapong	viriyapong	PROPN
ejpam-6009	412	13	.	.	PUNCT
ejpam-6009	413	1	continuous	continuous	ADJ
ejpam-6009	413	2	functions	function	NOUN
ejpam-6009	413	3	on	on	ADP
ejpam-6009	413	4	bigeneralized	bigeneralize	VERB
ejpam-6009	413	5	topological	topological	ADJ
ejpam-6009	413	6	spaces	space	NOUN
ejpam-6009	413	7	.	.	PUNCT
ejpam-6009	414	1	international	international	ADJ
ejpam-6009	414	2	journal	journal	PROPN
ejpam-6009	414	3	of	of	ADP
ejpam-6009	414	4	mathematical	mathematical	ADJ
ejpam-6009	414	5	analysis	analysis	NOUN
ejpam-6009	414	6	,	,	PUNCT
ejpam-6009	414	7	5(24):1165	5(24):1165	NUM
ejpam-6009	414	8	–	–	PUNCT
ejpam-6009	414	9	1174	1174	NUM
ejpam-6009	414	10	,	,	PUNCT
ejpam-6009	414	11	2011	2011	NUM
ejpam-6009	414	12	.	.	PUNCT
ejpam-6009	415	1	[	[	X
ejpam-6009	415	2	5	5	NUM
ejpam-6009	415	3	]	]	X
ejpam-6009	415	4	n.	n.	NOUN
ejpam-6009	415	5	srisarakham	srisarakham	PROPN
ejpam-6009	415	6	and	and	CCONJ
ejpam-6009	415	7	c.	c.	PROPN
ejpam-6009	415	8	boonpok	boonpok	PROPN
ejpam-6009	415	9	.	.	PUNCT
ejpam-6009	416	1	almost	almost	ADV
ejpam-6009	416	2	(	(	PUNCT
ejpam-6009	416	3	λ	λ	NOUN
ejpam-6009	416	4	,	,	PUNCT
ejpam-6009	416	5	p)-continuous	p)-continuous	ADJ
ejpam-6009	416	6	functions	function	NOUN
ejpam-6009	416	7	.	.	PUNCT
ejpam-6009	417	1	international	international	ADJ
ejpam-6009	417	2	journal	journal	PROPN
ejpam-6009	417	3	of	of	ADP
ejpam-6009	417	4	mathematics	mathematic	NOUN
ejpam-6009	417	5	and	and	CCONJ
ejpam-6009	417	6	computer	computer	NOUN
ejpam-6009	417	7	science	science	NOUN
ejpam-6009	417	8	,	,	PUNCT
ejpam-6009	417	9	18(2):255–259	18(2):255–259	NUM
ejpam-6009	417	10	,	,	PUNCT
ejpam-6009	417	11	2023	2023	NUM
ejpam-6009	417	12	.	.	PUNCT
ejpam-6009	418	1	[	[	X
ejpam-6009	418	2	6	6	NUM
ejpam-6009	418	3	]	]	PUNCT
ejpam-6009	418	4	m.	m.	NOUN
ejpam-6009	418	5	thongmoon	thongmoon	NOUN
ejpam-6009	418	6	and	and	CCONJ
ejpam-6009	418	7	c.	c.	PROPN
ejpam-6009	418	8	boonpok	boonpok	PROPN
ejpam-6009	418	9	.	.	PUNCT
ejpam-6009	419	1	strongly	strongly	ADV
ejpam-6009	419	2	θ(λ	θ(λ	PROPN
ejpam-6009	419	3	,	,	PUNCT
ejpam-6009	419	4	p)-continuous	p)-continuous	ADJ
ejpam-6009	419	5	functions	function	NOUN
ejpam-6009	419	6	.	.	PUNCT
ejpam-6009	420	1	international	international	ADJ
ejpam-6009	420	2	journal	journal	PROPN
ejpam-6009	420	3	of	of	ADP
ejpam-6009	420	4	mathematics	mathematic	NOUN
ejpam-6009	420	5	and	and	CCONJ
ejpam-6009	420	6	computer	computer	NOUN
ejpam-6009	420	7	science	science	NOUN
ejpam-6009	420	8	,	,	PUNCT
ejpam-6009	420	9	19(2):475–479	19(2):475–479	PROPN
ejpam-6009	420	10	,	,	PUNCT
ejpam-6009	420	11	2024	2024	NUM
ejpam-6009	420	12	.	.	PUNCT
ejpam-6009	421	1	[	[	X
ejpam-6009	421	2	7	7	X
ejpam-6009	421	3	]	]	X
ejpam-6009	421	4	c.	c.	PROPN
ejpam-6009	421	5	boonpok	boonpok	PROPN
ejpam-6009	421	6	and	and	CCONJ
ejpam-6009	421	7	j.	j.	PROPN
ejpam-6009	421	8	khampakdee	khampakdee	PROPN
ejpam-6009	421	9	.	.	PUNCT
ejpam-6009	422	1	almost	almost	ADV
ejpam-6009	422	2	strong	strong	ADJ
ejpam-6009	422	3	θ(λ	θ(λ	PROPN
ejpam-6009	422	4	,	,	PUNCT
ejpam-6009	422	5	p)-continuity	p)-continuity	NOUN
ejpam-6009	422	6	for	for	ADP
ejpam-6009	422	7	functions	function	NOUN
ejpam-6009	422	8	.	.	PUNCT
ejpam-6009	423	1	european	european	ADJ
ejpam-6009	423	2	journal	journal	PROPN
ejpam-6009	423	3	of	of	ADP
ejpam-6009	423	4	pure	pure	ADJ
ejpam-6009	423	5	and	and	CCONJ
ejpam-6009	423	6	applied	applied	ADJ
ejpam-6009	423	7	mathematics	mathematic	NOUN
ejpam-6009	423	8	,	,	PUNCT
ejpam-6009	423	9	17(1):300–309	17(1):300–309	PROPN
ejpam-6009	423	10	,	,	PUNCT
ejpam-6009	423	11	2024	2024	NUM
ejpam-6009	423	12	.	.	PUNCT
ejpam-6009	424	1	[	[	X
ejpam-6009	424	2	8	8	NUM
ejpam-6009	424	3	]	]	X
ejpam-6009	424	4	p.	p.	NOUN
ejpam-6009	424	5	pue	pue	NOUN
ejpam-6009	424	6	-	-	PUNCT
ejpam-6009	424	7	on	on	ADP
ejpam-6009	424	8	and	and	CCONJ
ejpam-6009	424	9	c.	c.	PROPN
ejpam-6009	424	10	boonpok	boonpok	PROPN
ejpam-6009	424	11	.	.	PUNCT
ejpam-6009	425	1	θ(λ	θ(λ	PROPN
ejpam-6009	425	2	,	,	PUNCT
ejpam-6009	425	3	p)-continuity	p)-continuity	NOUN
ejpam-6009	425	4	for	for	ADP
ejpam-6009	425	5	functions	function	NOUN
ejpam-6009	425	6	.	.	PUNCT
ejpam-6009	426	1	international	international	ADJ
ejpam-6009	426	2	journal	journal	NOUN
ejpam-6009	426	3	of	of	ADP
ejpam-6009	426	4	mathematics	mathematic	NOUN
ejpam-6009	426	5	and	and	CCONJ
ejpam-6009	426	6	computer	computer	NOUN
ejpam-6009	426	7	science	science	NOUN
ejpam-6009	426	8	,	,	PUNCT
ejpam-6009	426	9	19(2):491–495	19(2):491–495	NUM
ejpam-6009	426	10	,	,	PUNCT
ejpam-6009	426	11	2024	2024	NUM
ejpam-6009	426	12	.	.	PUNCT
ejpam-6009	427	1	[	[	X
ejpam-6009	427	2	9	9	NUM
ejpam-6009	427	3	]	]	PUNCT
ejpam-6009	427	4	c.	c.	NOUN
ejpam-6009	427	5	boonpok	boonpok	PROPN
ejpam-6009	427	6	and	and	CCONJ
ejpam-6009	427	7	n.	n.	PROPN
ejpam-6009	427	8	srisarakham	srisarakham	PROPN
ejpam-6009	427	9	.	.	PUNCT
ejpam-6009	428	1	weak	weak	ADJ
ejpam-6009	428	2	forms	form	NOUN
ejpam-6009	428	3	of	of	ADP
ejpam-6009	428	4	(	(	PUNCT
ejpam-6009	428	5	λ	λ	PROPN
ejpam-6009	428	6	,	,	PUNCT
ejpam-6009	428	7	b)-open	b)-open	VERB
ejpam-6009	428	8	sets	set	NOUN
ejpam-6009	428	9	and	and	CCONJ
ejpam-6009	428	10	weak	weak	ADJ
ejpam-6009	428	11	(	(	PUNCT
ejpam-6009	428	12	λ	λ	NOUN
ejpam-6009	428	13	,	,	PUNCT
ejpam-6009	428	14	b)continuity	b)continuity	NOUN
ejpam-6009	428	15	.	.	PUNCT
ejpam-6009	429	1	european	european	PROPN
ejpam-6009	429	2	journal	journal	PROPN
ejpam-6009	429	3	of	of	ADP
ejpam-6009	429	4	pure	pure	ADJ
ejpam-6009	429	5	and	and	CCONJ
ejpam-6009	429	6	applied	applied	ADJ
ejpam-6009	429	7	mathematics	mathematic	NOUN
ejpam-6009	429	8	,	,	PUNCT
ejpam-6009	429	9	16(1):29–43	16(1):29–43	NUM
ejpam-6009	429	10	,	,	PUNCT
ejpam-6009	429	11	2023	2023	NUM
ejpam-6009	429	12	.	.	PUNCT
ejpam-6009	430	1	[	[	X
ejpam-6009	430	2	10	10	NUM
ejpam-6009	430	3	]	]	X
ejpam-6009	430	4	c.	c.	PROPN
ejpam-6009	430	5	boonpok	boonpok	PROPN
ejpam-6009	430	6	.	.	PUNCT
ejpam-6009	431	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-6009	431	2	.	.	PUNCT
ejpam-6009	432	1	mathematica	mathematica	PROPN
ejpam-6009	432	2	,	,	PUNCT
ejpam-6009	432	3	65(1):31–42	65(1):31–42	NUM
ejpam-6009	432	4	,	,	PUNCT
ejpam-6009	432	5	2023	2023	NUM
ejpam-6009	432	6	.	.	PUNCT
ejpam-6009	433	1	[	[	X
ejpam-6009	433	2	11	11	NUM
ejpam-6009	433	3	]	]	PUNCT
ejpam-6009	433	4	c.	c.	PROPN
ejpam-6009	433	5	boonpok	boonpok	PROPN
ejpam-6009	433	6	.	.	PUNCT
ejpam-6009	434	1	on	on	ADP
ejpam-6009	434	2	some	some	DET
ejpam-6009	434	3	closed	closed	ADJ
ejpam-6009	434	4	sets	set	NOUN
ejpam-6009	434	5	and	and	CCONJ
ejpam-6009	434	6	low	low	ADJ
ejpam-6009	434	7	separation	separation	NOUN
ejpam-6009	434	8	axioms	axiom	NOUN
ejpam-6009	434	9	via	via	ADP
ejpam-6009	434	10	topological	topological	ADJ
ejpam-6009	434	11	ideals	ideal	NOUN
ejpam-6009	434	12	.	.	PUNCT
ejpam-6009	435	1	european	european	ADJ
ejpam-6009	435	2	journal	journal	PROPN
ejpam-6009	435	3	of	of	ADP
ejpam-6009	435	4	pure	pure	ADJ
ejpam-6009	435	5	and	and	CCONJ
ejpam-6009	435	6	applied	applied	ADJ
ejpam-6009	435	7	mathematics	mathematic	NOUN
ejpam-6009	435	8	,	,	PUNCT
ejpam-6009	435	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-6009	435	10	,	,	PUNCT
ejpam-6009	435	11	2022	2022	NUM
ejpam-6009	435	12	.	.	PUNCT
ejpam-6009	436	1	[	[	X
ejpam-6009	436	2	12	12	NUM
ejpam-6009	436	3	]	]	PUNCT
ejpam-6009	436	4	c.	c.	PROPN
ejpam-6009	436	5	boonpok	boonpok	PROPN
ejpam-6009	436	6	.	.	PUNCT
ejpam-6009	437	1	on	on	ADP
ejpam-6009	437	2	some	some	DET
ejpam-6009	437	3	spaces	space	NOUN
ejpam-6009	437	4	via	via	ADP
ejpam-6009	437	5	topological	topological	ADJ
ejpam-6009	437	6	ideals	ideal	NOUN
ejpam-6009	437	7	.	.	PUNCT
ejpam-6009	438	1	open	open	ADJ
ejpam-6009	438	2	mathematics	mathematic	NOUN
ejpam-6009	438	3	,	,	PUNCT
ejpam-6009	438	4	21:20230118	21:20230118	NUM
ejpam-6009	438	5	,	,	PUNCT
ejpam-6009	438	6	2023	2023	NUM
ejpam-6009	438	7	.	.	PUNCT
ejpam-6009	439	1	[	[	X
ejpam-6009	439	2	13	13	NUM
ejpam-6009	439	3	]	]	PUNCT
ejpam-6009	439	4	c.	c.	PROPN
ejpam-6009	439	5	boonpok	boonpok	PROPN
ejpam-6009	439	6	.	.	PUNCT
ejpam-6009	440	1	on	on	ADP
ejpam-6009	440	2	characterizations	characterization	NOUN
ejpam-6009	440	3	of	of	ADP
ejpam-6009	440	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-6009	440	5	ideal	ideal	ADJ
ejpam-6009	440	6	topological	topological	ADJ
ejpam-6009	440	7	spaces	space	NOUN
ejpam-6009	440	8	.	.	PUNCT
ejpam-6009	441	1	journal	journal	NOUN
ejpam-6009	441	2	of	of	ADP
ejpam-6009	441	3	mathematics	mathematic	NOUN
ejpam-6009	441	4	,	,	PUNCT
ejpam-6009	441	5	2020:9387601	2020:9387601	NUM
ejpam-6009	441	6	,	,	PUNCT
ejpam-6009	441	7	2020	2020	NUM
ejpam-6009	441	8	.	.	PUNCT
ejpam-6009	442	1	[	[	X
ejpam-6009	442	2	14	14	NUM
ejpam-6009	442	3	]	]	X
ejpam-6009	442	4	c.	c.	PROPN
ejpam-6009	442	5	boonpok	boonpok	PROPN
ejpam-6009	442	6	.	.	PUNCT
ejpam-6009	443	1	almost	almost	ADV
ejpam-6009	443	2	(	(	PUNCT
ejpam-6009	443	3	g	g	NOUN
ejpam-6009	443	4	,	,	PUNCT
ejpam-6009	443	5	m)-continuous	m)-continuous	ADJ
ejpam-6009	443	6	functions	function	NOUN
ejpam-6009	443	7	.	.	PUNCT
ejpam-6009	444	1	international	international	ADJ
ejpam-6009	444	2	journal	journal	PROPN
ejpam-6009	444	3	of	of	ADP
ejpam-6009	444	4	mathematical	mathematical	ADJ
ejpam-6009	444	5	analysis	analysis	NOUN
ejpam-6009	444	6	,	,	PUNCT
ejpam-6009	444	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-6009	444	8	,	,	PUNCT
ejpam-6009	444	9	2010	2010	NUM
ejpam-6009	444	10	.	.	PUNCT
ejpam-6009	445	1	[	[	X
ejpam-6009	445	2	15	15	NUM
ejpam-6009	445	3	]	]	X
ejpam-6009	445	4	c.	c.	PROPN
ejpam-6009	445	5	boonpok	boonpok	PROPN
ejpam-6009	445	6	.	.	PUNCT
ejpam-6009	446	1	m	m	VERB
ejpam-6009	446	2	-continuous	-continuous	ADJ
ejpam-6009	446	3	functions	function	NOUN
ejpam-6009	446	4	in	in	ADP
ejpam-6009	446	5	biminimal	biminimal	NOUN
ejpam-6009	446	6	structure	structure	NOUN
ejpam-6009	446	7	spaces	space	NOUN
ejpam-6009	446	8	.	.	PUNCT
ejpam-6009	447	1	far	far	PROPN
ejpam-6009	447	2	east	east	PROPN
ejpam-6009	447	3	journal	journal	PROPN
ejpam-6009	447	4	of	of	ADP
ejpam-6009	447	5	mathematical	mathematical	ADJ
ejpam-6009	447	6	sciences	science	NOUN
ejpam-6009	447	7	,	,	PUNCT
ejpam-6009	447	8	43(1):41–58	43(1):41–58	NUM
ejpam-6009	447	9	,	,	PUNCT
ejpam-6009	447	10	2010	2010	NUM
ejpam-6009	447	11	.	.	PUNCT
ejpam-6009	448	1	[	[	X
ejpam-6009	448	2	16	16	NUM
ejpam-6009	448	3	]	]	X
ejpam-6009	448	4	c.	c.	PROPN
ejpam-6009	448	5	boonpok	boonpok	PROPN
ejpam-6009	448	6	and	and	CCONJ
ejpam-6009	448	7	n.	n.	PROPN
ejpam-6009	448	8	srisarakham	srisarakham	PROPN
ejpam-6009	448	9	.	.	PUNCT
ejpam-6009	449	1	(	(	PUNCT
ejpam-6009	449	2	τ1	τ1	NOUN
ejpam-6009	449	3	,	,	PUNCT
ejpam-6009	449	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	449	5	for	for	ADP
ejpam-6009	449	6	functions	function	NOUN
ejpam-6009	449	7	.	.	PUNCT
ejpam-6009	450	1	asia	asia	PROPN
ejpam-6009	450	2	pacific	pacific	PROPN
ejpam-6009	450	3	journal	journal	PROPN
ejpam-6009	450	4	of	of	ADP
ejpam-6009	450	5	mathematics	mathematic	NOUN
ejpam-6009	450	6	,	,	PUNCT
ejpam-6009	450	7	11:21	11:21	NUM
ejpam-6009	450	8	,	,	PUNCT
ejpam-6009	450	9	2024	2024	NUM
ejpam-6009	450	10	.	.	PUNCT
ejpam-6009	451	1	[	[	X
ejpam-6009	451	2	17	17	NUM
ejpam-6009	451	3	]	]	X
ejpam-6009	451	4	c.	c.	PROPN
ejpam-6009	451	5	boonpok	boonpok	PROPN
ejpam-6009	451	6	and	and	CCONJ
ejpam-6009	451	7	p.	p.	NOUN
ejpam-6009	451	8	pue	pue	NOUN
ejpam-6009	451	9	-	-	PUNCT
ejpam-6009	451	10	on	on	ADP
ejpam-6009	451	11	.	.	PUNCT
ejpam-6009	452	1	characterizations	characterization	NOUN
ejpam-6009	452	2	of	of	ADP
ejpam-6009	452	3	almost	almost	ADV
ejpam-6009	452	4	(	(	PUNCT
ejpam-6009	452	5	τ1	τ1	NOUN
ejpam-6009	452	6	,	,	PUNCT
ejpam-6009	452	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	452	8	functions	function	NOUN
ejpam-6009	452	9	.	.	PUNCT
ejpam-6009	453	1	international	international	ADJ
ejpam-6009	453	2	journal	journal	NOUN
ejpam-6009	453	3	of	of	ADP
ejpam-6009	453	4	analysis	analysis	NOUN
ejpam-6009	453	5	and	and	CCONJ
ejpam-6009	453	6	applications	application	NOUN
ejpam-6009	453	7	,	,	PUNCT
ejpam-6009	453	8	22:33	22:33	NUM
ejpam-6009	453	9	,	,	PUNCT
ejpam-6009	453	10	2024	2024	NUM
ejpam-6009	453	11	.	.	PUNCT
ejpam-6009	454	1	[	[	X
ejpam-6009	454	2	18	18	NUM
ejpam-6009	454	3	]	]	PUNCT
ejpam-6009	454	4	c.	c.	PROPN
ejpam-6009	454	5	boonpok	boonpok	PROPN
ejpam-6009	454	6	and	and	CCONJ
ejpam-6009	454	7	c.	c.	PROPN
ejpam-6009	454	8	klanarong	klanarong	PROPN
ejpam-6009	454	9	.	.	PUNCT
ejpam-6009	455	1	on	on	ADP
ejpam-6009	455	2	weakly	weakly	ADJ
ejpam-6009	455	3	(	(	PUNCT
ejpam-6009	455	4	τ1	τ1	NOUN
ejpam-6009	455	5	,	,	PUNCT
ejpam-6009	455	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	455	7	functions	function	NOUN
ejpam-6009	455	8	.	.	PUNCT
ejpam-6009	456	1	european	european	ADJ
ejpam-6009	456	2	journal	journal	PROPN
ejpam-6009	456	3	of	of	ADP
ejpam-6009	456	4	pure	pure	ADJ
ejpam-6009	456	5	and	and	CCONJ
ejpam-6009	456	6	applied	applied	ADJ
ejpam-6009	456	7	mathematics	mathematic	NOUN
ejpam-6009	456	8	,	,	PUNCT
ejpam-6009	456	9	17(1):416–425	17(1):416–425	NUM
ejpam-6009	456	10	,	,	PUNCT
ejpam-6009	456	11	2024	2024	NUM
ejpam-6009	456	12	.	.	PUNCT
ejpam-6009	457	1	[	[	X
ejpam-6009	457	2	19	19	NUM
ejpam-6009	457	3	]	]	X
ejpam-6009	457	4	p.	p.	NOUN
ejpam-6009	457	5	pue	pue	NOUN
ejpam-6009	457	6	-	-	PUNCT
ejpam-6009	457	7	on	on	ADP
ejpam-6009	457	8	,	,	PUNCT
ejpam-6009	457	9	s.	s.	PROPN
ejpam-6009	457	10	sompong	sompong	PROPN
ejpam-6009	457	11	,	,	PUNCT
ejpam-6009	457	12	and	and	CCONJ
ejpam-6009	457	13	c.	c.	PROPN
ejpam-6009	457	14	boonpok	boonpok	PROPN
ejpam-6009	457	15	.	.	PUNCT
ejpam-6009	458	1	slightly	slightly	ADV
ejpam-6009	458	2	(	(	PUNCT
ejpam-6009	458	3	τ1	τ1	NOUN
ejpam-6009	458	4	,	,	PUNCT
ejpam-6009	458	5	τ2)s	τ2)s	ADJ
ejpam-6009	458	6	-	-	PUNCT
ejpam-6009	458	7	continuous	continuous	ADJ
ejpam-6009	458	8	functions	function	NOUN
ejpam-6009	458	9	.	.	PUNCT
ejpam-6009	459	1	international	international	ADJ
ejpam-6009	459	2	journal	journal	NOUN
ejpam-6009	459	3	of	of	ADP
ejpam-6009	459	4	mathematics	mathematic	NOUN
ejpam-6009	459	5	and	and	CCONJ
ejpam-6009	459	6	computer	computer	NOUN
ejpam-6009	459	7	science	science	NOUN
ejpam-6009	459	8	,	,	PUNCT
ejpam-6009	459	9	20(1):217–221	20(1):217–221	PROPN
ejpam-6009	459	10	,	,	PUNCT
ejpam-6009	459	11	2025	2025	NUM
ejpam-6009	459	12	.	.	PUNCT
ejpam-6009	460	1	[	[	X
ejpam-6009	460	2	20	20	NUM
ejpam-6009	460	3	]	]	PUNCT
ejpam-6009	460	4	b.	b.	PROPN
ejpam-6009	460	5	kong	kong	PROPN
ejpam-6009	460	6	-	-	PUNCT
ejpam-6009	460	7	ied	ied	PROPN
ejpam-6009	460	8	,	,	PUNCT
ejpam-6009	460	9	s.	s.	PROPN
ejpam-6009	460	10	sompong	sompong	PROPN
ejpam-6009	460	11	,	,	PUNCT
ejpam-6009	460	12	and	and	CCONJ
ejpam-6009	460	13	c.	c.	PROPN
ejpam-6009	460	14	boonpok	boonpok	PROPN
ejpam-6009	460	15	.	.	PUNCT
ejpam-6009	461	1	almost	almost	ADV
ejpam-6009	461	2	quasi	quasi	X
ejpam-6009	461	3	(	(	PUNCT
ejpam-6009	461	4	τ1	τ1	NOUN
ejpam-6009	461	5	,	,	PUNCT
ejpam-6009	461	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	461	7	functions	function	NOUN
ejpam-6009	461	8	.	.	PUNCT
ejpam-6009	462	1	asia	asia	PROPN
ejpam-6009	462	2	pacific	pacific	PROPN
ejpam-6009	462	3	journal	journal	PROPN
ejpam-6009	462	4	of	of	ADP
ejpam-6009	462	5	mathematics	mathematic	NOUN
ejpam-6009	462	6	,	,	PUNCT
ejpam-6009	462	7	11:64	11:64	NUM
ejpam-6009	462	8	,	,	PUNCT
ejpam-6009	462	9	2024	2024	NUM
ejpam-6009	462	10	.	.	PUNCT
ejpam-6009	463	1	[	[	X
ejpam-6009	463	2	21	21	NUM
ejpam-6009	463	3	]	]	PUNCT
ejpam-6009	463	4	m.	m.	NOUN
ejpam-6009	463	5	chiangpradit	chiangpradit	NOUN
ejpam-6009	463	6	,	,	PUNCT
ejpam-6009	463	7	s.	s.	PROPN
ejpam-6009	463	8	sompong	sompong	PROPN
ejpam-6009	463	9	,	,	PUNCT
ejpam-6009	463	10	and	and	CCONJ
ejpam-6009	463	11	c.	c.	PROPN
ejpam-6009	463	12	boonpok	boonpok	PROPN
ejpam-6009	463	13	.	.	PUNCT
ejpam-6009	464	1	weakly	weakly	ADJ
ejpam-6009	464	2	quasi	quasi	NOUN
ejpam-6009	464	3	(	(	PUNCT
ejpam-6009	464	4	τ1	τ1	PROPN
ejpam-6009	464	5	,	,	PUNCT
ejpam-6009	464	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	464	7	functions	function	NOUN
ejpam-6009	464	8	.	.	PUNCT
ejpam-6009	465	1	international	international	ADJ
ejpam-6009	465	2	journal	journal	NOUN
ejpam-6009	465	3	of	of	ADP
ejpam-6009	465	4	analysis	analysis	NOUN
ejpam-6009	465	5	and	and	CCONJ
ejpam-6009	465	6	applications	application	NOUN
ejpam-6009	465	7	,	,	PUNCT
ejpam-6009	465	8	22:125	22:125	NUM
ejpam-6009	465	9	,	,	PUNCT
ejpam-6009	465	10	2024	2024	NUM
ejpam-6009	465	11	.	.	PUNCT
ejpam-6009	466	1	[	[	X
ejpam-6009	466	2	22	22	NUM
ejpam-6009	466	3	]	]	PUNCT
ejpam-6009	466	4	m.	m.	NOUN
ejpam-6009	466	5	thongmoon	thongmoon	NOUN
ejpam-6009	466	6	,	,	PUNCT
ejpam-6009	466	7	s.	s.	PROPN
ejpam-6009	466	8	sompong	sompong	PROPN
ejpam-6009	466	9	,	,	PUNCT
ejpam-6009	466	10	and	and	CCONJ
ejpam-6009	466	11	c.	c.	PROPN
ejpam-6009	466	12	boonpok	boonpok	PROPN
ejpam-6009	466	13	.	.	PUNCT
ejpam-6009	467	1	rarely	rarely	ADV
ejpam-6009	467	2	(	(	PUNCT
ejpam-6009	467	3	τ1	τ1	NOUN
ejpam-6009	467	4	,	,	PUNCT
ejpam-6009	467	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	467	6	functions	function	NOUN
ejpam-6009	467	7	.	.	PUNCT
ejpam-6009	468	1	international	international	ADJ
ejpam-6009	468	2	journal	journal	NOUN
ejpam-6009	468	3	of	of	ADP
ejpam-6009	468	4	mathematics	mathematic	NOUN
ejpam-6009	468	5	and	and	CCONJ
ejpam-6009	468	6	computer	computer	NOUN
ejpam-6009	468	7	science	science	NOUN
ejpam-6009	468	8	,	,	PUNCT
ejpam-6009	468	9	20(1):423–427	20(1):423–427	NUM
ejpam-6009	468	10	,	,	PUNCT
ejpam-6009	468	11	2025	2025	NUM
ejpam-6009	468	12	.	.	PUNCT
ejpam-6009	469	1	[	[	X
ejpam-6009	469	2	23	23	NUM
ejpam-6009	469	3	]	]	X
ejpam-6009	469	4	n.	n.	PROPN
ejpam-6009	469	5	srisarakham	srisarakham	PROPN
ejpam-6009	469	6	,	,	PUNCT
ejpam-6009	469	7	a.	a.	PROPN
ejpam-6009	469	8	sama	sama	PROPN
ejpam-6009	469	9	-	-	PUNCT
ejpam-6009	469	10	ae	ae	PROPN
ejpam-6009	469	11	,	,	PUNCT
ejpam-6009	469	12	and	and	CCONJ
ejpam-6009	469	13	c.	c.	PROPN
ejpam-6009	469	14	boonpok	boonpok	PROPN
ejpam-6009	469	15	.	.	PUNCT
ejpam-6009	470	1	characterizations	characterization	NOUN
ejpam-6009	470	2	of	of	ADP
ejpam-6009	470	3	faintly	faintly	ADV
ejpam-6009	470	4	(	(	PUNCT
ejpam-6009	470	5	τ1	τ1	PROPN
ejpam-6009	470	6	,	,	PUNCT
ejpam-6009	470	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	470	8	functions	function	NOUN
ejpam-6009	470	9	.	.	PUNCT
ejpam-6009	471	1	european	european	ADJ
ejpam-6009	471	2	journal	journal	PROPN
ejpam-6009	471	3	of	of	ADP
ejpam-6009	471	4	pure	pure	ADJ
ejpam-6009	471	5	and	and	CCONJ
ejpam-6009	471	6	applied	applied	ADJ
ejpam-6009	471	7	mathematics	mathematic	NOUN
ejpam-6009	471	8	,	,	PUNCT
ejpam-6009	471	9	c.	c.	PROPN
ejpam-6009	471	10	viriyapong	viriyapong	PROPN
ejpam-6009	471	11	,	,	PUNCT
ejpam-6009	471	12	a.	a.	PROPN
ejpam-6009	471	13	sama	sama	PROPN
ejpam-6009	471	14	-	-	PUNCT
ejpam-6009	471	15	ae	ae	PROPN
ejpam-6009	471	16	,	,	PUNCT
ejpam-6009	471	17	c.	c.	PROPN
ejpam-6009	471	18	boonpok	boonpok	PROPN
ejpam-6009	471	19	/	/	SYM
ejpam-6009	471	20	eur	eur	PROPN
ejpam-6009	471	21	.	.	PUNCT
ejpam-6009	472	1	j.	j.	PROPN
ejpam-6009	472	2	pure	pure	PROPN
ejpam-6009	472	3	appl	appl	PROPN
ejpam-6009	472	4	.	.	PROPN
ejpam-6009	472	5	math	math	PROPN
ejpam-6009	472	6	,	,	PUNCT
ejpam-6009	472	7	18	18	NUM
ejpam-6009	472	8	(	(	PUNCT
ejpam-6009	472	9	2	2	NUM
ejpam-6009	472	10	)	)	PUNCT
ejpam-6009	472	11	(	(	PUNCT
ejpam-6009	472	12	2025	2025	NUM
ejpam-6009	472	13	)	)	PUNCT
ejpam-6009	472	14	,	,	PUNCT
ejpam-6009	472	15	6009	6009	NUM
ejpam-6009	472	16	16	16	NUM
ejpam-6009	472	17	of	of	ADP
ejpam-6009	472	18	18	18	NUM
ejpam-6009	472	19	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-6009	472	20	,	,	PUNCT
ejpam-6009	472	21	2024	2024	NUM
ejpam-6009	472	22	.	.	PUNCT
ejpam-6009	473	1	[	[	X
ejpam-6009	473	2	24	24	NUM
ejpam-6009	473	3	]	]	PUNCT
ejpam-6009	473	4	c.	c.	NOUN
ejpam-6009	473	5	prachanpol	prachanpol	NOUN
ejpam-6009	473	6	,	,	PUNCT
ejpam-6009	473	7	c.	c.	PROPN
ejpam-6009	473	8	boonpok	boonpok	PROPN
ejpam-6009	473	9	,	,	PUNCT
ejpam-6009	473	10	and	and	CCONJ
ejpam-6009	473	11	c.	c.	PROPN
ejpam-6009	473	12	viriyapong	viriyapong	PROPN
ejpam-6009	473	13	.	.	PUNCT
ejpam-6009	474	1	δ(τ1	δ(τ1	PROPN
ejpam-6009	474	2	,	,	PUNCT
ejpam-6009	474	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	474	4	functions	function	NOUN
ejpam-6009	474	5	.	.	PUNCT
ejpam-6009	475	1	european	european	ADJ
ejpam-6009	475	2	journal	journal	PROPN
ejpam-6009	475	3	of	of	ADP
ejpam-6009	475	4	pure	pure	ADJ
ejpam-6009	475	5	and	and	CCONJ
ejpam-6009	475	6	applied	applied	ADJ
ejpam-6009	475	7	mathematics	mathematic	NOUN
ejpam-6009	475	8	,	,	PUNCT
ejpam-6009	475	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-6009	475	10	,	,	PUNCT
ejpam-6009	475	11	2024	2024	NUM
ejpam-6009	475	12	.	.	PUNCT
ejpam-6009	476	1	[	[	X
ejpam-6009	476	2	25	25	NUM
ejpam-6009	476	3	]	]	X
ejpam-6009	476	4	n.	n.	NOUN
ejpam-6009	476	5	srisarakham	srisarakham	PROPN
ejpam-6009	476	6	,	,	PUNCT
ejpam-6009	476	7	s.	s.	PROPN
ejpam-6009	476	8	sompong	sompong	PROPN
ejpam-6009	476	9	,	,	PUNCT
ejpam-6009	476	10	and	and	CCONJ
ejpam-6009	476	11	c.	c.	PROPN
ejpam-6009	476	12	boonpok	boonpok	PROPN
ejpam-6009	476	13	.	.	PUNCT
ejpam-6009	477	1	quasi	quasi	PROPN
ejpam-6009	477	2	θ(τ1	θ(τ1	PROPN
ejpam-6009	477	3	,	,	PUNCT
ejpam-6009	477	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	477	5	functions	function	NOUN
ejpam-6009	477	6	.	.	PUNCT
ejpam-6009	478	1	european	european	ADJ
ejpam-6009	478	2	journal	journal	PROPN
ejpam-6009	478	3	of	of	ADP
ejpam-6009	478	4	pure	pure	ADJ
ejpam-6009	478	5	and	and	CCONJ
ejpam-6009	478	6	applied	applied	ADJ
ejpam-6009	478	7	mathematics	mathematic	NOUN
ejpam-6009	478	8	,	,	PUNCT
ejpam-6009	478	9	18(1):5722	18(1):5722	NUM
ejpam-6009	478	10	,	,	PUNCT
ejpam-6009	478	11	2025	2025	NUM
ejpam-6009	478	12	.	.	PUNCT
ejpam-6009	479	1	[	[	X
ejpam-6009	479	2	26	26	NUM
ejpam-6009	479	3	]	]	X
ejpam-6009	479	4	j.	j.	PROPN
ejpam-6009	479	5	khampakdee	khampakdee	PROPN
ejpam-6009	479	6	,	,	PUNCT
ejpam-6009	479	7	s.	s.	PROPN
ejpam-6009	479	8	sompong	sompong	PROPN
ejpam-6009	479	9	,	,	PUNCT
ejpam-6009	479	10	and	and	CCONJ
ejpam-6009	479	11	c.	c.	PROPN
ejpam-6009	479	12	boonpok	boonpok	PROPN
ejpam-6009	479	13	.	.	PUNCT
ejpam-6009	480	1	almost	almost	ADV
ejpam-6009	480	2	weakly	weakly	ADJ
ejpam-6009	480	3	(	(	PUNCT
ejpam-6009	480	4	τ1	τ1	NOUN
ejpam-6009	480	5	,	,	PUNCT
ejpam-6009	480	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	480	7	functions	function	NOUN
ejpam-6009	480	8	.	.	PUNCT
ejpam-6009	481	1	european	european	ADJ
ejpam-6009	481	2	journal	journal	PROPN
ejpam-6009	481	3	of	of	ADP
ejpam-6009	481	4	pure	pure	ADJ
ejpam-6009	481	5	and	and	CCONJ
ejpam-6009	481	6	applied	applied	ADJ
ejpam-6009	481	7	mathematics	mathematic	NOUN
ejpam-6009	481	8	,	,	PUNCT
ejpam-6009	481	9	18(1):5721	18(1):5721	NUM
ejpam-6009	481	10	,	,	PUNCT
ejpam-6009	481	11	2025	2025	NUM
ejpam-6009	481	12	.	.	PUNCT
ejpam-6009	482	1	[	[	X
ejpam-6009	482	2	27	27	NUM
ejpam-6009	482	3	]	]	X
ejpam-6009	482	4	b.	b.	PROPN
ejpam-6009	482	5	kong	kong	PROPN
ejpam-6009	482	6	-	-	PUNCT
ejpam-6009	482	7	ied	ied	PROPN
ejpam-6009	482	8	,	,	PUNCT
ejpam-6009	482	9	a.	a.	PROPN
ejpam-6009	482	10	sama	sama	PROPN
ejpam-6009	482	11	-	-	PUNCT
ejpam-6009	482	12	ae	ae	PROPN
ejpam-6009	482	13	,	,	PUNCT
ejpam-6009	482	14	and	and	CCONJ
ejpam-6009	482	15	c.	c.	PROPN
ejpam-6009	482	16	boonpok	boonpok	PROPN
ejpam-6009	482	17	.	.	PUNCT
ejpam-6009	483	1	almost	almost	ADV
ejpam-6009	483	2	nearly	nearly	ADV
ejpam-6009	483	3	(	(	PUNCT
ejpam-6009	483	4	τ1	τ1	NOUN
ejpam-6009	483	5	,	,	PUNCT
ejpam-6009	483	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	483	7	functions	function	NOUN
ejpam-6009	483	8	.	.	PUNCT
ejpam-6009	484	1	international	international	ADJ
ejpam-6009	484	2	journal	journal	NOUN
ejpam-6009	484	3	of	of	ADP
ejpam-6009	484	4	analysis	analysis	NOUN
ejpam-6009	484	5	and	and	CCONJ
ejpam-6009	484	6	applications	application	NOUN
ejpam-6009	484	7	,	,	PUNCT
ejpam-6009	484	8	23:14	23:14	NUM
ejpam-6009	484	9	,	,	PUNCT
ejpam-6009	484	10	2025	2025	NUM
ejpam-6009	484	11	.	.	PUNCT
ejpam-6009	485	1	[	[	X
ejpam-6009	485	2	28	28	NUM
ejpam-6009	485	3	]	]	X
ejpam-6009	485	4	j.	j.	PROPN
ejpam-6009	485	5	dontchev	dontchev	PROPN
ejpam-6009	485	6	.	.	PUNCT
ejpam-6009	486	1	contra	contra	ADJ
ejpam-6009	486	2	-	-	ADJ
ejpam-6009	486	3	continuous	continuous	ADJ
ejpam-6009	486	4	functions	function	NOUN
ejpam-6009	486	5	and	and	CCONJ
ejpam-6009	486	6	strongly	strongly	ADV
ejpam-6009	486	7	s	s	NOUN
ejpam-6009	486	8	-	-	PUNCT
ejpam-6009	486	9	closed	closed	ADJ
ejpam-6009	486	10	spaces	space	NOUN
ejpam-6009	486	11	.	.	PUNCT
ejpam-6009	487	1	international	international	ADJ
ejpam-6009	487	2	journal	journal	PROPN
ejpam-6009	487	3	of	of	ADP
ejpam-6009	487	4	mathematics	mathematics	PROPN
ejpam-6009	487	5	and	and	CCONJ
ejpam-6009	487	6	mathematical	mathematical	ADJ
ejpam-6009	487	7	sciences	science	NOUN
ejpam-6009	487	8	,	,	PUNCT
ejpam-6009	487	9	19:303–310	19:303–310	PROPN
ejpam-6009	487	10	,	,	PUNCT
ejpam-6009	487	11	1966	1966	NUM
ejpam-6009	487	12	.	.	PUNCT
ejpam-6009	488	1	[	[	X
ejpam-6009	488	2	29	29	NUM
ejpam-6009	488	3	]	]	PUNCT
ejpam-6009	488	4	j.	j.	PROPN
ejpam-6009	488	5	dontchev	dontchev	PROPN
ejpam-6009	488	6	,	,	PUNCT
ejpam-6009	488	7	m.	m.	NOUN
ejpam-6009	488	8	ganster	ganster	NOUN
ejpam-6009	488	9	,	,	PUNCT
ejpam-6009	488	10	and	and	CCONJ
ejpam-6009	488	11	i.	i.	PROPN
ejpam-6009	488	12	reilly	reilly	PROPN
ejpam-6009	488	13	.	.	PUNCT
ejpam-6009	489	1	more	more	ADV
ejpam-6009	489	2	on	on	ADP
ejpam-6009	489	3	almost	almost	ADV
ejpam-6009	489	4	s	s	NOUN
ejpam-6009	489	5	-	-	NOUN
ejpam-6009	489	6	continuity	continuity	NOUN
ejpam-6009	489	7	.	.	PUNCT
ejpam-6009	490	1	indian	indian	ADJ
ejpam-6009	490	2	journal	journal	PROPN
ejpam-6009	490	3	of	of	ADP
ejpam-6009	490	4	mathematics	mathematics	PROPN
ejpam-6009	490	5	,	,	PUNCT
ejpam-6009	490	6	41:139–146	41:139–146	PROPN
ejpam-6009	490	7	,	,	PUNCT
ejpam-6009	490	8	1999	1999	NUM
ejpam-6009	490	9	.	.	PUNCT
ejpam-6009	491	1	[	[	X
ejpam-6009	491	2	30	30	NUM
ejpam-6009	491	3	]	]	X
ejpam-6009	491	4	j.	j.	PROPN
ejpam-6009	491	5	dontchev	dontchev	PROPN
ejpam-6009	491	6	and	and	CCONJ
ejpam-6009	491	7	t.	t.	PROPN
ejpam-6009	491	8	noiri	noiri	PROPN
ejpam-6009	491	9	.	.	PUNCT
ejpam-6009	492	1	contra	contra	ADJ
ejpam-6009	492	2	-	-	ADJ
ejpam-6009	492	3	semicontinuous	semicontinuous	ADJ
ejpam-6009	492	4	functions	function	NOUN
ejpam-6009	492	5	.	.	PUNCT
ejpam-6009	493	1	mathematica	mathematica	PROPN
ejpam-6009	493	2	pannonica	pannonica	PROPN
ejpam-6009	493	3	,	,	PUNCT
ejpam-6009	493	4	10:159–168	10:159–168	NOUN
ejpam-6009	493	5	,	,	PUNCT
ejpam-6009	493	6	1999	1999	NUM
ejpam-6009	493	7	.	.	PUNCT
ejpam-6009	494	1	[	[	X
ejpam-6009	494	2	31	31	NUM
ejpam-6009	494	3	]	]	PUNCT
ejpam-6009	494	4	s.	s.	PROPN
ejpam-6009	494	5	jafari	jafari	PROPN
ejpam-6009	494	6	and	and	CCONJ
ejpam-6009	494	7	t.	t.	PROPN
ejpam-6009	494	8	noiri	noiri	PROPN
ejpam-6009	494	9	.	.	PUNCT
ejpam-6009	495	1	on	on	ADP
ejpam-6009	495	2	contra	contra	ADJ
ejpam-6009	495	3	-	-	ADJ
ejpam-6009	495	4	precontinuous	precontinuous	ADJ
ejpam-6009	495	5	functions	function	NOUN
ejpam-6009	495	6	.	.	PUNCT
ejpam-6009	496	1	bulletin	bulletin	NOUN
ejpam-6009	496	2	of	of	ADP
ejpam-6009	496	3	the	the	DET
ejpam-6009	496	4	malaysian	malaysian	PROPN
ejpam-6009	496	5	mathematical	mathematical	PROPN
ejpam-6009	496	6	sciences	sciences	PROPN
ejpam-6009	496	7	society	society	NOUN
ejpam-6009	496	8	,	,	PUNCT
ejpam-6009	496	9	25:115–128	25:115–128	PROPN
ejpam-6009	496	10	,	,	PUNCT
ejpam-6009	496	11	2002	2002	NUM
ejpam-6009	496	12	.	.	PUNCT
ejpam-6009	497	1	[	[	X
ejpam-6009	497	2	32	32	NUM
ejpam-6009	497	3	]	]	PUNCT
ejpam-6009	497	4	e.	e.	PROPN
ejpam-6009	497	5	ekici	ekici	PROPN
ejpam-6009	497	6	.	.	PUNCT
ejpam-6009	498	1	almost	almost	ADV
ejpam-6009	498	2	contra	contra	ADJ
ejpam-6009	498	3	-	-	ADJ
ejpam-6009	498	4	precontinuous	precontinuous	ADJ
ejpam-6009	498	5	functions	function	NOUN
ejpam-6009	498	6	.	.	PUNCT
ejpam-6009	499	1	bulletin	bulletin	NOUN
ejpam-6009	499	2	of	of	ADP
ejpam-6009	499	3	the	the	DET
ejpam-6009	499	4	malaysian	malaysian	PROPN
ejpam-6009	499	5	mathematical	mathematical	PROPN
ejpam-6009	499	6	sciences	sciences	PROPN
ejpam-6009	499	7	society	society	NOUN
ejpam-6009	499	8	,	,	PUNCT
ejpam-6009	499	9	27:53–65	27:53–65	NUM
ejpam-6009	499	10	,	,	PUNCT
ejpam-6009	499	11	2004	2004	NUM
ejpam-6009	499	12	.	.	PUNCT
ejpam-6009	500	1	[	[	X
ejpam-6009	500	2	33	33	NUM
ejpam-6009	500	3	]	]	PUNCT
ejpam-6009	500	4	t.	t.	PROPN
ejpam-6009	500	5	noiri	noiri	PROPN
ejpam-6009	500	6	,	,	PUNCT
ejpam-6009	500	7	b.	b.	PROPN
ejpam-6009	500	8	ahmad	ahmad	PROPN
ejpam-6009	500	9	,	,	PUNCT
ejpam-6009	500	10	and	and	CCONJ
ejpam-6009	500	11	m.	m.	PROPN
ejpam-6009	500	12	khan	khan	PROPN
ejpam-6009	500	13	.	.	PUNCT
ejpam-6009	501	1	almost	almost	ADV
ejpam-6009	501	2	s	s	NOUN
ejpam-6009	501	3	-	-	PUNCT
ejpam-6009	501	4	continuous	continuous	ADJ
ejpam-6009	501	5	functions	function	NOUN
ejpam-6009	501	6	.	.	PUNCT
ejpam-6009	502	1	kyungpook	kyungpook	PROPN
ejpam-6009	502	2	mathematical	mathematical	PROPN
ejpam-6009	502	3	journal	journal	PROPN
ejpam-6009	502	4	,	,	PUNCT
ejpam-6009	502	5	35:311–322	35:311–322	PROPN
ejpam-6009	502	6	,	,	PUNCT
ejpam-6009	502	7	1995	1995	NUM
ejpam-6009	502	8	.	.	PUNCT
ejpam-6009	503	1	[	[	X
ejpam-6009	503	2	34	34	NUM
ejpam-6009	503	3	]	]	PUNCT
ejpam-6009	503	4	t.	t.	PROPN
ejpam-6009	503	5	noiri	noiri	PROPN
ejpam-6009	503	6	.	.	PUNCT
ejpam-6009	504	1	super	super	ADJ
ejpam-6009	504	2	-	-	NOUN
ejpam-6009	504	3	continuity	continuity	NOUN
ejpam-6009	504	4	and	and	CCONJ
ejpam-6009	504	5	some	some	DET
ejpam-6009	504	6	strong	strong	ADJ
ejpam-6009	504	7	forms	form	NOUN
ejpam-6009	504	8	of	of	ADP
ejpam-6009	504	9	continuity	continuity	NOUN
ejpam-6009	504	10	.	.	PUNCT
ejpam-6009	505	1	indian	indian	ADJ
ejpam-6009	505	2	journal	journal	PROPN
ejpam-6009	505	3	of	of	ADP
ejpam-6009	505	4	pure	pure	ADJ
ejpam-6009	505	5	and	and	CCONJ
ejpam-6009	505	6	applied	applied	ADJ
ejpam-6009	505	7	mathematics	mathematic	NOUN
ejpam-6009	505	8	,	,	PUNCT
ejpam-6009	505	9	15:241–250	15:241–250	NUM
ejpam-6009	505	10	,	,	PUNCT
ejpam-6009	505	11	1984	1984	NUM
ejpam-6009	505	12	.	.	PUNCT
ejpam-6009	506	1	[	[	X
ejpam-6009	506	2	35	35	NUM
ejpam-6009	506	3	]	]	X
ejpam-6009	506	4	e.	e.	PROPN
ejpam-6009	506	5	ekici	ekici	PROPN
ejpam-6009	506	6	,	,	PUNCT
ejpam-6009	506	7	s.	s.	PROPN
ejpam-6009	506	8	jafari	jafari	PROPN
ejpam-6009	506	9	,	,	PUNCT
ejpam-6009	506	10	and	and	CCONJ
ejpam-6009	506	11	t.	t.	PROPN
ejpam-6009	506	12	noiri	noiri	PROPN
ejpam-6009	506	13	.	.	PUNCT
ejpam-6009	507	1	on	on	ADP
ejpam-6009	507	2	upper	upper	ADJ
ejpam-6009	507	3	and	and	CCONJ
ejpam-6009	507	4	lower	low	ADJ
ejpam-6009	507	5	contra	contra	ADJ
ejpam-6009	507	6	-	-	ADJ
ejpam-6009	507	7	continuous	continuous	ADJ
ejpam-6009	507	8	multifunctions	multifunction	NOUN
ejpam-6009	507	9	.	.	PUNCT
ejpam-6009	508	1	analele	analele	ADP
ejpam-6009	508	2	ştiinţifice	ştiinţifice	PROPN
ejpam-6009	508	3	ale	ale	NOUN
ejpam-6009	508	4	universităţii	universităţii	AUX
ejpam-6009	508	5	al	al	PROPN
ejpam-6009	508	6	.	.	PROPN
ejpam-6009	508	7	i.	i.	PROPN
ejpam-6009	508	8	cuza	cuza	AUX
ejpam-6009	508	9	din	din	PROPN
ejpam-6009	508	10	iaşi	iaşi	VERB
ejpam-6009	508	11	matematică	matematică	NOUN
ejpam-6009	508	12	,	,	PUNCT
ejpam-6009	508	13	54(1):75	54(1):75	NUM
ejpam-6009	508	14	–	–	PUNCT
ejpam-6009	508	15	85	85	NUM
ejpam-6009	508	16	,	,	PUNCT
ejpam-6009	508	17	2008	2008	NUM
ejpam-6009	508	18	.	.	PUNCT
ejpam-6009	509	1	[	[	X
ejpam-6009	509	2	36	36	NUM
ejpam-6009	509	3	]	]	PUNCT
ejpam-6009	509	4	t.	t.	PROPN
ejpam-6009	509	5	noiri	noiri	PROPN
ejpam-6009	509	6	and	and	CCONJ
ejpam-6009	509	7	v.	v.	ADP
ejpam-6009	509	8	popa	popa	NOUN
ejpam-6009	509	9	.	.	PUNCT
ejpam-6009	510	1	almost	almost	ADV
ejpam-6009	510	2	weakly	weakly	ADJ
ejpam-6009	510	3	continuous	continuous	ADJ
ejpam-6009	510	4	multifunctions	multifunction	NOUN
ejpam-6009	510	5	.	.	PUNCT
ejpam-6009	511	1	demonstratio	demonstratio	PROPN
ejpam-6009	511	2	mathematica	mathematica	PROPN
ejpam-6009	511	3	,	,	PUNCT
ejpam-6009	511	4	26:363–380	26:363–380	PROPN
ejpam-6009	511	5	,	,	PUNCT
ejpam-6009	511	6	1993	1993	NUM
ejpam-6009	511	7	.	.	PUNCT
ejpam-6009	512	1	[	[	X
ejpam-6009	512	2	37	37	NUM
ejpam-6009	512	3	]	]	PUNCT
ejpam-6009	512	4	e.	e.	PROPN
ejpam-6009	512	5	ekici	ekici	PROPN
ejpam-6009	512	6	,	,	PUNCT
ejpam-6009	512	7	s.	s.	PROPN
ejpam-6009	512	8	jafari	jafari	PROPN
ejpam-6009	512	9	,	,	PUNCT
ejpam-6009	512	10	and	and	CCONJ
ejpam-6009	512	11	v.	v.	ADP
ejpam-6009	512	12	popa	popa	NOUN
ejpam-6009	512	13	.	.	PUNCT
ejpam-6009	513	1	on	on	ADP
ejpam-6009	513	2	contra	contra	PROPN
ejpam-6009	513	3	-	-	ADJ
ejpam-6009	513	4	precontinuous	precontinuous	ADJ
ejpam-6009	513	5	and	and	CCONJ
ejpam-6009	513	6	almost	almost	ADV
ejpam-6009	513	7	contraprecontinuous	contraprecontinuous	ADJ
ejpam-6009	513	8	multifunctions	multifunction	NOUN
ejpam-6009	513	9	.	.	PUNCT
ejpam-6009	514	1	journal	journal	PROPN
ejpam-6009	514	2	of	of	ADP
ejpam-6009	514	3	advanced	advanced	ADJ
ejpam-6009	514	4	research	research	NOUN
ejpam-6009	514	5	in	in	ADP
ejpam-6009	514	6	pure	pure	ADJ
ejpam-6009	514	7	mathematics	mathematic	NOUN
ejpam-6009	514	8	,	,	PUNCT
ejpam-6009	514	9	2(1):11–25	2(1):11–25	NUM
ejpam-6009	514	10	,	,	PUNCT
ejpam-6009	514	11	2010	2010	NUM
ejpam-6009	514	12	.	.	PUNCT
ejpam-6009	515	1	[	[	X
ejpam-6009	515	2	38	38	NUM
ejpam-6009	515	3	]	]	PUNCT
ejpam-6009	515	4	k.	k.	PROPN
ejpam-6009	516	1	laprom	laprom	PROPN
ejpam-6009	516	2	,	,	PUNCT
ejpam-6009	516	3	c.	c.	PROPN
ejpam-6009	516	4	boonpok	boonpok	PROPN
ejpam-6009	516	5	,	,	PUNCT
ejpam-6009	516	6	and	and	CCONJ
ejpam-6009	516	7	c.	c.	PROPN
ejpam-6009	516	8	viriyapong	viriyapong	PROPN
ejpam-6009	516	9	.	.	PUNCT
ejpam-6009	517	1	β(τ1	β(τ1	PROPN
ejpam-6009	517	2	,	,	PUNCT
ejpam-6009	517	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	517	4	multifunctions	multifunction	NOUN
ejpam-6009	517	5	on	on	ADP
ejpam-6009	517	6	bitopological	bitopological	ADJ
ejpam-6009	517	7	spaces	space	NOUN
ejpam-6009	517	8	.	.	PUNCT
ejpam-6009	518	1	journal	journal	NOUN
ejpam-6009	518	2	of	of	ADP
ejpam-6009	518	3	mathematics	mathematic	NOUN
ejpam-6009	518	4	,	,	PUNCT
ejpam-6009	518	5	2020:4020971	2020:4020971	NUM
ejpam-6009	518	6	,	,	PUNCT
ejpam-6009	518	7	2020	2020	NUM
ejpam-6009	518	8	.	.	PUNCT
ejpam-6009	519	1	[	[	X
ejpam-6009	519	2	39	39	NUM
ejpam-6009	519	3	]	]	PUNCT
ejpam-6009	519	4	c.	c.	PROPN
ejpam-6009	519	5	boonpok	boonpok	PROPN
ejpam-6009	519	6	.	.	PUNCT
ejpam-6009	520	1	(	(	PUNCT
ejpam-6009	520	2	τ1	τ1	NOUN
ejpam-6009	520	3	,	,	PUNCT
ejpam-6009	520	4	τ2)δ	τ2)δ	ADJ
ejpam-6009	520	5	-	-	PUNCT
ejpam-6009	520	6	semicontinuous	semicontinuous	ADJ
ejpam-6009	520	7	multifunctions	multifunction	NOUN
ejpam-6009	520	8	.	.	PUNCT
ejpam-6009	521	1	heliyon	heliyon	NOUN
ejpam-6009	521	2	,	,	PUNCT
ejpam-6009	521	3	6	6	NUM
ejpam-6009	521	4	:	:	SYM
ejpam-6009	521	5	e05367	e05367	PROPN
ejpam-6009	521	6	,	,	PUNCT
ejpam-6009	521	7	2020	2020	NUM
ejpam-6009	521	8	.	.	PUNCT
ejpam-6009	522	1	[	[	X
ejpam-6009	522	2	40	40	NUM
ejpam-6009	522	3	]	]	PUNCT
ejpam-6009	522	4	c.	c.	PROPN
ejpam-6009	522	5	boonpok	boonpok	PROPN
ejpam-6009	522	6	and	and	CCONJ
ejpam-6009	522	7	c.	c.	PROPN
ejpam-6009	522	8	viriyapong	viriyapong	PROPN
ejpam-6009	522	9	.	.	PUNCT
ejpam-6009	523	1	upper	upper	ADJ
ejpam-6009	523	2	and	and	CCONJ
ejpam-6009	523	3	lower	low	ADJ
ejpam-6009	523	4	almost	almost	ADV
ejpam-6009	523	5	weak	weak	ADJ
ejpam-6009	523	6	(	(	PUNCT
ejpam-6009	523	7	τ1	τ1	NOUN
ejpam-6009	523	8	,	,	PUNCT
ejpam-6009	523	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	523	10	.	.	PUNCT
ejpam-6009	524	1	european	european	PROPN
ejpam-6009	524	2	journal	journal	PROPN
ejpam-6009	524	3	of	of	ADP
ejpam-6009	524	4	pure	pure	ADJ
ejpam-6009	524	5	and	and	CCONJ
ejpam-6009	524	6	applied	applied	ADJ
ejpam-6009	524	7	mathematics	mathematic	NOUN
ejpam-6009	524	8	,	,	PUNCT
ejpam-6009	524	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-6009	524	10	,	,	PUNCT
ejpam-6009	524	11	2021	2021	NUM
ejpam-6009	524	12	.	.	PUNCT
ejpam-6009	525	1	[	[	X
ejpam-6009	525	2	41	41	NUM
ejpam-6009	525	3	]	]	X
ejpam-6009	525	4	c.	c.	PROPN
ejpam-6009	525	5	viriyapong	viriyapong	PROPN
ejpam-6009	525	6	and	and	CCONJ
ejpam-6009	525	7	c.	c.	PROPN
ejpam-6009	525	8	boonpok	boonpok	PROPN
ejpam-6009	525	9	.	.	PUNCT
ejpam-6009	526	1	weak	weak	ADJ
ejpam-6009	526	2	quasi	quasi	NOUN
ejpam-6009	526	3	(	(	PUNCT
ejpam-6009	526	4	λ	λ	PROPN
ejpam-6009	526	5	,	,	PUNCT
ejpam-6009	526	6	sp)-continuity	sp)-continuity	NOUN
ejpam-6009	526	7	for	for	ADP
ejpam-6009	526	8	multifunctions	multifunction	NOUN
ejpam-6009	526	9	.	.	PUNCT
ejpam-6009	527	1	international	international	ADJ
ejpam-6009	527	2	journal	journal	PROPN
ejpam-6009	527	3	of	of	ADP
ejpam-6009	527	4	mathematics	mathematic	NOUN
ejpam-6009	527	5	and	and	CCONJ
ejpam-6009	527	6	computer	computer	NOUN
ejpam-6009	527	7	science	science	NOUN
ejpam-6009	527	8	,	,	PUNCT
ejpam-6009	527	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-6009	527	10	,	,	PUNCT
ejpam-6009	527	11	2022	2022	NUM
ejpam-6009	527	12	.	.	PUNCT
ejpam-6009	528	1	[	[	X
ejpam-6009	528	2	42	42	NUM
ejpam-6009	528	3	]	]	PUNCT
ejpam-6009	528	4	c.	c.	PROPN
ejpam-6009	528	5	boonpok	boonpok	PROPN
ejpam-6009	528	6	.	.	PUNCT
ejpam-6009	529	1	on	on	ADP
ejpam-6009	529	2	continuous	continuous	ADJ
ejpam-6009	529	3	multifunctions	multifunction	NOUN
ejpam-6009	529	4	in	in	ADP
ejpam-6009	529	5	ideal	ideal	ADJ
ejpam-6009	529	6	topological	topological	ADJ
ejpam-6009	529	7	spaces	space	NOUN
ejpam-6009	529	8	.	.	PUNCT
ejpam-6009	530	1	lobachevskii	lobachevskii	PROPN
ejpam-6009	530	2	journal	journal	PROPN
ejpam-6009	530	3	of	of	ADP
ejpam-6009	530	4	mathematics	mathematic	NOUN
ejpam-6009	530	5	,	,	PUNCT
ejpam-6009	530	6	40(1):24–35	40(1):24–35	NUM
ejpam-6009	530	7	,	,	PUNCT
ejpam-6009	530	8	2019	2019	NUM
ejpam-6009	530	9	.	.	PUNCT
ejpam-6009	531	1	[	[	X
ejpam-6009	531	2	43	43	NUM
ejpam-6009	531	3	]	]	X
ejpam-6009	531	4	c.	c.	PROPN
ejpam-6009	531	5	boonpok	boonpok	PROPN
ejpam-6009	531	6	.	.	PUNCT
ejpam-6009	532	1	upper	upper	ADJ
ejpam-6009	532	2	and	and	CCONJ
ejpam-6009	532	3	lower	low	ADJ
ejpam-6009	532	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-6009	532	5	.	.	PUNCT
ejpam-6009	532	6	heliyon	heliyon	NOUN
ejpam-6009	532	7	,	,	PUNCT
ejpam-6009	532	8	7	7	NUM
ejpam-6009	532	9	:	:	PUNCT
ejpam-6009	532	10	e05986	e05986	PROPN
ejpam-6009	532	11	,	,	PUNCT
ejpam-6009	532	12	2021	2021	NUM
ejpam-6009	532	13	.	.	PUNCT
ejpam-6009	533	1	[	[	X
ejpam-6009	533	2	44	44	NUM
ejpam-6009	533	3	]	]	PUNCT
ejpam-6009	533	4	c.	c.	PROPN
ejpam-6009	533	5	boonpok	boonpok	PROPN
ejpam-6009	533	6	and	and	CCONJ
ejpam-6009	533	7	j.	j.	PROPN
ejpam-6009	533	8	khampakdee	khampakdee	PROPN
ejpam-6009	533	9	.	.	PUNCT
ejpam-6009	534	1	upper	upper	ADJ
ejpam-6009	534	2	and	and	CCONJ
ejpam-6009	534	3	lower	low	ADJ
ejpam-6009	534	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-6009	534	5	.	.	PUNCT
ejpam-6009	534	6	european	european	PROPN
ejpam-6009	534	7	journal	journal	PROPN
ejpam-6009	534	8	of	of	ADP
ejpam-6009	534	9	pure	pure	ADJ
ejpam-6009	534	10	and	and	CCONJ
ejpam-6009	534	11	applied	applied	ADJ
ejpam-6009	534	12	mathematics	mathematic	NOUN
ejpam-6009	534	13	,	,	PUNCT
ejpam-6009	534	14	17(1):201–211	17(1):201–211	NUM
ejpam-6009	534	15	,	,	PUNCT
ejpam-6009	534	16	2024	2024	NUM
ejpam-6009	534	17	.	.	PUNCT
ejpam-6009	535	1	c.	c.	PROPN
ejpam-6009	535	2	viriyapong	viriyapong	PROPN
ejpam-6009	535	3	,	,	PUNCT
ejpam-6009	535	4	a.	a.	PROPN
ejpam-6009	535	5	sama	sama	PROPN
ejpam-6009	535	6	-	-	PUNCT
ejpam-6009	535	7	ae	ae	PROPN
ejpam-6009	535	8	,	,	PUNCT
ejpam-6009	535	9	c.	c.	PROPN
ejpam-6009	535	10	boonpok	boonpok	PROPN
ejpam-6009	535	11	/	/	SYM
ejpam-6009	535	12	eur	eur	PROPN
ejpam-6009	535	13	.	.	PUNCT
ejpam-6009	536	1	j.	j.	PROPN
ejpam-6009	536	2	pure	pure	PROPN
ejpam-6009	536	3	appl	appl	PROPN
ejpam-6009	536	4	.	.	PROPN
ejpam-6009	536	5	math	math	PROPN
ejpam-6009	536	6	,	,	PUNCT
ejpam-6009	536	7	18	18	NUM
ejpam-6009	536	8	(	(	PUNCT
ejpam-6009	536	9	2	2	NUM
ejpam-6009	536	10	)	)	PUNCT
ejpam-6009	536	11	(	(	PUNCT
ejpam-6009	536	12	2025	2025	NUM
ejpam-6009	536	13	)	)	PUNCT
ejpam-6009	536	14	,	,	PUNCT
ejpam-6009	536	15	6009	6009	NUM
ejpam-6009	536	16	17	17	NUM
ejpam-6009	536	17	of	of	ADP
ejpam-6009	536	18	18	18	NUM
ejpam-6009	536	19	[	[	SYM
ejpam-6009	536	20	45	45	NUM
ejpam-6009	536	21	]	]	PUNCT
ejpam-6009	536	22	c.	c.	PROPN
ejpam-6009	536	23	boonpok	boonpok	PROPN
ejpam-6009	536	24	and	and	CCONJ
ejpam-6009	536	25	n.	n.	PROPN
ejpam-6009	536	26	srisarakham	srisarakham	PROPN
ejpam-6009	536	27	.	.	PUNCT
ejpam-6009	537	1	almost	almost	ADV
ejpam-6009	537	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-6009	537	3	for	for	ADP
ejpam-6009	537	4	multifunctions	multifunction	NOUN
ejpam-6009	537	5	.	.	PUNCT
ejpam-6009	538	1	international	international	ADJ
ejpam-6009	538	2	journal	journal	NOUN
ejpam-6009	538	3	of	of	ADP
ejpam-6009	538	4	analysis	analysis	NOUN
ejpam-6009	538	5	and	and	CCONJ
ejpam-6009	538	6	applications	application	NOUN
ejpam-6009	538	7	,	,	PUNCT
ejpam-6009	538	8	21:107	21:107	NUM
ejpam-6009	538	9	,	,	PUNCT
ejpam-6009	538	10	2023	2023	NUM
ejpam-6009	538	11	.	.	PUNCT
ejpam-6009	539	1	[	[	X
ejpam-6009	539	2	46	46	NUM
ejpam-6009	539	3	]	]	X
ejpam-6009	539	4	c.	c.	PROPN
ejpam-6009	539	5	boonpok	boonpok	PROPN
ejpam-6009	539	6	.	.	PUNCT
ejpam-6009	540	1	weak	weak	ADJ
ejpam-6009	540	2	quasi	quasi	ADJ
ejpam-6009	540	3	continuity	continuity	NOUN
ejpam-6009	540	4	for	for	ADP
ejpam-6009	540	5	multifunctions	multifunction	NOUN
ejpam-6009	540	6	in	in	ADP
ejpam-6009	540	7	ideal	ideal	ADJ
ejpam-6009	540	8	topological	topological	ADJ
ejpam-6009	540	9	spaces	space	NOUN
ejpam-6009	540	10	.	.	PUNCT
ejpam-6009	541	1	advances	advance	NOUN
ejpam-6009	541	2	in	in	ADP
ejpam-6009	541	3	mathematics	mathematic	NOUN
ejpam-6009	541	4	:	:	PUNCT
ejpam-6009	541	5	scientific	scientific	ADJ
ejpam-6009	541	6	journal	journal	NOUN
ejpam-6009	541	7	,	,	PUNCT
ejpam-6009	541	8	9(1):339–355	9(1):339–355	NUM
ejpam-6009	541	9	,	,	PUNCT
ejpam-6009	541	10	2020	2020	NUM
ejpam-6009	541	11	.	.	PUNCT
ejpam-6009	542	1	[	[	X
ejpam-6009	542	2	47	47	NUM
ejpam-6009	542	3	]	]	X
ejpam-6009	542	4	c.	c.	PROPN
ejpam-6009	542	5	boonpok	boonpok	PROPN
ejpam-6009	542	6	and	and	CCONJ
ejpam-6009	542	7	p.	p.	NOUN
ejpam-6009	542	8	pue	pue	NOUN
ejpam-6009	542	9	-	-	PUNCT
ejpam-6009	542	10	on	on	ADP
ejpam-6009	542	11	.	.	PUNCT
ejpam-6009	543	1	upper	upper	ADJ
ejpam-6009	543	2	and	and	CCONJ
ejpam-6009	543	3	lower	low	ADJ
ejpam-6009	543	4	weakly	weakly	ADJ
ejpam-6009	543	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-6009	543	6	multifunctions	multifunction	NOUN
ejpam-6009	543	7	.	.	PUNCT
ejpam-6009	544	1	international	international	ADJ
ejpam-6009	544	2	journal	journal	NOUN
ejpam-6009	544	3	of	of	ADP
ejpam-6009	544	4	analysis	analysis	NOUN
ejpam-6009	544	5	and	and	CCONJ
ejpam-6009	544	6	applications	application	NOUN
ejpam-6009	544	7	,	,	PUNCT
ejpam-6009	544	8	21:90	21:90	NUM
ejpam-6009	544	9	,	,	PUNCT
ejpam-6009	544	10	2023	2023	NUM
ejpam-6009	544	11	.	.	PUNCT
ejpam-6009	545	1	[	[	X
ejpam-6009	545	2	48	48	NUM
ejpam-6009	545	3	]	]	PUNCT
ejpam-6009	545	4	c.	c.	PROPN
ejpam-6009	545	5	boonpok	boonpok	PROPN
ejpam-6009	545	6	and	and	CCONJ
ejpam-6009	545	7	p.	p.	NOUN
ejpam-6009	545	8	pue	pue	NOUN
ejpam-6009	545	9	-	-	PUNCT
ejpam-6009	545	10	on	on	ADP
ejpam-6009	545	11	.	.	PUNCT
ejpam-6009	546	1	upper	upper	ADJ
ejpam-6009	546	2	and	and	CCONJ
ejpam-6009	546	3	lower	low	ADJ
ejpam-6009	546	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-6009	546	5	multifunctions	multifunction	NOUN
ejpam-6009	546	6	.	.	PUNCT
ejpam-6009	547	1	european	european	ADJ
ejpam-6009	547	2	journal	journal	PROPN
ejpam-6009	547	3	of	of	ADP
ejpam-6009	547	4	pure	pure	ADJ
ejpam-6009	547	5	and	and	CCONJ
ejpam-6009	547	6	applied	applied	ADJ
ejpam-6009	547	7	mathematics	mathematic	NOUN
ejpam-6009	547	8	,	,	PUNCT
ejpam-6009	547	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-6009	547	10	,	,	PUNCT
ejpam-6009	547	11	2023	2023	NUM
ejpam-6009	547	12	.	.	PUNCT
ejpam-6009	548	1	[	[	X
ejpam-6009	548	2	49	49	NUM
ejpam-6009	548	3	]	]	PUNCT
ejpam-6009	548	4	c.	c.	PROPN
ejpam-6009	548	5	boonpok	boonpok	PROPN
ejpam-6009	548	6	and	and	CCONJ
ejpam-6009	548	7	j.	j.	PROPN
ejpam-6009	548	8	khampakdee	khampakdee	PROPN
ejpam-6009	548	9	.	.	PUNCT
ejpam-6009	549	1	upper	upper	ADJ
ejpam-6009	549	2	and	and	CCONJ
ejpam-6009	549	3	lower	low	ADJ
ejpam-6009	549	4	weak	weak	ADJ
ejpam-6009	549	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-6009	549	6	.	.	PUNCT
ejpam-6009	550	1	european	european	PROPN
ejpam-6009	550	2	journal	journal	PROPN
ejpam-6009	550	3	of	of	ADP
ejpam-6009	550	4	pure	pure	ADJ
ejpam-6009	550	5	and	and	CCONJ
ejpam-6009	550	6	applied	applied	ADJ
ejpam-6009	550	7	mathematics	mathematic	NOUN
ejpam-6009	550	8	,	,	PUNCT
ejpam-6009	550	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-6009	550	10	,	,	PUNCT
ejpam-6009	550	11	2023	2023	NUM
ejpam-6009	550	12	.	.	PUNCT
ejpam-6009	551	1	[	[	X
ejpam-6009	551	2	50	50	NUM
ejpam-6009	551	3	]	]	PUNCT
ejpam-6009	551	4	c.	c.	PROPN
ejpam-6009	551	5	boonpok	boonpok	PROPN
ejpam-6009	551	6	.	.	PUNCT
ejpam-6009	552	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-6009	552	2	continuity	continuity	NOUN
ejpam-6009	552	3	for	for	ADP
ejpam-6009	552	4	multifunctions	multifunction	NOUN
ejpam-6009	552	5	.	.	PUNCT
ejpam-6009	553	1	wseas	wseas	PROPN
ejpam-6009	553	2	transactions	transaction	NOUN
ejpam-6009	553	3	on	on	ADP
ejpam-6009	553	4	mathematics	mathematic	NOUN
ejpam-6009	553	5	,	,	PUNCT
ejpam-6009	553	6	21:245–251	21:245–251	NUM
ejpam-6009	553	7	,	,	PUNCT
ejpam-6009	553	8	2022	2022	NUM
ejpam-6009	553	9	.	.	PUNCT
ejpam-6009	554	1	[	[	X
ejpam-6009	554	2	51	51	NUM
ejpam-6009	554	3	]	]	PUNCT
ejpam-6009	554	4	c.	c.	PROPN
ejpam-6009	554	5	boonpok	boonpok	PROPN
ejpam-6009	554	6	and	and	CCONJ
ejpam-6009	554	7	p.	p.	NOUN
ejpam-6009	554	8	pue	pue	NOUN
ejpam-6009	554	9	-	-	PUNCT
ejpam-6009	554	10	on	on	ADP
ejpam-6009	554	11	.	.	PUNCT
ejpam-6009	555	1	continuity	continuity	NOUN
ejpam-6009	555	2	for	for	ADP
ejpam-6009	555	3	multifunctions	multifunction	NOUN
ejpam-6009	555	4	in	in	ADP
ejpam-6009	555	5	ideal	ideal	ADJ
ejpam-6009	555	6	topological	topological	ADJ
ejpam-6009	555	7	spaces	space	NOUN
ejpam-6009	555	8	.	.	PUNCT
ejpam-6009	556	1	wseas	wseas	VERB
ejpam-6009	556	2	transactions	transaction	NOUN
ejpam-6009	556	3	on	on	ADP
ejpam-6009	556	4	mathematics	mathematic	NOUN
ejpam-6009	556	5	,	,	PUNCT
ejpam-6009	556	6	19:624–631	19:624–631	NUM
ejpam-6009	556	7	,	,	PUNCT
ejpam-6009	556	8	2020	2020	NUM
ejpam-6009	556	9	.	.	PUNCT
ejpam-6009	557	1	[	[	X
ejpam-6009	557	2	52	52	NUM
ejpam-6009	557	3	]	]	PUNCT
ejpam-6009	557	4	c.	c.	PROPN
ejpam-6009	557	5	boonpok	boonpok	PROPN
ejpam-6009	557	6	and	and	CCONJ
ejpam-6009	557	7	p.	p.	NOUN
ejpam-6009	557	8	pue	pue	NOUN
ejpam-6009	557	9	-	-	PUNCT
ejpam-6009	557	10	on	on	ADP
ejpam-6009	557	11	.	.	PUNCT
ejpam-6009	558	1	upper	upper	ADJ
ejpam-6009	558	2	and	and	CCONJ
ejpam-6009	558	3	lower	low	ADJ
ejpam-6009	558	4	weakly	weakly	ADJ
ejpam-6009	558	5	(	(	PUNCT
ejpam-6009	558	6	λ	λ	NOUN
ejpam-6009	558	7	,	,	PUNCT
ejpam-6009	558	8	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	558	9	multifunctions	multifunction	NOUN
ejpam-6009	558	10	.	.	PUNCT
ejpam-6009	559	1	european	european	PROPN
ejpam-6009	559	2	journal	journal	PROPN
ejpam-6009	559	3	of	of	ADP
ejpam-6009	559	4	pure	pure	ADJ
ejpam-6009	559	5	and	and	CCONJ
ejpam-6009	559	6	applied	applied	ADJ
ejpam-6009	559	7	mathematics	mathematic	NOUN
ejpam-6009	559	8	,	,	PUNCT
ejpam-6009	559	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-6009	559	10	,	,	PUNCT
ejpam-6009	559	11	2023	2023	NUM
ejpam-6009	559	12	.	.	PUNCT
ejpam-6009	560	1	[	[	X
ejpam-6009	560	2	53	53	NUM
ejpam-6009	560	3	]	]	PUNCT
ejpam-6009	560	4	j.	j.	PROPN
ejpam-6009	560	5	khampakdee	khampakdee	PROPN
ejpam-6009	560	6	and	and	CCONJ
ejpam-6009	560	7	c.	c.	PROPN
ejpam-6009	560	8	boonpok	boonpok	PROPN
ejpam-6009	560	9	.	.	PUNCT
ejpam-6009	561	1	upper	upper	ADJ
ejpam-6009	561	2	and	and	CCONJ
ejpam-6009	561	3	lower	low	ADJ
ejpam-6009	561	4	α(λ	α(λ	PROPN
ejpam-6009	561	5	,	,	PUNCT
ejpam-6009	561	6	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	561	7	multifunctions	multifunction	NOUN
ejpam-6009	561	8	.	.	PUNCT
ejpam-6009	562	1	wseas	wseas	VERB
ejpam-6009	562	2	transactions	transaction	NOUN
ejpam-6009	562	3	on	on	ADP
ejpam-6009	562	4	mathematics	mathematic	NOUN
ejpam-6009	562	5	,	,	PUNCT
ejpam-6009	562	6	21:684–690	21:684–690	NUM
ejpam-6009	562	7	,	,	PUNCT
ejpam-6009	562	8	2022	2022	NUM
ejpam-6009	562	9	.	.	PUNCT
ejpam-6009	563	1	[	[	X
ejpam-6009	563	2	54	54	NUM
ejpam-6009	563	3	]	]	PUNCT
ejpam-6009	563	4	c.	c.	PROPN
ejpam-6009	563	5	boonpok	boonpok	PROPN
ejpam-6009	563	6	and	and	CCONJ
ejpam-6009	563	7	j.	j.	PROPN
ejpam-6009	563	8	khampakdee	khampakdee	PROPN
ejpam-6009	563	9	.	.	PUNCT
ejpam-6009	564	1	on	on	ADP
ejpam-6009	564	2	almost	almost	ADV
ejpam-6009	564	3	α(λ	α(λ	PROPN
ejpam-6009	564	4	,	,	PUNCT
ejpam-6009	564	5	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	564	6	multifunctions	multifunction	NOUN
ejpam-6009	564	7	.	.	PUNCT
ejpam-6009	565	1	european	european	PROPN
ejpam-6009	565	2	journal	journal	PROPN
ejpam-6009	565	3	of	of	ADP
ejpam-6009	565	4	pure	pure	ADJ
ejpam-6009	565	5	and	and	CCONJ
ejpam-6009	565	6	applied	applied	ADJ
ejpam-6009	565	7	mathematics	mathematic	NOUN
ejpam-6009	565	8	,	,	PUNCT
ejpam-6009	565	9	15(2):626–634	15(2):626–634	PROPN
ejpam-6009	565	10	,	,	PUNCT
ejpam-6009	565	11	2022	2022	NUM
ejpam-6009	565	12	.	.	PUNCT
ejpam-6009	566	1	[	[	X
ejpam-6009	566	2	55	55	NUM
ejpam-6009	566	3	]	]	PUNCT
ejpam-6009	566	4	c.	c.	PROPN
ejpam-6009	566	5	boonpok	boonpok	PROPN
ejpam-6009	566	6	and	and	CCONJ
ejpam-6009	566	7	m.	m.	NOUN
ejpam-6009	566	8	thongmoon	thongmoon	NOUN
ejpam-6009	566	9	.	.	PUNCT
ejpam-6009	567	1	weak	weak	ADJ
ejpam-6009	567	2	α(λ	α(λ	PROPN
ejpam-6009	567	3	,	,	PUNCT
ejpam-6009	567	4	sp)-continuity	sp)-continuity	NOUN
ejpam-6009	567	5	for	for	ADP
ejpam-6009	567	6	multifunctions	multifunction	NOUN
ejpam-6009	567	7	.	.	PUNCT
ejpam-6009	568	1	european	european	ADJ
ejpam-6009	568	2	journal	journal	PROPN
ejpam-6009	568	3	of	of	ADP
ejpam-6009	568	4	pure	pure	ADJ
ejpam-6009	568	5	and	and	CCONJ
ejpam-6009	568	6	applied	applied	ADJ
ejpam-6009	568	7	mathematics	mathematic	NOUN
ejpam-6009	568	8	,	,	PUNCT
ejpam-6009	568	9	16(1):465–478	16(1):465–478	NUM
ejpam-6009	568	10	,	,	PUNCT
ejpam-6009	568	11	2023	2023	NUM
ejpam-6009	568	12	.	.	PUNCT
ejpam-6009	569	1	[	[	X
ejpam-6009	569	2	56	56	NUM
ejpam-6009	569	3	]	]	PUNCT
ejpam-6009	569	4	m.	m.	NOUN
ejpam-6009	569	5	thongmoon	thongmoon	NOUN
ejpam-6009	569	6	and	and	CCONJ
ejpam-6009	569	7	c.	c.	PROPN
ejpam-6009	569	8	boonpok	boonpok	PROPN
ejpam-6009	569	9	.	.	PUNCT
ejpam-6009	570	1	upper	upper	ADJ
ejpam-6009	570	2	and	and	CCONJ
ejpam-6009	570	3	lower	low	ADJ
ejpam-6009	570	4	almost	almost	ADV
ejpam-6009	570	5	β(λ	β(λ	NOUN
ejpam-6009	570	6	,	,	PUNCT
ejpam-6009	570	7	sp)-continuous	sp)-continuous	ADJ
ejpam-6009	570	8	multifunctions	multifunction	NOUN
ejpam-6009	570	9	.	.	PUNCT
ejpam-6009	571	1	wseas	wseas	VERB
ejpam-6009	571	2	transactions	transaction	NOUN
ejpam-6009	571	3	on	on	ADP
ejpam-6009	571	4	mathematics	mathematic	NOUN
ejpam-6009	571	5	,	,	PUNCT
ejpam-6009	571	6	21:844–853	21:844–853	NUM
ejpam-6009	571	7	,	,	PUNCT
ejpam-6009	571	8	2022	2022	NUM
ejpam-6009	571	9	.	.	PUNCT
ejpam-6009	572	1	[	[	X
ejpam-6009	572	2	57	57	NUM
ejpam-6009	572	3	]	]	PUNCT
ejpam-6009	572	4	c.	c.	PROPN
ejpam-6009	572	5	boonpok	boonpok	PROPN
ejpam-6009	572	6	and	and	CCONJ
ejpam-6009	572	7	j.	j.	PROPN
ejpam-6009	572	8	khampakdee	khampakdee	PROPN
ejpam-6009	572	9	.	.	PUNCT
ejpam-6009	573	1	slight	slight	PROPN
ejpam-6009	573	2	(	(	PUNCT
ejpam-6009	573	3	λ	λ	NOUN
ejpam-6009	573	4	,	,	PUNCT
ejpam-6009	573	5	sp)-continuity	sp)-continuity	NOUN
ejpam-6009	573	6	and	and	CCONJ
ejpam-6009	573	7	λsp	λsp	NOUN
ejpam-6009	573	8	-	-	PUNCT
ejpam-6009	573	9	extremally	extremally	ADV
ejpam-6009	573	10	disconnectedness	disconnectedness	NOUN
ejpam-6009	573	11	.	.	PUNCT
ejpam-6009	574	1	european	european	ADJ
ejpam-6009	574	2	journal	journal	PROPN
ejpam-6009	574	3	of	of	ADP
ejpam-6009	574	4	pure	pure	ADJ
ejpam-6009	574	5	and	and	CCONJ
ejpam-6009	574	6	applied	applied	ADJ
ejpam-6009	574	7	mathematics	mathematic	NOUN
ejpam-6009	574	8	,	,	PUNCT
ejpam-6009	574	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-6009	574	10	,	,	PUNCT
ejpam-6009	574	11	2022	2022	NUM
ejpam-6009	574	12	.	.	PUNCT
ejpam-6009	575	1	[	[	X
ejpam-6009	575	2	58	58	NUM
ejpam-6009	575	3	]	]	PUNCT
ejpam-6009	575	4	p.	p.	NOUN
ejpam-6009	575	5	pue	pue	NOUN
ejpam-6009	575	6	-	-	PUNCT
ejpam-6009	575	7	on	on	ADP
ejpam-6009	575	8	,	,	PUNCT
ejpam-6009	575	9	s.	s.	PROPN
ejpam-6009	575	10	sompong	sompong	PROPN
ejpam-6009	575	11	,	,	PUNCT
ejpam-6009	575	12	and	and	CCONJ
ejpam-6009	575	13	c.	c.	PROPN
ejpam-6009	575	14	boonpok	boonpok	PROPN
ejpam-6009	575	15	.	.	PUNCT
ejpam-6009	576	1	weakly	weakly	ADJ
ejpam-6009	576	2	quasi	quasi	NOUN
ejpam-6009	576	3	(	(	PUNCT
ejpam-6009	576	4	τ1	τ1	PROPN
ejpam-6009	576	5	,	,	PUNCT
ejpam-6009	576	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	576	7	multifunctions	multifunction	NOUN
ejpam-6009	576	8	.	.	PUNCT
ejpam-6009	577	1	european	european	ADJ
ejpam-6009	577	2	journal	journal	PROPN
ejpam-6009	577	3	of	of	ADP
ejpam-6009	577	4	pure	pure	ADJ
ejpam-6009	577	5	and	and	CCONJ
ejpam-6009	577	6	applied	applied	ADJ
ejpam-6009	577	7	mathematics	mathematic	NOUN
ejpam-6009	577	8	,	,	PUNCT
ejpam-6009	577	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-6009	577	10	,	,	PUNCT
ejpam-6009	577	11	2024	2024	NUM
ejpam-6009	577	12	.	.	PUNCT
ejpam-6009	578	1	[	[	X
ejpam-6009	578	2	59	59	NUM
ejpam-6009	578	3	]	]	X
ejpam-6009	578	4	p.	p.	NOUN
ejpam-6009	578	5	pue	pue	NOUN
ejpam-6009	578	6	-	-	PUNCT
ejpam-6009	578	7	on	on	ADP
ejpam-6009	578	8	,	,	PUNCT
ejpam-6009	578	9	s.	s.	PROPN
ejpam-6009	578	10	sompong	sompong	PROPN
ejpam-6009	578	11	,	,	PUNCT
ejpam-6009	578	12	and	and	CCONJ
ejpam-6009	578	13	c.	c.	PROPN
ejpam-6009	578	14	boonpok	boonpok	PROPN
ejpam-6009	578	15	.	.	PUNCT
ejpam-6009	579	1	almost	almost	ADV
ejpam-6009	579	2	quasi	quasi	X
ejpam-6009	579	3	(	(	PUNCT
ejpam-6009	579	4	τ1	τ1	NOUN
ejpam-6009	579	5	,	,	PUNCT
ejpam-6009	579	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	579	7	for	for	ADP
ejpam-6009	579	8	multifunctions	multifunction	NOUN
ejpam-6009	579	9	.	.	PUNCT
ejpam-6009	580	1	international	international	ADJ
ejpam-6009	580	2	journal	journal	NOUN
ejpam-6009	580	3	of	of	ADP
ejpam-6009	580	4	analysis	analysis	NOUN
ejpam-6009	580	5	and	and	CCONJ
ejpam-6009	580	6	applications	application	NOUN
ejpam-6009	580	7	,	,	PUNCT
ejpam-6009	580	8	22:97	22:97	NUM
ejpam-6009	580	9	,	,	PUNCT
ejpam-6009	580	10	2024	2024	NUM
ejpam-6009	580	11	.	.	PUNCT
ejpam-6009	581	1	[	[	X
ejpam-6009	581	2	60	60	NUM
ejpam-6009	581	3	]	]	X
ejpam-6009	581	4	j.	j.	PROPN
ejpam-6009	581	5	khampakdee	khampakdee	PROPN
ejpam-6009	581	6	,	,	PUNCT
ejpam-6009	581	7	s.	s.	PROPN
ejpam-6009	581	8	sompong	sompong	PROPN
ejpam-6009	581	9	,	,	PUNCT
ejpam-6009	581	10	and	and	CCONJ
ejpam-6009	581	11	c.	c.	PROPN
ejpam-6009	581	12	boonpok	boonpok	PROPN
ejpam-6009	581	13	.	.	PUNCT
ejpam-6009	582	1	c-(τ1	c-(τ1	PROPN
ejpam-6009	582	2	,	,	PUNCT
ejpam-6009	582	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	582	4	for	for	ADP
ejpam-6009	582	5	multifunctions	multifunction	NOUN
ejpam-6009	582	6	.	.	PUNCT
ejpam-6009	583	1	european	european	ADJ
ejpam-6009	583	2	journal	journal	PROPN
ejpam-6009	583	3	of	of	ADP
ejpam-6009	583	4	pure	pure	ADJ
ejpam-6009	583	5	and	and	CCONJ
ejpam-6009	583	6	applied	applied	ADJ
ejpam-6009	583	7	mathematics	mathematic	NOUN
ejpam-6009	583	8	,	,	PUNCT
ejpam-6009	583	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-6009	583	10	,	,	PUNCT
ejpam-6009	583	11	2024	2024	NUM
ejpam-6009	583	12	.	.	PUNCT
ejpam-6009	584	1	[	[	X
ejpam-6009	584	2	61	61	NUM
ejpam-6009	584	3	]	]	X
ejpam-6009	584	4	p.	p.	NOUN
ejpam-6009	584	5	pue	pue	NOUN
ejpam-6009	584	6	-	-	PUNCT
ejpam-6009	584	7	on	on	ADP
ejpam-6009	584	8	,	,	PUNCT
ejpam-6009	584	9	a.	a.	PROPN
ejpam-6009	584	10	sama	sama	PROPN
ejpam-6009	584	11	-	-	PUNCT
ejpam-6009	584	12	ae	ae	PROPN
ejpam-6009	584	13	,	,	PUNCT
ejpam-6009	584	14	and	and	CCONJ
ejpam-6009	584	15	c.	c.	PROPN
ejpam-6009	584	16	boonpok	boonpok	PROPN
ejpam-6009	584	17	.	.	PUNCT
ejpam-6009	585	1	c	c	X
ejpam-6009	585	2	-	-	PUNCT
ejpam-6009	585	3	quasi	quasi	X
ejpam-6009	585	4	(	(	PUNCT
ejpam-6009	585	5	τ1	τ1	PROPN
ejpam-6009	585	6	,	,	PUNCT
ejpam-6009	585	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	585	8	multifunctions	multifunction	NOUN
ejpam-6009	585	9	.	.	PUNCT
ejpam-6009	586	1	european	european	ADJ
ejpam-6009	586	2	journal	journal	PROPN
ejpam-6009	586	3	of	of	ADP
ejpam-6009	586	4	pure	pure	ADJ
ejpam-6009	586	5	and	and	CCONJ
ejpam-6009	586	6	applied	applied	ADJ
ejpam-6009	586	7	mathematics	mathematic	NOUN
ejpam-6009	586	8	,	,	PUNCT
ejpam-6009	586	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-6009	586	10	,	,	PUNCT
ejpam-6009	586	11	2024	2024	NUM
ejpam-6009	586	12	.	.	PUNCT
ejpam-6009	587	1	[	[	X
ejpam-6009	587	2	62	62	NUM
ejpam-6009	587	3	]	]	X
ejpam-6009	587	4	n.	n.	PROPN
ejpam-6009	587	5	viriyapong	viriyapong	PROPN
ejpam-6009	587	6	,	,	PUNCT
ejpam-6009	587	7	s.	s.	PROPN
ejpam-6009	587	8	sompong	sompong	PROPN
ejpam-6009	587	9	,	,	PUNCT
ejpam-6009	587	10	and	and	CCONJ
ejpam-6009	587	11	c.	c.	PROPN
ejpam-6009	587	12	boonpok	boonpok	PROPN
ejpam-6009	587	13	.	.	PUNCT
ejpam-6009	588	1	upper	upper	ADJ
ejpam-6009	588	2	and	and	CCONJ
ejpam-6009	588	3	lower	low	ADJ
ejpam-6009	588	4	s-(τ1	s-(τ1	NOUN
ejpam-6009	588	5	,	,	PUNCT
ejpam-6009	588	6	τ2)p	τ2)p	ADJ
ejpam-6009	588	7	-	-	PUNCT
ejpam-6009	588	8	continuous	continuous	ADJ
ejpam-6009	588	9	multifunctions	multifunction	NOUN
ejpam-6009	588	10	.	.	PUNCT
ejpam-6009	589	1	european	european	ADJ
ejpam-6009	589	2	journal	journal	PROPN
ejpam-6009	589	3	of	of	ADP
ejpam-6009	589	4	pure	pure	ADJ
ejpam-6009	589	5	and	and	CCONJ
ejpam-6009	589	6	applied	applied	ADJ
ejpam-6009	589	7	mathematics	mathematic	NOUN
ejpam-6009	589	8	,	,	PUNCT
ejpam-6009	589	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-6009	589	10	,	,	PUNCT
ejpam-6009	589	11	2024	2024	NUM
ejpam-6009	589	12	.	.	PUNCT
ejpam-6009	590	1	[	[	X
ejpam-6009	590	2	63	63	NUM
ejpam-6009	590	3	]	]	PUNCT
ejpam-6009	590	4	c.	c.	PROPN
ejpam-6009	590	5	viriyapong	viriyapong	PROPN
ejpam-6009	590	6	,	,	PUNCT
ejpam-6009	590	7	s.	s.	PROPN
ejpam-6009	590	8	sompong	sompong	PROPN
ejpam-6009	590	9	,	,	PUNCT
ejpam-6009	590	10	and	and	CCONJ
ejpam-6009	590	11	c.	c.	PROPN
ejpam-6009	590	12	boonpok	boonpok	PROPN
ejpam-6009	590	13	.	.	PUNCT
ejpam-6009	591	1	upper	upper	ADJ
ejpam-6009	591	2	and	and	CCONJ
ejpam-6009	591	3	lower	low	ADJ
ejpam-6009	591	4	slight	slight	ADJ
ejpam-6009	591	5	α(τ1	α(τ1	NOUN
ejpam-6009	591	6	,	,	PUNCT
ejpam-6009	591	7	τ2)continuity	τ2)continuity	PROPN
ejpam-6009	591	8	.	.	PUNCT
ejpam-6009	592	1	european	european	PROPN
ejpam-6009	592	2	journal	journal	PROPN
ejpam-6009	592	3	of	of	ADP
ejpam-6009	592	4	pure	pure	ADJ
ejpam-6009	592	5	and	and	CCONJ
ejpam-6009	592	6	applied	applied	ADJ
ejpam-6009	592	7	mathematics	mathematic	NOUN
ejpam-6009	592	8	,	,	PUNCT
ejpam-6009	592	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-6009	592	10	,	,	PUNCT
ejpam-6009	592	11	2024	2024	NUM
ejpam-6009	592	12	.	.	PUNCT
ejpam-6009	593	1	[	[	X
ejpam-6009	593	2	64	64	NUM
ejpam-6009	593	3	]	]	X
ejpam-6009	593	4	n.	n.	PROPN
ejpam-6009	593	5	viriyapong	viriyapong	PROPN
ejpam-6009	593	6	,	,	PUNCT
ejpam-6009	593	7	s.	s.	PROPN
ejpam-6009	593	8	sompong	sompong	PROPN
ejpam-6009	593	9	,	,	PUNCT
ejpam-6009	593	10	and	and	CCONJ
ejpam-6009	593	11	c.	c.	PROPN
ejpam-6009	593	12	boonpok	boonpok	PROPN
ejpam-6009	593	13	.	.	PUNCT
ejpam-6009	594	1	slightly	slightly	ADV
ejpam-6009	594	2	(	(	PUNCT
ejpam-6009	594	3	τ1	τ1	NOUN
ejpam-6009	594	4	,	,	PUNCT
ejpam-6009	594	5	τ2)p	τ2)p	ADJ
ejpam-6009	594	6	-	-	ADJ
ejpam-6009	594	7	continuous	continuous	ADJ
ejpam-6009	594	8	multifunctions	multifunction	NOUN
ejpam-6009	594	9	.	.	PUNCT
ejpam-6009	595	1	international	international	ADJ
ejpam-6009	595	2	journal	journal	NOUN
ejpam-6009	595	3	of	of	ADP
ejpam-6009	595	4	analysis	analysis	NOUN
ejpam-6009	595	5	and	and	CCONJ
ejpam-6009	595	6	applications	application	NOUN
ejpam-6009	595	7	,	,	PUNCT
ejpam-6009	595	8	22:152	22:152	NUM
ejpam-6009	595	9	,	,	PUNCT
ejpam-6009	595	10	2024	2024	NUM
ejpam-6009	595	11	.	.	PUNCT
ejpam-6009	596	1	c.	c.	PROPN
ejpam-6009	596	2	viriyapong	viriyapong	PROPN
ejpam-6009	596	3	,	,	PUNCT
ejpam-6009	596	4	a.	a.	PROPN
ejpam-6009	596	5	sama	sama	PROPN
ejpam-6009	596	6	-	-	PUNCT
ejpam-6009	596	7	ae	ae	PROPN
ejpam-6009	596	8	,	,	PUNCT
ejpam-6009	596	9	c.	c.	PROPN
ejpam-6009	596	10	boonpok	boonpok	PROPN
ejpam-6009	596	11	/	/	SYM
ejpam-6009	596	12	eur	eur	PROPN
ejpam-6009	596	13	.	.	PUNCT
ejpam-6009	597	1	j.	j.	PROPN
ejpam-6009	597	2	pure	pure	PROPN
ejpam-6009	597	3	appl	appl	PROPN
ejpam-6009	597	4	.	.	PROPN
ejpam-6009	597	5	math	math	PROPN
ejpam-6009	597	6	,	,	PUNCT
ejpam-6009	597	7	18	18	NUM
ejpam-6009	597	8	(	(	PUNCT
ejpam-6009	597	9	2	2	NUM
ejpam-6009	597	10	)	)	PUNCT
ejpam-6009	597	11	(	(	PUNCT
ejpam-6009	597	12	2025	2025	NUM
ejpam-6009	597	13	)	)	PUNCT
ejpam-6009	597	14	,	,	PUNCT
ejpam-6009	597	15	6009	6009	NUM
ejpam-6009	597	16	18	18	NUM
ejpam-6009	597	17	of	of	ADP
ejpam-6009	597	18	18	18	NUM
ejpam-6009	597	19	[	[	SYM
ejpam-6009	597	20	65	65	NUM
ejpam-6009	597	21	]	]	X
ejpam-6009	597	22	b.	b.	PROPN
ejpam-6009	597	23	kong	kong	PROPN
ejpam-6009	597	24	-	-	PUNCT
ejpam-6009	597	25	ied	ied	PROPN
ejpam-6009	597	26	,	,	PUNCT
ejpam-6009	597	27	s.	s.	PROPN
ejpam-6009	597	28	sompong	sompong	PROPN
ejpam-6009	597	29	,	,	PUNCT
ejpam-6009	597	30	and	and	CCONJ
ejpam-6009	597	31	c.	c.	PROPN
ejpam-6009	597	32	boonpok	boonpok	PROPN
ejpam-6009	597	33	.	.	PUNCT
ejpam-6009	598	1	rarely	rarely	ADV
ejpam-6009	598	2	s-(τ1	s-(τ1	VERB
ejpam-6009	598	3	,	,	PUNCT
ejpam-6009	598	4	τ2)p	τ2)p	ADJ
ejpam-6009	598	5	-	-	PUNCT
ejpam-6009	598	6	continuous	continuous	ADJ
ejpam-6009	598	7	multifunctions	multifunction	NOUN
ejpam-6009	598	8	.	.	PUNCT
ejpam-6009	599	1	european	european	ADJ
ejpam-6009	599	2	journal	journal	PROPN
ejpam-6009	599	3	of	of	ADP
ejpam-6009	599	4	pure	pure	ADJ
ejpam-6009	599	5	and	and	CCONJ
ejpam-6009	599	6	applied	applied	ADJ
ejpam-6009	599	7	mathematics	mathematic	NOUN
ejpam-6009	599	8	,	,	PUNCT
ejpam-6009	599	9	18(1):5649	18(1):5649	NUM
ejpam-6009	599	10	,	,	PUNCT
ejpam-6009	599	11	2025	2025	NUM
ejpam-6009	599	12	.	.	PUNCT
ejpam-6009	600	1	[	[	X
ejpam-6009	600	2	66	66	NUM
ejpam-6009	600	3	]	]	X
ejpam-6009	600	4	n.	n.	NOUN
ejpam-6009	600	5	chutiman	chutiman	NOUN
ejpam-6009	600	6	,	,	PUNCT
ejpam-6009	600	7	a.	a.	PROPN
ejpam-6009	600	8	sama	sama	PROPN
ejpam-6009	600	9	-	-	PUNCT
ejpam-6009	600	10	ae	ae	PROPN
ejpam-6009	600	11	,	,	PUNCT
ejpam-6009	600	12	and	and	CCONJ
ejpam-6009	600	13	c.	c.	PROPN
ejpam-6009	600	14	boonpok	boonpok	PROPN
ejpam-6009	600	15	.	.	PUNCT
ejpam-6009	601	1	almost	almost	ADV
ejpam-6009	601	2	near	near	ADV
ejpam-6009	601	3	(	(	PUNCT
ejpam-6009	601	4	τ1	τ1	NOUN
ejpam-6009	601	5	,	,	PUNCT
ejpam-6009	601	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	601	7	for	for	ADP
ejpam-6009	601	8	multifunctions	multifunction	NOUN
ejpam-6009	601	9	.	.	PUNCT
ejpam-6009	602	1	european	european	ADJ
ejpam-6009	602	2	journal	journal	PROPN
ejpam-6009	602	3	of	of	ADP
ejpam-6009	602	4	pure	pure	ADJ
ejpam-6009	602	5	and	and	CCONJ
ejpam-6009	602	6	applied	applied	ADJ
ejpam-6009	602	7	mathematics	mathematic	NOUN
ejpam-6009	602	8	,	,	PUNCT
ejpam-6009	602	9	18(1):5650	18(1):5650	NUM
ejpam-6009	602	10	,	,	PUNCT
ejpam-6009	602	11	2025	2025	NUM
ejpam-6009	602	12	.	.	PUNCT
ejpam-6009	603	1	[	[	X
ejpam-6009	603	2	67	67	NUM
ejpam-6009	603	3	]	]	PUNCT
ejpam-6009	603	4	m.	m.	NOUN
ejpam-6009	603	5	chiangpradit	chiangpradit	NOUN
ejpam-6009	603	6	,	,	PUNCT
ejpam-6009	603	7	a.	a.	PROPN
ejpam-6009	603	8	sama	sama	PROPN
ejpam-6009	603	9	-	-	PUNCT
ejpam-6009	603	10	ae	ae	PROPN
ejpam-6009	603	11	,	,	PUNCT
ejpam-6009	603	12	and	and	CCONJ
ejpam-6009	603	13	c.	c.	PROPN
ejpam-6009	603	14	boonpok	boonpok	PROPN
ejpam-6009	603	15	.	.	PUNCT
ejpam-6009	604	1	s-(τ1	s-(τ1	PROPN
ejpam-6009	604	2	,	,	PUNCT
ejpam-6009	604	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	604	4	for	for	ADP
ejpam-6009	604	5	multifunctions	multifunction	NOUN
ejpam-6009	604	6	.	.	PUNCT
ejpam-6009	605	1	european	european	ADJ
ejpam-6009	605	2	journal	journal	PROPN
ejpam-6009	605	3	of	of	ADP
ejpam-6009	605	4	pure	pure	ADJ
ejpam-6009	605	5	and	and	CCONJ
ejpam-6009	605	6	applied	applied	ADJ
ejpam-6009	605	7	mathematics	mathematic	NOUN
ejpam-6009	605	8	,	,	PUNCT
ejpam-6009	605	9	18(1):5634	18(1):5634	NUM
ejpam-6009	605	10	,	,	PUNCT
ejpam-6009	605	11	2025	2025	NUM
ejpam-6009	605	12	.	.	PUNCT
ejpam-6009	606	1	[	[	X
ejpam-6009	606	2	68	68	NUM
ejpam-6009	606	3	]	]	X
ejpam-6009	606	4	p.	p.	NOUN
ejpam-6009	606	5	pue	pue	NOUN
ejpam-6009	606	6	-	-	PUNCT
ejpam-6009	606	7	on	on	ADP
ejpam-6009	606	8	,	,	PUNCT
ejpam-6009	606	9	a.	a.	PROPN
ejpam-6009	606	10	sama	sama	PROPN
ejpam-6009	606	11	-	-	PUNCT
ejpam-6009	606	12	ae	ae	PROPN
ejpam-6009	606	13	,	,	PUNCT
ejpam-6009	606	14	and	and	CCONJ
ejpam-6009	606	15	c.	c.	PROPN
ejpam-6009	606	16	boonpok	boonpok	PROPN
ejpam-6009	606	17	.	.	PUNCT
ejpam-6009	607	1	quasi	quasi	PROPN
ejpam-6009	607	2	θ(τ1	θ(τ1	PROPN
ejpam-6009	607	3	,	,	PUNCT
ejpam-6009	607	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	607	5	for	for	ADP
ejpam-6009	607	6	multifunctions	multifunction	NOUN
ejpam-6009	607	7	.	.	PUNCT
ejpam-6009	608	1	european	european	ADJ
ejpam-6009	608	2	journal	journal	PROPN
ejpam-6009	608	3	of	of	ADP
ejpam-6009	608	4	pure	pure	ADJ
ejpam-6009	608	5	and	and	CCONJ
ejpam-6009	608	6	applied	applied	ADJ
ejpam-6009	608	7	mathematics	mathematic	NOUN
ejpam-6009	608	8	,	,	PUNCT
ejpam-6009	608	9	18(1):5717	18(1):5717	NUM
ejpam-6009	608	10	,	,	PUNCT
ejpam-6009	608	11	2025	2025	NUM
ejpam-6009	608	12	.	.	PUNCT
ejpam-6009	609	1	[	[	X
ejpam-6009	609	2	69	69	NUM
ejpam-6009	609	3	]	]	PUNCT
ejpam-6009	609	4	j.	j.	PROPN
ejpam-6009	609	5	khampakdee	khampakdee	PROPN
ejpam-6009	609	6	,	,	PUNCT
ejpam-6009	609	7	a.	a.	PROPN
ejpam-6009	609	8	sama	sama	PROPN
ejpam-6009	609	9	-	-	PUNCT
ejpam-6009	609	10	ae	ae	PROPN
ejpam-6009	609	11	,	,	PUNCT
ejpam-6009	609	12	and	and	CCONJ
ejpam-6009	609	13	c.	c.	PROPN
ejpam-6009	609	14	boonpok	boonpok	PROPN
ejpam-6009	609	15	.	.	PUNCT
ejpam-6009	610	1	almost	almost	ADV
ejpam-6009	610	2	nearly	nearly	ADV
ejpam-6009	610	3	quasi	quasi	NOUN
ejpam-6009	610	4	(	(	PUNCT
ejpam-6009	610	5	τ1	τ1	NOUN
ejpam-6009	610	6	,	,	PUNCT
ejpam-6009	610	7	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	610	8	multifunctions	multifunction	NOUN
ejpam-6009	610	9	.	.	PUNCT
ejpam-6009	611	1	european	european	ADJ
ejpam-6009	611	2	journal	journal	PROPN
ejpam-6009	611	3	of	of	ADP
ejpam-6009	611	4	pure	pure	ADJ
ejpam-6009	611	5	and	and	CCONJ
ejpam-6009	611	6	applied	applied	ADJ
ejpam-6009	611	7	mathematics	mathematic	NOUN
ejpam-6009	611	8	,	,	PUNCT
ejpam-6009	611	9	18(1):5720	18(1):5720	NUM
ejpam-6009	611	10	,	,	PUNCT
ejpam-6009	611	11	2025	2025	NUM
ejpam-6009	611	12	.	.	PUNCT
ejpam-6009	612	1	[	[	X
ejpam-6009	612	2	70	70	X
ejpam-6009	612	3	]	]	X
ejpam-6009	612	4	p.	p.	NOUN
ejpam-6009	612	5	pue	pue	NOUN
ejpam-6009	612	6	-	-	PUNCT
ejpam-6009	612	7	on	on	ADP
ejpam-6009	612	8	,	,	PUNCT
ejpam-6009	612	9	a.	a.	PROPN
ejpam-6009	612	10	sama	sama	PROPN
ejpam-6009	612	11	-	-	PUNCT
ejpam-6009	612	12	ae	ae	PROPN
ejpam-6009	612	13	,	,	PUNCT
ejpam-6009	612	14	and	and	CCONJ
ejpam-6009	612	15	c.	c.	PROPN
ejpam-6009	612	16	boonpok	boonpok	PROPN
ejpam-6009	612	17	.	.	PUNCT
ejpam-6009	613	1	upper	upper	ADJ
ejpam-6009	613	2	and	and	CCONJ
ejpam-6009	613	3	lower	low	ADJ
ejpam-6009	613	4	weakly	weakly	ADJ
ejpam-6009	613	5	s-(τ1	s-(τ1	PROPN
ejpam-6009	613	6	,	,	PUNCT
ejpam-6009	613	7	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	613	8	multifunctions	multifunction	NOUN
ejpam-6009	613	9	.	.	PUNCT
ejpam-6009	614	1	european	european	ADJ
ejpam-6009	614	2	journal	journal	PROPN
ejpam-6009	614	3	of	of	ADP
ejpam-6009	614	4	pure	pure	ADJ
ejpam-6009	614	5	and	and	CCONJ
ejpam-6009	614	6	applied	applied	ADJ
ejpam-6009	614	7	mathematics	mathematic	NOUN
ejpam-6009	614	8	,	,	PUNCT
ejpam-6009	614	9	18(1):5718	18(1):5718	NUM
ejpam-6009	614	10	,	,	PUNCT
ejpam-6009	614	11	2025	2025	NUM
ejpam-6009	614	12	.	.	PUNCT
ejpam-6009	615	1	[	[	X
ejpam-6009	615	2	71	71	NUM
ejpam-6009	615	3	]	]	PUNCT
ejpam-6009	615	4	m.	m.	NOUN
ejpam-6009	615	5	thongmoon	thongmoon	NOUN
ejpam-6009	615	6	,	,	PUNCT
ejpam-6009	615	7	a.	a.	PROPN
ejpam-6009	615	8	sama	sama	PROPN
ejpam-6009	615	9	-	-	PUNCT
ejpam-6009	615	10	ae	ae	PROPN
ejpam-6009	615	11	,	,	PUNCT
ejpam-6009	615	12	and	and	CCONJ
ejpam-6009	615	13	c.	c.	PROPN
ejpam-6009	615	14	boonpok	boonpok	PROPN
ejpam-6009	615	15	.	.	PUNCT
ejpam-6009	616	1	upper	upper	ADJ
ejpam-6009	616	2	and	and	CCONJ
ejpam-6009	616	3	lower	low	ADJ
ejpam-6009	616	4	near	near	ADV
ejpam-6009	616	5	(	(	PUNCT
ejpam-6009	616	6	τ1	τ1	NOUN
ejpam-6009	616	7	,	,	PUNCT
ejpam-6009	616	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6009	616	9	.	.	PUNCT
ejpam-6009	617	1	european	european	PROPN
ejpam-6009	617	2	journal	journal	PROPN
ejpam-6009	617	3	of	of	ADP
ejpam-6009	617	4	pure	pure	ADJ
ejpam-6009	617	5	and	and	CCONJ
ejpam-6009	617	6	applied	applied	ADJ
ejpam-6009	617	7	mathematics	mathematic	NOUN
ejpam-6009	617	8	,	,	PUNCT
ejpam-6009	617	9	18(1):5633	18(1):5633	NUM
ejpam-6009	617	10	,	,	PUNCT
ejpam-6009	617	11	2025	2025	NUM
ejpam-6009	617	12	.	.	PUNCT
ejpam-6009	618	1	[	[	X
ejpam-6009	618	2	72	72	NUM
ejpam-6009	618	3	]	]	X
ejpam-6009	618	4	m.	m.	NOUN
ejpam-6009	618	5	chiangpradit	chiangpradit	NOUN
ejpam-6009	618	6	,	,	PUNCT
ejpam-6009	618	7	s.	s.	PROPN
ejpam-6009	618	8	sompong	sompong	PROPN
ejpam-6009	618	9	,	,	PUNCT
ejpam-6009	618	10	and	and	CCONJ
ejpam-6009	618	11	c.	c.	PROPN
ejpam-6009	618	12	boonpok	boonpok	PROPN
ejpam-6009	618	13	.	.	PUNCT
ejpam-6009	619	1	upper	upper	ADJ
ejpam-6009	619	2	and	and	CCONJ
ejpam-6009	619	3	lower	low	ADJ
ejpam-6009	619	4	almost	almost	ADV
ejpam-6009	619	5	quasi	quasi	NOUN
ejpam-6009	619	6	(	(	PUNCT
ejpam-6009	619	7	τ1	τ1	NOUN
ejpam-6009	619	8	,	,	PUNCT
ejpam-6009	619	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6009	619	10	.	.	PUNCT
ejpam-6009	619	11	asia	asia	PROPN
ejpam-6009	619	12	pacific	pacific	PROPN
ejpam-6009	619	13	journal	journal	PROPN
ejpam-6009	619	14	of	of	ADP
ejpam-6009	619	15	mathematics	mathematic	NOUN
ejpam-6009	619	16	,	,	PUNCT
ejpam-6009	619	17	12:12	12:12	NUM
ejpam-6009	619	18	,	,	PUNCT
ejpam-6009	619	19	2025	2025	NUM
ejpam-6009	619	20	.	.	PUNCT
ejpam-6009	620	1	[	[	X
ejpam-6009	620	2	73	73	NUM
ejpam-6009	620	3	]	]	PUNCT
ejpam-6009	620	4	c.	c.	PROPN
ejpam-6009	620	5	boonpok	boonpok	PROPN
ejpam-6009	620	6	and	and	CCONJ
ejpam-6009	620	7	j.	j.	PROPN
ejpam-6009	620	8	khampakdee	khampakdee	PROPN
ejpam-6009	620	9	.	.	PUNCT
ejpam-6009	621	1	upper	upper	ADJ
ejpam-6009	621	2	and	and	CCONJ
ejpam-6009	621	3	lower	low	ADJ
ejpam-6009	621	4	almost	almost	ADV
ejpam-6009	621	5	contra-(λ	contra-(λ	PROPN
ejpam-6009	621	6	,	,	PUNCT
ejpam-6009	621	7	sp)-continuity	sp)-continuity	NOUN
ejpam-6009	621	8	.	.	PUNCT
ejpam-6009	622	1	european	european	PROPN
ejpam-6009	622	2	journal	journal	PROPN
ejpam-6009	622	3	of	of	ADP
ejpam-6009	622	4	pure	pure	ADJ
ejpam-6009	622	5	and	and	CCONJ
ejpam-6009	622	6	applied	applied	ADJ
ejpam-6009	622	7	mathematics	mathematic	NOUN
ejpam-6009	622	8	,	,	PUNCT
ejpam-6009	622	9	16(1):156–168	16(1):156–168	PROPN
ejpam-6009	622	10	,	,	PUNCT
ejpam-6009	622	11	2023	2023	NUM
ejpam-6009	622	12	.	.	PUNCT
ejpam-6009	623	1	[	[	X
ejpam-6009	623	2	74	74	X
ejpam-6009	623	3	]	]	PUNCT
ejpam-6009	623	4	p.	p.	NOUN
ejpam-6009	623	5	pue	pue	NOUN
ejpam-6009	623	6	-	-	PUNCT
ejpam-6009	623	7	on	on	ADP
ejpam-6009	623	8	,	,	PUNCT
ejpam-6009	623	9	s.	s.	PROPN
ejpam-6009	623	10	sompong	sompong	PROPN
ejpam-6009	623	11	,	,	PUNCT
ejpam-6009	623	12	and	and	CCONJ
ejpam-6009	623	13	c.	c.	PROPN
ejpam-6009	623	14	boonpok	boonpok	PROPN
ejpam-6009	623	15	.	.	PUNCT
ejpam-6009	624	1	upper	upper	ADJ
ejpam-6009	624	2	and	and	CCONJ
ejpam-6009	624	3	lower	low	ADJ
ejpam-6009	624	4	(	(	PUNCT
ejpam-6009	624	5	τ1	τ1	NOUN
ejpam-6009	624	6	,	,	PUNCT
ejpam-6009	624	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	624	8	mulfunctions	mulfunction	NOUN
ejpam-6009	624	9	.	.	PUNCT
ejpam-6009	625	1	international	international	ADJ
ejpam-6009	625	2	journal	journal	NOUN
ejpam-6009	625	3	of	of	ADP
ejpam-6009	625	4	mathematics	mathematic	NOUN
ejpam-6009	625	5	and	and	CCONJ
ejpam-6009	625	6	computer	computer	NOUN
ejpam-6009	625	7	science	science	NOUN
ejpam-6009	625	8	,	,	PUNCT
ejpam-6009	625	9	19(4):1305	19(4):1305	NUM
ejpam-6009	625	10	–	–	PUNCT
ejpam-6009	625	11	1310	1310	NUM
ejpam-6009	625	12	,	,	PUNCT
ejpam-6009	625	13	2024	2024	NUM
ejpam-6009	625	14	.	.	PUNCT
ejpam-6009	626	1	[	[	X
ejpam-6009	626	2	75	75	NUM
ejpam-6009	626	3	]	]	PUNCT
ejpam-6009	626	4	c.	c.	PROPN
ejpam-6009	626	5	klanarong	klanarong	PROPN
ejpam-6009	626	6	,	,	PUNCT
ejpam-6009	626	7	s.	s.	PROPN
ejpam-6009	626	8	sompong	sompong	PROPN
ejpam-6009	626	9	,	,	PUNCT
ejpam-6009	626	10	and	and	CCONJ
ejpam-6009	626	11	c.	c.	PROPN
ejpam-6009	626	12	boonpok	boonpok	PROPN
ejpam-6009	626	13	.	.	PUNCT
ejpam-6009	627	1	upper	upper	ADJ
ejpam-6009	627	2	and	and	CCONJ
ejpam-6009	627	3	lower	low	ADJ
ejpam-6009	627	4	almost	almost	ADV
ejpam-6009	627	5	(	(	PUNCT
ejpam-6009	627	6	τ1	τ1	NOUN
ejpam-6009	627	7	,	,	PUNCT
ejpam-6009	627	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6009	627	9	multifunctions	multifunction	NOUN
ejpam-6009	627	10	.	.	PUNCT
ejpam-6009	628	1	european	european	ADJ
ejpam-6009	628	2	journal	journal	PROPN
ejpam-6009	628	3	of	of	ADP
ejpam-6009	628	4	pure	pure	ADJ
ejpam-6009	628	5	and	and	CCONJ
ejpam-6009	628	6	applied	applied	ADJ
ejpam-6009	628	7	mathematics	mathematic	NOUN
ejpam-6009	628	8	,	,	PUNCT
ejpam-6009	628	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-6009	628	10	,	,	PUNCT
ejpam-6009	628	11	2024	2024	NUM
ejpam-6009	628	12	.	.	PUNCT
ejpam-6009	629	1	[	[	X
ejpam-6009	629	2	76	76	NUM
ejpam-6009	629	3	]	]	X
ejpam-6009	629	4	m.	m.	NOUN
ejpam-6009	629	5	thongmoon	thongmoon	NOUN
ejpam-6009	629	6	,	,	PUNCT
ejpam-6009	629	7	s.	s.	PROPN
ejpam-6009	629	8	sompong	sompong	PROPN
ejpam-6009	629	9	,	,	PUNCT
ejpam-6009	629	10	and	and	CCONJ
ejpam-6009	629	11	c.	c.	PROPN
ejpam-6009	629	12	boonpok	boonpok	PROPN
ejpam-6009	629	13	.	.	PUNCT
ejpam-6009	630	1	upper	upper	ADJ
ejpam-6009	630	2	and	and	CCONJ
ejpam-6009	630	3	lower	low	ADJ
ejpam-6009	630	4	weak	weak	ADJ
ejpam-6009	630	5	(	(	PUNCT
ejpam-6009	630	6	τ1	τ1	NOUN
ejpam-6009	630	7	,	,	PUNCT
ejpam-6009	630	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6009	630	9	.	.	PUNCT
ejpam-6009	631	1	european	european	PROPN
ejpam-6009	631	2	journal	journal	PROPN
ejpam-6009	631	3	of	of	ADP
ejpam-6009	631	4	pure	pure	ADJ
ejpam-6009	631	5	and	and	CCONJ
ejpam-6009	631	6	applied	applied	ADJ
ejpam-6009	631	7	mathematics	mathematic	NOUN
ejpam-6009	631	8	,	,	PUNCT
ejpam-6009	631	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-6009	631	10	,	,	PUNCT
ejpam-6009	631	11	2024	2024	NUM
ejpam-6009	631	12	.	.	PUNCT
ejpam-6009	632	1	[	[	X
ejpam-6009	632	2	77	77	NUM
ejpam-6009	632	3	]	]	X
ejpam-6009	632	4	c.	c.	PROPN
ejpam-6009	632	5	boonpok	boonpok	PROPN
ejpam-6009	632	6	,	,	PUNCT
ejpam-6009	632	7	c.	c.	PROPN
ejpam-6009	632	8	viriyapong	viriyapong	PROPN
ejpam-6009	632	9	,	,	PUNCT
ejpam-6009	632	10	and	and	CCONJ
ejpam-6009	632	11	m.	m.	NOUN
ejpam-6009	632	12	thongmoon	thongmoon	NOUN
ejpam-6009	632	13	.	.	PUNCT
ejpam-6009	633	1	on	on	ADP
ejpam-6009	633	2	upper	upper	ADJ
ejpam-6009	633	3	and	and	CCONJ
ejpam-6009	633	4	lower	low	ADJ
ejpam-6009	633	5	(	(	PUNCT
ejpam-6009	633	6	τ1	τ1	NOUN
ejpam-6009	633	7	,	,	PUNCT
ejpam-6009	633	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6009	633	9	multifunctions	multifunction	NOUN
ejpam-6009	633	10	.	.	PUNCT
ejpam-6009	634	1	journal	journal	PROPN
ejpam-6009	634	2	of	of	ADP
ejpam-6009	634	3	mathematics	mathematics	PROPN
ejpam-6009	634	4	and	and	CCONJ
ejpam-6009	634	5	computer	computer	NOUN
ejpam-6009	634	6	science	science	NOUN
ejpam-6009	634	7	,	,	PUNCT
ejpam-6009	634	8	18:282–293	18:282–293	NUM
ejpam-6009	634	9	,	,	PUNCT
ejpam-6009	634	10	2018	2018	NUM
ejpam-6009	634	11	.	.	PUNCT
ejpam-6009	635	1	[	[	X
ejpam-6009	635	2	78	78	NUM
ejpam-6009	635	3	]	]	X
ejpam-6009	635	4	c.	c.	PROPN
ejpam-6009	635	5	viriyapong	viriyapong	PROPN
ejpam-6009	635	6	and	and	CCONJ
ejpam-6009	635	7	c.	c.	PROPN
ejpam-6009	635	8	boonpok	boonpok	PROPN
ejpam-6009	635	9	.	.	PUNCT
ejpam-6009	636	1	(	(	PUNCT
ejpam-6009	636	2	τ1	τ1	NOUN
ejpam-6009	636	3	,	,	PUNCT
ejpam-6009	636	4	τ2)α	τ2)α	NOUN
ejpam-6009	636	5	-	-	PUNCT
ejpam-6009	636	6	continuity	continuity	NOUN
ejpam-6009	636	7	for	for	ADP
ejpam-6009	636	8	multifunctions	multifunction	NOUN
ejpam-6009	636	9	.	.	PUNCT
ejpam-6009	637	1	journal	journal	PROPN
ejpam-6009	637	2	of	of	ADP
ejpam-6009	637	3	mathematics	mathematic	NOUN
ejpam-6009	637	4	,	,	PUNCT
ejpam-6009	637	5	2020:6285763	2020:6285763	NUM
ejpam-6009	637	6	,	,	PUNCT
ejpam-6009	637	7	2020	2020	NUM
ejpam-6009	637	8	.	.	PUNCT
ejpam-6009	638	1	[	[	X
ejpam-6009	638	2	79	79	NUM
ejpam-6009	638	3	]	]	X
ejpam-6009	638	4	n.	n.	PROPN
ejpam-6009	638	5	viriyapong	viriyapong	PROPN
ejpam-6009	638	6	,	,	PUNCT
ejpam-6009	638	7	s.	s.	PROPN
ejpam-6009	638	8	sompong	sompong	PROPN
ejpam-6009	638	9	,	,	PUNCT
ejpam-6009	638	10	and	and	CCONJ
ejpam-6009	638	11	c.	c.	PROPN
ejpam-6009	638	12	boonpok	boonpok	PROPN
ejpam-6009	638	13	.	.	PUNCT
ejpam-6009	639	1	(	(	PUNCT
ejpam-6009	639	2	τ1	τ1	NOUN
ejpam-6009	639	3	,	,	PUNCT
ejpam-6009	639	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6009	639	5	disconnectedness	disconnectedness	NOUN
ejpam-6009	639	6	in	in	ADP
ejpam-6009	639	7	bitopological	bitopological	ADJ
ejpam-6009	639	8	spaces	space	NOUN
ejpam-6009	639	9	.	.	PUNCT
ejpam-6009	640	1	international	international	ADJ
ejpam-6009	640	2	journal	journal	PROPN
ejpam-6009	640	3	of	of	ADP
ejpam-6009	640	4	mathematics	mathematic	NOUN
ejpam-6009	640	5	and	and	CCONJ
ejpam-6009	640	6	computer	computer	NOUN
ejpam-6009	640	7	science	science	NOUN
ejpam-6009	640	8	,	,	PUNCT
ejpam-6009	640	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6009	640	10	,	,	PUNCT
ejpam-6009	640	11	2024	2024	NUM
ejpam-6009	640	12	.	.	PUNCT
ejpam-6009	641	1	[	[	X
ejpam-6009	641	2	80	80	NUM
ejpam-6009	641	3	]	]	X
ejpam-6009	641	4	p.	p.	NOUN
ejpam-6009	641	5	pue	pue	NOUN
ejpam-6009	641	6	-	-	PUNCT
ejpam-6009	641	7	on	on	ADP
ejpam-6009	641	8	,	,	PUNCT
ejpam-6009	641	9	s.	s.	PROPN
ejpam-6009	641	10	sompong	sompong	PROPN
ejpam-6009	641	11	,	,	PUNCT
ejpam-6009	641	12	and	and	CCONJ
ejpam-6009	641	13	c.	c.	PROPN
ejpam-6009	641	14	boonpok	boonpok	PROPN
ejpam-6009	641	15	.	.	PUNCT
ejpam-6009	642	1	almost	almost	ADV
ejpam-6009	642	2	contra-(τ1	contra-(τ1	NOUN
ejpam-6009	642	3	,	,	PUNCT
ejpam-6009	642	4	τ2)p	τ2)p	NOUN
ejpam-6009	642	5	-	-	PUNCT
ejpam-6009	642	6	continuity	continuity	NOUN
ejpam-6009	642	7	for	for	ADP
ejpam-6009	642	8	functions	function	NOUN
ejpam-6009	642	9	.	.	PUNCT
ejpam-6009	643	1	(	(	PUNCT
ejpam-6009	643	2	accepted	accept	VERB
ejpam-6009	643	3	)	)	PUNCT
ejpam-6009	643	4	.	.	PUNCT
ejpam-6009	644	1	[	[	X
ejpam-6009	644	2	81	81	NUM
ejpam-6009	644	3	]	]	PUNCT
ejpam-6009	644	4	m.	m.	NOUN
ejpam-6009	644	5	thongmoon	thongmoon	NOUN
ejpam-6009	644	6	,	,	PUNCT
ejpam-6009	644	7	s.	s.	PROPN
ejpam-6009	644	8	sompong	sompong	PROPN
ejpam-6009	644	9	,	,	PUNCT
ejpam-6009	644	10	and	and	CCONJ
ejpam-6009	644	11	c.	c.	PROPN
ejpam-6009	644	12	boonpok	boonpok	PROPN
ejpam-6009	644	13	.	.	PUNCT
ejpam-6009	645	1	(	(	PUNCT
ejpam-6009	645	2	τ1	τ1	NOUN
ejpam-6009	645	3	,	,	PUNCT
ejpam-6009	645	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6009	645	5	multifunctions	multifunction	NOUN
ejpam-6009	645	6	and	and	CCONJ
ejpam-6009	645	7	τ1τ2	τ1τ2	NOUN
ejpam-6009	645	8	-	-	ADJ
ejpam-6009	645	9	δ	δ	NOUN
ejpam-6009	645	10	-	-	ADJ
ejpam-6009	645	11	open	open	ADJ
ejpam-6009	645	12	sets	set	NOUN
ejpam-6009	645	13	.	.	PUNCT
ejpam-6009	646	1	international	international	ADJ
ejpam-6009	646	2	journal	journal	NOUN
ejpam-6009	646	3	of	of	ADP
ejpam-6009	646	4	mathematics	mathematic	NOUN
ejpam-6009	646	5	and	and	CCONJ
ejpam-6009	646	6	computer	computer	NOUN
ejpam-6009	646	7	science	science	NOUN
ejpam-6009	646	8	,	,	PUNCT
ejpam-6009	646	9	19(4):1369–1375	19(4):1369–1375	NUM
ejpam-6009	646	10	,	,	PUNCT
ejpam-6009	646	11	2024	2024	NUM
ejpam-6009	646	12	.	.	PUNCT