id	sid	tid	token	lemma	pos
ejpam-5720	1	1	european	european	PROPN
ejpam-5720	1	2	journal	journal	PROPN
ejpam-5720	1	3	of	of	ADP
ejpam-5720	1	4	pure	pure	ADJ
ejpam-5720	1	5	and	and	CCONJ
ejpam-5720	1	6	applied	applied	ADJ
ejpam-5720	1	7	mathematics	mathematic	NOUN
ejpam-5720	1	8	2025	2025	NUM
ejpam-5720	1	9	,	,	PUNCT
ejpam-5720	1	10	vol	vol	NOUN
ejpam-5720	1	11	.	.	PROPN
ejpam-5720	1	12	18	18	NUM
ejpam-5720	1	13	,	,	PUNCT
ejpam-5720	1	14	issue	issue	NOUN
ejpam-5720	1	15	1	1	NUM
ejpam-5720	1	16	,	,	PUNCT
ejpam-5720	1	17	article	article	NOUN
ejpam-5720	1	18	number	number	NOUN
ejpam-5720	1	19	5720	5720	NUM
ejpam-5720	1	20	issn	issn	VERB
ejpam-5720	1	21	1307	1307	NUM
ejpam-5720	1	22	-	-	SYM
ejpam-5720	1	23	5543	5543	NUM
ejpam-5720	1	24	–	–	PUNCT
ejpam-5720	1	25	ejpam.com	ejpam.com	X
ejpam-5720	1	26	published	publish	VERB
ejpam-5720	1	27	by	by	ADP
ejpam-5720	1	28	new	new	PROPN
ejpam-5720	1	29	york	york	PROPN
ejpam-5720	1	30	business	business	NOUN
ejpam-5720	1	31	global	global	ADJ
ejpam-5720	1	32	almost	almost	ADV
ejpam-5720	1	33	nearly	nearly	ADV
ejpam-5720	1	34	quasi	quasi	NOUN
ejpam-5720	1	35	(	(	PUNCT
ejpam-5720	1	36	τ1	τ1	NOUN
ejpam-5720	1	37	,	,	PUNCT
ejpam-5720	1	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	1	39	multifunctions	multifunction	NOUN
ejpam-5720	1	40	jeeranunt	jeeranunt	PROPN
ejpam-5720	1	41	khampakdee1	khampakdee1	PROPN
ejpam-5720	1	42	,	,	PUNCT
ejpam-5720	1	43	areeyuth	areeyuth	NOUN
ejpam-5720	1	44	sama	sama	NOUN
ejpam-5720	1	45	-	-	PUNCT
ejpam-5720	1	46	ae2	ae2	PROPN
ejpam-5720	1	47	,	,	PUNCT
ejpam-5720	1	48	chawalit	chawalit	VERB
ejpam-5720	1	49	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5720	1	50	1	1	NUM
ejpam-5720	1	51	mathematics	mathematic	NOUN
ejpam-5720	1	52	and	and	CCONJ
ejpam-5720	1	53	applied	apply	VERB
ejpam-5720	1	54	mathematics	mathematics	PROPN
ejpam-5720	1	55	research	research	NOUN
ejpam-5720	1	56	unit	unit	NOUN
ejpam-5720	1	57	,	,	PUNCT
ejpam-5720	1	58	department	department	NOUN
ejpam-5720	1	59	of	of	ADP
ejpam-5720	1	60	mathematics	mathematic	NOUN
ejpam-5720	1	61	,	,	PUNCT
ejpam-5720	1	62	faculty	faculty	NOUN
ejpam-5720	1	63	of	of	ADP
ejpam-5720	1	64	science	science	NOUN
ejpam-5720	1	65	,	,	PUNCT
ejpam-5720	1	66	mahasarakham	mahasarakham	PROPN
ejpam-5720	1	67	university	university	PROPN
ejpam-5720	1	68	,	,	PUNCT
ejpam-5720	1	69	maha	maha	PROPN
ejpam-5720	1	70	sarakham	sarakham	PROPN
ejpam-5720	1	71	,	,	PUNCT
ejpam-5720	1	72	44150	44150	NUM
ejpam-5720	1	73	,	,	PUNCT
ejpam-5720	1	74	thailand	thailand	PROPN
ejpam-5720	1	75	2	2	NUM
ejpam-5720	1	76	department	department	NOUN
ejpam-5720	1	77	of	of	ADP
ejpam-5720	1	78	mathematics	mathematic	NOUN
ejpam-5720	1	79	and	and	CCONJ
ejpam-5720	1	80	computer	computer	NOUN
ejpam-5720	1	81	science	science	NOUN
ejpam-5720	1	82	,	,	PUNCT
ejpam-5720	1	83	faculty	faculty	NOUN
ejpam-5720	1	84	of	of	ADP
ejpam-5720	1	85	science	science	NOUN
ejpam-5720	1	86	and	and	CCONJ
ejpam-5720	1	87	technology	technology	NOUN
ejpam-5720	1	88	,	,	PUNCT
ejpam-5720	1	89	prince	prince	NOUN
ejpam-5720	1	90	of	of	ADP
ejpam-5720	1	91	songkla	songkla	PROPN
ejpam-5720	1	92	university	university	PROPN
ejpam-5720	1	93	,	,	PUNCT
ejpam-5720	1	94	pattani	pattani	NOUN
ejpam-5720	1	95	campus	campus	NOUN
ejpam-5720	1	96	,	,	PUNCT
ejpam-5720	1	97	pattani	pattani	NOUN
ejpam-5720	1	98	,	,	PUNCT
ejpam-5720	1	99	94000	94000	NUM
ejpam-5720	1	100	,	,	PUNCT
ejpam-5720	1	101	thailand	thailand	PROPN
ejpam-5720	1	102	abstract	abstract	PROPN
ejpam-5720	1	103	.	.	PUNCT
ejpam-5720	2	1	this	this	DET
ejpam-5720	2	2	paper	paper	NOUN
ejpam-5720	2	3	deals	deal	NOUN
ejpam-5720	2	4	with	with	ADP
ejpam-5720	2	5	the	the	DET
ejpam-5720	2	6	concept	concept	NOUN
ejpam-5720	2	7	of	of	ADP
ejpam-5720	2	8	almost	almost	ADV
ejpam-5720	2	9	nearly	nearly	ADV
ejpam-5720	2	10	quasi	quasi	NOUN
ejpam-5720	2	11	(	(	PUNCT
ejpam-5720	2	12	τ1	τ1	NOUN
ejpam-5720	2	13	,	,	PUNCT
ejpam-5720	2	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	2	15	multifunctions	multifunction	NOUN
ejpam-5720	2	16	.	.	PUNCT
ejpam-5720	3	1	moreover	moreover	ADV
ejpam-5720	3	2	,	,	PUNCT
ejpam-5720	3	3	several	several	ADJ
ejpam-5720	3	4	characterizations	characterization	NOUN
ejpam-5720	3	5	and	and	CCONJ
ejpam-5720	3	6	some	some	DET
ejpam-5720	3	7	properties	property	NOUN
ejpam-5720	3	8	concerning	concern	VERB
ejpam-5720	3	9	almost	almost	ADV
ejpam-5720	3	10	nearly	nearly	ADV
ejpam-5720	3	11	quasi	quasi	NOUN
ejpam-5720	3	12	(	(	PUNCT
ejpam-5720	3	13	τ1	τ1	NOUN
ejpam-5720	3	14	,	,	PUNCT
ejpam-5720	3	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	3	16	multifunctions	multifunction	NOUN
ejpam-5720	3	17	are	be	AUX
ejpam-5720	3	18	considered	consider	VERB
ejpam-5720	3	19	.	.	PUNCT
ejpam-5720	4	1	2020	2020	NUM
ejpam-5720	4	2	mathematics	mathematic	NOUN
ejpam-5720	4	3	subject	subject	NOUN
ejpam-5720	4	4	classifications	classification	NOUN
ejpam-5720	4	5	:	:	PUNCT
ejpam-5720	4	6	54c08	54c08	NUM
ejpam-5720	4	7	,	,	PUNCT
ejpam-5720	4	8	54c60	54c60	NUM
ejpam-5720	4	9	key	key	ADJ
ejpam-5720	4	10	words	word	NOUN
ejpam-5720	4	11	and	and	CCONJ
ejpam-5720	4	12	phrases	phrase	NOUN
ejpam-5720	4	13	:	:	PUNCT
ejpam-5720	4	14	upper	upper	ADJ
ejpam-5720	4	15	almost	almost	ADV
ejpam-5720	4	16	nearly	nearly	ADV
ejpam-5720	4	17	quasi	quasi	NOUN
ejpam-5720	4	18	(	(	PUNCT
ejpam-5720	4	19	τ1	τ1	NOUN
ejpam-5720	4	20	,	,	PUNCT
ejpam-5720	4	21	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	4	22	multifunction	multifunction	NOUN
ejpam-5720	4	23	,	,	PUNCT
ejpam-5720	4	24	lower	low	ADJ
ejpam-5720	4	25	almost	almost	ADV
ejpam-5720	4	26	nearly	nearly	ADV
ejpam-5720	4	27	quasi	quasi	NOUN
ejpam-5720	4	28	(	(	PUNCT
ejpam-5720	4	29	τ1	τ1	NOUN
ejpam-5720	4	30	,	,	PUNCT
ejpam-5720	4	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	4	32	multifunction	multifunction	NOUN
ejpam-5720	4	33	,	,	PUNCT
ejpam-5720	4	34	almost	almost	ADV
ejpam-5720	4	35	nearly	nearly	ADV
ejpam-5720	4	36	quasi	quasi	NOUN
ejpam-5720	4	37	(	(	PUNCT
ejpam-5720	4	38	τ1	τ1	NOUN
ejpam-5720	4	39	,	,	PUNCT
ejpam-5720	4	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	4	41	multifunction	multifunction	NOUN
ejpam-5720	4	42	1	1	NUM
ejpam-5720	4	43	.	.	PUNCT
ejpam-5720	4	44	introduction	introduction	NOUN
ejpam-5720	4	45	the	the	DET
ejpam-5720	4	46	concept	concept	NOUN
ejpam-5720	4	47	of	of	ADP
ejpam-5720	4	48	quasi	quasi	ADJ
ejpam-5720	4	49	continuous	continuous	ADJ
ejpam-5720	4	50	functions	function	NOUN
ejpam-5720	4	51	was	be	AUX
ejpam-5720	4	52	introduced	introduce	VERB
ejpam-5720	4	53	by	by	ADP
ejpam-5720	4	54	marcus	marcus	PROPN
ejpam-5720	5	1	[	[	X
ejpam-5720	5	2	44	44	NUM
ejpam-5720	5	3	]	]	PUNCT
ejpam-5720	5	4	.	.	PUNCT
ejpam-5720	6	1	popa	popa	NOUN
ejpam-5720	7	1	[	[	X
ejpam-5720	7	2	48	48	NUM
ejpam-5720	7	3	]	]	PUNCT
ejpam-5720	7	4	introduced	introduce	VERB
ejpam-5720	7	5	and	and	CCONJ
ejpam-5720	7	6	investigated	investigate	VERB
ejpam-5720	7	7	the	the	DET
ejpam-5720	7	8	notion	notion	NOUN
ejpam-5720	7	9	of	of	ADP
ejpam-5720	7	10	almost	almost	ADV
ejpam-5720	7	11	quasi	quasi	ADJ
ejpam-5720	7	12	continuous	continuous	ADJ
ejpam-5720	7	13	functions	function	NOUN
ejpam-5720	7	14	.	.	PUNCT
ejpam-5720	8	1	neubrunnovaá	neubrunnovaá	PUNCT
ejpam-5720	9	1	[	[	X
ejpam-5720	9	2	45	45	NUM
ejpam-5720	9	3	]	]	PUNCT
ejpam-5720	9	4	showed	show	VERB
ejpam-5720	9	5	that	that	SCONJ
ejpam-5720	9	6	quasi	quasi	NOUN
ejpam-5720	9	7	continuity	continuity	NOUN
ejpam-5720	9	8	is	be	AUX
ejpam-5720	9	9	equivalent	equivalent	ADJ
ejpam-5720	9	10	to	to	ADP
ejpam-5720	9	11	semi	semi	ADJ
ejpam-5720	9	12	-	-	NOUN
ejpam-5720	9	13	continuity	continuity	NOUN
ejpam-5720	9	14	due	due	ADP
ejpam-5720	9	15	to	to	ADP
ejpam-5720	9	16	levine	levine	PROPN
ejpam-5720	9	17	[	[	X
ejpam-5720	9	18	42	42	NUM
ejpam-5720	9	19	]	]	PUNCT
ejpam-5720	9	20	.	.	PUNCT
ejpam-5720	10	1	popa	popa	NOUN
ejpam-5720	10	2	and	and	CCONJ
ejpam-5720	10	3	noiri	noiri	ADV
ejpam-5720	11	1	[	[	X
ejpam-5720	11	2	50	50	NUM
ejpam-5720	11	3	]	]	PUNCT
ejpam-5720	11	4	introduced	introduce	VERB
ejpam-5720	11	5	the	the	DET
ejpam-5720	11	6	concept	concept	NOUN
ejpam-5720	11	7	of	of	ADP
ejpam-5720	11	8	almost	almost	ADV
ejpam-5720	11	9	quasi	quasi	ADJ
ejpam-5720	11	10	continuous	continuous	ADJ
ejpam-5720	11	11	multifunctions	multifunction	NOUN
ejpam-5720	11	12	and	and	CCONJ
ejpam-5720	11	13	investigated	investigate	VERB
ejpam-5720	11	14	some	some	DET
ejpam-5720	11	15	characterizations	characterization	NOUN
ejpam-5720	11	16	of	of	ADP
ejpam-5720	11	17	such	such	ADJ
ejpam-5720	11	18	multifunctions	multifunction	NOUN
ejpam-5720	11	19	.	.	PUNCT
ejpam-5720	12	1	malghan	malghan	PROPN
ejpam-5720	12	2	and	and	CCONJ
ejpam-5720	12	3	hanchinamani	hanchinamani	ADJ
ejpam-5720	12	4	[	[	X
ejpam-5720	12	5	43	43	NUM
ejpam-5720	12	6	]	]	PUNCT
ejpam-5720	12	7	introduced	introduce	VERB
ejpam-5720	12	8	the	the	DET
ejpam-5720	12	9	notion	notion	NOUN
ejpam-5720	12	10	of	of	ADP
ejpam-5720	12	11	n	n	CCONJ
ejpam-5720	12	12	-	-	PUNCT
ejpam-5720	12	13	continuous	continuous	ADJ
ejpam-5720	12	14	functions	function	NOUN
ejpam-5720	12	15	.	.	PUNCT
ejpam-5720	13	1	noiri	noiri	PROPN
ejpam-5720	13	2	and	and	CCONJ
ejpam-5720	13	3	ergun	ergun	NOUN
ejpam-5720	13	4	[	[	X
ejpam-5720	13	5	46	46	NUM
ejpam-5720	13	6	]	]	PUNCT
ejpam-5720	13	7	investigated	investigate	VERB
ejpam-5720	13	8	some	some	DET
ejpam-5720	13	9	characterizations	characterization	NOUN
ejpam-5720	13	10	of	of	ADP
ejpam-5720	13	11	n	n	CCONJ
ejpam-5720	13	12	-	-	PUNCT
ejpam-5720	13	13	continuous	continuous	ADJ
ejpam-5720	13	14	functions	function	NOUN
ejpam-5720	13	15	.	.	PUNCT
ejpam-5720	14	1	viriyapong	viriyapong	PROPN
ejpam-5720	14	2	and	and	CCONJ
ejpam-5720	14	3	boonpok	boonpok	VERB
ejpam-5720	14	4	[	[	X
ejpam-5720	14	5	68	68	NUM
ejpam-5720	14	6	]	]	PUNCT
ejpam-5720	14	7	investigated	investigate	VERB
ejpam-5720	14	8	some	some	DET
ejpam-5720	14	9	characterizations	characterization	NOUN
ejpam-5720	14	10	of	of	ADP
ejpam-5720	14	11	(	(	PUNCT
ejpam-5720	14	12	λ	λ	PROPN
ejpam-5720	14	13	,	,	PUNCT
ejpam-5720	14	14	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	14	15	functions	function	NOUN
ejpam-5720	14	16	by	by	ADP
ejpam-5720	14	17	utilizing	utilize	VERB
ejpam-5720	14	18	the	the	DET
ejpam-5720	14	19	notions	notion	NOUN
ejpam-5720	14	20	of	of	ADP
ejpam-5720	14	21	(	(	PUNCT
ejpam-5720	14	22	λ	λ	PROPN
ejpam-5720	14	23	,	,	PUNCT
ejpam-5720	14	24	sp)open	sp)open	NOUN
ejpam-5720	14	25	sets	set	NOUN
ejpam-5720	14	26	and	and	CCONJ
ejpam-5720	14	27	(	(	PUNCT
ejpam-5720	14	28	λ	λ	PROPN
ejpam-5720	14	29	,	,	PUNCT
ejpam-5720	14	30	sp)-closed	sp)-close	VERB
ejpam-5720	14	31	sets	set	NOUN
ejpam-5720	14	32	due	due	ADP
ejpam-5720	14	33	to	to	ADP
ejpam-5720	14	34	boonpok	boonpok	NOUN
ejpam-5720	14	35	and	and	CCONJ
ejpam-5720	14	36	khampakdee	khampakdee	NOUN
ejpam-5720	15	1	[	[	X
ejpam-5720	15	2	12	12	NUM
ejpam-5720	15	3	]	]	PUNCT
ejpam-5720	15	4	.	.	PUNCT
ejpam-5720	16	1	dungthaisong	dungthaisong	NOUN
ejpam-5720	16	2	et	et	PROPN
ejpam-5720	16	3	al	al	PROPN
ejpam-5720	16	4	.	.	PUNCT
ejpam-5720	17	1	[	[	X
ejpam-5720	17	2	35	35	NUM
ejpam-5720	17	3	]	]	PUNCT
ejpam-5720	17	4	introduced	introduce	VERB
ejpam-5720	17	5	and	and	CCONJ
ejpam-5720	17	6	studied	study	VERB
ejpam-5720	17	7	the	the	DET
ejpam-5720	17	8	concept	concept	NOUN
ejpam-5720	17	9	of	of	ADP
ejpam-5720	17	10	g(m	g(m	ADJ
ejpam-5720	17	11	,	,	PUNCT
ejpam-5720	17	12	n)-continuous	n)-continuous	ADJ
ejpam-5720	17	13	functions	function	NOUN
ejpam-5720	17	14	.	.	PUNCT
ejpam-5720	18	1	duangphui	duangphui	NOUN
ejpam-5720	18	2	et	et	PROPN
ejpam-5720	18	3	al	al	PROPN
ejpam-5720	18	4	.	.	PUNCT
ejpam-5720	19	1	[	[	X
ejpam-5720	19	2	34	34	NUM
ejpam-5720	19	3	]	]	PUNCT
ejpam-5720	19	4	introduced	introduce	VERB
ejpam-5720	19	5	and	and	CCONJ
ejpam-5720	19	6	investigated	investigate	VERB
ejpam-5720	19	7	the	the	DET
ejpam-5720	19	8	notion	notion	NOUN
ejpam-5720	19	9	of	of	ADP
ejpam-5720	19	10	(	(	PUNCT
ejpam-5720	19	11	µ	µ	NOUN
ejpam-5720	19	12	,	,	PUNCT
ejpam-5720	19	13	µ′)(m	µ′)(m	VERB
ejpam-5720	19	14	,	,	PUNCT
ejpam-5720	19	15	n)-continuous	n)-continuous	ADJ
ejpam-5720	19	16	functions	function	NOUN
ejpam-5720	19	17	.	.	PUNCT
ejpam-5720	20	1	srisarakham	srisarakham	PROPN
ejpam-5720	20	2	et	et	PROPN
ejpam-5720	20	3	al	al	PROPN
ejpam-5720	20	4	.	.	PUNCT
ejpam-5720	21	1	[	[	X
ejpam-5720	21	2	60	60	NUM
ejpam-5720	21	3	]	]	PUNCT
ejpam-5720	21	4	introduced	introduce	VERB
ejpam-5720	21	5	and	and	CCONJ
ejpam-5720	21	6	studied	study	VERB
ejpam-5720	21	7	the	the	DET
ejpam-5720	21	8	concept	concept	NOUN
ejpam-5720	21	9	of	of	ADP
ejpam-5720	21	10	almost	almost	ADV
ejpam-5720	21	11	(	(	PUNCT
ejpam-5720	21	12	λ	λ	PROPN
ejpam-5720	21	13	,	,	PUNCT
ejpam-5720	21	14	p)-continuous	p)-continuous	ADJ
ejpam-5720	21	15	functions	function	NOUN
ejpam-5720	21	16	.	.	PUNCT
ejpam-5720	22	1	furthermore	furthermore	ADV
ejpam-5720	22	2	,	,	PUNCT
ejpam-5720	22	3	several	several	ADJ
ejpam-5720	22	4	characterizations	characterization	NOUN
ejpam-5720	22	5	of	of	ADP
ejpam-5720	22	6	strongly	strongly	ADV
ejpam-5720	22	7	θ(λ	θ(λ	ADJ
ejpam-5720	22	8	,	,	PUNCT
ejpam-5720	22	9	p)-continuous	p)-continuous	ADJ
ejpam-5720	22	10	functions	function	NOUN
ejpam-5720	22	11	,	,	PUNCT
ejpam-5720	22	12	almost	almost	ADV
ejpam-5720	22	13	strongly	strongly	ADV
ejpam-5720	22	14	θ(λ	θ(λ	VERB
ejpam-5720	22	15	,	,	PUNCT
ejpam-5720	22	16	p)-continuous	p)-continuous	ADJ
ejpam-5720	22	17	functions	function	NOUN
ejpam-5720	22	18	,	,	PUNCT
ejpam-5720	22	19	θ(λ	θ(λ	PROPN
ejpam-5720	22	20	,	,	PUNCT
ejpam-5720	22	21	p)-continuous	p)-continuous	ADJ
ejpam-5720	22	22	functions	function	NOUN
ejpam-5720	22	23	,	,	PUNCT
ejpam-5720	22	24	weakly	weakly	ADJ
ejpam-5720	22	25	(	(	PUNCT
ejpam-5720	22	26	λ	λ	PROPN
ejpam-5720	22	27	,	,	PUNCT
ejpam-5720	22	28	b)-continuous	b)-continuous	ADJ
ejpam-5720	22	29	functions	function	NOUN
ejpam-5720	22	30	,	,	PUNCT
ejpam-5720	22	31	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5720	22	32	functions	function	NOUN
ejpam-5720	22	33	,	,	PUNCT
ejpam-5720	22	34	(	(	PUNCT
ejpam-5720	22	35	λ	λ	NOUN
ejpam-5720	22	36	,	,	PUNCT
ejpam-5720	22	37	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5720	22	38	functions	function	NOUN
ejpam-5720	22	39	,	,	PUNCT
ejpam-5720	22	40	∗corresponding	∗corresponde	VERB
ejpam-5720	22	41	author	author	NOUN
ejpam-5720	22	42	.	.	PUNCT
ejpam-5720	23	1	doi	doi	NOUN
ejpam-5720	23	2	:	:	PUNCT
ejpam-5720	23	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5720	https://doi.org/10.29020/nybg.ejpam.v18i1.5720	NOUN
ejpam-5720	23	4	email	email	NOUN
ejpam-5720	23	5	addresses	address	NOUN
ejpam-5720	23	6	:	:	PUNCT
ejpam-5720	23	7	jeeranunt.k@msu.ac.th	jeeranunt.k@msu.ac.th	INTJ
ejpam-5720	23	8	(	(	PUNCT
ejpam-5720	23	9	j.	j.	PROPN
ejpam-5720	23	10	khampakdee	khampakdee	PROPN
ejpam-5720	23	11	)	)	PUNCT
ejpam-5720	23	12	,	,	PUNCT
ejpam-5720	23	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-5720	23	14	(	(	PUNCT
ejpam-5720	23	15	a.	a.	PROPN
ejpam-5720	23	16	sama	sama	PROPN
ejpam-5720	23	17	-	-	PUNCT
ejpam-5720	23	18	ae	ae	PROPN
ejpam-5720	23	19	)	)	PUNCT
ejpam-5720	23	20	,	,	PUNCT
ejpam-5720	23	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5720	23	22	(	(	PUNCT
ejpam-5720	23	23	c.	c.	PROPN
ejpam-5720	23	24	boonpok	boonpok	PROPN
ejpam-5720	23	25	)	)	PUNCT
ejpam-5720	23	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5720	24	1	1	1	NUM
ejpam-5720	24	2	copyright	copyright	NOUN
ejpam-5720	24	3	:	:	PUNCT
ejpam-5720	24	4	©	©	PROPN
ejpam-5720	24	5	2025	2025	NUM
ejpam-5720	24	6	the	the	DET
ejpam-5720	24	7	author(s	author(s	NOUN
ejpam-5720	24	8	)	)	PUNCT
ejpam-5720	24	9	.	.	PUNCT
ejpam-5720	25	1	(	(	PUNCT
ejpam-5720	25	2	cc	cc	NOUN
ejpam-5720	25	3	by	by	ADP
ejpam-5720	25	4	-	-	PUNCT
ejpam-5720	25	5	nc	nc	PROPN
ejpam-5720	25	6	4.0	4.0	NUM
ejpam-5720	25	7	)	)	PUNCT
ejpam-5720	25	8	j.	j.	PROPN
ejpam-5720	25	9	khampakdee	khampakdee	PROPN
ejpam-5720	25	10	,	,	PUNCT
ejpam-5720	25	11	a.	a.	PROPN
ejpam-5720	25	12	sama	sama	PROPN
ejpam-5720	25	13	-	-	PUNCT
ejpam-5720	25	14	ae	ae	PROPN
ejpam-5720	25	15	,	,	PUNCT
ejpam-5720	25	16	c.	c.	PROPN
ejpam-5720	25	17	boonpok	boonpok	PROPN
ejpam-5720	25	18	/	/	SYM
ejpam-5720	25	19	eur	eur	PROPN
ejpam-5720	25	20	.	.	PUNCT
ejpam-5720	26	1	j.	j.	PROPN
ejpam-5720	26	2	pure	pure	PROPN
ejpam-5720	26	3	appl	appl	PROPN
ejpam-5720	26	4	.	.	PROPN
ejpam-5720	26	5	math	math	PROPN
ejpam-5720	26	6	,	,	PUNCT
ejpam-5720	26	7	18	18	NUM
ejpam-5720	26	8	(	(	PUNCT
ejpam-5720	26	9	1	1	NUM
ejpam-5720	26	10	)	)	PUNCT
ejpam-5720	26	11	(	(	PUNCT
ejpam-5720	26	12	2025	2025	NUM
ejpam-5720	26	13	)	)	PUNCT
ejpam-5720	26	14	,	,	PUNCT
ejpam-5720	26	15	5720	5720	NUM
ejpam-5720	26	16	2	2	NUM
ejpam-5720	26	17	of	of	ADP
ejpam-5720	26	18	15	15	NUM
ejpam-5720	26	19	⋆-continuous	⋆-continuous	ADJ
ejpam-5720	26	20	functions	function	NOUN
ejpam-5720	26	21	,	,	PUNCT
ejpam-5720	26	22	θ	θ	PROPN
ejpam-5720	26	23	-	-	ADJ
ejpam-5720	26	24	i	i	NOUN
ejpam-5720	26	25	-continuous	-continuous	ADJ
ejpam-5720	26	26	functions	function	NOUN
ejpam-5720	26	27	,	,	PUNCT
ejpam-5720	26	28	almost	almost	ADV
ejpam-5720	26	29	(	(	PUNCT
ejpam-5720	26	30	g	g	NOUN
ejpam-5720	26	31	,	,	PUNCT
ejpam-5720	26	32	m)-continuous	m)-continuous	ADJ
ejpam-5720	26	33	functions	function	NOUN
ejpam-5720	26	34	,	,	PUNCT
ejpam-5720	26	35	pairwise	pairwise	NOUN
ejpam-5720	26	36	almost	almost	ADV
ejpam-5720	26	37	m	m	VERB
ejpam-5720	26	38	-continuous	-continuous	ADJ
ejpam-5720	26	39	functions	function	NOUN
ejpam-5720	26	40	,	,	PUNCT
ejpam-5720	26	41	(	(	PUNCT
ejpam-5720	26	42	τ1	τ1	NOUN
ejpam-5720	26	43	,	,	PUNCT
ejpam-5720	26	44	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	26	45	functions	function	NOUN
ejpam-5720	26	46	,	,	PUNCT
ejpam-5720	26	47	almost	almost	ADV
ejpam-5720	26	48	(	(	PUNCT
ejpam-5720	26	49	τ1	τ1	NOUN
ejpam-5720	26	50	,	,	PUNCT
ejpam-5720	26	51	τ2)continuous	τ2)continuous	ADJ
ejpam-5720	26	52	functions	function	NOUN
ejpam-5720	26	53	,	,	PUNCT
ejpam-5720	26	54	weakly	weakly	ADJ
ejpam-5720	26	55	(	(	PUNCT
ejpam-5720	26	56	τ1	τ1	NOUN
ejpam-5720	26	57	,	,	PUNCT
ejpam-5720	26	58	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	26	59	functions	function	NOUN
ejpam-5720	26	60	,	,	PUNCT
ejpam-5720	26	61	slightly	slightly	ADV
ejpam-5720	26	62	(	(	PUNCT
ejpam-5720	26	63	τ1	τ1	NOUN
ejpam-5720	26	64	,	,	PUNCT
ejpam-5720	26	65	τ2)s	τ2)s	ADJ
ejpam-5720	26	66	-	-	PUNCT
ejpam-5720	26	67	continuous	continuous	ADJ
ejpam-5720	26	68	functions	function	NOUN
ejpam-5720	26	69	and	and	CCONJ
ejpam-5720	26	70	δ(τ1	δ(τ1	NOUN
ejpam-5720	26	71	,	,	PUNCT
ejpam-5720	26	72	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	26	73	functions	function	NOUN
ejpam-5720	26	74	were	be	AUX
ejpam-5720	26	75	presented	present	VERB
ejpam-5720	26	76	in	in	ADP
ejpam-5720	26	77	[	[	X
ejpam-5720	26	78	63	63	NUM
ejpam-5720	26	79	]	]	PUNCT
ejpam-5720	26	80	,	,	PUNCT
ejpam-5720	26	81	[	[	X
ejpam-5720	26	82	16	16	NUM
ejpam-5720	26	83	]	]	PUNCT
ejpam-5720	26	84	,	,	PUNCT
ejpam-5720	26	85	[	[	X
ejpam-5720	26	86	52	52	NUM
ejpam-5720	26	87	]	]	PUNCT
ejpam-5720	26	88	,	,	PUNCT
ejpam-5720	26	89	[	[	X
ejpam-5720	26	90	25	25	NUM
ejpam-5720	26	91	]	]	PUNCT
ejpam-5720	26	92	,	,	PUNCT
ejpam-5720	26	93	[	[	X
ejpam-5720	26	94	11	11	NUM
ejpam-5720	26	95	]	]	PUNCT
ejpam-5720	26	96	,	,	PUNCT
ejpam-5720	26	97	[	[	X
ejpam-5720	26	98	8	8	NUM
ejpam-5720	26	99	]	]	PUNCT
ejpam-5720	26	100	,	,	PUNCT
ejpam-5720	26	101	[	[	X
ejpam-5720	26	102	10	10	NUM
ejpam-5720	26	103	]	]	PUNCT
ejpam-5720	26	104	,	,	PUNCT
ejpam-5720	26	105	[	[	X
ejpam-5720	26	106	4	4	NUM
ejpam-5720	26	107	]	]	PUNCT
ejpam-5720	26	108	,	,	PUNCT
ejpam-5720	26	109	[	[	X
ejpam-5720	26	110	1	1	NUM
ejpam-5720	26	111	]	]	PUNCT
ejpam-5720	26	112	,	,	PUNCT
ejpam-5720	26	113	[	[	X
ejpam-5720	26	114	2	2	NUM
ejpam-5720	26	115	]	]	PUNCT
ejpam-5720	26	116	,	,	PUNCT
ejpam-5720	26	117	[	[	X
ejpam-5720	26	118	26	26	NUM
ejpam-5720	26	119	]	]	PUNCT
ejpam-5720	26	120	,	,	PUNCT
ejpam-5720	26	121	[	[	X
ejpam-5720	26	122	23	23	NUM
ejpam-5720	26	123	]	]	PUNCT
ejpam-5720	26	124	,	,	PUNCT
ejpam-5720	26	125	[	[	X
ejpam-5720	26	126	18	18	NUM
ejpam-5720	26	127	]	]	PUNCT
ejpam-5720	26	128	,	,	PUNCT
ejpam-5720	26	129	[	[	X
ejpam-5720	26	130	57	57	NUM
ejpam-5720	26	131	]	]	PUNCT
ejpam-5720	26	132	and	and	CCONJ
ejpam-5720	26	133	[	[	X
ejpam-5720	26	134	51	51	NUM
ejpam-5720	26	135	]	]	PUNCT
ejpam-5720	26	136	,	,	PUNCT
ejpam-5720	26	137	respectively	respectively	ADV
ejpam-5720	26	138	.	.	PUNCT
ejpam-5720	27	1	srisarakham	srisarakham	PROPN
ejpam-5720	27	2	et	et	PROPN
ejpam-5720	27	3	al	al	PROPN
ejpam-5720	27	4	.	.	PUNCT
ejpam-5720	28	1	[	[	X
ejpam-5720	28	2	61	61	NUM
ejpam-5720	28	3	]	]	PUNCT
ejpam-5720	28	4	introduced	introduce	VERB
ejpam-5720	28	5	and	and	CCONJ
ejpam-5720	28	6	studied	study	VERB
ejpam-5720	28	7	the	the	DET
ejpam-5720	28	8	concept	concept	NOUN
ejpam-5720	28	9	of	of	ADP
ejpam-5720	28	10	faintly	faintly	ADV
ejpam-5720	28	11	(	(	PUNCT
ejpam-5720	28	12	τ1	τ1	PROPN
ejpam-5720	28	13	,	,	PUNCT
ejpam-5720	28	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	28	15	functions	function	NOUN
ejpam-5720	28	16	.	.	PUNCT
ejpam-5720	29	1	thongmoon	thongmoon	NOUN
ejpam-5720	29	2	et	et	PROPN
ejpam-5720	29	3	al	al	PROPN
ejpam-5720	29	4	.	.	PUNCT
ejpam-5720	30	1	[	[	X
ejpam-5720	30	2	66	66	NUM
ejpam-5720	30	3	]	]	PUNCT
ejpam-5720	30	4	introduced	introduce	VERB
ejpam-5720	30	5	and	and	CCONJ
ejpam-5720	30	6	investigated	investigate	VERB
ejpam-5720	30	7	the	the	DET
ejpam-5720	30	8	notion	notion	NOUN
ejpam-5720	30	9	of	of	ADP
ejpam-5720	30	10	rarely	rarely	ADV
ejpam-5720	30	11	(	(	PUNCT
ejpam-5720	30	12	τ1	τ1	NOUN
ejpam-5720	30	13	,	,	PUNCT
ejpam-5720	30	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	30	15	functions	function	NOUN
ejpam-5720	30	16	.	.	PUNCT
ejpam-5720	31	1	chiangpradit	chiangpradit	NOUN
ejpam-5720	31	2	et	et	PROPN
ejpam-5720	31	3	al	al	PROPN
ejpam-5720	31	4	.	.	PUNCT
ejpam-5720	32	1	[	[	X
ejpam-5720	32	2	32	32	NUM
ejpam-5720	32	3	]	]	PUNCT
ejpam-5720	32	4	introduced	introduce	VERB
ejpam-5720	32	5	and	and	CCONJ
ejpam-5720	32	6	studied	study	VERB
ejpam-5720	32	7	the	the	DET
ejpam-5720	32	8	concept	concept	NOUN
ejpam-5720	32	9	of	of	ADP
ejpam-5720	32	10	weakly	weakly	ADJ
ejpam-5720	32	11	quasi	quasi	NOUN
ejpam-5720	32	12	(	(	PUNCT
ejpam-5720	32	13	τ1	τ1	PROPN
ejpam-5720	32	14	,	,	PUNCT
ejpam-5720	32	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	32	16	functions	function	NOUN
ejpam-5720	32	17	.	.	PUNCT
ejpam-5720	33	1	kong	kong	PROPN
ejpam-5720	33	2	-	-	PUNCT
ejpam-5720	33	3	ied	ied	PROPN
ejpam-5720	33	4	at	at	ADP
ejpam-5720	33	5	al	al	PROPN
ejpam-5720	33	6	.	.	PUNCT
ejpam-5720	34	1	[	[	X
ejpam-5720	34	2	41	41	NUM
ejpam-5720	34	3	]	]	PUNCT
ejpam-5720	34	4	introduced	introduce	VERB
ejpam-5720	34	5	and	and	CCONJ
ejpam-5720	34	6	investigated	investigate	VERB
ejpam-5720	34	7	the	the	DET
ejpam-5720	34	8	notion	notion	NOUN
ejpam-5720	34	9	of	of	ADP
ejpam-5720	34	10	almost	almost	ADV
ejpam-5720	34	11	quasi	quasi	X
ejpam-5720	34	12	(	(	PUNCT
ejpam-5720	34	13	τ1	τ1	NOUN
ejpam-5720	34	14	,	,	PUNCT
ejpam-5720	34	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	34	16	functions	function	NOUN
ejpam-5720	34	17	.	.	PUNCT
ejpam-5720	35	1	in	in	ADP
ejpam-5720	35	2	2003	2003	NUM
ejpam-5720	35	3	,	,	PUNCT
ejpam-5720	35	4	ekici	ekici	NOUN
ejpam-5720	35	5	[	[	X
ejpam-5720	35	6	36	36	NUM
ejpam-5720	35	7	]	]	PUNCT
ejpam-5720	35	8	introduced	introduce	VERB
ejpam-5720	35	9	and	and	CCONJ
ejpam-5720	35	10	studied	study	VERB
ejpam-5720	35	11	the	the	DET
ejpam-5720	35	12	concept	concept	NOUN
ejpam-5720	35	13	of	of	ADP
ejpam-5720	35	14	nearly	nearly	ADV
ejpam-5720	35	15	continuous	continuous	ADJ
ejpam-5720	35	16	multifunctions	multifunction	NOUN
ejpam-5720	35	17	as	as	ADP
ejpam-5720	35	18	a	a	DET
ejpam-5720	35	19	generalization	generalization	NOUN
ejpam-5720	35	20	of	of	ADP
ejpam-5720	35	21	semi	semi	ADJ
ejpam-5720	35	22	-	-	ADJ
ejpam-5720	35	23	continuous	continuous	ADJ
ejpam-5720	35	24	multifunctions	multifunction	NOUN
ejpam-5720	35	25	and	and	CCONJ
ejpam-5720	35	26	n	n	CCONJ
ejpam-5720	35	27	-	-	PUNCT
ejpam-5720	35	28	continuous	continuous	ADJ
ejpam-5720	35	29	functions	function	NOUN
ejpam-5720	35	30	.	.	PUNCT
ejpam-5720	36	1	ekici	ekici	NOUN
ejpam-5720	37	1	[	[	X
ejpam-5720	37	2	37	37	NUM
ejpam-5720	37	3	]	]	PUNCT
ejpam-5720	37	4	introduced	introduce	VERB
ejpam-5720	37	5	and	and	CCONJ
ejpam-5720	37	6	investigated	investigate	VERB
ejpam-5720	37	7	the	the	DET
ejpam-5720	37	8	notion	notion	NOUN
ejpam-5720	37	9	of	of	ADP
ejpam-5720	37	10	almost	almost	ADV
ejpam-5720	37	11	nearly	nearly	ADV
ejpam-5720	37	12	continuous	continuous	ADJ
ejpam-5720	37	13	multifunctions	multifunction	NOUN
ejpam-5720	37	14	as	as	ADP
ejpam-5720	37	15	a	a	DET
ejpam-5720	37	16	generalization	generalization	NOUN
ejpam-5720	37	17	of	of	ADP
ejpam-5720	37	18	nearly	nearly	ADV
ejpam-5720	37	19	continuous	continuous	ADJ
ejpam-5720	37	20	multifunctions	multifunction	NOUN
ejpam-5720	37	21	and	and	CCONJ
ejpam-5720	37	22	almost	almost	ADV
ejpam-5720	37	23	continuous	continuous	ADJ
ejpam-5720	37	24	multifunctions	multifunction	NOUN
ejpam-5720	37	25	[	[	X
ejpam-5720	37	26	48	48	NUM
ejpam-5720	37	27	]	]	PUNCT
ejpam-5720	37	28	.	.	PUNCT
ejpam-5720	38	1	noiri	noiri	PROPN
ejpam-5720	38	2	and	and	CCONJ
ejpam-5720	38	3	popa	popa	NOUN
ejpam-5720	38	4	[	[	X
ejpam-5720	38	5	47	47	NUM
ejpam-5720	38	6	]	]	PUNCT
ejpam-5720	38	7	introduced	introduce	VERB
ejpam-5720	38	8	and	and	CCONJ
ejpam-5720	38	9	studied	study	VERB
ejpam-5720	38	10	the	the	DET
ejpam-5720	38	11	notion	notion	NOUN
ejpam-5720	38	12	of	of	ADP
ejpam-5720	38	13	almost	almost	ADV
ejpam-5720	38	14	nearly	nearly	ADV
ejpam-5720	38	15	m	m	ADJ
ejpam-5720	38	16	-	-	ADJ
ejpam-5720	38	17	continuous	continuous	ADJ
ejpam-5720	38	18	multifunctions	multifunction	NOUN
ejpam-5720	38	19	as	as	ADP
ejpam-5720	38	20	multifunctions	multifunction	NOUN
ejpam-5720	38	21	from	from	ADP
ejpam-5720	38	22	a	a	DET
ejpam-5720	38	23	set	set	NOUN
ejpam-5720	38	24	satisfying	satisfy	VERB
ejpam-5720	38	25	some	some	DET
ejpam-5720	38	26	minimal	minimal	ADJ
ejpam-5720	38	27	conditions	condition	NOUN
ejpam-5720	38	28	into	into	ADP
ejpam-5720	38	29	a	a	DET
ejpam-5720	38	30	topological	topological	ADJ
ejpam-5720	38	31	spaces	space	NOUN
ejpam-5720	38	32	.	.	PUNCT
ejpam-5720	39	1	carpintero	carpintero	NOUN
ejpam-5720	39	2	et	et	PROPN
ejpam-5720	39	3	al	al	PROPN
ejpam-5720	39	4	.	.	PUNCT
ejpam-5720	40	1	[	[	X
ejpam-5720	40	2	30	30	NUM
ejpam-5720	40	3	]	]	PUNCT
ejpam-5720	40	4	introduced	introduce	VERB
ejpam-5720	40	5	and	and	CCONJ
ejpam-5720	40	6	studied	study	VERB
ejpam-5720	40	7	the	the	DET
ejpam-5720	40	8	notion	notion	NOUN
ejpam-5720	40	9	of	of	ADP
ejpam-5720	40	10	nearly	nearly	ADV
ejpam-5720	40	11	ω	ω	ADJ
ejpam-5720	40	12	-	-	ADJ
ejpam-5720	40	13	continuous	continuous	ADJ
ejpam-5720	40	14	multifunctions	multifunction	NOUN
ejpam-5720	40	15	as	as	ADP
ejpam-5720	40	16	a	a	DET
ejpam-5720	40	17	weaker	weak	ADJ
ejpam-5720	40	18	form	form	NOUN
ejpam-5720	40	19	of	of	ADP
ejpam-5720	40	20	nearly	nearly	ADV
ejpam-5720	40	21	continuous	continuous	ADJ
ejpam-5720	40	22	multifunctions	multifunction	NOUN
ejpam-5720	40	23	.	.	PUNCT
ejpam-5720	41	1	rosas	rosa	NOUN
ejpam-5720	41	2	et	et	PROPN
ejpam-5720	41	3	al	al	PROPN
ejpam-5720	41	4	.	.	PUNCT
ejpam-5720	42	1	[	[	X
ejpam-5720	42	2	58	58	NUM
ejpam-5720	42	3	]	]	PUNCT
ejpam-5720	42	4	introduced	introduce	VERB
ejpam-5720	42	5	and	and	CCONJ
ejpam-5720	42	6	studied	study	VERB
ejpam-5720	42	7	upper	upper	ADJ
ejpam-5720	42	8	and	and	CCONJ
ejpam-5720	42	9	lower	low	ADJ
ejpam-5720	42	10	almost	almost	ADV
ejpam-5720	42	11	nearly	nearly	ADV
ejpam-5720	42	12	continuous	continuous	ADJ
ejpam-5720	42	13	multifunctions	multifunction	NOUN
ejpam-5720	42	14	using	use	VERB
ejpam-5720	42	15	notions	notion	NOUN
ejpam-5720	42	16	of	of	ADP
ejpam-5720	42	17	topological	topological	ADJ
ejpam-5720	42	18	ideals	ideal	NOUN
ejpam-5720	42	19	.	.	PUNCT
ejpam-5720	43	1	moreover	moreover	ADV
ejpam-5720	43	2	,	,	PUNCT
ejpam-5720	43	3	several	several	ADJ
ejpam-5720	43	4	characterizations	characterization	NOUN
ejpam-5720	43	5	of	of	ADP
ejpam-5720	43	6	(	(	PUNCT
ejpam-5720	43	7	τ1	τ1	NOUN
ejpam-5720	43	8	,	,	PUNCT
ejpam-5720	43	9	τ2)δ	τ2)δ	ADJ
ejpam-5720	43	10	-	-	PUNCT
ejpam-5720	43	11	semicontinuous	semicontinuous	ADJ
ejpam-5720	43	12	multifunctions	multifunction	NOUN
ejpam-5720	43	13	,	,	PUNCT
ejpam-5720	43	14	almost	almost	ADV
ejpam-5720	43	15	weakly	weakly	ADJ
ejpam-5720	43	16	(	(	PUNCT
ejpam-5720	43	17	τ1	τ1	NOUN
ejpam-5720	43	18	,	,	PUNCT
ejpam-5720	43	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	20	multifunctions	multifunction	NOUN
ejpam-5720	43	21	,	,	PUNCT
ejpam-5720	43	22	weakly	weakly	ADJ
ejpam-5720	43	23	quasi	quasi	NOUN
ejpam-5720	43	24	(	(	PUNCT
ejpam-5720	43	25	λ	λ	PROPN
ejpam-5720	43	26	,	,	PUNCT
ejpam-5720	43	27	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	28	multifunctions	multifunction	NOUN
ejpam-5720	43	29	,	,	PUNCT
ejpam-5720	43	30	⋆-continuous	⋆-continuous	ADJ
ejpam-5720	43	31	multifunctions	multifunction	NOUN
ejpam-5720	43	32	,	,	PUNCT
ejpam-5720	43	33	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-5720	43	34	multifunctions	multifunction	NOUN
ejpam-5720	43	35	,	,	PUNCT
ejpam-5720	43	36	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5720	43	37	multifunctions	multifunction	NOUN
ejpam-5720	43	38	,	,	PUNCT
ejpam-5720	43	39	almost	almost	ADV
ejpam-5720	43	40	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5720	43	41	multifunctions	multifunction	NOUN
ejpam-5720	43	42	,	,	PUNCT
ejpam-5720	43	43	almost	almost	ADV
ejpam-5720	43	44	quasi	quasi	VERB
ejpam-5720	43	45	⋆-continuous	⋆-continuous	ADJ
ejpam-5720	43	46	multifunctions	multifunction	NOUN
ejpam-5720	43	47	,	,	PUNCT
ejpam-5720	43	48	weakly	weakly	ADJ
ejpam-5720	43	49	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5720	43	50	multifunctions	multifunction	NOUN
ejpam-5720	43	51	,	,	PUNCT
ejpam-5720	43	52	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5720	43	53	multifunctions	multifunction	NOUN
ejpam-5720	43	54	,	,	PUNCT
ejpam-5720	43	55	weakly	weakly	ADJ
ejpam-5720	43	56	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5720	43	57	multifunctions	multifunction	NOUN
ejpam-5720	43	58	,	,	PUNCT
ejpam-5720	43	59	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-5720	43	60	continuous	continuous	ADJ
ejpam-5720	43	61	multifunctions	multifunction	NOUN
ejpam-5720	43	62	,	,	PUNCT
ejpam-5720	43	63	almost	almost	ADV
ejpam-5720	43	64	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5720	43	65	multifunctions	multifunction	NOUN
ejpam-5720	43	66	,	,	PUNCT
ejpam-5720	43	67	weakly	weakly	ADJ
ejpam-5720	43	68	(	(	PUNCT
ejpam-5720	43	69	λ	λ	NOUN
ejpam-5720	43	70	,	,	PUNCT
ejpam-5720	43	71	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	72	multifunctions	multifunction	NOUN
ejpam-5720	43	73	,	,	PUNCT
ejpam-5720	43	74	α(λ	α(λ	PROPN
ejpam-5720	43	75	,	,	PUNCT
ejpam-5720	43	76	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	77	multifunctions	multifunction	NOUN
ejpam-5720	43	78	,	,	PUNCT
ejpam-5720	43	79	almost	almost	ADV
ejpam-5720	43	80	α(λ	α(λ	PROPN
ejpam-5720	43	81	,	,	PUNCT
ejpam-5720	43	82	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	83	multifunctions	multifunction	NOUN
ejpam-5720	43	84	,	,	PUNCT
ejpam-5720	43	85	weakly	weakly	ADJ
ejpam-5720	43	86	α(λ	α(λ	PROPN
ejpam-5720	43	87	,	,	PUNCT
ejpam-5720	43	88	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	89	multifunctions	multifunction	NOUN
ejpam-5720	43	90	,	,	PUNCT
ejpam-5720	43	91	almost	almost	ADV
ejpam-5720	43	92	β(λ	β(λ	NOUN
ejpam-5720	43	93	,	,	PUNCT
ejpam-5720	43	94	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	95	multifunctions	multifunction	NOUN
ejpam-5720	43	96	,	,	PUNCT
ejpam-5720	43	97	slightly	slightly	ADV
ejpam-5720	43	98	(	(	PUNCT
ejpam-5720	43	99	λ	λ	NOUN
ejpam-5720	43	100	,	,	PUNCT
ejpam-5720	43	101	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	43	102	multifunctions	multifunction	NOUN
ejpam-5720	43	103	,	,	PUNCT
ejpam-5720	43	104	(	(	PUNCT
ejpam-5720	43	105	τ1	τ1	NOUN
ejpam-5720	43	106	,	,	PUNCT
ejpam-5720	43	107	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	108	multifunctions	multifunction	NOUN
ejpam-5720	43	109	,	,	PUNCT
ejpam-5720	43	110	almost	almost	ADV
ejpam-5720	43	111	(	(	PUNCT
ejpam-5720	43	112	τ1	τ1	NOUN
ejpam-5720	43	113	,	,	PUNCT
ejpam-5720	43	114	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	115	multifunctions	multifunction	NOUN
ejpam-5720	43	116	,	,	PUNCT
ejpam-5720	43	117	weakly	weakly	ADJ
ejpam-5720	43	118	(	(	PUNCT
ejpam-5720	43	119	τ1	τ1	NOUN
ejpam-5720	43	120	,	,	PUNCT
ejpam-5720	43	121	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	122	multifunctions	multifunction	NOUN
ejpam-5720	43	123	,	,	PUNCT
ejpam-5720	43	124	weakly	weakly	ADJ
ejpam-5720	43	125	quasi	quasi	NOUN
ejpam-5720	43	126	(	(	PUNCT
ejpam-5720	43	127	τ1	τ1	PROPN
ejpam-5720	43	128	,	,	PUNCT
ejpam-5720	43	129	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	130	multifunctions	multifunction	NOUN
ejpam-5720	43	131	,	,	PUNCT
ejpam-5720	43	132	almost	almost	ADV
ejpam-5720	43	133	quasi	quasi	NOUN
ejpam-5720	43	134	(	(	PUNCT
ejpam-5720	43	135	τ1	τ1	NOUN
ejpam-5720	43	136	,	,	PUNCT
ejpam-5720	43	137	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	138	multifunctions	multifunction	NOUN
ejpam-5720	43	139	,	,	PUNCT
ejpam-5720	43	140	c-(τ1	c-(τ1	PROPN
ejpam-5720	43	141	,	,	PUNCT
ejpam-5720	43	142	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	143	multifunctions	multifunction	NOUN
ejpam-5720	43	144	,	,	PUNCT
ejpam-5720	43	145	c	c	NOUN
ejpam-5720	43	146	-	-	PUNCT
ejpam-5720	43	147	quasi	quasi	NOUN
ejpam-5720	43	148	(	(	PUNCT
ejpam-5720	43	149	τ1	τ1	PROPN
ejpam-5720	43	150	,	,	PUNCT
ejpam-5720	43	151	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	152	multifunctions	multifunction	NOUN
ejpam-5720	43	153	,	,	PUNCT
ejpam-5720	43	154	s-(τ1	s-(τ1	PROPN
ejpam-5720	43	155	,	,	PUNCT
ejpam-5720	43	156	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5720	43	157	multifunctions	multifunction	NOUN
ejpam-5720	43	158	,	,	PUNCT
ejpam-5720	43	159	slightly	slightly	ADV
ejpam-5720	43	160	(	(	PUNCT
ejpam-5720	43	161	τ1	τ1	NOUN
ejpam-5720	43	162	,	,	PUNCT
ejpam-5720	43	163	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	43	164	multifunctions	multifunction	NOUN
ejpam-5720	43	165	and	and	CCONJ
ejpam-5720	43	166	slightly	slightly	ADV
ejpam-5720	43	167	(	(	PUNCT
ejpam-5720	43	168	τ1	τ1	NOUN
ejpam-5720	43	169	,	,	PUNCT
ejpam-5720	43	170	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5720	43	171	multifunctions	multifunction	NOUN
ejpam-5720	43	172	were	be	AUX
ejpam-5720	43	173	established	establish	VERB
ejpam-5720	43	174	in	in	ADP
ejpam-5720	43	175	[	[	X
ejpam-5720	43	176	5	5	NUM
ejpam-5720	43	177	]	]	PUNCT
ejpam-5720	43	178	,	,	PUNCT
ejpam-5720	43	179	[	[	X
ejpam-5720	43	180	28	28	NUM
ejpam-5720	43	181	]	]	PUNCT
ejpam-5720	43	182	,	,	PUNCT
ejpam-5720	43	183	[	[	X
ejpam-5720	43	184	69	69	NUM
ejpam-5720	43	185	]	]	PUNCT
ejpam-5720	43	186	,	,	PUNCT
ejpam-5720	43	187	[	[	X
ejpam-5720	43	188	3	3	NUM
ejpam-5720	43	189	]	]	PUNCT
ejpam-5720	43	190	,	,	PUNCT
ejpam-5720	43	191	[	[	X
ejpam-5720	43	192	7	7	NUM
ejpam-5720	43	193	]	]	PUNCT
ejpam-5720	43	194	,	,	PUNCT
ejpam-5720	43	195	[	[	X
ejpam-5720	43	196	17	17	NUM
ejpam-5720	43	197	]	]	PUNCT
ejpam-5720	43	198	,	,	PUNCT
ejpam-5720	43	199	[	[	X
ejpam-5720	43	200	24	24	NUM
ejpam-5720	43	201	]	]	PUNCT
ejpam-5720	43	202	,	,	PUNCT
ejpam-5720	43	203	[	[	X
ejpam-5720	43	204	6	6	NUM
ejpam-5720	43	205	]	]	PUNCT
ejpam-5720	43	206	,	,	PUNCT
ejpam-5720	43	207	[	[	X
ejpam-5720	43	208	21	21	NUM
ejpam-5720	43	209	]	]	PUNCT
ejpam-5720	43	210	,	,	PUNCT
ejpam-5720	43	211	[	[	X
ejpam-5720	43	212	20	20	NUM
ejpam-5720	43	213	]	]	PUNCT
ejpam-5720	43	214	,	,	PUNCT
ejpam-5720	43	215	[	[	X
ejpam-5720	43	216	15	15	NUM
ejpam-5720	43	217	]	]	PUNCT
ejpam-5720	43	218	,	,	PUNCT
ejpam-5720	43	219	[	[	X
ejpam-5720	43	220	9	9	NUM
ejpam-5720	43	221	]	]	PUNCT
ejpam-5720	43	222	,	,	PUNCT
ejpam-5720	43	223	[	[	X
ejpam-5720	43	224	19	19	NUM
ejpam-5720	43	225	]	]	PUNCT
ejpam-5720	43	226	,	,	PUNCT
ejpam-5720	43	227	[	[	X
ejpam-5720	43	228	22	22	NUM
ejpam-5720	43	229	]	]	PUNCT
ejpam-5720	43	230	,	,	PUNCT
ejpam-5720	43	231	[	[	X
ejpam-5720	43	232	38	38	NUM
ejpam-5720	43	233	]	]	PUNCT
ejpam-5720	43	234	,	,	PUNCT
ejpam-5720	43	235	[	[	X
ejpam-5720	43	236	13	13	NUM
ejpam-5720	43	237	]	]	PUNCT
ejpam-5720	43	238	,	,	PUNCT
ejpam-5720	43	239	[	[	X
ejpam-5720	43	240	27	27	NUM
ejpam-5720	43	241	]	]	PUNCT
ejpam-5720	43	242	,	,	PUNCT
ejpam-5720	43	243	[	[	X
ejpam-5720	43	244	62	62	NUM
ejpam-5720	43	245	]	]	PUNCT
ejpam-5720	43	246	,	,	PUNCT
ejpam-5720	43	247	[	[	X
ejpam-5720	43	248	14	14	NUM
ejpam-5720	43	249	]	]	PUNCT
ejpam-5720	43	250	,	,	PUNCT
ejpam-5720	43	251	[	[	X
ejpam-5720	43	252	55	55	NUM
ejpam-5720	43	253	]	]	PUNCT
ejpam-5720	43	254	,	,	PUNCT
ejpam-5720	43	255	[	[	X
ejpam-5720	43	256	40	40	NUM
ejpam-5720	43	257	]	]	PUNCT
ejpam-5720	43	258	,	,	PUNCT
ejpam-5720	43	259	[	[	X
ejpam-5720	43	260	65	65	NUM
ejpam-5720	43	261	]	]	PUNCT
ejpam-5720	43	262	,	,	PUNCT
ejpam-5720	43	263	[	[	X
ejpam-5720	43	264	56	56	NUM
ejpam-5720	43	265	]	]	PUNCT
ejpam-5720	43	266	,	,	PUNCT
ejpam-5720	43	267	[	[	X
ejpam-5720	43	268	54	54	NUM
ejpam-5720	43	269	]	]	PUNCT
ejpam-5720	43	270	,	,	PUNCT
ejpam-5720	43	271	[	[	X
ejpam-5720	43	272	39	39	NUM
ejpam-5720	43	273	]	]	PUNCT
ejpam-5720	43	274	,	,	PUNCT
ejpam-5720	43	275	[	[	X
ejpam-5720	43	276	53	53	NUM
ejpam-5720	43	277	]	]	PUNCT
ejpam-5720	43	278	,	,	PUNCT
ejpam-5720	43	279	[	[	X
ejpam-5720	43	280	73	73	NUM
ejpam-5720	43	281	]	]	PUNCT
ejpam-5720	43	282	,	,	PUNCT
ejpam-5720	43	283	[	[	X
ejpam-5720	43	284	70	70	NUM
ejpam-5720	43	285	]	]	PUNCT
ejpam-5720	43	286	and	and	CCONJ
ejpam-5720	43	287	[	[	X
ejpam-5720	43	288	71	71	NUM
ejpam-5720	43	289	]	]	PUNCT
ejpam-5720	43	290	,	,	PUNCT
ejpam-5720	43	291	respectively	respectively	ADV
ejpam-5720	43	292	.	.	PUNCT
ejpam-5720	44	1	rychlewicz	rychlewicz	PROPN
ejpam-5720	45	1	[	[	X
ejpam-5720	45	2	59	59	NUM
ejpam-5720	45	3	]	]	PUNCT
ejpam-5720	45	4	introduced	introduce	VERB
ejpam-5720	45	5	and	and	CCONJ
ejpam-5720	45	6	studied	study	VERB
ejpam-5720	45	7	the	the	DET
ejpam-5720	45	8	notion	notion	NOUN
ejpam-5720	45	9	of	of	ADP
ejpam-5720	45	10	nearly	nearly	ADV
ejpam-5720	45	11	quasicontinuous	quasicontinuous	ADJ
ejpam-5720	45	12	multifunctions	multifunction	NOUN
ejpam-5720	45	13	as	as	ADP
ejpam-5720	45	14	a	a	DET
ejpam-5720	45	15	generalization	generalization	NOUN
ejpam-5720	45	16	of	of	ADP
ejpam-5720	45	17	almost	almost	ADV
ejpam-5720	45	18	nearly	nearly	ADV
ejpam-5720	45	19	continuous	continuous	ADJ
ejpam-5720	45	20	multifunctions	multifunction	NOUN
ejpam-5720	45	21	and	and	CCONJ
ejpam-5720	45	22	almost	almost	ADV
ejpam-5720	45	23	quasi	quasi	VERB
ejpam-5720	45	24	continuous	continuous	ADJ
ejpam-5720	45	25	multifunctions	multifunction	NOUN
ejpam-5720	46	1	[	[	X
ejpam-5720	46	2	49	49	NUM
ejpam-5720	46	3	]	]	PUNCT
ejpam-5720	46	4	.	.	PUNCT
ejpam-5720	47	1	in	in	ADP
ejpam-5720	47	2	this	this	DET
ejpam-5720	47	3	paper	paper	NOUN
ejpam-5720	47	4	,	,	PUNCT
ejpam-5720	47	5	we	we	PRON
ejpam-5720	47	6	introduce	introduce	VERB
ejpam-5720	47	7	the	the	DET
ejpam-5720	47	8	concept	concept	NOUN
ejpam-5720	47	9	of	of	ADP
ejpam-5720	47	10	almost	almost	ADV
ejpam-5720	47	11	nearly	nearly	ADV
ejpam-5720	47	12	quasi	quasi	NOUN
ejpam-5720	47	13	(	(	PUNCT
ejpam-5720	47	14	τ1	τ1	NOUN
ejpam-5720	47	15	,	,	PUNCT
ejpam-5720	47	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	47	17	multifunctions	multifunction	NOUN
ejpam-5720	47	18	.	.	PUNCT
ejpam-5720	48	1	we	we	PRON
ejpam-5720	48	2	also	also	ADV
ejpam-5720	48	3	investigate	investigate	VERB
ejpam-5720	48	4	several	several	ADJ
ejpam-5720	48	5	characterizations	characterization	NOUN
ejpam-5720	48	6	of	of	ADP
ejpam-5720	48	7	almost	almost	ADV
ejpam-5720	48	8	quasi	quasi	NOUN
ejpam-5720	48	9	(	(	PUNCT
ejpam-5720	48	10	τ1	τ1	NOUN
ejpam-5720	48	11	,	,	PUNCT
ejpam-5720	48	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	48	13	multifunctions	multifunction	NOUN
ejpam-5720	48	14	.	.	PUNCT
ejpam-5720	49	1	j.	j.	PROPN
ejpam-5720	49	2	khampakdee	khampakdee	PROPN
ejpam-5720	49	3	,	,	PUNCT
ejpam-5720	49	4	a.	a.	PROPN
ejpam-5720	49	5	sama	sama	PROPN
ejpam-5720	49	6	-	-	PUNCT
ejpam-5720	49	7	ae	ae	PROPN
ejpam-5720	49	8	,	,	PUNCT
ejpam-5720	49	9	c.	c.	PROPN
ejpam-5720	49	10	boonpok	boonpok	PROPN
ejpam-5720	49	11	/	/	SYM
ejpam-5720	49	12	eur	eur	PROPN
ejpam-5720	49	13	.	.	PUNCT
ejpam-5720	50	1	j.	j.	PROPN
ejpam-5720	50	2	pure	pure	PROPN
ejpam-5720	50	3	appl	appl	PROPN
ejpam-5720	50	4	.	.	PROPN
ejpam-5720	50	5	math	math	PROPN
ejpam-5720	50	6	,	,	PUNCT
ejpam-5720	50	7	18	18	NUM
ejpam-5720	50	8	(	(	PUNCT
ejpam-5720	50	9	1	1	NUM
ejpam-5720	50	10	)	)	PUNCT
ejpam-5720	50	11	(	(	PUNCT
ejpam-5720	50	12	2025	2025	NUM
ejpam-5720	50	13	)	)	PUNCT
ejpam-5720	50	14	,	,	PUNCT
ejpam-5720	50	15	5720	5720	NUM
ejpam-5720	50	16	3	3	NUM
ejpam-5720	50	17	of	of	ADP
ejpam-5720	50	18	15	15	NUM
ejpam-5720	50	19	2	2	NUM
ejpam-5720	50	20	.	.	PUNCT
ejpam-5720	50	21	preliminaries	preliminary	NOUN
ejpam-5720	50	22	throughout	throughout	ADP
ejpam-5720	50	23	the	the	DET
ejpam-5720	50	24	present	present	ADJ
ejpam-5720	50	25	paper	paper	NOUN
ejpam-5720	50	26	,	,	PUNCT
ejpam-5720	50	27	spaces	space	NOUN
ejpam-5720	50	28	(	(	PUNCT
ejpam-5720	50	29	x	x	NOUN
ejpam-5720	50	30	,	,	PUNCT
ejpam-5720	50	31	τ1	τ1	NOUN
ejpam-5720	50	32	,	,	PUNCT
ejpam-5720	50	33	τ2	τ2	NOUN
ejpam-5720	50	34	)	)	PUNCT
ejpam-5720	50	35	and	and	CCONJ
ejpam-5720	50	36	(	(	PUNCT
ejpam-5720	50	37	y	y	PROPN
ejpam-5720	50	38	,	,	PUNCT
ejpam-5720	50	39	σ1	σ1	PROPN
ejpam-5720	50	40	,	,	PUNCT
ejpam-5720	50	41	σ2	σ2	NOUN
ejpam-5720	50	42	)	)	PUNCT
ejpam-5720	50	43	(	(	PUNCT
ejpam-5720	50	44	or	or	CCONJ
ejpam-5720	50	45	simply	simply	ADV
ejpam-5720	50	46	x	x	X
ejpam-5720	50	47	and	and	CCONJ
ejpam-5720	50	48	y	y	PROPN
ejpam-5720	50	49	)	)	PUNCT
ejpam-5720	50	50	always	always	ADV
ejpam-5720	50	51	mean	mean	VERB
ejpam-5720	50	52	bitopological	bitopological	ADJ
ejpam-5720	50	53	spaces	space	NOUN
ejpam-5720	50	54	on	on	ADP
ejpam-5720	50	55	which	which	PRON
ejpam-5720	50	56	no	no	DET
ejpam-5720	50	57	separation	separation	NOUN
ejpam-5720	50	58	axioms	axiom	NOUN
ejpam-5720	50	59	are	be	AUX
ejpam-5720	50	60	assumed	assume	VERB
ejpam-5720	50	61	unless	unless	SCONJ
ejpam-5720	50	62	explicitly	explicitly	ADV
ejpam-5720	50	63	stated	state	VERB
ejpam-5720	50	64	.	.	PUNCT
ejpam-5720	51	1	let	let	VERB
ejpam-5720	51	2	a	a	DET
ejpam-5720	51	3	be	be	AUX
ejpam-5720	51	4	a	a	DET
ejpam-5720	51	5	subset	subset	NOUN
ejpam-5720	51	6	of	of	ADP
ejpam-5720	51	7	a	a	DET
ejpam-5720	51	8	bitopological	bitopological	ADJ
ejpam-5720	51	9	space	space	NOUN
ejpam-5720	51	10	(	(	PUNCT
ejpam-5720	51	11	x	x	NOUN
ejpam-5720	51	12	,	,	PUNCT
ejpam-5720	51	13	τ1	τ1	NOUN
ejpam-5720	51	14	,	,	PUNCT
ejpam-5720	51	15	τ2	τ2	NOUN
ejpam-5720	51	16	)	)	PUNCT
ejpam-5720	51	17	.	.	PUNCT
ejpam-5720	52	1	the	the	DET
ejpam-5720	52	2	closure	closure	NOUN
ejpam-5720	52	3	of	of	ADP
ejpam-5720	52	4	a	a	PRON
ejpam-5720	52	5	and	and	CCONJ
ejpam-5720	52	6	the	the	DET
ejpam-5720	52	7	interior	interior	NOUN
ejpam-5720	52	8	of	of	ADP
ejpam-5720	52	9	a	a	PRON
ejpam-5720	52	10	with	with	ADP
ejpam-5720	52	11	respect	respect	NOUN
ejpam-5720	52	12	to	to	ADP
ejpam-5720	52	13	τi	τi	PROPN
ejpam-5720	52	14	are	be	AUX
ejpam-5720	52	15	denoted	denote	VERB
ejpam-5720	52	16	by	by	ADP
ejpam-5720	52	17	τi	τi	NOUN
ejpam-5720	52	18	-	-	PUNCT
ejpam-5720	52	19	cl(a	cl(a	NUM
ejpam-5720	52	20	)	)	PUNCT
ejpam-5720	52	21	and	and	CCONJ
ejpam-5720	52	22	τi	τi	NOUN
ejpam-5720	52	23	-	-	PUNCT
ejpam-5720	52	24	int(a	int(a	NOUN
ejpam-5720	52	25	)	)	PUNCT
ejpam-5720	52	26	,	,	PUNCT
ejpam-5720	52	27	respectively	respectively	ADV
ejpam-5720	52	28	,	,	PUNCT
ejpam-5720	52	29	for	for	ADP
ejpam-5720	52	30	i	i	PROPN
ejpam-5720	52	31	=	=	SYM
ejpam-5720	52	32	1	1	NUM
ejpam-5720	52	33	,	,	PUNCT
ejpam-5720	52	34	2	2	NUM
ejpam-5720	52	35	.	.	X
ejpam-5720	52	36	a	a	DET
ejpam-5720	52	37	subset	subset	NOUN
ejpam-5720	52	38	a	a	PRON
ejpam-5720	52	39	of	of	ADP
ejpam-5720	52	40	a	a	DET
ejpam-5720	52	41	bitopological	bitopological	ADJ
ejpam-5720	52	42	space	space	NOUN
ejpam-5720	52	43	(	(	PUNCT
ejpam-5720	52	44	x	x	NOUN
ejpam-5720	52	45	,	,	PUNCT
ejpam-5720	52	46	τ1	τ1	NOUN
ejpam-5720	52	47	,	,	PUNCT
ejpam-5720	52	48	τ2	τ2	NOUN
ejpam-5720	52	49	)	)	PUNCT
ejpam-5720	52	50	is	be	AUX
ejpam-5720	52	51	called	call	VERB
ejpam-5720	52	52	τ1τ2	τ1τ2	VERB
ejpam-5720	52	53	-	-	ADJ
ejpam-5720	52	54	closed	closed	ADJ
ejpam-5720	52	55	[	[	X
ejpam-5720	52	56	29	29	NUM
ejpam-5720	52	57	]	]	X
ejpam-5720	52	58	if	if	SCONJ
ejpam-5720	52	59	a	a	DET
ejpam-5720	52	60	=	=	NOUN
ejpam-5720	52	61	τ1	τ1	NOUN
ejpam-5720	52	62	-	-	PUNCT
ejpam-5720	52	63	cl(τ2	cl(τ2	NOUN
ejpam-5720	52	64	-	-	PUNCT
ejpam-5720	52	65	cl(a	cl(a	NUM
ejpam-5720	52	66	)	)	PUNCT
ejpam-5720	52	67	)	)	PUNCT
ejpam-5720	52	68	.	.	PUNCT
ejpam-5720	53	1	the	the	DET
ejpam-5720	53	2	complement	complement	NOUN
ejpam-5720	53	3	of	of	ADP
ejpam-5720	53	4	a	a	DET
ejpam-5720	53	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	53	6	-	-	ADJ
ejpam-5720	53	7	closed	closed	ADJ
ejpam-5720	53	8	set	set	NOUN
ejpam-5720	53	9	is	be	AUX
ejpam-5720	53	10	called	call	VERB
ejpam-5720	53	11	τ1τ2	τ1τ2	NOUN
ejpam-5720	53	12	-	-	ADJ
ejpam-5720	53	13	open	open	ADJ
ejpam-5720	53	14	.	.	PUNCT
ejpam-5720	54	1	let	let	VERB
ejpam-5720	54	2	a	a	DET
ejpam-5720	54	3	be	be	AUX
ejpam-5720	54	4	a	a	DET
ejpam-5720	54	5	subset	subset	NOUN
ejpam-5720	54	6	of	of	ADP
ejpam-5720	54	7	a	a	DET
ejpam-5720	54	8	bitopological	bitopological	ADJ
ejpam-5720	54	9	space	space	NOUN
ejpam-5720	54	10	(	(	PUNCT
ejpam-5720	54	11	x	x	NOUN
ejpam-5720	54	12	,	,	PUNCT
ejpam-5720	54	13	τ1	τ1	NOUN
ejpam-5720	54	14	,	,	PUNCT
ejpam-5720	54	15	τ2	τ2	NOUN
ejpam-5720	54	16	)	)	PUNCT
ejpam-5720	54	17	.	.	PUNCT
ejpam-5720	55	1	the	the	DET
ejpam-5720	55	2	intersection	intersection	NOUN
ejpam-5720	55	3	of	of	ADP
ejpam-5720	55	4	all	all	DET
ejpam-5720	55	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	55	6	-	-	ADJ
ejpam-5720	55	7	closed	closed	ADJ
ejpam-5720	55	8	sets	set	NOUN
ejpam-5720	55	9	of	of	ADP
ejpam-5720	55	10	x	x	PUNCT
ejpam-5720	55	11	containing	contain	VERB
ejpam-5720	55	12	a	a	PRON
ejpam-5720	55	13	is	be	AUX
ejpam-5720	55	14	called	call	VERB
ejpam-5720	55	15	the	the	DET
ejpam-5720	55	16	τ1τ2	τ1τ2	NOUN
ejpam-5720	55	17	-	-	NOUN
ejpam-5720	55	18	closure	closure	NOUN
ejpam-5720	55	19	[	[	X
ejpam-5720	55	20	29	29	NUM
ejpam-5720	55	21	]	]	PUNCT
ejpam-5720	55	22	of	of	ADP
ejpam-5720	55	23	a	a	PRON
ejpam-5720	55	24	and	and	CCONJ
ejpam-5720	55	25	is	be	AUX
ejpam-5720	55	26	denoted	denote	VERB
ejpam-5720	55	27	by	by	ADP
ejpam-5720	55	28	τ1τ2	τ1τ2	NOUN
ejpam-5720	55	29	-	-	NUM
ejpam-5720	55	30	cl(a	cl(a	NUM
ejpam-5720	55	31	)	)	PUNCT
ejpam-5720	55	32	.	.	PUNCT
ejpam-5720	56	1	the	the	DET
ejpam-5720	56	2	union	union	NOUN
ejpam-5720	56	3	of	of	ADP
ejpam-5720	56	4	all	all	DET
ejpam-5720	56	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	56	6	-	-	ADJ
ejpam-5720	56	7	open	open	ADJ
ejpam-5720	56	8	sets	set	NOUN
ejpam-5720	56	9	of	of	ADP
ejpam-5720	56	10	x	x	PUNCT
ejpam-5720	56	11	contained	contain	VERB
ejpam-5720	56	12	in	in	ADP
ejpam-5720	56	13	a	a	PRON
ejpam-5720	56	14	is	be	AUX
ejpam-5720	56	15	called	call	VERB
ejpam-5720	56	16	the	the	DET
ejpam-5720	56	17	τ1τ2	τ1τ2	NOUN
ejpam-5720	56	18	-	-	ADJ
ejpam-5720	56	19	interior	interior	ADJ
ejpam-5720	56	20	[	[	X
ejpam-5720	56	21	29	29	NUM
ejpam-5720	56	22	]	]	PUNCT
ejpam-5720	56	23	of	of	ADP
ejpam-5720	56	24	a	a	PRON
ejpam-5720	56	25	and	and	CCONJ
ejpam-5720	56	26	is	be	AUX
ejpam-5720	56	27	denoted	denote	VERB
ejpam-5720	56	28	by	by	ADP
ejpam-5720	56	29	τ1τ2	τ1τ2	NOUN
ejpam-5720	56	30	-	-	ADJ
ejpam-5720	56	31	int(a	int(a	NOUN
ejpam-5720	56	32	)	)	PUNCT
ejpam-5720	56	33	.	.	PUNCT
ejpam-5720	57	1	lemma	lemma	PROPN
ejpam-5720	57	2	1	1	NUM
ejpam-5720	57	3	.	.	PUNCT
ejpam-5720	58	1	[	[	X
ejpam-5720	58	2	29	29	NUM
ejpam-5720	58	3	]	]	PUNCT
ejpam-5720	58	4	let	let	VERB
ejpam-5720	58	5	a	a	PRON
ejpam-5720	58	6	and	and	CCONJ
ejpam-5720	58	7	b	b	NOUN
ejpam-5720	58	8	be	be	AUX
ejpam-5720	58	9	subsets	subset	NOUN
ejpam-5720	58	10	of	of	ADP
ejpam-5720	58	11	a	a	DET
ejpam-5720	58	12	bitopological	bitopological	ADJ
ejpam-5720	58	13	space	space	NOUN
ejpam-5720	58	14	(	(	PUNCT
ejpam-5720	58	15	x	x	NOUN
ejpam-5720	58	16	,	,	PUNCT
ejpam-5720	58	17	τ1	τ1	NOUN
ejpam-5720	58	18	,	,	PUNCT
ejpam-5720	58	19	τ2	τ2	NOUN
ejpam-5720	58	20	)	)	PUNCT
ejpam-5720	58	21	.	.	PUNCT
ejpam-5720	59	1	for	for	ADP
ejpam-5720	59	2	the	the	DET
ejpam-5720	59	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5720	59	4	,	,	PUNCT
ejpam-5720	59	5	the	the	DET
ejpam-5720	59	6	following	follow	VERB
ejpam-5720	59	7	properties	property	NOUN
ejpam-5720	59	8	hold	hold	VERB
ejpam-5720	59	9	:	:	PUNCT
ejpam-5720	59	10	(	(	PUNCT
ejpam-5720	59	11	1	1	X
ejpam-5720	59	12	)	)	PUNCT
ejpam-5720	59	13	a	a	DET
ejpam-5720	59	14	⊆	⊆	NUM
ejpam-5720	59	15	τ1τ2	τ1τ2	NOUN
ejpam-5720	59	16	-	-	NUM
ejpam-5720	59	17	cl(a	cl(a	NUM
ejpam-5720	59	18	)	)	PUNCT
ejpam-5720	59	19	and	and	CCONJ
ejpam-5720	59	20	τ1τ2	τ1τ2	NOUN
ejpam-5720	59	21	-	-	ADJ
ejpam-5720	59	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	59	23	-	-	PUNCT
ejpam-5720	59	24	cl(a	cl(a	NUM
ejpam-5720	59	25	)	)	PUNCT
ejpam-5720	59	26	)	)	PUNCT
ejpam-5720	60	1	=	=	PUNCT
ejpam-5720	60	2	τ1τ2	τ1τ2	NOUN
ejpam-5720	60	3	-	-	NUM
ejpam-5720	60	4	cl(a	cl(a	NUM
ejpam-5720	60	5	)	)	PUNCT
ejpam-5720	60	6	.	.	PUNCT
ejpam-5720	61	1	(	(	PUNCT
ejpam-5720	61	2	2	2	X
ejpam-5720	61	3	)	)	PUNCT
ejpam-5720	61	4	if	if	SCONJ
ejpam-5720	61	5	a	a	DET
ejpam-5720	61	6	⊆	⊆	NUM
ejpam-5720	61	7	b	b	NOUN
ejpam-5720	61	8	,	,	PUNCT
ejpam-5720	61	9	then	then	ADV
ejpam-5720	61	10	τ1τ2	τ1τ2	NOUN
ejpam-5720	61	11	-	-	NUM
ejpam-5720	61	12	cl(a	cl(a	NUM
ejpam-5720	61	13	)	)	PUNCT
ejpam-5720	61	14	⊆	⊆	NUM
ejpam-5720	61	15	τ1τ2	τ1τ2	NOUN
ejpam-5720	61	16	-	-	NOUN
ejpam-5720	61	17	cl(b	cl(b	NOUN
ejpam-5720	61	18	)	)	PUNCT
ejpam-5720	61	19	.	.	PUNCT
ejpam-5720	62	1	(	(	PUNCT
ejpam-5720	62	2	3	3	X
ejpam-5720	62	3	)	)	PUNCT
ejpam-5720	62	4	τ1τ2	τ1τ2	NOUN
ejpam-5720	62	5	-	-	NUM
ejpam-5720	62	6	cl(a	cl(a	NUM
ejpam-5720	62	7	)	)	PUNCT
ejpam-5720	62	8	is	be	AUX
ejpam-5720	62	9	τ1τ2	τ1τ2	NOUN
ejpam-5720	62	10	-	-	ADJ
ejpam-5720	62	11	closed	closed	ADJ
ejpam-5720	62	12	.	.	PUNCT
ejpam-5720	63	1	(	(	PUNCT
ejpam-5720	63	2	4	4	X
ejpam-5720	63	3	)	)	PUNCT
ejpam-5720	63	4	a	a	PRON
ejpam-5720	63	5	is	be	AUX
ejpam-5720	63	6	τ1τ2	τ1τ2	NOUN
ejpam-5720	63	7	-	-	ADJ
ejpam-5720	63	8	closed	closed	ADJ
ejpam-5720	63	9	if	if	SCONJ
ejpam-5720	63	10	and	and	CCONJ
ejpam-5720	63	11	only	only	ADV
ejpam-5720	63	12	if	if	SCONJ
ejpam-5720	63	13	a	a	DET
ejpam-5720	63	14	=	=	PUNCT
ejpam-5720	63	15	τ1τ2	τ1τ2	NOUN
ejpam-5720	63	16	-	-	NUM
ejpam-5720	63	17	cl(a	cl(a	NUM
ejpam-5720	63	18	)	)	PUNCT
ejpam-5720	63	19	.	.	PUNCT
ejpam-5720	64	1	(	(	PUNCT
ejpam-5720	64	2	5	5	X
ejpam-5720	64	3	)	)	PUNCT
ejpam-5720	64	4	τ1τ2	τ1τ2	NOUN
ejpam-5720	64	5	-	-	NOUN
ejpam-5720	64	6	cl(x	cl(x	X
ejpam-5720	64	7	−a	−a	NOUN
ejpam-5720	64	8	)	)	PUNCT
ejpam-5720	65	1	=	=	PUNCT
ejpam-5720	65	2	x	x	X
ejpam-5720	66	1	−	−	ADP
ejpam-5720	66	2	τ1τ2	τ1τ2	NOUN
ejpam-5720	66	3	-	-	PUNCT
ejpam-5720	66	4	int(a	int(a	NOUN
ejpam-5720	66	5	)	)	PUNCT
ejpam-5720	66	6	.	.	PUNCT
ejpam-5720	67	1	a	a	DET
ejpam-5720	67	2	subset	subset	NOUN
ejpam-5720	67	3	a	a	PRON
ejpam-5720	67	4	of	of	ADP
ejpam-5720	67	5	a	a	DET
ejpam-5720	67	6	bitopological	bitopological	ADJ
ejpam-5720	67	7	space	space	NOUN
ejpam-5720	67	8	(	(	PUNCT
ejpam-5720	67	9	x	x	NOUN
ejpam-5720	67	10	,	,	PUNCT
ejpam-5720	67	11	τ1	τ1	NOUN
ejpam-5720	67	12	,	,	PUNCT
ejpam-5720	67	13	τ2	τ2	NOUN
ejpam-5720	67	14	)	)	PUNCT
ejpam-5720	67	15	is	be	AUX
ejpam-5720	67	16	said	say	VERB
ejpam-5720	67	17	to	to	PART
ejpam-5720	67	18	be	be	AUX
ejpam-5720	67	19	τ1τ2	τ1τ2	NOUN
ejpam-5720	67	20	-	-	ADJ
ejpam-5720	67	21	clopen	clopen	ADJ
ejpam-5720	67	22	[	[	X
ejpam-5720	67	23	29	29	NUM
ejpam-5720	67	24	]	]	X
ejpam-5720	67	25	if	if	SCONJ
ejpam-5720	67	26	a	a	PRON
ejpam-5720	67	27	is	be	AUX
ejpam-5720	67	28	both	both	PRON
ejpam-5720	67	29	τ1τ2	τ1τ2	ADJ
ejpam-5720	67	30	-	-	ADJ
ejpam-5720	67	31	open	open	ADJ
ejpam-5720	67	32	and	and	CCONJ
ejpam-5720	67	33	τ1τ2	τ1τ2	NOUN
ejpam-5720	67	34	-	-	ADJ
ejpam-5720	67	35	closed	closed	ADJ
ejpam-5720	67	36	.	.	PUNCT
ejpam-5720	68	1	a	a	DET
ejpam-5720	68	2	subset	subset	NOUN
ejpam-5720	68	3	a	a	PRON
ejpam-5720	68	4	of	of	ADP
ejpam-5720	68	5	a	a	DET
ejpam-5720	68	6	bitopological	bitopological	ADJ
ejpam-5720	68	7	space	space	NOUN
ejpam-5720	68	8	(	(	PUNCT
ejpam-5720	68	9	x	x	NOUN
ejpam-5720	68	10	,	,	PUNCT
ejpam-5720	68	11	τ1	τ1	NOUN
ejpam-5720	68	12	,	,	PUNCT
ejpam-5720	68	13	τ2	τ2	NOUN
ejpam-5720	68	14	)	)	PUNCT
ejpam-5720	68	15	is	be	AUX
ejpam-5720	68	16	said	say	VERB
ejpam-5720	68	17	to	to	PART
ejpam-5720	68	18	be	be	AUX
ejpam-5720	68	19	(	(	PUNCT
ejpam-5720	68	20	τ1	τ1	NOUN
ejpam-5720	68	21	,	,	PUNCT
ejpam-5720	68	22	τ2)r	τ2)r	NOUN
ejpam-5720	68	23	-	-	PUNCT
ejpam-5720	68	24	open	open	NOUN
ejpam-5720	69	1	[	[	X
ejpam-5720	69	2	67	67	NUM
ejpam-5720	69	3	]	]	X
ejpam-5720	69	4	(	(	PUNCT
ejpam-5720	69	5	resp	resp	NOUN
ejpam-5720	69	6	.	.	PUNCT
ejpam-5720	70	1	(	(	PUNCT
ejpam-5720	70	2	τ1	τ1	NOUN
ejpam-5720	70	3	,	,	PUNCT
ejpam-5720	70	4	τ2)s	τ2)s	NOUN
ejpam-5720	70	5	-	-	PUNCT
ejpam-5720	70	6	open	open	ADJ
ejpam-5720	70	7	[	[	X
ejpam-5720	70	8	5	5	NUM
ejpam-5720	70	9	]	]	PUNCT
ejpam-5720	70	10	,	,	PUNCT
ejpam-5720	70	11	(	(	PUNCT
ejpam-5720	70	12	τ1	τ1	NOUN
ejpam-5720	70	13	,	,	PUNCT
ejpam-5720	70	14	τ2)p	τ2)p	NOUN
ejpam-5720	70	15	-	-	ADJ
ejpam-5720	70	16	open	open	ADJ
ejpam-5720	70	17	[	[	X
ejpam-5720	70	18	5	5	NUM
ejpam-5720	70	19	]	]	PUNCT
ejpam-5720	70	20	,	,	PUNCT
ejpam-5720	70	21	(	(	PUNCT
ejpam-5720	70	22	τ1	τ1	NOUN
ejpam-5720	70	23	,	,	PUNCT
ejpam-5720	70	24	τ2)β	τ2)β	ADJ
ejpam-5720	70	25	-	-	PUNCT
ejpam-5720	70	26	open	open	ADJ
ejpam-5720	70	27	[	[	X
ejpam-5720	70	28	5	5	NUM
ejpam-5720	70	29	]	]	PUNCT
ejpam-5720	70	30	)	)	PUNCT
ejpam-5720	70	31	if	if	SCONJ
ejpam-5720	70	32	a	a	DET
ejpam-5720	70	33	=	=	PUNCT
ejpam-5720	70	34	τ1τ2	τ1τ2	NOUN
ejpam-5720	70	35	-	-	NOUN
ejpam-5720	70	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	70	37	-	-	PUNCT
ejpam-5720	70	38	cl(a	cl(a	NUM
ejpam-5720	70	39	)	)	PUNCT
ejpam-5720	70	40	)	)	PUNCT
ejpam-5720	70	41	(	(	PUNCT
ejpam-5720	70	42	resp	resp	NOUN
ejpam-5720	70	43	.	.	PUNCT
ejpam-5720	71	1	a	a	DET
ejpam-5720	71	2	⊆	⊆	NUM
ejpam-5720	71	3	τ1τ2	τ1τ2	NOUN
ejpam-5720	71	4	-	-	ADJ
ejpam-5720	71	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	71	6	-	-	PUNCT
ejpam-5720	71	7	int(a	int(a	NOUN
ejpam-5720	71	8	)	)	PUNCT
ejpam-5720	71	9	)	)	PUNCT
ejpam-5720	71	10	,	,	PUNCT
ejpam-5720	71	11	a	a	DET
ejpam-5720	71	12	⊆	⊆	NUM
ejpam-5720	71	13	τ1τ2	τ1τ2	NOUN
ejpam-5720	71	14	-	-	NOUN
ejpam-5720	71	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	71	16	-	-	PUNCT
ejpam-5720	71	17	cl(a	cl(a	NUM
ejpam-5720	71	18	)	)	PUNCT
ejpam-5720	71	19	)	)	PUNCT
ejpam-5720	71	20	,	,	PUNCT
ejpam-5720	71	21	a	a	DET
ejpam-5720	71	22	⊆	⊆	NUM
ejpam-5720	71	23	τ1τ2	τ1τ2	NOUN
ejpam-5720	71	24	-	-	PUNCT
ejpam-5720	71	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	71	26	-	-	PUNCT
ejpam-5720	71	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	71	28	-	-	PUNCT
ejpam-5720	71	29	cl(a	cl(a	NUM
ejpam-5720	71	30	)	)	PUNCT
ejpam-5720	71	31	)	)	PUNCT
ejpam-5720	71	32	)	)	PUNCT
ejpam-5720	71	33	)	)	PUNCT
ejpam-5720	71	34	.	.	PUNCT
ejpam-5720	72	1	the	the	DET
ejpam-5720	72	2	complement	complement	NOUN
ejpam-5720	72	3	of	of	ADP
ejpam-5720	72	4	a	a	DET
ejpam-5720	72	5	(	(	PUNCT
ejpam-5720	72	6	τ1	τ1	NOUN
ejpam-5720	72	7	,	,	PUNCT
ejpam-5720	72	8	τ2)r	τ2)r	NOUN
ejpam-5720	72	9	-	-	PUNCT
ejpam-5720	72	10	open	open	ADJ
ejpam-5720	72	11	(	(	PUNCT
ejpam-5720	72	12	resp	resp	NOUN
ejpam-5720	72	13	.	.	PUNCT
ejpam-5720	73	1	(	(	PUNCT
ejpam-5720	73	2	τ1	τ1	NOUN
ejpam-5720	73	3	,	,	PUNCT
ejpam-5720	73	4	τ2)s	τ2)s	NOUN
ejpam-5720	73	5	-	-	PUNCT
ejpam-5720	73	6	open	open	ADJ
ejpam-5720	73	7	,	,	PUNCT
ejpam-5720	73	8	(	(	PUNCT
ejpam-5720	73	9	τ1	τ1	NOUN
ejpam-5720	73	10	,	,	PUNCT
ejpam-5720	73	11	τ2)p	τ2)p	NOUN
ejpam-5720	73	12	-	-	ADJ
ejpam-5720	73	13	open	open	ADJ
ejpam-5720	73	14	,	,	PUNCT
ejpam-5720	73	15	(	(	PUNCT
ejpam-5720	73	16	τ1	τ1	NOUN
ejpam-5720	73	17	,	,	PUNCT
ejpam-5720	73	18	τ2)β	τ2)β	ADJ
ejpam-5720	73	19	-	-	PUNCT
ejpam-5720	73	20	open	open	ADJ
ejpam-5720	73	21	)	)	PUNCT
ejpam-5720	73	22	set	set	NOUN
ejpam-5720	73	23	is	be	AUX
ejpam-5720	73	24	called	call	VERB
ejpam-5720	73	25	(	(	PUNCT
ejpam-5720	73	26	τ1	τ1	NOUN
ejpam-5720	73	27	,	,	PUNCT
ejpam-5720	73	28	τ2)r	τ2)r	NOUN
ejpam-5720	73	29	-	-	PUNCT
ejpam-5720	73	30	closed	closed	ADJ
ejpam-5720	73	31	(	(	PUNCT
ejpam-5720	73	32	resp	resp	NOUN
ejpam-5720	73	33	.	.	PUNCT
ejpam-5720	74	1	(	(	PUNCT
ejpam-5720	74	2	τ1	τ1	NOUN
ejpam-5720	74	3	,	,	PUNCT
ejpam-5720	74	4	τ2)s	τ2)s	NOUN
ejpam-5720	74	5	-	-	PUNCT
ejpam-5720	74	6	closed	closed	ADJ
ejpam-5720	74	7	,	,	PUNCT
ejpam-5720	74	8	(	(	PUNCT
ejpam-5720	74	9	τ1	τ1	NOUN
ejpam-5720	74	10	,	,	PUNCT
ejpam-5720	74	11	τ2)pclosed	τ2)pclose	VERB
ejpam-5720	74	12	,	,	PUNCT
ejpam-5720	74	13	(	(	PUNCT
ejpam-5720	74	14	τ1	τ1	NOUN
ejpam-5720	74	15	,	,	PUNCT
ejpam-5720	74	16	τ2)β	τ2)β	ADJ
ejpam-5720	74	17	-	-	PUNCT
ejpam-5720	74	18	closed	closed	ADJ
ejpam-5720	74	19	)	)	PUNCT
ejpam-5720	74	20	.	.	PUNCT
ejpam-5720	75	1	a	a	DET
ejpam-5720	75	2	subset	subset	NOUN
ejpam-5720	75	3	a	a	PRON
ejpam-5720	75	4	of	of	ADP
ejpam-5720	75	5	a	a	DET
ejpam-5720	75	6	bitopological	bitopological	ADJ
ejpam-5720	75	7	space	space	NOUN
ejpam-5720	75	8	(	(	PUNCT
ejpam-5720	75	9	x	x	NOUN
ejpam-5720	75	10	,	,	PUNCT
ejpam-5720	75	11	τ1	τ1	NOUN
ejpam-5720	75	12	,	,	PUNCT
ejpam-5720	75	13	τ2	τ2	NOUN
ejpam-5720	75	14	)	)	PUNCT
ejpam-5720	75	15	is	be	AUX
ejpam-5720	75	16	said	say	VERB
ejpam-5720	75	17	to	to	PART
ejpam-5720	75	18	be	be	AUX
ejpam-5720	75	19	α(τ1	α(τ1	NOUN
ejpam-5720	75	20	,	,	PUNCT
ejpam-5720	75	21	τ2)-open	τ2)-open	ADJ
ejpam-5720	75	22	[	[	X
ejpam-5720	75	23	72	72	NUM
ejpam-5720	75	24	]	]	X
ejpam-5720	75	25	if	if	SCONJ
ejpam-5720	75	26	a	a	DET
ejpam-5720	75	27	⊆	⊆	NUM
ejpam-5720	75	28	τ1τ2	τ1τ2	NOUN
ejpam-5720	75	29	-	-	PUNCT
ejpam-5720	75	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	75	31	-	-	PUNCT
ejpam-5720	75	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	75	33	-	-	PUNCT
ejpam-5720	75	34	int(a	int(a	NOUN
ejpam-5720	75	35	)	)	PUNCT
ejpam-5720	75	36	)	)	PUNCT
ejpam-5720	75	37	)	)	PUNCT
ejpam-5720	75	38	.	.	PUNCT
ejpam-5720	76	1	the	the	DET
ejpam-5720	76	2	complement	complement	NOUN
ejpam-5720	76	3	of	of	ADP
ejpam-5720	76	4	an	an	DET
ejpam-5720	76	5	α(τ1	α(τ1	NOUN
ejpam-5720	76	6	,	,	PUNCT
ejpam-5720	76	7	τ2)open	τ2)open	PROPN
ejpam-5720	76	8	set	set	NOUN
ejpam-5720	76	9	is	be	AUX
ejpam-5720	76	10	said	say	VERB
ejpam-5720	76	11	to	to	PART
ejpam-5720	76	12	be	be	AUX
ejpam-5720	76	13	α(τ1	α(τ1	NOUN
ejpam-5720	76	14	,	,	PUNCT
ejpam-5720	76	15	τ2)-closed	τ2)-closed	ADJ
ejpam-5720	76	16	.	.	PUNCT
ejpam-5720	77	1	a	a	DET
ejpam-5720	77	2	subset	subset	NOUN
ejpam-5720	77	3	a	a	PRON
ejpam-5720	77	4	of	of	ADP
ejpam-5720	77	5	a	a	DET
ejpam-5720	77	6	bitopological	bitopological	ADJ
ejpam-5720	77	7	space	space	NOUN
ejpam-5720	77	8	(	(	PUNCT
ejpam-5720	77	9	x	x	NOUN
ejpam-5720	77	10	,	,	PUNCT
ejpam-5720	77	11	τ1	τ1	NOUN
ejpam-5720	77	12	,	,	PUNCT
ejpam-5720	77	13	τ2	τ2	NOUN
ejpam-5720	77	14	)	)	PUNCT
ejpam-5720	77	15	is	be	AUX
ejpam-5720	77	16	said	say	VERB
ejpam-5720	77	17	to	to	PART
ejpam-5720	77	18	be	be	AUX
ejpam-5720	77	19	n	n	PRON
ejpam-5720	77	20	(	(	PUNCT
ejpam-5720	77	21	τ1	τ1	PROPN
ejpam-5720	77	22	,	,	PUNCT
ejpam-5720	77	23	τ2)-closed	τ2)-close	VERB
ejpam-5720	78	1	[	[	X
ejpam-5720	78	2	64	64	NUM
ejpam-5720	78	3	]	]	PUNCT
ejpam-5720	78	4	if	if	SCONJ
ejpam-5720	78	5	every	every	DET
ejpam-5720	78	6	cover	cover	NOUN
ejpam-5720	78	7	of	of	ADP
ejpam-5720	78	8	a	a	DET
ejpam-5720	78	9	by	by	ADP
ejpam-5720	78	10	(	(	PUNCT
ejpam-5720	78	11	τ1	τ1	NOUN
ejpam-5720	78	12	,	,	PUNCT
ejpam-5720	78	13	τ2)r	τ2)r	ADJ
ejpam-5720	78	14	-	-	PUNCT
ejpam-5720	78	15	open	open	ADJ
ejpam-5720	78	16	sets	set	NOUN
ejpam-5720	78	17	of	of	ADP
ejpam-5720	78	18	x	x	PUNCT
ejpam-5720	78	19	has	have	VERB
ejpam-5720	78	20	a	a	DET
ejpam-5720	78	21	finite	finite	ADJ
ejpam-5720	78	22	subcover	subcover	PROPN
ejpam-5720	78	23	.	.	PUNCT
ejpam-5720	79	1	lemma	lemma	PROPN
ejpam-5720	79	2	2	2	NUM
ejpam-5720	79	3	.	.	X
ejpam-5720	80	1	for	for	ADP
ejpam-5720	80	2	a	a	DET
ejpam-5720	80	3	subset	subset	NOUN
ejpam-5720	80	4	a	a	PRON
ejpam-5720	80	5	of	of	ADP
ejpam-5720	80	6	a	a	DET
ejpam-5720	80	7	bitopological	bitopological	ADJ
ejpam-5720	80	8	space	space	NOUN
ejpam-5720	80	9	(	(	PUNCT
ejpam-5720	80	10	x	x	NOUN
ejpam-5720	80	11	,	,	PUNCT
ejpam-5720	80	12	τ1	τ1	NOUN
ejpam-5720	80	13	,	,	PUNCT
ejpam-5720	80	14	τ2	τ2	NOUN
ejpam-5720	80	15	)	)	PUNCT
ejpam-5720	80	16	,	,	PUNCT
ejpam-5720	80	17	the	the	DET
ejpam-5720	80	18	following	follow	VERB
ejpam-5720	80	19	properties	property	NOUN
ejpam-5720	80	20	hold	hold	VERB
ejpam-5720	80	21	:	:	PUNCT
ejpam-5720	80	22	(	(	PUNCT
ejpam-5720	80	23	1	1	X
ejpam-5720	80	24	)	)	PUNCT
ejpam-5720	80	25	(	(	PUNCT
ejpam-5720	80	26	τ1	τ1	NOUN
ejpam-5720	80	27	,	,	PUNCT
ejpam-5720	80	28	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5720	80	29	)	)	PUNCT
ejpam-5720	80	30	=	=	PUNCT
ejpam-5720	81	1	τ1τ2	τ1τ2	NOUN
ejpam-5720	81	2	-	-	NOUN
ejpam-5720	81	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	81	4	-	-	PUNCT
ejpam-5720	81	5	cl(a	cl(a	NUM
ejpam-5720	81	6	)	)	PUNCT
ejpam-5720	81	7	)	)	PUNCT
ejpam-5720	81	8	∪a	∪a	X
ejpam-5720	82	1	[	[	X
ejpam-5720	82	2	5	5	NUM
ejpam-5720	82	3	]	]	PUNCT
ejpam-5720	82	4	;	;	PUNCT
ejpam-5720	82	5	(	(	PUNCT
ejpam-5720	82	6	2	2	X
ejpam-5720	82	7	)	)	PUNCT
ejpam-5720	82	8	(	(	PUNCT
ejpam-5720	82	9	τ1	τ1	NOUN
ejpam-5720	82	10	,	,	PUNCT
ejpam-5720	82	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5720	82	12	)	)	PUNCT
ejpam-5720	82	13	=	=	PUNCT
ejpam-5720	82	14	τ1τ2	τ1τ2	NOUN
ejpam-5720	82	15	-	-	ADJ
ejpam-5720	82	16	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	82	17	-	-	PUNCT
ejpam-5720	82	18	int(a	int(a	NOUN
ejpam-5720	82	19	)	)	PUNCT
ejpam-5720	82	20	)	)	PUNCT
ejpam-5720	83	1	∩a	∩a	PROPN
ejpam-5720	84	1	[	[	X
ejpam-5720	84	2	54	54	NUM
ejpam-5720	84	3	]	]	PUNCT
ejpam-5720	84	4	.	.	PUNCT
ejpam-5720	85	1	lemma	lemma	PROPN
ejpam-5720	85	2	3	3	X
ejpam-5720	85	3	.	.	PUNCT
ejpam-5720	86	1	[	[	X
ejpam-5720	86	2	33	33	NUM
ejpam-5720	86	3	]	]	PUNCT
ejpam-5720	86	4	let	let	VERB
ejpam-5720	86	5	(	(	PUNCT
ejpam-5720	86	6	x	x	NOUN
ejpam-5720	86	7	,	,	PUNCT
ejpam-5720	86	8	τ1	τ1	NOUN
ejpam-5720	86	9	,	,	PUNCT
ejpam-5720	86	10	τ2	τ2	PROPN
ejpam-5720	86	11	)	)	PUNCT
ejpam-5720	86	12	be	be	VERB
ejpam-5720	86	13	a	a	DET
ejpam-5720	86	14	bitopological	bitopological	ADJ
ejpam-5720	86	15	space	space	NOUN
ejpam-5720	86	16	.	.	PUNCT
ejpam-5720	87	1	if	if	SCONJ
ejpam-5720	87	2	v	v	NOUN
ejpam-5720	87	3	is	be	AUX
ejpam-5720	87	4	a	a	DET
ejpam-5720	87	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	87	6	-	-	ADJ
ejpam-5720	87	7	open	open	ADJ
ejpam-5720	87	8	set	set	NOUN
ejpam-5720	87	9	of	of	ADP
ejpam-5720	87	10	x	x	PUNCT
ejpam-5720	87	11	having	have	VERB
ejpam-5720	87	12	n	n	X
ejpam-5720	87	13	(	(	PUNCT
ejpam-5720	87	14	τ1	τ1	PROPN
ejpam-5720	87	15	,	,	PUNCT
ejpam-5720	87	16	τ2)-closed	τ2)-closed	ADJ
ejpam-5720	87	17	complement	complement	NOUN
ejpam-5720	87	18	,	,	PUNCT
ejpam-5720	87	19	then	then	ADV
ejpam-5720	87	20	τ1τ2	τ1τ2	NOUN
ejpam-5720	87	21	-	-	NOUN
ejpam-5720	87	22	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	87	23	-	-	PUNCT
ejpam-5720	87	24	cl(v	cl(v	NOUN
ejpam-5720	87	25	)	)	PUNCT
ejpam-5720	87	26	)	)	PUNCT
ejpam-5720	87	27	is	be	AUX
ejpam-5720	87	28	a	a	DET
ejpam-5720	87	29	(	(	PUNCT
ejpam-5720	87	30	τ1	τ1	NOUN
ejpam-5720	87	31	,	,	PUNCT
ejpam-5720	87	32	τ2)r	τ2)r	ADJ
ejpam-5720	87	33	-	-	PUNCT
ejpam-5720	87	34	open	open	NOUN
ejpam-5720	87	35	set	set	NOUN
ejpam-5720	87	36	having	have	VERB
ejpam-5720	87	37	n	n	PRON
ejpam-5720	87	38	(	(	PUNCT
ejpam-5720	87	39	τ1	τ1	PROPN
ejpam-5720	87	40	,	,	PUNCT
ejpam-5720	87	41	τ2)-closed	τ2)-closed	ADJ
ejpam-5720	87	42	complement	complement	NOUN
ejpam-5720	87	43	.	.	PUNCT
ejpam-5720	88	1	j.	j.	PROPN
ejpam-5720	88	2	khampakdee	khampakdee	PROPN
ejpam-5720	88	3	,	,	PUNCT
ejpam-5720	88	4	a.	a.	PROPN
ejpam-5720	88	5	sama	sama	PROPN
ejpam-5720	88	6	-	-	PUNCT
ejpam-5720	88	7	ae	ae	PROPN
ejpam-5720	88	8	,	,	PUNCT
ejpam-5720	88	9	c.	c.	PROPN
ejpam-5720	88	10	boonpok	boonpok	PROPN
ejpam-5720	88	11	/	/	SYM
ejpam-5720	88	12	eur	eur	PROPN
ejpam-5720	88	13	.	.	PUNCT
ejpam-5720	89	1	j.	j.	PROPN
ejpam-5720	89	2	pure	pure	PROPN
ejpam-5720	89	3	appl	appl	PROPN
ejpam-5720	89	4	.	.	PROPN
ejpam-5720	89	5	math	math	PROPN
ejpam-5720	89	6	,	,	PUNCT
ejpam-5720	89	7	18	18	NUM
ejpam-5720	89	8	(	(	PUNCT
ejpam-5720	89	9	1	1	NUM
ejpam-5720	89	10	)	)	PUNCT
ejpam-5720	89	11	(	(	PUNCT
ejpam-5720	89	12	2025	2025	NUM
ejpam-5720	89	13	)	)	PUNCT
ejpam-5720	89	14	,	,	PUNCT
ejpam-5720	89	15	5720	5720	NUM
ejpam-5720	89	16	4	4	NUM
ejpam-5720	89	17	of	of	ADP
ejpam-5720	89	18	15	15	NUM
ejpam-5720	89	19	by	by	ADP
ejpam-5720	89	20	a	a	DET
ejpam-5720	89	21	multifunction	multifunction	NOUN
ejpam-5720	89	22	f	f	NOUN
ejpam-5720	89	23	:	:	PUNCT
ejpam-5720	89	24	x	x	X
ejpam-5720	89	25	→	→	SYM
ejpam-5720	89	26	y	y	PROPN
ejpam-5720	89	27	,	,	PUNCT
ejpam-5720	89	28	we	we	PRON
ejpam-5720	89	29	mean	mean	VERB
ejpam-5720	89	30	a	a	DET
ejpam-5720	89	31	point	point	NOUN
ejpam-5720	89	32	-	-	PUNCT
ejpam-5720	89	33	to	to	ADP
ejpam-5720	89	34	-	-	PUNCT
ejpam-5720	89	35	set	set	VERB
ejpam-5720	89	36	correspondence	correspondence	NOUN
ejpam-5720	89	37	from	from	ADP
ejpam-5720	89	38	x	x	PUNCT
ejpam-5720	89	39	into	into	ADP
ejpam-5720	89	40	y	y	PROPN
ejpam-5720	89	41	,	,	PUNCT
ejpam-5720	89	42	and	and	CCONJ
ejpam-5720	89	43	we	we	PRON
ejpam-5720	89	44	always	always	ADV
ejpam-5720	89	45	assume	assume	VERB
ejpam-5720	89	46	that	that	SCONJ
ejpam-5720	89	47	f	f	PROPN
ejpam-5720	89	48	(	(	PUNCT
ejpam-5720	89	49	x	x	X
ejpam-5720	89	50	)	)	PUNCT
ejpam-5720	89	51	̸=	̸=	NOUN
ejpam-5720	89	52	∅	∅	NOUN
ejpam-5720	89	53	for	for	ADP
ejpam-5720	89	54	all	all	PRON
ejpam-5720	89	55	x	x	SYM
ejpam-5720	89	56	∈	∈	ADJ
ejpam-5720	89	57	x.	x.	NOUN
ejpam-5720	89	58	for	for	ADP
ejpam-5720	89	59	a	a	DET
ejpam-5720	89	60	multifunction	multifunction	NOUN
ejpam-5720	89	61	f	f	NOUN
ejpam-5720	89	62	:	:	PUNCT
ejpam-5720	89	63	x	x	X
ejpam-5720	89	64	→	→	SYM
ejpam-5720	89	65	y	y	PROPN
ejpam-5720	89	66	,	,	PUNCT
ejpam-5720	89	67	we	we	PRON
ejpam-5720	89	68	shall	shall	AUX
ejpam-5720	89	69	denote	denote	VERB
ejpam-5720	89	70	the	the	DET
ejpam-5720	89	71	upper	upper	ADJ
ejpam-5720	89	72	and	and	CCONJ
ejpam-5720	89	73	lower	low	ADJ
ejpam-5720	89	74	inverse	inverse	NOUN
ejpam-5720	89	75	of	of	ADP
ejpam-5720	89	76	a	a	DET
ejpam-5720	89	77	set	set	NOUN
ejpam-5720	89	78	b	b	PROPN
ejpam-5720	89	79	of	of	ADP
ejpam-5720	89	80	y	y	PROPN
ejpam-5720	89	81	by	by	ADP
ejpam-5720	89	82	f+(b	f+(b	NOUN
ejpam-5720	89	83	)	)	PUNCT
ejpam-5720	89	84	and	and	CCONJ
ejpam-5720	89	85	f−(b	f−(b	NOUN
ejpam-5720	89	86	)	)	PUNCT
ejpam-5720	89	87	,	,	PUNCT
ejpam-5720	89	88	respectively	respectively	ADV
ejpam-5720	89	89	,	,	PUNCT
ejpam-5720	89	90	that	that	ADV
ejpam-5720	89	91	is	is	ADV
ejpam-5720	89	92	,	,	PUNCT
ejpam-5720	89	93	f+(b	f+(b	NOUN
ejpam-5720	89	94	)	)	PUNCT
ejpam-5720	89	95	=	=	PRON
ejpam-5720	90	1	{	{	PUNCT
ejpam-5720	90	2	x	x	PUNCT
ejpam-5720	90	3	∈	∈	PROPN
ejpam-5720	90	4	x	x	INTJ
ejpam-5720	91	1	|	|	NOUN
ejpam-5720	91	2	f	f	X
ejpam-5720	91	3	(	(	PUNCT
ejpam-5720	91	4	x	x	NOUN
ejpam-5720	91	5	)	)	PUNCT
ejpam-5720	91	6	⊆	⊆	NUM
ejpam-5720	91	7	b	b	NOUN
ejpam-5720	91	8	}	}	PUNCT
ejpam-5720	91	9	and	and	CCONJ
ejpam-5720	91	10	f−(b	f−(b	PROPN
ejpam-5720	91	11	)	)	PUNCT
ejpam-5720	91	12	=	=	PRON
ejpam-5720	92	1	{	{	PUNCT
ejpam-5720	92	2	x	x	PUNCT
ejpam-5720	92	3	∈	∈	PROPN
ejpam-5720	92	4	x	x	INTJ
ejpam-5720	93	1	|	|	NOUN
ejpam-5720	93	2	f	f	X
ejpam-5720	93	3	(	(	PUNCT
ejpam-5720	93	4	x	x	NOUN
ejpam-5720	93	5	)	)	PUNCT
ejpam-5720	93	6	∩	∩	NOUN
ejpam-5720	93	7	b	b	PROPN
ejpam-5720	93	8	̸=	̸=	PROPN
ejpam-5720	93	9	∅	∅	NOUN
ejpam-5720	93	10	}	}	PUNCT
ejpam-5720	93	11	.	.	PUNCT
ejpam-5720	94	1	in	in	ADP
ejpam-5720	94	2	particular	particular	ADJ
ejpam-5720	94	3	,	,	PUNCT
ejpam-5720	94	4	f−(y	f−(y	NOUN
ejpam-5720	94	5	)	)	PUNCT
ejpam-5720	94	6	=	=	SYM
ejpam-5720	95	1	{	{	PUNCT
ejpam-5720	95	2	x	x	PUNCT
ejpam-5720	95	3	∈	∈	PROPN
ejpam-5720	95	4	x	x	INTJ
ejpam-5720	96	1	|	|	ADV
ejpam-5720	96	2	y	y	PROPN
ejpam-5720	96	3	∈	∈	PROPN
ejpam-5720	96	4	f	f	X
ejpam-5720	96	5	(	(	PUNCT
ejpam-5720	96	6	x	x	NOUN
ejpam-5720	96	7	)	)	PUNCT
ejpam-5720	96	8	}	}	PUNCT
ejpam-5720	96	9	for	for	ADP
ejpam-5720	96	10	each	each	DET
ejpam-5720	96	11	point	point	NOUN
ejpam-5720	96	12	y	y	PROPN
ejpam-5720	96	13	∈	∈	PROPN
ejpam-5720	96	14	y	y	PROPN
ejpam-5720	96	15	.	.	PUNCT
ejpam-5720	97	1	for	for	ADP
ejpam-5720	97	2	each	each	DET
ejpam-5720	97	3	a	a	DET
ejpam-5720	97	4	⊆	⊆	NUM
ejpam-5720	97	5	x	x	SYM
ejpam-5720	97	6	,	,	PUNCT
ejpam-5720	97	7	f	f	PROPN
ejpam-5720	97	8	(	(	PUNCT
ejpam-5720	97	9	a	a	NOUN
ejpam-5720	97	10	)	)	PUNCT
ejpam-5720	97	11	=	=	SYM
ejpam-5720	97	12	∪x∈af	∪x∈af	NOUN
ejpam-5720	97	13	(	(	PUNCT
ejpam-5720	97	14	x	x	NOUN
ejpam-5720	97	15	)	)	PUNCT
ejpam-5720	97	16	.	.	PUNCT
ejpam-5720	98	1	3	3	X
ejpam-5720	98	2	.	.	X
ejpam-5720	98	3	upper	upper	ADJ
ejpam-5720	98	4	almost	almost	ADV
ejpam-5720	98	5	nearly	nearly	ADV
ejpam-5720	98	6	quasi	quasi	NOUN
ejpam-5720	98	7	(	(	PUNCT
ejpam-5720	98	8	τ1	τ1	NOUN
ejpam-5720	98	9	,	,	PUNCT
ejpam-5720	98	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	98	11	multifunctions	multifunction	NOUN
ejpam-5720	98	12	and	and	CCONJ
ejpam-5720	98	13	lower	low	ADJ
ejpam-5720	98	14	almost	almost	ADV
ejpam-5720	98	15	nearly	nearly	ADV
ejpam-5720	98	16	quasi	quasi	NOUN
ejpam-5720	98	17	(	(	PUNCT
ejpam-5720	98	18	τ1	τ1	NOUN
ejpam-5720	98	19	,	,	PUNCT
ejpam-5720	98	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	98	21	multifunctions	multifunction	NOUN
ejpam-5720	98	22	in	in	ADP
ejpam-5720	98	23	this	this	DET
ejpam-5720	98	24	section	section	NOUN
ejpam-5720	98	25	,	,	PUNCT
ejpam-5720	98	26	we	we	PRON
ejpam-5720	98	27	introduce	introduce	VERB
ejpam-5720	98	28	the	the	DET
ejpam-5720	98	29	notions	notion	NOUN
ejpam-5720	98	30	of	of	ADP
ejpam-5720	98	31	upper	upper	ADJ
ejpam-5720	98	32	almost	almost	ADV
ejpam-5720	98	33	nearly	nearly	ADV
ejpam-5720	98	34	quasi	quasi	NOUN
ejpam-5720	98	35	(	(	PUNCT
ejpam-5720	98	36	τ1	τ1	NOUN
ejpam-5720	98	37	,	,	PUNCT
ejpam-5720	98	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	98	39	multifunctions	multifunction	NOUN
ejpam-5720	98	40	and	and	CCONJ
ejpam-5720	98	41	lower	low	ADJ
ejpam-5720	98	42	almost	almost	ADV
ejpam-5720	98	43	nearly	nearly	ADV
ejpam-5720	98	44	quasi	quasi	NOUN
ejpam-5720	98	45	(	(	PUNCT
ejpam-5720	98	46	τ1	τ1	NOUN
ejpam-5720	98	47	,	,	PUNCT
ejpam-5720	98	48	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	98	49	multifunctions	multifunction	NOUN
ejpam-5720	98	50	.	.	PUNCT
ejpam-5720	99	1	furthermore	furthermore	ADV
ejpam-5720	99	2	,	,	PUNCT
ejpam-5720	99	3	several	several	ADJ
ejpam-5720	99	4	characterizations	characterization	NOUN
ejpam-5720	99	5	of	of	ADP
ejpam-5720	99	6	upper	upper	ADJ
ejpam-5720	99	7	almost	almost	ADV
ejpam-5720	99	8	nearly	nearly	ADV
ejpam-5720	99	9	quasi	quasi	NOUN
ejpam-5720	99	10	(	(	PUNCT
ejpam-5720	99	11	τ1	τ1	NOUN
ejpam-5720	99	12	,	,	PUNCT
ejpam-5720	99	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	99	14	multifunctions	multifunction	NOUN
ejpam-5720	99	15	and	and	CCONJ
ejpam-5720	99	16	lower	low	ADJ
ejpam-5720	99	17	almost	almost	ADV
ejpam-5720	99	18	nearly	nearly	ADV
ejpam-5720	99	19	quasi	quasi	NOUN
ejpam-5720	99	20	(	(	PUNCT
ejpam-5720	99	21	τ1	τ1	NOUN
ejpam-5720	99	22	,	,	PUNCT
ejpam-5720	99	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	99	24	multifunctions	multifunction	NOUN
ejpam-5720	99	25	are	be	AUX
ejpam-5720	99	26	discussed	discuss	VERB
ejpam-5720	99	27	.	.	PUNCT
ejpam-5720	100	1	definition	definition	NOUN
ejpam-5720	100	2	1	1	NUM
ejpam-5720	100	3	.	.	PUNCT
ejpam-5720	101	1	a	a	DET
ejpam-5720	101	2	multifunction	multifunction	NOUN
ejpam-5720	101	3	f	f	NOUN
ejpam-5720	101	4	:	:	PUNCT
ejpam-5720	101	5	(	(	PUNCT
ejpam-5720	101	6	x	x	NOUN
ejpam-5720	101	7	,	,	PUNCT
ejpam-5720	101	8	τ1	τ1	NOUN
ejpam-5720	101	9	,	,	PUNCT
ejpam-5720	101	10	τ2	τ2	NOUN
ejpam-5720	101	11	)	)	PUNCT
ejpam-5720	101	12	→	→	SYM
ejpam-5720	101	13	(	(	PUNCT
ejpam-5720	101	14	y	y	PROPN
ejpam-5720	101	15	,	,	PUNCT
ejpam-5720	101	16	σ1	σ1	PROPN
ejpam-5720	101	17	,	,	PUNCT
ejpam-5720	101	18	σ2	σ2	PROPN
ejpam-5720	101	19	)	)	PUNCT
ejpam-5720	101	20	is	be	AUX
ejpam-5720	101	21	said	say	VERB
ejpam-5720	101	22	to	to	PART
ejpam-5720	101	23	be	be	AUX
ejpam-5720	101	24	upper	upper	ADJ
ejpam-5720	101	25	almost	almost	ADV
ejpam-5720	101	26	nearly	nearly	ADV
ejpam-5720	101	27	quasi	quasi	NOUN
ejpam-5720	101	28	(	(	PUNCT
ejpam-5720	101	29	τ1	τ1	NOUN
ejpam-5720	101	30	,	,	PUNCT
ejpam-5720	101	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	101	32	at	at	ADP
ejpam-5720	101	33	a	a	DET
ejpam-5720	101	34	point	point	NOUN
ejpam-5720	101	35	x	x	SYM
ejpam-5720	101	36	∈	∈	NOUN
ejpam-5720	101	37	x	x	PUNCT
ejpam-5720	101	38	if	if	SCONJ
ejpam-5720	101	39	for	for	ADP
ejpam-5720	101	40	each	each	DET
ejpam-5720	101	41	σ1σ2	σ1σ2	VERB
ejpam-5720	101	42	-	-	ADJ
ejpam-5720	101	43	open	open	ADJ
ejpam-5720	101	44	set	set	NOUN
ejpam-5720	101	45	v	v	NOUN
ejpam-5720	101	46	of	of	ADP
ejpam-5720	101	47	y	y	PROPN
ejpam-5720	101	48	having	have	VERB
ejpam-5720	101	49	n	n	PROPN
ejpam-5720	101	50	(	(	PUNCT
ejpam-5720	101	51	σ1	σ1	PROPN
ejpam-5720	101	52	,	,	PUNCT
ejpam-5720	101	53	σ2)-closed	σ2)-close	VERB
ejpam-5720	101	54	complement	complement	NOUN
ejpam-5720	101	55	such	such	ADJ
ejpam-5720	101	56	that	that	SCONJ
ejpam-5720	101	57	x	x	SYM
ejpam-5720	101	58	∈	∈	PROPN
ejpam-5720	101	59	f+(v	f+(v	NOUN
ejpam-5720	101	60	)	)	PUNCT
ejpam-5720	101	61	and	and	CCONJ
ejpam-5720	101	62	for	for	ADP
ejpam-5720	101	63	every	every	DET
ejpam-5720	101	64	τ1τ2	τ1τ2	ADJ
ejpam-5720	101	65	-	-	ADJ
ejpam-5720	101	66	open	open	ADJ
ejpam-5720	101	67	set	set	ADJ
ejpam-5720	101	68	u	u	NOUN
ejpam-5720	101	69	of	of	ADP
ejpam-5720	101	70	x	x	PUNCT
ejpam-5720	101	71	containing	contain	VERB
ejpam-5720	101	72	x	x	PRON
ejpam-5720	101	73	,	,	PUNCT
ejpam-5720	101	74	there	there	PRON
ejpam-5720	101	75	exists	exist	VERB
ejpam-5720	101	76	a	a	DET
ejpam-5720	101	77	nonempty	nonempty	ADJ
ejpam-5720	101	78	τ1τ2	τ1τ2	NOUN
ejpam-5720	101	79	-	-	ADJ
ejpam-5720	101	80	open	open	ADJ
ejpam-5720	101	81	set	set	NOUN
ejpam-5720	101	82	w	w	ADP
ejpam-5720	101	83	such	such	ADJ
ejpam-5720	101	84	that	that	DET
ejpam-5720	101	85	w	w	ADP
ejpam-5720	101	86	⊆	⊆	NUM
ejpam-5720	101	87	u	u	NOUN
ejpam-5720	101	88	and	and	CCONJ
ejpam-5720	101	89	w	w	ADP
ejpam-5720	101	90	⊆	⊆	NUM
ejpam-5720	101	91	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	101	92	-	-	PUNCT
ejpam-5720	101	93	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	101	94	-	-	PUNCT
ejpam-5720	101	95	cl(v	cl(v	NOUN
ejpam-5720	101	96	)	)	PUNCT
ejpam-5720	101	97	)	)	PUNCT
ejpam-5720	101	98	)	)	PUNCT
ejpam-5720	101	99	.	.	PUNCT
ejpam-5720	102	1	a	a	DET
ejpam-5720	102	2	multifunction	multifunction	NOUN
ejpam-5720	102	3	f	f	NOUN
ejpam-5720	102	4	:	:	PUNCT
ejpam-5720	102	5	(	(	PUNCT
ejpam-5720	102	6	x	x	NOUN
ejpam-5720	102	7	,	,	PUNCT
ejpam-5720	102	8	τ1	τ1	NOUN
ejpam-5720	102	9	,	,	PUNCT
ejpam-5720	102	10	τ2	τ2	NOUN
ejpam-5720	102	11	)	)	PUNCT
ejpam-5720	102	12	→	→	SYM
ejpam-5720	102	13	(	(	PUNCT
ejpam-5720	102	14	y	y	PROPN
ejpam-5720	102	15	,	,	PUNCT
ejpam-5720	102	16	σ1	σ1	PROPN
ejpam-5720	102	17	,	,	PUNCT
ejpam-5720	102	18	σ2	σ2	PROPN
ejpam-5720	102	19	)	)	PUNCT
ejpam-5720	102	20	is	be	AUX
ejpam-5720	102	21	said	say	VERB
ejpam-5720	102	22	to	to	PART
ejpam-5720	102	23	be	be	AUX
ejpam-5720	102	24	upper	upper	ADJ
ejpam-5720	102	25	almost	almost	ADV
ejpam-5720	102	26	nearly	nearly	ADV
ejpam-5720	102	27	quasi	quasi	NOUN
ejpam-5720	102	28	(	(	PUNCT
ejpam-5720	102	29	τ1	τ1	NOUN
ejpam-5720	102	30	,	,	PUNCT
ejpam-5720	102	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	102	32	if	if	SCONJ
ejpam-5720	102	33	f	f	PROPN
ejpam-5720	102	34	is	be	AUX
ejpam-5720	102	35	upper	upper	ADJ
ejpam-5720	102	36	almost	almost	ADV
ejpam-5720	102	37	nearly	nearly	ADV
ejpam-5720	102	38	quasi	quasi	NOUN
ejpam-5720	102	39	(	(	PUNCT
ejpam-5720	102	40	τ1	τ1	NOUN
ejpam-5720	102	41	,	,	PUNCT
ejpam-5720	102	42	τ2)continuous	τ2)continuous	ADJ
ejpam-5720	102	43	at	at	ADP
ejpam-5720	102	44	each	each	DET
ejpam-5720	102	45	point	point	NOUN
ejpam-5720	102	46	x	x	PUNCT
ejpam-5720	102	47	of	of	ADP
ejpam-5720	102	48	x.	x.	PROPN
ejpam-5720	102	49	theorem	theorem	VERB
ejpam-5720	102	50	1	1	NUM
ejpam-5720	102	51	.	.	X
ejpam-5720	102	52	for	for	ADP
ejpam-5720	102	53	a	a	DET
ejpam-5720	102	54	multifunction	multifunction	NOUN
ejpam-5720	102	55	f	f	NOUN
ejpam-5720	102	56	:	:	PUNCT
ejpam-5720	102	57	(	(	PUNCT
ejpam-5720	102	58	x	x	NOUN
ejpam-5720	102	59	,	,	PUNCT
ejpam-5720	102	60	τ1	τ1	NOUN
ejpam-5720	102	61	,	,	PUNCT
ejpam-5720	102	62	τ2	τ2	NOUN
ejpam-5720	102	63	)	)	PUNCT
ejpam-5720	102	64	→	→	SYM
ejpam-5720	102	65	(	(	PUNCT
ejpam-5720	102	66	y	y	PROPN
ejpam-5720	102	67	,	,	PUNCT
ejpam-5720	102	68	σ1	σ1	PROPN
ejpam-5720	102	69	,	,	PUNCT
ejpam-5720	102	70	σ2	σ2	NOUN
ejpam-5720	102	71	)	)	PUNCT
ejpam-5720	102	72	,	,	PUNCT
ejpam-5720	102	73	the	the	DET
ejpam-5720	102	74	following	follow	VERB
ejpam-5720	102	75	properties	property	NOUN
ejpam-5720	102	76	are	be	AUX
ejpam-5720	102	77	equivalent	equivalent	ADJ
ejpam-5720	102	78	:	:	PUNCT
ejpam-5720	102	79	(	(	PUNCT
ejpam-5720	102	80	1	1	X
ejpam-5720	102	81	)	)	PUNCT
ejpam-5720	102	82	f	f	PROPN
ejpam-5720	102	83	is	be	AUX
ejpam-5720	102	84	upper	upper	ADJ
ejpam-5720	102	85	almost	almost	ADV
ejpam-5720	102	86	nearly	nearly	ADV
ejpam-5720	102	87	quasi	quasi	NOUN
ejpam-5720	102	88	(	(	PUNCT
ejpam-5720	102	89	τ1	τ1	NOUN
ejpam-5720	102	90	,	,	PUNCT
ejpam-5720	102	91	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	102	92	;	;	PUNCT
ejpam-5720	102	93	(	(	PUNCT
ejpam-5720	102	94	2	2	X
ejpam-5720	102	95	)	)	PUNCT
ejpam-5720	102	96	for	for	ADP
ejpam-5720	102	97	each	each	DET
ejpam-5720	102	98	x	x	SYM
ejpam-5720	102	99	∈	∈	PROPN
ejpam-5720	102	100	x	x	X
ejpam-5720	102	101	and	and	CCONJ
ejpam-5720	102	102	for	for	ADP
ejpam-5720	102	103	each	each	DET
ejpam-5720	102	104	(	(	PUNCT
ejpam-5720	102	105	σ1	σ1	PROPN
ejpam-5720	102	106	,	,	PUNCT
ejpam-5720	102	107	σ2)r	σ2)r	NOUN
ejpam-5720	102	108	-	-	PUNCT
ejpam-5720	102	109	open	open	ADJ
ejpam-5720	102	110	set	set	VERB
ejpam-5720	102	111	v	v	NOUN
ejpam-5720	102	112	of	of	ADP
ejpam-5720	102	113	y	y	PROPN
ejpam-5720	102	114	having	have	VERB
ejpam-5720	102	115	n	n	PROPN
ejpam-5720	102	116	(	(	PUNCT
ejpam-5720	102	117	σ1	σ1	PROPN
ejpam-5720	102	118	,	,	PUNCT
ejpam-5720	102	119	σ2)-closed	σ2)-close	VERB
ejpam-5720	102	120	complement	complement	NOUN
ejpam-5720	102	121	such	such	ADJ
ejpam-5720	102	122	that	that	SCONJ
ejpam-5720	102	123	x	x	SYM
ejpam-5720	102	124	∈	∈	PROPN
ejpam-5720	102	125	f+(v	f+(v	NOUN
ejpam-5720	102	126	)	)	PUNCT
ejpam-5720	102	127	and	and	CCONJ
ejpam-5720	102	128	for	for	ADP
ejpam-5720	102	129	every	every	DET
ejpam-5720	102	130	τ1τ2	τ1τ2	ADJ
ejpam-5720	102	131	-	-	ADJ
ejpam-5720	102	132	open	open	ADJ
ejpam-5720	102	133	set	set	ADJ
ejpam-5720	102	134	u	u	NOUN
ejpam-5720	102	135	of	of	ADP
ejpam-5720	102	136	x	x	PUNCT
ejpam-5720	102	137	containing	contain	VERB
ejpam-5720	102	138	x	x	PRON
ejpam-5720	102	139	,	,	PUNCT
ejpam-5720	102	140	there	there	PRON
ejpam-5720	102	141	exists	exist	VERB
ejpam-5720	102	142	a	a	DET
ejpam-5720	102	143	nonempty	nonempty	ADJ
ejpam-5720	102	144	τ1τ2	τ1τ2	NOUN
ejpam-5720	102	145	-	-	ADJ
ejpam-5720	102	146	open	open	ADJ
ejpam-5720	102	147	set	set	NOUN
ejpam-5720	102	148	w	w	ADP
ejpam-5720	102	149	such	such	ADJ
ejpam-5720	102	150	that	that	PRON
ejpam-5720	102	151	w	w	ADP
ejpam-5720	102	152	⊆	⊆	NUM
ejpam-5720	102	153	u	u	NOUN
ejpam-5720	102	154	and	and	CCONJ
ejpam-5720	102	155	w	w	NOUN
ejpam-5720	102	156	⊆	⊆	NUM
ejpam-5720	102	157	f+(v	f+(v	NOUN
ejpam-5720	102	158	)	)	PUNCT
ejpam-5720	102	159	;	;	PUNCT
ejpam-5720	102	160	(	(	PUNCT
ejpam-5720	102	161	3	3	X
ejpam-5720	102	162	)	)	PUNCT
ejpam-5720	102	163	for	for	ADP
ejpam-5720	102	164	each	each	DET
ejpam-5720	102	165	x	x	SYM
ejpam-5720	102	166	∈	∈	PROPN
ejpam-5720	102	167	x	x	X
ejpam-5720	102	168	and	and	CCONJ
ejpam-5720	102	169	for	for	ADP
ejpam-5720	102	170	every	every	DET
ejpam-5720	102	171	σ1σ2	σ1σ2	NOUN
ejpam-5720	102	172	-	-	PUNCT
ejpam-5720	102	173	closed	closed	ADJ
ejpam-5720	102	174	and	and	CCONJ
ejpam-5720	102	175	n	n	CCONJ
ejpam-5720	102	176	(	(	PUNCT
ejpam-5720	102	177	σ1	σ1	PROPN
ejpam-5720	102	178	,	,	PUNCT
ejpam-5720	102	179	σ2)-closed	σ2)-close	VERB
ejpam-5720	102	180	set	set	VERB
ejpam-5720	102	181	k	k	PROPN
ejpam-5720	102	182	of	of	ADP
ejpam-5720	102	183	y	y	PROPN
ejpam-5720	102	184	such	such	ADJ
ejpam-5720	102	185	that	that	SCONJ
ejpam-5720	102	186	x	x	SYM
ejpam-5720	102	187	∈	∈	PROPN
ejpam-5720	102	188	f+(y	f+(y	NOUN
ejpam-5720	102	189	−k	−k	PROPN
ejpam-5720	102	190	)	)	PUNCT
ejpam-5720	102	191	and	and	CCONJ
ejpam-5720	102	192	for	for	ADP
ejpam-5720	102	193	every	every	DET
ejpam-5720	102	194	τ1τ2	τ1τ2	ADJ
ejpam-5720	102	195	-	-	ADJ
ejpam-5720	102	196	closed	closed	ADJ
ejpam-5720	102	197	set	set	ADJ
ejpam-5720	102	198	h	h	NOUN
ejpam-5720	102	199	of	of	ADP
ejpam-5720	102	200	x	x	INTJ
ejpam-5720	102	201	such	such	ADJ
ejpam-5720	102	202	that	that	SCONJ
ejpam-5720	102	203	x	x	SYM
ejpam-5720	102	204	∈	∈	PROPN
ejpam-5720	102	205	x−h	x−h	PROPN
ejpam-5720	102	206	,	,	PUNCT
ejpam-5720	102	207	there	there	PRON
ejpam-5720	102	208	exists	exist	VERB
ejpam-5720	102	209	a	a	DET
ejpam-5720	102	210	τ1τ2	τ1τ2	ADJ
ejpam-5720	102	211	-	-	ADJ
ejpam-5720	102	212	closed	closed	ADJ
ejpam-5720	102	213	set	set	NOUN
ejpam-5720	102	214	m	m	VERB
ejpam-5720	102	215	such	such	ADJ
ejpam-5720	102	216	that	that	SCONJ
ejpam-5720	102	217	h	h	NOUN
ejpam-5720	102	218	⊆	⊆	NUM
ejpam-5720	102	219	m	m	NOUN
ejpam-5720	102	220	,	,	PUNCT
ejpam-5720	102	221	m	m	VERB
ejpam-5720	102	222	̸=	̸=	NOUN
ejpam-5720	102	223	x	x	PUNCT
ejpam-5720	102	224	and	and	CCONJ
ejpam-5720	102	225	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	102	226	-	-	PUNCT
ejpam-5720	102	227	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	102	228	-	-	PUNCT
ejpam-5720	102	229	int(k	int(k	NOUN
ejpam-5720	102	230	)	)	PUNCT
ejpam-5720	102	231	)	)	PUNCT
ejpam-5720	102	232	)	)	PUNCT
ejpam-5720	103	1	⊆	⊆	NUM
ejpam-5720	103	2	m	m	NOUN
ejpam-5720	103	3	;	;	PUNCT
ejpam-5720	103	4	(	(	PUNCT
ejpam-5720	103	5	4	4	X
ejpam-5720	103	6	)	)	PUNCT
ejpam-5720	103	7	for	for	ADP
ejpam-5720	103	8	each	each	DET
ejpam-5720	103	9	x	x	SYM
ejpam-5720	103	10	∈	∈	PROPN
ejpam-5720	103	11	x	x	X
ejpam-5720	103	12	and	and	CCONJ
ejpam-5720	103	13	for	for	ADP
ejpam-5720	103	14	every	every	DET
ejpam-5720	103	15	σ1σ2	σ1σ2	NOUN
ejpam-5720	103	16	-	-	ADJ
ejpam-5720	103	17	open	open	ADJ
ejpam-5720	103	18	set	set	NOUN
ejpam-5720	103	19	v	v	NOUN
ejpam-5720	103	20	of	of	ADP
ejpam-5720	103	21	y	y	PROPN
ejpam-5720	103	22	having	have	VERB
ejpam-5720	103	23	n	n	PROPN
ejpam-5720	103	24	(	(	PUNCT
ejpam-5720	103	25	σ1	σ1	PROPN
ejpam-5720	103	26	,	,	PUNCT
ejpam-5720	103	27	σ2)-closed	σ2)-close	VERB
ejpam-5720	103	28	complement	complement	NOUN
ejpam-5720	103	29	such	such	ADJ
ejpam-5720	103	30	that	that	SCONJ
ejpam-5720	103	31	x	x	SYM
ejpam-5720	103	32	∈	∈	PROPN
ejpam-5720	103	33	f+(v	f+(v	NOUN
ejpam-5720	103	34	)	)	PUNCT
ejpam-5720	103	35	,	,	PUNCT
ejpam-5720	103	36	there	there	PRON
ejpam-5720	103	37	exists	exist	VERB
ejpam-5720	103	38	a	a	DET
ejpam-5720	103	39	(	(	PUNCT
ejpam-5720	103	40	τ1	τ1	NOUN
ejpam-5720	103	41	,	,	PUNCT
ejpam-5720	103	42	τ2)s	τ2)s	NOUN
ejpam-5720	103	43	-	-	PUNCT
ejpam-5720	103	44	open	open	ADJ
ejpam-5720	103	45	set	set	NOUN
ejpam-5720	103	46	u	u	NOUN
ejpam-5720	103	47	of	of	ADP
ejpam-5720	103	48	x	x	PUNCT
ejpam-5720	103	49	containing	contain	VERB
ejpam-5720	103	50	x	x	PUNCT
ejpam-5720	103	51	such	such	ADJ
ejpam-5720	103	52	that	that	SCONJ
ejpam-5720	103	53	u	u	NOUN
ejpam-5720	103	54	⊆	⊆	NUM
ejpam-5720	103	55	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	103	56	-	-	PUNCT
ejpam-5720	103	57	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	103	58	-	-	PUNCT
ejpam-5720	103	59	cl(v	cl(v	NOUN
ejpam-5720	103	60	)	)	PUNCT
ejpam-5720	103	61	)	)	PUNCT
ejpam-5720	103	62	)	)	PUNCT
ejpam-5720	103	63	;	;	PUNCT
ejpam-5720	103	64	(	(	PUNCT
ejpam-5720	103	65	5	5	NUM
ejpam-5720	103	66	)	)	PUNCT
ejpam-5720	103	67	f+(v	f+(v	NOUN
ejpam-5720	103	68	)	)	PUNCT
ejpam-5720	104	1	is	be	AUX
ejpam-5720	104	2	(	(	PUNCT
ejpam-5720	104	3	τ1	τ1	NOUN
ejpam-5720	104	4	,	,	PUNCT
ejpam-5720	104	5	τ2)s	τ2)s	NOUN
ejpam-5720	104	6	-	-	PUNCT
ejpam-5720	104	7	open	open	ADJ
ejpam-5720	104	8	in	in	ADP
ejpam-5720	104	9	x	x	PUNCT
ejpam-5720	104	10	for	for	ADP
ejpam-5720	104	11	every	every	DET
ejpam-5720	104	12	(	(	PUNCT
ejpam-5720	104	13	σ1	σ1	PROPN
ejpam-5720	104	14	,	,	PUNCT
ejpam-5720	104	15	σ2)r	σ2)r	NOUN
ejpam-5720	104	16	-	-	PUNCT
ejpam-5720	104	17	open	open	ADJ
ejpam-5720	104	18	set	set	VERB
ejpam-5720	104	19	v	v	NOUN
ejpam-5720	104	20	of	of	ADP
ejpam-5720	104	21	y	y	PROPN
ejpam-5720	104	22	having	have	VERB
ejpam-5720	104	23	n	n	PROPN
ejpam-5720	104	24	(	(	PUNCT
ejpam-5720	104	25	σ1	σ1	PROPN
ejpam-5720	104	26	,	,	PUNCT
ejpam-5720	104	27	σ2)closed	σ2)close	VERB
ejpam-5720	104	28	complement	complement	NOUN
ejpam-5720	104	29	;	;	PUNCT
ejpam-5720	104	30	(	(	PUNCT
ejpam-5720	104	31	6	6	X
ejpam-5720	104	32	)	)	PUNCT
ejpam-5720	104	33	f−(k	f−(k	PROPN
ejpam-5720	104	34	)	)	PUNCT
ejpam-5720	104	35	is	be	AUX
ejpam-5720	104	36	(	(	PUNCT
ejpam-5720	104	37	τ1	τ1	NOUN
ejpam-5720	104	38	,	,	PUNCT
ejpam-5720	104	39	τ2)s	τ2)s	NOUN
ejpam-5720	104	40	-	-	PUNCT
ejpam-5720	104	41	closed	close	VERB
ejpam-5720	104	42	in	in	ADP
ejpam-5720	104	43	x	x	PUNCT
ejpam-5720	104	44	for	for	SCONJ
ejpam-5720	104	45	every	every	DET
ejpam-5720	104	46	(	(	PUNCT
ejpam-5720	104	47	σ1	σ1	PROPN
ejpam-5720	104	48	,	,	PUNCT
ejpam-5720	104	49	σ2)r	σ2)r	NOUN
ejpam-5720	104	50	-	-	PUNCT
ejpam-5720	104	51	closed	closed	ADJ
ejpam-5720	104	52	and	and	CCONJ
ejpam-5720	104	53	n	n	CCONJ
ejpam-5720	104	54	(	(	PUNCT
ejpam-5720	104	55	σ1	σ1	PROPN
ejpam-5720	104	56	,	,	PUNCT
ejpam-5720	104	57	σ2)-closed	σ2)-close	VERB
ejpam-5720	104	58	set	set	VERB
ejpam-5720	104	59	k	k	PROPN
ejpam-5720	104	60	of	of	ADP
ejpam-5720	104	61	y	y	PROPN
ejpam-5720	104	62	.	.	PUNCT
ejpam-5720	105	1	j.	j.	PROPN
ejpam-5720	105	2	khampakdee	khampakdee	PROPN
ejpam-5720	105	3	,	,	PUNCT
ejpam-5720	105	4	a.	a.	PROPN
ejpam-5720	105	5	sama	sama	PROPN
ejpam-5720	105	6	-	-	PUNCT
ejpam-5720	105	7	ae	ae	PROPN
ejpam-5720	105	8	,	,	PUNCT
ejpam-5720	105	9	c.	c.	PROPN
ejpam-5720	105	10	boonpok	boonpok	PROPN
ejpam-5720	105	11	/	/	SYM
ejpam-5720	105	12	eur	eur	PROPN
ejpam-5720	105	13	.	.	PUNCT
ejpam-5720	106	1	j.	j.	PROPN
ejpam-5720	106	2	pure	pure	PROPN
ejpam-5720	106	3	appl	appl	PROPN
ejpam-5720	106	4	.	.	PROPN
ejpam-5720	106	5	math	math	PROPN
ejpam-5720	106	6	,	,	PUNCT
ejpam-5720	106	7	18	18	NUM
ejpam-5720	106	8	(	(	PUNCT
ejpam-5720	106	9	1	1	NUM
ejpam-5720	106	10	)	)	PUNCT
ejpam-5720	106	11	(	(	PUNCT
ejpam-5720	106	12	2025	2025	NUM
ejpam-5720	106	13	)	)	PUNCT
ejpam-5720	106	14	,	,	PUNCT
ejpam-5720	106	15	5720	5720	NUM
ejpam-5720	106	16	5	5	NUM
ejpam-5720	106	17	of	of	ADP
ejpam-5720	106	18	15	15	NUM
ejpam-5720	106	19	proof	proof	NOUN
ejpam-5720	106	20	.	.	PUNCT
ejpam-5720	107	1	(	(	PUNCT
ejpam-5720	107	2	1	1	X
ejpam-5720	107	3	)	)	PUNCT
ejpam-5720	107	4	⇒	⇒	NOUN
ejpam-5720	107	5	(	(	PUNCT
ejpam-5720	107	6	2	2	NUM
ejpam-5720	107	7	):	):	PUNCT
ejpam-5720	107	8	let	let	VERB
ejpam-5720	107	9	x	x	PUNCT
ejpam-5720	107	10	∈	∈	PROPN
ejpam-5720	107	11	x	x	X
ejpam-5720	107	12	and	and	CCONJ
ejpam-5720	107	13	v	v	AUX
ejpam-5720	107	14	be	be	AUX
ejpam-5720	107	15	any	any	DET
ejpam-5720	107	16	(	(	PUNCT
ejpam-5720	107	17	σ1	σ1	NOUN
ejpam-5720	107	18	,	,	PUNCT
ejpam-5720	107	19	σ2)r	σ2)r	NOUN
ejpam-5720	107	20	-	-	PUNCT
ejpam-5720	107	21	open	open	ADJ
ejpam-5720	107	22	set	set	NOUN
ejpam-5720	107	23	of	of	ADP
ejpam-5720	107	24	y	y	PROPN
ejpam-5720	107	25	having	have	VERB
ejpam-5720	107	26	n	n	PROPN
ejpam-5720	107	27	(	(	PUNCT
ejpam-5720	107	28	σ1	σ1	PROPN
ejpam-5720	107	29	,	,	PUNCT
ejpam-5720	107	30	σ2)closed	σ2)close	VERB
ejpam-5720	107	31	complement	complement	NOUN
ejpam-5720	107	32	such	such	ADJ
ejpam-5720	107	33	that	that	SCONJ
ejpam-5720	107	34	f	f	PROPN
ejpam-5720	107	35	(	(	PUNCT
ejpam-5720	107	36	x	x	X
ejpam-5720	107	37	)	)	PUNCT
ejpam-5720	107	38	⊆	⊆	NUM
ejpam-5720	107	39	v	v	NOUN
ejpam-5720	107	40	and	and	CCONJ
ejpam-5720	107	41	let	let	VERB
ejpam-5720	107	42	u	u	PRON
ejpam-5720	107	43	be	be	AUX
ejpam-5720	107	44	any	any	DET
ejpam-5720	107	45	τ1τ2	τ1τ2	ADJ
ejpam-5720	107	46	-	-	ADJ
ejpam-5720	107	47	open	open	ADJ
ejpam-5720	107	48	set	set	NOUN
ejpam-5720	107	49	of	of	ADP
ejpam-5720	107	50	x	x	PUNCT
ejpam-5720	107	51	containing	contain	VERB
ejpam-5720	107	52	x.	x.	NOUN
ejpam-5720	107	53	by	by	ADP
ejpam-5720	107	54	(	(	PUNCT
ejpam-5720	107	55	1	1	NUM
ejpam-5720	107	56	)	)	PUNCT
ejpam-5720	107	57	,	,	PUNCT
ejpam-5720	107	58	there	there	PRON
ejpam-5720	107	59	exists	exist	VERB
ejpam-5720	107	60	a	a	DET
ejpam-5720	107	61	nonempty	nonempty	ADJ
ejpam-5720	107	62	τ1τ2	τ1τ2	NOUN
ejpam-5720	107	63	-	-	ADJ
ejpam-5720	107	64	open	open	ADJ
ejpam-5720	107	65	set	set	NOUN
ejpam-5720	107	66	w	w	ADP
ejpam-5720	107	67	such	such	ADJ
ejpam-5720	107	68	that	that	DET
ejpam-5720	107	69	w	w	ADP
ejpam-5720	107	70	⊆	⊆	NUM
ejpam-5720	107	71	u	u	NOUN
ejpam-5720	107	72	and	and	CCONJ
ejpam-5720	107	73	w	w	ADP
ejpam-5720	107	74	⊆	⊆	NUM
ejpam-5720	107	75	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	107	76	-	-	PUNCT
ejpam-5720	107	77	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	107	78	-	-	PUNCT
ejpam-5720	107	79	cl(v	cl(v	NOUN
ejpam-5720	107	80	)	)	PUNCT
ejpam-5720	107	81	)	)	PUNCT
ejpam-5720	107	82	)	)	PUNCT
ejpam-5720	108	1	=	=	PUNCT
ejpam-5720	108	2	f+(v	f+(v	NOUN
ejpam-5720	108	3	)	)	PUNCT
ejpam-5720	108	4	.	.	PUNCT
ejpam-5720	109	1	(	(	PUNCT
ejpam-5720	109	2	2	2	X
ejpam-5720	109	3	)	)	PUNCT
ejpam-5720	109	4	⇒	⇒	NOUN
ejpam-5720	109	5	(	(	PUNCT
ejpam-5720	109	6	1	1	NUM
ejpam-5720	109	7	):	):	PUNCT
ejpam-5720	109	8	let	let	VERB
ejpam-5720	109	9	x	x	PUNCT
ejpam-5720	109	10	∈	∈	PROPN
ejpam-5720	109	11	x	x	X
ejpam-5720	109	12	and	and	CCONJ
ejpam-5720	109	13	v	v	AUX
ejpam-5720	109	14	be	be	AUX
ejpam-5720	109	15	any	any	DET
ejpam-5720	109	16	(	(	PUNCT
ejpam-5720	109	17	σ1	σ1	NOUN
ejpam-5720	109	18	,	,	PUNCT
ejpam-5720	109	19	σ2)r	σ2)r	NOUN
ejpam-5720	109	20	-	-	PUNCT
ejpam-5720	109	21	open	open	ADJ
ejpam-5720	109	22	set	set	NOUN
ejpam-5720	109	23	of	of	ADP
ejpam-5720	109	24	y	y	PROPN
ejpam-5720	109	25	having	have	VERB
ejpam-5720	109	26	n	n	PROPN
ejpam-5720	109	27	(	(	PUNCT
ejpam-5720	109	28	σ1	σ1	PROPN
ejpam-5720	109	29	,	,	PUNCT
ejpam-5720	109	30	σ2)-closed	σ2)-close	VERB
ejpam-5720	109	31	complement	complement	NOUN
ejpam-5720	109	32	such	such	ADJ
ejpam-5720	109	33	that	that	SCONJ
ejpam-5720	109	34	f	f	PROPN
ejpam-5720	109	35	(	(	PUNCT
ejpam-5720	109	36	x	x	X
ejpam-5720	109	37	)	)	PUNCT
ejpam-5720	109	38	⊆	⊆	NUM
ejpam-5720	109	39	v	v	NOUN
ejpam-5720	109	40	and	and	CCONJ
ejpam-5720	109	41	let	let	VERB
ejpam-5720	109	42	u	u	PRON
ejpam-5720	109	43	be	be	AUX
ejpam-5720	109	44	any	any	DET
ejpam-5720	109	45	τ1τ2	τ1τ2	ADJ
ejpam-5720	109	46	-	-	ADJ
ejpam-5720	109	47	open	open	ADJ
ejpam-5720	109	48	set	set	NOUN
ejpam-5720	109	49	of	of	ADP
ejpam-5720	109	50	x	x	PUNCT
ejpam-5720	109	51	containing	contain	VERB
ejpam-5720	109	52	x.	x.	NOUN
ejpam-5720	109	53	by	by	ADP
ejpam-5720	109	54	lemma	lemma	PROPN
ejpam-5720	109	55	3	3	NUM
ejpam-5720	109	56	,	,	PUNCT
ejpam-5720	109	57	we	we	PRON
ejpam-5720	109	58	have	have	VERB
ejpam-5720	109	59	σ1σ2	σ1σ2	NOUN
ejpam-5720	109	60	-	-	PUNCT
ejpam-5720	109	61	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	109	62	-	-	PUNCT
ejpam-5720	109	63	cl(v	cl(v	NOUN
ejpam-5720	109	64	)	)	PUNCT
ejpam-5720	109	65	)	)	PUNCT
ejpam-5720	110	1	is	be	AUX
ejpam-5720	110	2	(	(	PUNCT
ejpam-5720	110	3	σ1	σ1	NOUN
ejpam-5720	110	4	,	,	PUNCT
ejpam-5720	110	5	σ2)r	σ2)r	NOUN
ejpam-5720	110	6	-	-	PUNCT
ejpam-5720	110	7	open	open	ADJ
ejpam-5720	110	8	and	and	CCONJ
ejpam-5720	110	9	y	y	PROPN
ejpam-5720	110	10	−σ1σ2	−σ1σ2	PROPN
ejpam-5720	110	11	-	-	PUNCT
ejpam-5720	110	12	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	110	13	-	-	PUNCT
ejpam-5720	110	14	cl(v	cl(v	NOUN
ejpam-5720	110	15	)	)	PUNCT
ejpam-5720	110	16	)	)	PUNCT
ejpam-5720	111	1	is	be	AUX
ejpam-5720	111	2	n	n	PROPN
ejpam-5720	111	3	(	(	PUNCT
ejpam-5720	111	4	σ1	σ1	PROPN
ejpam-5720	111	5	,	,	PUNCT
ejpam-5720	111	6	σ2)-closed	σ2)-close	VERB
ejpam-5720	111	7	.	.	PUNCT
ejpam-5720	112	1	since	since	SCONJ
ejpam-5720	112	2	f	f	PROPN
ejpam-5720	112	3	(	(	PUNCT
ejpam-5720	112	4	x	x	X
ejpam-5720	112	5	)	)	PUNCT
ejpam-5720	112	6	⊆	⊆	NUM
ejpam-5720	112	7	σ1σ2	σ1σ2	X
ejpam-5720	112	8	-	-	PUNCT
ejpam-5720	112	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	112	10	-	-	PUNCT
ejpam-5720	112	11	cl(v	cl(v	NOUN
ejpam-5720	112	12	)	)	PUNCT
ejpam-5720	112	13	)	)	PUNCT
ejpam-5720	112	14	,	,	PUNCT
ejpam-5720	112	15	therefore	therefore	ADV
ejpam-5720	112	16	there	there	PRON
ejpam-5720	112	17	exists	exist	VERB
ejpam-5720	112	18	a	a	DET
ejpam-5720	112	19	nonempty	nonempty	ADJ
ejpam-5720	112	20	τ1τ2	τ1τ2	NOUN
ejpam-5720	112	21	-	-	ADJ
ejpam-5720	112	22	open	open	ADJ
ejpam-5720	112	23	set	set	NOUN
ejpam-5720	112	24	w	w	ADP
ejpam-5720	112	25	such	such	ADJ
ejpam-5720	112	26	that	that	DET
ejpam-5720	112	27	w	w	ADP
ejpam-5720	112	28	⊆	⊆	NUM
ejpam-5720	112	29	u	u	NOUN
ejpam-5720	112	30	and	and	CCONJ
ejpam-5720	112	31	w	w	ADP
ejpam-5720	112	32	⊆	⊆	NUM
ejpam-5720	112	33	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	112	34	-	-	PUNCT
ejpam-5720	112	35	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	112	36	-	-	PUNCT
ejpam-5720	112	37	cl(v	cl(v	NOUN
ejpam-5720	112	38	)	)	PUNCT
ejpam-5720	112	39	)	)	PUNCT
ejpam-5720	112	40	)	)	PUNCT
ejpam-5720	112	41	.	.	PUNCT
ejpam-5720	113	1	(	(	PUNCT
ejpam-5720	113	2	1	1	X
ejpam-5720	113	3	)	)	PUNCT
ejpam-5720	113	4	⇒	⇒	NOUN
ejpam-5720	113	5	(	(	PUNCT
ejpam-5720	113	6	3	3	NUM
ejpam-5720	113	7	):	):	PUNCT
ejpam-5720	113	8	let	let	VERB
ejpam-5720	113	9	x	x	PUNCT
ejpam-5720	113	10	∈	∈	PROPN
ejpam-5720	113	11	x	x	X
ejpam-5720	113	12	and	and	CCONJ
ejpam-5720	113	13	k	k	PROPN
ejpam-5720	113	14	be	be	AUX
ejpam-5720	113	15	any	any	DET
ejpam-5720	113	16	σ1σ2	σ1σ2	NOUN
ejpam-5720	113	17	-	-	PUNCT
ejpam-5720	113	18	closed	closed	ADJ
ejpam-5720	113	19	n	n	CCONJ
ejpam-5720	113	20	(	(	PUNCT
ejpam-5720	113	21	σ1	σ1	PROPN
ejpam-5720	113	22	,	,	PUNCT
ejpam-5720	113	23	σ2)-closed	σ2)-close	VERB
ejpam-5720	113	24	set	set	NOUN
ejpam-5720	113	25	of	of	ADP
ejpam-5720	113	26	y	y	PRON
ejpam-5720	113	27	such	such	ADJ
ejpam-5720	113	28	that	that	SCONJ
ejpam-5720	113	29	x	x	SYM
ejpam-5720	113	30	∈	∈	PROPN
ejpam-5720	113	31	f+(y	f+(y	VERB
ejpam-5720	113	32	−k	−k	PROPN
ejpam-5720	113	33	)	)	PUNCT
ejpam-5720	113	34	.	.	PUNCT
ejpam-5720	114	1	it	it	PRON
ejpam-5720	114	2	is	be	AUX
ejpam-5720	114	3	clear	clear	ADJ
ejpam-5720	114	4	that	that	SCONJ
ejpam-5720	114	5	y	y	PROPN
ejpam-5720	114	6	−k	−k	PROPN
ejpam-5720	114	7	is	be	AUX
ejpam-5720	114	8	a	a	DET
ejpam-5720	114	9	σ1σ2	σ1σ2	NOUN
ejpam-5720	114	10	-	-	ADJ
ejpam-5720	114	11	open	open	ADJ
ejpam-5720	114	12	set	set	NOUN
ejpam-5720	114	13	of	of	ADP
ejpam-5720	114	14	y	y	PROPN
ejpam-5720	114	15	having	have	VERB
ejpam-5720	114	16	n	n	PROPN
ejpam-5720	114	17	(	(	PUNCT
ejpam-5720	114	18	σ1	σ1	PROPN
ejpam-5720	114	19	,	,	PUNCT
ejpam-5720	114	20	σ2)-closed	σ2)-close	VERB
ejpam-5720	114	21	complement	complement	NOUN
ejpam-5720	114	22	.	.	PUNCT
ejpam-5720	115	1	let	let	VERB
ejpam-5720	115	2	h	h	PRON
ejpam-5720	115	3	be	be	AUX
ejpam-5720	115	4	a	a	DET
ejpam-5720	115	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	115	6	-	-	ADJ
ejpam-5720	115	7	closed	closed	ADJ
ejpam-5720	115	8	set	set	NOUN
ejpam-5720	115	9	of	of	ADP
ejpam-5720	115	10	x	x	INTJ
ejpam-5720	115	11	such	such	ADJ
ejpam-5720	115	12	that	that	SCONJ
ejpam-5720	115	13	x	x	SYM
ejpam-5720	115	14	∈	∈	NOUN
ejpam-5720	115	15	x−h	x−h	PROPN
ejpam-5720	115	16	.	.	PUNCT
ejpam-5720	116	1	by	by	ADP
ejpam-5720	116	2	(	(	PUNCT
ejpam-5720	116	3	1	1	NUM
ejpam-5720	116	4	)	)	PUNCT
ejpam-5720	116	5	,	,	PUNCT
ejpam-5720	116	6	there	there	PRON
ejpam-5720	116	7	there	there	PRON
ejpam-5720	116	8	exists	exist	VERB
ejpam-5720	116	9	a	a	DET
ejpam-5720	116	10	nonempty	nonempty	ADJ
ejpam-5720	116	11	τ1τ2	τ1τ2	NOUN
ejpam-5720	116	12	-	-	ADJ
ejpam-5720	116	13	open	open	ADJ
ejpam-5720	116	14	setw	setw	NOUN
ejpam-5720	116	15	such	such	ADJ
ejpam-5720	116	16	thatw	thatw	VERB
ejpam-5720	116	17	⊆	⊆	NUM
ejpam-5720	116	18	x−h	x−h	NOUN
ejpam-5720	116	19	andw	andw	NOUN
ejpam-5720	116	20	⊆	⊆	NUM
ejpam-5720	116	21	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	116	22	-	-	PUNCT
ejpam-5720	116	23	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	116	24	-	-	PUNCT
ejpam-5720	116	25	cl(y−k	cl(y−k	NOUN
ejpam-5720	116	26	)	)	PUNCT
ejpam-5720	116	27	)	)	PUNCT
ejpam-5720	116	28	)	)	PUNCT
ejpam-5720	116	29	.	.	PUNCT
ejpam-5720	117	1	let	let	VERB
ejpam-5720	117	2	us	we	PRON
ejpam-5720	117	3	observe	observe	VERB
ejpam-5720	117	4	that	that	SCONJ
ejpam-5720	117	5	σ1σ2	σ1σ2	X
ejpam-5720	117	6	-	-	PUNCT
ejpam-5720	117	7	int(σ1σ2	int(σ1σ2	VERB
ejpam-5720	117	8	-	-	PUNCT
ejpam-5720	117	9	cl(y	cl(y	NOUN
ejpam-5720	117	10	−k	−k	NOUN
ejpam-5720	117	11	)	)	PUNCT
ejpam-5720	117	12	)	)	PUNCT
ejpam-5720	118	1	=	=	SYM
ejpam-5720	118	2	σ1σ2	σ1σ2	X
ejpam-5720	118	3	-	-	PUNCT
ejpam-5720	118	4	int(y	int(y	ADJ
ejpam-5720	118	5	−	−	NOUN
ejpam-5720	118	6	σ1σ2	σ1σ2	NUM
ejpam-5720	118	7	-	-	PUNCT
ejpam-5720	118	8	int(k	int(k	NOUN
ejpam-5720	118	9	)	)	PUNCT
ejpam-5720	118	10	)	)	PUNCT
ejpam-5720	119	1	=	=	PUNCT
ejpam-5720	119	2	y	y	PROPN
ejpam-5720	119	3	−	−	ADP
ejpam-5720	119	4	σ1σ2	σ1σ2	X
ejpam-5720	119	5	-	-	PUNCT
ejpam-5720	119	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	119	7	-	-	PUNCT
ejpam-5720	119	8	int(k	int(k	NOUN
ejpam-5720	119	9	)	)	PUNCT
ejpam-5720	119	10	)	)	PUNCT
ejpam-5720	119	11	.	.	PUNCT
ejpam-5720	120	1	it	it	PRON
ejpam-5720	120	2	follows	follow	VERB
ejpam-5720	120	3	that	that	SCONJ
ejpam-5720	120	4	w	w	ADP
ejpam-5720	120	5	⊆	⊆	NUM
ejpam-5720	120	6	f+(y	f+(y	ADP
ejpam-5720	120	7	−	−	NUM
ejpam-5720	120	8	σ1σ2	σ1σ2	X
ejpam-5720	120	9	-	-	PUNCT
ejpam-5720	120	10	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	120	11	-	-	PUNCT
ejpam-5720	120	12	int(k	int(k	NOUN
ejpam-5720	120	13	)	)	PUNCT
ejpam-5720	120	14	)	)	PUNCT
ejpam-5720	120	15	)	)	PUNCT
ejpam-5720	121	1	=	=	PUNCT
ejpam-5720	121	2	x	x	X
ejpam-5720	121	3	−	−	ADP
ejpam-5720	121	4	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	121	5	-	-	PUNCT
ejpam-5720	121	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	121	7	-	-	PUNCT
ejpam-5720	121	8	int(k	int(k	NOUN
ejpam-5720	121	9	)	)	PUNCT
ejpam-5720	121	10	)	)	PUNCT
ejpam-5720	121	11	)	)	PUNCT
ejpam-5720	121	12	.	.	PUNCT
ejpam-5720	122	1	let	let	VERB
ejpam-5720	122	2	m	m	VERB
ejpam-5720	122	3	=	=	PUNCT
ejpam-5720	122	4	x	x	PUNCT
ejpam-5720	122	5	−w	−w	ADV
ejpam-5720	122	6	,	,	PUNCT
ejpam-5720	122	7	then	then	ADV
ejpam-5720	122	8	x	x	SYM
ejpam-5720	122	9	−m	−m	PROPN
ejpam-5720	122	10	⊆	⊆	NUM
ejpam-5720	122	11	x	x	SYM
ejpam-5720	122	12	−	−	NOUN
ejpam-5720	122	13	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	122	14	-	-	PUNCT
ejpam-5720	122	15	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	122	16	-	-	PUNCT
ejpam-5720	122	17	int(k	int(k	NOUN
ejpam-5720	122	18	)	)	PUNCT
ejpam-5720	122	19	)	)	PUNCT
ejpam-5720	122	20	)	)	PUNCT
ejpam-5720	122	21	since	since	SCONJ
ejpam-5720	122	22	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	122	23	-	-	PUNCT
ejpam-5720	122	24	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5720	122	25	-	-	PUNCT
ejpam-5720	122	26	int(k	int(k	NOUN
ejpam-5720	122	27	)	)	PUNCT
ejpam-5720	122	28	)	)	PUNCT
ejpam-5720	122	29	)	)	PUNCT
ejpam-5720	123	1	⊆	⊆	NUM
ejpam-5720	123	2	m.	m.	NOUN
ejpam-5720	123	3	it	it	PRON
ejpam-5720	123	4	is	be	AUX
ejpam-5720	123	5	evident	evident	ADJ
ejpam-5720	123	6	that	that	SCONJ
ejpam-5720	123	7	m	m	PROPN
ejpam-5720	123	8	is	be	AUX
ejpam-5720	123	9	a	a	DET
ejpam-5720	123	10	τ1τ2	τ1τ2	ADJ
ejpam-5720	123	11	-	-	ADJ
ejpam-5720	123	12	closed	closed	ADJ
ejpam-5720	123	13	set	set	NOUN
ejpam-5720	123	14	and	and	CCONJ
ejpam-5720	123	15	m	m	PROPN
ejpam-5720	123	16	̸=	̸=	PROPN
ejpam-5720	123	17	x.	x.	NOUN
ejpam-5720	123	18	(	(	PUNCT
ejpam-5720	123	19	3	3	NUM
ejpam-5720	123	20	)	)	PUNCT
ejpam-5720	123	21	⇒	⇒	NOUN
ejpam-5720	123	22	(	(	PUNCT
ejpam-5720	123	23	1	1	NUM
ejpam-5720	123	24	):	):	PUNCT
ejpam-5720	123	25	let	let	VERB
ejpam-5720	123	26	x	x	PUNCT
ejpam-5720	123	27	∈	∈	PROPN
ejpam-5720	123	28	x	x	X
ejpam-5720	123	29	and	and	CCONJ
ejpam-5720	123	30	v	v	X
ejpam-5720	123	31	be	be	AUX
ejpam-5720	123	32	any	any	DET
ejpam-5720	123	33	σ1σ2	σ1σ2	NOUN
ejpam-5720	123	34	-	-	ADJ
ejpam-5720	123	35	open	open	ADJ
ejpam-5720	123	36	set	set	NOUN
ejpam-5720	123	37	of	of	ADP
ejpam-5720	123	38	y	y	PROPN
ejpam-5720	123	39	having	have	VERB
ejpam-5720	123	40	n	n	PROPN
ejpam-5720	123	41	(	(	PUNCT
ejpam-5720	123	42	σ1	σ1	PROPN
ejpam-5720	123	43	,	,	PUNCT
ejpam-5720	123	44	σ2)-closed	σ2)-close	VERB
ejpam-5720	123	45	complement	complement	NOUN
ejpam-5720	123	46	such	such	ADJ
ejpam-5720	123	47	that	that	SCONJ
ejpam-5720	123	48	f	f	PROPN
ejpam-5720	123	49	(	(	PUNCT
ejpam-5720	123	50	x	x	X
ejpam-5720	123	51	)	)	PUNCT
ejpam-5720	123	52	⊆	⊆	NUM
ejpam-5720	123	53	v	v	NOUN
ejpam-5720	123	54	.	.	PUNCT
ejpam-5720	124	1	then	then	ADV
ejpam-5720	124	2	,	,	PUNCT
ejpam-5720	124	3	we	we	PRON
ejpam-5720	124	4	have	have	VERB
ejpam-5720	124	5	k	k	NOUN
ejpam-5720	124	6	=	=	SYM
ejpam-5720	124	7	y	y	PROPN
ejpam-5720	124	8	−v	−v	NOUN
ejpam-5720	124	9	is	be	AUX
ejpam-5720	124	10	(	(	PUNCT
ejpam-5720	124	11	σ1	σ1	PROPN
ejpam-5720	124	12	,	,	PUNCT
ejpam-5720	124	13	σ2)-closed	σ2)-close	VERB
ejpam-5720	124	14	n	n	PROPN
ejpam-5720	124	15	(	(	PUNCT
ejpam-5720	124	16	σ1	σ1	PROPN
ejpam-5720	124	17	,	,	PUNCT
ejpam-5720	124	18	σ2)closed	σ2)close	VERB
ejpam-5720	124	19	set	set	NOUN
ejpam-5720	124	20	of	of	ADP
ejpam-5720	124	21	y	y	PROPN
ejpam-5720	124	22	and	and	CCONJ
ejpam-5720	124	23	x	x	PROPN
ejpam-5720	124	24	∈	∈	PROPN
ejpam-5720	124	25	f+(y	f+(y	VERB
ejpam-5720	124	26	−k	−k	PROPN
ejpam-5720	124	27	)	)	PUNCT
ejpam-5720	124	28	.	.	PUNCT
ejpam-5720	125	1	let	let	VERB
ejpam-5720	125	2	u	u	PRON
ejpam-5720	125	3	be	be	AUX
ejpam-5720	125	4	a	a	DET
ejpam-5720	125	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	125	6	-	-	ADJ
ejpam-5720	125	7	open	open	ADJ
ejpam-5720	125	8	set	set	NOUN
ejpam-5720	125	9	of	of	ADP
ejpam-5720	125	10	x	x	PUNCT
ejpam-5720	125	11	containing	contain	VERB
ejpam-5720	125	12	x.	x.	NOUN
ejpam-5720	125	13	then	then	ADV
ejpam-5720	125	14	,	,	PUNCT
ejpam-5720	125	15	h	h	NOUN
ejpam-5720	125	16	=	=	PUNCT
ejpam-5720	125	17	x−u	x−u	PROPN
ejpam-5720	125	18	is	be	AUX
ejpam-5720	125	19	a	a	DET
ejpam-5720	125	20	τ1τ2	τ1τ2	ADJ
ejpam-5720	125	21	-	-	ADJ
ejpam-5720	125	22	closed	closed	ADJ
ejpam-5720	125	23	set	set	NOUN
ejpam-5720	125	24	such	such	ADJ
ejpam-5720	125	25	that	that	SCONJ
ejpam-5720	125	26	x	x	SYM
ejpam-5720	125	27	∈	∈	NOUN
ejpam-5720	125	28	x−h	x−h	PROPN
ejpam-5720	125	29	.	.	PUNCT
ejpam-5720	126	1	by	by	ADP
ejpam-5720	126	2	the	the	DET
ejpam-5720	126	3	hypothesis	hypothesis	NOUN
ejpam-5720	126	4	,	,	PUNCT
ejpam-5720	126	5	there	there	PRON
ejpam-5720	126	6	exists	exist	VERB
ejpam-5720	126	7	a	a	DET
ejpam-5720	126	8	τ1τ2closed	τ1τ2close	VERB
ejpam-5720	126	9	set	set	NOUN
ejpam-5720	126	10	m	m	VERB
ejpam-5720	126	11	such	such	ADJ
ejpam-5720	126	12	that	that	SCONJ
ejpam-5720	126	13	h	h	NOUN
ejpam-5720	126	14	⊆	⊆	NUM
ejpam-5720	126	15	m	m	NOUN
ejpam-5720	126	16	,	,	PUNCT
ejpam-5720	126	17	m	m	VERB
ejpam-5720	126	18	̸=	̸=	NOUN
ejpam-5720	126	19	x	x	PUNCT
ejpam-5720	126	20	and	and	CCONJ
ejpam-5720	126	21	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	126	22	-	-	PUNCT
ejpam-5720	126	23	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	126	24	-	-	PUNCT
ejpam-5720	126	25	int(k	int(k	NOUN
ejpam-5720	126	26	)	)	PUNCT
ejpam-5720	126	27	)	)	PUNCT
ejpam-5720	126	28	)	)	PUNCT
ejpam-5720	127	1	⊆	⊆	NUM
ejpam-5720	127	2	m	m	NOUN
ejpam-5720	127	3	.	.	PUNCT
ejpam-5720	128	1	the	the	DET
ejpam-5720	128	2	last	last	ADJ
ejpam-5720	128	3	inclusion	inclusion	NOUN
ejpam-5720	128	4	implies	imply	VERB
ejpam-5720	128	5	that	that	SCONJ
ejpam-5720	128	6	x	x	PUNCT
ejpam-5720	128	7	−f+(σ1σ2	−f+(σ1σ2	X
ejpam-5720	128	8	-	-	PUNCT
ejpam-5720	128	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	128	10	-	-	PUNCT
ejpam-5720	128	11	cl(v	cl(v	NOUN
ejpam-5720	128	12	)	)	PUNCT
ejpam-5720	128	13	)	)	PUNCT
ejpam-5720	128	14	)	)	PUNCT
ejpam-5720	129	1	⊆	⊆	NUM
ejpam-5720	129	2	m	m	NOUN
ejpam-5720	129	3	=	=	PUNCT
ejpam-5720	129	4	x	x	PUNCT
ejpam-5720	129	5	−w	−w	ADV
ejpam-5720	129	6	,	,	PUNCT
ejpam-5720	129	7	where	where	SCONJ
ejpam-5720	129	8	w	w	NOUN
ejpam-5720	129	9	=	=	NOUN
ejpam-5720	129	10	x	x	SYM
ejpam-5720	129	11	−m	−m	NOUN
ejpam-5720	129	12	is	be	AUX
ejpam-5720	129	13	a	a	DET
ejpam-5720	129	14	nonempty	nonempty	ADJ
ejpam-5720	129	15	τ1τ2	τ1τ2	NOUN
ejpam-5720	129	16	-	-	ADJ
ejpam-5720	129	17	open	open	ADJ
ejpam-5720	129	18	set	set	NOUN
ejpam-5720	129	19	.	.	PUNCT
ejpam-5720	130	1	it	it	PRON
ejpam-5720	130	2	was	be	AUX
ejpam-5720	130	3	shown	show	VERB
ejpam-5720	130	4	that	that	SCONJ
ejpam-5720	130	5	w	w	ADP
ejpam-5720	130	6	⊆	⊆	NUM
ejpam-5720	130	7	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	130	8	-	-	PUNCT
ejpam-5720	130	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	130	10	-	-	PUNCT
ejpam-5720	130	11	cl(v	cl(v	NOUN
ejpam-5720	130	12	)	)	PUNCT
ejpam-5720	130	13	)	)	PUNCT
ejpam-5720	130	14	)	)	PUNCT
ejpam-5720	130	15	.	.	PUNCT
ejpam-5720	131	1	it	it	PRON
ejpam-5720	131	2	is	be	AUX
ejpam-5720	131	3	easy	easy	ADJ
ejpam-5720	131	4	to	to	PART
ejpam-5720	131	5	see	see	VERB
ejpam-5720	131	6	that	that	SCONJ
ejpam-5720	131	7	w	w	ADP
ejpam-5720	131	8	⊆	⊆	NUM
ejpam-5720	131	9	u	u	NOUN
ejpam-5720	131	10	.	.	PUNCT
ejpam-5720	132	1	(	(	PUNCT
ejpam-5720	132	2	1	1	X
ejpam-5720	132	3	)	)	PUNCT
ejpam-5720	132	4	⇒	⇒	NOUN
ejpam-5720	132	5	(	(	PUNCT
ejpam-5720	132	6	4	4	NUM
ejpam-5720	132	7	):	):	PUNCT
ejpam-5720	132	8	let	let	VERB
ejpam-5720	132	9	x	x	PUNCT
ejpam-5720	132	10	∈	∈	PROPN
ejpam-5720	132	11	x	x	X
ejpam-5720	132	12	and	and	CCONJ
ejpam-5720	132	13	v	v	X
ejpam-5720	132	14	be	be	AUX
ejpam-5720	132	15	any	any	DET
ejpam-5720	132	16	σ1σ2	σ1σ2	NOUN
ejpam-5720	132	17	-	-	ADJ
ejpam-5720	132	18	open	open	ADJ
ejpam-5720	132	19	set	set	NOUN
ejpam-5720	132	20	of	of	ADP
ejpam-5720	132	21	y	y	PROPN
ejpam-5720	132	22	having	have	VERB
ejpam-5720	132	23	n	n	PROPN
ejpam-5720	132	24	(	(	PUNCT
ejpam-5720	132	25	σ1	σ1	PROPN
ejpam-5720	132	26	,	,	PUNCT
ejpam-5720	132	27	σ2)-closed	σ2)-close	VERB
ejpam-5720	132	28	complement	complement	NOUN
ejpam-5720	132	29	such	such	ADJ
ejpam-5720	132	30	that	that	SCONJ
ejpam-5720	132	31	f	f	PROPN
ejpam-5720	132	32	(	(	PUNCT
ejpam-5720	132	33	x	x	X
ejpam-5720	132	34	)	)	PUNCT
ejpam-5720	132	35	⊆	⊆	NUM
ejpam-5720	132	36	v	v	NOUN
ejpam-5720	132	37	.	.	PUNCT
ejpam-5720	133	1	then	then	ADV
ejpam-5720	133	2	,	,	PUNCT
ejpam-5720	133	3	for	for	ADP
ejpam-5720	133	4	any	any	DET
ejpam-5720	133	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	133	6	-	-	ADJ
ejpam-5720	133	7	open	open	ADJ
ejpam-5720	133	8	set	set	ADJ
ejpam-5720	133	9	u	u	NOUN
ejpam-5720	133	10	of	of	ADP
ejpam-5720	133	11	x	x	PUNCT
ejpam-5720	133	12	containing	contain	VERB
ejpam-5720	133	13	x	x	PRON
ejpam-5720	133	14	,	,	PUNCT
ejpam-5720	133	15	there	there	PRON
ejpam-5720	133	16	exists	exist	VERB
ejpam-5720	133	17	a	a	DET
ejpam-5720	133	18	nonempty	nonempty	ADJ
ejpam-5720	133	19	τ1τ2	τ1τ2	NOUN
ejpam-5720	133	20	-	-	ADJ
ejpam-5720	133	21	open	open	ADJ
ejpam-5720	133	22	set	set	VERB
ejpam-5720	133	23	wu	wu	PROPN
ejpam-5720	133	24	such	such	ADJ
ejpam-5720	133	25	that	that	SCONJ
ejpam-5720	133	26	wu	wu	PROPN
ejpam-5720	133	27	⊆	⊆	NUM
ejpam-5720	133	28	u	u	NOUN
ejpam-5720	133	29	and	and	CCONJ
ejpam-5720	133	30	wu	wu	PROPN
ejpam-5720	133	31	⊆	⊆	NUM
ejpam-5720	133	32	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	133	33	-	-	PUNCT
ejpam-5720	133	34	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	133	35	-	-	PUNCT
ejpam-5720	133	36	cl(v	cl(v	NOUN
ejpam-5720	133	37	)	)	PUNCT
ejpam-5720	133	38	)	)	PUNCT
ejpam-5720	133	39	)	)	PUNCT
ejpam-5720	133	40	.	.	PUNCT
ejpam-5720	134	1	let	let	VERB
ejpam-5720	134	2	g	g	NOUN
ejpam-5720	134	3	=	=	SYM
ejpam-5720	134	4	{	{	PUNCT
ejpam-5720	134	5	x	x	NOUN
ejpam-5720	134	6	}	}	PUNCT
ejpam-5720	134	7	∪	∪	ADP
ejpam-5720	134	8	[	[	PUNCT
ejpam-5720	134	9	∪{wu	∪{wu	NUM
ejpam-5720	134	10	|	|	ADV
ejpam-5720	134	11	u	u	NOUN
ejpam-5720	134	12	is	be	AUX
ejpam-5720	134	13	a	a	DET
ejpam-5720	134	14	τ1τ2	τ1τ2	ADJ
ejpam-5720	134	15	-	-	ADJ
ejpam-5720	134	16	open	open	ADJ
ejpam-5720	134	17	set	set	NOUN
ejpam-5720	134	18	containing	contain	VERB
ejpam-5720	134	19	x	x	X
ejpam-5720	134	20	}	}	PUNCT
ejpam-5720	134	21	]	]	PUNCT
ejpam-5720	134	22	.	.	PUNCT
ejpam-5720	135	1	then	then	ADV
ejpam-5720	135	2	,	,	PUNCT
ejpam-5720	135	3	we	we	PRON
ejpam-5720	135	4	have	have	VERB
ejpam-5720	135	5	g	g	NOUN
ejpam-5720	135	6	⊆	⊆	NUM
ejpam-5720	135	7	τ1τ2	τ1τ2	NOUN
ejpam-5720	135	8	-	-	PUNCT
ejpam-5720	135	9	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	135	10	-	-	PUNCT
ejpam-5720	135	11	int(g	int(g	NOUN
ejpam-5720	135	12	)	)	PUNCT
ejpam-5720	135	13	)	)	PUNCT
ejpam-5720	135	14	and	and	CCONJ
ejpam-5720	135	15	hence	hence	ADV
ejpam-5720	135	16	g	g	PROPN
ejpam-5720	135	17	is	be	AUX
ejpam-5720	135	18	a	a	DET
ejpam-5720	135	19	(	(	PUNCT
ejpam-5720	135	20	τ1	τ1	NOUN
ejpam-5720	135	21	,	,	PUNCT
ejpam-5720	135	22	τ2)s	τ2)s	NOUN
ejpam-5720	135	23	-	-	PUNCT
ejpam-5720	135	24	open	open	NOUN
ejpam-5720	135	25	set	set	NOUN
ejpam-5720	135	26	such	such	ADJ
ejpam-5720	135	27	that	that	SCONJ
ejpam-5720	135	28	x	x	SYM
ejpam-5720	135	29	∈	∈	PROPN
ejpam-5720	135	30	g	g	NOUN
ejpam-5720	135	31	and	and	CCONJ
ejpam-5720	135	32	g	g	NOUN
ejpam-5720	135	33	⊆	⊆	NUM
ejpam-5720	135	34	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	135	35	-	-	PUNCT
ejpam-5720	135	36	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	135	37	-	-	PUNCT
ejpam-5720	135	38	cl(v	cl(v	NOUN
ejpam-5720	135	39	)	)	PUNCT
ejpam-5720	135	40	)	)	PUNCT
ejpam-5720	135	41	)	)	PUNCT
ejpam-5720	135	42	.	.	PUNCT
ejpam-5720	136	1	(	(	PUNCT
ejpam-5720	136	2	4	4	X
ejpam-5720	136	3	)	)	PUNCT
ejpam-5720	136	4	⇒	⇒	NOUN
ejpam-5720	136	5	(	(	PUNCT
ejpam-5720	136	6	1	1	NUM
ejpam-5720	136	7	):	):	PUNCT
ejpam-5720	136	8	let	let	VERB
ejpam-5720	136	9	x	x	PUNCT
ejpam-5720	136	10	∈	∈	PROPN
ejpam-5720	136	11	x	x	X
ejpam-5720	136	12	and	and	CCONJ
ejpam-5720	136	13	v	v	X
ejpam-5720	136	14	be	be	AUX
ejpam-5720	136	15	any	any	DET
ejpam-5720	136	16	σ1σ2	σ1σ2	NOUN
ejpam-5720	136	17	-	-	ADJ
ejpam-5720	136	18	open	open	ADJ
ejpam-5720	136	19	set	set	NOUN
ejpam-5720	136	20	of	of	ADP
ejpam-5720	136	21	y	y	PROPN
ejpam-5720	136	22	having	have	VERB
ejpam-5720	136	23	n	n	PROPN
ejpam-5720	136	24	(	(	PUNCT
ejpam-5720	136	25	σ1	σ1	PROPN
ejpam-5720	136	26	,	,	PUNCT
ejpam-5720	136	27	σ2)-closed	σ2)-close	VERB
ejpam-5720	136	28	complement	complement	NOUN
ejpam-5720	136	29	such	such	ADJ
ejpam-5720	136	30	that	that	SCONJ
ejpam-5720	136	31	f	f	PROPN
ejpam-5720	136	32	(	(	PUNCT
ejpam-5720	136	33	x	x	X
ejpam-5720	136	34	)	)	PUNCT
ejpam-5720	136	35	⊆	⊆	NUM
ejpam-5720	136	36	v	v	NOUN
ejpam-5720	136	37	.	.	PUNCT
ejpam-5720	137	1	let	let	VERB
ejpam-5720	137	2	u	u	PRON
ejpam-5720	137	3	be	be	AUX
ejpam-5720	137	4	a	a	DET
ejpam-5720	137	5	τ1τ2	τ1τ2	ADJ
ejpam-5720	137	6	-	-	ADJ
ejpam-5720	137	7	open	open	ADJ
ejpam-5720	137	8	set	set	NOUN
ejpam-5720	137	9	of	of	ADP
ejpam-5720	137	10	x	x	PUNCT
ejpam-5720	137	11	containing	contain	VERB
ejpam-5720	137	12	x.	x.	NOUN
ejpam-5720	137	13	by	by	ADP
ejpam-5720	137	14	the	the	DET
ejpam-5720	137	15	hypothesis	hypothesis	NOUN
ejpam-5720	137	16	,	,	PUNCT
ejpam-5720	137	17	there	there	PRON
ejpam-5720	137	18	exists	exist	VERB
ejpam-5720	137	19	a	a	DET
ejpam-5720	137	20	(	(	PUNCT
ejpam-5720	137	21	τ1	τ1	NOUN
ejpam-5720	137	22	,	,	PUNCT
ejpam-5720	137	23	τ2)s	τ2)s	NOUN
ejpam-5720	137	24	-	-	PUNCT
ejpam-5720	137	25	open	open	NOUN
ejpam-5720	137	26	set	set	NOUN
ejpam-5720	137	27	g	g	PROPN
ejpam-5720	137	28	such	such	ADJ
ejpam-5720	137	29	that	that	SCONJ
ejpam-5720	137	30	x	x	SYM
ejpam-5720	137	31	∈	∈	PROPN
ejpam-5720	137	32	g	g	NOUN
ejpam-5720	137	33	and	and	CCONJ
ejpam-5720	137	34	g	g	NOUN
ejpam-5720	137	35	⊆	⊆	NUM
ejpam-5720	137	36	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	137	37	-	-	PUNCT
ejpam-5720	137	38	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	137	39	-	-	PUNCT
ejpam-5720	137	40	cl(v	cl(v	NOUN
ejpam-5720	137	41	)	)	PUNCT
ejpam-5720	137	42	)	)	PUNCT
ejpam-5720	137	43	)	)	PUNCT
ejpam-5720	137	44	.	.	PUNCT
ejpam-5720	138	1	j.	j.	PROPN
ejpam-5720	138	2	khampakdee	khampakdee	PROPN
ejpam-5720	138	3	,	,	PUNCT
ejpam-5720	138	4	a.	a.	PROPN
ejpam-5720	138	5	sama	sama	PROPN
ejpam-5720	138	6	-	-	PUNCT
ejpam-5720	138	7	ae	ae	PROPN
ejpam-5720	138	8	,	,	PUNCT
ejpam-5720	138	9	c.	c.	PROPN
ejpam-5720	138	10	boonpok	boonpok	PROPN
ejpam-5720	138	11	/	/	SYM
ejpam-5720	138	12	eur	eur	PROPN
ejpam-5720	138	13	.	.	PUNCT
ejpam-5720	139	1	j.	j.	PROPN
ejpam-5720	139	2	pure	pure	PROPN
ejpam-5720	139	3	appl	appl	PROPN
ejpam-5720	139	4	.	.	PROPN
ejpam-5720	139	5	math	math	PROPN
ejpam-5720	139	6	,	,	PUNCT
ejpam-5720	139	7	18	18	NUM
ejpam-5720	139	8	(	(	PUNCT
ejpam-5720	139	9	1	1	NUM
ejpam-5720	139	10	)	)	PUNCT
ejpam-5720	139	11	(	(	PUNCT
ejpam-5720	139	12	2025	2025	NUM
ejpam-5720	139	13	)	)	PUNCT
ejpam-5720	139	14	,	,	PUNCT
ejpam-5720	139	15	5720	5720	NUM
ejpam-5720	139	16	6	6	NUM
ejpam-5720	139	17	of	of	ADP
ejpam-5720	139	18	15	15	NUM
ejpam-5720	139	19	let	let	VERB
ejpam-5720	139	20	w	w	NOUN
ejpam-5720	139	21	=	=	PUNCT
ejpam-5720	139	22	τ1τ2	τ1τ2	X
ejpam-5720	139	23	-	-	PUNCT
ejpam-5720	139	24	int(g	int(g	NOUN
ejpam-5720	139	25	)	)	PUNCT
ejpam-5720	139	26	∩	∩	NOUN
ejpam-5720	139	27	u	u	NOUN
ejpam-5720	139	28	.	.	PUNCT
ejpam-5720	140	1	since	since	SCONJ
ejpam-5720	140	2	u	u	NOUN
ejpam-5720	140	3	∩	∩	NOUN
ejpam-5720	140	4	g	g	PROPN
ejpam-5720	140	5	̸=	̸=	PROPN
ejpam-5720	140	6	∅	∅	NOUN
ejpam-5720	140	7	,	,	PUNCT
ejpam-5720	140	8	we	we	PRON
ejpam-5720	140	9	have	have	VERB
ejpam-5720	140	10	w	w	ADP
ejpam-5720	140	11	̸=	̸=	PROPN
ejpam-5720	140	12	∅.	∅.	ADP
ejpam-5720	140	13	it	it	PRON
ejpam-5720	140	14	is	be	AUX
ejpam-5720	140	15	easy	easy	ADJ
ejpam-5720	140	16	to	to	PART
ejpam-5720	140	17	check	check	VERB
ejpam-5720	140	18	that	that	PRON
ejpam-5720	140	19	w	w	ADP
ejpam-5720	140	20	⊆	⊆	NUM
ejpam-5720	140	21	u	u	NOUN
ejpam-5720	140	22	and	and	CCONJ
ejpam-5720	140	23	w	w	PROPN
ejpam-5720	140	24	⊆	⊆	NUM
ejpam-5720	140	25	g.	g.	NOUN
ejpam-5720	140	26	thus	thus	ADV
ejpam-5720	140	27	,	,	PUNCT
ejpam-5720	140	28	w	w	ADP
ejpam-5720	140	29	⊆	⊆	NUM
ejpam-5720	140	30	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	140	31	-	-	PUNCT
ejpam-5720	140	32	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	140	33	-	-	PUNCT
ejpam-5720	140	34	cl(v	cl(v	NOUN
ejpam-5720	140	35	)	)	PUNCT
ejpam-5720	140	36	)	)	PUNCT
ejpam-5720	140	37	)	)	PUNCT
ejpam-5720	140	38	.	.	PUNCT
ejpam-5720	141	1	(	(	PUNCT
ejpam-5720	141	2	4	4	X
ejpam-5720	141	3	)	)	PUNCT
ejpam-5720	141	4	⇒	⇒	NOUN
ejpam-5720	141	5	(	(	PUNCT
ejpam-5720	141	6	5	5	NUM
ejpam-5720	141	7	):	):	PUNCT
ejpam-5720	141	8	let	let	VERB
ejpam-5720	141	9	v	v	PART
ejpam-5720	141	10	be	be	AUX
ejpam-5720	141	11	any	any	DET
ejpam-5720	141	12	(	(	PUNCT
ejpam-5720	141	13	σ1	σ1	NOUN
ejpam-5720	141	14	,	,	PUNCT
ejpam-5720	141	15	σ2)r	σ2)r	NOUN
ejpam-5720	141	16	-	-	PUNCT
ejpam-5720	141	17	open	open	ADJ
ejpam-5720	141	18	set	set	NOUN
ejpam-5720	141	19	of	of	ADP
ejpam-5720	141	20	y	y	PROPN
ejpam-5720	141	21	having	have	VERB
ejpam-5720	141	22	n	n	PROPN
ejpam-5720	141	23	(	(	PUNCT
ejpam-5720	141	24	σ1	σ1	PROPN
ejpam-5720	141	25	,	,	PUNCT
ejpam-5720	141	26	σ2)-closed	σ2)-close	VERB
ejpam-5720	141	27	complement	complement	NOUN
ejpam-5720	141	28	and	and	CCONJ
ejpam-5720	141	29	x	x	NOUN
ejpam-5720	141	30	∈	∈	PROPN
ejpam-5720	141	31	f+(v	f+(v	NOUN
ejpam-5720	141	32	)	)	PUNCT
ejpam-5720	141	33	.	.	PUNCT
ejpam-5720	142	1	then	then	ADV
ejpam-5720	142	2	f	f	X
ejpam-5720	142	3	(	(	PUNCT
ejpam-5720	142	4	x	x	X
ejpam-5720	142	5	)	)	PUNCT
ejpam-5720	142	6	⊆	⊆	NUM
ejpam-5720	142	7	v	v	NOUN
ejpam-5720	142	8	.	.	PUNCT
ejpam-5720	143	1	under	under	ADP
ejpam-5720	143	2	the	the	DET
ejpam-5720	143	3	assumption	assumption	NOUN
ejpam-5720	143	4	,	,	PUNCT
ejpam-5720	143	5	there	there	PRON
ejpam-5720	143	6	exists	exist	VERB
ejpam-5720	143	7	a	a	DET
ejpam-5720	143	8	(	(	PUNCT
ejpam-5720	143	9	τ1	τ1	NOUN
ejpam-5720	143	10	,	,	PUNCT
ejpam-5720	143	11	τ2)s	τ2)s	NOUN
ejpam-5720	143	12	-	-	PUNCT
ejpam-5720	143	13	open	open	ADJ
ejpam-5720	143	14	set	set	VERB
ejpam-5720	143	15	gx	gx	PROPN
ejpam-5720	143	16	such	such	ADJ
ejpam-5720	143	17	that	that	SCONJ
ejpam-5720	143	18	x	x	SYM
ejpam-5720	143	19	∈	∈	PROPN
ejpam-5720	143	20	gx	gx	PROPN
ejpam-5720	143	21	and	and	CCONJ
ejpam-5720	143	22	gx	gx	PROPN
ejpam-5720	143	23	⊆	⊆	NUM
ejpam-5720	143	24	f+(v	f+(v	NOUN
ejpam-5720	143	25	)	)	PUNCT
ejpam-5720	144	1	=	=	SYM
ejpam-5720	144	2	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5720	144	3	-	-	PUNCT
ejpam-5720	144	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	144	5	-	-	PUNCT
ejpam-5720	144	6	cl(v	cl(v	NOUN
ejpam-5720	144	7	)	)	PUNCT
ejpam-5720	144	8	)	)	PUNCT
ejpam-5720	144	9	)	)	PUNCT
ejpam-5720	144	10	.	.	PUNCT
ejpam-5720	145	1	it	it	PRON
ejpam-5720	145	2	is	be	AUX
ejpam-5720	145	3	easily	easily	ADV
ejpam-5720	145	4	seen	see	VERB
ejpam-5720	145	5	that	that	SCONJ
ejpam-5720	145	6	the	the	DET
ejpam-5720	145	7	set	set	NOUN
ejpam-5720	145	8	g	g	PROPN
ejpam-5720	145	9	=	=	PUNCT
ejpam-5720	145	10	∪{gx	∪{gx	PROPN
ejpam-5720	145	11	|	|	NOUN
ejpam-5720	145	12	x	x	SYM
ejpam-5720	145	13	∈	∈	PROPN
ejpam-5720	145	14	f+(v	f+(v	NOUN
ejpam-5720	145	15	)	)	PUNCT
ejpam-5720	145	16	}	}	PUNCT
ejpam-5720	145	17	is	be	AUX
ejpam-5720	145	18	(	(	PUNCT
ejpam-5720	145	19	τ1	τ1	NOUN
ejpam-5720	145	20	,	,	PUNCT
ejpam-5720	145	21	τ2)s	τ2)s	NOUN
ejpam-5720	145	22	-	-	PUNCT
ejpam-5720	145	23	open	open	ADJ
ejpam-5720	145	24	and	and	CCONJ
ejpam-5720	145	25	equal	equal	ADJ
ejpam-5720	145	26	to	to	ADP
ejpam-5720	145	27	the	the	DET
ejpam-5720	145	28	set	set	NOUN
ejpam-5720	145	29	f+(v	f+(v	NOUN
ejpam-5720	145	30	)	)	PUNCT
ejpam-5720	145	31	.	.	PUNCT
ejpam-5720	146	1	(	(	PUNCT
ejpam-5720	146	2	5	5	X
ejpam-5720	146	3	)	)	PUNCT
ejpam-5720	146	4	⇒	⇒	NOUN
ejpam-5720	146	5	(	(	PUNCT
ejpam-5720	146	6	4	4	NUM
ejpam-5720	146	7	):	):	PUNCT
ejpam-5720	146	8	let	let	VERB
ejpam-5720	146	9	x	x	PUNCT
ejpam-5720	146	10	∈	∈	PROPN
ejpam-5720	146	11	x	x	X
ejpam-5720	146	12	and	and	CCONJ
ejpam-5720	146	13	v	v	X
ejpam-5720	146	14	be	be	AUX
ejpam-5720	146	15	any	any	DET
ejpam-5720	146	16	σ1σ2	σ1σ2	NOUN
ejpam-5720	146	17	-	-	ADJ
ejpam-5720	146	18	open	open	ADJ
ejpam-5720	146	19	set	set	NOUN
ejpam-5720	146	20	of	of	ADP
ejpam-5720	146	21	y	y	PROPN
ejpam-5720	146	22	having	have	VERB
ejpam-5720	146	23	n	n	PROPN
ejpam-5720	146	24	(	(	PUNCT
ejpam-5720	146	25	σ1	σ1	PROPN
ejpam-5720	146	26	,	,	PUNCT
ejpam-5720	146	27	σ2)-closed	σ2)-close	VERB
ejpam-5720	146	28	complement	complement	NOUN
ejpam-5720	146	29	such	such	ADJ
ejpam-5720	146	30	that	that	SCONJ
ejpam-5720	146	31	f	f	PROPN
ejpam-5720	146	32	(	(	PUNCT
ejpam-5720	146	33	x	x	X
ejpam-5720	146	34	)	)	PUNCT
ejpam-5720	146	35	⊆	⊆	NUM
ejpam-5720	146	36	v	v	NOUN
ejpam-5720	146	37	.	.	PUNCT
ejpam-5720	147	1	then	then	ADV
ejpam-5720	147	2	by	by	ADP
ejpam-5720	147	3	lemma	lemma	PROPN
ejpam-5720	147	4	3	3	NUM
ejpam-5720	147	5	,	,	PUNCT
ejpam-5720	147	6	σ1σ2	σ1σ2	X
ejpam-5720	147	7	-	-	PUNCT
ejpam-5720	147	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	147	9	-	-	PUNCT
ejpam-5720	147	10	cl(v	cl(v	NOUN
ejpam-5720	147	11	)	)	PUNCT
ejpam-5720	147	12	)	)	PUNCT
ejpam-5720	147	13	is	be	AUX
ejpam-5720	147	14	a	a	DET
ejpam-5720	147	15	(	(	PUNCT
ejpam-5720	147	16	σ1	σ1	NOUN
ejpam-5720	147	17	,	,	PUNCT
ejpam-5720	147	18	σ2)ropen	σ2)ropen	PROPN
ejpam-5720	147	19	set	set	VERB
ejpam-5720	147	20	having	have	VERB
ejpam-5720	147	21	n	n	PROPN
ejpam-5720	147	22	(	(	PUNCT
ejpam-5720	147	23	σ1	σ1	PROPN
ejpam-5720	147	24	,	,	PUNCT
ejpam-5720	147	25	σ2)-closed	σ2)-close	VERB
ejpam-5720	147	26	complement	complement	NOUN
ejpam-5720	147	27	.	.	PUNCT
ejpam-5720	148	1	by	by	ADP
ejpam-5720	148	2	(	(	PUNCT
ejpam-5720	148	3	5	5	NUM
ejpam-5720	148	4	)	)	PUNCT
ejpam-5720	148	5	,	,	PUNCT
ejpam-5720	148	6	we	we	PRON
ejpam-5720	148	7	have	have	VERB
ejpam-5720	148	8	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5720	148	9	-	-	PUNCT
ejpam-5720	148	10	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	148	11	-	-	PUNCT
ejpam-5720	148	12	cl(v	cl(v	NOUN
ejpam-5720	148	13	)	)	PUNCT
ejpam-5720	148	14	)	)	PUNCT
ejpam-5720	148	15	)	)	PUNCT
ejpam-5720	149	1	is	be	AUX
ejpam-5720	149	2	(	(	PUNCT
ejpam-5720	149	3	σ1	σ1	PROPN
ejpam-5720	149	4	,	,	PUNCT
ejpam-5720	149	5	σ2)s	σ2)s	NOUN
ejpam-5720	149	6	-	-	PUNCT
ejpam-5720	149	7	open	open	ADJ
ejpam-5720	149	8	in	in	ADP
ejpam-5720	149	9	x.	x.	NOUN
ejpam-5720	149	10	of	of	ADP
ejpam-5720	149	11	course	course	NOUN
ejpam-5720	149	12	,	,	PUNCT
ejpam-5720	149	13	x	x	X
ejpam-5720	149	14	∈	∈	NOUN
ejpam-5720	149	15	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	149	16	-	-	PUNCT
ejpam-5720	149	17	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	149	18	-	-	PUNCT
ejpam-5720	149	19	cl(v	cl(v	NOUN
ejpam-5720	149	20	)	)	PUNCT
ejpam-5720	149	21	)	)	PUNCT
ejpam-5720	149	22	)	)	PUNCT
ejpam-5720	149	23	.	.	PUNCT
ejpam-5720	150	1	(	(	PUNCT
ejpam-5720	150	2	5	5	X
ejpam-5720	150	3	)	)	PUNCT
ejpam-5720	150	4	⇒	⇒	NOUN
ejpam-5720	150	5	(	(	PUNCT
ejpam-5720	150	6	6	6	NUM
ejpam-5720	150	7	):	):	PUNCT
ejpam-5720	150	8	let	let	VERB
ejpam-5720	150	9	k	k	PRON
ejpam-5720	150	10	be	be	AUX
ejpam-5720	150	11	any	any	DET
ejpam-5720	150	12	(	(	PUNCT
ejpam-5720	150	13	σ1	σ1	NOUN
ejpam-5720	150	14	,	,	PUNCT
ejpam-5720	150	15	σ2)r	σ2)r	NOUN
ejpam-5720	150	16	-	-	PUNCT
ejpam-5720	150	17	closed	close	VERB
ejpam-5720	150	18	n	n	CCONJ
ejpam-5720	150	19	(	(	PUNCT
ejpam-5720	150	20	σ1	σ1	PROPN
ejpam-5720	150	21	,	,	PUNCT
ejpam-5720	150	22	σ2)-closed	σ2)-close	VERB
ejpam-5720	150	23	set	set	NOUN
ejpam-5720	150	24	of	of	ADP
ejpam-5720	150	25	y	y	PROPN
ejpam-5720	150	26	.	.	PUNCT
ejpam-5720	151	1	then	then	ADV
ejpam-5720	151	2	,	,	PUNCT
ejpam-5720	151	3	y	y	PROPN
ejpam-5720	151	4	−	−	PROPN
ejpam-5720	151	5	k	k	PROPN
ejpam-5720	151	6	is	be	AUX
ejpam-5720	151	7	a	a	DET
ejpam-5720	151	8	(	(	PUNCT
ejpam-5720	151	9	σ1	σ1	NOUN
ejpam-5720	151	10	,	,	PUNCT
ejpam-5720	151	11	σ2)r	σ2)r	NOUN
ejpam-5720	151	12	-	-	PUNCT
ejpam-5720	151	13	open	open	ADJ
ejpam-5720	151	14	set	set	NOUN
ejpam-5720	151	15	of	of	ADP
ejpam-5720	151	16	y	y	PROPN
ejpam-5720	151	17	having	have	VERB
ejpam-5720	151	18	n	n	PROPN
ejpam-5720	151	19	(	(	PUNCT
ejpam-5720	151	20	σ1	σ1	PROPN
ejpam-5720	151	21	,	,	PUNCT
ejpam-5720	151	22	σ2)-closed	σ2)-close	VERB
ejpam-5720	151	23	complement	complement	NOUN
ejpam-5720	151	24	.	.	PUNCT
ejpam-5720	152	1	by	by	ADP
ejpam-5720	152	2	(	(	PUNCT
ejpam-5720	152	3	5	5	NUM
ejpam-5720	152	4	)	)	PUNCT
ejpam-5720	152	5	,	,	PUNCT
ejpam-5720	152	6	f+(y	f+(y	PROPN
ejpam-5720	152	7	−k	−k	ADJ
ejpam-5720	152	8	)	)	PUNCT
ejpam-5720	152	9	=	=	PUNCT
ejpam-5720	152	10	x	x	X
ejpam-5720	152	11	−	−	PROPN
ejpam-5720	152	12	f−(k	f−(k	PROPN
ejpam-5720	152	13	)	)	PUNCT
ejpam-5720	152	14	is	be	AUX
ejpam-5720	152	15	(	(	PUNCT
ejpam-5720	152	16	τ1	τ1	NOUN
ejpam-5720	152	17	,	,	PUNCT
ejpam-5720	152	18	τ2)s	τ2)s	NOUN
ejpam-5720	152	19	-	-	PUNCT
ejpam-5720	152	20	open	open	ADJ
ejpam-5720	152	21	in	in	ADP
ejpam-5720	152	22	x	x	X
ejpam-5720	152	23	and	and	CCONJ
ejpam-5720	152	24	hence	hence	ADV
ejpam-5720	152	25	f−(k	f−(k	PROPN
ejpam-5720	152	26	)	)	PUNCT
ejpam-5720	152	27	is	be	AUX
ejpam-5720	152	28	(	(	PUNCT
ejpam-5720	152	29	τ1	τ1	NOUN
ejpam-5720	152	30	,	,	PUNCT
ejpam-5720	152	31	τ2)s	τ2)s	NOUN
ejpam-5720	152	32	-	-	PUNCT
ejpam-5720	152	33	closed	close	VERB
ejpam-5720	152	34	in	in	ADP
ejpam-5720	152	35	x.	x.	NOUN
ejpam-5720	152	36	(	(	PUNCT
ejpam-5720	152	37	6	6	NUM
ejpam-5720	152	38	)	)	PUNCT
ejpam-5720	152	39	⇒	⇒	NOUN
ejpam-5720	152	40	(	(	PUNCT
ejpam-5720	152	41	5	5	NUM
ejpam-5720	152	42	):	):	PUNCT
ejpam-5720	152	43	the	the	DET
ejpam-5720	152	44	proof	proof	NOUN
ejpam-5720	152	45	is	be	AUX
ejpam-5720	152	46	similar	similar	ADJ
ejpam-5720	152	47	to	to	ADP
ejpam-5720	152	48	the	the	DET
ejpam-5720	152	49	above	above	ADJ
ejpam-5720	152	50	.	.	PUNCT
ejpam-5720	153	1	definition	definition	NOUN
ejpam-5720	153	2	2	2	NUM
ejpam-5720	153	3	.	.	PUNCT
ejpam-5720	153	4	a	a	DET
ejpam-5720	153	5	multifunction	multifunction	NOUN
ejpam-5720	153	6	f	f	NOUN
ejpam-5720	153	7	:	:	PUNCT
ejpam-5720	153	8	(	(	PUNCT
ejpam-5720	153	9	x	x	NOUN
ejpam-5720	153	10	,	,	PUNCT
ejpam-5720	153	11	τ1	τ1	NOUN
ejpam-5720	153	12	,	,	PUNCT
ejpam-5720	153	13	τ2	τ2	NOUN
ejpam-5720	153	14	)	)	PUNCT
ejpam-5720	153	15	→	→	SYM
ejpam-5720	153	16	(	(	PUNCT
ejpam-5720	153	17	y	y	PROPN
ejpam-5720	153	18	,	,	PUNCT
ejpam-5720	153	19	σ1	σ1	PROPN
ejpam-5720	153	20	,	,	PUNCT
ejpam-5720	153	21	σ2	σ2	PROPN
ejpam-5720	153	22	)	)	PUNCT
ejpam-5720	153	23	is	be	AUX
ejpam-5720	153	24	said	say	VERB
ejpam-5720	153	25	to	to	PART
ejpam-5720	153	26	be	be	AUX
ejpam-5720	153	27	lower	low	ADJ
ejpam-5720	153	28	almost	almost	ADV
ejpam-5720	153	29	nearly	nearly	ADV
ejpam-5720	153	30	quasi	quasi	NOUN
ejpam-5720	153	31	(	(	PUNCT
ejpam-5720	153	32	τ1	τ1	NOUN
ejpam-5720	153	33	,	,	PUNCT
ejpam-5720	153	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	153	35	at	at	ADP
ejpam-5720	153	36	a	a	DET
ejpam-5720	153	37	point	point	NOUN
ejpam-5720	153	38	x	x	SYM
ejpam-5720	153	39	∈	∈	NOUN
ejpam-5720	153	40	x	x	PUNCT
ejpam-5720	153	41	if	if	SCONJ
ejpam-5720	153	42	for	for	ADP
ejpam-5720	153	43	each	each	DET
ejpam-5720	153	44	σ1σ2	σ1σ2	VERB
ejpam-5720	153	45	-	-	ADJ
ejpam-5720	153	46	open	open	ADJ
ejpam-5720	153	47	set	set	NOUN
ejpam-5720	153	48	v	v	NOUN
ejpam-5720	153	49	of	of	ADP
ejpam-5720	153	50	y	y	PROPN
ejpam-5720	153	51	having	have	VERB
ejpam-5720	153	52	n	n	PROPN
ejpam-5720	153	53	(	(	PUNCT
ejpam-5720	153	54	σ1	σ1	PROPN
ejpam-5720	153	55	,	,	PUNCT
ejpam-5720	153	56	σ2)-closed	σ2)-close	VERB
ejpam-5720	153	57	complement	complement	NOUN
ejpam-5720	153	58	such	such	ADJ
ejpam-5720	153	59	that	that	SCONJ
ejpam-5720	153	60	x	x	SYM
ejpam-5720	153	61	∈	∈	PROPN
ejpam-5720	153	62	f−(v	f−(v	NOUN
ejpam-5720	153	63	)	)	PUNCT
ejpam-5720	153	64	and	and	CCONJ
ejpam-5720	153	65	for	for	ADP
ejpam-5720	153	66	every	every	DET
ejpam-5720	153	67	τ1τ2	τ1τ2	ADJ
ejpam-5720	153	68	-	-	ADJ
ejpam-5720	153	69	open	open	ADJ
ejpam-5720	153	70	set	set	NOUN
ejpam-5720	153	71	of	of	ADP
ejpam-5720	153	72	x	x	PUNCT
ejpam-5720	153	73	containing	contain	VERB
ejpam-5720	153	74	x	x	PRON
ejpam-5720	153	75	,	,	PUNCT
ejpam-5720	153	76	there	there	PRON
ejpam-5720	153	77	exists	exist	VERB
ejpam-5720	153	78	a	a	DET
ejpam-5720	153	79	nonempty	nonempty	ADJ
ejpam-5720	153	80	τ1τ2	τ1τ2	NOUN
ejpam-5720	153	81	-	-	ADJ
ejpam-5720	153	82	open	open	ADJ
ejpam-5720	153	83	set	set	NOUN
ejpam-5720	153	84	w	w	ADP
ejpam-5720	153	85	such	such	ADJ
ejpam-5720	153	86	that	that	DET
ejpam-5720	153	87	w	w	ADP
ejpam-5720	153	88	⊆	⊆	NUM
ejpam-5720	153	89	u	u	NOUN
ejpam-5720	153	90	and	and	CCONJ
ejpam-5720	153	91	w	w	NOUN
ejpam-5720	153	92	⊆	⊆	NUM
ejpam-5720	153	93	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5720	153	94	-	-	PUNCT
ejpam-5720	153	95	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	153	96	-	-	PUNCT
ejpam-5720	153	97	cl(v	cl(v	NOUN
ejpam-5720	153	98	)	)	PUNCT
ejpam-5720	153	99	)	)	PUNCT
ejpam-5720	153	100	)	)	PUNCT
ejpam-5720	153	101	.	.	PUNCT
ejpam-5720	154	1	a	a	DET
ejpam-5720	154	2	multifunction	multifunction	NOUN
ejpam-5720	154	3	f	f	NOUN
ejpam-5720	154	4	:	:	PUNCT
ejpam-5720	154	5	(	(	PUNCT
ejpam-5720	154	6	x	x	NOUN
ejpam-5720	154	7	,	,	PUNCT
ejpam-5720	154	8	τ1	τ1	NOUN
ejpam-5720	154	9	,	,	PUNCT
ejpam-5720	154	10	τ2	τ2	NOUN
ejpam-5720	154	11	)	)	PUNCT
ejpam-5720	154	12	→	→	SYM
ejpam-5720	154	13	(	(	PUNCT
ejpam-5720	154	14	y	y	PROPN
ejpam-5720	154	15	,	,	PUNCT
ejpam-5720	154	16	σ1	σ1	PROPN
ejpam-5720	154	17	,	,	PUNCT
ejpam-5720	154	18	σ2	σ2	PROPN
ejpam-5720	154	19	)	)	PUNCT
ejpam-5720	154	20	is	be	AUX
ejpam-5720	154	21	said	say	VERB
ejpam-5720	154	22	to	to	PART
ejpam-5720	154	23	be	be	AUX
ejpam-5720	154	24	lower	low	ADJ
ejpam-5720	154	25	almost	almost	ADV
ejpam-5720	154	26	nearly	nearly	ADV
ejpam-5720	154	27	quasi	quasi	NOUN
ejpam-5720	154	28	(	(	PUNCT
ejpam-5720	154	29	τ1	τ1	NOUN
ejpam-5720	154	30	,	,	PUNCT
ejpam-5720	154	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	154	32	if	if	SCONJ
ejpam-5720	154	33	f	f	PROPN
ejpam-5720	154	34	is	be	AUX
ejpam-5720	154	35	lower	low	ADJ
ejpam-5720	154	36	almost	almost	ADV
ejpam-5720	154	37	nearly	nearly	ADV
ejpam-5720	154	38	quasi	quasi	NOUN
ejpam-5720	154	39	(	(	PUNCT
ejpam-5720	154	40	τ1	τ1	NOUN
ejpam-5720	154	41	,	,	PUNCT
ejpam-5720	154	42	τ2)continuous	τ2)continuous	ADJ
ejpam-5720	154	43	at	at	ADP
ejpam-5720	154	44	each	each	DET
ejpam-5720	154	45	point	point	NOUN
ejpam-5720	154	46	x	x	PUNCT
ejpam-5720	154	47	of	of	ADP
ejpam-5720	154	48	x.	x.	PROPN
ejpam-5720	154	49	theorem	theorem	VERB
ejpam-5720	154	50	2	2	NUM
ejpam-5720	154	51	.	.	X
ejpam-5720	154	52	for	for	ADP
ejpam-5720	154	53	a	a	DET
ejpam-5720	154	54	multifunction	multifunction	NOUN
ejpam-5720	154	55	f	f	NOUN
ejpam-5720	154	56	:	:	PUNCT
ejpam-5720	154	57	(	(	PUNCT
ejpam-5720	154	58	x	x	NOUN
ejpam-5720	154	59	,	,	PUNCT
ejpam-5720	154	60	τ1	τ1	NOUN
ejpam-5720	154	61	,	,	PUNCT
ejpam-5720	154	62	τ2	τ2	NOUN
ejpam-5720	154	63	)	)	PUNCT
ejpam-5720	154	64	→	→	SYM
ejpam-5720	154	65	(	(	PUNCT
ejpam-5720	154	66	y	y	PROPN
ejpam-5720	154	67	,	,	PUNCT
ejpam-5720	154	68	σ1	σ1	PROPN
ejpam-5720	154	69	,	,	PUNCT
ejpam-5720	154	70	σ2	σ2	NOUN
ejpam-5720	154	71	)	)	PUNCT
ejpam-5720	154	72	,	,	PUNCT
ejpam-5720	154	73	the	the	DET
ejpam-5720	154	74	following	follow	VERB
ejpam-5720	154	75	properties	property	NOUN
ejpam-5720	154	76	are	be	AUX
ejpam-5720	154	77	equivalent	equivalent	ADJ
ejpam-5720	154	78	:	:	PUNCT
ejpam-5720	154	79	(	(	PUNCT
ejpam-5720	154	80	1	1	X
ejpam-5720	154	81	)	)	PUNCT
ejpam-5720	154	82	f	f	PROPN
ejpam-5720	154	83	is	be	AUX
ejpam-5720	154	84	lower	low	ADJ
ejpam-5720	154	85	almost	almost	ADV
ejpam-5720	154	86	nearly	nearly	ADV
ejpam-5720	154	87	quasi	quasi	NOUN
ejpam-5720	154	88	(	(	PUNCT
ejpam-5720	154	89	τ1	τ1	NOUN
ejpam-5720	154	90	,	,	PUNCT
ejpam-5720	154	91	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	154	92	;	;	PUNCT
ejpam-5720	154	93	(	(	PUNCT
ejpam-5720	154	94	2	2	X
ejpam-5720	154	95	)	)	PUNCT
ejpam-5720	154	96	for	for	ADP
ejpam-5720	154	97	each	each	DET
ejpam-5720	154	98	x	x	SYM
ejpam-5720	154	99	∈	∈	PROPN
ejpam-5720	154	100	x	x	X
ejpam-5720	154	101	and	and	CCONJ
ejpam-5720	154	102	for	for	ADP
ejpam-5720	154	103	each	each	DET
ejpam-5720	154	104	(	(	PUNCT
ejpam-5720	154	105	σ1	σ1	PROPN
ejpam-5720	154	106	,	,	PUNCT
ejpam-5720	154	107	σ2)r	σ2)r	NOUN
ejpam-5720	154	108	-	-	PUNCT
ejpam-5720	154	109	open	open	ADJ
ejpam-5720	154	110	set	set	VERB
ejpam-5720	154	111	v	v	NOUN
ejpam-5720	154	112	of	of	ADP
ejpam-5720	154	113	y	y	PROPN
ejpam-5720	154	114	having	have	VERB
ejpam-5720	154	115	n	n	PROPN
ejpam-5720	154	116	(	(	PUNCT
ejpam-5720	154	117	σ1	σ1	PROPN
ejpam-5720	154	118	,	,	PUNCT
ejpam-5720	154	119	σ2)-closed	σ2)-close	VERB
ejpam-5720	154	120	complement	complement	NOUN
ejpam-5720	154	121	such	such	ADJ
ejpam-5720	154	122	that	that	SCONJ
ejpam-5720	154	123	x	x	SYM
ejpam-5720	154	124	∈	∈	PROPN
ejpam-5720	154	125	f−(v	f−(v	NOUN
ejpam-5720	154	126	)	)	PUNCT
ejpam-5720	154	127	and	and	CCONJ
ejpam-5720	154	128	for	for	ADP
ejpam-5720	154	129	every	every	DET
ejpam-5720	154	130	τ1τ2	τ1τ2	ADJ
ejpam-5720	154	131	-	-	ADJ
ejpam-5720	154	132	open	open	ADJ
ejpam-5720	154	133	set	set	ADJ
ejpam-5720	154	134	u	u	NOUN
ejpam-5720	154	135	of	of	ADP
ejpam-5720	154	136	x	x	PUNCT
ejpam-5720	154	137	containing	contain	VERB
ejpam-5720	154	138	x	x	PRON
ejpam-5720	154	139	,	,	PUNCT
ejpam-5720	154	140	there	there	PRON
ejpam-5720	154	141	exists	exist	VERB
ejpam-5720	154	142	a	a	DET
ejpam-5720	154	143	nonempty	nonempty	ADJ
ejpam-5720	154	144	τ1τ2	τ1τ2	NOUN
ejpam-5720	154	145	-	-	ADJ
ejpam-5720	154	146	open	open	ADJ
ejpam-5720	154	147	set	set	NOUN
ejpam-5720	154	148	w	w	ADP
ejpam-5720	154	149	such	such	ADJ
ejpam-5720	154	150	that	that	PRON
ejpam-5720	154	151	w	w	ADP
ejpam-5720	154	152	⊆	⊆	NUM
ejpam-5720	154	153	u	u	NOUN
ejpam-5720	154	154	and	and	CCONJ
ejpam-5720	154	155	w	w	NOUN
ejpam-5720	154	156	⊆	⊆	NUM
ejpam-5720	154	157	f−(v	f−(v	NOUN
ejpam-5720	154	158	)	)	PUNCT
ejpam-5720	154	159	;	;	PUNCT
ejpam-5720	154	160	(	(	PUNCT
ejpam-5720	154	161	3	3	X
ejpam-5720	154	162	)	)	PUNCT
ejpam-5720	154	163	for	for	ADP
ejpam-5720	154	164	each	each	DET
ejpam-5720	154	165	x	x	SYM
ejpam-5720	154	166	∈	∈	PROPN
ejpam-5720	154	167	x	x	X
ejpam-5720	154	168	and	and	CCONJ
ejpam-5720	154	169	for	for	ADP
ejpam-5720	154	170	every	every	DET
ejpam-5720	154	171	σ1σ2	σ1σ2	NOUN
ejpam-5720	154	172	-	-	PUNCT
ejpam-5720	154	173	closed	closed	ADJ
ejpam-5720	154	174	and	and	CCONJ
ejpam-5720	154	175	n	n	CCONJ
ejpam-5720	154	176	(	(	PUNCT
ejpam-5720	154	177	σ1	σ1	PROPN
ejpam-5720	154	178	,	,	PUNCT
ejpam-5720	154	179	σ2)-closed	σ2)-close	VERB
ejpam-5720	154	180	set	set	VERB
ejpam-5720	154	181	k	k	PROPN
ejpam-5720	154	182	of	of	ADP
ejpam-5720	154	183	y	y	PROPN
ejpam-5720	154	184	such	such	ADJ
ejpam-5720	154	185	that	that	SCONJ
ejpam-5720	154	186	x	x	SYM
ejpam-5720	154	187	∈	∈	NOUN
ejpam-5720	154	188	f−(y	f−(y	NOUN
ejpam-5720	154	189	−k	−k	NOUN
ejpam-5720	154	190	)	)	PUNCT
ejpam-5720	154	191	and	and	CCONJ
ejpam-5720	154	192	for	for	ADP
ejpam-5720	154	193	every	every	DET
ejpam-5720	154	194	τ1τ2	τ1τ2	ADJ
ejpam-5720	154	195	-	-	ADJ
ejpam-5720	154	196	closed	closed	ADJ
ejpam-5720	154	197	set	set	ADJ
ejpam-5720	154	198	h	h	NOUN
ejpam-5720	154	199	of	of	ADP
ejpam-5720	154	200	x	x	INTJ
ejpam-5720	154	201	such	such	ADJ
ejpam-5720	154	202	that	that	SCONJ
ejpam-5720	154	203	x	x	SYM
ejpam-5720	154	204	∈	∈	PROPN
ejpam-5720	154	205	x−h	x−h	PROPN
ejpam-5720	154	206	,	,	PUNCT
ejpam-5720	154	207	there	there	PRON
ejpam-5720	154	208	exists	exist	VERB
ejpam-5720	154	209	a	a	DET
ejpam-5720	154	210	τ1τ2	τ1τ2	ADJ
ejpam-5720	154	211	-	-	ADJ
ejpam-5720	154	212	closed	closed	ADJ
ejpam-5720	154	213	set	set	NOUN
ejpam-5720	154	214	m	m	VERB
ejpam-5720	154	215	such	such	ADJ
ejpam-5720	154	216	that	that	SCONJ
ejpam-5720	154	217	h	h	NOUN
ejpam-5720	154	218	⊆	⊆	NUM
ejpam-5720	154	219	m	m	NOUN
ejpam-5720	154	220	,	,	PUNCT
ejpam-5720	154	221	m	m	VERB
ejpam-5720	154	222	̸=	̸=	NOUN
ejpam-5720	154	223	x	x	PUNCT
ejpam-5720	154	224	and	and	CCONJ
ejpam-5720	154	225	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5720	154	226	-	-	PUNCT
ejpam-5720	154	227	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	154	228	-	-	PUNCT
ejpam-5720	154	229	int(k	int(k	NOUN
ejpam-5720	154	230	)	)	PUNCT
ejpam-5720	154	231	)	)	PUNCT
ejpam-5720	154	232	)	)	PUNCT
ejpam-5720	155	1	⊆	⊆	NUM
ejpam-5720	155	2	m	m	NOUN
ejpam-5720	155	3	;	;	PUNCT
ejpam-5720	155	4	(	(	PUNCT
ejpam-5720	155	5	4	4	X
ejpam-5720	155	6	)	)	PUNCT
ejpam-5720	155	7	for	for	ADP
ejpam-5720	155	8	each	each	DET
ejpam-5720	155	9	x	x	SYM
ejpam-5720	155	10	∈	∈	PROPN
ejpam-5720	155	11	x	x	X
ejpam-5720	155	12	and	and	CCONJ
ejpam-5720	155	13	for	for	ADP
ejpam-5720	155	14	every	every	DET
ejpam-5720	155	15	σ1σ2	σ1σ2	NOUN
ejpam-5720	155	16	-	-	ADJ
ejpam-5720	155	17	open	open	ADJ
ejpam-5720	155	18	set	set	NOUN
ejpam-5720	155	19	v	v	NOUN
ejpam-5720	155	20	of	of	ADP
ejpam-5720	155	21	y	y	PROPN
ejpam-5720	155	22	having	have	VERB
ejpam-5720	155	23	n	n	PROPN
ejpam-5720	155	24	(	(	PUNCT
ejpam-5720	155	25	σ1	σ1	PROPN
ejpam-5720	155	26	,	,	PUNCT
ejpam-5720	155	27	σ2)-closed	σ2)-close	VERB
ejpam-5720	155	28	complement	complement	NOUN
ejpam-5720	155	29	such	such	ADJ
ejpam-5720	155	30	that	that	SCONJ
ejpam-5720	155	31	x	x	SYM
ejpam-5720	155	32	∈	∈	PROPN
ejpam-5720	155	33	f−(v	f−(v	NOUN
ejpam-5720	155	34	)	)	PUNCT
ejpam-5720	155	35	,	,	PUNCT
ejpam-5720	155	36	there	there	PRON
ejpam-5720	155	37	exists	exist	VERB
ejpam-5720	155	38	a	a	DET
ejpam-5720	155	39	(	(	PUNCT
ejpam-5720	155	40	τ1	τ1	NOUN
ejpam-5720	155	41	,	,	PUNCT
ejpam-5720	155	42	τ2)s	τ2)s	NOUN
ejpam-5720	155	43	-	-	PUNCT
ejpam-5720	155	44	open	open	ADJ
ejpam-5720	155	45	set	set	NOUN
ejpam-5720	155	46	u	u	NOUN
ejpam-5720	155	47	of	of	ADP
ejpam-5720	155	48	x	x	PUNCT
ejpam-5720	155	49	containing	contain	VERB
ejpam-5720	155	50	x	x	PUNCT
ejpam-5720	155	51	such	such	ADJ
ejpam-5720	155	52	that	that	SCONJ
ejpam-5720	155	53	u	u	NOUN
ejpam-5720	155	54	⊆	⊆	NUM
ejpam-5720	155	55	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5720	155	56	-	-	PUNCT
ejpam-5720	155	57	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	155	58	-	-	PUNCT
ejpam-5720	155	59	cl(v	cl(v	NOUN
ejpam-5720	155	60	)	)	PUNCT
ejpam-5720	155	61	)	)	PUNCT
ejpam-5720	155	62	)	)	PUNCT
ejpam-5720	155	63	;	;	PUNCT
ejpam-5720	155	64	(	(	PUNCT
ejpam-5720	155	65	5	5	X
ejpam-5720	155	66	)	)	PUNCT
ejpam-5720	155	67	f−(v	f−(v	NOUN
ejpam-5720	155	68	)	)	PUNCT
ejpam-5720	155	69	is	be	AUX
ejpam-5720	155	70	(	(	PUNCT
ejpam-5720	155	71	τ1	τ1	NOUN
ejpam-5720	155	72	,	,	PUNCT
ejpam-5720	155	73	τ2)s	τ2)s	NOUN
ejpam-5720	155	74	-	-	PUNCT
ejpam-5720	155	75	open	open	ADJ
ejpam-5720	155	76	in	in	ADP
ejpam-5720	155	77	x	x	PUNCT
ejpam-5720	155	78	for	for	ADP
ejpam-5720	155	79	every	every	DET
ejpam-5720	155	80	(	(	PUNCT
ejpam-5720	155	81	σ1	σ1	PROPN
ejpam-5720	155	82	,	,	PUNCT
ejpam-5720	155	83	σ2)r	σ2)r	NOUN
ejpam-5720	155	84	-	-	PUNCT
ejpam-5720	155	85	open	open	ADJ
ejpam-5720	155	86	set	set	VERB
ejpam-5720	155	87	v	v	NOUN
ejpam-5720	155	88	of	of	ADP
ejpam-5720	155	89	y	y	PROPN
ejpam-5720	155	90	having	have	VERB
ejpam-5720	155	91	n	n	PROPN
ejpam-5720	155	92	(	(	PUNCT
ejpam-5720	155	93	σ1	σ1	PROPN
ejpam-5720	155	94	,	,	PUNCT
ejpam-5720	155	95	σ2)closed	σ2)close	VERB
ejpam-5720	155	96	complement	complement	NOUN
ejpam-5720	155	97	;	;	PUNCT
ejpam-5720	155	98	(	(	PUNCT
ejpam-5720	155	99	6	6	NUM
ejpam-5720	155	100	)	)	PUNCT
ejpam-5720	155	101	f+(k	f+(k	NOUN
ejpam-5720	155	102	)	)	PUNCT
ejpam-5720	155	103	is	be	AUX
ejpam-5720	155	104	(	(	PUNCT
ejpam-5720	155	105	τ1	τ1	NOUN
ejpam-5720	155	106	,	,	PUNCT
ejpam-5720	155	107	τ2)s	τ2)s	NOUN
ejpam-5720	155	108	-	-	PUNCT
ejpam-5720	155	109	closed	close	VERB
ejpam-5720	155	110	in	in	ADP
ejpam-5720	155	111	x	x	PUNCT
ejpam-5720	155	112	for	for	SCONJ
ejpam-5720	155	113	every	every	DET
ejpam-5720	155	114	(	(	PUNCT
ejpam-5720	155	115	σ1	σ1	PROPN
ejpam-5720	155	116	,	,	PUNCT
ejpam-5720	155	117	σ2)r	σ2)r	NOUN
ejpam-5720	155	118	-	-	PUNCT
ejpam-5720	155	119	closed	closed	ADJ
ejpam-5720	155	120	and	and	CCONJ
ejpam-5720	155	121	n	n	CCONJ
ejpam-5720	155	122	(	(	PUNCT
ejpam-5720	155	123	σ1	σ1	PROPN
ejpam-5720	155	124	,	,	PUNCT
ejpam-5720	155	125	σ2)-closed	σ2)-close	VERB
ejpam-5720	155	126	set	set	VERB
ejpam-5720	155	127	k	k	PROPN
ejpam-5720	155	128	of	of	ADP
ejpam-5720	155	129	y	y	PROPN
ejpam-5720	155	130	.	.	PUNCT
ejpam-5720	156	1	j.	j.	PROPN
ejpam-5720	156	2	khampakdee	khampakdee	PROPN
ejpam-5720	156	3	,	,	PUNCT
ejpam-5720	156	4	a.	a.	PROPN
ejpam-5720	156	5	sama	sama	PROPN
ejpam-5720	156	6	-	-	PUNCT
ejpam-5720	156	7	ae	ae	PROPN
ejpam-5720	156	8	,	,	PUNCT
ejpam-5720	156	9	c.	c.	PROPN
ejpam-5720	156	10	boonpok	boonpok	PROPN
ejpam-5720	156	11	/	/	SYM
ejpam-5720	156	12	eur	eur	PROPN
ejpam-5720	156	13	.	.	PUNCT
ejpam-5720	157	1	j.	j.	PROPN
ejpam-5720	157	2	pure	pure	PROPN
ejpam-5720	157	3	appl	appl	PROPN
ejpam-5720	157	4	.	.	PROPN
ejpam-5720	157	5	math	math	PROPN
ejpam-5720	157	6	,	,	PUNCT
ejpam-5720	157	7	18	18	NUM
ejpam-5720	157	8	(	(	PUNCT
ejpam-5720	157	9	1	1	NUM
ejpam-5720	157	10	)	)	PUNCT
ejpam-5720	157	11	(	(	PUNCT
ejpam-5720	157	12	2025	2025	NUM
ejpam-5720	157	13	)	)	PUNCT
ejpam-5720	157	14	,	,	PUNCT
ejpam-5720	157	15	5720	5720	NUM
ejpam-5720	157	16	7	7	NUM
ejpam-5720	157	17	of	of	ADP
ejpam-5720	157	18	15	15	NUM
ejpam-5720	157	19	proof	proof	NOUN
ejpam-5720	157	20	.	.	PUNCT
ejpam-5720	158	1	the	the	DET
ejpam-5720	158	2	proof	proof	NOUN
ejpam-5720	158	3	is	be	AUX
ejpam-5720	158	4	similar	similar	ADJ
ejpam-5720	158	5	to	to	ADP
ejpam-5720	158	6	that	that	PRON
ejpam-5720	158	7	of	of	ADP
ejpam-5720	158	8	theorem	theorem	NOUN
ejpam-5720	158	9	1	1	NUM
ejpam-5720	158	10	.	.	X
ejpam-5720	158	11	for	for	ADP
ejpam-5720	158	12	a	a	DET
ejpam-5720	158	13	multifunction	multifunction	NOUN
ejpam-5720	158	14	f	f	NOUN
ejpam-5720	158	15	:	:	PUNCT
ejpam-5720	158	16	(	(	PUNCT
ejpam-5720	158	17	x	x	NOUN
ejpam-5720	158	18	,	,	PUNCT
ejpam-5720	158	19	τ1	τ1	NOUN
ejpam-5720	158	20	,	,	PUNCT
ejpam-5720	158	21	τ2	τ2	NOUN
ejpam-5720	158	22	)	)	PUNCT
ejpam-5720	158	23	→	→	SYM
ejpam-5720	158	24	(	(	PUNCT
ejpam-5720	158	25	y	y	PROPN
ejpam-5720	158	26	,	,	PUNCT
ejpam-5720	158	27	σ1	σ1	PROPN
ejpam-5720	158	28	,	,	PUNCT
ejpam-5720	158	29	σ2	σ2	PROPN
ejpam-5720	158	30	)	)	PUNCT
ejpam-5720	158	31	,	,	PUNCT
ejpam-5720	158	32	a	a	DET
ejpam-5720	158	33	multifunction	multifunction	NOUN
ejpam-5720	158	34	sclf⊛	sclf⊛	PROPN
ejpam-5720	158	35	:	:	PUNCT
ejpam-5720	158	36	(	(	PUNCT
ejpam-5720	158	37	x	x	NOUN
ejpam-5720	158	38	,	,	PUNCT
ejpam-5720	158	39	τ1	τ1	NOUN
ejpam-5720	158	40	,	,	PUNCT
ejpam-5720	158	41	τ2	τ2	NOUN
ejpam-5720	158	42	)	)	PUNCT
ejpam-5720	158	43	→	→	SYM
ejpam-5720	158	44	(	(	PUNCT
ejpam-5720	158	45	y	y	PROPN
ejpam-5720	158	46	,	,	PUNCT
ejpam-5720	158	47	σ1	σ1	PROPN
ejpam-5720	158	48	,	,	PUNCT
ejpam-5720	158	49	σ2	σ2	PROPN
ejpam-5720	158	50	)	)	PUNCT
ejpam-5720	158	51	is	be	AUX
ejpam-5720	158	52	defined	define	VERB
ejpam-5720	158	53	in	in	ADP
ejpam-5720	158	54	[	[	X
ejpam-5720	158	55	31	31	NUM
ejpam-5720	158	56	]	]	PUNCT
ejpam-5720	158	57	as	as	SCONJ
ejpam-5720	158	58	follows	follow	VERB
ejpam-5720	158	59	:	:	PUNCT
ejpam-5720	158	60	sclf⊛(x	sclf⊛(x	NUM
ejpam-5720	158	61	)	)	PUNCT
ejpam-5720	159	1	=	=	SYM
ejpam-5720	159	2	(	(	PUNCT
ejpam-5720	159	3	σ1	σ1	PROPN
ejpam-5720	159	4	,	,	PUNCT
ejpam-5720	159	5	σ2)-scl(f	σ2)-scl(f	NOUN
ejpam-5720	159	6	(	(	PUNCT
ejpam-5720	159	7	x	x	NOUN
ejpam-5720	159	8	)	)	PUNCT
ejpam-5720	159	9	)	)	PUNCT
ejpam-5720	159	10	for	for	ADP
ejpam-5720	159	11	each	each	PRON
ejpam-5720	159	12	x	x	SYM
ejpam-5720	159	13	∈	∈	PROPN
ejpam-5720	159	14	x.	x.	NOUN
ejpam-5720	159	15	theorem	theorem	VERB
ejpam-5720	159	16	3	3	NUM
ejpam-5720	159	17	.	.	PUNCT
ejpam-5720	159	18	a	a	DET
ejpam-5720	159	19	multifunction	multifunction	NOUN
ejpam-5720	159	20	f	f	NOUN
ejpam-5720	159	21	:	:	PUNCT
ejpam-5720	159	22	(	(	PUNCT
ejpam-5720	159	23	x	x	NOUN
ejpam-5720	159	24	,	,	PUNCT
ejpam-5720	159	25	τ1	τ1	NOUN
ejpam-5720	159	26	,	,	PUNCT
ejpam-5720	159	27	τ2	τ2	NOUN
ejpam-5720	159	28	)	)	PUNCT
ejpam-5720	159	29	→	→	SYM
ejpam-5720	159	30	(	(	PUNCT
ejpam-5720	159	31	y	y	PROPN
ejpam-5720	159	32	,	,	PUNCT
ejpam-5720	159	33	σ1	σ1	PROPN
ejpam-5720	159	34	,	,	PUNCT
ejpam-5720	159	35	σ2	σ2	PROPN
ejpam-5720	159	36	)	)	PUNCT
ejpam-5720	159	37	is	be	AUX
ejpam-5720	159	38	upper	upper	ADJ
ejpam-5720	159	39	almost	almost	ADV
ejpam-5720	159	40	nearly	nearly	ADV
ejpam-5720	159	41	quasi	quasi	NOUN
ejpam-5720	159	42	(	(	PUNCT
ejpam-5720	159	43	τ1	τ1	NOUN
ejpam-5720	159	44	,	,	PUNCT
ejpam-5720	159	45	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	159	46	if	if	SCONJ
ejpam-5720	159	47	and	and	CCONJ
ejpam-5720	159	48	only	only	ADV
ejpam-5720	159	49	if	if	SCONJ
ejpam-5720	159	50	sclf⊛	sclf⊛	PRON
ejpam-5720	159	51	:	:	PUNCT
ejpam-5720	159	52	(	(	PUNCT
ejpam-5720	159	53	x	x	NOUN
ejpam-5720	159	54	,	,	PUNCT
ejpam-5720	159	55	τ1	τ1	NOUN
ejpam-5720	159	56	,	,	PUNCT
ejpam-5720	159	57	τ2	τ2	NOUN
ejpam-5720	159	58	)	)	PUNCT
ejpam-5720	159	59	→	→	SYM
ejpam-5720	159	60	(	(	PUNCT
ejpam-5720	159	61	y	y	PROPN
ejpam-5720	159	62	,	,	PUNCT
ejpam-5720	159	63	σ1	σ1	PROPN
ejpam-5720	159	64	,	,	PUNCT
ejpam-5720	159	65	σ2	σ2	PROPN
ejpam-5720	159	66	)	)	PUNCT
ejpam-5720	159	67	is	be	AUX
ejpam-5720	159	68	upper	upper	ADJ
ejpam-5720	159	69	almost	almost	ADV
ejpam-5720	159	70	nearly	nearly	ADV
ejpam-5720	159	71	quasi	quasi	NOUN
ejpam-5720	159	72	(	(	PUNCT
ejpam-5720	159	73	τ1	τ1	NOUN
ejpam-5720	159	74	,	,	PUNCT
ejpam-5720	159	75	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	159	76	.	.	PUNCT
ejpam-5720	160	1	proof	proof	NOUN
ejpam-5720	160	2	.	.	PUNCT
ejpam-5720	161	1	suppose	suppose	VERB
ejpam-5720	161	2	that	that	SCONJ
ejpam-5720	161	3	f	f	PROPN
ejpam-5720	161	4	is	be	AUX
ejpam-5720	161	5	upper	upper	ADJ
ejpam-5720	161	6	almost	almost	ADV
ejpam-5720	161	7	nearly	nearly	ADV
ejpam-5720	161	8	quasi	quasi	NOUN
ejpam-5720	161	9	(	(	PUNCT
ejpam-5720	161	10	τ1	τ1	NOUN
ejpam-5720	161	11	,	,	PUNCT
ejpam-5720	161	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	161	13	.	.	PUNCT
ejpam-5720	162	1	let	let	VERB
ejpam-5720	162	2	x	x	PUNCT
ejpam-5720	162	3	∈	∈	PROPN
ejpam-5720	162	4	x	x	X
ejpam-5720	162	5	and	and	CCONJ
ejpam-5720	162	6	v	v	X
ejpam-5720	162	7	be	be	AUX
ejpam-5720	162	8	any	any	DET
ejpam-5720	162	9	σ1σ2	σ1σ2	NOUN
ejpam-5720	162	10	-	-	ADJ
ejpam-5720	162	11	open	open	ADJ
ejpam-5720	162	12	set	set	NOUN
ejpam-5720	162	13	of	of	ADP
ejpam-5720	162	14	y	y	PROPN
ejpam-5720	162	15	having	have	VERB
ejpam-5720	162	16	n	n	PROPN
ejpam-5720	162	17	(	(	PUNCT
ejpam-5720	162	18	σ1	σ1	PROPN
ejpam-5720	162	19	,	,	PUNCT
ejpam-5720	162	20	σ2)-closed	σ2)-close	VERB
ejpam-5720	162	21	complement	complement	NOUN
ejpam-5720	162	22	such	such	ADJ
ejpam-5720	162	23	that	that	SCONJ
ejpam-5720	162	24	x	x	SYM
ejpam-5720	162	25	∈	∈	PROPN
ejpam-5720	162	26	sclf+	sclf+	ADP
ejpam-5720	162	27	⊛	⊛	NUM
ejpam-5720	162	28	(	(	PUNCT
ejpam-5720	162	29	v	v	NOUN
ejpam-5720	162	30	)	)	PUNCT
ejpam-5720	162	31	.	.	PUNCT
ejpam-5720	163	1	then	then	ADV
ejpam-5720	163	2	,	,	PUNCT
ejpam-5720	163	3	we	we	PRON
ejpam-5720	163	4	have	have	VERB
ejpam-5720	163	5	sclf⊛(x	sclf⊛(x	NUM
ejpam-5720	163	6	)	)	PUNCT
ejpam-5720	163	7	⊆	⊆	NUM
ejpam-5720	163	8	v	v	NOUN
ejpam-5720	163	9	and	and	CCONJ
ejpam-5720	163	10	hence	hence	ADV
ejpam-5720	163	11	f	f	PROPN
ejpam-5720	163	12	(	(	PUNCT
ejpam-5720	163	13	x	x	X
ejpam-5720	163	14	)	)	PUNCT
ejpam-5720	163	15	⊆	⊆	NUM
ejpam-5720	163	16	v	v	NOUN
ejpam-5720	163	17	.	.	PUNCT
ejpam-5720	164	1	since	since	SCONJ
ejpam-5720	164	2	f	f	PROPN
ejpam-5720	164	3	is	be	AUX
ejpam-5720	164	4	upper	upper	ADJ
ejpam-5720	164	5	almost	almost	ADV
ejpam-5720	164	6	nearly	nearly	ADV
ejpam-5720	164	7	quasi	quasi	NOUN
ejpam-5720	164	8	(	(	PUNCT
ejpam-5720	164	9	τ1	τ1	NOUN
ejpam-5720	164	10	,	,	PUNCT
ejpam-5720	164	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	164	12	,	,	PUNCT
ejpam-5720	164	13	by	by	ADP
ejpam-5720	164	14	theorem	theorem	NOUN
ejpam-5720	164	15	1	1	NUM
ejpam-5720	164	16	there	there	ADV
ejpam-5720	164	17	exists	exist	VERB
ejpam-5720	164	18	a	a	DET
ejpam-5720	164	19	(	(	PUNCT
ejpam-5720	164	20	τ1	τ1	NOUN
ejpam-5720	164	21	,	,	PUNCT
ejpam-5720	164	22	τ2)s	τ2)s	NOUN
ejpam-5720	164	23	-	-	PUNCT
ejpam-5720	164	24	open	open	ADJ
ejpam-5720	164	25	set	set	NOUN
ejpam-5720	164	26	u	u	NOUN
ejpam-5720	164	27	of	of	ADP
ejpam-5720	164	28	x	x	PUNCT
ejpam-5720	164	29	containing	contain	VERB
ejpam-5720	164	30	x	x	PUNCT
ejpam-5720	164	31	such	such	ADJ
ejpam-5720	164	32	that	that	SCONJ
ejpam-5720	164	33	u	u	NOUN
ejpam-5720	164	34	⊆	⊆	NUM
ejpam-5720	164	35	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5720	164	36	-	-	PUNCT
ejpam-5720	164	37	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	164	38	-	-	PUNCT
ejpam-5720	164	39	cl(v	cl(v	NOUN
ejpam-5720	164	40	)	)	PUNCT
ejpam-5720	164	41	)	)	PUNCT
ejpam-5720	164	42	)	)	PUNCT
ejpam-5720	164	43	.	.	PUNCT
ejpam-5720	165	1	thus	thus	ADV
ejpam-5720	165	2	by	by	ADP
ejpam-5720	165	3	lemma	lemma	PROPN
ejpam-5720	165	4	2	2	NUM
ejpam-5720	165	5	,	,	PUNCT
ejpam-5720	165	6	u	u	NOUN
ejpam-5720	165	7	⊆	⊆	NUM
ejpam-5720	165	8	f+((σ1	f+((σ1	NOUN
ejpam-5720	165	9	,	,	PUNCT
ejpam-5720	165	10	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5720	165	11	)	)	PUNCT
ejpam-5720	165	12	)	)	PUNCT
ejpam-5720	165	13	.	.	PUNCT
ejpam-5720	166	1	therefore	therefore	ADV
ejpam-5720	166	2	,	,	PUNCT
ejpam-5720	166	3	f	f	PROPN
ejpam-5720	166	4	(	(	PUNCT
ejpam-5720	166	5	u	u	NOUN
ejpam-5720	166	6	)	)	PUNCT
ejpam-5720	166	7	⊆	⊆	NUM
ejpam-5720	166	8	(	(	PUNCT
ejpam-5720	166	9	σ1	σ1	PROPN
ejpam-5720	166	10	,	,	PUNCT
ejpam-5720	166	11	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5720	166	12	)	)	PUNCT
ejpam-5720	166	13	.	.	PUNCT
ejpam-5720	167	1	for	for	ADP
ejpam-5720	167	2	each	each	DET
ejpam-5720	167	3	u	u	PROPN
ejpam-5720	167	4	∈	∈	PROPN
ejpam-5720	167	5	u	u	NOUN
ejpam-5720	167	6	,	,	PUNCT
ejpam-5720	167	7	(	(	PUNCT
ejpam-5720	167	8	σ1	σ1	PROPN
ejpam-5720	167	9	,	,	PUNCT
ejpam-5720	167	10	σ2)-scl(f	σ2)-scl(f	NOUN
ejpam-5720	167	11	(	(	PUNCT
ejpam-5720	167	12	u	u	NOUN
ejpam-5720	167	13	)	)	PUNCT
ejpam-5720	167	14	)	)	PUNCT
ejpam-5720	167	15	⊆	⊆	NUM
ejpam-5720	167	16	(	(	PUNCT
ejpam-5720	167	17	σ1	σ1	PROPN
ejpam-5720	167	18	,	,	PUNCT
ejpam-5720	167	19	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5720	167	20	)	)	PUNCT
ejpam-5720	167	21	and	and	CCONJ
ejpam-5720	167	22	so	so	ADV
ejpam-5720	167	23	(	(	PUNCT
ejpam-5720	167	24	σ1	σ1	PROPN
ejpam-5720	167	25	,	,	PUNCT
ejpam-5720	167	26	σ2)-scl(f	σ2)-scl(f	NOUN
ejpam-5720	167	27	(	(	PUNCT
ejpam-5720	167	28	u	u	NOUN
ejpam-5720	167	29	)	)	PUNCT
ejpam-5720	167	30	)	)	PUNCT
ejpam-5720	168	1	⊆	⊆	NUM
ejpam-5720	168	2	(	(	PUNCT
ejpam-5720	168	3	σ1	σ1	PROPN
ejpam-5720	168	4	,	,	PUNCT
ejpam-5720	168	5	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5720	168	6	)	)	PUNCT
ejpam-5720	168	7	.	.	PUNCT
ejpam-5720	169	1	thus	thus	ADV
ejpam-5720	169	2	,	,	PUNCT
ejpam-5720	169	3	sclf⊛(u	sclf⊛(u	NOUN
ejpam-5720	169	4	)	)	PUNCT
ejpam-5720	169	5	⊆	⊆	NUM
ejpam-5720	169	6	σ1σ2	σ1σ2	X
ejpam-5720	169	7	-	-	PUNCT
ejpam-5720	169	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	169	9	-	-	PUNCT
ejpam-5720	169	10	cl(v	cl(v	NOUN
ejpam-5720	169	11	)	)	PUNCT
ejpam-5720	169	12	)	)	PUNCT
ejpam-5720	169	13	and	and	CCONJ
ejpam-5720	169	14	hence	hence	ADV
ejpam-5720	169	15	x	x	X
ejpam-5720	169	16	∈	∈	PROPN
ejpam-5720	169	17	sclf+	sclf+	ADP
ejpam-5720	169	18	⊛	⊛	NUM
ejpam-5720	169	19	(	(	PUNCT
ejpam-5720	169	20	σ1σ2	σ1σ2	X
ejpam-5720	169	21	-	-	PUNCT
ejpam-5720	169	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	169	23	-	-	PUNCT
ejpam-5720	169	24	cl(v	cl(v	NOUN
ejpam-5720	169	25	)	)	PUNCT
ejpam-5720	169	26	)	)	PUNCT
ejpam-5720	169	27	)	)	PUNCT
ejpam-5720	169	28	.	.	PUNCT
ejpam-5720	170	1	by	by	ADP
ejpam-5720	170	2	theorem	theorem	NOUN
ejpam-5720	170	3	1	1	NUM
ejpam-5720	170	4	,	,	PUNCT
ejpam-5720	170	5	sclf⊛	sclf⊛	PROPN
ejpam-5720	170	6	is	be	AUX
ejpam-5720	170	7	upper	upper	ADJ
ejpam-5720	170	8	almost	almost	ADV
ejpam-5720	170	9	nearly	nearly	ADV
ejpam-5720	170	10	quasi	quasi	NOUN
ejpam-5720	170	11	(	(	PUNCT
ejpam-5720	170	12	τ1	τ1	NOUN
ejpam-5720	170	13	,	,	PUNCT
ejpam-5720	170	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	170	15	.	.	PUNCT
ejpam-5720	171	1	theorem	theorem	VERB
ejpam-5720	171	2	4	4	NUM
ejpam-5720	171	3	.	.	PUNCT
ejpam-5720	171	4	a	a	DET
ejpam-5720	171	5	multifunction	multifunction	NOUN
ejpam-5720	172	1	f	f	NOUN
ejpam-5720	172	2	:	:	PUNCT
ejpam-5720	172	3	(	(	PUNCT
ejpam-5720	172	4	x	x	NOUN
ejpam-5720	172	5	,	,	PUNCT
ejpam-5720	172	6	τ1	τ1	NOUN
ejpam-5720	172	7	,	,	PUNCT
ejpam-5720	172	8	τ2	τ2	NOUN
ejpam-5720	172	9	)	)	PUNCT
ejpam-5720	172	10	→	→	SYM
ejpam-5720	172	11	(	(	PUNCT
ejpam-5720	172	12	y	y	PROPN
ejpam-5720	172	13	,	,	PUNCT
ejpam-5720	172	14	σ1	σ1	PROPN
ejpam-5720	172	15	,	,	PUNCT
ejpam-5720	172	16	σ2	σ2	NOUN
ejpam-5720	172	17	)	)	PUNCT
ejpam-5720	172	18	is	be	AUX
ejpam-5720	172	19	lower	low	ADJ
ejpam-5720	172	20	almost	almost	ADV
ejpam-5720	172	21	nearly	nearly	ADV
ejpam-5720	172	22	quasi	quasi	NOUN
ejpam-5720	172	23	(	(	PUNCT
ejpam-5720	172	24	τ1	τ1	NOUN
ejpam-5720	172	25	,	,	PUNCT
ejpam-5720	172	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	172	27	if	if	SCONJ
ejpam-5720	172	28	and	and	CCONJ
ejpam-5720	172	29	only	only	ADV
ejpam-5720	172	30	if	if	SCONJ
ejpam-5720	172	31	sclf⊛	sclf⊛	PRON
ejpam-5720	172	32	:	:	PUNCT
ejpam-5720	172	33	(	(	PUNCT
ejpam-5720	172	34	x	x	NOUN
ejpam-5720	172	35	,	,	PUNCT
ejpam-5720	172	36	τ1	τ1	NOUN
ejpam-5720	172	37	,	,	PUNCT
ejpam-5720	172	38	τ2	τ2	NOUN
ejpam-5720	172	39	)	)	PUNCT
ejpam-5720	172	40	→	→	SYM
ejpam-5720	172	41	(	(	PUNCT
ejpam-5720	172	42	y	y	PROPN
ejpam-5720	172	43	,	,	PUNCT
ejpam-5720	172	44	σ1	σ1	PROPN
ejpam-5720	172	45	,	,	PUNCT
ejpam-5720	172	46	σ2	σ2	NOUN
ejpam-5720	172	47	)	)	PUNCT
ejpam-5720	172	48	is	be	AUX
ejpam-5720	172	49	lower	low	ADJ
ejpam-5720	172	50	almost	almost	ADV
ejpam-5720	172	51	nearly	nearly	ADV
ejpam-5720	172	52	quasi	quasi	NOUN
ejpam-5720	172	53	(	(	PUNCT
ejpam-5720	172	54	τ1	τ1	NOUN
ejpam-5720	172	55	,	,	PUNCT
ejpam-5720	172	56	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	172	57	.	.	PUNCT
ejpam-5720	173	1	proof	proof	NOUN
ejpam-5720	173	2	.	.	PUNCT
ejpam-5720	174	1	the	the	DET
ejpam-5720	174	2	proof	proof	NOUN
ejpam-5720	174	3	is	be	AUX
ejpam-5720	174	4	similar	similar	ADJ
ejpam-5720	174	5	to	to	ADP
ejpam-5720	174	6	that	that	PRON
ejpam-5720	174	7	of	of	ADP
ejpam-5720	174	8	theorem	theorem	ADJ
ejpam-5720	174	9	3	3	NUM
ejpam-5720	174	10	.	.	NOUN
ejpam-5720	174	11	recall	recall	VERB
ejpam-5720	174	12	that	that	SCONJ
ejpam-5720	174	13	a	a	DET
ejpam-5720	174	14	subset	subset	NOUN
ejpam-5720	174	15	a	a	PRON
ejpam-5720	174	16	of	of	ADP
ejpam-5720	174	17	a	a	DET
ejpam-5720	174	18	bitopological	bitopological	ADJ
ejpam-5720	174	19	space	space	NOUN
ejpam-5720	174	20	(	(	PUNCT
ejpam-5720	174	21	x	x	NOUN
ejpam-5720	174	22	,	,	PUNCT
ejpam-5720	174	23	τ1	τ1	NOUN
ejpam-5720	174	24	,	,	PUNCT
ejpam-5720	174	25	τ2	τ2	NOUN
ejpam-5720	174	26	)	)	PUNCT
ejpam-5720	174	27	is	be	AUX
ejpam-5720	174	28	said	say	VERB
ejpam-5720	174	29	to	to	PART
ejpam-5720	174	30	be	be	AUX
ejpam-5720	174	31	τ1τ2	τ1τ2	NOUN
ejpam-5720	174	32	-	-	ADJ
ejpam-5720	174	33	clopen	clopen	ADJ
ejpam-5720	174	34	[	[	X
ejpam-5720	174	35	29	29	NUM
ejpam-5720	174	36	]	]	X
ejpam-5720	174	37	if	if	SCONJ
ejpam-5720	174	38	a	a	PRON
ejpam-5720	174	39	is	be	AUX
ejpam-5720	174	40	both	both	PRON
ejpam-5720	174	41	τ1τ2	τ1τ2	ADJ
ejpam-5720	174	42	-	-	ADJ
ejpam-5720	174	43	open	open	ADJ
ejpam-5720	174	44	and	and	CCONJ
ejpam-5720	174	45	τ1τ2	τ1τ2	NOUN
ejpam-5720	174	46	-	-	ADJ
ejpam-5720	174	47	closed	closed	ADJ
ejpam-5720	174	48	.	.	PUNCT
ejpam-5720	175	1	definition	definition	NOUN
ejpam-5720	175	2	3	3	NUM
ejpam-5720	175	3	.	.	PUNCT
ejpam-5720	176	1	[	[	X
ejpam-5720	176	2	29	29	NUM
ejpam-5720	176	3	]	]	PUNCT
ejpam-5720	176	4	a	a	DET
ejpam-5720	176	5	bitopological	bitopological	ADJ
ejpam-5720	176	6	space	space	NOUN
ejpam-5720	176	7	(	(	PUNCT
ejpam-5720	176	8	x	x	NOUN
ejpam-5720	176	9	,	,	PUNCT
ejpam-5720	176	10	τ1	τ1	NOUN
ejpam-5720	176	11	,	,	PUNCT
ejpam-5720	176	12	τ2	τ2	NOUN
ejpam-5720	176	13	)	)	PUNCT
ejpam-5720	176	14	is	be	AUX
ejpam-5720	176	15	said	say	VERB
ejpam-5720	176	16	to	to	PART
ejpam-5720	176	17	be	be	AUX
ejpam-5720	176	18	τ1τ2	τ1τ2	NOUN
ejpam-5720	176	19	-	-	ADJ
ejpam-5720	176	20	connected	connected	ADJ
ejpam-5720	176	21	if	if	SCONJ
ejpam-5720	176	22	x	x	PRON
ejpam-5720	176	23	can	can	AUX
ejpam-5720	176	24	not	not	PART
ejpam-5720	176	25	be	be	AUX
ejpam-5720	176	26	written	write	VERB
ejpam-5720	176	27	as	as	ADP
ejpam-5720	176	28	the	the	DET
ejpam-5720	176	29	union	union	NOUN
ejpam-5720	176	30	of	of	ADP
ejpam-5720	176	31	two	two	NUM
ejpam-5720	176	32	disjoint	disjoint	NOUN
ejpam-5720	176	33	nonempty	nonempty	ADJ
ejpam-5720	176	34	τ1τ2	τ1τ2	ADJ
ejpam-5720	176	35	-	-	ADJ
ejpam-5720	176	36	open	open	ADJ
ejpam-5720	176	37	sets	set	NOUN
ejpam-5720	176	38	.	.	PUNCT
ejpam-5720	177	1	definition	definition	NOUN
ejpam-5720	177	2	4	4	NUM
ejpam-5720	177	3	.	.	PUNCT
ejpam-5720	178	1	[	[	X
ejpam-5720	178	2	33	33	NUM
ejpam-5720	178	3	]	]	PUNCT
ejpam-5720	178	4	a	a	DET
ejpam-5720	178	5	bitopological	bitopological	ADJ
ejpam-5720	178	6	space	space	NOUN
ejpam-5720	178	7	(	(	PUNCT
ejpam-5720	178	8	x	x	NOUN
ejpam-5720	178	9	,	,	PUNCT
ejpam-5720	178	10	τ1	τ1	NOUN
ejpam-5720	178	11	,	,	PUNCT
ejpam-5720	178	12	τ2	τ2	NOUN
ejpam-5720	178	13	)	)	PUNCT
ejpam-5720	178	14	is	be	AUX
ejpam-5720	178	15	said	say	VERB
ejpam-5720	178	16	to	to	PART
ejpam-5720	178	17	be	be	AUX
ejpam-5720	178	18	n	n	PRON
ejpam-5720	178	19	(	(	PUNCT
ejpam-5720	178	20	τ1	τ1	NOUN
ejpam-5720	178	21	,	,	PUNCT
ejpam-5720	178	22	τ2)-connected	τ2)-connecte	VERB
ejpam-5720	178	23	if	if	SCONJ
ejpam-5720	178	24	x	x	PRON
ejpam-5720	178	25	can	can	AUX
ejpam-5720	178	26	not	not	PART
ejpam-5720	178	27	be	be	AUX
ejpam-5720	178	28	written	write	VERB
ejpam-5720	178	29	as	as	ADP
ejpam-5720	178	30	the	the	DET
ejpam-5720	178	31	union	union	NOUN
ejpam-5720	178	32	of	of	ADP
ejpam-5720	178	33	two	two	NUM
ejpam-5720	178	34	disjoint	disjoint	NOUN
ejpam-5720	178	35	nonempty	nonempty	ADJ
ejpam-5720	178	36	τ1τ2	τ1τ2	ADJ
ejpam-5720	178	37	-	-	ADJ
ejpam-5720	178	38	open	open	ADJ
ejpam-5720	178	39	sets	set	NOUN
ejpam-5720	178	40	having	have	VERB
ejpam-5720	178	41	n	n	X
ejpam-5720	178	42	(	(	PUNCT
ejpam-5720	178	43	τ1	τ1	PROPN
ejpam-5720	178	44	,	,	PUNCT
ejpam-5720	178	45	τ2)closed	τ2)closed	ADJ
ejpam-5720	178	46	complements	complement	NOUN
ejpam-5720	178	47	.	.	PUNCT
ejpam-5720	179	1	definition	definition	NOUN
ejpam-5720	179	2	5	5	NUM
ejpam-5720	179	3	.	.	PUNCT
ejpam-5720	180	1	a	a	DET
ejpam-5720	180	2	bitopological	bitopological	ADJ
ejpam-5720	180	3	space	space	NOUN
ejpam-5720	180	4	(	(	PUNCT
ejpam-5720	180	5	x	x	NOUN
ejpam-5720	180	6	,	,	PUNCT
ejpam-5720	180	7	τ1	τ1	NOUN
ejpam-5720	180	8	,	,	PUNCT
ejpam-5720	180	9	τ2	τ2	NOUN
ejpam-5720	180	10	)	)	PUNCT
ejpam-5720	180	11	is	be	AUX
ejpam-5720	180	12	said	say	VERB
ejpam-5720	180	13	to	to	PART
ejpam-5720	180	14	be	be	AUX
ejpam-5720	180	15	(	(	PUNCT
ejpam-5720	180	16	τ1	τ1	NOUN
ejpam-5720	180	17	,	,	PUNCT
ejpam-5720	180	18	τ2)s	τ2)s	NOUN
ejpam-5720	180	19	-	-	PUNCT
ejpam-5720	180	20	connected	connect	VERB
ejpam-5720	180	21	if	if	SCONJ
ejpam-5720	180	22	x	x	PRON
ejpam-5720	180	23	can	can	AUX
ejpam-5720	180	24	not	not	PART
ejpam-5720	180	25	be	be	AUX
ejpam-5720	180	26	written	write	VERB
ejpam-5720	180	27	as	as	ADP
ejpam-5720	180	28	the	the	DET
ejpam-5720	180	29	union	union	NOUN
ejpam-5720	180	30	of	of	ADP
ejpam-5720	180	31	two	two	NUM
ejpam-5720	180	32	disjoint	disjoint	NOUN
ejpam-5720	180	33	nonempty	nonempty	NOUN
ejpam-5720	180	34	(	(	PUNCT
ejpam-5720	180	35	τ1	τ1	NOUN
ejpam-5720	180	36	,	,	PUNCT
ejpam-5720	180	37	τ2)s	τ2)s	NOUN
ejpam-5720	180	38	-	-	PUNCT
ejpam-5720	180	39	open	open	ADJ
ejpam-5720	180	40	sets	set	NOUN
ejpam-5720	180	41	.	.	PUNCT
ejpam-5720	181	1	theorem	theorem	NOUN
ejpam-5720	181	2	5	5	NUM
ejpam-5720	181	3	.	.	PUNCT
ejpam-5720	182	1	if	if	SCONJ
ejpam-5720	182	2	f	f	PROPN
ejpam-5720	182	3	:	:	PUNCT
ejpam-5720	182	4	(	(	PUNCT
ejpam-5720	182	5	x	x	NOUN
ejpam-5720	182	6	,	,	PUNCT
ejpam-5720	182	7	τ1	τ1	NOUN
ejpam-5720	182	8	,	,	PUNCT
ejpam-5720	182	9	τ2	τ2	NOUN
ejpam-5720	182	10	)	)	PUNCT
ejpam-5720	182	11	→	→	SYM
ejpam-5720	182	12	(	(	PUNCT
ejpam-5720	182	13	y	y	PROPN
ejpam-5720	182	14	,	,	PUNCT
ejpam-5720	182	15	σ1	σ1	PROPN
ejpam-5720	182	16	,	,	PUNCT
ejpam-5720	182	17	σ2	σ2	PROPN
ejpam-5720	182	18	)	)	PUNCT
ejpam-5720	182	19	is	be	AUX
ejpam-5720	182	20	an	an	DET
ejpam-5720	182	21	upper	upper	ADJ
ejpam-5720	182	22	or	or	CCONJ
ejpam-5720	182	23	lower	low	ADJ
ejpam-5720	182	24	almost	almost	ADV
ejpam-5720	182	25	nearly	nearly	ADV
ejpam-5720	182	26	quasi	quasi	NOUN
ejpam-5720	182	27	(	(	PUNCT
ejpam-5720	182	28	τ1	τ1	NOUN
ejpam-5720	182	29	,	,	PUNCT
ejpam-5720	182	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	182	31	surjective	surjective	ADJ
ejpam-5720	182	32	multifunction	multifunction	NOUN
ejpam-5720	182	33	such	such	ADJ
ejpam-5720	182	34	that	that	SCONJ
ejpam-5720	182	35	f	f	PROPN
ejpam-5720	182	36	(	(	PUNCT
ejpam-5720	182	37	x	x	X
ejpam-5720	182	38	)	)	PUNCT
ejpam-5720	182	39	is	be	AUX
ejpam-5720	182	40	σ1σ2	σ1σ2	NOUN
ejpam-5720	182	41	-	-	PUNCT
ejpam-5720	182	42	connected	connected	ADJ
ejpam-5720	182	43	for	for	ADP
ejpam-5720	182	44	every	every	DET
ejpam-5720	182	45	x	x	SYM
ejpam-5720	182	46	∈	∈	PROPN
ejpam-5720	182	47	x	x	X
ejpam-5720	182	48	and	and	CCONJ
ejpam-5720	182	49	(	(	PUNCT
ejpam-5720	182	50	x	x	NOUN
ejpam-5720	182	51	,	,	PUNCT
ejpam-5720	182	52	τ1	τ1	NOUN
ejpam-5720	182	53	,	,	PUNCT
ejpam-5720	182	54	τ2	τ2	NOUN
ejpam-5720	182	55	)	)	PUNCT
ejpam-5720	182	56	is	be	AUX
ejpam-5720	182	57	(	(	PUNCT
ejpam-5720	182	58	τ1	τ1	NOUN
ejpam-5720	182	59	,	,	PUNCT
ejpam-5720	182	60	τ2)s	τ2)s	NOUN
ejpam-5720	182	61	-	-	PUNCT
ejpam-5720	182	62	connected	connect	VERB
ejpam-5720	182	63	,	,	PUNCT
ejpam-5720	182	64	then	then	ADV
ejpam-5720	182	65	(	(	PUNCT
ejpam-5720	182	66	y	y	PROPN
ejpam-5720	182	67	,	,	PUNCT
ejpam-5720	182	68	σ1	σ1	PROPN
ejpam-5720	182	69	,	,	PUNCT
ejpam-5720	182	70	σ2	σ2	PROPN
ejpam-5720	182	71	)	)	PUNCT
ejpam-5720	182	72	is	be	AUX
ejpam-5720	182	73	n	n	PROPN
ejpam-5720	182	74	(	(	PUNCT
ejpam-5720	182	75	σ1	σ1	PROPN
ejpam-5720	182	76	,	,	PUNCT
ejpam-5720	182	77	σ2)-connected	σ2)-connecte	VERB
ejpam-5720	182	78	.	.	PUNCT
ejpam-5720	183	1	j.	j.	PROPN
ejpam-5720	183	2	khampakdee	khampakdee	PROPN
ejpam-5720	183	3	,	,	PUNCT
ejpam-5720	183	4	a.	a.	PROPN
ejpam-5720	183	5	sama	sama	PROPN
ejpam-5720	183	6	-	-	PUNCT
ejpam-5720	183	7	ae	ae	PROPN
ejpam-5720	183	8	,	,	PUNCT
ejpam-5720	183	9	c.	c.	PROPN
ejpam-5720	183	10	boonpok	boonpok	PROPN
ejpam-5720	183	11	/	/	SYM
ejpam-5720	183	12	eur	eur	PROPN
ejpam-5720	183	13	.	.	PUNCT
ejpam-5720	184	1	j.	j.	PROPN
ejpam-5720	184	2	pure	pure	PROPN
ejpam-5720	184	3	appl	appl	PROPN
ejpam-5720	184	4	.	.	PROPN
ejpam-5720	184	5	math	math	PROPN
ejpam-5720	184	6	,	,	PUNCT
ejpam-5720	184	7	18	18	NUM
ejpam-5720	184	8	(	(	PUNCT
ejpam-5720	184	9	1	1	NUM
ejpam-5720	184	10	)	)	PUNCT
ejpam-5720	184	11	(	(	PUNCT
ejpam-5720	184	12	2025	2025	NUM
ejpam-5720	184	13	)	)	PUNCT
ejpam-5720	184	14	,	,	PUNCT
ejpam-5720	184	15	5720	5720	NUM
ejpam-5720	184	16	8	8	NUM
ejpam-5720	184	17	of	of	ADP
ejpam-5720	184	18	15	15	NUM
ejpam-5720	184	19	proof	proof	NOUN
ejpam-5720	184	20	.	.	PUNCT
ejpam-5720	184	21	suppose	suppose	VERB
ejpam-5720	184	22	that	that	SCONJ
ejpam-5720	184	23	(	(	PUNCT
ejpam-5720	184	24	y	y	PROPN
ejpam-5720	184	25	,	,	PUNCT
ejpam-5720	184	26	σ1	σ1	PROPN
ejpam-5720	184	27	,	,	PUNCT
ejpam-5720	184	28	σ2	σ2	PROPN
ejpam-5720	184	29	)	)	PUNCT
ejpam-5720	184	30	is	be	AUX
ejpam-5720	184	31	not	not	PART
ejpam-5720	184	32	n	n	PROPN
ejpam-5720	184	33	(	(	PUNCT
ejpam-5720	184	34	σ1	σ1	PROPN
ejpam-5720	184	35	,	,	PUNCT
ejpam-5720	184	36	σ2)-connected	σ2)-connecte	VERB
ejpam-5720	184	37	.	.	PUNCT
ejpam-5720	185	1	there	there	PRON
ejpam-5720	185	2	exist	exist	VERB
ejpam-5720	185	3	nonempty	nonempty	ADJ
ejpam-5720	185	4	σ1σ2	σ1σ2	NOUN
ejpam-5720	185	5	-	-	ADJ
ejpam-5720	185	6	open	open	ADJ
ejpam-5720	185	7	sets	set	NOUN
ejpam-5720	185	8	u	u	NOUN
ejpam-5720	185	9	and	and	CCONJ
ejpam-5720	185	10	v	v	NOUN
ejpam-5720	185	11	of	of	ADP
ejpam-5720	185	12	y	y	PROPN
ejpam-5720	185	13	having	have	VERB
ejpam-5720	185	14	n	n	PROPN
ejpam-5720	185	15	(	(	PUNCT
ejpam-5720	185	16	σ1	σ1	PROPN
ejpam-5720	185	17	,	,	PUNCT
ejpam-5720	185	18	σ2)-closed	σ2)-close	VERB
ejpam-5720	185	19	complements	complement	NOUN
ejpam-5720	185	20	such	such	ADJ
ejpam-5720	185	21	that	that	SCONJ
ejpam-5720	185	22	u	u	PROPN
ejpam-5720	185	23	∩	∩	NOUN
ejpam-5720	185	24	v	v	NOUN
ejpam-5720	185	25	=	=	NOUN
ejpam-5720	185	26	∅	∅	NOUN
ejpam-5720	185	27	and	and	CCONJ
ejpam-5720	185	28	u	u	NOUN
ejpam-5720	185	29	∪	∪	NOUN
ejpam-5720	185	30	v	v	ADP
ejpam-5720	185	31	=	=	SYM
ejpam-5720	185	32	y	y	PROPN
ejpam-5720	185	33	.	.	PUNCT
ejpam-5720	186	1	since	since	SCONJ
ejpam-5720	186	2	f	f	PROPN
ejpam-5720	186	3	(	(	PUNCT
ejpam-5720	186	4	x	x	X
ejpam-5720	186	5	)	)	PUNCT
ejpam-5720	186	6	is	be	AUX
ejpam-5720	186	7	σ1σ2	σ1σ2	NOUN
ejpam-5720	186	8	-	-	PUNCT
ejpam-5720	186	9	connected	connected	ADJ
ejpam-5720	186	10	for	for	ADP
ejpam-5720	186	11	each	each	DET
ejpam-5720	186	12	x	x	SYM
ejpam-5720	186	13	∈	∈	PROPN
ejpam-5720	186	14	x	x	NOUN
ejpam-5720	186	15	,	,	PUNCT
ejpam-5720	186	16	either	either	CCONJ
ejpam-5720	186	17	f	f	PROPN
ejpam-5720	186	18	(	(	PUNCT
ejpam-5720	186	19	x	x	X
ejpam-5720	186	20	)	)	PUNCT
ejpam-5720	186	21	⊆	⊆	NUM
ejpam-5720	186	22	u	u	NOUN
ejpam-5720	186	23	or	or	CCONJ
ejpam-5720	186	24	f	f	PROPN
ejpam-5720	186	25	(	(	PUNCT
ejpam-5720	186	26	x	x	NOUN
ejpam-5720	186	27	)	)	PUNCT
ejpam-5720	186	28	⊆	⊆	NUM
ejpam-5720	186	29	v	v	NOUN
ejpam-5720	186	30	.	.	PUNCT
ejpam-5720	187	1	if	if	SCONJ
ejpam-5720	187	2	x	x	SYM
ejpam-5720	187	3	∈	∈	PROPN
ejpam-5720	187	4	f+(u∪v	f+(u∪v	PROPN
ejpam-5720	187	5	)	)	PUNCT
ejpam-5720	187	6	,	,	PUNCT
ejpam-5720	187	7	then	then	ADV
ejpam-5720	187	8	f	f	X
ejpam-5720	187	9	(	(	PUNCT
ejpam-5720	187	10	x	x	X
ejpam-5720	187	11	)	)	PUNCT
ejpam-5720	187	12	⊆	⊆	NUM
ejpam-5720	187	13	u∪v	u∪v	NOUN
ejpam-5720	187	14	and	and	CCONJ
ejpam-5720	187	15	hence	hence	ADV
ejpam-5720	187	16	x	x	PART
ejpam-5720	187	17	∈	∈	NOUN
ejpam-5720	187	18	f+(u)∪f+(v	f+(u)∪f+(v	NOUN
ejpam-5720	187	19	)	)	PUNCT
ejpam-5720	187	20	.	.	PUNCT
ejpam-5720	188	1	moreover	moreover	ADV
ejpam-5720	188	2	,	,	PUNCT
ejpam-5720	188	3	since	since	SCONJ
ejpam-5720	188	4	f	f	PROPN
ejpam-5720	188	5	is	be	AUX
ejpam-5720	188	6	surjective	surjective	ADJ
ejpam-5720	188	7	,	,	PUNCT
ejpam-5720	188	8	there	there	PRON
ejpam-5720	188	9	exist	exist	VERB
ejpam-5720	188	10	x	x	PUNCT
ejpam-5720	188	11	and	and	CCONJ
ejpam-5720	188	12	y	y	PROPN
ejpam-5720	188	13	in	in	ADP
ejpam-5720	188	14	x	x	PUNCT
ejpam-5720	188	15	such	such	ADJ
ejpam-5720	188	16	that	that	SCONJ
ejpam-5720	188	17	f	f	PROPN
ejpam-5720	188	18	(	(	PUNCT
ejpam-5720	188	19	x	x	X
ejpam-5720	188	20	)	)	PUNCT
ejpam-5720	188	21	⊆	⊆	NUM
ejpam-5720	188	22	u	u	NOUN
ejpam-5720	188	23	and	and	CCONJ
ejpam-5720	188	24	f	f	PROPN
ejpam-5720	188	25	(	(	PUNCT
ejpam-5720	188	26	y	y	PROPN
ejpam-5720	188	27	)	)	PUNCT
ejpam-5720	188	28	⊆	⊆	NUM
ejpam-5720	188	29	v	v	NOUN
ejpam-5720	188	30	;	;	PUNCT
ejpam-5720	188	31	hence	hence	ADV
ejpam-5720	188	32	x	x	SYM
ejpam-5720	188	33	∈	∈	PROPN
ejpam-5720	188	34	f+(u	f+(u	NUM
ejpam-5720	188	35	)	)	PUNCT
ejpam-5720	188	36	and	and	CCONJ
ejpam-5720	188	37	y	y	PROPN
ejpam-5720	188	38	∈	∈	PROPN
ejpam-5720	188	39	f+(v	f+(v	PROPN
ejpam-5720	188	40	)	)	PUNCT
ejpam-5720	188	41	.	.	PUNCT
ejpam-5720	189	1	therefore	therefore	ADV
ejpam-5720	189	2	,	,	PUNCT
ejpam-5720	189	3	we	we	PRON
ejpam-5720	189	4	obtain	obtain	VERB
ejpam-5720	189	5	the	the	DET
ejpam-5720	189	6	following	following	NOUN
ejpam-5720	189	7	:	:	PUNCT
ejpam-5720	189	8	(	(	PUNCT
ejpam-5720	189	9	1	1	X
ejpam-5720	189	10	)	)	PUNCT
ejpam-5720	189	11	f+(u	f+(u	NUM
ejpam-5720	189	12	)	)	PUNCT
ejpam-5720	189	13	∪	∪	ADP
ejpam-5720	189	14	f+(v	f+(v	NOUN
ejpam-5720	189	15	)	)	PUNCT
ejpam-5720	190	1	=	=	PUNCT
ejpam-5720	191	1	f+(u	f+(u	PUNCT
ejpam-5720	191	2	∪	∪	ADP
ejpam-5720	191	3	v	v	NOUN
ejpam-5720	191	4	)	)	PUNCT
ejpam-5720	191	5	=	=	SYM
ejpam-5720	192	1	x	x	X
ejpam-5720	192	2	;	;	PUNCT
ejpam-5720	192	3	(	(	PUNCT
ejpam-5720	192	4	2	2	X
ejpam-5720	192	5	)	)	PUNCT
ejpam-5720	192	6	f+(u	f+(u	NUM
ejpam-5720	192	7	)	)	PUNCT
ejpam-5720	192	8	∩	∩	NOUN
ejpam-5720	192	9	f+(v	f+(v	NOUN
ejpam-5720	192	10	)	)	PUNCT
ejpam-5720	192	11	=	=	SYM
ejpam-5720	193	1	f+(u	f+(u	NUM
ejpam-5720	193	2	∩	∩	NOUN
ejpam-5720	193	3	v	v	NOUN
ejpam-5720	193	4	)	)	PUNCT
ejpam-5720	193	5	=	=	NOUN
ejpam-5720	193	6	∅	∅	NOUN
ejpam-5720	193	7	;	;	PUNCT
ejpam-5720	193	8	(	(	PUNCT
ejpam-5720	193	9	3	3	X
ejpam-5720	193	10	)	)	PUNCT
ejpam-5720	193	11	f+(u	f+(u	NUM
ejpam-5720	193	12	)	)	PUNCT
ejpam-5720	193	13	̸=	̸=	PROPN
ejpam-5720	193	14	∅	∅	NOUN
ejpam-5720	193	15	and	and	CCONJ
ejpam-5720	193	16	f+(v	f+(v	NUM
ejpam-5720	193	17	)	)	PUNCT
ejpam-5720	194	1	̸=	̸=	PROPN
ejpam-5720	194	2	∅.	∅.	ADP
ejpam-5720	194	3	next	next	ADV
ejpam-5720	194	4	,	,	PUNCT
ejpam-5720	194	5	we	we	PRON
ejpam-5720	194	6	show	show	VERB
ejpam-5720	194	7	that	that	PRON
ejpam-5720	194	8	f+(u	f+(u	NUM
ejpam-5720	194	9	)	)	PUNCT
ejpam-5720	194	10	and	and	CCONJ
ejpam-5720	194	11	f+(v	f+(v	NUM
ejpam-5720	194	12	)	)	PUNCT
ejpam-5720	194	13	are	be	AUX
ejpam-5720	194	14	(	(	PUNCT
ejpam-5720	194	15	τ1	τ1	NOUN
ejpam-5720	194	16	,	,	PUNCT
ejpam-5720	194	17	τ2)s	τ2)s	NOUN
ejpam-5720	194	18	-	-	PUNCT
ejpam-5720	194	19	open	open	ADJ
ejpam-5720	194	20	in	in	ADP
ejpam-5720	194	21	x.	x.	PROPN
ejpam-5720	194	22	(	(	PUNCT
ejpam-5720	195	1	i	i	NOUN
ejpam-5720	195	2	)	)	PUNCT
ejpam-5720	195	3	let	let	VERB
ejpam-5720	195	4	f	f	PRON
ejpam-5720	195	5	be	be	AUX
ejpam-5720	195	6	upper	upper	ADJ
ejpam-5720	195	7	almost	almost	ADV
ejpam-5720	195	8	nearly	nearly	ADV
ejpam-5720	195	9	quasi	quasi	NOUN
ejpam-5720	195	10	(	(	PUNCT
ejpam-5720	195	11	τ1	τ1	NOUN
ejpam-5720	195	12	,	,	PUNCT
ejpam-5720	195	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	195	14	.	.	PUNCT
ejpam-5720	196	1	since	since	SCONJ
ejpam-5720	196	2	u	u	PROPN
ejpam-5720	196	3	and	and	CCONJ
ejpam-5720	196	4	v	v	NOUN
ejpam-5720	196	5	are	be	AUX
ejpam-5720	196	6	σ1σ2	σ1σ2	NOUN
ejpam-5720	196	7	-	-	PUNCT
ejpam-5720	196	8	clopen	clopen	ADJ
ejpam-5720	196	9	in	in	ADP
ejpam-5720	196	10	y	y	PROPN
ejpam-5720	196	11	,	,	PUNCT
ejpam-5720	196	12	σ1σ2	σ1σ2	NOUN
ejpam-5720	196	13	-	-	PUNCT
ejpam-5720	196	14	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	196	15	-	-	PUNCT
ejpam-5720	196	16	cl(u	cl(u	NUM
ejpam-5720	196	17	)	)	PUNCT
ejpam-5720	196	18	)	)	PUNCT
ejpam-5720	197	1	=	=	SYM
ejpam-5720	197	2	u	u	NOUN
ejpam-5720	197	3	and	and	CCONJ
ejpam-5720	197	4	σ1σ2	σ1σ2	NOUN
ejpam-5720	197	5	-	-	PUNCT
ejpam-5720	197	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	197	7	-	-	PUNCT
ejpam-5720	197	8	cl(v	cl(v	NOUN
ejpam-5720	197	9	)	)	PUNCT
ejpam-5720	197	10	)	)	PUNCT
ejpam-5720	198	1	=	=	SYM
ejpam-5720	198	2	v	v	X
ejpam-5720	198	3	.	.	PUNCT
ejpam-5720	199	1	thus	thus	ADV
ejpam-5720	199	2	,	,	PUNCT
ejpam-5720	199	3	u	u	NOUN
ejpam-5720	199	4	and	and	CCONJ
ejpam-5720	199	5	v	v	NOUN
ejpam-5720	199	6	are	be	AUX
ejpam-5720	199	7	(	(	PUNCT
ejpam-5720	199	8	σ1	σ1	NOUN
ejpam-5720	199	9	,	,	PUNCT
ejpam-5720	199	10	σ2)r	σ2)r	NOUN
ejpam-5720	199	11	-	-	PUNCT
ejpam-5720	199	12	open	open	ADJ
ejpam-5720	199	13	sets	set	NOUN
ejpam-5720	199	14	having	have	VERB
ejpam-5720	199	15	n	n	PRON
ejpam-5720	199	16	(	(	PUNCT
ejpam-5720	199	17	σ1	σ1	PROPN
ejpam-5720	199	18	,	,	PUNCT
ejpam-5720	199	19	σ2)closed	σ2)close	VERB
ejpam-5720	199	20	complements	complement	NOUN
ejpam-5720	199	21	.	.	PUNCT
ejpam-5720	200	1	since	since	SCONJ
ejpam-5720	200	2	f	f	PROPN
ejpam-5720	200	3	is	be	AUX
ejpam-5720	200	4	upper	upper	ADJ
ejpam-5720	200	5	almost	almost	ADV
ejpam-5720	200	6	nearly	nearly	ADV
ejpam-5720	200	7	quasi	quasi	NOUN
ejpam-5720	200	8	(	(	PUNCT
ejpam-5720	200	9	τ1	τ1	NOUN
ejpam-5720	200	10	,	,	PUNCT
ejpam-5720	200	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	200	12	,	,	PUNCT
ejpam-5720	200	13	by	by	ADP
ejpam-5720	200	14	theorem	theorem	NOUN
ejpam-5720	200	15	1	1	NUM
ejpam-5720	200	16	,	,	PUNCT
ejpam-5720	200	17	f+(u	f+(u	NUM
ejpam-5720	200	18	)	)	PUNCT
ejpam-5720	200	19	and	and	CCONJ
ejpam-5720	200	20	f+(v	f+(v	NUM
ejpam-5720	200	21	)	)	PUNCT
ejpam-5720	200	22	are	be	AUX
ejpam-5720	200	23	(	(	PUNCT
ejpam-5720	200	24	τ1	τ1	NOUN
ejpam-5720	200	25	,	,	PUNCT
ejpam-5720	200	26	τ2)s	τ2)s	NOUN
ejpam-5720	200	27	-	-	PUNCT
ejpam-5720	200	28	open	open	ADJ
ejpam-5720	200	29	sets	set	NOUN
ejpam-5720	200	30	.	.	PUNCT
ejpam-5720	201	1	(	(	PUNCT
ejpam-5720	201	2	ii	ii	NOUN
ejpam-5720	201	3	)	)	PUNCT
ejpam-5720	201	4	let	let	VERB
ejpam-5720	201	5	f	f	PRON
ejpam-5720	201	6	be	be	AUX
ejpam-5720	201	7	lower	low	ADJ
ejpam-5720	201	8	almost	almost	ADV
ejpam-5720	201	9	nearly	nearly	ADV
ejpam-5720	201	10	quasi	quasi	NOUN
ejpam-5720	201	11	(	(	PUNCT
ejpam-5720	201	12	τ1	τ1	NOUN
ejpam-5720	201	13	,	,	PUNCT
ejpam-5720	201	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	201	15	.	.	PUNCT
ejpam-5720	202	1	by	by	ADP
ejpam-5720	202	2	theorem	theorem	NOUN
ejpam-5720	202	3	2	2	NUM
ejpam-5720	202	4	,	,	PUNCT
ejpam-5720	202	5	f+(u	f+(u	NUM
ejpam-5720	202	6	)	)	PUNCT
ejpam-5720	202	7	is	be	AUX
ejpam-5720	202	8	(	(	PUNCT
ejpam-5720	202	9	τ1	τ1	NOUN
ejpam-5720	202	10	,	,	PUNCT
ejpam-5720	202	11	τ2)s	τ2)s	NOUN
ejpam-5720	202	12	-	-	PUNCT
ejpam-5720	202	13	closed	closed	ADJ
ejpam-5720	202	14	inx	inx	NOUN
ejpam-5720	202	15	because	because	SCONJ
ejpam-5720	202	16	u	u	NOUN
ejpam-5720	202	17	is	be	AUX
ejpam-5720	202	18	σ1σ2	σ1σ2	NOUN
ejpam-5720	202	19	-	-	PUNCT
ejpam-5720	202	20	clopen	clopen	ADJ
ejpam-5720	202	21	in	in	ADP
ejpam-5720	202	22	y	y	PROPN
ejpam-5720	202	23	.	.	PUNCT
ejpam-5720	203	1	thus	thus	ADV
ejpam-5720	203	2	,	,	PUNCT
ejpam-5720	203	3	f+(v	f+(v	PROPN
ejpam-5720	203	4	)	)	PUNCT
ejpam-5720	203	5	is	be	AUX
ejpam-5720	203	6	(	(	PUNCT
ejpam-5720	203	7	τ1	τ1	NOUN
ejpam-5720	203	8	,	,	PUNCT
ejpam-5720	203	9	τ2)s	τ2)s	NOUN
ejpam-5720	203	10	-	-	PUNCT
ejpam-5720	203	11	open	open	ADJ
ejpam-5720	203	12	in	in	ADP
ejpam-5720	203	13	x.	x.	NOUN
ejpam-5720	203	14	similarly	similarly	ADV
ejpam-5720	203	15	,	,	PUNCT
ejpam-5720	203	16	we	we	PRON
ejpam-5720	203	17	have	have	AUX
ejpam-5720	203	18	f+(u	f+(u	PUNCT
ejpam-5720	203	19	)	)	PUNCT
ejpam-5720	203	20	is	be	AUX
ejpam-5720	203	21	(	(	PUNCT
ejpam-5720	203	22	τ1	τ1	NOUN
ejpam-5720	203	23	,	,	PUNCT
ejpam-5720	203	24	τ2)-open	τ2)-open	ADJ
ejpam-5720	203	25	in	in	ADP
ejpam-5720	203	26	x.	x.	NOUN
ejpam-5720	203	27	therefore	therefore	ADV
ejpam-5720	203	28	,	,	PUNCT
ejpam-5720	203	29	(	(	PUNCT
ejpam-5720	203	30	x	x	NOUN
ejpam-5720	203	31	,	,	PUNCT
ejpam-5720	203	32	τ1	τ1	NOUN
ejpam-5720	203	33	,	,	PUNCT
ejpam-5720	203	34	τ2	τ2	NOUN
ejpam-5720	203	35	)	)	PUNCT
ejpam-5720	203	36	is	be	AUX
ejpam-5720	203	37	not	not	PART
ejpam-5720	203	38	(	(	PUNCT
ejpam-5720	203	39	τ1	τ1	NOUN
ejpam-5720	203	40	,	,	PUNCT
ejpam-5720	203	41	τ2)s	τ2)s	NOUN
ejpam-5720	203	42	-	-	PUNCT
ejpam-5720	203	43	connected	connect	VERB
ejpam-5720	203	44	.	.	PUNCT
ejpam-5720	204	1	4	4	X
ejpam-5720	204	2	.	.	X
ejpam-5720	204	3	almost	almost	ADV
ejpam-5720	204	4	nearly	nearly	ADV
ejpam-5720	204	5	quasi	quasi	NOUN
ejpam-5720	204	6	(	(	PUNCT
ejpam-5720	204	7	τ1	τ1	NOUN
ejpam-5720	204	8	,	,	PUNCT
ejpam-5720	204	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	204	10	multifunctions	multifunction	NOUN
ejpam-5720	204	11	in	in	ADP
ejpam-5720	204	12	this	this	DET
ejpam-5720	204	13	section	section	NOUN
ejpam-5720	204	14	,	,	PUNCT
ejpam-5720	204	15	we	we	PRON
ejpam-5720	204	16	introduce	introduce	VERB
ejpam-5720	204	17	the	the	DET
ejpam-5720	204	18	concept	concept	NOUN
ejpam-5720	204	19	of	of	ADP
ejpam-5720	204	20	almost	almost	ADV
ejpam-5720	204	21	nearly	nearly	ADV
ejpam-5720	204	22	quasi	quasi	NOUN
ejpam-5720	204	23	(	(	PUNCT
ejpam-5720	204	24	τ1	τ1	NOUN
ejpam-5720	204	25	,	,	PUNCT
ejpam-5720	204	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	204	27	multifunctions	multifunction	NOUN
ejpam-5720	204	28	.	.	PUNCT
ejpam-5720	205	1	we	we	PRON
ejpam-5720	205	2	also	also	ADV
ejpam-5720	205	3	investigate	investigate	VERB
ejpam-5720	205	4	some	some	DET
ejpam-5720	205	5	characterizations	characterization	NOUN
ejpam-5720	205	6	of	of	ADP
ejpam-5720	205	7	almost	almost	ADV
ejpam-5720	205	8	nearly	nearly	ADV
ejpam-5720	205	9	quasi	quasi	NOUN
ejpam-5720	205	10	(	(	PUNCT
ejpam-5720	205	11	τ1	τ1	NOUN
ejpam-5720	205	12	,	,	PUNCT
ejpam-5720	205	13	τ2)continuous	τ2)continuous	ADJ
ejpam-5720	205	14	multifunctions	multifunction	NOUN
ejpam-5720	205	15	.	.	PUNCT
ejpam-5720	206	1	definition	definition	NOUN
ejpam-5720	206	2	6	6	NUM
ejpam-5720	206	3	.	.	PUNCT
ejpam-5720	207	1	a	a	DET
ejpam-5720	207	2	multifunction	multifunction	NOUN
ejpam-5720	207	3	f	f	NOUN
ejpam-5720	207	4	:	:	PUNCT
ejpam-5720	207	5	(	(	PUNCT
ejpam-5720	207	6	x	x	NOUN
ejpam-5720	207	7	,	,	PUNCT
ejpam-5720	207	8	τ1	τ1	NOUN
ejpam-5720	207	9	,	,	PUNCT
ejpam-5720	207	10	τ2	τ2	NOUN
ejpam-5720	207	11	)	)	PUNCT
ejpam-5720	207	12	→	→	SYM
ejpam-5720	207	13	(	(	PUNCT
ejpam-5720	207	14	y	y	PROPN
ejpam-5720	207	15	,	,	PUNCT
ejpam-5720	207	16	σ1	σ1	PROPN
ejpam-5720	207	17	,	,	PUNCT
ejpam-5720	207	18	σ2	σ2	PROPN
ejpam-5720	207	19	)	)	PUNCT
ejpam-5720	207	20	is	be	AUX
ejpam-5720	207	21	said	say	VERB
ejpam-5720	207	22	to	to	PART
ejpam-5720	207	23	be	be	AUX
ejpam-5720	207	24	almost	almost	ADV
ejpam-5720	207	25	nearly	nearly	ADV
ejpam-5720	207	26	quasi	quasi	NOUN
ejpam-5720	207	27	(	(	PUNCT
ejpam-5720	207	28	τ1	τ1	NOUN
ejpam-5720	207	29	,	,	PUNCT
ejpam-5720	207	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	207	31	at	at	ADP
ejpam-5720	207	32	a	a	DET
ejpam-5720	207	33	point	point	NOUN
ejpam-5720	207	34	x	x	SYM
ejpam-5720	207	35	∈	∈	NOUN
ejpam-5720	207	36	x	x	PUNCT
ejpam-5720	207	37	if	if	SCONJ
ejpam-5720	207	38	for	for	ADP
ejpam-5720	207	39	each	each	DET
ejpam-5720	207	40	σ1σ2	σ1σ2	VERB
ejpam-5720	207	41	-	-	ADJ
ejpam-5720	207	42	open	open	ADJ
ejpam-5720	207	43	sets	set	NOUN
ejpam-5720	207	44	v1	v1	NOUN
ejpam-5720	207	45	,	,	PUNCT
ejpam-5720	207	46	v2	v2	PROPN
ejpam-5720	207	47	of	of	ADP
ejpam-5720	207	48	y	y	PROPN
ejpam-5720	207	49	having	have	VERB
ejpam-5720	207	50	n	n	PROPN
ejpam-5720	207	51	(	(	PUNCT
ejpam-5720	207	52	σ1	σ1	PROPN
ejpam-5720	207	53	,	,	PUNCT
ejpam-5720	207	54	σ2)-closed	σ2)-close	VERB
ejpam-5720	207	55	complements	complement	NOUN
ejpam-5720	207	56	such	such	ADJ
ejpam-5720	207	57	that	that	SCONJ
ejpam-5720	207	58	x	x	SYM
ejpam-5720	207	59	∈	∈	NOUN
ejpam-5720	207	60	f+(v1	f+(v1	NOUN
ejpam-5720	207	61	)	)	PUNCT
ejpam-5720	207	62	∩	∩	NOUN
ejpam-5720	207	63	f−(v2	f−(v2	NUM
ejpam-5720	207	64	)	)	PUNCT
ejpam-5720	207	65	and	and	CCONJ
ejpam-5720	207	66	for	for	ADP
ejpam-5720	207	67	every	every	DET
ejpam-5720	207	68	τ1τ2	τ1τ2	ADJ
ejpam-5720	207	69	-	-	ADJ
ejpam-5720	207	70	open	open	ADJ
ejpam-5720	207	71	set	set	ADJ
ejpam-5720	207	72	u	u	NOUN
ejpam-5720	207	73	of	of	ADP
ejpam-5720	207	74	x	x	PUNCT
ejpam-5720	207	75	containing	contain	VERB
ejpam-5720	207	76	x	x	PRON
ejpam-5720	207	77	,	,	PUNCT
ejpam-5720	207	78	there	there	PRON
ejpam-5720	207	79	exists	exist	VERB
ejpam-5720	207	80	a	a	DET
ejpam-5720	207	81	nonempty	nonempty	ADJ
ejpam-5720	207	82	τ1τ2	τ1τ2	NOUN
ejpam-5720	207	83	-	-	ADJ
ejpam-5720	207	84	open	open	ADJ
ejpam-5720	207	85	set	set	NOUN
ejpam-5720	207	86	w	w	ADP
ejpam-5720	207	87	such	such	ADJ
ejpam-5720	207	88	that	that	SCONJ
ejpam-5720	207	89	w	w	PROPN
ejpam-5720	207	90	⊆	⊆	NUM
ejpam-5720	207	91	u	u	NOUN
ejpam-5720	207	92	,	,	PUNCT
ejpam-5720	207	93	f	f	PROPN
ejpam-5720	207	94	(	(	PUNCT
ejpam-5720	207	95	w	w	PROPN
ejpam-5720	207	96	)	)	PUNCT
ejpam-5720	207	97	⊆	⊆	NUM
ejpam-5720	207	98	(	(	PUNCT
ejpam-5720	207	99	σ1	σ1	PROPN
ejpam-5720	207	100	,	,	PUNCT
ejpam-5720	207	101	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	207	102	)	)	PUNCT
ejpam-5720	207	103	and	and	CCONJ
ejpam-5720	207	104	(	(	PUNCT
ejpam-5720	207	105	σ1	σ1	PROPN
ejpam-5720	207	106	,	,	PUNCT
ejpam-5720	207	107	σ2)-scl(v2)∩f	σ2)-scl(v2)∩f	NOUN
ejpam-5720	207	108	(	(	PUNCT
ejpam-5720	207	109	z	z	NOUN
ejpam-5720	207	110	)	)	PUNCT
ejpam-5720	207	111	̸=	̸=	NOUN
ejpam-5720	207	112	∅	∅	NOUN
ejpam-5720	207	113	for	for	ADP
ejpam-5720	207	114	every	every	DET
ejpam-5720	207	115	z	z	PROPN
ejpam-5720	207	116	∈	∈	PROPN
ejpam-5720	207	117	w	w	PROPN
ejpam-5720	207	118	.	.	PUNCT
ejpam-5720	208	1	a	a	DET
ejpam-5720	208	2	multifunction	multifunction	NOUN
ejpam-5720	208	3	f	f	NOUN
ejpam-5720	208	4	:	:	PUNCT
ejpam-5720	208	5	(	(	PUNCT
ejpam-5720	208	6	x	x	NOUN
ejpam-5720	208	7	,	,	PUNCT
ejpam-5720	208	8	τ1	τ1	NOUN
ejpam-5720	208	9	,	,	PUNCT
ejpam-5720	208	10	τ2	τ2	NOUN
ejpam-5720	208	11	)	)	PUNCT
ejpam-5720	208	12	→	→	SYM
ejpam-5720	208	13	(	(	PUNCT
ejpam-5720	208	14	y	y	PROPN
ejpam-5720	208	15	,	,	PUNCT
ejpam-5720	208	16	σ1	σ1	PROPN
ejpam-5720	208	17	,	,	PUNCT
ejpam-5720	208	18	σ2	σ2	PROPN
ejpam-5720	208	19	)	)	PUNCT
ejpam-5720	208	20	is	be	AUX
ejpam-5720	208	21	said	say	VERB
ejpam-5720	208	22	to	to	PART
ejpam-5720	208	23	be	be	AUX
ejpam-5720	208	24	almost	almost	ADV
ejpam-5720	208	25	nearly	nearly	ADV
ejpam-5720	208	26	quasi	quasi	NOUN
ejpam-5720	208	27	(	(	PUNCT
ejpam-5720	208	28	τ1	τ1	NOUN
ejpam-5720	208	29	,	,	PUNCT
ejpam-5720	208	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	208	31	if	if	SCONJ
ejpam-5720	208	32	f	f	PROPN
ejpam-5720	208	33	is	be	AUX
ejpam-5720	208	34	almost	almost	ADV
ejpam-5720	208	35	nearly	nearly	ADV
ejpam-5720	208	36	quasi	quasi	NOUN
ejpam-5720	208	37	(	(	PUNCT
ejpam-5720	208	38	τ1	τ1	NOUN
ejpam-5720	208	39	,	,	PUNCT
ejpam-5720	208	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	208	41	at	at	ADP
ejpam-5720	208	42	each	each	DET
ejpam-5720	208	43	point	point	NOUN
ejpam-5720	208	44	x	x	PUNCT
ejpam-5720	208	45	of	of	ADP
ejpam-5720	208	46	x.	x.	PROPN
ejpam-5720	208	47	theorem	theorem	VERB
ejpam-5720	208	48	6	6	NUM
ejpam-5720	208	49	.	.	PUNCT
ejpam-5720	208	50	for	for	ADP
ejpam-5720	208	51	a	a	DET
ejpam-5720	208	52	multifunction	multifunction	NOUN
ejpam-5720	208	53	f	f	NOUN
ejpam-5720	208	54	:	:	PUNCT
ejpam-5720	208	55	(	(	PUNCT
ejpam-5720	208	56	x	x	NOUN
ejpam-5720	208	57	,	,	PUNCT
ejpam-5720	208	58	τ1	τ1	NOUN
ejpam-5720	208	59	,	,	PUNCT
ejpam-5720	208	60	τ2	τ2	NOUN
ejpam-5720	208	61	)	)	PUNCT
ejpam-5720	208	62	→	→	SYM
ejpam-5720	208	63	(	(	PUNCT
ejpam-5720	208	64	y	y	PROPN
ejpam-5720	208	65	,	,	PUNCT
ejpam-5720	208	66	σ1	σ1	PROPN
ejpam-5720	208	67	,	,	PUNCT
ejpam-5720	208	68	σ2	σ2	NOUN
ejpam-5720	208	69	)	)	PUNCT
ejpam-5720	208	70	,	,	PUNCT
ejpam-5720	208	71	the	the	DET
ejpam-5720	208	72	following	follow	VERB
ejpam-5720	208	73	properties	property	NOUN
ejpam-5720	208	74	are	be	AUX
ejpam-5720	208	75	equivalent	equivalent	ADJ
ejpam-5720	208	76	:	:	PUNCT
ejpam-5720	208	77	(	(	PUNCT
ejpam-5720	208	78	1	1	X
ejpam-5720	208	79	)	)	PUNCT
ejpam-5720	208	80	f	f	NOUN
ejpam-5720	208	81	is	be	AUX
ejpam-5720	208	82	almost	almost	ADV
ejpam-5720	208	83	nearly	nearly	ADV
ejpam-5720	208	84	quasi	quasi	NOUN
ejpam-5720	208	85	(	(	PUNCT
ejpam-5720	208	86	τ1	τ1	NOUN
ejpam-5720	208	87	,	,	PUNCT
ejpam-5720	208	88	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	208	89	at	at	ADP
ejpam-5720	208	90	a	a	DET
ejpam-5720	208	91	point	point	NOUN
ejpam-5720	208	92	x	x	X
ejpam-5720	208	93	∈	∈	NOUN
ejpam-5720	208	94	x	x	X
ejpam-5720	208	95	;	;	PUNCT
ejpam-5720	208	96	(	(	PUNCT
ejpam-5720	208	97	2	2	X
ejpam-5720	208	98	)	)	PUNCT
ejpam-5720	208	99	for	for	ADP
ejpam-5720	208	100	every	every	DET
ejpam-5720	208	101	σ1σ2	σ1σ2	NUM
ejpam-5720	208	102	-	-	ADJ
ejpam-5720	208	103	open	open	ADJ
ejpam-5720	208	104	sets	set	NOUN
ejpam-5720	208	105	v1	v1	NOUN
ejpam-5720	208	106	,	,	PUNCT
ejpam-5720	208	107	v2	v2	PROPN
ejpam-5720	208	108	of	of	ADP
ejpam-5720	208	109	y	y	PROPN
ejpam-5720	208	110	having	have	VERB
ejpam-5720	208	111	n	n	PROPN
ejpam-5720	208	112	(	(	PUNCT
ejpam-5720	208	113	σ1	σ1	PROPN
ejpam-5720	208	114	,	,	PUNCT
ejpam-5720	208	115	σ2)-closed	σ2)-close	VERB
ejpam-5720	208	116	complements	complement	NOUN
ejpam-5720	208	117	such	such	ADJ
ejpam-5720	208	118	that	that	SCONJ
ejpam-5720	208	119	x	x	SYM
ejpam-5720	208	120	∈	∈	PROPN
ejpam-5720	208	121	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5720	208	122	)	)	PUNCT
ejpam-5720	208	123	,	,	PUNCT
ejpam-5720	208	124	there	there	PRON
ejpam-5720	208	125	exists	exist	VERB
ejpam-5720	208	126	a	a	DET
ejpam-5720	208	127	(	(	PUNCT
ejpam-5720	208	128	τ1	τ1	NOUN
ejpam-5720	208	129	,	,	PUNCT
ejpam-5720	208	130	τ2)s	τ2)s	NOUN
ejpam-5720	208	131	-	-	PUNCT
ejpam-5720	208	132	open	open	ADJ
ejpam-5720	208	133	set	set	NOUN
ejpam-5720	208	134	u	u	NOUN
ejpam-5720	208	135	of	of	ADP
ejpam-5720	208	136	x	x	PUNCT
ejpam-5720	208	137	containing	contain	VERB
ejpam-5720	208	138	x	x	PUNCT
ejpam-5720	208	139	such	such	ADJ
ejpam-5720	208	140	that	that	SCONJ
ejpam-5720	208	141	f	f	PROPN
ejpam-5720	208	142	(	(	PUNCT
ejpam-5720	208	143	u	u	NOUN
ejpam-5720	208	144	)	)	PUNCT
ejpam-5720	208	145	⊆	⊆	NUM
ejpam-5720	208	146	(	(	PUNCT
ejpam-5720	208	147	σ1	σ1	PROPN
ejpam-5720	208	148	,	,	PUNCT
ejpam-5720	208	149	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	208	150	)	)	PUNCT
ejpam-5720	208	151	and	and	CCONJ
ejpam-5720	208	152	(	(	PUNCT
ejpam-5720	208	153	σ1	σ1	PROPN
ejpam-5720	208	154	,	,	PUNCT
ejpam-5720	208	155	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	208	156	)	)	PUNCT
ejpam-5720	208	157	∩	∩	PROPN
ejpam-5720	208	158	f	f	X
ejpam-5720	208	159	(	(	PUNCT
ejpam-5720	208	160	z	z	NOUN
ejpam-5720	208	161	)	)	PUNCT
ejpam-5720	208	162	̸=	̸=	NOUN
ejpam-5720	208	163	∅	∅	NOUN
ejpam-5720	208	164	for	for	ADP
ejpam-5720	208	165	every	every	DET
ejpam-5720	208	166	z	z	PROPN
ejpam-5720	208	167	∈	∈	PROPN
ejpam-5720	208	168	u	u	NOUN
ejpam-5720	208	169	;	;	PUNCT
ejpam-5720	208	170	j.	j.	PROPN
ejpam-5720	208	171	khampakdee	khampakdee	PROPN
ejpam-5720	208	172	,	,	PUNCT
ejpam-5720	208	173	a.	a.	PROPN
ejpam-5720	208	174	sama	sama	PROPN
ejpam-5720	208	175	-	-	PUNCT
ejpam-5720	208	176	ae	ae	PROPN
ejpam-5720	208	177	,	,	PUNCT
ejpam-5720	208	178	c.	c.	PROPN
ejpam-5720	208	179	boonpok	boonpok	PROPN
ejpam-5720	208	180	/	/	SYM
ejpam-5720	208	181	eur	eur	PROPN
ejpam-5720	208	182	.	.	PUNCT
ejpam-5720	209	1	j.	j.	PROPN
ejpam-5720	209	2	pure	pure	PROPN
ejpam-5720	209	3	appl	appl	PROPN
ejpam-5720	209	4	.	.	PROPN
ejpam-5720	209	5	math	math	PROPN
ejpam-5720	209	6	,	,	PUNCT
ejpam-5720	209	7	18	18	NUM
ejpam-5720	209	8	(	(	PUNCT
ejpam-5720	209	9	1	1	NUM
ejpam-5720	209	10	)	)	PUNCT
ejpam-5720	209	11	(	(	PUNCT
ejpam-5720	209	12	2025	2025	NUM
ejpam-5720	209	13	)	)	PUNCT
ejpam-5720	209	14	,	,	PUNCT
ejpam-5720	209	15	5720	5720	NUM
ejpam-5720	209	16	9	9	NUM
ejpam-5720	209	17	of	of	ADP
ejpam-5720	209	18	15	15	NUM
ejpam-5720	209	19	(	(	PUNCT
ejpam-5720	209	20	3	3	NUM
ejpam-5720	209	21	)	)	PUNCT
ejpam-5720	209	22	x	x	SYM
ejpam-5720	209	23	∈	∈	PROPN
ejpam-5720	209	24	(	(	PUNCT
ejpam-5720	209	25	τ1	τ1	NOUN
ejpam-5720	209	26	,	,	PUNCT
ejpam-5720	209	27	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	210	1	+	+	ADJ
ejpam-5720	210	2	(	(	PUNCT
ejpam-5720	210	3	(	(	PUNCT
ejpam-5720	210	4	σ1	σ1	PROPN
ejpam-5720	210	5	,	,	PUNCT
ejpam-5720	210	6	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	210	7	)	)	PUNCT
ejpam-5720	210	8	)	)	PUNCT
ejpam-5720	210	9	∩	∩	ADJ
ejpam-5720	210	10	f−((σ1	f−((σ1	NOUN
ejpam-5720	210	11	,	,	PUNCT
ejpam-5720	210	12	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	210	13	)	)	PUNCT
ejpam-5720	210	14	)	)	PUNCT
ejpam-5720	210	15	)	)	PUNCT
ejpam-5720	211	1	for	for	ADP
ejpam-5720	211	2	every	every	DET
ejpam-5720	211	3	σ1σ2	σ1σ2	NUM
ejpam-5720	211	4	-	-	ADJ
ejpam-5720	211	5	open	open	ADJ
ejpam-5720	211	6	sets	set	NOUN
ejpam-5720	211	7	v1	v1	NOUN
ejpam-5720	211	8	,	,	PUNCT
ejpam-5720	211	9	v2	v2	PROPN
ejpam-5720	211	10	of	of	ADP
ejpam-5720	211	11	y	y	PROPN
ejpam-5720	211	12	having	have	VERB
ejpam-5720	211	13	n	n	PROPN
ejpam-5720	211	14	(	(	PUNCT
ejpam-5720	211	15	σ1	σ1	PROPN
ejpam-5720	211	16	,	,	PUNCT
ejpam-5720	211	17	σ2)-closed	σ2)-close	VERB
ejpam-5720	211	18	complements	complement	NOUN
ejpam-5720	211	19	such	such	ADJ
ejpam-5720	211	20	that	that	SCONJ
ejpam-5720	211	21	x	x	SYM
ejpam-5720	211	22	∈	∈	NOUN
ejpam-5720	211	23	f+(v1	f+(v1	NOUN
ejpam-5720	211	24	)	)	PUNCT
ejpam-5720	211	25	∩	∩	NOUN
ejpam-5720	211	26	f−(v2	f−(v2	NUM
ejpam-5720	211	27	)	)	PUNCT
ejpam-5720	211	28	;	;	PUNCT
ejpam-5720	211	29	(	(	PUNCT
ejpam-5720	211	30	4	4	X
ejpam-5720	211	31	)	)	PUNCT
ejpam-5720	211	32	x	x	SYM
ejpam-5720	211	33	∈	∈	X
ejpam-5720	211	34	τ1τ2	τ1τ2	NOUN
ejpam-5720	211	35	-	-	ADJ
ejpam-5720	211	36	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	211	37	-	-	PUNCT
ejpam-5720	211	38	int(f	int(f	VERB
ejpam-5720	211	39	+	+	ADJ
ejpam-5720	211	40	(	(	PUNCT
ejpam-5720	211	41	(	(	PUNCT
ejpam-5720	211	42	σ1	σ1	PROPN
ejpam-5720	211	43	,	,	PUNCT
ejpam-5720	211	44	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	211	45	)	)	PUNCT
ejpam-5720	211	46	)	)	PUNCT
ejpam-5720	211	47	∩	∩	ADJ
ejpam-5720	211	48	f−((σ1	f−((σ1	NOUN
ejpam-5720	211	49	,	,	PUNCT
ejpam-5720	211	50	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	211	51	)	)	PUNCT
ejpam-5720	211	52	)	)	PUNCT
ejpam-5720	211	53	)	)	PUNCT
ejpam-5720	211	54	)	)	PUNCT
ejpam-5720	211	55	for	for	ADP
ejpam-5720	211	56	every	every	DET
ejpam-5720	211	57	σ1σ2open	σ1σ2open	NUM
ejpam-5720	211	58	sets	set	NOUN
ejpam-5720	211	59	v1	v1	NOUN
ejpam-5720	211	60	,	,	PUNCT
ejpam-5720	211	61	v2	v2	PROPN
ejpam-5720	211	62	of	of	ADP
ejpam-5720	211	63	y	y	PROPN
ejpam-5720	211	64	having	have	VERB
ejpam-5720	211	65	n	n	PROPN
ejpam-5720	211	66	(	(	PUNCT
ejpam-5720	211	67	σ1	σ1	PROPN
ejpam-5720	211	68	,	,	PUNCT
ejpam-5720	211	69	σ2)-closed	σ2)-close	VERB
ejpam-5720	211	70	complements	complement	NOUN
ejpam-5720	211	71	such	such	ADJ
ejpam-5720	211	72	that	that	SCONJ
ejpam-5720	211	73	x	x	SYM
ejpam-5720	211	74	∈	∈	NOUN
ejpam-5720	211	75	f+(v1	f+(v1	NOUN
ejpam-5720	211	76	)	)	PUNCT
ejpam-5720	211	77	∩	∩	NOUN
ejpam-5720	211	78	f−(v2	f−(v2	NUM
ejpam-5720	211	79	)	)	PUNCT
ejpam-5720	211	80	.	.	PUNCT
ejpam-5720	212	1	proof	proof	NOUN
ejpam-5720	212	2	.	.	PUNCT
ejpam-5720	213	1	(	(	PUNCT
ejpam-5720	213	2	1	1	X
ejpam-5720	213	3	)	)	PUNCT
ejpam-5720	213	4	⇒	⇒	NOUN
ejpam-5720	213	5	(	(	PUNCT
ejpam-5720	213	6	2	2	NUM
ejpam-5720	213	7	):	):	PUNCT
ejpam-5720	213	8	let	let	VERB
ejpam-5720	213	9	u(x	u(x	NOUN
ejpam-5720	213	10	)	)	PUNCT
ejpam-5720	213	11	be	be	VERB
ejpam-5720	213	12	the	the	DET
ejpam-5720	213	13	family	family	NOUN
ejpam-5720	213	14	of	of	ADP
ejpam-5720	213	15	all	all	DET
ejpam-5720	213	16	τ1τ2	τ1τ2	ADJ
ejpam-5720	213	17	-	-	ADJ
ejpam-5720	213	18	open	open	ADJ
ejpam-5720	213	19	sets	set	NOUN
ejpam-5720	213	20	of	of	ADP
ejpam-5720	213	21	x	x	PUNCT
ejpam-5720	213	22	containing	contain	VERB
ejpam-5720	213	23	x.	x.	NOUN
ejpam-5720	213	24	let	let	VERB
ejpam-5720	213	25	v1	v1	NOUN
ejpam-5720	213	26	,	,	PUNCT
ejpam-5720	213	27	v2	v2	PROPN
ejpam-5720	213	28	be	be	AUX
ejpam-5720	213	29	any	any	DET
ejpam-5720	213	30	σ1σ2	σ1σ2	NOUN
ejpam-5720	213	31	-	-	PUNCT
ejpam-5720	213	32	open	open	ADJ
ejpam-5720	213	33	sets	set	NOUN
ejpam-5720	213	34	of	of	ADP
ejpam-5720	213	35	y	y	PROPN
ejpam-5720	213	36	having	have	VERB
ejpam-5720	213	37	n	n	PROPN
ejpam-5720	213	38	(	(	PUNCT
ejpam-5720	213	39	σ1	σ1	PROPN
ejpam-5720	213	40	,	,	PUNCT
ejpam-5720	213	41	σ2)-closed	σ2)-close	VERB
ejpam-5720	213	42	complements	complement	NOUN
ejpam-5720	213	43	such	such	ADJ
ejpam-5720	213	44	that	that	SCONJ
ejpam-5720	213	45	x	x	SYM
ejpam-5720	213	46	∈	∈	NOUN
ejpam-5720	213	47	f+(v1	f+(v1	NOUN
ejpam-5720	213	48	)	)	PUNCT
ejpam-5720	213	49	∩	∩	NOUN
ejpam-5720	213	50	f−(v2	f−(v2	NUM
ejpam-5720	213	51	)	)	PUNCT
ejpam-5720	213	52	.	.	PUNCT
ejpam-5720	214	1	for	for	ADP
ejpam-5720	214	2	each	each	DET
ejpam-5720	214	3	h	h	NOUN
ejpam-5720	214	4	∈	∈	PROPN
ejpam-5720	214	5	u(x	u(x	PROPN
ejpam-5720	214	6	)	)	PUNCT
ejpam-5720	214	7	,	,	PUNCT
ejpam-5720	214	8	there	there	PRON
ejpam-5720	214	9	exists	exist	VERB
ejpam-5720	214	10	a	a	DET
ejpam-5720	214	11	nonempty	nonempty	ADJ
ejpam-5720	214	12	τ1τ2	τ1τ2	NOUN
ejpam-5720	214	13	-	-	ADJ
ejpam-5720	214	14	open	open	ADJ
ejpam-5720	214	15	set	set	ADJ
ejpam-5720	214	16	gh	gh	PROPN
ejpam-5720	214	17	of	of	ADP
ejpam-5720	214	18	x	x	PRON
ejpam-5720	214	19	such	such	ADJ
ejpam-5720	214	20	that	that	SCONJ
ejpam-5720	214	21	gh	gh	PROPN
ejpam-5720	214	22	⊆	⊆	NUM
ejpam-5720	214	23	h	h	NOUN
ejpam-5720	214	24	,	,	PUNCT
ejpam-5720	214	25	f	f	PROPN
ejpam-5720	214	26	(	(	PUNCT
ejpam-5720	214	27	gh	gh	PROPN
ejpam-5720	214	28	)	)	PUNCT
ejpam-5720	214	29	⊆	⊆	NUM
ejpam-5720	214	30	(	(	PUNCT
ejpam-5720	214	31	σ1	σ1	PROPN
ejpam-5720	214	32	,	,	PUNCT
ejpam-5720	214	33	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	214	34	)	)	PUNCT
ejpam-5720	214	35	and	and	CCONJ
ejpam-5720	214	36	(	(	PUNCT
ejpam-5720	214	37	σ1	σ1	PROPN
ejpam-5720	214	38	,	,	PUNCT
ejpam-5720	214	39	σ2)-scl(v2)∩f	σ2)-scl(v2)∩f	NOUN
ejpam-5720	214	40	(	(	PUNCT
ejpam-5720	214	41	z	z	NOUN
ejpam-5720	214	42	)	)	PUNCT
ejpam-5720	214	43	̸=	̸=	NOUN
ejpam-5720	214	44	∅	∅	NOUN
ejpam-5720	214	45	for	for	ADP
ejpam-5720	214	46	every	every	DET
ejpam-5720	214	47	z	z	PROPN
ejpam-5720	214	48	∈	∈	PROPN
ejpam-5720	214	49	gh	gh	PROPN
ejpam-5720	214	50	.	.	PUNCT
ejpam-5720	215	1	let	let	VERB
ejpam-5720	215	2	w	w	NOUN
ejpam-5720	215	3	=	=	PUNCT
ejpam-5720	215	4	∪{gh	∪{gh	ADP
ejpam-5720	215	5	|	|	ADV
ejpam-5720	215	6	h	h	NOUN
ejpam-5720	215	7	∈	∈	NOUN
ejpam-5720	215	8	u(x	u(x	PROPN
ejpam-5720	215	9	)	)	PUNCT
ejpam-5720	215	10	}	}	PUNCT
ejpam-5720	215	11	.	.	PUNCT
ejpam-5720	216	1	then	then	ADV
ejpam-5720	216	2	,	,	PUNCT
ejpam-5720	216	3	w	w	PROPN
ejpam-5720	216	4	is	be	AUX
ejpam-5720	216	5	τ1τ2	τ1τ2	NOUN
ejpam-5720	216	6	-	-	ADJ
ejpam-5720	216	7	open	open	ADJ
ejpam-5720	216	8	in	in	ADP
ejpam-5720	216	9	x	x	X
ejpam-5720	216	10	,	,	PUNCT
ejpam-5720	216	11	x	x	SYM
ejpam-5720	216	12	∈	∈	PROPN
ejpam-5720	216	13	τ1τ2	τ1τ2	NOUN
ejpam-5720	216	14	-	-	NOUN
ejpam-5720	216	15	cl(w	cl(w	NOUN
ejpam-5720	216	16	)	)	PUNCT
ejpam-5720	216	17	,	,	PUNCT
ejpam-5720	216	18	f	f	PROPN
ejpam-5720	216	19	(	(	PUNCT
ejpam-5720	216	20	w	w	PROPN
ejpam-5720	216	21	)	)	PUNCT
ejpam-5720	216	22	⊆	⊆	NUM
ejpam-5720	216	23	(	(	PUNCT
ejpam-5720	216	24	σ1	σ1	PROPN
ejpam-5720	216	25	,	,	PUNCT
ejpam-5720	216	26	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	216	27	)	)	PUNCT
ejpam-5720	216	28	and	and	CCONJ
ejpam-5720	216	29	(	(	PUNCT
ejpam-5720	216	30	σ1	σ1	PROPN
ejpam-5720	216	31	,	,	PUNCT
ejpam-5720	216	32	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	216	33	)	)	PUNCT
ejpam-5720	216	34	∩	∩	PROPN
ejpam-5720	216	35	f	f	PROPN
ejpam-5720	216	36	(	(	PUNCT
ejpam-5720	216	37	w	w	NOUN
ejpam-5720	216	38	)	)	PUNCT
ejpam-5720	216	39	̸=	̸=	NOUN
ejpam-5720	216	40	∅	∅	NOUN
ejpam-5720	216	41	for	for	ADP
ejpam-5720	216	42	every	every	DET
ejpam-5720	216	43	w	w	PROPN
ejpam-5720	216	44	∈	∈	PROPN
ejpam-5720	216	45	w	w	PROPN
ejpam-5720	216	46	.	.	PUNCT
ejpam-5720	217	1	put	put	VERB
ejpam-5720	217	2	u	u	NOUN
ejpam-5720	218	1	=	=	NOUN
ejpam-5720	218	2	w	w	NOUN
ejpam-5720	218	3	∪	∪	X
ejpam-5720	218	4	{	{	PUNCT
ejpam-5720	218	5	x	x	NOUN
ejpam-5720	218	6	}	}	PUNCT
ejpam-5720	218	7	.	.	PUNCT
ejpam-5720	219	1	then	then	ADV
ejpam-5720	219	2	,	,	PUNCT
ejpam-5720	219	3	w	w	PROPN
ejpam-5720	219	4	⊆	⊆	NUM
ejpam-5720	219	5	u	u	NOUN
ejpam-5720	219	6	⊆	⊆	NUM
ejpam-5720	219	7	τ1τ2	τ1τ2	NOUN
ejpam-5720	219	8	-	-	NOUN
ejpam-5720	219	9	cl(w	cl(w	NOUN
ejpam-5720	219	10	)	)	PUNCT
ejpam-5720	219	11	.	.	PUNCT
ejpam-5720	220	1	thus	thus	ADV
ejpam-5720	220	2	,	,	PUNCT
ejpam-5720	220	3	u	u	NOUN
ejpam-5720	220	4	is	be	AUX
ejpam-5720	220	5	a	a	DET
ejpam-5720	220	6	(	(	PUNCT
ejpam-5720	220	7	τ1	τ1	NOUN
ejpam-5720	220	8	,	,	PUNCT
ejpam-5720	220	9	τ2)s	τ2)s	NOUN
ejpam-5720	220	10	-	-	PUNCT
ejpam-5720	220	11	open	open	ADJ
ejpam-5720	220	12	set	set	NOUN
ejpam-5720	220	13	of	of	ADP
ejpam-5720	220	14	x	x	PUNCT
ejpam-5720	220	15	containing	contain	VERB
ejpam-5720	220	16	x	x	PUNCT
ejpam-5720	220	17	such	such	ADJ
ejpam-5720	220	18	that	that	SCONJ
ejpam-5720	220	19	f	f	PROPN
ejpam-5720	220	20	(	(	PUNCT
ejpam-5720	220	21	u	u	NOUN
ejpam-5720	220	22	)	)	PUNCT
ejpam-5720	220	23	⊆	⊆	NUM
ejpam-5720	220	24	(	(	PUNCT
ejpam-5720	220	25	(	(	PUNCT
ejpam-5720	220	26	σ1	σ1	PROPN
ejpam-5720	220	27	,	,	PUNCT
ejpam-5720	220	28	σ2)-scl(v1	σ2)-scl(v1	NOUN
ejpam-5720	220	29	)	)	PUNCT
ejpam-5720	220	30	)	)	PUNCT
ejpam-5720	220	31	and	and	CCONJ
ejpam-5720	220	32	(	(	PUNCT
ejpam-5720	220	33	σ1	σ1	PROPN
ejpam-5720	220	34	,	,	PUNCT
ejpam-5720	220	35	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	220	36	)	)	PUNCT
ejpam-5720	220	37	∩	∩	PROPN
ejpam-5720	220	38	f	f	X
ejpam-5720	220	39	(	(	PUNCT
ejpam-5720	220	40	z	z	NOUN
ejpam-5720	220	41	)	)	PUNCT
ejpam-5720	220	42	̸=	̸=	NOUN
ejpam-5720	220	43	∅	∅	NOUN
ejpam-5720	220	44	for	for	ADP
ejpam-5720	220	45	every	every	DET
ejpam-5720	220	46	z	z	NOUN
ejpam-5720	220	47	∈	∈	PROPN
ejpam-5720	220	48	u	u	NOUN
ejpam-5720	220	49	.	.	PUNCT
ejpam-5720	221	1	(	(	PUNCT
ejpam-5720	221	2	2	2	X
ejpam-5720	221	3	)	)	PUNCT
ejpam-5720	221	4	⇒	⇒	NOUN
ejpam-5720	221	5	(	(	PUNCT
ejpam-5720	221	6	3	3	NUM
ejpam-5720	221	7	):	):	PUNCT
ejpam-5720	221	8	let	let	VERB
ejpam-5720	221	9	v1	v1	NOUN
ejpam-5720	221	10	,	,	PUNCT
ejpam-5720	221	11	v2	v2	PROPN
ejpam-5720	221	12	be	be	AUX
ejpam-5720	221	13	any	any	DET
ejpam-5720	221	14	σ1σ2	σ1σ2	NOUN
ejpam-5720	221	15	-	-	PUNCT
ejpam-5720	221	16	open	open	ADJ
ejpam-5720	221	17	sets	set	NOUN
ejpam-5720	221	18	of	of	ADP
ejpam-5720	221	19	y	y	PROPN
ejpam-5720	221	20	having	have	VERB
ejpam-5720	221	21	n	n	PROPN
ejpam-5720	221	22	(	(	PUNCT
ejpam-5720	221	23	σ1	σ1	PROPN
ejpam-5720	221	24	,	,	PUNCT
ejpam-5720	221	25	σ2)-closed	σ2)-close	VERB
ejpam-5720	221	26	complements	complement	NOUN
ejpam-5720	221	27	such	such	ADJ
ejpam-5720	221	28	that	that	SCONJ
ejpam-5720	221	29	x	x	SYM
ejpam-5720	221	30	∈	∈	NOUN
ejpam-5720	221	31	f+(v1	f+(v1	NOUN
ejpam-5720	221	32	)	)	PUNCT
ejpam-5720	221	33	∩	∩	NOUN
ejpam-5720	221	34	f−(v2	f−(v2	NUM
ejpam-5720	221	35	)	)	PUNCT
ejpam-5720	221	36	.	.	PUNCT
ejpam-5720	222	1	then	then	ADV
ejpam-5720	222	2	,	,	PUNCT
ejpam-5720	222	3	there	there	PRON
ejpam-5720	222	4	exists	exist	VERB
ejpam-5720	222	5	a	a	DET
ejpam-5720	222	6	(	(	PUNCT
ejpam-5720	222	7	τ1	τ1	NOUN
ejpam-5720	222	8	,	,	PUNCT
ejpam-5720	222	9	τ2)s	τ2)s	NOUN
ejpam-5720	222	10	-	-	PUNCT
ejpam-5720	222	11	open	open	ADJ
ejpam-5720	222	12	set	set	NOUN
ejpam-5720	222	13	of	of	ADP
ejpam-5720	222	14	x	x	PUNCT
ejpam-5720	222	15	containing	contain	VERB
ejpam-5720	222	16	x	x	PUNCT
ejpam-5720	222	17	such	such	ADJ
ejpam-5720	222	18	that	that	SCONJ
ejpam-5720	222	19	f	f	PROPN
ejpam-5720	222	20	(	(	PUNCT
ejpam-5720	222	21	u	u	NOUN
ejpam-5720	222	22	)	)	PUNCT
ejpam-5720	222	23	⊆	⊆	NUM
ejpam-5720	222	24	(	(	PUNCT
ejpam-5720	222	25	σ1	σ1	PROPN
ejpam-5720	222	26	,	,	PUNCT
ejpam-5720	222	27	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	222	28	)	)	PUNCT
ejpam-5720	222	29	and	and	CCONJ
ejpam-5720	222	30	(	(	PUNCT
ejpam-5720	222	31	σ1	σ1	PROPN
ejpam-5720	222	32	,	,	PUNCT
ejpam-5720	222	33	σ2)-scl(v2)∩	σ2)-scl(v2)∩	PROPN
ejpam-5720	222	34	f	f	X
ejpam-5720	222	35	(	(	PUNCT
ejpam-5720	222	36	z	z	NOUN
ejpam-5720	222	37	)	)	PUNCT
ejpam-5720	222	38	̸=	̸=	NOUN
ejpam-5720	222	39	∅	∅	NOUN
ejpam-5720	222	40	for	for	ADP
ejpam-5720	222	41	every	every	DET
ejpam-5720	222	42	z	z	NOUN
ejpam-5720	222	43	∈	∈	PROPN
ejpam-5720	222	44	u	u	NOUN
ejpam-5720	222	45	.	.	PUNCT
ejpam-5720	223	1	thus	thus	ADV
ejpam-5720	223	2	,	,	PUNCT
ejpam-5720	223	3	x	x	PUNCT
ejpam-5720	223	4	∈	∈	PROPN
ejpam-5720	223	5	u	u	NOUN
ejpam-5720	223	6	⊆	⊆	NUM
ejpam-5720	223	7	f+((σ1	f+((σ1	NOUN
ejpam-5720	223	8	,	,	PUNCT
ejpam-5720	223	9	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	223	10	)	)	PUNCT
ejpam-5720	223	11	)	)	PUNCT
ejpam-5720	223	12	∩	∩	ADJ
ejpam-5720	223	13	f−((σ1	f−((σ1	NOUN
ejpam-5720	223	14	,	,	PUNCT
ejpam-5720	223	15	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	223	16	)	)	PUNCT
ejpam-5720	223	17	)	)	PUNCT
ejpam-5720	223	18	.	.	PUNCT
ejpam-5720	224	1	since	since	SCONJ
ejpam-5720	224	2	u	u	NOUN
ejpam-5720	224	3	is	be	AUX
ejpam-5720	224	4	(	(	PUNCT
ejpam-5720	224	5	τ1	τ1	NOUN
ejpam-5720	224	6	,	,	PUNCT
ejpam-5720	224	7	τ2)s	τ2)s	NOUN
ejpam-5720	224	8	-	-	PUNCT
ejpam-5720	224	9	open	open	ADJ
ejpam-5720	224	10	,	,	PUNCT
ejpam-5720	224	11	we	we	PRON
ejpam-5720	224	12	have	have	VERB
ejpam-5720	224	13	x	x	PROPN
ejpam-5720	224	14	∈	∈	PROPN
ejpam-5720	224	15	(	(	PUNCT
ejpam-5720	224	16	τ1	τ1	NOUN
ejpam-5720	224	17	,	,	PUNCT
ejpam-5720	224	18	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	225	1	+	+	ADJ
ejpam-5720	225	2	(	(	PUNCT
ejpam-5720	225	3	(	(	PUNCT
ejpam-5720	225	4	σ1	σ1	PROPN
ejpam-5720	225	5	,	,	PUNCT
ejpam-5720	225	6	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	225	7	)	)	PUNCT
ejpam-5720	225	8	)	)	PUNCT
ejpam-5720	225	9	∩	∩	ADJ
ejpam-5720	225	10	f−((σ1	f−((σ1	NOUN
ejpam-5720	225	11	,	,	PUNCT
ejpam-5720	225	12	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	225	13	)	)	PUNCT
ejpam-5720	225	14	)	)	PUNCT
ejpam-5720	225	15	)	)	PUNCT
ejpam-5720	225	16	.	.	PUNCT
ejpam-5720	226	1	(	(	PUNCT
ejpam-5720	226	2	3	3	X
ejpam-5720	226	3	)	)	PUNCT
ejpam-5720	226	4	⇒	⇒	NOUN
ejpam-5720	226	5	(	(	PUNCT
ejpam-5720	226	6	4	4	NUM
ejpam-5720	226	7	):	):	PUNCT
ejpam-5720	226	8	let	let	VERB
ejpam-5720	226	9	v1	v1	NOUN
ejpam-5720	226	10	,	,	PUNCT
ejpam-5720	226	11	v2	v2	PROPN
ejpam-5720	226	12	be	be	AUX
ejpam-5720	226	13	any	any	DET
ejpam-5720	226	14	σ1σ2	σ1σ2	NOUN
ejpam-5720	226	15	-	-	PUNCT
ejpam-5720	226	16	open	open	ADJ
ejpam-5720	226	17	sets	set	NOUN
ejpam-5720	226	18	of	of	ADP
ejpam-5720	226	19	y	y	PROPN
ejpam-5720	226	20	having	have	VERB
ejpam-5720	226	21	n	n	PROPN
ejpam-5720	226	22	(	(	PUNCT
ejpam-5720	226	23	σ1	σ1	PROPN
ejpam-5720	226	24	,	,	PUNCT
ejpam-5720	226	25	σ2)-closed	σ2)-close	VERB
ejpam-5720	226	26	complements	complement	NOUN
ejpam-5720	226	27	such	such	ADJ
ejpam-5720	226	28	that	that	SCONJ
ejpam-5720	226	29	x	x	SYM
ejpam-5720	226	30	∈	∈	NOUN
ejpam-5720	226	31	f+(v1	f+(v1	NOUN
ejpam-5720	226	32	)	)	PUNCT
ejpam-5720	226	33	∩	∩	NOUN
ejpam-5720	226	34	f−(v2	f−(v2	NUM
ejpam-5720	226	35	)	)	PUNCT
ejpam-5720	226	36	.	.	PUNCT
ejpam-5720	227	1	now	now	ADV
ejpam-5720	227	2	put	put	VERB
ejpam-5720	227	3	u	u	NOUN
ejpam-5720	227	4	=	=	PUNCT
ejpam-5720	227	5	(	(	PUNCT
ejpam-5720	227	6	τ1	τ1	NOUN
ejpam-5720	227	7	,	,	PUNCT
ejpam-5720	227	8	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	228	1	+	+	ADJ
ejpam-5720	228	2	(	(	PUNCT
ejpam-5720	228	3	(	(	PUNCT
ejpam-5720	228	4	σ1	σ1	PROPN
ejpam-5720	228	5	,	,	PUNCT
ejpam-5720	228	6	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	228	7	)	)	PUNCT
ejpam-5720	228	8	)	)	PUNCT
ejpam-5720	228	9	∩	∩	ADJ
ejpam-5720	228	10	f−((σ1	f−((σ1	NOUN
ejpam-5720	228	11	,	,	PUNCT
ejpam-5720	228	12	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	228	13	)	)	PUNCT
ejpam-5720	228	14	)	)	PUNCT
ejpam-5720	228	15	)	)	PUNCT
ejpam-5720	228	16	.	.	PUNCT
ejpam-5720	229	1	then	then	ADV
ejpam-5720	229	2	,	,	PUNCT
ejpam-5720	229	3	u	u	NOUN
ejpam-5720	229	4	is	be	AUX
ejpam-5720	229	5	(	(	PUNCT
ejpam-5720	229	6	τ1	τ1	NOUN
ejpam-5720	229	7	,	,	PUNCT
ejpam-5720	229	8	τ2)s	τ2)s	NOUN
ejpam-5720	229	9	-	-	PUNCT
ejpam-5720	229	10	open	open	ADJ
ejpam-5720	229	11	in	in	ADP
ejpam-5720	229	12	x	x	PUNCT
ejpam-5720	229	13	and	and	CCONJ
ejpam-5720	229	14	x	x	PUNCT
ejpam-5720	229	15	∈	∈	PROPN
ejpam-5720	229	16	τ1τ2	τ1τ2	NOUN
ejpam-5720	229	17	-	-	ADJ
ejpam-5720	229	18	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	229	19	-	-	PUNCT
ejpam-5720	229	20	int(f	int(f	VERB
ejpam-5720	229	21	+	+	ADJ
ejpam-5720	229	22	(	(	PUNCT
ejpam-5720	229	23	(	(	PUNCT
ejpam-5720	229	24	σ1	σ1	PROPN
ejpam-5720	229	25	,	,	PUNCT
ejpam-5720	229	26	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	229	27	)	)	PUNCT
ejpam-5720	229	28	)	)	PUNCT
ejpam-5720	229	29	∩	∩	ADJ
ejpam-5720	229	30	f−((σ1	f−((σ1	NOUN
ejpam-5720	229	31	,	,	PUNCT
ejpam-5720	229	32	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	229	33	)	)	PUNCT
ejpam-5720	229	34	)	)	PUNCT
ejpam-5720	229	35	)	)	PUNCT
ejpam-5720	229	36	)	)	PUNCT
ejpam-5720	229	37	.	.	PUNCT
ejpam-5720	230	1	(	(	PUNCT
ejpam-5720	230	2	4	4	X
ejpam-5720	230	3	)	)	PUNCT
ejpam-5720	230	4	⇒	⇒	NOUN
ejpam-5720	230	5	(	(	PUNCT
ejpam-5720	230	6	1	1	NUM
ejpam-5720	230	7	):	):	PUNCT
ejpam-5720	230	8	let	let	VERB
ejpam-5720	230	9	u	u	PRON
ejpam-5720	230	10	be	be	AUX
ejpam-5720	230	11	any	any	DET
ejpam-5720	230	12	τ1τ2	τ1τ2	ADJ
ejpam-5720	230	13	-	-	ADJ
ejpam-5720	230	14	open	open	ADJ
ejpam-5720	230	15	set	set	NOUN
ejpam-5720	230	16	of	of	ADP
ejpam-5720	230	17	x	x	PUNCT
ejpam-5720	230	18	containing	contain	VERB
ejpam-5720	230	19	x	x	X
ejpam-5720	230	20	and	and	CCONJ
ejpam-5720	230	21	v1	v1	NOUN
ejpam-5720	230	22	,	,	PUNCT
ejpam-5720	230	23	v2	v2	PROPN
ejpam-5720	230	24	be	be	AUX
ejpam-5720	230	25	any	any	DET
ejpam-5720	230	26	σ1σ2	σ1σ2	NOUN
ejpam-5720	230	27	-	-	PUNCT
ejpam-5720	230	28	open	open	ADJ
ejpam-5720	230	29	sets	set	NOUN
ejpam-5720	230	30	of	of	ADP
ejpam-5720	230	31	y	y	PROPN
ejpam-5720	230	32	having	have	VERB
ejpam-5720	230	33	n	n	PROPN
ejpam-5720	230	34	(	(	PUNCT
ejpam-5720	230	35	σ1	σ1	PROPN
ejpam-5720	230	36	,	,	PUNCT
ejpam-5720	230	37	σ2)-closed	σ2)-close	VERB
ejpam-5720	230	38	complements	complement	NOUN
ejpam-5720	230	39	such	such	ADJ
ejpam-5720	230	40	that	that	SCONJ
ejpam-5720	230	41	x	x	SYM
ejpam-5720	230	42	∈	∈	NOUN
ejpam-5720	230	43	f+(v1	f+(v1	NOUN
ejpam-5720	230	44	)	)	PUNCT
ejpam-5720	230	45	∩	∩	NOUN
ejpam-5720	230	46	f−(v2	f−(v2	NUM
ejpam-5720	230	47	)	)	PUNCT
ejpam-5720	230	48	.	.	PUNCT
ejpam-5720	231	1	then	then	ADV
ejpam-5720	231	2	,	,	PUNCT
ejpam-5720	231	3	we	we	PRON
ejpam-5720	231	4	have	have	VERB
ejpam-5720	231	5	x	x	PART
ejpam-5720	231	6	∈	∈	PRON
ejpam-5720	231	7	τ1τ2	τ1τ2	NOUN
ejpam-5720	231	8	-	-	NOUN
ejpam-5720	231	9	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	231	10	-	-	PUNCT
ejpam-5720	231	11	int(f	int(f	VERB
ejpam-5720	231	12	+	+	ADJ
ejpam-5720	231	13	(	(	PUNCT
ejpam-5720	231	14	(	(	PUNCT
ejpam-5720	231	15	σ1	σ1	PROPN
ejpam-5720	231	16	,	,	PUNCT
ejpam-5720	231	17	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	231	18	)	)	PUNCT
ejpam-5720	231	19	)	)	PUNCT
ejpam-5720	231	20	∩	∩	ADJ
ejpam-5720	231	21	f−((σ1	f−((σ1	NOUN
ejpam-5720	231	22	,	,	PUNCT
ejpam-5720	231	23	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	231	24	)	)	PUNCT
ejpam-5720	231	25	)	)	PUNCT
ejpam-5720	231	26	)	)	PUNCT
ejpam-5720	231	27	)	)	PUNCT
ejpam-5720	231	28	.	.	PUNCT
ejpam-5720	232	1	put	put	VERB
ejpam-5720	232	2	w	w	NOUN
ejpam-5720	232	3	=	=	PUNCT
ejpam-5720	232	4	τ1τ2	τ1τ2	NOUN
ejpam-5720	232	5	-	-	NUM
ejpam-5720	232	6	int(f	int(f	VERB
ejpam-5720	232	7	+	+	ADJ
ejpam-5720	232	8	(	(	PUNCT
ejpam-5720	232	9	(	(	PUNCT
ejpam-5720	232	10	σ1	σ1	PROPN
ejpam-5720	232	11	,	,	PUNCT
ejpam-5720	232	12	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	232	13	)	)	PUNCT
ejpam-5720	232	14	)	)	PUNCT
ejpam-5720	232	15	∩	∩	ADJ
ejpam-5720	232	16	f−((σ1	f−((σ1	NOUN
ejpam-5720	232	17	,	,	PUNCT
ejpam-5720	232	18	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	232	19	)	)	PUNCT
ejpam-5720	232	20	)	)	PUNCT
ejpam-5720	232	21	)	)	PUNCT
ejpam-5720	233	1	∩	∩	PROPN
ejpam-5720	233	2	u.	u.	PROPN
ejpam-5720	233	3	then	then	ADV
ejpam-5720	233	4	,	,	PUNCT
ejpam-5720	233	5	w	w	PROPN
ejpam-5720	233	6	is	be	AUX
ejpam-5720	233	7	a	a	DET
ejpam-5720	233	8	nonempty	nonempty	ADJ
ejpam-5720	233	9	τ1τ2	τ1τ2	NOUN
ejpam-5720	233	10	-	-	ADJ
ejpam-5720	233	11	open	open	ADJ
ejpam-5720	233	12	set	set	NOUN
ejpam-5720	233	13	of	of	ADP
ejpam-5720	233	14	x	x	PUNCT
ejpam-5720	233	15	such	such	ADJ
ejpam-5720	233	16	that	that	SCONJ
ejpam-5720	233	17	w	w	PROPN
ejpam-5720	233	18	⊆	⊆	NUM
ejpam-5720	233	19	u	u	NOUN
ejpam-5720	233	20	,	,	PUNCT
ejpam-5720	233	21	f	f	PROPN
ejpam-5720	233	22	(	(	PUNCT
ejpam-5720	233	23	w	w	PROPN
ejpam-5720	233	24	)	)	PUNCT
ejpam-5720	233	25	⊆	⊆	NUM
ejpam-5720	233	26	(	(	PUNCT
ejpam-5720	233	27	σ1	σ1	PROPN
ejpam-5720	233	28	,	,	PUNCT
ejpam-5720	233	29	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	233	30	)	)	PUNCT
ejpam-5720	233	31	and	and	CCONJ
ejpam-5720	233	32	(	(	PUNCT
ejpam-5720	233	33	σ1	σ1	PROPN
ejpam-5720	233	34	,	,	PUNCT
ejpam-5720	233	35	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	233	36	)	)	PUNCT
ejpam-5720	233	37	∩	∩	PROPN
ejpam-5720	233	38	f	f	PROPN
ejpam-5720	233	39	(	(	PUNCT
ejpam-5720	233	40	w	w	NOUN
ejpam-5720	233	41	)	)	PUNCT
ejpam-5720	233	42	̸=	̸=	NOUN
ejpam-5720	233	43	∅	∅	NOUN
ejpam-5720	233	44	for	for	ADP
ejpam-5720	233	45	every	every	DET
ejpam-5720	233	46	w	w	PROPN
ejpam-5720	233	47	∈	∈	PROPN
ejpam-5720	233	48	w	w	NOUN
ejpam-5720	233	49	.	.	PUNCT
ejpam-5720	234	1	this	this	PRON
ejpam-5720	234	2	shows	show	VERB
ejpam-5720	234	3	that	that	SCONJ
ejpam-5720	234	4	f	f	PROPN
ejpam-5720	234	5	is	be	AUX
ejpam-5720	234	6	almost	almost	ADV
ejpam-5720	234	7	nearly	nearly	ADV
ejpam-5720	234	8	quasi	quasi	NOUN
ejpam-5720	234	9	(	(	PUNCT
ejpam-5720	234	10	τ1	τ1	NOUN
ejpam-5720	234	11	,	,	PUNCT
ejpam-5720	234	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	234	13	at	at	ADP
ejpam-5720	234	14	x.	x.	NOUN
ejpam-5720	234	15	theorem	theorem	VERB
ejpam-5720	234	16	7	7	NUM
ejpam-5720	234	17	.	.	X
ejpam-5720	234	18	for	for	ADP
ejpam-5720	234	19	a	a	DET
ejpam-5720	234	20	multifunction	multifunction	NOUN
ejpam-5720	234	21	f	f	NOUN
ejpam-5720	234	22	:	:	PUNCT
ejpam-5720	234	23	(	(	PUNCT
ejpam-5720	234	24	x	x	NOUN
ejpam-5720	234	25	,	,	PUNCT
ejpam-5720	234	26	τ1	τ1	NOUN
ejpam-5720	234	27	,	,	PUNCT
ejpam-5720	234	28	τ2	τ2	NOUN
ejpam-5720	234	29	)	)	PUNCT
ejpam-5720	234	30	→	→	SYM
ejpam-5720	234	31	(	(	PUNCT
ejpam-5720	234	32	y	y	PROPN
ejpam-5720	234	33	,	,	PUNCT
ejpam-5720	234	34	σ1	σ1	PROPN
ejpam-5720	234	35	,	,	PUNCT
ejpam-5720	234	36	σ2	σ2	NOUN
ejpam-5720	234	37	)	)	PUNCT
ejpam-5720	234	38	,	,	PUNCT
ejpam-5720	234	39	the	the	DET
ejpam-5720	234	40	following	follow	VERB
ejpam-5720	234	41	properties	property	NOUN
ejpam-5720	234	42	are	be	AUX
ejpam-5720	234	43	equivalent	equivalent	ADJ
ejpam-5720	234	44	:	:	PUNCT
ejpam-5720	234	45	(	(	PUNCT
ejpam-5720	234	46	1	1	X
ejpam-5720	234	47	)	)	PUNCT
ejpam-5720	234	48	f	f	NOUN
ejpam-5720	234	49	is	be	AUX
ejpam-5720	234	50	almost	almost	ADV
ejpam-5720	234	51	nearly	nearly	ADV
ejpam-5720	234	52	quasi	quasi	NOUN
ejpam-5720	234	53	(	(	PUNCT
ejpam-5720	234	54	τ1	τ1	NOUN
ejpam-5720	234	55	,	,	PUNCT
ejpam-5720	234	56	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	234	57	;	;	PUNCT
ejpam-5720	234	58	j.	j.	PROPN
ejpam-5720	234	59	khampakdee	khampakdee	PROPN
ejpam-5720	234	60	,	,	PUNCT
ejpam-5720	234	61	a.	a.	PROPN
ejpam-5720	234	62	sama	sama	PROPN
ejpam-5720	234	63	-	-	PUNCT
ejpam-5720	234	64	ae	ae	PROPN
ejpam-5720	234	65	,	,	PUNCT
ejpam-5720	234	66	c.	c.	PROPN
ejpam-5720	234	67	boonpok	boonpok	PROPN
ejpam-5720	234	68	/	/	SYM
ejpam-5720	234	69	eur	eur	PROPN
ejpam-5720	234	70	.	.	PUNCT
ejpam-5720	235	1	j.	j.	PROPN
ejpam-5720	235	2	pure	pure	PROPN
ejpam-5720	235	3	appl	appl	PROPN
ejpam-5720	235	4	.	.	PROPN
ejpam-5720	235	5	math	math	PROPN
ejpam-5720	235	6	,	,	PUNCT
ejpam-5720	235	7	18	18	NUM
ejpam-5720	235	8	(	(	PUNCT
ejpam-5720	235	9	1	1	NUM
ejpam-5720	235	10	)	)	PUNCT
ejpam-5720	235	11	(	(	PUNCT
ejpam-5720	235	12	2025	2025	NUM
ejpam-5720	235	13	)	)	PUNCT
ejpam-5720	235	14	,	,	PUNCT
ejpam-5720	235	15	5720	5720	NUM
ejpam-5720	235	16	10	10	NUM
ejpam-5720	235	17	of	of	ADP
ejpam-5720	235	18	15	15	NUM
ejpam-5720	235	19	(	(	PUNCT
ejpam-5720	235	20	2	2	NUM
ejpam-5720	235	21	)	)	PUNCT
ejpam-5720	235	22	for	for	ADP
ejpam-5720	235	23	each	each	DET
ejpam-5720	235	24	x	x	SYM
ejpam-5720	235	25	∈	∈	PROPN
ejpam-5720	235	26	x	x	X
ejpam-5720	235	27	and	and	CCONJ
ejpam-5720	235	28	for	for	ADP
ejpam-5720	235	29	every	every	DET
ejpam-5720	235	30	σ1σ2	σ1σ2	NUM
ejpam-5720	235	31	-	-	ADJ
ejpam-5720	235	32	open	open	ADJ
ejpam-5720	235	33	sets	set	NOUN
ejpam-5720	235	34	v1	v1	NOUN
ejpam-5720	235	35	,	,	PUNCT
ejpam-5720	235	36	v2	v2	PROPN
ejpam-5720	235	37	of	of	ADP
ejpam-5720	235	38	y	y	PROPN
ejpam-5720	235	39	having	have	VERB
ejpam-5720	235	40	n	n	PROPN
ejpam-5720	235	41	(	(	PUNCT
ejpam-5720	235	42	σ1	σ1	PROPN
ejpam-5720	235	43	,	,	PUNCT
ejpam-5720	235	44	σ2)-closed	σ2)-close	VERB
ejpam-5720	235	45	complements	complement	NOUN
ejpam-5720	235	46	such	such	ADJ
ejpam-5720	235	47	that	that	SCONJ
ejpam-5720	235	48	x	x	SYM
ejpam-5720	235	49	∈	∈	NOUN
ejpam-5720	235	50	f+(v1	f+(v1	NOUN
ejpam-5720	235	51	)	)	PUNCT
ejpam-5720	235	52	∩	∩	NOUN
ejpam-5720	235	53	f−(v2	f−(v2	NUM
ejpam-5720	235	54	)	)	PUNCT
ejpam-5720	235	55	,	,	PUNCT
ejpam-5720	235	56	there	there	PRON
ejpam-5720	235	57	exists	exist	VERB
ejpam-5720	235	58	a	a	DET
ejpam-5720	235	59	(	(	PUNCT
ejpam-5720	235	60	τ1	τ1	NOUN
ejpam-5720	235	61	,	,	PUNCT
ejpam-5720	235	62	τ2)s	τ2)s	NOUN
ejpam-5720	235	63	-	-	PUNCT
ejpam-5720	235	64	open	open	ADJ
ejpam-5720	235	65	set	set	NOUN
ejpam-5720	235	66	u	u	NOUN
ejpam-5720	235	67	of	of	ADP
ejpam-5720	235	68	x	x	PUNCT
ejpam-5720	235	69	containing	contain	VERB
ejpam-5720	235	70	x	x	PUNCT
ejpam-5720	235	71	such	such	ADJ
ejpam-5720	235	72	that	that	SCONJ
ejpam-5720	235	73	f	f	PROPN
ejpam-5720	235	74	(	(	PUNCT
ejpam-5720	235	75	u	u	NOUN
ejpam-5720	235	76	)	)	PUNCT
ejpam-5720	235	77	⊆	⊆	NUM
ejpam-5720	235	78	(	(	PUNCT
ejpam-5720	235	79	σ1	σ1	PROPN
ejpam-5720	235	80	,	,	PUNCT
ejpam-5720	235	81	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	235	82	)	)	PUNCT
ejpam-5720	235	83	and	and	CCONJ
ejpam-5720	235	84	(	(	PUNCT
ejpam-5720	235	85	σ1	σ1	PROPN
ejpam-5720	235	86	,	,	PUNCT
ejpam-5720	235	87	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	235	88	)	)	PUNCT
ejpam-5720	235	89	∩	∩	PROPN
ejpam-5720	235	90	f	f	X
ejpam-5720	235	91	(	(	PUNCT
ejpam-5720	235	92	z	z	NOUN
ejpam-5720	235	93	)	)	PUNCT
ejpam-5720	235	94	̸=	̸=	NOUN
ejpam-5720	235	95	∅	∅	NOUN
ejpam-5720	235	96	for	for	ADP
ejpam-5720	235	97	every	every	DET
ejpam-5720	235	98	z	z	NOUN
ejpam-5720	235	99	∈	∈	PROPN
ejpam-5720	235	100	u	u	NOUN
ejpam-5720	235	101	;	;	PUNCT
ejpam-5720	235	102	(	(	PUNCT
ejpam-5720	235	103	3	3	X
ejpam-5720	235	104	)	)	PUNCT
ejpam-5720	235	105	f+(v1	f+(v1	NOUN
ejpam-5720	235	106	)	)	PUNCT
ejpam-5720	235	107	∩	∩	NOUN
ejpam-5720	235	108	f−(v2	f−(v2	X
ejpam-5720	235	109	)	)	PUNCT
ejpam-5720	235	110	is	be	AUX
ejpam-5720	235	111	(	(	PUNCT
ejpam-5720	235	112	τ1	τ1	NOUN
ejpam-5720	235	113	,	,	PUNCT
ejpam-5720	235	114	τ2)s	τ2)s	NOUN
ejpam-5720	235	115	-	-	PUNCT
ejpam-5720	235	116	open	open	ADJ
ejpam-5720	235	117	in	in	ADP
ejpam-5720	235	118	x	x	PUNCT
ejpam-5720	235	119	for	for	ADP
ejpam-5720	235	120	every	every	DET
ejpam-5720	235	121	(	(	PUNCT
ejpam-5720	235	122	σ1	σ1	PROPN
ejpam-5720	235	123	,	,	PUNCT
ejpam-5720	235	124	σ2)r	σ2)r	NOUN
ejpam-5720	235	125	-	-	PUNCT
ejpam-5720	235	126	open	open	ADJ
ejpam-5720	235	127	sets	set	NOUN
ejpam-5720	235	128	v1	v1	NOUN
ejpam-5720	235	129	,	,	PUNCT
ejpam-5720	235	130	v2	v2	PROPN
ejpam-5720	235	131	of	of	ADP
ejpam-5720	235	132	y	y	PROPN
ejpam-5720	235	133	having	have	VERB
ejpam-5720	235	134	n	n	PROPN
ejpam-5720	235	135	(	(	PUNCT
ejpam-5720	235	136	σ1	σ1	PROPN
ejpam-5720	235	137	,	,	PUNCT
ejpam-5720	235	138	σ2)-closed	σ2)-close	VERB
ejpam-5720	235	139	complements	complement	NOUN
ejpam-5720	235	140	;	;	PUNCT
ejpam-5720	235	141	(	(	PUNCT
ejpam-5720	235	142	4	4	X
ejpam-5720	235	143	)	)	PUNCT
ejpam-5720	235	144	f+(v1	f+(v1	NOUN
ejpam-5720	235	145	)	)	PUNCT
ejpam-5720	235	146	∩	∩	NOUN
ejpam-5720	235	147	f−(v2	f−(v2	X
ejpam-5720	235	148	)	)	PUNCT
ejpam-5720	235	149	⊆	⊆	NUM
ejpam-5720	235	150	(	(	PUNCT
ejpam-5720	235	151	τ1	τ1	NOUN
ejpam-5720	235	152	,	,	PUNCT
ejpam-5720	235	153	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	236	1	+	+	ADJ
ejpam-5720	236	2	(	(	PUNCT
ejpam-5720	236	3	(	(	PUNCT
ejpam-5720	236	4	σ1	σ1	PROPN
ejpam-5720	236	5	,	,	PUNCT
ejpam-5720	236	6	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	236	7	)	)	PUNCT
ejpam-5720	236	8	)	)	PUNCT
ejpam-5720	236	9	∩	∩	ADJ
ejpam-5720	236	10	f−((σ1	f−((σ1	NOUN
ejpam-5720	236	11	,	,	PUNCT
ejpam-5720	236	12	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	236	13	)	)	PUNCT
ejpam-5720	236	14	)	)	PUNCT
ejpam-5720	236	15	)	)	PUNCT
ejpam-5720	237	1	for	for	ADP
ejpam-5720	237	2	every	every	DET
ejpam-5720	237	3	σ1σ2	σ1σ2	NUM
ejpam-5720	237	4	-	-	ADJ
ejpam-5720	237	5	open	open	ADJ
ejpam-5720	237	6	sets	set	NOUN
ejpam-5720	237	7	v1	v1	NOUN
ejpam-5720	237	8	,	,	PUNCT
ejpam-5720	237	9	v2	v2	PROPN
ejpam-5720	237	10	of	of	ADP
ejpam-5720	237	11	y	y	PROPN
ejpam-5720	237	12	having	have	VERB
ejpam-5720	237	13	n	n	PROPN
ejpam-5720	237	14	(	(	PUNCT
ejpam-5720	237	15	σ1	σ1	PROPN
ejpam-5720	237	16	,	,	PUNCT
ejpam-5720	237	17	σ2)-closed	σ2)-close	VERB
ejpam-5720	237	18	complements	complement	NOUN
ejpam-5720	237	19	;	;	PUNCT
ejpam-5720	237	20	(	(	PUNCT
ejpam-5720	237	21	5	5	NUM
ejpam-5720	237	22	)	)	PUNCT
ejpam-5720	237	23	(	(	PUNCT
ejpam-5720	237	24	τ1	τ1	NOUN
ejpam-5720	237	25	,	,	PUNCT
ejpam-5720	237	26	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5720	237	27	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5720	237	28	-	-	PUNCT
ejpam-5720	237	29	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	237	30	-	-	PUNCT
ejpam-5720	237	31	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	237	32	-	-	PUNCT
ejpam-5720	237	33	cl(b1	cl(b1	NOUN
ejpam-5720	237	34	)	)	PUNCT
ejpam-5720	237	35	)	)	PUNCT
ejpam-5720	237	36	)	)	PUNCT
ejpam-5720	237	37	)	)	PUNCT
ejpam-5720	237	38	∪	∪	ADP
ejpam-5720	237	39	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5720	237	40	-	-	PUNCT
ejpam-5720	237	41	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	237	42	-	-	PUNCT
ejpam-5720	237	43	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	237	44	-	-	PUNCT
ejpam-5720	237	45	cl(b2	cl(b2	NOUN
ejpam-5720	237	46	)	)	PUNCT
ejpam-5720	237	47	)	)	PUNCT
ejpam-5720	237	48	)	)	PUNCT
ejpam-5720	237	49	)	)	PUNCT
ejpam-5720	237	50	)	)	PUNCT
ejpam-5720	238	1	⊆	⊆	X
ejpam-5720	238	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5720	238	3	-	-	PUNCT
ejpam-5720	238	4	cl(b1	cl(b1	NOUN
ejpam-5720	238	5	)	)	PUNCT
ejpam-5720	238	6	)	)	PUNCT
ejpam-5720	238	7	∪	∪	ADP
ejpam-5720	238	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	238	9	-	-	PUNCT
ejpam-5720	238	10	cl(b2	cl(b2	NOUN
ejpam-5720	238	11	)	)	PUNCT
ejpam-5720	238	12	)	)	PUNCT
ejpam-5720	238	13	for	for	ADP
ejpam-5720	238	14	every	every	DET
ejpam-5720	238	15	subsets	subset	NOUN
ejpam-5720	238	16	b1	b1	NOUN
ejpam-5720	238	17	,	,	PUNCT
ejpam-5720	238	18	b2	b2	NOUN
ejpam-5720	238	19	of	of	ADP
ejpam-5720	238	20	y	y	PROPN
ejpam-5720	238	21	having	have	VERB
ejpam-5720	238	22	the	the	DET
ejpam-5720	238	23	n	n	PROPN
ejpam-5720	238	24	(	(	PUNCT
ejpam-5720	238	25	σ1	σ1	PROPN
ejpam-5720	238	26	,	,	PUNCT
ejpam-5720	238	27	σ2)-closed	σ2)-close	VERB
ejpam-5720	238	28	σ1σ2	σ1σ2	NOUN
ejpam-5720	238	29	-	-	NOUN
ejpam-5720	238	30	closure	closure	NOUN
ejpam-5720	238	31	;	;	PUNCT
ejpam-5720	238	32	(	(	PUNCT
ejpam-5720	238	33	6	6	X
ejpam-5720	238	34	)	)	PUNCT
ejpam-5720	238	35	f+(v1	f+(v1	NOUN
ejpam-5720	238	36	)	)	PUNCT
ejpam-5720	238	37	∩	∩	NOUN
ejpam-5720	238	38	f−(v2	f−(v2	X
ejpam-5720	238	39	)	)	PUNCT
ejpam-5720	238	40	⊆	⊆	NUM
ejpam-5720	238	41	τ1τ2	τ1τ2	NOUN
ejpam-5720	238	42	-	-	NUM
ejpam-5720	238	43	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	238	44	-	-	PUNCT
ejpam-5720	238	45	int((f	int((f	VERB
ejpam-5720	238	46	+	+	NOUN
ejpam-5720	238	47	(	(	PUNCT
ejpam-5720	238	48	(	(	PUNCT
ejpam-5720	238	49	σ1	σ1	PROPN
ejpam-5720	238	50	,	,	PUNCT
ejpam-5720	238	51	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	238	52	)	)	PUNCT
ejpam-5720	238	53	)	)	PUNCT
ejpam-5720	238	54	∩	∩	ADJ
ejpam-5720	238	55	f−((σ1	f−((σ1	NOUN
ejpam-5720	238	56	,	,	PUNCT
ejpam-5720	238	57	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	238	58	)	)	PUNCT
ejpam-5720	238	59	)	)	PUNCT
ejpam-5720	238	60	)	)	PUNCT
ejpam-5720	238	61	)	)	PUNCT
ejpam-5720	239	1	for	for	ADP
ejpam-5720	239	2	every	every	DET
ejpam-5720	239	3	σ1σ2	σ1σ2	NUM
ejpam-5720	239	4	-	-	ADJ
ejpam-5720	239	5	open	open	ADJ
ejpam-5720	239	6	sets	set	NOUN
ejpam-5720	239	7	v1	v1	NOUN
ejpam-5720	239	8	,	,	PUNCT
ejpam-5720	239	9	v2	v2	PROPN
ejpam-5720	239	10	of	of	ADP
ejpam-5720	239	11	y	y	PROPN
ejpam-5720	239	12	having	have	VERB
ejpam-5720	239	13	n	n	PROPN
ejpam-5720	239	14	(	(	PUNCT
ejpam-5720	239	15	σ1	σ1	PROPN
ejpam-5720	239	16	,	,	PUNCT
ejpam-5720	239	17	σ2)-closed	σ2)-close	VERB
ejpam-5720	239	18	complements	complement	NOUN
ejpam-5720	239	19	.	.	PUNCT
ejpam-5720	240	1	proof	proof	NOUN
ejpam-5720	240	2	.	.	PUNCT
ejpam-5720	241	1	(	(	PUNCT
ejpam-5720	241	2	1	1	X
ejpam-5720	241	3	)	)	PUNCT
ejpam-5720	241	4	⇒	⇒	NOUN
ejpam-5720	241	5	(	(	PUNCT
ejpam-5720	241	6	2	2	NUM
ejpam-5720	241	7	):	):	PUNCT
ejpam-5720	241	8	the	the	DET
ejpam-5720	241	9	proof	proof	NOUN
ejpam-5720	241	10	follows	follow	VERB
ejpam-5720	241	11	immediately	immediately	ADV
ejpam-5720	241	12	from	from	ADP
ejpam-5720	241	13	theorem	theorem	ADJ
ejpam-5720	241	14	6	6	NUM
ejpam-5720	241	15	,	,	PUNCT
ejpam-5720	241	16	since	since	SCONJ
ejpam-5720	241	17	f	f	PROPN
ejpam-5720	241	18	is	be	AUX
ejpam-5720	241	19	almost	almost	ADV
ejpam-5720	241	20	nearly	nearly	ADV
ejpam-5720	241	21	quasi	quasi	NOUN
ejpam-5720	241	22	(	(	PUNCT
ejpam-5720	241	23	τ1	τ1	NOUN
ejpam-5720	241	24	,	,	PUNCT
ejpam-5720	241	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	241	26	at	at	ADP
ejpam-5720	241	27	each	each	DET
ejpam-5720	241	28	point	point	NOUN
ejpam-5720	241	29	of	of	ADP
ejpam-5720	241	30	x.	x.	NOUN
ejpam-5720	241	31	(	(	PUNCT
ejpam-5720	241	32	2	2	NUM
ejpam-5720	241	33	)	)	PUNCT
ejpam-5720	241	34	⇒	⇒	NOUN
ejpam-5720	241	35	(	(	PUNCT
ejpam-5720	241	36	3	3	NUM
ejpam-5720	241	37	):	):	PUNCT
ejpam-5720	241	38	let	let	VERB
ejpam-5720	241	39	v1	v1	NOUN
ejpam-5720	241	40	,	,	PUNCT
ejpam-5720	241	41	v2	v2	PROPN
ejpam-5720	241	42	be	be	VERB
ejpam-5720	241	43	any	any	DET
ejpam-5720	241	44	(	(	PUNCT
ejpam-5720	241	45	σ1	σ1	NOUN
ejpam-5720	241	46	,	,	PUNCT
ejpam-5720	241	47	σ2)r	σ2)r	NOUN
ejpam-5720	241	48	-	-	PUNCT
ejpam-5720	241	49	open	open	ADJ
ejpam-5720	241	50	sets	set	NOUN
ejpam-5720	241	51	of	of	ADP
ejpam-5720	241	52	y	y	PROPN
ejpam-5720	241	53	having	have	VERB
ejpam-5720	241	54	n	n	PROPN
ejpam-5720	241	55	(	(	PUNCT
ejpam-5720	241	56	σ1	σ1	PROPN
ejpam-5720	241	57	,	,	PUNCT
ejpam-5720	241	58	σ2)-closed	σ2)-close	VERB
ejpam-5720	241	59	complements	complement	NOUN
ejpam-5720	241	60	and	and	CCONJ
ejpam-5720	241	61	x	x	PUNCT
ejpam-5720	241	62	∈	∈	PROPN
ejpam-5720	241	63	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5720	241	64	)	)	PUNCT
ejpam-5720	241	65	.	.	PUNCT
ejpam-5720	242	1	then	then	ADV
ejpam-5720	242	2	,	,	PUNCT
ejpam-5720	242	3	there	there	PRON
ejpam-5720	242	4	exists	exist	VERB
ejpam-5720	242	5	a	a	DET
ejpam-5720	242	6	a	a	DET
ejpam-5720	242	7	(	(	PUNCT
ejpam-5720	242	8	τ1	τ1	NOUN
ejpam-5720	242	9	,	,	PUNCT
ejpam-5720	242	10	τ2)s	τ2)s	NOUN
ejpam-5720	242	11	-	-	PUNCT
ejpam-5720	242	12	open	open	ADJ
ejpam-5720	242	13	set	set	NOUN
ejpam-5720	242	14	u	u	NOUN
ejpam-5720	242	15	of	of	ADP
ejpam-5720	242	16	x	x	PUNCT
ejpam-5720	242	17	containing	contain	VERB
ejpam-5720	242	18	x	x	PUNCT
ejpam-5720	242	19	such	such	ADJ
ejpam-5720	242	20	that	that	SCONJ
ejpam-5720	242	21	f	f	PROPN
ejpam-5720	242	22	(	(	PUNCT
ejpam-5720	242	23	u	u	NOUN
ejpam-5720	242	24	)	)	PUNCT
ejpam-5720	242	25	⊆	⊆	NUM
ejpam-5720	242	26	(	(	PUNCT
ejpam-5720	242	27	σ1	σ1	PROPN
ejpam-5720	242	28	,	,	PUNCT
ejpam-5720	242	29	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	242	30	)	)	PUNCT
ejpam-5720	242	31	and	and	CCONJ
ejpam-5720	242	32	(	(	PUNCT
ejpam-5720	242	33	σ1	σ1	PROPN
ejpam-5720	242	34	,	,	PUNCT
ejpam-5720	242	35	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	242	36	)	)	PUNCT
ejpam-5720	242	37	∩	∩	PROPN
ejpam-5720	242	38	f	f	X
ejpam-5720	242	39	(	(	PUNCT
ejpam-5720	242	40	z	z	NOUN
ejpam-5720	242	41	)	)	PUNCT
ejpam-5720	242	42	̸=	̸=	NOUN
ejpam-5720	242	43	∅	∅	NOUN
ejpam-5720	242	44	for	for	ADP
ejpam-5720	242	45	every	every	DET
ejpam-5720	242	46	z	z	NOUN
ejpam-5720	242	47	∈	∈	PROPN
ejpam-5720	242	48	u	u	NOUN
ejpam-5720	242	49	.	.	PUNCT
ejpam-5720	243	1	thus	thus	ADV
ejpam-5720	243	2	,	,	PUNCT
ejpam-5720	243	3	x	x	PUNCT
ejpam-5720	243	4	∈	∈	PROPN
ejpam-5720	243	5	u	u	NOUN
ejpam-5720	243	6	⊆	⊆	NUM
ejpam-5720	243	7	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5720	243	8	)	)	PUNCT
ejpam-5720	243	9	and	and	CCONJ
ejpam-5720	243	10	hence	hence	ADV
ejpam-5720	243	11	x	x	X
ejpam-5720	243	12	∈	∈	PROPN
ejpam-5720	243	13	(	(	PUNCT
ejpam-5720	243	14	τ1	τ1	NOUN
ejpam-5720	243	15	,	,	PUNCT
ejpam-5720	243	16	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	244	1	+	+	ADJ
ejpam-5720	244	2	(	(	PUNCT
ejpam-5720	244	3	v1)∩f−(v2	v1)∩f−(v2	PROPN
ejpam-5720	244	4	)	)	PUNCT
ejpam-5720	244	5	)	)	PUNCT
ejpam-5720	244	6	.	.	PUNCT
ejpam-5720	245	1	therefore	therefore	ADV
ejpam-5720	245	2	,	,	PUNCT
ejpam-5720	245	3	f+(v1	f+(v1	ADJ
ejpam-5720	245	4	)	)	PUNCT
ejpam-5720	245	5	∩	∩	NOUN
ejpam-5720	245	6	f−(v2	f−(v2	X
ejpam-5720	245	7	)	)	PUNCT
ejpam-5720	245	8	⊆	⊆	NUM
ejpam-5720	245	9	(	(	PUNCT
ejpam-5720	245	10	τ1	τ1	NOUN
ejpam-5720	245	11	,	,	PUNCT
ejpam-5720	245	12	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	245	13	+	+	ADJ
ejpam-5720	245	14	(	(	PUNCT
ejpam-5720	245	15	v1	v1	NOUN
ejpam-5720	245	16	)	)	PUNCT
ejpam-5720	245	17	∩	∩	NOUN
ejpam-5720	245	18	f−(v2	f−(v2	NUM
ejpam-5720	245	19	)	)	PUNCT
ejpam-5720	245	20	)	)	PUNCT
ejpam-5720	245	21	.	.	PUNCT
ejpam-5720	246	1	this	this	PRON
ejpam-5720	246	2	shows	show	VERB
ejpam-5720	246	3	that	that	SCONJ
ejpam-5720	246	4	f+(v1	f+(v1	VERB
ejpam-5720	246	5	)	)	PUNCT
ejpam-5720	246	6	∩	∩	NOUN
ejpam-5720	246	7	f−(v2	f−(v2	X
ejpam-5720	246	8	)	)	PUNCT
ejpam-5720	246	9	is	be	AUX
ejpam-5720	246	10	(	(	PUNCT
ejpam-5720	246	11	τ1	τ1	NOUN
ejpam-5720	246	12	,	,	PUNCT
ejpam-5720	246	13	τ2)s	τ2)s	NOUN
ejpam-5720	246	14	-	-	PUNCT
ejpam-5720	246	15	open	open	ADJ
ejpam-5720	246	16	in	in	ADP
ejpam-5720	246	17	x.	x.	NOUN
ejpam-5720	246	18	(	(	PUNCT
ejpam-5720	246	19	3	3	NUM
ejpam-5720	246	20	)	)	PUNCT
ejpam-5720	246	21	⇒	⇒	NOUN
ejpam-5720	246	22	(	(	PUNCT
ejpam-5720	246	23	4	4	NUM
ejpam-5720	246	24	):	):	PUNCT
ejpam-5720	246	25	let	let	VERB
ejpam-5720	246	26	v1	v1	NOUN
ejpam-5720	246	27	,	,	PUNCT
ejpam-5720	246	28	v2	v2	PROPN
ejpam-5720	246	29	be	be	AUX
ejpam-5720	246	30	any	any	DET
ejpam-5720	246	31	σ1σ2	σ1σ2	NOUN
ejpam-5720	246	32	-	-	PUNCT
ejpam-5720	246	33	open	open	ADJ
ejpam-5720	246	34	sets	set	NOUN
ejpam-5720	246	35	of	of	ADP
ejpam-5720	246	36	y	y	PROPN
ejpam-5720	246	37	having	have	VERB
ejpam-5720	246	38	n	n	PROPN
ejpam-5720	246	39	(	(	PUNCT
ejpam-5720	246	40	σ1	σ1	PROPN
ejpam-5720	246	41	,	,	PUNCT
ejpam-5720	246	42	σ2)-closed	σ2)-close	VERB
ejpam-5720	246	43	complements	complement	NOUN
ejpam-5720	246	44	such	such	ADJ
ejpam-5720	246	45	that	that	SCONJ
ejpam-5720	246	46	x	x	SYM
ejpam-5720	246	47	∈	∈	NOUN
ejpam-5720	246	48	f+(v1	f+(v1	NOUN
ejpam-5720	246	49	)	)	PUNCT
ejpam-5720	246	50	∩	∩	NOUN
ejpam-5720	246	51	f−(v2	f−(v2	NUM
ejpam-5720	246	52	)	)	PUNCT
ejpam-5720	246	53	.	.	PUNCT
ejpam-5720	247	1	then	then	ADV
ejpam-5720	247	2	,	,	PUNCT
ejpam-5720	247	3	we	we	PRON
ejpam-5720	247	4	have	have	VERB
ejpam-5720	247	5	f	f	PROPN
ejpam-5720	247	6	(	(	PUNCT
ejpam-5720	247	7	x	x	NOUN
ejpam-5720	247	8	)	)	PUNCT
ejpam-5720	247	9	⊆	⊆	NUM
ejpam-5720	247	10	v1	v1	NOUN
ejpam-5720	247	11	⊆	⊆	NUM
ejpam-5720	247	12	(	(	PUNCT
ejpam-5720	247	13	σ1	σ1	PROPN
ejpam-5720	247	14	,	,	PUNCT
ejpam-5720	247	15	σ2)-scl(v1	σ2)-scl(v1	X
ejpam-5720	247	16	)	)	PUNCT
ejpam-5720	247	17	and	and	CCONJ
ejpam-5720	247	18	∅	∅	NOUN
ejpam-5720	247	19	=	=	NOUN
ejpam-5720	247	20	̸	̸	ADV
ejpam-5720	247	21	v2	v2	PROPN
ejpam-5720	247	22	∩	∩	ADJ
ejpam-5720	247	23	f	f	X
ejpam-5720	247	24	(	(	PUNCT
ejpam-5720	247	25	x	x	X
ejpam-5720	247	26	)	)	PUNCT
ejpam-5720	247	27	⊆	⊆	NUM
ejpam-5720	247	28	(	(	PUNCT
ejpam-5720	247	29	σ1	σ1	PROPN
ejpam-5720	247	30	,	,	PUNCT
ejpam-5720	247	31	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	247	32	)	)	PUNCT
ejpam-5720	247	33	∩	∩	PROPN
ejpam-5720	247	34	f	f	PROPN
ejpam-5720	247	35	(	(	PUNCT
ejpam-5720	247	36	x	x	NOUN
ejpam-5720	247	37	)	)	PUNCT
ejpam-5720	247	38	.	.	PUNCT
ejpam-5720	248	1	thus	thus	ADV
ejpam-5720	248	2	,	,	PUNCT
ejpam-5720	248	3	x	x	SYM
ejpam-5720	248	4	∈	∈	NOUN
ejpam-5720	248	5	f+((σ1	f+((σ1	NOUN
ejpam-5720	248	6	,	,	PUNCT
ejpam-5720	248	7	σ2)-scl(v1	σ2)-scl(v1	NOUN
ejpam-5720	248	8	)	)	PUNCT
ejpam-5720	248	9	)	)	PUNCT
ejpam-5720	249	1	and	and	CCONJ
ejpam-5720	249	2	x	x	PUNCT
ejpam-5720	249	3	∈	∈	NOUN
ejpam-5720	249	4	f−((σ1	f−((σ1	NOUN
ejpam-5720	249	5	,	,	PUNCT
ejpam-5720	249	6	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	249	7	)	)	PUNCT
ejpam-5720	249	8	)	)	PUNCT
ejpam-5720	249	9	.	.	PUNCT
ejpam-5720	250	1	by	by	ADP
ejpam-5720	250	2	(	(	PUNCT
ejpam-5720	250	3	3	3	NUM
ejpam-5720	250	4	)	)	PUNCT
ejpam-5720	250	5	,	,	PUNCT
ejpam-5720	250	6	we	we	PRON
ejpam-5720	250	7	have	have	VERB
ejpam-5720	250	8	f+((σ1	f+((σ1	NOUN
ejpam-5720	250	9	,	,	PUNCT
ejpam-5720	250	10	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	250	11	)	)	PUNCT
ejpam-5720	250	12	)	)	PUNCT
ejpam-5720	250	13	∩	∩	ADJ
ejpam-5720	250	14	f−((σ1	f−((σ1	NOUN
ejpam-5720	250	15	,	,	PUNCT
ejpam-5720	250	16	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	250	17	)	)	PUNCT
ejpam-5720	250	18	)	)	PUNCT
ejpam-5720	250	19	is	be	AUX
ejpam-5720	250	20	(	(	PUNCT
ejpam-5720	250	21	τ1	τ1	NOUN
ejpam-5720	250	22	,	,	PUNCT
ejpam-5720	250	23	τ2)s	τ2)s	NOUN
ejpam-5720	250	24	-	-	PUNCT
ejpam-5720	250	25	open	open	ADJ
ejpam-5720	250	26	in	in	ADP
ejpam-5720	250	27	x	x	PUNCT
ejpam-5720	250	28	and	and	CCONJ
ejpam-5720	250	29	x	x	SYM
ejpam-5720	250	30	∈	∈	PROPN
ejpam-5720	250	31	(	(	PUNCT
ejpam-5720	250	32	τ1	τ1	NOUN
ejpam-5720	250	33	,	,	PUNCT
ejpam-5720	250	34	τ2)s	τ2)s	NOUN
ejpam-5720	250	35	-	-	PUNCT
ejpam-5720	250	36	int(f	int(f	VERB
ejpam-5720	250	37	+	+	ADJ
ejpam-5720	250	38	(	(	PUNCT
ejpam-5720	250	39	(	(	PUNCT
ejpam-5720	250	40	σ1	σ1	PROPN
ejpam-5720	250	41	,	,	PUNCT
ejpam-5720	250	42	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	250	43	)	)	PUNCT
ejpam-5720	250	44	)	)	PUNCT
ejpam-5720	250	45	∩	∩	ADJ
ejpam-5720	250	46	f−((σ1	f−((σ1	NOUN
ejpam-5720	250	47	,	,	PUNCT
ejpam-5720	250	48	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	250	49	)	)	PUNCT
ejpam-5720	250	50	)	)	PUNCT
ejpam-5720	250	51	)	)	PUNCT
ejpam-5720	250	52	.	.	PUNCT
ejpam-5720	251	1	therefore	therefore	ADV
ejpam-5720	251	2	,	,	PUNCT
ejpam-5720	251	3	f+(v1	f+(v1	ADJ
ejpam-5720	251	4	)	)	PUNCT
ejpam-5720	251	5	∩	∩	NOUN
ejpam-5720	251	6	f−(v2	f−(v2	X
ejpam-5720	251	7	)	)	PUNCT
ejpam-5720	251	8	⊆	⊆	NUM
ejpam-5720	251	9	(	(	PUNCT
ejpam-5720	251	10	τ1	τ1	NOUN
ejpam-5720	251	11	,	,	PUNCT
ejpam-5720	251	12	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	251	13	+	+	ADJ
ejpam-5720	251	14	(	(	PUNCT
ejpam-5720	251	15	(	(	PUNCT
ejpam-5720	251	16	σ1	σ1	PROPN
ejpam-5720	251	17	,	,	PUNCT
ejpam-5720	251	18	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	251	19	)	)	PUNCT
ejpam-5720	251	20	)	)	PUNCT
ejpam-5720	251	21	∩	∩	ADJ
ejpam-5720	251	22	f−((σ1	f−((σ1	NOUN
ejpam-5720	251	23	,	,	PUNCT
ejpam-5720	251	24	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	251	25	)	)	PUNCT
ejpam-5720	251	26	)	)	PUNCT
ejpam-5720	251	27	)	)	PUNCT
ejpam-5720	251	28	.	.	PUNCT
ejpam-5720	252	1	(	(	PUNCT
ejpam-5720	252	2	4	4	X
ejpam-5720	252	3	)	)	PUNCT
ejpam-5720	252	4	⇒	⇒	NOUN
ejpam-5720	252	5	(	(	PUNCT
ejpam-5720	252	6	5	5	NUM
ejpam-5720	252	7	):	):	PUNCT
ejpam-5720	252	8	let	let	VERB
ejpam-5720	252	9	b1	b1	NOUN
ejpam-5720	252	10	,	,	PUNCT
ejpam-5720	252	11	b2	b2	NOUN
ejpam-5720	252	12	be	be	VERB
ejpam-5720	252	13	any	any	DET
ejpam-5720	252	14	subsets	subset	NOUN
ejpam-5720	252	15	of	of	ADP
ejpam-5720	252	16	y	y	PROPN
ejpam-5720	252	17	having	have	VERB
ejpam-5720	252	18	the	the	DET
ejpam-5720	252	19	n	n	PROPN
ejpam-5720	252	20	(	(	PUNCT
ejpam-5720	252	21	σ1	σ1	PROPN
ejpam-5720	252	22	,	,	PUNCT
ejpam-5720	252	23	σ2)-closed	σ2)-close	VERB
ejpam-5720	252	24	σ1σ2	σ1σ2	NOUN
ejpam-5720	252	25	-	-	NOUN
ejpam-5720	252	26	closure	closure	NOUN
ejpam-5720	252	27	.	.	PUNCT
ejpam-5720	253	1	then	then	ADV
ejpam-5720	253	2	,	,	PUNCT
ejpam-5720	253	3	y	y	PROPN
ejpam-5720	253	4	−	−	NUM
ejpam-5720	253	5	σ1σ2	σ1σ2	NOUN
ejpam-5720	253	6	-	-	PUNCT
ejpam-5720	253	7	cl(b1	cl(b1	NOUN
ejpam-5720	253	8	)	)	PUNCT
ejpam-5720	253	9	and	and	CCONJ
ejpam-5720	253	10	y	y	PROPN
ejpam-5720	253	11	−	−	PROPN
ejpam-5720	253	12	σ1σ2	σ1σ2	NOUN
ejpam-5720	253	13	-	-	PUNCT
ejpam-5720	253	14	cl(b2	cl(b2	NOUN
ejpam-5720	253	15	)	)	PUNCT
ejpam-5720	253	16	are	be	AUX
ejpam-5720	253	17	σ1σ2	σ1σ2	NOUN
ejpam-5720	253	18	-	-	ADJ
ejpam-5720	253	19	open	open	ADJ
ejpam-5720	253	20	sets	set	NOUN
ejpam-5720	253	21	of	of	ADP
ejpam-5720	253	22	y	y	PROPN
ejpam-5720	253	23	having	have	VERB
ejpam-5720	253	24	n	n	PROPN
ejpam-5720	253	25	(	(	PUNCT
ejpam-5720	253	26	σ1	σ1	PROPN
ejpam-5720	253	27	,	,	PUNCT
ejpam-5720	253	28	σ2)closed	σ2)close	VERB
ejpam-5720	253	29	complements	complement	NOUN
ejpam-5720	253	30	.	.	PUNCT
ejpam-5720	254	1	thus	thus	ADV
ejpam-5720	254	2	by	by	ADP
ejpam-5720	254	3	(	(	PUNCT
ejpam-5720	254	4	4	4	NUM
ejpam-5720	254	5	)	)	PUNCT
ejpam-5720	254	6	,	,	PUNCT
ejpam-5720	254	7	we	we	PRON
ejpam-5720	254	8	have	have	VERB
ejpam-5720	254	9	x	x	X
ejpam-5720	254	10	−	−	X
ejpam-5720	254	11	(	(	PUNCT
ejpam-5720	254	12	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5720	254	13	-	-	PUNCT
ejpam-5720	254	14	cl(b1	cl(b1	NOUN
ejpam-5720	254	15	)	)	PUNCT
ejpam-5720	254	16	)	)	PUNCT
ejpam-5720	254	17	∪	∪	ADP
ejpam-5720	254	18	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	254	19	-	-	PUNCT
ejpam-5720	254	20	cl(b2	cl(b2	NOUN
ejpam-5720	254	21	)	)	PUNCT
ejpam-5720	254	22	)	)	PUNCT
ejpam-5720	254	23	)	)	PUNCT
ejpam-5720	255	1	=	=	PUNCT
ejpam-5720	255	2	(	(	PUNCT
ejpam-5720	255	3	x	x	X
ejpam-5720	255	4	−	−	NOUN
ejpam-5720	255	5	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5720	255	6	-	-	PUNCT
ejpam-5720	255	7	cl(b1	cl(b1	NOUN
ejpam-5720	255	8	)	)	PUNCT
ejpam-5720	255	9	)	)	PUNCT
ejpam-5720	255	10	)	)	PUNCT
ejpam-5720	256	1	∩	∩	NOUN
ejpam-5720	256	2	(	(	PUNCT
ejpam-5720	256	3	x	x	SYM
ejpam-5720	256	4	−	−	PRON
ejpam-5720	256	5	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	256	6	-	-	PUNCT
ejpam-5720	256	7	cl(b2	cl(b2	NOUN
ejpam-5720	256	8	)	)	PUNCT
ejpam-5720	256	9	)	)	PUNCT
ejpam-5720	256	10	)	)	PUNCT
ejpam-5720	257	1	=	=	PUNCT
ejpam-5720	258	1	f+(y	f+(y	NOUN
ejpam-5720	258	2	−	−	NUM
ejpam-5720	258	3	σ1σ2	σ1σ2	NUM
ejpam-5720	258	4	-	-	PUNCT
ejpam-5720	258	5	cl(b1	cl(b1	NOUN
ejpam-5720	258	6	)	)	PUNCT
ejpam-5720	258	7	)	)	PUNCT
ejpam-5720	259	1	∩	∩	NOUN
ejpam-5720	259	2	f−(y	f−(y	NOUN
ejpam-5720	259	3	−	−	NUM
ejpam-5720	259	4	σ1σ2	σ1σ2	NOUN
ejpam-5720	259	5	-	-	PUNCT
ejpam-5720	259	6	cl(b2	cl(b2	NOUN
ejpam-5720	259	7	)	)	PUNCT
ejpam-5720	259	8	)	)	PUNCT
ejpam-5720	260	1	⊆	⊆	NUM
ejpam-5720	260	2	(	(	PUNCT
ejpam-5720	260	3	τ1	τ1	NOUN
ejpam-5720	260	4	,	,	PUNCT
ejpam-5720	260	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	260	6	+	+	ADJ
ejpam-5720	260	7	(	(	PUNCT
ejpam-5720	260	8	(	(	PUNCT
ejpam-5720	260	9	σ1	σ1	PROPN
ejpam-5720	260	10	,	,	PUNCT
ejpam-5720	260	11	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-5720	260	12	−	−	NOUN
ejpam-5720	260	13	σ1σ2	σ1σ2	NOUN
ejpam-5720	260	14	-	-	PUNCT
ejpam-5720	260	15	cl(b1	cl(b1	NOUN
ejpam-5720	260	16	)	)	PUNCT
ejpam-5720	260	17	)	)	PUNCT
ejpam-5720	260	18	)	)	PUNCT
ejpam-5720	260	19	∩	∩	ADJ
ejpam-5720	260	20	f−((σ1	f−((σ1	NOUN
ejpam-5720	260	21	,	,	PUNCT
ejpam-5720	260	22	σ2)-scl(y	σ2)-scl(y	ADJ
ejpam-5720	260	23	−	−	CCONJ
ejpam-5720	260	24	σ1σ2	σ1σ2	NOUN
ejpam-5720	260	25	-	-	PUNCT
ejpam-5720	260	26	cl(b2	cl(b2	NOUN
ejpam-5720	260	27	)	)	PUNCT
ejpam-5720	260	28	)	)	PUNCT
ejpam-5720	260	29	)	)	PUNCT
ejpam-5720	260	30	)	)	PUNCT
ejpam-5720	261	1	=	=	PUNCT
ejpam-5720	261	2	x	x	X
ejpam-5720	261	3	−	−	PROPN
ejpam-5720	261	4	(	(	PUNCT
ejpam-5720	261	5	τ1	τ1	PROPN
ejpam-5720	261	6	,	,	PUNCT
ejpam-5720	261	7	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5720	261	8	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5720	261	9	-	-	PUNCT
ejpam-5720	261	10	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	261	11	-	-	PUNCT
ejpam-5720	261	12	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	261	13	-	-	PUNCT
ejpam-5720	261	14	cl(b1	cl(b1	NOUN
ejpam-5720	261	15	)	)	PUNCT
ejpam-5720	261	16	)	)	PUNCT
ejpam-5720	261	17	)	)	PUNCT
ejpam-5720	261	18	)	)	PUNCT
ejpam-5720	261	19	∪	∪	ADP
ejpam-5720	261	20	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5720	261	21	-	-	PUNCT
ejpam-5720	261	22	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	261	23	-	-	PUNCT
ejpam-5720	261	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	261	25	-	-	PUNCT
ejpam-5720	261	26	cl(b2	cl(b2	NOUN
ejpam-5720	261	27	)	)	PUNCT
ejpam-5720	261	28	)	)	PUNCT
ejpam-5720	261	29	)	)	PUNCT
ejpam-5720	261	30	)	)	PUNCT
ejpam-5720	261	31	)	)	PUNCT
ejpam-5720	262	1	j.	j.	PROPN
ejpam-5720	262	2	khampakdee	khampakdee	PROPN
ejpam-5720	262	3	,	,	PUNCT
ejpam-5720	262	4	a.	a.	PROPN
ejpam-5720	262	5	sama	sama	PROPN
ejpam-5720	262	6	-	-	PUNCT
ejpam-5720	262	7	ae	ae	PROPN
ejpam-5720	262	8	,	,	PUNCT
ejpam-5720	262	9	c.	c.	PROPN
ejpam-5720	262	10	boonpok	boonpok	PROPN
ejpam-5720	262	11	/	/	SYM
ejpam-5720	262	12	eur	eur	PROPN
ejpam-5720	262	13	.	.	PUNCT
ejpam-5720	263	1	j.	j.	PROPN
ejpam-5720	263	2	pure	pure	PROPN
ejpam-5720	263	3	appl	appl	PROPN
ejpam-5720	263	4	.	.	PROPN
ejpam-5720	263	5	math	math	PROPN
ejpam-5720	263	6	,	,	PUNCT
ejpam-5720	263	7	18	18	NUM
ejpam-5720	263	8	(	(	PUNCT
ejpam-5720	263	9	1	1	NUM
ejpam-5720	263	10	)	)	PUNCT
ejpam-5720	263	11	(	(	PUNCT
ejpam-5720	263	12	2025	2025	NUM
ejpam-5720	263	13	)	)	PUNCT
ejpam-5720	263	14	,	,	PUNCT
ejpam-5720	263	15	5720	5720	NUM
ejpam-5720	263	16	11	11	NUM
ejpam-5720	263	17	of	of	ADP
ejpam-5720	263	18	15	15	NUM
ejpam-5720	263	19	and	and	CCONJ
ejpam-5720	263	20	hence	hence	ADV
ejpam-5720	263	21	(	(	PUNCT
ejpam-5720	263	22	τ1	τ1	NOUN
ejpam-5720	263	23	,	,	PUNCT
ejpam-5720	263	24	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5720	263	25	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5720	263	26	-	-	PUNCT
ejpam-5720	263	27	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	263	28	-	-	PUNCT
ejpam-5720	263	29	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	263	30	-	-	PUNCT
ejpam-5720	263	31	cl(b1	cl(b1	NOUN
ejpam-5720	263	32	)	)	PUNCT
ejpam-5720	263	33	)	)	PUNCT
ejpam-5720	263	34	)	)	PUNCT
ejpam-5720	263	35	)	)	PUNCT
ejpam-5720	264	1	∪	∪	ADP
ejpam-5720	264	2	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5720	264	3	-	-	PUNCT
ejpam-5720	264	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	264	5	-	-	PUNCT
ejpam-5720	264	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	264	7	-	-	PUNCT
ejpam-5720	264	8	cl(b2	cl(b2	NOUN
ejpam-5720	264	9	)	)	PUNCT
ejpam-5720	264	10	)	)	PUNCT
ejpam-5720	264	11	)	)	PUNCT
ejpam-5720	264	12	)	)	PUNCT
ejpam-5720	264	13	)	)	PUNCT
ejpam-5720	265	1	⊆	⊆	X
ejpam-5720	265	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5720	265	3	-	-	PUNCT
ejpam-5720	265	4	cl(b1	cl(b1	NOUN
ejpam-5720	265	5	)	)	PUNCT
ejpam-5720	265	6	)	)	PUNCT
ejpam-5720	265	7	∪	∪	ADP
ejpam-5720	265	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5720	265	9	-	-	PUNCT
ejpam-5720	265	10	cl(b2	cl(b2	NOUN
ejpam-5720	265	11	)	)	PUNCT
ejpam-5720	265	12	)	)	PUNCT
ejpam-5720	265	13	.	.	PUNCT
ejpam-5720	266	1	(	(	PUNCT
ejpam-5720	266	2	5	5	X
ejpam-5720	266	3	)	)	PUNCT
ejpam-5720	266	4	⇒	⇒	NOUN
ejpam-5720	266	5	(	(	PUNCT
ejpam-5720	266	6	6	6	NUM
ejpam-5720	266	7	):	):	PUNCT
ejpam-5720	266	8	let	let	VERB
ejpam-5720	266	9	v1	v1	NOUN
ejpam-5720	266	10	,	,	PUNCT
ejpam-5720	266	11	v2	v2	PROPN
ejpam-5720	266	12	be	be	AUX
ejpam-5720	266	13	any	any	DET
ejpam-5720	266	14	σ1σ2	σ1σ2	NOUN
ejpam-5720	266	15	-	-	PUNCT
ejpam-5720	266	16	open	open	ADJ
ejpam-5720	266	17	sets	set	NOUN
ejpam-5720	266	18	of	of	ADP
ejpam-5720	266	19	y	y	PROPN
ejpam-5720	266	20	having	have	VERB
ejpam-5720	266	21	n	n	PROPN
ejpam-5720	266	22	(	(	PUNCT
ejpam-5720	266	23	σ1	σ1	PROPN
ejpam-5720	266	24	,	,	PUNCT
ejpam-5720	266	25	σ2)-closed	σ2)-close	VERB
ejpam-5720	266	26	complements	complement	NOUN
ejpam-5720	266	27	.	.	PUNCT
ejpam-5720	267	1	then	then	ADV
ejpam-5720	267	2	,	,	PUNCT
ejpam-5720	267	3	y	y	PROPN
ejpam-5720	267	4	−	−	PROPN
ejpam-5720	267	5	v1	v1	PROPN
ejpam-5720	267	6	and	and	CCONJ
ejpam-5720	267	7	y	y	PROPN
ejpam-5720	267	8	−	−	PROPN
ejpam-5720	267	9	v2	v2	PROPN
ejpam-5720	267	10	are	be	AUX
ejpam-5720	267	11	n	n	PROPN
ejpam-5720	267	12	(	(	PUNCT
ejpam-5720	267	13	σ1	σ1	PROPN
ejpam-5720	267	14	,	,	PUNCT
ejpam-5720	267	15	σ2)-closed	σ2)-close	VERB
ejpam-5720	267	16	and	and	CCONJ
ejpam-5720	267	17	σ1σ2	σ1σ2	NOUN
ejpam-5720	267	18	-	-	PUNCT
ejpam-5720	267	19	closed	closed	ADJ
ejpam-5720	267	20	sets	set	NOUN
ejpam-5720	267	21	of	of	ADP
ejpam-5720	267	22	y	y	PROPN
ejpam-5720	267	23	.	.	PUNCT
ejpam-5720	268	1	by	by	ADP
ejpam-5720	268	2	(	(	PUNCT
ejpam-5720	268	3	5	5	NUM
ejpam-5720	268	4	)	)	PUNCT
ejpam-5720	268	5	and	and	CCONJ
ejpam-5720	268	6	lemma	lemma	PROPN
ejpam-5720	268	7	2	2	NUM
ejpam-5720	268	8	,	,	PUNCT
ejpam-5720	268	9	τ1τ2	τ1τ2	NOUN
ejpam-5720	268	10	-	-	NOUN
ejpam-5720	268	11	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	268	12	-	-	PUNCT
ejpam-5720	268	13	cl(f	cl(f	NOUN
ejpam-5720	268	14	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5720	268	15	-	-	PUNCT
ejpam-5720	268	16	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	268	17	-	-	PUNCT
ejpam-5720	268	18	int(y	int(y	PROPN
ejpam-5720	268	19	−	−	PROPN
ejpam-5720	268	20	v1	v1	NOUN
ejpam-5720	268	21	)	)	PUNCT
ejpam-5720	268	22	)	)	PUNCT
ejpam-5720	268	23	)	)	PUNCT
ejpam-5720	268	24	∪	∪	ADP
ejpam-5720	268	25	f+(y	f+(y	NUM
ejpam-5720	268	26	−	−	PROPN
ejpam-5720	268	27	σ1σ2	σ1σ2	SYM
ejpam-5720	268	28	-	-	PUNCT
ejpam-5720	268	29	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	268	30	-	-	PUNCT
ejpam-5720	268	31	int(v2	int(v2	NOUN
ejpam-5720	268	32	)	)	PUNCT
ejpam-5720	268	33	)	)	PUNCT
ejpam-5720	268	34	)	)	PUNCT
ejpam-5720	268	35	)	)	PUNCT
ejpam-5720	268	36	)	)	PUNCT
ejpam-5720	269	1	⊆	⊆	NUM
ejpam-5720	269	2	f−(y	f−(y	NOUN
ejpam-5720	269	3	−	−	NOUN
ejpam-5720	269	4	v1	v1	NOUN
ejpam-5720	269	5	)	)	PUNCT
ejpam-5720	269	6	∪	∪	NOUN
ejpam-5720	269	7	f+(y	f+(y	ADP
ejpam-5720	269	8	−	−	PROPN
ejpam-5720	269	9	v2	v2	PROPN
ejpam-5720	269	10	)	)	PUNCT
ejpam-5720	269	11	=	=	SYM
ejpam-5720	269	12	(	(	PUNCT
ejpam-5720	269	13	x	x	SYM
ejpam-5720	269	14	−	−	NOUN
ejpam-5720	269	15	f+(v1	f+(v1	NOUN
ejpam-5720	269	16	)	)	PUNCT
ejpam-5720	269	17	)	)	PUNCT
ejpam-5720	269	18	∪	∪	ADP
ejpam-5720	269	19	(	(	PUNCT
ejpam-5720	269	20	x	x	NOUN
ejpam-5720	269	21	−	−	NOUN
ejpam-5720	269	22	f−(v2	f−(v2	NUM
ejpam-5720	269	23	)	)	PUNCT
ejpam-5720	269	24	)	)	PUNCT
ejpam-5720	270	1	=	=	PUNCT
ejpam-5720	270	2	x	x	X
ejpam-5720	270	3	−	−	PROPN
ejpam-5720	270	4	(	(	PUNCT
ejpam-5720	270	5	f+(v1	f+(v1	NOUN
ejpam-5720	270	6	)	)	PUNCT
ejpam-5720	270	7	∩	∩	NOUN
ejpam-5720	270	8	f−(v2	f−(v2	NUM
ejpam-5720	270	9	)	)	PUNCT
ejpam-5720	270	10	)	)	PUNCT
ejpam-5720	270	11	.	.	PUNCT
ejpam-5720	271	1	moreover	moreover	ADV
ejpam-5720	271	2	,	,	PUNCT
ejpam-5720	271	3	we	we	PRON
ejpam-5720	271	4	have	have	VERB
ejpam-5720	271	5	τ1τ2	τ1τ2	NOUN
ejpam-5720	271	6	-	-	NOUN
ejpam-5720	271	7	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	271	8	-	-	PUNCT
ejpam-5720	271	9	cl(f	cl(f	NOUN
ejpam-5720	271	10	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5720	271	11	-	-	PUNCT
ejpam-5720	271	12	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	271	13	-	-	PUNCT
ejpam-5720	271	14	int(y	int(y	PROPN
ejpam-5720	271	15	−	−	PROPN
ejpam-5720	271	16	v1	v1	NOUN
ejpam-5720	271	17	)	)	PUNCT
ejpam-5720	271	18	)	)	PUNCT
ejpam-5720	271	19	)	)	PUNCT
ejpam-5720	272	1	∪	∪	ADP
ejpam-5720	272	2	f+(y	f+(y	NUM
ejpam-5720	272	3	−	−	PROPN
ejpam-5720	272	4	σ1σ2	σ1σ2	SYM
ejpam-5720	272	5	-	-	PUNCT
ejpam-5720	272	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5720	272	7	-	-	PUNCT
ejpam-5720	272	8	int(v2	int(v2	NOUN
ejpam-5720	272	9	)	)	PUNCT
ejpam-5720	272	10	)	)	PUNCT
ejpam-5720	272	11	)	)	PUNCT
ejpam-5720	272	12	)	)	PUNCT
ejpam-5720	272	13	)	)	PUNCT
ejpam-5720	273	1	=	=	PUNCT
ejpam-5720	274	1	τ1τ2	τ1τ2	NOUN
ejpam-5720	274	2	-	-	NOUN
ejpam-5720	274	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	274	4	-	-	PUNCT
ejpam-5720	274	5	cl(f	cl(f	NOUN
ejpam-5720	274	6	−(y	−(y	NOUN
ejpam-5720	274	7	−	−	NOUN
ejpam-5720	274	8	σ1σ2	σ1σ2	SYM
ejpam-5720	274	9	-	-	PUNCT
ejpam-5720	274	10	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	274	11	-	-	PUNCT
ejpam-5720	274	12	cl(v1	cl(v1	NOUN
ejpam-5720	274	13	)	)	PUNCT
ejpam-5720	274	14	)	)	PUNCT
ejpam-5720	274	15	)	)	PUNCT
ejpam-5720	274	16	∪	∪	ADP
ejpam-5720	274	17	f+(y	f+(y	NUM
ejpam-5720	274	18	−	−	PROPN
ejpam-5720	274	19	σ1σ2	σ1σ2	SYM
ejpam-5720	274	20	-	-	PUNCT
ejpam-5720	274	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	274	22	-	-	PUNCT
ejpam-5720	274	23	cl(v2	cl(v2	NOUN
ejpam-5720	274	24	)	)	PUNCT
ejpam-5720	274	25	)	)	PUNCT
ejpam-5720	274	26	)	)	PUNCT
ejpam-5720	274	27	)	)	PUNCT
ejpam-5720	274	28	)	)	PUNCT
ejpam-5720	275	1	=	=	PUNCT
ejpam-5720	275	2	τ1τ2	τ1τ2	NOUN
ejpam-5720	275	3	-	-	NOUN
ejpam-5720	275	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	275	5	-	-	PUNCT
ejpam-5720	275	6	cl((x	cl((x	NOUN
ejpam-5720	275	7	−	−	NOUN
ejpam-5720	275	8	f+((σ1	f+((σ1	NOUN
ejpam-5720	275	9	,	,	PUNCT
ejpam-5720	275	10	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	275	11	)	)	PUNCT
ejpam-5720	275	12	)	)	PUNCT
ejpam-5720	275	13	)	)	PUNCT
ejpam-5720	276	1	∪	∪	ADV
ejpam-5720	276	2	(	(	PUNCT
ejpam-5720	276	3	x	x	NOUN
ejpam-5720	276	4	−	−	NOUN
ejpam-5720	276	5	f−((σ1	f−((σ1	NOUN
ejpam-5720	276	6	,	,	PUNCT
ejpam-5720	276	7	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	276	8	)	)	PUNCT
ejpam-5720	276	9	)	)	PUNCT
ejpam-5720	276	10	)	)	PUNCT
ejpam-5720	276	11	)	)	PUNCT
ejpam-5720	276	12	)	)	PUNCT
ejpam-5720	277	1	=	=	PUNCT
ejpam-5720	278	1	τ1τ2	τ1τ2	NOUN
ejpam-5720	278	2	-	-	NOUN
ejpam-5720	278	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5720	278	4	-	-	PUNCT
ejpam-5720	278	5	cl(x	cl(x	NUM
ejpam-5720	278	6	−	−	PROPN
ejpam-5720	278	7	(	(	PUNCT
ejpam-5720	278	8	f+((σ1	f+((σ1	ADV
ejpam-5720	278	9	,	,	PUNCT
ejpam-5720	278	10	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	278	11	)	)	PUNCT
ejpam-5720	278	12	)	)	PUNCT
ejpam-5720	278	13	∩	∩	ADJ
ejpam-5720	278	14	f−((σ1	f−((σ1	NOUN
ejpam-5720	278	15	,	,	PUNCT
ejpam-5720	278	16	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	278	17	)	)	PUNCT
ejpam-5720	278	18	)	)	PUNCT
ejpam-5720	278	19	)	)	PUNCT
ejpam-5720	278	20	)	)	PUNCT
ejpam-5720	278	21	)	)	PUNCT
ejpam-5720	279	1	=	=	PUNCT
ejpam-5720	279	2	x	x	X
ejpam-5720	280	1	−	−	ADP
ejpam-5720	280	2	τ1τ2	τ1τ2	NOUN
ejpam-5720	280	3	-	-	NUM
ejpam-5720	280	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	280	5	-	-	PUNCT
ejpam-5720	280	6	int(f	int(f	VERB
ejpam-5720	280	7	+	+	ADJ
ejpam-5720	280	8	(	(	PUNCT
ejpam-5720	280	9	(	(	PUNCT
ejpam-5720	280	10	σ1	σ1	PROPN
ejpam-5720	280	11	,	,	PUNCT
ejpam-5720	280	12	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	280	13	)	)	PUNCT
ejpam-5720	280	14	)	)	PUNCT
ejpam-5720	280	15	∩	∩	ADJ
ejpam-5720	280	16	f−((σ1	f−((σ1	NOUN
ejpam-5720	280	17	,	,	PUNCT
ejpam-5720	280	18	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	280	19	)	)	PUNCT
ejpam-5720	280	20	)	)	PUNCT
ejpam-5720	280	21	)	)	PUNCT
ejpam-5720	280	22	)	)	PUNCT
ejpam-5720	280	23	.	.	PUNCT
ejpam-5720	281	1	thus	thus	ADV
ejpam-5720	281	2	,	,	PUNCT
ejpam-5720	281	3	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5720	281	4	)	)	PUNCT
ejpam-5720	281	5	⊆	⊆	NUM
ejpam-5720	281	6	τ1τ2	τ1τ2	NOUN
ejpam-5720	281	7	-	-	NUM
ejpam-5720	281	8	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5720	281	9	-	-	PUNCT
ejpam-5720	281	10	int((f	int((f	VERB
ejpam-5720	281	11	+	+	NOUN
ejpam-5720	281	12	(	(	PUNCT
ejpam-5720	281	13	(	(	PUNCT
ejpam-5720	281	14	σ1	σ1	NOUN
ejpam-5720	281	15	,	,	PUNCT
ejpam-5720	281	16	σ2)-scl(v1))∩f−((σ1	σ2)-scl(v1))∩f−((σ1	PROPN
ejpam-5720	281	17	,	,	PUNCT
ejpam-5720	281	18	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	281	19	)	)	PUNCT
ejpam-5720	281	20	)	)	PUNCT
ejpam-5720	281	21	)	)	PUNCT
ejpam-5720	281	22	)	)	PUNCT
ejpam-5720	281	23	.	.	PUNCT
ejpam-5720	282	1	(	(	PUNCT
ejpam-5720	282	2	6	6	X
ejpam-5720	282	3	)	)	PUNCT
ejpam-5720	282	4	⇒	⇒	NOUN
ejpam-5720	282	5	(	(	PUNCT
ejpam-5720	282	6	1	1	NUM
ejpam-5720	282	7	):	):	PUNCT
ejpam-5720	282	8	let	let	VERB
ejpam-5720	282	9	x	x	PUNCT
ejpam-5720	282	10	∈	∈	PROPN
ejpam-5720	282	11	x	x	PUNCT
ejpam-5720	282	12	and	and	CCONJ
ejpam-5720	282	13	let	let	VERB
ejpam-5720	282	14	v1	v1	NOUN
ejpam-5720	282	15	,	,	PUNCT
ejpam-5720	282	16	v2	v2	PROPN
ejpam-5720	282	17	be	be	AUX
ejpam-5720	282	18	any	any	DET
ejpam-5720	282	19	σ1σ2	σ1σ2	NOUN
ejpam-5720	282	20	-	-	PUNCT
ejpam-5720	282	21	open	open	ADJ
ejpam-5720	282	22	sets	set	NOUN
ejpam-5720	282	23	of	of	ADP
ejpam-5720	282	24	y	y	PROPN
ejpam-5720	282	25	having	have	VERB
ejpam-5720	282	26	n	n	PROPN
ejpam-5720	282	27	(	(	PUNCT
ejpam-5720	282	28	σ1	σ1	PROPN
ejpam-5720	282	29	,	,	PUNCT
ejpam-5720	282	30	σ2)closed	σ2)close	VERB
ejpam-5720	282	31	complements	complement	NOUN
ejpam-5720	282	32	such	such	ADJ
ejpam-5720	282	33	that	that	SCONJ
ejpam-5720	282	34	x	x	SYM
ejpam-5720	282	35	∈	∈	NOUN
ejpam-5720	282	36	f+(v1	f+(v1	NOUN
ejpam-5720	282	37	)	)	PUNCT
ejpam-5720	282	38	∩	∩	NOUN
ejpam-5720	282	39	f−(v2	f−(v2	NUM
ejpam-5720	282	40	)	)	PUNCT
ejpam-5720	282	41	.	.	PUNCT
ejpam-5720	283	1	by	by	ADP
ejpam-5720	283	2	(	(	PUNCT
ejpam-5720	283	3	6	6	NUM
ejpam-5720	283	4	)	)	PUNCT
ejpam-5720	283	5	and	and	CCONJ
ejpam-5720	283	6	lemma	lemma	PROPN
ejpam-5720	283	7	2	2	NUM
ejpam-5720	283	8	,	,	PUNCT
ejpam-5720	283	9	we	we	PRON
ejpam-5720	283	10	have	have	VERB
ejpam-5720	283	11	x	x	X
ejpam-5720	283	12	∈	∈	NOUN
ejpam-5720	283	13	f+(v1	f+(v1	NOUN
ejpam-5720	283	14	)	)	PUNCT
ejpam-5720	283	15	∩	∩	NOUN
ejpam-5720	283	16	f−(v2	f−(v2	X
ejpam-5720	283	17	)	)	PUNCT
ejpam-5720	283	18	⊆	⊆	NUM
ejpam-5720	283	19	(	(	PUNCT
ejpam-5720	283	20	τ1	τ1	NOUN
ejpam-5720	283	21	,	,	PUNCT
ejpam-5720	283	22	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	284	1	+	+	ADJ
ejpam-5720	284	2	(	(	PUNCT
ejpam-5720	284	3	(	(	PUNCT
ejpam-5720	284	4	σ1	σ1	PROPN
ejpam-5720	284	5	,	,	PUNCT
ejpam-5720	284	6	σ2)-scl(v1	σ2)-scl(v1	ADJ
ejpam-5720	284	7	)	)	PUNCT
ejpam-5720	284	8	)	)	PUNCT
ejpam-5720	284	9	∩	∩	ADJ
ejpam-5720	284	10	f−((σ1	f−((σ1	NOUN
ejpam-5720	284	11	,	,	PUNCT
ejpam-5720	284	12	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	284	13	)	)	PUNCT
ejpam-5720	284	14	)	)	PUNCT
ejpam-5720	284	15	)	)	PUNCT
ejpam-5720	284	16	.	.	PUNCT
ejpam-5720	285	1	put	put	VERB
ejpam-5720	285	2	u	u	NOUN
ejpam-5720	285	3	=	=	PUNCT
ejpam-5720	285	4	(	(	PUNCT
ejpam-5720	285	5	τ1	τ1	NOUN
ejpam-5720	285	6	,	,	PUNCT
ejpam-5720	285	7	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	286	1	+	+	ADJ
ejpam-5720	286	2	(	(	PUNCT
ejpam-5720	286	3	(	(	PUNCT
ejpam-5720	286	4	σ1	σ1	NOUN
ejpam-5720	286	5	,	,	PUNCT
ejpam-5720	286	6	σ2)-scl(v1))∩f−((σ1	σ2)-scl(v1))∩f−((σ1	PROPN
ejpam-5720	286	7	,	,	PUNCT
ejpam-5720	286	8	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	286	9	)	)	PUNCT
ejpam-5720	286	10	)	)	PUNCT
ejpam-5720	286	11	)	)	PUNCT
ejpam-5720	286	12	.	.	PUNCT
ejpam-5720	287	1	then	then	ADV
ejpam-5720	287	2	,	,	PUNCT
ejpam-5720	287	3	u	u	NOUN
ejpam-5720	287	4	is	be	AUX
ejpam-5720	287	5	a	a	DET
ejpam-5720	287	6	(	(	PUNCT
ejpam-5720	287	7	τ1	τ1	NOUN
ejpam-5720	287	8	,	,	PUNCT
ejpam-5720	287	9	τ2)sopen	τ2)sopen	ADJ
ejpam-5720	287	10	set	set	NOUN
ejpam-5720	287	11	of	of	ADP
ejpam-5720	287	12	x	x	PUNCT
ejpam-5720	287	13	containing	contain	VERB
ejpam-5720	287	14	x	x	PROPN
ejpam-5720	287	15	,	,	PUNCT
ejpam-5720	287	16	f	f	PROPN
ejpam-5720	287	17	(	(	PUNCT
ejpam-5720	287	18	u	u	NOUN
ejpam-5720	287	19	)	)	PUNCT
ejpam-5720	287	20	⊆	⊆	NUM
ejpam-5720	287	21	(	(	PUNCT
ejpam-5720	287	22	σ1	σ1	PROPN
ejpam-5720	287	23	,	,	PUNCT
ejpam-5720	287	24	σ2)-scl(v1	σ2)-scl(v1	VERB
ejpam-5720	287	25	)	)	PUNCT
ejpam-5720	287	26	and	and	CCONJ
ejpam-5720	287	27	(	(	PUNCT
ejpam-5720	287	28	σ1	σ1	PROPN
ejpam-5720	287	29	,	,	PUNCT
ejpam-5720	287	30	σ2)-scl(v2	σ2)-scl(v2	NOUN
ejpam-5720	287	31	)	)	PUNCT
ejpam-5720	287	32	∩	∩	PROPN
ejpam-5720	287	33	f	f	X
ejpam-5720	287	34	(	(	PUNCT
ejpam-5720	287	35	z	z	NOUN
ejpam-5720	287	36	)	)	PUNCT
ejpam-5720	287	37	̸=	̸=	NOUN
ejpam-5720	287	38	∅	∅	NOUN
ejpam-5720	287	39	for	for	ADP
ejpam-5720	287	40	every	every	DET
ejpam-5720	287	41	z	z	NOUN
ejpam-5720	287	42	∈	∈	PROPN
ejpam-5720	287	43	u	u	NOUN
ejpam-5720	287	44	.	.	PUNCT
ejpam-5720	288	1	this	this	PRON
ejpam-5720	288	2	shows	show	VERB
ejpam-5720	288	3	that	that	SCONJ
ejpam-5720	288	4	f	f	PROPN
ejpam-5720	288	5	is	be	AUX
ejpam-5720	288	6	almost	almost	ADV
ejpam-5720	288	7	nearly	nearly	ADV
ejpam-5720	288	8	quasi	quasi	NOUN
ejpam-5720	288	9	(	(	PUNCT
ejpam-5720	288	10	τ1	τ1	NOUN
ejpam-5720	288	11	,	,	PUNCT
ejpam-5720	288	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	288	13	.	.	PUNCT
ejpam-5720	289	1	theorem	theorem	VERB
ejpam-5720	289	2	8	8	NUM
ejpam-5720	289	3	.	.	PUNCT
ejpam-5720	290	1	for	for	ADP
ejpam-5720	290	2	a	a	DET
ejpam-5720	290	3	multifunction	multifunction	NOUN
ejpam-5720	290	4	f	f	NOUN
ejpam-5720	290	5	:	:	PUNCT
ejpam-5720	290	6	(	(	PUNCT
ejpam-5720	290	7	x	x	NOUN
ejpam-5720	290	8	,	,	PUNCT
ejpam-5720	290	9	τ1	τ1	NOUN
ejpam-5720	290	10	,	,	PUNCT
ejpam-5720	290	11	τ2	τ2	NOUN
ejpam-5720	290	12	)	)	PUNCT
ejpam-5720	290	13	→	→	SYM
ejpam-5720	290	14	(	(	PUNCT
ejpam-5720	290	15	y	y	PROPN
ejpam-5720	290	16	,	,	PUNCT
ejpam-5720	290	17	σ1	σ1	PROPN
ejpam-5720	290	18	,	,	PUNCT
ejpam-5720	290	19	σ2	σ2	NOUN
ejpam-5720	290	20	)	)	PUNCT
ejpam-5720	290	21	,	,	PUNCT
ejpam-5720	290	22	the	the	DET
ejpam-5720	290	23	following	follow	VERB
ejpam-5720	290	24	properties	property	NOUN
ejpam-5720	290	25	are	be	AUX
ejpam-5720	290	26	equivalent	equivalent	ADJ
ejpam-5720	290	27	:	:	PUNCT
ejpam-5720	290	28	(	(	PUNCT
ejpam-5720	290	29	1	1	X
ejpam-5720	290	30	)	)	PUNCT
ejpam-5720	290	31	f	f	NOUN
ejpam-5720	290	32	is	be	AUX
ejpam-5720	290	33	almost	almost	ADV
ejpam-5720	290	34	nearly	nearly	ADV
ejpam-5720	290	35	quasi	quasi	NOUN
ejpam-5720	290	36	(	(	PUNCT
ejpam-5720	290	37	τ1	τ1	NOUN
ejpam-5720	290	38	,	,	PUNCT
ejpam-5720	290	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	290	40	;	;	PUNCT
ejpam-5720	290	41	(	(	PUNCT
ejpam-5720	290	42	2	2	X
ejpam-5720	290	43	)	)	PUNCT
ejpam-5720	290	44	(	(	PUNCT
ejpam-5720	290	45	τ1	τ1	NOUN
ejpam-5720	290	46	,	,	PUNCT
ejpam-5720	290	47	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5720	290	48	−(v1)∪f+(v2	−(v1)∪f+(v2	PROPN
ejpam-5720	290	49	)	)	PUNCT
ejpam-5720	290	50	)	)	PUNCT
ejpam-5720	291	1	⊆	⊆	X
ejpam-5720	291	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	291	3	-	-	PUNCT
ejpam-5720	291	4	cl(v1))∪f+(σ1σ2	cl(v1))∪f+(σ1σ2	NOUN
ejpam-5720	291	5	-	-	NOUN
ejpam-5720	291	6	cl(v2	cl(v2	NOUN
ejpam-5720	291	7	)	)	PUNCT
ejpam-5720	291	8	)	)	PUNCT
ejpam-5720	291	9	for	for	ADP
ejpam-5720	291	10	every	every	DET
ejpam-5720	291	11	(	(	PUNCT
ejpam-5720	291	12	σ1	σ1	PROPN
ejpam-5720	291	13	,	,	PUNCT
ejpam-5720	291	14	σ2)βopen	σ2)βopen	NOUN
ejpam-5720	291	15	sets	set	NOUN
ejpam-5720	291	16	v1	v1	NOUN
ejpam-5720	291	17	,	,	PUNCT
ejpam-5720	291	18	v2	v2	PROPN
ejpam-5720	291	19	of	of	ADP
ejpam-5720	291	20	y	y	PROPN
ejpam-5720	291	21	having	have	VERB
ejpam-5720	291	22	n	n	PROPN
ejpam-5720	291	23	(	(	PUNCT
ejpam-5720	291	24	σ1	σ1	PROPN
ejpam-5720	291	25	,	,	PUNCT
ejpam-5720	291	26	σ2)-closed	σ2)-close	VERB
ejpam-5720	291	27	complements	complement	NOUN
ejpam-5720	291	28	;	;	PUNCT
ejpam-5720	291	29	(	(	PUNCT
ejpam-5720	291	30	3	3	X
ejpam-5720	291	31	)	)	PUNCT
ejpam-5720	291	32	(	(	PUNCT
ejpam-5720	291	33	τ1	τ1	PROPN
ejpam-5720	291	34	,	,	PUNCT
ejpam-5720	291	35	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5720	291	36	−(v1)∪f+(v2	−(v1)∪f+(v2	PROPN
ejpam-5720	291	37	)	)	PUNCT
ejpam-5720	291	38	)	)	PUNCT
ejpam-5720	291	39	⊆	⊆	X
ejpam-5720	291	40	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5720	291	41	-	-	PUNCT
ejpam-5720	291	42	cl(v1))∪f+(σ1σ2	cl(v1))∪f+(σ1σ2	NOUN
ejpam-5720	291	43	-	-	NOUN
ejpam-5720	291	44	cl(v2	cl(v2	NOUN
ejpam-5720	291	45	)	)	PUNCT
ejpam-5720	291	46	)	)	PUNCT
ejpam-5720	292	1	for	for	ADP
ejpam-5720	292	2	every	every	DET
ejpam-5720	292	3	(	(	PUNCT
ejpam-5720	292	4	σ1	σ1	PROPN
ejpam-5720	292	5	,	,	PUNCT
ejpam-5720	292	6	σ2)sopen	σ2)sopen	NOUN
ejpam-5720	292	7	sets	set	NOUN
ejpam-5720	292	8	v1	v1	NOUN
ejpam-5720	292	9	,	,	PUNCT
ejpam-5720	292	10	v2	v2	PROPN
ejpam-5720	292	11	of	of	ADP
ejpam-5720	292	12	y	y	PROPN
ejpam-5720	292	13	having	have	VERB
ejpam-5720	292	14	n	n	PROPN
ejpam-5720	292	15	(	(	PUNCT
ejpam-5720	292	16	σ1	σ1	PROPN
ejpam-5720	292	17	,	,	PUNCT
ejpam-5720	292	18	σ2)-closed	σ2)-close	VERB
ejpam-5720	292	19	complements	complement	NOUN
ejpam-5720	292	20	;	;	PUNCT
ejpam-5720	292	21	(	(	PUNCT
ejpam-5720	292	22	4	4	X
ejpam-5720	292	23	)	)	PUNCT
ejpam-5720	292	24	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5720	292	25	)	)	PUNCT
ejpam-5720	292	26	⊆	⊆	NUM
ejpam-5720	292	27	(	(	PUNCT
ejpam-5720	292	28	τ1	τ1	NOUN
ejpam-5720	292	29	,	,	PUNCT
ejpam-5720	292	30	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5720	293	1	+	+	ADJ
ejpam-5720	293	2	(	(	PUNCT
ejpam-5720	293	3	σ1σ2	σ1σ2	ADJ
ejpam-5720	293	4	-	-	PUNCT
ejpam-5720	293	5	int(σ1σ2	int(σ1σ2	VERB
ejpam-5720	293	6	-	-	PUNCT
ejpam-5720	293	7	cl(v1)))∩f−(σ1σ2	cl(v1)))∩f−(σ1σ2	NOUN
ejpam-5720	293	8	-	-	PUNCT
ejpam-5720	293	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5720	293	10	-	-	PUNCT
ejpam-5720	293	11	cl(v2	cl(v2	NOUN
ejpam-5720	293	12	)	)	PUNCT
ejpam-5720	293	13	)	)	PUNCT
ejpam-5720	293	14	)	)	PUNCT
ejpam-5720	293	15	)	)	PUNCT
ejpam-5720	293	16	for	for	ADP
ejpam-5720	293	17	every	every	DET
ejpam-5720	293	18	(	(	PUNCT
ejpam-5720	293	19	σ1	σ1	PROPN
ejpam-5720	293	20	,	,	PUNCT
ejpam-5720	293	21	σ2)p	σ2)p	NOUN
ejpam-5720	293	22	-	-	PUNCT
ejpam-5720	293	23	open	open	ADJ
ejpam-5720	293	24	sets	set	NOUN
ejpam-5720	293	25	v1	v1	NOUN
ejpam-5720	293	26	,	,	PUNCT
ejpam-5720	293	27	v2	v2	PROPN
ejpam-5720	293	28	of	of	ADP
ejpam-5720	293	29	y	y	PROPN
ejpam-5720	293	30	having	having	AUX
ejpam-5720	293	31	n	n	PROPN
ejpam-5720	293	32	(	(	PUNCT
ejpam-5720	293	33	σ1	σ1	PROPN
ejpam-5720	293	34	,	,	PUNCT
ejpam-5720	293	35	σ2)-closed	σ2)-close	VERB
ejpam-5720	293	36	complements	complement	NOUN
ejpam-5720	293	37	.	.	PUNCT
ejpam-5720	294	1	proof	proof	NOUN
ejpam-5720	294	2	.	.	PUNCT
ejpam-5720	295	1	the	the	DET
ejpam-5720	295	2	proof	proof	NOUN
ejpam-5720	295	3	follows	follow	VERB
ejpam-5720	295	4	from	from	ADP
ejpam-5720	295	5	theorem	theorem	ADJ
ejpam-5720	295	6	7	7	NUM
ejpam-5720	295	7	and	and	CCONJ
ejpam-5720	295	8	is	be	AUX
ejpam-5720	295	9	thus	thus	ADV
ejpam-5720	295	10	omitted	omit	VERB
ejpam-5720	295	11	.	.	PUNCT
ejpam-5720	296	1	j.	j.	PROPN
ejpam-5720	296	2	khampakdee	khampakdee	PROPN
ejpam-5720	296	3	,	,	PUNCT
ejpam-5720	296	4	a.	a.	PROPN
ejpam-5720	296	5	sama	sama	PROPN
ejpam-5720	296	6	-	-	PUNCT
ejpam-5720	296	7	ae	ae	PROPN
ejpam-5720	296	8	,	,	PUNCT
ejpam-5720	296	9	c.	c.	PROPN
ejpam-5720	296	10	boonpok	boonpok	PROPN
ejpam-5720	296	11	/	/	SYM
ejpam-5720	296	12	eur	eur	PROPN
ejpam-5720	296	13	.	.	PUNCT
ejpam-5720	297	1	j.	j.	PROPN
ejpam-5720	297	2	pure	pure	PROPN
ejpam-5720	297	3	appl	appl	PROPN
ejpam-5720	297	4	.	.	PROPN
ejpam-5720	297	5	math	math	PROPN
ejpam-5720	297	6	,	,	PUNCT
ejpam-5720	297	7	18	18	NUM
ejpam-5720	297	8	(	(	PUNCT
ejpam-5720	297	9	1	1	NUM
ejpam-5720	297	10	)	)	PUNCT
ejpam-5720	297	11	(	(	PUNCT
ejpam-5720	297	12	2025	2025	NUM
ejpam-5720	297	13	)	)	PUNCT
ejpam-5720	297	14	,	,	PUNCT
ejpam-5720	297	15	5720	5720	NUM
ejpam-5720	297	16	12	12	NUM
ejpam-5720	297	17	of	of	ADP
ejpam-5720	297	18	15	15	NUM
ejpam-5720	297	19	acknowledgements	acknowledgement	NOUN
ejpam-5720	297	20	this	this	DET
ejpam-5720	297	21	research	research	NOUN
ejpam-5720	297	22	project	project	NOUN
ejpam-5720	297	23	was	be	AUX
ejpam-5720	297	24	financially	financially	ADV
ejpam-5720	297	25	supported	support	VERB
ejpam-5720	297	26	by	by	ADP
ejpam-5720	297	27	mahasarakham	mahasarakham	PROPN
ejpam-5720	297	28	university	university	PROPN
ejpam-5720	297	29	.	.	PUNCT
ejpam-5720	298	1	references	reference	NOUN
ejpam-5720	298	2	[	[	X
ejpam-5720	298	3	1	1	NUM
ejpam-5720	298	4	]	]	PUNCT
ejpam-5720	298	5	c.	c.	PROPN
ejpam-5720	298	6	boonpok	boonpok	PROPN
ejpam-5720	298	7	.	.	PUNCT
ejpam-5720	299	1	almost	almost	ADV
ejpam-5720	299	2	(	(	PUNCT
ejpam-5720	299	3	g	g	NOUN
ejpam-5720	299	4	,	,	PUNCT
ejpam-5720	299	5	m)-continuous	m)-continuous	ADJ
ejpam-5720	299	6	functions	function	NOUN
ejpam-5720	299	7	.	.	PUNCT
ejpam-5720	300	1	international	international	ADJ
ejpam-5720	300	2	journal	journal	PROPN
ejpam-5720	300	3	of	of	ADP
ejpam-5720	300	4	mathematical	mathematical	ADJ
ejpam-5720	300	5	analysis	analysis	NOUN
ejpam-5720	300	6	,	,	PUNCT
ejpam-5720	300	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5720	300	8	,	,	PUNCT
ejpam-5720	300	9	2010	2010	NUM
ejpam-5720	300	10	.	.	PUNCT
ejpam-5720	301	1	[	[	X
ejpam-5720	301	2	2	2	NUM
ejpam-5720	301	3	]	]	PUNCT
ejpam-5720	301	4	c.	c.	PROPN
ejpam-5720	301	5	boonpok	boonpok	PROPN
ejpam-5720	301	6	.	.	PUNCT
ejpam-5720	302	1	m	m	VERB
ejpam-5720	302	2	-continuous	-continuous	ADJ
ejpam-5720	302	3	functions	function	NOUN
ejpam-5720	302	4	in	in	ADP
ejpam-5720	302	5	biminimal	biminimal	NOUN
ejpam-5720	302	6	structure	structure	NOUN
ejpam-5720	302	7	spaces	space	NOUN
ejpam-5720	302	8	.	.	PUNCT
ejpam-5720	303	1	far	far	PROPN
ejpam-5720	303	2	east	east	PROPN
ejpam-5720	303	3	journal	journal	PROPN
ejpam-5720	303	4	of	of	ADP
ejpam-5720	303	5	mathematical	mathematical	ADJ
ejpam-5720	303	6	sciences	science	NOUN
ejpam-5720	303	7	,	,	PUNCT
ejpam-5720	303	8	43(1):41–58	43(1):41–58	NUM
ejpam-5720	303	9	,	,	PUNCT
ejpam-5720	303	10	2010	2010	NUM
ejpam-5720	303	11	.	.	PUNCT
ejpam-5720	304	1	[	[	X
ejpam-5720	304	2	3	3	X
ejpam-5720	304	3	]	]	PUNCT
ejpam-5720	304	4	c.	c.	PROPN
ejpam-5720	304	5	boonpok	boonpok	PROPN
ejpam-5720	304	6	.	.	PUNCT
ejpam-5720	305	1	on	on	ADP
ejpam-5720	305	2	continuous	continuous	ADJ
ejpam-5720	305	3	multifunctions	multifunction	NOUN
ejpam-5720	305	4	in	in	ADP
ejpam-5720	305	5	ideal	ideal	ADJ
ejpam-5720	305	6	topological	topological	ADJ
ejpam-5720	305	7	spaces	space	NOUN
ejpam-5720	305	8	.	.	PUNCT
ejpam-5720	306	1	lobachevskii	lobachevskii	PROPN
ejpam-5720	306	2	journal	journal	PROPN
ejpam-5720	306	3	of	of	ADP
ejpam-5720	306	4	mathematics	mathematic	NOUN
ejpam-5720	306	5	,	,	PUNCT
ejpam-5720	306	6	40(1):24–35	40(1):24–35	NUM
ejpam-5720	306	7	,	,	PUNCT
ejpam-5720	306	8	2019	2019	NUM
ejpam-5720	306	9	.	.	PUNCT
ejpam-5720	307	1	[	[	X
ejpam-5720	307	2	4	4	NUM
ejpam-5720	307	3	]	]	PUNCT
ejpam-5720	307	4	c.	c.	PROPN
ejpam-5720	307	5	boonpok	boonpok	PROPN
ejpam-5720	307	6	.	.	PUNCT
ejpam-5720	308	1	on	on	ADP
ejpam-5720	308	2	characterizations	characterization	NOUN
ejpam-5720	308	3	of	of	ADP
ejpam-5720	308	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5720	308	5	ideal	ideal	ADJ
ejpam-5720	308	6	topological	topological	ADJ
ejpam-5720	308	7	spaces	space	NOUN
ejpam-5720	308	8	.	.	PUNCT
ejpam-5720	309	1	journal	journal	NOUN
ejpam-5720	309	2	of	of	ADP
ejpam-5720	309	3	mathematics	mathematic	NOUN
ejpam-5720	309	4	,	,	PUNCT
ejpam-5720	309	5	2020:9387601	2020:9387601	NUM
ejpam-5720	309	6	,	,	PUNCT
ejpam-5720	309	7	2020	2020	NUM
ejpam-5720	309	8	.	.	PUNCT
ejpam-5720	310	1	[	[	X
ejpam-5720	310	2	5	5	X
ejpam-5720	310	3	]	]	PUNCT
ejpam-5720	310	4	c.	c.	PROPN
ejpam-5720	310	5	boonpok	boonpok	PROPN
ejpam-5720	310	6	.	.	PUNCT
ejpam-5720	311	1	(	(	PUNCT
ejpam-5720	311	2	τ1	τ1	NOUN
ejpam-5720	311	3	,	,	PUNCT
ejpam-5720	311	4	τ2)δ	τ2)δ	ADJ
ejpam-5720	311	5	-	-	PUNCT
ejpam-5720	311	6	semicontinuous	semicontinuous	ADJ
ejpam-5720	311	7	multifunctions	multifunction	NOUN
ejpam-5720	311	8	.	.	PUNCT
ejpam-5720	312	1	heliyon	heliyon	NOUN
ejpam-5720	312	2	,	,	PUNCT
ejpam-5720	312	3	6	6	NUM
ejpam-5720	312	4	:	:	SYM
ejpam-5720	312	5	e05367	e05367	PROPN
ejpam-5720	312	6	,	,	PUNCT
ejpam-5720	312	7	2020	2020	NUM
ejpam-5720	312	8	.	.	PUNCT
ejpam-5720	313	1	[	[	X
ejpam-5720	313	2	6	6	NUM
ejpam-5720	313	3	]	]	PUNCT
ejpam-5720	313	4	c.	c.	PROPN
ejpam-5720	313	5	boonpok	boonpok	PROPN
ejpam-5720	313	6	.	.	PUNCT
ejpam-5720	314	1	weak	weak	ADJ
ejpam-5720	314	2	quasi	quasi	ADJ
ejpam-5720	314	3	continuity	continuity	NOUN
ejpam-5720	314	4	for	for	ADP
ejpam-5720	314	5	multifunctions	multifunction	NOUN
ejpam-5720	314	6	in	in	ADP
ejpam-5720	314	7	ideal	ideal	ADJ
ejpam-5720	314	8	topological	topological	ADJ
ejpam-5720	314	9	spaces	space	NOUN
ejpam-5720	314	10	.	.	PUNCT
ejpam-5720	315	1	advances	advance	NOUN
ejpam-5720	315	2	in	in	ADP
ejpam-5720	315	3	mathematics	mathematic	NOUN
ejpam-5720	315	4	:	:	PUNCT
ejpam-5720	315	5	scientific	scientific	ADJ
ejpam-5720	315	6	journal	journal	NOUN
ejpam-5720	315	7	,	,	PUNCT
ejpam-5720	315	8	9(1):339–355	9(1):339–355	NUM
ejpam-5720	315	9	,	,	PUNCT
ejpam-5720	315	10	2020	2020	NUM
ejpam-5720	315	11	.	.	PUNCT
ejpam-5720	316	1	[	[	X
ejpam-5720	316	2	7	7	X
ejpam-5720	316	3	]	]	X
ejpam-5720	316	4	c.	c.	PROPN
ejpam-5720	316	5	boonpok	boonpok	PROPN
ejpam-5720	316	6	.	.	PUNCT
ejpam-5720	317	1	upper	upper	ADJ
ejpam-5720	317	2	and	and	CCONJ
ejpam-5720	317	3	lower	low	ADJ
ejpam-5720	317	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5720	317	5	.	.	PUNCT
ejpam-5720	317	6	heliyon	heliyon	NOUN
ejpam-5720	317	7	,	,	PUNCT
ejpam-5720	317	8	7	7	NUM
ejpam-5720	317	9	:	:	PUNCT
ejpam-5720	317	10	e05986	e05986	PROPN
ejpam-5720	317	11	,	,	PUNCT
ejpam-5720	317	12	2021	2021	NUM
ejpam-5720	317	13	.	.	PUNCT
ejpam-5720	318	1	[	[	X
ejpam-5720	318	2	8	8	NUM
ejpam-5720	318	3	]	]	X
ejpam-5720	318	4	c.	c.	PROPN
ejpam-5720	318	5	boonpok	boonpok	PROPN
ejpam-5720	318	6	.	.	PUNCT
ejpam-5720	319	1	on	on	ADP
ejpam-5720	319	2	some	some	DET
ejpam-5720	319	3	closed	closed	ADJ
ejpam-5720	319	4	sets	set	NOUN
ejpam-5720	319	5	and	and	CCONJ
ejpam-5720	319	6	low	low	ADJ
ejpam-5720	319	7	separation	separation	NOUN
ejpam-5720	319	8	axioms	axiom	NOUN
ejpam-5720	319	9	via	via	ADP
ejpam-5720	319	10	topological	topological	ADJ
ejpam-5720	319	11	ideals	ideal	NOUN
ejpam-5720	319	12	.	.	PUNCT
ejpam-5720	320	1	european	european	ADJ
ejpam-5720	320	2	journal	journal	PROPN
ejpam-5720	320	3	of	of	ADP
ejpam-5720	320	4	pure	pure	ADJ
ejpam-5720	320	5	and	and	CCONJ
ejpam-5720	320	6	applied	applied	ADJ
ejpam-5720	320	7	mathematics	mathematic	NOUN
ejpam-5720	320	8	,	,	PUNCT
ejpam-5720	320	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5720	320	10	,	,	PUNCT
ejpam-5720	320	11	2022	2022	NUM
ejpam-5720	320	12	.	.	PUNCT
ejpam-5720	321	1	[	[	X
ejpam-5720	321	2	9	9	NUM
ejpam-5720	321	3	]	]	PUNCT
ejpam-5720	321	4	c.	c.	PROPN
ejpam-5720	321	5	boonpok	boonpok	PROPN
ejpam-5720	321	6	.	.	PUNCT
ejpam-5720	322	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-5720	322	2	continuity	continuity	NOUN
ejpam-5720	322	3	for	for	ADP
ejpam-5720	322	4	multifunctions	multifunction	NOUN
ejpam-5720	322	5	.	.	PUNCT
ejpam-5720	323	1	wseas	wseas	PROPN
ejpam-5720	323	2	transactions	transaction	NOUN
ejpam-5720	323	3	on	on	ADP
ejpam-5720	323	4	mathematics	mathematic	NOUN
ejpam-5720	323	5	,	,	PUNCT
ejpam-5720	323	6	21:245–251	21:245–251	NUM
ejpam-5720	323	7	,	,	PUNCT
ejpam-5720	323	8	2022	2022	NUM
ejpam-5720	323	9	.	.	PUNCT
ejpam-5720	324	1	[	[	X
ejpam-5720	324	2	10	10	NUM
ejpam-5720	324	3	]	]	X
ejpam-5720	324	4	c.	c.	PROPN
ejpam-5720	324	5	boonpok	boonpok	PROPN
ejpam-5720	324	6	.	.	PUNCT
ejpam-5720	325	1	on	on	ADP
ejpam-5720	325	2	some	some	DET
ejpam-5720	325	3	spaces	space	NOUN
ejpam-5720	325	4	via	via	ADP
ejpam-5720	325	5	topological	topological	ADJ
ejpam-5720	325	6	ideals	ideal	NOUN
ejpam-5720	325	7	.	.	PUNCT
ejpam-5720	326	1	open	open	ADJ
ejpam-5720	326	2	mathematics	mathematic	NOUN
ejpam-5720	326	3	,	,	PUNCT
ejpam-5720	326	4	21:20230118	21:20230118	NUM
ejpam-5720	326	5	,	,	PUNCT
ejpam-5720	326	6	2023	2023	NUM
ejpam-5720	326	7	.	.	PUNCT
ejpam-5720	327	1	[	[	X
ejpam-5720	327	2	11	11	NUM
ejpam-5720	327	3	]	]	PUNCT
ejpam-5720	327	4	c.	c.	PROPN
ejpam-5720	327	5	boonpok	boonpok	PROPN
ejpam-5720	327	6	.	.	PUNCT
ejpam-5720	328	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5720	328	2	.	.	PUNCT
ejpam-5720	329	1	mathematica	mathematica	PROPN
ejpam-5720	329	2	,	,	PUNCT
ejpam-5720	329	3	65(1):31–42	65(1):31–42	NUM
ejpam-5720	329	4	,	,	PUNCT
ejpam-5720	329	5	2023	2023	NUM
ejpam-5720	329	6	.	.	PUNCT
ejpam-5720	330	1	[	[	X
ejpam-5720	330	2	12	12	NUM
ejpam-5720	330	3	]	]	X
ejpam-5720	330	4	c.	c.	PROPN
ejpam-5720	330	5	boonpok	boonpok	PROPN
ejpam-5720	330	6	and	and	CCONJ
ejpam-5720	330	7	j.	j.	PROPN
ejpam-5720	330	8	khampakdee	khampakdee	PROPN
ejpam-5720	330	9	.	.	PUNCT
ejpam-5720	331	1	(	(	PUNCT
ejpam-5720	331	2	λ	λ	NOUN
ejpam-5720	331	3	,	,	PUNCT
ejpam-5720	331	4	sp)-open	sp)-open	ADJ
ejpam-5720	331	5	sets	set	NOUN
ejpam-5720	331	6	in	in	ADP
ejpam-5720	331	7	topological	topological	ADJ
ejpam-5720	331	8	spaces	space	NOUN
ejpam-5720	331	9	.	.	PUNCT
ejpam-5720	332	1	european	european	ADJ
ejpam-5720	332	2	journal	journal	PROPN
ejpam-5720	332	3	of	of	ADP
ejpam-5720	332	4	pure	pure	ADJ
ejpam-5720	332	5	and	and	CCONJ
ejpam-5720	332	6	applied	applied	ADJ
ejpam-5720	332	7	mathematics	mathematic	NOUN
ejpam-5720	332	8	,	,	PUNCT
ejpam-5720	332	9	15(2):572–588	15(2):572–588	NUM
ejpam-5720	332	10	,	,	PUNCT
ejpam-5720	332	11	2022	2022	NUM
ejpam-5720	332	12	.	.	PUNCT
ejpam-5720	333	1	[	[	X
ejpam-5720	333	2	13	13	NUM
ejpam-5720	333	3	]	]	PUNCT
ejpam-5720	333	4	c.	c.	PROPN
ejpam-5720	333	5	boonpok	boonpok	PROPN
ejpam-5720	333	6	and	and	CCONJ
ejpam-5720	333	7	j.	j.	PROPN
ejpam-5720	333	8	khampakdee	khampakdee	PROPN
ejpam-5720	333	9	.	.	PUNCT
ejpam-5720	334	1	on	on	ADP
ejpam-5720	334	2	almost	almost	ADV
ejpam-5720	334	3	α(λ	α(λ	PROPN
ejpam-5720	334	4	,	,	PUNCT
ejpam-5720	334	5	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	334	6	multifunctions	multifunction	NOUN
ejpam-5720	334	7	.	.	PUNCT
ejpam-5720	335	1	european	european	PROPN
ejpam-5720	335	2	journal	journal	PROPN
ejpam-5720	335	3	of	of	ADP
ejpam-5720	335	4	pure	pure	ADJ
ejpam-5720	335	5	and	and	CCONJ
ejpam-5720	335	6	applied	applied	ADJ
ejpam-5720	335	7	mathematics	mathematic	NOUN
ejpam-5720	335	8	,	,	PUNCT
ejpam-5720	335	9	15(2):626–634	15(2):626–634	PROPN
ejpam-5720	335	10	,	,	PUNCT
ejpam-5720	335	11	2022	2022	NUM
ejpam-5720	335	12	.	.	PUNCT
ejpam-5720	336	1	[	[	X
ejpam-5720	336	2	14	14	NUM
ejpam-5720	336	3	]	]	X
ejpam-5720	336	4	c.	c.	PROPN
ejpam-5720	336	5	boonpok	boonpok	PROPN
ejpam-5720	336	6	and	and	CCONJ
ejpam-5720	336	7	j.	j.	PROPN
ejpam-5720	336	8	khampakdee	khampakdee	PROPN
ejpam-5720	336	9	.	.	PUNCT
ejpam-5720	337	1	slight	slight	PROPN
ejpam-5720	337	2	(	(	PUNCT
ejpam-5720	337	3	λ	λ	NOUN
ejpam-5720	337	4	,	,	PUNCT
ejpam-5720	337	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5720	337	6	and	and	CCONJ
ejpam-5720	337	7	λsp	λsp	NOUN
ejpam-5720	337	8	-	-	PUNCT
ejpam-5720	337	9	extremally	extremally	ADV
ejpam-5720	337	10	disconnectedness	disconnectedness	NOUN
ejpam-5720	337	11	.	.	PUNCT
ejpam-5720	338	1	european	european	ADJ
ejpam-5720	338	2	journal	journal	PROPN
ejpam-5720	338	3	of	of	ADP
ejpam-5720	338	4	pure	pure	ADJ
ejpam-5720	338	5	and	and	CCONJ
ejpam-5720	338	6	applied	applied	ADJ
ejpam-5720	338	7	mathematics	mathematic	NOUN
ejpam-5720	338	8	,	,	PUNCT
ejpam-5720	338	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-5720	338	10	,	,	PUNCT
ejpam-5720	338	11	2022	2022	NUM
ejpam-5720	338	12	.	.	PUNCT
ejpam-5720	339	1	[	[	X
ejpam-5720	339	2	15	15	NUM
ejpam-5720	339	3	]	]	X
ejpam-5720	339	4	c.	c.	PROPN
ejpam-5720	339	5	boonpok	boonpok	PROPN
ejpam-5720	339	6	and	and	CCONJ
ejpam-5720	339	7	j.	j.	PROPN
ejpam-5720	339	8	khampakdee	khampakdee	PROPN
ejpam-5720	339	9	.	.	PUNCT
ejpam-5720	340	1	upper	upper	ADJ
ejpam-5720	340	2	and	and	CCONJ
ejpam-5720	340	3	lower	low	ADJ
ejpam-5720	340	4	weak	weak	ADJ
ejpam-5720	340	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-5720	340	6	.	.	PUNCT
ejpam-5720	341	1	european	european	PROPN
ejpam-5720	341	2	journal	journal	PROPN
ejpam-5720	341	3	of	of	ADP
ejpam-5720	341	4	pure	pure	ADJ
ejpam-5720	341	5	and	and	CCONJ
ejpam-5720	341	6	applied	applied	ADJ
ejpam-5720	341	7	mathematics	mathematic	NOUN
ejpam-5720	341	8	,	,	PUNCT
ejpam-5720	341	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-5720	341	10	,	,	PUNCT
ejpam-5720	341	11	2023	2023	NUM
ejpam-5720	341	12	.	.	PUNCT
ejpam-5720	342	1	[	[	X
ejpam-5720	342	2	16	16	NUM
ejpam-5720	342	3	]	]	X
ejpam-5720	342	4	c.	c.	PROPN
ejpam-5720	342	5	boonpok	boonpok	PROPN
ejpam-5720	342	6	and	and	CCONJ
ejpam-5720	342	7	j.	j.	PROPN
ejpam-5720	342	8	khampakdee	khampakdee	PROPN
ejpam-5720	342	9	.	.	PUNCT
ejpam-5720	343	1	almost	almost	ADV
ejpam-5720	343	2	strong	strong	ADJ
ejpam-5720	343	3	θ(λ	θ(λ	PROPN
ejpam-5720	343	4	,	,	PUNCT
ejpam-5720	343	5	p)-continuity	p)-continuity	NOUN
ejpam-5720	343	6	for	for	ADP
ejpam-5720	343	7	functions	function	NOUN
ejpam-5720	343	8	.	.	PUNCT
ejpam-5720	344	1	european	european	ADJ
ejpam-5720	344	2	journal	journal	PROPN
ejpam-5720	344	3	of	of	ADP
ejpam-5720	344	4	pure	pure	ADJ
ejpam-5720	344	5	and	and	CCONJ
ejpam-5720	344	6	applied	applied	ADJ
ejpam-5720	344	7	mathematics	mathematic	NOUN
ejpam-5720	344	8	,	,	PUNCT
ejpam-5720	344	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5720	344	10	,	,	PUNCT
ejpam-5720	344	11	2024	2024	NUM
ejpam-5720	344	12	.	.	PUNCT
ejpam-5720	345	1	[	[	X
ejpam-5720	345	2	17	17	NUM
ejpam-5720	345	3	]	]	X
ejpam-5720	345	4	c.	c.	PROPN
ejpam-5720	345	5	boonpok	boonpok	PROPN
ejpam-5720	345	6	and	and	CCONJ
ejpam-5720	345	7	j.	j.	PROPN
ejpam-5720	345	8	khampakdee	khampakdee	PROPN
ejpam-5720	345	9	.	.	PUNCT
ejpam-5720	346	1	upper	upper	ADJ
ejpam-5720	346	2	and	and	CCONJ
ejpam-5720	346	3	lower	low	ADJ
ejpam-5720	346	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5720	346	5	.	.	PUNCT
ejpam-5720	346	6	european	european	PROPN
ejpam-5720	346	7	journal	journal	PROPN
ejpam-5720	346	8	of	of	ADP
ejpam-5720	346	9	pure	pure	ADJ
ejpam-5720	346	10	and	and	CCONJ
ejpam-5720	346	11	applied	applied	ADJ
ejpam-5720	346	12	mathematics	mathematic	NOUN
ejpam-5720	346	13	,	,	PUNCT
ejpam-5720	346	14	17(1):201–211	17(1):201–211	NUM
ejpam-5720	346	15	,	,	PUNCT
ejpam-5720	346	16	2024	2024	NUM
ejpam-5720	346	17	.	.	PUNCT
ejpam-5720	347	1	[	[	X
ejpam-5720	347	2	18	18	NUM
ejpam-5720	347	3	]	]	PUNCT
ejpam-5720	347	4	c.	c.	PROPN
ejpam-5720	347	5	boonpok	boonpok	PROPN
ejpam-5720	347	6	and	and	CCONJ
ejpam-5720	347	7	c.	c.	PROPN
ejpam-5720	347	8	klanarong	klanarong	PROPN
ejpam-5720	347	9	.	.	PUNCT
ejpam-5720	348	1	on	on	ADP
ejpam-5720	348	2	weakly	weakly	ADJ
ejpam-5720	348	3	(	(	PUNCT
ejpam-5720	348	4	τ1	τ1	NOUN
ejpam-5720	348	5	,	,	PUNCT
ejpam-5720	348	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	348	7	functions	function	NOUN
ejpam-5720	348	8	.	.	PUNCT
ejpam-5720	349	1	european	european	ADJ
ejpam-5720	349	2	journal	journal	PROPN
ejpam-5720	349	3	of	of	ADP
ejpam-5720	349	4	pure	pure	ADJ
ejpam-5720	349	5	and	and	CCONJ
ejpam-5720	349	6	applied	applied	ADJ
ejpam-5720	349	7	mathematics	mathematic	NOUN
ejpam-5720	349	8	,	,	PUNCT
ejpam-5720	349	9	17(1):416–425	17(1):416–425	NUM
ejpam-5720	349	10	,	,	PUNCT
ejpam-5720	349	11	2024	2024	NUM
ejpam-5720	349	12	.	.	PUNCT
ejpam-5720	350	1	[	[	X
ejpam-5720	350	2	19	19	NUM
ejpam-5720	350	3	]	]	X
ejpam-5720	350	4	c.	c.	PROPN
ejpam-5720	350	5	boonpok	boonpok	PROPN
ejpam-5720	350	6	and	and	CCONJ
ejpam-5720	350	7	p.	p.	NOUN
ejpam-5720	350	8	pue	pue	NOUN
ejpam-5720	350	9	-	-	PUNCT
ejpam-5720	350	10	on	on	ADP
ejpam-5720	350	11	.	.	PUNCT
ejpam-5720	351	1	continuity	continuity	NOUN
ejpam-5720	351	2	for	for	ADP
ejpam-5720	351	3	multifunctions	multifunction	NOUN
ejpam-5720	351	4	in	in	ADP
ejpam-5720	351	5	ideal	ideal	ADJ
ejpam-5720	351	6	topological	topological	ADJ
ejpam-5720	351	7	spaces	space	NOUN
ejpam-5720	351	8	.	.	PUNCT
ejpam-5720	352	1	wseas	wseas	VERB
ejpam-5720	352	2	transactions	transaction	NOUN
ejpam-5720	352	3	on	on	ADP
ejpam-5720	352	4	mathematics	mathematic	NOUN
ejpam-5720	352	5	,	,	PUNCT
ejpam-5720	352	6	19:624–631	19:624–631	NUM
ejpam-5720	352	7	,	,	PUNCT
ejpam-5720	352	8	2020	2020	NUM
ejpam-5720	352	9	.	.	PUNCT
ejpam-5720	353	1	j.	j.	PROPN
ejpam-5720	353	2	khampakdee	khampakdee	PROPN
ejpam-5720	353	3	,	,	PUNCT
ejpam-5720	353	4	a.	a.	PROPN
ejpam-5720	353	5	sama	sama	PROPN
ejpam-5720	353	6	-	-	PUNCT
ejpam-5720	353	7	ae	ae	PROPN
ejpam-5720	353	8	,	,	PUNCT
ejpam-5720	353	9	c.	c.	PROPN
ejpam-5720	353	10	boonpok	boonpok	PROPN
ejpam-5720	353	11	/	/	SYM
ejpam-5720	353	12	eur	eur	PROPN
ejpam-5720	353	13	.	.	PUNCT
ejpam-5720	354	1	j.	j.	PROPN
ejpam-5720	354	2	pure	pure	PROPN
ejpam-5720	354	3	appl	appl	PROPN
ejpam-5720	354	4	.	.	PROPN
ejpam-5720	354	5	math	math	PROPN
ejpam-5720	354	6	,	,	PUNCT
ejpam-5720	354	7	18	18	NUM
ejpam-5720	354	8	(	(	PUNCT
ejpam-5720	354	9	1	1	NUM
ejpam-5720	354	10	)	)	PUNCT
ejpam-5720	354	11	(	(	PUNCT
ejpam-5720	354	12	2025	2025	NUM
ejpam-5720	354	13	)	)	PUNCT
ejpam-5720	354	14	,	,	PUNCT
ejpam-5720	354	15	5720	5720	NUM
ejpam-5720	354	16	13	13	NUM
ejpam-5720	354	17	of	of	ADP
ejpam-5720	354	18	15	15	NUM
ejpam-5720	354	19	[	[	SYM
ejpam-5720	354	20	20	20	NUM
ejpam-5720	354	21	]	]	PUNCT
ejpam-5720	354	22	c.	c.	PROPN
ejpam-5720	354	23	boonpok	boonpok	PROPN
ejpam-5720	354	24	and	and	CCONJ
ejpam-5720	354	25	p.	p.	NOUN
ejpam-5720	354	26	pue	pue	NOUN
ejpam-5720	354	27	-	-	PUNCT
ejpam-5720	354	28	on	on	ADP
ejpam-5720	354	29	.	.	PUNCT
ejpam-5720	355	1	upper	upper	ADJ
ejpam-5720	355	2	and	and	CCONJ
ejpam-5720	355	3	lower	low	ADJ
ejpam-5720	355	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5720	355	5	multifunctions	multifunction	NOUN
ejpam-5720	355	6	.	.	PUNCT
ejpam-5720	356	1	european	european	ADJ
ejpam-5720	356	2	journal	journal	PROPN
ejpam-5720	356	3	of	of	ADP
ejpam-5720	356	4	pure	pure	ADJ
ejpam-5720	356	5	and	and	CCONJ
ejpam-5720	356	6	applied	applied	ADJ
ejpam-5720	356	7	mathematics	mathematic	NOUN
ejpam-5720	356	8	,	,	PUNCT
ejpam-5720	356	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-5720	356	10	,	,	PUNCT
ejpam-5720	356	11	2023	2023	NUM
ejpam-5720	356	12	.	.	PUNCT
ejpam-5720	357	1	[	[	X
ejpam-5720	357	2	21	21	NUM
ejpam-5720	357	3	]	]	X
ejpam-5720	357	4	c.	c.	PROPN
ejpam-5720	357	5	boonpok	boonpok	PROPN
ejpam-5720	357	6	and	and	CCONJ
ejpam-5720	357	7	p.	p.	NOUN
ejpam-5720	357	8	pue	pue	NOUN
ejpam-5720	357	9	-	-	PUNCT
ejpam-5720	357	10	on	on	ADP
ejpam-5720	357	11	.	.	PUNCT
ejpam-5720	358	1	upper	upper	ADJ
ejpam-5720	358	2	and	and	CCONJ
ejpam-5720	358	3	lower	low	ADJ
ejpam-5720	358	4	weakly	weakly	ADJ
ejpam-5720	358	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5720	358	6	multifunctions	multifunction	NOUN
ejpam-5720	358	7	.	.	PUNCT
ejpam-5720	359	1	international	international	ADJ
ejpam-5720	359	2	journal	journal	NOUN
ejpam-5720	359	3	of	of	ADP
ejpam-5720	359	4	analysis	analysis	NOUN
ejpam-5720	359	5	and	and	CCONJ
ejpam-5720	359	6	applications	application	NOUN
ejpam-5720	359	7	,	,	PUNCT
ejpam-5720	359	8	21:90	21:90	NUM
ejpam-5720	359	9	,	,	PUNCT
ejpam-5720	359	10	2023	2023	NUM
ejpam-5720	359	11	.	.	PUNCT
ejpam-5720	360	1	[	[	X
ejpam-5720	360	2	22	22	NUM
ejpam-5720	360	3	]	]	PUNCT
ejpam-5720	360	4	c.	c.	PROPN
ejpam-5720	360	5	boonpok	boonpok	PROPN
ejpam-5720	360	6	and	and	CCONJ
ejpam-5720	360	7	p.	p.	NOUN
ejpam-5720	360	8	pue	pue	NOUN
ejpam-5720	360	9	-	-	PUNCT
ejpam-5720	360	10	on	on	ADP
ejpam-5720	360	11	.	.	PUNCT
ejpam-5720	361	1	upper	upper	ADJ
ejpam-5720	361	2	and	and	CCONJ
ejpam-5720	361	3	lower	low	ADJ
ejpam-5720	361	4	weakly	weakly	ADJ
ejpam-5720	361	5	(	(	PUNCT
ejpam-5720	361	6	λ	λ	NOUN
ejpam-5720	361	7	,	,	PUNCT
ejpam-5720	361	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	361	9	multifunctions	multifunction	NOUN
ejpam-5720	361	10	.	.	PUNCT
ejpam-5720	362	1	european	european	PROPN
ejpam-5720	362	2	journal	journal	PROPN
ejpam-5720	362	3	of	of	ADP
ejpam-5720	362	4	pure	pure	ADJ
ejpam-5720	362	5	and	and	CCONJ
ejpam-5720	362	6	applied	applied	ADJ
ejpam-5720	362	7	mathematics	mathematic	NOUN
ejpam-5720	362	8	,	,	PUNCT
ejpam-5720	362	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5720	362	10	,	,	PUNCT
ejpam-5720	362	11	2023	2023	NUM
ejpam-5720	362	12	.	.	PUNCT
ejpam-5720	363	1	[	[	X
ejpam-5720	363	2	23	23	NUM
ejpam-5720	363	3	]	]	X
ejpam-5720	363	4	c.	c.	PROPN
ejpam-5720	363	5	boonpok	boonpok	PROPN
ejpam-5720	363	6	and	and	CCONJ
ejpam-5720	363	7	p.	p.	NOUN
ejpam-5720	363	8	pue	pue	NOUN
ejpam-5720	363	9	-	-	PUNCT
ejpam-5720	363	10	on	on	ADP
ejpam-5720	363	11	.	.	PUNCT
ejpam-5720	364	1	characterizations	characterization	NOUN
ejpam-5720	364	2	of	of	ADP
ejpam-5720	364	3	almost	almost	ADV
ejpam-5720	364	4	(	(	PUNCT
ejpam-5720	364	5	τ1	τ1	NOUN
ejpam-5720	364	6	,	,	PUNCT
ejpam-5720	364	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	364	8	functions	function	NOUN
ejpam-5720	364	9	.	.	PUNCT
ejpam-5720	365	1	international	international	ADJ
ejpam-5720	365	2	journal	journal	NOUN
ejpam-5720	365	3	of	of	ADP
ejpam-5720	365	4	analysis	analysis	NOUN
ejpam-5720	365	5	and	and	CCONJ
ejpam-5720	365	6	applications	application	NOUN
ejpam-5720	365	7	,	,	PUNCT
ejpam-5720	365	8	22:33	22:33	NUM
ejpam-5720	365	9	,	,	PUNCT
ejpam-5720	365	10	2024	2024	NUM
ejpam-5720	365	11	.	.	PUNCT
ejpam-5720	366	1	[	[	X
ejpam-5720	366	2	24	24	NUM
ejpam-5720	366	3	]	]	PUNCT
ejpam-5720	366	4	c.	c.	PROPN
ejpam-5720	366	5	boonpok	boonpok	PROPN
ejpam-5720	366	6	and	and	CCONJ
ejpam-5720	366	7	n.	n.	PROPN
ejpam-5720	366	8	srisarakham	srisarakham	PROPN
ejpam-5720	366	9	.	.	PUNCT
ejpam-5720	367	1	almost	almost	ADV
ejpam-5720	367	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5720	367	3	for	for	ADP
ejpam-5720	367	4	multifunctions	multifunction	NOUN
ejpam-5720	367	5	.	.	PUNCT
ejpam-5720	368	1	international	international	ADJ
ejpam-5720	368	2	journal	journal	NOUN
ejpam-5720	368	3	of	of	ADP
ejpam-5720	368	4	analysis	analysis	NOUN
ejpam-5720	368	5	and	and	CCONJ
ejpam-5720	368	6	applications	application	NOUN
ejpam-5720	368	7	,	,	PUNCT
ejpam-5720	368	8	21:107	21:107	NUM
ejpam-5720	368	9	,	,	PUNCT
ejpam-5720	368	10	2023	2023	NUM
ejpam-5720	368	11	.	.	PUNCT
ejpam-5720	369	1	[	[	X
ejpam-5720	369	2	25	25	NUM
ejpam-5720	369	3	]	]	PUNCT
ejpam-5720	369	4	c.	c.	PROPN
ejpam-5720	369	5	boonpok	boonpok	PROPN
ejpam-5720	369	6	and	and	CCONJ
ejpam-5720	369	7	n.	n.	PROPN
ejpam-5720	369	8	srisarakham	srisarakham	PROPN
ejpam-5720	369	9	.	.	PUNCT
ejpam-5720	370	1	weak	weak	ADJ
ejpam-5720	370	2	forms	form	NOUN
ejpam-5720	370	3	of	of	ADP
ejpam-5720	370	4	(	(	PUNCT
ejpam-5720	370	5	λ	λ	PROPN
ejpam-5720	370	6	,	,	PUNCT
ejpam-5720	370	7	b)-open	b)-open	VERB
ejpam-5720	370	8	sets	set	NOUN
ejpam-5720	370	9	and	and	CCONJ
ejpam-5720	370	10	weak	weak	ADJ
ejpam-5720	370	11	(	(	PUNCT
ejpam-5720	370	12	λ	λ	NOUN
ejpam-5720	370	13	,	,	PUNCT
ejpam-5720	370	14	b)continuity	b)continuity	NOUN
ejpam-5720	370	15	.	.	PUNCT
ejpam-5720	371	1	european	european	PROPN
ejpam-5720	371	2	journal	journal	PROPN
ejpam-5720	371	3	of	of	ADP
ejpam-5720	371	4	pure	pure	ADJ
ejpam-5720	371	5	and	and	CCONJ
ejpam-5720	371	6	applied	applied	ADJ
ejpam-5720	371	7	mathematics	mathematic	NOUN
ejpam-5720	371	8	,	,	PUNCT
ejpam-5720	371	9	16(1):29–43	16(1):29–43	NUM
ejpam-5720	371	10	,	,	PUNCT
ejpam-5720	371	11	2023	2023	NUM
ejpam-5720	371	12	.	.	PUNCT
ejpam-5720	372	1	[	[	X
ejpam-5720	372	2	26	26	NUM
ejpam-5720	372	3	]	]	X
ejpam-5720	372	4	c.	c.	PROPN
ejpam-5720	372	5	boonpok	boonpok	PROPN
ejpam-5720	372	6	and	and	CCONJ
ejpam-5720	372	7	n.	n.	PROPN
ejpam-5720	372	8	srisarakham	srisarakham	PROPN
ejpam-5720	372	9	.	.	PUNCT
ejpam-5720	373	1	(	(	PUNCT
ejpam-5720	373	2	τ1	τ1	NOUN
ejpam-5720	373	3	,	,	PUNCT
ejpam-5720	373	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5720	373	5	for	for	ADP
ejpam-5720	373	6	functions	function	NOUN
ejpam-5720	373	7	.	.	PUNCT
ejpam-5720	374	1	asia	asia	PROPN
ejpam-5720	374	2	pacific	pacific	PROPN
ejpam-5720	374	3	journal	journal	PROPN
ejpam-5720	374	4	of	of	ADP
ejpam-5720	374	5	mathematics	mathematic	NOUN
ejpam-5720	374	6	,	,	PUNCT
ejpam-5720	374	7	11:21	11:21	NUM
ejpam-5720	374	8	,	,	PUNCT
ejpam-5720	374	9	2024	2024	NUM
ejpam-5720	374	10	.	.	PUNCT
ejpam-5720	375	1	[	[	X
ejpam-5720	375	2	27	27	NUM
ejpam-5720	375	3	]	]	X
ejpam-5720	375	4	c.	c.	PROPN
ejpam-5720	375	5	boonpok	boonpok	PROPN
ejpam-5720	375	6	and	and	CCONJ
ejpam-5720	375	7	m.	m.	NOUN
ejpam-5720	375	8	thongmoon	thongmoon	NOUN
ejpam-5720	375	9	.	.	PUNCT
ejpam-5720	376	1	weak	weak	ADJ
ejpam-5720	376	2	α(λ	α(λ	PROPN
ejpam-5720	376	3	,	,	PUNCT
ejpam-5720	376	4	sp)-continuity	sp)-continuity	NOUN
ejpam-5720	376	5	for	for	ADP
ejpam-5720	376	6	multifunctions	multifunction	NOUN
ejpam-5720	376	7	.	.	PUNCT
ejpam-5720	377	1	european	european	ADJ
ejpam-5720	377	2	journal	journal	PROPN
ejpam-5720	377	3	of	of	ADP
ejpam-5720	377	4	pure	pure	ADJ
ejpam-5720	377	5	and	and	CCONJ
ejpam-5720	377	6	applied	applied	ADJ
ejpam-5720	377	7	mathematics	mathematic	NOUN
ejpam-5720	377	8	,	,	PUNCT
ejpam-5720	377	9	16(1):465–478	16(1):465–478	NUM
ejpam-5720	377	10	,	,	PUNCT
ejpam-5720	377	11	2023	2023	NUM
ejpam-5720	377	12	.	.	PUNCT
ejpam-5720	378	1	[	[	X
ejpam-5720	378	2	28	28	NUM
ejpam-5720	378	3	]	]	X
ejpam-5720	378	4	c.	c.	PROPN
ejpam-5720	378	5	boonpok	boonpok	PROPN
ejpam-5720	378	6	and	and	CCONJ
ejpam-5720	378	7	c.	c.	PROPN
ejpam-5720	378	8	viriyapong	viriyapong	PROPN
ejpam-5720	378	9	.	.	PUNCT
ejpam-5720	379	1	upper	upper	ADJ
ejpam-5720	379	2	and	and	CCONJ
ejpam-5720	379	3	lower	low	ADJ
ejpam-5720	379	4	almost	almost	ADV
ejpam-5720	379	5	weak	weak	ADJ
ejpam-5720	379	6	(	(	PUNCT
ejpam-5720	379	7	τ1	τ1	NOUN
ejpam-5720	379	8	,	,	PUNCT
ejpam-5720	379	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5720	379	10	.	.	PUNCT
ejpam-5720	380	1	european	european	PROPN
ejpam-5720	380	2	journal	journal	PROPN
ejpam-5720	380	3	of	of	ADP
ejpam-5720	380	4	pure	pure	ADJ
ejpam-5720	380	5	and	and	CCONJ
ejpam-5720	380	6	applied	applied	ADJ
ejpam-5720	380	7	mathematics	mathematic	NOUN
ejpam-5720	380	8	,	,	PUNCT
ejpam-5720	380	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5720	380	10	,	,	PUNCT
ejpam-5720	380	11	2021	2021	NUM
ejpam-5720	380	12	.	.	PUNCT
ejpam-5720	381	1	[	[	X
ejpam-5720	381	2	29	29	NUM
ejpam-5720	381	3	]	]	X
ejpam-5720	381	4	c.	c.	PROPN
ejpam-5720	381	5	boonpok	boonpok	PROPN
ejpam-5720	381	6	,	,	PUNCT
ejpam-5720	381	7	c.	c.	PROPN
ejpam-5720	381	8	viriyapong	viriyapong	PROPN
ejpam-5720	381	9	,	,	PUNCT
ejpam-5720	381	10	and	and	CCONJ
ejpam-5720	381	11	m.	m.	NOUN
ejpam-5720	381	12	thongmoon	thongmoon	NOUN
ejpam-5720	381	13	.	.	PUNCT
ejpam-5720	382	1	on	on	ADP
ejpam-5720	382	2	upper	upper	ADJ
ejpam-5720	382	3	and	and	CCONJ
ejpam-5720	382	4	lower	low	ADJ
ejpam-5720	382	5	(	(	PUNCT
ejpam-5720	382	6	τ1	τ1	NOUN
ejpam-5720	382	7	,	,	PUNCT
ejpam-5720	382	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5720	382	9	multifunctions	multifunction	NOUN
ejpam-5720	382	10	.	.	PUNCT
ejpam-5720	383	1	journal	journal	PROPN
ejpam-5720	383	2	of	of	ADP
ejpam-5720	383	3	mathematics	mathematics	PROPN
ejpam-5720	383	4	and	and	CCONJ
ejpam-5720	383	5	computer	computer	NOUN
ejpam-5720	383	6	science	science	NOUN
ejpam-5720	383	7	,	,	PUNCT
ejpam-5720	383	8	18:282–293	18:282–293	NUM
ejpam-5720	383	9	,	,	PUNCT
ejpam-5720	383	10	2018	2018	NUM
ejpam-5720	383	11	.	.	PUNCT
ejpam-5720	384	1	[	[	X
ejpam-5720	384	2	30	30	NUM
ejpam-5720	384	3	]	]	X
ejpam-5720	384	4	c.	c.	PROPN
ejpam-5720	384	5	carpintero	carpintero	PROPN
ejpam-5720	384	6	,	,	PUNCT
ejpam-5720	384	7	j.	j.	PROPN
ejpam-5720	384	8	pacheco	pacheco	PROPN
ejpam-5720	384	9	,	,	PUNCT
ejpam-5720	384	10	n.	n.	PROPN
ejpam-5720	384	11	rajesh	rajesh	PROPN
ejpam-5720	384	12	,	,	PUNCT
ejpam-5720	384	13	e.	e.	PROPN
ejpam-5720	384	14	rosas	rosas	PROPN
ejpam-5720	384	15	,	,	PUNCT
ejpam-5720	384	16	and	and	CCONJ
ejpam-5720	384	17	s.	s.	PROPN
ejpam-5720	384	18	saranyasri	saranyasri	PROPN
ejpam-5720	384	19	.	.	PUNCT
ejpam-5720	385	1	properties	property	NOUN
ejpam-5720	385	2	of	of	ADP
ejpam-5720	385	3	nearly	nearly	ADV
ejpam-5720	385	4	ω	ω	ADJ
ejpam-5720	385	5	-	-	ADJ
ejpam-5720	385	6	continuous	continuous	ADJ
ejpam-5720	385	7	multifunctions	multifunction	NOUN
ejpam-5720	385	8	.	.	PUNCT
ejpam-5720	386	1	acta	acta	PROPN
ejpam-5720	386	2	universitatis	universitatis	PROPN
ejpam-5720	386	3	sapientiae	sapientiae	PROPN
ejpam-5720	386	4	,	,	PUNCT
ejpam-5720	386	5	mathematica	mathematica	PROPN
ejpam-5720	386	6	,	,	PUNCT
ejpam-5720	386	7	9(1):13–25	9(1):13–25	NUM
ejpam-5720	386	8	,	,	PUNCT
ejpam-5720	386	9	2017	2017	NUM
ejpam-5720	386	10	.	.	PUNCT
ejpam-5720	387	1	[	[	X
ejpam-5720	387	2	31	31	NUM
ejpam-5720	387	3	]	]	PUNCT
ejpam-5720	387	4	m.	m.	NOUN
ejpam-5720	387	5	chiangpradit	chiangpradit	NOUN
ejpam-5720	387	6	,	,	PUNCT
ejpam-5720	387	7	a.	a.	PROPN
ejpam-5720	387	8	sama	sama	PROPN
ejpam-5720	387	9	-	-	PUNCT
ejpam-5720	387	10	ae	ae	PROPN
ejpam-5720	387	11	,	,	PUNCT
ejpam-5720	387	12	and	and	CCONJ
ejpam-5720	387	13	c.	c.	PROPN
ejpam-5720	387	14	boonpok	boonpok	PROPN
ejpam-5720	387	15	.	.	PUNCT
ejpam-5720	388	1	almost	almost	ADV
ejpam-5720	388	2	nearly	nearly	ADV
ejpam-5720	388	3	quasi	quasi	NOUN
ejpam-5720	388	4	(	(	PUNCT
ejpam-5720	388	5	τ1	τ1	NOUN
ejpam-5720	388	6	,	,	PUNCT
ejpam-5720	388	7	τ2)continuous	τ2)continuous	ADJ
ejpam-5720	388	8	multifunctions	multifunction	NOUN
ejpam-5720	388	9	.	.	PUNCT
ejpam-5720	389	1	(	(	PUNCT
ejpam-5720	389	2	accepted	accept	VERB
ejpam-5720	389	3	)	)	PUNCT
ejpam-5720	389	4	.	.	PUNCT
ejpam-5720	390	1	[	[	X
ejpam-5720	390	2	32	32	NUM
ejpam-5720	390	3	]	]	PUNCT
ejpam-5720	390	4	m.	m.	NOUN
ejpam-5720	390	5	chiangpradit	chiangpradit	NOUN
ejpam-5720	390	6	,	,	PUNCT
ejpam-5720	390	7	s.	s.	PROPN
ejpam-5720	390	8	sompong	sompong	PROPN
ejpam-5720	390	9	,	,	PUNCT
ejpam-5720	390	10	and	and	CCONJ
ejpam-5720	390	11	c.	c.	PROPN
ejpam-5720	390	12	boonpok	boonpok	PROPN
ejpam-5720	390	13	.	.	PUNCT
ejpam-5720	391	1	weakly	weakly	ADJ
ejpam-5720	391	2	quasi	quasi	NOUN
ejpam-5720	391	3	(	(	PUNCT
ejpam-5720	391	4	τ1	τ1	PROPN
ejpam-5720	391	5	,	,	PUNCT
ejpam-5720	391	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	391	7	functions	function	NOUN
ejpam-5720	391	8	.	.	PUNCT
ejpam-5720	392	1	international	international	ADJ
ejpam-5720	392	2	journal	journal	NOUN
ejpam-5720	392	3	of	of	ADP
ejpam-5720	392	4	analysis	analysis	NOUN
ejpam-5720	392	5	and	and	CCONJ
ejpam-5720	392	6	applications	application	NOUN
ejpam-5720	392	7	,	,	PUNCT
ejpam-5720	392	8	22:125	22:125	NUM
ejpam-5720	392	9	,	,	PUNCT
ejpam-5720	392	10	2024	2024	NUM
ejpam-5720	392	11	.	.	PUNCT
ejpam-5720	393	1	[	[	X
ejpam-5720	393	2	33	33	NUM
ejpam-5720	393	3	]	]	X
ejpam-5720	393	4	n.	n.	NOUN
ejpam-5720	393	5	chutiman	chutiman	NOUN
ejpam-5720	393	6	,	,	PUNCT
ejpam-5720	393	7	a.	a.	PROPN
ejpam-5720	393	8	sama	sama	PROPN
ejpam-5720	393	9	-	-	PUNCT
ejpam-5720	393	10	ae	ae	PROPN
ejpam-5720	393	11	,	,	PUNCT
ejpam-5720	393	12	and	and	CCONJ
ejpam-5720	393	13	c.	c.	PROPN
ejpam-5720	393	14	boonpok	boonpok	PROPN
ejpam-5720	393	15	.	.	PUNCT
ejpam-5720	394	1	almost	almost	ADV
ejpam-5720	394	2	near	near	ADV
ejpam-5720	394	3	(	(	PUNCT
ejpam-5720	394	4	τ1	τ1	NOUN
ejpam-5720	394	5	,	,	PUNCT
ejpam-5720	394	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5720	394	7	for	for	ADP
ejpam-5720	394	8	multifunctions	multifunction	NOUN
ejpam-5720	394	9	.	.	PUNCT
ejpam-5720	395	1	(	(	PUNCT
ejpam-5720	395	2	accepted	accept	VERB
ejpam-5720	395	3	)	)	PUNCT
ejpam-5720	395	4	.	.	PUNCT
ejpam-5720	396	1	[	[	X
ejpam-5720	396	2	34	34	NUM
ejpam-5720	396	3	]	]	X
ejpam-5720	396	4	t.	t.	PROPN
ejpam-5720	396	5	duangphui	duangphui	PROPN
ejpam-5720	396	6	,	,	PUNCT
ejpam-5720	396	7	c.	c.	PROPN
ejpam-5720	396	8	boonpok	boonpok	PROPN
ejpam-5720	396	9	,	,	PUNCT
ejpam-5720	396	10	and	and	CCONJ
ejpam-5720	396	11	c.	c.	PROPN
ejpam-5720	396	12	viriyapong	viriyapong	PROPN
ejpam-5720	396	13	.	.	PUNCT
ejpam-5720	397	1	continuous	continuous	ADJ
ejpam-5720	397	2	functions	function	NOUN
ejpam-5720	397	3	on	on	ADP
ejpam-5720	397	4	bigeneralized	bigeneralize	VERB
ejpam-5720	397	5	topological	topological	ADJ
ejpam-5720	397	6	spaces	space	NOUN
ejpam-5720	397	7	.	.	PUNCT
ejpam-5720	398	1	international	international	ADJ
ejpam-5720	398	2	journal	journal	PROPN
ejpam-5720	398	3	of	of	ADP
ejpam-5720	398	4	mathematical	mathematical	ADJ
ejpam-5720	398	5	analysis	analysis	NOUN
ejpam-5720	398	6	,	,	PUNCT
ejpam-5720	398	7	5(24):1165	5(24):1165	NUM
ejpam-5720	398	8	–	–	PUNCT
ejpam-5720	398	9	1174	1174	NUM
ejpam-5720	398	10	,	,	PUNCT
ejpam-5720	398	11	2011	2011	NUM
ejpam-5720	398	12	.	.	PUNCT
ejpam-5720	399	1	[	[	X
ejpam-5720	399	2	35	35	NUM
ejpam-5720	399	3	]	]	PUNCT
ejpam-5720	399	4	t.	t.	NOUN
ejpam-5720	399	5	dungthaisong	dungthaisong	PROPN
ejpam-5720	399	6	,	,	PUNCT
ejpam-5720	399	7	c.	c.	PROPN
ejpam-5720	399	8	boonpok	boonpok	PROPN
ejpam-5720	399	9	,	,	PUNCT
ejpam-5720	399	10	and	and	CCONJ
ejpam-5720	399	11	c.	c.	PROPN
ejpam-5720	399	12	viriyapong	viriyapong	PROPN
ejpam-5720	399	13	.	.	PUNCT
ejpam-5720	400	1	generalized	generalize	VERB
ejpam-5720	400	2	closed	close	VERB
ejpam-5720	400	3	sets	set	NOUN
ejpam-5720	400	4	in	in	ADP
ejpam-5720	400	5	bigeneralized	bigeneralize	VERB
ejpam-5720	400	6	topological	topological	ADJ
ejpam-5720	400	7	spaces	space	NOUN
ejpam-5720	400	8	.	.	PUNCT
ejpam-5720	401	1	international	international	ADJ
ejpam-5720	401	2	journal	journal	PROPN
ejpam-5720	401	3	of	of	ADP
ejpam-5720	401	4	mathematical	mathematical	ADJ
ejpam-5720	401	5	analysis	analysis	NOUN
ejpam-5720	401	6	,	,	PUNCT
ejpam-5720	401	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5720	401	8	,	,	PUNCT
ejpam-5720	401	9	2011	2011	NUM
ejpam-5720	401	10	.	.	PUNCT
ejpam-5720	402	1	[	[	X
ejpam-5720	402	2	36	36	NUM
ejpam-5720	402	3	]	]	X
ejpam-5720	402	4	e.	e.	PROPN
ejpam-5720	402	5	ekici	ekici	PROPN
ejpam-5720	402	6	.	.	PUNCT
ejpam-5720	403	1	nearly	nearly	ADV
ejpam-5720	403	2	continuous	continuous	ADJ
ejpam-5720	403	3	multifunctions	multifunction	NOUN
ejpam-5720	403	4	.	.	PUNCT
ejpam-5720	404	1	acta	acta	PROPN
ejpam-5720	404	2	mathematica	mathematica	PROPN
ejpam-5720	404	3	universitatis	universitatis	PROPN
ejpam-5720	404	4	comenianae	comenianae	PROPN
ejpam-5720	404	5	,	,	PUNCT
ejpam-5720	404	6	72:229–235	72:229–235	PROPN
ejpam-5720	404	7	,	,	PUNCT
ejpam-5720	404	8	2003	2003	NUM
ejpam-5720	404	9	.	.	PUNCT
ejpam-5720	405	1	[	[	X
ejpam-5720	405	2	37	37	NUM
ejpam-5720	405	3	]	]	PUNCT
ejpam-5720	405	4	e.	e.	PROPN
ejpam-5720	405	5	ekici	ekici	PROPN
ejpam-5720	405	6	.	.	PUNCT
ejpam-5720	406	1	almost	almost	ADV
ejpam-5720	406	2	nearly	nearly	ADV
ejpam-5720	406	3	continuous	continuous	ADJ
ejpam-5720	406	4	multifunctions	multifunction	NOUN
ejpam-5720	406	5	.	.	PUNCT
ejpam-5720	407	1	acta	acta	PROPN
ejpam-5720	407	2	mathematica	mathematica	PROPN
ejpam-5720	407	3	universitatis	universitatis	PROPN
ejpam-5720	407	4	comenianae	comenianae	PROPN
ejpam-5720	407	5	,	,	PUNCT
ejpam-5720	407	6	73:175–186	73:175–186	PROPN
ejpam-5720	407	7	,	,	PUNCT
ejpam-5720	407	8	2004	2004	NUM
ejpam-5720	407	9	.	.	PUNCT
ejpam-5720	408	1	[	[	X
ejpam-5720	408	2	38	38	NUM
ejpam-5720	408	3	]	]	PUNCT
ejpam-5720	408	4	j.	j.	PROPN
ejpam-5720	408	5	khampakdee	khampakdee	PROPN
ejpam-5720	408	6	and	and	CCONJ
ejpam-5720	408	7	c.	c.	PROPN
ejpam-5720	408	8	boonpok	boonpok	PROPN
ejpam-5720	408	9	.	.	PUNCT
ejpam-5720	409	1	upper	upper	ADJ
ejpam-5720	409	2	and	and	CCONJ
ejpam-5720	409	3	lower	low	ADJ
ejpam-5720	409	4	α(λ	α(λ	PROPN
ejpam-5720	409	5	,	,	PUNCT
ejpam-5720	409	6	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	409	7	multifunctions	multifunction	NOUN
ejpam-5720	409	8	.	.	PUNCT
ejpam-5720	410	1	wseas	wseas	VERB
ejpam-5720	410	2	transactions	transaction	NOUN
ejpam-5720	410	3	on	on	ADP
ejpam-5720	410	4	mathematics	mathematic	NOUN
ejpam-5720	410	5	,	,	PUNCT
ejpam-5720	410	6	21:684–690	21:684–690	NUM
ejpam-5720	410	7	,	,	PUNCT
ejpam-5720	410	8	2022	2022	NUM
ejpam-5720	410	9	.	.	PUNCT
ejpam-5720	411	1	[	[	X
ejpam-5720	411	2	39	39	NUM
ejpam-5720	411	3	]	]	PUNCT
ejpam-5720	411	4	j.	j.	PROPN
ejpam-5720	411	5	khampakdee	khampakdee	PROPN
ejpam-5720	411	6	,	,	PUNCT
ejpam-5720	411	7	s.	s.	PROPN
ejpam-5720	411	8	sompong	sompong	PROPN
ejpam-5720	411	9	,	,	PUNCT
ejpam-5720	411	10	and	and	CCONJ
ejpam-5720	411	11	c.	c.	PROPN
ejpam-5720	411	12	boonpok	boonpok	PROPN
ejpam-5720	411	13	.	.	PUNCT
ejpam-5720	412	1	c-(τ1	c-(τ1	PROPN
ejpam-5720	412	2	,	,	PUNCT
ejpam-5720	412	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5720	412	4	for	for	ADP
ejpam-5720	412	5	multifuncj	multifuncj	NOUN
ejpam-5720	412	6	.	.	PUNCT
ejpam-5720	413	1	khampakdee	khampakdee	PROPN
ejpam-5720	413	2	,	,	PUNCT
ejpam-5720	413	3	a.	a.	PROPN
ejpam-5720	413	4	sama	sama	PROPN
ejpam-5720	413	5	-	-	PUNCT
ejpam-5720	413	6	ae	ae	PROPN
ejpam-5720	413	7	,	,	PUNCT
ejpam-5720	413	8	c.	c.	PROPN
ejpam-5720	413	9	boonpok	boonpok	PROPN
ejpam-5720	413	10	/	/	SYM
ejpam-5720	413	11	eur	eur	PROPN
ejpam-5720	413	12	.	.	PUNCT
ejpam-5720	414	1	j.	j.	PROPN
ejpam-5720	414	2	pure	pure	PROPN
ejpam-5720	414	3	appl	appl	PROPN
ejpam-5720	414	4	.	.	PROPN
ejpam-5720	414	5	math	math	PROPN
ejpam-5720	414	6	,	,	PUNCT
ejpam-5720	414	7	18	18	NUM
ejpam-5720	414	8	(	(	PUNCT
ejpam-5720	414	9	1	1	NUM
ejpam-5720	414	10	)	)	PUNCT
ejpam-5720	414	11	(	(	PUNCT
ejpam-5720	414	12	2025	2025	NUM
ejpam-5720	414	13	)	)	PUNCT
ejpam-5720	414	14	,	,	PUNCT
ejpam-5720	414	15	5720	5720	NUM
ejpam-5720	414	16	14	14	NUM
ejpam-5720	414	17	of	of	ADP
ejpam-5720	414	18	15	15	NUM
ejpam-5720	414	19	tions	tion	NOUN
ejpam-5720	414	20	.	.	PUNCT
ejpam-5720	415	1	european	european	ADJ
ejpam-5720	415	2	journal	journal	PROPN
ejpam-5720	415	3	of	of	ADP
ejpam-5720	415	4	pure	pure	ADJ
ejpam-5720	415	5	and	and	CCONJ
ejpam-5720	415	6	applied	applied	ADJ
ejpam-5720	415	7	mathematics	mathematic	NOUN
ejpam-5720	415	8	,	,	PUNCT
ejpam-5720	415	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-5720	415	10	,	,	PUNCT
ejpam-5720	415	11	2024	2024	NUM
ejpam-5720	415	12	.	.	PUNCT
ejpam-5720	416	1	[	[	X
ejpam-5720	416	2	40	40	NUM
ejpam-5720	416	3	]	]	X
ejpam-5720	416	4	c.	c.	PROPN
ejpam-5720	416	5	klanarong	klanarong	PROPN
ejpam-5720	416	6	,	,	PUNCT
ejpam-5720	416	7	s.	s.	PROPN
ejpam-5720	416	8	sompong	sompong	PROPN
ejpam-5720	416	9	,	,	PUNCT
ejpam-5720	416	10	and	and	CCONJ
ejpam-5720	416	11	c.	c.	PROPN
ejpam-5720	416	12	boonpok	boonpok	PROPN
ejpam-5720	416	13	.	.	PUNCT
ejpam-5720	417	1	upper	upper	ADJ
ejpam-5720	417	2	and	and	CCONJ
ejpam-5720	417	3	lower	low	ADJ
ejpam-5720	417	4	almost	almost	ADV
ejpam-5720	417	5	(	(	PUNCT
ejpam-5720	417	6	τ1	τ1	NOUN
ejpam-5720	417	7	,	,	PUNCT
ejpam-5720	417	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5720	417	9	multifunctions	multifunction	NOUN
ejpam-5720	417	10	.	.	PUNCT
ejpam-5720	418	1	european	european	ADJ
ejpam-5720	418	2	journal	journal	PROPN
ejpam-5720	418	3	of	of	ADP
ejpam-5720	418	4	pure	pure	ADJ
ejpam-5720	418	5	and	and	CCONJ
ejpam-5720	418	6	applied	applied	ADJ
ejpam-5720	418	7	mathematics	mathematic	NOUN
ejpam-5720	418	8	,	,	PUNCT
ejpam-5720	418	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5720	418	10	,	,	PUNCT
ejpam-5720	418	11	2024	2024	NUM
ejpam-5720	418	12	.	.	PUNCT
ejpam-5720	419	1	[	[	X
ejpam-5720	419	2	41	41	NUM
ejpam-5720	419	3	]	]	X
ejpam-5720	419	4	b.	b.	PROPN
ejpam-5720	419	5	kong	kong	PROPN
ejpam-5720	419	6	-	-	PUNCT
ejpam-5720	419	7	ied	ied	PROPN
ejpam-5720	419	8	,	,	PUNCT
ejpam-5720	419	9	s.	s.	PROPN
ejpam-5720	419	10	sompong	sompong	PROPN
ejpam-5720	419	11	,	,	PUNCT
ejpam-5720	419	12	and	and	CCONJ
ejpam-5720	419	13	c.	c.	PROPN
ejpam-5720	419	14	boonpok	boonpok	PROPN
ejpam-5720	419	15	.	.	PUNCT
ejpam-5720	420	1	almost	almost	ADV
ejpam-5720	420	2	quasi	quasi	X
ejpam-5720	420	3	(	(	PUNCT
ejpam-5720	420	4	τ1	τ1	NOUN
ejpam-5720	420	5	,	,	PUNCT
ejpam-5720	420	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	420	7	functions	function	NOUN
ejpam-5720	420	8	.	.	PUNCT
ejpam-5720	421	1	asia	asia	PROPN
ejpam-5720	421	2	pacific	pacific	PROPN
ejpam-5720	421	3	journal	journal	PROPN
ejpam-5720	421	4	of	of	ADP
ejpam-5720	421	5	mathematics	mathematic	NOUN
ejpam-5720	421	6	,	,	PUNCT
ejpam-5720	421	7	11:64	11:64	NUM
ejpam-5720	421	8	,	,	PUNCT
ejpam-5720	421	9	2024	2024	NUM
ejpam-5720	421	10	.	.	PUNCT
ejpam-5720	422	1	[	[	X
ejpam-5720	422	2	42	42	NUM
ejpam-5720	422	3	]	]	X
ejpam-5720	422	4	n.	n.	PROPN
ejpam-5720	422	5	levine	levine	PROPN
ejpam-5720	422	6	.	.	PUNCT
ejpam-5720	423	1	semi	semi	ADJ
ejpam-5720	423	2	-	-	ADJ
ejpam-5720	423	3	open	open	ADJ
ejpam-5720	423	4	sets	set	NOUN
ejpam-5720	423	5	and	and	CCONJ
ejpam-5720	423	6	semi	semi	ADJ
ejpam-5720	423	7	-	-	NOUN
ejpam-5720	423	8	continuity	continuity	NOUN
ejpam-5720	423	9	in	in	ADP
ejpam-5720	423	10	topological	topological	ADJ
ejpam-5720	423	11	spaces	space	NOUN
ejpam-5720	423	12	.	.	PUNCT
ejpam-5720	424	1	the	the	DET
ejpam-5720	424	2	american	american	PROPN
ejpam-5720	424	3	mathematical	mathematical	PROPN
ejpam-5720	424	4	monthly	monthly	ADV
ejpam-5720	424	5	,	,	PUNCT
ejpam-5720	424	6	70:36–41	70:36–41	NUM
ejpam-5720	424	7	,	,	PUNCT
ejpam-5720	424	8	1963	1963	NUM
ejpam-5720	424	9	.	.	PUNCT
ejpam-5720	425	1	[	[	X
ejpam-5720	425	2	43	43	NUM
ejpam-5720	425	3	]	]	X
ejpam-5720	425	4	s.	s.	PROPN
ejpam-5720	425	5	r.	r.	PROPN
ejpam-5720	425	6	malghan	malghan	PROPN
ejpam-5720	425	7	and	and	CCONJ
ejpam-5720	425	8	v.	v.	ADP
ejpam-5720	425	9	v.	v.	CCONJ
ejpam-5720	425	10	hanchinamani	hanchinamani	PROPN
ejpam-5720	425	11	.	.	PUNCT
ejpam-5720	426	1	n	n	CCONJ
ejpam-5720	426	2	-	-	PUNCT
ejpam-5720	426	3	continuous	continuous	ADJ
ejpam-5720	426	4	functions	function	NOUN
ejpam-5720	426	5	.	.	PUNCT
ejpam-5720	427	1	annales	annales	PROPN
ejpam-5720	427	2	de	de	ADP
ejpam-5720	427	3	la	la	PROPN
ejpam-5720	427	4	société	société	PROPN
ejpam-5720	427	5	scientifique	scientifique	PROPN
ejpam-5720	427	6	de	de	X
ejpam-5720	427	7	bruxelles	bruxelle	NOUN
ejpam-5720	427	8	,	,	PUNCT
ejpam-5720	427	9	98:69–79	98:69–79	ADV
ejpam-5720	427	10	,	,	PUNCT
ejpam-5720	427	11	1984	1984	NUM
ejpam-5720	427	12	.	.	PUNCT
ejpam-5720	428	1	[	[	X
ejpam-5720	428	2	44	44	NUM
ejpam-5720	428	3	]	]	PUNCT
ejpam-5720	428	4	s.	s.	PROPN
ejpam-5720	428	5	marcus	marcus	PROPN
ejpam-5720	428	6	.	.	PUNCT
ejpam-5720	429	1	sur	sur	PROPN
ejpam-5720	429	2	les	les	PROPN
ejpam-5720	429	3	fonctions	fonctions	PROPN
ejpam-5720	429	4	quasicontinues	quasicontinue	NOUN
ejpam-5720	429	5	au	au	PROPN
ejpam-5720	429	6	sens	sens	X
ejpam-5720	429	7	de	de	PROPN
ejpam-5720	429	8	s.	s.	PROPN
ejpam-5720	429	9	kempisty	kempisty	PROPN
ejpam-5720	429	10	.	.	PUNCT
ejpam-5720	430	1	colloquium	colloquium	NOUN
ejpam-5720	430	2	mathematicum	mathematicum	PROPN
ejpam-5720	430	3	,	,	PUNCT
ejpam-5720	430	4	8:47–53	8:47–53	NUM
ejpam-5720	430	5	,	,	PUNCT
ejpam-5720	430	6	1961	1961	NUM
ejpam-5720	430	7	.	.	PUNCT
ejpam-5720	431	1	[	[	X
ejpam-5720	431	2	45	45	NUM
ejpam-5720	431	3	]	]	PUNCT
ejpam-5720	431	4	a.	a.	NOUN
ejpam-5720	431	5	neubrunnová.	neubrunnová.	PROPN
ejpam-5720	431	6	on	on	ADP
ejpam-5720	431	7	certain	certain	ADJ
ejpam-5720	431	8	generalizations	generalization	NOUN
ejpam-5720	431	9	of	of	ADP
ejpam-5720	431	10	the	the	DET
ejpam-5720	431	11	notion	notion	NOUN
ejpam-5720	431	12	of	of	ADP
ejpam-5720	431	13	continuity	continuity	NOUN
ejpam-5720	431	14	.	.	PUNCT
ejpam-5720	432	1	matematický	matematický	ADJ
ejpam-5720	432	2	časopis	časopis	PROPN
ejpam-5720	432	3	,	,	PUNCT
ejpam-5720	432	4	23:374–380	23:374–380	NUM
ejpam-5720	432	5	,	,	PUNCT
ejpam-5720	432	6	1973	1973	NUM
ejpam-5720	432	7	.	.	PUNCT
ejpam-5720	433	1	[	[	X
ejpam-5720	433	2	46	46	NUM
ejpam-5720	433	3	]	]	PUNCT
ejpam-5720	433	4	t.	t.	PROPN
ejpam-5720	433	5	noiri	noiri	PROPN
ejpam-5720	433	6	and	and	CCONJ
ejpam-5720	433	7	n.	n.	PROPN
ejpam-5720	433	8	ergun	ergun	PROPN
ejpam-5720	433	9	.	.	PUNCT
ejpam-5720	434	1	notes	note	NOUN
ejpam-5720	434	2	on	on	ADP
ejpam-5720	434	3	n	n	CCONJ
ejpam-5720	434	4	-	-	PUNCT
ejpam-5720	434	5	continuous	continuous	ADJ
ejpam-5720	434	6	functions	function	NOUN
ejpam-5720	434	7	.	.	PUNCT
ejpam-5720	435	1	research	research	NOUN
ejpam-5720	435	2	reports	report	NOUN
ejpam-5720	435	3	of	of	ADP
ejpam-5720	435	4	yatsushiro	yatsushiro	PROPN
ejpam-5720	435	5	national	national	PROPN
ejpam-5720	435	6	college	college	PROPN
ejpam-5720	435	7	of	of	ADP
ejpam-5720	435	8	technology	technology	NOUN
ejpam-5720	435	9	,	,	PUNCT
ejpam-5720	435	10	11:65–68	11:65–68	NUM
ejpam-5720	435	11	,	,	PUNCT
ejpam-5720	435	12	1989	1989	NUM
ejpam-5720	435	13	.	.	PUNCT
ejpam-5720	436	1	[	[	X
ejpam-5720	436	2	47	47	NUM
ejpam-5720	436	3	]	]	PUNCT
ejpam-5720	436	4	t.	t.	PROPN
ejpam-5720	436	5	noiri	noiri	PROPN
ejpam-5720	436	6	and	and	CCONJ
ejpam-5720	436	7	v.	v.	ADP
ejpam-5720	436	8	popa	popa	NOUN
ejpam-5720	436	9	.	.	PUNCT
ejpam-5720	437	1	a	a	DET
ejpam-5720	437	2	unified	unified	ADJ
ejpam-5720	437	3	theory	theory	NOUN
ejpam-5720	437	4	of	of	ADP
ejpam-5720	437	5	upper	upper	ADJ
ejpam-5720	437	6	and	and	CCONJ
ejpam-5720	437	7	lower	low	ADJ
ejpam-5720	437	8	almost	almost	ADV
ejpam-5720	437	9	nearly	nearly	ADV
ejpam-5720	437	10	continuous	continuous	ADJ
ejpam-5720	437	11	multifunctions	multifunction	NOUN
ejpam-5720	437	12	.	.	PUNCT
ejpam-5720	438	1	mathematica	mathematica	PROPN
ejpam-5720	438	2	balkanica	balkanica	PROPN
ejpam-5720	438	3	,	,	PUNCT
ejpam-5720	438	4	23:51–72	23:51–72	PROPN
ejpam-5720	438	5	,	,	PUNCT
ejpam-5720	438	6	2009	2009	NUM
ejpam-5720	438	7	.	.	PUNCT
ejpam-5720	439	1	[	[	X
ejpam-5720	439	2	48	48	NUM
ejpam-5720	439	3	]	]	PUNCT
ejpam-5720	439	4	v.	v.	CCONJ
ejpam-5720	439	5	popa	popa	NOUN
ejpam-5720	439	6	.	.	PUNCT
ejpam-5720	440	1	almost	almost	ADV
ejpam-5720	440	2	continuous	continuous	ADJ
ejpam-5720	440	3	multifunctions	multifunction	NOUN
ejpam-5720	440	4	.	.	PUNCT
ejpam-5720	441	1	matematički	matematički	PROPN
ejpam-5720	441	2	vesnik	vesnik	PROPN
ejpam-5720	441	3	,	,	PUNCT
ejpam-5720	441	4	34:75–84	34:75–84	NUM
ejpam-5720	441	5	,	,	PUNCT
ejpam-5720	441	6	1982	1982	NUM
ejpam-5720	441	7	.	.	PUNCT
ejpam-5720	442	1	[	[	X
ejpam-5720	442	2	49	49	X
ejpam-5720	442	3	]	]	PUNCT
ejpam-5720	442	4	v.	v.	CCONJ
ejpam-5720	442	5	popa	popa	NOUN
ejpam-5720	442	6	and	and	CCONJ
ejpam-5720	442	7	noiri	noiri	NOUN
ejpam-5720	442	8	.	.	PUNCT
ejpam-5720	443	1	on	on	ADP
ejpam-5720	443	2	upper	upper	ADJ
ejpam-5720	443	3	and	and	CCONJ
ejpam-5720	443	4	lower	low	ADJ
ejpam-5720	443	5	almost	almost	ADV
ejpam-5720	443	6	quasi	quasi	ADJ
ejpam-5720	443	7	continuous	continuous	ADJ
ejpam-5720	443	8	multifunctions	multifunction	NOUN
ejpam-5720	443	9	.	.	PUNCT
ejpam-5720	444	1	bulletin	bulletin	NOUN
ejpam-5720	444	2	of	of	ADP
ejpam-5720	444	3	the	the	DET
ejpam-5720	444	4	institute	institute	PROPN
ejpam-5720	444	5	of	of	ADP
ejpam-5720	444	6	mathematics	mathematics	PROPN
ejpam-5720	444	7	academia	academia	PROPN
ejpam-5720	444	8	sinica	sinica	PROPN
ejpam-5720	444	9	,	,	PUNCT
ejpam-5720	444	10	21:337–349	21:337–349	NUM
ejpam-5720	444	11	,	,	PUNCT
ejpam-5720	444	12	1993	1993	NUM
ejpam-5720	444	13	.	.	PUNCT
ejpam-5720	445	1	[	[	X
ejpam-5720	445	2	50	50	NUM
ejpam-5720	445	3	]	]	PUNCT
ejpam-5720	445	4	v.	v.	CCONJ
ejpam-5720	445	5	popa	popa	NOUN
ejpam-5720	445	6	and	and	CCONJ
ejpam-5720	445	7	t.	t.	NOUN
ejpam-5720	445	8	noiri	noiri	PROPN
ejpam-5720	445	9	.	.	PUNCT
ejpam-5720	446	1	almost	almost	ADV
ejpam-5720	446	2	quasi	quasi	VERB
ejpam-5720	446	3	continuous	continuous	ADJ
ejpam-5720	446	4	multifunctions	multifunction	NOUN
ejpam-5720	446	5	.	.	PUNCT
ejpam-5720	447	1	tatra	tatra	PROPN
ejpam-5720	447	2	mountains	mountains	PROPN
ejpam-5720	447	3	mathematical	mathematical	ADJ
ejpam-5720	447	4	publications	publication	NOUN
ejpam-5720	447	5	,	,	PUNCT
ejpam-5720	447	6	14:81–90	14:81–90	PROPN
ejpam-5720	447	7	,	,	PUNCT
ejpam-5720	447	8	1998	1998	NUM
ejpam-5720	447	9	.	.	PUNCT
ejpam-5720	448	1	[	[	X
ejpam-5720	448	2	51	51	NUM
ejpam-5720	448	3	]	]	PUNCT
ejpam-5720	448	4	c.	c.	NOUN
ejpam-5720	448	5	prachanpol	prachanpol	NOUN
ejpam-5720	448	6	,	,	PUNCT
ejpam-5720	448	7	c.	c.	PROPN
ejpam-5720	448	8	boonpok	boonpok	PROPN
ejpam-5720	448	9	,	,	PUNCT
ejpam-5720	448	10	and	and	CCONJ
ejpam-5720	448	11	c.	c.	PROPN
ejpam-5720	448	12	viriyapong	viriyapong	PROPN
ejpam-5720	448	13	.	.	PUNCT
ejpam-5720	449	1	δ(τ1	δ(τ1	PROPN
ejpam-5720	449	2	,	,	PUNCT
ejpam-5720	449	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	449	4	functions	function	NOUN
ejpam-5720	449	5	.	.	PUNCT
ejpam-5720	450	1	european	european	ADJ
ejpam-5720	450	2	journal	journal	PROPN
ejpam-5720	450	3	of	of	ADP
ejpam-5720	450	4	pure	pure	ADJ
ejpam-5720	450	5	and	and	CCONJ
ejpam-5720	450	6	applied	applied	ADJ
ejpam-5720	450	7	mathematics	mathematic	NOUN
ejpam-5720	450	8	,	,	PUNCT
ejpam-5720	450	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-5720	450	10	,	,	PUNCT
ejpam-5720	450	11	2024	2024	NUM
ejpam-5720	450	12	.	.	PUNCT
ejpam-5720	451	1	[	[	X
ejpam-5720	451	2	52	52	NUM
ejpam-5720	451	3	]	]	PUNCT
ejpam-5720	451	4	p.	p.	NOUN
ejpam-5720	451	5	pue	pue	NOUN
ejpam-5720	451	6	-	-	PUNCT
ejpam-5720	451	7	on	on	ADP
ejpam-5720	451	8	and	and	CCONJ
ejpam-5720	451	9	c.	c.	PROPN
ejpam-5720	451	10	boonpok	boonpok	PROPN
ejpam-5720	451	11	.	.	PUNCT
ejpam-5720	452	1	θ(λ	θ(λ	PROPN
ejpam-5720	452	2	,	,	PUNCT
ejpam-5720	452	3	p)-continuity	p)-continuity	NOUN
ejpam-5720	452	4	for	for	ADP
ejpam-5720	452	5	functions	function	NOUN
ejpam-5720	452	6	.	.	PUNCT
ejpam-5720	453	1	international	international	ADJ
ejpam-5720	453	2	journal	journal	NOUN
ejpam-5720	453	3	of	of	ADP
ejpam-5720	453	4	mathematics	mathematic	NOUN
ejpam-5720	453	5	and	and	CCONJ
ejpam-5720	453	6	computer	computer	NOUN
ejpam-5720	453	7	science	science	NOUN
ejpam-5720	453	8	,	,	PUNCT
ejpam-5720	453	9	19(2):491–495	19(2):491–495	NUM
ejpam-5720	453	10	,	,	PUNCT
ejpam-5720	453	11	2024	2024	NUM
ejpam-5720	453	12	.	.	PUNCT
ejpam-5720	454	1	[	[	X
ejpam-5720	454	2	53	53	NUM
ejpam-5720	454	3	]	]	PUNCT
ejpam-5720	454	4	p.	p.	NOUN
ejpam-5720	454	5	pue	pue	NOUN
ejpam-5720	454	6	-	-	PUNCT
ejpam-5720	454	7	on	on	ADP
ejpam-5720	454	8	,	,	PUNCT
ejpam-5720	454	9	a.	a.	PROPN
ejpam-5720	454	10	sama	sama	PROPN
ejpam-5720	454	11	-	-	PUNCT
ejpam-5720	454	12	ae	ae	PROPN
ejpam-5720	454	13	,	,	PUNCT
ejpam-5720	454	14	and	and	CCONJ
ejpam-5720	454	15	c.	c.	PROPN
ejpam-5720	454	16	boonpok	boonpok	PROPN
ejpam-5720	454	17	.	.	PUNCT
ejpam-5720	455	1	c	c	X
ejpam-5720	455	2	-	-	PUNCT
ejpam-5720	455	3	quasi	quasi	X
ejpam-5720	455	4	(	(	PUNCT
ejpam-5720	455	5	τ1	τ1	PROPN
ejpam-5720	455	6	,	,	PUNCT
ejpam-5720	455	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	455	8	multifunctions	multifunction	NOUN
ejpam-5720	455	9	.	.	PUNCT
ejpam-5720	456	1	european	european	ADJ
ejpam-5720	456	2	journal	journal	PROPN
ejpam-5720	456	3	of	of	ADP
ejpam-5720	456	4	pure	pure	ADJ
ejpam-5720	456	5	and	and	CCONJ
ejpam-5720	456	6	applied	applied	ADJ
ejpam-5720	456	7	mathematics	mathematic	NOUN
ejpam-5720	456	8	,	,	PUNCT
ejpam-5720	456	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-5720	456	10	,	,	PUNCT
ejpam-5720	456	11	2024	2024	NUM
ejpam-5720	456	12	.	.	PUNCT
ejpam-5720	457	1	[	[	X
ejpam-5720	457	2	54	54	NUM
ejpam-5720	457	3	]	]	PUNCT
ejpam-5720	457	4	p.	p.	NOUN
ejpam-5720	457	5	pue	pue	NOUN
ejpam-5720	457	6	-	-	PUNCT
ejpam-5720	457	7	on	on	ADP
ejpam-5720	457	8	,	,	PUNCT
ejpam-5720	457	9	s.	s.	PROPN
ejpam-5720	457	10	sompong	sompong	PROPN
ejpam-5720	457	11	,	,	PUNCT
ejpam-5720	457	12	and	and	CCONJ
ejpam-5720	457	13	c.	c.	PROPN
ejpam-5720	457	14	boonpok	boonpok	PROPN
ejpam-5720	457	15	.	.	PUNCT
ejpam-5720	458	1	almost	almost	ADV
ejpam-5720	458	2	quasi	quasi	X
ejpam-5720	458	3	(	(	PUNCT
ejpam-5720	458	4	τ1	τ1	NOUN
ejpam-5720	458	5	,	,	PUNCT
ejpam-5720	458	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5720	458	7	for	for	ADP
ejpam-5720	458	8	multifunctions	multifunction	NOUN
ejpam-5720	458	9	.	.	PUNCT
ejpam-5720	459	1	international	international	ADJ
ejpam-5720	459	2	journal	journal	NOUN
ejpam-5720	459	3	of	of	ADP
ejpam-5720	459	4	analysis	analysis	NOUN
ejpam-5720	459	5	and	and	CCONJ
ejpam-5720	459	6	applications	application	NOUN
ejpam-5720	459	7	,	,	PUNCT
ejpam-5720	459	8	22:97	22:97	NUM
ejpam-5720	459	9	,	,	PUNCT
ejpam-5720	459	10	2024	2024	NUM
ejpam-5720	459	11	.	.	PUNCT
ejpam-5720	460	1	[	[	X
ejpam-5720	460	2	55	55	NUM
ejpam-5720	460	3	]	]	X
ejpam-5720	460	4	p.	p.	NOUN
ejpam-5720	460	5	pue	pue	NOUN
ejpam-5720	460	6	-	-	PUNCT
ejpam-5720	460	7	on	on	ADP
ejpam-5720	460	8	,	,	PUNCT
ejpam-5720	460	9	s.	s.	PROPN
ejpam-5720	460	10	sompong	sompong	PROPN
ejpam-5720	460	11	,	,	PUNCT
ejpam-5720	460	12	and	and	CCONJ
ejpam-5720	460	13	c.	c.	PROPN
ejpam-5720	460	14	boonpok	boonpok	PROPN
ejpam-5720	460	15	.	.	PUNCT
ejpam-5720	461	1	upper	upper	ADJ
ejpam-5720	461	2	and	and	CCONJ
ejpam-5720	461	3	lower	low	ADJ
ejpam-5720	461	4	(	(	PUNCT
ejpam-5720	461	5	τ1	τ1	NOUN
ejpam-5720	461	6	,	,	PUNCT
ejpam-5720	461	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	461	8	mulfunctions	mulfunction	NOUN
ejpam-5720	461	9	.	.	PUNCT
ejpam-5720	462	1	international	international	ADJ
ejpam-5720	462	2	journal	journal	NOUN
ejpam-5720	462	3	of	of	ADP
ejpam-5720	462	4	mathematics	mathematic	NOUN
ejpam-5720	462	5	and	and	CCONJ
ejpam-5720	462	6	computer	computer	NOUN
ejpam-5720	462	7	science	science	NOUN
ejpam-5720	462	8	,	,	PUNCT
ejpam-5720	462	9	19(4):1305	19(4):1305	NUM
ejpam-5720	462	10	–	–	PUNCT
ejpam-5720	462	11	1310	1310	NUM
ejpam-5720	462	12	,	,	PUNCT
ejpam-5720	462	13	2024	2024	NUM
ejpam-5720	462	14	.	.	PUNCT
ejpam-5720	463	1	[	[	X
ejpam-5720	463	2	56	56	NUM
ejpam-5720	463	3	]	]	X
ejpam-5720	463	4	p.	p.	NOUN
ejpam-5720	463	5	pue	pue	NOUN
ejpam-5720	463	6	-	-	PUNCT
ejpam-5720	463	7	on	on	ADP
ejpam-5720	463	8	,	,	PUNCT
ejpam-5720	463	9	s.	s.	PROPN
ejpam-5720	463	10	sompong	sompong	PROPN
ejpam-5720	463	11	,	,	PUNCT
ejpam-5720	463	12	and	and	CCONJ
ejpam-5720	463	13	c.	c.	PROPN
ejpam-5720	463	14	boonpok	boonpok	PROPN
ejpam-5720	463	15	.	.	PUNCT
ejpam-5720	464	1	weakly	weakly	ADJ
ejpam-5720	464	2	quasi	quasi	NOUN
ejpam-5720	464	3	(	(	PUNCT
ejpam-5720	464	4	τ1	τ1	PROPN
ejpam-5720	464	5	,	,	PUNCT
ejpam-5720	464	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	464	7	multifunctions	multifunction	NOUN
ejpam-5720	464	8	.	.	PUNCT
ejpam-5720	465	1	european	european	ADJ
ejpam-5720	465	2	journal	journal	PROPN
ejpam-5720	465	3	of	of	ADP
ejpam-5720	465	4	pure	pure	ADJ
ejpam-5720	465	5	and	and	CCONJ
ejpam-5720	465	6	applied	applied	ADJ
ejpam-5720	465	7	mathematics	mathematic	NOUN
ejpam-5720	465	8	,	,	PUNCT
ejpam-5720	465	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-5720	465	10	,	,	PUNCT
ejpam-5720	465	11	2024	2024	NUM
ejpam-5720	465	12	.	.	PUNCT
ejpam-5720	466	1	[	[	X
ejpam-5720	466	2	57	57	NUM
ejpam-5720	466	3	]	]	X
ejpam-5720	466	4	p.	p.	NOUN
ejpam-5720	466	5	pue	pue	NOUN
ejpam-5720	466	6	-	-	PUNCT
ejpam-5720	466	7	on	on	ADP
ejpam-5720	466	8	,	,	PUNCT
ejpam-5720	466	9	s.	s.	PROPN
ejpam-5720	466	10	sompong	sompong	PROPN
ejpam-5720	466	11	,	,	PUNCT
ejpam-5720	466	12	and	and	CCONJ
ejpam-5720	466	13	c.	c.	PROPN
ejpam-5720	466	14	boonpok	boonpok	PROPN
ejpam-5720	466	15	.	.	PUNCT
ejpam-5720	467	1	slightly	slightly	ADV
ejpam-5720	467	2	(	(	PUNCT
ejpam-5720	467	3	τ1	τ1	NOUN
ejpam-5720	467	4	,	,	PUNCT
ejpam-5720	467	5	τ2)s	τ2)s	ADJ
ejpam-5720	467	6	-	-	PUNCT
ejpam-5720	467	7	continuous	continuous	ADJ
ejpam-5720	467	8	functions	function	NOUN
ejpam-5720	467	9	.	.	PUNCT
ejpam-5720	468	1	international	international	ADJ
ejpam-5720	468	2	journal	journal	NOUN
ejpam-5720	468	3	of	of	ADP
ejpam-5720	468	4	mathematics	mathematic	NOUN
ejpam-5720	468	5	and	and	CCONJ
ejpam-5720	468	6	computer	computer	NOUN
ejpam-5720	468	7	science	science	NOUN
ejpam-5720	468	8	,	,	PUNCT
ejpam-5720	468	9	20(1):217–221	20(1):217–221	PROPN
ejpam-5720	468	10	,	,	PUNCT
ejpam-5720	468	11	2025	2025	NUM
ejpam-5720	468	12	.	.	PUNCT
ejpam-5720	469	1	[	[	X
ejpam-5720	469	2	58	58	NUM
ejpam-5720	469	3	]	]	PUNCT
ejpam-5720	469	4	e.	e.	PROPN
ejpam-5720	469	5	rosas	rosas	PROPN
ejpam-5720	469	6	,	,	PUNCT
ejpam-5720	469	7	c.	c.	PROPN
ejpam-5720	469	8	carpintero	carpintero	PROPN
ejpam-5720	469	9	,	,	PUNCT
ejpam-5720	469	10	and	and	CCONJ
ejpam-5720	469	11	j.	j.	PROPN
ejpam-5720	469	12	moreno	moreno	PROPN
ejpam-5720	469	13	.	.	PUNCT
ejpam-5720	470	1	more	more	ADV
ejpam-5720	470	2	on	on	ADP
ejpam-5720	470	3	upper	upper	ADJ
ejpam-5720	470	4	and	and	CCONJ
ejpam-5720	470	5	lower	low	ADJ
ejpam-5720	470	6	almost	almost	ADV
ejpam-5720	470	7	nearly	nearly	ADV
ejpam-5720	470	8	icontinuous	icontinuous	ADJ
ejpam-5720	470	9	multifunctions	multifunction	NOUN
ejpam-5720	470	10	.	.	PUNCT
ejpam-5720	471	1	international	international	ADJ
ejpam-5720	471	2	journal	journal	NOUN
ejpam-5720	471	3	of	of	ADP
ejpam-5720	471	4	pure	pure	ADJ
ejpam-5720	471	5	and	and	CCONJ
ejpam-5720	471	6	applied	applied	ADJ
ejpam-5720	471	7	mathematics	mathematic	NOUN
ejpam-5720	471	8	,	,	PUNCT
ejpam-5720	471	9	117(3):521–537	117(3):521–537	NUM
ejpam-5720	471	10	,	,	PUNCT
ejpam-5720	471	11	2017	2017	NUM
ejpam-5720	471	12	.	.	PUNCT
ejpam-5720	472	1	[	[	X
ejpam-5720	472	2	59	59	NUM
ejpam-5720	472	3	]	]	PUNCT
ejpam-5720	472	4	a.	a.	NOUN
ejpam-5720	472	5	rychlewicz	rychlewicz	NOUN
ejpam-5720	472	6	.	.	PUNCT
ejpam-5720	473	1	on	on	ADP
ejpam-5720	473	2	almost	almost	ADV
ejpam-5720	473	3	nearly	nearly	ADV
ejpam-5720	473	4	continuous	continuous	ADJ
ejpam-5720	473	5	functions	function	NOUN
ejpam-5720	473	6	with	with	ADP
ejpam-5720	473	7	reference	reference	NOUN
ejpam-5720	473	8	to	to	ADP
ejpam-5720	473	9	multifunctions	multifunction	NOUN
ejpam-5720	473	10	.	.	PUNCT
ejpam-5720	474	1	tatra	tatra	PROPN
ejpam-5720	474	2	mountains	mountains	PROPN
ejpam-5720	474	3	mathematical	mathematical	ADJ
ejpam-5720	474	4	publications	publication	NOUN
ejpam-5720	474	5	,	,	PUNCT
ejpam-5720	474	6	42:61–72	42:61–72	NUM
ejpam-5720	474	7	,	,	PUNCT
ejpam-5720	474	8	2009	2009	NUM
ejpam-5720	474	9	.	.	PUNCT
ejpam-5720	475	1	j.	j.	PROPN
ejpam-5720	475	2	khampakdee	khampakdee	PROPN
ejpam-5720	475	3	,	,	PUNCT
ejpam-5720	475	4	a.	a.	PROPN
ejpam-5720	475	5	sama	sama	PROPN
ejpam-5720	475	6	-	-	PUNCT
ejpam-5720	475	7	ae	ae	PROPN
ejpam-5720	475	8	,	,	PUNCT
ejpam-5720	475	9	c.	c.	PROPN
ejpam-5720	475	10	boonpok	boonpok	PROPN
ejpam-5720	475	11	/	/	SYM
ejpam-5720	475	12	eur	eur	PROPN
ejpam-5720	475	13	.	.	PUNCT
ejpam-5720	476	1	j.	j.	PROPN
ejpam-5720	476	2	pure	pure	PROPN
ejpam-5720	476	3	appl	appl	PROPN
ejpam-5720	476	4	.	.	PROPN
ejpam-5720	476	5	math	math	PROPN
ejpam-5720	476	6	,	,	PUNCT
ejpam-5720	476	7	18	18	NUM
ejpam-5720	476	8	(	(	PUNCT
ejpam-5720	476	9	1	1	NUM
ejpam-5720	476	10	)	)	PUNCT
ejpam-5720	476	11	(	(	PUNCT
ejpam-5720	476	12	2025	2025	NUM
ejpam-5720	476	13	)	)	PUNCT
ejpam-5720	476	14	,	,	PUNCT
ejpam-5720	476	15	5720	5720	NUM
ejpam-5720	476	16	15	15	NUM
ejpam-5720	476	17	of	of	ADP
ejpam-5720	476	18	15	15	NUM
ejpam-5720	476	19	[	[	SYM
ejpam-5720	476	20	60	60	NUM
ejpam-5720	476	21	]	]	X
ejpam-5720	476	22	n.	n.	NOUN
ejpam-5720	476	23	srisarakham	srisarakham	PROPN
ejpam-5720	476	24	and	and	CCONJ
ejpam-5720	476	25	c.	c.	PROPN
ejpam-5720	476	26	boonpok	boonpok	PROPN
ejpam-5720	476	27	.	.	PUNCT
ejpam-5720	477	1	almost	almost	ADV
ejpam-5720	477	2	(	(	PUNCT
ejpam-5720	477	3	λ	λ	NOUN
ejpam-5720	477	4	,	,	PUNCT
ejpam-5720	477	5	p)-continuous	p)-continuous	ADJ
ejpam-5720	477	6	functions	function	NOUN
ejpam-5720	477	7	.	.	PUNCT
ejpam-5720	478	1	international	international	ADJ
ejpam-5720	478	2	journal	journal	PROPN
ejpam-5720	478	3	of	of	ADP
ejpam-5720	478	4	mathematics	mathematic	NOUN
ejpam-5720	478	5	and	and	CCONJ
ejpam-5720	478	6	computer	computer	NOUN
ejpam-5720	478	7	science	science	NOUN
ejpam-5720	478	8	,	,	PUNCT
ejpam-5720	478	9	18(2):255–259	18(2):255–259	NUM
ejpam-5720	478	10	,	,	PUNCT
ejpam-5720	478	11	2023	2023	NUM
ejpam-5720	478	12	.	.	PUNCT
ejpam-5720	479	1	[	[	X
ejpam-5720	479	2	61	61	NUM
ejpam-5720	479	3	]	]	X
ejpam-5720	479	4	n.	n.	NOUN
ejpam-5720	479	5	srisarakham	srisarakham	PROPN
ejpam-5720	479	6	,	,	PUNCT
ejpam-5720	479	7	a.	a.	PROPN
ejpam-5720	479	8	sama	sama	PROPN
ejpam-5720	479	9	-	-	PUNCT
ejpam-5720	479	10	ae	ae	PROPN
ejpam-5720	479	11	,	,	PUNCT
ejpam-5720	479	12	and	and	CCONJ
ejpam-5720	479	13	c.	c.	PROPN
ejpam-5720	479	14	boonpok	boonpok	PROPN
ejpam-5720	479	15	.	.	PUNCT
ejpam-5720	480	1	characterizations	characterization	NOUN
ejpam-5720	480	2	of	of	ADP
ejpam-5720	480	3	faintly	faintly	ADV
ejpam-5720	480	4	(	(	PUNCT
ejpam-5720	480	5	τ1	τ1	PROPN
ejpam-5720	480	6	,	,	PUNCT
ejpam-5720	480	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	480	8	functions	function	NOUN
ejpam-5720	480	9	.	.	PUNCT
ejpam-5720	481	1	european	european	ADJ
ejpam-5720	481	2	journal	journal	PROPN
ejpam-5720	481	3	of	of	ADP
ejpam-5720	481	4	pure	pure	ADJ
ejpam-5720	481	5	and	and	CCONJ
ejpam-5720	481	6	applied	applied	ADJ
ejpam-5720	481	7	mathematics	mathematic	NOUN
ejpam-5720	481	8	,	,	PUNCT
ejpam-5720	481	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-5720	481	10	,	,	PUNCT
ejpam-5720	481	11	2024	2024	NUM
ejpam-5720	481	12	.	.	PUNCT
ejpam-5720	482	1	[	[	X
ejpam-5720	482	2	62	62	NUM
ejpam-5720	482	3	]	]	PUNCT
ejpam-5720	482	4	m.	m.	NOUN
ejpam-5720	482	5	thongmoon	thongmoon	NOUN
ejpam-5720	482	6	and	and	CCONJ
ejpam-5720	482	7	c.	c.	PROPN
ejpam-5720	482	8	boonpok	boonpok	PROPN
ejpam-5720	482	9	.	.	PUNCT
ejpam-5720	483	1	upper	upper	ADJ
ejpam-5720	483	2	and	and	CCONJ
ejpam-5720	483	3	lower	low	ADJ
ejpam-5720	483	4	almost	almost	ADV
ejpam-5720	483	5	β(λ	β(λ	NOUN
ejpam-5720	483	6	,	,	PUNCT
ejpam-5720	483	7	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	483	8	multifunctions	multifunction	NOUN
ejpam-5720	483	9	.	.	PUNCT
ejpam-5720	484	1	wseas	wseas	VERB
ejpam-5720	484	2	transactions	transaction	NOUN
ejpam-5720	484	3	on	on	ADP
ejpam-5720	484	4	mathematics	mathematic	NOUN
ejpam-5720	484	5	,	,	PUNCT
ejpam-5720	484	6	21:844–853	21:844–853	NUM
ejpam-5720	484	7	,	,	PUNCT
ejpam-5720	484	8	2022	2022	NUM
ejpam-5720	484	9	.	.	PUNCT
ejpam-5720	485	1	[	[	X
ejpam-5720	485	2	63	63	NUM
ejpam-5720	485	3	]	]	PUNCT
ejpam-5720	485	4	m.	m.	NOUN
ejpam-5720	485	5	thongmoon	thongmoon	NOUN
ejpam-5720	485	6	and	and	CCONJ
ejpam-5720	485	7	c.	c.	PROPN
ejpam-5720	485	8	boonpok	boonpok	PROPN
ejpam-5720	485	9	.	.	PUNCT
ejpam-5720	486	1	strongly	strongly	ADV
ejpam-5720	486	2	θ(λ	θ(λ	PROPN
ejpam-5720	486	3	,	,	PUNCT
ejpam-5720	486	4	p)-continuous	p)-continuous	ADJ
ejpam-5720	486	5	functions	function	NOUN
ejpam-5720	486	6	.	.	PUNCT
ejpam-5720	487	1	international	international	ADJ
ejpam-5720	487	2	journal	journal	PROPN
ejpam-5720	487	3	of	of	ADP
ejpam-5720	487	4	mathematics	mathematic	NOUN
ejpam-5720	487	5	and	and	CCONJ
ejpam-5720	487	6	computer	computer	NOUN
ejpam-5720	487	7	science	science	NOUN
ejpam-5720	487	8	,	,	PUNCT
ejpam-5720	487	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5720	487	10	,	,	PUNCT
ejpam-5720	487	11	2024	2024	NUM
ejpam-5720	487	12	.	.	PUNCT
ejpam-5720	488	1	[	[	X
ejpam-5720	488	2	64	64	NUM
ejpam-5720	488	3	]	]	PUNCT
ejpam-5720	488	4	m.	m.	NOUN
ejpam-5720	488	5	thongmoon	thongmoon	NOUN
ejpam-5720	488	6	,	,	PUNCT
ejpam-5720	488	7	a.	a.	PROPN
ejpam-5720	488	8	sama	sama	PROPN
ejpam-5720	488	9	-	-	PUNCT
ejpam-5720	488	10	ae	ae	PROPN
ejpam-5720	488	11	,	,	PUNCT
ejpam-5720	488	12	and	and	CCONJ
ejpam-5720	488	13	c.	c.	PROPN
ejpam-5720	488	14	boonpok	boonpok	PROPN
ejpam-5720	488	15	.	.	PUNCT
ejpam-5720	489	1	upper	upper	ADJ
ejpam-5720	489	2	and	and	CCONJ
ejpam-5720	489	3	lower	low	ADJ
ejpam-5720	489	4	near	near	ADV
ejpam-5720	489	5	(	(	PUNCT
ejpam-5720	489	6	τ1	τ1	NOUN
ejpam-5720	489	7	,	,	PUNCT
ejpam-5720	489	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5720	489	9	.	.	PUNCT
ejpam-5720	490	1	(	(	PUNCT
ejpam-5720	490	2	accepted	accept	VERB
ejpam-5720	490	3	)	)	PUNCT
ejpam-5720	490	4	.	.	PUNCT
ejpam-5720	491	1	[	[	X
ejpam-5720	491	2	65	65	NUM
ejpam-5720	491	3	]	]	X
ejpam-5720	491	4	m.	m.	NOUN
ejpam-5720	491	5	thongmoon	thongmoon	NOUN
ejpam-5720	491	6	,	,	PUNCT
ejpam-5720	491	7	s.	s.	PROPN
ejpam-5720	491	8	sompong	sompong	PROPN
ejpam-5720	491	9	,	,	PUNCT
ejpam-5720	491	10	and	and	CCONJ
ejpam-5720	491	11	c.	c.	PROPN
ejpam-5720	491	12	boonpok	boonpok	PROPN
ejpam-5720	491	13	.	.	PUNCT
ejpam-5720	492	1	upper	upper	ADJ
ejpam-5720	492	2	and	and	CCONJ
ejpam-5720	492	3	lower	low	ADJ
ejpam-5720	492	4	weak	weak	ADJ
ejpam-5720	492	5	(	(	PUNCT
ejpam-5720	492	6	τ1	τ1	NOUN
ejpam-5720	492	7	,	,	PUNCT
ejpam-5720	492	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5720	492	9	.	.	PUNCT
ejpam-5720	493	1	european	european	PROPN
ejpam-5720	493	2	journal	journal	PROPN
ejpam-5720	493	3	of	of	ADP
ejpam-5720	493	4	pure	pure	ADJ
ejpam-5720	493	5	and	and	CCONJ
ejpam-5720	493	6	applied	applied	ADJ
ejpam-5720	493	7	mathematics	mathematic	NOUN
ejpam-5720	493	8	,	,	PUNCT
ejpam-5720	493	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5720	493	10	,	,	PUNCT
ejpam-5720	493	11	2024	2024	NUM
ejpam-5720	493	12	.	.	PUNCT
ejpam-5720	494	1	[	[	X
ejpam-5720	494	2	66	66	NUM
ejpam-5720	494	3	]	]	PUNCT
ejpam-5720	494	4	m.	m.	NOUN
ejpam-5720	494	5	thongmoon	thongmoon	NOUN
ejpam-5720	494	6	,	,	PUNCT
ejpam-5720	494	7	s.	s.	PROPN
ejpam-5720	494	8	sompong	sompong	PROPN
ejpam-5720	494	9	,	,	PUNCT
ejpam-5720	494	10	and	and	CCONJ
ejpam-5720	494	11	c.	c.	PROPN
ejpam-5720	494	12	boonpok	boonpok	PROPN
ejpam-5720	494	13	.	.	PUNCT
ejpam-5720	495	1	rarely	rarely	ADV
ejpam-5720	495	2	(	(	PUNCT
ejpam-5720	495	3	τ1	τ1	NOUN
ejpam-5720	495	4	,	,	PUNCT
ejpam-5720	495	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5720	495	6	functions	function	NOUN
ejpam-5720	495	7	.	.	PUNCT
ejpam-5720	496	1	international	international	ADJ
ejpam-5720	496	2	journal	journal	NOUN
ejpam-5720	496	3	of	of	ADP
ejpam-5720	496	4	mathematics	mathematic	NOUN
ejpam-5720	496	5	and	and	CCONJ
ejpam-5720	496	6	computer	computer	NOUN
ejpam-5720	496	7	science	science	NOUN
ejpam-5720	496	8	,	,	PUNCT
ejpam-5720	496	9	20(1):423–427	20(1):423–427	NUM
ejpam-5720	496	10	,	,	PUNCT
ejpam-5720	496	11	2025	2025	NUM
ejpam-5720	496	12	.	.	PUNCT
ejpam-5720	497	1	[	[	X
ejpam-5720	497	2	67	67	NUM
ejpam-5720	497	3	]	]	X
ejpam-5720	497	4	c.	c.	PROPN
ejpam-5720	497	5	viriyapong	viriyapong	PROPN
ejpam-5720	497	6	and	and	CCONJ
ejpam-5720	497	7	c.	c.	PROPN
ejpam-5720	497	8	boonpok	boonpok	PROPN
ejpam-5720	497	9	.	.	PUNCT
ejpam-5720	498	1	(	(	PUNCT
ejpam-5720	498	2	τ1	τ1	NOUN
ejpam-5720	498	3	,	,	PUNCT
ejpam-5720	498	4	τ2)α	τ2)α	NOUN
ejpam-5720	498	5	-	-	PUNCT
ejpam-5720	498	6	continuity	continuity	NOUN
ejpam-5720	498	7	for	for	ADP
ejpam-5720	498	8	multifunctions	multifunction	NOUN
ejpam-5720	498	9	.	.	PUNCT
ejpam-5720	499	1	journal	journal	PROPN
ejpam-5720	499	2	of	of	ADP
ejpam-5720	499	3	mathematics	mathematic	NOUN
ejpam-5720	499	4	,	,	PUNCT
ejpam-5720	499	5	2020:6285763	2020:6285763	NUM
ejpam-5720	499	6	,	,	PUNCT
ejpam-5720	499	7	2020	2020	NUM
ejpam-5720	499	8	.	.	PUNCT
ejpam-5720	500	1	[	[	X
ejpam-5720	500	2	68	68	NUM
ejpam-5720	500	3	]	]	X
ejpam-5720	500	4	c.	c.	PROPN
ejpam-5720	500	5	viriyapong	viriyapong	PROPN
ejpam-5720	500	6	and	and	CCONJ
ejpam-5720	500	7	c.	c.	PROPN
ejpam-5720	500	8	boonpok	boonpok	PROPN
ejpam-5720	500	9	.	.	PUNCT
ejpam-5720	501	1	(	(	PUNCT
ejpam-5720	501	2	λ	λ	X
ejpam-5720	501	3	,	,	PUNCT
ejpam-5720	501	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5720	501	5	functions	function	NOUN
ejpam-5720	501	6	.	.	PUNCT
ejpam-5720	502	1	wseas	wseas	VERB
ejpam-5720	502	2	transactions	transaction	NOUN
ejpam-5720	502	3	on	on	ADP
ejpam-5720	502	4	mathematics	mathematic	NOUN
ejpam-5720	502	5	,	,	PUNCT
ejpam-5720	502	6	21:380–385	21:380–385	NUM
ejpam-5720	502	7	,	,	PUNCT
ejpam-5720	502	8	2022	2022	NUM
ejpam-5720	502	9	.	.	PUNCT
ejpam-5720	503	1	[	[	X
ejpam-5720	503	2	69	69	NUM
ejpam-5720	503	3	]	]	X
ejpam-5720	503	4	c.	c.	PROPN
ejpam-5720	503	5	viriyapong	viriyapong	PROPN
ejpam-5720	503	6	and	and	CCONJ
ejpam-5720	503	7	c.	c.	PROPN
ejpam-5720	503	8	boonpok	boonpok	PROPN
ejpam-5720	503	9	.	.	PUNCT
ejpam-5720	504	1	weak	weak	ADJ
ejpam-5720	504	2	quasi	quasi	NOUN
ejpam-5720	504	3	(	(	PUNCT
ejpam-5720	504	4	λ	λ	PROPN
ejpam-5720	504	5	,	,	PUNCT
ejpam-5720	504	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5720	504	7	for	for	ADP
ejpam-5720	504	8	multifunctions	multifunction	NOUN
ejpam-5720	504	9	.	.	PUNCT
ejpam-5720	505	1	international	international	ADJ
ejpam-5720	505	2	journal	journal	PROPN
ejpam-5720	505	3	of	of	ADP
ejpam-5720	505	4	mathematics	mathematic	NOUN
ejpam-5720	505	5	and	and	CCONJ
ejpam-5720	505	6	computer	computer	NOUN
ejpam-5720	505	7	science	science	NOUN
ejpam-5720	505	8	,	,	PUNCT
ejpam-5720	505	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5720	505	10	,	,	PUNCT
ejpam-5720	505	11	2022	2022	NUM
ejpam-5720	505	12	.	.	PUNCT
ejpam-5720	506	1	[	[	X
ejpam-5720	506	2	70	70	NUM
ejpam-5720	506	3	]	]	X
ejpam-5720	506	4	c.	c.	PROPN
ejpam-5720	506	5	viriyapong	viriyapong	PROPN
ejpam-5720	506	6	,	,	PUNCT
ejpam-5720	506	7	s.	s.	PROPN
ejpam-5720	506	8	sompong	sompong	PROPN
ejpam-5720	506	9	,	,	PUNCT
ejpam-5720	506	10	and	and	CCONJ
ejpam-5720	506	11	c.	c.	PROPN
ejpam-5720	506	12	boonpok	boonpok	PROPN
ejpam-5720	506	13	.	.	PUNCT
ejpam-5720	507	1	upper	upper	ADJ
ejpam-5720	507	2	and	and	CCONJ
ejpam-5720	507	3	lower	low	ADJ
ejpam-5720	507	4	slight	slight	ADJ
ejpam-5720	507	5	(	(	PUNCT
ejpam-5720	507	6	τ1	τ1	NOUN
ejpam-5720	507	7	,	,	PUNCT
ejpam-5720	507	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5720	507	9	.	.	PUNCT
ejpam-5720	508	1	european	european	PROPN
ejpam-5720	508	2	journal	journal	PROPN
ejpam-5720	508	3	of	of	ADP
ejpam-5720	508	4	pure	pure	ADJ
ejpam-5720	508	5	and	and	CCONJ
ejpam-5720	508	6	applied	applied	ADJ
ejpam-5720	508	7	mathematics	mathematic	NOUN
ejpam-5720	508	8	,	,	PUNCT
ejpam-5720	508	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-5720	508	10	,	,	PUNCT
ejpam-5720	508	11	2024	2024	NUM
ejpam-5720	508	12	.	.	PUNCT
ejpam-5720	509	1	[	[	X
ejpam-5720	509	2	71	71	NUM
ejpam-5720	509	3	]	]	X
ejpam-5720	509	4	n.	n.	PROPN
ejpam-5720	509	5	viriyapong	viriyapong	PROPN
ejpam-5720	509	6	,	,	PUNCT
ejpam-5720	509	7	s.	s.	PROPN
ejpam-5720	509	8	sompong	sompong	PROPN
ejpam-5720	509	9	,	,	PUNCT
ejpam-5720	509	10	and	and	CCONJ
ejpam-5720	509	11	c.	c.	PROPN
ejpam-5720	509	12	boonpok	boonpok	PROPN
ejpam-5720	509	13	.	.	PUNCT
ejpam-5720	510	1	slightly	slightly	ADV
ejpam-5720	510	2	(	(	PUNCT
ejpam-5720	510	3	τ1	τ1	NOUN
ejpam-5720	510	4	,	,	PUNCT
ejpam-5720	510	5	τ2)p	τ2)p	ADJ
ejpam-5720	510	6	-	-	ADJ
ejpam-5720	510	7	continuous	continuous	ADJ
ejpam-5720	510	8	multifunctions	multifunction	NOUN
ejpam-5720	510	9	.	.	PUNCT
ejpam-5720	511	1	international	international	ADJ
ejpam-5720	511	2	journal	journal	NOUN
ejpam-5720	511	3	of	of	ADP
ejpam-5720	511	4	analysis	analysis	NOUN
ejpam-5720	511	5	and	and	CCONJ
ejpam-5720	511	6	applications	application	NOUN
ejpam-5720	511	7	,	,	PUNCT
ejpam-5720	511	8	22:152	22:152	NUM
ejpam-5720	511	9	,	,	PUNCT
ejpam-5720	511	10	2024	2024	NUM
ejpam-5720	511	11	.	.	PUNCT
ejpam-5720	512	1	[	[	X
ejpam-5720	512	2	72	72	NUM
ejpam-5720	512	3	]	]	X
ejpam-5720	512	4	n.	n.	PROPN
ejpam-5720	512	5	viriyapong	viriyapong	PROPN
ejpam-5720	512	6	,	,	PUNCT
ejpam-5720	512	7	s.	s.	PROPN
ejpam-5720	512	8	sompong	sompong	PROPN
ejpam-5720	512	9	,	,	PUNCT
ejpam-5720	512	10	and	and	CCONJ
ejpam-5720	512	11	c.	c.	PROPN
ejpam-5720	512	12	boonpok	boonpok	PROPN
ejpam-5720	512	13	.	.	PUNCT
ejpam-5720	513	1	(	(	PUNCT
ejpam-5720	513	2	τ1	τ1	NOUN
ejpam-5720	513	3	,	,	PUNCT
ejpam-5720	513	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5720	513	5	disconnectedness	disconnectedness	NOUN
ejpam-5720	513	6	in	in	ADP
ejpam-5720	513	7	bitopological	bitopological	ADJ
ejpam-5720	513	8	spaces	space	NOUN
ejpam-5720	513	9	.	.	PUNCT
ejpam-5720	514	1	international	international	ADJ
ejpam-5720	514	2	journal	journal	PROPN
ejpam-5720	514	3	of	of	ADP
ejpam-5720	514	4	mathematics	mathematic	NOUN
ejpam-5720	514	5	and	and	CCONJ
ejpam-5720	514	6	computer	computer	NOUN
ejpam-5720	514	7	science	science	NOUN
ejpam-5720	514	8	,	,	PUNCT
ejpam-5720	514	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5720	514	10	,	,	PUNCT
ejpam-5720	514	11	2024	2024	NUM
ejpam-5720	514	12	.	.	PUNCT
ejpam-5720	515	1	[	[	X
ejpam-5720	515	2	73	73	NUM
ejpam-5720	515	3	]	]	X
ejpam-5720	515	4	n.	n.	PROPN
ejpam-5720	515	5	viriyapong	viriyapong	PROPN
ejpam-5720	515	6	,	,	PUNCT
ejpam-5720	515	7	s.	s.	PROPN
ejpam-5720	515	8	sompong	sompong	PROPN
ejpam-5720	515	9	,	,	PUNCT
ejpam-5720	515	10	and	and	CCONJ
ejpam-5720	515	11	c.	c.	PROPN
ejpam-5720	515	12	boonpok	boonpok	PROPN
ejpam-5720	515	13	.	.	PUNCT
ejpam-5720	516	1	upper	upper	ADJ
ejpam-5720	516	2	and	and	CCONJ
ejpam-5720	516	3	lower	low	ADJ
ejpam-5720	516	4	s-(τ1	s-(τ1	NOUN
ejpam-5720	516	5	,	,	PUNCT
ejpam-5720	516	6	τ2)p	τ2)p	ADJ
ejpam-5720	516	7	-	-	PUNCT
ejpam-5720	516	8	continuous	continuous	ADJ
ejpam-5720	516	9	multifunctions	multifunction	NOUN
ejpam-5720	516	10	.	.	PUNCT
ejpam-5720	517	1	european	european	ADJ
ejpam-5720	517	2	journal	journal	PROPN
ejpam-5720	517	3	of	of	ADP
ejpam-5720	517	4	pure	pure	ADJ
ejpam-5720	517	5	and	and	CCONJ
ejpam-5720	517	6	applied	applied	ADJ
ejpam-5720	517	7	mathematics	mathematic	NOUN
ejpam-5720	517	8	,	,	PUNCT
ejpam-5720	517	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-5720	517	10	,	,	PUNCT
ejpam-5720	517	11	2024	2024	NUM
ejpam-5720	517	12	.	.	PUNCT