id	sid	tid	token	lemma	pos
ejpam-5650	1	1	european	european	PROPN
ejpam-5650	1	2	journal	journal	PROPN
ejpam-5650	1	3	of	of	ADP
ejpam-5650	1	4	pure	pure	ADJ
ejpam-5650	1	5	and	and	CCONJ
ejpam-5650	1	6	applied	applied	ADJ
ejpam-5650	1	7	mathematics	mathematic	NOUN
ejpam-5650	1	8	2025	2025	NUM
ejpam-5650	1	9	,	,	PUNCT
ejpam-5650	1	10	vol	vol	NOUN
ejpam-5650	1	11	.	.	PROPN
ejpam-5650	1	12	18	18	NUM
ejpam-5650	1	13	,	,	PUNCT
ejpam-5650	1	14	issue	issue	NOUN
ejpam-5650	1	15	1	1	NUM
ejpam-5650	1	16	,	,	PUNCT
ejpam-5650	1	17	article	article	NOUN
ejpam-5650	1	18	number	number	NOUN
ejpam-5650	1	19	5650	5650	NUM
ejpam-5650	1	20	issn	issn	PROPN
ejpam-5650	1	21	1307	1307	NUM
ejpam-5650	1	22	-	-	SYM
ejpam-5650	1	23	5543	5543	NUM
ejpam-5650	1	24	–	–	PUNCT
ejpam-5650	1	25	ejpam.com	ejpam.com	X
ejpam-5650	1	26	published	publish	VERB
ejpam-5650	1	27	by	by	ADP
ejpam-5650	1	28	new	new	PROPN
ejpam-5650	1	29	york	york	PROPN
ejpam-5650	1	30	business	business	PROPN
ejpam-5650	1	31	global	global	PROPN
ejpam-5650	1	32	almost	almost	ADV
ejpam-5650	1	33	near	near	ADV
ejpam-5650	1	34	(	(	PUNCT
ejpam-5650	1	35	τ1	τ1	NOUN
ejpam-5650	1	36	,	,	PUNCT
ejpam-5650	1	37	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5650	1	38	for	for	ADP
ejpam-5650	1	39	multifunctions	multifunction	NOUN
ejpam-5650	1	40	nipaporn	nipaporn	ADV
ejpam-5650	1	41	chutiman1	chutiman1	PROPN
ejpam-5650	1	42	,	,	PUNCT
ejpam-5650	1	43	areeyuth	areeyuth	NOUN
ejpam-5650	1	44	sama	sama	NOUN
ejpam-5650	1	45	-	-	PUNCT
ejpam-5650	1	46	ae2	ae2	PROPN
ejpam-5650	1	47	,	,	PUNCT
ejpam-5650	1	48	chawalit	chawalit	VERB
ejpam-5650	1	49	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5650	1	50	1	1	NUM
ejpam-5650	1	51	mathematics	mathematic	NOUN
ejpam-5650	1	52	and	and	CCONJ
ejpam-5650	1	53	applied	apply	VERB
ejpam-5650	1	54	mathematics	mathematics	PROPN
ejpam-5650	1	55	research	research	NOUN
ejpam-5650	1	56	unit	unit	NOUN
ejpam-5650	1	57	,	,	PUNCT
ejpam-5650	1	58	department	department	NOUN
ejpam-5650	1	59	of	of	ADP
ejpam-5650	1	60	mathematics	mathematic	NOUN
ejpam-5650	1	61	,	,	PUNCT
ejpam-5650	1	62	faculty	faculty	NOUN
ejpam-5650	1	63	of	of	ADP
ejpam-5650	1	64	science	science	NOUN
ejpam-5650	1	65	,	,	PUNCT
ejpam-5650	1	66	mahasarakham	mahasarakham	PROPN
ejpam-5650	1	67	university	university	PROPN
ejpam-5650	1	68	,	,	PUNCT
ejpam-5650	1	69	maha	maha	PROPN
ejpam-5650	1	70	sarakham	sarakham	PROPN
ejpam-5650	1	71	,	,	PUNCT
ejpam-5650	1	72	44150	44150	NUM
ejpam-5650	1	73	,	,	PUNCT
ejpam-5650	1	74	thailand	thailand	PROPN
ejpam-5650	1	75	2	2	NUM
ejpam-5650	1	76	department	department	NOUN
ejpam-5650	1	77	of	of	ADP
ejpam-5650	1	78	mathematics	mathematic	NOUN
ejpam-5650	1	79	and	and	CCONJ
ejpam-5650	1	80	computer	computer	NOUN
ejpam-5650	1	81	science	science	NOUN
ejpam-5650	1	82	,	,	PUNCT
ejpam-5650	1	83	faculty	faculty	NOUN
ejpam-5650	1	84	of	of	ADP
ejpam-5650	1	85	science	science	NOUN
ejpam-5650	1	86	and	and	CCONJ
ejpam-5650	1	87	technology	technology	NOUN
ejpam-5650	1	88	,	,	PUNCT
ejpam-5650	1	89	prince	prince	NOUN
ejpam-5650	1	90	of	of	ADP
ejpam-5650	1	91	songkla	songkla	PROPN
ejpam-5650	1	92	university	university	PROPN
ejpam-5650	1	93	,	,	PUNCT
ejpam-5650	1	94	pattani	pattani	NOUN
ejpam-5650	1	95	campus	campus	NOUN
ejpam-5650	1	96	,	,	PUNCT
ejpam-5650	1	97	pattani	pattani	NOUN
ejpam-5650	1	98	,	,	PUNCT
ejpam-5650	1	99	94000	94000	NUM
ejpam-5650	1	100	,	,	PUNCT
ejpam-5650	1	101	thailand	thailand	PROPN
ejpam-5650	1	102	abstract	abstract	PROPN
ejpam-5650	1	103	.	.	PUNCT
ejpam-5650	2	1	this	this	DET
ejpam-5650	2	2	paper	paper	NOUN
ejpam-5650	2	3	presents	present	VERB
ejpam-5650	2	4	new	new	ADJ
ejpam-5650	2	5	classes	class	NOUN
ejpam-5650	2	6	of	of	ADP
ejpam-5650	2	7	multifunctions	multifunction	NOUN
ejpam-5650	2	8	called	call	VERB
ejpam-5650	2	9	upper	upper	ADV
ejpam-5650	2	10	almost	almost	ADV
ejpam-5650	2	11	nearly	nearly	ADV
ejpam-5650	2	12	(	(	PUNCT
ejpam-5650	2	13	τ1	τ1	NOUN
ejpam-5650	2	14	,	,	PUNCT
ejpam-5650	2	15	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	2	16	multifunctions	multifunction	NOUN
ejpam-5650	2	17	and	and	CCONJ
ejpam-5650	2	18	lower	low	ADJ
ejpam-5650	2	19	almost	almost	ADV
ejpam-5650	2	20	nearly	nearly	ADV
ejpam-5650	2	21	(	(	PUNCT
ejpam-5650	2	22	τ1	τ1	NOUN
ejpam-5650	2	23	,	,	PUNCT
ejpam-5650	2	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	2	25	multifunctions	multifunction	NOUN
ejpam-5650	2	26	.	.	PUNCT
ejpam-5650	3	1	moreover	moreover	ADV
ejpam-5650	3	2	,	,	PUNCT
ejpam-5650	3	3	several	several	ADJ
ejpam-5650	3	4	characterizations	characterization	NOUN
ejpam-5650	3	5	and	and	CCONJ
ejpam-5650	3	6	some	some	DET
ejpam-5650	3	7	properties	property	NOUN
ejpam-5650	3	8	concerning	concern	VERB
ejpam-5650	3	9	upper	upper	ADJ
ejpam-5650	3	10	almost	almost	ADV
ejpam-5650	3	11	nearly	nearly	ADV
ejpam-5650	3	12	(	(	PUNCT
ejpam-5650	3	13	τ1	τ1	NOUN
ejpam-5650	3	14	,	,	PUNCT
ejpam-5650	3	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	3	16	multifunctions	multifunction	NOUN
ejpam-5650	3	17	and	and	CCONJ
ejpam-5650	3	18	lower	low	ADJ
ejpam-5650	3	19	almost	almost	ADV
ejpam-5650	3	20	nearly	nearly	ADV
ejpam-5650	3	21	(	(	PUNCT
ejpam-5650	3	22	τ1	τ1	NOUN
ejpam-5650	3	23	,	,	PUNCT
ejpam-5650	3	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	3	25	multifunctions	multifunction	NOUN
ejpam-5650	3	26	are	be	AUX
ejpam-5650	3	27	established	establish	VERB
ejpam-5650	3	28	.	.	PUNCT
ejpam-5650	4	1	2020	2020	NUM
ejpam-5650	4	2	mathematics	mathematics	PROPN
ejpam-5650	4	3	subject	subject	NOUN
ejpam-5650	4	4	classifications	classification	NOUN
ejpam-5650	4	5	:	:	PUNCT
ejpam-5650	4	6	54c08	54c08	NUM
ejpam-5650	4	7	,	,	PUNCT
ejpam-5650	4	8	54c60	54c60	NUM
ejpam-5650	4	9	key	key	ADJ
ejpam-5650	4	10	words	word	NOUN
ejpam-5650	4	11	and	and	CCONJ
ejpam-5650	4	12	phrases	phrase	NOUN
ejpam-5650	4	13	:	:	PUNCT
ejpam-5650	4	14	upper	upper	ADJ
ejpam-5650	4	15	almost	almost	ADV
ejpam-5650	4	16	nearly	nearly	ADV
ejpam-5650	4	17	(	(	PUNCT
ejpam-5650	4	18	τ1	τ1	NOUN
ejpam-5650	4	19	,	,	PUNCT
ejpam-5650	4	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	4	21	multifunction	multifunction	NOUN
ejpam-5650	4	22	,	,	PUNCT
ejpam-5650	4	23	lower	low	ADJ
ejpam-5650	4	24	almost	almost	ADV
ejpam-5650	4	25	nearly	nearly	ADV
ejpam-5650	4	26	(	(	PUNCT
ejpam-5650	4	27	τ1	τ1	NOUN
ejpam-5650	4	28	,	,	PUNCT
ejpam-5650	4	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	4	30	multifunction	multifunction	NOUN
ejpam-5650	4	31	1	1	NUM
ejpam-5650	4	32	.	.	PUNCT
ejpam-5650	4	33	introduction	introduction	NOUN
ejpam-5650	4	34	in	in	ADP
ejpam-5650	4	35	1968	1968	NUM
ejpam-5650	4	36	,	,	PUNCT
ejpam-5650	4	37	singal	singal	NOUN
ejpam-5650	4	38	and	and	CCONJ
ejpam-5650	4	39	singal	singal	ADJ
ejpam-5650	5	1	[	[	X
ejpam-5650	5	2	56	56	NUM
ejpam-5650	5	3	]	]	PUNCT
ejpam-5650	5	4	introduced	introduce	VERB
ejpam-5650	5	5	the	the	DET
ejpam-5650	5	6	concept	concept	NOUN
ejpam-5650	5	7	of	of	ADP
ejpam-5650	5	8	almost	almost	ADV
ejpam-5650	5	9	continuous	continuous	ADJ
ejpam-5650	5	10	functions	function	NOUN
ejpam-5650	5	11	as	as	ADP
ejpam-5650	5	12	a	a	DET
ejpam-5650	5	13	generalization	generalization	NOUN
ejpam-5650	5	14	of	of	ADP
ejpam-5650	5	15	continuity	continuity	NOUN
ejpam-5650	5	16	.	.	PUNCT
ejpam-5650	6	1	popa	popa	NOUN
ejpam-5650	7	1	[	[	X
ejpam-5650	7	2	46	46	NUM
ejpam-5650	7	3	]	]	X
ejpam-5650	7	4	defined	define	VERB
ejpam-5650	7	5	almost	almost	ADV
ejpam-5650	7	6	quasi	quasi	ADJ
ejpam-5650	7	7	-	-	ADJ
ejpam-5650	7	8	continuous	continuous	ADJ
ejpam-5650	7	9	functions	function	NOUN
ejpam-5650	7	10	as	as	ADP
ejpam-5650	7	11	a	a	DET
ejpam-5650	7	12	generalization	generalization	NOUN
ejpam-5650	7	13	of	of	ADP
ejpam-5650	7	14	almost	almost	ADV
ejpam-5650	7	15	continuity	continuity	NOUN
ejpam-5650	7	16	and	and	CCONJ
ejpam-5650	7	17	quasi	quasi	NOUN
ejpam-5650	7	18	-	-	NOUN
ejpam-5650	7	19	continuity	continuity	NOUN
ejpam-5650	7	20	[	[	X
ejpam-5650	7	21	42	42	NUM
ejpam-5650	7	22	]	]	PUNCT
ejpam-5650	7	23	.	.	PUNCT
ejpam-5650	8	1	munshi	munshi	PROPN
ejpam-5650	8	2	and	and	CCONJ
ejpam-5650	8	3	bassan	bassan	NOUN
ejpam-5650	8	4	[	[	X
ejpam-5650	8	5	43	43	NUM
ejpam-5650	8	6	]	]	PUNCT
ejpam-5650	8	7	studied	study	VERB
ejpam-5650	8	8	the	the	DET
ejpam-5650	8	9	notion	notion	NOUN
ejpam-5650	8	10	of	of	ADP
ejpam-5650	8	11	almost	almost	ADV
ejpam-5650	8	12	semi	semi	ADJ
ejpam-5650	8	13	-	-	ADJ
ejpam-5650	8	14	continuous	continuous	ADJ
ejpam-5650	8	15	functions	function	NOUN
ejpam-5650	8	16	.	.	PUNCT
ejpam-5650	9	1	maheshwari	maheshwari	PROPN
ejpam-5650	9	2	et	et	PROPN
ejpam-5650	9	3	al	al	PROPN
ejpam-5650	9	4	.	.	PUNCT
ejpam-5650	10	1	[	[	X
ejpam-5650	10	2	40	40	NUM
ejpam-5650	10	3	]	]	PUNCT
ejpam-5650	10	4	introduced	introduce	VERB
ejpam-5650	10	5	the	the	DET
ejpam-5650	10	6	concept	concept	NOUN
ejpam-5650	10	7	of	of	ADP
ejpam-5650	10	8	almost	almost	ADV
ejpam-5650	10	9	feebly	feebly	ADV
ejpam-5650	10	10	continuous	continuous	ADJ
ejpam-5650	10	11	functions	function	NOUN
ejpam-5650	10	12	as	as	ADP
ejpam-5650	10	13	a	a	DET
ejpam-5650	10	14	generalization	generalization	NOUN
ejpam-5650	10	15	of	of	ADP
ejpam-5650	10	16	almost	almost	ADV
ejpam-5650	10	17	continuity	continuity	NOUN
ejpam-5650	10	18	.	.	PUNCT
ejpam-5650	11	1	in	in	ADP
ejpam-5650	11	2	1984	1984	NUM
ejpam-5650	11	3	,	,	PUNCT
ejpam-5650	11	4	malghan	malghan	NOUN
ejpam-5650	11	5	and	and	CCONJ
ejpam-5650	11	6	hanchinamani	hanchinamani	ADJ
ejpam-5650	11	7	[	[	X
ejpam-5650	11	8	41	41	NUM
ejpam-5650	11	9	]	]	PUNCT
ejpam-5650	11	10	introduced	introduce	VERB
ejpam-5650	11	11	the	the	DET
ejpam-5650	11	12	concept	concept	NOUN
ejpam-5650	11	13	of	of	ADP
ejpam-5650	11	14	n	n	CCONJ
ejpam-5650	11	15	-	-	PUNCT
ejpam-5650	11	16	continuous	continuous	ADJ
ejpam-5650	11	17	functions	function	NOUN
ejpam-5650	11	18	.	.	PUNCT
ejpam-5650	12	1	noiri	noiri	PROPN
ejpam-5650	12	2	and	and	CCONJ
ejpam-5650	12	3	ergun	ergun	NOUN
ejpam-5650	12	4	[	[	X
ejpam-5650	12	5	44	44	NUM
ejpam-5650	12	6	]	]	PUNCT
ejpam-5650	12	7	investigated	investigate	VERB
ejpam-5650	12	8	some	some	DET
ejpam-5650	12	9	characterizations	characterization	NOUN
ejpam-5650	12	10	of	of	ADP
ejpam-5650	12	11	n	n	CCONJ
ejpam-5650	12	12	-	-	PUNCT
ejpam-5650	12	13	continuous	continuous	ADJ
ejpam-5650	12	14	functions	function	NOUN
ejpam-5650	12	15	.	.	PUNCT
ejpam-5650	13	1	ekici	ekici	NOUN
ejpam-5650	14	1	[	[	X
ejpam-5650	14	2	34	34	NUM
ejpam-5650	14	3	]	]	PUNCT
ejpam-5650	14	4	introduced	introduce	VERB
ejpam-5650	14	5	and	and	CCONJ
ejpam-5650	14	6	studied	study	VERB
ejpam-5650	14	7	the	the	DET
ejpam-5650	14	8	concept	concept	NOUN
ejpam-5650	14	9	of	of	ADP
ejpam-5650	14	10	nearly	nearly	ADV
ejpam-5650	14	11	continuous	continuous	ADJ
ejpam-5650	14	12	multifunctions	multifunction	NOUN
ejpam-5650	14	13	as	as	ADP
ejpam-5650	14	14	a	a	DET
ejpam-5650	14	15	generalization	generalization	NOUN
ejpam-5650	14	16	of	of	ADP
ejpam-5650	14	17	semi	semi	ADJ
ejpam-5650	14	18	-	-	ADJ
ejpam-5650	14	19	continuous	continuous	ADJ
ejpam-5650	14	20	multifunctions	multifunction	NOUN
ejpam-5650	14	21	and	and	CCONJ
ejpam-5650	14	22	n	n	CCONJ
ejpam-5650	14	23	-	-	PUNCT
ejpam-5650	14	24	continuous	continuous	ADJ
ejpam-5650	14	25	functions	function	NOUN
ejpam-5650	14	26	.	.	PUNCT
ejpam-5650	15	1	viriyapong	viriyapong	PROPN
ejpam-5650	15	2	and	and	CCONJ
ejpam-5650	15	3	boonpok	boonpok	VERB
ejpam-5650	16	1	[	[	X
ejpam-5650	16	2	65	65	NUM
ejpam-5650	16	3	]	]	PUNCT
ejpam-5650	16	4	investigated	investigate	VERB
ejpam-5650	16	5	some	some	DET
ejpam-5650	16	6	characterizations	characterization	NOUN
ejpam-5650	16	7	of	of	ADP
ejpam-5650	16	8	(	(	PUNCT
ejpam-5650	16	9	λ	λ	PROPN
ejpam-5650	16	10	,	,	PUNCT
ejpam-5650	16	11	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	16	12	functions	function	NOUN
ejpam-5650	16	13	by	by	ADP
ejpam-5650	16	14	utilizing	utilize	VERB
ejpam-5650	16	15	the	the	DET
ejpam-5650	16	16	notions	notion	NOUN
ejpam-5650	16	17	of	of	ADP
ejpam-5650	16	18	(	(	PUNCT
ejpam-5650	16	19	λ	λ	PROPN
ejpam-5650	16	20	,	,	PUNCT
ejpam-5650	16	21	sp)-open	sp)-open	ADJ
ejpam-5650	16	22	sets	set	NOUN
ejpam-5650	16	23	and	and	CCONJ
ejpam-5650	16	24	(	(	PUNCT
ejpam-5650	16	25	λ	λ	PROPN
ejpam-5650	16	26	,	,	PUNCT
ejpam-5650	16	27	sp)-closed	sp)-close	VERB
ejpam-5650	16	28	sets	set	NOUN
ejpam-5650	16	29	due	due	ADP
ejpam-5650	16	30	to	to	ADP
ejpam-5650	16	31	boonpok	boonpok	NOUN
ejpam-5650	16	32	and	and	CCONJ
ejpam-5650	16	33	khampakdee	khampakdee	NOUN
ejpam-5650	16	34	[	[	X
ejpam-5650	16	35	12	12	NUM
ejpam-5650	16	36	]	]	PUNCT
ejpam-5650	16	37	.	.	PUNCT
ejpam-5650	17	1	dungthaisong	dungthaisong	NOUN
ejpam-5650	17	2	et	et	PROPN
ejpam-5650	17	3	al	al	PROPN
ejpam-5650	17	4	.	.	PUNCT
ejpam-5650	18	1	[	[	X
ejpam-5650	18	2	33	33	NUM
ejpam-5650	18	3	]	]	PUNCT
ejpam-5650	18	4	introduced	introduce	VERB
ejpam-5650	18	5	and	and	CCONJ
ejpam-5650	18	6	studied	study	VERB
ejpam-5650	18	7	the	the	DET
ejpam-5650	18	8	concept	concept	NOUN
ejpam-5650	18	9	of	of	ADP
ejpam-5650	18	10	g(m	g(m	ADJ
ejpam-5650	18	11	,	,	PUNCT
ejpam-5650	18	12	n)-continuous	n)-continuous	ADJ
ejpam-5650	18	13	functions	function	NOUN
ejpam-5650	18	14	.	.	PUNCT
ejpam-5650	19	1	duangphui	duangphui	NOUN
ejpam-5650	19	2	et	et	PROPN
ejpam-5650	19	3	al	al	PROPN
ejpam-5650	19	4	.	.	PUNCT
ejpam-5650	20	1	[	[	X
ejpam-5650	20	2	32	32	NUM
ejpam-5650	20	3	]	]	PUNCT
ejpam-5650	20	4	introduced	introduce	VERB
ejpam-5650	20	5	and	and	CCONJ
ejpam-5650	20	6	investigated	investigate	VERB
ejpam-5650	20	7	the	the	DET
ejpam-5650	20	8	notion	notion	NOUN
ejpam-5650	20	9	of	of	ADP
ejpam-5650	20	10	(	(	PUNCT
ejpam-5650	20	11	µ	µ	NOUN
ejpam-5650	20	12	,	,	PUNCT
ejpam-5650	20	13	µ′)(m	µ′)(m	VERB
ejpam-5650	20	14	,	,	PUNCT
ejpam-5650	20	15	n)-continuous	n)-continuous	ADJ
ejpam-5650	20	16	functions	function	NOUN
ejpam-5650	20	17	.	.	PUNCT
ejpam-5650	21	1	furthermore	furthermore	ADV
ejpam-5650	21	2	,	,	PUNCT
ejpam-5650	21	3	several	several	ADJ
ejpam-5650	21	4	characterizations	characterization	NOUN
ejpam-5650	21	5	of	of	ADP
ejpam-5650	21	6	almost	almost	ADV
ejpam-5650	21	7	∗corresponding	∗corresponde	VERB
ejpam-5650	21	8	author	author	NOUN
ejpam-5650	21	9	.	.	PUNCT
ejpam-5650	22	1	doi	doi	NOUN
ejpam-5650	22	2	:	:	PUNCT
ejpam-5650	22	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5650	https://doi.org/10.29020/nybg.ejpam.v18i1.5650	PROPN
ejpam-5650	22	4	email	email	NOUN
ejpam-5650	22	5	addresses	address	NOUN
ejpam-5650	22	6	:	:	PUNCT
ejpam-5650	22	7	nipaporn.c@msu.ac.th	nipaporn.c@msu.ac.th	PROPN
ejpam-5650	22	8	(	(	PUNCT
ejpam-5650	22	9	n.	n.	NOUN
ejpam-5650	22	10	chutiman	chutiman	NOUN
ejpam-5650	22	11	)	)	PUNCT
ejpam-5650	22	12	,	,	PUNCT
ejpam-5650	22	13	areeyuth.s@snru.ac.th	areeyuth.s@snru.ac.th	PROPN
ejpam-5650	22	14	(	(	PUNCT
ejpam-5650	22	15	a.	a.	PROPN
ejpam-5650	22	16	sama	sama	PROPN
ejpam-5650	22	17	-	-	PUNCT
ejpam-5650	22	18	ae	ae	PROPN
ejpam-5650	22	19	)	)	PUNCT
ejpam-5650	22	20	,	,	PUNCT
ejpam-5650	22	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5650	22	22	(	(	PUNCT
ejpam-5650	22	23	c.	c.	PROPN
ejpam-5650	22	24	boonpok	boonpok	PROPN
ejpam-5650	22	25	)	)	PUNCT
ejpam-5650	22	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5650	23	1	1	1	NUM
ejpam-5650	23	2	copyright	copyright	NOUN
ejpam-5650	23	3	:	:	PUNCT
ejpam-5650	23	4	©	©	PROPN
ejpam-5650	23	5	2025	2025	NUM
ejpam-5650	23	6	the	the	DET
ejpam-5650	23	7	author(s	author(s	NOUN
ejpam-5650	23	8	)	)	PUNCT
ejpam-5650	23	9	.	.	PUNCT
ejpam-5650	24	1	(	(	PUNCT
ejpam-5650	24	2	cc	cc	NOUN
ejpam-5650	24	3	by	by	ADP
ejpam-5650	24	4	-	-	PUNCT
ejpam-5650	24	5	nc	nc	PROPN
ejpam-5650	24	6	4.0	4.0	NUM
ejpam-5650	24	7	)	)	PUNCT
ejpam-5650	24	8	n.	n.	NOUN
ejpam-5650	24	9	chutiman	chutiman	NOUN
ejpam-5650	24	10	,	,	PUNCT
ejpam-5650	24	11	a.	a.	PROPN
ejpam-5650	24	12	sama	sama	PROPN
ejpam-5650	24	13	-	-	PUNCT
ejpam-5650	24	14	ae	ae	PROPN
ejpam-5650	24	15	,	,	PUNCT
ejpam-5650	24	16	c.	c.	PROPN
ejpam-5650	24	17	boonpok	boonpok	PROPN
ejpam-5650	24	18	/	/	SYM
ejpam-5650	24	19	eur	eur	PROPN
ejpam-5650	24	20	.	.	PUNCT
ejpam-5650	25	1	j.	j.	PROPN
ejpam-5650	25	2	pure	pure	PROPN
ejpam-5650	25	3	appl	appl	PROPN
ejpam-5650	25	4	.	.	PROPN
ejpam-5650	25	5	math	math	PROPN
ejpam-5650	25	6	,	,	PUNCT
ejpam-5650	25	7	18	18	NUM
ejpam-5650	25	8	(	(	PUNCT
ejpam-5650	25	9	1	1	NUM
ejpam-5650	25	10	)	)	PUNCT
ejpam-5650	25	11	(	(	PUNCT
ejpam-5650	25	12	2025	2025	NUM
ejpam-5650	25	13	)	)	PUNCT
ejpam-5650	25	14	,	,	PUNCT
ejpam-5650	25	15	5650	5650	NUM
ejpam-5650	25	16	2	2	NUM
ejpam-5650	25	17	of	of	ADP
ejpam-5650	25	18	18	18	NUM
ejpam-5650	25	19	(	(	PUNCT
ejpam-5650	25	20	λ	λ	PROPN
ejpam-5650	25	21	,	,	PUNCT
ejpam-5650	25	22	p)-continuous	p)-continuous	ADJ
ejpam-5650	25	23	functions	function	NOUN
ejpam-5650	25	24	,	,	PUNCT
ejpam-5650	25	25	strongly	strongly	ADV
ejpam-5650	25	26	θ(λ	θ(λ	PROPN
ejpam-5650	25	27	,	,	PUNCT
ejpam-5650	25	28	p)-continuous	p)-continuous	ADJ
ejpam-5650	25	29	functions	function	NOUN
ejpam-5650	25	30	,	,	PUNCT
ejpam-5650	25	31	almost	almost	ADV
ejpam-5650	25	32	strongly	strongly	ADV
ejpam-5650	25	33	θ(λ	θ(λ	VERB
ejpam-5650	25	34	,	,	PUNCT
ejpam-5650	25	35	p)continuous	p)continuous	ADJ
ejpam-5650	25	36	functions	function	NOUN
ejpam-5650	25	37	,	,	PUNCT
ejpam-5650	25	38	θ(λ	θ(λ	PROPN
ejpam-5650	25	39	,	,	PUNCT
ejpam-5650	25	40	p)-continuous	p)-continuous	ADJ
ejpam-5650	25	41	functions	function	NOUN
ejpam-5650	25	42	,	,	PUNCT
ejpam-5650	25	43	weakly	weakly	ADJ
ejpam-5650	25	44	(	(	PUNCT
ejpam-5650	25	45	λ	λ	PROPN
ejpam-5650	25	46	,	,	PUNCT
ejpam-5650	25	47	b)-continuous	b)-continuous	ADJ
ejpam-5650	25	48	functions	function	NOUN
ejpam-5650	25	49	,	,	PUNCT
ejpam-5650	25	50	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5650	25	51	functions	function	NOUN
ejpam-5650	25	52	,	,	PUNCT
ejpam-5650	25	53	(	(	PUNCT
ejpam-5650	25	54	λ	λ	NOUN
ejpam-5650	25	55	,	,	PUNCT
ejpam-5650	25	56	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5650	25	57	functions	function	NOUN
ejpam-5650	25	58	,	,	PUNCT
ejpam-5650	25	59	⋆-continuous	⋆-continuous	ADJ
ejpam-5650	25	60	functions	function	NOUN
ejpam-5650	25	61	,	,	PUNCT
ejpam-5650	25	62	θ	θ	PROPN
ejpam-5650	25	63	-	-	ADJ
ejpam-5650	25	64	i	i	VERB
ejpam-5650	25	65	continuous	continuous	ADJ
ejpam-5650	25	66	functions	function	NOUN
ejpam-5650	25	67	,	,	PUNCT
ejpam-5650	25	68	almost	almost	ADV
ejpam-5650	25	69	(	(	PUNCT
ejpam-5650	25	70	g	g	NOUN
ejpam-5650	25	71	,	,	PUNCT
ejpam-5650	25	72	m)-continuous	m)-continuous	ADJ
ejpam-5650	25	73	functions	function	NOUN
ejpam-5650	25	74	,	,	PUNCT
ejpam-5650	25	75	pairwise	pairwise	NOUN
ejpam-5650	25	76	almost	almost	ADV
ejpam-5650	25	77	m	m	VERB
ejpam-5650	25	78	-continuous	-continuous	ADJ
ejpam-5650	25	79	functions	function	NOUN
ejpam-5650	25	80	,	,	PUNCT
ejpam-5650	25	81	(	(	PUNCT
ejpam-5650	25	82	τ1	τ1	NOUN
ejpam-5650	25	83	,	,	PUNCT
ejpam-5650	25	84	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	25	85	functions	function	NOUN
ejpam-5650	25	86	,	,	PUNCT
ejpam-5650	25	87	almost	almost	ADV
ejpam-5650	25	88	(	(	PUNCT
ejpam-5650	25	89	τ1	τ1	NOUN
ejpam-5650	25	90	,	,	PUNCT
ejpam-5650	25	91	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	25	92	functions	function	NOUN
ejpam-5650	25	93	and	and	CCONJ
ejpam-5650	25	94	weakly	weakly	ADJ
ejpam-5650	25	95	(	(	PUNCT
ejpam-5650	25	96	τ1	τ1	NOUN
ejpam-5650	25	97	,	,	PUNCT
ejpam-5650	25	98	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	25	99	functions	function	NOUN
ejpam-5650	25	100	were	be	AUX
ejpam-5650	25	101	presented	present	VERB
ejpam-5650	25	102	in	in	ADP
ejpam-5650	25	103	[	[	X
ejpam-5650	25	104	57	57	NUM
ejpam-5650	25	105	]	]	PUNCT
ejpam-5650	25	106	,	,	PUNCT
ejpam-5650	25	107	[	[	X
ejpam-5650	25	108	60	60	NUM
ejpam-5650	25	109	]	]	PUNCT
ejpam-5650	25	110	,	,	PUNCT
ejpam-5650	25	111	[	[	X
ejpam-5650	25	112	16	16	NUM
ejpam-5650	25	113	]	]	PUNCT
ejpam-5650	25	114	,	,	PUNCT
ejpam-5650	25	115	[	[	X
ejpam-5650	25	116	49	49	NUM
ejpam-5650	25	117	]	]	PUNCT
ejpam-5650	25	118	,	,	PUNCT
ejpam-5650	25	119	[	[	X
ejpam-5650	25	120	25	25	NUM
ejpam-5650	25	121	]	]	PUNCT
ejpam-5650	25	122	,	,	PUNCT
ejpam-5650	25	123	[	[	X
ejpam-5650	25	124	11	11	NUM
ejpam-5650	25	125	]	]	PUNCT
ejpam-5650	25	126	,	,	PUNCT
ejpam-5650	25	127	[	[	X
ejpam-5650	25	128	8	8	NUM
ejpam-5650	25	129	]	]	PUNCT
ejpam-5650	25	130	,	,	PUNCT
ejpam-5650	25	131	[	[	X
ejpam-5650	25	132	10	10	NUM
ejpam-5650	25	133	]	]	PUNCT
ejpam-5650	25	134	,	,	PUNCT
ejpam-5650	25	135	[	[	X
ejpam-5650	25	136	4	4	NUM
ejpam-5650	25	137	]	]	PUNCT
ejpam-5650	25	138	,	,	PUNCT
ejpam-5650	25	139	[	[	X
ejpam-5650	25	140	1	1	NUM
ejpam-5650	25	141	]	]	PUNCT
ejpam-5650	25	142	,	,	PUNCT
ejpam-5650	25	143	[	[	X
ejpam-5650	25	144	2	2	NUM
ejpam-5650	25	145	]	]	PUNCT
ejpam-5650	25	146	,	,	PUNCT
ejpam-5650	25	147	[	[	X
ejpam-5650	25	148	26	26	NUM
ejpam-5650	25	149	]	]	PUNCT
ejpam-5650	25	150	,	,	PUNCT
ejpam-5650	25	151	[	[	X
ejpam-5650	25	152	23	23	NUM
ejpam-5650	25	153	]	]	PUNCT
ejpam-5650	25	154	and	and	CCONJ
ejpam-5650	25	155	[	[	X
ejpam-5650	25	156	18	18	NUM
ejpam-5650	25	157	]	]	PUNCT
ejpam-5650	25	158	,	,	PUNCT
ejpam-5650	25	159	respectively	respectively	ADV
ejpam-5650	25	160	.	.	PUNCT
ejpam-5650	26	1	srisarakham	srisarakham	PROPN
ejpam-5650	26	2	et	et	PROPN
ejpam-5650	26	3	al	al	PROPN
ejpam-5650	26	4	.	.	PUNCT
ejpam-5650	27	1	[	[	X
ejpam-5650	27	2	58	58	NUM
ejpam-5650	27	3	]	]	PUNCT
ejpam-5650	27	4	introduced	introduce	VERB
ejpam-5650	27	5	and	and	CCONJ
ejpam-5650	27	6	studied	study	VERB
ejpam-5650	27	7	the	the	DET
ejpam-5650	27	8	concept	concept	NOUN
ejpam-5650	27	9	of	of	ADP
ejpam-5650	27	10	faintly	faintly	ADV
ejpam-5650	27	11	(	(	PUNCT
ejpam-5650	27	12	τ1	τ1	PROPN
ejpam-5650	27	13	,	,	PUNCT
ejpam-5650	27	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	27	15	functions	function	NOUN
ejpam-5650	27	16	.	.	PUNCT
ejpam-5650	28	1	kong	kong	PROPN
ejpam-5650	28	2	-	-	PUNCT
ejpam-5650	28	3	ied	ied	PROPN
ejpam-5650	28	4	et	et	PROPN
ejpam-5650	28	5	al	al	PROPN
ejpam-5650	28	6	.	.	PUNCT
ejpam-5650	29	1	[	[	X
ejpam-5650	29	2	39	39	NUM
ejpam-5650	29	3	]	]	PUNCT
ejpam-5650	29	4	introduced	introduce	VERB
ejpam-5650	29	5	and	and	CCONJ
ejpam-5650	29	6	investigated	investigate	VERB
ejpam-5650	29	7	the	the	DET
ejpam-5650	29	8	notion	notion	NOUN
ejpam-5650	29	9	of	of	ADP
ejpam-5650	29	10	almost	almost	ADV
ejpam-5650	29	11	quasi	quasi	X
ejpam-5650	29	12	(	(	PUNCT
ejpam-5650	29	13	τ1	τ1	NOUN
ejpam-5650	29	14	,	,	PUNCT
ejpam-5650	29	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	29	16	functions	function	NOUN
ejpam-5650	29	17	.	.	PUNCT
ejpam-5650	30	1	chiangpradit	chiangpradit	NOUN
ejpam-5650	30	2	et	et	PROPN
ejpam-5650	30	3	al	al	PROPN
ejpam-5650	30	4	.	.	PUNCT
ejpam-5650	31	1	[	[	X
ejpam-5650	31	2	31	31	NUM
ejpam-5650	31	3	]	]	PUNCT
ejpam-5650	31	4	introduced	introduce	VERB
ejpam-5650	31	5	and	and	CCONJ
ejpam-5650	31	6	studied	study	VERB
ejpam-5650	31	7	the	the	DET
ejpam-5650	31	8	concept	concept	NOUN
ejpam-5650	31	9	of	of	ADP
ejpam-5650	31	10	weakly	weakly	ADJ
ejpam-5650	31	11	quasi	quasi	NOUN
ejpam-5650	31	12	(	(	PUNCT
ejpam-5650	31	13	τ1	τ1	PROPN
ejpam-5650	31	14	,	,	PUNCT
ejpam-5650	31	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	31	16	functions	function	NOUN
ejpam-5650	31	17	.	.	PUNCT
ejpam-5650	32	1	thongmoon	thongmoon	NOUN
ejpam-5650	32	2	et	et	PROPN
ejpam-5650	32	3	al	al	PROPN
ejpam-5650	32	4	.	.	PUNCT
ejpam-5650	33	1	[	[	X
ejpam-5650	33	2	63	63	NUM
ejpam-5650	33	3	]	]	PUNCT
ejpam-5650	33	4	introduced	introduce	VERB
ejpam-5650	33	5	and	and	CCONJ
ejpam-5650	33	6	investigated	investigate	VERB
ejpam-5650	33	7	the	the	DET
ejpam-5650	33	8	notion	notion	NOUN
ejpam-5650	33	9	of	of	ADP
ejpam-5650	33	10	rarely	rarely	ADV
ejpam-5650	33	11	(	(	PUNCT
ejpam-5650	33	12	τ1	τ1	NOUN
ejpam-5650	33	13	,	,	PUNCT
ejpam-5650	33	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	33	15	functions	function	NOUN
ejpam-5650	33	16	.	.	PUNCT
ejpam-5650	34	1	in	in	ADP
ejpam-5650	34	2	2004	2004	NUM
ejpam-5650	34	3	,	,	PUNCT
ejpam-5650	34	4	ekici	ekici	NOUN
ejpam-5650	34	5	[	[	X
ejpam-5650	34	6	35	35	NUM
ejpam-5650	34	7	]	]	PUNCT
ejpam-5650	34	8	introduced	introduce	VERB
ejpam-5650	34	9	and	and	CCONJ
ejpam-5650	34	10	investigated	investigate	VERB
ejpam-5650	34	11	the	the	DET
ejpam-5650	34	12	notion	notion	NOUN
ejpam-5650	34	13	of	of	ADP
ejpam-5650	34	14	almost	almost	ADV
ejpam-5650	34	15	nearly	nearly	ADV
ejpam-5650	34	16	continuous	continuous	ADJ
ejpam-5650	34	17	multifunctions	multifunction	NOUN
ejpam-5650	34	18	as	as	ADP
ejpam-5650	34	19	a	a	DET
ejpam-5650	34	20	generalization	generalization	NOUN
ejpam-5650	34	21	of	of	ADP
ejpam-5650	34	22	nearly	nearly	ADV
ejpam-5650	34	23	continuous	continuous	ADJ
ejpam-5650	34	24	multifunctions	multifunction	NOUN
ejpam-5650	34	25	and	and	CCONJ
ejpam-5650	34	26	almost	almost	ADV
ejpam-5650	34	27	continuous	continuous	ADJ
ejpam-5650	34	28	multifunctions	multifunction	NOUN
ejpam-5650	34	29	[	[	X
ejpam-5650	34	30	47	47	NUM
ejpam-5650	34	31	]	]	PUNCT
ejpam-5650	34	32	.	.	PUNCT
ejpam-5650	35	1	in	in	ADP
ejpam-5650	35	2	2009	2009	NUM
ejpam-5650	35	3	,	,	PUNCT
ejpam-5650	35	4	noiri	noiri	PRON
ejpam-5650	35	5	and	and	CCONJ
ejpam-5650	35	6	popa	popa	NOUN
ejpam-5650	35	7	[	[	X
ejpam-5650	35	8	45	45	NUM
ejpam-5650	35	9	]	]	PUNCT
ejpam-5650	35	10	introduced	introduce	VERB
ejpam-5650	35	11	and	and	CCONJ
ejpam-5650	35	12	studied	study	VERB
ejpam-5650	35	13	the	the	DET
ejpam-5650	35	14	notion	notion	NOUN
ejpam-5650	35	15	of	of	ADP
ejpam-5650	35	16	almost	almost	ADV
ejpam-5650	35	17	nearlym	nearlym	ADJ
ejpam-5650	35	18	-	-	PUNCT
ejpam-5650	35	19	continuous	continuous	ADJ
ejpam-5650	35	20	multifunctions	multifunction	NOUN
ejpam-5650	35	21	as	as	ADP
ejpam-5650	35	22	multifunctions	multifunction	NOUN
ejpam-5650	35	23	from	from	ADP
ejpam-5650	35	24	a	a	DET
ejpam-5650	35	25	set	set	NOUN
ejpam-5650	35	26	satisfying	satisfy	VERB
ejpam-5650	35	27	some	some	DET
ejpam-5650	35	28	minimal	minimal	ADJ
ejpam-5650	35	29	conditions	condition	NOUN
ejpam-5650	35	30	into	into	ADP
ejpam-5650	35	31	a	a	DET
ejpam-5650	35	32	topological	topological	ADJ
ejpam-5650	35	33	spaces	space	NOUN
ejpam-5650	35	34	.	.	PUNCT
ejpam-5650	36	1	carpintero	carpintero	NOUN
ejpam-5650	36	2	et	et	PROPN
ejpam-5650	36	3	al	al	PROPN
ejpam-5650	36	4	.	.	PUNCT
ejpam-5650	37	1	[	[	X
ejpam-5650	37	2	30	30	NUM
ejpam-5650	37	3	]	]	PUNCT
ejpam-5650	37	4	introduced	introduce	VERB
ejpam-5650	37	5	and	and	CCONJ
ejpam-5650	37	6	studied	study	VERB
ejpam-5650	37	7	the	the	DET
ejpam-5650	37	8	notion	notion	NOUN
ejpam-5650	37	9	of	of	ADP
ejpam-5650	37	10	nearly	nearly	ADV
ejpam-5650	37	11	ω	ω	ADJ
ejpam-5650	37	12	-	-	ADJ
ejpam-5650	37	13	continuous	continuous	ADJ
ejpam-5650	37	14	multifunctions	multifunction	NOUN
ejpam-5650	37	15	as	as	ADP
ejpam-5650	37	16	a	a	DET
ejpam-5650	37	17	weaker	weak	ADJ
ejpam-5650	37	18	form	form	NOUN
ejpam-5650	37	19	of	of	ADP
ejpam-5650	37	20	nearly	nearly	ADV
ejpam-5650	37	21	continuous	continuous	ADJ
ejpam-5650	37	22	multifunctions	multifunction	NOUN
ejpam-5650	37	23	.	.	PUNCT
ejpam-5650	38	1	moreover	moreover	ADV
ejpam-5650	38	2	,	,	PUNCT
ejpam-5650	38	3	several	several	ADJ
ejpam-5650	38	4	characterizations	characterization	NOUN
ejpam-5650	38	5	and	and	CCONJ
ejpam-5650	38	6	some	some	DET
ejpam-5650	38	7	properties	property	NOUN
ejpam-5650	38	8	concerning	concern	VERB
ejpam-5650	38	9	(	(	PUNCT
ejpam-5650	38	10	τ1	τ1	NOUN
ejpam-5650	38	11	,	,	PUNCT
ejpam-5650	38	12	τ2)δ	τ2)δ	ADJ
ejpam-5650	38	13	-	-	PUNCT
ejpam-5650	38	14	semicontinuous	semicontinuous	ADJ
ejpam-5650	38	15	multifunctions	multifunction	NOUN
ejpam-5650	38	16	,	,	PUNCT
ejpam-5650	38	17	almost	almost	ADV
ejpam-5650	38	18	weakly	weakly	ADJ
ejpam-5650	38	19	(	(	PUNCT
ejpam-5650	38	20	τ1	τ1	NOUN
ejpam-5650	38	21	,	,	PUNCT
ejpam-5650	38	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	23	multifunctions	multifunction	NOUN
ejpam-5650	38	24	,	,	PUNCT
ejpam-5650	38	25	weakly	weakly	ADJ
ejpam-5650	38	26	quasi	quasi	NOUN
ejpam-5650	38	27	(	(	PUNCT
ejpam-5650	38	28	λ	λ	PROPN
ejpam-5650	38	29	,	,	PUNCT
ejpam-5650	38	30	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	31	multifunctions	multifunction	NOUN
ejpam-5650	38	32	,	,	PUNCT
ejpam-5650	38	33	⋆-continuous	⋆-continuous	ADJ
ejpam-5650	38	34	multifunctions	multifunction	NOUN
ejpam-5650	38	35	,	,	PUNCT
ejpam-5650	38	36	β(⋆)continuous	β(⋆)continuous	ADJ
ejpam-5650	38	37	multifunctions	multifunction	NOUN
ejpam-5650	38	38	,	,	PUNCT
ejpam-5650	38	39	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5650	38	40	multifunctions	multifunction	NOUN
ejpam-5650	38	41	,	,	PUNCT
ejpam-5650	38	42	almost	almost	ADV
ejpam-5650	38	43	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5650	38	44	multifunctions	multifunction	NOUN
ejpam-5650	38	45	,	,	PUNCT
ejpam-5650	38	46	almost	almost	ADV
ejpam-5650	38	47	quasi	quasi	VERB
ejpam-5650	38	48	⋆-continuous	⋆-continuous	ADJ
ejpam-5650	38	49	multifunctions	multifunction	NOUN
ejpam-5650	38	50	,	,	PUNCT
ejpam-5650	38	51	weakly	weakly	ADJ
ejpam-5650	38	52	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5650	38	53	multifunctions	multifunction	NOUN
ejpam-5650	38	54	,	,	PUNCT
ejpam-5650	38	55	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5650	38	56	multifunctions	multifunction	NOUN
ejpam-5650	38	57	,	,	PUNCT
ejpam-5650	38	58	weakly	weakly	ADJ
ejpam-5650	38	59	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5650	38	60	multifunctions	multifunction	NOUN
ejpam-5650	38	61	,	,	PUNCT
ejpam-5650	38	62	θ(⋆)-quasi	θ(⋆)-quasi	NUM
ejpam-5650	38	63	continuous	continuous	ADJ
ejpam-5650	38	64	multifunctions	multifunction	NOUN
ejpam-5650	38	65	,	,	PUNCT
ejpam-5650	38	66	almost	almost	ADV
ejpam-5650	38	67	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5650	38	68	multifunctions	multifunction	NOUN
ejpam-5650	38	69	,	,	PUNCT
ejpam-5650	38	70	weakly	weakly	ADJ
ejpam-5650	38	71	(	(	PUNCT
ejpam-5650	38	72	λ	λ	NOUN
ejpam-5650	38	73	,	,	PUNCT
ejpam-5650	38	74	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	75	multifunctions	multifunction	NOUN
ejpam-5650	38	76	,	,	PUNCT
ejpam-5650	38	77	α(λ	α(λ	PROPN
ejpam-5650	38	78	,	,	PUNCT
ejpam-5650	38	79	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	80	multifunctions	multifunction	NOUN
ejpam-5650	38	81	,	,	PUNCT
ejpam-5650	38	82	almost	almost	ADV
ejpam-5650	38	83	α(λ	α(λ	PROPN
ejpam-5650	38	84	,	,	PUNCT
ejpam-5650	38	85	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	86	multifunctions	multifunction	NOUN
ejpam-5650	38	87	,	,	PUNCT
ejpam-5650	38	88	weakly	weakly	ADJ
ejpam-5650	38	89	α(λ	α(λ	PROPN
ejpam-5650	38	90	,	,	PUNCT
ejpam-5650	38	91	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	92	multifunctions	multifunction	NOUN
ejpam-5650	38	93	,	,	PUNCT
ejpam-5650	38	94	almost	almost	ADV
ejpam-5650	38	95	β(λ	β(λ	NOUN
ejpam-5650	38	96	,	,	PUNCT
ejpam-5650	38	97	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	98	multifunctions	multifunction	NOUN
ejpam-5650	38	99	,	,	PUNCT
ejpam-5650	38	100	slightly	slightly	ADV
ejpam-5650	38	101	(	(	PUNCT
ejpam-5650	38	102	λ	λ	NOUN
ejpam-5650	38	103	,	,	PUNCT
ejpam-5650	38	104	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	38	105	multifunctions	multifunction	NOUN
ejpam-5650	38	106	,	,	PUNCT
ejpam-5650	38	107	(	(	PUNCT
ejpam-5650	38	108	τ1	τ1	NOUN
ejpam-5650	38	109	,	,	PUNCT
ejpam-5650	38	110	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	111	multifunctions	multifunction	NOUN
ejpam-5650	38	112	,	,	PUNCT
ejpam-5650	38	113	almost	almost	ADV
ejpam-5650	38	114	(	(	PUNCT
ejpam-5650	38	115	τ1	τ1	NOUN
ejpam-5650	38	116	,	,	PUNCT
ejpam-5650	38	117	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	118	multifunctions	multifunction	NOUN
ejpam-5650	38	119	,	,	PUNCT
ejpam-5650	38	120	weakly	weakly	ADJ
ejpam-5650	38	121	(	(	PUNCT
ejpam-5650	38	122	τ1	τ1	NOUN
ejpam-5650	38	123	,	,	PUNCT
ejpam-5650	38	124	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	125	multifunctions	multifunction	NOUN
ejpam-5650	38	126	,	,	PUNCT
ejpam-5650	38	127	weakly	weakly	ADJ
ejpam-5650	38	128	quasi	quasi	NOUN
ejpam-5650	38	129	(	(	PUNCT
ejpam-5650	38	130	τ1	τ1	PROPN
ejpam-5650	38	131	,	,	PUNCT
ejpam-5650	38	132	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	133	multifunctions	multifunction	NOUN
ejpam-5650	38	134	,	,	PUNCT
ejpam-5650	38	135	almost	almost	ADV
ejpam-5650	38	136	quasi	quasi	NOUN
ejpam-5650	38	137	(	(	PUNCT
ejpam-5650	38	138	τ1	τ1	NOUN
ejpam-5650	38	139	,	,	PUNCT
ejpam-5650	38	140	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	141	multifunctions	multifunction	NOUN
ejpam-5650	38	142	,	,	PUNCT
ejpam-5650	38	143	c(τ1	c(τ1	PROPN
ejpam-5650	38	144	,	,	PUNCT
ejpam-5650	38	145	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	146	multifunctions	multifunction	NOUN
ejpam-5650	38	147	,	,	PUNCT
ejpam-5650	38	148	c	c	NOUN
ejpam-5650	38	149	-	-	PUNCT
ejpam-5650	38	150	quasi	quasi	NOUN
ejpam-5650	38	151	(	(	PUNCT
ejpam-5650	38	152	τ1	τ1	PROPN
ejpam-5650	38	153	,	,	PUNCT
ejpam-5650	38	154	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	38	155	multifunctions	multifunction	NOUN
ejpam-5650	38	156	and	and	CCONJ
ejpam-5650	38	157	s-(τ1	s-(τ1	PROPN
ejpam-5650	38	158	,	,	PUNCT
ejpam-5650	38	159	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-5650	38	160	multifunctions	multifunction	NOUN
ejpam-5650	38	161	were	be	AUX
ejpam-5650	38	162	established	establish	VERB
ejpam-5650	38	163	in	in	ADP
ejpam-5650	38	164	[	[	X
ejpam-5650	38	165	5	5	NUM
ejpam-5650	38	166	]	]	PUNCT
ejpam-5650	38	167	,	,	PUNCT
ejpam-5650	39	1	[	[	X
ejpam-5650	39	2	28	28	NUM
ejpam-5650	39	3	]	]	PUNCT
ejpam-5650	39	4	,	,	PUNCT
ejpam-5650	40	1	[	[	X
ejpam-5650	40	2	66	66	NUM
ejpam-5650	40	3	]	]	PUNCT
ejpam-5650	40	4	,	,	PUNCT
ejpam-5650	41	1	[	[	X
ejpam-5650	41	2	3	3	NUM
ejpam-5650	41	3	]	]	PUNCT
ejpam-5650	41	4	,	,	PUNCT
ejpam-5650	41	5	[	[	X
ejpam-5650	41	6	7	7	NUM
ejpam-5650	41	7	]	]	PUNCT
ejpam-5650	41	8	,	,	PUNCT
ejpam-5650	41	9	[	[	X
ejpam-5650	41	10	17	17	NUM
ejpam-5650	41	11	]	]	PUNCT
ejpam-5650	41	12	,	,	PUNCT
ejpam-5650	41	13	[	[	X
ejpam-5650	41	14	24	24	NUM
ejpam-5650	41	15	]	]	PUNCT
ejpam-5650	41	16	,	,	PUNCT
ejpam-5650	41	17	[	[	X
ejpam-5650	41	18	6	6	NUM
ejpam-5650	41	19	]	]	PUNCT
ejpam-5650	41	20	,	,	PUNCT
ejpam-5650	41	21	[	[	X
ejpam-5650	41	22	21	21	NUM
ejpam-5650	41	23	]	]	PUNCT
ejpam-5650	41	24	,	,	PUNCT
ejpam-5650	41	25	[	[	X
ejpam-5650	41	26	20	20	NUM
ejpam-5650	41	27	]	]	PUNCT
ejpam-5650	41	28	,	,	PUNCT
ejpam-5650	41	29	[	[	X
ejpam-5650	41	30	15	15	NUM
ejpam-5650	41	31	]	]	PUNCT
ejpam-5650	41	32	,	,	PUNCT
ejpam-5650	41	33	[	[	X
ejpam-5650	41	34	9	9	NUM
ejpam-5650	41	35	]	]	PUNCT
ejpam-5650	41	36	,	,	PUNCT
ejpam-5650	41	37	[	[	X
ejpam-5650	41	38	19	19	NUM
ejpam-5650	41	39	]	]	PUNCT
ejpam-5650	41	40	,	,	PUNCT
ejpam-5650	41	41	[	[	X
ejpam-5650	41	42	22	22	NUM
ejpam-5650	41	43	]	]	PUNCT
ejpam-5650	41	44	,	,	PUNCT
ejpam-5650	41	45	[	[	X
ejpam-5650	41	46	36	36	NUM
ejpam-5650	41	47	]	]	PUNCT
ejpam-5650	41	48	,	,	PUNCT
ejpam-5650	41	49	[	[	X
ejpam-5650	41	50	13	13	NUM
ejpam-5650	41	51	]	]	PUNCT
ejpam-5650	41	52	,	,	PUNCT
ejpam-5650	41	53	[	[	X
ejpam-5650	41	54	27	27	NUM
ejpam-5650	41	55	]	]	PUNCT
ejpam-5650	41	56	,	,	PUNCT
ejpam-5650	41	57	[	[	X
ejpam-5650	41	58	59	59	NUM
ejpam-5650	41	59	]	]	PUNCT
ejpam-5650	41	60	,	,	PUNCT
ejpam-5650	41	61	[	[	X
ejpam-5650	41	62	14	14	NUM
ejpam-5650	41	63	]	]	PUNCT
ejpam-5650	41	64	,	,	PUNCT
ejpam-5650	41	65	[	[	X
ejpam-5650	41	66	52	52	NUM
ejpam-5650	41	67	]	]	PUNCT
ejpam-5650	41	68	,	,	PUNCT
ejpam-5650	41	69	[	[	X
ejpam-5650	41	70	38	38	NUM
ejpam-5650	41	71	]	]	PUNCT
ejpam-5650	41	72	,	,	PUNCT
ejpam-5650	42	1	[	[	X
ejpam-5650	42	2	62	62	NUM
ejpam-5650	42	3	]	]	PUNCT
ejpam-5650	42	4	,	,	PUNCT
ejpam-5650	42	5	[	[	X
ejpam-5650	42	6	53	53	NUM
ejpam-5650	42	7	]	]	PUNCT
ejpam-5650	42	8	,	,	PUNCT
ejpam-5650	42	9	[	[	X
ejpam-5650	42	10	51	51	NUM
ejpam-5650	42	11	]	]	PUNCT
ejpam-5650	42	12	,	,	PUNCT
ejpam-5650	42	13	[	[	X
ejpam-5650	42	14	37	37	NUM
ejpam-5650	42	15	]	]	PUNCT
ejpam-5650	42	16	,	,	PUNCT
ejpam-5650	42	17	[	[	X
ejpam-5650	42	18	50	50	NUM
ejpam-5650	42	19	]	]	PUNCT
ejpam-5650	42	20	and	and	CCONJ
ejpam-5650	42	21	[	[	X
ejpam-5650	43	1	70	70	NUM
ejpam-5650	43	2	]	]	PUNCT
ejpam-5650	43	3	,	,	PUNCT
ejpam-5650	43	4	respectively	respectively	ADV
ejpam-5650	43	5	.	.	PUNCT
ejpam-5650	44	1	rosas	rosa	NOUN
ejpam-5650	44	2	et	et	PROPN
ejpam-5650	44	3	al	al	PROPN
ejpam-5650	44	4	.	.	PUNCT
ejpam-5650	45	1	[	[	X
ejpam-5650	45	2	54	54	NUM
ejpam-5650	45	3	]	]	PUNCT
ejpam-5650	45	4	introduced	introduce	VERB
ejpam-5650	45	5	and	and	CCONJ
ejpam-5650	45	6	studied	study	VERB
ejpam-5650	45	7	upper	upper	ADJ
ejpam-5650	45	8	almost	almost	ADV
ejpam-5650	45	9	nearly	nearly	ADV
ejpam-5650	45	10	continuous	continuous	ADJ
ejpam-5650	45	11	multifunctions	multifunction	NOUN
ejpam-5650	45	12	and	and	CCONJ
ejpam-5650	45	13	lower	low	ADJ
ejpam-5650	45	14	almost	almost	ADV
ejpam-5650	45	15	nearly	nearly	ADV
ejpam-5650	45	16	continuous	continuous	ADJ
ejpam-5650	45	17	multifunctions	multifunction	NOUN
ejpam-5650	45	18	using	use	VERB
ejpam-5650	45	19	notions	notion	NOUN
ejpam-5650	45	20	of	of	ADP
ejpam-5650	45	21	topological	topological	ADJ
ejpam-5650	45	22	ideals	ideal	NOUN
ejpam-5650	45	23	.	.	PUNCT
ejpam-5650	46	1	rychlewicz	rychlewicz	PROPN
ejpam-5650	47	1	[	[	X
ejpam-5650	47	2	55	55	NUM
ejpam-5650	47	3	]	]	PUNCT
ejpam-5650	47	4	introduced	introduce	VERB
ejpam-5650	47	5	and	and	CCONJ
ejpam-5650	47	6	studied	study	VERB
ejpam-5650	47	7	the	the	DET
ejpam-5650	47	8	notion	notion	NOUN
ejpam-5650	47	9	of	of	ADP
ejpam-5650	47	10	nearly	nearly	ADV
ejpam-5650	47	11	quasi	quasi	ADJ
ejpam-5650	47	12	-	-	ADJ
ejpam-5650	47	13	continuous	continuous	ADJ
ejpam-5650	47	14	multifunctions	multifunction	NOUN
ejpam-5650	47	15	as	as	ADP
ejpam-5650	47	16	a	a	DET
ejpam-5650	47	17	generalization	generalization	NOUN
ejpam-5650	47	18	of	of	ADP
ejpam-5650	47	19	almost	almost	ADV
ejpam-5650	47	20	nearly	nearly	ADV
ejpam-5650	47	21	continuous	continuous	ADJ
ejpam-5650	47	22	multifunctions	multifunction	NOUN
ejpam-5650	47	23	and	and	CCONJ
ejpam-5650	47	24	almost	almost	ADV
ejpam-5650	47	25	quasi	quasi	VERB
ejpam-5650	47	26	continuous	continuous	ADJ
ejpam-5650	47	27	multifunctions	multifunction	NOUN
ejpam-5650	47	28	[	[	X
ejpam-5650	47	29	48	48	NUM
ejpam-5650	47	30	]	]	PUNCT
ejpam-5650	47	31	.	.	PUNCT
ejpam-5650	48	1	in	in	ADP
ejpam-5650	48	2	this	this	DET
ejpam-5650	48	3	paper	paper	NOUN
ejpam-5650	48	4	,	,	PUNCT
ejpam-5650	48	5	we	we	PRON
ejpam-5650	48	6	introduce	introduce	VERB
ejpam-5650	48	7	the	the	DET
ejpam-5650	48	8	concepts	concept	NOUN
ejpam-5650	48	9	of	of	ADP
ejpam-5650	48	10	upper	upper	ADJ
ejpam-5650	48	11	almost	almost	ADV
ejpam-5650	48	12	nearly	nearly	ADV
ejpam-5650	48	13	(	(	PUNCT
ejpam-5650	48	14	τ1	τ1	NOUN
ejpam-5650	48	15	,	,	PUNCT
ejpam-5650	48	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	48	17	multifunctions	multifunction	NOUN
ejpam-5650	48	18	and	and	CCONJ
ejpam-5650	48	19	lower	low	ADJ
ejpam-5650	48	20	almost	almost	ADV
ejpam-5650	48	21	nearly	nearly	ADV
ejpam-5650	48	22	(	(	PUNCT
ejpam-5650	48	23	τ1	τ1	NOUN
ejpam-5650	48	24	,	,	PUNCT
ejpam-5650	48	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	48	26	multifunctions	multifunction	NOUN
ejpam-5650	48	27	.	.	PUNCT
ejpam-5650	49	1	we	we	PRON
ejpam-5650	49	2	also	also	ADV
ejpam-5650	49	3	investigate	investigate	VERB
ejpam-5650	49	4	several	several	ADJ
ejpam-5650	49	5	characterizations	characterization	NOUN
ejpam-5650	49	6	of	of	ADP
ejpam-5650	49	7	upper	upper	ADJ
ejpam-5650	49	8	almost	almost	ADV
ejpam-5650	49	9	nearly	nearly	ADV
ejpam-5650	49	10	(	(	PUNCT
ejpam-5650	49	11	τ1	τ1	NOUN
ejpam-5650	49	12	,	,	PUNCT
ejpam-5650	49	13	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	49	14	multifunctions	multifunction	NOUN
ejpam-5650	49	15	and	and	CCONJ
ejpam-5650	49	16	lower	low	ADJ
ejpam-5650	49	17	almost	almost	ADV
ejpam-5650	49	18	nearly	nearly	ADV
ejpam-5650	49	19	(	(	PUNCT
ejpam-5650	49	20	τ1	τ1	NOUN
ejpam-5650	49	21	,	,	PUNCT
ejpam-5650	49	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	49	23	multifunctions	multifunction	NOUN
ejpam-5650	49	24	.	.	PUNCT
ejpam-5650	50	1	n.	n.	PROPN
ejpam-5650	50	2	chutiman	chutiman	PROPN
ejpam-5650	50	3	,	,	PUNCT
ejpam-5650	50	4	a.	a.	PROPN
ejpam-5650	50	5	sama	sama	PROPN
ejpam-5650	50	6	-	-	PUNCT
ejpam-5650	50	7	ae	ae	PROPN
ejpam-5650	50	8	,	,	PUNCT
ejpam-5650	50	9	c.	c.	PROPN
ejpam-5650	50	10	boonpok	boonpok	PROPN
ejpam-5650	50	11	/	/	SYM
ejpam-5650	50	12	eur	eur	PROPN
ejpam-5650	50	13	.	.	PUNCT
ejpam-5650	51	1	j.	j.	PROPN
ejpam-5650	51	2	pure	pure	PROPN
ejpam-5650	51	3	appl	appl	PROPN
ejpam-5650	51	4	.	.	PROPN
ejpam-5650	51	5	math	math	PROPN
ejpam-5650	51	6	,	,	PUNCT
ejpam-5650	51	7	18	18	NUM
ejpam-5650	51	8	(	(	PUNCT
ejpam-5650	51	9	1	1	NUM
ejpam-5650	51	10	)	)	PUNCT
ejpam-5650	51	11	(	(	PUNCT
ejpam-5650	51	12	2025	2025	NUM
ejpam-5650	51	13	)	)	PUNCT
ejpam-5650	51	14	,	,	PUNCT
ejpam-5650	51	15	5650	5650	NUM
ejpam-5650	51	16	3	3	NUM
ejpam-5650	51	17	of	of	ADP
ejpam-5650	51	18	18	18	NUM
ejpam-5650	51	19	2	2	NUM
ejpam-5650	51	20	.	.	PUNCT
ejpam-5650	51	21	preliminaries	preliminary	NOUN
ejpam-5650	51	22	throughout	throughout	ADP
ejpam-5650	51	23	the	the	DET
ejpam-5650	51	24	present	present	ADJ
ejpam-5650	51	25	paper	paper	NOUN
ejpam-5650	51	26	,	,	PUNCT
ejpam-5650	51	27	spaces	space	NOUN
ejpam-5650	51	28	(	(	PUNCT
ejpam-5650	51	29	x	x	NOUN
ejpam-5650	51	30	,	,	PUNCT
ejpam-5650	51	31	τ1	τ1	NOUN
ejpam-5650	51	32	,	,	PUNCT
ejpam-5650	51	33	τ2	τ2	NOUN
ejpam-5650	51	34	)	)	PUNCT
ejpam-5650	51	35	and	and	CCONJ
ejpam-5650	51	36	(	(	PUNCT
ejpam-5650	51	37	y	y	PROPN
ejpam-5650	51	38	,	,	PUNCT
ejpam-5650	51	39	σ1	σ1	PROPN
ejpam-5650	51	40	,	,	PUNCT
ejpam-5650	51	41	σ2	σ2	NOUN
ejpam-5650	51	42	)	)	PUNCT
ejpam-5650	51	43	(	(	PUNCT
ejpam-5650	51	44	or	or	CCONJ
ejpam-5650	51	45	simply	simply	ADV
ejpam-5650	51	46	x	x	X
ejpam-5650	51	47	and	and	CCONJ
ejpam-5650	51	48	y	y	PROPN
ejpam-5650	51	49	)	)	PUNCT
ejpam-5650	51	50	always	always	ADV
ejpam-5650	51	51	mean	mean	VERB
ejpam-5650	51	52	bitopological	bitopological	ADJ
ejpam-5650	51	53	spaces	space	NOUN
ejpam-5650	51	54	on	on	ADP
ejpam-5650	51	55	which	which	PRON
ejpam-5650	51	56	no	no	DET
ejpam-5650	51	57	separation	separation	NOUN
ejpam-5650	51	58	axioms	axiom	NOUN
ejpam-5650	51	59	are	be	AUX
ejpam-5650	51	60	assumed	assume	VERB
ejpam-5650	51	61	unless	unless	SCONJ
ejpam-5650	51	62	explicitly	explicitly	ADV
ejpam-5650	51	63	stated	state	VERB
ejpam-5650	51	64	.	.	PUNCT
ejpam-5650	52	1	let	let	VERB
ejpam-5650	52	2	a	a	DET
ejpam-5650	52	3	be	be	AUX
ejpam-5650	52	4	a	a	DET
ejpam-5650	52	5	subset	subset	NOUN
ejpam-5650	52	6	of	of	ADP
ejpam-5650	52	7	a	a	DET
ejpam-5650	52	8	bitopological	bitopological	ADJ
ejpam-5650	52	9	space	space	NOUN
ejpam-5650	52	10	(	(	PUNCT
ejpam-5650	52	11	x	x	NOUN
ejpam-5650	52	12	,	,	PUNCT
ejpam-5650	52	13	τ1	τ1	NOUN
ejpam-5650	52	14	,	,	PUNCT
ejpam-5650	52	15	τ2	τ2	NOUN
ejpam-5650	52	16	)	)	PUNCT
ejpam-5650	52	17	.	.	PUNCT
ejpam-5650	53	1	the	the	DET
ejpam-5650	53	2	closure	closure	NOUN
ejpam-5650	53	3	of	of	ADP
ejpam-5650	53	4	a	a	PRON
ejpam-5650	53	5	and	and	CCONJ
ejpam-5650	53	6	the	the	DET
ejpam-5650	53	7	interior	interior	NOUN
ejpam-5650	53	8	of	of	ADP
ejpam-5650	53	9	a	a	PRON
ejpam-5650	53	10	with	with	ADP
ejpam-5650	53	11	respect	respect	NOUN
ejpam-5650	53	12	to	to	ADP
ejpam-5650	53	13	τi	τi	PROPN
ejpam-5650	53	14	are	be	AUX
ejpam-5650	53	15	denoted	denote	VERB
ejpam-5650	53	16	by	by	ADP
ejpam-5650	53	17	τi	τi	NOUN
ejpam-5650	53	18	-	-	PUNCT
ejpam-5650	53	19	cl(a	cl(a	NUM
ejpam-5650	53	20	)	)	PUNCT
ejpam-5650	53	21	and	and	CCONJ
ejpam-5650	53	22	τi	τi	NOUN
ejpam-5650	53	23	-	-	PUNCT
ejpam-5650	53	24	int(a	int(a	NOUN
ejpam-5650	53	25	)	)	PUNCT
ejpam-5650	53	26	,	,	PUNCT
ejpam-5650	53	27	respectively	respectively	ADV
ejpam-5650	53	28	,	,	PUNCT
ejpam-5650	53	29	for	for	ADP
ejpam-5650	53	30	i	i	PROPN
ejpam-5650	53	31	=	=	SYM
ejpam-5650	53	32	1	1	NUM
ejpam-5650	53	33	,	,	PUNCT
ejpam-5650	53	34	2	2	NUM
ejpam-5650	53	35	.	.	X
ejpam-5650	53	36	a	a	DET
ejpam-5650	53	37	subset	subset	NOUN
ejpam-5650	53	38	a	a	PRON
ejpam-5650	53	39	of	of	ADP
ejpam-5650	53	40	a	a	DET
ejpam-5650	53	41	bitopological	bitopological	ADJ
ejpam-5650	53	42	space	space	NOUN
ejpam-5650	53	43	(	(	PUNCT
ejpam-5650	53	44	x	x	NOUN
ejpam-5650	53	45	,	,	PUNCT
ejpam-5650	53	46	τ1	τ1	NOUN
ejpam-5650	53	47	,	,	PUNCT
ejpam-5650	53	48	τ2	τ2	NOUN
ejpam-5650	53	49	)	)	PUNCT
ejpam-5650	53	50	is	be	AUX
ejpam-5650	53	51	called	call	VERB
ejpam-5650	53	52	τ1τ2	τ1τ2	VERB
ejpam-5650	53	53	-	-	ADJ
ejpam-5650	53	54	closed	closed	ADJ
ejpam-5650	53	55	[	[	X
ejpam-5650	53	56	29	29	NUM
ejpam-5650	53	57	]	]	X
ejpam-5650	53	58	if	if	SCONJ
ejpam-5650	53	59	a	a	DET
ejpam-5650	53	60	=	=	NOUN
ejpam-5650	53	61	τ1	τ1	NOUN
ejpam-5650	53	62	-	-	PUNCT
ejpam-5650	53	63	cl(τ2	cl(τ2	NOUN
ejpam-5650	53	64	-	-	PUNCT
ejpam-5650	53	65	cl(a	cl(a	NUM
ejpam-5650	53	66	)	)	PUNCT
ejpam-5650	53	67	)	)	PUNCT
ejpam-5650	53	68	.	.	PUNCT
ejpam-5650	54	1	the	the	DET
ejpam-5650	54	2	complement	complement	NOUN
ejpam-5650	54	3	of	of	ADP
ejpam-5650	54	4	a	a	DET
ejpam-5650	54	5	τ1τ2	τ1τ2	ADJ
ejpam-5650	54	6	-	-	ADJ
ejpam-5650	54	7	closed	closed	ADJ
ejpam-5650	54	8	set	set	NOUN
ejpam-5650	54	9	is	be	AUX
ejpam-5650	54	10	called	call	VERB
ejpam-5650	54	11	τ1τ2	τ1τ2	NOUN
ejpam-5650	54	12	-	-	ADJ
ejpam-5650	54	13	open	open	ADJ
ejpam-5650	54	14	.	.	PUNCT
ejpam-5650	55	1	let	let	VERB
ejpam-5650	55	2	a	a	DET
ejpam-5650	55	3	be	be	AUX
ejpam-5650	55	4	a	a	DET
ejpam-5650	55	5	subset	subset	NOUN
ejpam-5650	55	6	of	of	ADP
ejpam-5650	55	7	a	a	DET
ejpam-5650	55	8	bitopological	bitopological	ADJ
ejpam-5650	55	9	space	space	NOUN
ejpam-5650	55	10	(	(	PUNCT
ejpam-5650	55	11	x	x	NOUN
ejpam-5650	55	12	,	,	PUNCT
ejpam-5650	55	13	τ1	τ1	NOUN
ejpam-5650	55	14	,	,	PUNCT
ejpam-5650	55	15	τ2	τ2	NOUN
ejpam-5650	55	16	)	)	PUNCT
ejpam-5650	55	17	.	.	PUNCT
ejpam-5650	56	1	the	the	DET
ejpam-5650	56	2	intersection	intersection	NOUN
ejpam-5650	56	3	of	of	ADP
ejpam-5650	56	4	all	all	DET
ejpam-5650	56	5	τ1τ2	τ1τ2	ADJ
ejpam-5650	56	6	-	-	ADJ
ejpam-5650	56	7	closed	closed	ADJ
ejpam-5650	56	8	sets	set	NOUN
ejpam-5650	56	9	of	of	ADP
ejpam-5650	56	10	x	x	PUNCT
ejpam-5650	56	11	containing	contain	VERB
ejpam-5650	56	12	a	a	PRON
ejpam-5650	56	13	is	be	AUX
ejpam-5650	56	14	called	call	VERB
ejpam-5650	56	15	the	the	DET
ejpam-5650	56	16	τ1τ2	τ1τ2	NOUN
ejpam-5650	56	17	-	-	NOUN
ejpam-5650	56	18	closure	closure	NOUN
ejpam-5650	56	19	[	[	X
ejpam-5650	56	20	29	29	NUM
ejpam-5650	56	21	]	]	PUNCT
ejpam-5650	56	22	of	of	ADP
ejpam-5650	56	23	a	a	PRON
ejpam-5650	56	24	and	and	CCONJ
ejpam-5650	56	25	is	be	AUX
ejpam-5650	56	26	denoted	denote	VERB
ejpam-5650	56	27	by	by	ADP
ejpam-5650	56	28	τ1τ2	τ1τ2	NOUN
ejpam-5650	56	29	-	-	NUM
ejpam-5650	56	30	cl(a	cl(a	NUM
ejpam-5650	56	31	)	)	PUNCT
ejpam-5650	56	32	.	.	PUNCT
ejpam-5650	57	1	the	the	DET
ejpam-5650	57	2	union	union	NOUN
ejpam-5650	57	3	of	of	ADP
ejpam-5650	57	4	all	all	DET
ejpam-5650	57	5	τ1τ2	τ1τ2	ADJ
ejpam-5650	57	6	-	-	ADJ
ejpam-5650	57	7	open	open	ADJ
ejpam-5650	57	8	sets	set	NOUN
ejpam-5650	57	9	of	of	ADP
ejpam-5650	57	10	x	x	PUNCT
ejpam-5650	57	11	contained	contain	VERB
ejpam-5650	57	12	in	in	ADP
ejpam-5650	57	13	a	a	PRON
ejpam-5650	57	14	is	be	AUX
ejpam-5650	57	15	called	call	VERB
ejpam-5650	57	16	the	the	DET
ejpam-5650	57	17	τ1τ2	τ1τ2	NOUN
ejpam-5650	57	18	-	-	ADJ
ejpam-5650	57	19	interior	interior	ADJ
ejpam-5650	57	20	[	[	X
ejpam-5650	57	21	29	29	NUM
ejpam-5650	57	22	]	]	PUNCT
ejpam-5650	57	23	of	of	ADP
ejpam-5650	57	24	a	a	PRON
ejpam-5650	57	25	and	and	CCONJ
ejpam-5650	57	26	is	be	AUX
ejpam-5650	57	27	denoted	denote	VERB
ejpam-5650	57	28	by	by	ADP
ejpam-5650	57	29	τ1τ2	τ1τ2	NOUN
ejpam-5650	57	30	-	-	ADJ
ejpam-5650	57	31	int(a	int(a	NOUN
ejpam-5650	57	32	)	)	PUNCT
ejpam-5650	57	33	.	.	PUNCT
ejpam-5650	58	1	a	a	DET
ejpam-5650	58	2	subset	subset	NOUN
ejpam-5650	58	3	a	a	PRON
ejpam-5650	58	4	of	of	ADP
ejpam-5650	58	5	a	a	DET
ejpam-5650	58	6	bitopological	bitopological	ADJ
ejpam-5650	58	7	space	space	NOUN
ejpam-5650	58	8	(	(	PUNCT
ejpam-5650	58	9	x	x	NOUN
ejpam-5650	58	10	,	,	PUNCT
ejpam-5650	58	11	τ1	τ1	NOUN
ejpam-5650	58	12	,	,	PUNCT
ejpam-5650	58	13	τ2	τ2	NOUN
ejpam-5650	58	14	)	)	PUNCT
ejpam-5650	58	15	is	be	AUX
ejpam-5650	58	16	said	say	VERB
ejpam-5650	58	17	to	to	PART
ejpam-5650	58	18	be	be	AUX
ejpam-5650	58	19	(	(	PUNCT
ejpam-5650	58	20	τ1	τ1	NOUN
ejpam-5650	58	21	,	,	PUNCT
ejpam-5650	58	22	τ2)r	τ2)r	NOUN
ejpam-5650	58	23	-	-	PUNCT
ejpam-5650	58	24	open	open	NOUN
ejpam-5650	59	1	[	[	X
ejpam-5650	59	2	64	64	NUM
ejpam-5650	59	3	]	]	PUNCT
ejpam-5650	59	4	(	(	PUNCT
ejpam-5650	59	5	resp	resp	NOUN
ejpam-5650	59	6	.	.	PUNCT
ejpam-5650	60	1	(	(	PUNCT
ejpam-5650	60	2	τ1	τ1	NOUN
ejpam-5650	60	3	,	,	PUNCT
ejpam-5650	60	4	τ2)s	τ2)s	NOUN
ejpam-5650	60	5	-	-	PUNCT
ejpam-5650	60	6	open	open	ADJ
ejpam-5650	60	7	[	[	X
ejpam-5650	60	8	5	5	NUM
ejpam-5650	60	9	]	]	PUNCT
ejpam-5650	60	10	,	,	PUNCT
ejpam-5650	60	11	(	(	PUNCT
ejpam-5650	60	12	τ1	τ1	NOUN
ejpam-5650	60	13	,	,	PUNCT
ejpam-5650	60	14	τ2)p	τ2)p	NOUN
ejpam-5650	60	15	-	-	ADJ
ejpam-5650	60	16	open	open	ADJ
ejpam-5650	60	17	[	[	X
ejpam-5650	60	18	5	5	NUM
ejpam-5650	60	19	]	]	PUNCT
ejpam-5650	60	20	,	,	PUNCT
ejpam-5650	60	21	(	(	PUNCT
ejpam-5650	60	22	τ1	τ1	NOUN
ejpam-5650	60	23	,	,	PUNCT
ejpam-5650	60	24	τ2)β	τ2)β	ADJ
ejpam-5650	60	25	-	-	PUNCT
ejpam-5650	60	26	open	open	ADJ
ejpam-5650	60	27	[	[	X
ejpam-5650	60	28	5	5	NUM
ejpam-5650	60	29	]	]	PUNCT
ejpam-5650	60	30	)	)	PUNCT
ejpam-5650	60	31	if	if	SCONJ
ejpam-5650	60	32	a	a	DET
ejpam-5650	60	33	=	=	PUNCT
ejpam-5650	60	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	60	35	-	-	NOUN
ejpam-5650	60	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	60	37	-	-	PUNCT
ejpam-5650	60	38	cl(a	cl(a	NUM
ejpam-5650	60	39	)	)	PUNCT
ejpam-5650	60	40	)	)	PUNCT
ejpam-5650	60	41	(	(	PUNCT
ejpam-5650	60	42	resp	resp	NOUN
ejpam-5650	60	43	.	.	PUNCT
ejpam-5650	61	1	a	a	DET
ejpam-5650	61	2	⊆	⊆	NUM
ejpam-5650	61	3	τ1τ2	τ1τ2	NOUN
ejpam-5650	61	4	-	-	ADJ
ejpam-5650	61	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5650	61	6	-	-	PUNCT
ejpam-5650	61	7	int(a	int(a	NOUN
ejpam-5650	61	8	)	)	PUNCT
ejpam-5650	61	9	)	)	PUNCT
ejpam-5650	61	10	,	,	PUNCT
ejpam-5650	61	11	a	a	DET
ejpam-5650	61	12	⊆	⊆	NUM
ejpam-5650	61	13	τ1τ2	τ1τ2	NOUN
ejpam-5650	61	14	-	-	NOUN
ejpam-5650	61	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	61	16	-	-	PUNCT
ejpam-5650	61	17	cl(a	cl(a	NUM
ejpam-5650	61	18	)	)	PUNCT
ejpam-5650	61	19	)	)	PUNCT
ejpam-5650	61	20	,	,	PUNCT
ejpam-5650	61	21	a	a	DET
ejpam-5650	61	22	⊆	⊆	NUM
ejpam-5650	61	23	τ1τ2	τ1τ2	NOUN
ejpam-5650	61	24	-	-	PUNCT
ejpam-5650	61	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5650	61	26	-	-	PUNCT
ejpam-5650	61	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	61	28	-	-	PUNCT
ejpam-5650	61	29	cl(a	cl(a	NUM
ejpam-5650	61	30	)	)	PUNCT
ejpam-5650	61	31	)	)	PUNCT
ejpam-5650	61	32	)	)	PUNCT
ejpam-5650	61	33	)	)	PUNCT
ejpam-5650	61	34	.	.	PUNCT
ejpam-5650	62	1	the	the	DET
ejpam-5650	62	2	complement	complement	NOUN
ejpam-5650	62	3	of	of	ADP
ejpam-5650	62	4	a	a	DET
ejpam-5650	62	5	(	(	PUNCT
ejpam-5650	62	6	τ1	τ1	NOUN
ejpam-5650	62	7	,	,	PUNCT
ejpam-5650	62	8	τ2)r	τ2)r	NOUN
ejpam-5650	62	9	-	-	PUNCT
ejpam-5650	62	10	open	open	ADJ
ejpam-5650	62	11	(	(	PUNCT
ejpam-5650	62	12	resp	resp	NOUN
ejpam-5650	62	13	.	.	PUNCT
ejpam-5650	63	1	(	(	PUNCT
ejpam-5650	63	2	τ1	τ1	NOUN
ejpam-5650	63	3	,	,	PUNCT
ejpam-5650	63	4	τ2)sopen	τ2)sopen	ADJ
ejpam-5650	63	5	,	,	PUNCT
ejpam-5650	63	6	(	(	PUNCT
ejpam-5650	63	7	τ1	τ1	NOUN
ejpam-5650	63	8	,	,	PUNCT
ejpam-5650	63	9	τ2)p	τ2)p	NOUN
ejpam-5650	63	10	-	-	ADJ
ejpam-5650	63	11	open	open	ADJ
ejpam-5650	63	12	,	,	PUNCT
ejpam-5650	63	13	(	(	PUNCT
ejpam-5650	63	14	τ1	τ1	NOUN
ejpam-5650	63	15	,	,	PUNCT
ejpam-5650	63	16	τ2)β	τ2)β	ADJ
ejpam-5650	63	17	-	-	PUNCT
ejpam-5650	63	18	open	open	ADJ
ejpam-5650	63	19	)	)	PUNCT
ejpam-5650	63	20	set	set	NOUN
ejpam-5650	63	21	is	be	AUX
ejpam-5650	63	22	called	call	VERB
ejpam-5650	63	23	(	(	PUNCT
ejpam-5650	63	24	τ1	τ1	NOUN
ejpam-5650	63	25	,	,	PUNCT
ejpam-5650	63	26	τ2)r	τ2)r	NOUN
ejpam-5650	63	27	-	-	PUNCT
ejpam-5650	63	28	closed	closed	ADJ
ejpam-5650	63	29	(	(	PUNCT
ejpam-5650	63	30	resp	resp	NOUN
ejpam-5650	63	31	.	.	PUNCT
ejpam-5650	64	1	(	(	PUNCT
ejpam-5650	64	2	τ1	τ1	NOUN
ejpam-5650	64	3	,	,	PUNCT
ejpam-5650	64	4	τ2)s	τ2)s	NOUN
ejpam-5650	64	5	-	-	PUNCT
ejpam-5650	64	6	closed	closed	ADJ
ejpam-5650	64	7	,	,	PUNCT
ejpam-5650	64	8	(	(	PUNCT
ejpam-5650	64	9	τ1	τ1	NOUN
ejpam-5650	64	10	,	,	PUNCT
ejpam-5650	64	11	τ2)p	τ2)p	NOUN
ejpam-5650	64	12	-	-	PUNCT
ejpam-5650	64	13	closed	closed	ADJ
ejpam-5650	64	14	,	,	PUNCT
ejpam-5650	64	15	(	(	PUNCT
ejpam-5650	64	16	τ1	τ1	NOUN
ejpam-5650	64	17	,	,	PUNCT
ejpam-5650	64	18	τ2)β	τ2)β	ADJ
ejpam-5650	64	19	-	-	PUNCT
ejpam-5650	64	20	closed	closed	ADJ
ejpam-5650	64	21	)	)	PUNCT
ejpam-5650	64	22	.	.	PUNCT
ejpam-5650	65	1	a	a	DET
ejpam-5650	65	2	subset	subset	NOUN
ejpam-5650	65	3	a	a	PRON
ejpam-5650	65	4	of	of	ADP
ejpam-5650	65	5	a	a	DET
ejpam-5650	65	6	bitopological	bitopological	ADJ
ejpam-5650	65	7	space	space	NOUN
ejpam-5650	65	8	(	(	PUNCT
ejpam-5650	65	9	x	x	NOUN
ejpam-5650	65	10	,	,	PUNCT
ejpam-5650	65	11	τ1	τ1	NOUN
ejpam-5650	65	12	,	,	PUNCT
ejpam-5650	65	13	τ2	τ2	NOUN
ejpam-5650	65	14	)	)	PUNCT
ejpam-5650	65	15	is	be	AUX
ejpam-5650	65	16	said	say	VERB
ejpam-5650	65	17	to	to	PART
ejpam-5650	65	18	be	be	AUX
ejpam-5650	65	19	α(τ1	α(τ1	NOUN
ejpam-5650	65	20	,	,	PUNCT
ejpam-5650	65	21	τ2)-open	τ2)-open	ADJ
ejpam-5650	65	22	[	[	X
ejpam-5650	65	23	69	69	NUM
ejpam-5650	65	24	]	]	PUNCT
ejpam-5650	65	25	if	if	SCONJ
ejpam-5650	65	26	a	a	DET
ejpam-5650	65	27	⊆	⊆	NUM
ejpam-5650	65	28	τ1τ2	τ1τ2	NOUN
ejpam-5650	65	29	-	-	PUNCT
ejpam-5650	65	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	65	31	-	-	PUNCT
ejpam-5650	65	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5650	65	33	-	-	PUNCT
ejpam-5650	65	34	int(a	int(a	NOUN
ejpam-5650	65	35	)	)	PUNCT
ejpam-5650	65	36	)	)	PUNCT
ejpam-5650	65	37	)	)	PUNCT
ejpam-5650	65	38	.	.	PUNCT
ejpam-5650	66	1	the	the	DET
ejpam-5650	66	2	complement	complement	NOUN
ejpam-5650	66	3	of	of	ADP
ejpam-5650	66	4	an	an	DET
ejpam-5650	66	5	α(τ1	α(τ1	NOUN
ejpam-5650	66	6	,	,	PUNCT
ejpam-5650	66	7	τ2)-open	τ2)-open	ADJ
ejpam-5650	66	8	set	set	NOUN
ejpam-5650	66	9	is	be	AUX
ejpam-5650	66	10	said	say	VERB
ejpam-5650	66	11	to	to	PART
ejpam-5650	66	12	be	be	AUX
ejpam-5650	66	13	α(τ1	α(τ1	NOUN
ejpam-5650	66	14	,	,	PUNCT
ejpam-5650	66	15	τ2)-closed	τ2)-close	VERB
ejpam-5650	66	16	.	.	PUNCT
ejpam-5650	67	1	let	let	VERB
ejpam-5650	67	2	a	a	DET
ejpam-5650	67	3	be	be	AUX
ejpam-5650	67	4	a	a	DET
ejpam-5650	67	5	subset	subset	NOUN
ejpam-5650	67	6	of	of	ADP
ejpam-5650	67	7	a	a	DET
ejpam-5650	67	8	bitopological	bitopological	ADJ
ejpam-5650	67	9	space	space	NOUN
ejpam-5650	67	10	(	(	PUNCT
ejpam-5650	67	11	x	x	NOUN
ejpam-5650	67	12	,	,	PUNCT
ejpam-5650	67	13	τ1	τ1	NOUN
ejpam-5650	67	14	,	,	PUNCT
ejpam-5650	67	15	τ2	τ2	NOUN
ejpam-5650	67	16	)	)	PUNCT
ejpam-5650	67	17	.	.	PUNCT
ejpam-5650	68	1	the	the	DET
ejpam-5650	68	2	intersection	intersection	NOUN
ejpam-5650	68	3	of	of	ADP
ejpam-5650	68	4	all	all	DET
ejpam-5650	68	5	(	(	PUNCT
ejpam-5650	68	6	τ1	τ1	NOUN
ejpam-5650	68	7	,	,	PUNCT
ejpam-5650	68	8	τ2)p	τ2)p	NOUN
ejpam-5650	68	9	-	-	PUNCT
ejpam-5650	68	10	closed	closed	ADJ
ejpam-5650	68	11	(	(	PUNCT
ejpam-5650	68	12	resp	resp	NOUN
ejpam-5650	68	13	.	.	PUNCT
ejpam-5650	69	1	(	(	PUNCT
ejpam-5650	69	2	τ1	τ1	NOUN
ejpam-5650	69	3	,	,	PUNCT
ejpam-5650	69	4	τ2)s	τ2)s	NOUN
ejpam-5650	69	5	-	-	PUNCT
ejpam-5650	69	6	closed	closed	ADJ
ejpam-5650	69	7	,	,	PUNCT
ejpam-5650	69	8	α(τ1	α(τ1	NOUN
ejpam-5650	69	9	,	,	PUNCT
ejpam-5650	69	10	τ2)closed	τ2)closed	ADJ
ejpam-5650	69	11	)	)	PUNCT
ejpam-5650	69	12	sets	set	NOUN
ejpam-5650	69	13	of	of	ADP
ejpam-5650	69	14	x	x	PUNCT
ejpam-5650	69	15	containing	contain	VERB
ejpam-5650	69	16	a	a	PRON
ejpam-5650	69	17	is	be	AUX
ejpam-5650	69	18	called	call	VERB
ejpam-5650	69	19	the	the	DET
ejpam-5650	69	20	(	(	PUNCT
ejpam-5650	69	21	τ1	τ1	NOUN
ejpam-5650	69	22	,	,	PUNCT
ejpam-5650	69	23	τ2)p	τ2)p	NOUN
ejpam-5650	69	24	-	-	NOUN
ejpam-5650	69	25	closure	closure	NOUN
ejpam-5650	69	26	[	[	X
ejpam-5650	69	27	68	68	NUM
ejpam-5650	69	28	]	]	X
ejpam-5650	69	29	(	(	PUNCT
ejpam-5650	69	30	resp	resp	NOUN
ejpam-5650	69	31	.	.	PUNCT
ejpam-5650	70	1	(	(	PUNCT
ejpam-5650	70	2	τ1	τ1	NOUN
ejpam-5650	70	3	,	,	PUNCT
ejpam-5650	70	4	τ2)s	τ2)s	NOUN
ejpam-5650	70	5	-	-	PUNCT
ejpam-5650	70	6	closure	closure	NOUN
ejpam-5650	70	7	[	[	X
ejpam-5650	70	8	5	5	NUM
ejpam-5650	70	9	]	]	PUNCT
ejpam-5650	70	10	,	,	PUNCT
ejpam-5650	70	11	α(τ1	α(τ1	NOUN
ejpam-5650	70	12	,	,	PUNCT
ejpam-5650	70	13	τ2)-closure	τ2)-closure	NOUN
ejpam-5650	70	14	[	[	X
ejpam-5650	70	15	67	67	NUM
ejpam-5650	70	16	]	]	SYM
ejpam-5650	70	17	)	)	PUNCT
ejpam-5650	70	18	of	of	ADP
ejpam-5650	70	19	a	a	PRON
ejpam-5650	70	20	and	and	CCONJ
ejpam-5650	70	21	is	be	AUX
ejpam-5650	70	22	denoted	denote	VERB
ejpam-5650	70	23	by	by	ADP
ejpam-5650	70	24	(	(	PUNCT
ejpam-5650	70	25	τ1	τ1	NOUN
ejpam-5650	70	26	,	,	PUNCT
ejpam-5650	70	27	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-5650	70	28	)	)	PUNCT
ejpam-5650	70	29	(	(	PUNCT
ejpam-5650	70	30	resp	resp	NOUN
ejpam-5650	70	31	.	.	PUNCT
ejpam-5650	71	1	(	(	PUNCT
ejpam-5650	71	2	τ1	τ1	NOUN
ejpam-5650	71	3	,	,	PUNCT
ejpam-5650	71	4	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5650	71	5	)	)	PUNCT
ejpam-5650	71	6	,	,	PUNCT
ejpam-5650	71	7	α(τ1	α(τ1	NOUN
ejpam-5650	71	8	,	,	PUNCT
ejpam-5650	71	9	τ2)-cl(a	τ2)-cl(a	NUM
ejpam-5650	71	10	)	)	PUNCT
ejpam-5650	71	11	)	)	PUNCT
ejpam-5650	71	12	.	.	PUNCT
ejpam-5650	72	1	the	the	DET
ejpam-5650	72	2	union	union	NOUN
ejpam-5650	72	3	of	of	ADP
ejpam-5650	72	4	all	all	DET
ejpam-5650	72	5	(	(	PUNCT
ejpam-5650	72	6	τ1	τ1	NOUN
ejpam-5650	72	7	,	,	PUNCT
ejpam-5650	72	8	τ2)p	τ2)p	NOUN
ejpam-5650	72	9	-	-	ADJ
ejpam-5650	72	10	open	open	ADJ
ejpam-5650	72	11	(	(	PUNCT
ejpam-5650	72	12	resp	resp	NOUN
ejpam-5650	72	13	.	.	PUNCT
ejpam-5650	73	1	(	(	PUNCT
ejpam-5650	73	2	τ1	τ1	NOUN
ejpam-5650	73	3	,	,	PUNCT
ejpam-5650	73	4	τ2)s	τ2)s	NOUN
ejpam-5650	73	5	-	-	PUNCT
ejpam-5650	73	6	open	open	ADJ
ejpam-5650	73	7	,	,	PUNCT
ejpam-5650	73	8	α(τ1	α(τ1	NOUN
ejpam-5650	73	9	,	,	PUNCT
ejpam-5650	73	10	τ2)-open	τ2)-open	ADJ
ejpam-5650	73	11	)	)	PUNCT
ejpam-5650	73	12	sets	set	NOUN
ejpam-5650	73	13	of	of	ADP
ejpam-5650	73	14	x	x	PUNCT
ejpam-5650	73	15	contained	contain	VERB
ejpam-5650	73	16	in	in	ADP
ejpam-5650	73	17	a	a	PRON
ejpam-5650	73	18	is	be	AUX
ejpam-5650	73	19	called	call	VERB
ejpam-5650	73	20	the	the	DET
ejpam-5650	73	21	(	(	PUNCT
ejpam-5650	73	22	τ1	τ1	NOUN
ejpam-5650	73	23	,	,	PUNCT
ejpam-5650	73	24	τ2)p	τ2)p	ADJ
ejpam-5650	73	25	-	-	NOUN
ejpam-5650	73	26	interior	interior	ADJ
ejpam-5650	73	27	[	[	X
ejpam-5650	73	28	68	68	NUM
ejpam-5650	73	29	]	]	PUNCT
ejpam-5650	73	30	(	(	PUNCT
ejpam-5650	73	31	resp	resp	NOUN
ejpam-5650	73	32	.	.	PUNCT
ejpam-5650	74	1	(	(	PUNCT
ejpam-5650	74	2	τ1	τ1	NOUN
ejpam-5650	74	3	,	,	PUNCT
ejpam-5650	74	4	τ2)s	τ2)s	NOUN
ejpam-5650	74	5	-	-	ADJ
ejpam-5650	74	6	interior	interior	ADJ
ejpam-5650	74	7	[	[	X
ejpam-5650	74	8	5	5	NUM
ejpam-5650	74	9	]	]	PUNCT
ejpam-5650	74	10	,	,	PUNCT
ejpam-5650	74	11	α(τ1	α(τ1	NOUN
ejpam-5650	74	12	,	,	PUNCT
ejpam-5650	74	13	τ2)-interior	τ2)-interior	PROPN
ejpam-5650	74	14	[	[	X
ejpam-5650	74	15	67	67	NUM
ejpam-5650	74	16	]	]	SYM
ejpam-5650	74	17	)	)	PUNCT
ejpam-5650	74	18	of	of	ADP
ejpam-5650	74	19	a	a	PRON
ejpam-5650	74	20	and	and	CCONJ
ejpam-5650	74	21	is	be	AUX
ejpam-5650	74	22	denoted	denote	VERB
ejpam-5650	74	23	by	by	ADP
ejpam-5650	74	24	(	(	PUNCT
ejpam-5650	74	25	τ1	τ1	NOUN
ejpam-5650	74	26	,	,	PUNCT
ejpam-5650	74	27	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-5650	74	28	)	)	PUNCT
ejpam-5650	74	29	(	(	PUNCT
ejpam-5650	74	30	resp	resp	NOUN
ejpam-5650	74	31	.	.	PUNCT
ejpam-5650	75	1	(	(	PUNCT
ejpam-5650	75	2	τ1	τ1	NOUN
ejpam-5650	75	3	,	,	PUNCT
ejpam-5650	75	4	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5650	75	5	)	)	PUNCT
ejpam-5650	75	6	,	,	PUNCT
ejpam-5650	75	7	α(τ1	α(τ1	NOUN
ejpam-5650	75	8	,	,	PUNCT
ejpam-5650	75	9	τ2)-int(a	τ2)-int(a	NOUN
ejpam-5650	75	10	)	)	PUNCT
ejpam-5650	75	11	)	)	PUNCT
ejpam-5650	75	12	.	.	PUNCT
ejpam-5650	76	1	a	a	DET
ejpam-5650	76	2	subset	subset	NOUN
ejpam-5650	76	3	a	a	PRON
ejpam-5650	76	4	of	of	ADP
ejpam-5650	76	5	a	a	DET
ejpam-5650	76	6	bitopological	bitopological	ADJ
ejpam-5650	76	7	space	space	NOUN
ejpam-5650	76	8	(	(	PUNCT
ejpam-5650	76	9	x	x	NOUN
ejpam-5650	76	10	,	,	PUNCT
ejpam-5650	76	11	τ1	τ1	NOUN
ejpam-5650	76	12	,	,	PUNCT
ejpam-5650	76	13	τ2	τ2	NOUN
ejpam-5650	76	14	)	)	PUNCT
ejpam-5650	76	15	is	be	AUX
ejpam-5650	76	16	said	say	VERB
ejpam-5650	76	17	to	to	PART
ejpam-5650	76	18	be	be	AUX
ejpam-5650	76	19	n	n	PRON
ejpam-5650	76	20	(	(	PUNCT
ejpam-5650	76	21	τ1	τ1	PROPN
ejpam-5650	76	22	,	,	PUNCT
ejpam-5650	76	23	τ2)closed	τ2)close	VERB
ejpam-5650	77	1	[	[	X
ejpam-5650	77	2	61	61	NUM
ejpam-5650	77	3	]	]	X
ejpam-5650	77	4	if	if	SCONJ
ejpam-5650	77	5	every	every	DET
ejpam-5650	77	6	cover	cover	NOUN
ejpam-5650	77	7	of	of	ADP
ejpam-5650	77	8	a	a	DET
ejpam-5650	77	9	by	by	ADP
ejpam-5650	77	10	(	(	PUNCT
ejpam-5650	77	11	τ1	τ1	NOUN
ejpam-5650	77	12	,	,	PUNCT
ejpam-5650	77	13	τ2)r	τ2)r	ADJ
ejpam-5650	77	14	-	-	PUNCT
ejpam-5650	77	15	open	open	ADJ
ejpam-5650	77	16	sets	set	NOUN
ejpam-5650	77	17	of	of	ADP
ejpam-5650	77	18	x	x	PUNCT
ejpam-5650	77	19	has	have	VERB
ejpam-5650	77	20	a	a	DET
ejpam-5650	77	21	finite	finite	ADJ
ejpam-5650	77	22	subcover	subcover	PROPN
ejpam-5650	77	23	.	.	PUNCT
ejpam-5650	78	1	lemma	lemma	PROPN
ejpam-5650	78	2	1	1	NUM
ejpam-5650	78	3	.	.	PUNCT
ejpam-5650	79	1	for	for	ADP
ejpam-5650	79	2	a	a	DET
ejpam-5650	79	3	subset	subset	NOUN
ejpam-5650	79	4	a	a	PRON
ejpam-5650	79	5	of	of	ADP
ejpam-5650	79	6	a	a	DET
ejpam-5650	79	7	bitopological	bitopological	ADJ
ejpam-5650	79	8	space	space	NOUN
ejpam-5650	79	9	(	(	PUNCT
ejpam-5650	79	10	x	x	NOUN
ejpam-5650	79	11	,	,	PUNCT
ejpam-5650	79	12	τ1	τ1	NOUN
ejpam-5650	79	13	,	,	PUNCT
ejpam-5650	79	14	τ2	τ2	NOUN
ejpam-5650	79	15	)	)	PUNCT
ejpam-5650	79	16	,	,	PUNCT
ejpam-5650	79	17	the	the	DET
ejpam-5650	79	18	following	follow	VERB
ejpam-5650	79	19	properties	property	NOUN
ejpam-5650	79	20	hold	hold	VERB
ejpam-5650	79	21	:	:	PUNCT
ejpam-5650	79	22	(	(	PUNCT
ejpam-5650	79	23	1	1	X
ejpam-5650	79	24	)	)	PUNCT
ejpam-5650	79	25	(	(	PUNCT
ejpam-5650	79	26	τ1	τ1	NOUN
ejpam-5650	79	27	,	,	PUNCT
ejpam-5650	79	28	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5650	79	29	)	)	PUNCT
ejpam-5650	79	30	=	=	PUNCT
ejpam-5650	80	1	τ1τ2	τ1τ2	NOUN
ejpam-5650	80	2	-	-	NOUN
ejpam-5650	80	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	80	4	-	-	PUNCT
ejpam-5650	80	5	cl(a	cl(a	NUM
ejpam-5650	80	6	)	)	PUNCT
ejpam-5650	80	7	)	)	PUNCT
ejpam-5650	80	8	∪a	∪a	X
ejpam-5650	81	1	[	[	X
ejpam-5650	81	2	5	5	NUM
ejpam-5650	81	3	]	]	PUNCT
ejpam-5650	81	4	;	;	PUNCT
ejpam-5650	81	5	(	(	PUNCT
ejpam-5650	81	6	2	2	X
ejpam-5650	81	7	)	)	PUNCT
ejpam-5650	81	8	(	(	PUNCT
ejpam-5650	81	9	τ1	τ1	NOUN
ejpam-5650	81	10	,	,	PUNCT
ejpam-5650	81	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5650	81	12	)	)	PUNCT
ejpam-5650	81	13	=	=	PUNCT
ejpam-5650	81	14	τ1τ2	τ1τ2	NOUN
ejpam-5650	81	15	-	-	ADJ
ejpam-5650	81	16	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5650	81	17	-	-	PUNCT
ejpam-5650	81	18	int(a	int(a	NOUN
ejpam-5650	81	19	)	)	PUNCT
ejpam-5650	81	20	)	)	PUNCT
ejpam-5650	82	1	∩a	∩a	PROPN
ejpam-5650	83	1	[	[	X
ejpam-5650	83	2	52	52	NUM
ejpam-5650	83	3	]	]	PUNCT
ejpam-5650	83	4	.	.	PUNCT
ejpam-5650	84	1	lemma	lemma	PROPN
ejpam-5650	84	2	2	2	X
ejpam-5650	84	3	.	.	PUNCT
ejpam-5650	85	1	let	let	AUX
ejpam-5650	85	2	(	(	PUNCT
ejpam-5650	85	3	x	x	NOUN
ejpam-5650	85	4	,	,	PUNCT
ejpam-5650	85	5	τ1	τ1	NOUN
ejpam-5650	85	6	,	,	PUNCT
ejpam-5650	85	7	τ2	τ2	PROPN
ejpam-5650	85	8	)	)	PUNCT
ejpam-5650	85	9	be	be	VERB
ejpam-5650	85	10	a	a	DET
ejpam-5650	85	11	bitopological	bitopological	ADJ
ejpam-5650	85	12	space	space	NOUN
ejpam-5650	85	13	.	.	PUNCT
ejpam-5650	86	1	if	if	SCONJ
ejpam-5650	86	2	v	v	NOUN
ejpam-5650	86	3	is	be	AUX
ejpam-5650	86	4	a	a	DET
ejpam-5650	86	5	τ1τ2	τ1τ2	ADJ
ejpam-5650	86	6	-	-	ADJ
ejpam-5650	86	7	open	open	ADJ
ejpam-5650	86	8	set	set	NOUN
ejpam-5650	86	9	of	of	ADP
ejpam-5650	86	10	x	x	PUNCT
ejpam-5650	86	11	having	have	VERB
ejpam-5650	86	12	n	n	X
ejpam-5650	86	13	(	(	PUNCT
ejpam-5650	86	14	τ1	τ1	PROPN
ejpam-5650	86	15	,	,	PUNCT
ejpam-5650	86	16	τ2)-closed	τ2)-closed	ADJ
ejpam-5650	86	17	complement	complement	NOUN
ejpam-5650	86	18	,	,	PUNCT
ejpam-5650	86	19	then	then	ADV
ejpam-5650	86	20	τ1τ2	τ1τ2	NOUN
ejpam-5650	86	21	-	-	NOUN
ejpam-5650	86	22	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	86	23	-	-	PUNCT
ejpam-5650	86	24	cl(v	cl(v	NOUN
ejpam-5650	86	25	)	)	PUNCT
ejpam-5650	86	26	)	)	PUNCT
ejpam-5650	86	27	is	be	AUX
ejpam-5650	86	28	a	a	DET
ejpam-5650	86	29	(	(	PUNCT
ejpam-5650	86	30	τ1	τ1	NOUN
ejpam-5650	86	31	,	,	PUNCT
ejpam-5650	86	32	τ2)r	τ2)r	ADJ
ejpam-5650	86	33	-	-	PUNCT
ejpam-5650	86	34	open	open	NOUN
ejpam-5650	86	35	set	set	NOUN
ejpam-5650	86	36	having	have	VERB
ejpam-5650	86	37	n	n	PRON
ejpam-5650	86	38	(	(	PUNCT
ejpam-5650	86	39	τ1	τ1	PROPN
ejpam-5650	86	40	,	,	PUNCT
ejpam-5650	86	41	τ2)-closed	τ2)-closed	ADJ
ejpam-5650	86	42	complement	complement	NOUN
ejpam-5650	86	43	.	.	PUNCT
ejpam-5650	87	1	proof	proof	NOUN
ejpam-5650	87	2	.	.	PUNCT
ejpam-5650	88	1	it	it	PRON
ejpam-5650	88	2	is	be	AUX
ejpam-5650	88	3	obvious	obvious	ADJ
ejpam-5650	88	4	that	that	SCONJ
ejpam-5650	88	5	τ1τ2	τ1τ2	NOUN
ejpam-5650	88	6	-	-	NOUN
ejpam-5650	88	7	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	88	8	-	-	PUNCT
ejpam-5650	88	9	cl(v	cl(v	NOUN
ejpam-5650	88	10	)	)	PUNCT
ejpam-5650	88	11	)	)	PUNCT
ejpam-5650	88	12	is	be	AUX
ejpam-5650	88	13	a	a	DET
ejpam-5650	88	14	(	(	PUNCT
ejpam-5650	88	15	τ1	τ1	NOUN
ejpam-5650	88	16	,	,	PUNCT
ejpam-5650	88	17	τ2)r	τ2)r	ADJ
ejpam-5650	88	18	-	-	PUNCT
ejpam-5650	88	19	open	open	NOUN
ejpam-5650	88	20	set	set	NOUN
ejpam-5650	88	21	.	.	PUNCT
ejpam-5650	89	1	let	let	VERB
ejpam-5650	89	2	us	we	PRON
ejpam-5650	89	3	denote	denote	VERB
ejpam-5650	89	4	k	k	PROPN
ejpam-5650	90	1	=	=	PUNCT
ejpam-5650	90	2	x	x	X
ejpam-5650	90	3	−	−	ADP
ejpam-5650	90	4	τ1τ2	τ1τ2	NOUN
ejpam-5650	90	5	-	-	NOUN
ejpam-5650	90	6	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	90	7	-	-	PUNCT
ejpam-5650	90	8	cl(v	cl(v	NOUN
ejpam-5650	90	9	)	)	PUNCT
ejpam-5650	90	10	)	)	PUNCT
ejpam-5650	90	11	.	.	PUNCT
ejpam-5650	91	1	of	of	ADP
ejpam-5650	91	2	course	course	NOUN
ejpam-5650	91	3	,	,	PUNCT
ejpam-5650	91	4	k	k	PROPN
ejpam-5650	91	5	⊆	⊆	NUM
ejpam-5650	91	6	x	x	SYM
ejpam-5650	91	7	−	−	NOUN
ejpam-5650	91	8	v	v	NOUN
ejpam-5650	91	9	.	.	PUNCT
ejpam-5650	92	1	let	let	VERB
ejpam-5650	92	2	{	{	PUNCT
ejpam-5650	92	3	uγ	uγ	ADV
ejpam-5650	92	4	|	|	ADV
ejpam-5650	92	5	γ	γ	PROPN
ejpam-5650	92	6	∈	∈	PROPN
ejpam-5650	92	7	γ	γ	AUX
ejpam-5650	92	8	}	}	PUNCT
ejpam-5650	92	9	be	be	AUX
ejpam-5650	92	10	a	a	DET
ejpam-5650	92	11	τ1τ2	τ1τ2	ADJ
ejpam-5650	92	12	-	-	ADJ
ejpam-5650	92	13	open	open	ADJ
ejpam-5650	92	14	cover	cover	NOUN
ejpam-5650	92	15	of	of	ADP
ejpam-5650	92	16	the	the	DET
ejpam-5650	92	17	set	set	NOUN
ejpam-5650	93	1	k.	k.	PROPN
ejpam-5650	93	2	then	then	ADV
ejpam-5650	93	3	,	,	PUNCT
ejpam-5650	93	4	{	{	PUNCT
ejpam-5650	93	5	uγ	uγ	ADV
ejpam-5650	93	6	|	|	ADV
ejpam-5650	93	7	γ	γ	PROPN
ejpam-5650	93	8	∈	∈	PROPN
ejpam-5650	93	9	γ	γ	X
ejpam-5650	93	10	}	}	PUNCT
ejpam-5650	93	11	∪	∪	NOUN
ejpam-5650	93	12	(	(	PUNCT
ejpam-5650	93	13	x	x	NOUN
ejpam-5650	93	14	−k	−k	ADV
ejpam-5650	93	15	)	)	PUNCT
ejpam-5650	93	16	is	be	AUX
ejpam-5650	93	17	a	a	DET
ejpam-5650	93	18	τ1τ2	τ1τ2	ADJ
ejpam-5650	93	19	-	-	ADJ
ejpam-5650	93	20	open	open	ADJ
ejpam-5650	93	21	cover	cover	NOUN
ejpam-5650	93	22	of	of	ADP
ejpam-5650	93	23	the	the	DET
ejpam-5650	93	24	set	set	NOUN
ejpam-5650	93	25	x	x	PUNCT
ejpam-5650	93	26	−	−	PROPN
ejpam-5650	93	27	v	v	NOUN
ejpam-5650	93	28	.	.	PUNCT
ejpam-5650	94	1	thus	thus	ADV
ejpam-5650	94	2	,	,	PUNCT
ejpam-5650	94	3	there	there	PRON
ejpam-5650	94	4	exist	exist	VERB
ejpam-5650	94	5	indexes	index	NOUN
ejpam-5650	94	6	γ1	γ1	NOUN
ejpam-5650	94	7	,	,	PUNCT
ejpam-5650	94	8	γ2	γ2	PROPN
ejpam-5650	94	9	,	,	PUNCT
ejpam-5650	94	10	...	...	PUNCT
ejpam-5650	94	11	,	,	PUNCT
ejpam-5650	94	12	γk	γk	ADP
ejpam-5650	94	13	such	such	ADJ
ejpam-5650	94	14	that	that	SCONJ
ejpam-5650	95	1	x	x	X
ejpam-5650	95	2	−	−	NOUN
ejpam-5650	95	3	v	v	PRON
ejpam-5650	95	4	⊆	⊆	NUM
ejpam-5650	95	5	k	k	X
ejpam-5650	95	6	∪	∪	ADV
ejpam-5650	95	7	i=1	i=1	ADP
ejpam-5650	95	8	τ1τ2	τ1τ2	NOUN
ejpam-5650	95	9	-	-	NOUN
ejpam-5650	95	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	95	11	-	-	PUNCT
ejpam-5650	95	12	cl(uγi	cl(uγi	NOUN
ejpam-5650	95	13	)	)	PUNCT
ejpam-5650	95	14	)	)	PUNCT
ejpam-5650	95	15	∪	∪	ADP
ejpam-5650	95	16	τ1τ2	τ1τ2	NOUN
ejpam-5650	95	17	-	-	NOUN
ejpam-5650	95	18	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	95	19	-	-	PUNCT
ejpam-5650	95	20	cl(x	cl(x	NOUN
ejpam-5650	95	21	−k	−k	NOUN
ejpam-5650	95	22	)	)	PUNCT
ejpam-5650	95	23	)	)	PUNCT
ejpam-5650	95	24	.	.	PUNCT
ejpam-5650	96	1	n.	n.	PROPN
ejpam-5650	96	2	chutiman	chutiman	PROPN
ejpam-5650	96	3	,	,	PUNCT
ejpam-5650	96	4	a.	a.	PROPN
ejpam-5650	96	5	sama	sama	PROPN
ejpam-5650	96	6	-	-	PUNCT
ejpam-5650	96	7	ae	ae	PROPN
ejpam-5650	96	8	,	,	PUNCT
ejpam-5650	96	9	c.	c.	PROPN
ejpam-5650	96	10	boonpok	boonpok	PROPN
ejpam-5650	96	11	/	/	SYM
ejpam-5650	96	12	eur	eur	PROPN
ejpam-5650	96	13	.	.	PUNCT
ejpam-5650	97	1	j.	j.	PROPN
ejpam-5650	97	2	pure	pure	PROPN
ejpam-5650	97	3	appl	appl	PROPN
ejpam-5650	97	4	.	.	PROPN
ejpam-5650	97	5	math	math	PROPN
ejpam-5650	97	6	,	,	PUNCT
ejpam-5650	97	7	18	18	NUM
ejpam-5650	97	8	(	(	PUNCT
ejpam-5650	97	9	1	1	NUM
ejpam-5650	97	10	)	)	PUNCT
ejpam-5650	97	11	(	(	PUNCT
ejpam-5650	97	12	2025	2025	NUM
ejpam-5650	97	13	)	)	PUNCT
ejpam-5650	97	14	,	,	PUNCT
ejpam-5650	97	15	5650	5650	NUM
ejpam-5650	97	16	4	4	NUM
ejpam-5650	97	17	of	of	ADP
ejpam-5650	97	18	18	18	NUM
ejpam-5650	97	19	since	since	SCONJ
ejpam-5650	97	20	τ1τ2	τ1τ2	NOUN
ejpam-5650	97	21	-	-	NOUN
ejpam-5650	97	22	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	97	23	-	-	PUNCT
ejpam-5650	97	24	cl(x−k	cl(x−k	PRON
ejpam-5650	97	25	)	)	PUNCT
ejpam-5650	97	26	)	)	PUNCT
ejpam-5650	98	1	=	=	PUNCT
ejpam-5650	98	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	98	3	-	-	NOUN
ejpam-5650	98	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	98	5	-	-	PUNCT
ejpam-5650	98	6	cl(v	cl(v	NOUN
ejpam-5650	98	7	)	)	PUNCT
ejpam-5650	98	8	)	)	PUNCT
ejpam-5650	98	9	,	,	PUNCT
ejpam-5650	98	10	τ1τ2	τ1τ2	NOUN
ejpam-5650	98	11	-	-	NOUN
ejpam-5650	98	12	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	98	13	-	-	PUNCT
ejpam-5650	98	14	cl(x−k))∩k	cl(x−k))∩k	NOUN
ejpam-5650	98	15	=	=	PUNCT
ejpam-5650	98	16	∅.	∅.	NOUN
ejpam-5650	98	17	it	it	PRON
ejpam-5650	98	18	was	be	AUX
ejpam-5650	98	19	shown	show	VERB
ejpam-5650	98	20	that	that	SCONJ
ejpam-5650	98	21	k	k	PROPN
ejpam-5650	98	22	⊆	⊆	NUM
ejpam-5650	98	23	k	k	PROPN
ejpam-5650	98	24	∪	∪	ADP
ejpam-5650	98	25	i=1	i=1	ADP
ejpam-5650	98	26	τ1τ2	τ1τ2	NOUN
ejpam-5650	98	27	-	-	NOUN
ejpam-5650	98	28	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	98	29	-	-	PUNCT
ejpam-5650	98	30	cl(uγi	cl(uγi	NOUN
ejpam-5650	98	31	)	)	PUNCT
ejpam-5650	98	32	)	)	PUNCT
ejpam-5650	98	33	.	.	PUNCT
ejpam-5650	99	1	the	the	DET
ejpam-5650	99	2	proof	proof	NOUN
ejpam-5650	99	3	of	of	ADP
ejpam-5650	99	4	n	n	PROPN
ejpam-5650	99	5	(	(	PUNCT
ejpam-5650	99	6	τ1	τ1	PROPN
ejpam-5650	99	7	,	,	PUNCT
ejpam-5650	99	8	τ2)-closedness	τ2)-closedness	NOUN
ejpam-5650	99	9	of	of	ADP
ejpam-5650	99	10	the	the	DET
ejpam-5650	99	11	set	set	NOUN
ejpam-5650	99	12	k	k	PROPN
ejpam-5650	99	13	is	be	AUX
ejpam-5650	99	14	finished	finish	VERB
ejpam-5650	99	15	.	.	PUNCT
ejpam-5650	100	1	lemma	lemma	PROPN
ejpam-5650	100	2	3	3	X
ejpam-5650	100	3	.	.	PUNCT
ejpam-5650	101	1	let	let	AUX
ejpam-5650	101	2	(	(	PUNCT
ejpam-5650	101	3	x	x	NOUN
ejpam-5650	101	4	,	,	PUNCT
ejpam-5650	101	5	τ1	τ1	NOUN
ejpam-5650	101	6	,	,	PUNCT
ejpam-5650	101	7	τ2	τ2	PROPN
ejpam-5650	101	8	)	)	PUNCT
ejpam-5650	101	9	be	be	VERB
ejpam-5650	101	10	a	a	DET
ejpam-5650	101	11	bitopological	bitopological	ADJ
ejpam-5650	101	12	space	space	NOUN
ejpam-5650	101	13	.	.	PUNCT
ejpam-5650	102	1	if	if	SCONJ
ejpam-5650	102	2	v	v	NOUN
ejpam-5650	102	3	is	be	AUX
ejpam-5650	102	4	a	a	DET
ejpam-5650	102	5	(	(	PUNCT
ejpam-5650	102	6	τ1	τ1	NOUN
ejpam-5650	102	7	,	,	PUNCT
ejpam-5650	102	8	τ2)p	τ2)p	ADJ
ejpam-5650	102	9	-	-	PUNCT
ejpam-5650	102	10	open	open	ADJ
ejpam-5650	102	11	set	set	NOUN
ejpam-5650	102	12	of	of	ADP
ejpam-5650	102	13	x	x	PUNCT
ejpam-5650	102	14	having	have	VERB
ejpam-5650	102	15	n	n	X
ejpam-5650	102	16	(	(	PUNCT
ejpam-5650	102	17	τ1	τ1	PROPN
ejpam-5650	102	18	,	,	PUNCT
ejpam-5650	102	19	τ2)-closed	τ2)-closed	ADJ
ejpam-5650	102	20	complement	complement	NOUN
ejpam-5650	102	21	,	,	PUNCT
ejpam-5650	102	22	then	then	ADV
ejpam-5650	102	23	τ1τ2	τ1τ2	NOUN
ejpam-5650	102	24	-	-	NOUN
ejpam-5650	102	25	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	102	26	-	-	PUNCT
ejpam-5650	102	27	cl(v	cl(v	NOUN
ejpam-5650	102	28	)	)	PUNCT
ejpam-5650	102	29	)	)	PUNCT
ejpam-5650	102	30	is	be	AUX
ejpam-5650	102	31	a	a	DET
ejpam-5650	102	32	(	(	PUNCT
ejpam-5650	102	33	τ1	τ1	NOUN
ejpam-5650	102	34	,	,	PUNCT
ejpam-5650	102	35	τ2)r	τ2)r	ADJ
ejpam-5650	102	36	-	-	PUNCT
ejpam-5650	102	37	open	open	NOUN
ejpam-5650	102	38	set	set	NOUN
ejpam-5650	102	39	having	have	VERB
ejpam-5650	102	40	n	n	PRON
ejpam-5650	102	41	(	(	PUNCT
ejpam-5650	102	42	τ1	τ1	PROPN
ejpam-5650	102	43	,	,	PUNCT
ejpam-5650	102	44	τ2)-closed	τ2)-closed	ADJ
ejpam-5650	102	45	complement	complement	NOUN
ejpam-5650	102	46	.	.	PUNCT
ejpam-5650	103	1	proof	proof	NOUN
ejpam-5650	103	2	.	.	PUNCT
ejpam-5650	104	1	it	it	PRON
ejpam-5650	104	2	is	be	AUX
ejpam-5650	104	3	evident	evident	ADJ
ejpam-5650	104	4	that	that	SCONJ
ejpam-5650	104	5	τ1τ2	τ1τ2	NOUN
ejpam-5650	104	6	-	-	NOUN
ejpam-5650	104	7	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	104	8	-	-	PUNCT
ejpam-5650	104	9	cl(v	cl(v	NOUN
ejpam-5650	104	10	)	)	PUNCT
ejpam-5650	104	11	)	)	PUNCT
ejpam-5650	104	12	is	be	AUX
ejpam-5650	104	13	a	a	DET
ejpam-5650	104	14	(	(	PUNCT
ejpam-5650	104	15	τ1	τ1	NOUN
ejpam-5650	104	16	,	,	PUNCT
ejpam-5650	104	17	τ2)r	τ2)r	ADJ
ejpam-5650	104	18	-	-	PUNCT
ejpam-5650	104	19	open	open	ADJ
ejpam-5650	104	20	set	set	NOUN
ejpam-5650	104	21	.	.	PUNCT
ejpam-5650	105	1	since	since	SCONJ
ejpam-5650	105	2	v	v	NOUN
ejpam-5650	105	3	is	be	AUX
ejpam-5650	105	4	(	(	PUNCT
ejpam-5650	105	5	τ1	τ1	NOUN
ejpam-5650	105	6	,	,	PUNCT
ejpam-5650	105	7	τ2)popen	τ2)popen	ADJ
ejpam-5650	105	8	,	,	PUNCT
ejpam-5650	105	9	v	v	ADP
ejpam-5650	105	10	⊆	⊆	NUM
ejpam-5650	105	11	τ1τ2	τ1τ2	NOUN
ejpam-5650	105	12	-	-	NOUN
ejpam-5650	105	13	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	105	14	-	-	PUNCT
ejpam-5650	105	15	cl(v	cl(v	NOUN
ejpam-5650	105	16	)	)	PUNCT
ejpam-5650	105	17	)	)	PUNCT
ejpam-5650	105	18	and	and	CCONJ
ejpam-5650	105	19	hence	hence	ADV
ejpam-5650	105	20	x	x	X
ejpam-5650	105	21	−	−	ADP
ejpam-5650	105	22	τ1τ2	τ1τ2	NOUN
ejpam-5650	105	23	-	-	NOUN
ejpam-5650	105	24	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	105	25	-	-	PUNCT
ejpam-5650	105	26	cl(v	cl(v	NOUN
ejpam-5650	105	27	)	)	PUNCT
ejpam-5650	105	28	)	)	PUNCT
ejpam-5650	106	1	⊆	⊆	NUM
ejpam-5650	106	2	x	x	SYM
ejpam-5650	106	3	−	−	NUM
ejpam-5650	106	4	v	v	NOUN
ejpam-5650	106	5	.	.	PUNCT
ejpam-5650	107	1	by	by	ADP
ejpam-5650	107	2	the	the	DET
ejpam-5650	107	3	hypothesis	hypothesis	NOUN
ejpam-5650	107	4	,	,	PUNCT
ejpam-5650	107	5	x	x	PUNCT
ejpam-5650	107	6	−	−	PROPN
ejpam-5650	107	7	v	v	NOUN
ejpam-5650	107	8	is	be	AUX
ejpam-5650	107	9	n	n	PRON
ejpam-5650	107	10	(	(	PUNCT
ejpam-5650	107	11	τ1	τ1	PROPN
ejpam-5650	107	12	,	,	PUNCT
ejpam-5650	107	13	τ2)-closed	τ2)-closed	ADJ
ejpam-5650	107	14	and	and	CCONJ
ejpam-5650	107	15	x	x	X
ejpam-5650	108	1	−	−	ADP
ejpam-5650	108	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	108	3	-	-	NOUN
ejpam-5650	108	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	108	5	-	-	PUNCT
ejpam-5650	108	6	cl(v	cl(v	NOUN
ejpam-5650	108	7	)	)	PUNCT
ejpam-5650	108	8	)	)	PUNCT
ejpam-5650	108	9	is	be	AUX
ejpam-5650	108	10	(	(	PUNCT
ejpam-5650	108	11	τ1	τ1	NOUN
ejpam-5650	108	12	,	,	PUNCT
ejpam-5650	108	13	τ2)r	τ2)r	NOUN
ejpam-5650	108	14	-	-	PUNCT
ejpam-5650	108	15	closed	closed	ADJ
ejpam-5650	108	16	.	.	PUNCT
ejpam-5650	109	1	thus	thus	ADV
ejpam-5650	109	2	,	,	PUNCT
ejpam-5650	109	3	it	it	PRON
ejpam-5650	109	4	follows	follow	VERB
ejpam-5650	109	5	from	from	ADP
ejpam-5650	109	6	lemma	lemma	PROPN
ejpam-5650	109	7	2	2	NUM
ejpam-5650	109	8	that	that	PRON
ejpam-5650	109	9	x	x	X
ejpam-5650	110	1	−	−	ADP
ejpam-5650	110	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	110	3	-	-	NOUN
ejpam-5650	110	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5650	110	5	-	-	PUNCT
ejpam-5650	110	6	cl(v	cl(v	NOUN
ejpam-5650	110	7	)	)	PUNCT
ejpam-5650	110	8	)	)	PUNCT
ejpam-5650	110	9	is	be	AUX
ejpam-5650	110	10	n	n	PROPN
ejpam-5650	110	11	(	(	PUNCT
ejpam-5650	110	12	τ1	τ1	PROPN
ejpam-5650	110	13	,	,	PUNCT
ejpam-5650	110	14	τ2)-closed	τ2)-closed	PROPN
ejpam-5650	110	15	.	.	PUNCT
ejpam-5650	111	1	by	by	ADP
ejpam-5650	111	2	a	a	DET
ejpam-5650	111	3	multifunction	multifunction	NOUN
ejpam-5650	111	4	f	f	NOUN
ejpam-5650	111	5	:	:	PUNCT
ejpam-5650	111	6	x	x	X
ejpam-5650	111	7	→	→	SYM
ejpam-5650	111	8	y	y	PROPN
ejpam-5650	111	9	,	,	PUNCT
ejpam-5650	111	10	we	we	PRON
ejpam-5650	111	11	mean	mean	VERB
ejpam-5650	111	12	a	a	DET
ejpam-5650	111	13	point	point	NOUN
ejpam-5650	111	14	-	-	PUNCT
ejpam-5650	111	15	to	to	ADP
ejpam-5650	111	16	-	-	PUNCT
ejpam-5650	111	17	set	set	VERB
ejpam-5650	111	18	correspondence	correspondence	NOUN
ejpam-5650	111	19	from	from	ADP
ejpam-5650	111	20	x	x	PUNCT
ejpam-5650	111	21	into	into	ADP
ejpam-5650	111	22	y	y	PROPN
ejpam-5650	111	23	,	,	PUNCT
ejpam-5650	111	24	and	and	CCONJ
ejpam-5650	111	25	we	we	PRON
ejpam-5650	111	26	always	always	ADV
ejpam-5650	111	27	assume	assume	VERB
ejpam-5650	111	28	that	that	SCONJ
ejpam-5650	111	29	f	f	PROPN
ejpam-5650	111	30	(	(	PUNCT
ejpam-5650	111	31	x	x	X
ejpam-5650	111	32	)	)	PUNCT
ejpam-5650	111	33	̸=	̸=	NOUN
ejpam-5650	111	34	∅	∅	NOUN
ejpam-5650	111	35	for	for	ADP
ejpam-5650	111	36	all	all	PRON
ejpam-5650	111	37	x	x	SYM
ejpam-5650	111	38	∈	∈	ADJ
ejpam-5650	111	39	x.	x.	NOUN
ejpam-5650	111	40	for	for	ADP
ejpam-5650	111	41	a	a	DET
ejpam-5650	111	42	multifunction	multifunction	NOUN
ejpam-5650	111	43	f	f	NOUN
ejpam-5650	111	44	:	:	PUNCT
ejpam-5650	111	45	x	x	X
ejpam-5650	111	46	→	→	SYM
ejpam-5650	111	47	y	y	PROPN
ejpam-5650	111	48	,	,	PUNCT
ejpam-5650	111	49	we	we	PRON
ejpam-5650	111	50	shall	shall	AUX
ejpam-5650	111	51	denote	denote	VERB
ejpam-5650	111	52	the	the	DET
ejpam-5650	111	53	upper	upper	ADJ
ejpam-5650	111	54	and	and	CCONJ
ejpam-5650	111	55	lower	low	ADJ
ejpam-5650	111	56	inverse	inverse	NOUN
ejpam-5650	111	57	of	of	ADP
ejpam-5650	111	58	a	a	DET
ejpam-5650	111	59	set	set	NOUN
ejpam-5650	111	60	b	b	PROPN
ejpam-5650	111	61	of	of	ADP
ejpam-5650	111	62	y	y	PROPN
ejpam-5650	111	63	by	by	ADP
ejpam-5650	111	64	f+(b	f+(b	NOUN
ejpam-5650	111	65	)	)	PUNCT
ejpam-5650	111	66	and	and	CCONJ
ejpam-5650	111	67	f−(b	f−(b	NOUN
ejpam-5650	111	68	)	)	PUNCT
ejpam-5650	111	69	,	,	PUNCT
ejpam-5650	111	70	respectively	respectively	ADV
ejpam-5650	111	71	,	,	PUNCT
ejpam-5650	111	72	that	that	ADV
ejpam-5650	111	73	is	is	ADV
ejpam-5650	111	74	,	,	PUNCT
ejpam-5650	111	75	f+(b	f+(b	NOUN
ejpam-5650	111	76	)	)	PUNCT
ejpam-5650	111	77	=	=	PRON
ejpam-5650	112	1	{	{	PUNCT
ejpam-5650	112	2	x	x	PUNCT
ejpam-5650	112	3	∈	∈	PROPN
ejpam-5650	112	4	x	x	INTJ
ejpam-5650	113	1	|	|	NOUN
ejpam-5650	113	2	f	f	X
ejpam-5650	113	3	(	(	PUNCT
ejpam-5650	113	4	x	x	NOUN
ejpam-5650	113	5	)	)	PUNCT
ejpam-5650	113	6	⊆	⊆	NUM
ejpam-5650	113	7	b	b	NOUN
ejpam-5650	113	8	}	}	PUNCT
ejpam-5650	113	9	and	and	CCONJ
ejpam-5650	113	10	f−(b	f−(b	PROPN
ejpam-5650	113	11	)	)	PUNCT
ejpam-5650	113	12	=	=	PRON
ejpam-5650	114	1	{	{	PUNCT
ejpam-5650	114	2	x	x	PUNCT
ejpam-5650	114	3	∈	∈	PROPN
ejpam-5650	114	4	x	x	INTJ
ejpam-5650	115	1	|	|	NOUN
ejpam-5650	115	2	f	f	X
ejpam-5650	115	3	(	(	PUNCT
ejpam-5650	115	4	x	x	NOUN
ejpam-5650	115	5	)	)	PUNCT
ejpam-5650	115	6	∩	∩	NOUN
ejpam-5650	115	7	b	b	PROPN
ejpam-5650	115	8	̸=	̸=	PROPN
ejpam-5650	115	9	∅	∅	NOUN
ejpam-5650	115	10	}	}	PUNCT
ejpam-5650	115	11	.	.	PUNCT
ejpam-5650	116	1	in	in	ADP
ejpam-5650	116	2	particular	particular	ADJ
ejpam-5650	116	3	,	,	PUNCT
ejpam-5650	116	4	f−(y	f−(y	NOUN
ejpam-5650	116	5	)	)	PUNCT
ejpam-5650	116	6	=	=	SYM
ejpam-5650	117	1	{	{	PUNCT
ejpam-5650	117	2	x	x	PUNCT
ejpam-5650	117	3	∈	∈	PROPN
ejpam-5650	117	4	x	x	INTJ
ejpam-5650	118	1	|	|	ADV
ejpam-5650	118	2	y	y	PROPN
ejpam-5650	118	3	∈	∈	PROPN
ejpam-5650	118	4	f	f	X
ejpam-5650	118	5	(	(	PUNCT
ejpam-5650	118	6	x	x	NOUN
ejpam-5650	118	7	)	)	PUNCT
ejpam-5650	118	8	}	}	PUNCT
ejpam-5650	118	9	for	for	ADP
ejpam-5650	118	10	each	each	DET
ejpam-5650	118	11	point	point	NOUN
ejpam-5650	118	12	y	y	PROPN
ejpam-5650	118	13	∈	∈	PROPN
ejpam-5650	118	14	y	y	PROPN
ejpam-5650	118	15	.	.	PUNCT
ejpam-5650	119	1	for	for	ADP
ejpam-5650	119	2	each	each	DET
ejpam-5650	119	3	a	a	DET
ejpam-5650	119	4	⊆	⊆	NUM
ejpam-5650	119	5	x	x	SYM
ejpam-5650	119	6	,	,	PUNCT
ejpam-5650	119	7	f	f	PROPN
ejpam-5650	119	8	(	(	PUNCT
ejpam-5650	119	9	a	a	NOUN
ejpam-5650	119	10	)	)	PUNCT
ejpam-5650	119	11	=	=	SYM
ejpam-5650	119	12	∪x∈af	∪x∈af	NOUN
ejpam-5650	119	13	(	(	PUNCT
ejpam-5650	119	14	x	x	NOUN
ejpam-5650	119	15	)	)	PUNCT
ejpam-5650	119	16	.	.	PUNCT
ejpam-5650	120	1	3	3	X
ejpam-5650	120	2	.	.	X
ejpam-5650	120	3	upper	upper	ADJ
ejpam-5650	120	4	and	and	CCONJ
ejpam-5650	120	5	lower	low	ADJ
ejpam-5650	120	6	almost	almost	ADV
ejpam-5650	120	7	nearly	nearly	ADV
ejpam-5650	120	8	(	(	PUNCT
ejpam-5650	120	9	τ1	τ1	NOUN
ejpam-5650	120	10	,	,	PUNCT
ejpam-5650	120	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	120	12	multifunctions	multifunction	NOUN
ejpam-5650	120	13	in	in	ADP
ejpam-5650	120	14	this	this	DET
ejpam-5650	120	15	section	section	NOUN
ejpam-5650	120	16	,	,	PUNCT
ejpam-5650	120	17	we	we	PRON
ejpam-5650	120	18	introduce	introduce	VERB
ejpam-5650	120	19	the	the	DET
ejpam-5650	120	20	notions	notion	NOUN
ejpam-5650	120	21	of	of	ADP
ejpam-5650	120	22	upper	upper	ADJ
ejpam-5650	120	23	almost	almost	ADV
ejpam-5650	120	24	nearly	nearly	ADV
ejpam-5650	120	25	(	(	PUNCT
ejpam-5650	120	26	τ1	τ1	NOUN
ejpam-5650	120	27	,	,	PUNCT
ejpam-5650	120	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	120	29	multifunctions	multifunction	NOUN
ejpam-5650	120	30	and	and	CCONJ
ejpam-5650	120	31	lower	low	ADJ
ejpam-5650	120	32	almost	almost	ADV
ejpam-5650	120	33	nearly	nearly	ADV
ejpam-5650	120	34	(	(	PUNCT
ejpam-5650	120	35	τ1	τ1	NOUN
ejpam-5650	120	36	,	,	PUNCT
ejpam-5650	120	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	120	38	multifunctions	multifunction	NOUN
ejpam-5650	120	39	.	.	PUNCT
ejpam-5650	121	1	furthermore	furthermore	ADV
ejpam-5650	121	2	,	,	PUNCT
ejpam-5650	121	3	several	several	ADJ
ejpam-5650	121	4	characterizations	characterization	NOUN
ejpam-5650	121	5	of	of	ADP
ejpam-5650	121	6	upper	upper	ADJ
ejpam-5650	121	7	almost	almost	ADV
ejpam-5650	121	8	nearly	nearly	ADV
ejpam-5650	121	9	(	(	PUNCT
ejpam-5650	121	10	τ1	τ1	NOUN
ejpam-5650	121	11	,	,	PUNCT
ejpam-5650	121	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	121	13	multifunctions	multifunction	NOUN
ejpam-5650	121	14	and	and	CCONJ
ejpam-5650	121	15	lower	low	ADJ
ejpam-5650	121	16	almost	almost	ADV
ejpam-5650	121	17	nearly	nearly	ADV
ejpam-5650	121	18	(	(	PUNCT
ejpam-5650	121	19	τ1	τ1	NOUN
ejpam-5650	121	20	,	,	PUNCT
ejpam-5650	121	21	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	121	22	multifunctions	multifunction	NOUN
ejpam-5650	121	23	are	be	AUX
ejpam-5650	121	24	discussed	discuss	VERB
ejpam-5650	121	25	.	.	PUNCT
ejpam-5650	122	1	definition	definition	NOUN
ejpam-5650	122	2	1	1	NUM
ejpam-5650	122	3	.	.	PUNCT
ejpam-5650	123	1	a	a	DET
ejpam-5650	123	2	multifunction	multifunction	NOUN
ejpam-5650	123	3	f	f	NOUN
ejpam-5650	123	4	:	:	PUNCT
ejpam-5650	123	5	(	(	PUNCT
ejpam-5650	123	6	x	x	NOUN
ejpam-5650	123	7	,	,	PUNCT
ejpam-5650	123	8	τ1	τ1	NOUN
ejpam-5650	123	9	,	,	PUNCT
ejpam-5650	123	10	τ2	τ2	NOUN
ejpam-5650	123	11	)	)	PUNCT
ejpam-5650	123	12	→	→	SYM
ejpam-5650	123	13	(	(	PUNCT
ejpam-5650	123	14	y	y	PROPN
ejpam-5650	123	15	,	,	PUNCT
ejpam-5650	123	16	σ1	σ1	PROPN
ejpam-5650	123	17	,	,	PUNCT
ejpam-5650	123	18	σ2	σ2	PROPN
ejpam-5650	123	19	)	)	PUNCT
ejpam-5650	123	20	is	be	AUX
ejpam-5650	123	21	called	call	VERB
ejpam-5650	123	22	upper	upper	ADV
ejpam-5650	123	23	almost	almost	ADV
ejpam-5650	123	24	nearly	nearly	ADV
ejpam-5650	123	25	(	(	PUNCT
ejpam-5650	123	26	τ1	τ1	NOUN
ejpam-5650	123	27	,	,	PUNCT
ejpam-5650	123	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	123	29	at	at	ADP
ejpam-5650	123	30	a	a	DET
ejpam-5650	123	31	point	point	NOUN
ejpam-5650	123	32	x	x	SYM
ejpam-5650	123	33	∈	∈	NOUN
ejpam-5650	123	34	x	x	PUNCT
ejpam-5650	123	35	if	if	SCONJ
ejpam-5650	123	36	for	for	ADP
ejpam-5650	123	37	each	each	DET
ejpam-5650	123	38	σ1σ2	σ1σ2	VERB
ejpam-5650	123	39	-	-	ADJ
ejpam-5650	123	40	open	open	ADJ
ejpam-5650	123	41	set	set	NOUN
ejpam-5650	123	42	v	v	NOUN
ejpam-5650	123	43	of	of	ADP
ejpam-5650	123	44	y	y	PROPN
ejpam-5650	123	45	containing	contain	VERB
ejpam-5650	123	46	f	f	PROPN
ejpam-5650	123	47	(	(	PUNCT
ejpam-5650	123	48	x	x	NOUN
ejpam-5650	123	49	)	)	PUNCT
ejpam-5650	123	50	and	and	CCONJ
ejpam-5650	123	51	having	have	VERB
ejpam-5650	123	52	n	n	PRON
ejpam-5650	123	53	(	(	PUNCT
ejpam-5650	123	54	σ1	σ1	PROPN
ejpam-5650	123	55	,	,	PUNCT
ejpam-5650	123	56	σ2)-closed	σ2)-close	VERB
ejpam-5650	123	57	complement	complement	NOUN
ejpam-5650	123	58	,	,	PUNCT
ejpam-5650	123	59	there	there	PRON
ejpam-5650	123	60	exists	exist	VERB
ejpam-5650	123	61	a	a	DET
ejpam-5650	123	62	τ1τ2	τ1τ2	NOUN
ejpam-5650	123	63	-	-	ADJ
ejpam-5650	123	64	open	open	ADJ
ejpam-5650	123	65	set	set	ADJ
ejpam-5650	123	66	u	u	NOUN
ejpam-5650	123	67	of	of	ADP
ejpam-5650	123	68	x	x	PUNCT
ejpam-5650	123	69	containing	contain	VERB
ejpam-5650	123	70	x	x	PUNCT
ejpam-5650	123	71	such	such	ADJ
ejpam-5650	123	72	that	that	SCONJ
ejpam-5650	123	73	f	f	PROPN
ejpam-5650	123	74	(	(	PUNCT
ejpam-5650	123	75	u	u	NOUN
ejpam-5650	123	76	)	)	PUNCT
ejpam-5650	123	77	⊆	⊆	NUM
ejpam-5650	123	78	σ1σ2	σ1σ2	X
ejpam-5650	123	79	-	-	PUNCT
ejpam-5650	123	80	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	123	81	-	-	PUNCT
ejpam-5650	123	82	cl(v	cl(v	NOUN
ejpam-5650	123	83	)	)	PUNCT
ejpam-5650	123	84	)	)	PUNCT
ejpam-5650	123	85	.	.	PUNCT
ejpam-5650	124	1	a	a	DET
ejpam-5650	124	2	multifunction	multifunction	NOUN
ejpam-5650	124	3	f	f	NOUN
ejpam-5650	124	4	:	:	PUNCT
ejpam-5650	124	5	(	(	PUNCT
ejpam-5650	124	6	x	x	NOUN
ejpam-5650	124	7	,	,	PUNCT
ejpam-5650	124	8	τ1	τ1	NOUN
ejpam-5650	124	9	,	,	PUNCT
ejpam-5650	124	10	τ2	τ2	NOUN
ejpam-5650	124	11	)	)	PUNCT
ejpam-5650	124	12	→	→	SYM
ejpam-5650	124	13	(	(	PUNCT
ejpam-5650	124	14	y	y	PROPN
ejpam-5650	124	15	,	,	PUNCT
ejpam-5650	124	16	σ1	σ1	PROPN
ejpam-5650	124	17	,	,	PUNCT
ejpam-5650	124	18	σ2	σ2	PROPN
ejpam-5650	124	19	)	)	PUNCT
ejpam-5650	124	20	is	be	AUX
ejpam-5650	124	21	called	call	VERB
ejpam-5650	124	22	upper	upper	ADV
ejpam-5650	124	23	almost	almost	ADV
ejpam-5650	124	24	nearly	nearly	ADV
ejpam-5650	124	25	(	(	PUNCT
ejpam-5650	124	26	τ1	τ1	NOUN
ejpam-5650	124	27	,	,	PUNCT
ejpam-5650	124	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	124	29	if	if	SCONJ
ejpam-5650	124	30	f	f	PROPN
ejpam-5650	124	31	is	be	AUX
ejpam-5650	124	32	upper	upper	ADJ
ejpam-5650	124	33	almost	almost	ADV
ejpam-5650	124	34	nearly	nearly	ADV
ejpam-5650	124	35	(	(	PUNCT
ejpam-5650	124	36	τ1	τ1	NOUN
ejpam-5650	124	37	,	,	PUNCT
ejpam-5650	124	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	124	39	at	at	ADP
ejpam-5650	124	40	each	each	DET
ejpam-5650	124	41	point	point	NOUN
ejpam-5650	124	42	x	x	PUNCT
ejpam-5650	124	43	of	of	ADP
ejpam-5650	124	44	x.	x.	PROPN
ejpam-5650	124	45	theorem	theorem	VERB
ejpam-5650	124	46	1	1	NUM
ejpam-5650	124	47	.	.	X
ejpam-5650	124	48	for	for	ADP
ejpam-5650	124	49	a	a	DET
ejpam-5650	124	50	multifunction	multifunction	NOUN
ejpam-5650	124	51	f	f	NOUN
ejpam-5650	124	52	:	:	PUNCT
ejpam-5650	124	53	(	(	PUNCT
ejpam-5650	124	54	x	x	NOUN
ejpam-5650	124	55	,	,	PUNCT
ejpam-5650	124	56	τ1	τ1	NOUN
ejpam-5650	124	57	,	,	PUNCT
ejpam-5650	124	58	τ2	τ2	NOUN
ejpam-5650	124	59	)	)	PUNCT
ejpam-5650	124	60	→	→	SYM
ejpam-5650	124	61	(	(	PUNCT
ejpam-5650	124	62	y	y	PROPN
ejpam-5650	124	63	,	,	PUNCT
ejpam-5650	124	64	σ1	σ1	PROPN
ejpam-5650	124	65	,	,	PUNCT
ejpam-5650	124	66	σ2	σ2	NOUN
ejpam-5650	124	67	)	)	PUNCT
ejpam-5650	124	68	,	,	PUNCT
ejpam-5650	124	69	the	the	DET
ejpam-5650	124	70	following	follow	VERB
ejpam-5650	124	71	properties	property	NOUN
ejpam-5650	124	72	are	be	AUX
ejpam-5650	124	73	equivalent	equivalent	ADJ
ejpam-5650	124	74	:	:	PUNCT
ejpam-5650	124	75	(	(	PUNCT
ejpam-5650	124	76	1	1	X
ejpam-5650	124	77	)	)	PUNCT
ejpam-5650	124	78	f	f	PROPN
ejpam-5650	124	79	is	be	AUX
ejpam-5650	124	80	upper	upper	ADJ
ejpam-5650	124	81	almost	almost	ADV
ejpam-5650	124	82	nearly	nearly	ADV
ejpam-5650	124	83	(	(	PUNCT
ejpam-5650	124	84	τ1	τ1	NOUN
ejpam-5650	124	85	,	,	PUNCT
ejpam-5650	124	86	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	124	87	at	at	ADP
ejpam-5650	124	88	x	x	X
ejpam-5650	124	89	∈	∈	PROPN
ejpam-5650	124	90	x	x	X
ejpam-5650	124	91	;	;	PUNCT
ejpam-5650	124	92	(	(	PUNCT
ejpam-5650	124	93	2	2	X
ejpam-5650	124	94	)	)	PUNCT
ejpam-5650	124	95	x	x	SYM
ejpam-5650	124	96	∈	∈	PRON
ejpam-5650	124	97	τ1τ2	τ1τ2	NOUN
ejpam-5650	124	98	-	-	NUM
ejpam-5650	124	99	int(f	int(f	VERB
ejpam-5650	124	100	+	+	ADJ
ejpam-5650	124	101	(	(	PUNCT
ejpam-5650	124	102	σ1σ2	σ1σ2	NUM
ejpam-5650	124	103	-	-	PUNCT
ejpam-5650	124	104	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	124	105	-	-	PUNCT
ejpam-5650	124	106	cl(v	cl(v	NOUN
ejpam-5650	124	107	)	)	PUNCT
ejpam-5650	124	108	)	)	PUNCT
ejpam-5650	124	109	)	)	PUNCT
ejpam-5650	124	110	)	)	PUNCT
ejpam-5650	124	111	for	for	ADP
ejpam-5650	124	112	each	each	DET
ejpam-5650	124	113	σ1σ2	σ1σ2	VERB
ejpam-5650	124	114	-	-	ADJ
ejpam-5650	124	115	open	open	ADJ
ejpam-5650	124	116	set	set	NOUN
ejpam-5650	124	117	v	v	NOUN
ejpam-5650	124	118	of	of	ADP
ejpam-5650	124	119	y	y	PROPN
ejpam-5650	124	120	containing	contain	VERB
ejpam-5650	124	121	f	f	PROPN
ejpam-5650	124	122	(	(	PUNCT
ejpam-5650	124	123	x	x	NOUN
ejpam-5650	124	124	)	)	PUNCT
ejpam-5650	124	125	and	and	CCONJ
ejpam-5650	124	126	having	have	VERB
ejpam-5650	124	127	n	n	PRON
ejpam-5650	124	128	(	(	PUNCT
ejpam-5650	124	129	σ1	σ1	PROPN
ejpam-5650	124	130	,	,	PUNCT
ejpam-5650	124	131	σ2)-closed	σ2)-close	VERB
ejpam-5650	124	132	complement	complement	NOUN
ejpam-5650	124	133	;	;	PUNCT
ejpam-5650	124	134	(	(	PUNCT
ejpam-5650	124	135	3	3	X
ejpam-5650	124	136	)	)	PUNCT
ejpam-5650	124	137	x	x	SYM
ejpam-5650	124	138	∈	∈	PRON
ejpam-5650	124	139	τ1τ2	τ1τ2	PUNCT
ejpam-5650	124	140	-	-	NUM
ejpam-5650	124	141	int(f	int(f	VERB
ejpam-5650	124	142	+	+	ADJ
ejpam-5650	124	143	(	(	PUNCT
ejpam-5650	124	144	(	(	PUNCT
ejpam-5650	124	145	σ1	σ1	PROPN
ejpam-5650	124	146	,	,	PUNCT
ejpam-5650	124	147	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5650	124	148	)	)	PUNCT
ejpam-5650	124	149	)	)	PUNCT
ejpam-5650	124	150	)	)	PUNCT
ejpam-5650	124	151	for	for	ADP
ejpam-5650	124	152	each	each	DET
ejpam-5650	124	153	σ1σ2	σ1σ2	VERB
ejpam-5650	124	154	-	-	ADJ
ejpam-5650	124	155	open	open	ADJ
ejpam-5650	124	156	set	set	NOUN
ejpam-5650	124	157	v	v	NOUN
ejpam-5650	124	158	of	of	ADP
ejpam-5650	124	159	y	y	PROPN
ejpam-5650	124	160	containing	contain	VERB
ejpam-5650	124	161	f	f	PROPN
ejpam-5650	124	162	(	(	PUNCT
ejpam-5650	124	163	x	x	NOUN
ejpam-5650	124	164	)	)	PUNCT
ejpam-5650	124	165	and	and	CCONJ
ejpam-5650	124	166	having	have	VERB
ejpam-5650	124	167	n	n	PRON
ejpam-5650	124	168	(	(	PUNCT
ejpam-5650	124	169	σ1	σ1	PROPN
ejpam-5650	124	170	,	,	PUNCT
ejpam-5650	124	171	σ2)-closed	σ2)-close	VERB
ejpam-5650	124	172	complement	complement	NOUN
ejpam-5650	124	173	;	;	PUNCT
ejpam-5650	124	174	n.	n.	NOUN
ejpam-5650	124	175	chutiman	chutiman	NOUN
ejpam-5650	124	176	,	,	PUNCT
ejpam-5650	124	177	a.	a.	PROPN
ejpam-5650	124	178	sama	sama	PROPN
ejpam-5650	124	179	-	-	PUNCT
ejpam-5650	124	180	ae	ae	PROPN
ejpam-5650	124	181	,	,	PUNCT
ejpam-5650	124	182	c.	c.	PROPN
ejpam-5650	124	183	boonpok	boonpok	PROPN
ejpam-5650	124	184	/	/	SYM
ejpam-5650	124	185	eur	eur	PROPN
ejpam-5650	124	186	.	.	PUNCT
ejpam-5650	125	1	j.	j.	PROPN
ejpam-5650	125	2	pure	pure	PROPN
ejpam-5650	125	3	appl	appl	PROPN
ejpam-5650	125	4	.	.	PROPN
ejpam-5650	125	5	math	math	PROPN
ejpam-5650	125	6	,	,	PUNCT
ejpam-5650	125	7	18	18	NUM
ejpam-5650	125	8	(	(	PUNCT
ejpam-5650	125	9	1	1	NUM
ejpam-5650	125	10	)	)	PUNCT
ejpam-5650	125	11	(	(	PUNCT
ejpam-5650	125	12	2025	2025	NUM
ejpam-5650	125	13	)	)	PUNCT
ejpam-5650	125	14	,	,	PUNCT
ejpam-5650	125	15	5650	5650	NUM
ejpam-5650	125	16	5	5	NUM
ejpam-5650	125	17	of	of	ADP
ejpam-5650	125	18	18	18	NUM
ejpam-5650	125	19	(	(	PUNCT
ejpam-5650	125	20	4	4	NUM
ejpam-5650	125	21	)	)	PUNCT
ejpam-5650	125	22	x	x	SYM
ejpam-5650	125	23	∈	∈	PRON
ejpam-5650	125	24	τ1τ2	τ1τ2	PUNCT
ejpam-5650	125	25	-	-	NUM
ejpam-5650	125	26	int(f	int(f	VERB
ejpam-5650	125	27	+	+	ADJ
ejpam-5650	125	28	(	(	PUNCT
ejpam-5650	125	29	v	v	NOUN
ejpam-5650	125	30	)	)	PUNCT
ejpam-5650	125	31	)	)	PUNCT
ejpam-5650	126	1	for	for	ADP
ejpam-5650	126	2	each	each	DET
ejpam-5650	126	3	(	(	PUNCT
ejpam-5650	126	4	σ1	σ1	PROPN
ejpam-5650	126	5	,	,	PUNCT
ejpam-5650	126	6	σ2)r	σ2)r	NOUN
ejpam-5650	126	7	-	-	PUNCT
ejpam-5650	126	8	open	open	ADJ
ejpam-5650	126	9	set	set	VERB
ejpam-5650	126	10	v	v	NOUN
ejpam-5650	126	11	of	of	ADP
ejpam-5650	126	12	y	y	PROPN
ejpam-5650	126	13	containing	contain	VERB
ejpam-5650	126	14	f	f	PROPN
ejpam-5650	126	15	(	(	PUNCT
ejpam-5650	126	16	x	x	NOUN
ejpam-5650	126	17	)	)	PUNCT
ejpam-5650	126	18	and	and	CCONJ
ejpam-5650	126	19	having	have	VERB
ejpam-5650	126	20	n	n	PRON
ejpam-5650	126	21	(	(	PUNCT
ejpam-5650	126	22	σ1	σ1	PROPN
ejpam-5650	126	23	,	,	PUNCT
ejpam-5650	126	24	σ2)-closed	σ2)-close	VERB
ejpam-5650	126	25	complement	complement	NOUN
ejpam-5650	126	26	;	;	PUNCT
ejpam-5650	126	27	(	(	PUNCT
ejpam-5650	126	28	5	5	X
ejpam-5650	126	29	)	)	PUNCT
ejpam-5650	126	30	for	for	ADP
ejpam-5650	126	31	each	each	DET
ejpam-5650	126	32	(	(	PUNCT
ejpam-5650	126	33	σ1	σ1	PROPN
ejpam-5650	126	34	,	,	PUNCT
ejpam-5650	126	35	σ2)r	σ2)r	NOUN
ejpam-5650	126	36	-	-	PUNCT
ejpam-5650	126	37	open	open	ADJ
ejpam-5650	126	38	set	set	VERB
ejpam-5650	126	39	v	v	NOUN
ejpam-5650	126	40	of	of	ADP
ejpam-5650	126	41	y	y	PROPN
ejpam-5650	126	42	containing	contain	VERB
ejpam-5650	126	43	f	f	PROPN
ejpam-5650	126	44	(	(	PUNCT
ejpam-5650	126	45	x	x	NOUN
ejpam-5650	126	46	)	)	PUNCT
ejpam-5650	126	47	and	and	CCONJ
ejpam-5650	126	48	having	have	VERB
ejpam-5650	126	49	n	n	PRON
ejpam-5650	126	50	(	(	PUNCT
ejpam-5650	126	51	σ1	σ1	PROPN
ejpam-5650	126	52	,	,	PUNCT
ejpam-5650	126	53	σ2)-closed	σ2)-close	VERB
ejpam-5650	126	54	complement	complement	NOUN
ejpam-5650	126	55	,	,	PUNCT
ejpam-5650	126	56	there	there	PRON
ejpam-5650	126	57	exists	exist	VERB
ejpam-5650	126	58	a	a	DET
ejpam-5650	126	59	τ1τ2	τ1τ2	NOUN
ejpam-5650	126	60	-	-	ADJ
ejpam-5650	126	61	open	open	ADJ
ejpam-5650	126	62	set	set	ADJ
ejpam-5650	126	63	u	u	NOUN
ejpam-5650	126	64	of	of	ADP
ejpam-5650	126	65	x	x	PUNCT
ejpam-5650	126	66	containing	contain	VERB
ejpam-5650	126	67	x	x	PUNCT
ejpam-5650	126	68	such	such	ADJ
ejpam-5650	126	69	that	that	SCONJ
ejpam-5650	126	70	f	f	PROPN
ejpam-5650	126	71	(	(	PUNCT
ejpam-5650	126	72	u	u	NOUN
ejpam-5650	126	73	)	)	PUNCT
ejpam-5650	126	74	⊆	⊆	NUM
ejpam-5650	126	75	v	v	NOUN
ejpam-5650	126	76	.	.	PUNCT
ejpam-5650	127	1	proof	proof	NOUN
ejpam-5650	127	2	.	.	PUNCT
ejpam-5650	128	1	(	(	PUNCT
ejpam-5650	128	2	1	1	X
ejpam-5650	128	3	)	)	PUNCT
ejpam-5650	128	4	⇒	⇒	NOUN
ejpam-5650	128	5	(	(	PUNCT
ejpam-5650	128	6	2	2	NUM
ejpam-5650	128	7	):	):	PUNCT
ejpam-5650	128	8	let	let	VERB
ejpam-5650	128	9	v	v	PART
ejpam-5650	128	10	be	be	AUX
ejpam-5650	128	11	any	any	DET
ejpam-5650	128	12	σ1σ2	σ1σ2	NOUN
ejpam-5650	128	13	-	-	ADJ
ejpam-5650	128	14	open	open	ADJ
ejpam-5650	128	15	set	set	NOUN
ejpam-5650	128	16	of	of	ADP
ejpam-5650	128	17	y	y	PROPN
ejpam-5650	128	18	containing	contain	VERB
ejpam-5650	128	19	f	f	PROPN
ejpam-5650	128	20	(	(	PUNCT
ejpam-5650	128	21	x	x	NOUN
ejpam-5650	128	22	)	)	PUNCT
ejpam-5650	128	23	and	and	CCONJ
ejpam-5650	128	24	having	have	VERB
ejpam-5650	128	25	n	n	PRON
ejpam-5650	128	26	(	(	PUNCT
ejpam-5650	128	27	σ1	σ1	PROPN
ejpam-5650	128	28	,	,	PUNCT
ejpam-5650	128	29	σ2)-closed	σ2)-close	VERB
ejpam-5650	128	30	complement	complement	NOUN
ejpam-5650	128	31	.	.	PUNCT
ejpam-5650	129	1	by	by	ADP
ejpam-5650	129	2	(	(	PUNCT
ejpam-5650	129	3	1	1	NUM
ejpam-5650	129	4	)	)	PUNCT
ejpam-5650	129	5	,	,	PUNCT
ejpam-5650	129	6	there	there	PRON
ejpam-5650	129	7	exists	exist	VERB
ejpam-5650	129	8	a	a	DET
ejpam-5650	129	9	τ1τ2	τ1τ2	NOUN
ejpam-5650	129	10	-	-	ADJ
ejpam-5650	129	11	open	open	ADJ
ejpam-5650	129	12	set	set	ADJ
ejpam-5650	129	13	u	u	NOUN
ejpam-5650	129	14	of	of	ADP
ejpam-5650	129	15	x	x	PUNCT
ejpam-5650	129	16	containing	contain	VERB
ejpam-5650	129	17	x	x	PUNCT
ejpam-5650	129	18	such	such	ADJ
ejpam-5650	129	19	that	that	SCONJ
ejpam-5650	129	20	f	f	PROPN
ejpam-5650	129	21	(	(	PUNCT
ejpam-5650	129	22	u	u	NOUN
ejpam-5650	129	23	)	)	PUNCT
ejpam-5650	129	24	⊆	⊆	NUM
ejpam-5650	129	25	σ1σ2	σ1σ2	X
ejpam-5650	129	26	-	-	PUNCT
ejpam-5650	129	27	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	129	28	-	-	PUNCT
ejpam-5650	129	29	cl(v	cl(v	NOUN
ejpam-5650	129	30	)	)	PUNCT
ejpam-5650	129	31	)	)	PUNCT
ejpam-5650	129	32	.	.	PUNCT
ejpam-5650	130	1	thus	thus	ADV
ejpam-5650	130	2	,	,	PUNCT
ejpam-5650	130	3	we	we	PRON
ejpam-5650	130	4	have	have	VERB
ejpam-5650	130	5	x	x	X
ejpam-5650	130	6	∈	∈	PROPN
ejpam-5650	130	7	u	u	NOUN
ejpam-5650	130	8	⊆	⊆	NUM
ejpam-5650	130	9	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5650	130	10	-	-	PUNCT
ejpam-5650	130	11	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	130	12	-	-	PUNCT
ejpam-5650	130	13	cl(v	cl(v	NOUN
ejpam-5650	130	14	)	)	PUNCT
ejpam-5650	130	15	)	)	PUNCT
ejpam-5650	130	16	and	and	CCONJ
ejpam-5650	130	17	hence	hence	ADV
ejpam-5650	130	18	x	x	X
ejpam-5650	130	19	∈	∈	PRON
ejpam-5650	130	20	τ1τ2	τ1τ2	NOUN
ejpam-5650	130	21	-	-	NUM
ejpam-5650	130	22	int(f	int(f	VERB
ejpam-5650	130	23	+	+	ADJ
ejpam-5650	130	24	(	(	PUNCT
ejpam-5650	130	25	σ1σ2	σ1σ2	NUM
ejpam-5650	130	26	-	-	PUNCT
ejpam-5650	130	27	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	130	28	-	-	PUNCT
ejpam-5650	130	29	cl(v	cl(v	NOUN
ejpam-5650	130	30	)	)	PUNCT
ejpam-5650	130	31	)	)	PUNCT
ejpam-5650	130	32	)	)	PUNCT
ejpam-5650	130	33	)	)	PUNCT
ejpam-5650	130	34	.	.	PUNCT
ejpam-5650	131	1	(	(	PUNCT
ejpam-5650	131	2	2	2	X
ejpam-5650	131	3	)	)	PUNCT
ejpam-5650	131	4	⇒	⇒	NOUN
ejpam-5650	131	5	(	(	PUNCT
ejpam-5650	131	6	3	3	NUM
ejpam-5650	131	7	):	):	PUNCT
ejpam-5650	131	8	this	this	PRON
ejpam-5650	131	9	follows	follow	VERB
ejpam-5650	131	10	from	from	ADP
ejpam-5650	131	11	lemma	lemma	PROPN
ejpam-5650	131	12	1	1	NUM
ejpam-5650	131	13	.	.	PUNCT
ejpam-5650	131	14	(	(	PUNCT
ejpam-5650	131	15	3	3	X
ejpam-5650	131	16	)	)	PUNCT
ejpam-5650	131	17	⇒	⇒	NOUN
ejpam-5650	131	18	(	(	PUNCT
ejpam-5650	131	19	4	4	NUM
ejpam-5650	131	20	):	):	PUNCT
ejpam-5650	131	21	let	let	VERB
ejpam-5650	131	22	v	v	PART
ejpam-5650	131	23	be	be	AUX
ejpam-5650	131	24	any	any	DET
ejpam-5650	131	25	(	(	PUNCT
ejpam-5650	131	26	σ1	σ1	NOUN
ejpam-5650	131	27	,	,	PUNCT
ejpam-5650	131	28	σ2)r	σ2)r	NOUN
ejpam-5650	131	29	-	-	PUNCT
ejpam-5650	131	30	open	open	ADJ
ejpam-5650	131	31	set	set	NOUN
ejpam-5650	131	32	of	of	ADP
ejpam-5650	131	33	y	y	PROPN
ejpam-5650	131	34	containing	contain	VERB
ejpam-5650	131	35	f	f	PROPN
ejpam-5650	131	36	(	(	PUNCT
ejpam-5650	131	37	x	x	NOUN
ejpam-5650	131	38	)	)	PUNCT
ejpam-5650	131	39	and	and	CCONJ
ejpam-5650	131	40	having	have	VERB
ejpam-5650	131	41	n	n	PRON
ejpam-5650	131	42	(	(	PUNCT
ejpam-5650	131	43	σ1	σ1	PROPN
ejpam-5650	131	44	,	,	PUNCT
ejpam-5650	131	45	σ2)closed	σ2)close	VERB
ejpam-5650	131	46	complement	complement	NOUN
ejpam-5650	131	47	.	.	PUNCT
ejpam-5650	132	1	it	it	PRON
ejpam-5650	132	2	follows	follow	VERB
ejpam-5650	132	3	from	from	ADP
ejpam-5650	132	4	lemma	lemma	PROPN
ejpam-5650	132	5	1	1	NUM
ejpam-5650	132	6	that	that	PRON
ejpam-5650	132	7	v	v	NOUN
ejpam-5650	132	8	=	=	SYM
ejpam-5650	132	9	σ1σ2	σ1σ2	NOUN
ejpam-5650	132	10	-	-	PUNCT
ejpam-5650	132	11	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	132	12	-	-	PUNCT
ejpam-5650	132	13	cl(v	cl(v	NOUN
ejpam-5650	132	14	)	)	PUNCT
ejpam-5650	132	15	)	)	PUNCT
ejpam-5650	133	1	=	=	SYM
ejpam-5650	133	2	(	(	PUNCT
ejpam-5650	133	3	σ1	σ1	PROPN
ejpam-5650	133	4	,	,	PUNCT
ejpam-5650	133	5	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5650	133	6	)	)	PUNCT
ejpam-5650	133	7	.	.	PUNCT
ejpam-5650	134	1	(	(	PUNCT
ejpam-5650	134	2	4	4	X
ejpam-5650	134	3	)	)	PUNCT
ejpam-5650	134	4	⇒	⇒	NOUN
ejpam-5650	134	5	(	(	PUNCT
ejpam-5650	134	6	5	5	NUM
ejpam-5650	134	7	):	):	PUNCT
ejpam-5650	134	8	let	let	VERB
ejpam-5650	134	9	v	v	PART
ejpam-5650	134	10	be	be	AUX
ejpam-5650	134	11	any	any	DET
ejpam-5650	134	12	(	(	PUNCT
ejpam-5650	134	13	σ1	σ1	NOUN
ejpam-5650	134	14	,	,	PUNCT
ejpam-5650	134	15	σ2)r	σ2)r	NOUN
ejpam-5650	134	16	-	-	PUNCT
ejpam-5650	134	17	open	open	ADJ
ejpam-5650	134	18	set	set	NOUN
ejpam-5650	134	19	of	of	ADP
ejpam-5650	134	20	y	y	PROPN
ejpam-5650	134	21	containing	contain	VERB
ejpam-5650	134	22	f	f	PROPN
ejpam-5650	134	23	(	(	PUNCT
ejpam-5650	134	24	x	x	NOUN
ejpam-5650	134	25	)	)	PUNCT
ejpam-5650	134	26	and	and	CCONJ
ejpam-5650	134	27	having	have	VERB
ejpam-5650	134	28	n	n	PRON
ejpam-5650	134	29	(	(	PUNCT
ejpam-5650	134	30	σ1	σ1	PROPN
ejpam-5650	134	31	,	,	PUNCT
ejpam-5650	134	32	σ2)closed	σ2)close	VERB
ejpam-5650	134	33	complement	complement	NOUN
ejpam-5650	134	34	.	.	PUNCT
ejpam-5650	135	1	by	by	ADP
ejpam-5650	135	2	(	(	PUNCT
ejpam-5650	135	3	4	4	NUM
ejpam-5650	135	4	)	)	PUNCT
ejpam-5650	135	5	,	,	PUNCT
ejpam-5650	135	6	x	x	PUNCT
ejpam-5650	135	7	∈	∈	PROPN
ejpam-5650	135	8	τ1τ2	τ1τ2	NOUN
ejpam-5650	135	9	-	-	NOUN
ejpam-5650	135	10	cl(f	cl(f	NOUN
ejpam-5650	135	11	+	+	NOUN
ejpam-5650	135	12	(	(	PUNCT
ejpam-5650	135	13	v	v	NOUN
ejpam-5650	135	14	)	)	PUNCT
ejpam-5650	135	15	)	)	PUNCT
ejpam-5650	135	16	and	and	CCONJ
ejpam-5650	135	17	therefore	therefore	ADV
ejpam-5650	135	18	there	there	PRON
ejpam-5650	135	19	exists	exist	VERB
ejpam-5650	135	20	a	a	DET
ejpam-5650	135	21	τ1τ2	τ1τ2	NOUN
ejpam-5650	135	22	-	-	ADJ
ejpam-5650	135	23	open	open	ADJ
ejpam-5650	135	24	set	set	ADJ
ejpam-5650	135	25	u	u	NOUN
ejpam-5650	135	26	of	of	ADP
ejpam-5650	135	27	x	x	SYM
ejpam-5650	135	28	such	such	ADJ
ejpam-5650	135	29	that	that	SCONJ
ejpam-5650	135	30	x	x	SYM
ejpam-5650	135	31	∈	∈	NUM
ejpam-5650	135	32	u	u	NOUN
ejpam-5650	135	33	⊆	⊆	NUM
ejpam-5650	135	34	f+(v	f+(v	NOUN
ejpam-5650	135	35	)	)	PUNCT
ejpam-5650	135	36	;	;	PUNCT
ejpam-5650	135	37	hence	hence	ADV
ejpam-5650	135	38	f	f	PROPN
ejpam-5650	135	39	(	(	PUNCT
ejpam-5650	135	40	u	u	NOUN
ejpam-5650	135	41	)	)	PUNCT
ejpam-5650	135	42	⊆	⊆	NUM
ejpam-5650	135	43	v	v	NOUN
ejpam-5650	135	44	.	.	PUNCT
ejpam-5650	136	1	(	(	PUNCT
ejpam-5650	136	2	5	5	X
ejpam-5650	136	3	)	)	PUNCT
ejpam-5650	136	4	⇒	⇒	NOUN
ejpam-5650	136	5	(	(	PUNCT
ejpam-5650	136	6	1	1	NUM
ejpam-5650	136	7	):	):	PUNCT
ejpam-5650	136	8	let	let	VERB
ejpam-5650	136	9	v	v	PART
ejpam-5650	136	10	be	be	AUX
ejpam-5650	136	11	any	any	DET
ejpam-5650	136	12	σ1σ2	σ1σ2	NOUN
ejpam-5650	136	13	-	-	ADJ
ejpam-5650	136	14	open	open	ADJ
ejpam-5650	136	15	set	set	NOUN
ejpam-5650	136	16	of	of	ADP
ejpam-5650	136	17	y	y	PROPN
ejpam-5650	136	18	containing	contain	VERB
ejpam-5650	136	19	f	f	PROPN
ejpam-5650	136	20	(	(	PUNCT
ejpam-5650	136	21	x	x	NOUN
ejpam-5650	136	22	)	)	PUNCT
ejpam-5650	136	23	and	and	CCONJ
ejpam-5650	136	24	having	have	VERB
ejpam-5650	136	25	n	n	PRON
ejpam-5650	136	26	(	(	PUNCT
ejpam-5650	136	27	σ1	σ1	PROPN
ejpam-5650	136	28	,	,	PUNCT
ejpam-5650	136	29	σ2)closed	σ2)close	VERB
ejpam-5650	136	30	complement	complement	NOUN
ejpam-5650	136	31	.	.	PUNCT
ejpam-5650	137	1	by	by	ADP
ejpam-5650	137	2	lemma	lemma	PROPN
ejpam-5650	137	3	2	2	NUM
ejpam-5650	137	4	,	,	PUNCT
ejpam-5650	137	5	σ1σ2	σ1σ2	X
ejpam-5650	137	6	-	-	PUNCT
ejpam-5650	137	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	137	8	-	-	PUNCT
ejpam-5650	137	9	cl(v	cl(v	NOUN
ejpam-5650	137	10	)	)	PUNCT
ejpam-5650	137	11	)	)	PUNCT
ejpam-5650	137	12	is	be	AUX
ejpam-5650	137	13	a	a	DET
ejpam-5650	137	14	(	(	PUNCT
ejpam-5650	137	15	σ1	σ1	NOUN
ejpam-5650	137	16	,	,	PUNCT
ejpam-5650	137	17	σ2)r	σ2)r	NOUN
ejpam-5650	137	18	-	-	PUNCT
ejpam-5650	137	19	open	open	ADJ
ejpam-5650	137	20	set	set	NOUN
ejpam-5650	137	21	of	of	ADP
ejpam-5650	137	22	y	y	PROPN
ejpam-5650	137	23	containing	contain	VERB
ejpam-5650	137	24	f	f	PROPN
ejpam-5650	137	25	(	(	PUNCT
ejpam-5650	137	26	x	x	NOUN
ejpam-5650	137	27	)	)	PUNCT
ejpam-5650	137	28	and	and	CCONJ
ejpam-5650	137	29	having	have	VERB
ejpam-5650	137	30	n	n	PRON
ejpam-5650	137	31	(	(	PUNCT
ejpam-5650	137	32	σ1	σ1	PROPN
ejpam-5650	137	33	,	,	PUNCT
ejpam-5650	137	34	σ2)-closed	σ2)-close	VERB
ejpam-5650	137	35	complement	complement	NOUN
ejpam-5650	137	36	.	.	PUNCT
ejpam-5650	138	1	thus	thus	ADV
ejpam-5650	138	2	by	by	ADP
ejpam-5650	138	3	(	(	PUNCT
ejpam-5650	138	4	5	5	NUM
ejpam-5650	138	5	)	)	PUNCT
ejpam-5650	138	6	,	,	PUNCT
ejpam-5650	138	7	there	there	PRON
ejpam-5650	138	8	exists	exist	VERB
ejpam-5650	138	9	a	a	DET
ejpam-5650	138	10	τ1τ2open	τ1τ2open	ADJ
ejpam-5650	138	11	set	set	NOUN
ejpam-5650	138	12	u	u	NOUN
ejpam-5650	138	13	of	of	ADP
ejpam-5650	138	14	x	x	PUNCT
ejpam-5650	138	15	containing	contain	VERB
ejpam-5650	138	16	x	x	PUNCT
ejpam-5650	138	17	such	such	ADJ
ejpam-5650	138	18	that	that	SCONJ
ejpam-5650	138	19	f	f	PROPN
ejpam-5650	138	20	(	(	PUNCT
ejpam-5650	138	21	u	u	NOUN
ejpam-5650	138	22	)	)	PUNCT
ejpam-5650	138	23	⊆	⊆	NUM
ejpam-5650	138	24	σ1σ2	σ1σ2	X
ejpam-5650	138	25	-	-	PUNCT
ejpam-5650	138	26	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	138	27	-	-	PUNCT
ejpam-5650	138	28	cl(v	cl(v	NOUN
ejpam-5650	138	29	)	)	PUNCT
ejpam-5650	138	30	)	)	PUNCT
ejpam-5650	138	31	.	.	PUNCT
ejpam-5650	139	1	this	this	PRON
ejpam-5650	139	2	shows	show	VERB
ejpam-5650	139	3	that	that	SCONJ
ejpam-5650	139	4	f	f	PROPN
ejpam-5650	139	5	is	be	AUX
ejpam-5650	139	6	upper	upper	ADJ
ejpam-5650	139	7	almost	almost	ADV
ejpam-5650	139	8	nearly	nearly	ADV
ejpam-5650	139	9	(	(	PUNCT
ejpam-5650	139	10	τ1	τ1	NOUN
ejpam-5650	139	11	,	,	PUNCT
ejpam-5650	139	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	139	13	.	.	PUNCT
ejpam-5650	140	1	definition	definition	NOUN
ejpam-5650	140	2	2	2	NUM
ejpam-5650	140	3	.	.	PUNCT
ejpam-5650	140	4	a	a	DET
ejpam-5650	140	5	multifunction	multifunction	NOUN
ejpam-5650	140	6	f	f	NOUN
ejpam-5650	140	7	:	:	PUNCT
ejpam-5650	140	8	(	(	PUNCT
ejpam-5650	140	9	x	x	NOUN
ejpam-5650	140	10	,	,	PUNCT
ejpam-5650	140	11	τ1	τ1	NOUN
ejpam-5650	140	12	,	,	PUNCT
ejpam-5650	140	13	τ2	τ2	NOUN
ejpam-5650	140	14	)	)	PUNCT
ejpam-5650	140	15	→	→	SYM
ejpam-5650	140	16	(	(	PUNCT
ejpam-5650	140	17	y	y	PROPN
ejpam-5650	140	18	,	,	PUNCT
ejpam-5650	140	19	σ1	σ1	PROPN
ejpam-5650	140	20	,	,	PUNCT
ejpam-5650	140	21	σ2	σ2	PROPN
ejpam-5650	140	22	)	)	PUNCT
ejpam-5650	140	23	is	be	AUX
ejpam-5650	140	24	said	say	VERB
ejpam-5650	140	25	to	to	PART
ejpam-5650	140	26	be	be	AUX
ejpam-5650	140	27	lower	low	ADJ
ejpam-5650	140	28	almost	almost	ADV
ejpam-5650	140	29	nearly	nearly	ADV
ejpam-5650	140	30	(	(	PUNCT
ejpam-5650	140	31	τ1	τ1	NOUN
ejpam-5650	140	32	,	,	PUNCT
ejpam-5650	140	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	140	34	at	at	ADP
ejpam-5650	140	35	a	a	DET
ejpam-5650	140	36	point	point	NOUN
ejpam-5650	140	37	x	x	SYM
ejpam-5650	140	38	∈	∈	NOUN
ejpam-5650	140	39	x	x	PUNCT
ejpam-5650	140	40	if	if	SCONJ
ejpam-5650	140	41	for	for	ADP
ejpam-5650	140	42	each	each	DET
ejpam-5650	140	43	σ1σ2	σ1σ2	VERB
ejpam-5650	140	44	-	-	ADJ
ejpam-5650	140	45	open	open	ADJ
ejpam-5650	140	46	set	set	NOUN
ejpam-5650	140	47	v	v	NOUN
ejpam-5650	140	48	of	of	ADP
ejpam-5650	140	49	y	y	PRON
ejpam-5650	140	50	such	such	ADJ
ejpam-5650	140	51	that	that	SCONJ
ejpam-5650	140	52	f	f	PROPN
ejpam-5650	140	53	(	(	PUNCT
ejpam-5650	140	54	x)∩v	x)∩v	PROPN
ejpam-5650	140	55	̸=	̸=	PROPN
ejpam-5650	140	56	∅	∅	NOUN
ejpam-5650	140	57	and	and	CCONJ
ejpam-5650	140	58	having	have	VERB
ejpam-5650	140	59	n	n	PROPN
ejpam-5650	140	60	(	(	PUNCT
ejpam-5650	140	61	σ1	σ1	PROPN
ejpam-5650	140	62	,	,	PUNCT
ejpam-5650	140	63	σ2)-closed	σ2)-close	VERB
ejpam-5650	140	64	complement	complement	NOUN
ejpam-5650	140	65	,	,	PUNCT
ejpam-5650	140	66	there	there	PRON
ejpam-5650	140	67	exists	exist	VERB
ejpam-5650	140	68	a	a	DET
ejpam-5650	140	69	τ1τ2	τ1τ2	NOUN
ejpam-5650	140	70	-	-	ADJ
ejpam-5650	140	71	open	open	ADJ
ejpam-5650	140	72	set	set	ADJ
ejpam-5650	140	73	u	u	NOUN
ejpam-5650	140	74	of	of	ADP
ejpam-5650	140	75	x	x	PUNCT
ejpam-5650	140	76	containing	contain	VERB
ejpam-5650	140	77	x	x	PUNCT
ejpam-5650	140	78	such	such	ADJ
ejpam-5650	140	79	that	that	SCONJ
ejpam-5650	140	80	σ1σ2	σ1σ2	ADV
ejpam-5650	140	81	-	-	PUNCT
ejpam-5650	140	82	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	140	83	-	-	PUNCT
ejpam-5650	140	84	cl(v	cl(v	NOUN
ejpam-5650	140	85	)	)	PUNCT
ejpam-5650	140	86	)	)	PUNCT
ejpam-5650	140	87	∩	∩	PROPN
ejpam-5650	140	88	f	f	X
ejpam-5650	140	89	(	(	PUNCT
ejpam-5650	140	90	z	z	NOUN
ejpam-5650	140	91	)	)	PUNCT
ejpam-5650	140	92	̸=	̸=	NOUN
ejpam-5650	140	93	∅	∅	NOUN
ejpam-5650	140	94	for	for	ADP
ejpam-5650	140	95	each	each	DET
ejpam-5650	140	96	z	z	NOUN
ejpam-5650	140	97	∈	∈	PROPN
ejpam-5650	140	98	u	u	NOUN
ejpam-5650	140	99	.	.	PUNCT
ejpam-5650	141	1	a	a	DET
ejpam-5650	141	2	multifunction	multifunction	NOUN
ejpam-5650	141	3	f	f	NOUN
ejpam-5650	141	4	:	:	PUNCT
ejpam-5650	141	5	(	(	PUNCT
ejpam-5650	141	6	x	x	NOUN
ejpam-5650	141	7	,	,	PUNCT
ejpam-5650	141	8	τ1	τ1	NOUN
ejpam-5650	141	9	,	,	PUNCT
ejpam-5650	141	10	τ2	τ2	NOUN
ejpam-5650	141	11	)	)	PUNCT
ejpam-5650	141	12	→	→	SYM
ejpam-5650	141	13	(	(	PUNCT
ejpam-5650	141	14	y	y	PROPN
ejpam-5650	141	15	,	,	PUNCT
ejpam-5650	141	16	σ1	σ1	PROPN
ejpam-5650	141	17	,	,	PUNCT
ejpam-5650	141	18	σ2	σ2	PROPN
ejpam-5650	141	19	)	)	PUNCT
ejpam-5650	141	20	is	be	AUX
ejpam-5650	141	21	said	say	VERB
ejpam-5650	141	22	to	to	PART
ejpam-5650	141	23	be	be	AUX
ejpam-5650	141	24	lower	low	ADJ
ejpam-5650	141	25	almost	almost	ADV
ejpam-5650	141	26	nearly	nearly	ADV
ejpam-5650	141	27	(	(	PUNCT
ejpam-5650	141	28	τ1	τ1	NOUN
ejpam-5650	141	29	,	,	PUNCT
ejpam-5650	141	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	141	31	if	if	SCONJ
ejpam-5650	141	32	f	f	PROPN
ejpam-5650	141	33	is	be	AUX
ejpam-5650	141	34	lower	low	ADJ
ejpam-5650	141	35	almost	almost	ADV
ejpam-5650	141	36	nearly	nearly	ADV
ejpam-5650	141	37	(	(	PUNCT
ejpam-5650	141	38	τ1	τ1	NOUN
ejpam-5650	141	39	,	,	PUNCT
ejpam-5650	141	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	141	41	at	at	ADP
ejpam-5650	141	42	each	each	DET
ejpam-5650	141	43	point	point	NOUN
ejpam-5650	141	44	x	x	PUNCT
ejpam-5650	141	45	of	of	ADP
ejpam-5650	141	46	x.	x.	PROPN
ejpam-5650	141	47	theorem	theorem	VERB
ejpam-5650	141	48	2	2	NUM
ejpam-5650	141	49	.	.	X
ejpam-5650	141	50	for	for	ADP
ejpam-5650	141	51	a	a	DET
ejpam-5650	141	52	multifunction	multifunction	NOUN
ejpam-5650	141	53	f	f	NOUN
ejpam-5650	141	54	:	:	PUNCT
ejpam-5650	141	55	(	(	PUNCT
ejpam-5650	141	56	x	x	NOUN
ejpam-5650	141	57	,	,	PUNCT
ejpam-5650	141	58	τ1	τ1	NOUN
ejpam-5650	141	59	,	,	PUNCT
ejpam-5650	141	60	τ2	τ2	NOUN
ejpam-5650	141	61	)	)	PUNCT
ejpam-5650	141	62	→	→	SYM
ejpam-5650	141	63	(	(	PUNCT
ejpam-5650	141	64	y	y	PROPN
ejpam-5650	141	65	,	,	PUNCT
ejpam-5650	141	66	σ1	σ1	PROPN
ejpam-5650	141	67	,	,	PUNCT
ejpam-5650	141	68	σ2	σ2	NOUN
ejpam-5650	141	69	)	)	PUNCT
ejpam-5650	141	70	,	,	PUNCT
ejpam-5650	141	71	the	the	DET
ejpam-5650	141	72	following	follow	VERB
ejpam-5650	141	73	properties	property	NOUN
ejpam-5650	141	74	are	be	AUX
ejpam-5650	141	75	equivalent	equivalent	ADJ
ejpam-5650	141	76	:	:	PUNCT
ejpam-5650	141	77	(	(	PUNCT
ejpam-5650	141	78	1	1	X
ejpam-5650	141	79	)	)	PUNCT
ejpam-5650	141	80	f	f	PROPN
ejpam-5650	141	81	is	be	AUX
ejpam-5650	141	82	lower	low	ADJ
ejpam-5650	141	83	almost	almost	ADV
ejpam-5650	141	84	nearly	nearly	ADV
ejpam-5650	141	85	(	(	PUNCT
ejpam-5650	141	86	τ1	τ1	NOUN
ejpam-5650	141	87	,	,	PUNCT
ejpam-5650	141	88	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	141	89	at	at	ADP
ejpam-5650	141	90	x	x	X
ejpam-5650	141	91	∈	∈	PROPN
ejpam-5650	141	92	x	x	X
ejpam-5650	141	93	;	;	PUNCT
ejpam-5650	141	94	(	(	PUNCT
ejpam-5650	141	95	2	2	X
ejpam-5650	141	96	)	)	PUNCT
ejpam-5650	141	97	x	x	SYM
ejpam-5650	141	98	∈	∈	PRON
ejpam-5650	141	99	τ1τ2	τ1τ2	NOUN
ejpam-5650	141	100	-	-	PUNCT
ejpam-5650	141	101	int(f	int(f	NOUN
ejpam-5650	141	102	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	141	103	-	-	PUNCT
ejpam-5650	141	104	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	141	105	-	-	PUNCT
ejpam-5650	141	106	cl(v	cl(v	NOUN
ejpam-5650	141	107	)	)	PUNCT
ejpam-5650	141	108	)	)	PUNCT
ejpam-5650	141	109	)	)	PUNCT
ejpam-5650	141	110	)	)	PUNCT
ejpam-5650	142	1	for	for	ADP
ejpam-5650	142	2	each	each	DET
ejpam-5650	142	3	σ1σ2	σ1σ2	VERB
ejpam-5650	142	4	-	-	ADJ
ejpam-5650	142	5	open	open	ADJ
ejpam-5650	142	6	set	set	NOUN
ejpam-5650	142	7	v	v	NOUN
ejpam-5650	142	8	of	of	ADP
ejpam-5650	142	9	y	y	PRON
ejpam-5650	142	10	such	such	ADJ
ejpam-5650	142	11	that	that	SCONJ
ejpam-5650	142	12	f	f	PROPN
ejpam-5650	142	13	(	(	PUNCT
ejpam-5650	142	14	x	x	NOUN
ejpam-5650	142	15	)	)	PUNCT
ejpam-5650	142	16	∩	∩	NOUN
ejpam-5650	142	17	v	v	ADP
ejpam-5650	142	18	̸=	̸=	PROPN
ejpam-5650	142	19	∅	∅	NOUN
ejpam-5650	142	20	and	and	CCONJ
ejpam-5650	142	21	having	have	VERB
ejpam-5650	142	22	n	n	PROPN
ejpam-5650	142	23	(	(	PUNCT
ejpam-5650	142	24	σ1	σ1	PROPN
ejpam-5650	142	25	,	,	PUNCT
ejpam-5650	142	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	142	27	complement	complement	NOUN
ejpam-5650	142	28	;	;	PUNCT
ejpam-5650	142	29	(	(	PUNCT
ejpam-5650	142	30	3	3	X
ejpam-5650	142	31	)	)	PUNCT
ejpam-5650	142	32	x	x	SYM
ejpam-5650	142	33	∈	∈	PRON
ejpam-5650	142	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	142	35	-	-	ADJ
ejpam-5650	142	36	int(f	int(f	NUM
ejpam-5650	142	37	−((σ1	−((σ1	NOUN
ejpam-5650	142	38	,	,	PUNCT
ejpam-5650	142	39	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5650	142	40	)	)	PUNCT
ejpam-5650	142	41	)	)	PUNCT
ejpam-5650	142	42	)	)	PUNCT
ejpam-5650	142	43	for	for	ADP
ejpam-5650	142	44	each	each	DET
ejpam-5650	142	45	σ1σ2	σ1σ2	VERB
ejpam-5650	142	46	-	-	ADJ
ejpam-5650	142	47	open	open	ADJ
ejpam-5650	142	48	set	set	NOUN
ejpam-5650	142	49	v	v	NOUN
ejpam-5650	142	50	of	of	ADP
ejpam-5650	142	51	y	y	PRON
ejpam-5650	142	52	such	such	ADJ
ejpam-5650	142	53	that	that	SCONJ
ejpam-5650	142	54	f	f	PROPN
ejpam-5650	142	55	(	(	PUNCT
ejpam-5650	142	56	x	x	NOUN
ejpam-5650	142	57	)	)	PUNCT
ejpam-5650	142	58	∩	∩	NOUN
ejpam-5650	142	59	v	v	ADP
ejpam-5650	142	60	̸=	̸=	PROPN
ejpam-5650	142	61	∅	∅	NOUN
ejpam-5650	142	62	and	and	CCONJ
ejpam-5650	142	63	having	have	VERB
ejpam-5650	142	64	n	n	PROPN
ejpam-5650	142	65	(	(	PUNCT
ejpam-5650	142	66	σ1	σ1	PROPN
ejpam-5650	142	67	,	,	PUNCT
ejpam-5650	142	68	σ2)-closed	σ2)-close	VERB
ejpam-5650	142	69	complement	complement	NOUN
ejpam-5650	142	70	;	;	PUNCT
ejpam-5650	142	71	n.	n.	NOUN
ejpam-5650	142	72	chutiman	chutiman	NOUN
ejpam-5650	142	73	,	,	PUNCT
ejpam-5650	142	74	a.	a.	PROPN
ejpam-5650	142	75	sama	sama	PROPN
ejpam-5650	142	76	-	-	PUNCT
ejpam-5650	142	77	ae	ae	PROPN
ejpam-5650	142	78	,	,	PUNCT
ejpam-5650	142	79	c.	c.	PROPN
ejpam-5650	142	80	boonpok	boonpok	PROPN
ejpam-5650	142	81	/	/	SYM
ejpam-5650	142	82	eur	eur	PROPN
ejpam-5650	142	83	.	.	PUNCT
ejpam-5650	143	1	j.	j.	PROPN
ejpam-5650	143	2	pure	pure	PROPN
ejpam-5650	143	3	appl	appl	PROPN
ejpam-5650	143	4	.	.	PROPN
ejpam-5650	143	5	math	math	PROPN
ejpam-5650	143	6	,	,	PUNCT
ejpam-5650	143	7	18	18	NUM
ejpam-5650	143	8	(	(	PUNCT
ejpam-5650	143	9	1	1	NUM
ejpam-5650	143	10	)	)	PUNCT
ejpam-5650	143	11	(	(	PUNCT
ejpam-5650	143	12	2025	2025	NUM
ejpam-5650	143	13	)	)	PUNCT
ejpam-5650	143	14	,	,	PUNCT
ejpam-5650	143	15	5650	5650	NUM
ejpam-5650	143	16	6	6	NUM
ejpam-5650	143	17	of	of	ADP
ejpam-5650	143	18	18	18	NUM
ejpam-5650	143	19	(	(	PUNCT
ejpam-5650	143	20	4	4	NUM
ejpam-5650	143	21	)	)	PUNCT
ejpam-5650	143	22	x	x	SYM
ejpam-5650	143	23	∈	∈	PRON
ejpam-5650	143	24	τ1τ2	τ1τ2	NOUN
ejpam-5650	143	25	-	-	ADJ
ejpam-5650	143	26	int(f	int(f	NUM
ejpam-5650	143	27	−(v	−(v	NOUN
ejpam-5650	143	28	)	)	PUNCT
ejpam-5650	143	29	)	)	PUNCT
ejpam-5650	144	1	for	for	ADP
ejpam-5650	144	2	each	each	DET
ejpam-5650	144	3	(	(	PUNCT
ejpam-5650	144	4	σ1	σ1	PROPN
ejpam-5650	144	5	,	,	PUNCT
ejpam-5650	144	6	σ2)r	σ2)r	NOUN
ejpam-5650	144	7	-	-	PUNCT
ejpam-5650	144	8	open	open	ADJ
ejpam-5650	144	9	set	set	VERB
ejpam-5650	144	10	v	v	NOUN
ejpam-5650	144	11	of	of	ADP
ejpam-5650	144	12	y	y	PRON
ejpam-5650	144	13	such	such	ADJ
ejpam-5650	144	14	that	that	SCONJ
ejpam-5650	144	15	f	f	PROPN
ejpam-5650	144	16	(	(	PUNCT
ejpam-5650	144	17	x)∩	x)∩	PROPN
ejpam-5650	144	18	v	v	ADP
ejpam-5650	144	19	̸=	̸=	PROPN
ejpam-5650	144	20	∅	∅	NOUN
ejpam-5650	144	21	and	and	CCONJ
ejpam-5650	144	22	having	have	VERB
ejpam-5650	144	23	n	n	PROPN
ejpam-5650	144	24	(	(	PUNCT
ejpam-5650	144	25	σ1	σ1	PROPN
ejpam-5650	144	26	,	,	PUNCT
ejpam-5650	144	27	σ2)-closed	σ2)-close	VERB
ejpam-5650	144	28	complement	complement	NOUN
ejpam-5650	144	29	;	;	PUNCT
ejpam-5650	144	30	(	(	PUNCT
ejpam-5650	144	31	5	5	X
ejpam-5650	144	32	)	)	PUNCT
ejpam-5650	144	33	for	for	ADP
ejpam-5650	144	34	each	each	DET
ejpam-5650	144	35	(	(	PUNCT
ejpam-5650	144	36	σ1	σ1	PROPN
ejpam-5650	144	37	,	,	PUNCT
ejpam-5650	144	38	σ2)r	σ2)r	NOUN
ejpam-5650	144	39	-	-	PUNCT
ejpam-5650	144	40	open	open	ADJ
ejpam-5650	144	41	set	set	VERB
ejpam-5650	144	42	v	v	NOUN
ejpam-5650	144	43	of	of	ADP
ejpam-5650	144	44	y	y	PRON
ejpam-5650	144	45	such	such	ADJ
ejpam-5650	144	46	that	that	SCONJ
ejpam-5650	144	47	f	f	PROPN
ejpam-5650	144	48	(	(	PUNCT
ejpam-5650	144	49	x	x	NOUN
ejpam-5650	144	50	)	)	PUNCT
ejpam-5650	144	51	∩	∩	NOUN
ejpam-5650	144	52	v	v	ADP
ejpam-5650	144	53	̸=	̸=	PROPN
ejpam-5650	144	54	∅	∅	NOUN
ejpam-5650	144	55	and	and	CCONJ
ejpam-5650	144	56	having	have	VERB
ejpam-5650	144	57	n	n	PROPN
ejpam-5650	144	58	(	(	PUNCT
ejpam-5650	144	59	σ1	σ1	PROPN
ejpam-5650	144	60	,	,	PUNCT
ejpam-5650	144	61	σ2)closed	σ2)close	VERB
ejpam-5650	144	62	complement	complement	NOUN
ejpam-5650	145	1	,	,	PUNCT
ejpam-5650	145	2	there	there	PRON
ejpam-5650	145	3	exists	exist	VERB
ejpam-5650	145	4	a	a	DET
ejpam-5650	145	5	τ1τ2	τ1τ2	NOUN
ejpam-5650	145	6	-	-	ADJ
ejpam-5650	145	7	open	open	ADJ
ejpam-5650	145	8	set	set	ADJ
ejpam-5650	145	9	u	u	NOUN
ejpam-5650	145	10	of	of	ADP
ejpam-5650	145	11	x	x	PUNCT
ejpam-5650	145	12	containing	contain	VERB
ejpam-5650	145	13	x	x	PUNCT
ejpam-5650	145	14	such	such	ADJ
ejpam-5650	145	15	that	that	SCONJ
ejpam-5650	145	16	f	f	PROPN
ejpam-5650	145	17	(	(	PUNCT
ejpam-5650	145	18	z	z	NOUN
ejpam-5650	145	19	)	)	PUNCT
ejpam-5650	145	20	∩	∩	NOUN
ejpam-5650	145	21	v	v	ADP
ejpam-5650	145	22	̸=	̸=	PROPN
ejpam-5650	145	23	∅	∅	NOUN
ejpam-5650	145	24	for	for	ADP
ejpam-5650	145	25	every	every	DET
ejpam-5650	145	26	z	z	NOUN
ejpam-5650	145	27	∈	∈	PROPN
ejpam-5650	145	28	u	u	NOUN
ejpam-5650	145	29	.	.	PUNCT
ejpam-5650	146	1	proof	proof	NOUN
ejpam-5650	146	2	.	.	PUNCT
ejpam-5650	147	1	the	the	DET
ejpam-5650	147	2	proof	proof	NOUN
ejpam-5650	147	3	is	be	AUX
ejpam-5650	147	4	similar	similar	ADJ
ejpam-5650	147	5	to	to	ADP
ejpam-5650	147	6	that	that	PRON
ejpam-5650	147	7	of	of	ADP
ejpam-5650	147	8	theorem	theorem	ADJ
ejpam-5650	147	9	1	1	NUM
ejpam-5650	147	10	.	.	PUNCT
ejpam-5650	147	11	theorem	theorem	NOUN
ejpam-5650	147	12	3	3	NUM
ejpam-5650	147	13	.	.	X
ejpam-5650	147	14	for	for	ADP
ejpam-5650	147	15	a	a	DET
ejpam-5650	147	16	multifunction	multifunction	NOUN
ejpam-5650	147	17	f	f	NOUN
ejpam-5650	147	18	:	:	PUNCT
ejpam-5650	147	19	(	(	PUNCT
ejpam-5650	147	20	x	x	NOUN
ejpam-5650	147	21	,	,	PUNCT
ejpam-5650	147	22	τ1	τ1	NOUN
ejpam-5650	147	23	,	,	PUNCT
ejpam-5650	147	24	τ2	τ2	NOUN
ejpam-5650	147	25	)	)	PUNCT
ejpam-5650	147	26	→	→	SYM
ejpam-5650	147	27	(	(	PUNCT
ejpam-5650	147	28	y	y	PROPN
ejpam-5650	147	29	,	,	PUNCT
ejpam-5650	147	30	σ1	σ1	PROPN
ejpam-5650	147	31	,	,	PUNCT
ejpam-5650	147	32	σ2	σ2	NOUN
ejpam-5650	147	33	)	)	PUNCT
ejpam-5650	147	34	,	,	PUNCT
ejpam-5650	147	35	the	the	DET
ejpam-5650	147	36	following	follow	VERB
ejpam-5650	147	37	properties	property	NOUN
ejpam-5650	147	38	are	be	AUX
ejpam-5650	147	39	equivalent	equivalent	ADJ
ejpam-5650	147	40	:	:	PUNCT
ejpam-5650	147	41	(	(	PUNCT
ejpam-5650	147	42	1	1	X
ejpam-5650	147	43	)	)	PUNCT
ejpam-5650	147	44	f	f	PROPN
ejpam-5650	147	45	is	be	AUX
ejpam-5650	147	46	upper	upper	ADJ
ejpam-5650	147	47	almost	almost	ADV
ejpam-5650	147	48	nearly	nearly	ADV
ejpam-5650	147	49	(	(	PUNCT
ejpam-5650	147	50	τ1	τ1	NOUN
ejpam-5650	147	51	,	,	PUNCT
ejpam-5650	147	52	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	147	53	;	;	PUNCT
ejpam-5650	147	54	(	(	PUNCT
ejpam-5650	147	55	2	2	NUM
ejpam-5650	147	56	)	)	PUNCT
ejpam-5650	147	57	f+(v	f+(v	NOUN
ejpam-5650	147	58	)	)	PUNCT
ejpam-5650	148	1	⊆	⊆	X
ejpam-5650	148	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	148	3	-	-	NUM
ejpam-5650	148	4	int(f	int(f	VERB
ejpam-5650	148	5	+	+	ADJ
ejpam-5650	148	6	(	(	PUNCT
ejpam-5650	148	7	σ1σ2	σ1σ2	NUM
ejpam-5650	148	8	-	-	PUNCT
ejpam-5650	148	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	148	10	-	-	PUNCT
ejpam-5650	148	11	cl(v	cl(v	NOUN
ejpam-5650	148	12	)	)	PUNCT
ejpam-5650	148	13	)	)	PUNCT
ejpam-5650	148	14	)	)	PUNCT
ejpam-5650	148	15	)	)	PUNCT
ejpam-5650	148	16	for	for	ADP
ejpam-5650	148	17	each	each	DET
ejpam-5650	148	18	σ1σ2	σ1σ2	VERB
ejpam-5650	148	19	-	-	ADJ
ejpam-5650	148	20	open	open	ADJ
ejpam-5650	148	21	set	set	NOUN
ejpam-5650	148	22	v	v	NOUN
ejpam-5650	148	23	of	of	ADP
ejpam-5650	148	24	y	y	PROPN
ejpam-5650	148	25	having	have	VERB
ejpam-5650	148	26	n	n	PROPN
ejpam-5650	148	27	(	(	PUNCT
ejpam-5650	148	28	σ1	σ1	PROPN
ejpam-5650	148	29	,	,	PUNCT
ejpam-5650	148	30	σ2)-closed	σ2)-close	VERB
ejpam-5650	148	31	complement	complement	NOUN
ejpam-5650	148	32	;	;	PUNCT
ejpam-5650	148	33	(	(	PUNCT
ejpam-5650	148	34	3	3	X
ejpam-5650	148	35	)	)	PUNCT
ejpam-5650	148	36	τ1τ2	τ1τ2	NOUN
ejpam-5650	148	37	-	-	NOUN
ejpam-5650	148	38	cl(f	cl(f	NOUN
ejpam-5650	148	39	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	148	40	-	-	PUNCT
ejpam-5650	148	41	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	148	42	-	-	PUNCT
ejpam-5650	148	43	int(k	int(k	NOUN
ejpam-5650	148	44	)	)	PUNCT
ejpam-5650	148	45	)	)	PUNCT
ejpam-5650	148	46	)	)	PUNCT
ejpam-5650	148	47	)	)	PUNCT
ejpam-5650	149	1	⊆	⊆	X
ejpam-5650	149	2	f−(k	f−(k	PROPN
ejpam-5650	149	3	)	)	PUNCT
ejpam-5650	149	4	for	for	ADP
ejpam-5650	149	5	every	every	DET
ejpam-5650	149	6	n	n	PROPN
ejpam-5650	149	7	(	(	PUNCT
ejpam-5650	149	8	σ1	σ1	PROPN
ejpam-5650	149	9	,	,	PUNCT
ejpam-5650	149	10	σ2)-closed	σ2)-close	VERB
ejpam-5650	149	11	and	and	CCONJ
ejpam-5650	149	12	σ1σ2closed	σ1σ2close	VERB
ejpam-5650	149	13	set	set	VERB
ejpam-5650	149	14	k	k	PROPN
ejpam-5650	149	15	of	of	ADP
ejpam-5650	149	16	y	y	PROPN
ejpam-5650	149	17	;	;	PUNCT
ejpam-5650	149	18	(	(	PUNCT
ejpam-5650	149	19	4	4	X
ejpam-5650	149	20	)	)	PUNCT
ejpam-5650	149	21	τ1τ2	τ1τ2	NOUN
ejpam-5650	149	22	-	-	NOUN
ejpam-5650	149	23	cl(f	cl(f	NOUN
ejpam-5650	149	24	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	149	25	-	-	PUNCT
ejpam-5650	149	26	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	149	27	-	-	PUNCT
ejpam-5650	149	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	149	29	-	-	PUNCT
ejpam-5650	149	30	cl(b	cl(b	NOUN
ejpam-5650	149	31	)	)	PUNCT
ejpam-5650	149	32	)	)	PUNCT
ejpam-5650	149	33	)	)	PUNCT
ejpam-5650	149	34	)	)	PUNCT
ejpam-5650	149	35	)	)	PUNCT
ejpam-5650	150	1	⊆	⊆	X
ejpam-5650	150	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5650	150	3	-	-	PUNCT
ejpam-5650	150	4	cl(b	cl(b	NOUN
ejpam-5650	150	5	)	)	PUNCT
ejpam-5650	150	6	)	)	PUNCT
ejpam-5650	150	7	for	for	ADP
ejpam-5650	150	8	every	every	DET
ejpam-5650	150	9	every	every	DET
ejpam-5650	150	10	subset	subset	NOUN
ejpam-5650	150	11	b	b	PROPN
ejpam-5650	150	12	of	of	ADP
ejpam-5650	150	13	y	y	PROPN
ejpam-5650	150	14	having	have	VERB
ejpam-5650	150	15	the	the	DET
ejpam-5650	150	16	n	n	PROPN
ejpam-5650	150	17	(	(	PUNCT
ejpam-5650	150	18	σ1	σ1	PROPN
ejpam-5650	150	19	,	,	PUNCT
ejpam-5650	150	20	σ2)-closed	σ2)-close	VERB
ejpam-5650	150	21	σ1σ2	σ1σ2	NOUN
ejpam-5650	150	22	-	-	NOUN
ejpam-5650	150	23	closure	closure	NOUN
ejpam-5650	150	24	;	;	PUNCT
ejpam-5650	150	25	(	(	PUNCT
ejpam-5650	150	26	5	5	X
ejpam-5650	150	27	)	)	PUNCT
ejpam-5650	150	28	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	150	29	-	-	PUNCT
ejpam-5650	150	30	int(b	int(b	NOUN
ejpam-5650	150	31	)	)	PUNCT
ejpam-5650	150	32	)	)	PUNCT
ejpam-5650	151	1	⊆	⊆	X
ejpam-5650	151	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	151	3	-	-	NUM
ejpam-5650	151	4	int(f	int(f	VERB
ejpam-5650	151	5	+	+	ADJ
ejpam-5650	151	6	(	(	PUNCT
ejpam-5650	151	7	σ1σ2	σ1σ2	NUM
ejpam-5650	151	8	-	-	PUNCT
ejpam-5650	151	9	int(σ1σ2	int(σ1σ2	ADV
ejpam-5650	151	10	-	-	PUNCT
ejpam-5650	151	11	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	151	12	-	-	PUNCT
ejpam-5650	151	13	int(b	int(b	NOUN
ejpam-5650	151	14	)	)	PUNCT
ejpam-5650	151	15	)	)	PUNCT
ejpam-5650	151	16	)	)	PUNCT
ejpam-5650	151	17	)	)	PUNCT
ejpam-5650	151	18	)	)	PUNCT
ejpam-5650	152	1	for	for	ADP
ejpam-5650	152	2	every	every	DET
ejpam-5650	152	3	every	every	DET
ejpam-5650	152	4	subset	subset	NOUN
ejpam-5650	152	5	b	b	NOUN
ejpam-5650	152	6	of	of	ADP
ejpam-5650	152	7	y	y	PRON
ejpam-5650	152	8	such	such	ADJ
ejpam-5650	152	9	that	that	SCONJ
ejpam-5650	152	10	y	y	PROPN
ejpam-5650	152	11	−	−	ADP
ejpam-5650	152	12	σ1σ2	σ1σ2	NUM
ejpam-5650	152	13	-	-	PUNCT
ejpam-5650	152	14	int(b	int(b	NOUN
ejpam-5650	152	15	)	)	PUNCT
ejpam-5650	152	16	is	be	AUX
ejpam-5650	152	17	n	n	PROPN
ejpam-5650	152	18	(	(	PUNCT
ejpam-5650	152	19	σ1	σ1	PROPN
ejpam-5650	152	20	,	,	PUNCT
ejpam-5650	152	21	σ2)-closed	σ2)-close	VERB
ejpam-5650	152	22	;	;	PUNCT
ejpam-5650	152	23	(	(	PUNCT
ejpam-5650	152	24	6	6	NUM
ejpam-5650	152	25	)	)	PUNCT
ejpam-5650	152	26	f+(v	f+(v	NOUN
ejpam-5650	152	27	)	)	PUNCT
ejpam-5650	152	28	is	be	AUX
ejpam-5650	152	29	τ1τ2	τ1τ2	NOUN
ejpam-5650	152	30	-	-	ADJ
ejpam-5650	152	31	open	open	ADJ
ejpam-5650	152	32	in	in	ADP
ejpam-5650	152	33	x	x	PUNCT
ejpam-5650	152	34	for	for	ADP
ejpam-5650	152	35	each	each	DET
ejpam-5650	152	36	(	(	PUNCT
ejpam-5650	152	37	σ1	σ1	PROPN
ejpam-5650	152	38	,	,	PUNCT
ejpam-5650	152	39	σ2)r	σ2)r	NOUN
ejpam-5650	152	40	-	-	PUNCT
ejpam-5650	152	41	open	open	ADJ
ejpam-5650	152	42	set	set	VERB
ejpam-5650	152	43	v	v	NOUN
ejpam-5650	152	44	of	of	ADP
ejpam-5650	152	45	y	y	PROPN
ejpam-5650	152	46	having	have	VERB
ejpam-5650	152	47	n	n	PROPN
ejpam-5650	152	48	(	(	PUNCT
ejpam-5650	152	49	σ1	σ1	PROPN
ejpam-5650	152	50	,	,	PUNCT
ejpam-5650	152	51	σ2)-closed	σ2)-close	VERB
ejpam-5650	152	52	complement	complement	NOUN
ejpam-5650	152	53	;	;	PUNCT
ejpam-5650	152	54	(	(	PUNCT
ejpam-5650	152	55	7	7	X
ejpam-5650	152	56	)	)	PUNCT
ejpam-5650	152	57	f−(k	f−(k	PROPN
ejpam-5650	152	58	)	)	PUNCT
ejpam-5650	152	59	is	be	AUX
ejpam-5650	152	60	τ1τ2	τ1τ2	NOUN
ejpam-5650	152	61	-	-	ADJ
ejpam-5650	152	62	closed	closed	ADJ
ejpam-5650	152	63	in	in	ADP
ejpam-5650	152	64	x	x	PUNCT
ejpam-5650	152	65	for	for	ADP
ejpam-5650	152	66	every	every	DET
ejpam-5650	152	67	n	n	PROPN
ejpam-5650	152	68	(	(	PUNCT
ejpam-5650	152	69	σ1	σ1	PROPN
ejpam-5650	152	70	,	,	PUNCT
ejpam-5650	152	71	σ2)-closed	σ2)-close	VERB
ejpam-5650	152	72	and	and	CCONJ
ejpam-5650	152	73	(	(	PUNCT
ejpam-5650	152	74	σ1	σ1	PROPN
ejpam-5650	152	75	,	,	PUNCT
ejpam-5650	152	76	σ2)r	σ2)r	NOUN
ejpam-5650	152	77	-	-	PUNCT
ejpam-5650	152	78	closed	close	VERB
ejpam-5650	152	79	set	set	ADJ
ejpam-5650	152	80	k	k	PROPN
ejpam-5650	152	81	of	of	ADP
ejpam-5650	152	82	y	y	PROPN
ejpam-5650	152	83	.	.	PUNCT
ejpam-5650	153	1	proof	proof	NOUN
ejpam-5650	153	2	.	.	PUNCT
ejpam-5650	154	1	(	(	PUNCT
ejpam-5650	154	2	1	1	X
ejpam-5650	154	3	)	)	PUNCT
ejpam-5650	154	4	⇒	⇒	NOUN
ejpam-5650	154	5	(	(	PUNCT
ejpam-5650	154	6	2	2	NUM
ejpam-5650	154	7	):	):	PUNCT
ejpam-5650	154	8	let	let	VERB
ejpam-5650	154	9	v	v	PART
ejpam-5650	154	10	be	be	AUX
ejpam-5650	154	11	any	any	DET
ejpam-5650	154	12	σ1σ2	σ1σ2	NOUN
ejpam-5650	154	13	-	-	ADJ
ejpam-5650	154	14	open	open	ADJ
ejpam-5650	154	15	set	set	NOUN
ejpam-5650	154	16	of	of	ADP
ejpam-5650	154	17	y	y	PROPN
ejpam-5650	154	18	containing	contain	VERB
ejpam-5650	154	19	f	f	PROPN
ejpam-5650	154	20	(	(	PUNCT
ejpam-5650	154	21	x	x	X
ejpam-5650	154	22	)	)	PUNCT
ejpam-5650	154	23	having	have	VERB
ejpam-5650	154	24	n	n	PRON
ejpam-5650	154	25	(	(	PUNCT
ejpam-5650	154	26	σ1	σ1	PROPN
ejpam-5650	154	27	,	,	PUNCT
ejpam-5650	154	28	σ2)closed	σ2)close	VERB
ejpam-5650	154	29	complement	complement	NOUN
ejpam-5650	154	30	and	and	CCONJ
ejpam-5650	154	31	x	x	NOUN
ejpam-5650	154	32	∈	∈	PROPN
ejpam-5650	154	33	f+(v	f+(v	NOUN
ejpam-5650	154	34	)	)	PUNCT
ejpam-5650	154	35	.	.	PUNCT
ejpam-5650	155	1	then	then	ADV
ejpam-5650	155	2	,	,	PUNCT
ejpam-5650	155	3	f	f	PROPN
ejpam-5650	155	4	(	(	PUNCT
ejpam-5650	155	5	x	x	X
ejpam-5650	155	6	)	)	PUNCT
ejpam-5650	155	7	⊆	⊆	NUM
ejpam-5650	155	8	v	v	NOUN
ejpam-5650	155	9	.	.	PUNCT
ejpam-5650	156	1	by	by	ADP
ejpam-5650	156	2	theorem	theorem	NOUN
ejpam-5650	156	3	1	1	NUM
ejpam-5650	156	4	,	,	PUNCT
ejpam-5650	156	5	we	we	PRON
ejpam-5650	156	6	have	have	VERB
ejpam-5650	156	7	x	x	PART
ejpam-5650	156	8	∈	∈	PRON
ejpam-5650	156	9	τ1τ2	τ1τ2	NOUN
ejpam-5650	156	10	-	-	NUM
ejpam-5650	156	11	int(f	int(f	VERB
ejpam-5650	156	12	+	+	ADJ
ejpam-5650	156	13	(	(	PUNCT
ejpam-5650	156	14	σ1σ2	σ1σ2	NUM
ejpam-5650	156	15	-	-	PUNCT
ejpam-5650	156	16	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	156	17	-	-	PUNCT
ejpam-5650	156	18	cl(v	cl(v	NOUN
ejpam-5650	156	19	)	)	PUNCT
ejpam-5650	156	20	)	)	PUNCT
ejpam-5650	156	21	)	)	PUNCT
ejpam-5650	156	22	)	)	PUNCT
ejpam-5650	156	23	and	and	CCONJ
ejpam-5650	156	24	hence	hence	ADV
ejpam-5650	156	25	f+(v	f+(v	NOUN
ejpam-5650	156	26	)	)	PUNCT
ejpam-5650	157	1	⊆	⊆	X
ejpam-5650	157	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	157	3	-	-	NUM
ejpam-5650	157	4	int(f	int(f	VERB
ejpam-5650	157	5	+	+	ADJ
ejpam-5650	157	6	(	(	PUNCT
ejpam-5650	157	7	σ1σ2	σ1σ2	NUM
ejpam-5650	157	8	-	-	PUNCT
ejpam-5650	157	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	157	10	-	-	PUNCT
ejpam-5650	157	11	cl(v	cl(v	NOUN
ejpam-5650	157	12	)	)	PUNCT
ejpam-5650	157	13	)	)	PUNCT
ejpam-5650	157	14	)	)	PUNCT
ejpam-5650	157	15	)	)	PUNCT
ejpam-5650	157	16	.	.	PUNCT
ejpam-5650	158	1	(	(	PUNCT
ejpam-5650	158	2	2	2	X
ejpam-5650	158	3	)	)	PUNCT
ejpam-5650	158	4	⇒	⇒	NOUN
ejpam-5650	158	5	(	(	PUNCT
ejpam-5650	158	6	3	3	NUM
ejpam-5650	158	7	):	):	PUNCT
ejpam-5650	158	8	let	let	VERB
ejpam-5650	158	9	k	k	PRON
ejpam-5650	158	10	be	be	AUX
ejpam-5650	158	11	any	any	DET
ejpam-5650	158	12	n	n	PROPN
ejpam-5650	158	13	(	(	PUNCT
ejpam-5650	158	14	σ1	σ1	PROPN
ejpam-5650	158	15	,	,	PUNCT
ejpam-5650	158	16	σ2)-closed	σ2)-close	VERB
ejpam-5650	158	17	and	and	CCONJ
ejpam-5650	158	18	σ1σ2	σ1σ2	NOUN
ejpam-5650	158	19	-	-	PUNCT
ejpam-5650	158	20	closed	closed	ADJ
ejpam-5650	158	21	set	set	NOUN
ejpam-5650	158	22	k	k	PROPN
ejpam-5650	158	23	of	of	ADP
ejpam-5650	158	24	y	y	PROPN
ejpam-5650	158	25	.	.	PUNCT
ejpam-5650	159	1	then	then	ADV
ejpam-5650	159	2	,	,	PUNCT
ejpam-5650	159	3	y	y	PROPN
ejpam-5650	159	4	−k	−k	PROPN
ejpam-5650	159	5	is	be	AUX
ejpam-5650	159	6	a	a	DET
ejpam-5650	159	7	σ1σ2	σ1σ2	NOUN
ejpam-5650	159	8	-	-	ADJ
ejpam-5650	159	9	open	open	ADJ
ejpam-5650	159	10	set	set	NOUN
ejpam-5650	159	11	of	of	ADP
ejpam-5650	159	12	y	y	PROPN
ejpam-5650	159	13	having	have	VERB
ejpam-5650	159	14	n	n	PROPN
ejpam-5650	159	15	(	(	PUNCT
ejpam-5650	159	16	σ1	σ1	PROPN
ejpam-5650	159	17	,	,	PUNCT
ejpam-5650	159	18	σ2)-closed	σ2)-close	VERB
ejpam-5650	159	19	complement	complement	NOUN
ejpam-5650	159	20	.	.	PUNCT
ejpam-5650	160	1	by	by	ADP
ejpam-5650	160	2	(	(	PUNCT
ejpam-5650	160	3	2	2	NUM
ejpam-5650	160	4	)	)	PUNCT
ejpam-5650	160	5	,	,	PUNCT
ejpam-5650	160	6	we	we	PRON
ejpam-5650	160	7	have	have	VERB
ejpam-5650	160	8	x	x	INTJ
ejpam-5650	160	9	−	−	DET
ejpam-5650	160	10	f−(k	f−(k	PROPN
ejpam-5650	160	11	)	)	PUNCT
ejpam-5650	160	12	=	=	PUNCT
ejpam-5650	161	1	f+(y	f+(y	PROPN
ejpam-5650	161	2	−k	−k	PROPN
ejpam-5650	161	3	)	)	PUNCT
ejpam-5650	161	4	⊆	⊆	NUM
ejpam-5650	161	5	τ1τ2	τ1τ2	NOUN
ejpam-5650	161	6	-	-	NUM
ejpam-5650	161	7	int(f	int(f	VERB
ejpam-5650	161	8	+	+	ADJ
ejpam-5650	161	9	(	(	PUNCT
ejpam-5650	161	10	σ1σ2	σ1σ2	NUM
ejpam-5650	161	11	-	-	PUNCT
ejpam-5650	161	12	int(σ1σ2	int(σ1σ2	VERB
ejpam-5650	161	13	-	-	PUNCT
ejpam-5650	161	14	cl(y	cl(y	NOUN
ejpam-5650	161	15	−k	−k	NOUN
ejpam-5650	161	16	)	)	PUNCT
ejpam-5650	161	17	)	)	PUNCT
ejpam-5650	161	18	)	)	PUNCT
ejpam-5650	161	19	)	)	PUNCT
ejpam-5650	162	1	=	=	PUNCT
ejpam-5650	163	1	τ1τ2	τ1τ2	NOUN
ejpam-5650	163	2	-	-	ADJ
ejpam-5650	163	3	int(x	int(x	ADJ
ejpam-5650	163	4	−	−	NOUN
ejpam-5650	163	5	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5650	163	6	-	-	PUNCT
ejpam-5650	163	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	163	8	-	-	PUNCT
ejpam-5650	163	9	int(k	int(k	NOUN
ejpam-5650	163	10	)	)	PUNCT
ejpam-5650	163	11	)	)	PUNCT
ejpam-5650	163	12	)	)	PUNCT
ejpam-5650	163	13	)	)	PUNCT
ejpam-5650	164	1	n.	n.	NOUN
ejpam-5650	164	2	chutiman	chutiman	NOUN
ejpam-5650	164	3	,	,	PUNCT
ejpam-5650	164	4	a.	a.	PROPN
ejpam-5650	164	5	sama	sama	PROPN
ejpam-5650	164	6	-	-	PUNCT
ejpam-5650	164	7	ae	ae	PROPN
ejpam-5650	164	8	,	,	PUNCT
ejpam-5650	164	9	c.	c.	PROPN
ejpam-5650	164	10	boonpok	boonpok	PROPN
ejpam-5650	164	11	/	/	SYM
ejpam-5650	164	12	eur	eur	PROPN
ejpam-5650	164	13	.	.	PUNCT
ejpam-5650	165	1	j.	j.	PROPN
ejpam-5650	165	2	pure	pure	PROPN
ejpam-5650	165	3	appl	appl	PROPN
ejpam-5650	165	4	.	.	PROPN
ejpam-5650	165	5	math	math	PROPN
ejpam-5650	165	6	,	,	PUNCT
ejpam-5650	165	7	18	18	NUM
ejpam-5650	165	8	(	(	PUNCT
ejpam-5650	165	9	1	1	NUM
ejpam-5650	165	10	)	)	PUNCT
ejpam-5650	165	11	(	(	PUNCT
ejpam-5650	165	12	2025	2025	NUM
ejpam-5650	165	13	)	)	PUNCT
ejpam-5650	165	14	,	,	PUNCT
ejpam-5650	165	15	5650	5650	NUM
ejpam-5650	165	16	7	7	NUM
ejpam-5650	165	17	of	of	ADP
ejpam-5650	165	18	18	18	NUM
ejpam-5650	165	19	=	=	SYM
ejpam-5650	165	20	x	x	NOUN
ejpam-5650	165	21	−	−	ADP
ejpam-5650	165	22	τ1τ2	τ1τ2	NOUN
ejpam-5650	165	23	-	-	ADJ
ejpam-5650	165	24	cl(f	cl(f	NOUN
ejpam-5650	165	25	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	165	26	-	-	PUNCT
ejpam-5650	165	27	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	165	28	-	-	PUNCT
ejpam-5650	165	29	int(k	int(k	NOUN
ejpam-5650	165	30	)	)	PUNCT
ejpam-5650	165	31	)	)	PUNCT
ejpam-5650	165	32	)	)	PUNCT
ejpam-5650	165	33	)	)	PUNCT
ejpam-5650	165	34	.	.	PUNCT
ejpam-5650	166	1	thus	thus	ADV
ejpam-5650	166	2	,	,	PUNCT
ejpam-5650	166	3	τ1τ2	τ1τ2	NOUN
ejpam-5650	166	4	-	-	ADJ
ejpam-5650	166	5	cl(f	cl(f	NOUN
ejpam-5650	166	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	166	7	-	-	PUNCT
ejpam-5650	166	8	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	166	9	-	-	PUNCT
ejpam-5650	166	10	int(k	int(k	NOUN
ejpam-5650	166	11	)	)	PUNCT
ejpam-5650	166	12	)	)	PUNCT
ejpam-5650	166	13	)	)	PUNCT
ejpam-5650	166	14	)	)	PUNCT
ejpam-5650	167	1	⊆	⊆	NUM
ejpam-5650	167	2	f−(k	f−(k	PROPN
ejpam-5650	167	3	)	)	PUNCT
ejpam-5650	167	4	.	.	PUNCT
ejpam-5650	168	1	(	(	PUNCT
ejpam-5650	168	2	3	3	X
ejpam-5650	168	3	)	)	PUNCT
ejpam-5650	168	4	⇒	⇒	NOUN
ejpam-5650	168	5	(	(	PUNCT
ejpam-5650	168	6	4	4	NUM
ejpam-5650	168	7	):	):	PUNCT
ejpam-5650	168	8	let	let	VERB
ejpam-5650	168	9	b	b	X
ejpam-5650	168	10	be	be	AUX
ejpam-5650	168	11	any	any	DET
ejpam-5650	168	12	subset	subset	NOUN
ejpam-5650	168	13	of	of	ADP
ejpam-5650	168	14	y	y	PROPN
ejpam-5650	168	15	having	have	VERB
ejpam-5650	168	16	the	the	DET
ejpam-5650	168	17	n	n	PROPN
ejpam-5650	168	18	(	(	PUNCT
ejpam-5650	168	19	σ1	σ1	PROPN
ejpam-5650	168	20	,	,	PUNCT
ejpam-5650	168	21	σ2)-closed	σ2)-close	VERB
ejpam-5650	168	22	σ1σ2	σ1σ2	NOUN
ejpam-5650	168	23	-	-	NOUN
ejpam-5650	168	24	closure	closure	NOUN
ejpam-5650	168	25	.	.	PUNCT
ejpam-5650	169	1	then	then	ADV
ejpam-5650	169	2	,	,	PUNCT
ejpam-5650	169	3	σ1σ2	σ1σ2	NOUN
ejpam-5650	169	4	-	-	NOUN
ejpam-5650	169	5	cl(b	cl(b	NOUN
ejpam-5650	169	6	)	)	PUNCT
ejpam-5650	169	7	is	be	AUX
ejpam-5650	169	8	a	a	DET
ejpam-5650	169	9	σ1σ2	σ1σ2	NUM
ejpam-5650	169	10	-	-	PUNCT
ejpam-5650	169	11	closed	closed	ADJ
ejpam-5650	169	12	and	and	CCONJ
ejpam-5650	169	13	n	n	CCONJ
ejpam-5650	169	14	(	(	PUNCT
ejpam-5650	169	15	σ1	σ1	PROPN
ejpam-5650	169	16	,	,	PUNCT
ejpam-5650	169	17	σ2)-closed	σ2)-close	VERB
ejpam-5650	169	18	set	set	NOUN
ejpam-5650	169	19	of	of	ADP
ejpam-5650	169	20	y	y	PROPN
ejpam-5650	169	21	.	.	PUNCT
ejpam-5650	170	1	thus	thus	ADV
ejpam-5650	170	2	by	by	ADP
ejpam-5650	170	3	(	(	PUNCT
ejpam-5650	170	4	3	3	NUM
ejpam-5650	170	5	)	)	PUNCT
ejpam-5650	170	6	,	,	PUNCT
ejpam-5650	170	7	τ1τ2	τ1τ2	NOUN
ejpam-5650	170	8	-	-	ADJ
ejpam-5650	170	9	cl(f	cl(f	NOUN
ejpam-5650	170	10	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	170	11	-	-	PUNCT
ejpam-5650	170	12	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	170	13	-	-	PUNCT
ejpam-5650	170	14	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	170	15	-	-	PUNCT
ejpam-5650	170	16	cl(b	cl(b	NOUN
ejpam-5650	170	17	)	)	PUNCT
ejpam-5650	170	18	)	)	PUNCT
ejpam-5650	170	19	)	)	PUNCT
ejpam-5650	170	20	)	)	PUNCT
ejpam-5650	170	21	)	)	PUNCT
ejpam-5650	171	1	⊆	⊆	X
ejpam-5650	171	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5650	171	3	-	-	PUNCT
ejpam-5650	171	4	cl(b	cl(b	NOUN
ejpam-5650	171	5	)	)	PUNCT
ejpam-5650	171	6	)	)	PUNCT
ejpam-5650	171	7	.	.	PUNCT
ejpam-5650	172	1	(	(	PUNCT
ejpam-5650	172	2	4	4	X
ejpam-5650	172	3	)	)	PUNCT
ejpam-5650	172	4	⇒	⇒	NOUN
ejpam-5650	172	5	(	(	PUNCT
ejpam-5650	172	6	5	5	NUM
ejpam-5650	172	7	):	):	PUNCT
ejpam-5650	172	8	let	let	VERB
ejpam-5650	172	9	b	b	X
ejpam-5650	172	10	be	be	AUX
ejpam-5650	172	11	any	any	DET
ejpam-5650	172	12	subset	subset	NOUN
ejpam-5650	172	13	of	of	ADP
ejpam-5650	172	14	y	y	PRON
ejpam-5650	172	15	such	such	ADJ
ejpam-5650	172	16	that	that	SCONJ
ejpam-5650	172	17	y	y	PROPN
ejpam-5650	172	18	−	−	ADP
ejpam-5650	172	19	σ1σ2	σ1σ2	NUM
ejpam-5650	172	20	-	-	PUNCT
ejpam-5650	172	21	int(b	int(b	NOUN
ejpam-5650	172	22	)	)	PUNCT
ejpam-5650	172	23	is	be	AUX
ejpam-5650	172	24	n	n	PROPN
ejpam-5650	172	25	(	(	PUNCT
ejpam-5650	172	26	σ1	σ1	PROPN
ejpam-5650	172	27	,	,	PUNCT
ejpam-5650	172	28	σ2)-closed	σ2)-close	VERB
ejpam-5650	172	29	.	.	PUNCT
ejpam-5650	173	1	since	since	SCONJ
ejpam-5650	173	2	y	y	PROPN
ejpam-5650	173	3	−	−	PROPN
ejpam-5650	173	4	σ1σ2	σ1σ2	X
ejpam-5650	173	5	-	-	PUNCT
ejpam-5650	173	6	int(b	int(b	NOUN
ejpam-5650	173	7	)	)	PUNCT
ejpam-5650	173	8	is	be	AUX
ejpam-5650	173	9	σ1σ2	σ1σ2	NOUN
ejpam-5650	173	10	-	-	ADJ
ejpam-5650	173	11	closed	closed	ADJ
ejpam-5650	173	12	and	and	CCONJ
ejpam-5650	173	13	n	n	CCONJ
ejpam-5650	173	14	(	(	PUNCT
ejpam-5650	173	15	σ1	σ1	PROPN
ejpam-5650	173	16	,	,	PUNCT
ejpam-5650	173	17	σ2)-closed	σ2)-close	VERB
ejpam-5650	173	18	.	.	PUNCT
ejpam-5650	174	1	then	then	ADV
ejpam-5650	174	2	by	by	ADP
ejpam-5650	174	3	(	(	PUNCT
ejpam-5650	174	4	4	4	NUM
ejpam-5650	174	5	)	)	PUNCT
ejpam-5650	174	6	,	,	PUNCT
ejpam-5650	174	7	we	we	PRON
ejpam-5650	174	8	have	have	VERB
ejpam-5650	174	9	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	174	10	-	-	PUNCT
ejpam-5650	174	11	int(b	int(b	NOUN
ejpam-5650	174	12	)	)	PUNCT
ejpam-5650	174	13	)	)	PUNCT
ejpam-5650	175	1	=	=	PUNCT
ejpam-5650	175	2	x	x	PUNCT
ejpam-5650	176	1	−	−	NOUN
ejpam-5650	176	2	f−(y	f−(y	NOUN
ejpam-5650	176	3	−	−	NOUN
ejpam-5650	176	4	σ1σ2	σ1σ2	NOUN
ejpam-5650	176	5	-	-	PUNCT
ejpam-5650	176	6	int(b	int(b	NOUN
ejpam-5650	176	7	)	)	PUNCT
ejpam-5650	176	8	)	)	PUNCT
ejpam-5650	177	1	=	=	PUNCT
ejpam-5650	178	1	x	x	PUNCT
ejpam-5650	178	2	−	−	ADP
ejpam-5650	178	3	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5650	178	4	-	-	PUNCT
ejpam-5650	178	5	cl(y	cl(y	NOUN
ejpam-5650	178	6	−b	−b	NOUN
ejpam-5650	178	7	)	)	PUNCT
ejpam-5650	178	8	)	)	PUNCT
ejpam-5650	179	1	⊆	⊆	NUM
ejpam-5650	179	2	x	x	SYM
ejpam-5650	179	3	−	−	NUM
ejpam-5650	179	4	τ1τ2	τ1τ2	NOUN
ejpam-5650	179	5	-	-	ADJ
ejpam-5650	179	6	cl(f	cl(f	NOUN
ejpam-5650	179	7	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	179	8	-	-	PUNCT
ejpam-5650	179	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	179	10	-	-	PUNCT
ejpam-5650	179	11	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	179	12	-	-	PUNCT
ejpam-5650	179	13	cl(y	cl(y	NOUN
ejpam-5650	179	14	−b	−b	NOUN
ejpam-5650	179	15	)	)	PUNCT
ejpam-5650	179	16	)	)	PUNCT
ejpam-5650	179	17	)	)	PUNCT
ejpam-5650	179	18	)	)	PUNCT
ejpam-5650	179	19	)	)	PUNCT
ejpam-5650	180	1	=	=	PUNCT
ejpam-5650	181	1	x	x	X
ejpam-5650	181	2	−	−	ADP
ejpam-5650	181	3	τ1τ2	τ1τ2	NOUN
ejpam-5650	181	4	-	-	NOUN
ejpam-5650	181	5	cl(f	cl(f	NOUN
ejpam-5650	181	6	−(y	−(y	NOUN
ejpam-5650	181	7	−	−	NOUN
ejpam-5650	181	8	σ1σ2	σ1σ2	SYM
ejpam-5650	181	9	-	-	PUNCT
ejpam-5650	181	10	int(σ1σ2	int(σ1σ2	ADV
ejpam-5650	181	11	-	-	PUNCT
ejpam-5650	181	12	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	181	13	-	-	PUNCT
ejpam-5650	181	14	int(b	int(b	NOUN
ejpam-5650	181	15	)	)	PUNCT
ejpam-5650	181	16	)	)	PUNCT
ejpam-5650	181	17	)	)	PUNCT
ejpam-5650	181	18	)	)	PUNCT
ejpam-5650	181	19	)	)	PUNCT
ejpam-5650	182	1	=	=	PUNCT
ejpam-5650	182	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	182	3	-	-	NUM
ejpam-5650	182	4	int(f	int(f	VERB
ejpam-5650	182	5	+	+	ADJ
ejpam-5650	182	6	(	(	PUNCT
ejpam-5650	182	7	σ1σ2	σ1σ2	NUM
ejpam-5650	182	8	-	-	PUNCT
ejpam-5650	182	9	int(σ1σ2	int(σ1σ2	ADV
ejpam-5650	182	10	-	-	PUNCT
ejpam-5650	182	11	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	182	12	-	-	PUNCT
ejpam-5650	182	13	int(b	int(b	NOUN
ejpam-5650	182	14	)	)	PUNCT
ejpam-5650	182	15	)	)	PUNCT
ejpam-5650	182	16	)	)	PUNCT
ejpam-5650	182	17	)	)	PUNCT
ejpam-5650	182	18	)	)	PUNCT
ejpam-5650	182	19	.	.	PUNCT
ejpam-5650	183	1	(	(	PUNCT
ejpam-5650	183	2	5	5	X
ejpam-5650	183	3	)	)	PUNCT
ejpam-5650	183	4	⇒	⇒	NOUN
ejpam-5650	183	5	(	(	PUNCT
ejpam-5650	183	6	6	6	NUM
ejpam-5650	183	7	):	):	PUNCT
ejpam-5650	183	8	let	let	VERB
ejpam-5650	183	9	v	v	PART
ejpam-5650	183	10	be	be	AUX
ejpam-5650	183	11	any	any	DET
ejpam-5650	183	12	(	(	PUNCT
ejpam-5650	183	13	σ1	σ1	NOUN
ejpam-5650	183	14	,	,	PUNCT
ejpam-5650	183	15	σ2)r	σ2)r	NOUN
ejpam-5650	183	16	-	-	PUNCT
ejpam-5650	183	17	open	open	ADJ
ejpam-5650	183	18	set	set	VERB
ejpam-5650	183	19	v	v	NOUN
ejpam-5650	183	20	of	of	ADP
ejpam-5650	183	21	y	y	PROPN
ejpam-5650	183	22	having	have	VERB
ejpam-5650	183	23	n	n	PROPN
ejpam-5650	183	24	(	(	PUNCT
ejpam-5650	183	25	σ1	σ1	PROPN
ejpam-5650	183	26	,	,	PUNCT
ejpam-5650	183	27	σ2)-closed	σ2)-close	VERB
ejpam-5650	183	28	complement	complement	NOUN
ejpam-5650	183	29	.	.	PUNCT
ejpam-5650	184	1	then	then	ADV
ejpam-5650	184	2	,	,	PUNCT
ejpam-5650	184	3	y	y	PROPN
ejpam-5650	184	4	−	−	PROPN
ejpam-5650	184	5	σ1σ2	σ1σ2	PROPN
ejpam-5650	184	6	-	-	PUNCT
ejpam-5650	184	7	int(v	int(v	NOUN
ejpam-5650	184	8	)	)	PUNCT
ejpam-5650	184	9	is	be	AUX
ejpam-5650	184	10	n	n	PROPN
ejpam-5650	184	11	(	(	PUNCT
ejpam-5650	184	12	σ1	σ1	PROPN
ejpam-5650	184	13	,	,	PUNCT
ejpam-5650	184	14	σ2)-closed	σ2)-close	VERB
ejpam-5650	184	15	.	.	PUNCT
ejpam-5650	185	1	thus	thus	ADV
ejpam-5650	185	2	by	by	ADP
ejpam-5650	185	3	(	(	PUNCT
ejpam-5650	185	4	5	5	NUM
ejpam-5650	185	5	)	)	PUNCT
ejpam-5650	185	6	,	,	PUNCT
ejpam-5650	185	7	we	we	PRON
ejpam-5650	185	8	have	have	VERB
ejpam-5650	185	9	f+(v	f+(v	NOUN
ejpam-5650	185	10	)	)	PUNCT
ejpam-5650	186	1	⊆	⊆	X
ejpam-5650	186	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	186	3	-	-	NUM
ejpam-5650	186	4	int(f	int(f	VERB
ejpam-5650	186	5	+	+	ADJ
ejpam-5650	186	6	(	(	PUNCT
ejpam-5650	186	7	v	v	NOUN
ejpam-5650	186	8	)	)	PUNCT
ejpam-5650	186	9	)	)	PUNCT
ejpam-5650	186	10	and	and	CCONJ
ejpam-5650	186	11	hence	hence	ADV
ejpam-5650	186	12	f+(v	f+(v	PROPN
ejpam-5650	186	13	)	)	PUNCT
ejpam-5650	186	14	is	be	AUX
ejpam-5650	186	15	τ1τ2	τ1τ2	NOUN
ejpam-5650	186	16	-	-	ADJ
ejpam-5650	186	17	open	open	ADJ
ejpam-5650	186	18	in	in	ADP
ejpam-5650	186	19	x.	x.	NOUN
ejpam-5650	186	20	(	(	PUNCT
ejpam-5650	186	21	6	6	NUM
ejpam-5650	186	22	)	)	PUNCT
ejpam-5650	186	23	⇒	⇒	NOUN
ejpam-5650	186	24	(	(	PUNCT
ejpam-5650	186	25	7	7	NUM
ejpam-5650	186	26	):	):	PUNCT
ejpam-5650	186	27	let	let	VERB
ejpam-5650	186	28	k	k	PRON
ejpam-5650	186	29	be	be	AUX
ejpam-5650	186	30	any	any	DET
ejpam-5650	186	31	n	n	PROPN
ejpam-5650	186	32	(	(	PUNCT
ejpam-5650	186	33	σ1	σ1	PROPN
ejpam-5650	186	34	,	,	PUNCT
ejpam-5650	186	35	σ2)-closed	σ2)-close	VERB
ejpam-5650	186	36	and	and	CCONJ
ejpam-5650	186	37	(	(	PUNCT
ejpam-5650	186	38	σ1	σ1	PROPN
ejpam-5650	186	39	,	,	PUNCT
ejpam-5650	186	40	σ2)r	σ2)r	NOUN
ejpam-5650	186	41	-	-	PUNCT
ejpam-5650	186	42	closed	close	VERB
ejpam-5650	186	43	set	set	NOUN
ejpam-5650	186	44	of	of	ADP
ejpam-5650	186	45	y	y	PROPN
ejpam-5650	186	46	.	.	PUNCT
ejpam-5650	187	1	then	then	ADV
ejpam-5650	187	2	,	,	PUNCT
ejpam-5650	187	3	y	y	PROPN
ejpam-5650	187	4	−k	−k	PROPN
ejpam-5650	187	5	is	be	AUX
ejpam-5650	187	6	a	a	DET
ejpam-5650	187	7	(	(	PUNCT
ejpam-5650	187	8	σ1	σ1	NOUN
ejpam-5650	187	9	,	,	PUNCT
ejpam-5650	187	10	σ2)r	σ2)r	NOUN
ejpam-5650	187	11	-	-	PUNCT
ejpam-5650	187	12	open	open	ADJ
ejpam-5650	187	13	set	set	NOUN
ejpam-5650	187	14	of	of	ADP
ejpam-5650	187	15	y	y	PROPN
ejpam-5650	187	16	having	have	VERB
ejpam-5650	187	17	n	n	PROPN
ejpam-5650	187	18	(	(	PUNCT
ejpam-5650	187	19	σ1	σ1	PROPN
ejpam-5650	187	20	,	,	PUNCT
ejpam-5650	187	21	σ2)-closed	σ2)-close	VERB
ejpam-5650	187	22	complement	complement	NOUN
ejpam-5650	187	23	.	.	PUNCT
ejpam-5650	188	1	by	by	ADP
ejpam-5650	188	2	(	(	PUNCT
ejpam-5650	188	3	6	6	NUM
ejpam-5650	188	4	)	)	PUNCT
ejpam-5650	188	5	,	,	PUNCT
ejpam-5650	188	6	we	we	PRON
ejpam-5650	188	7	have	have	VERB
ejpam-5650	188	8	f+(y	f+(y	VERB
ejpam-5650	188	9	−k	−k	ADV
ejpam-5650	188	10	)	)	PUNCT
ejpam-5650	188	11	=	=	PUNCT
ejpam-5650	189	1	x	x	X
ejpam-5650	189	2	−	−	PROPN
ejpam-5650	189	3	f−(k	f−(k	PROPN
ejpam-5650	189	4	)	)	PUNCT
ejpam-5650	189	5	is	be	AUX
ejpam-5650	189	6	τ1τ2	τ1τ2	NOUN
ejpam-5650	189	7	-	-	ADJ
ejpam-5650	189	8	open	open	ADJ
ejpam-5650	189	9	in	in	ADP
ejpam-5650	189	10	x	x	X
ejpam-5650	189	11	and	and	CCONJ
ejpam-5650	189	12	hence	hence	ADV
ejpam-5650	189	13	f−(k	f−(k	PROPN
ejpam-5650	189	14	)	)	PUNCT
ejpam-5650	189	15	is	be	AUX
ejpam-5650	189	16	τ1τ2	τ1τ2	NOUN
ejpam-5650	189	17	-	-	ADJ
ejpam-5650	189	18	closed	closed	ADJ
ejpam-5650	189	19	in	in	ADP
ejpam-5650	189	20	x.	x.	NOUN
ejpam-5650	189	21	(	(	PUNCT
ejpam-5650	189	22	7	7	NUM
ejpam-5650	189	23	)	)	PUNCT
ejpam-5650	189	24	⇒	⇒	NOUN
ejpam-5650	189	25	(	(	PUNCT
ejpam-5650	189	26	1	1	NUM
ejpam-5650	189	27	):	):	PUNCT
ejpam-5650	189	28	let	let	VERB
ejpam-5650	189	29	x	x	PUNCT
ejpam-5650	189	30	∈	∈	PROPN
ejpam-5650	189	31	x	x	X
ejpam-5650	189	32	and	and	CCONJ
ejpam-5650	189	33	v	v	AUX
ejpam-5650	189	34	be	be	AUX
ejpam-5650	189	35	any	any	DET
ejpam-5650	189	36	(	(	PUNCT
ejpam-5650	189	37	σ1	σ1	NOUN
ejpam-5650	189	38	,	,	PUNCT
ejpam-5650	189	39	σ2)r	σ2)r	NOUN
ejpam-5650	189	40	-	-	PUNCT
ejpam-5650	189	41	open	open	ADJ
ejpam-5650	189	42	set	set	NOUN
ejpam-5650	189	43	of	of	ADP
ejpam-5650	189	44	y	y	PROPN
ejpam-5650	189	45	containing	contain	VERB
ejpam-5650	189	46	f	f	PROPN
ejpam-5650	189	47	(	(	PUNCT
ejpam-5650	189	48	x	x	NOUN
ejpam-5650	189	49	)	)	PUNCT
ejpam-5650	189	50	and	and	CCONJ
ejpam-5650	189	51	having	have	VERB
ejpam-5650	189	52	n	n	PRON
ejpam-5650	189	53	(	(	PUNCT
ejpam-5650	189	54	σ1	σ1	PROPN
ejpam-5650	189	55	,	,	PUNCT
ejpam-5650	189	56	σ2)-closed	σ2)-close	VERB
ejpam-5650	189	57	complement	complement	NOUN
ejpam-5650	189	58	.	.	PUNCT
ejpam-5650	190	1	then	then	ADV
ejpam-5650	190	2	,	,	PUNCT
ejpam-5650	190	3	y	y	PROPN
ejpam-5650	190	4	−	−	PROPN
ejpam-5650	190	5	v	v	NOUN
ejpam-5650	190	6	is	be	AUX
ejpam-5650	190	7	(	(	PUNCT
ejpam-5650	190	8	σ1	σ1	NOUN
ejpam-5650	190	9	,	,	PUNCT
ejpam-5650	190	10	σ2)r	σ2)r	NOUN
ejpam-5650	190	11	-	-	PUNCT
ejpam-5650	190	12	closed	closed	ADJ
ejpam-5650	190	13	and	and	CCONJ
ejpam-5650	190	14	n	n	CCONJ
ejpam-5650	190	15	(	(	PUNCT
ejpam-5650	190	16	σ1	σ1	PROPN
ejpam-5650	190	17	,	,	PUNCT
ejpam-5650	190	18	σ2)-closed	σ2)-close	VERB
ejpam-5650	190	19	.	.	PUNCT
ejpam-5650	191	1	by	by	ADP
ejpam-5650	191	2	(	(	PUNCT
ejpam-5650	191	3	7	7	NUM
ejpam-5650	191	4	)	)	PUNCT
ejpam-5650	191	5	,	,	PUNCT
ejpam-5650	191	6	f−(y	f−(y	NOUN
ejpam-5650	191	7	−v	−v	NOUN
ejpam-5650	191	8	)	)	PUNCT
ejpam-5650	191	9	=	=	PUNCT
ejpam-5650	191	10	x	x	PUNCT
ejpam-5650	191	11	−f+(v	−f+(v	NOUN
ejpam-5650	191	12	)	)	PUNCT
ejpam-5650	191	13	is	be	AUX
ejpam-5650	191	14	τ1τ2	τ1τ2	NOUN
ejpam-5650	191	15	-	-	ADJ
ejpam-5650	191	16	closed	closed	ADJ
ejpam-5650	191	17	in	in	ADP
ejpam-5650	191	18	x.	x.	NOUN
ejpam-5650	191	19	thus	thus	ADV
ejpam-5650	191	20	,	,	PUNCT
ejpam-5650	191	21	f+(v	f+(v	PROPN
ejpam-5650	191	22	)	)	PUNCT
ejpam-5650	192	1	is	be	AUX
ejpam-5650	192	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	192	3	-	-	ADJ
ejpam-5650	192	4	open	open	ADJ
ejpam-5650	192	5	in	in	ADP
ejpam-5650	192	6	x.	x.	NOUN
ejpam-5650	192	7	then	then	ADV
ejpam-5650	192	8	,	,	PUNCT
ejpam-5650	192	9	there	there	PRON
ejpam-5650	192	10	exists	exist	VERB
ejpam-5650	192	11	a	a	DET
ejpam-5650	192	12	τ1τ2	τ1τ2	NOUN
ejpam-5650	192	13	-	-	ADJ
ejpam-5650	192	14	open	open	ADJ
ejpam-5650	192	15	set	set	ADJ
ejpam-5650	192	16	u	u	NOUN
ejpam-5650	192	17	of	of	ADP
ejpam-5650	192	18	x	x	PUNCT
ejpam-5650	192	19	containing	contain	VERB
ejpam-5650	192	20	x	x	PUNCT
ejpam-5650	192	21	such	such	ADJ
ejpam-5650	192	22	that	that	SCONJ
ejpam-5650	192	23	f	f	PROPN
ejpam-5650	192	24	(	(	PUNCT
ejpam-5650	192	25	u	u	NOUN
ejpam-5650	192	26	)	)	PUNCT
ejpam-5650	192	27	⊆	⊆	NUM
ejpam-5650	192	28	v	v	NOUN
ejpam-5650	192	29	.	.	PUNCT
ejpam-5650	193	1	it	it	PRON
ejpam-5650	193	2	follows	follow	VERB
ejpam-5650	193	3	from	from	ADP
ejpam-5650	193	4	theorem	theorem	ADJ
ejpam-5650	193	5	1	1	NUM
ejpam-5650	193	6	that	that	SCONJ
ejpam-5650	193	7	f	f	PROPN
ejpam-5650	193	8	is	be	AUX
ejpam-5650	193	9	upper	upper	ADJ
ejpam-5650	193	10	almost	almost	ADV
ejpam-5650	193	11	nearly	nearly	ADV
ejpam-5650	193	12	(	(	PUNCT
ejpam-5650	193	13	τ1	τ1	NOUN
ejpam-5650	193	14	,	,	PUNCT
ejpam-5650	193	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	193	16	at	at	ADP
ejpam-5650	193	17	x.	x.	NOUN
ejpam-5650	193	18	this	this	PRON
ejpam-5650	193	19	shows	show	VERB
ejpam-5650	193	20	that	that	SCONJ
ejpam-5650	193	21	f	f	PROPN
ejpam-5650	193	22	is	be	AUX
ejpam-5650	193	23	upper	upper	ADJ
ejpam-5650	193	24	almost	almost	ADV
ejpam-5650	193	25	nearly	nearly	ADV
ejpam-5650	193	26	(	(	PUNCT
ejpam-5650	193	27	τ1	τ1	NOUN
ejpam-5650	193	28	,	,	PUNCT
ejpam-5650	193	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	193	30	.	.	PUNCT
ejpam-5650	194	1	theorem	theorem	NOUN
ejpam-5650	194	2	4	4	NUM
ejpam-5650	194	3	.	.	X
ejpam-5650	194	4	for	for	ADP
ejpam-5650	194	5	a	a	DET
ejpam-5650	194	6	multifunction	multifunction	NOUN
ejpam-5650	195	1	f	f	NOUN
ejpam-5650	195	2	:	:	PUNCT
ejpam-5650	195	3	(	(	PUNCT
ejpam-5650	195	4	x	x	NOUN
ejpam-5650	195	5	,	,	PUNCT
ejpam-5650	195	6	τ1	τ1	NOUN
ejpam-5650	195	7	,	,	PUNCT
ejpam-5650	195	8	τ2	τ2	NOUN
ejpam-5650	195	9	)	)	PUNCT
ejpam-5650	195	10	→	→	SYM
ejpam-5650	195	11	(	(	PUNCT
ejpam-5650	195	12	y	y	PROPN
ejpam-5650	195	13	,	,	PUNCT
ejpam-5650	195	14	σ1	σ1	PROPN
ejpam-5650	195	15	,	,	PUNCT
ejpam-5650	195	16	σ2	σ2	NOUN
ejpam-5650	195	17	)	)	PUNCT
ejpam-5650	195	18	,	,	PUNCT
ejpam-5650	195	19	the	the	DET
ejpam-5650	195	20	following	follow	VERB
ejpam-5650	195	21	properties	property	NOUN
ejpam-5650	195	22	are	be	AUX
ejpam-5650	195	23	equivalent	equivalent	ADJ
ejpam-5650	195	24	:	:	PUNCT
ejpam-5650	195	25	(	(	PUNCT
ejpam-5650	195	26	1	1	X
ejpam-5650	195	27	)	)	PUNCT
ejpam-5650	195	28	f	f	PROPN
ejpam-5650	195	29	is	be	AUX
ejpam-5650	195	30	lower	low	ADJ
ejpam-5650	195	31	nearly	nearly	ADV
ejpam-5650	195	32	almost	almost	ADV
ejpam-5650	195	33	(	(	PUNCT
ejpam-5650	195	34	τ1	τ1	NOUN
ejpam-5650	195	35	,	,	PUNCT
ejpam-5650	195	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	195	37	;	;	PUNCT
ejpam-5650	195	38	(	(	PUNCT
ejpam-5650	195	39	2	2	X
ejpam-5650	195	40	)	)	PUNCT
ejpam-5650	195	41	f−(v	f−(v	NOUN
ejpam-5650	195	42	)	)	PUNCT
ejpam-5650	195	43	⊆	⊆	NUM
ejpam-5650	195	44	τ1τ2	τ1τ2	NOUN
ejpam-5650	195	45	-	-	NUM
ejpam-5650	195	46	int(f	int(f	VERB
ejpam-5650	195	47	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	195	48	-	-	PUNCT
ejpam-5650	195	49	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	195	50	-	-	PUNCT
ejpam-5650	195	51	cl(v	cl(v	NOUN
ejpam-5650	195	52	)	)	PUNCT
ejpam-5650	195	53	)	)	PUNCT
ejpam-5650	195	54	)	)	PUNCT
ejpam-5650	195	55	)	)	PUNCT
ejpam-5650	196	1	for	for	ADP
ejpam-5650	196	2	each	each	DET
ejpam-5650	196	3	σ1σ2	σ1σ2	VERB
ejpam-5650	196	4	-	-	ADJ
ejpam-5650	196	5	open	open	ADJ
ejpam-5650	196	6	set	set	NOUN
ejpam-5650	196	7	v	v	NOUN
ejpam-5650	196	8	of	of	ADP
ejpam-5650	196	9	y	y	PROPN
ejpam-5650	196	10	having	have	VERB
ejpam-5650	196	11	n	n	PROPN
ejpam-5650	196	12	(	(	PUNCT
ejpam-5650	196	13	σ1	σ1	PROPN
ejpam-5650	196	14	,	,	PUNCT
ejpam-5650	196	15	σ2)-closed	σ2)-close	VERB
ejpam-5650	196	16	complement	complement	NOUN
ejpam-5650	196	17	;	;	PUNCT
ejpam-5650	196	18	(	(	PUNCT
ejpam-5650	196	19	3	3	X
ejpam-5650	196	20	)	)	PUNCT
ejpam-5650	196	21	τ1τ2	τ1τ2	NOUN
ejpam-5650	196	22	-	-	NOUN
ejpam-5650	196	23	cl(f	cl(f	NOUN
ejpam-5650	196	24	+	+	NOUN
ejpam-5650	196	25	(	(	PUNCT
ejpam-5650	196	26	σ1σ2	σ1σ2	NUM
ejpam-5650	196	27	-	-	PUNCT
ejpam-5650	196	28	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	196	29	-	-	PUNCT
ejpam-5650	196	30	int(k	int(k	NOUN
ejpam-5650	196	31	)	)	PUNCT
ejpam-5650	196	32	)	)	PUNCT
ejpam-5650	196	33	)	)	PUNCT
ejpam-5650	196	34	)	)	PUNCT
ejpam-5650	197	1	⊆	⊆	NUM
ejpam-5650	197	2	f+(k	f+(k	NOUN
ejpam-5650	197	3	)	)	PUNCT
ejpam-5650	197	4	for	for	ADP
ejpam-5650	197	5	every	every	DET
ejpam-5650	197	6	n	n	PROPN
ejpam-5650	197	7	(	(	PUNCT
ejpam-5650	197	8	σ1	σ1	PROPN
ejpam-5650	197	9	,	,	PUNCT
ejpam-5650	197	10	σ2)-closed	σ2)-close	VERB
ejpam-5650	197	11	and	and	CCONJ
ejpam-5650	197	12	σ1σ2closed	σ1σ2close	VERB
ejpam-5650	197	13	set	set	VERB
ejpam-5650	197	14	k	k	PROPN
ejpam-5650	197	15	of	of	ADP
ejpam-5650	197	16	y	y	PROPN
ejpam-5650	197	17	;	;	PUNCT
ejpam-5650	197	18	(	(	PUNCT
ejpam-5650	197	19	4	4	X
ejpam-5650	197	20	)	)	PUNCT
ejpam-5650	197	21	τ1τ2	τ1τ2	NOUN
ejpam-5650	197	22	-	-	NOUN
ejpam-5650	197	23	cl(f	cl(f	NOUN
ejpam-5650	197	24	+	+	NOUN
ejpam-5650	197	25	(	(	PUNCT
ejpam-5650	197	26	σ1σ2	σ1σ2	NUM
ejpam-5650	197	27	-	-	PUNCT
ejpam-5650	197	28	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	197	29	-	-	PUNCT
ejpam-5650	197	30	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	197	31	-	-	PUNCT
ejpam-5650	197	32	cl(b	cl(b	NOUN
ejpam-5650	197	33	)	)	PUNCT
ejpam-5650	197	34	)	)	PUNCT
ejpam-5650	197	35	)	)	PUNCT
ejpam-5650	197	36	)	)	PUNCT
ejpam-5650	197	37	)	)	PUNCT
ejpam-5650	197	38	⊆	⊆	X
ejpam-5650	197	39	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	197	40	-	-	PUNCT
ejpam-5650	197	41	cl(b	cl(b	NOUN
ejpam-5650	197	42	)	)	PUNCT
ejpam-5650	197	43	)	)	PUNCT
ejpam-5650	197	44	for	for	ADP
ejpam-5650	197	45	every	every	DET
ejpam-5650	197	46	every	every	DET
ejpam-5650	197	47	subset	subset	NOUN
ejpam-5650	197	48	b	b	PROPN
ejpam-5650	197	49	of	of	ADP
ejpam-5650	197	50	y	y	PROPN
ejpam-5650	197	51	having	have	VERB
ejpam-5650	197	52	the	the	DET
ejpam-5650	197	53	n	n	PROPN
ejpam-5650	197	54	(	(	PUNCT
ejpam-5650	197	55	σ1	σ1	PROPN
ejpam-5650	197	56	,	,	PUNCT
ejpam-5650	197	57	σ2)-closed	σ2)-close	VERB
ejpam-5650	197	58	σ1σ2	σ1σ2	NOUN
ejpam-5650	197	59	-	-	NOUN
ejpam-5650	197	60	closure	closure	NOUN
ejpam-5650	197	61	;	;	PUNCT
ejpam-5650	197	62	n.	n.	NOUN
ejpam-5650	197	63	chutiman	chutiman	NOUN
ejpam-5650	197	64	,	,	PUNCT
ejpam-5650	197	65	a.	a.	PROPN
ejpam-5650	197	66	sama	sama	PROPN
ejpam-5650	197	67	-	-	PUNCT
ejpam-5650	197	68	ae	ae	PROPN
ejpam-5650	197	69	,	,	PUNCT
ejpam-5650	197	70	c.	c.	PROPN
ejpam-5650	197	71	boonpok	boonpok	PROPN
ejpam-5650	197	72	/	/	SYM
ejpam-5650	197	73	eur	eur	PROPN
ejpam-5650	197	74	.	.	PUNCT
ejpam-5650	198	1	j.	j.	PROPN
ejpam-5650	198	2	pure	pure	PROPN
ejpam-5650	198	3	appl	appl	PROPN
ejpam-5650	198	4	.	.	PROPN
ejpam-5650	198	5	math	math	PROPN
ejpam-5650	198	6	,	,	PUNCT
ejpam-5650	198	7	18	18	NUM
ejpam-5650	198	8	(	(	PUNCT
ejpam-5650	198	9	1	1	NUM
ejpam-5650	198	10	)	)	PUNCT
ejpam-5650	198	11	(	(	PUNCT
ejpam-5650	198	12	2025	2025	NUM
ejpam-5650	198	13	)	)	PUNCT
ejpam-5650	198	14	,	,	PUNCT
ejpam-5650	198	15	5650	5650	NUM
ejpam-5650	198	16	8	8	NUM
ejpam-5650	198	17	of	of	ADP
ejpam-5650	198	18	18	18	NUM
ejpam-5650	198	19	(	(	PUNCT
ejpam-5650	198	20	5	5	NUM
ejpam-5650	198	21	)	)	PUNCT
ejpam-5650	198	22	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	198	23	-	-	PUNCT
ejpam-5650	198	24	int(b	int(b	NOUN
ejpam-5650	198	25	)	)	PUNCT
ejpam-5650	198	26	)	)	PUNCT
ejpam-5650	199	1	⊆	⊆	X
ejpam-5650	199	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	199	3	-	-	NUM
ejpam-5650	199	4	int(f	int(f	VERB
ejpam-5650	199	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	199	6	-	-	PUNCT
ejpam-5650	199	7	int(σ1σ2	int(σ1σ2	ADV
ejpam-5650	199	8	-	-	PUNCT
ejpam-5650	199	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	199	10	-	-	PUNCT
ejpam-5650	199	11	int(b	int(b	NOUN
ejpam-5650	199	12	)	)	PUNCT
ejpam-5650	199	13	)	)	PUNCT
ejpam-5650	199	14	)	)	PUNCT
ejpam-5650	199	15	)	)	PUNCT
ejpam-5650	199	16	)	)	PUNCT
ejpam-5650	199	17	for	for	ADP
ejpam-5650	199	18	every	every	DET
ejpam-5650	199	19	every	every	DET
ejpam-5650	199	20	subset	subset	NOUN
ejpam-5650	199	21	b	b	NOUN
ejpam-5650	199	22	of	of	ADP
ejpam-5650	199	23	y	y	PRON
ejpam-5650	199	24	such	such	ADJ
ejpam-5650	199	25	that	that	SCONJ
ejpam-5650	199	26	y	y	PROPN
ejpam-5650	199	27	−	−	ADP
ejpam-5650	199	28	σ1σ2	σ1σ2	NUM
ejpam-5650	199	29	-	-	PUNCT
ejpam-5650	199	30	int(b	int(b	NOUN
ejpam-5650	199	31	)	)	PUNCT
ejpam-5650	199	32	is	be	AUX
ejpam-5650	199	33	n	n	PROPN
ejpam-5650	199	34	(	(	PUNCT
ejpam-5650	199	35	σ1	σ1	PROPN
ejpam-5650	199	36	,	,	PUNCT
ejpam-5650	199	37	σ2)-closed	σ2)-close	VERB
ejpam-5650	199	38	;	;	PUNCT
ejpam-5650	199	39	(	(	PUNCT
ejpam-5650	199	40	6	6	X
ejpam-5650	199	41	)	)	PUNCT
ejpam-5650	199	42	f−(v	f−(v	NOUN
ejpam-5650	199	43	)	)	PUNCT
ejpam-5650	199	44	is	be	AUX
ejpam-5650	199	45	τ1τ2	τ1τ2	NOUN
ejpam-5650	199	46	-	-	ADJ
ejpam-5650	199	47	open	open	ADJ
ejpam-5650	199	48	in	in	ADP
ejpam-5650	199	49	x	x	PUNCT
ejpam-5650	199	50	for	for	ADP
ejpam-5650	199	51	each	each	DET
ejpam-5650	199	52	(	(	PUNCT
ejpam-5650	199	53	σ1	σ1	PROPN
ejpam-5650	199	54	,	,	PUNCT
ejpam-5650	199	55	σ2)r	σ2)r	NOUN
ejpam-5650	199	56	-	-	PUNCT
ejpam-5650	199	57	open	open	ADJ
ejpam-5650	199	58	set	set	VERB
ejpam-5650	199	59	v	v	NOUN
ejpam-5650	199	60	of	of	ADP
ejpam-5650	199	61	y	y	PROPN
ejpam-5650	199	62	having	have	VERB
ejpam-5650	199	63	n	n	PROPN
ejpam-5650	199	64	(	(	PUNCT
ejpam-5650	199	65	σ1	σ1	PROPN
ejpam-5650	199	66	,	,	PUNCT
ejpam-5650	199	67	σ2)-closed	σ2)-close	VERB
ejpam-5650	199	68	complement	complement	NOUN
ejpam-5650	199	69	;	;	PUNCT
ejpam-5650	199	70	(	(	PUNCT
ejpam-5650	199	71	7	7	X
ejpam-5650	199	72	)	)	PUNCT
ejpam-5650	199	73	f+(k	f+(k	NOUN
ejpam-5650	199	74	)	)	PUNCT
ejpam-5650	199	75	is	be	AUX
ejpam-5650	199	76	τ1τ2	τ1τ2	NOUN
ejpam-5650	199	77	-	-	ADJ
ejpam-5650	199	78	closed	closed	ADJ
ejpam-5650	199	79	in	in	ADP
ejpam-5650	199	80	x	x	PUNCT
ejpam-5650	199	81	for	for	ADP
ejpam-5650	199	82	every	every	DET
ejpam-5650	199	83	n	n	PROPN
ejpam-5650	199	84	(	(	PUNCT
ejpam-5650	199	85	σ1	σ1	PROPN
ejpam-5650	199	86	,	,	PUNCT
ejpam-5650	199	87	σ2)-closed	σ2)-close	VERB
ejpam-5650	199	88	and	and	CCONJ
ejpam-5650	199	89	(	(	PUNCT
ejpam-5650	199	90	σ1	σ1	PROPN
ejpam-5650	199	91	,	,	PUNCT
ejpam-5650	200	1	σ2)r	σ2)r	NOUN
ejpam-5650	200	2	-	-	PUNCT
ejpam-5650	200	3	closed	close	VERB
ejpam-5650	200	4	set	set	ADJ
ejpam-5650	200	5	k	k	PROPN
ejpam-5650	200	6	of	of	ADP
ejpam-5650	200	7	y	y	PROPN
ejpam-5650	200	8	.	.	PUNCT
ejpam-5650	201	1	proof	proof	NOUN
ejpam-5650	201	2	.	.	PUNCT
ejpam-5650	202	1	the	the	DET
ejpam-5650	202	2	proof	proof	NOUN
ejpam-5650	202	3	is	be	AUX
ejpam-5650	202	4	similar	similar	ADJ
ejpam-5650	202	5	to	to	ADP
ejpam-5650	202	6	that	that	PRON
ejpam-5650	202	7	of	of	ADP
ejpam-5650	202	8	theorem	theorem	ADJ
ejpam-5650	202	9	3	3	NUM
ejpam-5650	202	10	.	.	PUNCT
ejpam-5650	202	11	corollary	corollary	ADJ
ejpam-5650	202	12	1	1	NUM
ejpam-5650	202	13	.	.	PUNCT
ejpam-5650	203	1	a	a	DET
ejpam-5650	203	2	multifunction	multifunction	NOUN
ejpam-5650	203	3	f	f	NOUN
ejpam-5650	203	4	:	:	PUNCT
ejpam-5650	203	5	(	(	PUNCT
ejpam-5650	203	6	x	x	NOUN
ejpam-5650	203	7	,	,	PUNCT
ejpam-5650	203	8	τ1	τ1	NOUN
ejpam-5650	203	9	,	,	PUNCT
ejpam-5650	203	10	τ2	τ2	NOUN
ejpam-5650	203	11	)	)	PUNCT
ejpam-5650	203	12	→	→	SYM
ejpam-5650	203	13	(	(	PUNCT
ejpam-5650	203	14	y	y	PROPN
ejpam-5650	203	15	,	,	PUNCT
ejpam-5650	203	16	σ1	σ1	PROPN
ejpam-5650	203	17	,	,	PUNCT
ejpam-5650	203	18	σ2	σ2	PROPN
ejpam-5650	203	19	)	)	PUNCT
ejpam-5650	203	20	is	be	AUX
ejpam-5650	203	21	upper	upper	ADJ
ejpam-5650	203	22	almost	almost	ADV
ejpam-5650	203	23	nearly	nearly	ADV
ejpam-5650	203	24	(	(	PUNCT
ejpam-5650	203	25	τ1	τ1	NOUN
ejpam-5650	203	26	,	,	PUNCT
ejpam-5650	203	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	203	28	if	if	SCONJ
ejpam-5650	203	29	f−(k	f−(k	PROPN
ejpam-5650	203	30	)	)	PUNCT
ejpam-5650	203	31	is	be	AUX
ejpam-5650	203	32	τ1τ2	τ1τ2	NOUN
ejpam-5650	203	33	-	-	ADJ
ejpam-5650	203	34	closed	closed	ADJ
ejpam-5650	203	35	in	in	ADP
ejpam-5650	203	36	x	x	PUNCT
ejpam-5650	203	37	for	for	SCONJ
ejpam-5650	203	38	every	every	DET
ejpam-5650	203	39	n	n	PROPN
ejpam-5650	203	40	(	(	PUNCT
ejpam-5650	203	41	σ1	σ1	PROPN
ejpam-5650	203	42	,	,	PUNCT
ejpam-5650	203	43	σ2)-closed	σ2)-close	VERB
ejpam-5650	203	44	set	set	VERB
ejpam-5650	203	45	k	k	PROPN
ejpam-5650	203	46	of	of	ADP
ejpam-5650	203	47	y	y	PROPN
ejpam-5650	203	48	.	.	PUNCT
ejpam-5650	204	1	proof	proof	NOUN
ejpam-5650	204	2	.	.	PUNCT
ejpam-5650	205	1	let	let	VERB
ejpam-5650	205	2	v	v	PART
ejpam-5650	205	3	be	be	AUX
ejpam-5650	205	4	any	any	DET
ejpam-5650	205	5	(	(	PUNCT
ejpam-5650	205	6	σ1	σ1	NOUN
ejpam-5650	205	7	,	,	PUNCT
ejpam-5650	205	8	σ2)r	σ2)r	NOUN
ejpam-5650	205	9	-	-	PUNCT
ejpam-5650	205	10	open	open	ADJ
ejpam-5650	205	11	set	set	NOUN
ejpam-5650	205	12	of	of	ADP
ejpam-5650	205	13	y	y	PROPN
ejpam-5650	205	14	having	have	VERB
ejpam-5650	205	15	n	n	PROPN
ejpam-5650	205	16	(	(	PUNCT
ejpam-5650	205	17	σ1	σ1	PROPN
ejpam-5650	205	18	,	,	PUNCT
ejpam-5650	205	19	σ2)-closed	σ2)-close	VERB
ejpam-5650	205	20	complement	complement	NOUN
ejpam-5650	205	21	.	.	PUNCT
ejpam-5650	206	1	then	then	ADV
ejpam-5650	206	2	,	,	PUNCT
ejpam-5650	206	3	y	y	PROPN
ejpam-5650	206	4	−	−	PROPN
ejpam-5650	206	5	v	v	NOUN
ejpam-5650	206	6	is	be	AUX
ejpam-5650	206	7	n	n	PRON
ejpam-5650	206	8	(	(	PUNCT
ejpam-5650	206	9	σ1	σ1	PROPN
ejpam-5650	206	10	,	,	PUNCT
ejpam-5650	206	11	σ2)-closed	σ2)-close	VERB
ejpam-5650	206	12	and	and	CCONJ
ejpam-5650	206	13	(	(	PUNCT
ejpam-5650	206	14	σ1	σ1	PROPN
ejpam-5650	206	15	,	,	PUNCT
ejpam-5650	206	16	σ2)r	σ2)r	NOUN
ejpam-5650	206	17	-	-	PUNCT
ejpam-5650	206	18	closed	closed	ADJ
ejpam-5650	206	19	.	.	PUNCT
ejpam-5650	207	1	by	by	ADP
ejpam-5650	207	2	the	the	DET
ejpam-5650	207	3	hypothesis	hypothesis	NOUN
ejpam-5650	207	4	,	,	PUNCT
ejpam-5650	207	5	x	x	NOUN
ejpam-5650	207	6	−	−	PROPN
ejpam-5650	207	7	f+(v	f+(v	NOUN
ejpam-5650	207	8	)	)	PUNCT
ejpam-5650	208	1	=	=	PUNCT
ejpam-5650	208	2	f−(y	f−(y	NOUN
ejpam-5650	208	3	−	−	NOUN
ejpam-5650	208	4	v	v	NOUN
ejpam-5650	208	5	)	)	PUNCT
ejpam-5650	208	6	is	be	AUX
ejpam-5650	208	7	τ1τ2	τ1τ2	NOUN
ejpam-5650	208	8	-	-	ADJ
ejpam-5650	208	9	closed	closed	ADJ
ejpam-5650	208	10	in	in	ADP
ejpam-5650	208	11	x	x	X
ejpam-5650	208	12	and	and	CCONJ
ejpam-5650	208	13	hence	hence	ADV
ejpam-5650	208	14	f+(v	f+(v	PROPN
ejpam-5650	208	15	)	)	PUNCT
ejpam-5650	208	16	is	be	AUX
ejpam-5650	208	17	τ1τ2	τ1τ2	NOUN
ejpam-5650	208	18	-	-	ADJ
ejpam-5650	208	19	open	open	ADJ
ejpam-5650	208	20	in	in	ADP
ejpam-5650	208	21	x.	x.	NOUN
ejpam-5650	208	22	it	it	PRON
ejpam-5650	208	23	follows	follow	VERB
ejpam-5650	208	24	from	from	ADP
ejpam-5650	208	25	theorem	theorem	ADJ
ejpam-5650	208	26	3	3	NUM
ejpam-5650	208	27	that	that	SCONJ
ejpam-5650	208	28	f	f	PROPN
ejpam-5650	208	29	is	be	AUX
ejpam-5650	208	30	upper	upper	ADJ
ejpam-5650	208	31	almost	almost	ADV
ejpam-5650	208	32	nearly	nearly	ADV
ejpam-5650	208	33	(	(	PUNCT
ejpam-5650	208	34	τ1	τ1	NOUN
ejpam-5650	208	35	,	,	PUNCT
ejpam-5650	208	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	208	37	.	.	PUNCT
ejpam-5650	209	1	corollary	corollary	ADJ
ejpam-5650	209	2	2	2	NUM
ejpam-5650	209	3	.	.	PUNCT
ejpam-5650	209	4	a	a	DET
ejpam-5650	209	5	multifunction	multifunction	NOUN
ejpam-5650	210	1	f	f	NOUN
ejpam-5650	210	2	:	:	PUNCT
ejpam-5650	210	3	(	(	PUNCT
ejpam-5650	210	4	x	x	NOUN
ejpam-5650	210	5	,	,	PUNCT
ejpam-5650	210	6	τ1	τ1	NOUN
ejpam-5650	210	7	,	,	PUNCT
ejpam-5650	210	8	τ2	τ2	NOUN
ejpam-5650	210	9	)	)	PUNCT
ejpam-5650	210	10	→	→	SYM
ejpam-5650	210	11	(	(	PUNCT
ejpam-5650	210	12	y	y	PROPN
ejpam-5650	210	13	,	,	PUNCT
ejpam-5650	210	14	σ1	σ1	PROPN
ejpam-5650	210	15	,	,	PUNCT
ejpam-5650	210	16	σ2	σ2	NOUN
ejpam-5650	210	17	)	)	PUNCT
ejpam-5650	210	18	is	be	AUX
ejpam-5650	210	19	lower	low	ADJ
ejpam-5650	210	20	almost	almost	ADV
ejpam-5650	210	21	nearly	nearly	ADV
ejpam-5650	210	22	(	(	PUNCT
ejpam-5650	210	23	τ1	τ1	NOUN
ejpam-5650	210	24	,	,	PUNCT
ejpam-5650	210	25	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	210	26	if	if	SCONJ
ejpam-5650	210	27	f+(k	f+(k	NUM
ejpam-5650	210	28	)	)	PUNCT
ejpam-5650	210	29	is	be	AUX
ejpam-5650	210	30	τ1τ2	τ1τ2	NOUN
ejpam-5650	210	31	-	-	ADJ
ejpam-5650	210	32	closed	closed	ADJ
ejpam-5650	210	33	in	in	ADP
ejpam-5650	210	34	x	x	PUNCT
ejpam-5650	210	35	for	for	SCONJ
ejpam-5650	210	36	every	every	DET
ejpam-5650	210	37	n	n	PROPN
ejpam-5650	210	38	(	(	PUNCT
ejpam-5650	210	39	σ1	σ1	PROPN
ejpam-5650	210	40	,	,	PUNCT
ejpam-5650	210	41	σ2)-closed	σ2)-close	VERB
ejpam-5650	210	42	set	set	VERB
ejpam-5650	210	43	k	k	PROPN
ejpam-5650	210	44	of	of	ADP
ejpam-5650	210	45	y	y	PROPN
ejpam-5650	210	46	.	.	PUNCT
ejpam-5650	211	1	proof	proof	NOUN
ejpam-5650	211	2	.	.	PUNCT
ejpam-5650	212	1	the	the	DET
ejpam-5650	212	2	proof	proof	NOUN
ejpam-5650	212	3	is	be	AUX
ejpam-5650	212	4	similar	similar	ADJ
ejpam-5650	212	5	to	to	ADP
ejpam-5650	212	6	that	that	PRON
ejpam-5650	212	7	of	of	ADP
ejpam-5650	212	8	corollary	corollary	ADJ
ejpam-5650	212	9	1	1	NUM
ejpam-5650	212	10	.	.	PUNCT
ejpam-5650	212	11	theorem	theorem	NOUN
ejpam-5650	212	12	5	5	NUM
ejpam-5650	212	13	.	.	X
ejpam-5650	212	14	for	for	ADP
ejpam-5650	212	15	a	a	DET
ejpam-5650	212	16	multifunction	multifunction	NOUN
ejpam-5650	212	17	f	f	NOUN
ejpam-5650	212	18	:	:	PUNCT
ejpam-5650	212	19	(	(	PUNCT
ejpam-5650	212	20	x	x	NOUN
ejpam-5650	212	21	,	,	PUNCT
ejpam-5650	212	22	τ1	τ1	NOUN
ejpam-5650	212	23	,	,	PUNCT
ejpam-5650	212	24	τ2	τ2	NOUN
ejpam-5650	212	25	)	)	PUNCT
ejpam-5650	212	26	→	→	SYM
ejpam-5650	212	27	(	(	PUNCT
ejpam-5650	212	28	y	y	PROPN
ejpam-5650	212	29	,	,	PUNCT
ejpam-5650	212	30	σ1	σ1	PROPN
ejpam-5650	212	31	,	,	PUNCT
ejpam-5650	212	32	σ2	σ2	NOUN
ejpam-5650	212	33	)	)	PUNCT
ejpam-5650	212	34	,	,	PUNCT
ejpam-5650	212	35	the	the	DET
ejpam-5650	212	36	following	follow	VERB
ejpam-5650	212	37	properties	property	NOUN
ejpam-5650	212	38	are	be	AUX
ejpam-5650	212	39	equivalent	equivalent	ADJ
ejpam-5650	212	40	:	:	PUNCT
ejpam-5650	212	41	(	(	PUNCT
ejpam-5650	212	42	1	1	X
ejpam-5650	212	43	)	)	PUNCT
ejpam-5650	212	44	f	f	PROPN
ejpam-5650	212	45	is	be	AUX
ejpam-5650	212	46	upper	upper	ADJ
ejpam-5650	212	47	almost	almost	ADV
ejpam-5650	212	48	nearly	nearly	ADV
ejpam-5650	212	49	(	(	PUNCT
ejpam-5650	212	50	τ1	τ1	NOUN
ejpam-5650	212	51	,	,	PUNCT
ejpam-5650	212	52	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	212	53	;	;	PUNCT
ejpam-5650	212	54	(	(	PUNCT
ejpam-5650	212	55	2	2	X
ejpam-5650	212	56	)	)	PUNCT
ejpam-5650	212	57	τ1τ2	τ1τ2	NOUN
ejpam-5650	212	58	-	-	NOUN
ejpam-5650	212	59	cl(f	cl(f	NUM
ejpam-5650	212	60	−(v	−(v	NOUN
ejpam-5650	212	61	)	)	PUNCT
ejpam-5650	212	62	)	)	PUNCT
ejpam-5650	213	1	⊆	⊆	X
ejpam-5650	213	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	213	3	-	-	PUNCT
ejpam-5650	213	4	cl(v	cl(v	NOUN
ejpam-5650	213	5	)	)	PUNCT
ejpam-5650	213	6	)	)	PUNCT
ejpam-5650	213	7	for	for	ADP
ejpam-5650	213	8	every	every	DET
ejpam-5650	213	9	every	every	DET
ejpam-5650	213	10	(	(	PUNCT
ejpam-5650	213	11	σ1	σ1	PROPN
ejpam-5650	213	12	,	,	PUNCT
ejpam-5650	213	13	σ2)β	σ2)β	NOUN
ejpam-5650	213	14	-	-	PUNCT
ejpam-5650	213	15	open	open	NOUN
ejpam-5650	213	16	set	set	NOUN
ejpam-5650	213	17	v	v	NOUN
ejpam-5650	213	18	of	of	ADP
ejpam-5650	213	19	y	y	PROPN
ejpam-5650	213	20	having	have	VERB
ejpam-5650	213	21	the	the	DET
ejpam-5650	213	22	n	n	PROPN
ejpam-5650	213	23	(	(	PUNCT
ejpam-5650	213	24	σ1	σ1	PROPN
ejpam-5650	213	25	,	,	PUNCT
ejpam-5650	213	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	213	27	σ1σ2	σ1σ2	NOUN
ejpam-5650	213	28	-	-	NOUN
ejpam-5650	213	29	closure	closure	NOUN
ejpam-5650	213	30	;	;	PUNCT
ejpam-5650	213	31	(	(	PUNCT
ejpam-5650	213	32	3	3	X
ejpam-5650	213	33	)	)	PUNCT
ejpam-5650	213	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	213	35	-	-	NOUN
ejpam-5650	213	36	cl(f	cl(f	NUM
ejpam-5650	213	37	−(v	−(v	NOUN
ejpam-5650	213	38	)	)	PUNCT
ejpam-5650	213	39	)	)	PUNCT
ejpam-5650	214	1	⊆	⊆	X
ejpam-5650	214	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	214	3	-	-	PUNCT
ejpam-5650	214	4	cl(v	cl(v	NOUN
ejpam-5650	214	5	)	)	PUNCT
ejpam-5650	214	6	)	)	PUNCT
ejpam-5650	214	7	for	for	ADP
ejpam-5650	214	8	every	every	DET
ejpam-5650	214	9	every	every	DET
ejpam-5650	214	10	(	(	PUNCT
ejpam-5650	214	11	σ1	σ1	PROPN
ejpam-5650	214	12	,	,	PUNCT
ejpam-5650	214	13	σ2)s	σ2)s	NOUN
ejpam-5650	214	14	-	-	PUNCT
ejpam-5650	214	15	open	open	NOUN
ejpam-5650	214	16	set	set	NOUN
ejpam-5650	214	17	v	v	NOUN
ejpam-5650	214	18	of	of	ADP
ejpam-5650	214	19	y	y	PROPN
ejpam-5650	214	20	having	have	VERB
ejpam-5650	215	1	the	the	DET
ejpam-5650	215	2	n	n	PROPN
ejpam-5650	215	3	(	(	PUNCT
ejpam-5650	215	4	σ1	σ1	PROPN
ejpam-5650	215	5	,	,	PUNCT
ejpam-5650	215	6	σ2)-closed	σ2)-close	VERB
ejpam-5650	215	7	σ1σ2	σ1σ2	NOUN
ejpam-5650	215	8	-	-	NOUN
ejpam-5650	215	9	closure	closure	NOUN
ejpam-5650	215	10	;	;	PUNCT
ejpam-5650	215	11	(	(	PUNCT
ejpam-5650	215	12	4	4	NUM
ejpam-5650	215	13	)	)	PUNCT
ejpam-5650	215	14	f+(v	f+(v	NOUN
ejpam-5650	215	15	)	)	PUNCT
ejpam-5650	216	1	⊆	⊆	X
ejpam-5650	216	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	216	3	-	-	NUM
ejpam-5650	216	4	int(f	int(f	VERB
ejpam-5650	216	5	+	+	ADJ
ejpam-5650	216	6	(	(	PUNCT
ejpam-5650	216	7	σ1σ2	σ1σ2	NUM
ejpam-5650	216	8	-	-	PUNCT
ejpam-5650	216	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	216	10	-	-	PUNCT
ejpam-5650	216	11	cl(v	cl(v	NOUN
ejpam-5650	216	12	)	)	PUNCT
ejpam-5650	216	13	)	)	PUNCT
ejpam-5650	216	14	)	)	PUNCT
ejpam-5650	216	15	)	)	PUNCT
ejpam-5650	216	16	for	for	ADP
ejpam-5650	216	17	every	every	DET
ejpam-5650	216	18	every	every	DET
ejpam-5650	216	19	(	(	PUNCT
ejpam-5650	216	20	σ1	σ1	PROPN
ejpam-5650	216	21	,	,	PUNCT
ejpam-5650	216	22	σ2)p	σ2)p	NOUN
ejpam-5650	216	23	-	-	PUNCT
ejpam-5650	216	24	open	open	NOUN
ejpam-5650	216	25	set	set	NOUN
ejpam-5650	216	26	v	v	NOUN
ejpam-5650	216	27	of	of	ADP
ejpam-5650	216	28	y	y	PROPN
ejpam-5650	216	29	having	have	VERB
ejpam-5650	216	30	n	n	PROPN
ejpam-5650	216	31	(	(	PUNCT
ejpam-5650	216	32	σ1	σ1	PROPN
ejpam-5650	216	33	,	,	PUNCT
ejpam-5650	216	34	σ2)-closed	σ2)-close	VERB
ejpam-5650	216	35	complement	complement	NOUN
ejpam-5650	216	36	.	.	PUNCT
ejpam-5650	217	1	proof	proof	NOUN
ejpam-5650	217	2	.	.	PUNCT
ejpam-5650	218	1	(	(	PUNCT
ejpam-5650	218	2	1	1	X
ejpam-5650	218	3	)	)	PUNCT
ejpam-5650	218	4	⇒	⇒	NOUN
ejpam-5650	218	5	(	(	PUNCT
ejpam-5650	218	6	2	2	NUM
ejpam-5650	218	7	):	):	PUNCT
ejpam-5650	218	8	let	let	VERB
ejpam-5650	218	9	v	v	PART
ejpam-5650	218	10	be	be	AUX
ejpam-5650	218	11	any	any	DET
ejpam-5650	218	12	(	(	PUNCT
ejpam-5650	218	13	σ1	σ1	PROPN
ejpam-5650	218	14	,	,	PUNCT
ejpam-5650	218	15	σ2)β	σ2)β	NOUN
ejpam-5650	218	16	-	-	PUNCT
ejpam-5650	218	17	open	open	ADJ
ejpam-5650	218	18	set	set	NOUN
ejpam-5650	218	19	of	of	ADP
ejpam-5650	218	20	y	y	PROPN
ejpam-5650	218	21	having	have	VERB
ejpam-5650	218	22	the	the	DET
ejpam-5650	218	23	n	n	PROPN
ejpam-5650	218	24	(	(	PUNCT
ejpam-5650	218	25	σ1	σ1	PROPN
ejpam-5650	218	26	,	,	PUNCT
ejpam-5650	218	27	σ2)-closed	σ2)-close	VERB
ejpam-5650	218	28	σ1σ2	σ1σ2	NOUN
ejpam-5650	218	29	-	-	NOUN
ejpam-5650	218	30	closure	closure	NOUN
ejpam-5650	218	31	.	.	PUNCT
ejpam-5650	219	1	then	then	ADV
ejpam-5650	219	2	,	,	PUNCT
ejpam-5650	219	3	σ1σ2	σ1σ2	NOUN
ejpam-5650	219	4	-	-	NUM
ejpam-5650	219	5	cl(v	cl(v	NOUN
ejpam-5650	219	6	)	)	PUNCT
ejpam-5650	219	7	is	be	AUX
ejpam-5650	219	8	(	(	PUNCT
ejpam-5650	219	9	σ1	σ1	NOUN
ejpam-5650	219	10	,	,	PUNCT
ejpam-5650	219	11	σ2)r	σ2)r	NOUN
ejpam-5650	219	12	-	-	PUNCT
ejpam-5650	219	13	closed	closed	ADJ
ejpam-5650	219	14	in	in	ADP
ejpam-5650	219	15	y	y	PROPN
ejpam-5650	219	16	.	.	PUNCT
ejpam-5650	220	1	since	since	SCONJ
ejpam-5650	220	2	f	f	PROPN
ejpam-5650	220	3	is	be	AUX
ejpam-5650	220	4	upper	upper	ADJ
ejpam-5650	220	5	almost	almost	ADV
ejpam-5650	220	6	nearly	nearly	ADV
ejpam-5650	220	7	(	(	PUNCT
ejpam-5650	220	8	τ1	τ1	NOUN
ejpam-5650	220	9	,	,	PUNCT
ejpam-5650	220	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	220	11	,	,	PUNCT
ejpam-5650	220	12	by	by	ADP
ejpam-5650	220	13	theorem	theorem	NOUN
ejpam-5650	220	14	3	3	NUM
ejpam-5650	220	15	we	we	PRON
ejpam-5650	220	16	have	have	VERB
ejpam-5650	220	17	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	220	18	-	-	PUNCT
ejpam-5650	220	19	cl(v	cl(v	NOUN
ejpam-5650	220	20	)	)	PUNCT
ejpam-5650	220	21	)	)	PUNCT
ejpam-5650	220	22	is	be	AUX
ejpam-5650	220	23	τ1τ2	τ1τ2	NOUN
ejpam-5650	220	24	-	-	ADJ
ejpam-5650	220	25	closed	closed	ADJ
ejpam-5650	220	26	in	in	ADP
ejpam-5650	220	27	x.	x.	NOUN
ejpam-5650	220	28	thus	thus	ADV
ejpam-5650	220	29	,	,	PUNCT
ejpam-5650	220	30	τ1τ2	τ1τ2	NOUN
ejpam-5650	220	31	-	-	ADJ
ejpam-5650	220	32	cl(f	cl(f	NUM
ejpam-5650	220	33	−(v	−(v	NOUN
ejpam-5650	220	34	)	)	PUNCT
ejpam-5650	220	35	)	)	PUNCT
ejpam-5650	221	1	⊆	⊆	X
ejpam-5650	221	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	221	3	-	-	ADJ
ejpam-5650	221	4	cl(f	cl(f	NOUN
ejpam-5650	221	5	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	221	6	-	-	NOUN
ejpam-5650	221	7	cl(v	cl(v	NOUN
ejpam-5650	221	8	)	)	PUNCT
ejpam-5650	221	9	)	)	PUNCT
ejpam-5650	221	10	)	)	PUNCT
ejpam-5650	222	1	=	=	PUNCT
ejpam-5650	222	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	222	3	-	-	PUNCT
ejpam-5650	222	4	cl(v	cl(v	NOUN
ejpam-5650	222	5	)	)	PUNCT
ejpam-5650	222	6	)	)	PUNCT
ejpam-5650	222	7	.	.	PUNCT
ejpam-5650	223	1	(	(	PUNCT
ejpam-5650	223	2	2	2	X
ejpam-5650	223	3	)	)	PUNCT
ejpam-5650	223	4	⇒	⇒	NOUN
ejpam-5650	223	5	(	(	PUNCT
ejpam-5650	223	6	3	3	NUM
ejpam-5650	223	7	):	):	PUNCT
ejpam-5650	223	8	the	the	DET
ejpam-5650	223	9	proof	proof	NOUN
ejpam-5650	223	10	is	be	AUX
ejpam-5650	223	11	obvious	obvious	ADJ
ejpam-5650	223	12	since	since	SCONJ
ejpam-5650	223	13	every	every	DET
ejpam-5650	223	14	(	(	PUNCT
ejpam-5650	223	15	σ1	σ1	PROPN
ejpam-5650	223	16	,	,	PUNCT
ejpam-5650	223	17	σ2)s	σ2)s	NOUN
ejpam-5650	223	18	-	-	PUNCT
ejpam-5650	223	19	open	open	ADJ
ejpam-5650	223	20	set	set	NOUN
ejpam-5650	223	21	is	be	AUX
ejpam-5650	223	22	(	(	PUNCT
ejpam-5650	223	23	σ1	σ1	PROPN
ejpam-5650	223	24	,	,	PUNCT
ejpam-5650	223	25	σ2)β	σ2)β	NOUN
ejpam-5650	223	26	-	-	PUNCT
ejpam-5650	223	27	open	open	ADJ
ejpam-5650	223	28	.	.	PUNCT
ejpam-5650	224	1	n.	n.	NOUN
ejpam-5650	224	2	chutiman	chutiman	PROPN
ejpam-5650	224	3	,	,	PUNCT
ejpam-5650	224	4	a.	a.	PROPN
ejpam-5650	224	5	sama	sama	PROPN
ejpam-5650	224	6	-	-	PUNCT
ejpam-5650	224	7	ae	ae	PROPN
ejpam-5650	224	8	,	,	PUNCT
ejpam-5650	224	9	c.	c.	PROPN
ejpam-5650	224	10	boonpok	boonpok	PROPN
ejpam-5650	224	11	/	/	SYM
ejpam-5650	224	12	eur	eur	PROPN
ejpam-5650	224	13	.	.	PUNCT
ejpam-5650	225	1	j.	j.	PROPN
ejpam-5650	225	2	pure	pure	PROPN
ejpam-5650	225	3	appl	appl	PROPN
ejpam-5650	225	4	.	.	PROPN
ejpam-5650	225	5	math	math	PROPN
ejpam-5650	225	6	,	,	PUNCT
ejpam-5650	225	7	18	18	NUM
ejpam-5650	225	8	(	(	PUNCT
ejpam-5650	225	9	1	1	NUM
ejpam-5650	225	10	)	)	PUNCT
ejpam-5650	225	11	(	(	PUNCT
ejpam-5650	225	12	2025	2025	NUM
ejpam-5650	225	13	)	)	PUNCT
ejpam-5650	225	14	,	,	PUNCT
ejpam-5650	225	15	5650	5650	NUM
ejpam-5650	225	16	9	9	NUM
ejpam-5650	225	17	of	of	ADP
ejpam-5650	225	18	18	18	NUM
ejpam-5650	225	19	(	(	PUNCT
ejpam-5650	225	20	3	3	NUM
ejpam-5650	225	21	)	)	PUNCT
ejpam-5650	225	22	⇒	⇒	NOUN
ejpam-5650	225	23	(	(	PUNCT
ejpam-5650	225	24	4	4	NUM
ejpam-5650	225	25	):	):	PUNCT
ejpam-5650	225	26	let	let	VERB
ejpam-5650	225	27	v	v	PART
ejpam-5650	225	28	be	be	AUX
ejpam-5650	225	29	any	any	DET
ejpam-5650	225	30	(	(	PUNCT
ejpam-5650	225	31	σ1	σ1	PROPN
ejpam-5650	225	32	,	,	PUNCT
ejpam-5650	225	33	σ2)p	σ2)p	NOUN
ejpam-5650	225	34	-	-	PUNCT
ejpam-5650	225	35	open	open	ADJ
ejpam-5650	225	36	set	set	NOUN
ejpam-5650	225	37	of	of	ADP
ejpam-5650	225	38	y	y	PROPN
ejpam-5650	225	39	having	have	VERB
ejpam-5650	225	40	n	n	PROPN
ejpam-5650	225	41	(	(	PUNCT
ejpam-5650	225	42	σ1	σ1	PROPN
ejpam-5650	225	43	,	,	PUNCT
ejpam-5650	225	44	σ2)-closed	σ2)-close	VERB
ejpam-5650	225	45	complement	complement	NOUN
ejpam-5650	225	46	.	.	PUNCT
ejpam-5650	226	1	then	then	ADV
ejpam-5650	226	2	by	by	ADP
ejpam-5650	226	3	lemma	lemma	PROPN
ejpam-5650	226	4	3	3	NUM
ejpam-5650	226	5	,	,	PUNCT
ejpam-5650	226	6	σ1σ2	σ1σ2	X
ejpam-5650	226	7	-	-	PUNCT
ejpam-5650	226	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	226	9	-	-	PUNCT
ejpam-5650	226	10	cl(v	cl(v	NOUN
ejpam-5650	226	11	)	)	PUNCT
ejpam-5650	226	12	)	)	PUNCT
ejpam-5650	226	13	is	be	AUX
ejpam-5650	226	14	a	a	DET
ejpam-5650	226	15	(	(	PUNCT
ejpam-5650	226	16	σ1	σ1	NOUN
ejpam-5650	226	17	,	,	PUNCT
ejpam-5650	226	18	σ2)r	σ2)r	NOUN
ejpam-5650	226	19	-	-	PUNCT
ejpam-5650	226	20	open	open	ADJ
ejpam-5650	226	21	set	set	NOUN
ejpam-5650	226	22	having	have	VERB
ejpam-5650	226	23	n	n	PROPN
ejpam-5650	226	24	(	(	PUNCT
ejpam-5650	226	25	σ1	σ1	PROPN
ejpam-5650	226	26	,	,	PUNCT
ejpam-5650	226	27	σ2)-closed	σ2)-close	VERB
ejpam-5650	226	28	complement	complement	NOUN
ejpam-5650	226	29	.	.	PUNCT
ejpam-5650	227	1	then	then	ADV
ejpam-5650	227	2	,	,	PUNCT
ejpam-5650	227	3	y	y	PROPN
ejpam-5650	227	4	−	−	NUM
ejpam-5650	227	5	σ1σ2	σ1σ2	NUM
ejpam-5650	227	6	-	-	PUNCT
ejpam-5650	227	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	227	8	-	-	PUNCT
ejpam-5650	227	9	cl(v	cl(v	NOUN
ejpam-5650	227	10	)	)	PUNCT
ejpam-5650	227	11	)	)	PUNCT
ejpam-5650	227	12	is	be	AUX
ejpam-5650	227	13	a	a	DET
ejpam-5650	227	14	(	(	PUNCT
ejpam-5650	227	15	σ1	σ1	NOUN
ejpam-5650	227	16	,	,	PUNCT
ejpam-5650	227	17	σ2)r	σ2)r	NOUN
ejpam-5650	227	18	-	-	PUNCT
ejpam-5650	227	19	closed	closed	ADJ
ejpam-5650	227	20	and	and	CCONJ
ejpam-5650	227	21	n	n	CCONJ
ejpam-5650	227	22	(	(	PUNCT
ejpam-5650	227	23	σ1	σ1	PROPN
ejpam-5650	227	24	,	,	PUNCT
ejpam-5650	227	25	σ2)-closed	σ2)-close	VERB
ejpam-5650	227	26	set	set	NOUN
ejpam-5650	227	27	.	.	PUNCT
ejpam-5650	228	1	therefore	therefore	ADV
ejpam-5650	228	2	,	,	PUNCT
ejpam-5650	228	3	y	y	PROPN
ejpam-5650	228	4	−	−	NUM
ejpam-5650	228	5	σ1σ2	σ1σ2	NUM
ejpam-5650	228	6	-	-	PUNCT
ejpam-5650	228	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	228	8	-	-	PUNCT
ejpam-5650	228	9	cl(v	cl(v	NOUN
ejpam-5650	228	10	)	)	PUNCT
ejpam-5650	228	11	)	)	PUNCT
ejpam-5650	228	12	is	be	AUX
ejpam-5650	228	13	a	a	DET
ejpam-5650	228	14	(	(	PUNCT
ejpam-5650	228	15	σ1	σ1	NOUN
ejpam-5650	228	16	,	,	PUNCT
ejpam-5650	228	17	σ2)s	σ2)s	NOUN
ejpam-5650	228	18	-	-	PUNCT
ejpam-5650	228	19	open	open	ADJ
ejpam-5650	228	20	set	set	NOUN
ejpam-5650	228	21	having	have	VERB
ejpam-5650	228	22	the	the	DET
ejpam-5650	228	23	n	n	PROPN
ejpam-5650	228	24	(	(	PUNCT
ejpam-5650	228	25	σ1	σ1	PROPN
ejpam-5650	228	26	,	,	PUNCT
ejpam-5650	228	27	σ2)closed	σ2)close	VERB
ejpam-5650	228	28	σ1σ2	σ1σ2	NOUN
ejpam-5650	228	29	-	-	NOUN
ejpam-5650	228	30	closure	closure	NOUN
ejpam-5650	228	31	.	.	PUNCT
ejpam-5650	229	1	by	by	ADP
ejpam-5650	229	2	(	(	PUNCT
ejpam-5650	229	3	3	3	NUM
ejpam-5650	229	4	)	)	PUNCT
ejpam-5650	229	5	,	,	PUNCT
ejpam-5650	229	6	we	we	PRON
ejpam-5650	229	7	have	have	VERB
ejpam-5650	229	8	x	x	INTJ
ejpam-5650	229	9	−	−	ADP
ejpam-5650	229	10	τ1τ2	τ1τ2	NOUN
ejpam-5650	229	11	-	-	NUM
ejpam-5650	229	12	int(f	int(f	VERB
ejpam-5650	229	13	+	+	ADJ
ejpam-5650	229	14	(	(	PUNCT
ejpam-5650	229	15	σ1σ2	σ1σ2	NUM
ejpam-5650	229	16	-	-	PUNCT
ejpam-5650	229	17	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	229	18	-	-	PUNCT
ejpam-5650	229	19	cl(v	cl(v	NOUN
ejpam-5650	229	20	)	)	PUNCT
ejpam-5650	229	21	)	)	PUNCT
ejpam-5650	229	22	)	)	PUNCT
ejpam-5650	229	23	)	)	PUNCT
ejpam-5650	230	1	=	=	PUNCT
ejpam-5650	231	1	τ1τ2	τ1τ2	NOUN
ejpam-5650	231	2	-	-	PROPN
ejpam-5650	231	3	cl(f	cl(f	NOUN
ejpam-5650	231	4	−(y	−(y	NOUN
ejpam-5650	231	5	−	−	NOUN
ejpam-5650	231	6	σ1σ2	σ1σ2	SYM
ejpam-5650	231	7	-	-	PUNCT
ejpam-5650	231	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	231	9	-	-	PUNCT
ejpam-5650	231	10	cl(v	cl(v	NOUN
ejpam-5650	231	11	)	)	PUNCT
ejpam-5650	231	12	)	)	PUNCT
ejpam-5650	231	13	)	)	PUNCT
ejpam-5650	231	14	)	)	PUNCT
ejpam-5650	232	1	⊆	⊆	X
ejpam-5650	232	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5650	232	3	-	-	PUNCT
ejpam-5650	232	4	cl(y	cl(y	NOUN
ejpam-5650	232	5	−	−	NOUN
ejpam-5650	232	6	σ1σ2	σ1σ2	NUM
ejpam-5650	232	7	-	-	PUNCT
ejpam-5650	232	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	232	9	-	-	PUNCT
ejpam-5650	232	10	cl(v	cl(v	NOUN
ejpam-5650	232	11	)	)	PUNCT
ejpam-5650	232	12	)	)	PUNCT
ejpam-5650	232	13	)	)	PUNCT
ejpam-5650	232	14	)	)	PUNCT
ejpam-5650	233	1	=	=	PUNCT
ejpam-5650	233	2	x	x	X
ejpam-5650	233	3	−	−	ADP
ejpam-5650	233	4	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5650	233	5	-	-	PUNCT
ejpam-5650	233	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	233	7	-	-	PUNCT
ejpam-5650	233	8	cl(v	cl(v	NOUN
ejpam-5650	233	9	)	)	PUNCT
ejpam-5650	233	10	)	)	PUNCT
ejpam-5650	233	11	)	)	PUNCT
ejpam-5650	234	1	⊆	⊆	NUM
ejpam-5650	234	2	x	x	SYM
ejpam-5650	234	3	−	−	NOUN
ejpam-5650	234	4	f+(v	f+(v	NOUN
ejpam-5650	234	5	)	)	PUNCT
ejpam-5650	234	6	and	and	CCONJ
ejpam-5650	234	7	hence	hence	ADV
ejpam-5650	234	8	f+(v	f+(v	NOUN
ejpam-5650	234	9	)	)	PUNCT
ejpam-5650	235	1	⊆	⊆	X
ejpam-5650	235	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	235	3	-	-	NUM
ejpam-5650	235	4	int(f	int(f	VERB
ejpam-5650	235	5	+	+	ADJ
ejpam-5650	235	6	(	(	PUNCT
ejpam-5650	235	7	σ1σ2	σ1σ2	NUM
ejpam-5650	235	8	-	-	PUNCT
ejpam-5650	235	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	235	10	-	-	PUNCT
ejpam-5650	235	11	cl(v	cl(v	NOUN
ejpam-5650	235	12	)	)	PUNCT
ejpam-5650	235	13	)	)	PUNCT
ejpam-5650	235	14	)	)	PUNCT
ejpam-5650	235	15	)	)	PUNCT
ejpam-5650	235	16	.	.	PUNCT
ejpam-5650	236	1	(	(	PUNCT
ejpam-5650	236	2	4	4	X
ejpam-5650	236	3	)	)	PUNCT
ejpam-5650	236	4	⇒	⇒	NOUN
ejpam-5650	236	5	(	(	PUNCT
ejpam-5650	236	6	1	1	NUM
ejpam-5650	236	7	):	):	PUNCT
ejpam-5650	236	8	let	let	VERB
ejpam-5650	236	9	v	v	PART
ejpam-5650	236	10	be	be	AUX
ejpam-5650	236	11	any	any	DET
ejpam-5650	236	12	(	(	PUNCT
ejpam-5650	236	13	σ1	σ1	NOUN
ejpam-5650	236	14	,	,	PUNCT
ejpam-5650	236	15	σ2)r	σ2)r	NOUN
ejpam-5650	236	16	-	-	PUNCT
ejpam-5650	236	17	open	open	ADJ
ejpam-5650	236	18	set	set	NOUN
ejpam-5650	236	19	of	of	ADP
ejpam-5650	236	20	y	y	PROPN
ejpam-5650	236	21	having	have	VERB
ejpam-5650	236	22	n	n	PROPN
ejpam-5650	236	23	(	(	PUNCT
ejpam-5650	236	24	σ1	σ1	PROPN
ejpam-5650	236	25	,	,	PUNCT
ejpam-5650	236	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	236	27	complement	complement	NOUN
ejpam-5650	236	28	.	.	PUNCT
ejpam-5650	237	1	then	then	ADV
ejpam-5650	237	2	,	,	PUNCT
ejpam-5650	237	3	v	v	NOUN
ejpam-5650	237	4	is	be	AUX
ejpam-5650	237	5	a	a	DET
ejpam-5650	237	6	(	(	PUNCT
ejpam-5650	237	7	σ1	σ1	PROPN
ejpam-5650	237	8	,	,	PUNCT
ejpam-5650	237	9	σ2)p	σ2)p	NOUN
ejpam-5650	237	10	-	-	PUNCT
ejpam-5650	237	11	open	open	NOUN
ejpam-5650	237	12	set	set	NOUN
ejpam-5650	237	13	having	have	VERB
ejpam-5650	237	14	n	n	PROPN
ejpam-5650	237	15	(	(	PUNCT
ejpam-5650	237	16	σ1	σ1	PROPN
ejpam-5650	237	17	,	,	PUNCT
ejpam-5650	237	18	σ2)-closed	σ2)-close	VERB
ejpam-5650	237	19	complement	complement	NOUN
ejpam-5650	237	20	.	.	PUNCT
ejpam-5650	238	1	by	by	ADP
ejpam-5650	238	2	(	(	PUNCT
ejpam-5650	238	3	4	4	NUM
ejpam-5650	238	4	)	)	PUNCT
ejpam-5650	238	5	,	,	PUNCT
ejpam-5650	238	6	we	we	PRON
ejpam-5650	238	7	have	have	VERB
ejpam-5650	238	8	f+(v	f+(v	NOUN
ejpam-5650	238	9	)	)	PUNCT
ejpam-5650	239	1	⊆	⊆	X
ejpam-5650	239	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	239	3	-	-	NUM
ejpam-5650	239	4	int(f	int(f	VERB
ejpam-5650	239	5	+	+	ADJ
ejpam-5650	239	6	(	(	PUNCT
ejpam-5650	239	7	σ1σ2	σ1σ2	NUM
ejpam-5650	239	8	-	-	PUNCT
ejpam-5650	239	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	239	10	-	-	PUNCT
ejpam-5650	239	11	cl(v	cl(v	NOUN
ejpam-5650	239	12	)	)	PUNCT
ejpam-5650	239	13	)	)	PUNCT
ejpam-5650	239	14	)	)	PUNCT
ejpam-5650	239	15	)	)	PUNCT
ejpam-5650	240	1	=	=	PUNCT
ejpam-5650	240	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	240	3	-	-	NUM
ejpam-5650	240	4	int(f	int(f	VERB
ejpam-5650	240	5	+	+	ADJ
ejpam-5650	240	6	(	(	PUNCT
ejpam-5650	240	7	v	v	NOUN
ejpam-5650	240	8	)	)	PUNCT
ejpam-5650	240	9	)	)	PUNCT
ejpam-5650	240	10	and	and	CCONJ
ejpam-5650	240	11	hence	hence	ADV
ejpam-5650	240	12	f+(v	f+(v	PROPN
ejpam-5650	240	13	)	)	PUNCT
ejpam-5650	240	14	is	be	AUX
ejpam-5650	240	15	τ1τ2	τ1τ2	NOUN
ejpam-5650	240	16	-	-	ADJ
ejpam-5650	240	17	open	open	ADJ
ejpam-5650	240	18	in	in	ADP
ejpam-5650	240	19	x.	x.	NOUN
ejpam-5650	240	20	thus	thus	ADV
ejpam-5650	240	21	by	by	ADP
ejpam-5650	240	22	theorem	theorem	NOUN
ejpam-5650	240	23	3	3	NUM
ejpam-5650	240	24	,	,	PUNCT
ejpam-5650	240	25	f	f	PROPN
ejpam-5650	240	26	is	be	AUX
ejpam-5650	240	27	upper	upper	ADJ
ejpam-5650	240	28	almost	almost	ADV
ejpam-5650	240	29	nearly	nearly	ADV
ejpam-5650	240	30	(	(	PUNCT
ejpam-5650	240	31	τ1	τ1	NOUN
ejpam-5650	240	32	,	,	PUNCT
ejpam-5650	240	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	240	34	.	.	PUNCT
ejpam-5650	241	1	theorem	theorem	VERB
ejpam-5650	241	2	6	6	NUM
ejpam-5650	241	3	.	.	PUNCT
ejpam-5650	241	4	for	for	ADP
ejpam-5650	241	5	a	a	DET
ejpam-5650	241	6	multifunction	multifunction	NOUN
ejpam-5650	242	1	f	f	NOUN
ejpam-5650	242	2	:	:	PUNCT
ejpam-5650	242	3	(	(	PUNCT
ejpam-5650	242	4	x	x	NOUN
ejpam-5650	242	5	,	,	PUNCT
ejpam-5650	242	6	τ1	τ1	NOUN
ejpam-5650	242	7	,	,	PUNCT
ejpam-5650	242	8	τ2	τ2	NOUN
ejpam-5650	242	9	)	)	PUNCT
ejpam-5650	242	10	→	→	SYM
ejpam-5650	242	11	(	(	PUNCT
ejpam-5650	242	12	y	y	PROPN
ejpam-5650	242	13	,	,	PUNCT
ejpam-5650	242	14	σ1	σ1	PROPN
ejpam-5650	242	15	,	,	PUNCT
ejpam-5650	242	16	σ2	σ2	NOUN
ejpam-5650	242	17	)	)	PUNCT
ejpam-5650	242	18	,	,	PUNCT
ejpam-5650	242	19	the	the	DET
ejpam-5650	242	20	following	follow	VERB
ejpam-5650	242	21	properties	property	NOUN
ejpam-5650	242	22	are	be	AUX
ejpam-5650	242	23	equivalent	equivalent	ADJ
ejpam-5650	242	24	:	:	PUNCT
ejpam-5650	242	25	(	(	PUNCT
ejpam-5650	242	26	1	1	X
ejpam-5650	242	27	)	)	PUNCT
ejpam-5650	242	28	f	f	PROPN
ejpam-5650	242	29	is	be	AUX
ejpam-5650	242	30	lower	low	ADJ
ejpam-5650	242	31	almost	almost	ADV
ejpam-5650	242	32	nearly	nearly	ADV
ejpam-5650	242	33	(	(	PUNCT
ejpam-5650	242	34	τ1	τ1	NOUN
ejpam-5650	242	35	,	,	PUNCT
ejpam-5650	242	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	242	37	;	;	PUNCT
ejpam-5650	242	38	(	(	PUNCT
ejpam-5650	242	39	2	2	X
ejpam-5650	242	40	)	)	PUNCT
ejpam-5650	242	41	τ1τ2	τ1τ2	NOUN
ejpam-5650	242	42	-	-	NOUN
ejpam-5650	242	43	cl(f	cl(f	NOUN
ejpam-5650	242	44	+	+	NOUN
ejpam-5650	242	45	(	(	PUNCT
ejpam-5650	242	46	v	v	NOUN
ejpam-5650	242	47	)	)	PUNCT
ejpam-5650	242	48	)	)	PUNCT
ejpam-5650	243	1	⊆	⊆	NUM
ejpam-5650	243	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	243	3	-	-	PUNCT
ejpam-5650	243	4	cl(v	cl(v	NOUN
ejpam-5650	243	5	)	)	PUNCT
ejpam-5650	243	6	)	)	PUNCT
ejpam-5650	243	7	for	for	ADP
ejpam-5650	243	8	every	every	DET
ejpam-5650	243	9	every	every	DET
ejpam-5650	243	10	(	(	PUNCT
ejpam-5650	243	11	σ1	σ1	PROPN
ejpam-5650	243	12	,	,	PUNCT
ejpam-5650	243	13	σ2)β	σ2)β	NOUN
ejpam-5650	243	14	-	-	PUNCT
ejpam-5650	243	15	open	open	NOUN
ejpam-5650	243	16	set	set	NOUN
ejpam-5650	243	17	v	v	NOUN
ejpam-5650	243	18	of	of	ADP
ejpam-5650	243	19	y	y	PROPN
ejpam-5650	243	20	having	have	VERB
ejpam-5650	243	21	the	the	DET
ejpam-5650	243	22	n	n	PROPN
ejpam-5650	243	23	(	(	PUNCT
ejpam-5650	243	24	σ1	σ1	PROPN
ejpam-5650	243	25	,	,	PUNCT
ejpam-5650	243	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	243	27	σ1σ2	σ1σ2	NOUN
ejpam-5650	243	28	-	-	NOUN
ejpam-5650	243	29	closure	closure	NOUN
ejpam-5650	243	30	;	;	PUNCT
ejpam-5650	243	31	(	(	PUNCT
ejpam-5650	243	32	3	3	X
ejpam-5650	243	33	)	)	PUNCT
ejpam-5650	243	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	243	35	-	-	NOUN
ejpam-5650	243	36	cl(f	cl(f	NOUN
ejpam-5650	243	37	+	+	NOUN
ejpam-5650	243	38	(	(	PUNCT
ejpam-5650	243	39	v	v	NOUN
ejpam-5650	243	40	)	)	PUNCT
ejpam-5650	243	41	)	)	PUNCT
ejpam-5650	244	1	⊆	⊆	NUM
ejpam-5650	244	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	244	3	-	-	PUNCT
ejpam-5650	244	4	cl(v	cl(v	NOUN
ejpam-5650	244	5	)	)	PUNCT
ejpam-5650	244	6	)	)	PUNCT
ejpam-5650	244	7	for	for	SCONJ
ejpam-5650	244	8	every	every	DET
ejpam-5650	244	9	every	every	DET
ejpam-5650	244	10	(	(	PUNCT
ejpam-5650	244	11	σ1	σ1	PROPN
ejpam-5650	244	12	,	,	PUNCT
ejpam-5650	244	13	σ2)s	σ2)s	NOUN
ejpam-5650	244	14	-	-	PUNCT
ejpam-5650	244	15	open	open	NOUN
ejpam-5650	244	16	set	set	NOUN
ejpam-5650	244	17	v	v	NOUN
ejpam-5650	244	18	of	of	ADP
ejpam-5650	244	19	y	y	PROPN
ejpam-5650	244	20	having	have	VERB
ejpam-5650	244	21	the	the	DET
ejpam-5650	244	22	n	n	PROPN
ejpam-5650	244	23	(	(	PUNCT
ejpam-5650	244	24	σ1	σ1	PROPN
ejpam-5650	244	25	,	,	PUNCT
ejpam-5650	244	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	244	27	σ1σ2	σ1σ2	NOUN
ejpam-5650	244	28	-	-	NOUN
ejpam-5650	244	29	closure	closure	NOUN
ejpam-5650	244	30	;	;	PUNCT
ejpam-5650	244	31	(	(	PUNCT
ejpam-5650	244	32	4	4	X
ejpam-5650	244	33	)	)	PUNCT
ejpam-5650	244	34	f−(v	f−(v	NOUN
ejpam-5650	244	35	)	)	PUNCT
ejpam-5650	244	36	⊆	⊆	NUM
ejpam-5650	244	37	τ1τ2	τ1τ2	NOUN
ejpam-5650	244	38	-	-	NUM
ejpam-5650	244	39	int(f	int(f	VERB
ejpam-5650	244	40	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5650	244	41	-	-	PUNCT
ejpam-5650	244	42	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	244	43	-	-	PUNCT
ejpam-5650	244	44	cl(v	cl(v	NOUN
ejpam-5650	244	45	)	)	PUNCT
ejpam-5650	244	46	)	)	PUNCT
ejpam-5650	244	47	)	)	PUNCT
ejpam-5650	244	48	)	)	PUNCT
ejpam-5650	245	1	for	for	ADP
ejpam-5650	245	2	every	every	DET
ejpam-5650	245	3	every	every	DET
ejpam-5650	245	4	(	(	PUNCT
ejpam-5650	245	5	σ1	σ1	PROPN
ejpam-5650	245	6	,	,	PUNCT
ejpam-5650	245	7	σ2)p	σ2)p	NOUN
ejpam-5650	245	8	-	-	PUNCT
ejpam-5650	245	9	open	open	NOUN
ejpam-5650	245	10	set	set	NOUN
ejpam-5650	245	11	v	v	NOUN
ejpam-5650	245	12	of	of	ADP
ejpam-5650	245	13	y	y	PROPN
ejpam-5650	245	14	having	have	VERB
ejpam-5650	245	15	n	n	PROPN
ejpam-5650	245	16	(	(	PUNCT
ejpam-5650	245	17	σ1	σ1	PROPN
ejpam-5650	245	18	,	,	PUNCT
ejpam-5650	245	19	σ2)-closed	σ2)-close	VERB
ejpam-5650	245	20	complement	complement	NOUN
ejpam-5650	245	21	.	.	PUNCT
ejpam-5650	246	1	proof	proof	NOUN
ejpam-5650	246	2	.	.	PUNCT
ejpam-5650	247	1	the	the	DET
ejpam-5650	247	2	proof	proof	NOUN
ejpam-5650	247	3	is	be	AUX
ejpam-5650	247	4	similar	similar	ADJ
ejpam-5650	247	5	to	to	ADP
ejpam-5650	247	6	that	that	PRON
ejpam-5650	247	7	of	of	ADP
ejpam-5650	247	8	theorem	theorem	NOUN
ejpam-5650	247	9	5	5	NUM
ejpam-5650	247	10	.	.	PUNCT
ejpam-5650	247	11	lemma	lemma	PROPN
ejpam-5650	247	12	4	4	NUM
ejpam-5650	247	13	.	.	PUNCT
ejpam-5650	247	14	for	for	ADP
ejpam-5650	247	15	a	a	DET
ejpam-5650	247	16	bitopological	bitopological	ADJ
ejpam-5650	247	17	space	space	NOUN
ejpam-5650	247	18	(	(	PUNCT
ejpam-5650	247	19	x	x	NOUN
ejpam-5650	247	20	,	,	PUNCT
ejpam-5650	247	21	τ1	τ1	NOUN
ejpam-5650	247	22	,	,	PUNCT
ejpam-5650	247	23	τ2	τ2	NOUN
ejpam-5650	247	24	)	)	PUNCT
ejpam-5650	247	25	,	,	PUNCT
ejpam-5650	247	26	the	the	DET
ejpam-5650	247	27	following	follow	VERB
ejpam-5650	247	28	properties	property	NOUN
ejpam-5650	247	29	hold	hold	VERB
ejpam-5650	247	30	:	:	PUNCT
ejpam-5650	247	31	(	(	PUNCT
ejpam-5650	247	32	1	1	X
ejpam-5650	247	33	)	)	PUNCT
ejpam-5650	247	34	α(τ1	α(τ1	NOUN
ejpam-5650	247	35	,	,	PUNCT
ejpam-5650	247	36	τ2)-cl(u	τ2)-cl(u	NOUN
ejpam-5650	247	37	)	)	PUNCT
ejpam-5650	247	38	=	=	PUNCT
ejpam-5650	248	1	τ1τ2	τ1τ2	NOUN
ejpam-5650	248	2	-	-	NOUN
ejpam-5650	248	3	cl(u	cl(u	NOUN
ejpam-5650	248	4	)	)	PUNCT
ejpam-5650	248	5	for	for	ADP
ejpam-5650	248	6	every	every	DET
ejpam-5650	248	7	(	(	PUNCT
ejpam-5650	248	8	τ1	τ1	NOUN
ejpam-5650	248	9	,	,	PUNCT
ejpam-5650	248	10	τ2)β	τ2)β	ADJ
ejpam-5650	248	11	-	-	PUNCT
ejpam-5650	248	12	open	open	ADJ
ejpam-5650	248	13	set	set	NOUN
ejpam-5650	248	14	u	u	NOUN
ejpam-5650	248	15	of	of	ADP
ejpam-5650	248	16	x	x	PRON
ejpam-5650	248	17	;	;	PUNCT
ejpam-5650	248	18	(	(	PUNCT
ejpam-5650	248	19	2	2	X
ejpam-5650	248	20	)	)	PUNCT
ejpam-5650	248	21	(	(	PUNCT
ejpam-5650	248	22	τ1	τ1	NOUN
ejpam-5650	248	23	,	,	PUNCT
ejpam-5650	248	24	τ2)-pcl(u	τ2)-pcl(u	NOUN
ejpam-5650	248	25	)	)	PUNCT
ejpam-5650	248	26	=	=	PUNCT
ejpam-5650	249	1	τ1τ2	τ1τ2	NOUN
ejpam-5650	249	2	-	-	NOUN
ejpam-5650	249	3	cl(u	cl(u	NOUN
ejpam-5650	249	4	)	)	PUNCT
ejpam-5650	249	5	for	for	ADP
ejpam-5650	249	6	every	every	DET
ejpam-5650	249	7	(	(	PUNCT
ejpam-5650	249	8	τ1	τ1	NOUN
ejpam-5650	249	9	,	,	PUNCT
ejpam-5650	249	10	τ2)s	τ2)s	NOUN
ejpam-5650	249	11	-	-	PUNCT
ejpam-5650	249	12	open	open	ADJ
ejpam-5650	249	13	set	set	NOUN
ejpam-5650	249	14	u	u	NOUN
ejpam-5650	249	15	of	of	ADP
ejpam-5650	249	16	x.	x.	PROPN
ejpam-5650	249	17	corollary	corollary	PROPN
ejpam-5650	249	18	3	3	X
ejpam-5650	249	19	.	.	PUNCT
ejpam-5650	249	20	for	for	ADP
ejpam-5650	249	21	a	a	DET
ejpam-5650	249	22	multifunction	multifunction	NOUN
ejpam-5650	249	23	f	f	NOUN
ejpam-5650	249	24	:	:	PUNCT
ejpam-5650	249	25	(	(	PUNCT
ejpam-5650	249	26	x	x	NOUN
ejpam-5650	249	27	,	,	PUNCT
ejpam-5650	249	28	τ1	τ1	NOUN
ejpam-5650	249	29	,	,	PUNCT
ejpam-5650	249	30	τ2	τ2	NOUN
ejpam-5650	249	31	)	)	PUNCT
ejpam-5650	249	32	→	→	SYM
ejpam-5650	249	33	(	(	PUNCT
ejpam-5650	249	34	y	y	PROPN
ejpam-5650	249	35	,	,	PUNCT
ejpam-5650	249	36	σ1	σ1	PROPN
ejpam-5650	249	37	,	,	PUNCT
ejpam-5650	249	38	σ2	σ2	NOUN
ejpam-5650	249	39	)	)	PUNCT
ejpam-5650	249	40	,	,	PUNCT
ejpam-5650	249	41	the	the	DET
ejpam-5650	249	42	following	follow	VERB
ejpam-5650	249	43	properties	property	NOUN
ejpam-5650	249	44	are	be	AUX
ejpam-5650	249	45	equivalent	equivalent	ADJ
ejpam-5650	249	46	:	:	PUNCT
ejpam-5650	249	47	(	(	PUNCT
ejpam-5650	249	48	1	1	X
ejpam-5650	249	49	)	)	PUNCT
ejpam-5650	249	50	f	f	PROPN
ejpam-5650	249	51	is	be	AUX
ejpam-5650	249	52	upper	upper	ADJ
ejpam-5650	249	53	almost	almost	ADV
ejpam-5650	249	54	nearly	nearly	ADV
ejpam-5650	249	55	(	(	PUNCT
ejpam-5650	249	56	τ1	τ1	NOUN
ejpam-5650	249	57	,	,	PUNCT
ejpam-5650	249	58	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	249	59	;	;	PUNCT
ejpam-5650	249	60	(	(	PUNCT
ejpam-5650	249	61	2	2	X
ejpam-5650	249	62	)	)	PUNCT
ejpam-5650	249	63	τ1τ2	τ1τ2	NOUN
ejpam-5650	249	64	-	-	NOUN
ejpam-5650	249	65	cl(f	cl(f	NUM
ejpam-5650	249	66	−(v	−(v	NOUN
ejpam-5650	249	67	)	)	PUNCT
ejpam-5650	249	68	)	)	PUNCT
ejpam-5650	250	1	⊆	⊆	NUM
ejpam-5650	250	2	f−(α(σ1	f−(α(σ1	NOUN
ejpam-5650	250	3	,	,	PUNCT
ejpam-5650	250	4	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-5650	250	5	)	)	PUNCT
ejpam-5650	250	6	)	)	PUNCT
ejpam-5650	250	7	for	for	ADP
ejpam-5650	250	8	every	every	DET
ejpam-5650	250	9	every	every	DET
ejpam-5650	250	10	(	(	PUNCT
ejpam-5650	250	11	σ1	σ1	PROPN
ejpam-5650	250	12	,	,	PUNCT
ejpam-5650	250	13	σ2)β	σ2)β	NOUN
ejpam-5650	250	14	-	-	PUNCT
ejpam-5650	250	15	open	open	NOUN
ejpam-5650	250	16	set	set	NOUN
ejpam-5650	250	17	v	v	NOUN
ejpam-5650	250	18	of	of	ADP
ejpam-5650	250	19	y	y	PROPN
ejpam-5650	250	20	having	have	VERB
ejpam-5650	250	21	the	the	DET
ejpam-5650	250	22	n	n	PROPN
ejpam-5650	250	23	(	(	PUNCT
ejpam-5650	250	24	σ1	σ1	PROPN
ejpam-5650	250	25	,	,	PUNCT
ejpam-5650	250	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	250	27	σ1σ2	σ1σ2	NOUN
ejpam-5650	250	28	-	-	NOUN
ejpam-5650	250	29	closure	closure	NOUN
ejpam-5650	250	30	;	;	PUNCT
ejpam-5650	250	31	n.	n.	NOUN
ejpam-5650	250	32	chutiman	chutiman	NOUN
ejpam-5650	250	33	,	,	PUNCT
ejpam-5650	250	34	a.	a.	PROPN
ejpam-5650	250	35	sama	sama	PROPN
ejpam-5650	250	36	-	-	PUNCT
ejpam-5650	250	37	ae	ae	PROPN
ejpam-5650	250	38	,	,	PUNCT
ejpam-5650	250	39	c.	c.	PROPN
ejpam-5650	250	40	boonpok	boonpok	PROPN
ejpam-5650	250	41	/	/	SYM
ejpam-5650	250	42	eur	eur	PROPN
ejpam-5650	250	43	.	.	PUNCT
ejpam-5650	251	1	j.	j.	PROPN
ejpam-5650	251	2	pure	pure	PROPN
ejpam-5650	251	3	appl	appl	PROPN
ejpam-5650	251	4	.	.	PROPN
ejpam-5650	251	5	math	math	PROPN
ejpam-5650	251	6	,	,	PUNCT
ejpam-5650	251	7	18	18	NUM
ejpam-5650	251	8	(	(	PUNCT
ejpam-5650	251	9	1	1	NUM
ejpam-5650	251	10	)	)	PUNCT
ejpam-5650	251	11	(	(	PUNCT
ejpam-5650	251	12	2025	2025	NUM
ejpam-5650	251	13	)	)	PUNCT
ejpam-5650	251	14	,	,	PUNCT
ejpam-5650	251	15	5650	5650	NUM
ejpam-5650	251	16	10	10	NUM
ejpam-5650	251	17	of	of	ADP
ejpam-5650	251	18	18	18	NUM
ejpam-5650	251	19	(	(	PUNCT
ejpam-5650	251	20	3	3	NUM
ejpam-5650	251	21	)	)	PUNCT
ejpam-5650	251	22	τ1τ2	τ1τ2	NOUN
ejpam-5650	251	23	-	-	NOUN
ejpam-5650	251	24	cl(f	cl(f	NUM
ejpam-5650	251	25	−(v	−(v	NOUN
ejpam-5650	251	26	)	)	PUNCT
ejpam-5650	251	27	)	)	PUNCT
ejpam-5650	252	1	⊆	⊆	NUM
ejpam-5650	252	2	f−((σ1	f−((σ1	NOUN
ejpam-5650	252	3	,	,	PUNCT
ejpam-5650	252	4	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-5650	252	5	)	)	PUNCT
ejpam-5650	252	6	)	)	PUNCT
ejpam-5650	252	7	for	for	ADP
ejpam-5650	252	8	every	every	DET
ejpam-5650	252	9	every	every	DET
ejpam-5650	252	10	(	(	PUNCT
ejpam-5650	252	11	σ1	σ1	PROPN
ejpam-5650	252	12	,	,	PUNCT
ejpam-5650	252	13	σ2)s	σ2)s	NOUN
ejpam-5650	252	14	-	-	PUNCT
ejpam-5650	252	15	open	open	NOUN
ejpam-5650	252	16	set	set	NOUN
ejpam-5650	252	17	v	v	NOUN
ejpam-5650	252	18	of	of	ADP
ejpam-5650	252	19	y	y	PROPN
ejpam-5650	252	20	having	have	VERB
ejpam-5650	252	21	the	the	DET
ejpam-5650	252	22	n	n	PROPN
ejpam-5650	252	23	(	(	PUNCT
ejpam-5650	252	24	σ1	σ1	PROPN
ejpam-5650	252	25	,	,	PUNCT
ejpam-5650	252	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	252	27	σ1σ2	σ1σ2	NOUN
ejpam-5650	252	28	-	-	NOUN
ejpam-5650	252	29	closure	closure	NOUN
ejpam-5650	252	30	.	.	PUNCT
ejpam-5650	253	1	corollary	corollary	ADJ
ejpam-5650	253	2	4	4	NUM
ejpam-5650	253	3	.	.	PUNCT
ejpam-5650	253	4	for	for	ADP
ejpam-5650	253	5	a	a	DET
ejpam-5650	253	6	multifunction	multifunction	NOUN
ejpam-5650	254	1	f	f	NOUN
ejpam-5650	254	2	:	:	PUNCT
ejpam-5650	254	3	(	(	PUNCT
ejpam-5650	254	4	x	x	NOUN
ejpam-5650	254	5	,	,	PUNCT
ejpam-5650	254	6	τ1	τ1	NOUN
ejpam-5650	254	7	,	,	PUNCT
ejpam-5650	254	8	τ2	τ2	NOUN
ejpam-5650	254	9	)	)	PUNCT
ejpam-5650	254	10	→	→	SYM
ejpam-5650	254	11	(	(	PUNCT
ejpam-5650	254	12	y	y	PROPN
ejpam-5650	254	13	,	,	PUNCT
ejpam-5650	254	14	σ1	σ1	PROPN
ejpam-5650	254	15	,	,	PUNCT
ejpam-5650	254	16	σ2	σ2	NOUN
ejpam-5650	254	17	)	)	PUNCT
ejpam-5650	254	18	,	,	PUNCT
ejpam-5650	254	19	the	the	DET
ejpam-5650	254	20	following	follow	VERB
ejpam-5650	254	21	properties	property	NOUN
ejpam-5650	254	22	are	be	AUX
ejpam-5650	254	23	equivalent	equivalent	ADJ
ejpam-5650	254	24	:	:	PUNCT
ejpam-5650	254	25	(	(	PUNCT
ejpam-5650	254	26	1	1	X
ejpam-5650	254	27	)	)	PUNCT
ejpam-5650	254	28	f	f	PROPN
ejpam-5650	254	29	is	be	AUX
ejpam-5650	254	30	lower	low	ADJ
ejpam-5650	254	31	almost	almost	ADV
ejpam-5650	254	32	nearly	nearly	ADV
ejpam-5650	254	33	(	(	PUNCT
ejpam-5650	254	34	τ1	τ1	NOUN
ejpam-5650	254	35	,	,	PUNCT
ejpam-5650	254	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	254	37	;	;	PUNCT
ejpam-5650	254	38	(	(	PUNCT
ejpam-5650	254	39	2	2	X
ejpam-5650	254	40	)	)	PUNCT
ejpam-5650	254	41	τ1τ2	τ1τ2	NOUN
ejpam-5650	254	42	-	-	NOUN
ejpam-5650	254	43	cl(f	cl(f	NOUN
ejpam-5650	254	44	+	+	NOUN
ejpam-5650	254	45	(	(	PUNCT
ejpam-5650	254	46	v	v	NOUN
ejpam-5650	254	47	)	)	PUNCT
ejpam-5650	254	48	)	)	PUNCT
ejpam-5650	255	1	⊆	⊆	NUM
ejpam-5650	255	2	f+(α(σ1	f+(α(σ1	NOUN
ejpam-5650	255	3	,	,	PUNCT
ejpam-5650	255	4	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-5650	255	5	)	)	PUNCT
ejpam-5650	255	6	)	)	PUNCT
ejpam-5650	255	7	for	for	ADP
ejpam-5650	255	8	every	every	DET
ejpam-5650	255	9	every	every	DET
ejpam-5650	255	10	(	(	PUNCT
ejpam-5650	255	11	σ1	σ1	PROPN
ejpam-5650	255	12	,	,	PUNCT
ejpam-5650	255	13	σ2)β	σ2)β	NOUN
ejpam-5650	255	14	-	-	PUNCT
ejpam-5650	255	15	open	open	NOUN
ejpam-5650	255	16	set	set	NOUN
ejpam-5650	255	17	v	v	NOUN
ejpam-5650	255	18	of	of	ADP
ejpam-5650	255	19	y	y	PROPN
ejpam-5650	255	20	having	have	VERB
ejpam-5650	255	21	the	the	DET
ejpam-5650	255	22	n	n	PROPN
ejpam-5650	255	23	(	(	PUNCT
ejpam-5650	255	24	σ1	σ1	PROPN
ejpam-5650	255	25	,	,	PUNCT
ejpam-5650	255	26	σ2)-closed	σ2)-close	VERB
ejpam-5650	255	27	σ1σ2	σ1σ2	NOUN
ejpam-5650	255	28	-	-	NOUN
ejpam-5650	255	29	closure	closure	NOUN
ejpam-5650	255	30	;	;	PUNCT
ejpam-5650	255	31	(	(	PUNCT
ejpam-5650	255	32	3	3	X
ejpam-5650	255	33	)	)	PUNCT
ejpam-5650	255	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	255	35	-	-	NOUN
ejpam-5650	255	36	cl(f	cl(f	NOUN
ejpam-5650	255	37	+	+	NOUN
ejpam-5650	255	38	(	(	PUNCT
ejpam-5650	255	39	v	v	NOUN
ejpam-5650	255	40	)	)	PUNCT
ejpam-5650	255	41	)	)	PUNCT
ejpam-5650	256	1	⊆	⊆	NUM
ejpam-5650	256	2	f+((σ1	f+((σ1	NOUN
ejpam-5650	256	3	,	,	PUNCT
ejpam-5650	256	4	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-5650	256	5	)	)	PUNCT
ejpam-5650	256	6	)	)	PUNCT
ejpam-5650	257	1	for	for	SCONJ
ejpam-5650	257	2	every	every	DET
ejpam-5650	257	3	every	every	DET
ejpam-5650	257	4	(	(	PUNCT
ejpam-5650	257	5	σ1	σ1	PROPN
ejpam-5650	257	6	,	,	PUNCT
ejpam-5650	257	7	σ2)s	σ2)s	NOUN
ejpam-5650	257	8	-	-	PUNCT
ejpam-5650	257	9	open	open	NOUN
ejpam-5650	257	10	set	set	NOUN
ejpam-5650	257	11	v	v	NOUN
ejpam-5650	257	12	of	of	ADP
ejpam-5650	257	13	y	y	PROPN
ejpam-5650	257	14	having	have	VERB
ejpam-5650	257	15	the	the	DET
ejpam-5650	257	16	n	n	PROPN
ejpam-5650	257	17	(	(	PUNCT
ejpam-5650	257	18	σ1	σ1	PROPN
ejpam-5650	257	19	,	,	PUNCT
ejpam-5650	257	20	σ2)-closed	σ2)-close	VERB
ejpam-5650	257	21	σ1σ2	σ1σ2	NOUN
ejpam-5650	257	22	-	-	NOUN
ejpam-5650	257	23	closure	closure	NOUN
ejpam-5650	257	24	.	.	PUNCT
ejpam-5650	258	1	theorem	theorem	VERB
ejpam-5650	258	2	7	7	NUM
ejpam-5650	258	3	.	.	X
ejpam-5650	258	4	for	for	ADP
ejpam-5650	258	5	a	a	DET
ejpam-5650	258	6	multifunction	multifunction	NOUN
ejpam-5650	259	1	f	f	NOUN
ejpam-5650	259	2	:	:	PUNCT
ejpam-5650	259	3	(	(	PUNCT
ejpam-5650	259	4	x	x	NOUN
ejpam-5650	259	5	,	,	PUNCT
ejpam-5650	259	6	τ1	τ1	NOUN
ejpam-5650	259	7	,	,	PUNCT
ejpam-5650	259	8	τ2	τ2	NOUN
ejpam-5650	259	9	)	)	PUNCT
ejpam-5650	259	10	→	→	SYM
ejpam-5650	259	11	(	(	PUNCT
ejpam-5650	259	12	y	y	PROPN
ejpam-5650	259	13	,	,	PUNCT
ejpam-5650	259	14	σ1	σ1	PROPN
ejpam-5650	259	15	,	,	PUNCT
ejpam-5650	259	16	σ2	σ2	NOUN
ejpam-5650	259	17	)	)	PUNCT
ejpam-5650	259	18	,	,	PUNCT
ejpam-5650	259	19	the	the	DET
ejpam-5650	259	20	following	follow	VERB
ejpam-5650	259	21	properties	property	NOUN
ejpam-5650	259	22	are	be	AUX
ejpam-5650	259	23	equivalent	equivalent	ADJ
ejpam-5650	259	24	:	:	PUNCT
ejpam-5650	259	25	(	(	PUNCT
ejpam-5650	259	26	1	1	X
ejpam-5650	259	27	)	)	PUNCT
ejpam-5650	259	28	f	f	PROPN
ejpam-5650	259	29	is	be	AUX
ejpam-5650	259	30	upper	upper	ADJ
ejpam-5650	259	31	almost	almost	ADV
ejpam-5650	259	32	nearly	nearly	ADV
ejpam-5650	259	33	(	(	PUNCT
ejpam-5650	259	34	τ1	τ1	NOUN
ejpam-5650	259	35	,	,	PUNCT
ejpam-5650	259	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	259	37	;	;	PUNCT
ejpam-5650	259	38	(	(	PUNCT
ejpam-5650	259	39	2	2	X
ejpam-5650	259	40	)	)	PUNCT
ejpam-5650	259	41	for	for	ADP
ejpam-5650	259	42	each	each	DET
ejpam-5650	259	43	x	x	SYM
ejpam-5650	259	44	∈	∈	PROPN
ejpam-5650	259	45	x	x	X
ejpam-5650	259	46	and	and	CCONJ
ejpam-5650	259	47	for	for	ADP
ejpam-5650	259	48	every	every	DET
ejpam-5650	259	49	σ1σ2	σ1σ2	NOUN
ejpam-5650	259	50	-	-	PUNCT
ejpam-5650	259	51	closed	closed	ADJ
ejpam-5650	259	52	and	and	CCONJ
ejpam-5650	259	53	n	n	CCONJ
ejpam-5650	259	54	(	(	PUNCT
ejpam-5650	259	55	σ1	σ1	PROPN
ejpam-5650	259	56	,	,	PUNCT
ejpam-5650	259	57	σ2)-closed	σ2)-close	VERB
ejpam-5650	259	58	set	set	VERB
ejpam-5650	259	59	k	k	PROPN
ejpam-5650	259	60	of	of	ADP
ejpam-5650	259	61	y	y	PROPN
ejpam-5650	259	62	such	such	ADJ
ejpam-5650	259	63	that	that	SCONJ
ejpam-5650	259	64	x	x	SYM
ejpam-5650	259	65	∈	∈	PROPN
ejpam-5650	259	66	f+(y	f+(y	NOUN
ejpam-5650	259	67	−k	−k	PROPN
ejpam-5650	259	68	)	)	PUNCT
ejpam-5650	259	69	,	,	PUNCT
ejpam-5650	259	70	there	there	PRON
ejpam-5650	259	71	exists	exist	VERB
ejpam-5650	259	72	a	a	DET
ejpam-5650	259	73	τ1τ2	τ1τ2	ADJ
ejpam-5650	259	74	-	-	ADJ
ejpam-5650	259	75	closed	closed	ADJ
ejpam-5650	259	76	set	set	ADJ
ejpam-5650	259	77	h	h	NOUN
ejpam-5650	259	78	of	of	ADP
ejpam-5650	259	79	x	x	INTJ
ejpam-5650	259	80	such	such	ADJ
ejpam-5650	259	81	that	that	SCONJ
ejpam-5650	259	82	x	x	SYM
ejpam-5650	259	83	∈	∈	NOUN
ejpam-5650	259	84	x	x	SYM
ejpam-5650	259	85	−h	−h	ADJ
ejpam-5650	259	86	and	and	CCONJ
ejpam-5650	259	87	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5650	259	88	-	-	PUNCT
ejpam-5650	259	89	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	259	90	-	-	PUNCT
ejpam-5650	259	91	int(k	int(k	NOUN
ejpam-5650	259	92	)	)	PUNCT
ejpam-5650	259	93	)	)	PUNCT
ejpam-5650	259	94	)	)	PUNCT
ejpam-5650	260	1	⊆	⊆	NUM
ejpam-5650	260	2	h	h	NOUN
ejpam-5650	260	3	;	;	PUNCT
ejpam-5650	260	4	(	(	PUNCT
ejpam-5650	260	5	3	3	X
ejpam-5650	260	6	)	)	PUNCT
ejpam-5650	260	7	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	260	8	-	-	PUNCT
ejpam-5650	260	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	260	10	-	-	PUNCT
ejpam-5650	260	11	cl(v	cl(v	NOUN
ejpam-5650	260	12	)	)	PUNCT
ejpam-5650	260	13	)	)	PUNCT
ejpam-5650	260	14	)	)	PUNCT
ejpam-5650	260	15	is	be	AUX
ejpam-5650	260	16	τ1τ2	τ1τ2	NOUN
ejpam-5650	260	17	-	-	ADJ
ejpam-5650	260	18	open	open	ADJ
ejpam-5650	260	19	in	in	ADP
ejpam-5650	260	20	x	x	PUNCT
ejpam-5650	260	21	for	for	ADP
ejpam-5650	260	22	every	every	DET
ejpam-5650	260	23	σ1σ2	σ1σ2	NOUN
ejpam-5650	260	24	-	-	ADJ
ejpam-5650	260	25	open	open	ADJ
ejpam-5650	260	26	set	set	NOUN
ejpam-5650	260	27	v	v	NOUN
ejpam-5650	260	28	of	of	ADP
ejpam-5650	260	29	y	y	PROPN
ejpam-5650	260	30	having	have	VERB
ejpam-5650	260	31	n	n	PROPN
ejpam-5650	260	32	(	(	PUNCT
ejpam-5650	260	33	σ1	σ1	PROPN
ejpam-5650	260	34	,	,	PUNCT
ejpam-5650	260	35	σ2)-closed	σ2)-close	VERB
ejpam-5650	260	36	complement	complement	NOUN
ejpam-5650	260	37	;	;	PUNCT
ejpam-5650	260	38	(	(	PUNCT
ejpam-5650	260	39	4	4	X
ejpam-5650	260	40	)	)	PUNCT
ejpam-5650	260	41	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	260	42	-	-	PUNCT
ejpam-5650	260	43	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	260	44	-	-	PUNCT
ejpam-5650	260	45	int(k	int(k	NOUN
ejpam-5650	260	46	)	)	PUNCT
ejpam-5650	260	47	)	)	PUNCT
ejpam-5650	260	48	)	)	PUNCT
ejpam-5650	261	1	is	be	AUX
ejpam-5650	261	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	261	3	-	-	ADJ
ejpam-5650	261	4	closed	closed	ADJ
ejpam-5650	261	5	in	in	ADP
ejpam-5650	261	6	x	x	PUNCT
ejpam-5650	261	7	for	for	ADP
ejpam-5650	261	8	every	every	DET
ejpam-5650	261	9	σ1σ2	σ1σ2	NOUN
ejpam-5650	261	10	-	-	PUNCT
ejpam-5650	261	11	closed	closed	ADJ
ejpam-5650	261	12	and	and	CCONJ
ejpam-5650	261	13	n	n	CCONJ
ejpam-5650	261	14	(	(	PUNCT
ejpam-5650	261	15	σ1	σ1	PROPN
ejpam-5650	261	16	,	,	PUNCT
ejpam-5650	261	17	σ2)closed	σ2)close	VERB
ejpam-5650	261	18	set	set	VERB
ejpam-5650	261	19	k	k	PROPN
ejpam-5650	261	20	of	of	ADP
ejpam-5650	261	21	y	y	PROPN
ejpam-5650	261	22	.	.	PUNCT
ejpam-5650	262	1	proof	proof	NOUN
ejpam-5650	262	2	.	.	PUNCT
ejpam-5650	263	1	(	(	PUNCT
ejpam-5650	263	2	1	1	X
ejpam-5650	263	3	)	)	PUNCT
ejpam-5650	263	4	⇒	⇒	NOUN
ejpam-5650	263	5	(	(	PUNCT
ejpam-5650	263	6	2	2	NUM
ejpam-5650	263	7	):	):	PUNCT
ejpam-5650	263	8	let	let	VERB
ejpam-5650	263	9	x	x	PUNCT
ejpam-5650	263	10	∈	∈	PROPN
ejpam-5650	263	11	x	x	X
ejpam-5650	263	12	and	and	CCONJ
ejpam-5650	263	13	k	k	PROPN
ejpam-5650	263	14	be	be	AUX
ejpam-5650	263	15	any	any	DET
ejpam-5650	263	16	σ1σ2	σ1σ2	NOUN
ejpam-5650	263	17	-	-	PUNCT
ejpam-5650	263	18	closed	closed	ADJ
ejpam-5650	263	19	and	and	CCONJ
ejpam-5650	263	20	n	n	CCONJ
ejpam-5650	263	21	(	(	PUNCT
ejpam-5650	263	22	σ1	σ1	PROPN
ejpam-5650	263	23	,	,	PUNCT
ejpam-5650	263	24	σ2)-closed	σ2)-close	VERB
ejpam-5650	263	25	set	set	NOUN
ejpam-5650	263	26	of	of	ADP
ejpam-5650	263	27	y	y	PRON
ejpam-5650	263	28	such	such	ADJ
ejpam-5650	263	29	that	that	SCONJ
ejpam-5650	263	30	x	x	SYM
ejpam-5650	263	31	∈	∈	PROPN
ejpam-5650	263	32	f+(y	f+(y	VERB
ejpam-5650	263	33	−k	−k	PROPN
ejpam-5650	263	34	)	)	PUNCT
ejpam-5650	263	35	.	.	PUNCT
ejpam-5650	264	1	then	then	ADV
ejpam-5650	264	2	,	,	PUNCT
ejpam-5650	264	3	y	y	PROPN
ejpam-5650	264	4	−k	−k	PROPN
ejpam-5650	264	5	is	be	AUX
ejpam-5650	264	6	a	a	DET
ejpam-5650	264	7	σ1σ2	σ1σ2	NUM
ejpam-5650	264	8	-	-	ADJ
ejpam-5650	264	9	open	open	ADJ
ejpam-5650	264	10	set	set	NOUN
ejpam-5650	264	11	having	have	VERB
ejpam-5650	264	12	n	n	PROPN
ejpam-5650	264	13	(	(	PUNCT
ejpam-5650	264	14	σ1	σ1	PROPN
ejpam-5650	264	15	,	,	PUNCT
ejpam-5650	264	16	σ2)-closed	σ2)-close	VERB
ejpam-5650	264	17	complement	complement	NOUN
ejpam-5650	264	18	.	.	PUNCT
ejpam-5650	265	1	since	since	SCONJ
ejpam-5650	265	2	f	f	PROPN
ejpam-5650	265	3	is	be	AUX
ejpam-5650	265	4	upper	upper	ADJ
ejpam-5650	265	5	almost	almost	ADV
ejpam-5650	265	6	nearly	nearly	ADV
ejpam-5650	265	7	(	(	PUNCT
ejpam-5650	265	8	τ1	τ1	NOUN
ejpam-5650	265	9	,	,	PUNCT
ejpam-5650	265	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	265	11	,	,	PUNCT
ejpam-5650	265	12	there	there	PRON
ejpam-5650	265	13	exists	exist	VERB
ejpam-5650	265	14	a	a	DET
ejpam-5650	265	15	τ1τ2	τ1τ2	NOUN
ejpam-5650	265	16	-	-	ADJ
ejpam-5650	265	17	open	open	ADJ
ejpam-5650	265	18	set	set	ADJ
ejpam-5650	265	19	u	u	NOUN
ejpam-5650	265	20	of	of	ADP
ejpam-5650	265	21	x	x	PUNCT
ejpam-5650	265	22	containing	contain	VERB
ejpam-5650	265	23	x	x	PUNCT
ejpam-5650	265	24	such	such	ADJ
ejpam-5650	265	25	that	that	SCONJ
ejpam-5650	265	26	u	u	NOUN
ejpam-5650	265	27	⊆	⊆	NUM
ejpam-5650	265	28	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5650	265	29	-	-	PUNCT
ejpam-5650	265	30	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	265	31	-	-	PUNCT
ejpam-5650	265	32	cl(y	cl(y	NOUN
ejpam-5650	265	33	−k	−k	NOUN
ejpam-5650	265	34	)	)	PUNCT
ejpam-5650	265	35	)	)	PUNCT
ejpam-5650	265	36	)	)	PUNCT
ejpam-5650	266	1	=	=	PUNCT
ejpam-5650	266	2	x	x	X
ejpam-5650	266	3	−	−	ADP
ejpam-5650	266	4	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5650	266	5	-	-	PUNCT
ejpam-5650	266	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	266	7	-	-	PUNCT
ejpam-5650	266	8	int(k	int(k	NOUN
ejpam-5650	266	9	)	)	PUNCT
ejpam-5650	266	10	)	)	PUNCT
ejpam-5650	266	11	)	)	PUNCT
ejpam-5650	266	12	.	.	PUNCT
ejpam-5650	267	1	it	it	PRON
ejpam-5650	267	2	is	be	AUX
ejpam-5650	267	3	clear	clear	ADJ
ejpam-5650	267	4	that	that	SCONJ
ejpam-5650	267	5	h	h	NOUN
ejpam-5650	268	1	=	=	NOUN
ejpam-5650	268	2	x	x	SYM
ejpam-5650	268	3	−	−	NOUN
ejpam-5650	268	4	u	u	NOUN
ejpam-5650	268	5	is	be	AUX
ejpam-5650	268	6	τ1τ2	τ1τ2	NOUN
ejpam-5650	268	7	-	-	ADJ
ejpam-5650	268	8	closed	closed	ADJ
ejpam-5650	268	9	in	in	ADP
ejpam-5650	268	10	x	x	X
ejpam-5650	268	11	and	and	CCONJ
ejpam-5650	268	12	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5650	268	13	-	-	PUNCT
ejpam-5650	268	14	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	268	15	-	-	PUNCT
ejpam-5650	268	16	int(k	int(k	NOUN
ejpam-5650	268	17	)	)	PUNCT
ejpam-5650	268	18	)	)	PUNCT
ejpam-5650	268	19	)	)	PUNCT
ejpam-5650	269	1	⊆	⊆	NUM
ejpam-5650	269	2	h.	h.	NOUN
ejpam-5650	269	3	(	(	PUNCT
ejpam-5650	269	4	2	2	NUM
ejpam-5650	269	5	)	)	PUNCT
ejpam-5650	269	6	⇒	⇒	NOUN
ejpam-5650	269	7	(	(	PUNCT
ejpam-5650	269	8	1	1	NUM
ejpam-5650	269	9	):	):	PUNCT
ejpam-5650	269	10	the	the	DET
ejpam-5650	269	11	proof	proof	NOUN
ejpam-5650	269	12	is	be	AUX
ejpam-5650	269	13	similar	similar	ADJ
ejpam-5650	269	14	to	to	ADP
ejpam-5650	269	15	the	the	DET
ejpam-5650	269	16	proof	proof	NOUN
ejpam-5650	269	17	(	(	PUNCT
ejpam-5650	269	18	1	1	X
ejpam-5650	269	19	)	)	PUNCT
ejpam-5650	269	20	⇒	⇒	NOUN
ejpam-5650	269	21	(	(	PUNCT
ejpam-5650	269	22	2	2	NUM
ejpam-5650	269	23	)	)	PUNCT
ejpam-5650	269	24	.	.	PUNCT
ejpam-5650	270	1	(	(	PUNCT
ejpam-5650	270	2	1	1	X
ejpam-5650	270	3	)	)	PUNCT
ejpam-5650	270	4	⇒	⇒	NOUN
ejpam-5650	270	5	(	(	PUNCT
ejpam-5650	270	6	3	3	NUM
ejpam-5650	270	7	):	):	PUNCT
ejpam-5650	270	8	let	let	VERB
ejpam-5650	270	9	v	v	PART
ejpam-5650	270	10	be	be	AUX
ejpam-5650	270	11	any	any	DET
ejpam-5650	270	12	σ1σ2	σ1σ2	NOUN
ejpam-5650	270	13	-	-	ADJ
ejpam-5650	270	14	open	open	ADJ
ejpam-5650	270	15	set	set	NOUN
ejpam-5650	270	16	of	of	ADP
ejpam-5650	270	17	y	y	PROPN
ejpam-5650	270	18	having	have	VERB
ejpam-5650	270	19	n	n	PROPN
ejpam-5650	270	20	(	(	PUNCT
ejpam-5650	270	21	σ1	σ1	PROPN
ejpam-5650	270	22	,	,	PUNCT
ejpam-5650	270	23	σ2)-closed	σ2)-close	VERB
ejpam-5650	270	24	complement	complement	NOUN
ejpam-5650	270	25	and	and	CCONJ
ejpam-5650	270	26	x	x	PART
ejpam-5650	270	27	∈	∈	NOUN
ejpam-5650	270	28	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5650	270	29	-	-	PUNCT
ejpam-5650	270	30	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	270	31	-	-	PUNCT
ejpam-5650	270	32	cl(v	cl(v	NOUN
ejpam-5650	270	33	)	)	PUNCT
ejpam-5650	270	34	)	)	PUNCT
ejpam-5650	270	35	)	)	PUNCT
ejpam-5650	270	36	.	.	PUNCT
ejpam-5650	271	1	then	then	ADV
ejpam-5650	271	2	,	,	PUNCT
ejpam-5650	271	3	we	we	PRON
ejpam-5650	271	4	have	have	VERB
ejpam-5650	271	5	σ1σ2	σ1σ2	NOUN
ejpam-5650	271	6	-	-	PUNCT
ejpam-5650	271	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	271	8	-	-	PUNCT
ejpam-5650	271	9	cl(v	cl(v	NOUN
ejpam-5650	271	10	)	)	PUNCT
ejpam-5650	271	11	)	)	PUNCT
ejpam-5650	271	12	is	be	AUX
ejpam-5650	271	13	a	a	DET
ejpam-5650	271	14	σ1σ2	σ1σ2	NUM
ejpam-5650	271	15	-	-	ADJ
ejpam-5650	271	16	open	open	ADJ
ejpam-5650	271	17	set	set	NOUN
ejpam-5650	271	18	of	of	ADP
ejpam-5650	271	19	y	y	PROPN
ejpam-5650	271	20	having	have	VERB
ejpam-5650	271	21	n	n	PROPN
ejpam-5650	271	22	(	(	PUNCT
ejpam-5650	271	23	σ1	σ1	PROPN
ejpam-5650	271	24	,	,	PUNCT
ejpam-5650	271	25	σ2)-closed	σ2)-close	VERB
ejpam-5650	271	26	complement	complement	NOUN
ejpam-5650	271	27	.	.	PUNCT
ejpam-5650	272	1	thus	thus	ADV
ejpam-5650	272	2	by	by	ADP
ejpam-5650	272	3	(	(	PUNCT
ejpam-5650	272	4	1	1	NUM
ejpam-5650	272	5	)	)	PUNCT
ejpam-5650	272	6	,	,	PUNCT
ejpam-5650	272	7	there	there	PRON
ejpam-5650	272	8	exists	exist	VERB
ejpam-5650	272	9	a	a	DET
ejpam-5650	272	10	τ1τ2	τ1τ2	NOUN
ejpam-5650	272	11	-	-	ADJ
ejpam-5650	272	12	open	open	ADJ
ejpam-5650	272	13	set	set	ADJ
ejpam-5650	272	14	u	u	NOUN
ejpam-5650	272	15	of	of	ADP
ejpam-5650	272	16	x	x	PUNCT
ejpam-5650	272	17	containing	contain	VERB
ejpam-5650	272	18	x	x	PUNCT
ejpam-5650	272	19	such	such	ADJ
ejpam-5650	272	20	that	that	SCONJ
ejpam-5650	272	21	u	u	NOUN
ejpam-5650	272	22	⊆	⊆	NUM
ejpam-5650	272	23	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5650	272	24	-	-	PUNCT
ejpam-5650	272	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	272	26	-	-	PUNCT
ejpam-5650	272	27	cl(v	cl(v	NOUN
ejpam-5650	272	28	)	)	PUNCT
ejpam-5650	272	29	)	)	PUNCT
ejpam-5650	272	30	)	)	PUNCT
ejpam-5650	272	31	.	.	PUNCT
ejpam-5650	273	1	since	since	SCONJ
ejpam-5650	273	2	u	u	NOUN
ejpam-5650	273	3	is	be	AUX
ejpam-5650	273	4	τ1τ2	τ1τ2	VERB
ejpam-5650	273	5	-	-	ADJ
ejpam-5650	273	6	open	open	ADJ
ejpam-5650	273	7	,	,	PUNCT
ejpam-5650	273	8	we	we	PRON
ejpam-5650	273	9	have	have	VERB
ejpam-5650	273	10	x	x	PART
ejpam-5650	273	11	∈	∈	PRON
ejpam-5650	273	12	τ1τ2	τ1τ2	NOUN
ejpam-5650	273	13	-	-	NUM
ejpam-5650	273	14	int(f	int(f	VERB
ejpam-5650	273	15	+	+	ADJ
ejpam-5650	273	16	(	(	PUNCT
ejpam-5650	273	17	σ1σ2	σ1σ2	NUM
ejpam-5650	273	18	-	-	PUNCT
ejpam-5650	273	19	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	273	20	-	-	PUNCT
ejpam-5650	273	21	cl(v	cl(v	NOUN
ejpam-5650	273	22	)	)	PUNCT
ejpam-5650	273	23	)	)	PUNCT
ejpam-5650	273	24	)	)	PUNCT
ejpam-5650	273	25	)	)	PUNCT
ejpam-5650	273	26	and	and	CCONJ
ejpam-5650	273	27	hence	hence	ADV
ejpam-5650	273	28	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5650	273	29	-	-	PUNCT
ejpam-5650	273	30	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	273	31	-	-	PUNCT
ejpam-5650	273	32	cl(v	cl(v	NOUN
ejpam-5650	273	33	)	)	PUNCT
ejpam-5650	273	34	)	)	PUNCT
ejpam-5650	273	35	)	)	PUNCT
ejpam-5650	274	1	⊆	⊆	X
ejpam-5650	274	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	274	3	-	-	NUM
ejpam-5650	274	4	int(f	int(f	VERB
ejpam-5650	274	5	+	+	ADJ
ejpam-5650	274	6	(	(	PUNCT
ejpam-5650	274	7	σ1σ2	σ1σ2	NUM
ejpam-5650	274	8	-	-	PUNCT
ejpam-5650	274	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	274	10	-	-	PUNCT
ejpam-5650	274	11	cl(v	cl(v	NOUN
ejpam-5650	274	12	)	)	PUNCT
ejpam-5650	274	13	)	)	PUNCT
ejpam-5650	274	14	)	)	PUNCT
ejpam-5650	274	15	)	)	PUNCT
ejpam-5650	274	16	.	.	PUNCT
ejpam-5650	275	1	thus	thus	ADV
ejpam-5650	275	2	,	,	PUNCT
ejpam-5650	275	3	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	275	4	-	-	PUNCT
ejpam-5650	275	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	275	6	-	-	PUNCT
ejpam-5650	275	7	cl(v	cl(v	NOUN
ejpam-5650	275	8	)	)	PUNCT
ejpam-5650	275	9	)	)	PUNCT
ejpam-5650	275	10	)	)	PUNCT
ejpam-5650	275	11	is	be	AUX
ejpam-5650	275	12	τ1τ2	τ1τ2	NOUN
ejpam-5650	275	13	-	-	ADJ
ejpam-5650	275	14	open	open	ADJ
ejpam-5650	275	15	in	in	ADP
ejpam-5650	275	16	x.	x.	NOUN
ejpam-5650	275	17	(	(	PUNCT
ejpam-5650	275	18	3	3	NUM
ejpam-5650	275	19	)	)	PUNCT
ejpam-5650	275	20	⇒	⇒	NOUN
ejpam-5650	275	21	(	(	PUNCT
ejpam-5650	275	22	1	1	NUM
ejpam-5650	275	23	):	):	PUNCT
ejpam-5650	275	24	the	the	DET
ejpam-5650	275	25	proof	proof	NOUN
ejpam-5650	275	26	is	be	AUX
ejpam-5650	275	27	clear	clear	ADJ
ejpam-5650	275	28	.	.	PUNCT
ejpam-5650	276	1	n.	n.	NOUN
ejpam-5650	276	2	chutiman	chutiman	PROPN
ejpam-5650	276	3	,	,	PUNCT
ejpam-5650	276	4	a.	a.	PROPN
ejpam-5650	276	5	sama	sama	PROPN
ejpam-5650	276	6	-	-	PUNCT
ejpam-5650	276	7	ae	ae	PROPN
ejpam-5650	276	8	,	,	PUNCT
ejpam-5650	276	9	c.	c.	PROPN
ejpam-5650	276	10	boonpok	boonpok	PROPN
ejpam-5650	276	11	/	/	SYM
ejpam-5650	276	12	eur	eur	PROPN
ejpam-5650	276	13	.	.	PUNCT
ejpam-5650	277	1	j.	j.	PROPN
ejpam-5650	277	2	pure	pure	PROPN
ejpam-5650	277	3	appl	appl	PROPN
ejpam-5650	277	4	.	.	PROPN
ejpam-5650	277	5	math	math	PROPN
ejpam-5650	277	6	,	,	PUNCT
ejpam-5650	277	7	18	18	NUM
ejpam-5650	277	8	(	(	PUNCT
ejpam-5650	277	9	1	1	NUM
ejpam-5650	277	10	)	)	PUNCT
ejpam-5650	277	11	(	(	PUNCT
ejpam-5650	277	12	2025	2025	NUM
ejpam-5650	277	13	)	)	PUNCT
ejpam-5650	277	14	,	,	PUNCT
ejpam-5650	277	15	5650	5650	NUM
ejpam-5650	277	16	11	11	NUM
ejpam-5650	277	17	of	of	ADP
ejpam-5650	277	18	18	18	NUM
ejpam-5650	277	19	(	(	PUNCT
ejpam-5650	277	20	3	3	NUM
ejpam-5650	277	21	)	)	PUNCT
ejpam-5650	277	22	⇒	⇒	NOUN
ejpam-5650	277	23	(	(	PUNCT
ejpam-5650	277	24	4	4	NUM
ejpam-5650	277	25	):	):	PUNCT
ejpam-5650	277	26	let	let	VERB
ejpam-5650	277	27	k	k	PRON
ejpam-5650	277	28	be	be	AUX
ejpam-5650	277	29	any	any	DET
ejpam-5650	277	30	σ1σ2	σ1σ2	NOUN
ejpam-5650	277	31	-	-	PUNCT
ejpam-5650	277	32	closed	closed	ADJ
ejpam-5650	277	33	n	n	CCONJ
ejpam-5650	277	34	(	(	PUNCT
ejpam-5650	277	35	σ1	σ1	PROPN
ejpam-5650	277	36	,	,	PUNCT
ejpam-5650	277	37	σ2)-closed	σ2)-close	VERB
ejpam-5650	277	38	set	set	NOUN
ejpam-5650	277	39	of	of	ADP
ejpam-5650	277	40	y	y	PROPN
ejpam-5650	277	41	.	.	PUNCT
ejpam-5650	278	1	then	then	ADV
ejpam-5650	278	2	,	,	PUNCT
ejpam-5650	278	3	y	y	PROPN
ejpam-5650	278	4	−k	−k	PROPN
ejpam-5650	278	5	is	be	AUX
ejpam-5650	278	6	a	a	DET
ejpam-5650	278	7	σ1σ2open	σ1σ2open	NOUN
ejpam-5650	278	8	set	set	NOUN
ejpam-5650	278	9	having	have	VERB
ejpam-5650	278	10	n	n	PRON
ejpam-5650	278	11	(	(	PUNCT
ejpam-5650	278	12	σ1	σ1	PROPN
ejpam-5650	278	13	,	,	PUNCT
ejpam-5650	278	14	σ2)-closed	σ2)-close	VERB
ejpam-5650	278	15	complement	complement	NOUN
ejpam-5650	278	16	.	.	PUNCT
ejpam-5650	279	1	by	by	ADP
ejpam-5650	279	2	(	(	PUNCT
ejpam-5650	279	3	3	3	NUM
ejpam-5650	279	4	)	)	PUNCT
ejpam-5650	279	5	,	,	PUNCT
ejpam-5650	279	6	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	279	7	-	-	PUNCT
ejpam-5650	279	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	279	9	-	-	PUNCT
ejpam-5650	279	10	cl(y	cl(y	NOUN
ejpam-5650	279	11	−k	−k	NOUN
ejpam-5650	279	12	)	)	PUNCT
ejpam-5650	279	13	)	)	PUNCT
ejpam-5650	279	14	)	)	PUNCT
ejpam-5650	279	15	is	be	AUX
ejpam-5650	279	16	τ1τ2	τ1τ2	NOUN
ejpam-5650	279	17	-	-	ADJ
ejpam-5650	279	18	open	open	ADJ
ejpam-5650	279	19	in	in	ADP
ejpam-5650	279	20	x.	x.	NOUN
ejpam-5650	279	21	since	since	SCONJ
ejpam-5650	279	22	σ1σ2	σ1σ2	NOUN
ejpam-5650	279	23	-	-	PUNCT
ejpam-5650	279	24	int(σ1σ2	int(σ1σ2	VERB
ejpam-5650	279	25	-	-	PUNCT
ejpam-5650	279	26	cl(y	cl(y	NOUN
ejpam-5650	279	27	−k	−k	NOUN
ejpam-5650	279	28	)	)	PUNCT
ejpam-5650	279	29	)	)	PUNCT
ejpam-5650	280	1	=	=	PUNCT
ejpam-5650	280	2	y	y	PROPN
ejpam-5650	280	3	−	−	ADP
ejpam-5650	280	4	σ1σ2	σ1σ2	X
ejpam-5650	280	5	-	-	PUNCT
ejpam-5650	280	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	280	7	-	-	PUNCT
ejpam-5650	280	8	int(k	int(k	NOUN
ejpam-5650	280	9	)	)	PUNCT
ejpam-5650	280	10	)	)	PUNCT
ejpam-5650	280	11	,	,	PUNCT
ejpam-5650	280	12	it	it	PRON
ejpam-5650	280	13	follows	follow	VERB
ejpam-5650	280	14	that	that	SCONJ
ejpam-5650	280	15	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5650	280	16	-	-	PUNCT
ejpam-5650	280	17	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	280	18	-	-	PUNCT
ejpam-5650	280	19	cl(y	cl(y	NOUN
ejpam-5650	280	20	−k	−k	NOUN
ejpam-5650	280	21	)	)	PUNCT
ejpam-5650	280	22	)	)	PUNCT
ejpam-5650	280	23	)	)	PUNCT
ejpam-5650	281	1	=	=	PUNCT
ejpam-5650	282	1	f+(y	f+(y	NOUN
ejpam-5650	282	2	−	−	NUM
ejpam-5650	282	3	σ1σ2	σ1σ2	X
ejpam-5650	282	4	-	-	PUNCT
ejpam-5650	282	5	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	282	6	-	-	PUNCT
ejpam-5650	282	7	int(k	int(k	NOUN
ejpam-5650	282	8	)	)	PUNCT
ejpam-5650	282	9	)	)	PUNCT
ejpam-5650	282	10	)	)	PUNCT
ejpam-5650	283	1	=	=	PUNCT
ejpam-5650	283	2	x	x	X
ejpam-5650	283	3	−	−	ADP
ejpam-5650	283	4	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5650	283	5	-	-	PUNCT
ejpam-5650	283	6	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	283	7	-	-	PUNCT
ejpam-5650	283	8	int(k	int(k	NOUN
ejpam-5650	283	9	)	)	PUNCT
ejpam-5650	283	10	)	)	PUNCT
ejpam-5650	283	11	)	)	PUNCT
ejpam-5650	283	12	.	.	PUNCT
ejpam-5650	284	1	thus	thus	ADV
ejpam-5650	284	2	,	,	PUNCT
ejpam-5650	284	3	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5650	284	4	-	-	PUNCT
ejpam-5650	284	5	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5650	284	6	-	-	PUNCT
ejpam-5650	284	7	int(k	int(k	NOUN
ejpam-5650	284	8	)	)	PUNCT
ejpam-5650	284	9	)	)	PUNCT
ejpam-5650	284	10	)	)	PUNCT
ejpam-5650	284	11	is	be	AUX
ejpam-5650	284	12	τ1τ2	τ1τ2	NOUN
ejpam-5650	284	13	-	-	ADJ
ejpam-5650	284	14	closed	closed	ADJ
ejpam-5650	284	15	in	in	ADP
ejpam-5650	284	16	x.	x.	NOUN
ejpam-5650	284	17	(	(	PUNCT
ejpam-5650	284	18	4	4	NUM
ejpam-5650	284	19	)	)	PUNCT
ejpam-5650	284	20	⇒	⇒	NOUN
ejpam-5650	284	21	(	(	PUNCT
ejpam-5650	284	22	3	3	NUM
ejpam-5650	284	23	):	):	PUNCT
ejpam-5650	284	24	it	it	PRON
ejpam-5650	284	25	can	can	AUX
ejpam-5650	284	26	be	be	AUX
ejpam-5650	284	27	obtained	obtain	VERB
ejpam-5650	284	28	similarly	similarly	ADV
ejpam-5650	284	29	as	as	ADP
ejpam-5650	284	30	(	(	PUNCT
ejpam-5650	284	31	3	3	X
ejpam-5650	284	32	)	)	PUNCT
ejpam-5650	284	33	⇒	⇒	NOUN
ejpam-5650	284	34	(	(	PUNCT
ejpam-5650	284	35	4	4	NUM
ejpam-5650	284	36	)	)	PUNCT
ejpam-5650	284	37	.	.	PUNCT
ejpam-5650	285	1	theorem	theorem	ADJ
ejpam-5650	285	2	8	8	NUM
ejpam-5650	285	3	.	.	PUNCT
ejpam-5650	286	1	for	for	ADP
ejpam-5650	286	2	a	a	DET
ejpam-5650	286	3	multifunction	multifunction	NOUN
ejpam-5650	286	4	f	f	NOUN
ejpam-5650	286	5	:	:	PUNCT
ejpam-5650	286	6	(	(	PUNCT
ejpam-5650	286	7	x	x	NOUN
ejpam-5650	286	8	,	,	PUNCT
ejpam-5650	286	9	τ1	τ1	NOUN
ejpam-5650	286	10	,	,	PUNCT
ejpam-5650	286	11	τ2	τ2	NOUN
ejpam-5650	286	12	)	)	PUNCT
ejpam-5650	286	13	→	→	SYM
ejpam-5650	286	14	(	(	PUNCT
ejpam-5650	286	15	y	y	PROPN
ejpam-5650	286	16	,	,	PUNCT
ejpam-5650	286	17	σ1	σ1	PROPN
ejpam-5650	286	18	,	,	PUNCT
ejpam-5650	286	19	σ2	σ2	NOUN
ejpam-5650	286	20	)	)	PUNCT
ejpam-5650	286	21	,	,	PUNCT
ejpam-5650	286	22	the	the	DET
ejpam-5650	286	23	following	follow	VERB
ejpam-5650	286	24	properties	property	NOUN
ejpam-5650	286	25	are	be	AUX
ejpam-5650	286	26	equivalent	equivalent	ADJ
ejpam-5650	286	27	:	:	PUNCT
ejpam-5650	286	28	(	(	PUNCT
ejpam-5650	286	29	1	1	X
ejpam-5650	286	30	)	)	PUNCT
ejpam-5650	286	31	f	f	PROPN
ejpam-5650	286	32	is	be	AUX
ejpam-5650	286	33	lower	low	ADJ
ejpam-5650	286	34	almost	almost	ADV
ejpam-5650	286	35	nearly	nearly	ADV
ejpam-5650	286	36	(	(	PUNCT
ejpam-5650	286	37	τ1	τ1	NOUN
ejpam-5650	286	38	,	,	PUNCT
ejpam-5650	286	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	286	40	;	;	PUNCT
ejpam-5650	286	41	(	(	PUNCT
ejpam-5650	286	42	2	2	X
ejpam-5650	286	43	)	)	PUNCT
ejpam-5650	286	44	for	for	ADP
ejpam-5650	286	45	each	each	DET
ejpam-5650	286	46	x	x	SYM
ejpam-5650	286	47	∈	∈	PROPN
ejpam-5650	286	48	x	x	X
ejpam-5650	286	49	and	and	CCONJ
ejpam-5650	286	50	for	for	ADP
ejpam-5650	286	51	every	every	DET
ejpam-5650	286	52	σ1σ2	σ1σ2	NOUN
ejpam-5650	286	53	-	-	PUNCT
ejpam-5650	286	54	closed	closed	ADJ
ejpam-5650	286	55	and	and	CCONJ
ejpam-5650	286	56	n	n	CCONJ
ejpam-5650	286	57	(	(	PUNCT
ejpam-5650	286	58	σ1	σ1	PROPN
ejpam-5650	286	59	,	,	PUNCT
ejpam-5650	286	60	σ2)-closed	σ2)-close	VERB
ejpam-5650	286	61	set	set	VERB
ejpam-5650	286	62	k	k	PROPN
ejpam-5650	286	63	of	of	ADP
ejpam-5650	286	64	y	y	PROPN
ejpam-5650	286	65	such	such	ADJ
ejpam-5650	286	66	that	that	SCONJ
ejpam-5650	286	67	x	x	SYM
ejpam-5650	286	68	∈	∈	NOUN
ejpam-5650	286	69	f−(y	f−(y	NOUN
ejpam-5650	286	70	−k	−k	NOUN
ejpam-5650	286	71	)	)	PUNCT
ejpam-5650	286	72	,	,	PUNCT
ejpam-5650	286	73	there	there	PRON
ejpam-5650	286	74	exists	exist	VERB
ejpam-5650	286	75	a	a	DET
ejpam-5650	286	76	τ1τ2	τ1τ2	ADJ
ejpam-5650	286	77	-	-	ADJ
ejpam-5650	286	78	closed	closed	ADJ
ejpam-5650	286	79	set	set	ADJ
ejpam-5650	286	80	h	h	NOUN
ejpam-5650	286	81	of	of	ADP
ejpam-5650	286	82	x	x	INTJ
ejpam-5650	286	83	such	such	ADJ
ejpam-5650	286	84	that	that	SCONJ
ejpam-5650	286	85	x	x	SYM
ejpam-5650	286	86	∈	∈	NOUN
ejpam-5650	286	87	x	x	SYM
ejpam-5650	286	88	−h	−h	ADJ
ejpam-5650	286	89	and	and	CCONJ
ejpam-5650	286	90	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5650	286	91	-	-	PUNCT
ejpam-5650	286	92	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	286	93	-	-	PUNCT
ejpam-5650	286	94	int(k	int(k	NOUN
ejpam-5650	286	95	)	)	PUNCT
ejpam-5650	286	96	)	)	PUNCT
ejpam-5650	286	97	)	)	PUNCT
ejpam-5650	287	1	⊆	⊆	NUM
ejpam-5650	287	2	h	h	NOUN
ejpam-5650	287	3	;	;	PUNCT
ejpam-5650	287	4	(	(	PUNCT
ejpam-5650	287	5	3	3	X
ejpam-5650	287	6	)	)	PUNCT
ejpam-5650	287	7	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5650	287	8	-	-	PUNCT
ejpam-5650	287	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	287	10	-	-	PUNCT
ejpam-5650	287	11	cl(v	cl(v	NOUN
ejpam-5650	287	12	)	)	PUNCT
ejpam-5650	287	13	)	)	PUNCT
ejpam-5650	287	14	)	)	PUNCT
ejpam-5650	287	15	is	be	AUX
ejpam-5650	287	16	τ1τ2	τ1τ2	NOUN
ejpam-5650	287	17	-	-	ADJ
ejpam-5650	287	18	open	open	ADJ
ejpam-5650	287	19	in	in	ADP
ejpam-5650	287	20	x	x	PUNCT
ejpam-5650	287	21	for	for	ADP
ejpam-5650	287	22	every	every	DET
ejpam-5650	287	23	σ1σ2	σ1σ2	NOUN
ejpam-5650	287	24	-	-	ADJ
ejpam-5650	287	25	open	open	ADJ
ejpam-5650	287	26	set	set	NOUN
ejpam-5650	287	27	v	v	NOUN
ejpam-5650	287	28	of	of	ADP
ejpam-5650	287	29	y	y	PROPN
ejpam-5650	287	30	having	have	VERB
ejpam-5650	287	31	n	n	PROPN
ejpam-5650	287	32	(	(	PUNCT
ejpam-5650	287	33	σ1	σ1	PROPN
ejpam-5650	287	34	,	,	PUNCT
ejpam-5650	287	35	σ2)-closed	σ2)-close	VERB
ejpam-5650	287	36	complement	complement	NOUN
ejpam-5650	287	37	;	;	PUNCT
ejpam-5650	287	38	(	(	PUNCT
ejpam-5650	287	39	4	4	X
ejpam-5650	287	40	)	)	PUNCT
ejpam-5650	287	41	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5650	287	42	-	-	PUNCT
ejpam-5650	287	43	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5650	287	44	-	-	PUNCT
ejpam-5650	287	45	int(k	int(k	NOUN
ejpam-5650	287	46	)	)	PUNCT
ejpam-5650	287	47	)	)	PUNCT
ejpam-5650	287	48	)	)	PUNCT
ejpam-5650	288	1	is	be	AUX
ejpam-5650	288	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	288	3	-	-	ADJ
ejpam-5650	288	4	closed	closed	ADJ
ejpam-5650	288	5	in	in	ADP
ejpam-5650	288	6	x	x	PUNCT
ejpam-5650	288	7	for	for	ADP
ejpam-5650	288	8	every	every	DET
ejpam-5650	288	9	σ1σ2	σ1σ2	NOUN
ejpam-5650	288	10	-	-	PUNCT
ejpam-5650	288	11	closed	closed	ADJ
ejpam-5650	288	12	and	and	CCONJ
ejpam-5650	288	13	n	n	CCONJ
ejpam-5650	288	14	(	(	PUNCT
ejpam-5650	288	15	σ1	σ1	PROPN
ejpam-5650	288	16	,	,	PUNCT
ejpam-5650	288	17	σ2)closed	σ2)close	VERB
ejpam-5650	288	18	set	set	VERB
ejpam-5650	288	19	k	k	PROPN
ejpam-5650	288	20	of	of	ADP
ejpam-5650	288	21	y	y	PROPN
ejpam-5650	288	22	.	.	PUNCT
ejpam-5650	289	1	proof	proof	NOUN
ejpam-5650	289	2	.	.	PUNCT
ejpam-5650	290	1	the	the	DET
ejpam-5650	290	2	proof	proof	NOUN
ejpam-5650	290	3	is	be	AUX
ejpam-5650	290	4	similar	similar	ADJ
ejpam-5650	290	5	to	to	ADP
ejpam-5650	290	6	that	that	PRON
ejpam-5650	290	7	of	of	ADP
ejpam-5650	290	8	theorem	theorem	ADJ
ejpam-5650	290	9	7	7	NUM
ejpam-5650	290	10	.	.	NOUN
ejpam-5650	290	11	recall	recall	VERB
ejpam-5650	290	12	that	that	SCONJ
ejpam-5650	290	13	a	a	DET
ejpam-5650	290	14	net	net	NOUN
ejpam-5650	290	15	(	(	PUNCT
ejpam-5650	290	16	xγ	xγ	PROPN
ejpam-5650	290	17	)	)	PUNCT
ejpam-5650	290	18	in	in	ADP
ejpam-5650	290	19	a	a	DET
ejpam-5650	290	20	topological	topological	ADJ
ejpam-5650	290	21	space	space	NOUN
ejpam-5650	290	22	(	(	PUNCT
ejpam-5650	290	23	x	x	X
ejpam-5650	290	24	,	,	PUNCT
ejpam-5650	290	25	τ	τ	X
ejpam-5650	290	26	)	)	PUNCT
ejpam-5650	290	27	is	be	AUX
ejpam-5650	290	28	said	say	VERB
ejpam-5650	290	29	to	to	PART
ejpam-5650	290	30	be	be	AUX
ejpam-5650	290	31	eventually	eventually	ADV
ejpam-5650	290	32	in	in	ADP
ejpam-5650	290	33	the	the	DET
ejpam-5650	290	34	set	set	NOUN
ejpam-5650	290	35	u	u	NOUN
ejpam-5650	290	36	⊆	⊆	NUM
ejpam-5650	290	37	x	x	SYM
ejpam-5650	290	38	if	if	SCONJ
ejpam-5650	290	39	there	there	PRON
ejpam-5650	290	40	exists	exist	VERB
ejpam-5650	290	41	an	an	DET
ejpam-5650	290	42	index	index	NOUN
ejpam-5650	290	43	γ0	γ0	NOUN
ejpam-5650	290	44	∈	∈	PROPN
ejpam-5650	290	45	∇	∇	X
ejpam-5650	290	46	such	such	ADJ
ejpam-5650	290	47	that	that	SCONJ
ejpam-5650	290	48	xγ	xγ	VERB
ejpam-5650	290	49	∈	∈	PROPN
ejpam-5650	290	50	u	u	NOUN
ejpam-5650	290	51	for	for	ADP
ejpam-5650	290	52	all	all	DET
ejpam-5650	290	53	γ	γ	PROPN
ejpam-5650	290	54	≥	≥	PROPN
ejpam-5650	290	55	γ0	γ0	PROPN
ejpam-5650	290	56	.	.	PUNCT
ejpam-5650	291	1	a	a	PRON
ejpam-5650	291	2	net	net	ADJ
ejpam-5650	291	3	(	(	PUNCT
ejpam-5650	291	4	xγ	xγ	NOUN
ejpam-5650	291	5	)	)	PUNCT
ejpam-5650	291	6	is	be	AUX
ejpam-5650	291	7	called	call	VERB
ejpam-5650	291	8	(	(	PUNCT
ejpam-5650	291	9	τ1	τ1	NOUN
ejpam-5650	291	10	,	,	PUNCT
ejpam-5650	291	11	τ2)-converge	τ2)-converge	VERB
ejpam-5650	291	12	to	to	ADP
ejpam-5650	291	13	a	a	DET
ejpam-5650	291	14	point	point	NOUN
ejpam-5650	291	15	x	x	PUNCT
ejpam-5650	291	16	if	if	SCONJ
ejpam-5650	291	17	for	for	ADP
ejpam-5650	291	18	every	every	DET
ejpam-5650	291	19	τ1τ2	τ1τ2	NOUN
ejpam-5650	291	20	-	-	ADJ
ejpam-5650	291	21	open	open	ADJ
ejpam-5650	291	22	set	set	ADJ
ejpam-5650	291	23	v	v	NOUN
ejpam-5650	291	24	containing	contain	VERB
ejpam-5650	291	25	x	x	X
ejpam-5650	291	26	,	,	PUNCT
ejpam-5650	291	27	there	there	PRON
ejpam-5650	291	28	exists	exist	VERB
ejpam-5650	291	29	an	an	DET
ejpam-5650	291	30	index	index	NOUN
ejpam-5650	291	31	γ0	γ0	NOUN
ejpam-5650	291	32	∈	∈	PROPN
ejpam-5650	291	33	∇	∇	X
ejpam-5650	291	34	such	such	ADJ
ejpam-5650	291	35	that	that	SCONJ
ejpam-5650	291	36	xγ	xγ	PROPN
ejpam-5650	291	37	∈	∈	PROPN
ejpam-5650	291	38	v	v	NOUN
ejpam-5650	291	39	for	for	ADP
ejpam-5650	291	40	all	all	DET
ejpam-5650	291	41	γ	γ	PROPN
ejpam-5650	291	42	≥	≥	PROPN
ejpam-5650	291	43	γ0	γ0	PROPN
ejpam-5650	291	44	.	.	PUNCT
ejpam-5650	291	45	theorem	theorem	VERB
ejpam-5650	291	46	9	9	NUM
ejpam-5650	291	47	.	.	PUNCT
ejpam-5650	292	1	a	a	DET
ejpam-5650	292	2	multifunction	multifunction	NOUN
ejpam-5650	292	3	f	f	NOUN
ejpam-5650	292	4	:	:	PUNCT
ejpam-5650	292	5	(	(	PUNCT
ejpam-5650	292	6	x	x	NOUN
ejpam-5650	292	7	,	,	PUNCT
ejpam-5650	292	8	τ1	τ1	NOUN
ejpam-5650	292	9	,	,	PUNCT
ejpam-5650	292	10	τ2	τ2	NOUN
ejpam-5650	292	11	)	)	PUNCT
ejpam-5650	292	12	→	→	SYM
ejpam-5650	292	13	(	(	PUNCT
ejpam-5650	292	14	y	y	PROPN
ejpam-5650	292	15	,	,	PUNCT
ejpam-5650	292	16	σ1	σ1	PROPN
ejpam-5650	292	17	,	,	PUNCT
ejpam-5650	292	18	σ2	σ2	PROPN
ejpam-5650	292	19	)	)	PUNCT
ejpam-5650	292	20	is	be	AUX
ejpam-5650	292	21	upper	upper	ADJ
ejpam-5650	292	22	almost	almost	ADV
ejpam-5650	292	23	nearly	nearly	ADV
ejpam-5650	292	24	(	(	PUNCT
ejpam-5650	292	25	τ1	τ1	NOUN
ejpam-5650	292	26	,	,	PUNCT
ejpam-5650	292	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	292	28	if	if	SCONJ
ejpam-5650	292	29	and	and	CCONJ
ejpam-5650	292	30	only	only	ADV
ejpam-5650	292	31	if	if	SCONJ
ejpam-5650	292	32	for	for	ADP
ejpam-5650	292	33	each	each	DET
ejpam-5650	292	34	x	x	SYM
ejpam-5650	292	35	∈	∈	PROPN
ejpam-5650	292	36	x	x	X
ejpam-5650	292	37	and	and	CCONJ
ejpam-5650	292	38	for	for	ADP
ejpam-5650	292	39	each	each	DET
ejpam-5650	292	40	net	net	NOUN
ejpam-5650	292	41	(	(	PUNCT
ejpam-5650	292	42	xγ	xγ	PROPN
ejpam-5650	292	43	)	)	PUNCT
ejpam-5650	292	44	which	which	DET
ejpam-5650	292	45	(	(	PUNCT
ejpam-5650	292	46	τ1	τ1	NOUN
ejpam-5650	292	47	,	,	PUNCT
ejpam-5650	292	48	τ2)-converges	τ2)-converge	NOUN
ejpam-5650	292	49	to	to	ADP
ejpam-5650	292	50	x	x	PUNCT
ejpam-5650	292	51	in	in	ADP
ejpam-5650	292	52	x	x	X
ejpam-5650	292	53	and	and	CCONJ
ejpam-5650	292	54	for	for	ADP
ejpam-5650	292	55	each	each	DET
ejpam-5650	292	56	σ1σ2	σ1σ2	VERB
ejpam-5650	292	57	-	-	ADJ
ejpam-5650	292	58	open	open	ADJ
ejpam-5650	292	59	set	set	NOUN
ejpam-5650	292	60	v	v	NOUN
ejpam-5650	292	61	of	of	ADP
ejpam-5650	292	62	y	y	PROPN
ejpam-5650	292	63	having	have	VERB
ejpam-5650	292	64	n	n	PROPN
ejpam-5650	292	65	(	(	PUNCT
ejpam-5650	292	66	σ1	σ1	PROPN
ejpam-5650	292	67	,	,	PUNCT
ejpam-5650	292	68	σ2)-closed	σ2)-close	VERB
ejpam-5650	292	69	complement	complement	NOUN
ejpam-5650	292	70	such	such	ADJ
ejpam-5650	292	71	that	that	SCONJ
ejpam-5650	292	72	x	x	SYM
ejpam-5650	292	73	∈	∈	PROPN
ejpam-5650	292	74	f+(v	f+(v	NOUN
ejpam-5650	292	75	)	)	PUNCT
ejpam-5650	292	76	,	,	PUNCT
ejpam-5650	292	77	the	the	DET
ejpam-5650	292	78	net	net	NOUN
ejpam-5650	292	79	(	(	PUNCT
ejpam-5650	292	80	xγ	xγ	PROPN
ejpam-5650	292	81	)	)	PUNCT
ejpam-5650	292	82	is	be	AUX
ejpam-5650	292	83	eventually	eventually	ADV
ejpam-5650	292	84	in	in	ADP
ejpam-5650	292	85	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5650	292	86	-	-	PUNCT
ejpam-5650	292	87	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	292	88	-	-	PUNCT
ejpam-5650	292	89	cl(v	cl(v	NOUN
ejpam-5650	292	90	)	)	PUNCT
ejpam-5650	292	91	)	)	PUNCT
ejpam-5650	292	92	)	)	PUNCT
ejpam-5650	292	93	.	.	PUNCT
ejpam-5650	293	1	proof	proof	NOUN
ejpam-5650	293	2	.	.	PUNCT
ejpam-5650	294	1	let	let	AUX
ejpam-5650	294	2	(	(	PUNCT
ejpam-5650	294	3	xγ	xγ	VERB
ejpam-5650	294	4	)	)	PUNCT
ejpam-5650	294	5	be	be	AUX
ejpam-5650	294	6	a	a	DET
ejpam-5650	294	7	net	net	NOUN
ejpam-5650	294	8	which	which	PRON
ejpam-5650	294	9	(	(	PUNCT
ejpam-5650	294	10	τ1	τ1	NOUN
ejpam-5650	294	11	,	,	PUNCT
ejpam-5650	294	12	τ2)-converges	τ2)-converge	NOUN
ejpam-5650	294	13	to	to	ADP
ejpam-5650	294	14	x	x	PUNCT
ejpam-5650	294	15	in	in	ADP
ejpam-5650	294	16	x	x	X
ejpam-5650	294	17	and	and	CCONJ
ejpam-5650	294	18	v	v	X
ejpam-5650	294	19	be	be	AUX
ejpam-5650	294	20	any	any	DET
ejpam-5650	294	21	σ1σ2	σ1σ2	NOUN
ejpam-5650	294	22	-	-	ADJ
ejpam-5650	294	23	open	open	ADJ
ejpam-5650	294	24	set	set	NOUN
ejpam-5650	294	25	of	of	ADP
ejpam-5650	294	26	y	y	PROPN
ejpam-5650	294	27	having	have	VERB
ejpam-5650	294	28	n	n	PROPN
ejpam-5650	294	29	(	(	PUNCT
ejpam-5650	294	30	σ1	σ1	PROPN
ejpam-5650	294	31	,	,	PUNCT
ejpam-5650	294	32	σ2)-closed	σ2)-close	VERB
ejpam-5650	294	33	complement	complement	NOUN
ejpam-5650	294	34	such	such	ADJ
ejpam-5650	294	35	that	that	SCONJ
ejpam-5650	294	36	x	x	SYM
ejpam-5650	294	37	∈	∈	PROPN
ejpam-5650	294	38	f+(v	f+(v	NOUN
ejpam-5650	294	39	)	)	PUNCT
ejpam-5650	294	40	.	.	PUNCT
ejpam-5650	295	1	since	since	SCONJ
ejpam-5650	295	2	f	f	PROPN
ejpam-5650	295	3	is	be	AUX
ejpam-5650	295	4	upper	upper	ADJ
ejpam-5650	295	5	almost	almost	ADV
ejpam-5650	295	6	nearly	nearly	ADV
ejpam-5650	295	7	(	(	PUNCT
ejpam-5650	295	8	τ1	τ1	NOUN
ejpam-5650	295	9	,	,	PUNCT
ejpam-5650	295	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	295	11	,	,	PUNCT
ejpam-5650	295	12	there	there	PRON
ejpam-5650	295	13	exists	exist	VERB
ejpam-5650	295	14	a	a	DET
ejpam-5650	295	15	τ1τ2	τ1τ2	NOUN
ejpam-5650	295	16	-	-	ADJ
ejpam-5650	295	17	open	open	ADJ
ejpam-5650	295	18	set	set	ADJ
ejpam-5650	295	19	u	u	NOUN
ejpam-5650	295	20	of	of	ADP
ejpam-5650	295	21	x	x	PUNCT
ejpam-5650	295	22	containing	contain	VERB
ejpam-5650	295	23	x	x	PUNCT
ejpam-5650	295	24	such	such	ADJ
ejpam-5650	295	25	that	that	SCONJ
ejpam-5650	295	26	u	u	NOUN
ejpam-5650	295	27	⊆	⊆	NUM
ejpam-5650	295	28	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5650	295	29	-	-	PUNCT
ejpam-5650	295	30	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	295	31	-	-	PUNCT
ejpam-5650	295	32	cl(v	cl(v	NOUN
ejpam-5650	295	33	)	)	PUNCT
ejpam-5650	295	34	)	)	PUNCT
ejpam-5650	295	35	)	)	PUNCT
ejpam-5650	295	36	.	.	PUNCT
ejpam-5650	296	1	since	since	SCONJ
ejpam-5650	296	2	(	(	PUNCT
ejpam-5650	296	3	xγ	xγ	PROPN
ejpam-5650	296	4	)	)	PUNCT
ejpam-5650	296	5	(	(	PUNCT
ejpam-5650	296	6	τ1	τ1	NOUN
ejpam-5650	296	7	,	,	PUNCT
ejpam-5650	296	8	τ2)-converges	τ2)-converge	NOUN
ejpam-5650	296	9	to	to	ADP
ejpam-5650	296	10	x	x	PRON
ejpam-5650	296	11	,	,	PUNCT
ejpam-5650	296	12	it	it	PRON
ejpam-5650	296	13	follows	follow	VERB
ejpam-5650	296	14	that	that	SCONJ
ejpam-5650	296	15	there	there	PRON
ejpam-5650	296	16	exists	exist	VERB
ejpam-5650	296	17	an	an	DET
ejpam-5650	296	18	index	index	NOUN
ejpam-5650	296	19	γ0	γ0	NOUN
ejpam-5650	296	20	∈	∈	PROPN
ejpam-5650	296	21	∇	∇	X
ejpam-5650	296	22	such	such	ADJ
ejpam-5650	296	23	that	that	SCONJ
ejpam-5650	296	24	xγ	xγ	VERB
ejpam-5650	296	25	∈	∈	PROPN
ejpam-5650	296	26	u	u	NOUN
ejpam-5650	296	27	for	for	ADP
ejpam-5650	296	28	all	all	DET
ejpam-5650	296	29	γ	γ	PROPN
ejpam-5650	296	30	≥	≥	PROPN
ejpam-5650	296	31	γ0	γ0	PROPN
ejpam-5650	296	32	.	.	PUNCT
ejpam-5650	297	1	therefore	therefore	ADV
ejpam-5650	297	2	,	,	PUNCT
ejpam-5650	297	3	xγ	xγ	PROPN
ejpam-5650	297	4	∈	∈	PROPN
ejpam-5650	297	5	u	u	NOUN
ejpam-5650	297	6	⊆	⊆	NUM
ejpam-5650	297	7	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5650	297	8	-	-	PUNCT
ejpam-5650	297	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	297	10	-	-	PUNCT
ejpam-5650	297	11	cl(v	cl(v	NOUN
ejpam-5650	297	12	)	)	PUNCT
ejpam-5650	297	13	)	)	PUNCT
ejpam-5650	297	14	)	)	PUNCT
ejpam-5650	298	1	for	for	ADP
ejpam-5650	298	2	all	all	DET
ejpam-5650	298	3	γ	γ	PROPN
ejpam-5650	298	4	≥	≥	PROPN
ejpam-5650	298	5	γ0	γ0	PROPN
ejpam-5650	298	6	.	.	PUNCT
ejpam-5650	299	1	thus	thus	ADV
ejpam-5650	299	2	,	,	PUNCT
ejpam-5650	299	3	the	the	DET
ejpam-5650	299	4	net	net	NOUN
ejpam-5650	299	5	(	(	PUNCT
ejpam-5650	299	6	xγ	xγ	PROPN
ejpam-5650	299	7	)	)	PUNCT
ejpam-5650	299	8	is	be	AUX
ejpam-5650	299	9	eventually	eventually	ADV
ejpam-5650	299	10	in	in	ADP
ejpam-5650	299	11	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5650	299	12	-	-	PUNCT
ejpam-5650	299	13	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	299	14	-	-	PUNCT
ejpam-5650	299	15	cl(v	cl(v	NOUN
ejpam-5650	299	16	)	)	PUNCT
ejpam-5650	299	17	)	)	PUNCT
ejpam-5650	299	18	)	)	PUNCT
ejpam-5650	299	19	.	.	PUNCT
ejpam-5650	300	1	n.	n.	PROPN
ejpam-5650	300	2	chutiman	chutiman	PROPN
ejpam-5650	300	3	,	,	PUNCT
ejpam-5650	300	4	a.	a.	PROPN
ejpam-5650	300	5	sama	sama	PROPN
ejpam-5650	300	6	-	-	PUNCT
ejpam-5650	300	7	ae	ae	PROPN
ejpam-5650	300	8	,	,	PUNCT
ejpam-5650	300	9	c.	c.	PROPN
ejpam-5650	300	10	boonpok	boonpok	PROPN
ejpam-5650	300	11	/	/	SYM
ejpam-5650	300	12	eur	eur	PROPN
ejpam-5650	300	13	.	.	PUNCT
ejpam-5650	301	1	j.	j.	PROPN
ejpam-5650	301	2	pure	pure	PROPN
ejpam-5650	301	3	appl	appl	PROPN
ejpam-5650	301	4	.	.	PROPN
ejpam-5650	301	5	math	math	PROPN
ejpam-5650	301	6	,	,	PUNCT
ejpam-5650	301	7	18	18	NUM
ejpam-5650	301	8	(	(	PUNCT
ejpam-5650	301	9	1	1	NUM
ejpam-5650	301	10	)	)	PUNCT
ejpam-5650	301	11	(	(	PUNCT
ejpam-5650	301	12	2025	2025	NUM
ejpam-5650	301	13	)	)	PUNCT
ejpam-5650	301	14	,	,	PUNCT
ejpam-5650	301	15	5650	5650	NUM
ejpam-5650	301	16	12	12	NUM
ejpam-5650	301	17	of	of	ADP
ejpam-5650	301	18	18	18	NUM
ejpam-5650	301	19	conversely	conversely	ADV
ejpam-5650	301	20	,	,	PUNCT
ejpam-5650	301	21	suppose	suppose	VERB
ejpam-5650	301	22	that	that	SCONJ
ejpam-5650	301	23	f	f	PROPN
ejpam-5650	301	24	is	be	AUX
ejpam-5650	301	25	not	not	PART
ejpam-5650	301	26	upper	upper	ADJ
ejpam-5650	301	27	almost	almost	ADV
ejpam-5650	301	28	nearly	nearly	ADV
ejpam-5650	301	29	(	(	PUNCT
ejpam-5650	301	30	τ1	τ1	NOUN
ejpam-5650	301	31	,	,	PUNCT
ejpam-5650	301	32	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5650	301	33	.	.	PUNCT
ejpam-5650	302	1	then	then	ADV
ejpam-5650	302	2	,	,	PUNCT
ejpam-5650	302	3	there	there	PRON
ejpam-5650	302	4	exists	exist	VERB
ejpam-5650	302	5	a	a	DET
ejpam-5650	302	6	point	point	NOUN
ejpam-5650	302	7	x	x	PUNCT
ejpam-5650	302	8	of	of	ADP
ejpam-5650	302	9	x	x	X
ejpam-5650	302	10	and	and	CCONJ
ejpam-5650	302	11	a	a	DET
ejpam-5650	302	12	σ1σ2	σ1σ2	NUM
ejpam-5650	302	13	-	-	ADJ
ejpam-5650	302	14	open	open	ADJ
ejpam-5650	302	15	set	set	NOUN
ejpam-5650	302	16	v	v	NOUN
ejpam-5650	302	17	of	of	ADP
ejpam-5650	302	18	y	y	PROPN
ejpam-5650	302	19	having	have	VERB
ejpam-5650	302	20	n	n	PROPN
ejpam-5650	302	21	(	(	PUNCT
ejpam-5650	302	22	σ1	σ1	PROPN
ejpam-5650	302	23	,	,	PUNCT
ejpam-5650	302	24	σ2)-closed	σ2)-close	VERB
ejpam-5650	302	25	complement	complement	NOUN
ejpam-5650	302	26	with	with	ADP
ejpam-5650	302	27	x	x	PROPN
ejpam-5650	302	28	∈	∈	PROPN
ejpam-5650	302	29	f+(v	f+(v	NOUN
ejpam-5650	302	30	)	)	PUNCT
ejpam-5650	302	31	such	such	ADJ
ejpam-5650	302	32	that	that	SCONJ
ejpam-5650	302	33	u	u	NOUN
ejpam-5650	302	34	̸⊆	̸⊆	ADV
ejpam-5650	302	35	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5650	302	36	-	-	PUNCT
ejpam-5650	302	37	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	302	38	-	-	PUNCT
ejpam-5650	302	39	cl(v	cl(v	NOUN
ejpam-5650	302	40	)	)	PUNCT
ejpam-5650	302	41	)	)	PUNCT
ejpam-5650	302	42	)	)	PUNCT
ejpam-5650	302	43	for	for	ADP
ejpam-5650	302	44	each	each	DET
ejpam-5650	302	45	τ1τ2	τ1τ2	ADJ
ejpam-5650	302	46	-	-	ADJ
ejpam-5650	302	47	open	open	ADJ
ejpam-5650	302	48	set	set	ADJ
ejpam-5650	302	49	u	u	NOUN
ejpam-5650	302	50	of	of	ADP
ejpam-5650	302	51	x	x	SYM
ejpam-5650	302	52	containing	contain	VERB
ejpam-5650	302	53	x.	x.	NOUN
ejpam-5650	302	54	let	let	VERB
ejpam-5650	302	55	xu	xu	PROPN
ejpam-5650	302	56	∈	∈	PROPN
ejpam-5650	302	57	u	u	PROPN
ejpam-5650	302	58	and	and	CCONJ
ejpam-5650	302	59	xu	xu	PROPN
ejpam-5650	302	60	̸∈	̸∈	PROPN
ejpam-5650	302	61	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5650	302	62	-	-	PUNCT
ejpam-5650	302	63	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	302	64	-	-	PUNCT
ejpam-5650	302	65	cl(v	cl(v	NOUN
ejpam-5650	302	66	)	)	PUNCT
ejpam-5650	302	67	)	)	PUNCT
ejpam-5650	302	68	)	)	PUNCT
ejpam-5650	302	69	for	for	ADP
ejpam-5650	302	70	each	each	DET
ejpam-5650	302	71	τ1τ2	τ1τ2	ADJ
ejpam-5650	302	72	-	-	ADJ
ejpam-5650	302	73	open	open	ADJ
ejpam-5650	302	74	set	set	ADJ
ejpam-5650	302	75	u	u	NOUN
ejpam-5650	302	76	of	of	ADP
ejpam-5650	302	77	x	x	SYM
ejpam-5650	302	78	containing	contain	VERB
ejpam-5650	302	79	x.	x.	NOUN
ejpam-5650	302	80	then	then	ADV
ejpam-5650	302	81	,	,	PUNCT
ejpam-5650	302	82	for	for	ADP
ejpam-5650	302	83	each	each	DET
ejpam-5650	302	84	τ1τ2	τ1τ2	ADJ
ejpam-5650	302	85	-	-	ADJ
ejpam-5650	302	86	neighbourhood	neighbourhood	ADJ
ejpam-5650	302	87	net	net	NOUN
ejpam-5650	302	88	(	(	PUNCT
ejpam-5650	302	89	xu	xu	PROPN
ejpam-5650	302	90	)	)	PUNCT
ejpam-5650	302	91	,	,	PUNCT
ejpam-5650	302	92	(	(	PUNCT
ejpam-5650	302	93	xu	xu	INTJ
ejpam-5650	302	94	)	)	PUNCT
ejpam-5650	302	95	(	(	PUNCT
ejpam-5650	302	96	τ1	τ1	NOUN
ejpam-5650	302	97	,	,	PUNCT
ejpam-5650	302	98	τ2)-converges	τ2)-converge	NOUN
ejpam-5650	302	99	to	to	ADP
ejpam-5650	302	100	x	x	PRON
ejpam-5650	302	101	,	,	PUNCT
ejpam-5650	302	102	but	but	CCONJ
ejpam-5650	302	103	(	(	PUNCT
ejpam-5650	302	104	xu	xu	INTJ
ejpam-5650	302	105	)	)	PUNCT
ejpam-5650	302	106	is	be	AUX
ejpam-5650	302	107	not	not	PART
ejpam-5650	302	108	eventually	eventually	ADV
ejpam-5650	302	109	in	in	ADP
ejpam-5650	302	110	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5650	302	111	-	-	PUNCT
ejpam-5650	302	112	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	302	113	-	-	PUNCT
ejpam-5650	302	114	cl(v	cl(v	NOUN
ejpam-5650	302	115	)	)	PUNCT
ejpam-5650	302	116	)	)	PUNCT
ejpam-5650	302	117	)	)	PUNCT
ejpam-5650	302	118	.	.	PUNCT
ejpam-5650	303	1	this	this	PRON
ejpam-5650	303	2	is	be	AUX
ejpam-5650	303	3	a	a	DET
ejpam-5650	303	4	contradiction	contradiction	NOUN
ejpam-5650	303	5	.	.	PUNCT
ejpam-5650	304	1	thus	thus	ADV
ejpam-5650	304	2	,	,	PUNCT
ejpam-5650	304	3	f	f	PROPN
ejpam-5650	304	4	is	be	AUX
ejpam-5650	304	5	upper	upper	ADJ
ejpam-5650	304	6	almost	almost	ADV
ejpam-5650	304	7	nearly	nearly	ADV
ejpam-5650	304	8	(	(	PUNCT
ejpam-5650	304	9	τ1	τ1	NOUN
ejpam-5650	304	10	,	,	PUNCT
ejpam-5650	304	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	304	12	.	.	PUNCT
ejpam-5650	305	1	theorem	theorem	VERB
ejpam-5650	305	2	10	10	NUM
ejpam-5650	305	3	.	.	PUNCT
ejpam-5650	306	1	a	a	DET
ejpam-5650	306	2	multifunction	multifunction	NOUN
ejpam-5650	306	3	f	f	NOUN
ejpam-5650	306	4	:	:	PUNCT
ejpam-5650	306	5	(	(	PUNCT
ejpam-5650	306	6	x	x	NOUN
ejpam-5650	306	7	,	,	PUNCT
ejpam-5650	306	8	τ1	τ1	NOUN
ejpam-5650	306	9	,	,	PUNCT
ejpam-5650	306	10	τ2	τ2	NOUN
ejpam-5650	306	11	)	)	PUNCT
ejpam-5650	306	12	→	→	SYM
ejpam-5650	306	13	(	(	PUNCT
ejpam-5650	306	14	y	y	PROPN
ejpam-5650	306	15	,	,	PUNCT
ejpam-5650	306	16	σ1	σ1	PROPN
ejpam-5650	306	17	,	,	PUNCT
ejpam-5650	306	18	σ2	σ2	NOUN
ejpam-5650	306	19	)	)	PUNCT
ejpam-5650	306	20	is	be	AUX
ejpam-5650	306	21	lower	low	ADJ
ejpam-5650	306	22	almost	almost	ADV
ejpam-5650	306	23	nearly	nearly	ADV
ejpam-5650	306	24	(	(	PUNCT
ejpam-5650	306	25	τ1	τ1	NOUN
ejpam-5650	306	26	,	,	PUNCT
ejpam-5650	306	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	306	28	if	if	SCONJ
ejpam-5650	306	29	and	and	CCONJ
ejpam-5650	306	30	only	only	ADV
ejpam-5650	306	31	if	if	SCONJ
ejpam-5650	306	32	for	for	ADP
ejpam-5650	306	33	each	each	DET
ejpam-5650	306	34	x	x	SYM
ejpam-5650	306	35	∈	∈	PROPN
ejpam-5650	306	36	x	x	X
ejpam-5650	306	37	and	and	CCONJ
ejpam-5650	306	38	for	for	ADP
ejpam-5650	306	39	each	each	DET
ejpam-5650	306	40	net	net	NOUN
ejpam-5650	306	41	(	(	PUNCT
ejpam-5650	306	42	xγ	xγ	PROPN
ejpam-5650	306	43	)	)	PUNCT
ejpam-5650	306	44	which	which	DET
ejpam-5650	306	45	(	(	PUNCT
ejpam-5650	306	46	τ1	τ1	NOUN
ejpam-5650	306	47	,	,	PUNCT
ejpam-5650	306	48	τ2)-converges	τ2)-converge	NOUN
ejpam-5650	306	49	to	to	ADP
ejpam-5650	306	50	x	x	PUNCT
ejpam-5650	306	51	in	in	ADP
ejpam-5650	306	52	x	x	X
ejpam-5650	306	53	and	and	CCONJ
ejpam-5650	306	54	for	for	ADP
ejpam-5650	306	55	each	each	DET
ejpam-5650	306	56	σ1σ2	σ1σ2	VERB
ejpam-5650	306	57	-	-	ADJ
ejpam-5650	306	58	open	open	ADJ
ejpam-5650	306	59	set	set	NOUN
ejpam-5650	306	60	v	v	NOUN
ejpam-5650	306	61	of	of	ADP
ejpam-5650	306	62	y	y	PROPN
ejpam-5650	306	63	having	have	VERB
ejpam-5650	306	64	n	n	PROPN
ejpam-5650	306	65	(	(	PUNCT
ejpam-5650	306	66	σ1	σ1	PROPN
ejpam-5650	306	67	,	,	PUNCT
ejpam-5650	306	68	σ2)-closed	σ2)-close	VERB
ejpam-5650	306	69	complement	complement	NOUN
ejpam-5650	306	70	such	such	ADJ
ejpam-5650	306	71	that	that	SCONJ
ejpam-5650	306	72	x	x	SYM
ejpam-5650	306	73	∈	∈	PROPN
ejpam-5650	306	74	f−(v	f−(v	NOUN
ejpam-5650	306	75	)	)	PUNCT
ejpam-5650	306	76	,	,	PUNCT
ejpam-5650	306	77	the	the	DET
ejpam-5650	306	78	net	net	NOUN
ejpam-5650	306	79	(	(	PUNCT
ejpam-5650	306	80	xγ	xγ	PROPN
ejpam-5650	306	81	)	)	PUNCT
ejpam-5650	306	82	is	be	AUX
ejpam-5650	306	83	eventually	eventually	ADV
ejpam-5650	306	84	in	in	ADP
ejpam-5650	306	85	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5650	306	86	-	-	PUNCT
ejpam-5650	306	87	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	306	88	-	-	PUNCT
ejpam-5650	306	89	cl(v	cl(v	NOUN
ejpam-5650	306	90	)	)	PUNCT
ejpam-5650	306	91	)	)	PUNCT
ejpam-5650	306	92	)	)	PUNCT
ejpam-5650	306	93	.	.	PUNCT
ejpam-5650	307	1	proof	proof	NOUN
ejpam-5650	307	2	.	.	PUNCT
ejpam-5650	308	1	the	the	DET
ejpam-5650	308	2	proof	proof	NOUN
ejpam-5650	308	3	is	be	AUX
ejpam-5650	308	4	similar	similar	ADJ
ejpam-5650	308	5	to	to	ADP
ejpam-5650	308	6	that	that	PRON
ejpam-5650	308	7	of	of	ADP
ejpam-5650	308	8	theorem	theorem	NOUN
ejpam-5650	308	9	9	9	NUM
ejpam-5650	308	10	.	.	X
ejpam-5650	308	11	for	for	ADP
ejpam-5650	308	12	a	a	DET
ejpam-5650	308	13	multifunction	multifunction	NOUN
ejpam-5650	308	14	f	f	NOUN
ejpam-5650	308	15	:	:	PUNCT
ejpam-5650	308	16	(	(	PUNCT
ejpam-5650	308	17	x	x	NOUN
ejpam-5650	308	18	,	,	PUNCT
ejpam-5650	308	19	τ1	τ1	NOUN
ejpam-5650	308	20	,	,	PUNCT
ejpam-5650	308	21	τ2	τ2	NOUN
ejpam-5650	308	22	)	)	PUNCT
ejpam-5650	308	23	→	→	SYM
ejpam-5650	308	24	(	(	PUNCT
ejpam-5650	308	25	y	y	PROPN
ejpam-5650	308	26	,	,	PUNCT
ejpam-5650	308	27	σ1	σ1	PROPN
ejpam-5650	308	28	,	,	PUNCT
ejpam-5650	308	29	σ2	σ2	PROPN
ejpam-5650	308	30	)	)	PUNCT
ejpam-5650	308	31	,	,	PUNCT
ejpam-5650	308	32	a	a	DET
ejpam-5650	308	33	multifunction	multifunction	NOUN
ejpam-5650	308	34	clf⊛	clf⊛	NOUN
ejpam-5650	308	35	:	:	PUNCT
ejpam-5650	308	36	(	(	PUNCT
ejpam-5650	308	37	x	x	NOUN
ejpam-5650	308	38	,	,	PUNCT
ejpam-5650	308	39	τ1	τ1	NOUN
ejpam-5650	308	40	,	,	PUNCT
ejpam-5650	308	41	τ2	τ2	NOUN
ejpam-5650	308	42	)	)	PUNCT
ejpam-5650	308	43	→	→	SYM
ejpam-5650	308	44	(	(	PUNCT
ejpam-5650	308	45	y	y	PROPN
ejpam-5650	308	46	,	,	PUNCT
ejpam-5650	308	47	σ1	σ1	PROPN
ejpam-5650	308	48	,	,	PUNCT
ejpam-5650	308	49	σ2	σ2	PROPN
ejpam-5650	308	50	)	)	PUNCT
ejpam-5650	308	51	is	be	AUX
ejpam-5650	308	52	defined	define	VERB
ejpam-5650	308	53	in	in	ADP
ejpam-5650	308	54	[	[	X
ejpam-5650	308	55	29	29	NUM
ejpam-5650	308	56	]	]	PUNCT
ejpam-5650	308	57	as	as	SCONJ
ejpam-5650	308	58	follows	follow	VERB
ejpam-5650	308	59	:	:	PUNCT
ejpam-5650	308	60	clf⊛(x	clf⊛(x	PROPN
ejpam-5650	308	61	)	)	PUNCT
ejpam-5650	309	1	=	=	PUNCT
ejpam-5650	309	2	σ1σ2	σ1σ2	X
ejpam-5650	309	3	-	-	NUM
ejpam-5650	309	4	cl(f	cl(f	NOUN
ejpam-5650	309	5	(	(	PUNCT
ejpam-5650	309	6	x	x	NOUN
ejpam-5650	309	7	)	)	PUNCT
ejpam-5650	309	8	)	)	PUNCT
ejpam-5650	309	9	for	for	ADP
ejpam-5650	309	10	each	each	DET
ejpam-5650	309	11	x	x	SYM
ejpam-5650	309	12	∈	∈	PROPN
ejpam-5650	309	13	x.	x.	NOUN
ejpam-5650	309	14	definition	definition	NOUN
ejpam-5650	309	15	3	3	NUM
ejpam-5650	309	16	.	.	PUNCT
ejpam-5650	310	1	[	[	X
ejpam-5650	310	2	29	29	NUM
ejpam-5650	310	3	]	]	PUNCT
ejpam-5650	310	4	a	a	DET
ejpam-5650	310	5	subset	subset	NOUN
ejpam-5650	310	6	a	a	PRON
ejpam-5650	310	7	of	of	ADP
ejpam-5650	310	8	a	a	DET
ejpam-5650	310	9	bitopological	bitopological	ADJ
ejpam-5650	310	10	space	space	NOUN
ejpam-5650	310	11	(	(	PUNCT
ejpam-5650	310	12	x	x	NOUN
ejpam-5650	310	13	,	,	PUNCT
ejpam-5650	310	14	τ1	τ1	NOUN
ejpam-5650	310	15	,	,	PUNCT
ejpam-5650	310	16	τ2	τ2	NOUN
ejpam-5650	310	17	)	)	PUNCT
ejpam-5650	310	18	is	be	AUX
ejpam-5650	310	19	said	say	VERB
ejpam-5650	310	20	to	to	PART
ejpam-5650	310	21	be	be	AUX
ejpam-5650	310	22	:	:	PUNCT
ejpam-5650	310	23	(	(	PUNCT
ejpam-5650	310	24	1	1	X
ejpam-5650	310	25	)	)	PUNCT
ejpam-5650	310	26	τ1τ2	τ1τ2	NOUN
ejpam-5650	310	27	-	-	NOUN
ejpam-5650	310	28	paracompact	paracompact	ADJ
ejpam-5650	310	29	if	if	SCONJ
ejpam-5650	310	30	every	every	DET
ejpam-5650	310	31	cover	cover	NOUN
ejpam-5650	310	32	of	of	ADP
ejpam-5650	310	33	a	a	PRON
ejpam-5650	310	34	by	by	ADP
ejpam-5650	310	35	τ1τ2	τ1τ2	ADJ
ejpam-5650	310	36	-	-	ADJ
ejpam-5650	310	37	open	open	ADJ
ejpam-5650	310	38	sets	set	NOUN
ejpam-5650	310	39	of	of	ADP
ejpam-5650	310	40	x	x	VERB
ejpam-5650	310	41	is	be	AUX
ejpam-5650	310	42	refined	refine	VERB
ejpam-5650	310	43	by	by	ADP
ejpam-5650	310	44	a	a	DET
ejpam-5650	310	45	cover	cover	NOUN
ejpam-5650	310	46	of	of	ADP
ejpam-5650	310	47	a	a	PRON
ejpam-5650	310	48	which	which	PRON
ejpam-5650	310	49	consists	consist	VERB
ejpam-5650	310	50	of	of	ADP
ejpam-5650	310	51	τ1τ2	τ1τ2	ADJ
ejpam-5650	310	52	-	-	ADJ
ejpam-5650	310	53	open	open	ADJ
ejpam-5650	310	54	sets	set	NOUN
ejpam-5650	310	55	of	of	ADP
ejpam-5650	310	56	x	x	PUNCT
ejpam-5650	310	57	and	and	CCONJ
ejpam-5650	310	58	is	be	AUX
ejpam-5650	310	59	τ1τ2	τ1τ2	NOUN
ejpam-5650	310	60	-	-	ADJ
ejpam-5650	310	61	locally	locally	ADV
ejpam-5650	310	62	finite	finite	NOUN
ejpam-5650	310	63	in	in	ADP
ejpam-5650	310	64	x	x	PRON
ejpam-5650	310	65	;	;	PUNCT
ejpam-5650	310	66	(	(	PUNCT
ejpam-5650	310	67	2	2	X
ejpam-5650	310	68	)	)	PUNCT
ejpam-5650	310	69	τ1τ2	τ1τ2	NOUN
ejpam-5650	310	70	-	-	NOUN
ejpam-5650	310	71	regular	regular	ADJ
ejpam-5650	310	72	if	if	SCONJ
ejpam-5650	310	73	for	for	ADP
ejpam-5650	310	74	each	each	DET
ejpam-5650	310	75	x	x	SYM
ejpam-5650	310	76	∈	∈	PROPN
ejpam-5650	310	77	a	a	PRON
ejpam-5650	310	78	and	and	CCONJ
ejpam-5650	310	79	each	each	DET
ejpam-5650	310	80	τ1τ2	τ1τ2	ADJ
ejpam-5650	310	81	-	-	ADJ
ejpam-5650	310	82	open	open	ADJ
ejpam-5650	310	83	set	set	ADJ
ejpam-5650	310	84	u	u	NOUN
ejpam-5650	310	85	of	of	ADP
ejpam-5650	310	86	x	x	PUNCT
ejpam-5650	310	87	containing	contain	VERB
ejpam-5650	310	88	x	x	PRON
ejpam-5650	310	89	,	,	PUNCT
ejpam-5650	310	90	there	there	PRON
ejpam-5650	310	91	exists	exist	VERB
ejpam-5650	310	92	a	a	DET
ejpam-5650	310	93	τ1τ2	τ1τ2	NOUN
ejpam-5650	310	94	-	-	ADJ
ejpam-5650	310	95	open	open	ADJ
ejpam-5650	310	96	set	set	NOUN
ejpam-5650	310	97	v	v	NOUN
ejpam-5650	310	98	of	of	ADP
ejpam-5650	310	99	x	x	PUNCT
ejpam-5650	310	100	such	such	ADJ
ejpam-5650	310	101	that	that	SCONJ
ejpam-5650	310	102	x	x	SYM
ejpam-5650	310	103	∈	∈	NOUN
ejpam-5650	310	104	v	v	ADP
ejpam-5650	310	105	⊆	⊆	NUM
ejpam-5650	310	106	τ1τ2	τ1τ2	NOUN
ejpam-5650	310	107	-	-	NOUN
ejpam-5650	310	108	cl(v	cl(v	X
ejpam-5650	310	109	)	)	PUNCT
ejpam-5650	310	110	⊆	⊆	NUM
ejpam-5650	310	111	u	u	NOUN
ejpam-5650	310	112	.	.	PUNCT
ejpam-5650	311	1	lemma	lemma	PROPN
ejpam-5650	311	2	5	5	NUM
ejpam-5650	311	3	.	.	PUNCT
ejpam-5650	312	1	[	[	X
ejpam-5650	312	2	29	29	NUM
ejpam-5650	312	3	]	]	X
ejpam-5650	312	4	if	if	SCONJ
ejpam-5650	312	5	a	a	PRON
ejpam-5650	312	6	is	be	AUX
ejpam-5650	312	7	a	a	DET
ejpam-5650	312	8	τ1τ2	τ1τ2	ADJ
ejpam-5650	312	9	-	-	ADJ
ejpam-5650	312	10	regular	regular	ADJ
ejpam-5650	312	11	τ1τ2	τ1τ2	NOUN
ejpam-5650	312	12	-	-	ADJ
ejpam-5650	312	13	paracompact	paracompact	ADJ
ejpam-5650	312	14	set	set	NOUN
ejpam-5650	312	15	of	of	ADP
ejpam-5650	312	16	a	a	DET
ejpam-5650	312	17	bitopological	bitopological	ADJ
ejpam-5650	312	18	space	space	NOUN
ejpam-5650	312	19	(	(	PUNCT
ejpam-5650	312	20	x	x	NOUN
ejpam-5650	312	21	,	,	PUNCT
ejpam-5650	312	22	τ1	τ1	NOUN
ejpam-5650	312	23	,	,	PUNCT
ejpam-5650	312	24	τ2	τ2	NOUN
ejpam-5650	312	25	)	)	PUNCT
ejpam-5650	312	26	and	and	CCONJ
ejpam-5650	312	27	u	u	NOUN
ejpam-5650	312	28	is	be	AUX
ejpam-5650	312	29	a	a	DET
ejpam-5650	312	30	τ1τ2	τ1τ2	ADJ
ejpam-5650	312	31	-	-	ADJ
ejpam-5650	312	32	open	open	ADJ
ejpam-5650	312	33	neighbourhood	neighbourhood	NOUN
ejpam-5650	312	34	of	of	ADP
ejpam-5650	312	35	a	a	PRON
ejpam-5650	312	36	,	,	PUNCT
ejpam-5650	312	37	then	then	ADV
ejpam-5650	312	38	there	there	PRON
ejpam-5650	312	39	exists	exist	VERB
ejpam-5650	312	40	a	a	DET
ejpam-5650	312	41	τ1τ2	τ1τ2	NOUN
ejpam-5650	312	42	-	-	ADJ
ejpam-5650	312	43	open	open	ADJ
ejpam-5650	312	44	set	set	NOUN
ejpam-5650	312	45	v	v	NOUN
ejpam-5650	312	46	of	of	ADP
ejpam-5650	312	47	x	x	PUNCT
ejpam-5650	312	48	such	such	ADJ
ejpam-5650	312	49	that	that	SCONJ
ejpam-5650	312	50	a	a	DET
ejpam-5650	312	51	⊆	⊆	NUM
ejpam-5650	312	52	v	v	ADP
ejpam-5650	312	53	⊆	⊆	NUM
ejpam-5650	312	54	τ1τ2	τ1τ2	NOUN
ejpam-5650	312	55	-	-	NOUN
ejpam-5650	312	56	cl(v	cl(v	X
ejpam-5650	312	57	)	)	PUNCT
ejpam-5650	312	58	⊆	⊆	NUM
ejpam-5650	312	59	u	u	NOUN
ejpam-5650	312	60	.	.	PUNCT
ejpam-5650	313	1	lemma	lemma	PROPN
ejpam-5650	313	2	6	6	NUM
ejpam-5650	313	3	.	.	PUNCT
ejpam-5650	314	1	[	[	X
ejpam-5650	314	2	29	29	NUM
ejpam-5650	314	3	]	]	X
ejpam-5650	314	4	if	if	SCONJ
ejpam-5650	314	5	f	f	PROPN
ejpam-5650	314	6	:	:	PUNCT
ejpam-5650	314	7	(	(	PUNCT
ejpam-5650	314	8	x	x	NOUN
ejpam-5650	314	9	,	,	PUNCT
ejpam-5650	314	10	τ1	τ1	NOUN
ejpam-5650	314	11	,	,	PUNCT
ejpam-5650	314	12	τ2	τ2	NOUN
ejpam-5650	314	13	)	)	PUNCT
ejpam-5650	314	14	→	→	SYM
ejpam-5650	314	15	(	(	PUNCT
ejpam-5650	314	16	y	y	PROPN
ejpam-5650	314	17	,	,	PUNCT
ejpam-5650	314	18	σ1	σ1	PROPN
ejpam-5650	314	19	,	,	PUNCT
ejpam-5650	314	20	σ2	σ2	PROPN
ejpam-5650	314	21	)	)	PUNCT
ejpam-5650	314	22	is	be	AUX
ejpam-5650	314	23	a	a	DET
ejpam-5650	314	24	multifunction	multifunction	NOUN
ejpam-5650	314	25	such	such	ADJ
ejpam-5650	314	26	that	that	SCONJ
ejpam-5650	314	27	f	f	PROPN
ejpam-5650	314	28	(	(	PUNCT
ejpam-5650	314	29	x	x	X
ejpam-5650	314	30	)	)	PUNCT
ejpam-5650	314	31	is	be	AUX
ejpam-5650	314	32	τ1τ2regular	τ1τ2regular	NUM
ejpam-5650	314	33	and	and	CCONJ
ejpam-5650	314	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	314	35	-	-	ADJ
ejpam-5650	314	36	paracompact	paracompact	ADJ
ejpam-5650	314	37	for	for	ADP
ejpam-5650	314	38	each	each	DET
ejpam-5650	314	39	x	x	SYM
ejpam-5650	314	40	∈	∈	PROPN
ejpam-5650	314	41	x	x	NOUN
ejpam-5650	314	42	,	,	PUNCT
ejpam-5650	314	43	then	then	ADV
ejpam-5650	314	44	clf+	clf+	PROPN
ejpam-5650	314	45	⊛	⊛	X
ejpam-5650	314	46	(	(	PUNCT
ejpam-5650	314	47	v	v	NOUN
ejpam-5650	314	48	)	)	PUNCT
ejpam-5650	314	49	=	=	PUNCT
ejpam-5650	314	50	f+(v	f+(v	NOUN
ejpam-5650	314	51	)	)	PUNCT
ejpam-5650	314	52	for	for	ADP
ejpam-5650	314	53	each	each	DET
ejpam-5650	314	54	σ1σ2	σ1σ2	VERB
ejpam-5650	314	55	-	-	ADJ
ejpam-5650	314	56	open	open	ADJ
ejpam-5650	314	57	set	set	NOUN
ejpam-5650	314	58	v	v	NOUN
ejpam-5650	314	59	of	of	ADP
ejpam-5650	314	60	y	y	PROPN
ejpam-5650	314	61	.	.	PUNCT
ejpam-5650	315	1	theorem	theorem	ADJ
ejpam-5650	315	2	11	11	NUM
ejpam-5650	315	3	.	.	PUNCT
ejpam-5650	316	1	let	let	VERB
ejpam-5650	316	2	f	f	NOUN
ejpam-5650	316	3	:	:	PUNCT
ejpam-5650	316	4	(	(	PUNCT
ejpam-5650	316	5	x	x	NOUN
ejpam-5650	316	6	,	,	PUNCT
ejpam-5650	316	7	τ1	τ1	NOUN
ejpam-5650	316	8	,	,	PUNCT
ejpam-5650	316	9	τ2	τ2	NOUN
ejpam-5650	316	10	)	)	PUNCT
ejpam-5650	316	11	→	→	SYM
ejpam-5650	316	12	(	(	PUNCT
ejpam-5650	316	13	y	y	PROPN
ejpam-5650	316	14	,	,	PUNCT
ejpam-5650	316	15	σ1	σ1	PROPN
ejpam-5650	316	16	,	,	PUNCT
ejpam-5650	316	17	σ2	σ2	PROPN
ejpam-5650	316	18	)	)	PUNCT
ejpam-5650	316	19	be	be	VERB
ejpam-5650	316	20	a	a	DET
ejpam-5650	316	21	multifunction	multifunction	NOUN
ejpam-5650	316	22	such	such	ADJ
ejpam-5650	316	23	that	that	SCONJ
ejpam-5650	316	24	f	f	PROPN
ejpam-5650	316	25	(	(	PUNCT
ejpam-5650	316	26	x	x	X
ejpam-5650	316	27	)	)	PUNCT
ejpam-5650	316	28	is	be	AUX
ejpam-5650	316	29	σ1σ2	σ1σ2	NOUN
ejpam-5650	316	30	-	-	ADJ
ejpam-5650	316	31	paracompact	paracompact	ADJ
ejpam-5650	316	32	and	and	CCONJ
ejpam-5650	316	33	σ1σ2	σ1σ2	NOUN
ejpam-5650	316	34	-	-	ADJ
ejpam-5650	316	35	regular	regular	ADJ
ejpam-5650	316	36	for	for	ADP
ejpam-5650	316	37	each	each	DET
ejpam-5650	316	38	x	x	SYM
ejpam-5650	316	39	∈	∈	PROPN
ejpam-5650	316	40	x.	x.	NOUN
ejpam-5650	316	41	then	then	ADV
ejpam-5650	316	42	,	,	PUNCT
ejpam-5650	316	43	f	f	PROPN
ejpam-5650	316	44	is	be	AUX
ejpam-5650	316	45	upper	upper	ADJ
ejpam-5650	316	46	almost	almost	ADV
ejpam-5650	316	47	nearly	nearly	ADV
ejpam-5650	316	48	(	(	PUNCT
ejpam-5650	316	49	τ1	τ1	NOUN
ejpam-5650	316	50	,	,	PUNCT
ejpam-5650	316	51	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	316	52	if	if	SCONJ
ejpam-5650	316	53	and	and	CCONJ
ejpam-5650	316	54	only	only	ADV
ejpam-5650	316	55	if	if	SCONJ
ejpam-5650	316	56	g	g	NOUN
ejpam-5650	316	57	:	:	PUNCT
ejpam-5650	316	58	(	(	PUNCT
ejpam-5650	316	59	x	x	NOUN
ejpam-5650	316	60	,	,	PUNCT
ejpam-5650	316	61	τ1	τ1	NOUN
ejpam-5650	316	62	,	,	PUNCT
ejpam-5650	316	63	τ2	τ2	NOUN
ejpam-5650	316	64	)	)	PUNCT
ejpam-5650	316	65	→	→	SYM
ejpam-5650	316	66	(	(	PUNCT
ejpam-5650	316	67	y	y	PROPN
ejpam-5650	316	68	,	,	PUNCT
ejpam-5650	316	69	σ1	σ1	PROPN
ejpam-5650	316	70	,	,	PUNCT
ejpam-5650	316	71	σ2	σ2	PROPN
ejpam-5650	316	72	)	)	PUNCT
ejpam-5650	316	73	is	be	AUX
ejpam-5650	316	74	upper	upper	ADJ
ejpam-5650	316	75	almost	almost	ADV
ejpam-5650	316	76	nearly	nearly	ADV
ejpam-5650	316	77	(	(	PUNCT
ejpam-5650	316	78	τ1	τ1	NOUN
ejpam-5650	316	79	,	,	PUNCT
ejpam-5650	316	80	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	316	81	,	,	PUNCT
ejpam-5650	316	82	where	where	SCONJ
ejpam-5650	316	83	g	g	PROPN
ejpam-5650	316	84	denote	denote	VERB
ejpam-5650	316	85	clf⊛.	clf⊛.	DET
ejpam-5650	316	86	proof	proof	NOUN
ejpam-5650	316	87	.	.	PUNCT
ejpam-5650	317	1	suppose	suppose	VERB
ejpam-5650	317	2	that	that	SCONJ
ejpam-5650	317	3	f	f	PROPN
ejpam-5650	317	4	is	be	AUX
ejpam-5650	317	5	upper	upper	ADJ
ejpam-5650	317	6	almost	almost	ADV
ejpam-5650	317	7	nearly	nearly	ADV
ejpam-5650	317	8	(	(	PUNCT
ejpam-5650	317	9	τ1	τ1	NOUN
ejpam-5650	317	10	,	,	PUNCT
ejpam-5650	317	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	317	12	.	.	PUNCT
ejpam-5650	318	1	let	let	VERB
ejpam-5650	318	2	v	v	PART
ejpam-5650	318	3	be	be	AUX
ejpam-5650	318	4	any	any	DET
ejpam-5650	318	5	(	(	PUNCT
ejpam-5650	318	6	σ1	σ1	NOUN
ejpam-5650	318	7	,	,	PUNCT
ejpam-5650	318	8	σ2)r	σ2)r	NOUN
ejpam-5650	318	9	-	-	PUNCT
ejpam-5650	318	10	open	open	ADJ
ejpam-5650	318	11	set	set	NOUN
ejpam-5650	318	12	of	of	ADP
ejpam-5650	318	13	y	y	PROPN
ejpam-5650	318	14	having	have	VERB
ejpam-5650	318	15	n	n	PROPN
ejpam-5650	318	16	(	(	PUNCT
ejpam-5650	318	17	σ1	σ1	PROPN
ejpam-5650	318	18	,	,	PUNCT
ejpam-5650	318	19	σ2)-connected	σ2)-connecte	VERB
ejpam-5650	318	20	complement	complement	NOUN
ejpam-5650	318	21	.	.	PUNCT
ejpam-5650	319	1	it	it	PRON
ejpam-5650	319	2	follows	follow	VERB
ejpam-5650	319	3	from	from	ADP
ejpam-5650	319	4	lemma	lemma	PROPN
ejpam-5650	319	5	6	6	NUM
ejpam-5650	319	6	and	and	CCONJ
ejpam-5650	319	7	theorem	theorem	VERB
ejpam-5650	319	8	3	3	NUM
ejpam-5650	319	9	that	that	DET
ejpam-5650	319	10	g+(v	g+(v	PROPN
ejpam-5650	319	11	)	)	PUNCT
ejpam-5650	320	1	=	=	PUNCT
ejpam-5650	320	2	f+(v	f+(v	PROPN
ejpam-5650	320	3	)	)	PUNCT
ejpam-5650	320	4	is	be	AUX
ejpam-5650	320	5	τ1τ2	τ1τ2	NOUN
ejpam-5650	320	6	-	-	ADJ
ejpam-5650	320	7	open	open	ADJ
ejpam-5650	320	8	in	in	ADP
ejpam-5650	320	9	x.	x.	NOUN
ejpam-5650	320	10	by	by	ADP
ejpam-5650	320	11	theorem	theorem	NOUN
ejpam-5650	320	12	3	3	NUM
ejpam-5650	320	13	,	,	PUNCT
ejpam-5650	320	14	g	g	PROPN
ejpam-5650	320	15	is	be	AUX
ejpam-5650	320	16	upper	upper	ADJ
ejpam-5650	320	17	almost	almost	ADV
ejpam-5650	320	18	nearly	nearly	ADV
ejpam-5650	320	19	(	(	PUNCT
ejpam-5650	320	20	τ1	τ1	NOUN
ejpam-5650	320	21	,	,	PUNCT
ejpam-5650	320	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	320	23	.	.	PUNCT
ejpam-5650	321	1	n.	n.	PROPN
ejpam-5650	321	2	chutiman	chutiman	PROPN
ejpam-5650	321	3	,	,	PUNCT
ejpam-5650	321	4	a.	a.	PROPN
ejpam-5650	321	5	sama	sama	PROPN
ejpam-5650	321	6	-	-	PUNCT
ejpam-5650	321	7	ae	ae	PROPN
ejpam-5650	321	8	,	,	PUNCT
ejpam-5650	321	9	c.	c.	PROPN
ejpam-5650	321	10	boonpok	boonpok	PROPN
ejpam-5650	321	11	/	/	SYM
ejpam-5650	321	12	eur	eur	PROPN
ejpam-5650	321	13	.	.	PUNCT
ejpam-5650	322	1	j.	j.	PROPN
ejpam-5650	322	2	pure	pure	PROPN
ejpam-5650	322	3	appl	appl	PROPN
ejpam-5650	322	4	.	.	PROPN
ejpam-5650	322	5	math	math	PROPN
ejpam-5650	322	6	,	,	PUNCT
ejpam-5650	322	7	18	18	NUM
ejpam-5650	322	8	(	(	PUNCT
ejpam-5650	322	9	1	1	NUM
ejpam-5650	322	10	)	)	PUNCT
ejpam-5650	322	11	(	(	PUNCT
ejpam-5650	322	12	2025	2025	NUM
ejpam-5650	322	13	)	)	PUNCT
ejpam-5650	322	14	,	,	PUNCT
ejpam-5650	322	15	5650	5650	NUM
ejpam-5650	322	16	13	13	NUM
ejpam-5650	322	17	of	of	ADP
ejpam-5650	322	18	18	18	NUM
ejpam-5650	322	19	conversely	conversely	ADV
ejpam-5650	322	20	,	,	PUNCT
ejpam-5650	322	21	suppose	suppose	VERB
ejpam-5650	322	22	that	that	SCONJ
ejpam-5650	322	23	g	g	PROPN
ejpam-5650	322	24	is	be	AUX
ejpam-5650	322	25	upper	upper	ADJ
ejpam-5650	322	26	almost	almost	ADV
ejpam-5650	322	27	nearly	nearly	ADV
ejpam-5650	322	28	(	(	PUNCT
ejpam-5650	322	29	τ1	τ1	NOUN
ejpam-5650	322	30	,	,	PUNCT
ejpam-5650	322	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	322	32	.	.	PUNCT
ejpam-5650	323	1	let	let	VERB
ejpam-5650	323	2	v	v	PART
ejpam-5650	323	3	be	be	AUX
ejpam-5650	323	4	any	any	DET
ejpam-5650	323	5	(	(	PUNCT
ejpam-5650	323	6	σ1	σ1	NOUN
ejpam-5650	323	7	,	,	PUNCT
ejpam-5650	323	8	σ2)r	σ2)r	NOUN
ejpam-5650	323	9	-	-	PUNCT
ejpam-5650	323	10	open	open	ADJ
ejpam-5650	323	11	set	set	NOUN
ejpam-5650	323	12	of	of	ADP
ejpam-5650	323	13	y	y	PROPN
ejpam-5650	323	14	having	have	VERB
ejpam-5650	323	15	n	n	PROPN
ejpam-5650	323	16	(	(	PUNCT
ejpam-5650	323	17	σ1	σ1	PROPN
ejpam-5650	323	18	,	,	PUNCT
ejpam-5650	323	19	σ2)-connected	σ2)-connecte	VERB
ejpam-5650	323	20	complement	complement	NOUN
ejpam-5650	323	21	.	.	PUNCT
ejpam-5650	324	1	by	by	ADP
ejpam-5650	324	2	lemma	lemma	PROPN
ejpam-5650	324	3	6	6	NUM
ejpam-5650	324	4	and	and	CCONJ
ejpam-5650	324	5	theorem	theorem	VERB
ejpam-5650	324	6	3	3	NUM
ejpam-5650	324	7	,	,	PUNCT
ejpam-5650	324	8	f+(v	f+(v	PROPN
ejpam-5650	324	9	)	)	PUNCT
ejpam-5650	324	10	=	=	PUNCT
ejpam-5650	324	11	g+(v	g+(v	PROPN
ejpam-5650	324	12	)	)	PUNCT
ejpam-5650	324	13	is	be	AUX
ejpam-5650	324	14	τ1τ2	τ1τ2	NOUN
ejpam-5650	324	15	-	-	ADJ
ejpam-5650	324	16	open	open	ADJ
ejpam-5650	324	17	in	in	ADP
ejpam-5650	324	18	x.	x.	NOUN
ejpam-5650	324	19	thus	thus	ADV
ejpam-5650	324	20	by	by	ADP
ejpam-5650	324	21	theorem	theorem	NOUN
ejpam-5650	324	22	3	3	NUM
ejpam-5650	324	23	,	,	PUNCT
ejpam-5650	324	24	f	f	PROPN
ejpam-5650	324	25	is	be	AUX
ejpam-5650	324	26	upper	upper	ADJ
ejpam-5650	324	27	almost	almost	ADV
ejpam-5650	324	28	nearly	nearly	ADV
ejpam-5650	324	29	(	(	PUNCT
ejpam-5650	324	30	τ1	τ1	NOUN
ejpam-5650	324	31	,	,	PUNCT
ejpam-5650	324	32	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5650	324	33	.	.	PUNCT
ejpam-5650	325	1	lemma	lemma	PROPN
ejpam-5650	325	2	7	7	NUM
ejpam-5650	325	3	.	.	PUNCT
ejpam-5650	326	1	[	[	X
ejpam-5650	326	2	29	29	NUM
ejpam-5650	326	3	]	]	PUNCT
ejpam-5650	326	4	for	for	ADP
ejpam-5650	326	5	a	a	DET
ejpam-5650	326	6	multifunction	multifunction	NOUN
ejpam-5650	326	7	f	f	NOUN
ejpam-5650	326	8	:	:	PUNCT
ejpam-5650	326	9	(	(	PUNCT
ejpam-5650	326	10	x	x	NOUN
ejpam-5650	326	11	,	,	PUNCT
ejpam-5650	326	12	τ1	τ1	NOUN
ejpam-5650	326	13	,	,	PUNCT
ejpam-5650	326	14	τ2	τ2	NOUN
ejpam-5650	326	15	)	)	PUNCT
ejpam-5650	326	16	→	→	SYM
ejpam-5650	326	17	(	(	PUNCT
ejpam-5650	326	18	y	y	PROPN
ejpam-5650	326	19	,	,	PUNCT
ejpam-5650	326	20	σ1	σ1	PROPN
ejpam-5650	326	21	,	,	PUNCT
ejpam-5650	326	22	σ2	σ2	NOUN
ejpam-5650	326	23	)	)	PUNCT
ejpam-5650	326	24	,	,	PUNCT
ejpam-5650	326	25	clf	clf	PROPN
ejpam-5650	326	26	−	−	PROPN
ejpam-5650	326	27	⊛	⊛	NUM
ejpam-5650	326	28	(	(	PUNCT
ejpam-5650	326	29	v	v	NOUN
ejpam-5650	326	30	)	)	PUNCT
ejpam-5650	326	31	=	=	SYM
ejpam-5650	326	32	f−(v	f−(v	ADJ
ejpam-5650	326	33	)	)	PUNCT
ejpam-5650	326	34	for	for	ADP
ejpam-5650	326	35	each	each	DET
ejpam-5650	326	36	σ1σ2	σ1σ2	VERB
ejpam-5650	326	37	-	-	ADJ
ejpam-5650	326	38	open	open	ADJ
ejpam-5650	326	39	set	set	NOUN
ejpam-5650	326	40	v	v	NOUN
ejpam-5650	326	41	of	of	ADP
ejpam-5650	326	42	y	y	PROPN
ejpam-5650	326	43	.	.	PUNCT
ejpam-5650	327	1	theorem	theorem	PROPN
ejpam-5650	327	2	12	12	NUM
ejpam-5650	327	3	.	.	PUNCT
ejpam-5650	328	1	a	a	DET
ejpam-5650	328	2	multifunction	multifunction	NOUN
ejpam-5650	328	3	f	f	NOUN
ejpam-5650	328	4	:	:	PUNCT
ejpam-5650	328	5	(	(	PUNCT
ejpam-5650	328	6	x	x	NOUN
ejpam-5650	328	7	,	,	PUNCT
ejpam-5650	328	8	τ1	τ1	NOUN
ejpam-5650	328	9	,	,	PUNCT
ejpam-5650	328	10	τ2	τ2	NOUN
ejpam-5650	328	11	)	)	PUNCT
ejpam-5650	328	12	→	→	SYM
ejpam-5650	328	13	(	(	PUNCT
ejpam-5650	328	14	y	y	PROPN
ejpam-5650	328	15	,	,	PUNCT
ejpam-5650	328	16	σ1	σ1	PROPN
ejpam-5650	328	17	,	,	PUNCT
ejpam-5650	328	18	σ2	σ2	NOUN
ejpam-5650	328	19	)	)	PUNCT
ejpam-5650	328	20	is	be	AUX
ejpam-5650	328	21	lower	low	ADJ
ejpam-5650	328	22	almost	almost	ADV
ejpam-5650	328	23	nearly	nearly	ADV
ejpam-5650	328	24	(	(	PUNCT
ejpam-5650	328	25	τ1	τ1	NOUN
ejpam-5650	328	26	,	,	PUNCT
ejpam-5650	328	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	328	28	if	if	SCONJ
ejpam-5650	328	29	and	and	CCONJ
ejpam-5650	328	30	only	only	ADV
ejpam-5650	328	31	if	if	SCONJ
ejpam-5650	328	32	g	g	NOUN
ejpam-5650	328	33	:	:	PUNCT
ejpam-5650	328	34	(	(	PUNCT
ejpam-5650	328	35	x	x	NOUN
ejpam-5650	328	36	,	,	PUNCT
ejpam-5650	328	37	τ1	τ1	NOUN
ejpam-5650	328	38	,	,	PUNCT
ejpam-5650	328	39	τ2	τ2	NOUN
ejpam-5650	328	40	)	)	PUNCT
ejpam-5650	328	41	→	→	SYM
ejpam-5650	328	42	(	(	PUNCT
ejpam-5650	328	43	y	y	PROPN
ejpam-5650	328	44	,	,	PUNCT
ejpam-5650	328	45	σ1	σ1	PROPN
ejpam-5650	328	46	,	,	PUNCT
ejpam-5650	328	47	σ2	σ2	NOUN
ejpam-5650	328	48	)	)	PUNCT
ejpam-5650	328	49	is	be	AUX
ejpam-5650	328	50	lower	low	ADJ
ejpam-5650	328	51	almost	almost	ADV
ejpam-5650	328	52	nearly	nearly	ADV
ejpam-5650	328	53	(	(	PUNCT
ejpam-5650	328	54	τ1	τ1	NOUN
ejpam-5650	328	55	,	,	PUNCT
ejpam-5650	328	56	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	328	57	,	,	PUNCT
ejpam-5650	328	58	where	where	SCONJ
ejpam-5650	328	59	g	g	PROPN
ejpam-5650	328	60	denote	denote	VERB
ejpam-5650	328	61	clf⊛.	clf⊛.	DET
ejpam-5650	328	62	proof	proof	NOUN
ejpam-5650	328	63	.	.	PUNCT
ejpam-5650	329	1	by	by	ADP
ejpam-5650	329	2	using	use	VERB
ejpam-5650	329	3	lemma	lemma	PROPN
ejpam-5650	329	4	7	7	NUM
ejpam-5650	329	5	this	this	PRON
ejpam-5650	329	6	can	can	AUX
ejpam-5650	329	7	be	be	AUX
ejpam-5650	329	8	shown	show	VERB
ejpam-5650	329	9	similarly	similarly	ADV
ejpam-5650	329	10	as	as	ADP
ejpam-5650	329	11	in	in	ADP
ejpam-5650	329	12	theorem	theorem	NOUN
ejpam-5650	329	13	11	11	NUM
ejpam-5650	329	14	.	.	PUNCT
ejpam-5650	329	15	4	4	NUM
ejpam-5650	329	16	.	.	X
ejpam-5650	329	17	several	several	ADJ
ejpam-5650	329	18	characterizations	characterization	NOUN
ejpam-5650	329	19	the	the	DET
ejpam-5650	329	20	τ1τ2	τ1τ2	NOUN
ejpam-5650	329	21	-	-	NOUN
ejpam-5650	329	22	frontier	frontier	NOUN
ejpam-5650	329	23	[	[	X
ejpam-5650	329	24	26	26	NUM
ejpam-5650	329	25	]	]	PUNCT
ejpam-5650	329	26	of	of	ADP
ejpam-5650	329	27	a	a	DET
ejpam-5650	329	28	subset	subset	NOUN
ejpam-5650	329	29	a	a	PRON
ejpam-5650	329	30	of	of	ADP
ejpam-5650	329	31	a	a	DET
ejpam-5650	329	32	bitopological	bitopological	ADJ
ejpam-5650	329	33	space	space	NOUN
ejpam-5650	329	34	(	(	PUNCT
ejpam-5650	329	35	x	x	NOUN
ejpam-5650	329	36	,	,	PUNCT
ejpam-5650	329	37	τ1	τ1	NOUN
ejpam-5650	329	38	,	,	PUNCT
ejpam-5650	329	39	τ2	τ2	PROPN
ejpam-5650	329	40	)	)	PUNCT
ejpam-5650	329	41	,	,	PUNCT
ejpam-5650	329	42	denoted	denote	VERB
ejpam-5650	329	43	by	by	ADP
ejpam-5650	329	44	τ1τ2	τ1τ2	NOUN
ejpam-5650	329	45	-	-	ADJ
ejpam-5650	329	46	fr(a	fr(a	NUM
ejpam-5650	329	47	)	)	PUNCT
ejpam-5650	329	48	,	,	PUNCT
ejpam-5650	329	49	is	be	AUX
ejpam-5650	329	50	defined	define	VERB
ejpam-5650	329	51	by	by	ADP
ejpam-5650	329	52	τ1τ2	τ1τ2	NOUN
ejpam-5650	329	53	-	-	ADJ
ejpam-5650	329	54	fr(a	fr(a	ADJ
ejpam-5650	329	55	)	)	PUNCT
ejpam-5650	330	1	=	=	PUNCT
ejpam-5650	330	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	330	3	-	-	NUM
ejpam-5650	330	4	cl(a	cl(a	NUM
ejpam-5650	330	5	)	)	PUNCT
ejpam-5650	330	6	∩	∩	NOUN
ejpam-5650	330	7	τ1τ2	τ1τ2	NOUN
ejpam-5650	330	8	-	-	ADJ
ejpam-5650	330	9	cl(x	cl(x	SYM
ejpam-5650	330	10	−a	−a	NOUN
ejpam-5650	330	11	)	)	PUNCT
ejpam-5650	330	12	=	=	PUNCT
ejpam-5650	331	1	τ1τ2	τ1τ2	ADJ
ejpam-5650	331	2	-	-	ADJ
ejpam-5650	331	3	cl(a)−	cl(a)−	ADJ
ejpam-5650	331	4	τ1τ2	τ1τ2	NOUN
ejpam-5650	331	5	-	-	ADJ
ejpam-5650	331	6	int(a	int(a	NOUN
ejpam-5650	331	7	)	)	PUNCT
ejpam-5650	331	8	.	.	PUNCT
ejpam-5650	332	1	theorem	theorem	VERB
ejpam-5650	332	2	13	13	NUM
ejpam-5650	332	3	.	.	PUNCT
ejpam-5650	333	1	the	the	DET
ejpam-5650	333	2	set	set	NOUN
ejpam-5650	333	3	of	of	ADP
ejpam-5650	333	4	all	all	DET
ejpam-5650	333	5	points	point	NOUN
ejpam-5650	333	6	x	x	PUNCT
ejpam-5650	333	7	of	of	ADP
ejpam-5650	333	8	x	x	SYM
ejpam-5650	333	9	at	at	ADP
ejpam-5650	333	10	which	which	PRON
ejpam-5650	333	11	a	a	DET
ejpam-5650	333	12	multifunction	multifunction	NOUN
ejpam-5650	334	1	f	f	NOUN
ejpam-5650	334	2	:	:	PUNCT
ejpam-5650	334	3	(	(	PUNCT
ejpam-5650	334	4	x	x	NOUN
ejpam-5650	334	5	,	,	PUNCT
ejpam-5650	334	6	τ1	τ1	NOUN
ejpam-5650	334	7	,	,	PUNCT
ejpam-5650	334	8	τ2	τ2	NOUN
ejpam-5650	334	9	)	)	PUNCT
ejpam-5650	334	10	→	→	SYM
ejpam-5650	334	11	(	(	PUNCT
ejpam-5650	334	12	y	y	PROPN
ejpam-5650	334	13	,	,	PUNCT
ejpam-5650	334	14	σ1	σ1	PROPN
ejpam-5650	334	15	,	,	PUNCT
ejpam-5650	334	16	σ2	σ2	PROPN
ejpam-5650	334	17	)	)	PUNCT
ejpam-5650	334	18	is	be	AUX
ejpam-5650	334	19	not	not	PART
ejpam-5650	334	20	upper	upper	ADJ
ejpam-5650	334	21	almost	almost	ADV
ejpam-5650	334	22	nearly	nearly	ADV
ejpam-5650	334	23	(	(	PUNCT
ejpam-5650	334	24	τ1	τ1	NOUN
ejpam-5650	334	25	,	,	PUNCT
ejpam-5650	334	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	334	27	is	be	AUX
ejpam-5650	334	28	identical	identical	ADJ
ejpam-5650	334	29	with	with	ADP
ejpam-5650	334	30	the	the	DET
ejpam-5650	334	31	union	union	NOUN
ejpam-5650	334	32	of	of	ADP
ejpam-5650	334	33	the	the	DET
ejpam-5650	334	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	334	35	-	-	NOUN
ejpam-5650	334	36	frontier	frontier	NOUN
ejpam-5650	334	37	of	of	ADP
ejpam-5650	334	38	the	the	DET
ejpam-5650	334	39	upper	upper	ADJ
ejpam-5650	334	40	inverse	inverse	NOUN
ejpam-5650	334	41	images	image	NOUN
ejpam-5650	334	42	of	of	ADP
ejpam-5650	334	43	(	(	PUNCT
ejpam-5650	334	44	σ1	σ1	PROPN
ejpam-5650	334	45	,	,	PUNCT
ejpam-5650	334	46	σ2)r	σ2)r	NOUN
ejpam-5650	334	47	-	-	PUNCT
ejpam-5650	334	48	open	open	ADJ
ejpam-5650	334	49	sets	set	NOUN
ejpam-5650	334	50	containing	contain	VERB
ejpam-5650	334	51	f	f	X
ejpam-5650	334	52	(	(	PUNCT
ejpam-5650	334	53	x	x	NOUN
ejpam-5650	334	54	)	)	PUNCT
ejpam-5650	334	55	and	and	CCONJ
ejpam-5650	334	56	having	have	VERB
ejpam-5650	334	57	n	n	PRON
ejpam-5650	334	58	(	(	PUNCT
ejpam-5650	334	59	σ1	σ1	PROPN
ejpam-5650	334	60	,	,	PUNCT
ejpam-5650	334	61	σ2)closed	σ2)close	VERB
ejpam-5650	334	62	complement	complement	NOUN
ejpam-5650	334	63	.	.	PUNCT
ejpam-5650	335	1	proof	proof	NOUN
ejpam-5650	335	2	.	.	PUNCT
ejpam-5650	336	1	let	let	VERB
ejpam-5650	336	2	x	x	PRON
ejpam-5650	336	3	be	be	AUX
ejpam-5650	336	4	a	a	DET
ejpam-5650	336	5	point	point	NOUN
ejpam-5650	336	6	of	of	ADP
ejpam-5650	336	7	x	x	PUNCT
ejpam-5650	336	8	at	at	ADP
ejpam-5650	336	9	which	which	PRON
ejpam-5650	336	10	f	f	NOUN
ejpam-5650	336	11	is	be	AUX
ejpam-5650	336	12	not	not	PART
ejpam-5650	336	13	upper	upper	ADJ
ejpam-5650	336	14	almost	almost	ADV
ejpam-5650	336	15	nearly	nearly	ADV
ejpam-5650	336	16	(	(	PUNCT
ejpam-5650	336	17	τ1	τ1	NOUN
ejpam-5650	336	18	,	,	PUNCT
ejpam-5650	336	19	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5650	336	20	.	.	PUNCT
ejpam-5650	337	1	then	then	ADV
ejpam-5650	337	2	,	,	PUNCT
ejpam-5650	337	3	by	by	ADP
ejpam-5650	337	4	theorem	theorem	NOUN
ejpam-5650	337	5	1	1	NUM
ejpam-5650	337	6	there	there	ADV
ejpam-5650	337	7	exists	exist	VERB
ejpam-5650	337	8	a	a	DET
ejpam-5650	337	9	(	(	PUNCT
ejpam-5650	337	10	σ1	σ1	NOUN
ejpam-5650	337	11	,	,	PUNCT
ejpam-5650	337	12	σ2)r	σ2)r	NOUN
ejpam-5650	337	13	-	-	PUNCT
ejpam-5650	337	14	open	open	ADJ
ejpam-5650	337	15	set	set	VERB
ejpam-5650	337	16	v	v	NOUN
ejpam-5650	337	17	of	of	ADP
ejpam-5650	337	18	y	y	PROPN
ejpam-5650	337	19	containing	contain	VERB
ejpam-5650	337	20	f	f	PROPN
ejpam-5650	337	21	(	(	PUNCT
ejpam-5650	337	22	x	x	NOUN
ejpam-5650	337	23	)	)	PUNCT
ejpam-5650	337	24	and	and	CCONJ
ejpam-5650	337	25	having	have	VERB
ejpam-5650	337	26	n	n	PRON
ejpam-5650	337	27	(	(	PUNCT
ejpam-5650	337	28	σ1	σ1	PROPN
ejpam-5650	337	29	,	,	PUNCT
ejpam-5650	337	30	σ2)-closed	σ2)-close	VERB
ejpam-5650	337	31	complement	complement	NOUN
ejpam-5650	337	32	such	such	ADJ
ejpam-5650	337	33	that	that	SCONJ
ejpam-5650	337	34	u	u	PROPN
ejpam-5650	337	35	∩	∩	NOUN
ejpam-5650	337	36	(	(	PUNCT
ejpam-5650	337	37	x	x	NOUN
ejpam-5650	337	38	−	−	PROPN
ejpam-5650	337	39	f+(v	f+(v	NOUN
ejpam-5650	337	40	)	)	PUNCT
ejpam-5650	337	41	)	)	PUNCT
ejpam-5650	338	1	̸=	̸=	NOUN
ejpam-5650	338	2	∅	∅	NOUN
ejpam-5650	338	3	for	for	ADP
ejpam-5650	338	4	every	every	DET
ejpam-5650	338	5	τ1τ2	τ1τ2	ADJ
ejpam-5650	338	6	-	-	ADJ
ejpam-5650	338	7	open	open	ADJ
ejpam-5650	338	8	set	set	ADJ
ejpam-5650	338	9	u	u	NOUN
ejpam-5650	338	10	of	of	ADP
ejpam-5650	338	11	x	x	SYM
ejpam-5650	338	12	containing	contain	VERB
ejpam-5650	338	13	x.	x.	NOUN
ejpam-5650	338	14	thus	thus	ADV
ejpam-5650	338	15	,	,	PUNCT
ejpam-5650	338	16	x	x	SYM
ejpam-5650	338	17	∈	∈	PROPN
ejpam-5650	338	18	τ1τ2	τ1τ2	NOUN
ejpam-5650	338	19	-	-	NOUN
ejpam-5650	338	20	cl(x	cl(x	NUM
ejpam-5650	338	21	−	−	NOUN
ejpam-5650	338	22	f+(v	f+(v	NOUN
ejpam-5650	338	23	)	)	PUNCT
ejpam-5650	338	24	)	)	PUNCT
ejpam-5650	338	25	.	.	PUNCT
ejpam-5650	339	1	on	on	ADP
ejpam-5650	339	2	the	the	DET
ejpam-5650	339	3	other	other	ADJ
ejpam-5650	339	4	hand	hand	NOUN
ejpam-5650	339	5	,	,	PUNCT
ejpam-5650	339	6	we	we	PRON
ejpam-5650	339	7	have	have	VERB
ejpam-5650	339	8	x	x	X
ejpam-5650	339	9	∈	∈	NOUN
ejpam-5650	339	10	f+(v	f+(v	NOUN
ejpam-5650	339	11	)	)	PUNCT
ejpam-5650	340	1	⊆	⊆	X
ejpam-5650	340	2	τ1τ2	τ1τ2	NOUN
ejpam-5650	340	3	-	-	NOUN
ejpam-5650	340	4	cl(f	cl(f	NOUN
ejpam-5650	340	5	+	+	NOUN
ejpam-5650	340	6	(	(	PUNCT
ejpam-5650	340	7	v	v	NOUN
ejpam-5650	340	8	)	)	PUNCT
ejpam-5650	340	9	)	)	PUNCT
ejpam-5650	340	10	and	and	CCONJ
ejpam-5650	340	11	hence	hence	ADV
ejpam-5650	340	12	x	x	X
ejpam-5650	340	13	∈	∈	PRON
ejpam-5650	340	14	τ1τ2	τ1τ2	NOUN
ejpam-5650	340	15	-	-	ADJ
ejpam-5650	340	16	fr(f	fr(f	PUNCT
ejpam-5650	340	17	+	+	ADJ
ejpam-5650	340	18	(	(	PUNCT
ejpam-5650	340	19	v	v	NOUN
ejpam-5650	340	20	)	)	PUNCT
ejpam-5650	340	21	)	)	PUNCT
ejpam-5650	340	22	.	.	PUNCT
ejpam-5650	341	1	conversely	conversely	ADV
ejpam-5650	341	2	,	,	PUNCT
ejpam-5650	341	3	suppose	suppose	VERB
ejpam-5650	341	4	that	that	SCONJ
ejpam-5650	341	5	v	v	NOUN
ejpam-5650	341	6	is	be	AUX
ejpam-5650	341	7	a	a	DET
ejpam-5650	341	8	(	(	PUNCT
ejpam-5650	341	9	σ1	σ1	NOUN
ejpam-5650	341	10	,	,	PUNCT
ejpam-5650	341	11	σ2)r	σ2)r	NOUN
ejpam-5650	341	12	-	-	PUNCT
ejpam-5650	341	13	open	open	ADJ
ejpam-5650	341	14	set	set	NOUN
ejpam-5650	341	15	of	of	ADP
ejpam-5650	341	16	y	y	PROPN
ejpam-5650	341	17	containing	contain	VERB
ejpam-5650	341	18	f	f	PROPN
ejpam-5650	341	19	(	(	PUNCT
ejpam-5650	341	20	x	x	NOUN
ejpam-5650	341	21	)	)	PUNCT
ejpam-5650	341	22	and	and	CCONJ
ejpam-5650	341	23	having	have	VERB
ejpam-5650	341	24	n	n	PRON
ejpam-5650	341	25	(	(	PUNCT
ejpam-5650	341	26	σ1	σ1	PROPN
ejpam-5650	341	27	,	,	PUNCT
ejpam-5650	341	28	σ2)-closed	σ2)-close	VERB
ejpam-5650	341	29	complement	complement	NOUN
ejpam-5650	341	30	such	such	ADJ
ejpam-5650	341	31	that	that	SCONJ
ejpam-5650	341	32	x	x	PUNCT
ejpam-5650	341	33	∈	∈	PRON
ejpam-5650	341	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	341	35	-	-	ADJ
ejpam-5650	341	36	fr(f	fr(f	PUNCT
ejpam-5650	341	37	+	+	ADJ
ejpam-5650	341	38	(	(	PUNCT
ejpam-5650	341	39	v	v	NOUN
ejpam-5650	341	40	)	)	PUNCT
ejpam-5650	341	41	)	)	PUNCT
ejpam-5650	341	42	.	.	PUNCT
ejpam-5650	342	1	if	if	SCONJ
ejpam-5650	342	2	f	f	PROPN
ejpam-5650	342	3	is	be	AUX
ejpam-5650	342	4	upper	upper	ADJ
ejpam-5650	342	5	almost	almost	ADV
ejpam-5650	342	6	nearly	nearly	ADV
ejpam-5650	342	7	(	(	PUNCT
ejpam-5650	342	8	τ1	τ1	NOUN
ejpam-5650	342	9	,	,	PUNCT
ejpam-5650	342	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	342	11	at	at	ADP
ejpam-5650	342	12	x	x	SYM
ejpam-5650	342	13	∈	∈	PROPN
ejpam-5650	342	14	x.	x.	NOUN
ejpam-5650	342	15	then	then	ADV
ejpam-5650	342	16	by	by	ADP
ejpam-5650	342	17	theorem	theorem	NOUN
ejpam-5650	342	18	1	1	NUM
ejpam-5650	342	19	,	,	PUNCT
ejpam-5650	342	20	we	we	PRON
ejpam-5650	342	21	have	have	VERB
ejpam-5650	342	22	x	x	PART
ejpam-5650	342	23	∈	∈	PRON
ejpam-5650	342	24	τ1τ2	τ1τ2	NOUN
ejpam-5650	342	25	-	-	NUM
ejpam-5650	342	26	int(f	int(f	VERB
ejpam-5650	342	27	+	+	ADJ
ejpam-5650	342	28	(	(	PUNCT
ejpam-5650	342	29	v	v	NOUN
ejpam-5650	342	30	)	)	PUNCT
ejpam-5650	342	31	)	)	PUNCT
ejpam-5650	342	32	.	.	PUNCT
ejpam-5650	343	1	this	this	PRON
ejpam-5650	343	2	is	be	AUX
ejpam-5650	343	3	a	a	DET
ejpam-5650	343	4	contradiction	contradiction	NOUN
ejpam-5650	343	5	and	and	CCONJ
ejpam-5650	343	6	hence	hence	ADV
ejpam-5650	343	7	f	f	PROPN
ejpam-5650	343	8	is	be	AUX
ejpam-5650	343	9	not	not	PART
ejpam-5650	343	10	upper	upper	ADJ
ejpam-5650	343	11	almost	almost	ADV
ejpam-5650	343	12	nearly	nearly	ADV
ejpam-5650	343	13	(	(	PUNCT
ejpam-5650	343	14	τ1	τ1	NOUN
ejpam-5650	343	15	,	,	PUNCT
ejpam-5650	343	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	343	17	at	at	ADP
ejpam-5650	343	18	x.	x.	NOUN
ejpam-5650	343	19	theorem	theorem	VERB
ejpam-5650	343	20	14	14	NUM
ejpam-5650	343	21	.	.	PUNCT
ejpam-5650	344	1	the	the	DET
ejpam-5650	344	2	set	set	NOUN
ejpam-5650	344	3	of	of	ADP
ejpam-5650	344	4	all	all	DET
ejpam-5650	344	5	points	point	NOUN
ejpam-5650	344	6	x	x	PUNCT
ejpam-5650	344	7	of	of	ADP
ejpam-5650	344	8	x	x	SYM
ejpam-5650	344	9	at	at	ADP
ejpam-5650	344	10	which	which	PRON
ejpam-5650	344	11	a	a	DET
ejpam-5650	344	12	multifunction	multifunction	NOUN
ejpam-5650	345	1	f	f	NOUN
ejpam-5650	345	2	:	:	PUNCT
ejpam-5650	345	3	(	(	PUNCT
ejpam-5650	345	4	x	x	NOUN
ejpam-5650	345	5	,	,	PUNCT
ejpam-5650	345	6	τ1	τ1	NOUN
ejpam-5650	345	7	,	,	PUNCT
ejpam-5650	345	8	τ2	τ2	NOUN
ejpam-5650	345	9	)	)	PUNCT
ejpam-5650	345	10	→	→	SYM
ejpam-5650	345	11	(	(	PUNCT
ejpam-5650	345	12	y	y	PROPN
ejpam-5650	345	13	,	,	PUNCT
ejpam-5650	345	14	σ1	σ1	PROPN
ejpam-5650	345	15	,	,	PUNCT
ejpam-5650	345	16	σ2	σ2	PROPN
ejpam-5650	345	17	)	)	PUNCT
ejpam-5650	345	18	is	be	AUX
ejpam-5650	345	19	not	not	PART
ejpam-5650	345	20	lower	low	ADJ
ejpam-5650	345	21	almost	almost	ADV
ejpam-5650	345	22	nearly	nearly	ADV
ejpam-5650	345	23	(	(	PUNCT
ejpam-5650	345	24	τ1	τ1	NOUN
ejpam-5650	345	25	,	,	PUNCT
ejpam-5650	345	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	345	27	is	be	AUX
ejpam-5650	345	28	identical	identical	ADJ
ejpam-5650	345	29	with	with	ADP
ejpam-5650	345	30	the	the	DET
ejpam-5650	345	31	union	union	NOUN
ejpam-5650	345	32	of	of	ADP
ejpam-5650	345	33	the	the	DET
ejpam-5650	345	34	τ1τ2	τ1τ2	NOUN
ejpam-5650	345	35	-	-	NOUN
ejpam-5650	345	36	frontier	frontier	NOUN
ejpam-5650	345	37	of	of	ADP
ejpam-5650	345	38	the	the	DET
ejpam-5650	345	39	lower	low	ADJ
ejpam-5650	345	40	inverse	inverse	NOUN
ejpam-5650	345	41	images	image	NOUN
ejpam-5650	345	42	of	of	ADP
ejpam-5650	345	43	(	(	PUNCT
ejpam-5650	345	44	σ1	σ1	PROPN
ejpam-5650	345	45	,	,	PUNCT
ejpam-5650	345	46	σ2)r	σ2)r	NOUN
ejpam-5650	345	47	-	-	PUNCT
ejpam-5650	345	48	open	open	ADJ
ejpam-5650	345	49	sets	set	NOUN
ejpam-5650	345	50	meeting	meet	VERB
ejpam-5650	345	51	f	f	X
ejpam-5650	345	52	(	(	PUNCT
ejpam-5650	345	53	x	x	NOUN
ejpam-5650	345	54	)	)	PUNCT
ejpam-5650	345	55	and	and	CCONJ
ejpam-5650	345	56	having	have	VERB
ejpam-5650	345	57	n	n	PRON
ejpam-5650	345	58	(	(	PUNCT
ejpam-5650	345	59	σ1	σ1	PROPN
ejpam-5650	345	60	,	,	PUNCT
ejpam-5650	345	61	σ2)closed	σ2)close	VERB
ejpam-5650	345	62	complement	complement	NOUN
ejpam-5650	345	63	.	.	PUNCT
ejpam-5650	346	1	n.	n.	PROPN
ejpam-5650	346	2	chutiman	chutiman	PROPN
ejpam-5650	346	3	,	,	PUNCT
ejpam-5650	346	4	a.	a.	PROPN
ejpam-5650	346	5	sama	sama	PROPN
ejpam-5650	346	6	-	-	PUNCT
ejpam-5650	346	7	ae	ae	PROPN
ejpam-5650	346	8	,	,	PUNCT
ejpam-5650	346	9	c.	c.	PROPN
ejpam-5650	346	10	boonpok	boonpok	PROPN
ejpam-5650	346	11	/	/	SYM
ejpam-5650	346	12	eur	eur	PROPN
ejpam-5650	346	13	.	.	PUNCT
ejpam-5650	347	1	j.	j.	PROPN
ejpam-5650	347	2	pure	pure	PROPN
ejpam-5650	347	3	appl	appl	PROPN
ejpam-5650	347	4	.	.	PROPN
ejpam-5650	347	5	math	math	PROPN
ejpam-5650	347	6	,	,	PUNCT
ejpam-5650	347	7	18	18	NUM
ejpam-5650	347	8	(	(	PUNCT
ejpam-5650	347	9	1	1	NUM
ejpam-5650	347	10	)	)	PUNCT
ejpam-5650	347	11	(	(	PUNCT
ejpam-5650	347	12	2025	2025	NUM
ejpam-5650	347	13	)	)	PUNCT
ejpam-5650	347	14	,	,	PUNCT
ejpam-5650	347	15	5650	5650	NUM
ejpam-5650	347	16	14	14	NUM
ejpam-5650	347	17	of	of	ADP
ejpam-5650	347	18	18	18	NUM
ejpam-5650	347	19	proof	proof	NOUN
ejpam-5650	347	20	.	.	PUNCT
ejpam-5650	348	1	the	the	DET
ejpam-5650	348	2	proof	proof	NOUN
ejpam-5650	348	3	is	be	AUX
ejpam-5650	348	4	similar	similar	ADJ
ejpam-5650	348	5	to	to	ADP
ejpam-5650	348	6	that	that	PRON
ejpam-5650	348	7	of	of	ADP
ejpam-5650	348	8	theorem	theorem	ADJ
ejpam-5650	348	9	13	13	NUM
ejpam-5650	348	10	.	.	PUNCT
ejpam-5650	348	11	recall	recall	VERB
ejpam-5650	348	12	that	that	SCONJ
ejpam-5650	348	13	a	a	DET
ejpam-5650	348	14	subset	subset	NOUN
ejpam-5650	348	15	a	a	PRON
ejpam-5650	348	16	of	of	ADP
ejpam-5650	348	17	a	a	DET
ejpam-5650	348	18	bitopological	bitopological	ADJ
ejpam-5650	348	19	space	space	NOUN
ejpam-5650	348	20	(	(	PUNCT
ejpam-5650	348	21	x	x	NOUN
ejpam-5650	348	22	,	,	PUNCT
ejpam-5650	348	23	τ1	τ1	NOUN
ejpam-5650	348	24	,	,	PUNCT
ejpam-5650	348	25	τ2	τ2	NOUN
ejpam-5650	348	26	)	)	PUNCT
ejpam-5650	348	27	is	be	AUX
ejpam-5650	348	28	said	say	VERB
ejpam-5650	348	29	to	to	PART
ejpam-5650	348	30	be	be	AUX
ejpam-5650	348	31	τ1τ2	τ1τ2	NOUN
ejpam-5650	348	32	-	-	ADJ
ejpam-5650	348	33	clopen	clopen	ADJ
ejpam-5650	348	34	[	[	X
ejpam-5650	348	35	29	29	NUM
ejpam-5650	348	36	]	]	X
ejpam-5650	348	37	if	if	SCONJ
ejpam-5650	348	38	a	a	PRON
ejpam-5650	348	39	is	be	AUX
ejpam-5650	348	40	both	both	PRON
ejpam-5650	348	41	τ1τ2	τ1τ2	ADJ
ejpam-5650	348	42	-	-	ADJ
ejpam-5650	348	43	open	open	ADJ
ejpam-5650	348	44	and	and	CCONJ
ejpam-5650	348	45	τ1τ2	τ1τ2	NOUN
ejpam-5650	348	46	-	-	ADJ
ejpam-5650	348	47	closed	closed	ADJ
ejpam-5650	348	48	.	.	PUNCT
ejpam-5650	349	1	definition	definition	NOUN
ejpam-5650	349	2	4	4	NUM
ejpam-5650	349	3	.	.	PUNCT
ejpam-5650	350	1	[	[	X
ejpam-5650	350	2	29	29	NUM
ejpam-5650	350	3	]	]	PUNCT
ejpam-5650	350	4	a	a	DET
ejpam-5650	350	5	bitopological	bitopological	ADJ
ejpam-5650	350	6	space	space	NOUN
ejpam-5650	350	7	(	(	PUNCT
ejpam-5650	350	8	x	x	NOUN
ejpam-5650	350	9	,	,	PUNCT
ejpam-5650	350	10	τ1	τ1	NOUN
ejpam-5650	350	11	,	,	PUNCT
ejpam-5650	350	12	τ2	τ2	NOUN
ejpam-5650	350	13	)	)	PUNCT
ejpam-5650	350	14	is	be	AUX
ejpam-5650	350	15	said	say	VERB
ejpam-5650	350	16	to	to	PART
ejpam-5650	350	17	be	be	AUX
ejpam-5650	350	18	τ1τ2	τ1τ2	NOUN
ejpam-5650	350	19	-	-	ADJ
ejpam-5650	350	20	connected	connected	ADJ
ejpam-5650	350	21	if	if	SCONJ
ejpam-5650	350	22	x	x	PRON
ejpam-5650	350	23	can	can	AUX
ejpam-5650	350	24	not	not	PART
ejpam-5650	350	25	be	be	AUX
ejpam-5650	350	26	written	write	VERB
ejpam-5650	350	27	as	as	ADP
ejpam-5650	350	28	the	the	DET
ejpam-5650	350	29	union	union	NOUN
ejpam-5650	350	30	of	of	ADP
ejpam-5650	350	31	two	two	NUM
ejpam-5650	350	32	disjoint	disjoint	NOUN
ejpam-5650	350	33	nonempty	nonempty	ADJ
ejpam-5650	350	34	τ1τ2	τ1τ2	ADJ
ejpam-5650	350	35	-	-	ADJ
ejpam-5650	350	36	open	open	ADJ
ejpam-5650	350	37	sets	set	NOUN
ejpam-5650	350	38	.	.	PUNCT
ejpam-5650	351	1	definition	definition	NOUN
ejpam-5650	351	2	5	5	NUM
ejpam-5650	351	3	.	.	PUNCT
ejpam-5650	352	1	a	a	DET
ejpam-5650	352	2	bitopological	bitopological	ADJ
ejpam-5650	352	3	space	space	NOUN
ejpam-5650	352	4	(	(	PUNCT
ejpam-5650	352	5	x	x	NOUN
ejpam-5650	352	6	,	,	PUNCT
ejpam-5650	352	7	τ1	τ1	NOUN
ejpam-5650	352	8	,	,	PUNCT
ejpam-5650	352	9	τ2	τ2	NOUN
ejpam-5650	352	10	)	)	PUNCT
ejpam-5650	352	11	is	be	AUX
ejpam-5650	352	12	said	say	VERB
ejpam-5650	352	13	to	to	PART
ejpam-5650	352	14	be	be	AUX
ejpam-5650	352	15	n	n	PRON
ejpam-5650	352	16	(	(	PUNCT
ejpam-5650	352	17	τ1	τ1	NOUN
ejpam-5650	352	18	,	,	PUNCT
ejpam-5650	352	19	τ2)-connected	τ2)-connecte	VERB
ejpam-5650	352	20	if	if	SCONJ
ejpam-5650	352	21	x	x	PRON
ejpam-5650	352	22	can	can	AUX
ejpam-5650	352	23	not	not	PART
ejpam-5650	352	24	be	be	AUX
ejpam-5650	352	25	written	write	VERB
ejpam-5650	352	26	as	as	ADP
ejpam-5650	352	27	the	the	DET
ejpam-5650	352	28	union	union	NOUN
ejpam-5650	352	29	of	of	ADP
ejpam-5650	352	30	two	two	NUM
ejpam-5650	352	31	disjoint	disjoint	NOUN
ejpam-5650	352	32	nonempty	nonempty	ADJ
ejpam-5650	352	33	τ1τ2	τ1τ2	ADJ
ejpam-5650	352	34	-	-	ADJ
ejpam-5650	352	35	open	open	ADJ
ejpam-5650	352	36	sets	set	NOUN
ejpam-5650	352	37	having	have	VERB
ejpam-5650	352	38	n	n	X
ejpam-5650	352	39	(	(	PUNCT
ejpam-5650	352	40	τ1	τ1	PROPN
ejpam-5650	352	41	,	,	PUNCT
ejpam-5650	352	42	τ2)closed	τ2)closed	ADJ
ejpam-5650	352	43	complements	complement	NOUN
ejpam-5650	352	44	.	.	PUNCT
ejpam-5650	353	1	theorem	theorem	NOUN
ejpam-5650	353	2	15	15	NUM
ejpam-5650	353	3	.	.	PUNCT
ejpam-5650	354	1	if	if	SCONJ
ejpam-5650	354	2	f	f	PROPN
ejpam-5650	354	3	:	:	PUNCT
ejpam-5650	354	4	(	(	PUNCT
ejpam-5650	354	5	x	x	NOUN
ejpam-5650	354	6	,	,	PUNCT
ejpam-5650	354	7	τ1	τ1	NOUN
ejpam-5650	354	8	,	,	PUNCT
ejpam-5650	354	9	τ2	τ2	NOUN
ejpam-5650	354	10	)	)	PUNCT
ejpam-5650	354	11	→	→	SYM
ejpam-5650	354	12	(	(	PUNCT
ejpam-5650	354	13	y	y	PROPN
ejpam-5650	354	14	,	,	PUNCT
ejpam-5650	354	15	σ1	σ1	PROPN
ejpam-5650	354	16	,	,	PUNCT
ejpam-5650	354	17	σ2	σ2	PROPN
ejpam-5650	354	18	)	)	PUNCT
ejpam-5650	354	19	is	be	AUX
ejpam-5650	354	20	an	an	DET
ejpam-5650	354	21	upper	upper	ADJ
ejpam-5650	354	22	or	or	CCONJ
ejpam-5650	354	23	lower	low	ADJ
ejpam-5650	354	24	almost	almost	ADV
ejpam-5650	354	25	nearly	nearly	ADV
ejpam-5650	354	26	(	(	PUNCT
ejpam-5650	354	27	τ1	τ1	NOUN
ejpam-5650	354	28	,	,	PUNCT
ejpam-5650	354	29	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	354	30	surjective	surjective	ADJ
ejpam-5650	354	31	multifunction	multifunction	NOUN
ejpam-5650	354	32	such	such	ADJ
ejpam-5650	354	33	that	that	SCONJ
ejpam-5650	354	34	f	f	PROPN
ejpam-5650	354	35	(	(	PUNCT
ejpam-5650	354	36	x	x	X
ejpam-5650	354	37	)	)	PUNCT
ejpam-5650	354	38	is	be	AUX
ejpam-5650	354	39	σ1σ2	σ1σ2	NOUN
ejpam-5650	354	40	-	-	PUNCT
ejpam-5650	354	41	connected	connected	ADJ
ejpam-5650	354	42	for	for	ADP
ejpam-5650	354	43	each	each	DET
ejpam-5650	354	44	x	x	SYM
ejpam-5650	354	45	∈	∈	PROPN
ejpam-5650	354	46	x	x	X
ejpam-5650	354	47	and	and	CCONJ
ejpam-5650	354	48	(	(	PUNCT
ejpam-5650	354	49	x	x	NOUN
ejpam-5650	354	50	,	,	PUNCT
ejpam-5650	354	51	τ1	τ1	NOUN
ejpam-5650	354	52	,	,	PUNCT
ejpam-5650	354	53	τ2	τ2	NOUN
ejpam-5650	354	54	)	)	PUNCT
ejpam-5650	354	55	is	be	AUX
ejpam-5650	354	56	τ1τ2	τ1τ2	NOUN
ejpam-5650	354	57	-	-	ADJ
ejpam-5650	354	58	connected	connected	ADJ
ejpam-5650	354	59	,	,	PUNCT
ejpam-5650	354	60	then	then	ADV
ejpam-5650	354	61	(	(	PUNCT
ejpam-5650	354	62	y	y	PROPN
ejpam-5650	354	63	,	,	PUNCT
ejpam-5650	354	64	σ1	σ1	PROPN
ejpam-5650	354	65	,	,	PUNCT
ejpam-5650	354	66	σ2	σ2	PROPN
ejpam-5650	354	67	)	)	PUNCT
ejpam-5650	354	68	is	be	AUX
ejpam-5650	354	69	n	n	PROPN
ejpam-5650	354	70	(	(	PUNCT
ejpam-5650	354	71	σ1	σ1	PROPN
ejpam-5650	354	72	,	,	PUNCT
ejpam-5650	354	73	σ2)-connected	σ2)-connecte	VERB
ejpam-5650	354	74	.	.	PUNCT
ejpam-5650	355	1	proof	proof	NOUN
ejpam-5650	355	2	.	.	PUNCT
ejpam-5650	356	1	suppose	suppose	VERB
ejpam-5650	356	2	that	that	SCONJ
ejpam-5650	356	3	(	(	PUNCT
ejpam-5650	356	4	y	y	PROPN
ejpam-5650	356	5	,	,	PUNCT
ejpam-5650	356	6	σ1	σ1	PROPN
ejpam-5650	356	7	,	,	PUNCT
ejpam-5650	356	8	σ2	σ2	PROPN
ejpam-5650	356	9	)	)	PUNCT
ejpam-5650	356	10	is	be	AUX
ejpam-5650	356	11	not	not	PART
ejpam-5650	356	12	n	n	PROPN
ejpam-5650	356	13	(	(	PUNCT
ejpam-5650	356	14	σ1	σ1	PROPN
ejpam-5650	356	15	,	,	PUNCT
ejpam-5650	356	16	σ2)-connected	σ2)-connecte	VERB
ejpam-5650	356	17	.	.	PUNCT
ejpam-5650	357	1	there	there	PRON
ejpam-5650	357	2	exist	exist	VERB
ejpam-5650	357	3	nonempty	nonempty	ADJ
ejpam-5650	357	4	σ1σ2	σ1σ2	NOUN
ejpam-5650	357	5	-	-	ADJ
ejpam-5650	357	6	open	open	ADJ
ejpam-5650	357	7	sets	set	NOUN
ejpam-5650	357	8	u	u	NOUN
ejpam-5650	357	9	and	and	CCONJ
ejpam-5650	357	10	v	v	NOUN
ejpam-5650	357	11	of	of	ADP
ejpam-5650	357	12	y	y	PROPN
ejpam-5650	357	13	having	have	VERB
ejpam-5650	357	14	n	n	PROPN
ejpam-5650	357	15	(	(	PUNCT
ejpam-5650	357	16	σ1	σ1	PROPN
ejpam-5650	357	17	,	,	PUNCT
ejpam-5650	357	18	σ2)-closed	σ2)-close	VERB
ejpam-5650	357	19	complements	complement	NOUN
ejpam-5650	357	20	such	such	ADJ
ejpam-5650	357	21	that	that	SCONJ
ejpam-5650	357	22	u	u	PROPN
ejpam-5650	357	23	∩	∩	NOUN
ejpam-5650	357	24	v	v	NOUN
ejpam-5650	357	25	=	=	NOUN
ejpam-5650	357	26	∅	∅	NOUN
ejpam-5650	357	27	and	and	CCONJ
ejpam-5650	357	28	u	u	NOUN
ejpam-5650	357	29	∪	∪	NOUN
ejpam-5650	357	30	v	v	ADP
ejpam-5650	357	31	=	=	SYM
ejpam-5650	357	32	y	y	PROPN
ejpam-5650	357	33	.	.	PUNCT
ejpam-5650	358	1	since	since	SCONJ
ejpam-5650	358	2	f	f	PROPN
ejpam-5650	358	3	(	(	PUNCT
ejpam-5650	358	4	x	x	X
ejpam-5650	358	5	)	)	PUNCT
ejpam-5650	358	6	is	be	AUX
ejpam-5650	358	7	σ1σ2	σ1σ2	NOUN
ejpam-5650	358	8	-	-	PUNCT
ejpam-5650	358	9	connected	connected	ADJ
ejpam-5650	358	10	for	for	ADP
ejpam-5650	358	11	each	each	DET
ejpam-5650	358	12	x	x	SYM
ejpam-5650	358	13	∈	∈	PROPN
ejpam-5650	358	14	x	x	NOUN
ejpam-5650	358	15	,	,	PUNCT
ejpam-5650	358	16	either	either	CCONJ
ejpam-5650	358	17	f	f	PROPN
ejpam-5650	358	18	(	(	PUNCT
ejpam-5650	358	19	x	x	X
ejpam-5650	358	20	)	)	PUNCT
ejpam-5650	358	21	⊆	⊆	NUM
ejpam-5650	358	22	u	u	NOUN
ejpam-5650	358	23	or	or	CCONJ
ejpam-5650	358	24	f	f	PROPN
ejpam-5650	358	25	(	(	PUNCT
ejpam-5650	358	26	x	x	NOUN
ejpam-5650	358	27	)	)	PUNCT
ejpam-5650	358	28	⊆	⊆	NUM
ejpam-5650	358	29	v	v	NOUN
ejpam-5650	358	30	.	.	PUNCT
ejpam-5650	359	1	if	if	SCONJ
ejpam-5650	359	2	x	x	SYM
ejpam-5650	359	3	∈	∈	PROPN
ejpam-5650	359	4	f+(u∪v	f+(u∪v	PROPN
ejpam-5650	359	5	)	)	PUNCT
ejpam-5650	359	6	,	,	PUNCT
ejpam-5650	359	7	then	then	ADV
ejpam-5650	359	8	f	f	X
ejpam-5650	359	9	(	(	PUNCT
ejpam-5650	359	10	x	x	X
ejpam-5650	359	11	)	)	PUNCT
ejpam-5650	359	12	⊆	⊆	NUM
ejpam-5650	359	13	u∪v	u∪v	NOUN
ejpam-5650	359	14	and	and	CCONJ
ejpam-5650	359	15	hence	hence	ADV
ejpam-5650	359	16	x	x	PART
ejpam-5650	359	17	∈	∈	NOUN
ejpam-5650	359	18	f+(u)∪f+(v	f+(u)∪f+(v	NOUN
ejpam-5650	359	19	)	)	PUNCT
ejpam-5650	359	20	.	.	PUNCT
ejpam-5650	360	1	moreover	moreover	ADV
ejpam-5650	360	2	,	,	PUNCT
ejpam-5650	360	3	since	since	SCONJ
ejpam-5650	360	4	f	f	PROPN
ejpam-5650	360	5	is	be	AUX
ejpam-5650	360	6	surjective	surjective	ADJ
ejpam-5650	360	7	,	,	PUNCT
ejpam-5650	360	8	there	there	PRON
ejpam-5650	360	9	exist	exist	VERB
ejpam-5650	360	10	x	x	PUNCT
ejpam-5650	360	11	and	and	CCONJ
ejpam-5650	360	12	y	y	PROPN
ejpam-5650	360	13	in	in	ADP
ejpam-5650	360	14	x	x	PUNCT
ejpam-5650	360	15	such	such	ADJ
ejpam-5650	360	16	that	that	SCONJ
ejpam-5650	360	17	f	f	PROPN
ejpam-5650	360	18	(	(	PUNCT
ejpam-5650	360	19	x	x	X
ejpam-5650	360	20	)	)	PUNCT
ejpam-5650	360	21	⊆	⊆	NUM
ejpam-5650	360	22	u	u	NOUN
ejpam-5650	360	23	and	and	CCONJ
ejpam-5650	360	24	f	f	PROPN
ejpam-5650	360	25	(	(	PUNCT
ejpam-5650	360	26	y	y	PROPN
ejpam-5650	360	27	)	)	PUNCT
ejpam-5650	360	28	⊆	⊆	NUM
ejpam-5650	360	29	v	v	NOUN
ejpam-5650	360	30	;	;	PUNCT
ejpam-5650	360	31	hence	hence	ADV
ejpam-5650	360	32	x	x	SYM
ejpam-5650	360	33	∈	∈	PROPN
ejpam-5650	360	34	f+(u	f+(u	NUM
ejpam-5650	360	35	)	)	PUNCT
ejpam-5650	360	36	and	and	CCONJ
ejpam-5650	360	37	y	y	PROPN
ejpam-5650	360	38	∈	∈	PROPN
ejpam-5650	360	39	f+(v	f+(v	PROPN
ejpam-5650	360	40	)	)	PUNCT
ejpam-5650	360	41	.	.	PUNCT
ejpam-5650	361	1	therefore	therefore	ADV
ejpam-5650	361	2	,	,	PUNCT
ejpam-5650	361	3	we	we	PRON
ejpam-5650	361	4	obtain	obtain	VERB
ejpam-5650	361	5	the	the	DET
ejpam-5650	361	6	following	following	NOUN
ejpam-5650	361	7	:	:	PUNCT
ejpam-5650	361	8	(	(	PUNCT
ejpam-5650	361	9	1	1	X
ejpam-5650	361	10	)	)	PUNCT
ejpam-5650	361	11	f+(u	f+(u	NUM
ejpam-5650	361	12	)	)	PUNCT
ejpam-5650	361	13	∪	∪	ADP
ejpam-5650	361	14	f+(v	f+(v	NOUN
ejpam-5650	361	15	)	)	PUNCT
ejpam-5650	362	1	=	=	PUNCT
ejpam-5650	362	2	x	x	X
ejpam-5650	362	3	;	;	PUNCT
ejpam-5650	362	4	(	(	PUNCT
ejpam-5650	362	5	2	2	X
ejpam-5650	362	6	)	)	PUNCT
ejpam-5650	362	7	f+(u	f+(u	NUM
ejpam-5650	362	8	)	)	PUNCT
ejpam-5650	362	9	∩	∩	NOUN
ejpam-5650	362	10	f+(v	f+(v	NOUN
ejpam-5650	362	11	)	)	PUNCT
ejpam-5650	362	12	=	=	NOUN
ejpam-5650	362	13	∅	∅	NOUN
ejpam-5650	362	14	;	;	PUNCT
ejpam-5650	362	15	(	(	PUNCT
ejpam-5650	362	16	3	3	X
ejpam-5650	362	17	)	)	PUNCT
ejpam-5650	362	18	f+(u	f+(u	NUM
ejpam-5650	362	19	)	)	PUNCT
ejpam-5650	362	20	̸=	̸=	PROPN
ejpam-5650	362	21	∅	∅	NOUN
ejpam-5650	362	22	and	and	CCONJ
ejpam-5650	362	23	f+(v	f+(v	NUM
ejpam-5650	362	24	)	)	PUNCT
ejpam-5650	363	1	̸=	̸=	PROPN
ejpam-5650	363	2	∅.	∅.	ADP
ejpam-5650	363	3	next	next	ADV
ejpam-5650	363	4	,	,	PUNCT
ejpam-5650	363	5	we	we	PRON
ejpam-5650	363	6	show	show	VERB
ejpam-5650	363	7	that	that	PRON
ejpam-5650	363	8	f+(u	f+(u	NUM
ejpam-5650	363	9	)	)	PUNCT
ejpam-5650	363	10	and	and	CCONJ
ejpam-5650	363	11	f+(v	f+(v	NUM
ejpam-5650	363	12	)	)	PUNCT
ejpam-5650	363	13	are	be	AUX
ejpam-5650	363	14	τ1τ2	τ1τ2	NOUN
ejpam-5650	363	15	-	-	ADJ
ejpam-5650	363	16	open	open	ADJ
ejpam-5650	363	17	in	in	ADP
ejpam-5650	363	18	x.	x.	PROPN
ejpam-5650	363	19	(	(	PUNCT
ejpam-5650	363	20	i	i	NOUN
ejpam-5650	363	21	)	)	PUNCT
ejpam-5650	363	22	let	let	VERB
ejpam-5650	363	23	f	f	PRON
ejpam-5650	363	24	be	be	AUX
ejpam-5650	363	25	upper	upper	ADJ
ejpam-5650	363	26	almost	almost	ADV
ejpam-5650	363	27	nearly	nearly	ADV
ejpam-5650	363	28	(	(	PUNCT
ejpam-5650	363	29	τ1	τ1	NOUN
ejpam-5650	363	30	,	,	PUNCT
ejpam-5650	363	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	363	32	.	.	PUNCT
ejpam-5650	364	1	since	since	SCONJ
ejpam-5650	364	2	u	u	PROPN
ejpam-5650	364	3	and	and	CCONJ
ejpam-5650	364	4	v	v	NOUN
ejpam-5650	364	5	are	be	AUX
ejpam-5650	364	6	σ1σ2	σ1σ2	NOUN
ejpam-5650	364	7	-	-	PUNCT
ejpam-5650	364	8	clopen	clopen	ADJ
ejpam-5650	364	9	in	in	ADP
ejpam-5650	364	10	y	y	PROPN
ejpam-5650	364	11	,	,	PUNCT
ejpam-5650	364	12	σ1σ2	σ1σ2	NOUN
ejpam-5650	364	13	-	-	PUNCT
ejpam-5650	364	14	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	364	15	-	-	PUNCT
ejpam-5650	364	16	cl(u	cl(u	NUM
ejpam-5650	364	17	)	)	PUNCT
ejpam-5650	364	18	)	)	PUNCT
ejpam-5650	365	1	=	=	SYM
ejpam-5650	365	2	u	u	NOUN
ejpam-5650	365	3	and	and	CCONJ
ejpam-5650	365	4	σ1σ2	σ1σ2	NOUN
ejpam-5650	365	5	-	-	PUNCT
ejpam-5650	365	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5650	365	7	-	-	PUNCT
ejpam-5650	365	8	cl(v	cl(v	NOUN
ejpam-5650	365	9	)	)	PUNCT
ejpam-5650	365	10	)	)	PUNCT
ejpam-5650	366	1	=	=	SYM
ejpam-5650	366	2	v	v	X
ejpam-5650	366	3	.	.	PUNCT
ejpam-5650	367	1	thus	thus	ADV
ejpam-5650	367	2	,	,	PUNCT
ejpam-5650	367	3	u	u	NOUN
ejpam-5650	367	4	and	and	CCONJ
ejpam-5650	367	5	v	v	NOUN
ejpam-5650	367	6	are	be	AUX
ejpam-5650	367	7	(	(	PUNCT
ejpam-5650	367	8	σ1	σ1	NOUN
ejpam-5650	367	9	,	,	PUNCT
ejpam-5650	367	10	σ2)r	σ2)r	NOUN
ejpam-5650	367	11	-	-	PUNCT
ejpam-5650	367	12	open	open	ADJ
ejpam-5650	367	13	sets	set	NOUN
ejpam-5650	367	14	having	have	VERB
ejpam-5650	367	15	n	n	PRON
ejpam-5650	367	16	(	(	PUNCT
ejpam-5650	367	17	σ1	σ1	PROPN
ejpam-5650	367	18	,	,	PUNCT
ejpam-5650	367	19	σ2)closed	σ2)close	VERB
ejpam-5650	367	20	complements	complement	NOUN
ejpam-5650	367	21	.	.	PUNCT
ejpam-5650	368	1	since	since	SCONJ
ejpam-5650	368	2	f	f	PROPN
ejpam-5650	368	3	is	be	AUX
ejpam-5650	368	4	upper	upper	ADJ
ejpam-5650	368	5	almost	almost	ADV
ejpam-5650	368	6	nearly	nearly	ADV
ejpam-5650	368	7	(	(	PUNCT
ejpam-5650	368	8	τ1	τ1	NOUN
ejpam-5650	368	9	,	,	PUNCT
ejpam-5650	368	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	368	11	,	,	PUNCT
ejpam-5650	368	12	by	by	ADP
ejpam-5650	368	13	theorem	theorem	NOUN
ejpam-5650	368	14	3	3	NUM
ejpam-5650	368	15	f+(u	f+(u	NUM
ejpam-5650	368	16	)	)	PUNCT
ejpam-5650	368	17	and	and	CCONJ
ejpam-5650	368	18	f+(v	f+(v	NUM
ejpam-5650	368	19	)	)	PUNCT
ejpam-5650	368	20	are	be	AUX
ejpam-5650	368	21	τ1τ2	τ1τ2	ADJ
ejpam-5650	368	22	-	-	ADJ
ejpam-5650	368	23	open	open	ADJ
ejpam-5650	368	24	sets	set	NOUN
ejpam-5650	368	25	.	.	PUNCT
ejpam-5650	369	1	(	(	PUNCT
ejpam-5650	369	2	ii	ii	NOUN
ejpam-5650	369	3	)	)	PUNCT
ejpam-5650	369	4	let	let	VERB
ejpam-5650	369	5	f	f	PRON
ejpam-5650	369	6	be	be	AUX
ejpam-5650	369	7	lower	low	ADJ
ejpam-5650	369	8	almost	almost	ADV
ejpam-5650	369	9	nearly	nearly	ADV
ejpam-5650	369	10	(	(	PUNCT
ejpam-5650	369	11	τ1	τ1	NOUN
ejpam-5650	369	12	,	,	PUNCT
ejpam-5650	369	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	369	14	.	.	PUNCT
ejpam-5650	370	1	by	by	ADP
ejpam-5650	370	2	theorem	theorem	ADJ
ejpam-5650	370	3	4	4	NUM
ejpam-5650	370	4	,	,	PUNCT
ejpam-5650	370	5	f+(u	f+(u	NUM
ejpam-5650	370	6	)	)	PUNCT
ejpam-5650	370	7	is	be	AUX
ejpam-5650	370	8	τ1τ2	τ1τ2	VERB
ejpam-5650	370	9	-	-	ADJ
ejpam-5650	370	10	closed	closed	ADJ
ejpam-5650	370	11	inx	inx	NOUN
ejpam-5650	370	12	because	because	SCONJ
ejpam-5650	370	13	u	u	NOUN
ejpam-5650	370	14	is	be	AUX
ejpam-5650	370	15	σ1σ2	σ1σ2	NOUN
ejpam-5650	370	16	-	-	PUNCT
ejpam-5650	370	17	clopen	clopen	ADJ
ejpam-5650	370	18	in	in	ADP
ejpam-5650	370	19	y	y	PROPN
ejpam-5650	370	20	.	.	PUNCT
ejpam-5650	371	1	therefore	therefore	ADV
ejpam-5650	371	2	,	,	PUNCT
ejpam-5650	371	3	f+(v	f+(v	PROPN
ejpam-5650	371	4	)	)	PUNCT
ejpam-5650	371	5	is	be	AUX
ejpam-5650	371	6	τ1τ2	τ1τ2	NOUN
ejpam-5650	371	7	-	-	ADJ
ejpam-5650	371	8	open	open	ADJ
ejpam-5650	371	9	in	in	ADP
ejpam-5650	371	10	x.	x.	NOUN
ejpam-5650	371	11	similarly	similarly	ADV
ejpam-5650	371	12	,	,	PUNCT
ejpam-5650	371	13	we	we	PRON
ejpam-5650	371	14	have	have	AUX
ejpam-5650	371	15	f+(u	f+(u	PUNCT
ejpam-5650	371	16	)	)	PUNCT
ejpam-5650	371	17	is	be	AUX
ejpam-5650	371	18	τ1τ2	τ1τ2	NOUN
ejpam-5650	371	19	-	-	ADJ
ejpam-5650	371	20	open	open	ADJ
ejpam-5650	371	21	in	in	ADP
ejpam-5650	371	22	x.	x.	NOUN
ejpam-5650	371	23	thus	thus	ADV
ejpam-5650	371	24	,	,	PUNCT
ejpam-5650	371	25	(	(	PUNCT
ejpam-5650	371	26	x	x	NOUN
ejpam-5650	371	27	,	,	PUNCT
ejpam-5650	371	28	τ1	τ1	NOUN
ejpam-5650	371	29	,	,	PUNCT
ejpam-5650	371	30	τ2	τ2	NOUN
ejpam-5650	371	31	)	)	PUNCT
ejpam-5650	371	32	is	be	AUX
ejpam-5650	371	33	not	not	PART
ejpam-5650	371	34	τ1τ2	τ1τ2	ADJ
ejpam-5650	371	35	-	-	VERB
ejpam-5650	371	36	connected	connected	ADJ
ejpam-5650	371	37	.	.	PUNCT
ejpam-5650	372	1	acknowledgements	acknowledgement	NOUN
ejpam-5650	372	2	this	this	DET
ejpam-5650	372	3	research	research	NOUN
ejpam-5650	372	4	project	project	NOUN
ejpam-5650	372	5	was	be	AUX
ejpam-5650	372	6	financially	financially	ADV
ejpam-5650	372	7	supported	support	VERB
ejpam-5650	372	8	by	by	ADP
ejpam-5650	372	9	mahasarakham	mahasarakham	PROPN
ejpam-5650	372	10	university	university	PROPN
ejpam-5650	372	11	.	.	PUNCT
ejpam-5650	373	1	references	reference	NOUN
ejpam-5650	373	2	[	[	X
ejpam-5650	373	3	1	1	NUM
ejpam-5650	373	4	]	]	PUNCT
ejpam-5650	373	5	c.	c.	PROPN
ejpam-5650	373	6	boonpok	boonpok	PROPN
ejpam-5650	373	7	.	.	PUNCT
ejpam-5650	374	1	almost	almost	ADV
ejpam-5650	374	2	(	(	PUNCT
ejpam-5650	374	3	g	g	NOUN
ejpam-5650	374	4	,	,	PUNCT
ejpam-5650	374	5	m)-continuous	m)-continuous	ADJ
ejpam-5650	374	6	functions	function	NOUN
ejpam-5650	374	7	.	.	PUNCT
ejpam-5650	375	1	international	international	ADJ
ejpam-5650	375	2	journal	journal	PROPN
ejpam-5650	375	3	of	of	ADP
ejpam-5650	375	4	mathematical	mathematical	ADJ
ejpam-5650	375	5	analysis	analysis	NOUN
ejpam-5650	375	6	,	,	PUNCT
ejpam-5650	375	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5650	375	8	,	,	PUNCT
ejpam-5650	375	9	2010	2010	NUM
ejpam-5650	375	10	.	.	PUNCT
ejpam-5650	376	1	n.	n.	PROPN
ejpam-5650	376	2	chutiman	chutiman	PROPN
ejpam-5650	376	3	,	,	PUNCT
ejpam-5650	376	4	a.	a.	PROPN
ejpam-5650	376	5	sama	sama	PROPN
ejpam-5650	376	6	-	-	PUNCT
ejpam-5650	376	7	ae	ae	PROPN
ejpam-5650	376	8	,	,	PUNCT
ejpam-5650	376	9	c.	c.	PROPN
ejpam-5650	376	10	boonpok	boonpok	PROPN
ejpam-5650	376	11	/	/	SYM
ejpam-5650	376	12	eur	eur	PROPN
ejpam-5650	376	13	.	.	PUNCT
ejpam-5650	377	1	j.	j.	PROPN
ejpam-5650	377	2	pure	pure	PROPN
ejpam-5650	377	3	appl	appl	PROPN
ejpam-5650	377	4	.	.	PROPN
ejpam-5650	377	5	math	math	PROPN
ejpam-5650	377	6	,	,	PUNCT
ejpam-5650	377	7	18	18	NUM
ejpam-5650	377	8	(	(	PUNCT
ejpam-5650	377	9	1	1	NUM
ejpam-5650	377	10	)	)	PUNCT
ejpam-5650	377	11	(	(	PUNCT
ejpam-5650	377	12	2025	2025	NUM
ejpam-5650	377	13	)	)	PUNCT
ejpam-5650	377	14	,	,	PUNCT
ejpam-5650	377	15	5650	5650	NUM
ejpam-5650	377	16	15	15	NUM
ejpam-5650	377	17	of	of	ADP
ejpam-5650	377	18	18	18	NUM
ejpam-5650	377	19	[	[	SYM
ejpam-5650	377	20	2	2	NUM
ejpam-5650	377	21	]	]	PUNCT
ejpam-5650	377	22	c.	c.	PROPN
ejpam-5650	377	23	boonpok	boonpok	PROPN
ejpam-5650	377	24	.	.	PUNCT
ejpam-5650	378	1	m	m	VERB
ejpam-5650	378	2	-continuous	-continuous	ADJ
ejpam-5650	378	3	functions	function	NOUN
ejpam-5650	378	4	in	in	ADP
ejpam-5650	378	5	biminimal	biminimal	NOUN
ejpam-5650	378	6	structure	structure	NOUN
ejpam-5650	378	7	spaces	space	NOUN
ejpam-5650	378	8	.	.	PUNCT
ejpam-5650	379	1	far	far	PROPN
ejpam-5650	379	2	east	east	PROPN
ejpam-5650	379	3	journal	journal	PROPN
ejpam-5650	379	4	of	of	ADP
ejpam-5650	379	5	mathematical	mathematical	ADJ
ejpam-5650	379	6	sciences	science	NOUN
ejpam-5650	379	7	,	,	PUNCT
ejpam-5650	379	8	43(1):41–58	43(1):41–58	NUM
ejpam-5650	379	9	,	,	PUNCT
ejpam-5650	379	10	2010	2010	NUM
ejpam-5650	379	11	.	.	PUNCT
ejpam-5650	380	1	[	[	X
ejpam-5650	380	2	3	3	X
ejpam-5650	380	3	]	]	PUNCT
ejpam-5650	380	4	c.	c.	PROPN
ejpam-5650	380	5	boonpok	boonpok	PROPN
ejpam-5650	380	6	.	.	PUNCT
ejpam-5650	381	1	on	on	ADP
ejpam-5650	381	2	continuous	continuous	ADJ
ejpam-5650	381	3	multifunctions	multifunction	NOUN
ejpam-5650	381	4	in	in	ADP
ejpam-5650	381	5	ideal	ideal	ADJ
ejpam-5650	381	6	topological	topological	ADJ
ejpam-5650	381	7	spaces	space	NOUN
ejpam-5650	381	8	.	.	PUNCT
ejpam-5650	382	1	lobachevskii	lobachevskii	PROPN
ejpam-5650	382	2	journal	journal	PROPN
ejpam-5650	382	3	of	of	ADP
ejpam-5650	382	4	mathematics	mathematic	NOUN
ejpam-5650	382	5	,	,	PUNCT
ejpam-5650	382	6	40(1):24–35	40(1):24–35	NUM
ejpam-5650	382	7	,	,	PUNCT
ejpam-5650	382	8	2019	2019	NUM
ejpam-5650	382	9	.	.	PUNCT
ejpam-5650	383	1	[	[	X
ejpam-5650	383	2	4	4	NUM
ejpam-5650	383	3	]	]	PUNCT
ejpam-5650	383	4	c.	c.	PROPN
ejpam-5650	383	5	boonpok	boonpok	PROPN
ejpam-5650	383	6	.	.	PUNCT
ejpam-5650	384	1	on	on	ADP
ejpam-5650	384	2	characterizations	characterization	NOUN
ejpam-5650	384	3	of	of	ADP
ejpam-5650	384	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5650	384	5	ideal	ideal	ADJ
ejpam-5650	384	6	topological	topological	ADJ
ejpam-5650	384	7	spaces	space	NOUN
ejpam-5650	384	8	.	.	PUNCT
ejpam-5650	385	1	journal	journal	NOUN
ejpam-5650	385	2	of	of	ADP
ejpam-5650	385	3	mathematics	mathematic	NOUN
ejpam-5650	385	4	,	,	PUNCT
ejpam-5650	385	5	2020:9387601	2020:9387601	NUM
ejpam-5650	385	6	,	,	PUNCT
ejpam-5650	385	7	2020	2020	NUM
ejpam-5650	385	8	.	.	PUNCT
ejpam-5650	386	1	[	[	X
ejpam-5650	386	2	5	5	X
ejpam-5650	386	3	]	]	PUNCT
ejpam-5650	386	4	c.	c.	PROPN
ejpam-5650	386	5	boonpok	boonpok	PROPN
ejpam-5650	386	6	.	.	PUNCT
ejpam-5650	387	1	(	(	PUNCT
ejpam-5650	387	2	τ1	τ1	NOUN
ejpam-5650	387	3	,	,	PUNCT
ejpam-5650	387	4	τ2)δ	τ2)δ	ADJ
ejpam-5650	387	5	-	-	PUNCT
ejpam-5650	387	6	semicontinuous	semicontinuous	ADJ
ejpam-5650	387	7	multifunctions	multifunction	NOUN
ejpam-5650	387	8	.	.	PUNCT
ejpam-5650	388	1	heliyon	heliyon	NOUN
ejpam-5650	388	2	,	,	PUNCT
ejpam-5650	388	3	6	6	NUM
ejpam-5650	388	4	:	:	SYM
ejpam-5650	388	5	e05367	e05367	PROPN
ejpam-5650	388	6	,	,	PUNCT
ejpam-5650	388	7	2020	2020	NUM
ejpam-5650	388	8	.	.	PUNCT
ejpam-5650	389	1	[	[	X
ejpam-5650	389	2	6	6	NUM
ejpam-5650	389	3	]	]	PUNCT
ejpam-5650	389	4	c.	c.	PROPN
ejpam-5650	389	5	boonpok	boonpok	PROPN
ejpam-5650	389	6	.	.	PUNCT
ejpam-5650	390	1	weak	weak	ADJ
ejpam-5650	390	2	quasi	quasi	ADJ
ejpam-5650	390	3	continuity	continuity	NOUN
ejpam-5650	390	4	for	for	ADP
ejpam-5650	390	5	multifunctions	multifunction	NOUN
ejpam-5650	390	6	in	in	ADP
ejpam-5650	390	7	ideal	ideal	ADJ
ejpam-5650	390	8	topological	topological	ADJ
ejpam-5650	390	9	spaces	space	NOUN
ejpam-5650	390	10	.	.	PUNCT
ejpam-5650	391	1	advances	advance	NOUN
ejpam-5650	391	2	in	in	ADP
ejpam-5650	391	3	mathematics	mathematic	NOUN
ejpam-5650	391	4	:	:	PUNCT
ejpam-5650	391	5	scientific	scientific	ADJ
ejpam-5650	391	6	journal	journal	NOUN
ejpam-5650	391	7	,	,	PUNCT
ejpam-5650	391	8	9(1):339–355	9(1):339–355	NUM
ejpam-5650	391	9	,	,	PUNCT
ejpam-5650	391	10	2020	2020	NUM
ejpam-5650	391	11	.	.	PUNCT
ejpam-5650	392	1	[	[	X
ejpam-5650	392	2	7	7	X
ejpam-5650	392	3	]	]	X
ejpam-5650	392	4	c.	c.	PROPN
ejpam-5650	392	5	boonpok	boonpok	PROPN
ejpam-5650	392	6	.	.	PUNCT
ejpam-5650	393	1	upper	upper	ADJ
ejpam-5650	393	2	and	and	CCONJ
ejpam-5650	393	3	lower	low	ADJ
ejpam-5650	393	4	β(⋆)-continuity	β(⋆)-continuity	NOUN
ejpam-5650	393	5	.	.	PUNCT
ejpam-5650	393	6	heliyon	heliyon	NOUN
ejpam-5650	393	7	,	,	PUNCT
ejpam-5650	393	8	7	7	NUM
ejpam-5650	393	9	:	:	PUNCT
ejpam-5650	393	10	e05986	e05986	PROPN
ejpam-5650	393	11	,	,	PUNCT
ejpam-5650	393	12	2021	2021	NUM
ejpam-5650	393	13	.	.	PUNCT
ejpam-5650	394	1	[	[	X
ejpam-5650	394	2	8	8	NUM
ejpam-5650	394	3	]	]	X
ejpam-5650	394	4	c.	c.	PROPN
ejpam-5650	394	5	boonpok	boonpok	PROPN
ejpam-5650	394	6	.	.	PUNCT
ejpam-5650	395	1	on	on	ADP
ejpam-5650	395	2	some	some	DET
ejpam-5650	395	3	closed	closed	ADJ
ejpam-5650	395	4	sets	set	NOUN
ejpam-5650	395	5	and	and	CCONJ
ejpam-5650	395	6	low	low	ADJ
ejpam-5650	395	7	separation	separation	NOUN
ejpam-5650	395	8	axioms	axiom	NOUN
ejpam-5650	395	9	via	via	ADP
ejpam-5650	395	10	topological	topological	ADJ
ejpam-5650	395	11	ideals	ideal	NOUN
ejpam-5650	395	12	.	.	PUNCT
ejpam-5650	396	1	european	european	ADJ
ejpam-5650	396	2	journal	journal	PROPN
ejpam-5650	396	3	of	of	ADP
ejpam-5650	396	4	pure	pure	ADJ
ejpam-5650	396	5	and	and	CCONJ
ejpam-5650	396	6	applied	applied	ADJ
ejpam-5650	396	7	mathematics	mathematic	NOUN
ejpam-5650	396	8	,	,	PUNCT
ejpam-5650	396	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5650	396	10	,	,	PUNCT
ejpam-5650	396	11	2022	2022	NUM
ejpam-5650	396	12	.	.	PUNCT
ejpam-5650	397	1	[	[	X
ejpam-5650	397	2	9	9	NUM
ejpam-5650	397	3	]	]	PUNCT
ejpam-5650	397	4	c.	c.	PROPN
ejpam-5650	397	5	boonpok	boonpok	PROPN
ejpam-5650	397	6	.	.	PUNCT
ejpam-5650	398	1	θ(⋆)-quasi	θ(⋆)-quasi	DET
ejpam-5650	398	2	continuity	continuity	NOUN
ejpam-5650	398	3	for	for	ADP
ejpam-5650	398	4	multifunctions	multifunction	NOUN
ejpam-5650	398	5	.	.	PUNCT
ejpam-5650	399	1	wseas	wseas	PROPN
ejpam-5650	399	2	transactions	transaction	NOUN
ejpam-5650	399	3	on	on	ADP
ejpam-5650	399	4	mathematics	mathematic	NOUN
ejpam-5650	399	5	,	,	PUNCT
ejpam-5650	399	6	21:245–251	21:245–251	NUM
ejpam-5650	399	7	,	,	PUNCT
ejpam-5650	399	8	2022	2022	NUM
ejpam-5650	399	9	.	.	PUNCT
ejpam-5650	400	1	[	[	X
ejpam-5650	400	2	10	10	NUM
ejpam-5650	400	3	]	]	X
ejpam-5650	400	4	c.	c.	PROPN
ejpam-5650	400	5	boonpok	boonpok	PROPN
ejpam-5650	400	6	.	.	PUNCT
ejpam-5650	401	1	on	on	ADP
ejpam-5650	401	2	some	some	DET
ejpam-5650	401	3	spaces	space	NOUN
ejpam-5650	401	4	via	via	ADP
ejpam-5650	401	5	topological	topological	ADJ
ejpam-5650	401	6	ideals	ideal	NOUN
ejpam-5650	401	7	.	.	PUNCT
ejpam-5650	402	1	open	open	ADJ
ejpam-5650	402	2	mathematics	mathematic	NOUN
ejpam-5650	402	3	,	,	PUNCT
ejpam-5650	402	4	21:20230118	21:20230118	NUM
ejpam-5650	402	5	,	,	PUNCT
ejpam-5650	402	6	2023	2023	NUM
ejpam-5650	402	7	.	.	PUNCT
ejpam-5650	403	1	[	[	X
ejpam-5650	403	2	11	11	NUM
ejpam-5650	403	3	]	]	PUNCT
ejpam-5650	403	4	c.	c.	PROPN
ejpam-5650	403	5	boonpok	boonpok	PROPN
ejpam-5650	403	6	.	.	PUNCT
ejpam-5650	404	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5650	404	2	.	.	PUNCT
ejpam-5650	405	1	mathematica	mathematica	PROPN
ejpam-5650	405	2	,	,	PUNCT
ejpam-5650	405	3	65(1):31–42	65(1):31–42	NUM
ejpam-5650	405	4	,	,	PUNCT
ejpam-5650	405	5	2023	2023	NUM
ejpam-5650	405	6	.	.	PUNCT
ejpam-5650	406	1	[	[	X
ejpam-5650	406	2	12	12	NUM
ejpam-5650	406	3	]	]	X
ejpam-5650	406	4	c.	c.	PROPN
ejpam-5650	406	5	boonpok	boonpok	PROPN
ejpam-5650	406	6	and	and	CCONJ
ejpam-5650	406	7	j.	j.	PROPN
ejpam-5650	406	8	khampakdee	khampakdee	PROPN
ejpam-5650	406	9	.	.	PUNCT
ejpam-5650	407	1	(	(	PUNCT
ejpam-5650	407	2	λ	λ	NOUN
ejpam-5650	407	3	,	,	PUNCT
ejpam-5650	407	4	sp)-open	sp)-open	ADJ
ejpam-5650	407	5	sets	set	NOUN
ejpam-5650	407	6	in	in	ADP
ejpam-5650	407	7	topological	topological	ADJ
ejpam-5650	407	8	spaces	space	NOUN
ejpam-5650	407	9	.	.	PUNCT
ejpam-5650	408	1	european	european	ADJ
ejpam-5650	408	2	journal	journal	PROPN
ejpam-5650	408	3	of	of	ADP
ejpam-5650	408	4	pure	pure	ADJ
ejpam-5650	408	5	and	and	CCONJ
ejpam-5650	408	6	applied	applied	ADJ
ejpam-5650	408	7	mathematics	mathematic	NOUN
ejpam-5650	408	8	,	,	PUNCT
ejpam-5650	408	9	15(2):572–588	15(2):572–588	NUM
ejpam-5650	408	10	,	,	PUNCT
ejpam-5650	408	11	2022	2022	NUM
ejpam-5650	408	12	.	.	PUNCT
ejpam-5650	409	1	[	[	X
ejpam-5650	409	2	13	13	NUM
ejpam-5650	409	3	]	]	PUNCT
ejpam-5650	409	4	c.	c.	PROPN
ejpam-5650	409	5	boonpok	boonpok	PROPN
ejpam-5650	409	6	and	and	CCONJ
ejpam-5650	409	7	j.	j.	PROPN
ejpam-5650	409	8	khampakdee	khampakdee	PROPN
ejpam-5650	409	9	.	.	PUNCT
ejpam-5650	410	1	on	on	ADP
ejpam-5650	410	2	almost	almost	ADV
ejpam-5650	410	3	α(λ	α(λ	PROPN
ejpam-5650	410	4	,	,	PUNCT
ejpam-5650	410	5	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	410	6	multifunctions	multifunction	NOUN
ejpam-5650	410	7	.	.	PUNCT
ejpam-5650	411	1	european	european	PROPN
ejpam-5650	411	2	journal	journal	PROPN
ejpam-5650	411	3	of	of	ADP
ejpam-5650	411	4	pure	pure	ADJ
ejpam-5650	411	5	and	and	CCONJ
ejpam-5650	411	6	applied	applied	ADJ
ejpam-5650	411	7	mathematics	mathematic	NOUN
ejpam-5650	411	8	,	,	PUNCT
ejpam-5650	411	9	15(2):626–634	15(2):626–634	PROPN
ejpam-5650	411	10	,	,	PUNCT
ejpam-5650	411	11	2022	2022	NUM
ejpam-5650	411	12	.	.	PUNCT
ejpam-5650	412	1	[	[	X
ejpam-5650	412	2	14	14	NUM
ejpam-5650	412	3	]	]	X
ejpam-5650	412	4	c.	c.	PROPN
ejpam-5650	412	5	boonpok	boonpok	PROPN
ejpam-5650	412	6	and	and	CCONJ
ejpam-5650	412	7	j.	j.	PROPN
ejpam-5650	412	8	khampakdee	khampakdee	PROPN
ejpam-5650	412	9	.	.	PUNCT
ejpam-5650	413	1	slight	slight	PROPN
ejpam-5650	413	2	(	(	PUNCT
ejpam-5650	413	3	λ	λ	NOUN
ejpam-5650	413	4	,	,	PUNCT
ejpam-5650	413	5	sp)-continuity	sp)-continuity	NOUN
ejpam-5650	413	6	and	and	CCONJ
ejpam-5650	413	7	λsp	λsp	NOUN
ejpam-5650	413	8	-	-	PUNCT
ejpam-5650	413	9	extremally	extremally	ADV
ejpam-5650	413	10	disconnectedness	disconnectedness	NOUN
ejpam-5650	413	11	.	.	PUNCT
ejpam-5650	414	1	european	european	ADJ
ejpam-5650	414	2	journal	journal	PROPN
ejpam-5650	414	3	of	of	ADP
ejpam-5650	414	4	pure	pure	ADJ
ejpam-5650	414	5	and	and	CCONJ
ejpam-5650	414	6	applied	applied	ADJ
ejpam-5650	414	7	mathematics	mathematic	NOUN
ejpam-5650	414	8	,	,	PUNCT
ejpam-5650	414	9	15(3):1180–1188	15(3):1180–1188	NUM
ejpam-5650	414	10	,	,	PUNCT
ejpam-5650	414	11	2022	2022	NUM
ejpam-5650	414	12	.	.	PUNCT
ejpam-5650	415	1	[	[	X
ejpam-5650	415	2	15	15	NUM
ejpam-5650	415	3	]	]	X
ejpam-5650	415	4	c.	c.	PROPN
ejpam-5650	415	5	boonpok	boonpok	PROPN
ejpam-5650	415	6	and	and	CCONJ
ejpam-5650	415	7	j.	j.	PROPN
ejpam-5650	415	8	khampakdee	khampakdee	PROPN
ejpam-5650	415	9	.	.	PUNCT
ejpam-5650	416	1	upper	upper	ADJ
ejpam-5650	416	2	and	and	CCONJ
ejpam-5650	416	3	lower	low	ADJ
ejpam-5650	416	4	weak	weak	ADJ
ejpam-5650	416	5	sβ(⋆)-continuity	sβ(⋆)-continuity	NOUN
ejpam-5650	416	6	.	.	PUNCT
ejpam-5650	417	1	european	european	PROPN
ejpam-5650	417	2	journal	journal	PROPN
ejpam-5650	417	3	of	of	ADP
ejpam-5650	417	4	pure	pure	ADJ
ejpam-5650	417	5	and	and	CCONJ
ejpam-5650	417	6	applied	applied	ADJ
ejpam-5650	417	7	mathematics	mathematic	NOUN
ejpam-5650	417	8	,	,	PUNCT
ejpam-5650	417	9	16(4):2544–2556	16(4):2544–2556	NUM
ejpam-5650	417	10	,	,	PUNCT
ejpam-5650	417	11	2023	2023	NUM
ejpam-5650	417	12	.	.	PUNCT
ejpam-5650	418	1	[	[	X
ejpam-5650	418	2	16	16	NUM
ejpam-5650	418	3	]	]	X
ejpam-5650	418	4	c.	c.	PROPN
ejpam-5650	418	5	boonpok	boonpok	PROPN
ejpam-5650	418	6	and	and	CCONJ
ejpam-5650	418	7	j.	j.	PROPN
ejpam-5650	418	8	khampakdee	khampakdee	PROPN
ejpam-5650	418	9	.	.	PUNCT
ejpam-5650	419	1	almost	almost	ADV
ejpam-5650	419	2	strong	strong	ADJ
ejpam-5650	419	3	θ(λ	θ(λ	PROPN
ejpam-5650	419	4	,	,	PUNCT
ejpam-5650	419	5	p)-continuity	p)-continuity	NOUN
ejpam-5650	419	6	for	for	ADP
ejpam-5650	419	7	functions	function	NOUN
ejpam-5650	419	8	.	.	PUNCT
ejpam-5650	420	1	european	european	ADJ
ejpam-5650	420	2	journal	journal	PROPN
ejpam-5650	420	3	of	of	ADP
ejpam-5650	420	4	pure	pure	ADJ
ejpam-5650	420	5	and	and	CCONJ
ejpam-5650	420	6	applied	applied	ADJ
ejpam-5650	420	7	mathematics	mathematic	NOUN
ejpam-5650	420	8	,	,	PUNCT
ejpam-5650	420	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5650	420	10	,	,	PUNCT
ejpam-5650	420	11	2024	2024	NUM
ejpam-5650	420	12	.	.	PUNCT
ejpam-5650	421	1	[	[	X
ejpam-5650	421	2	17	17	NUM
ejpam-5650	421	3	]	]	X
ejpam-5650	421	4	c.	c.	PROPN
ejpam-5650	421	5	boonpok	boonpok	PROPN
ejpam-5650	421	6	and	and	CCONJ
ejpam-5650	421	7	j.	j.	PROPN
ejpam-5650	421	8	khampakdee	khampakdee	PROPN
ejpam-5650	421	9	.	.	PUNCT
ejpam-5650	422	1	upper	upper	ADJ
ejpam-5650	422	2	and	and	CCONJ
ejpam-5650	422	3	lower	low	ADJ
ejpam-5650	422	4	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5650	422	5	.	.	PUNCT
ejpam-5650	422	6	european	european	PROPN
ejpam-5650	422	7	journal	journal	PROPN
ejpam-5650	422	8	of	of	ADP
ejpam-5650	422	9	pure	pure	ADJ
ejpam-5650	422	10	and	and	CCONJ
ejpam-5650	422	11	applied	applied	ADJ
ejpam-5650	422	12	mathematics	mathematic	NOUN
ejpam-5650	422	13	,	,	PUNCT
ejpam-5650	422	14	17(1):201–211	17(1):201–211	NUM
ejpam-5650	422	15	,	,	PUNCT
ejpam-5650	422	16	2024	2024	NUM
ejpam-5650	422	17	.	.	PUNCT
ejpam-5650	423	1	[	[	X
ejpam-5650	423	2	18	18	NUM
ejpam-5650	423	3	]	]	PUNCT
ejpam-5650	423	4	c.	c.	PROPN
ejpam-5650	423	5	boonpok	boonpok	PROPN
ejpam-5650	423	6	and	and	CCONJ
ejpam-5650	423	7	c.	c.	PROPN
ejpam-5650	423	8	klanarong	klanarong	PROPN
ejpam-5650	423	9	.	.	PUNCT
ejpam-5650	424	1	on	on	ADP
ejpam-5650	424	2	weakly	weakly	ADJ
ejpam-5650	424	3	(	(	PUNCT
ejpam-5650	424	4	τ1	τ1	NOUN
ejpam-5650	424	5	,	,	PUNCT
ejpam-5650	424	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	424	7	functions	function	NOUN
ejpam-5650	424	8	.	.	PUNCT
ejpam-5650	425	1	european	european	ADJ
ejpam-5650	425	2	journal	journal	PROPN
ejpam-5650	425	3	of	of	ADP
ejpam-5650	425	4	pure	pure	ADJ
ejpam-5650	425	5	and	and	CCONJ
ejpam-5650	425	6	applied	applied	ADJ
ejpam-5650	425	7	mathematics	mathematic	NOUN
ejpam-5650	425	8	,	,	PUNCT
ejpam-5650	425	9	17(1):416–425	17(1):416–425	NUM
ejpam-5650	425	10	,	,	PUNCT
ejpam-5650	425	11	2024	2024	NUM
ejpam-5650	425	12	.	.	PUNCT
ejpam-5650	426	1	[	[	X
ejpam-5650	426	2	19	19	NUM
ejpam-5650	426	3	]	]	X
ejpam-5650	426	4	c.	c.	PROPN
ejpam-5650	426	5	boonpok	boonpok	PROPN
ejpam-5650	426	6	and	and	CCONJ
ejpam-5650	426	7	p.	p.	NOUN
ejpam-5650	426	8	pue	pue	NOUN
ejpam-5650	426	9	-	-	PUNCT
ejpam-5650	426	10	on	on	ADP
ejpam-5650	426	11	.	.	PUNCT
ejpam-5650	427	1	continuity	continuity	NOUN
ejpam-5650	427	2	for	for	ADP
ejpam-5650	427	3	multifunctions	multifunction	NOUN
ejpam-5650	427	4	in	in	ADP
ejpam-5650	427	5	ideal	ideal	ADJ
ejpam-5650	427	6	topological	topological	ADJ
ejpam-5650	427	7	spaces	space	NOUN
ejpam-5650	427	8	.	.	PUNCT
ejpam-5650	428	1	wseas	wseas	VERB
ejpam-5650	428	2	transactions	transaction	NOUN
ejpam-5650	428	3	on	on	ADP
ejpam-5650	428	4	mathematics	mathematic	NOUN
ejpam-5650	428	5	,	,	PUNCT
ejpam-5650	428	6	19:624–631	19:624–631	NUM
ejpam-5650	428	7	,	,	PUNCT
ejpam-5650	428	8	2020	2020	NUM
ejpam-5650	428	9	.	.	PUNCT
ejpam-5650	429	1	[	[	X
ejpam-5650	429	2	20	20	NUM
ejpam-5650	429	3	]	]	PUNCT
ejpam-5650	429	4	c.	c.	PROPN
ejpam-5650	429	5	boonpok	boonpok	PROPN
ejpam-5650	429	6	and	and	CCONJ
ejpam-5650	429	7	p.	p.	NOUN
ejpam-5650	429	8	pue	pue	NOUN
ejpam-5650	429	9	-	-	PUNCT
ejpam-5650	429	10	on	on	ADP
ejpam-5650	429	11	.	.	PUNCT
ejpam-5650	430	1	upper	upper	ADJ
ejpam-5650	430	2	and	and	CCONJ
ejpam-5650	430	3	lower	low	ADJ
ejpam-5650	430	4	sβ(⋆)-continuous	sβ(⋆)-continuous	ADJ
ejpam-5650	430	5	multifunctions	multifunction	NOUN
ejpam-5650	430	6	.	.	PUNCT
ejpam-5650	431	1	european	european	ADJ
ejpam-5650	431	2	journal	journal	PROPN
ejpam-5650	431	3	of	of	ADP
ejpam-5650	431	4	pure	pure	ADJ
ejpam-5650	431	5	and	and	CCONJ
ejpam-5650	431	6	applied	applied	ADJ
ejpam-5650	431	7	mathematics	mathematic	NOUN
ejpam-5650	431	8	,	,	PUNCT
ejpam-5650	431	9	16(3):1634–1646	16(3):1634–1646	NUM
ejpam-5650	431	10	,	,	PUNCT
ejpam-5650	431	11	2023	2023	NUM
ejpam-5650	431	12	.	.	PUNCT
ejpam-5650	432	1	[	[	X
ejpam-5650	432	2	21	21	NUM
ejpam-5650	432	3	]	]	X
ejpam-5650	432	4	c.	c.	PROPN
ejpam-5650	432	5	boonpok	boonpok	PROPN
ejpam-5650	432	6	and	and	CCONJ
ejpam-5650	432	7	p.	p.	NOUN
ejpam-5650	432	8	pue	pue	NOUN
ejpam-5650	432	9	-	-	PUNCT
ejpam-5650	432	10	on	on	ADP
ejpam-5650	432	11	.	.	PUNCT
ejpam-5650	433	1	upper	upper	ADJ
ejpam-5650	433	2	and	and	CCONJ
ejpam-5650	433	3	lower	low	ADJ
ejpam-5650	433	4	weakly	weakly	ADJ
ejpam-5650	433	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5650	433	6	multifunctions	multifunction	NOUN
ejpam-5650	433	7	.	.	PUNCT
ejpam-5650	434	1	international	international	ADJ
ejpam-5650	434	2	journal	journal	NOUN
ejpam-5650	434	3	of	of	ADP
ejpam-5650	434	4	analysis	analysis	NOUN
ejpam-5650	434	5	and	and	CCONJ
ejpam-5650	434	6	applications	application	NOUN
ejpam-5650	434	7	,	,	PUNCT
ejpam-5650	434	8	21:90	21:90	NUM
ejpam-5650	434	9	,	,	PUNCT
ejpam-5650	434	10	2023	2023	NUM
ejpam-5650	434	11	.	.	PUNCT
ejpam-5650	435	1	[	[	X
ejpam-5650	435	2	22	22	NUM
ejpam-5650	435	3	]	]	PUNCT
ejpam-5650	435	4	c.	c.	PROPN
ejpam-5650	435	5	boonpok	boonpok	PROPN
ejpam-5650	435	6	and	and	CCONJ
ejpam-5650	435	7	p.	p.	NOUN
ejpam-5650	435	8	pue	pue	NOUN
ejpam-5650	435	9	-	-	PUNCT
ejpam-5650	435	10	on	on	ADP
ejpam-5650	435	11	.	.	PUNCT
ejpam-5650	436	1	upper	upper	ADJ
ejpam-5650	436	2	and	and	CCONJ
ejpam-5650	436	3	lower	low	ADJ
ejpam-5650	436	4	weakly	weakly	ADJ
ejpam-5650	436	5	(	(	PUNCT
ejpam-5650	436	6	λ	λ	NOUN
ejpam-5650	436	7	,	,	PUNCT
ejpam-5650	436	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	436	9	multifunctions	multifunction	NOUN
ejpam-5650	436	10	.	.	PUNCT
ejpam-5650	437	1	european	european	PROPN
ejpam-5650	437	2	journal	journal	PROPN
ejpam-5650	437	3	of	of	ADP
ejpam-5650	437	4	pure	pure	ADJ
ejpam-5650	437	5	and	and	CCONJ
ejpam-5650	437	6	applied	applied	ADJ
ejpam-5650	437	7	mathematics	mathematic	NOUN
ejpam-5650	437	8	,	,	PUNCT
ejpam-5650	437	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5650	437	10	,	,	PUNCT
ejpam-5650	437	11	2023	2023	NUM
ejpam-5650	437	12	.	.	PUNCT
ejpam-5650	438	1	[	[	X
ejpam-5650	438	2	23	23	NUM
ejpam-5650	438	3	]	]	X
ejpam-5650	438	4	c.	c.	PROPN
ejpam-5650	438	5	boonpok	boonpok	PROPN
ejpam-5650	438	6	and	and	CCONJ
ejpam-5650	438	7	p.	p.	NOUN
ejpam-5650	438	8	pue	pue	NOUN
ejpam-5650	438	9	-	-	PUNCT
ejpam-5650	438	10	on	on	ADP
ejpam-5650	438	11	.	.	PUNCT
ejpam-5650	439	1	characterizations	characterization	NOUN
ejpam-5650	439	2	of	of	ADP
ejpam-5650	439	3	almost	almost	ADV
ejpam-5650	439	4	(	(	PUNCT
ejpam-5650	439	5	τ1	τ1	NOUN
ejpam-5650	439	6	,	,	PUNCT
ejpam-5650	439	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	439	8	functions	function	NOUN
ejpam-5650	439	9	.	.	PUNCT
ejpam-5650	440	1	international	international	ADJ
ejpam-5650	440	2	journal	journal	NOUN
ejpam-5650	440	3	of	of	ADP
ejpam-5650	440	4	analysis	analysis	NOUN
ejpam-5650	440	5	and	and	CCONJ
ejpam-5650	440	6	applications	application	NOUN
ejpam-5650	440	7	,	,	PUNCT
ejpam-5650	440	8	22:33	22:33	NUM
ejpam-5650	440	9	,	,	PUNCT
ejpam-5650	440	10	2024	2024	NUM
ejpam-5650	440	11	.	.	PUNCT
ejpam-5650	441	1	[	[	X
ejpam-5650	441	2	24	24	NUM
ejpam-5650	441	3	]	]	PUNCT
ejpam-5650	441	4	c.	c.	PROPN
ejpam-5650	441	5	boonpok	boonpok	PROPN
ejpam-5650	441	6	and	and	CCONJ
ejpam-5650	441	7	n.	n.	PROPN
ejpam-5650	441	8	srisarakham	srisarakham	PROPN
ejpam-5650	441	9	.	.	PUNCT
ejpam-5650	442	1	almost	almost	ADV
ejpam-5650	442	2	α-⋆-continuity	α-⋆-continuity	NUM
ejpam-5650	442	3	for	for	ADP
ejpam-5650	442	4	multifunctions	multifunction	NOUN
ejpam-5650	442	5	.	.	PUNCT
ejpam-5650	443	1	internan	internan	PROPN
ejpam-5650	443	2	.	.	PUNCT
ejpam-5650	444	1	chutiman	chutiman	NOUN
ejpam-5650	444	2	,	,	PUNCT
ejpam-5650	444	3	a.	a.	PROPN
ejpam-5650	444	4	sama	sama	PROPN
ejpam-5650	444	5	-	-	PUNCT
ejpam-5650	444	6	ae	ae	PROPN
ejpam-5650	444	7	,	,	PUNCT
ejpam-5650	444	8	c.	c.	PROPN
ejpam-5650	444	9	boonpok	boonpok	PROPN
ejpam-5650	444	10	/	/	SYM
ejpam-5650	444	11	eur	eur	PROPN
ejpam-5650	444	12	.	.	PUNCT
ejpam-5650	445	1	j.	j.	PROPN
ejpam-5650	445	2	pure	pure	PROPN
ejpam-5650	445	3	appl	appl	PROPN
ejpam-5650	445	4	.	.	PROPN
ejpam-5650	445	5	math	math	PROPN
ejpam-5650	445	6	,	,	PUNCT
ejpam-5650	445	7	18	18	NUM
ejpam-5650	445	8	(	(	PUNCT
ejpam-5650	445	9	1	1	NUM
ejpam-5650	445	10	)	)	PUNCT
ejpam-5650	445	11	(	(	PUNCT
ejpam-5650	445	12	2025	2025	NUM
ejpam-5650	445	13	)	)	PUNCT
ejpam-5650	445	14	,	,	PUNCT
ejpam-5650	445	15	5650	5650	NUM
ejpam-5650	445	16	16	16	NUM
ejpam-5650	445	17	of	of	ADP
ejpam-5650	445	18	18	18	NUM
ejpam-5650	445	19	tional	tional	ADJ
ejpam-5650	445	20	journal	journal	NOUN
ejpam-5650	445	21	of	of	ADP
ejpam-5650	445	22	analysis	analysis	NOUN
ejpam-5650	445	23	and	and	CCONJ
ejpam-5650	445	24	applications	application	NOUN
ejpam-5650	445	25	,	,	PUNCT
ejpam-5650	445	26	21:107	21:107	NUM
ejpam-5650	445	27	,	,	PUNCT
ejpam-5650	445	28	2023	2023	NUM
ejpam-5650	445	29	.	.	PUNCT
ejpam-5650	446	1	[	[	X
ejpam-5650	446	2	25	25	NUM
ejpam-5650	446	3	]	]	PUNCT
ejpam-5650	446	4	c.	c.	PROPN
ejpam-5650	446	5	boonpok	boonpok	PROPN
ejpam-5650	446	6	and	and	CCONJ
ejpam-5650	446	7	n.	n.	PROPN
ejpam-5650	446	8	srisarakham	srisarakham	PROPN
ejpam-5650	446	9	.	.	PUNCT
ejpam-5650	447	1	weak	weak	ADJ
ejpam-5650	447	2	forms	form	NOUN
ejpam-5650	447	3	of	of	ADP
ejpam-5650	447	4	(	(	PUNCT
ejpam-5650	447	5	λ	λ	PROPN
ejpam-5650	447	6	,	,	PUNCT
ejpam-5650	447	7	b)-open	b)-open	VERB
ejpam-5650	447	8	sets	set	NOUN
ejpam-5650	447	9	and	and	CCONJ
ejpam-5650	447	10	weak	weak	ADJ
ejpam-5650	447	11	(	(	PUNCT
ejpam-5650	447	12	λ	λ	NOUN
ejpam-5650	447	13	,	,	PUNCT
ejpam-5650	447	14	b)continuity	b)continuity	NOUN
ejpam-5650	447	15	.	.	PUNCT
ejpam-5650	448	1	european	european	PROPN
ejpam-5650	448	2	journal	journal	PROPN
ejpam-5650	448	3	of	of	ADP
ejpam-5650	448	4	pure	pure	ADJ
ejpam-5650	448	5	and	and	CCONJ
ejpam-5650	448	6	applied	applied	ADJ
ejpam-5650	448	7	mathematics	mathematic	NOUN
ejpam-5650	448	8	,	,	PUNCT
ejpam-5650	448	9	16(1):29–43	16(1):29–43	NUM
ejpam-5650	448	10	,	,	PUNCT
ejpam-5650	448	11	2023	2023	NUM
ejpam-5650	448	12	.	.	PUNCT
ejpam-5650	449	1	[	[	X
ejpam-5650	449	2	26	26	NUM
ejpam-5650	449	3	]	]	X
ejpam-5650	449	4	c.	c.	PROPN
ejpam-5650	449	5	boonpok	boonpok	PROPN
ejpam-5650	449	6	and	and	CCONJ
ejpam-5650	449	7	n.	n.	PROPN
ejpam-5650	449	8	srisarakham	srisarakham	PROPN
ejpam-5650	449	9	.	.	PUNCT
ejpam-5650	450	1	(	(	PUNCT
ejpam-5650	450	2	τ1	τ1	NOUN
ejpam-5650	450	3	,	,	PUNCT
ejpam-5650	450	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5650	450	5	for	for	ADP
ejpam-5650	450	6	functions	function	NOUN
ejpam-5650	450	7	.	.	PUNCT
ejpam-5650	451	1	asia	asia	PROPN
ejpam-5650	451	2	pacific	pacific	PROPN
ejpam-5650	451	3	journal	journal	PROPN
ejpam-5650	451	4	of	of	ADP
ejpam-5650	451	5	mathematics	mathematic	NOUN
ejpam-5650	451	6	,	,	PUNCT
ejpam-5650	451	7	11:21	11:21	NUM
ejpam-5650	451	8	,	,	PUNCT
ejpam-5650	451	9	2024	2024	NUM
ejpam-5650	451	10	.	.	PUNCT
ejpam-5650	452	1	[	[	X
ejpam-5650	452	2	27	27	NUM
ejpam-5650	452	3	]	]	X
ejpam-5650	452	4	c.	c.	PROPN
ejpam-5650	452	5	boonpok	boonpok	PROPN
ejpam-5650	452	6	and	and	CCONJ
ejpam-5650	452	7	m.	m.	NOUN
ejpam-5650	452	8	thongmoon	thongmoon	NOUN
ejpam-5650	452	9	.	.	PUNCT
ejpam-5650	453	1	weak	weak	ADJ
ejpam-5650	453	2	α(λ	α(λ	PROPN
ejpam-5650	453	3	,	,	PUNCT
ejpam-5650	453	4	sp)-continuity	sp)-continuity	NOUN
ejpam-5650	453	5	for	for	ADP
ejpam-5650	453	6	multifunctions	multifunction	NOUN
ejpam-5650	453	7	.	.	PUNCT
ejpam-5650	454	1	european	european	ADJ
ejpam-5650	454	2	journal	journal	PROPN
ejpam-5650	454	3	of	of	ADP
ejpam-5650	454	4	pure	pure	ADJ
ejpam-5650	454	5	and	and	CCONJ
ejpam-5650	454	6	applied	applied	ADJ
ejpam-5650	454	7	mathematics	mathematic	NOUN
ejpam-5650	454	8	,	,	PUNCT
ejpam-5650	454	9	16(1):465–478	16(1):465–478	NUM
ejpam-5650	454	10	,	,	PUNCT
ejpam-5650	454	11	2023	2023	NUM
ejpam-5650	454	12	.	.	PUNCT
ejpam-5650	455	1	[	[	X
ejpam-5650	455	2	28	28	NUM
ejpam-5650	455	3	]	]	X
ejpam-5650	455	4	c.	c.	PROPN
ejpam-5650	455	5	boonpok	boonpok	PROPN
ejpam-5650	455	6	and	and	CCONJ
ejpam-5650	455	7	c.	c.	PROPN
ejpam-5650	455	8	viriyapong	viriyapong	PROPN
ejpam-5650	455	9	.	.	PUNCT
ejpam-5650	456	1	upper	upper	ADJ
ejpam-5650	456	2	and	and	CCONJ
ejpam-5650	456	3	lower	low	ADJ
ejpam-5650	456	4	almost	almost	ADV
ejpam-5650	456	5	weak	weak	ADJ
ejpam-5650	456	6	(	(	PUNCT
ejpam-5650	456	7	τ1	τ1	NOUN
ejpam-5650	456	8	,	,	PUNCT
ejpam-5650	456	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5650	456	10	.	.	PUNCT
ejpam-5650	457	1	european	european	PROPN
ejpam-5650	457	2	journal	journal	PROPN
ejpam-5650	457	3	of	of	ADP
ejpam-5650	457	4	pure	pure	ADJ
ejpam-5650	457	5	and	and	CCONJ
ejpam-5650	457	6	applied	applied	ADJ
ejpam-5650	457	7	mathematics	mathematic	NOUN
ejpam-5650	457	8	,	,	PUNCT
ejpam-5650	457	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5650	457	10	,	,	PUNCT
ejpam-5650	457	11	2021	2021	NUM
ejpam-5650	457	12	.	.	PUNCT
ejpam-5650	458	1	[	[	X
ejpam-5650	458	2	29	29	NUM
ejpam-5650	458	3	]	]	X
ejpam-5650	458	4	c.	c.	PROPN
ejpam-5650	458	5	boonpok	boonpok	PROPN
ejpam-5650	458	6	,	,	PUNCT
ejpam-5650	458	7	c.	c.	PROPN
ejpam-5650	458	8	viriyapong	viriyapong	PROPN
ejpam-5650	458	9	,	,	PUNCT
ejpam-5650	458	10	and	and	CCONJ
ejpam-5650	458	11	m.	m.	NOUN
ejpam-5650	458	12	thongmoon	thongmoon	NOUN
ejpam-5650	458	13	.	.	PUNCT
ejpam-5650	459	1	on	on	ADP
ejpam-5650	459	2	upper	upper	ADJ
ejpam-5650	459	3	and	and	CCONJ
ejpam-5650	459	4	lower	low	ADJ
ejpam-5650	459	5	(	(	PUNCT
ejpam-5650	459	6	τ1	τ1	NOUN
ejpam-5650	459	7	,	,	PUNCT
ejpam-5650	459	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5650	459	9	multifunctions	multifunction	NOUN
ejpam-5650	459	10	.	.	PUNCT
ejpam-5650	460	1	journal	journal	PROPN
ejpam-5650	460	2	of	of	ADP
ejpam-5650	460	3	mathematics	mathematics	PROPN
ejpam-5650	460	4	and	and	CCONJ
ejpam-5650	460	5	computer	computer	NOUN
ejpam-5650	460	6	science	science	NOUN
ejpam-5650	460	7	,	,	PUNCT
ejpam-5650	460	8	18:282–293	18:282–293	NUM
ejpam-5650	460	9	,	,	PUNCT
ejpam-5650	460	10	2018	2018	NUM
ejpam-5650	460	11	.	.	PUNCT
ejpam-5650	461	1	[	[	X
ejpam-5650	461	2	30	30	NUM
ejpam-5650	461	3	]	]	X
ejpam-5650	461	4	c.	c.	PROPN
ejpam-5650	461	5	carpintero	carpintero	PROPN
ejpam-5650	461	6	,	,	PUNCT
ejpam-5650	461	7	j.	j.	PROPN
ejpam-5650	461	8	pacheco	pacheco	PROPN
ejpam-5650	461	9	,	,	PUNCT
ejpam-5650	461	10	n.	n.	PROPN
ejpam-5650	461	11	rajesh	rajesh	PROPN
ejpam-5650	461	12	,	,	PUNCT
ejpam-5650	461	13	e.	e.	PROPN
ejpam-5650	461	14	rosas	rosas	PROPN
ejpam-5650	461	15	,	,	PUNCT
ejpam-5650	461	16	and	and	CCONJ
ejpam-5650	461	17	s.	s.	PROPN
ejpam-5650	461	18	saranyasri	saranyasri	PROPN
ejpam-5650	461	19	.	.	PUNCT
ejpam-5650	462	1	properties	property	NOUN
ejpam-5650	462	2	of	of	ADP
ejpam-5650	462	3	nearly	nearly	ADV
ejpam-5650	462	4	ω	ω	ADJ
ejpam-5650	462	5	-	-	ADJ
ejpam-5650	462	6	continuous	continuous	ADJ
ejpam-5650	462	7	multifunctions	multifunction	NOUN
ejpam-5650	462	8	.	.	PUNCT
ejpam-5650	463	1	acta	acta	PROPN
ejpam-5650	463	2	universitatis	universitatis	PROPN
ejpam-5650	463	3	sapientiae	sapientiae	PROPN
ejpam-5650	463	4	,	,	PUNCT
ejpam-5650	463	5	mathematica	mathematica	PROPN
ejpam-5650	463	6	,	,	PUNCT
ejpam-5650	463	7	9(1):13–25	9(1):13–25	NUM
ejpam-5650	463	8	,	,	PUNCT
ejpam-5650	463	9	2017	2017	NUM
ejpam-5650	463	10	.	.	PUNCT
ejpam-5650	464	1	[	[	X
ejpam-5650	464	2	31	31	NUM
ejpam-5650	464	3	]	]	PUNCT
ejpam-5650	464	4	m.	m.	NOUN
ejpam-5650	464	5	chiangpradit	chiangpradit	NOUN
ejpam-5650	464	6	,	,	PUNCT
ejpam-5650	464	7	s.	s.	PROPN
ejpam-5650	464	8	sompong	sompong	PROPN
ejpam-5650	464	9	,	,	PUNCT
ejpam-5650	464	10	and	and	CCONJ
ejpam-5650	464	11	c.	c.	PROPN
ejpam-5650	464	12	boonpok	boonpok	PROPN
ejpam-5650	464	13	.	.	PUNCT
ejpam-5650	465	1	weakly	weakly	ADJ
ejpam-5650	465	2	quasi	quasi	NOUN
ejpam-5650	465	3	(	(	PUNCT
ejpam-5650	465	4	τ1	τ1	PROPN
ejpam-5650	465	5	,	,	PUNCT
ejpam-5650	465	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	465	7	functions	function	NOUN
ejpam-5650	465	8	.	.	PUNCT
ejpam-5650	466	1	international	international	ADJ
ejpam-5650	466	2	journal	journal	NOUN
ejpam-5650	466	3	of	of	ADP
ejpam-5650	466	4	analysis	analysis	NOUN
ejpam-5650	466	5	and	and	CCONJ
ejpam-5650	466	6	applications	application	NOUN
ejpam-5650	466	7	,	,	PUNCT
ejpam-5650	466	8	22:125	22:125	NUM
ejpam-5650	466	9	,	,	PUNCT
ejpam-5650	466	10	2024	2024	NUM
ejpam-5650	466	11	.	.	PUNCT
ejpam-5650	467	1	[	[	X
ejpam-5650	467	2	32	32	NUM
ejpam-5650	467	3	]	]	PUNCT
ejpam-5650	467	4	t.	t.	PROPN
ejpam-5650	467	5	duangphui	duangphui	PROPN
ejpam-5650	467	6	,	,	PUNCT
ejpam-5650	467	7	c.	c.	PROPN
ejpam-5650	467	8	boonpok	boonpok	PROPN
ejpam-5650	467	9	,	,	PUNCT
ejpam-5650	467	10	and	and	CCONJ
ejpam-5650	467	11	c.	c.	PROPN
ejpam-5650	467	12	viriyapong	viriyapong	PROPN
ejpam-5650	467	13	.	.	PUNCT
ejpam-5650	468	1	continuous	continuous	ADJ
ejpam-5650	468	2	functions	function	NOUN
ejpam-5650	468	3	on	on	ADP
ejpam-5650	468	4	bigeneralized	bigeneralize	VERB
ejpam-5650	468	5	topological	topological	ADJ
ejpam-5650	468	6	spaces	space	NOUN
ejpam-5650	468	7	.	.	PUNCT
ejpam-5650	469	1	international	international	ADJ
ejpam-5650	469	2	journal	journal	PROPN
ejpam-5650	469	3	of	of	ADP
ejpam-5650	469	4	mathematical	mathematical	ADJ
ejpam-5650	469	5	analysis	analysis	NOUN
ejpam-5650	469	6	,	,	PUNCT
ejpam-5650	469	7	5(24):1165	5(24):1165	NUM
ejpam-5650	469	8	–	–	PUNCT
ejpam-5650	469	9	1174	1174	NUM
ejpam-5650	469	10	,	,	PUNCT
ejpam-5650	469	11	2011	2011	NUM
ejpam-5650	469	12	.	.	PUNCT
ejpam-5650	470	1	[	[	X
ejpam-5650	470	2	33	33	NUM
ejpam-5650	470	3	]	]	PUNCT
ejpam-5650	470	4	t.	t.	NOUN
ejpam-5650	470	5	dungthaisong	dungthaisong	PROPN
ejpam-5650	470	6	,	,	PUNCT
ejpam-5650	470	7	c.	c.	PROPN
ejpam-5650	470	8	boonpok	boonpok	PROPN
ejpam-5650	470	9	,	,	PUNCT
ejpam-5650	470	10	and	and	CCONJ
ejpam-5650	470	11	c.	c.	PROPN
ejpam-5650	470	12	viriyapong	viriyapong	PROPN
ejpam-5650	470	13	.	.	PUNCT
ejpam-5650	471	1	generalized	generalize	VERB
ejpam-5650	471	2	closed	close	VERB
ejpam-5650	471	3	sets	set	NOUN
ejpam-5650	471	4	in	in	ADP
ejpam-5650	471	5	bigeneralized	bigeneralize	VERB
ejpam-5650	471	6	topological	topological	ADJ
ejpam-5650	471	7	spaces	space	NOUN
ejpam-5650	471	8	.	.	PUNCT
ejpam-5650	472	1	international	international	ADJ
ejpam-5650	472	2	journal	journal	PROPN
ejpam-5650	472	3	of	of	ADP
ejpam-5650	472	4	mathematical	mathematical	ADJ
ejpam-5650	472	5	analysis	analysis	NOUN
ejpam-5650	472	6	,	,	PUNCT
ejpam-5650	472	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5650	472	8	,	,	PUNCT
ejpam-5650	472	9	2011	2011	NUM
ejpam-5650	472	10	.	.	PUNCT
ejpam-5650	473	1	[	[	X
ejpam-5650	473	2	34	34	NUM
ejpam-5650	473	3	]	]	X
ejpam-5650	473	4	e.	e.	PROPN
ejpam-5650	473	5	ekici	ekici	PROPN
ejpam-5650	473	6	.	.	PUNCT
ejpam-5650	474	1	nearly	nearly	ADV
ejpam-5650	474	2	continuous	continuous	ADJ
ejpam-5650	474	3	multifunctions	multifunction	NOUN
ejpam-5650	474	4	.	.	PUNCT
ejpam-5650	475	1	acta	acta	PROPN
ejpam-5650	475	2	mathematica	mathematica	PROPN
ejpam-5650	475	3	universitatis	universitatis	PROPN
ejpam-5650	475	4	comenianae	comenianae	PROPN
ejpam-5650	475	5	,	,	PUNCT
ejpam-5650	475	6	72:229–235	72:229–235	PROPN
ejpam-5650	475	7	,	,	PUNCT
ejpam-5650	475	8	2003	2003	NUM
ejpam-5650	475	9	.	.	PUNCT
ejpam-5650	476	1	[	[	X
ejpam-5650	476	2	35	35	NUM
ejpam-5650	476	3	]	]	X
ejpam-5650	476	4	e.	e.	PROPN
ejpam-5650	476	5	ekici	ekici	PROPN
ejpam-5650	476	6	.	.	PUNCT
ejpam-5650	477	1	almost	almost	ADV
ejpam-5650	477	2	nearly	nearly	ADV
ejpam-5650	477	3	continuous	continuous	ADJ
ejpam-5650	477	4	multifunctions	multifunction	NOUN
ejpam-5650	477	5	.	.	PUNCT
ejpam-5650	478	1	acta	acta	PROPN
ejpam-5650	478	2	mathematica	mathematica	PROPN
ejpam-5650	478	3	universitatis	universitatis	PROPN
ejpam-5650	478	4	comenianae	comenianae	PROPN
ejpam-5650	478	5	,	,	PUNCT
ejpam-5650	478	6	73:175–186	73:175–186	PROPN
ejpam-5650	478	7	,	,	PUNCT
ejpam-5650	478	8	2004	2004	NUM
ejpam-5650	478	9	.	.	PUNCT
ejpam-5650	479	1	[	[	X
ejpam-5650	479	2	36	36	NUM
ejpam-5650	479	3	]	]	X
ejpam-5650	479	4	j.	j.	PROPN
ejpam-5650	479	5	khampakdee	khampakdee	PROPN
ejpam-5650	479	6	and	and	CCONJ
ejpam-5650	479	7	c.	c.	PROPN
ejpam-5650	479	8	boonpok	boonpok	PROPN
ejpam-5650	479	9	.	.	PUNCT
ejpam-5650	480	1	upper	upper	ADJ
ejpam-5650	480	2	and	and	CCONJ
ejpam-5650	480	3	lower	low	ADJ
ejpam-5650	480	4	α(λ	α(λ	PROPN
ejpam-5650	480	5	,	,	PUNCT
ejpam-5650	480	6	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	480	7	multifunctions	multifunction	NOUN
ejpam-5650	480	8	.	.	PUNCT
ejpam-5650	481	1	wseas	wseas	VERB
ejpam-5650	481	2	transactions	transaction	NOUN
ejpam-5650	481	3	on	on	ADP
ejpam-5650	481	4	mathematics	mathematic	NOUN
ejpam-5650	481	5	,	,	PUNCT
ejpam-5650	481	6	21:684–690	21:684–690	NUM
ejpam-5650	481	7	,	,	PUNCT
ejpam-5650	481	8	2022	2022	NUM
ejpam-5650	481	9	.	.	PUNCT
ejpam-5650	482	1	[	[	X
ejpam-5650	482	2	37	37	NUM
ejpam-5650	482	3	]	]	X
ejpam-5650	482	4	j.	j.	PROPN
ejpam-5650	482	5	khampakdee	khampakdee	PROPN
ejpam-5650	482	6	,	,	PUNCT
ejpam-5650	482	7	s.	s.	PROPN
ejpam-5650	482	8	sompong	sompong	PROPN
ejpam-5650	482	9	,	,	PUNCT
ejpam-5650	482	10	and	and	CCONJ
ejpam-5650	482	11	c.	c.	PROPN
ejpam-5650	482	12	boonpok	boonpok	PROPN
ejpam-5650	482	13	.	.	PUNCT
ejpam-5650	483	1	c-(τ1	c-(τ1	PROPN
ejpam-5650	483	2	,	,	PUNCT
ejpam-5650	483	3	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5650	483	4	for	for	ADP
ejpam-5650	483	5	multifunctions	multifunction	NOUN
ejpam-5650	483	6	.	.	PUNCT
ejpam-5650	484	1	european	european	ADJ
ejpam-5650	484	2	journal	journal	PROPN
ejpam-5650	484	3	of	of	ADP
ejpam-5650	484	4	pure	pure	ADJ
ejpam-5650	484	5	and	and	CCONJ
ejpam-5650	484	6	applied	applied	ADJ
ejpam-5650	484	7	mathematics	mathematic	NOUN
ejpam-5650	484	8	,	,	PUNCT
ejpam-5650	484	9	17(3):2289–2299	17(3):2289–2299	NUM
ejpam-5650	484	10	,	,	PUNCT
ejpam-5650	484	11	2024	2024	NUM
ejpam-5650	484	12	.	.	PUNCT
ejpam-5650	485	1	[	[	X
ejpam-5650	485	2	38	38	NUM
ejpam-5650	485	3	]	]	PUNCT
ejpam-5650	485	4	c.	c.	PROPN
ejpam-5650	485	5	klanarong	klanarong	PROPN
ejpam-5650	485	6	,	,	PUNCT
ejpam-5650	485	7	s.	s.	PROPN
ejpam-5650	485	8	sompong	sompong	PROPN
ejpam-5650	485	9	,	,	PUNCT
ejpam-5650	485	10	and	and	CCONJ
ejpam-5650	485	11	c.	c.	PROPN
ejpam-5650	485	12	boonpok	boonpok	PROPN
ejpam-5650	485	13	.	.	PUNCT
ejpam-5650	486	1	upper	upper	ADJ
ejpam-5650	486	2	and	and	CCONJ
ejpam-5650	486	3	lower	low	ADJ
ejpam-5650	486	4	almost	almost	ADV
ejpam-5650	486	5	(	(	PUNCT
ejpam-5650	486	6	τ1	τ1	NOUN
ejpam-5650	486	7	,	,	PUNCT
ejpam-5650	486	8	τ2)continuous	τ2)continuous	ADJ
ejpam-5650	486	9	multifunctions	multifunction	NOUN
ejpam-5650	486	10	.	.	PUNCT
ejpam-5650	487	1	european	european	ADJ
ejpam-5650	487	2	journal	journal	PROPN
ejpam-5650	487	3	of	of	ADP
ejpam-5650	487	4	pure	pure	ADJ
ejpam-5650	487	5	and	and	CCONJ
ejpam-5650	487	6	applied	applied	ADJ
ejpam-5650	487	7	mathematics	mathematic	NOUN
ejpam-5650	487	8	,	,	PUNCT
ejpam-5650	487	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-5650	487	10	,	,	PUNCT
ejpam-5650	487	11	2024	2024	NUM
ejpam-5650	487	12	.	.	PUNCT
ejpam-5650	488	1	[	[	X
ejpam-5650	488	2	39	39	NUM
ejpam-5650	488	3	]	]	PUNCT
ejpam-5650	488	4	b.	b.	PROPN
ejpam-5650	488	5	kong	kong	PROPN
ejpam-5650	488	6	-	-	PUNCT
ejpam-5650	488	7	ied	ied	PROPN
ejpam-5650	488	8	,	,	PUNCT
ejpam-5650	488	9	s.	s.	PROPN
ejpam-5650	488	10	sompong	sompong	PROPN
ejpam-5650	488	11	,	,	PUNCT
ejpam-5650	488	12	and	and	CCONJ
ejpam-5650	488	13	c.	c.	PROPN
ejpam-5650	488	14	boonpok	boonpok	PROPN
ejpam-5650	488	15	.	.	PUNCT
ejpam-5650	489	1	almost	almost	ADV
ejpam-5650	489	2	quasi	quasi	X
ejpam-5650	489	3	(	(	PUNCT
ejpam-5650	489	4	τ1	τ1	NOUN
ejpam-5650	489	5	,	,	PUNCT
ejpam-5650	489	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	489	7	functions	function	NOUN
ejpam-5650	489	8	.	.	PUNCT
ejpam-5650	490	1	asia	asia	PROPN
ejpam-5650	490	2	pacific	pacific	PROPN
ejpam-5650	490	3	journal	journal	PROPN
ejpam-5650	490	4	of	of	ADP
ejpam-5650	490	5	mathematics	mathematic	NOUN
ejpam-5650	490	6	,	,	PUNCT
ejpam-5650	490	7	11:64	11:64	NUM
ejpam-5650	490	8	,	,	PUNCT
ejpam-5650	490	9	2024	2024	NUM
ejpam-5650	490	10	.	.	PUNCT
ejpam-5650	491	1	[	[	X
ejpam-5650	491	2	40	40	NUM
ejpam-5650	491	3	]	]	PUNCT
ejpam-5650	491	4	s.	s.	PROPN
ejpam-5650	491	5	n.	n.	PROPN
ejpam-5650	491	6	maheshwari	maheshwari	PROPN
ejpam-5650	491	7	,	,	PUNCT
ejpam-5650	491	8	gyn	gyn	NOUN
ejpam-5650	491	9	-	-	PUNCT
ejpam-5650	491	10	ihn	ihn	NOUN
ejpam-5650	491	11	chae	chae	PROPN
ejpam-5650	491	12	,	,	PUNCT
ejpam-5650	491	13	and	and	CCONJ
ejpam-5650	491	14	p.	p.	PROPN
ejpam-5650	491	15	c.	c.	PROPN
ejpam-5650	491	16	jain	jain	PROPN
ejpam-5650	491	17	.	.	PUNCT
ejpam-5650	492	1	almost	almost	ADV
ejpam-5650	492	2	feebly	feebly	ADV
ejpam-5650	492	3	continuous	continuous	ADJ
ejpam-5650	492	4	functions	function	NOUN
ejpam-5650	492	5	.	.	PUNCT
ejpam-5650	493	1	uit	uit	PROPN
ejpam-5650	493	2	report	report	PROPN
ejpam-5650	493	3	,	,	PUNCT
ejpam-5650	493	4	13(1):195–197	13(1):195–197	NUM
ejpam-5650	493	5	,	,	PUNCT
ejpam-5650	493	6	1982	1982	NUM
ejpam-5650	493	7	.	.	PUNCT
ejpam-5650	494	1	[	[	X
ejpam-5650	494	2	41	41	NUM
ejpam-5650	494	3	]	]	X
ejpam-5650	494	4	s.	s.	PROPN
ejpam-5650	494	5	r.	r.	PROPN
ejpam-5650	494	6	malghan	malghan	PROPN
ejpam-5650	494	7	and	and	CCONJ
ejpam-5650	494	8	v.	v.	ADP
ejpam-5650	494	9	v.	v.	CCONJ
ejpam-5650	494	10	hanchinamani	hanchinamani	PROPN
ejpam-5650	494	11	.	.	PUNCT
ejpam-5650	495	1	n	n	CCONJ
ejpam-5650	495	2	-	-	PUNCT
ejpam-5650	495	3	continuous	continuous	ADJ
ejpam-5650	495	4	functions	function	NOUN
ejpam-5650	495	5	.	.	PUNCT
ejpam-5650	496	1	annales	annales	PROPN
ejpam-5650	496	2	de	de	ADP
ejpam-5650	496	3	la	la	PROPN
ejpam-5650	496	4	société	société	PROPN
ejpam-5650	496	5	scientifique	scientifique	PROPN
ejpam-5650	496	6	de	de	X
ejpam-5650	496	7	bruxelles	bruxelle	NOUN
ejpam-5650	496	8	,	,	PUNCT
ejpam-5650	496	9	98:69–79	98:69–79	ADV
ejpam-5650	496	10	,	,	PUNCT
ejpam-5650	496	11	1984	1984	NUM
ejpam-5650	496	12	.	.	PUNCT
ejpam-5650	497	1	[	[	X
ejpam-5650	497	2	42	42	NUM
ejpam-5650	497	3	]	]	PUNCT
ejpam-5650	497	4	s.	s.	PROPN
ejpam-5650	497	5	marcus	marcus	PROPN
ejpam-5650	497	6	.	.	PUNCT
ejpam-5650	498	1	sur	sur	PROPN
ejpam-5650	498	2	les	les	PROPN
ejpam-5650	498	3	fonctions	fonctions	PROPN
ejpam-5650	498	4	quasicontinues	quasicontinue	NOUN
ejpam-5650	498	5	au	au	PROPN
ejpam-5650	498	6	sens	sens	X
ejpam-5650	498	7	de	de	PROPN
ejpam-5650	498	8	s.	s.	PROPN
ejpam-5650	498	9	kempisty	kempisty	PROPN
ejpam-5650	498	10	.	.	PUNCT
ejpam-5650	499	1	colloquium	colloquium	NOUN
ejpam-5650	499	2	mathematicum	mathematicum	PROPN
ejpam-5650	499	3	,	,	PUNCT
ejpam-5650	499	4	8:47–53	8:47–53	NUM
ejpam-5650	499	5	,	,	PUNCT
ejpam-5650	499	6	1961	1961	NUM
ejpam-5650	499	7	.	.	PUNCT
ejpam-5650	500	1	[	[	X
ejpam-5650	500	2	43	43	NUM
ejpam-5650	500	3	]	]	X
ejpam-5650	500	4	b.	b.	PROPN
ejpam-5650	500	5	m.	m.	PROPN
ejpam-5650	500	6	munshi	munshi	PROPN
ejpam-5650	500	7	and	and	CCONJ
ejpam-5650	500	8	d.	d.	PROPN
ejpam-5650	500	9	s.	s.	PROPN
ejpam-5650	500	10	bassan	bassan	PROPN
ejpam-5650	500	11	.	.	PUNCT
ejpam-5650	501	1	almost	almost	ADV
ejpam-5650	501	2	semi	semi	ADJ
ejpam-5650	501	3	-	-	ADJ
ejpam-5650	501	4	continuous	continuous	ADJ
ejpam-5650	501	5	mappings	mapping	NOUN
ejpam-5650	501	6	.	.	PUNCT
ejpam-5650	502	1	the	the	DET
ejpam-5650	502	2	mathematics	mathematics	PROPN
ejpam-5650	502	3	n.	n.	PROPN
ejpam-5650	502	4	chutiman	chutiman	PROPN
ejpam-5650	502	5	,	,	PUNCT
ejpam-5650	502	6	a.	a.	PROPN
ejpam-5650	502	7	sama	sama	PROPN
ejpam-5650	502	8	-	-	PUNCT
ejpam-5650	502	9	ae	ae	PROPN
ejpam-5650	502	10	,	,	PUNCT
ejpam-5650	502	11	c.	c.	PROPN
ejpam-5650	502	12	boonpok	boonpok	PROPN
ejpam-5650	502	13	/	/	SYM
ejpam-5650	502	14	eur	eur	PROPN
ejpam-5650	502	15	.	.	PUNCT
ejpam-5650	503	1	j.	j.	PROPN
ejpam-5650	503	2	pure	pure	PROPN
ejpam-5650	503	3	appl	appl	PROPN
ejpam-5650	503	4	.	.	PROPN
ejpam-5650	503	5	math	math	PROPN
ejpam-5650	503	6	,	,	PUNCT
ejpam-5650	503	7	18	18	NUM
ejpam-5650	503	8	(	(	PUNCT
ejpam-5650	503	9	1	1	NUM
ejpam-5650	503	10	)	)	PUNCT
ejpam-5650	503	11	(	(	PUNCT
ejpam-5650	503	12	2025	2025	NUM
ejpam-5650	503	13	)	)	PUNCT
ejpam-5650	503	14	,	,	PUNCT
ejpam-5650	503	15	5650	5650	NUM
ejpam-5650	503	16	17	17	NUM
ejpam-5650	503	17	of	of	ADP
ejpam-5650	503	18	18	18	NUM
ejpam-5650	503	19	student	student	NOUN
ejpam-5650	503	20	,	,	PUNCT
ejpam-5650	503	21	49(3):239–248	49(3):239–248	PROPN
ejpam-5650	503	22	,	,	PUNCT
ejpam-5650	503	23	1981	1981	NUM
ejpam-5650	503	24	.	.	PUNCT
ejpam-5650	504	1	[	[	X
ejpam-5650	504	2	44	44	NUM
ejpam-5650	504	3	]	]	PUNCT
ejpam-5650	504	4	t.	t.	PROPN
ejpam-5650	504	5	noiri	noiri	PROPN
ejpam-5650	504	6	and	and	CCONJ
ejpam-5650	504	7	n.	n.	PROPN
ejpam-5650	504	8	ergun	ergun	PROPN
ejpam-5650	504	9	.	.	PUNCT
ejpam-5650	505	1	notes	note	NOUN
ejpam-5650	505	2	on	on	ADP
ejpam-5650	505	3	n	n	CCONJ
ejpam-5650	505	4	-	-	PUNCT
ejpam-5650	505	5	continuous	continuous	ADJ
ejpam-5650	505	6	functions	function	NOUN
ejpam-5650	505	7	.	.	PUNCT
ejpam-5650	506	1	research	research	NOUN
ejpam-5650	506	2	reports	report	NOUN
ejpam-5650	506	3	of	of	ADP
ejpam-5650	506	4	yatsushiro	yatsushiro	PROPN
ejpam-5650	506	5	national	national	PROPN
ejpam-5650	506	6	college	college	PROPN
ejpam-5650	506	7	of	of	ADP
ejpam-5650	506	8	technology	technology	NOUN
ejpam-5650	506	9	,	,	PUNCT
ejpam-5650	506	10	11:65–68	11:65–68	NUM
ejpam-5650	506	11	,	,	PUNCT
ejpam-5650	506	12	1989	1989	NUM
ejpam-5650	506	13	.	.	PUNCT
ejpam-5650	507	1	[	[	X
ejpam-5650	507	2	45	45	NUM
ejpam-5650	507	3	]	]	PUNCT
ejpam-5650	507	4	t.	t.	PROPN
ejpam-5650	507	5	noiri	noiri	PROPN
ejpam-5650	507	6	and	and	CCONJ
ejpam-5650	507	7	v.	v.	ADP
ejpam-5650	507	8	popa	popa	NOUN
ejpam-5650	507	9	.	.	PUNCT
ejpam-5650	508	1	a	a	DET
ejpam-5650	508	2	unified	unified	ADJ
ejpam-5650	508	3	theory	theory	NOUN
ejpam-5650	508	4	of	of	ADP
ejpam-5650	508	5	upper	upper	ADJ
ejpam-5650	508	6	and	and	CCONJ
ejpam-5650	508	7	lower	low	ADJ
ejpam-5650	508	8	almost	almost	ADV
ejpam-5650	508	9	nearly	nearly	ADV
ejpam-5650	508	10	continuous	continuous	ADJ
ejpam-5650	508	11	multifunctions	multifunction	NOUN
ejpam-5650	508	12	.	.	PUNCT
ejpam-5650	509	1	mathematica	mathematica	PROPN
ejpam-5650	509	2	balkanica	balkanica	PROPN
ejpam-5650	509	3	,	,	PUNCT
ejpam-5650	509	4	23:51–72	23:51–72	PROPN
ejpam-5650	509	5	,	,	PUNCT
ejpam-5650	509	6	2009	2009	NUM
ejpam-5650	509	7	.	.	PUNCT
ejpam-5650	510	1	[	[	X
ejpam-5650	510	2	46	46	NUM
ejpam-5650	510	3	]	]	X
ejpam-5650	510	4	v.	v.	CCONJ
ejpam-5650	510	5	popa	popa	NOUN
ejpam-5650	510	6	.	.	PUNCT
ejpam-5650	511	1	on	on	ADP
ejpam-5650	511	2	a	a	DET
ejpam-5650	511	3	decomposition	decomposition	NOUN
ejpam-5650	511	4	of	of	ADP
ejpam-5650	511	5	quasi	quasi	NOUN
ejpam-5650	511	6	-	-	NOUN
ejpam-5650	511	7	continuity	continuity	NOUN
ejpam-5650	511	8	in	in	ADP
ejpam-5650	511	9	topological	topological	ADJ
ejpam-5650	511	10	spaces	space	NOUN
ejpam-5650	511	11	.	.	PUNCT
ejpam-5650	512	1	studii	studii	PROPN
ejpam-5650	512	2	şi	şi	PROPN
ejpam-5650	512	3	cercetǎri	cercetǎri	NOUN
ejpam-5650	512	4	matematicǎ	matematicǎ	VERB
ejpam-5650	512	5	,	,	PUNCT
ejpam-5650	512	6	30:31–35	30:31–35	NUM
ejpam-5650	512	7	,	,	PUNCT
ejpam-5650	512	8	1978	1978	NUM
ejpam-5650	512	9	.	.	PUNCT
ejpam-5650	513	1	[	[	X
ejpam-5650	513	2	47	47	NUM
ejpam-5650	513	3	]	]	X
ejpam-5650	513	4	v.	v.	CCONJ
ejpam-5650	513	5	popa	popa	NOUN
ejpam-5650	513	6	.	.	PUNCT
ejpam-5650	514	1	almost	almost	ADV
ejpam-5650	514	2	continuous	continuous	ADJ
ejpam-5650	514	3	multifunctions	multifunction	NOUN
ejpam-5650	514	4	.	.	PUNCT
ejpam-5650	515	1	matematički	matematički	PROPN
ejpam-5650	515	2	vesnik	vesnik	PROPN
ejpam-5650	515	3	,	,	PUNCT
ejpam-5650	515	4	34:75–84	34:75–84	NUM
ejpam-5650	515	5	,	,	PUNCT
ejpam-5650	515	6	1982	1982	NUM
ejpam-5650	515	7	.	.	PUNCT
ejpam-5650	516	1	[	[	X
ejpam-5650	516	2	48	48	NUM
ejpam-5650	516	3	]	]	PUNCT
ejpam-5650	516	4	v.	v.	CCONJ
ejpam-5650	516	5	popa	popa	NOUN
ejpam-5650	516	6	and	and	CCONJ
ejpam-5650	516	7	noiri	noiri	NOUN
ejpam-5650	516	8	.	.	PUNCT
ejpam-5650	517	1	on	on	ADP
ejpam-5650	517	2	upper	upper	ADJ
ejpam-5650	517	3	and	and	CCONJ
ejpam-5650	517	4	lower	low	ADJ
ejpam-5650	517	5	almost	almost	ADV
ejpam-5650	517	6	quasi	quasi	ADJ
ejpam-5650	517	7	continuous	continuous	ADJ
ejpam-5650	517	8	multifunctions	multifunction	NOUN
ejpam-5650	517	9	.	.	PUNCT
ejpam-5650	518	1	bulletin	bulletin	NOUN
ejpam-5650	518	2	of	of	ADP
ejpam-5650	518	3	the	the	DET
ejpam-5650	518	4	institute	institute	PROPN
ejpam-5650	518	5	of	of	ADP
ejpam-5650	518	6	mathematics	mathematics	PROPN
ejpam-5650	518	7	academia	academia	PROPN
ejpam-5650	518	8	sinica	sinica	PROPN
ejpam-5650	518	9	,	,	PUNCT
ejpam-5650	518	10	21:337–349	21:337–349	NUM
ejpam-5650	518	11	,	,	PUNCT
ejpam-5650	518	12	1993	1993	NUM
ejpam-5650	518	13	.	.	PUNCT
ejpam-5650	519	1	[	[	X
ejpam-5650	519	2	49	49	NUM
ejpam-5650	519	3	]	]	PUNCT
ejpam-5650	519	4	p.	p.	NOUN
ejpam-5650	519	5	pue	pue	NOUN
ejpam-5650	519	6	-	-	PUNCT
ejpam-5650	519	7	on	on	ADP
ejpam-5650	519	8	and	and	CCONJ
ejpam-5650	519	9	c.	c.	PROPN
ejpam-5650	519	10	boonpok	boonpok	PROPN
ejpam-5650	519	11	.	.	PUNCT
ejpam-5650	520	1	θ(λ	θ(λ	PROPN
ejpam-5650	520	2	,	,	PUNCT
ejpam-5650	520	3	p)-continuity	p)-continuity	NOUN
ejpam-5650	520	4	for	for	ADP
ejpam-5650	520	5	functions	function	NOUN
ejpam-5650	520	6	.	.	PUNCT
ejpam-5650	521	1	international	international	ADJ
ejpam-5650	521	2	journal	journal	NOUN
ejpam-5650	521	3	of	of	ADP
ejpam-5650	521	4	mathematics	mathematic	NOUN
ejpam-5650	521	5	and	and	CCONJ
ejpam-5650	521	6	computer	computer	NOUN
ejpam-5650	521	7	science	science	NOUN
ejpam-5650	521	8	,	,	PUNCT
ejpam-5650	521	9	19(2):491–495	19(2):491–495	NUM
ejpam-5650	521	10	,	,	PUNCT
ejpam-5650	521	11	2024	2024	NUM
ejpam-5650	521	12	.	.	PUNCT
ejpam-5650	522	1	[	[	X
ejpam-5650	522	2	50	50	NUM
ejpam-5650	522	3	]	]	PUNCT
ejpam-5650	522	4	p.	p.	NOUN
ejpam-5650	522	5	pue	pue	NOUN
ejpam-5650	522	6	-	-	PUNCT
ejpam-5650	522	7	on	on	ADP
ejpam-5650	522	8	,	,	PUNCT
ejpam-5650	522	9	a.	a.	PROPN
ejpam-5650	522	10	sama	sama	PROPN
ejpam-5650	522	11	-	-	PUNCT
ejpam-5650	522	12	ae	ae	PROPN
ejpam-5650	522	13	,	,	PUNCT
ejpam-5650	522	14	and	and	CCONJ
ejpam-5650	522	15	c.	c.	PROPN
ejpam-5650	522	16	boonpok	boonpok	PROPN
ejpam-5650	522	17	.	.	PUNCT
ejpam-5650	523	1	c	c	X
ejpam-5650	523	2	-	-	PUNCT
ejpam-5650	523	3	quasi	quasi	X
ejpam-5650	523	4	(	(	PUNCT
ejpam-5650	523	5	τ1	τ1	PROPN
ejpam-5650	523	6	,	,	PUNCT
ejpam-5650	523	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	523	8	multifunctions	multifunction	NOUN
ejpam-5650	523	9	.	.	PUNCT
ejpam-5650	524	1	european	european	ADJ
ejpam-5650	524	2	journal	journal	PROPN
ejpam-5650	524	3	of	of	ADP
ejpam-5650	524	4	pure	pure	ADJ
ejpam-5650	524	5	and	and	CCONJ
ejpam-5650	524	6	applied	applied	ADJ
ejpam-5650	524	7	mathematics	mathematic	NOUN
ejpam-5650	524	8	,	,	PUNCT
ejpam-5650	524	9	17(4):3242–3253	17(4):3242–3253	NUM
ejpam-5650	524	10	,	,	PUNCT
ejpam-5650	524	11	2024	2024	NUM
ejpam-5650	524	12	.	.	PUNCT
ejpam-5650	525	1	[	[	X
ejpam-5650	525	2	51	51	NUM
ejpam-5650	525	3	]	]	X
ejpam-5650	525	4	p.	p.	NOUN
ejpam-5650	525	5	pue	pue	NOUN
ejpam-5650	525	6	-	-	PUNCT
ejpam-5650	525	7	on	on	ADP
ejpam-5650	525	8	,	,	PUNCT
ejpam-5650	525	9	s.	s.	PROPN
ejpam-5650	525	10	sompong	sompong	PROPN
ejpam-5650	525	11	,	,	PUNCT
ejpam-5650	525	12	and	and	CCONJ
ejpam-5650	525	13	c.	c.	PROPN
ejpam-5650	525	14	boonpok	boonpok	PROPN
ejpam-5650	525	15	.	.	PUNCT
ejpam-5650	526	1	almost	almost	ADV
ejpam-5650	526	2	quasi	quasi	X
ejpam-5650	526	3	(	(	PUNCT
ejpam-5650	526	4	τ1	τ1	NOUN
ejpam-5650	526	5	,	,	PUNCT
ejpam-5650	526	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5650	526	7	for	for	ADP
ejpam-5650	526	8	multifunctions	multifunction	NOUN
ejpam-5650	526	9	.	.	PUNCT
ejpam-5650	527	1	international	international	ADJ
ejpam-5650	527	2	journal	journal	NOUN
ejpam-5650	527	3	of	of	ADP
ejpam-5650	527	4	analysis	analysis	NOUN
ejpam-5650	527	5	and	and	CCONJ
ejpam-5650	527	6	applications	application	NOUN
ejpam-5650	527	7	,	,	PUNCT
ejpam-5650	527	8	22:97	22:97	NUM
ejpam-5650	527	9	,	,	PUNCT
ejpam-5650	527	10	2024	2024	NUM
ejpam-5650	527	11	.	.	PUNCT
ejpam-5650	528	1	[	[	X
ejpam-5650	528	2	52	52	NUM
ejpam-5650	528	3	]	]	PUNCT
ejpam-5650	528	4	p.	p.	NOUN
ejpam-5650	528	5	pue	pue	NOUN
ejpam-5650	528	6	-	-	PUNCT
ejpam-5650	528	7	on	on	ADP
ejpam-5650	528	8	,	,	PUNCT
ejpam-5650	528	9	s.	s.	PROPN
ejpam-5650	528	10	sompong	sompong	PROPN
ejpam-5650	528	11	,	,	PUNCT
ejpam-5650	528	12	and	and	CCONJ
ejpam-5650	528	13	c.	c.	PROPN
ejpam-5650	528	14	boonpok	boonpok	PROPN
ejpam-5650	528	15	.	.	PUNCT
ejpam-5650	529	1	upper	upper	ADJ
ejpam-5650	529	2	and	and	CCONJ
ejpam-5650	529	3	lower	low	ADJ
ejpam-5650	529	4	(	(	PUNCT
ejpam-5650	529	5	τ1	τ1	NOUN
ejpam-5650	529	6	,	,	PUNCT
ejpam-5650	529	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	529	8	mulfunctions	mulfunction	NOUN
ejpam-5650	529	9	.	.	PUNCT
ejpam-5650	530	1	international	international	ADJ
ejpam-5650	530	2	journal	journal	NOUN
ejpam-5650	530	3	of	of	ADP
ejpam-5650	530	4	mathematics	mathematic	NOUN
ejpam-5650	530	5	and	and	CCONJ
ejpam-5650	530	6	computer	computer	NOUN
ejpam-5650	530	7	science	science	NOUN
ejpam-5650	530	8	,	,	PUNCT
ejpam-5650	530	9	19(4):1305	19(4):1305	NUM
ejpam-5650	530	10	–	–	PUNCT
ejpam-5650	530	11	1310	1310	NUM
ejpam-5650	530	12	,	,	PUNCT
ejpam-5650	530	13	2024	2024	NUM
ejpam-5650	530	14	.	.	PUNCT
ejpam-5650	531	1	[	[	X
ejpam-5650	531	2	53	53	NUM
ejpam-5650	531	3	]	]	PUNCT
ejpam-5650	531	4	p.	p.	NOUN
ejpam-5650	531	5	pue	pue	NOUN
ejpam-5650	531	6	-	-	PUNCT
ejpam-5650	531	7	on	on	ADP
ejpam-5650	531	8	,	,	PUNCT
ejpam-5650	531	9	s.	s.	PROPN
ejpam-5650	531	10	sompong	sompong	PROPN
ejpam-5650	531	11	,	,	PUNCT
ejpam-5650	531	12	and	and	CCONJ
ejpam-5650	531	13	c.	c.	PROPN
ejpam-5650	531	14	boonpok	boonpok	PROPN
ejpam-5650	531	15	.	.	PUNCT
ejpam-5650	532	1	weakly	weakly	ADJ
ejpam-5650	532	2	quasi	quasi	NOUN
ejpam-5650	532	3	(	(	PUNCT
ejpam-5650	532	4	τ1	τ1	PROPN
ejpam-5650	532	5	,	,	PUNCT
ejpam-5650	532	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	532	7	multifunctions	multifunction	NOUN
ejpam-5650	532	8	.	.	PUNCT
ejpam-5650	533	1	european	european	ADJ
ejpam-5650	533	2	journal	journal	PROPN
ejpam-5650	533	3	of	of	ADP
ejpam-5650	533	4	pure	pure	ADJ
ejpam-5650	533	5	and	and	CCONJ
ejpam-5650	533	6	applied	applied	ADJ
ejpam-5650	533	7	mathematics	mathematic	NOUN
ejpam-5650	533	8	,	,	PUNCT
ejpam-5650	533	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-5650	533	10	,	,	PUNCT
ejpam-5650	533	11	2024	2024	NUM
ejpam-5650	533	12	.	.	PUNCT
ejpam-5650	534	1	[	[	X
ejpam-5650	534	2	54	54	NUM
ejpam-5650	534	3	]	]	PUNCT
ejpam-5650	534	4	e.	e.	PROPN
ejpam-5650	534	5	rosas	rosas	PROPN
ejpam-5650	534	6	,	,	PUNCT
ejpam-5650	534	7	c.	c.	PROPN
ejpam-5650	534	8	carpintero	carpintero	PROPN
ejpam-5650	534	9	,	,	PUNCT
ejpam-5650	534	10	and	and	CCONJ
ejpam-5650	534	11	j.	j.	PROPN
ejpam-5650	534	12	moreno	moreno	PROPN
ejpam-5650	534	13	.	.	PUNCT
ejpam-5650	535	1	more	more	ADV
ejpam-5650	535	2	on	on	ADP
ejpam-5650	535	3	upper	upper	ADJ
ejpam-5650	535	4	and	and	CCONJ
ejpam-5650	535	5	lower	low	ADJ
ejpam-5650	535	6	almost	almost	ADV
ejpam-5650	535	7	nearly	nearly	ADV
ejpam-5650	535	8	icontinuous	icontinuous	ADJ
ejpam-5650	535	9	multifunctions	multifunction	NOUN
ejpam-5650	535	10	.	.	PUNCT
ejpam-5650	536	1	international	international	ADJ
ejpam-5650	536	2	journal	journal	NOUN
ejpam-5650	536	3	of	of	ADP
ejpam-5650	536	4	pure	pure	ADJ
ejpam-5650	536	5	and	and	CCONJ
ejpam-5650	536	6	applied	applied	ADJ
ejpam-5650	536	7	mathematics	mathematic	NOUN
ejpam-5650	536	8	,	,	PUNCT
ejpam-5650	536	9	117(3):521–537	117(3):521–537	NUM
ejpam-5650	536	10	,	,	PUNCT
ejpam-5650	536	11	2017	2017	NUM
ejpam-5650	536	12	.	.	PUNCT
ejpam-5650	537	1	[	[	X
ejpam-5650	537	2	55	55	NUM
ejpam-5650	537	3	]	]	PUNCT
ejpam-5650	537	4	a.	a.	NOUN
ejpam-5650	537	5	rychlewicz	rychlewicz	NOUN
ejpam-5650	537	6	.	.	PUNCT
ejpam-5650	538	1	on	on	ADP
ejpam-5650	538	2	almost	almost	ADV
ejpam-5650	538	3	nearly	nearly	ADV
ejpam-5650	538	4	continuous	continuous	ADJ
ejpam-5650	538	5	functions	function	NOUN
ejpam-5650	538	6	with	with	ADP
ejpam-5650	538	7	reference	reference	NOUN
ejpam-5650	538	8	to	to	ADP
ejpam-5650	538	9	multifunctions	multifunction	NOUN
ejpam-5650	538	10	.	.	PUNCT
ejpam-5650	539	1	tatra	tatra	PROPN
ejpam-5650	539	2	mountains	mountains	PROPN
ejpam-5650	539	3	mathematical	mathematical	ADJ
ejpam-5650	539	4	publications	publication	NOUN
ejpam-5650	539	5	,	,	PUNCT
ejpam-5650	539	6	42:61–72	42:61–72	NUM
ejpam-5650	539	7	,	,	PUNCT
ejpam-5650	539	8	2009	2009	NUM
ejpam-5650	539	9	.	.	PUNCT
ejpam-5650	540	1	[	[	X
ejpam-5650	540	2	56	56	NUM
ejpam-5650	540	3	]	]	PUNCT
ejpam-5650	540	4	m.	m.	NOUN
ejpam-5650	540	5	k.	k.	PROPN
ejpam-5650	540	6	singal	singal	PROPN
ejpam-5650	540	7	and	and	CCONJ
ejpam-5650	540	8	a.	a.	PROPN
ejpam-5650	540	9	r.	r.	PROPN
ejpam-5650	540	10	singal	singal	PROPN
ejpam-5650	540	11	.	.	PUNCT
ejpam-5650	541	1	almost	almost	ADV
ejpam-5650	541	2	continuous	continuous	ADJ
ejpam-5650	541	3	mappings	mapping	NOUN
ejpam-5650	541	4	.	.	PUNCT
ejpam-5650	542	1	yokohama	yokohama	PROPN
ejpam-5650	542	2	mathematical	mathematical	PROPN
ejpam-5650	542	3	journal	journal	PROPN
ejpam-5650	542	4	,	,	PUNCT
ejpam-5650	542	5	16:63–73	16:63–73	PROPN
ejpam-5650	542	6	,	,	PUNCT
ejpam-5650	542	7	1968	1968	NUM
ejpam-5650	542	8	.	.	PUNCT
ejpam-5650	543	1	[	[	X
ejpam-5650	543	2	57	57	NUM
ejpam-5650	543	3	]	]	X
ejpam-5650	543	4	n.	n.	NOUN
ejpam-5650	543	5	srisarakham	srisarakham	PROPN
ejpam-5650	543	6	and	and	CCONJ
ejpam-5650	543	7	c.	c.	PROPN
ejpam-5650	543	8	boonpok	boonpok	PROPN
ejpam-5650	543	9	.	.	PUNCT
ejpam-5650	544	1	almost	almost	ADV
ejpam-5650	544	2	(	(	PUNCT
ejpam-5650	544	3	λ	λ	NOUN
ejpam-5650	544	4	,	,	PUNCT
ejpam-5650	544	5	p)-continuous	p)-continuous	ADJ
ejpam-5650	544	6	functions	function	NOUN
ejpam-5650	544	7	.	.	PUNCT
ejpam-5650	545	1	international	international	ADJ
ejpam-5650	545	2	journal	journal	PROPN
ejpam-5650	545	3	of	of	ADP
ejpam-5650	545	4	mathematics	mathematic	NOUN
ejpam-5650	545	5	and	and	CCONJ
ejpam-5650	545	6	computer	computer	NOUN
ejpam-5650	545	7	science	science	NOUN
ejpam-5650	545	8	,	,	PUNCT
ejpam-5650	545	9	18(2):255–259	18(2):255–259	NUM
ejpam-5650	545	10	,	,	PUNCT
ejpam-5650	545	11	2023	2023	NUM
ejpam-5650	545	12	.	.	PUNCT
ejpam-5650	546	1	[	[	X
ejpam-5650	546	2	58	58	NUM
ejpam-5650	546	3	]	]	X
ejpam-5650	546	4	n.	n.	PROPN
ejpam-5650	546	5	srisarakham	srisarakham	PROPN
ejpam-5650	546	6	,	,	PUNCT
ejpam-5650	546	7	a.	a.	PROPN
ejpam-5650	546	8	sama	sama	PROPN
ejpam-5650	546	9	-	-	PUNCT
ejpam-5650	546	10	ae	ae	PROPN
ejpam-5650	546	11	,	,	PUNCT
ejpam-5650	546	12	and	and	CCONJ
ejpam-5650	546	13	c.	c.	PROPN
ejpam-5650	546	14	boonpok	boonpok	PROPN
ejpam-5650	546	15	.	.	PUNCT
ejpam-5650	547	1	characterizations	characterization	NOUN
ejpam-5650	547	2	of	of	ADP
ejpam-5650	547	3	faintly	faintly	ADV
ejpam-5650	547	4	(	(	PUNCT
ejpam-5650	547	5	τ1	τ1	PROPN
ejpam-5650	547	6	,	,	PUNCT
ejpam-5650	547	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	547	8	functions	function	NOUN
ejpam-5650	547	9	.	.	PUNCT
ejpam-5650	548	1	european	european	ADJ
ejpam-5650	548	2	journal	journal	PROPN
ejpam-5650	548	3	of	of	ADP
ejpam-5650	548	4	pure	pure	ADJ
ejpam-5650	548	5	and	and	CCONJ
ejpam-5650	548	6	applied	applied	ADJ
ejpam-5650	548	7	mathematics	mathematic	NOUN
ejpam-5650	548	8	,	,	PUNCT
ejpam-5650	548	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-5650	548	10	,	,	PUNCT
ejpam-5650	548	11	2024	2024	NUM
ejpam-5650	548	12	.	.	PUNCT
ejpam-5650	549	1	[	[	X
ejpam-5650	549	2	59	59	NUM
ejpam-5650	549	3	]	]	PUNCT
ejpam-5650	549	4	m.	m.	NOUN
ejpam-5650	549	5	thongmoon	thongmoon	NOUN
ejpam-5650	549	6	and	and	CCONJ
ejpam-5650	549	7	c.	c.	PROPN
ejpam-5650	549	8	boonpok	boonpok	PROPN
ejpam-5650	549	9	.	.	PUNCT
ejpam-5650	550	1	upper	upper	ADJ
ejpam-5650	550	2	and	and	CCONJ
ejpam-5650	550	3	lower	low	ADJ
ejpam-5650	550	4	almost	almost	ADV
ejpam-5650	550	5	β(λ	β(λ	NOUN
ejpam-5650	550	6	,	,	PUNCT
ejpam-5650	550	7	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	550	8	multifunctions	multifunction	NOUN
ejpam-5650	550	9	.	.	PUNCT
ejpam-5650	551	1	wseas	wseas	VERB
ejpam-5650	551	2	transactions	transaction	NOUN
ejpam-5650	551	3	on	on	ADP
ejpam-5650	551	4	mathematics	mathematic	NOUN
ejpam-5650	551	5	,	,	PUNCT
ejpam-5650	551	6	21:844–853	21:844–853	NUM
ejpam-5650	551	7	,	,	PUNCT
ejpam-5650	551	8	2022	2022	NUM
ejpam-5650	551	9	.	.	PUNCT
ejpam-5650	552	1	[	[	X
ejpam-5650	552	2	60	60	NUM
ejpam-5650	552	3	]	]	PUNCT
ejpam-5650	552	4	m.	m.	NOUN
ejpam-5650	552	5	thongmoon	thongmoon	NOUN
ejpam-5650	552	6	and	and	CCONJ
ejpam-5650	552	7	c.	c.	PROPN
ejpam-5650	552	8	boonpok	boonpok	PROPN
ejpam-5650	552	9	.	.	PUNCT
ejpam-5650	553	1	strongly	strongly	ADV
ejpam-5650	553	2	θ(λ	θ(λ	PROPN
ejpam-5650	553	3	,	,	PUNCT
ejpam-5650	553	4	p)-continuous	p)-continuous	ADJ
ejpam-5650	553	5	functions	function	NOUN
ejpam-5650	553	6	.	.	PUNCT
ejpam-5650	554	1	international	international	ADJ
ejpam-5650	554	2	journal	journal	PROPN
ejpam-5650	554	3	of	of	ADP
ejpam-5650	554	4	mathematics	mathematic	NOUN
ejpam-5650	554	5	and	and	CCONJ
ejpam-5650	554	6	computer	computer	NOUN
ejpam-5650	554	7	science	science	NOUN
ejpam-5650	554	8	,	,	PUNCT
ejpam-5650	554	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5650	554	10	,	,	PUNCT
ejpam-5650	554	11	2024	2024	NUM
ejpam-5650	554	12	.	.	PUNCT
ejpam-5650	555	1	[	[	X
ejpam-5650	555	2	61	61	NUM
ejpam-5650	555	3	]	]	PUNCT
ejpam-5650	555	4	m.	m.	NOUN
ejpam-5650	555	5	thongmoon	thongmoon	NOUN
ejpam-5650	555	6	,	,	PUNCT
ejpam-5650	555	7	a.	a.	PROPN
ejpam-5650	555	8	sama	sama	PROPN
ejpam-5650	555	9	-	-	PUNCT
ejpam-5650	555	10	ae	ae	PROPN
ejpam-5650	555	11	,	,	PUNCT
ejpam-5650	555	12	and	and	CCONJ
ejpam-5650	555	13	c.	c.	PROPN
ejpam-5650	555	14	boonpok	boonpok	PROPN
ejpam-5650	555	15	.	.	PUNCT
ejpam-5650	556	1	upper	upper	ADJ
ejpam-5650	556	2	and	and	CCONJ
ejpam-5650	556	3	lower	low	ADJ
ejpam-5650	556	4	near	near	ADV
ejpam-5650	556	5	(	(	PUNCT
ejpam-5650	556	6	τ1	τ1	NOUN
ejpam-5650	556	7	,	,	PUNCT
ejpam-5650	556	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5650	556	9	.	.	PUNCT
ejpam-5650	557	1	(	(	PUNCT
ejpam-5650	557	2	accepted	accept	VERB
ejpam-5650	557	3	)	)	PUNCT
ejpam-5650	557	4	.	.	PUNCT
ejpam-5650	558	1	[	[	X
ejpam-5650	558	2	62	62	NUM
ejpam-5650	558	3	]	]	PUNCT
ejpam-5650	558	4	m.	m.	NOUN
ejpam-5650	558	5	thongmoon	thongmoon	NOUN
ejpam-5650	558	6	,	,	PUNCT
ejpam-5650	558	7	s.	s.	PROPN
ejpam-5650	558	8	sompong	sompong	PROPN
ejpam-5650	558	9	,	,	PUNCT
ejpam-5650	558	10	and	and	CCONJ
ejpam-5650	558	11	c.	c.	PROPN
ejpam-5650	558	12	boonpok	boonpok	PROPN
ejpam-5650	558	13	.	.	PUNCT
ejpam-5650	559	1	upper	upper	ADJ
ejpam-5650	559	2	and	and	CCONJ
ejpam-5650	559	3	lower	low	ADJ
ejpam-5650	559	4	weak	weak	ADJ
ejpam-5650	559	5	(	(	PUNCT
ejpam-5650	559	6	τ1	τ1	NOUN
ejpam-5650	559	7	,	,	PUNCT
ejpam-5650	559	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5650	559	9	.	.	PUNCT
ejpam-5650	560	1	european	european	PROPN
ejpam-5650	560	2	journal	journal	PROPN
ejpam-5650	560	3	of	of	ADP
ejpam-5650	560	4	pure	pure	ADJ
ejpam-5650	560	5	and	and	CCONJ
ejpam-5650	560	6	applied	applied	ADJ
ejpam-5650	560	7	mathematics	mathematic	NOUN
ejpam-5650	560	8	,	,	PUNCT
ejpam-5650	560	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5650	560	10	,	,	PUNCT
ejpam-5650	560	11	2024	2024	NUM
ejpam-5650	560	12	.	.	PUNCT
ejpam-5650	561	1	[	[	X
ejpam-5650	561	2	63	63	NUM
ejpam-5650	561	3	]	]	PUNCT
ejpam-5650	561	4	m.	m.	NOUN
ejpam-5650	561	5	thongmoon	thongmoon	NOUN
ejpam-5650	561	6	,	,	PUNCT
ejpam-5650	561	7	s.	s.	PROPN
ejpam-5650	561	8	sompong	sompong	PROPN
ejpam-5650	561	9	,	,	PUNCT
ejpam-5650	561	10	and	and	CCONJ
ejpam-5650	561	11	c.	c.	PROPN
ejpam-5650	561	12	boonpok	boonpok	PROPN
ejpam-5650	561	13	.	.	PUNCT
ejpam-5650	562	1	rarely	rarely	ADV
ejpam-5650	562	2	(	(	PUNCT
ejpam-5650	562	3	τ1	τ1	NOUN
ejpam-5650	562	4	,	,	PUNCT
ejpam-5650	562	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5650	562	6	functions	function	NOUN
ejpam-5650	562	7	.	.	PUNCT
ejpam-5650	563	1	n.	n.	NOUN
ejpam-5650	563	2	chutiman	chutiman	PROPN
ejpam-5650	563	3	,	,	PUNCT
ejpam-5650	563	4	a.	a.	PROPN
ejpam-5650	563	5	sama	sama	PROPN
ejpam-5650	563	6	-	-	PUNCT
ejpam-5650	563	7	ae	ae	PROPN
ejpam-5650	563	8	,	,	PUNCT
ejpam-5650	563	9	c.	c.	PROPN
ejpam-5650	563	10	boonpok	boonpok	PROPN
ejpam-5650	563	11	/	/	SYM
ejpam-5650	563	12	eur	eur	PROPN
ejpam-5650	563	13	.	.	PUNCT
ejpam-5650	564	1	j.	j.	PROPN
ejpam-5650	564	2	pure	pure	PROPN
ejpam-5650	564	3	appl	appl	PROPN
ejpam-5650	564	4	.	.	PROPN
ejpam-5650	564	5	math	math	PROPN
ejpam-5650	564	6	,	,	PUNCT
ejpam-5650	564	7	18	18	NUM
ejpam-5650	564	8	(	(	PUNCT
ejpam-5650	564	9	1	1	NUM
ejpam-5650	564	10	)	)	PUNCT
ejpam-5650	564	11	(	(	PUNCT
ejpam-5650	564	12	2025	2025	NUM
ejpam-5650	564	13	)	)	PUNCT
ejpam-5650	564	14	,	,	PUNCT
ejpam-5650	564	15	5650	5650	NUM
ejpam-5650	564	16	18	18	NUM
ejpam-5650	564	17	of	of	ADP
ejpam-5650	564	18	18	18	NUM
ejpam-5650	564	19	international	international	ADJ
ejpam-5650	564	20	journal	journal	NOUN
ejpam-5650	564	21	of	of	ADP
ejpam-5650	564	22	mathematics	mathematic	NOUN
ejpam-5650	564	23	and	and	CCONJ
ejpam-5650	564	24	computer	computer	NOUN
ejpam-5650	564	25	science	science	NOUN
ejpam-5650	564	26	,	,	PUNCT
ejpam-5650	564	27	20(1):423–427	20(1):423–427	NUM
ejpam-5650	564	28	,	,	PUNCT
ejpam-5650	564	29	2025	2025	NUM
ejpam-5650	564	30	.	.	PUNCT
ejpam-5650	565	1	[	[	X
ejpam-5650	565	2	64	64	NUM
ejpam-5650	565	3	]	]	PUNCT
ejpam-5650	565	4	c.	c.	PROPN
ejpam-5650	565	5	viriyapong	viriyapong	PROPN
ejpam-5650	565	6	and	and	CCONJ
ejpam-5650	565	7	c.	c.	PROPN
ejpam-5650	565	8	boonpok	boonpok	PROPN
ejpam-5650	565	9	.	.	PUNCT
ejpam-5650	566	1	(	(	PUNCT
ejpam-5650	566	2	τ1	τ1	NOUN
ejpam-5650	566	3	,	,	PUNCT
ejpam-5650	566	4	τ2)α	τ2)α	NOUN
ejpam-5650	566	5	-	-	PUNCT
ejpam-5650	566	6	continuity	continuity	NOUN
ejpam-5650	566	7	for	for	ADP
ejpam-5650	566	8	multifunctions	multifunction	NOUN
ejpam-5650	566	9	.	.	PUNCT
ejpam-5650	567	1	journal	journal	PROPN
ejpam-5650	567	2	of	of	ADP
ejpam-5650	567	3	mathematics	mathematic	NOUN
ejpam-5650	567	4	,	,	PUNCT
ejpam-5650	567	5	2020:6285763	2020:6285763	NUM
ejpam-5650	567	6	,	,	PUNCT
ejpam-5650	567	7	2020	2020	NUM
ejpam-5650	567	8	.	.	PUNCT
ejpam-5650	568	1	[	[	X
ejpam-5650	568	2	65	65	NUM
ejpam-5650	568	3	]	]	X
ejpam-5650	568	4	c.	c.	PROPN
ejpam-5650	568	5	viriyapong	viriyapong	PROPN
ejpam-5650	568	6	and	and	CCONJ
ejpam-5650	568	7	c.	c.	PROPN
ejpam-5650	568	8	boonpok	boonpok	PROPN
ejpam-5650	568	9	.	.	PUNCT
ejpam-5650	569	1	(	(	PUNCT
ejpam-5650	569	2	λ	λ	X
ejpam-5650	569	3	,	,	PUNCT
ejpam-5650	569	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5650	569	5	functions	function	NOUN
ejpam-5650	569	6	.	.	PUNCT
ejpam-5650	570	1	wseas	wseas	VERB
ejpam-5650	570	2	transactions	transaction	NOUN
ejpam-5650	570	3	on	on	ADP
ejpam-5650	570	4	mathematics	mathematic	NOUN
ejpam-5650	570	5	,	,	PUNCT
ejpam-5650	570	6	21:380–385	21:380–385	NUM
ejpam-5650	570	7	,	,	PUNCT
ejpam-5650	570	8	2022	2022	NUM
ejpam-5650	570	9	.	.	PUNCT
ejpam-5650	571	1	[	[	X
ejpam-5650	571	2	66	66	NUM
ejpam-5650	571	3	]	]	PUNCT
ejpam-5650	571	4	c.	c.	PROPN
ejpam-5650	571	5	viriyapong	viriyapong	PROPN
ejpam-5650	571	6	and	and	CCONJ
ejpam-5650	571	7	c.	c.	PROPN
ejpam-5650	571	8	boonpok	boonpok	PROPN
ejpam-5650	571	9	.	.	PUNCT
ejpam-5650	572	1	weak	weak	ADJ
ejpam-5650	572	2	quasi	quasi	NOUN
ejpam-5650	572	3	(	(	PUNCT
ejpam-5650	572	4	λ	λ	PROPN
ejpam-5650	572	5	,	,	PUNCT
ejpam-5650	572	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5650	572	7	for	for	ADP
ejpam-5650	572	8	multifunctions	multifunction	NOUN
ejpam-5650	572	9	.	.	PUNCT
ejpam-5650	573	1	international	international	ADJ
ejpam-5650	573	2	journal	journal	PROPN
ejpam-5650	573	3	of	of	ADP
ejpam-5650	573	4	mathematics	mathematic	NOUN
ejpam-5650	573	5	and	and	CCONJ
ejpam-5650	573	6	computer	computer	NOUN
ejpam-5650	573	7	science	science	NOUN
ejpam-5650	573	8	,	,	PUNCT
ejpam-5650	573	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5650	573	10	,	,	PUNCT
ejpam-5650	573	11	2022	2022	NUM
ejpam-5650	573	12	.	.	PUNCT
ejpam-5650	574	1	[	[	X
ejpam-5650	574	2	67	67	NUM
ejpam-5650	574	3	]	]	X
ejpam-5650	574	4	c.	c.	PROPN
ejpam-5650	574	5	viriyapong	viriyapong	PROPN
ejpam-5650	574	6	,	,	PUNCT
ejpam-5650	574	7	s.	s.	PROPN
ejpam-5650	574	8	sompong	sompong	PROPN
ejpam-5650	574	9	,	,	PUNCT
ejpam-5650	574	10	and	and	CCONJ
ejpam-5650	574	11	c.	c.	PROPN
ejpam-5650	574	12	boonpok	boonpok	PROPN
ejpam-5650	574	13	.	.	PUNCT
ejpam-5650	575	1	upper	upper	ADJ
ejpam-5650	575	2	and	and	CCONJ
ejpam-5650	575	3	lower	low	ADJ
ejpam-5650	575	4	slight	slight	ADJ
ejpam-5650	575	5	(	(	PUNCT
ejpam-5650	575	6	τ1	τ1	NOUN
ejpam-5650	575	7	,	,	PUNCT
ejpam-5650	575	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5650	575	9	.	.	PUNCT
ejpam-5650	576	1	european	european	PROPN
ejpam-5650	576	2	journal	journal	PROPN
ejpam-5650	576	3	of	of	ADP
ejpam-5650	576	4	pure	pure	ADJ
ejpam-5650	576	5	and	and	CCONJ
ejpam-5650	576	6	applied	applied	ADJ
ejpam-5650	576	7	mathematics	mathematic	NOUN
ejpam-5650	576	8	,	,	PUNCT
ejpam-5650	576	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-5650	576	10	,	,	PUNCT
ejpam-5650	576	11	2024	2024	NUM
ejpam-5650	576	12	.	.	PUNCT
ejpam-5650	577	1	[	[	X
ejpam-5650	577	2	68	68	NUM
ejpam-5650	577	3	]	]	X
ejpam-5650	577	4	n.	n.	PROPN
ejpam-5650	577	5	viriyapong	viriyapong	PROPN
ejpam-5650	577	6	,	,	PUNCT
ejpam-5650	577	7	s.	s.	PROPN
ejpam-5650	577	8	sompong	sompong	PROPN
ejpam-5650	577	9	,	,	PUNCT
ejpam-5650	577	10	and	and	CCONJ
ejpam-5650	577	11	c.	c.	PROPN
ejpam-5650	577	12	boonpok	boonpok	PROPN
ejpam-5650	577	13	.	.	PUNCT
ejpam-5650	578	1	slightly	slightly	ADV
ejpam-5650	578	2	(	(	PUNCT
ejpam-5650	578	3	τ1	τ1	NOUN
ejpam-5650	578	4	,	,	PUNCT
ejpam-5650	578	5	τ2)p	τ2)p	ADJ
ejpam-5650	578	6	-	-	ADJ
ejpam-5650	578	7	continuous	continuous	ADJ
ejpam-5650	578	8	multifunctions	multifunction	NOUN
ejpam-5650	578	9	.	.	PUNCT
ejpam-5650	579	1	international	international	ADJ
ejpam-5650	579	2	journal	journal	NOUN
ejpam-5650	579	3	of	of	ADP
ejpam-5650	579	4	analysis	analysis	NOUN
ejpam-5650	579	5	and	and	CCONJ
ejpam-5650	579	6	applications	application	NOUN
ejpam-5650	579	7	,	,	PUNCT
ejpam-5650	579	8	22:152	22:152	NUM
ejpam-5650	579	9	,	,	PUNCT
ejpam-5650	579	10	2024	2024	NUM
ejpam-5650	579	11	.	.	PUNCT
ejpam-5650	580	1	[	[	X
ejpam-5650	580	2	69	69	NUM
ejpam-5650	580	3	]	]	X
ejpam-5650	580	4	n.	n.	PROPN
ejpam-5650	580	5	viriyapong	viriyapong	PROPN
ejpam-5650	580	6	,	,	PUNCT
ejpam-5650	580	7	s.	s.	PROPN
ejpam-5650	580	8	sompong	sompong	PROPN
ejpam-5650	580	9	,	,	PUNCT
ejpam-5650	580	10	and	and	CCONJ
ejpam-5650	580	11	c.	c.	PROPN
ejpam-5650	580	12	boonpok	boonpok	PROPN
ejpam-5650	580	13	.	.	PUNCT
ejpam-5650	581	1	(	(	PUNCT
ejpam-5650	581	2	τ1	τ1	NOUN
ejpam-5650	581	3	,	,	PUNCT
ejpam-5650	581	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5650	581	5	disconnectedness	disconnectedness	NOUN
ejpam-5650	581	6	in	in	ADP
ejpam-5650	581	7	bitopological	bitopological	ADJ
ejpam-5650	581	8	spaces	space	NOUN
ejpam-5650	581	9	.	.	PUNCT
ejpam-5650	582	1	international	international	ADJ
ejpam-5650	582	2	journal	journal	PROPN
ejpam-5650	582	3	of	of	ADP
ejpam-5650	582	4	mathematics	mathematic	NOUN
ejpam-5650	582	5	and	and	CCONJ
ejpam-5650	582	6	computer	computer	NOUN
ejpam-5650	582	7	science	science	NOUN
ejpam-5650	582	8	,	,	PUNCT
ejpam-5650	582	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5650	582	10	,	,	PUNCT
ejpam-5650	582	11	2024	2024	NUM
ejpam-5650	582	12	.	.	PUNCT
ejpam-5650	583	1	[	[	X
ejpam-5650	583	2	70	70	NUM
ejpam-5650	583	3	]	]	X
ejpam-5650	583	4	n.	n.	PROPN
ejpam-5650	583	5	viriyapong	viriyapong	PROPN
ejpam-5650	583	6	,	,	PUNCT
ejpam-5650	583	7	s.	s.	PROPN
ejpam-5650	583	8	sompong	sompong	PROPN
ejpam-5650	583	9	,	,	PUNCT
ejpam-5650	583	10	and	and	CCONJ
ejpam-5650	583	11	c.	c.	PROPN
ejpam-5650	583	12	boonpok	boonpok	PROPN
ejpam-5650	583	13	.	.	PUNCT
ejpam-5650	584	1	upper	upper	ADJ
ejpam-5650	584	2	and	and	CCONJ
ejpam-5650	584	3	lower	low	ADJ
ejpam-5650	584	4	s-(τ1	s-(τ1	NOUN
ejpam-5650	584	5	,	,	PUNCT
ejpam-5650	584	6	τ2)p	τ2)p	ADJ
ejpam-5650	584	7	-	-	PUNCT
ejpam-5650	584	8	continuous	continuous	ADJ
ejpam-5650	584	9	multifunctions	multifunction	NOUN
ejpam-5650	584	10	.	.	PUNCT
ejpam-5650	585	1	european	european	ADJ
ejpam-5650	585	2	journal	journal	PROPN
ejpam-5650	585	3	of	of	ADP
ejpam-5650	585	4	pure	pure	ADJ
ejpam-5650	585	5	and	and	CCONJ
ejpam-5650	585	6	applied	applied	ADJ
ejpam-5650	585	7	mathematics	mathematic	NOUN
ejpam-5650	585	8	,	,	PUNCT
ejpam-5650	585	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-5650	585	10	,	,	PUNCT
ejpam-5650	585	11	2024	2024	NUM
ejpam-5650	585	12	.	.	PUNCT