id	sid	tid	token	lemma	pos
ejpam-6571	1	1	european	european	PROPN
ejpam-6571	1	2	journal	journal	PROPN
ejpam-6571	1	3	of	of	ADP
ejpam-6571	1	4	pure	pure	ADJ
ejpam-6571	1	5	and	and	CCONJ
ejpam-6571	1	6	applied	applied	ADJ
ejpam-6571	1	7	mathematics	mathematic	NOUN
ejpam-6571	1	8	2025	2025	NUM
ejpam-6571	1	9	,	,	PUNCT
ejpam-6571	1	10	vol	vol	NOUN
ejpam-6571	1	11	.	.	PROPN
ejpam-6571	1	12	18	18	NUM
ejpam-6571	1	13	,	,	PUNCT
ejpam-6571	1	14	issue	issue	NOUN
ejpam-6571	1	15	3	3	NUM
ejpam-6571	1	16	,	,	PUNCT
ejpam-6571	1	17	article	article	NOUN
ejpam-6571	1	18	number	number	NOUN
ejpam-6571	1	19	6571	6571	NUM
ejpam-6571	1	20	issn	issn	VERB
ejpam-6571	1	21	1307	1307	NUM
ejpam-6571	1	22	-	-	SYM
ejpam-6571	1	23	5543	5543	NUM
ejpam-6571	1	24	–	–	PUNCT
ejpam-6571	1	25	ejpam.com	ejpam.com	X
ejpam-6571	1	26	published	publish	VERB
ejpam-6571	1	27	by	by	ADP
ejpam-6571	1	28	new	new	PROPN
ejpam-6571	1	29	york	york	PROPN
ejpam-6571	1	30	business	business	PROPN
ejpam-6571	1	31	global	global	PROPN
ejpam-6571	1	32	almost	almost	ADV
ejpam-6571	1	33	quasi	quasi	ADJ
ejpam-6571	1	34	continuity	continuity	NOUN
ejpam-6571	1	35	and	and	CCONJ
ejpam-6571	1	36	weak	weak	ADJ
ejpam-6571	1	37	quasi	quasi	NOUN
ejpam-6571	1	38	continuity	continuity	NOUN
ejpam-6571	1	39	for	for	ADP
ejpam-6571	1	40	multifunctions	multifunction	NOUN
ejpam-6571	1	41	between	between	ADP
ejpam-6571	1	42	an	an	DET
ejpam-6571	1	43	ideal	ideal	ADJ
ejpam-6571	1	44	topological	topological	ADJ
ejpam-6571	1	45	space	space	NOUN
ejpam-6571	1	46	and	and	CCONJ
ejpam-6571	1	47	a	a	DET
ejpam-6571	1	48	bitopological	bitopological	ADJ
ejpam-6571	1	49	space	space	NOUN
ejpam-6571	1	50	montri	montri	PROPN
ejpam-6571	1	51	thongmoon1	thongmoon1	PROPN
ejpam-6571	1	52	,	,	PUNCT
ejpam-6571	1	53	areeyuth	areeyuth	NOUN
ejpam-6571	1	54	sama	sama	NOUN
ejpam-6571	1	55	-	-	PUNCT
ejpam-6571	1	56	ae2	ae2	PROPN
ejpam-6571	1	57	,	,	PUNCT
ejpam-6571	1	58	chawalit	chawalit	VERB
ejpam-6571	1	59	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6571	1	60	1	1	NUM
ejpam-6571	1	61	mathematics	mathematic	NOUN
ejpam-6571	1	62	and	and	CCONJ
ejpam-6571	1	63	applied	apply	VERB
ejpam-6571	1	64	mathematics	mathematics	PROPN
ejpam-6571	1	65	research	research	NOUN
ejpam-6571	1	66	unit	unit	NOUN
ejpam-6571	1	67	,	,	PUNCT
ejpam-6571	1	68	department	department	NOUN
ejpam-6571	1	69	of	of	ADP
ejpam-6571	1	70	mathematics	mathematic	NOUN
ejpam-6571	1	71	,	,	PUNCT
ejpam-6571	1	72	faculty	faculty	NOUN
ejpam-6571	1	73	of	of	ADP
ejpam-6571	1	74	science	science	NOUN
ejpam-6571	1	75	,	,	PUNCT
ejpam-6571	1	76	mahasarakham	mahasarakham	PROPN
ejpam-6571	1	77	university	university	PROPN
ejpam-6571	1	78	,	,	PUNCT
ejpam-6571	1	79	maha	maha	PROPN
ejpam-6571	1	80	sarakham	sarakham	PROPN
ejpam-6571	1	81	,	,	PUNCT
ejpam-6571	1	82	44150	44150	NUM
ejpam-6571	1	83	,	,	PUNCT
ejpam-6571	1	84	thailand	thailand	PROPN
ejpam-6571	1	85	2	2	NUM
ejpam-6571	1	86	department	department	NOUN
ejpam-6571	1	87	of	of	ADP
ejpam-6571	1	88	mathematics	mathematic	NOUN
ejpam-6571	1	89	and	and	CCONJ
ejpam-6571	1	90	computer	computer	NOUN
ejpam-6571	1	91	science	science	NOUN
ejpam-6571	1	92	,	,	PUNCT
ejpam-6571	1	93	faculty	faculty	NOUN
ejpam-6571	1	94	of	of	ADP
ejpam-6571	1	95	science	science	NOUN
ejpam-6571	1	96	and	and	CCONJ
ejpam-6571	1	97	technology	technology	NOUN
ejpam-6571	1	98	,	,	PUNCT
ejpam-6571	1	99	prince	prince	NOUN
ejpam-6571	1	100	of	of	ADP
ejpam-6571	1	101	songkla	songkla	PROPN
ejpam-6571	1	102	university	university	PROPN
ejpam-6571	1	103	,	,	PUNCT
ejpam-6571	1	104	pattani	pattani	NOUN
ejpam-6571	1	105	campus	campus	NOUN
ejpam-6571	1	106	,	,	PUNCT
ejpam-6571	1	107	pattani	pattani	NOUN
ejpam-6571	1	108	,	,	PUNCT
ejpam-6571	1	109	94000	94000	NUM
ejpam-6571	1	110	,	,	PUNCT
ejpam-6571	1	111	thailand	thailand	PROPN
ejpam-6571	1	112	abstract	abstract	PROPN
ejpam-6571	1	113	.	.	PUNCT
ejpam-6571	2	1	this	this	DET
ejpam-6571	2	2	paper	paper	NOUN
ejpam-6571	2	3	introduces	introduce	VERB
ejpam-6571	2	4	four	four	NUM
ejpam-6571	2	5	classes	class	NOUN
ejpam-6571	2	6	of	of	ADP
ejpam-6571	2	7	continuous	continuous	ADJ
ejpam-6571	2	8	multifunctions	multifunction	NOUN
ejpam-6571	2	9	defined	define	VERB
ejpam-6571	2	10	from	from	ADP
ejpam-6571	2	11	an	an	DET
ejpam-6571	2	12	ideal	ideal	ADJ
ejpam-6571	2	13	topological	topological	ADJ
ejpam-6571	2	14	space	space	NOUN
ejpam-6571	2	15	into	into	ADP
ejpam-6571	2	16	a	a	DET
ejpam-6571	2	17	bitopological	bitopological	ADJ
ejpam-6571	2	18	space	space	NOUN
ejpam-6571	2	19	,	,	PUNCT
ejpam-6571	2	20	namely	namely	ADV
ejpam-6571	2	21	upper	upper	ADJ
ejpam-6571	2	22	almost	almost	ADV
ejpam-6571	2	23	quasi	quasi	ADJ
ejpam-6571	2	24	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	2	25	,	,	PUNCT
ejpam-6571	2	26	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	2	27	multifunctions	multifunction	NOUN
ejpam-6571	2	28	,	,	PUNCT
ejpam-6571	2	29	lower	low	ADJ
ejpam-6571	2	30	almost	almost	ADV
ejpam-6571	2	31	quasi	quasi	ADJ
ejpam-6571	2	32	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	2	33	,	,	PUNCT
ejpam-6571	2	34	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	2	35	multifunctions	multifunction	NOUN
ejpam-6571	2	36	,	,	PUNCT
ejpam-6571	2	37	upper	upper	ADJ
ejpam-6571	2	38	weakly	weakly	ADJ
ejpam-6571	2	39	quasi	quasi	NOUN
ejpam-6571	2	40	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	2	41	,	,	PUNCT
ejpam-6571	2	42	σ2)continuous	σ2)continuous	ADJ
ejpam-6571	2	43	multifunctions	multifunction	NOUN
ejpam-6571	2	44	and	and	CCONJ
ejpam-6571	2	45	lower	low	ADJ
ejpam-6571	2	46	weakly	weakly	ADJ
ejpam-6571	2	47	quasi	quasi	NOUN
ejpam-6571	2	48	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	2	49	,	,	PUNCT
ejpam-6571	2	50	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	2	51	multifunctions	multifunction	NOUN
ejpam-6571	2	52	.	.	PUNCT
ejpam-6571	3	1	moreover	moreover	ADV
ejpam-6571	3	2	,	,	PUNCT
ejpam-6571	3	3	several	several	ADJ
ejpam-6571	3	4	characterizations	characterization	NOUN
ejpam-6571	3	5	of	of	ADP
ejpam-6571	3	6	upper	upper	ADJ
ejpam-6571	3	7	almost	almost	ADV
ejpam-6571	3	8	quasi	quasi	ADJ
ejpam-6571	3	9	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	3	10	,	,	PUNCT
ejpam-6571	3	11	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	3	12	multifunctions	multifunction	NOUN
ejpam-6571	3	13	,	,	PUNCT
ejpam-6571	3	14	lower	low	ADJ
ejpam-6571	3	15	almost	almost	ADV
ejpam-6571	3	16	quasi	quasi	ADJ
ejpam-6571	3	17	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	3	18	,	,	PUNCT
ejpam-6571	3	19	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	3	20	multifunctions	multifunction	NOUN
ejpam-6571	3	21	,	,	PUNCT
ejpam-6571	3	22	upper	upper	ADJ
ejpam-6571	3	23	weakly	weakly	ADJ
ejpam-6571	3	24	quasi	quasi	NOUN
ejpam-6571	3	25	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	3	26	,	,	PUNCT
ejpam-6571	3	27	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	3	28	multifunctions	multifunction	NOUN
ejpam-6571	3	29	and	and	CCONJ
ejpam-6571	3	30	lower	low	ADJ
ejpam-6571	3	31	weakly	weakly	ADJ
ejpam-6571	3	32	quasi	quasi	NOUN
ejpam-6571	3	33	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	3	34	,	,	PUNCT
ejpam-6571	3	35	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	3	36	multifunctions	multifunction	NOUN
ejpam-6571	3	37	are	be	AUX
ejpam-6571	3	38	established	establish	VERB
ejpam-6571	3	39	.	.	PUNCT
ejpam-6571	4	1	furthermore	furthermore	ADV
ejpam-6571	4	2	,	,	PUNCT
ejpam-6571	4	3	the	the	DET
ejpam-6571	4	4	relationships	relationship	NOUN
ejpam-6571	4	5	between	between	ADP
ejpam-6571	4	6	almost	almost	ADV
ejpam-6571	4	7	quasi	quasi	ADJ
ejpam-6571	4	8	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	4	9	,	,	PUNCT
ejpam-6571	4	10	σ2)-continuity	σ2)-continuity	NOUN
ejpam-6571	4	11	and	and	CCONJ
ejpam-6571	4	12	weak	weak	ADJ
ejpam-6571	4	13	quasi	quasi	NOUN
ejpam-6571	4	14	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	4	15	,	,	PUNCT
ejpam-6571	4	16	σ2)-continuity	σ2)-continuity	NOUN
ejpam-6571	4	17	are	be	AUX
ejpam-6571	4	18	discussed	discuss	VERB
ejpam-6571	4	19	.	.	PUNCT
ejpam-6571	5	1	2020	2020	NUM
ejpam-6571	5	2	mathematics	mathematic	NOUN
ejpam-6571	5	3	subject	subject	NOUN
ejpam-6571	5	4	classifications	classification	NOUN
ejpam-6571	5	5	:	:	PUNCT
ejpam-6571	5	6	54c08	54c08	NUM
ejpam-6571	5	7	,	,	PUNCT
ejpam-6571	5	8	54c60	54c60	NUM
ejpam-6571	5	9	key	key	ADJ
ejpam-6571	5	10	words	word	NOUN
ejpam-6571	5	11	and	and	CCONJ
ejpam-6571	5	12	phrases	phrase	NOUN
ejpam-6571	5	13	:	:	PUNCT
ejpam-6571	5	14	upper	upper	ADJ
ejpam-6571	5	15	almost	almost	ADV
ejpam-6571	5	16	quasi	quasi	ADJ
ejpam-6571	5	17	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	5	18	,	,	PUNCT
ejpam-6571	5	19	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	5	20	multifunction	multifunction	NOUN
ejpam-6571	5	21	,	,	PUNCT
ejpam-6571	5	22	lower	low	ADJ
ejpam-6571	5	23	almost	almost	ADV
ejpam-6571	5	24	quasi	quasi	ADJ
ejpam-6571	5	25	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	5	26	,	,	PUNCT
ejpam-6571	5	27	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	5	28	multifunction	multifunction	NOUN
ejpam-6571	5	29	,	,	PUNCT
ejpam-6571	5	30	upper	upper	ADJ
ejpam-6571	5	31	weakly	weakly	ADJ
ejpam-6571	5	32	quasi	quasi	NOUN
ejpam-6571	5	33	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	5	34	,	,	PUNCT
ejpam-6571	5	35	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	5	36	multifunction	multifunction	NOUN
ejpam-6571	5	37	,	,	PUNCT
ejpam-6571	5	38	lower	low	ADJ
ejpam-6571	5	39	weakly	weakly	ADJ
ejpam-6571	5	40	quasi	quasi	NOUN
ejpam-6571	5	41	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	5	42	,	,	PUNCT
ejpam-6571	5	43	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	5	44	multifunction	multifunction	NOUN
ejpam-6571	5	45	1	1	NUM
ejpam-6571	5	46	.	.	PUNCT
ejpam-6571	5	47	introduction	introduction	NOUN
ejpam-6571	5	48	the	the	DET
ejpam-6571	5	49	concept	concept	NOUN
ejpam-6571	5	50	of	of	ADP
ejpam-6571	5	51	quasi	quasi	ADJ
ejpam-6571	5	52	continuous	continuous	ADJ
ejpam-6571	5	53	functions	function	NOUN
ejpam-6571	5	54	was	be	AUX
ejpam-6571	5	55	introduced	introduce	VERB
ejpam-6571	5	56	by	by	ADP
ejpam-6571	5	57	marcus	marcus	PROPN
ejpam-6571	6	1	[	[	X
ejpam-6571	6	2	1	1	NUM
ejpam-6571	6	3	]	]	PUNCT
ejpam-6571	6	4	.	.	PUNCT
ejpam-6571	7	1	popa	popa	NOUN
ejpam-6571	8	1	[	[	X
ejpam-6571	8	2	2	2	NUM
ejpam-6571	8	3	]	]	PUNCT
ejpam-6571	8	4	introduced	introduce	VERB
ejpam-6571	8	5	and	and	CCONJ
ejpam-6571	8	6	investigated	investigate	VERB
ejpam-6571	8	7	the	the	DET
ejpam-6571	8	8	notion	notion	NOUN
ejpam-6571	8	9	of	of	ADP
ejpam-6571	8	10	almost	almost	ADV
ejpam-6571	8	11	quasi	quasi	ADJ
ejpam-6571	8	12	continuous	continuous	ADJ
ejpam-6571	8	13	functions	function	NOUN
ejpam-6571	8	14	.	.	PUNCT
ejpam-6571	9	1	neubrunnovaá	neubrunnovaá	PUNCT
ejpam-6571	10	1	[	[	X
ejpam-6571	10	2	3	3	NUM
ejpam-6571	10	3	]	]	PUNCT
ejpam-6571	10	4	showed	show	VERB
ejpam-6571	10	5	that	that	SCONJ
ejpam-6571	10	6	quasi	quasi	NOUN
ejpam-6571	10	7	continuity	continuity	NOUN
ejpam-6571	10	8	is	be	AUX
ejpam-6571	10	9	equivalent	equivalent	ADJ
ejpam-6571	10	10	to	to	ADP
ejpam-6571	10	11	semi	semi	ADJ
ejpam-6571	10	12	-	-	NOUN
ejpam-6571	10	13	continuity	continuity	NOUN
ejpam-6571	10	14	due	due	ADP
ejpam-6571	10	15	to	to	ADP
ejpam-6571	10	16	levine	levine	PROPN
ejpam-6571	10	17	[	[	X
ejpam-6571	10	18	4	4	NUM
ejpam-6571	10	19	]	]	PUNCT
ejpam-6571	10	20	.	.	PUNCT
ejpam-6571	11	1	popa	popa	NOUN
ejpam-6571	11	2	and	and	CCONJ
ejpam-6571	11	3	stan	stan	PROPN
ejpam-6571	12	1	[	[	X
ejpam-6571	12	2	5	5	NUM
ejpam-6571	12	3	]	]	PUNCT
ejpam-6571	12	4	introduced	introduce	VERB
ejpam-6571	12	5	and	and	CCONJ
ejpam-6571	12	6	studied	study	VERB
ejpam-6571	12	7	the	the	DET
ejpam-6571	12	8	notion	notion	NOUN
ejpam-6571	12	9	of	of	ADP
ejpam-6571	12	10	weakly	weakly	ADJ
ejpam-6571	12	11	quasi	quasi	ADJ
ejpam-6571	12	12	continuous	continuous	ADJ
ejpam-6571	12	13	functions	function	NOUN
ejpam-6571	12	14	.	.	PUNCT
ejpam-6571	13	1	weak	weak	ADJ
ejpam-6571	13	2	quasi	quasi	NOUN
ejpam-6571	13	3	continuity	continuity	NOUN
ejpam-6571	13	4	is	be	AUX
ejpam-6571	13	5	implied	imply	VERB
ejpam-6571	13	6	by	by	ADP
ejpam-6571	13	7	quasi	quasi	NOUN
ejpam-6571	13	8	continuity	continuity	NOUN
ejpam-6571	13	9	and	and	CCONJ
ejpam-6571	13	10	weak	weak	ADJ
ejpam-6571	13	11	continuity	continuity	NOUN
ejpam-6571	13	12	[	[	X
ejpam-6571	13	13	6	6	NUM
ejpam-6571	13	14	]	]	PUNCT
ejpam-6571	13	15	which	which	PRON
ejpam-6571	13	16	are	be	AUX
ejpam-6571	13	17	independent	independent	ADJ
ejpam-6571	13	18	of	of	ADP
ejpam-6571	13	19	each	each	DET
ejpam-6571	13	20	other	other	ADJ
ejpam-6571	13	21	.	.	PUNCT
ejpam-6571	14	1	it	it	PRON
ejpam-6571	14	2	is	be	AUX
ejpam-6571	14	3	shown	show	VERB
ejpam-6571	14	4	in	in	ADP
ejpam-6571	14	5	[	[	X
ejpam-6571	14	6	7	7	X
ejpam-6571	14	7	]	]	PUNCT
ejpam-6571	14	8	that	that	SCONJ
ejpam-6571	14	9	weak	weak	ADJ
ejpam-6571	14	10	quasi	quasi	NOUN
ejpam-6571	14	11	continuity	continuity	NOUN
ejpam-6571	14	12	∗corresponding	∗corresponde	VERB
ejpam-6571	14	13	author	author	NOUN
ejpam-6571	14	14	.	.	PUNCT
ejpam-6571	15	1	doi	doi	NOUN
ejpam-6571	15	2	:	:	PUNCT
ejpam-6571	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6571	https://doi.org/10.29020/nybg.ejpam.v18i3.6571	ADJ
ejpam-6571	15	4	email	email	NOUN
ejpam-6571	15	5	addresses	address	VERB
ejpam-6571	15	6	:	:	PUNCT
ejpam-6571	15	7	montri.t@msu.ac.th	montri.t@msu.ac.th	PROPN
ejpam-6571	15	8	(	(	PUNCT
ejpam-6571	15	9	m.	m.	NOUN
ejpam-6571	15	10	thongmoon	thongmoon	PROPN
ejpam-6571	15	11	)	)	PUNCT
ejpam-6571	15	12	,	,	PUNCT
ejpam-6571	15	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-6571	15	14	(	(	PUNCT
ejpam-6571	15	15	a.	a.	PROPN
ejpam-6571	15	16	sama	sama	PROPN
ejpam-6571	15	17	-	-	PUNCT
ejpam-6571	15	18	ae	ae	PROPN
ejpam-6571	15	19	)	)	PUNCT
ejpam-6571	15	20	,	,	PUNCT
ejpam-6571	15	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6571	15	22	(	(	PUNCT
ejpam-6571	15	23	c.	c.	PROPN
ejpam-6571	15	24	boonpok	boonpok	PROPN
ejpam-6571	15	25	)	)	PUNCT
ejpam-6571	15	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6571	16	1	1	1	NUM
ejpam-6571	16	2	copyright	copyright	NOUN
ejpam-6571	16	3	:	:	PUNCT
ejpam-6571	16	4	©	©	PROPN
ejpam-6571	16	5	2025	2025	NUM
ejpam-6571	16	6	the	the	DET
ejpam-6571	16	7	author(s	author(s	NOUN
ejpam-6571	16	8	)	)	PUNCT
ejpam-6571	16	9	.	.	PUNCT
ejpam-6571	17	1	(	(	PUNCT
ejpam-6571	17	2	cc	cc	NOUN
ejpam-6571	17	3	by	by	ADP
ejpam-6571	17	4	-	-	PUNCT
ejpam-6571	17	5	nc	nc	PROPN
ejpam-6571	17	6	4.0	4.0	NUM
ejpam-6571	17	7	)	)	PUNCT
ejpam-6571	17	8	m.	m.	NOUN
ejpam-6571	17	9	thongmoon	thongmoon	NOUN
ejpam-6571	17	10	,	,	PUNCT
ejpam-6571	17	11	a.	a.	PROPN
ejpam-6571	17	12	sama	sama	PROPN
ejpam-6571	17	13	-	-	PUNCT
ejpam-6571	17	14	ae	ae	PROPN
ejpam-6571	17	15	,	,	PUNCT
ejpam-6571	17	16	c.	c.	PROPN
ejpam-6571	17	17	boonpok	boonpok	PROPN
ejpam-6571	17	18	/	/	SYM
ejpam-6571	17	19	eur	eur	PROPN
ejpam-6571	17	20	.	.	PUNCT
ejpam-6571	18	1	j.	j.	PROPN
ejpam-6571	18	2	pure	pure	PROPN
ejpam-6571	18	3	appl	appl	PROPN
ejpam-6571	18	4	.	.	PROPN
ejpam-6571	18	5	math	math	PROPN
ejpam-6571	18	6	,	,	PUNCT
ejpam-6571	18	7	18	18	NUM
ejpam-6571	18	8	(	(	PUNCT
ejpam-6571	18	9	3	3	NUM
ejpam-6571	18	10	)	)	PUNCT
ejpam-6571	18	11	(	(	PUNCT
ejpam-6571	18	12	2025	2025	NUM
ejpam-6571	18	13	)	)	PUNCT
ejpam-6571	18	14	,	,	PUNCT
ejpam-6571	18	15	6571	6571	NUM
ejpam-6571	18	16	2	2	NUM
ejpam-6571	18	17	of	of	ADP
ejpam-6571	18	18	15	15	NUM
ejpam-6571	18	19	is	be	AUX
ejpam-6571	18	20	equivalent	equivalent	ADJ
ejpam-6571	18	21	to	to	AUX
ejpam-6571	18	22	weak	weak	ADJ
ejpam-6571	18	23	semi	semi	ADJ
ejpam-6571	18	24	-	-	NOUN
ejpam-6571	18	25	continuity	continuity	NOUN
ejpam-6571	18	26	due	due	ADP
ejpam-6571	18	27	to	to	ADP
ejpam-6571	18	28	arya	arya	PROPN
ejpam-6571	18	29	and	and	CCONJ
ejpam-6571	18	30	bhamini	bhamini	PROPN
ejpam-6571	19	1	[	[	X
ejpam-6571	19	2	8	8	NUM
ejpam-6571	19	3	]	]	PUNCT
ejpam-6571	19	4	and	and	CCONJ
ejpam-6571	19	5	kar	kar	NOUN
ejpam-6571	19	6	and	and	CCONJ
ejpam-6571	19	7	bhattacharyya	bhattacharyya	ADJ
ejpam-6571	20	1	[	[	X
ejpam-6571	20	2	9	9	NUM
ejpam-6571	20	3	]	]	PUNCT
ejpam-6571	20	4	.	.	PUNCT
ejpam-6571	21	1	janković	janković	PROPN
ejpam-6571	22	1	and	and	CCONJ
ejpam-6571	22	2	hamlett	hamlett	PROPN
ejpam-6571	22	3	[	[	X
ejpam-6571	22	4	10	10	NUM
ejpam-6571	22	5	]	]	PUNCT
ejpam-6571	22	6	introduced	introduce	VERB
ejpam-6571	22	7	the	the	DET
ejpam-6571	22	8	concept	concept	NOUN
ejpam-6571	22	9	of	of	ADP
ejpam-6571	22	10	i	i	PRON
ejpam-6571	22	11	-open	-open	PROPN
ejpam-6571	22	12	sets	set	NOUN
ejpam-6571	22	13	in	in	ADP
ejpam-6571	22	14	ideal	ideal	ADJ
ejpam-6571	22	15	topological	topological	ADJ
ejpam-6571	22	16	spaces	space	NOUN
ejpam-6571	22	17	.	.	PUNCT
ejpam-6571	23	1	abd	abd	PROPN
ejpam-6571	23	2	el	el	PROPN
ejpam-6571	23	3	-	-	PROPN
ejpam-6571	23	4	monsef	monsef	PROPN
ejpam-6571	23	5	et	et	PROPN
ejpam-6571	23	6	al	al	PROPN
ejpam-6571	23	7	.	.	PUNCT
ejpam-6571	24	1	[	[	X
ejpam-6571	24	2	11	11	NUM
ejpam-6571	24	3	]	]	PUNCT
ejpam-6571	24	4	introduced	introduce	VERB
ejpam-6571	24	5	and	and	CCONJ
ejpam-6571	24	6	studied	study	VERB
ejpam-6571	24	7	the	the	DET
ejpam-6571	24	8	notions	notion	NOUN
ejpam-6571	24	9	of	of	ADP
ejpam-6571	24	10	i	i	PRON
ejpam-6571	24	11	closed	close	VERB
ejpam-6571	24	12	sets	set	NOUN
ejpam-6571	24	13	and	and	CCONJ
ejpam-6571	24	14	i	i	PRON
ejpam-6571	24	15	-continuous	-continuous	ADJ
ejpam-6571	24	16	functions	function	NOUN
ejpam-6571	24	17	.	.	PUNCT
ejpam-6571	25	1	semi	semi	ADJ
ejpam-6571	25	2	-	-	ADJ
ejpam-6571	25	3	i	i	ADJ
ejpam-6571	25	4	-open	-open	NOUN
ejpam-6571	25	5	sets	set	NOUN
ejpam-6571	25	6	,	,	PUNCT
ejpam-6571	25	7	pre	pre	ADJ
ejpam-6571	25	8	-	-	ADJ
ejpam-6571	25	9	i	i	ADJ
ejpam-6571	25	10	-open	-open	NOUN
ejpam-6571	25	11	sets	set	NOUN
ejpam-6571	25	12	,	,	PUNCT
ejpam-6571	25	13	α	α	X
ejpam-6571	25	14	-	-	PUNCT
ejpam-6571	25	15	i	i	PRON
ejpam-6571	25	16	-open	-open	NOUN
ejpam-6571	25	17	sets	set	NOUN
ejpam-6571	25	18	,	,	PUNCT
ejpam-6571	25	19	β	β	X
ejpam-6571	25	20	-	-	ADJ
ejpam-6571	25	21	i	i	PRON
ejpam-6571	25	22	-open	-open	NOUN
ejpam-6571	25	23	sets	set	NOUN
ejpam-6571	25	24	and	and	CCONJ
ejpam-6571	25	25	δ	δ	PROPN
ejpam-6571	25	26	-	-	PUNCT
ejpam-6571	25	27	i	i	PRON
ejpam-6571	25	28	-open	-open	NOUN
ejpam-6571	25	29	sets	set	NOUN
ejpam-6571	25	30	play	play	VERB
ejpam-6571	25	31	an	an	DET
ejpam-6571	25	32	important	important	ADJ
ejpam-6571	25	33	role	role	NOUN
ejpam-6571	25	34	in	in	ADP
ejpam-6571	25	35	the	the	DET
ejpam-6571	25	36	research	research	NOUN
ejpam-6571	25	37	of	of	ADP
ejpam-6571	25	38	generalizations	generalization	NOUN
ejpam-6571	25	39	of	of	ADP
ejpam-6571	25	40	continuity	continuity	NOUN
ejpam-6571	25	41	in	in	ADP
ejpam-6571	25	42	ideal	ideal	ADJ
ejpam-6571	25	43	topological	topological	ADJ
ejpam-6571	25	44	spaces	space	NOUN
ejpam-6571	25	45	.	.	PUNCT
ejpam-6571	26	1	using	use	VERB
ejpam-6571	26	2	these	these	DET
ejpam-6571	26	3	notions	notion	NOUN
ejpam-6571	26	4	many	many	ADJ
ejpam-6571	26	5	authors	author	NOUN
ejpam-6571	26	6	introduced	introduce	VERB
ejpam-6571	26	7	and	and	CCONJ
ejpam-6571	26	8	studied	study	VERB
ejpam-6571	26	9	various	various	ADJ
ejpam-6571	26	10	types	type	NOUN
ejpam-6571	26	11	of	of	ADP
ejpam-6571	26	12	generalizations	generalization	NOUN
ejpam-6571	26	13	of	of	ADP
ejpam-6571	26	14	continuity	continuity	NOUN
ejpam-6571	26	15	for	for	ADP
ejpam-6571	26	16	functions	function	NOUN
ejpam-6571	26	17	and	and	CCONJ
ejpam-6571	26	18	multifunctions	multifunction	NOUN
ejpam-6571	26	19	.	.	PUNCT
ejpam-6571	27	1	hatir	hatir	PROPN
ejpam-6571	27	2	and	and	CCONJ
ejpam-6571	27	3	noiri	noiri	ADV
ejpam-6571	28	1	[	[	X
ejpam-6571	28	2	12	12	NUM
ejpam-6571	28	3	]	]	PUNCT
ejpam-6571	28	4	introduced	introduce	VERB
ejpam-6571	28	5	and	and	CCONJ
ejpam-6571	28	6	investigated	investigate	VERB
ejpam-6571	28	7	the	the	DET
ejpam-6571	28	8	notions	notion	NOUN
ejpam-6571	28	9	of	of	ADP
ejpam-6571	28	10	weakly	weakly	ADJ
ejpam-6571	28	11	pre	pre	ADJ
ejpam-6571	28	12	-	-	ADJ
ejpam-6571	28	13	i	i	PRON
ejpam-6571	28	14	-open	-open	NOUN
ejpam-6571	28	15	sets	set	NOUN
ejpam-6571	28	16	and	and	CCONJ
ejpam-6571	28	17	weakly	weakly	ADJ
ejpam-6571	28	18	pre	pre	ADJ
ejpam-6571	28	19	-	-	ADJ
ejpam-6571	28	20	i	i	ADJ
ejpam-6571	28	21	-continuous	-continuous	ADJ
ejpam-6571	28	22	functions	function	NOUN
ejpam-6571	28	23	.	.	PUNCT
ejpam-6571	29	1	moreover	moreover	ADV
ejpam-6571	29	2	,	,	PUNCT
ejpam-6571	29	3	hatir	hatir	PROPN
ejpam-6571	29	4	and	and	CCONJ
ejpam-6571	29	5	noiri	noiri	ADV
ejpam-6571	30	1	[	[	X
ejpam-6571	30	2	13	13	NUM
ejpam-6571	30	3	]	]	PUNCT
ejpam-6571	30	4	investigated	investigate	VERB
ejpam-6571	30	5	further	further	ADJ
ejpam-6571	30	6	properties	property	NOUN
ejpam-6571	30	7	of	of	ADP
ejpam-6571	30	8	semi	semi	ADJ
ejpam-6571	30	9	-	-	ADJ
ejpam-6571	30	10	i	i	PRON
ejpam-6571	30	11	-open	-open	NOUN
ejpam-6571	30	12	sets	set	NOUN
ejpam-6571	30	13	and	and	CCONJ
ejpam-6571	30	14	semi	semi	ADJ
ejpam-6571	30	15	-	-	ADJ
ejpam-6571	30	16	i	i	ADV
ejpam-6571	30	17	-continuous	-continuous	ADJ
ejpam-6571	30	18	functions	function	NOUN
ejpam-6571	30	19	.	.	PUNCT
ejpam-6571	31	1	on	on	ADP
ejpam-6571	31	2	the	the	DET
ejpam-6571	31	3	other	other	ADJ
ejpam-6571	31	4	hand	hand	NOUN
ejpam-6571	31	5	,	,	PUNCT
ejpam-6571	31	6	the	the	DET
ejpam-6571	31	7	present	present	ADJ
ejpam-6571	31	8	author	author	NOUN
ejpam-6571	31	9	introduced	introduce	VERB
ejpam-6571	31	10	and	and	CCONJ
ejpam-6571	31	11	investigated	investigate	VERB
ejpam-6571	31	12	the	the	DET
ejpam-6571	31	13	concepts	concept	NOUN
ejpam-6571	31	14	of	of	ADP
ejpam-6571	31	15	almost	almost	ADV
ejpam-6571	31	16	quasi	quasi	ADJ
ejpam-6571	31	17	⋆-continuous	⋆-continuous	ADJ
ejpam-6571	31	18	multifunctions	multifunction	NOUN
ejpam-6571	32	1	[	[	X
ejpam-6571	32	2	14	14	NUM
ejpam-6571	32	3	]	]	PUNCT
ejpam-6571	32	4	,	,	PUNCT
ejpam-6571	32	5	weakly	weakly	ADJ
ejpam-6571	32	6	quasi	quasi	ADJ
ejpam-6571	32	7	⋆-continuous	⋆-continuous	ADJ
ejpam-6571	32	8	multifunctions	multifunction	NOUN
ejpam-6571	33	1	[	[	X
ejpam-6571	33	2	14	14	NUM
ejpam-6571	33	3	]	]	PUNCT
ejpam-6571	33	4	,	,	PUNCT
ejpam-6571	33	5	pıcontinuous	pıcontinuous	ADJ
ejpam-6571	33	6	multifunctions	multifunction	NOUN
ejpam-6571	34	1	[	[	X
ejpam-6571	34	2	15	15	NUM
ejpam-6571	34	3	]	]	PUNCT
ejpam-6571	34	4	and	and	CCONJ
ejpam-6571	34	5	weakly	weakly	ADJ
ejpam-6571	34	6	pı	pı	ADJ
ejpam-6571	34	7	-	-	ADJ
ejpam-6571	34	8	continuous	continuous	ADJ
ejpam-6571	34	9	multifunctions	multifunction	NOUN
ejpam-6571	35	1	[	[	X
ejpam-6571	35	2	15	15	NUM
ejpam-6571	35	3	]	]	PUNCT
ejpam-6571	35	4	.	.	PUNCT
ejpam-6571	36	1	pue	pue	NOUN
ejpam-6571	36	2	-	-	PUNCT
ejpam-6571	36	3	on	on	NOUN
ejpam-6571	36	4	et	et	PROPN
ejpam-6571	36	5	al	al	PROPN
ejpam-6571	36	6	.	.	PUNCT
ejpam-6571	37	1	[	[	X
ejpam-6571	37	2	16	16	NUM
ejpam-6571	37	3	]	]	PUNCT
ejpam-6571	37	4	introduced	introduce	VERB
ejpam-6571	37	5	and	and	CCONJ
ejpam-6571	37	6	studied	study	VERB
ejpam-6571	37	7	the	the	DET
ejpam-6571	37	8	concepts	concept	NOUN
ejpam-6571	37	9	of	of	ADP
ejpam-6571	37	10	upper	upper	ADJ
ejpam-6571	37	11	(	(	PUNCT
ejpam-6571	37	12	τ1	τ1	NOUN
ejpam-6571	37	13	,	,	PUNCT
ejpam-6571	37	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	37	15	multifunctions	multifunction	NOUN
ejpam-6571	37	16	and	and	CCONJ
ejpam-6571	37	17	lower	low	ADJ
ejpam-6571	37	18	(	(	PUNCT
ejpam-6571	37	19	τ1	τ1	NOUN
ejpam-6571	37	20	,	,	PUNCT
ejpam-6571	37	21	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	37	22	multifunctions	multifunction	NOUN
ejpam-6571	37	23	.	.	PUNCT
ejpam-6571	38	1	klanarong	klanarong	NOUN
ejpam-6571	38	2	et	et	PROPN
ejpam-6571	38	3	al	al	PROPN
ejpam-6571	38	4	.	.	PUNCT
ejpam-6571	39	1	[	[	X
ejpam-6571	39	2	17	17	NUM
ejpam-6571	39	3	]	]	PUNCT
ejpam-6571	39	4	introduced	introduce	VERB
ejpam-6571	39	5	and	and	CCONJ
ejpam-6571	39	6	investigated	investigate	VERB
ejpam-6571	39	7	the	the	DET
ejpam-6571	39	8	notions	notion	NOUN
ejpam-6571	39	9	of	of	ADP
ejpam-6571	39	10	upper	upper	ADJ
ejpam-6571	39	11	almost	almost	ADV
ejpam-6571	39	12	(	(	PUNCT
ejpam-6571	39	13	τ1	τ1	NOUN
ejpam-6571	39	14	,	,	PUNCT
ejpam-6571	39	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	39	16	multifunctions	multifunction	NOUN
ejpam-6571	39	17	and	and	CCONJ
ejpam-6571	39	18	lower	low	ADJ
ejpam-6571	39	19	almost	almost	ADV
ejpam-6571	39	20	(	(	PUNCT
ejpam-6571	39	21	τ1	τ1	NOUN
ejpam-6571	39	22	,	,	PUNCT
ejpam-6571	39	23	τ2)continuous	τ2)continuous	ADJ
ejpam-6571	39	24	multifunctions	multifunction	NOUN
ejpam-6571	39	25	.	.	PUNCT
ejpam-6571	40	1	thongmoon	thongmoon	NOUN
ejpam-6571	40	2	et	et	PROPN
ejpam-6571	40	3	al	al	PROPN
ejpam-6571	40	4	.	.	PUNCT
ejpam-6571	41	1	[	[	X
ejpam-6571	41	2	18	18	NUM
ejpam-6571	41	3	]	]	PUNCT
ejpam-6571	41	4	introduced	introduce	VERB
ejpam-6571	41	5	and	and	CCONJ
ejpam-6571	41	6	studied	study	VERB
ejpam-6571	41	7	the	the	DET
ejpam-6571	41	8	concepts	concept	NOUN
ejpam-6571	41	9	of	of	ADP
ejpam-6571	41	10	upper	upper	ADJ
ejpam-6571	41	11	weakly	weakly	ADJ
ejpam-6571	41	12	(	(	PUNCT
ejpam-6571	41	13	τ1	τ1	NOUN
ejpam-6571	41	14	,	,	PUNCT
ejpam-6571	41	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	41	16	multifunctions	multifunction	NOUN
ejpam-6571	41	17	and	and	CCONJ
ejpam-6571	41	18	lower	low	ADJ
ejpam-6571	41	19	weakly	weakly	ADJ
ejpam-6571	41	20	(	(	PUNCT
ejpam-6571	41	21	τ1	τ1	NOUN
ejpam-6571	41	22	,	,	PUNCT
ejpam-6571	41	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	41	24	multifunctions	multifunction	NOUN
ejpam-6571	41	25	.	.	PUNCT
ejpam-6571	42	1	chiangpradit	chiangpradit	NOUN
ejpam-6571	42	2	et	et	PROPN
ejpam-6571	42	3	al	al	PROPN
ejpam-6571	42	4	.	.	PUNCT
ejpam-6571	43	1	[	[	X
ejpam-6571	43	2	19	19	NUM
ejpam-6571	43	3	]	]	PUNCT
ejpam-6571	43	4	introduced	introduce	VERB
ejpam-6571	43	5	and	and	CCONJ
ejpam-6571	43	6	investigated	investigate	VERB
ejpam-6571	43	7	the	the	DET
ejpam-6571	43	8	notions	notion	NOUN
ejpam-6571	43	9	of	of	ADP
ejpam-6571	43	10	upper	upper	ADJ
ejpam-6571	43	11	almost	almost	ADV
ejpam-6571	43	12	quasi	quasi	NOUN
ejpam-6571	43	13	(	(	PUNCT
ejpam-6571	43	14	τ1	τ1	NOUN
ejpam-6571	43	15	,	,	PUNCT
ejpam-6571	43	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	43	17	multifunctions	multifunction	NOUN
ejpam-6571	43	18	and	and	CCONJ
ejpam-6571	43	19	lower	low	ADJ
ejpam-6571	43	20	almost	almost	ADV
ejpam-6571	43	21	quasi	quasi	NOUN
ejpam-6571	43	22	(	(	PUNCT
ejpam-6571	43	23	τ1	τ1	NOUN
ejpam-6571	43	24	,	,	PUNCT
ejpam-6571	43	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	43	26	multifunctions	multifunction	NOUN
ejpam-6571	43	27	.	.	PUNCT
ejpam-6571	44	1	quite	quite	ADV
ejpam-6571	44	2	recently	recently	ADV
ejpam-6571	44	3	,	,	PUNCT
ejpam-6571	44	4	pue	pue	NOUN
ejpam-6571	44	5	-	-	PUNCT
ejpam-6571	44	6	on	on	NOUN
ejpam-6571	44	7	et	et	PROPN
ejpam-6571	44	8	al	al	PROPN
ejpam-6571	44	9	.	.	PUNCT
ejpam-6571	45	1	[	[	X
ejpam-6571	45	2	20	20	NUM
ejpam-6571	45	3	]	]	PUNCT
ejpam-6571	45	4	introduced	introduce	VERB
ejpam-6571	45	5	and	and	CCONJ
ejpam-6571	45	6	studied	study	VERB
ejpam-6571	45	7	the	the	DET
ejpam-6571	45	8	concepts	concept	NOUN
ejpam-6571	45	9	of	of	ADP
ejpam-6571	45	10	upper	upper	ADJ
ejpam-6571	45	11	weakly	weakly	ADJ
ejpam-6571	45	12	quasi	quasi	NOUN
ejpam-6571	45	13	(	(	PUNCT
ejpam-6571	45	14	τ1	τ1	PROPN
ejpam-6571	45	15	,	,	PUNCT
ejpam-6571	45	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	45	17	multifunctions	multifunction	NOUN
ejpam-6571	45	18	and	and	CCONJ
ejpam-6571	45	19	lower	low	ADJ
ejpam-6571	45	20	weakly	weakly	ADJ
ejpam-6571	45	21	quasi	quasi	NOUN
ejpam-6571	45	22	(	(	PUNCT
ejpam-6571	45	23	τ1	τ1	NOUN
ejpam-6571	45	24	,	,	PUNCT
ejpam-6571	45	25	τ2)continuous	τ2)continuous	ADJ
ejpam-6571	45	26	multifunctions	multifunction	NOUN
ejpam-6571	45	27	.	.	PUNCT
ejpam-6571	46	1	in	in	ADP
ejpam-6571	46	2	this	this	DET
ejpam-6571	46	3	paper	paper	NOUN
ejpam-6571	46	4	,	,	PUNCT
ejpam-6571	46	5	we	we	PRON
ejpam-6571	46	6	introduce	introduce	VERB
ejpam-6571	46	7	new	new	ADJ
ejpam-6571	46	8	classes	class	NOUN
ejpam-6571	46	9	of	of	ADP
ejpam-6571	46	10	continuous	continuous	ADJ
ejpam-6571	46	11	multifunctions	multifunction	NOUN
ejpam-6571	46	12	between	between	ADP
ejpam-6571	46	13	an	an	DET
ejpam-6571	46	14	ideal	ideal	ADJ
ejpam-6571	46	15	topological	topological	ADJ
ejpam-6571	46	16	space	space	NOUN
ejpam-6571	46	17	and	and	CCONJ
ejpam-6571	46	18	a	a	DET
ejpam-6571	46	19	bitopological	bitopological	ADJ
ejpam-6571	46	20	space	space	NOUN
ejpam-6571	46	21	,	,	PUNCT
ejpam-6571	46	22	namely	namely	ADV
ejpam-6571	46	23	upper	upper	ADJ
ejpam-6571	46	24	almost	almost	ADV
ejpam-6571	46	25	quasi	quasi	ADJ
ejpam-6571	46	26	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	46	27	,	,	PUNCT
ejpam-6571	46	28	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	46	29	multifunctions	multifunction	NOUN
ejpam-6571	46	30	,	,	PUNCT
ejpam-6571	46	31	lower	low	ADJ
ejpam-6571	46	32	almost	almost	ADV
ejpam-6571	46	33	quasi	quasi	ADJ
ejpam-6571	46	34	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	46	35	,	,	PUNCT
ejpam-6571	46	36	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	46	37	multifunctions	multifunction	NOUN
ejpam-6571	46	38	,	,	PUNCT
ejpam-6571	46	39	upper	upper	ADJ
ejpam-6571	46	40	weakly	weakly	ADJ
ejpam-6571	46	41	quasi	quasi	NOUN
ejpam-6571	46	42	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	46	43	,	,	PUNCT
ejpam-6571	46	44	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	46	45	multifunctions	multifunction	NOUN
ejpam-6571	46	46	and	and	CCONJ
ejpam-6571	46	47	lower	low	ADJ
ejpam-6571	46	48	weakly	weakly	ADJ
ejpam-6571	46	49	quasi	quasi	NOUN
ejpam-6571	46	50	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	46	51	,	,	PUNCT
ejpam-6571	46	52	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	46	53	multifunctions	multifunction	NOUN
ejpam-6571	46	54	.	.	PUNCT
ejpam-6571	47	1	we	we	PRON
ejpam-6571	47	2	also	also	ADV
ejpam-6571	47	3	investigate	investigate	VERB
ejpam-6571	47	4	several	several	ADJ
ejpam-6571	47	5	characterizations	characterization	NOUN
ejpam-6571	47	6	of	of	ADP
ejpam-6571	47	7	upper	upper	ADJ
ejpam-6571	47	8	almost	almost	ADV
ejpam-6571	47	9	quasi	quasi	ADJ
ejpam-6571	47	10	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	47	11	,	,	PUNCT
ejpam-6571	47	12	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	47	13	multifunctions	multifunction	NOUN
ejpam-6571	47	14	,	,	PUNCT
ejpam-6571	47	15	lower	low	ADJ
ejpam-6571	47	16	almost	almost	ADV
ejpam-6571	47	17	quasi	quasi	ADJ
ejpam-6571	47	18	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	47	19	,	,	PUNCT
ejpam-6571	47	20	σ2)continuous	σ2)continuous	ADJ
ejpam-6571	47	21	multifunctions	multifunction	NOUN
ejpam-6571	47	22	,	,	PUNCT
ejpam-6571	47	23	upper	upper	ADJ
ejpam-6571	47	24	weakly	weakly	ADJ
ejpam-6571	47	25	quasi	quasi	NOUN
ejpam-6571	47	26	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	47	27	,	,	PUNCT
ejpam-6571	47	28	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	47	29	multifunctions	multifunction	NOUN
ejpam-6571	47	30	and	and	CCONJ
ejpam-6571	47	31	lower	low	ADJ
ejpam-6571	47	32	weakly	weakly	ADJ
ejpam-6571	47	33	quasi	quasi	NOUN
ejpam-6571	47	34	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	47	35	,	,	PUNCT
ejpam-6571	47	36	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	47	37	multifunctions	multifunction	NOUN
ejpam-6571	47	38	.	.	PUNCT
ejpam-6571	48	1	2	2	X
ejpam-6571	48	2	.	.	X
ejpam-6571	48	3	preliminaries	preliminary	NOUN
ejpam-6571	48	4	throughout	throughout	ADP
ejpam-6571	48	5	the	the	DET
ejpam-6571	48	6	present	present	ADJ
ejpam-6571	48	7	paper	paper	NOUN
ejpam-6571	48	8	,	,	PUNCT
ejpam-6571	48	9	spaces	space	NOUN
ejpam-6571	48	10	(	(	PUNCT
ejpam-6571	48	11	x	x	NOUN
ejpam-6571	48	12	,	,	PUNCT
ejpam-6571	48	13	τ1	τ1	NOUN
ejpam-6571	48	14	,	,	PUNCT
ejpam-6571	48	15	τ2	τ2	NOUN
ejpam-6571	48	16	)	)	PUNCT
ejpam-6571	48	17	and	and	CCONJ
ejpam-6571	48	18	(	(	PUNCT
ejpam-6571	48	19	y	y	PROPN
ejpam-6571	48	20	,	,	PUNCT
ejpam-6571	48	21	σ1	σ1	PROPN
ejpam-6571	48	22	,	,	PUNCT
ejpam-6571	48	23	σ2	σ2	NOUN
ejpam-6571	48	24	)	)	PUNCT
ejpam-6571	48	25	(	(	PUNCT
ejpam-6571	48	26	or	or	CCONJ
ejpam-6571	48	27	simply	simply	ADV
ejpam-6571	48	28	x	x	X
ejpam-6571	48	29	and	and	CCONJ
ejpam-6571	48	30	y	y	PROPN
ejpam-6571	48	31	)	)	PUNCT
ejpam-6571	48	32	always	always	ADV
ejpam-6571	48	33	mean	mean	VERB
ejpam-6571	48	34	bitopological	bitopological	ADJ
ejpam-6571	48	35	spaces	space	NOUN
ejpam-6571	48	36	on	on	ADP
ejpam-6571	48	37	which	which	PRON
ejpam-6571	48	38	no	no	DET
ejpam-6571	48	39	separation	separation	NOUN
ejpam-6571	48	40	axioms	axiom	NOUN
ejpam-6571	48	41	are	be	AUX
ejpam-6571	48	42	assumed	assume	VERB
ejpam-6571	48	43	unless	unless	SCONJ
ejpam-6571	48	44	explicitly	explicitly	ADV
ejpam-6571	48	45	stated	state	VERB
ejpam-6571	48	46	.	.	PUNCT
ejpam-6571	49	1	let	let	VERB
ejpam-6571	49	2	a	a	DET
ejpam-6571	49	3	be	be	AUX
ejpam-6571	49	4	a	a	DET
ejpam-6571	49	5	subset	subset	NOUN
ejpam-6571	49	6	of	of	ADP
ejpam-6571	49	7	a	a	DET
ejpam-6571	49	8	bitopological	bitopological	ADJ
ejpam-6571	49	9	space	space	NOUN
ejpam-6571	49	10	(	(	PUNCT
ejpam-6571	49	11	x	x	NOUN
ejpam-6571	49	12	,	,	PUNCT
ejpam-6571	49	13	τ1	τ1	NOUN
ejpam-6571	49	14	,	,	PUNCT
ejpam-6571	49	15	τ2	τ2	NOUN
ejpam-6571	49	16	)	)	PUNCT
ejpam-6571	49	17	.	.	PUNCT
ejpam-6571	50	1	the	the	DET
ejpam-6571	50	2	closure	closure	NOUN
ejpam-6571	50	3	of	of	ADP
ejpam-6571	50	4	a	a	PRON
ejpam-6571	50	5	and	and	CCONJ
ejpam-6571	50	6	the	the	DET
ejpam-6571	50	7	interior	interior	NOUN
ejpam-6571	50	8	of	of	ADP
ejpam-6571	50	9	a	a	PRON
ejpam-6571	50	10	with	with	ADP
ejpam-6571	50	11	respect	respect	NOUN
ejpam-6571	50	12	to	to	ADP
ejpam-6571	50	13	τi	τi	PROPN
ejpam-6571	50	14	are	be	AUX
ejpam-6571	50	15	denoted	denote	VERB
ejpam-6571	50	16	by	by	ADP
ejpam-6571	50	17	τi	τi	NOUN
ejpam-6571	50	18	-	-	PUNCT
ejpam-6571	50	19	cl(a	cl(a	NUM
ejpam-6571	50	20	)	)	PUNCT
ejpam-6571	50	21	and	and	CCONJ
ejpam-6571	50	22	τi	τi	NOUN
ejpam-6571	50	23	-	-	PUNCT
ejpam-6571	50	24	int(a	int(a	NOUN
ejpam-6571	50	25	)	)	PUNCT
ejpam-6571	50	26	,	,	PUNCT
ejpam-6571	50	27	respectively	respectively	ADV
ejpam-6571	50	28	,	,	PUNCT
ejpam-6571	50	29	for	for	ADP
ejpam-6571	50	30	i	i	PROPN
ejpam-6571	50	31	=	=	SYM
ejpam-6571	50	32	1	1	NUM
ejpam-6571	50	33	,	,	PUNCT
ejpam-6571	50	34	2	2	NUM
ejpam-6571	50	35	.	.	X
ejpam-6571	50	36	a	a	DET
ejpam-6571	50	37	subset	subset	NOUN
ejpam-6571	50	38	a	a	PRON
ejpam-6571	50	39	of	of	ADP
ejpam-6571	50	40	a	a	DET
ejpam-6571	50	41	bitopological	bitopological	ADJ
ejpam-6571	50	42	space	space	NOUN
ejpam-6571	50	43	(	(	PUNCT
ejpam-6571	50	44	x	x	NOUN
ejpam-6571	50	45	,	,	PUNCT
ejpam-6571	50	46	τ1	τ1	NOUN
ejpam-6571	50	47	,	,	PUNCT
ejpam-6571	50	48	τ2	τ2	NOUN
ejpam-6571	50	49	)	)	PUNCT
ejpam-6571	50	50	is	be	AUX
ejpam-6571	50	51	called	call	VERB
ejpam-6571	50	52	τ1τ2	τ1τ2	VERB
ejpam-6571	50	53	-	-	ADJ
ejpam-6571	50	54	closed	closed	ADJ
ejpam-6571	50	55	[	[	X
ejpam-6571	50	56	21	21	NUM
ejpam-6571	50	57	]	]	X
ejpam-6571	50	58	if	if	SCONJ
ejpam-6571	50	59	a	a	DET
ejpam-6571	50	60	=	=	NOUN
ejpam-6571	50	61	τ1	τ1	NOUN
ejpam-6571	50	62	-	-	PUNCT
ejpam-6571	50	63	cl(τ2	cl(τ2	NOUN
ejpam-6571	50	64	-	-	PUNCT
ejpam-6571	50	65	cl(a	cl(a	NUM
ejpam-6571	50	66	)	)	PUNCT
ejpam-6571	50	67	)	)	PUNCT
ejpam-6571	50	68	.	.	PUNCT
ejpam-6571	51	1	the	the	DET
ejpam-6571	51	2	complement	complement	NOUN
ejpam-6571	51	3	of	of	ADP
ejpam-6571	51	4	a	a	DET
ejpam-6571	51	5	τ1τ2	τ1τ2	ADJ
ejpam-6571	51	6	-	-	ADJ
ejpam-6571	51	7	closed	closed	ADJ
ejpam-6571	51	8	set	set	NOUN
ejpam-6571	51	9	is	be	AUX
ejpam-6571	51	10	called	call	VERB
ejpam-6571	51	11	τ1τ2	τ1τ2	NOUN
ejpam-6571	51	12	-	-	ADJ
ejpam-6571	51	13	open	open	ADJ
ejpam-6571	51	14	.	.	PUNCT
ejpam-6571	52	1	the	the	DET
ejpam-6571	52	2	intersection	intersection	NOUN
ejpam-6571	52	3	of	of	ADP
ejpam-6571	52	4	all	all	DET
ejpam-6571	52	5	τ1τ2	τ1τ2	ADJ
ejpam-6571	52	6	-	-	ADJ
ejpam-6571	52	7	closed	closed	ADJ
ejpam-6571	52	8	sets	set	NOUN
ejpam-6571	52	9	of	of	ADP
ejpam-6571	52	10	x	x	PUNCT
ejpam-6571	52	11	containing	contain	VERB
ejpam-6571	52	12	a	a	PRON
ejpam-6571	52	13	is	be	AUX
ejpam-6571	52	14	called	call	VERB
ejpam-6571	52	15	the	the	DET
ejpam-6571	52	16	τ1τ2	τ1τ2	NOUN
ejpam-6571	52	17	-	-	NOUN
ejpam-6571	52	18	closure	closure	NOUN
ejpam-6571	52	19	[	[	X
ejpam-6571	52	20	21	21	NUM
ejpam-6571	52	21	]	]	PUNCT
ejpam-6571	52	22	of	of	ADP
ejpam-6571	52	23	a	a	PRON
ejpam-6571	52	24	and	and	CCONJ
ejpam-6571	52	25	is	be	AUX
ejpam-6571	52	26	denoted	denote	VERB
ejpam-6571	52	27	by	by	ADP
ejpam-6571	52	28	τ1τ2	τ1τ2	NOUN
ejpam-6571	52	29	-	-	NUM
ejpam-6571	52	30	cl(a	cl(a	NUM
ejpam-6571	52	31	)	)	PUNCT
ejpam-6571	52	32	.	.	PUNCT
ejpam-6571	53	1	the	the	DET
ejpam-6571	53	2	union	union	NOUN
ejpam-6571	53	3	of	of	ADP
ejpam-6571	53	4	all	all	DET
ejpam-6571	53	5	τ1τ2	τ1τ2	ADJ
ejpam-6571	53	6	-	-	ADJ
ejpam-6571	53	7	open	open	ADJ
ejpam-6571	53	8	sets	set	NOUN
ejpam-6571	53	9	of	of	ADP
ejpam-6571	53	10	x	x	PUNCT
ejpam-6571	53	11	contained	contain	VERB
ejpam-6571	53	12	in	in	ADP
ejpam-6571	53	13	a	a	PRON
ejpam-6571	53	14	is	be	AUX
ejpam-6571	53	15	called	call	VERB
ejpam-6571	53	16	the	the	DET
ejpam-6571	53	17	τ1τ2	τ1τ2	NOUN
ejpam-6571	53	18	-	-	ADJ
ejpam-6571	53	19	interior	interior	ADJ
ejpam-6571	53	20	[	[	X
ejpam-6571	53	21	21	21	NUM
ejpam-6571	53	22	]	]	PUNCT
ejpam-6571	53	23	of	of	ADP
ejpam-6571	53	24	a	a	PRON
ejpam-6571	53	25	and	and	CCONJ
ejpam-6571	53	26	is	be	AUX
ejpam-6571	53	27	denoted	denote	VERB
ejpam-6571	53	28	by	by	ADP
ejpam-6571	53	29	τ1τ2	τ1τ2	NOUN
ejpam-6571	53	30	-	-	ADJ
ejpam-6571	53	31	int(a	int(a	NOUN
ejpam-6571	53	32	)	)	PUNCT
ejpam-6571	53	33	.	.	PUNCT
ejpam-6571	54	1	lemma	lemma	PROPN
ejpam-6571	54	2	1	1	NUM
ejpam-6571	54	3	.	.	PUNCT
ejpam-6571	55	1	[	[	X
ejpam-6571	55	2	21	21	NUM
ejpam-6571	55	3	]	]	PUNCT
ejpam-6571	55	4	let	let	VERB
ejpam-6571	55	5	a	a	PRON
ejpam-6571	55	6	and	and	CCONJ
ejpam-6571	55	7	b	b	NOUN
ejpam-6571	55	8	be	be	AUX
ejpam-6571	55	9	subsets	subset	NOUN
ejpam-6571	55	10	of	of	ADP
ejpam-6571	55	11	a	a	DET
ejpam-6571	55	12	bitopological	bitopological	ADJ
ejpam-6571	55	13	space	space	NOUN
ejpam-6571	55	14	(	(	PUNCT
ejpam-6571	55	15	x	x	NOUN
ejpam-6571	55	16	,	,	PUNCT
ejpam-6571	55	17	τ1	τ1	NOUN
ejpam-6571	55	18	,	,	PUNCT
ejpam-6571	55	19	τ2	τ2	NOUN
ejpam-6571	55	20	)	)	PUNCT
ejpam-6571	55	21	.	.	PUNCT
ejpam-6571	56	1	for	for	ADP
ejpam-6571	56	2	the	the	DET
ejpam-6571	56	3	τ1τ2	τ1τ2	NOUN
ejpam-6571	56	4	m.	m.	NOUN
ejpam-6571	56	5	thongmoon	thongmoon	NOUN
ejpam-6571	56	6	,	,	PUNCT
ejpam-6571	56	7	a.	a.	PROPN
ejpam-6571	56	8	sama	sama	PROPN
ejpam-6571	56	9	-	-	PUNCT
ejpam-6571	56	10	ae	ae	PROPN
ejpam-6571	56	11	,	,	PUNCT
ejpam-6571	56	12	c.	c.	PROPN
ejpam-6571	56	13	boonpok	boonpok	PROPN
ejpam-6571	56	14	/	/	SYM
ejpam-6571	56	15	eur	eur	PROPN
ejpam-6571	56	16	.	.	PUNCT
ejpam-6571	57	1	j.	j.	PROPN
ejpam-6571	57	2	pure	pure	PROPN
ejpam-6571	57	3	appl	appl	PROPN
ejpam-6571	57	4	.	.	PROPN
ejpam-6571	57	5	math	math	PROPN
ejpam-6571	57	6	,	,	PUNCT
ejpam-6571	57	7	18	18	NUM
ejpam-6571	57	8	(	(	PUNCT
ejpam-6571	57	9	3	3	NUM
ejpam-6571	57	10	)	)	PUNCT
ejpam-6571	57	11	(	(	PUNCT
ejpam-6571	57	12	2025	2025	NUM
ejpam-6571	57	13	)	)	PUNCT
ejpam-6571	57	14	,	,	PUNCT
ejpam-6571	57	15	6571	6571	NUM
ejpam-6571	57	16	3	3	NUM
ejpam-6571	57	17	of	of	ADP
ejpam-6571	57	18	15	15	NUM
ejpam-6571	57	19	closure	closure	NOUN
ejpam-6571	57	20	,	,	PUNCT
ejpam-6571	57	21	the	the	DET
ejpam-6571	57	22	following	follow	VERB
ejpam-6571	57	23	properties	property	NOUN
ejpam-6571	57	24	hold	hold	VERB
ejpam-6571	57	25	:	:	PUNCT
ejpam-6571	57	26	(	(	PUNCT
ejpam-6571	57	27	1	1	X
ejpam-6571	57	28	)	)	PUNCT
ejpam-6571	57	29	a	a	DET
ejpam-6571	57	30	⊆	⊆	NUM
ejpam-6571	57	31	τ1τ2	τ1τ2	NOUN
ejpam-6571	57	32	-	-	NUM
ejpam-6571	57	33	cl(a	cl(a	NUM
ejpam-6571	57	34	)	)	PUNCT
ejpam-6571	57	35	and	and	CCONJ
ejpam-6571	57	36	τ1τ2	τ1τ2	NOUN
ejpam-6571	57	37	-	-	ADJ
ejpam-6571	57	38	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6571	57	39	-	-	PUNCT
ejpam-6571	57	40	cl(a	cl(a	NUM
ejpam-6571	57	41	)	)	PUNCT
ejpam-6571	57	42	)	)	PUNCT
ejpam-6571	58	1	=	=	PUNCT
ejpam-6571	58	2	τ1τ2	τ1τ2	NOUN
ejpam-6571	58	3	-	-	NUM
ejpam-6571	58	4	cl(a	cl(a	NUM
ejpam-6571	58	5	)	)	PUNCT
ejpam-6571	58	6	.	.	PUNCT
ejpam-6571	59	1	(	(	PUNCT
ejpam-6571	59	2	2	2	X
ejpam-6571	59	3	)	)	PUNCT
ejpam-6571	59	4	if	if	SCONJ
ejpam-6571	59	5	a	a	DET
ejpam-6571	59	6	⊆	⊆	NUM
ejpam-6571	59	7	b	b	NOUN
ejpam-6571	59	8	,	,	PUNCT
ejpam-6571	59	9	then	then	ADV
ejpam-6571	59	10	τ1τ2	τ1τ2	NOUN
ejpam-6571	59	11	-	-	NUM
ejpam-6571	59	12	cl(a	cl(a	NUM
ejpam-6571	59	13	)	)	PUNCT
ejpam-6571	59	14	⊆	⊆	NUM
ejpam-6571	59	15	τ1τ2	τ1τ2	NOUN
ejpam-6571	59	16	-	-	NOUN
ejpam-6571	59	17	cl(b	cl(b	NOUN
ejpam-6571	59	18	)	)	PUNCT
ejpam-6571	59	19	.	.	PUNCT
ejpam-6571	60	1	(	(	PUNCT
ejpam-6571	60	2	3	3	X
ejpam-6571	60	3	)	)	PUNCT
ejpam-6571	60	4	τ1τ2	τ1τ2	NOUN
ejpam-6571	60	5	-	-	NUM
ejpam-6571	60	6	cl(a	cl(a	NUM
ejpam-6571	60	7	)	)	PUNCT
ejpam-6571	60	8	is	be	AUX
ejpam-6571	60	9	τ1τ2	τ1τ2	NOUN
ejpam-6571	60	10	-	-	ADJ
ejpam-6571	60	11	closed	closed	ADJ
ejpam-6571	60	12	.	.	PUNCT
ejpam-6571	61	1	(	(	PUNCT
ejpam-6571	61	2	4	4	X
ejpam-6571	61	3	)	)	PUNCT
ejpam-6571	61	4	a	a	PRON
ejpam-6571	61	5	is	be	AUX
ejpam-6571	61	6	τ1τ2	τ1τ2	NOUN
ejpam-6571	61	7	-	-	ADJ
ejpam-6571	61	8	closed	closed	ADJ
ejpam-6571	61	9	if	if	SCONJ
ejpam-6571	61	10	and	and	CCONJ
ejpam-6571	61	11	only	only	ADV
ejpam-6571	61	12	if	if	SCONJ
ejpam-6571	61	13	a	a	DET
ejpam-6571	61	14	=	=	PUNCT
ejpam-6571	61	15	τ1τ2	τ1τ2	NOUN
ejpam-6571	61	16	-	-	NUM
ejpam-6571	61	17	cl(a	cl(a	NUM
ejpam-6571	61	18	)	)	PUNCT
ejpam-6571	61	19	.	.	PUNCT
ejpam-6571	62	1	(	(	PUNCT
ejpam-6571	62	2	5	5	X
ejpam-6571	62	3	)	)	PUNCT
ejpam-6571	62	4	τ1τ2	τ1τ2	NOUN
ejpam-6571	62	5	-	-	NOUN
ejpam-6571	62	6	cl(x	cl(x	X
ejpam-6571	62	7	−a	−a	NOUN
ejpam-6571	62	8	)	)	PUNCT
ejpam-6571	63	1	=	=	PUNCT
ejpam-6571	63	2	x	x	X
ejpam-6571	64	1	−	−	ADP
ejpam-6571	64	2	τ1τ2	τ1τ2	NOUN
ejpam-6571	64	3	-	-	PUNCT
ejpam-6571	64	4	int(a	int(a	NOUN
ejpam-6571	64	5	)	)	PUNCT
ejpam-6571	64	6	.	.	PUNCT
ejpam-6571	65	1	a	a	DET
ejpam-6571	65	2	subset	subset	NOUN
ejpam-6571	65	3	a	a	PRON
ejpam-6571	65	4	of	of	ADP
ejpam-6571	65	5	a	a	DET
ejpam-6571	65	6	bitopological	bitopological	ADJ
ejpam-6571	65	7	space	space	NOUN
ejpam-6571	65	8	(	(	PUNCT
ejpam-6571	65	9	x	x	NOUN
ejpam-6571	65	10	,	,	PUNCT
ejpam-6571	65	11	τ1	τ1	NOUN
ejpam-6571	65	12	,	,	PUNCT
ejpam-6571	65	13	τ2	τ2	NOUN
ejpam-6571	65	14	)	)	PUNCT
ejpam-6571	65	15	is	be	AUX
ejpam-6571	65	16	said	say	VERB
ejpam-6571	65	17	to	to	PART
ejpam-6571	65	18	be	be	AUX
ejpam-6571	65	19	(	(	PUNCT
ejpam-6571	65	20	τ1	τ1	NOUN
ejpam-6571	65	21	,	,	PUNCT
ejpam-6571	65	22	τ2)r	τ2)r	NOUN
ejpam-6571	65	23	-	-	PUNCT
ejpam-6571	65	24	open	open	NOUN
ejpam-6571	66	1	[	[	X
ejpam-6571	66	2	22	22	NUM
ejpam-6571	66	3	]	]	PUNCT
ejpam-6571	66	4	(	(	PUNCT
ejpam-6571	66	5	resp	resp	NOUN
ejpam-6571	66	6	.	.	PUNCT
ejpam-6571	67	1	(	(	PUNCT
ejpam-6571	67	2	τ1	τ1	NOUN
ejpam-6571	67	3	,	,	PUNCT
ejpam-6571	67	4	τ2)s	τ2)s	NOUN
ejpam-6571	67	5	-	-	PUNCT
ejpam-6571	67	6	open	open	ADJ
ejpam-6571	67	7	[	[	X
ejpam-6571	67	8	23	23	NUM
ejpam-6571	67	9	]	]	PUNCT
ejpam-6571	67	10	,	,	PUNCT
ejpam-6571	67	11	(	(	PUNCT
ejpam-6571	67	12	τ1	τ1	NOUN
ejpam-6571	67	13	,	,	PUNCT
ejpam-6571	67	14	τ2)p	τ2)p	NOUN
ejpam-6571	67	15	-	-	ADJ
ejpam-6571	67	16	open	open	ADJ
ejpam-6571	67	17	[	[	X
ejpam-6571	67	18	23	23	NUM
ejpam-6571	67	19	]	]	PUNCT
ejpam-6571	67	20	,	,	PUNCT
ejpam-6571	67	21	(	(	PUNCT
ejpam-6571	67	22	τ1	τ1	NOUN
ejpam-6571	67	23	,	,	PUNCT
ejpam-6571	67	24	τ2)β	τ2)β	ADJ
ejpam-6571	67	25	-	-	PUNCT
ejpam-6571	67	26	open	open	NOUN
ejpam-6571	68	1	[	[	X
ejpam-6571	68	2	23	23	NUM
ejpam-6571	68	3	]	]	SYM
ejpam-6571	68	4	)	)	PUNCT
ejpam-6571	68	5	if	if	SCONJ
ejpam-6571	68	6	a	a	DET
ejpam-6571	68	7	=	=	PUNCT
ejpam-6571	68	8	τ1τ2	τ1τ2	NOUN
ejpam-6571	68	9	-	-	NOUN
ejpam-6571	68	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6571	68	11	-	-	PUNCT
ejpam-6571	68	12	cl(a	cl(a	NUM
ejpam-6571	68	13	)	)	PUNCT
ejpam-6571	68	14	)	)	PUNCT
ejpam-6571	68	15	(	(	PUNCT
ejpam-6571	68	16	resp	resp	NOUN
ejpam-6571	68	17	.	.	PUNCT
ejpam-6571	69	1	a	a	DET
ejpam-6571	69	2	⊆	⊆	NUM
ejpam-6571	69	3	τ1τ2	τ1τ2	NOUN
ejpam-6571	69	4	-	-	ADJ
ejpam-6571	69	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6571	69	6	-	-	PUNCT
ejpam-6571	69	7	int(a	int(a	NOUN
ejpam-6571	69	8	)	)	PUNCT
ejpam-6571	69	9	)	)	PUNCT
ejpam-6571	69	10	,	,	PUNCT
ejpam-6571	69	11	a	a	DET
ejpam-6571	69	12	⊆	⊆	NUM
ejpam-6571	69	13	τ1τ2	τ1τ2	NOUN
ejpam-6571	69	14	-	-	NOUN
ejpam-6571	69	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6571	69	16	-	-	PUNCT
ejpam-6571	69	17	cl(a	cl(a	NUM
ejpam-6571	69	18	)	)	PUNCT
ejpam-6571	69	19	)	)	PUNCT
ejpam-6571	69	20	,	,	PUNCT
ejpam-6571	69	21	a	a	DET
ejpam-6571	69	22	⊆	⊆	NUM
ejpam-6571	69	23	τ1τ2	τ1τ2	NOUN
ejpam-6571	69	24	-	-	PUNCT
ejpam-6571	69	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6571	69	26	-	-	PUNCT
ejpam-6571	69	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6571	69	28	-	-	PUNCT
ejpam-6571	69	29	cl(a	cl(a	NUM
ejpam-6571	69	30	)	)	PUNCT
ejpam-6571	69	31	)	)	PUNCT
ejpam-6571	69	32	)	)	PUNCT
ejpam-6571	69	33	)	)	PUNCT
ejpam-6571	69	34	.	.	PUNCT
ejpam-6571	70	1	the	the	DET
ejpam-6571	70	2	complement	complement	NOUN
ejpam-6571	70	3	of	of	ADP
ejpam-6571	70	4	a	a	DET
ejpam-6571	70	5	(	(	PUNCT
ejpam-6571	70	6	τ1	τ1	NOUN
ejpam-6571	70	7	,	,	PUNCT
ejpam-6571	70	8	τ2)r	τ2)r	NOUN
ejpam-6571	70	9	-	-	PUNCT
ejpam-6571	70	10	open	open	ADJ
ejpam-6571	70	11	(	(	PUNCT
ejpam-6571	70	12	resp	resp	NOUN
ejpam-6571	70	13	.	.	PUNCT
ejpam-6571	71	1	(	(	PUNCT
ejpam-6571	71	2	τ1	τ1	NOUN
ejpam-6571	71	3	,	,	PUNCT
ejpam-6571	71	4	τ2)s	τ2)s	NOUN
ejpam-6571	71	5	-	-	PUNCT
ejpam-6571	71	6	open	open	ADJ
ejpam-6571	71	7	,	,	PUNCT
ejpam-6571	71	8	(	(	PUNCT
ejpam-6571	71	9	τ1	τ1	NOUN
ejpam-6571	71	10	,	,	PUNCT
ejpam-6571	71	11	τ2)p	τ2)p	NOUN
ejpam-6571	71	12	-	-	ADJ
ejpam-6571	71	13	open	open	ADJ
ejpam-6571	71	14	,	,	PUNCT
ejpam-6571	71	15	(	(	PUNCT
ejpam-6571	71	16	τ1	τ1	NOUN
ejpam-6571	71	17	,	,	PUNCT
ejpam-6571	71	18	τ2)β	τ2)β	ADJ
ejpam-6571	71	19	-	-	PUNCT
ejpam-6571	71	20	open	open	ADJ
ejpam-6571	71	21	)	)	PUNCT
ejpam-6571	71	22	set	set	NOUN
ejpam-6571	71	23	is	be	AUX
ejpam-6571	71	24	said	say	VERB
ejpam-6571	71	25	to	to	PART
ejpam-6571	71	26	be	be	AUX
ejpam-6571	71	27	(	(	PUNCT
ejpam-6571	71	28	τ1	τ1	NOUN
ejpam-6571	71	29	,	,	PUNCT
ejpam-6571	71	30	τ2)r	τ2)r	NOUN
ejpam-6571	71	31	-	-	PUNCT
ejpam-6571	71	32	closed	closed	ADJ
ejpam-6571	71	33	(	(	PUNCT
ejpam-6571	71	34	resp	resp	NOUN
ejpam-6571	71	35	.	.	PUNCT
ejpam-6571	72	1	(	(	PUNCT
ejpam-6571	72	2	τ1	τ1	NOUN
ejpam-6571	72	3	,	,	PUNCT
ejpam-6571	72	4	τ2)s	τ2)s	NOUN
ejpam-6571	72	5	-	-	PUNCT
ejpam-6571	72	6	closed	closed	ADJ
ejpam-6571	72	7	,	,	PUNCT
ejpam-6571	72	8	(	(	PUNCT
ejpam-6571	72	9	τ1	τ1	NOUN
ejpam-6571	72	10	,	,	PUNCT
ejpam-6571	72	11	τ2)p	τ2)p	NOUN
ejpam-6571	72	12	-	-	PUNCT
ejpam-6571	72	13	closed	closed	ADJ
ejpam-6571	72	14	,	,	PUNCT
ejpam-6571	72	15	(	(	PUNCT
ejpam-6571	72	16	τ1	τ1	NOUN
ejpam-6571	72	17	,	,	PUNCT
ejpam-6571	72	18	τ2)β	τ2)β	ADJ
ejpam-6571	72	19	-	-	PUNCT
ejpam-6571	72	20	closed	closed	ADJ
ejpam-6571	72	21	)	)	PUNCT
ejpam-6571	72	22	.	.	PUNCT
ejpam-6571	73	1	a	a	DET
ejpam-6571	73	2	subset	subset	NOUN
ejpam-6571	73	3	a	a	PRON
ejpam-6571	73	4	of	of	ADP
ejpam-6571	73	5	a	a	DET
ejpam-6571	73	6	bitopological	bitopological	ADJ
ejpam-6571	73	7	space	space	NOUN
ejpam-6571	73	8	(	(	PUNCT
ejpam-6571	73	9	x	x	NOUN
ejpam-6571	73	10	,	,	PUNCT
ejpam-6571	73	11	τ1	τ1	NOUN
ejpam-6571	73	12	,	,	PUNCT
ejpam-6571	73	13	τ2	τ2	NOUN
ejpam-6571	73	14	)	)	PUNCT
ejpam-6571	73	15	is	be	AUX
ejpam-6571	73	16	said	say	VERB
ejpam-6571	73	17	to	to	PART
ejpam-6571	73	18	be	be	AUX
ejpam-6571	73	19	α(τ1	α(τ1	NOUN
ejpam-6571	73	20	,	,	PUNCT
ejpam-6571	73	21	τ2)-open	τ2)-open	ADJ
ejpam-6571	73	22	[	[	X
ejpam-6571	73	23	24	24	NUM
ejpam-6571	73	24	]	]	X
ejpam-6571	73	25	if	if	SCONJ
ejpam-6571	73	26	a	a	DET
ejpam-6571	73	27	⊆	⊆	NUM
ejpam-6571	73	28	τ1τ2	τ1τ2	NOUN
ejpam-6571	73	29	-	-	PUNCT
ejpam-6571	73	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6571	73	31	-	-	PUNCT
ejpam-6571	73	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6571	73	33	-	-	PUNCT
ejpam-6571	73	34	int(a	int(a	NOUN
ejpam-6571	73	35	)	)	PUNCT
ejpam-6571	73	36	)	)	PUNCT
ejpam-6571	73	37	)	)	PUNCT
ejpam-6571	73	38	.	.	PUNCT
ejpam-6571	74	1	the	the	DET
ejpam-6571	74	2	complement	complement	NOUN
ejpam-6571	74	3	of	of	ADP
ejpam-6571	74	4	an	an	DET
ejpam-6571	74	5	α(τ1	α(τ1	NOUN
ejpam-6571	74	6	,	,	PUNCT
ejpam-6571	74	7	τ2)-open	τ2)-open	ADJ
ejpam-6571	74	8	set	set	NOUN
ejpam-6571	74	9	is	be	AUX
ejpam-6571	74	10	said	say	VERB
ejpam-6571	74	11	to	to	PART
ejpam-6571	74	12	be	be	AUX
ejpam-6571	74	13	α(τ1	α(τ1	NOUN
ejpam-6571	74	14	,	,	PUNCT
ejpam-6571	74	15	τ2)-closed	τ2)-close	VERB
ejpam-6571	74	16	.	.	PUNCT
ejpam-6571	75	1	let	let	VERB
ejpam-6571	75	2	a	a	DET
ejpam-6571	75	3	be	be	AUX
ejpam-6571	75	4	a	a	DET
ejpam-6571	75	5	subset	subset	NOUN
ejpam-6571	75	6	of	of	ADP
ejpam-6571	75	7	a	a	DET
ejpam-6571	75	8	bitopological	bitopological	ADJ
ejpam-6571	75	9	space	space	NOUN
ejpam-6571	75	10	(	(	PUNCT
ejpam-6571	75	11	x	x	NOUN
ejpam-6571	75	12	,	,	PUNCT
ejpam-6571	75	13	τ1	τ1	NOUN
ejpam-6571	75	14	,	,	PUNCT
ejpam-6571	75	15	τ2	τ2	NOUN
ejpam-6571	75	16	)	)	PUNCT
ejpam-6571	75	17	.	.	PUNCT
ejpam-6571	76	1	the	the	DET
ejpam-6571	76	2	intersection	intersection	NOUN
ejpam-6571	76	3	of	of	ADP
ejpam-6571	76	4	all	all	DET
ejpam-6571	76	5	(	(	PUNCT
ejpam-6571	76	6	τ1	τ1	NOUN
ejpam-6571	76	7	,	,	PUNCT
ejpam-6571	76	8	τ2)p	τ2)p	NOUN
ejpam-6571	76	9	-	-	PUNCT
ejpam-6571	76	10	closed	closed	ADJ
ejpam-6571	76	11	(	(	PUNCT
ejpam-6571	76	12	resp	resp	NOUN
ejpam-6571	76	13	.	.	PUNCT
ejpam-6571	77	1	(	(	PUNCT
ejpam-6571	77	2	τ1	τ1	NOUN
ejpam-6571	77	3	,	,	PUNCT
ejpam-6571	77	4	τ2)s	τ2)s	NOUN
ejpam-6571	77	5	-	-	PUNCT
ejpam-6571	77	6	closed	closed	ADJ
ejpam-6571	77	7	,	,	PUNCT
ejpam-6571	77	8	α(τ1	α(τ1	NOUN
ejpam-6571	77	9	,	,	PUNCT
ejpam-6571	77	10	τ2)-closed	τ2)-closed	ADJ
ejpam-6571	77	11	)	)	PUNCT
ejpam-6571	77	12	sets	set	NOUN
ejpam-6571	77	13	of	of	ADP
ejpam-6571	77	14	x	x	PUNCT
ejpam-6571	77	15	containing	contain	VERB
ejpam-6571	77	16	a	a	PRON
ejpam-6571	77	17	is	be	AUX
ejpam-6571	77	18	called	call	VERB
ejpam-6571	77	19	the	the	DET
ejpam-6571	77	20	(	(	PUNCT
ejpam-6571	77	21	τ1	τ1	NOUN
ejpam-6571	77	22	,	,	PUNCT
ejpam-6571	77	23	τ2)p	τ2)p	NOUN
ejpam-6571	77	24	-	-	NOUN
ejpam-6571	77	25	closure	closure	NOUN
ejpam-6571	77	26	[	[	X
ejpam-6571	77	27	25	25	NUM
ejpam-6571	77	28	]	]	PUNCT
ejpam-6571	77	29	(	(	PUNCT
ejpam-6571	77	30	resp	resp	NOUN
ejpam-6571	77	31	.	.	PUNCT
ejpam-6571	78	1	(	(	PUNCT
ejpam-6571	78	2	τ1	τ1	NOUN
ejpam-6571	78	3	,	,	PUNCT
ejpam-6571	78	4	τ2)s	τ2)s	NOUN
ejpam-6571	78	5	-	-	PUNCT
ejpam-6571	78	6	closure	closure	NOUN
ejpam-6571	78	7	[	[	X
ejpam-6571	78	8	23	23	NUM
ejpam-6571	78	9	]	]	PUNCT
ejpam-6571	78	10	,	,	PUNCT
ejpam-6571	78	11	α(τ1	α(τ1	NOUN
ejpam-6571	78	12	,	,	PUNCT
ejpam-6571	78	13	τ2)-closure	τ2)-closure	NOUN
ejpam-6571	78	14	[	[	X
ejpam-6571	78	15	26	26	NUM
ejpam-6571	78	16	]	]	PUNCT
ejpam-6571	78	17	)	)	PUNCT
ejpam-6571	78	18	of	of	ADP
ejpam-6571	78	19	a	a	PRON
ejpam-6571	78	20	and	and	CCONJ
ejpam-6571	78	21	is	be	AUX
ejpam-6571	78	22	denoted	denote	VERB
ejpam-6571	78	23	by	by	ADP
ejpam-6571	78	24	(	(	PUNCT
ejpam-6571	78	25	τ1	τ1	NOUN
ejpam-6571	78	26	,	,	PUNCT
ejpam-6571	78	27	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6571	78	28	)	)	PUNCT
ejpam-6571	78	29	(	(	PUNCT
ejpam-6571	78	30	resp	resp	NOUN
ejpam-6571	78	31	.	.	PUNCT
ejpam-6571	79	1	(	(	PUNCT
ejpam-6571	79	2	τ1	τ1	NOUN
ejpam-6571	79	3	,	,	PUNCT
ejpam-6571	79	4	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6571	79	5	)	)	PUNCT
ejpam-6571	79	6	,	,	PUNCT
ejpam-6571	79	7	α(τ1	α(τ1	NOUN
ejpam-6571	79	8	,	,	PUNCT
ejpam-6571	79	9	τ2)-cl(a	τ2)-cl(a	NUM
ejpam-6571	79	10	)	)	PUNCT
ejpam-6571	79	11	)	)	PUNCT
ejpam-6571	79	12	.	.	PUNCT
ejpam-6571	80	1	the	the	DET
ejpam-6571	80	2	union	union	NOUN
ejpam-6571	80	3	of	of	ADP
ejpam-6571	80	4	all	all	DET
ejpam-6571	80	5	(	(	PUNCT
ejpam-6571	80	6	τ1	τ1	NOUN
ejpam-6571	80	7	,	,	PUNCT
ejpam-6571	80	8	τ2)p	τ2)p	NOUN
ejpam-6571	80	9	-	-	ADJ
ejpam-6571	80	10	open	open	ADJ
ejpam-6571	80	11	(	(	PUNCT
ejpam-6571	80	12	resp	resp	NOUN
ejpam-6571	80	13	.	.	PUNCT
ejpam-6571	81	1	(	(	PUNCT
ejpam-6571	81	2	τ1	τ1	NOUN
ejpam-6571	81	3	,	,	PUNCT
ejpam-6571	81	4	τ2)s	τ2)s	NOUN
ejpam-6571	81	5	-	-	PUNCT
ejpam-6571	81	6	open	open	ADJ
ejpam-6571	81	7	,	,	PUNCT
ejpam-6571	81	8	α(τ1	α(τ1	NOUN
ejpam-6571	81	9	,	,	PUNCT
ejpam-6571	81	10	τ2)-open	τ2)-open	ADJ
ejpam-6571	81	11	)	)	PUNCT
ejpam-6571	81	12	sets	set	NOUN
ejpam-6571	81	13	of	of	ADP
ejpam-6571	81	14	x	x	PUNCT
ejpam-6571	81	15	contained	contain	VERB
ejpam-6571	81	16	in	in	ADP
ejpam-6571	81	17	a	a	PRON
ejpam-6571	81	18	is	be	AUX
ejpam-6571	81	19	called	call	VERB
ejpam-6571	81	20	the	the	DET
ejpam-6571	81	21	(	(	PUNCT
ejpam-6571	81	22	τ1	τ1	NOUN
ejpam-6571	81	23	,	,	PUNCT
ejpam-6571	81	24	τ2)p	τ2)p	ADJ
ejpam-6571	81	25	-	-	NOUN
ejpam-6571	81	26	interior	interior	ADJ
ejpam-6571	81	27	[	[	X
ejpam-6571	81	28	25	25	NUM
ejpam-6571	81	29	]	]	PUNCT
ejpam-6571	81	30	(	(	PUNCT
ejpam-6571	81	31	resp	resp	NOUN
ejpam-6571	81	32	.	.	PUNCT
ejpam-6571	82	1	(	(	PUNCT
ejpam-6571	82	2	τ1	τ1	NOUN
ejpam-6571	82	3	,	,	PUNCT
ejpam-6571	82	4	τ2)s	τ2)s	NOUN
ejpam-6571	82	5	-	-	NOUN
ejpam-6571	82	6	interior	interior	NOUN
ejpam-6571	82	7	[	[	X
ejpam-6571	82	8	23	23	NUM
ejpam-6571	82	9	]	]	PUNCT
ejpam-6571	82	10	,	,	PUNCT
ejpam-6571	82	11	α(τ1	α(τ1	NOUN
ejpam-6571	82	12	,	,	PUNCT
ejpam-6571	82	13	τ2)-interior	τ2)-interior	PROPN
ejpam-6571	82	14	[	[	X
ejpam-6571	82	15	26	26	NUM
ejpam-6571	82	16	]	]	PUNCT
ejpam-6571	82	17	)	)	PUNCT
ejpam-6571	82	18	of	of	ADP
ejpam-6571	82	19	a	a	PRON
ejpam-6571	82	20	and	and	CCONJ
ejpam-6571	82	21	is	be	AUX
ejpam-6571	82	22	denoted	denote	VERB
ejpam-6571	82	23	by	by	ADP
ejpam-6571	82	24	(	(	PUNCT
ejpam-6571	82	25	τ1	τ1	NOUN
ejpam-6571	82	26	,	,	PUNCT
ejpam-6571	82	27	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6571	82	28	)	)	PUNCT
ejpam-6571	82	29	(	(	PUNCT
ejpam-6571	82	30	resp	resp	NOUN
ejpam-6571	82	31	.	.	PUNCT
ejpam-6571	83	1	(	(	PUNCT
ejpam-6571	83	2	τ1	τ1	NOUN
ejpam-6571	83	3	,	,	PUNCT
ejpam-6571	83	4	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6571	83	5	)	)	PUNCT
ejpam-6571	83	6	,	,	PUNCT
ejpam-6571	83	7	α(τ1	α(τ1	NOUN
ejpam-6571	83	8	,	,	PUNCT
ejpam-6571	83	9	τ2)-int(a	τ2)-int(a	NOUN
ejpam-6571	83	10	)	)	PUNCT
ejpam-6571	83	11	)	)	PUNCT
ejpam-6571	83	12	.	.	PUNCT
ejpam-6571	84	1	for	for	ADP
ejpam-6571	84	2	a	a	DET
ejpam-6571	84	3	subset	subset	NOUN
ejpam-6571	84	4	a	a	PRON
ejpam-6571	84	5	of	of	ADP
ejpam-6571	84	6	a	a	DET
ejpam-6571	84	7	bitopological	bitopological	ADJ
ejpam-6571	84	8	space	space	NOUN
ejpam-6571	84	9	(	(	PUNCT
ejpam-6571	84	10	x	x	NOUN
ejpam-6571	84	11	,	,	PUNCT
ejpam-6571	84	12	τ1	τ1	NOUN
ejpam-6571	84	13	,	,	PUNCT
ejpam-6571	84	14	τ2	τ2	PROPN
ejpam-6571	84	15	)	)	PUNCT
ejpam-6571	84	16	,	,	PUNCT
ejpam-6571	84	17	a	a	DET
ejpam-6571	84	18	point	point	NOUN
ejpam-6571	84	19	x	x	X
ejpam-6571	84	20	∈	∈	NOUN
ejpam-6571	84	21	x	x	PUNCT
ejpam-6571	84	22	is	be	AUX
ejpam-6571	84	23	called	call	VERB
ejpam-6571	84	24	a	a	DET
ejpam-6571	84	25	(	(	PUNCT
ejpam-6571	84	26	τ1	τ1	NOUN
ejpam-6571	84	27	,	,	PUNCT
ejpam-6571	84	28	τ2)θ	τ2)θ	ADJ
ejpam-6571	84	29	-	-	PUNCT
ejpam-6571	84	30	cluster	cluster	NOUN
ejpam-6571	84	31	point	point	NOUN
ejpam-6571	84	32	[	[	X
ejpam-6571	84	33	22	22	NUM
ejpam-6571	84	34	]	]	PUNCT
ejpam-6571	84	35	of	of	ADP
ejpam-6571	84	36	a	a	DET
ejpam-6571	84	37	if	if	SCONJ
ejpam-6571	84	38	τ1τ2	τ1τ2	NOUN
ejpam-6571	84	39	-	-	NOUN
ejpam-6571	84	40	cl(u	cl(u	NOUN
ejpam-6571	84	41	)	)	PUNCT
ejpam-6571	84	42	∩	∩	NOUN
ejpam-6571	84	43	a	a	DET
ejpam-6571	84	44	̸=	̸=	PROPN
ejpam-6571	84	45	∅	∅	NOUN
ejpam-6571	84	46	for	for	ADP
ejpam-6571	84	47	every	every	DET
ejpam-6571	84	48	τ1τ2	τ1τ2	ADJ
ejpam-6571	84	49	-	-	ADJ
ejpam-6571	84	50	open	open	ADJ
ejpam-6571	84	51	set	set	NOUN
ejpam-6571	84	52	u	u	NOUN
ejpam-6571	84	53	containing	contain	VERB
ejpam-6571	84	54	x.	x.	NOUN
ejpam-6571	84	55	the	the	DET
ejpam-6571	84	56	set	set	NOUN
ejpam-6571	84	57	of	of	ADP
ejpam-6571	84	58	all	all	DET
ejpam-6571	84	59	(	(	PUNCT
ejpam-6571	84	60	τ1	τ1	NOUN
ejpam-6571	84	61	,	,	PUNCT
ejpam-6571	84	62	τ2)θ	τ2)θ	ADJ
ejpam-6571	84	63	-	-	PUNCT
ejpam-6571	84	64	cluster	cluster	NOUN
ejpam-6571	84	65	points	point	NOUN
ejpam-6571	84	66	of	of	ADP
ejpam-6571	84	67	a	a	PRON
ejpam-6571	84	68	is	be	AUX
ejpam-6571	84	69	called	call	VERB
ejpam-6571	84	70	the	the	DET
ejpam-6571	84	71	(	(	PUNCT
ejpam-6571	84	72	τ1	τ1	NOUN
ejpam-6571	84	73	,	,	PUNCT
ejpam-6571	84	74	τ2)θ	τ2)θ	ADJ
ejpam-6571	84	75	-	-	PUNCT
ejpam-6571	84	76	closure	closure	NOUN
ejpam-6571	84	77	[	[	X
ejpam-6571	84	78	22	22	NUM
ejpam-6571	84	79	]	]	PUNCT
ejpam-6571	84	80	of	of	ADP
ejpam-6571	84	81	a	a	PRON
ejpam-6571	84	82	and	and	CCONJ
ejpam-6571	84	83	is	be	AUX
ejpam-6571	84	84	denoted	denote	VERB
ejpam-6571	84	85	by	by	ADP
ejpam-6571	84	86	(	(	PUNCT
ejpam-6571	84	87	τ1	τ1	NOUN
ejpam-6571	84	88	,	,	PUNCT
ejpam-6571	84	89	τ2)θ	τ2)θ	NOUN
ejpam-6571	84	90	-	-	PUNCT
ejpam-6571	84	91	cl(a	cl(a	NUM
ejpam-6571	84	92	)	)	PUNCT
ejpam-6571	84	93	.	.	PUNCT
ejpam-6571	85	1	a	a	DET
ejpam-6571	85	2	subset	subset	NOUN
ejpam-6571	85	3	a	a	PRON
ejpam-6571	85	4	of	of	ADP
ejpam-6571	85	5	a	a	DET
ejpam-6571	85	6	bitopological	bitopological	ADJ
ejpam-6571	85	7	space	space	NOUN
ejpam-6571	85	8	(	(	PUNCT
ejpam-6571	85	9	x	x	NOUN
ejpam-6571	85	10	,	,	PUNCT
ejpam-6571	85	11	τ1	τ1	NOUN
ejpam-6571	85	12	,	,	PUNCT
ejpam-6571	85	13	τ2	τ2	NOUN
ejpam-6571	85	14	)	)	PUNCT
ejpam-6571	85	15	is	be	AUX
ejpam-6571	85	16	said	say	VERB
ejpam-6571	85	17	to	to	PART
ejpam-6571	85	18	be	be	AUX
ejpam-6571	85	19	(	(	PUNCT
ejpam-6571	85	20	τ1	τ1	NOUN
ejpam-6571	85	21	,	,	PUNCT
ejpam-6571	85	22	τ2)θ	τ2)θ	NOUN
ejpam-6571	85	23	-	-	PUNCT
ejpam-6571	85	24	closed	closed	ADJ
ejpam-6571	85	25	[	[	X
ejpam-6571	85	26	22	22	NUM
ejpam-6571	85	27	]	]	X
ejpam-6571	85	28	if	if	SCONJ
ejpam-6571	85	29	(	(	PUNCT
ejpam-6571	85	30	τ1	τ1	NOUN
ejpam-6571	85	31	,	,	PUNCT
ejpam-6571	85	32	τ2)θ	τ2)θ	NOUN
ejpam-6571	85	33	-	-	PUNCT
ejpam-6571	85	34	cl(a	cl(a	NUM
ejpam-6571	85	35	)	)	PUNCT
ejpam-6571	86	1	=	=	PUNCT
ejpam-6571	86	2	a.	a.	NOUN
ejpam-6571	86	3	the	the	DET
ejpam-6571	86	4	complement	complement	NOUN
ejpam-6571	86	5	of	of	ADP
ejpam-6571	86	6	a	a	DET
ejpam-6571	86	7	(	(	PUNCT
ejpam-6571	86	8	τ1	τ1	NOUN
ejpam-6571	86	9	,	,	PUNCT
ejpam-6571	86	10	τ2)θ	τ2)θ	ADJ
ejpam-6571	86	11	-	-	PUNCT
ejpam-6571	86	12	closed	close	VERB
ejpam-6571	86	13	set	set	NOUN
ejpam-6571	86	14	is	be	AUX
ejpam-6571	86	15	said	say	VERB
ejpam-6571	86	16	to	to	PART
ejpam-6571	86	17	be	be	AUX
ejpam-6571	86	18	(	(	PUNCT
ejpam-6571	86	19	τ1	τ1	NOUN
ejpam-6571	86	20	,	,	PUNCT
ejpam-6571	86	21	τ2)θopen	τ2)θopen	PROPN
ejpam-6571	86	22	.	.	PUNCT
ejpam-6571	87	1	the	the	DET
ejpam-6571	87	2	union	union	NOUN
ejpam-6571	87	3	of	of	ADP
ejpam-6571	87	4	all	all	DET
ejpam-6571	87	5	(	(	PUNCT
ejpam-6571	87	6	τ1	τ1	NOUN
ejpam-6571	87	7	,	,	PUNCT
ejpam-6571	87	8	τ2)θ	τ2)θ	ADJ
ejpam-6571	87	9	-	-	PUNCT
ejpam-6571	87	10	open	open	ADJ
ejpam-6571	87	11	sets	set	NOUN
ejpam-6571	87	12	of	of	ADP
ejpam-6571	87	13	x	x	PUNCT
ejpam-6571	87	14	contained	contain	VERB
ejpam-6571	87	15	in	in	ADP
ejpam-6571	87	16	a	a	PRON
ejpam-6571	87	17	is	be	AUX
ejpam-6571	87	18	called	call	VERB
ejpam-6571	87	19	the	the	DET
ejpam-6571	87	20	(	(	PUNCT
ejpam-6571	87	21	τ1	τ1	NOUN
ejpam-6571	87	22	,	,	PUNCT
ejpam-6571	87	23	τ2)θ	τ2)θ	ADJ
ejpam-6571	87	24	-	-	PUNCT
ejpam-6571	87	25	interior	interior	NOUN
ejpam-6571	87	26	[	[	X
ejpam-6571	87	27	22	22	NUM
ejpam-6571	87	28	]	]	PUNCT
ejpam-6571	87	29	of	of	ADP
ejpam-6571	87	30	a	a	PRON
ejpam-6571	87	31	and	and	CCONJ
ejpam-6571	87	32	is	be	AUX
ejpam-6571	87	33	denoted	denote	VERB
ejpam-6571	87	34	by	by	ADP
ejpam-6571	87	35	(	(	PUNCT
ejpam-6571	87	36	τ1	τ1	NOUN
ejpam-6571	87	37	,	,	PUNCT
ejpam-6571	87	38	τ2)θ	τ2)θ	NOUN
ejpam-6571	87	39	-	-	PUNCT
ejpam-6571	87	40	int(a	int(a	NOUN
ejpam-6571	87	41	)	)	PUNCT
ejpam-6571	87	42	.	.	PUNCT
ejpam-6571	88	1	lemma	lemma	PROPN
ejpam-6571	88	2	2	2	NUM
ejpam-6571	88	3	.	.	PUNCT
ejpam-6571	89	1	[	[	X
ejpam-6571	89	2	27	27	NUM
ejpam-6571	89	3	]	]	PUNCT
ejpam-6571	89	4	for	for	ADP
ejpam-6571	89	5	a	a	DET
ejpam-6571	89	6	subset	subset	NOUN
ejpam-6571	89	7	a	a	PRON
ejpam-6571	89	8	of	of	ADP
ejpam-6571	89	9	a	a	DET
ejpam-6571	89	10	bitopological	bitopological	ADJ
ejpam-6571	89	11	space	space	NOUN
ejpam-6571	89	12	(	(	PUNCT
ejpam-6571	89	13	x	x	NOUN
ejpam-6571	89	14	,	,	PUNCT
ejpam-6571	89	15	τ1	τ1	NOUN
ejpam-6571	89	16	,	,	PUNCT
ejpam-6571	89	17	τ2	τ2	NOUN
ejpam-6571	89	18	)	)	PUNCT
ejpam-6571	89	19	,	,	PUNCT
ejpam-6571	89	20	the	the	DET
ejpam-6571	89	21	following	follow	VERB
ejpam-6571	89	22	properties	property	NOUN
ejpam-6571	89	23	hold	hold	VERB
ejpam-6571	89	24	:	:	PUNCT
ejpam-6571	89	25	(	(	PUNCT
ejpam-6571	89	26	1	1	X
ejpam-6571	89	27	)	)	PUNCT
ejpam-6571	89	28	(	(	PUNCT
ejpam-6571	89	29	τ1	τ1	NOUN
ejpam-6571	89	30	,	,	PUNCT
ejpam-6571	89	31	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6571	89	32	)	)	PUNCT
ejpam-6571	89	33	=	=	PUNCT
ejpam-6571	90	1	τ1τ2	τ1τ2	NOUN
ejpam-6571	90	2	-	-	NOUN
ejpam-6571	90	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6571	90	4	-	-	PUNCT
ejpam-6571	90	5	cl(a	cl(a	NUM
ejpam-6571	90	6	)	)	PUNCT
ejpam-6571	90	7	)	)	PUNCT
ejpam-6571	90	8	∪a	∪a	X
ejpam-6571	91	1	[	[	X
ejpam-6571	91	2	28	28	NUM
ejpam-6571	91	3	]	]	X
ejpam-6571	91	4	;	;	PUNCT
ejpam-6571	91	5	(	(	PUNCT
ejpam-6571	91	6	2	2	X
ejpam-6571	91	7	)	)	PUNCT
ejpam-6571	91	8	(	(	PUNCT
ejpam-6571	91	9	τ1	τ1	NOUN
ejpam-6571	91	10	,	,	PUNCT
ejpam-6571	91	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6571	91	12	)	)	PUNCT
ejpam-6571	92	1	=	=	PUNCT
ejpam-6571	92	2	τ1τ2	τ1τ2	NOUN
ejpam-6571	92	3	-	-	ADJ
ejpam-6571	92	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6571	92	5	-	-	PUNCT
ejpam-6571	92	6	int(a	int(a	NOUN
ejpam-6571	92	7	)	)	PUNCT
ejpam-6571	92	8	)	)	PUNCT
ejpam-6571	93	1	∩a	∩a	PROPN
ejpam-6571	93	2	.	.	PUNCT
ejpam-6571	94	1	an	an	DET
ejpam-6571	94	2	ideal	ideal	NOUN
ejpam-6571	94	3	i	i	PRON
ejpam-6571	94	4	on	on	ADP
ejpam-6571	94	5	a	a	DET
ejpam-6571	94	6	topological	topological	ADJ
ejpam-6571	94	7	space	space	NOUN
ejpam-6571	94	8	(	(	PUNCT
ejpam-6571	94	9	x	x	X
ejpam-6571	94	10	,	,	PUNCT
ejpam-6571	94	11	τ	τ	X
ejpam-6571	94	12	)	)	PUNCT
ejpam-6571	94	13	is	be	AUX
ejpam-6571	94	14	a	a	DET
ejpam-6571	94	15	nonempty	nonempty	ADJ
ejpam-6571	94	16	collection	collection	NOUN
ejpam-6571	94	17	of	of	ADP
ejpam-6571	94	18	subsets	subset	NOUN
ejpam-6571	94	19	of	of	ADP
ejpam-6571	94	20	x	x	PUNCT
ejpam-6571	94	21	satisfying	satisfy	VERB
ejpam-6571	94	22	the	the	DET
ejpam-6571	94	23	following	follow	VERB
ejpam-6571	94	24	properties	property	NOUN
ejpam-6571	94	25	:	:	PUNCT
ejpam-6571	94	26	(	(	PUNCT
ejpam-6571	94	27	1	1	X
ejpam-6571	94	28	)	)	PUNCT
ejpam-6571	94	29	a	a	DET
ejpam-6571	94	30	∈	∈	NOUN
ejpam-6571	94	31	i	i	PRON
ejpam-6571	94	32	and	and	CCONJ
ejpam-6571	94	33	b	b	X
ejpam-6571	94	34	⊆	⊆	NUM
ejpam-6571	94	35	a	a	DET
ejpam-6571	94	36	imply	imply	NOUN
ejpam-6571	94	37	b	b	X
ejpam-6571	94	38	∈	∈	PROPN
ejpam-6571	94	39	i	i	PRON
ejpam-6571	94	40	;	;	PUNCT
ejpam-6571	94	41	(	(	PUNCT
ejpam-6571	94	42	2	2	X
ejpam-6571	94	43	)	)	PUNCT
ejpam-6571	95	1	a	a	PRON
ejpam-6571	95	2	∈	∈	NOUN
ejpam-6571	96	1	i	i	PRON
ejpam-6571	96	2	and	and	CCONJ
ejpam-6571	96	3	b	b	X
ejpam-6571	96	4	∈	∈	NOUN
ejpam-6571	97	1	i	i	PRON
ejpam-6571	97	2	imply	imply	VERB
ejpam-6571	97	3	a	a	DET
ejpam-6571	97	4	∪	∪	X
ejpam-6571	97	5	b	b	NOUN
ejpam-6571	97	6	∈	∈	NOUN
ejpam-6571	98	1	i	i	PRON
ejpam-6571	98	2	.	.	PUNCT
ejpam-6571	99	1	a	a	DET
ejpam-6571	99	2	topological	topological	ADJ
ejpam-6571	99	3	space	space	NOUN
ejpam-6571	99	4	(	(	PUNCT
ejpam-6571	99	5	x	x	X
ejpam-6571	99	6	,	,	PUNCT
ejpam-6571	99	7	τ	τ	X
ejpam-6571	99	8	)	)	PUNCT
ejpam-6571	99	9	with	with	ADP
ejpam-6571	99	10	an	an	DET
ejpam-6571	99	11	ideal	ideal	ADJ
ejpam-6571	99	12	i	i	PRON
ejpam-6571	99	13	on	on	ADP
ejpam-6571	99	14	x	x	SYM
ejpam-6571	99	15	is	be	AUX
ejpam-6571	99	16	called	call	VERB
ejpam-6571	99	17	an	an	DET
ejpam-6571	99	18	ideal	ideal	ADJ
ejpam-6571	99	19	topological	topological	ADJ
ejpam-6571	99	20	space	space	NOUN
ejpam-6571	99	21	and	and	CCONJ
ejpam-6571	99	22	is	be	AUX
ejpam-6571	99	23	denoted	denote	VERB
ejpam-6571	99	24	by	by	ADP
ejpam-6571	99	25	(	(	PUNCT
ejpam-6571	99	26	x	x	X
ejpam-6571	99	27	,	,	PUNCT
ejpam-6571	99	28	τ	τ	PROPN
ejpam-6571	99	29	,	,	PUNCT
ejpam-6571	99	30	i	i	NOUN
ejpam-6571	99	31	)	)	PUNCT
ejpam-6571	99	32	.	.	PUNCT
ejpam-6571	100	1	for	for	ADP
ejpam-6571	100	2	an	an	DET
ejpam-6571	100	3	ideal	ideal	ADJ
ejpam-6571	100	4	topological	topological	ADJ
ejpam-6571	100	5	space	space	NOUN
ejpam-6571	100	6	(	(	PUNCT
ejpam-6571	100	7	x	x	X
ejpam-6571	100	8	,	,	PUNCT
ejpam-6571	100	9	τ	τ	PROPN
ejpam-6571	100	10	,	,	PUNCT
ejpam-6571	100	11	i	i	PROPN
ejpam-6571	100	12	)	)	PUNCT
ejpam-6571	100	13	and	and	CCONJ
ejpam-6571	100	14	a	a	DET
ejpam-6571	100	15	subset	subset	NOUN
ejpam-6571	100	16	a	a	PRON
ejpam-6571	100	17	of	of	ADP
ejpam-6571	100	18	x	x	PRON
ejpam-6571	100	19	,	,	PUNCT
ejpam-6571	100	20	a⋆(i	a⋆(i	PROPN
ejpam-6571	100	21	)	)	PUNCT
ejpam-6571	100	22	is	be	AUX
ejpam-6571	100	23	defined	define	VERB
ejpam-6571	100	24	as	as	SCONJ
ejpam-6571	100	25	follows	follow	VERB
ejpam-6571	100	26	:	:	PUNCT
ejpam-6571	100	27	a⋆(i	a⋆(i	NOUN
ejpam-6571	100	28	)	)	PUNCT
ejpam-6571	101	1	=	=	PUNCT
ejpam-6571	101	2	{	{	PUNCT
ejpam-6571	101	3	x	x	PUNCT
ejpam-6571	101	4	∈	∈	PROPN
ejpam-6571	101	5	x	x	X
ejpam-6571	101	6	:	:	PUNCT
ejpam-6571	101	7	u	u	X
ejpam-6571	101	8	∩a	∩a	PROPN
ejpam-6571	101	9	̸∈	̸∈	PROPN
ejpam-6571	101	10	i	i	PRON
ejpam-6571	101	11	for	for	ADP
ejpam-6571	101	12	every	every	DET
ejpam-6571	101	13	open	open	ADJ
ejpam-6571	101	14	neighbourhood	neighbourhood	NOUN
ejpam-6571	101	15	u	u	NOUN
ejpam-6571	101	16	of	of	ADP
ejpam-6571	101	17	x	x	NOUN
ejpam-6571	101	18	}	}	PUNCT
ejpam-6571	101	19	.	.	PUNCT
ejpam-6571	102	1	m.	m.	NOUN
ejpam-6571	102	2	thongmoon	thongmoon	PROPN
ejpam-6571	102	3	,	,	PUNCT
ejpam-6571	102	4	a.	a.	PROPN
ejpam-6571	102	5	sama	sama	PROPN
ejpam-6571	102	6	-	-	PUNCT
ejpam-6571	102	7	ae	ae	PROPN
ejpam-6571	102	8	,	,	PUNCT
ejpam-6571	102	9	c.	c.	PROPN
ejpam-6571	102	10	boonpok	boonpok	PROPN
ejpam-6571	102	11	/	/	SYM
ejpam-6571	102	12	eur	eur	PROPN
ejpam-6571	102	13	.	.	PUNCT
ejpam-6571	103	1	j.	j.	PROPN
ejpam-6571	103	2	pure	pure	PROPN
ejpam-6571	103	3	appl	appl	PROPN
ejpam-6571	103	4	.	.	PROPN
ejpam-6571	103	5	math	math	PROPN
ejpam-6571	103	6	,	,	PUNCT
ejpam-6571	103	7	18	18	NUM
ejpam-6571	103	8	(	(	PUNCT
ejpam-6571	103	9	3	3	NUM
ejpam-6571	103	10	)	)	PUNCT
ejpam-6571	103	11	(	(	PUNCT
ejpam-6571	103	12	2025	2025	NUM
ejpam-6571	103	13	)	)	PUNCT
ejpam-6571	103	14	,	,	PUNCT
ejpam-6571	103	15	6571	6571	NUM
ejpam-6571	103	16	4	4	NUM
ejpam-6571	103	17	of	of	ADP
ejpam-6571	103	18	15	15	NUM
ejpam-6571	103	19	in	in	ADP
ejpam-6571	103	20	case	case	NOUN
ejpam-6571	103	21	there	there	PRON
ejpam-6571	103	22	is	be	VERB
ejpam-6571	103	23	no	no	DET
ejpam-6571	103	24	chance	chance	NOUN
ejpam-6571	103	25	for	for	ADP
ejpam-6571	103	26	confusion	confusion	NOUN
ejpam-6571	103	27	,	,	PUNCT
ejpam-6571	103	28	a⋆(i	a⋆(i	NOUN
ejpam-6571	103	29	)	)	PUNCT
ejpam-6571	103	30	is	be	AUX
ejpam-6571	103	31	simply	simply	ADV
ejpam-6571	103	32	written	write	VERB
ejpam-6571	103	33	as	as	ADP
ejpam-6571	103	34	a⋆.	a⋆.	NOUN
ejpam-6571	103	35	in	in	ADP
ejpam-6571	103	36	[	[	X
ejpam-6571	103	37	29	29	NUM
ejpam-6571	103	38	]	]	PUNCT
ejpam-6571	103	39	,	,	PUNCT
ejpam-6571	103	40	a⋆	a⋆	ADV
ejpam-6571	103	41	is	be	AUX
ejpam-6571	103	42	called	call	VERB
ejpam-6571	103	43	the	the	DET
ejpam-6571	103	44	local	local	ADJ
ejpam-6571	103	45	function	function	NOUN
ejpam-6571	103	46	of	of	ADP
ejpam-6571	103	47	a	a	PRON
ejpam-6571	103	48	with	with	ADP
ejpam-6571	103	49	respect	respect	NOUN
ejpam-6571	103	50	to	to	ADP
ejpam-6571	103	51	i	i	PRON
ejpam-6571	103	52	and	and	CCONJ
ejpam-6571	103	53	τ	τ	PROPN
ejpam-6571	103	54	and	and	CCONJ
ejpam-6571	103	55	cl⋆(a	cl⋆(a	PROPN
ejpam-6571	103	56	)	)	PUNCT
ejpam-6571	103	57	=	=	NOUN
ejpam-6571	103	58	a⋆∪a	a⋆∪a	NOUN
ejpam-6571	103	59	defines	define	VERB
ejpam-6571	103	60	a	a	DET
ejpam-6571	103	61	kuratowski	kuratowski	ADJ
ejpam-6571	103	62	closure	closure	NOUN
ejpam-6571	103	63	operator	operator	NOUN
ejpam-6571	103	64	for	for	ADP
ejpam-6571	103	65	a	a	DET
ejpam-6571	103	66	topology	topology	NOUN
ejpam-6571	103	67	τ⋆(i	τ⋆(i	NOUN
ejpam-6571	103	68	)	)	PUNCT
ejpam-6571	103	69	finer	fine	ADJ
ejpam-6571	103	70	than	than	ADP
ejpam-6571	103	71	τ	τ	PROPN
ejpam-6571	103	72	.	.	PUNCT
ejpam-6571	104	1	a	a	DET
ejpam-6571	104	2	subset	subset	NOUN
ejpam-6571	104	3	a	a	PRON
ejpam-6571	104	4	is	be	AUX
ejpam-6571	104	5	said	say	VERB
ejpam-6571	104	6	to	to	PART
ejpam-6571	104	7	be	be	AUX
ejpam-6571	104	8	⋆-closed	⋆-close	VERB
ejpam-6571	104	9	[	[	X
ejpam-6571	104	10	10	10	NUM
ejpam-6571	104	11	]	]	X
ejpam-6571	104	12	if	if	SCONJ
ejpam-6571	104	13	a⋆	a⋆	ADJ
ejpam-6571	104	14	⊆	⊆	NUM
ejpam-6571	104	15	a.	a.	NOUN
ejpam-6571	104	16	the	the	DET
ejpam-6571	104	17	interior	interior	NOUN
ejpam-6571	104	18	of	of	ADP
ejpam-6571	104	19	a	a	DET
ejpam-6571	104	20	subset	subset	NOUN
ejpam-6571	104	21	a	a	DET
ejpam-6571	104	22	in	in	ADP
ejpam-6571	104	23	(	(	PUNCT
ejpam-6571	104	24	x	x	X
ejpam-6571	104	25	,	,	PUNCT
ejpam-6571	104	26	τ⋆(i	τ⋆(i	NOUN
ejpam-6571	104	27	)	)	PUNCT
ejpam-6571	104	28	)	)	PUNCT
ejpam-6571	104	29	is	be	AUX
ejpam-6571	104	30	denoted	denote	VERB
ejpam-6571	104	31	by	by	ADP
ejpam-6571	104	32	int⋆(a	int⋆(a	NOUN
ejpam-6571	104	33	)	)	PUNCT
ejpam-6571	104	34	.	.	PUNCT
ejpam-6571	105	1	a	a	DET
ejpam-6571	105	2	subset	subset	NOUN
ejpam-6571	105	3	a	a	PRON
ejpam-6571	105	4	of	of	ADP
ejpam-6571	105	5	an	an	DET
ejpam-6571	105	6	ideal	ideal	ADJ
ejpam-6571	105	7	topological	topological	ADJ
ejpam-6571	105	8	space	space	NOUN
ejpam-6571	105	9	(	(	PUNCT
ejpam-6571	105	10	x	x	X
ejpam-6571	105	11	,	,	PUNCT
ejpam-6571	105	12	τ	τ	PROPN
ejpam-6571	105	13	,	,	PUNCT
ejpam-6571	105	14	i	i	PROPN
ejpam-6571	105	15	)	)	PUNCT
ejpam-6571	105	16	is	be	AUX
ejpam-6571	105	17	said	say	VERB
ejpam-6571	105	18	to	to	PART
ejpam-6571	105	19	be	be	AUX
ejpam-6571	105	20	semi⋆-i	semi⋆-i	PUNCT
ejpam-6571	105	21	-open	-open	VERB
ejpam-6571	105	22	[	[	PUNCT
ejpam-6571	105	23	30	30	NUM
ejpam-6571	105	24	]	]	PUNCT
ejpam-6571	105	25	(	(	PUNCT
ejpam-6571	105	26	resp	resp	NOUN
ejpam-6571	105	27	.	.	PUNCT
ejpam-6571	106	1	semi	semi	ADJ
ejpam-6571	106	2	-	-	VERB
ejpam-6571	106	3	i	i	PRON
ejpam-6571	106	4	-open	-open	NOUN
ejpam-6571	107	1	[	[	X
ejpam-6571	107	2	13	13	NUM
ejpam-6571	107	3	]	]	SYM
ejpam-6571	107	4	)	)	PUNCT
ejpam-6571	107	5	if	if	SCONJ
ejpam-6571	107	6	a	a	DET
ejpam-6571	107	7	⊆	⊆	NUM
ejpam-6571	107	8	cl(int⋆(a	cl(int⋆(a	NUM
ejpam-6571	107	9	)	)	PUNCT
ejpam-6571	107	10	)	)	PUNCT
ejpam-6571	107	11	(	(	PUNCT
ejpam-6571	107	12	resp	resp	NOUN
ejpam-6571	107	13	.	.	PUNCT
ejpam-6571	108	1	a	a	DET
ejpam-6571	108	2	⊆	⊆	NUM
ejpam-6571	108	3	cl⋆(int(a	cl⋆(int(a	PROPN
ejpam-6571	108	4	)	)	PUNCT
ejpam-6571	108	5	)	)	PUNCT
ejpam-6571	108	6	)	)	PUNCT
ejpam-6571	108	7	.	.	PUNCT
ejpam-6571	109	1	the	the	DET
ejpam-6571	109	2	complement	complement	NOUN
ejpam-6571	109	3	of	of	ADP
ejpam-6571	109	4	a	a	DET
ejpam-6571	109	5	semi⋆-i	semi⋆-i	PUNCT
ejpam-6571	109	6	-open	-open	ADJ
ejpam-6571	109	7	(	(	PUNCT
ejpam-6571	109	8	resp	resp	NOUN
ejpam-6571	109	9	.	.	PUNCT
ejpam-6571	110	1	semi	semi	ADJ
ejpam-6571	110	2	-	-	VERB
ejpam-6571	110	3	i	i	PRON
ejpam-6571	110	4	-open	-open	NOUN
ejpam-6571	110	5	)	)	PUNCT
ejpam-6571	111	1	set	set	NOUN
ejpam-6571	111	2	is	be	AUX
ejpam-6571	111	3	said	say	VERB
ejpam-6571	111	4	to	to	PART
ejpam-6571	111	5	be	be	AUX
ejpam-6571	111	6	semi⋆-i	semi⋆-i	PUNCT
ejpam-6571	111	7	-closed	-close	VERB
ejpam-6571	111	8	[	[	PUNCT
ejpam-6571	111	9	30	30	NUM
ejpam-6571	111	10	]	]	PUNCT
ejpam-6571	111	11	(	(	PUNCT
ejpam-6571	111	12	resp	resp	NOUN
ejpam-6571	111	13	.	.	PUNCT
ejpam-6571	112	1	semi	semi	ADJ
ejpam-6571	112	2	-	-	VERB
ejpam-6571	112	3	i	i	PRON
ejpam-6571	112	4	-closed	-close	VERB
ejpam-6571	113	1	[	[	PUNCT
ejpam-6571	113	2	13	13	NUM
ejpam-6571	113	3	]	]	NUM
ejpam-6571	113	4	)	)	PUNCT
ejpam-6571	113	5	.	.	PUNCT
ejpam-6571	114	1	a	a	DET
ejpam-6571	114	2	subset	subset	NOUN
ejpam-6571	114	3	a	a	PRON
ejpam-6571	114	4	of	of	ADP
ejpam-6571	114	5	an	an	DET
ejpam-6571	114	6	ideal	ideal	ADJ
ejpam-6571	114	7	topological	topological	ADJ
ejpam-6571	114	8	space	space	NOUN
ejpam-6571	114	9	(	(	PUNCT
ejpam-6571	114	10	x	x	X
ejpam-6571	114	11	,	,	PUNCT
ejpam-6571	114	12	τ	τ	PROPN
ejpam-6571	114	13	,	,	PUNCT
ejpam-6571	114	14	i	i	PROPN
ejpam-6571	114	15	)	)	PUNCT
ejpam-6571	114	16	is	be	AUX
ejpam-6571	114	17	said	say	VERB
ejpam-6571	114	18	to	to	PART
ejpam-6571	114	19	be	be	AUX
ejpam-6571	114	20	semi	semi	ADJ
ejpam-6571	114	21	-	-	ADJ
ejpam-6571	114	22	i	i	PRON
ejpam-6571	114	23	⋆-open	⋆-open	VERB
ejpam-6571	115	1	[	[	X
ejpam-6571	115	2	14	14	NUM
ejpam-6571	115	3	]	]	X
ejpam-6571	115	4	if	if	SCONJ
ejpam-6571	115	5	a	a	DET
ejpam-6571	115	6	⊆	⊆	NUM
ejpam-6571	115	7	cl⋆(int⋆(a	cl⋆(int⋆(a	NOUN
ejpam-6571	115	8	)	)	PUNCT
ejpam-6571	115	9	)	)	PUNCT
ejpam-6571	115	10	.	.	PUNCT
ejpam-6571	116	1	the	the	DET
ejpam-6571	116	2	complement	complement	NOUN
ejpam-6571	116	3	of	of	ADP
ejpam-6571	116	4	a	a	DET
ejpam-6571	116	5	semi	semi	NOUN
ejpam-6571	116	6	-	-	ADJ
ejpam-6571	116	7	i	i	PRON
ejpam-6571	116	8	⋆-open	⋆-open	ADJ
ejpam-6571	116	9	set	set	VERB
ejpam-6571	116	10	is	be	AUX
ejpam-6571	116	11	called	call	VERB
ejpam-6571	116	12	semi	semi	ADJ
ejpam-6571	116	13	-	-	ADJ
ejpam-6571	116	14	i	i	PRON
ejpam-6571	116	15	⋆-closed	⋆-close	VERB
ejpam-6571	116	16	[	[	X
ejpam-6571	116	17	14	14	NUM
ejpam-6571	116	18	]	]	PUNCT
ejpam-6571	116	19	.	.	PUNCT
ejpam-6571	117	1	for	for	ADP
ejpam-6571	117	2	a	a	DET
ejpam-6571	117	3	subset	subset	NOUN
ejpam-6571	117	4	a	a	PRON
ejpam-6571	117	5	of	of	ADP
ejpam-6571	117	6	an	an	DET
ejpam-6571	117	7	ideal	ideal	ADJ
ejpam-6571	117	8	topological	topological	ADJ
ejpam-6571	117	9	space	space	NOUN
ejpam-6571	117	10	(	(	PUNCT
ejpam-6571	117	11	x	x	X
ejpam-6571	117	12	,	,	PUNCT
ejpam-6571	117	13	τ	τ	PROPN
ejpam-6571	117	14	,	,	PUNCT
ejpam-6571	117	15	i	i	NOUN
ejpam-6571	117	16	)	)	PUNCT
ejpam-6571	117	17	,	,	PUNCT
ejpam-6571	117	18	the	the	DET
ejpam-6571	117	19	intersection	intersection	NOUN
ejpam-6571	117	20	of	of	ADP
ejpam-6571	117	21	all	all	DET
ejpam-6571	117	22	semi	semi	ADJ
ejpam-6571	117	23	-	-	ADJ
ejpam-6571	117	24	i	i	PRON
ejpam-6571	117	25	-closed	-closed	ADJ
ejpam-6571	117	26	sets	set	NOUN
ejpam-6571	117	27	containing	contain	VERB
ejpam-6571	117	28	a	a	PRON
ejpam-6571	117	29	is	be	AUX
ejpam-6571	117	30	called	call	VERB
ejpam-6571	117	31	the	the	DET
ejpam-6571	117	32	semi	semi	NOUN
ejpam-6571	117	33	-	-	ADJ
ejpam-6571	117	34	i	i	PRON
ejpam-6571	117	35	⋆-closure	⋆-closure	NOUN
ejpam-6571	118	1	[	[	X
ejpam-6571	118	2	14	14	NUM
ejpam-6571	118	3	]	]	PUNCT
ejpam-6571	118	4	of	of	ADP
ejpam-6571	118	5	a	a	PRON
ejpam-6571	118	6	and	and	CCONJ
ejpam-6571	118	7	is	be	AUX
ejpam-6571	118	8	denoted	denote	VERB
ejpam-6571	118	9	by	by	ADP
ejpam-6571	118	10	scl⋆(a	scl⋆(a	NOUN
ejpam-6571	118	11	)	)	PUNCT
ejpam-6571	118	12	(	(	PUNCT
ejpam-6571	118	13	scli	scli	PROPN
ejpam-6571	118	14	⋆(a	⋆(a	PRON
ejpam-6571	118	15	)	)	PUNCT
ejpam-6571	119	1	[	[	X
ejpam-6571	119	2	14	14	NUM
ejpam-6571	119	3	]	]	SYM
ejpam-6571	119	4	)	)	PUNCT
ejpam-6571	119	5	.	.	PUNCT
ejpam-6571	120	1	the	the	DET
ejpam-6571	120	2	union	union	NOUN
ejpam-6571	120	3	of	of	ADP
ejpam-6571	120	4	all	all	DET
ejpam-6571	120	5	semi	semi	ADJ
ejpam-6571	120	6	-	-	ADJ
ejpam-6571	120	7	i	i	PRON
ejpam-6571	120	8	-open	-open	NOUN
ejpam-6571	120	9	sets	set	NOUN
ejpam-6571	120	10	contained	contain	VERB
ejpam-6571	120	11	in	in	ADP
ejpam-6571	120	12	a	a	PRON
ejpam-6571	120	13	is	be	AUX
ejpam-6571	120	14	called	call	VERB
ejpam-6571	120	15	the	the	DET
ejpam-6571	120	16	semi	semi	NOUN
ejpam-6571	120	17	-	-	ADJ
ejpam-6571	120	18	i	i	PRON
ejpam-6571	120	19	⋆-interior	⋆-interior	PUNCT
ejpam-6571	121	1	[	[	X
ejpam-6571	121	2	14	14	NUM
ejpam-6571	121	3	]	]	PUNCT
ejpam-6571	121	4	of	of	ADP
ejpam-6571	121	5	a	a	PRON
ejpam-6571	121	6	and	and	CCONJ
ejpam-6571	121	7	is	be	AUX
ejpam-6571	121	8	denoted	denote	VERB
ejpam-6571	121	9	by	by	ADP
ejpam-6571	121	10	sint⋆(a	sint⋆(a	PROPN
ejpam-6571	121	11	)	)	PUNCT
ejpam-6571	122	1	(	(	PUNCT
ejpam-6571	122	2	sinti	sinti	PROPN
ejpam-6571	122	3	⋆(a	⋆(a	NOUN
ejpam-6571	122	4	)	)	PUNCT
ejpam-6571	123	1	[	[	X
ejpam-6571	123	2	14	14	NUM
ejpam-6571	123	3	]	]	SYM
ejpam-6571	123	4	)	)	PUNCT
ejpam-6571	123	5	.	.	PUNCT
ejpam-6571	124	1	lemma	lemma	PROPN
ejpam-6571	124	2	3	3	X
ejpam-6571	124	3	.	.	PUNCT
ejpam-6571	125	1	[	[	X
ejpam-6571	125	2	14	14	NUM
ejpam-6571	125	3	]	]	PUNCT
ejpam-6571	125	4	for	for	ADP
ejpam-6571	125	5	a	a	DET
ejpam-6571	125	6	subset	subset	NOUN
ejpam-6571	125	7	a	a	PRON
ejpam-6571	125	8	of	of	ADP
ejpam-6571	125	9	a	a	DET
ejpam-6571	125	10	an	an	DET
ejpam-6571	125	11	ideal	ideal	ADJ
ejpam-6571	125	12	topological	topological	ADJ
ejpam-6571	125	13	space	space	NOUN
ejpam-6571	125	14	(	(	PUNCT
ejpam-6571	125	15	x	x	X
ejpam-6571	125	16	,	,	PUNCT
ejpam-6571	125	17	τ	τ	PROPN
ejpam-6571	125	18	,	,	PUNCT
ejpam-6571	125	19	i	i	NOUN
ejpam-6571	125	20	)	)	PUNCT
ejpam-6571	125	21	,	,	PUNCT
ejpam-6571	125	22	the	the	DET
ejpam-6571	125	23	following	follow	VERB
ejpam-6571	125	24	properties	property	NOUN
ejpam-6571	125	25	hold	hold	VERB
ejpam-6571	125	26	:	:	PUNCT
ejpam-6571	125	27	(	(	PUNCT
ejpam-6571	125	28	1	1	X
ejpam-6571	125	29	)	)	PUNCT
ejpam-6571	125	30	scl⋆(a	scl⋆(a	NUM
ejpam-6571	125	31	)	)	PUNCT
ejpam-6571	125	32	=	=	PUNCT
ejpam-6571	125	33	a	a	DET
ejpam-6571	125	34	∪	∪	ADJ
ejpam-6571	125	35	int⋆(cl⋆(a	int⋆(cl⋆(a	NOUN
ejpam-6571	125	36	)	)	PUNCT
ejpam-6571	125	37	)	)	PUNCT
ejpam-6571	125	38	;	;	PUNCT
ejpam-6571	125	39	(	(	PUNCT
ejpam-6571	125	40	2	2	X
ejpam-6571	125	41	)	)	PUNCT
ejpam-6571	125	42	sint⋆(a	sint⋆(a	PROPN
ejpam-6571	125	43	)	)	PUNCT
ejpam-6571	126	1	=	=	PUNCT
ejpam-6571	126	2	a	a	DET
ejpam-6571	126	3	∩	∩	ADJ
ejpam-6571	126	4	cl⋆(int⋆(a	cl⋆(int⋆(a	NOUN
ejpam-6571	126	5	)	)	PUNCT
ejpam-6571	126	6	)	)	PUNCT
ejpam-6571	126	7	.	.	PUNCT
ejpam-6571	127	1	by	by	ADP
ejpam-6571	127	2	a	a	DET
ejpam-6571	127	3	multifunction	multifunction	NOUN
ejpam-6571	127	4	f	f	NOUN
ejpam-6571	127	5	:	:	PUNCT
ejpam-6571	127	6	x	x	X
ejpam-6571	127	7	→	→	SYM
ejpam-6571	127	8	y	y	PROPN
ejpam-6571	127	9	,	,	PUNCT
ejpam-6571	127	10	we	we	PRON
ejpam-6571	127	11	mean	mean	VERB
ejpam-6571	127	12	a	a	DET
ejpam-6571	127	13	point	point	NOUN
ejpam-6571	127	14	-	-	PUNCT
ejpam-6571	127	15	to	to	ADP
ejpam-6571	127	16	-	-	PUNCT
ejpam-6571	127	17	set	set	VERB
ejpam-6571	127	18	correspondence	correspondence	NOUN
ejpam-6571	127	19	from	from	ADP
ejpam-6571	127	20	x	x	PUNCT
ejpam-6571	127	21	into	into	ADP
ejpam-6571	127	22	y	y	PROPN
ejpam-6571	127	23	,	,	PUNCT
ejpam-6571	127	24	and	and	CCONJ
ejpam-6571	127	25	we	we	PRON
ejpam-6571	127	26	always	always	ADV
ejpam-6571	127	27	assume	assume	VERB
ejpam-6571	127	28	that	that	SCONJ
ejpam-6571	127	29	f	f	PROPN
ejpam-6571	127	30	(	(	PUNCT
ejpam-6571	127	31	x	x	X
ejpam-6571	127	32	)	)	PUNCT
ejpam-6571	127	33	̸=	̸=	NOUN
ejpam-6571	127	34	∅	∅	NOUN
ejpam-6571	127	35	for	for	ADP
ejpam-6571	127	36	all	all	PRON
ejpam-6571	127	37	x	x	SYM
ejpam-6571	127	38	∈	∈	ADJ
ejpam-6571	127	39	x.	x.	NOUN
ejpam-6571	127	40	for	for	ADP
ejpam-6571	127	41	a	a	DET
ejpam-6571	127	42	multifunction	multifunction	NOUN
ejpam-6571	127	43	f	f	NOUN
ejpam-6571	127	44	:	:	PUNCT
ejpam-6571	127	45	x	x	X
ejpam-6571	127	46	→	→	SYM
ejpam-6571	127	47	y	y	PROPN
ejpam-6571	127	48	,	,	PUNCT
ejpam-6571	127	49	we	we	PRON
ejpam-6571	127	50	shall	shall	AUX
ejpam-6571	127	51	denote	denote	VERB
ejpam-6571	127	52	the	the	DET
ejpam-6571	127	53	upper	upper	ADJ
ejpam-6571	127	54	and	and	CCONJ
ejpam-6571	127	55	lower	low	ADJ
ejpam-6571	127	56	inverse	inverse	NOUN
ejpam-6571	127	57	of	of	ADP
ejpam-6571	127	58	a	a	DET
ejpam-6571	127	59	set	set	NOUN
ejpam-6571	127	60	b	b	PROPN
ejpam-6571	127	61	of	of	ADP
ejpam-6571	127	62	y	y	PROPN
ejpam-6571	127	63	by	by	ADP
ejpam-6571	127	64	f+(b	f+(b	NOUN
ejpam-6571	127	65	)	)	PUNCT
ejpam-6571	127	66	and	and	CCONJ
ejpam-6571	127	67	f−(b	f−(b	NOUN
ejpam-6571	127	68	)	)	PUNCT
ejpam-6571	127	69	,	,	PUNCT
ejpam-6571	127	70	respectively	respectively	ADV
ejpam-6571	127	71	,	,	PUNCT
ejpam-6571	127	72	that	that	ADV
ejpam-6571	127	73	is	is	ADV
ejpam-6571	127	74	,	,	PUNCT
ejpam-6571	127	75	f+(b	f+(b	NOUN
ejpam-6571	127	76	)	)	PUNCT
ejpam-6571	127	77	=	=	PRON
ejpam-6571	128	1	{	{	PUNCT
ejpam-6571	128	2	x	x	PUNCT
ejpam-6571	128	3	∈	∈	PROPN
ejpam-6571	128	4	x	x	INTJ
ejpam-6571	129	1	|	|	NOUN
ejpam-6571	129	2	f	f	X
ejpam-6571	129	3	(	(	PUNCT
ejpam-6571	129	4	x	x	NOUN
ejpam-6571	129	5	)	)	PUNCT
ejpam-6571	129	6	⊆	⊆	NUM
ejpam-6571	129	7	b	b	NOUN
ejpam-6571	129	8	}	}	PUNCT
ejpam-6571	129	9	and	and	CCONJ
ejpam-6571	129	10	f−(b	f−(b	PROPN
ejpam-6571	129	11	)	)	PUNCT
ejpam-6571	129	12	=	=	PRON
ejpam-6571	130	1	{	{	PUNCT
ejpam-6571	130	2	x	x	PUNCT
ejpam-6571	130	3	∈	∈	PROPN
ejpam-6571	130	4	x	x	INTJ
ejpam-6571	131	1	|	|	NOUN
ejpam-6571	131	2	f	f	X
ejpam-6571	131	3	(	(	PUNCT
ejpam-6571	131	4	x	x	NOUN
ejpam-6571	131	5	)	)	PUNCT
ejpam-6571	131	6	∩	∩	NOUN
ejpam-6571	131	7	b	b	PROPN
ejpam-6571	131	8	̸=	̸=	PROPN
ejpam-6571	131	9	∅	∅	NOUN
ejpam-6571	131	10	}	}	PUNCT
ejpam-6571	131	11	.	.	PUNCT
ejpam-6571	132	1	in	in	ADP
ejpam-6571	132	2	particular	particular	ADJ
ejpam-6571	132	3	,	,	PUNCT
ejpam-6571	132	4	f−(y	f−(y	NOUN
ejpam-6571	132	5	)	)	PUNCT
ejpam-6571	132	6	=	=	SYM
ejpam-6571	133	1	{	{	PUNCT
ejpam-6571	133	2	x	x	PUNCT
ejpam-6571	133	3	∈	∈	PROPN
ejpam-6571	133	4	x	x	INTJ
ejpam-6571	134	1	|	|	ADV
ejpam-6571	134	2	y	y	PROPN
ejpam-6571	134	3	∈	∈	PROPN
ejpam-6571	134	4	f	f	X
ejpam-6571	134	5	(	(	PUNCT
ejpam-6571	134	6	x	x	NOUN
ejpam-6571	134	7	)	)	PUNCT
ejpam-6571	134	8	}	}	PUNCT
ejpam-6571	134	9	for	for	ADP
ejpam-6571	134	10	each	each	DET
ejpam-6571	134	11	point	point	NOUN
ejpam-6571	134	12	y	y	PROPN
ejpam-6571	134	13	∈	∈	PROPN
ejpam-6571	134	14	y	y	PROPN
ejpam-6571	134	15	.	.	PUNCT
ejpam-6571	135	1	for	for	ADP
ejpam-6571	135	2	each	each	DET
ejpam-6571	135	3	a	a	DET
ejpam-6571	135	4	⊆	⊆	NUM
ejpam-6571	135	5	x	x	SYM
ejpam-6571	135	6	,	,	PUNCT
ejpam-6571	135	7	f	f	PROPN
ejpam-6571	135	8	(	(	PUNCT
ejpam-6571	135	9	a	a	NOUN
ejpam-6571	135	10	)	)	PUNCT
ejpam-6571	135	11	=	=	SYM
ejpam-6571	135	12	∪x∈af	∪x∈af	NOUN
ejpam-6571	135	13	(	(	PUNCT
ejpam-6571	135	14	x	x	NOUN
ejpam-6571	135	15	)	)	PUNCT
ejpam-6571	135	16	.	.	PUNCT
ejpam-6571	136	1	3	3	X
ejpam-6571	136	2	.	.	X
ejpam-6571	136	3	upper	upper	ADJ
ejpam-6571	136	4	and	and	CCONJ
ejpam-6571	136	5	lower	low	ADJ
ejpam-6571	136	6	almost	almost	ADV
ejpam-6571	136	7	quasi	quasi	ADJ
ejpam-6571	136	8	τ	τ	PROPN
ejpam-6571	136	9	⋆(σ1	⋆(σ1	PROPN
ejpam-6571	136	10	,	,	PUNCT
ejpam-6571	136	11	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	136	12	multifunctions	multifunction	NOUN
ejpam-6571	136	13	in	in	ADP
ejpam-6571	136	14	this	this	DET
ejpam-6571	136	15	section	section	NOUN
ejpam-6571	136	16	,	,	PUNCT
ejpam-6571	136	17	we	we	PRON
ejpam-6571	136	18	introduce	introduce	VERB
ejpam-6571	136	19	the	the	DET
ejpam-6571	136	20	concepts	concept	NOUN
ejpam-6571	136	21	of	of	ADP
ejpam-6571	136	22	upper	upper	ADJ
ejpam-6571	136	23	almost	almost	ADV
ejpam-6571	136	24	quasi	quasi	ADJ
ejpam-6571	136	25	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	136	26	,	,	PUNCT
ejpam-6571	136	27	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	136	28	multifunctions	multifunction	NOUN
ejpam-6571	136	29	and	and	CCONJ
ejpam-6571	136	30	lower	low	ADJ
ejpam-6571	136	31	almost	almost	ADV
ejpam-6571	136	32	quasi	quasi	ADJ
ejpam-6571	136	33	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	136	34	,	,	PUNCT
ejpam-6571	136	35	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	136	36	multifunctions	multifunction	NOUN
ejpam-6571	136	37	.	.	PUNCT
ejpam-6571	137	1	furthermore	furthermore	ADV
ejpam-6571	137	2	,	,	PUNCT
ejpam-6571	137	3	several	several	ADJ
ejpam-6571	137	4	characterizations	characterization	NOUN
ejpam-6571	137	5	of	of	ADP
ejpam-6571	137	6	upper	upper	ADJ
ejpam-6571	137	7	almost	almost	ADV
ejpam-6571	137	8	quasi	quasi	ADJ
ejpam-6571	137	9	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	137	10	,	,	PUNCT
ejpam-6571	137	11	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	137	12	multifunctions	multifunction	NOUN
ejpam-6571	137	13	and	and	CCONJ
ejpam-6571	137	14	lower	low	ADJ
ejpam-6571	137	15	almost	almost	ADV
ejpam-6571	137	16	quasi	quasi	ADJ
ejpam-6571	137	17	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	137	18	,	,	PUNCT
ejpam-6571	137	19	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	137	20	multifunctions	multifunction	NOUN
ejpam-6571	137	21	are	be	AUX
ejpam-6571	137	22	discussed	discuss	VERB
ejpam-6571	137	23	.	.	PUNCT
ejpam-6571	138	1	definition	definition	NOUN
ejpam-6571	138	2	1	1	NUM
ejpam-6571	138	3	.	.	PUNCT
ejpam-6571	139	1	a	a	DET
ejpam-6571	139	2	multifunction	multifunction	NOUN
ejpam-6571	139	3	f	f	NOUN
ejpam-6571	139	4	:	:	PUNCT
ejpam-6571	139	5	(	(	PUNCT
ejpam-6571	139	6	x	x	X
ejpam-6571	139	7	,	,	PUNCT
ejpam-6571	139	8	τ	τ	PROPN
ejpam-6571	139	9	,	,	PUNCT
ejpam-6571	139	10	i	i	NOUN
ejpam-6571	139	11	)	)	PUNCT
ejpam-6571	139	12	→	→	PUNCT
ejpam-6571	139	13	(	(	PUNCT
ejpam-6571	139	14	y	y	PROPN
ejpam-6571	139	15	,	,	PUNCT
ejpam-6571	139	16	σ1	σ1	PROPN
ejpam-6571	139	17	,	,	PUNCT
ejpam-6571	139	18	σ2	σ2	PROPN
ejpam-6571	139	19	)	)	PUNCT
ejpam-6571	139	20	is	be	AUX
ejpam-6571	139	21	said	say	VERB
ejpam-6571	139	22	to	to	PART
ejpam-6571	139	23	be	be	AUX
ejpam-6571	139	24	upper	upper	ADJ
ejpam-6571	139	25	almost	almost	ADV
ejpam-6571	139	26	quasi	quasi	ADJ
ejpam-6571	139	27	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	139	28	,	,	PUNCT
ejpam-6571	139	29	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	139	30	at	at	ADP
ejpam-6571	139	31	a	a	DET
ejpam-6571	139	32	point	point	NOUN
ejpam-6571	139	33	x	x	SYM
ejpam-6571	139	34	∈	∈	NOUN
ejpam-6571	139	35	x	x	INTJ
ejpam-6571	139	36	if	if	SCONJ
ejpam-6571	139	37	for	for	ADP
ejpam-6571	139	38	every	every	DET
ejpam-6571	139	39	σ1σ2	σ1σ2	NOUN
ejpam-6571	139	40	-	-	ADJ
ejpam-6571	139	41	open	open	ADJ
ejpam-6571	139	42	set	set	NOUN
ejpam-6571	139	43	v	v	NOUN
ejpam-6571	139	44	of	of	ADP
ejpam-6571	139	45	y	y	PRON
ejpam-6571	139	46	such	such	ADJ
ejpam-6571	139	47	that	that	SCONJ
ejpam-6571	139	48	f	f	PROPN
ejpam-6571	139	49	(	(	PUNCT
ejpam-6571	139	50	x	x	X
ejpam-6571	139	51	)	)	PUNCT
ejpam-6571	139	52	⊆	⊆	NUM
ejpam-6571	139	53	v	v	NOUN
ejpam-6571	139	54	and	and	CCONJ
ejpam-6571	139	55	each	each	DET
ejpam-6571	139	56	⋆-open	⋆-open	ADV
ejpam-6571	139	57	set	set	VERB
ejpam-6571	139	58	u	u	NOUN
ejpam-6571	139	59	of	of	ADP
ejpam-6571	139	60	x	x	SYM
ejpam-6571	139	61	containing	contain	VERB
ejpam-6571	139	62	x	x	PRON
ejpam-6571	139	63	,	,	PUNCT
ejpam-6571	139	64	there	there	PRON
ejpam-6571	139	65	exists	exist	VERB
ejpam-6571	139	66	a	a	DET
ejpam-6571	139	67	nonempty	nonempty	ADJ
ejpam-6571	139	68	⋆-open	⋆-open	NOUN
ejpam-6571	139	69	set	set	VERB
ejpam-6571	139	70	g	g	PROPN
ejpam-6571	139	71	such	such	ADJ
ejpam-6571	139	72	that	that	SCONJ
ejpam-6571	139	73	g	g	PROPN
ejpam-6571	139	74	⊆	⊆	NUM
ejpam-6571	139	75	u	u	NOUN
ejpam-6571	139	76	and	and	CCONJ
ejpam-6571	139	77	f	f	PROPN
ejpam-6571	139	78	(	(	PUNCT
ejpam-6571	139	79	g	g	NOUN
ejpam-6571	139	80	)	)	PUNCT
ejpam-6571	139	81	⊆	⊆	NUM
ejpam-6571	139	82	(	(	PUNCT
ejpam-6571	139	83	σ1	σ1	PROPN
ejpam-6571	139	84	,	,	PUNCT
ejpam-6571	139	85	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	139	86	)	)	PUNCT
ejpam-6571	139	87	.	.	PUNCT
ejpam-6571	140	1	a	a	DET
ejpam-6571	140	2	multifunction	multifunction	NOUN
ejpam-6571	140	3	f	f	NOUN
ejpam-6571	140	4	:	:	PUNCT
ejpam-6571	140	5	(	(	PUNCT
ejpam-6571	140	6	x	x	X
ejpam-6571	140	7	,	,	PUNCT
ejpam-6571	140	8	τ	τ	PROPN
ejpam-6571	140	9	,	,	PUNCT
ejpam-6571	140	10	i	i	NOUN
ejpam-6571	140	11	)	)	PUNCT
ejpam-6571	140	12	→	→	PUNCT
ejpam-6571	140	13	(	(	PUNCT
ejpam-6571	140	14	y	y	PROPN
ejpam-6571	140	15	,	,	PUNCT
ejpam-6571	140	16	σ1	σ1	PROPN
ejpam-6571	140	17	,	,	PUNCT
ejpam-6571	140	18	σ2	σ2	PROPN
ejpam-6571	140	19	)	)	PUNCT
ejpam-6571	140	20	is	be	AUX
ejpam-6571	140	21	said	say	VERB
ejpam-6571	140	22	to	to	PART
ejpam-6571	140	23	be	be	AUX
ejpam-6571	140	24	upper	upper	ADJ
ejpam-6571	140	25	almost	almost	ADV
ejpam-6571	140	26	quasi	quasi	ADJ
ejpam-6571	140	27	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	140	28	,	,	PUNCT
ejpam-6571	140	29	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	140	30	if	if	SCONJ
ejpam-6571	140	31	f	f	PROPN
ejpam-6571	140	32	is	be	AUX
ejpam-6571	140	33	upper	upper	ADJ
ejpam-6571	140	34	almost	almost	ADV
ejpam-6571	140	35	quasi	quasi	ADJ
ejpam-6571	140	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	140	37	,	,	PUNCT
ejpam-6571	140	38	σ2)continuous	σ2)continuous	ADJ
ejpam-6571	140	39	at	at	ADP
ejpam-6571	140	40	each	each	DET
ejpam-6571	140	41	point	point	NOUN
ejpam-6571	140	42	x	x	PUNCT
ejpam-6571	140	43	of	of	ADP
ejpam-6571	140	44	x.	x.	PROPN
ejpam-6571	140	45	theorem	theorem	VERB
ejpam-6571	140	46	1	1	NUM
ejpam-6571	140	47	.	.	X
ejpam-6571	140	48	for	for	ADP
ejpam-6571	140	49	a	a	DET
ejpam-6571	140	50	multifunction	multifunction	NOUN
ejpam-6571	141	1	f	f	NOUN
ejpam-6571	141	2	:	:	PUNCT
ejpam-6571	141	3	(	(	PUNCT
ejpam-6571	141	4	x	x	X
ejpam-6571	141	5	,	,	PUNCT
ejpam-6571	141	6	τ	τ	PROPN
ejpam-6571	141	7	,	,	PUNCT
ejpam-6571	141	8	i	i	NOUN
ejpam-6571	141	9	)	)	PUNCT
ejpam-6571	141	10	→	→	PUNCT
ejpam-6571	141	11	(	(	PUNCT
ejpam-6571	141	12	y	y	PROPN
ejpam-6571	141	13	,	,	PUNCT
ejpam-6571	141	14	σ1	σ1	PROPN
ejpam-6571	141	15	,	,	PUNCT
ejpam-6571	141	16	σ2	σ2	NOUN
ejpam-6571	141	17	)	)	PUNCT
ejpam-6571	141	18	,	,	PUNCT
ejpam-6571	141	19	the	the	DET
ejpam-6571	141	20	following	follow	VERB
ejpam-6571	141	21	properties	property	NOUN
ejpam-6571	141	22	are	be	AUX
ejpam-6571	141	23	equivalent	equivalent	ADJ
ejpam-6571	141	24	:	:	PUNCT
ejpam-6571	141	25	(	(	PUNCT
ejpam-6571	141	26	1	1	X
ejpam-6571	141	27	)	)	PUNCT
ejpam-6571	141	28	f	f	PROPN
ejpam-6571	141	29	is	be	AUX
ejpam-6571	141	30	upper	upper	ADJ
ejpam-6571	141	31	almost	almost	ADV
ejpam-6571	141	32	quasi	quasi	ADJ
ejpam-6571	141	33	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	141	34	,	,	PUNCT
ejpam-6571	141	35	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	141	36	at	at	ADP
ejpam-6571	141	37	x	x	X
ejpam-6571	141	38	∈	∈	PROPN
ejpam-6571	141	39	x	x	NOUN
ejpam-6571	141	40	;	;	PUNCT
ejpam-6571	141	41	m.	m.	NOUN
ejpam-6571	141	42	thongmoon	thongmoon	NOUN
ejpam-6571	141	43	,	,	PUNCT
ejpam-6571	141	44	a.	a.	PROPN
ejpam-6571	141	45	sama	sama	PROPN
ejpam-6571	141	46	-	-	PUNCT
ejpam-6571	141	47	ae	ae	PROPN
ejpam-6571	141	48	,	,	PUNCT
ejpam-6571	141	49	c.	c.	PROPN
ejpam-6571	141	50	boonpok	boonpok	PROPN
ejpam-6571	141	51	/	/	SYM
ejpam-6571	141	52	eur	eur	PROPN
ejpam-6571	141	53	.	.	PUNCT
ejpam-6571	142	1	j.	j.	PROPN
ejpam-6571	142	2	pure	pure	PROPN
ejpam-6571	142	3	appl	appl	PROPN
ejpam-6571	142	4	.	.	PROPN
ejpam-6571	142	5	math	math	PROPN
ejpam-6571	142	6	,	,	PUNCT
ejpam-6571	142	7	18	18	NUM
ejpam-6571	142	8	(	(	PUNCT
ejpam-6571	142	9	3	3	NUM
ejpam-6571	142	10	)	)	PUNCT
ejpam-6571	142	11	(	(	PUNCT
ejpam-6571	142	12	2025	2025	NUM
ejpam-6571	142	13	)	)	PUNCT
ejpam-6571	142	14	,	,	PUNCT
ejpam-6571	142	15	6571	6571	NUM
ejpam-6571	142	16	5	5	NUM
ejpam-6571	142	17	of	of	ADP
ejpam-6571	142	18	15	15	NUM
ejpam-6571	142	19	(	(	PUNCT
ejpam-6571	142	20	2	2	NUM
ejpam-6571	142	21	)	)	PUNCT
ejpam-6571	142	22	for	for	ADP
ejpam-6571	142	23	every	every	DET
ejpam-6571	142	24	σ1σ2	σ1σ2	NOUN
ejpam-6571	142	25	-	-	ADJ
ejpam-6571	142	26	open	open	ADJ
ejpam-6571	142	27	set	set	NOUN
ejpam-6571	142	28	v	v	NOUN
ejpam-6571	142	29	of	of	ADP
ejpam-6571	142	30	y	y	PRON
ejpam-6571	142	31	such	such	ADJ
ejpam-6571	142	32	that	that	SCONJ
ejpam-6571	142	33	f	f	PROPN
ejpam-6571	142	34	(	(	PUNCT
ejpam-6571	142	35	x	x	X
ejpam-6571	142	36	)	)	PUNCT
ejpam-6571	142	37	⊆	⊆	NUM
ejpam-6571	142	38	v	v	NOUN
ejpam-6571	143	1	,	,	PUNCT
ejpam-6571	143	2	there	there	PRON
ejpam-6571	143	3	exists	exist	VERB
ejpam-6571	143	4	a	a	DET
ejpam-6571	143	5	semi	semi	NOUN
ejpam-6571	143	6	-	-	ADJ
ejpam-6571	143	7	i	i	PRON
ejpam-6571	143	8	⋆-open	⋆-open	VERB
ejpam-6571	143	9	set	set	VERB
ejpam-6571	143	10	u	u	NOUN
ejpam-6571	143	11	of	of	ADP
ejpam-6571	143	12	x	x	PUNCT
ejpam-6571	143	13	containing	contain	VERB
ejpam-6571	143	14	x	x	PUNCT
ejpam-6571	143	15	such	such	ADJ
ejpam-6571	143	16	that	that	SCONJ
ejpam-6571	143	17	f	f	PROPN
ejpam-6571	143	18	(	(	PUNCT
ejpam-6571	143	19	u	u	NOUN
ejpam-6571	143	20	)	)	PUNCT
ejpam-6571	143	21	⊆	⊆	NUM
ejpam-6571	143	22	(	(	PUNCT
ejpam-6571	143	23	σ1	σ1	PROPN
ejpam-6571	143	24	,	,	PUNCT
ejpam-6571	143	25	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	143	26	)	)	PUNCT
ejpam-6571	143	27	;	;	PUNCT
ejpam-6571	143	28	(	(	PUNCT
ejpam-6571	143	29	3	3	X
ejpam-6571	143	30	)	)	PUNCT
ejpam-6571	143	31	x	x	SYM
ejpam-6571	143	32	∈	∈	NOUN
ejpam-6571	143	33	sint⋆(f+((σ1	sint⋆(f+((σ1	NOUN
ejpam-6571	143	34	,	,	PUNCT
ejpam-6571	143	35	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	143	36	)	)	PUNCT
ejpam-6571	143	37	)	)	PUNCT
ejpam-6571	143	38	)	)	PUNCT
ejpam-6571	144	1	for	for	ADP
ejpam-6571	144	2	every	every	DET
ejpam-6571	144	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	144	4	-	-	ADJ
ejpam-6571	144	5	open	open	ADJ
ejpam-6571	144	6	set	set	NOUN
ejpam-6571	144	7	v	v	NOUN
ejpam-6571	144	8	of	of	ADP
ejpam-6571	144	9	y	y	PRON
ejpam-6571	144	10	such	such	ADJ
ejpam-6571	144	11	that	that	SCONJ
ejpam-6571	144	12	f	f	PROPN
ejpam-6571	144	13	(	(	PUNCT
ejpam-6571	144	14	x	x	X
ejpam-6571	144	15	)	)	PUNCT
ejpam-6571	144	16	⊆	⊆	NUM
ejpam-6571	144	17	v	v	NOUN
ejpam-6571	144	18	;	;	PUNCT
ejpam-6571	144	19	(	(	PUNCT
ejpam-6571	144	20	4	4	X
ejpam-6571	144	21	)	)	PUNCT
ejpam-6571	144	22	x	x	SYM
ejpam-6571	144	23	∈	∈	NOUN
ejpam-6571	144	24	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	144	25	,	,	PUNCT
ejpam-6571	144	26	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	144	27	)	)	PUNCT
ejpam-6571	144	28	)	)	PUNCT
ejpam-6571	144	29	)	)	PUNCT
ejpam-6571	144	30	)	)	PUNCT
ejpam-6571	145	1	for	for	ADP
ejpam-6571	145	2	every	every	DET
ejpam-6571	145	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	145	4	-	-	ADJ
ejpam-6571	145	5	open	open	ADJ
ejpam-6571	145	6	set	set	NOUN
ejpam-6571	145	7	v	v	NOUN
ejpam-6571	145	8	of	of	ADP
ejpam-6571	145	9	y	y	PRON
ejpam-6571	145	10	such	such	ADJ
ejpam-6571	145	11	that	that	SCONJ
ejpam-6571	145	12	f	f	PROPN
ejpam-6571	145	13	(	(	PUNCT
ejpam-6571	145	14	x	x	X
ejpam-6571	145	15	)	)	PUNCT
ejpam-6571	145	16	⊆	⊆	NUM
ejpam-6571	145	17	v	v	NOUN
ejpam-6571	145	18	.	.	PUNCT
ejpam-6571	146	1	proof	proof	NOUN
ejpam-6571	146	2	.	.	PUNCT
ejpam-6571	147	1	(	(	PUNCT
ejpam-6571	147	2	1	1	X
ejpam-6571	147	3	)	)	PUNCT
ejpam-6571	147	4	⇒	⇒	NOUN
ejpam-6571	147	5	(	(	PUNCT
ejpam-6571	147	6	2	2	NUM
ejpam-6571	147	7	):	):	PUNCT
ejpam-6571	147	8	let	let	VERB
ejpam-6571	147	9	u	u	PRON
ejpam-6571	147	10	(	(	PUNCT
ejpam-6571	147	11	x	x	NOUN
ejpam-6571	147	12	)	)	PUNCT
ejpam-6571	147	13	be	be	VERB
ejpam-6571	147	14	the	the	DET
ejpam-6571	147	15	family	family	NOUN
ejpam-6571	147	16	of	of	ADP
ejpam-6571	147	17	all	all	DET
ejpam-6571	147	18	⋆-open	⋆-open	ADJ
ejpam-6571	147	19	sets	set	NOUN
ejpam-6571	147	20	of	of	ADP
ejpam-6571	147	21	x	x	PUNCT
ejpam-6571	147	22	containing	contain	VERB
ejpam-6571	147	23	x.	x.	NOUN
ejpam-6571	147	24	let	let	VERB
ejpam-6571	147	25	v	v	PART
ejpam-6571	147	26	be	be	AUX
ejpam-6571	147	27	any	any	DET
ejpam-6571	147	28	σ1σ2	σ1σ2	NOUN
ejpam-6571	147	29	-	-	ADJ
ejpam-6571	147	30	open	open	ADJ
ejpam-6571	147	31	set	set	NOUN
ejpam-6571	147	32	of	of	ADP
ejpam-6571	147	33	y	y	PRON
ejpam-6571	147	34	such	such	ADJ
ejpam-6571	147	35	that	that	SCONJ
ejpam-6571	147	36	f	f	PROPN
ejpam-6571	147	37	(	(	PUNCT
ejpam-6571	147	38	x	x	X
ejpam-6571	147	39	)	)	PUNCT
ejpam-6571	147	40	⊆	⊆	NUM
ejpam-6571	147	41	v	v	NOUN
ejpam-6571	147	42	.	.	PUNCT
ejpam-6571	148	1	for	for	ADP
ejpam-6571	148	2	each	each	DET
ejpam-6571	148	3	h	h	NOUN
ejpam-6571	148	4	∈	∈	PROPN
ejpam-6571	148	5	u	u	NOUN
ejpam-6571	148	6	(	(	PUNCT
ejpam-6571	148	7	x	x	NOUN
ejpam-6571	148	8	)	)	PUNCT
ejpam-6571	148	9	,	,	PUNCT
ejpam-6571	148	10	there	there	PRON
ejpam-6571	148	11	exists	exist	VERB
ejpam-6571	148	12	a	a	DET
ejpam-6571	148	13	nonempty	nonempty	ADJ
ejpam-6571	148	14	⋆-open	⋆-open	NOUN
ejpam-6571	148	15	set	set	NOUN
ejpam-6571	148	16	gh	gh	PROPN
ejpam-6571	148	17	such	such	ADJ
ejpam-6571	148	18	that	that	SCONJ
ejpam-6571	148	19	gh	gh	PROPN
ejpam-6571	148	20	⊆	⊆	NUM
ejpam-6571	148	21	h	h	PROPN
ejpam-6571	148	22	and	and	CCONJ
ejpam-6571	148	23	f	f	PROPN
ejpam-6571	148	24	(	(	PUNCT
ejpam-6571	148	25	gh	gh	PROPN
ejpam-6571	148	26	)	)	PUNCT
ejpam-6571	148	27	⊆	⊆	NUM
ejpam-6571	148	28	(	(	PUNCT
ejpam-6571	148	29	σ1	σ1	PROPN
ejpam-6571	148	30	,	,	PUNCT
ejpam-6571	148	31	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	148	32	)	)	PUNCT
ejpam-6571	148	33	.	.	PUNCT
ejpam-6571	149	1	put	put	VERB
ejpam-6571	149	2	w	w	NOUN
ejpam-6571	149	3	=	=	PUNCT
ejpam-6571	149	4	∪{gh	∪{gh	ADP
ejpam-6571	150	1	|	|	ADV
ejpam-6571	150	2	h	h	NOUN
ejpam-6571	150	3	∈	∈	PROPN
ejpam-6571	150	4	u	u	NOUN
ejpam-6571	150	5	(	(	PUNCT
ejpam-6571	150	6	x	x	NOUN
ejpam-6571	150	7	)	)	PUNCT
ejpam-6571	150	8	}	}	PUNCT
ejpam-6571	150	9	.	.	PUNCT
ejpam-6571	151	1	then	then	ADV
ejpam-6571	151	2	,	,	PUNCT
ejpam-6571	151	3	w	w	PROPN
ejpam-6571	151	4	is	be	AUX
ejpam-6571	151	5	⋆-open	⋆-open	ADJ
ejpam-6571	151	6	in	in	ADP
ejpam-6571	151	7	x	x	X
ejpam-6571	151	8	,	,	PUNCT
ejpam-6571	151	9	x	x	PROPN
ejpam-6571	151	10	∈	∈	PROPN
ejpam-6571	151	11	cl⋆(w	cl⋆(w	PROPN
ejpam-6571	151	12	)	)	PUNCT
ejpam-6571	151	13	and	and	CCONJ
ejpam-6571	151	14	f	f	PROPN
ejpam-6571	151	15	(	(	PUNCT
ejpam-6571	151	16	w	w	PROPN
ejpam-6571	151	17	)	)	PUNCT
ejpam-6571	151	18	⊆	⊆	NUM
ejpam-6571	151	19	(	(	PUNCT
ejpam-6571	151	20	σ1	σ1	PROPN
ejpam-6571	151	21	,	,	PUNCT
ejpam-6571	151	22	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	151	23	)	)	PUNCT
ejpam-6571	151	24	.	.	PUNCT
ejpam-6571	152	1	put	put	VERB
ejpam-6571	152	2	u	u	NOUN
ejpam-6571	152	3	=	=	X
ejpam-6571	152	4	w	w	PROPN
ejpam-6571	152	5	∪{x	∪{x	NOUN
ejpam-6571	152	6	}	}	PUNCT
ejpam-6571	152	7	,	,	PUNCT
ejpam-6571	152	8	then	then	ADV
ejpam-6571	152	9	w	w	PROPN
ejpam-6571	152	10	⊆	⊆	NUM
ejpam-6571	152	11	u	u	NOUN
ejpam-6571	152	12	⊆	⊆	NUM
ejpam-6571	152	13	cl⋆(w	cl⋆(w	NOUN
ejpam-6571	152	14	)	)	PUNCT
ejpam-6571	152	15	.	.	PUNCT
ejpam-6571	153	1	thus	thus	ADV
ejpam-6571	153	2	,	,	PUNCT
ejpam-6571	153	3	u	u	NOUN
ejpam-6571	153	4	is	be	AUX
ejpam-6571	153	5	a	a	DET
ejpam-6571	153	6	semi	semi	ADJ
ejpam-6571	153	7	-	-	ADJ
ejpam-6571	153	8	i	i	PRON
ejpam-6571	153	9	⋆-open	⋆-open	VERB
ejpam-6571	153	10	set	set	VERB
ejpam-6571	153	11	of	of	ADP
ejpam-6571	153	12	x	x	PUNCT
ejpam-6571	153	13	containing	contain	VERB
ejpam-6571	153	14	x	x	PUNCT
ejpam-6571	153	15	such	such	ADJ
ejpam-6571	153	16	that	that	SCONJ
ejpam-6571	153	17	f	f	PROPN
ejpam-6571	153	18	(	(	PUNCT
ejpam-6571	153	19	u	u	NOUN
ejpam-6571	153	20	)	)	PUNCT
ejpam-6571	153	21	⊆	⊆	NUM
ejpam-6571	153	22	(	(	PUNCT
ejpam-6571	153	23	σ1	σ1	PROPN
ejpam-6571	153	24	,	,	PUNCT
ejpam-6571	153	25	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	153	26	)	)	PUNCT
ejpam-6571	153	27	.	.	PUNCT
ejpam-6571	154	1	(	(	PUNCT
ejpam-6571	154	2	2	2	X
ejpam-6571	154	3	)	)	PUNCT
ejpam-6571	154	4	⇒	⇒	NOUN
ejpam-6571	154	5	(	(	PUNCT
ejpam-6571	154	6	3	3	NUM
ejpam-6571	154	7	):	):	PUNCT
ejpam-6571	154	8	let	let	VERB
ejpam-6571	154	9	v	v	PART
ejpam-6571	154	10	be	be	AUX
ejpam-6571	154	11	any	any	DET
ejpam-6571	154	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	154	13	-	-	ADJ
ejpam-6571	154	14	open	open	ADJ
ejpam-6571	154	15	set	set	NOUN
ejpam-6571	154	16	of	of	ADP
ejpam-6571	154	17	y	y	PROPN
ejpam-6571	154	18	and	and	CCONJ
ejpam-6571	154	19	f	f	PROPN
ejpam-6571	154	20	(	(	PUNCT
ejpam-6571	154	21	x	x	X
ejpam-6571	154	22	)	)	PUNCT
ejpam-6571	154	23	⊆	⊆	NUM
ejpam-6571	154	24	v	v	NOUN
ejpam-6571	154	25	.	.	PUNCT
ejpam-6571	155	1	then	then	ADV
ejpam-6571	155	2	,	,	PUNCT
ejpam-6571	155	3	there	there	PRON
ejpam-6571	155	4	exists	exist	VERB
ejpam-6571	155	5	a	a	DET
ejpam-6571	155	6	semi	semi	NOUN
ejpam-6571	155	7	-	-	ADJ
ejpam-6571	155	8	i	i	PRON
ejpam-6571	155	9	⋆-open	⋆-open	VERB
ejpam-6571	155	10	set	set	VERB
ejpam-6571	155	11	u	u	NOUN
ejpam-6571	155	12	of	of	ADP
ejpam-6571	155	13	x	x	PUNCT
ejpam-6571	155	14	containing	contain	VERB
ejpam-6571	155	15	x	x	PUNCT
ejpam-6571	155	16	such	such	ADJ
ejpam-6571	155	17	that	that	SCONJ
ejpam-6571	155	18	f	f	PROPN
ejpam-6571	155	19	(	(	PUNCT
ejpam-6571	155	20	u	u	NOUN
ejpam-6571	155	21	)	)	PUNCT
ejpam-6571	155	22	⊆	⊆	NUM
ejpam-6571	155	23	(	(	PUNCT
ejpam-6571	155	24	σ1	σ1	PROPN
ejpam-6571	155	25	,	,	PUNCT
ejpam-6571	155	26	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	155	27	)	)	PUNCT
ejpam-6571	155	28	.	.	PUNCT
ejpam-6571	156	1	thus	thus	ADV
ejpam-6571	156	2	,	,	PUNCT
ejpam-6571	156	3	x	x	PUNCT
ejpam-6571	156	4	∈	∈	PROPN
ejpam-6571	156	5	u	u	NOUN
ejpam-6571	156	6	⊆	⊆	NUM
ejpam-6571	156	7	f+((σ1	f+((σ1	NOUN
ejpam-6571	156	8	,	,	PUNCT
ejpam-6571	156	9	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	156	10	)	)	PUNCT
ejpam-6571	156	11	)	)	PUNCT
ejpam-6571	156	12	and	and	CCONJ
ejpam-6571	156	13	hence	hence	ADV
ejpam-6571	156	14	x	x	PART
ejpam-6571	156	15	∈	∈	PROPN
ejpam-6571	156	16	u	u	NOUN
ejpam-6571	156	17	⊆	⊆	NUM
ejpam-6571	156	18	sint⋆(f+((σ1	sint⋆(f+((σ1	NUM
ejpam-6571	156	19	,	,	PUNCT
ejpam-6571	156	20	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	156	21	)	)	PUNCT
ejpam-6571	156	22	)	)	PUNCT
ejpam-6571	156	23	)	)	PUNCT
ejpam-6571	156	24	.	.	PUNCT
ejpam-6571	157	1	(	(	PUNCT
ejpam-6571	157	2	3	3	X
ejpam-6571	157	3	)	)	PUNCT
ejpam-6571	157	4	⇒	⇒	NOUN
ejpam-6571	157	5	(	(	PUNCT
ejpam-6571	157	6	4	4	NUM
ejpam-6571	157	7	):	):	PUNCT
ejpam-6571	157	8	let	let	VERB
ejpam-6571	157	9	v	v	PART
ejpam-6571	157	10	be	be	AUX
ejpam-6571	157	11	any	any	DET
ejpam-6571	157	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	157	13	-	-	ADJ
ejpam-6571	157	14	open	open	ADJ
ejpam-6571	157	15	set	set	NOUN
ejpam-6571	157	16	of	of	ADP
ejpam-6571	157	17	y	y	PRON
ejpam-6571	157	18	such	such	ADJ
ejpam-6571	157	19	that	that	SCONJ
ejpam-6571	157	20	f	f	PROPN
ejpam-6571	157	21	(	(	PUNCT
ejpam-6571	157	22	x	x	X
ejpam-6571	157	23	)	)	PUNCT
ejpam-6571	157	24	⊆	⊆	NUM
ejpam-6571	157	25	v	v	NOUN
ejpam-6571	157	26	.	.	PUNCT
ejpam-6571	158	1	by	by	ADP
ejpam-6571	158	2	(	(	PUNCT
ejpam-6571	158	3	3	3	NUM
ejpam-6571	158	4	)	)	PUNCT
ejpam-6571	158	5	,	,	PUNCT
ejpam-6571	158	6	we	we	PRON
ejpam-6571	158	7	have	have	VERB
ejpam-6571	158	8	x	x	X
ejpam-6571	158	9	∈	∈	NOUN
ejpam-6571	158	10	sint⋆(f+((σ1	sint⋆(f+((σ1	NOUN
ejpam-6571	158	11	,	,	PUNCT
ejpam-6571	158	12	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	158	13	)	)	PUNCT
ejpam-6571	158	14	)	)	PUNCT
ejpam-6571	158	15	)	)	PUNCT
ejpam-6571	158	16	.	.	PUNCT
ejpam-6571	159	1	now	now	ADV
ejpam-6571	159	2	,	,	PUNCT
ejpam-6571	159	3	put	put	VERB
ejpam-6571	159	4	u	u	PRON
ejpam-6571	159	5	=	=	NOUN
ejpam-6571	159	6	sint⋆(f+((σ1	sint⋆(f+((σ1	X
ejpam-6571	159	7	,	,	PUNCT
ejpam-6571	159	8	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	159	9	)	)	PUNCT
ejpam-6571	159	10	)	)	PUNCT
ejpam-6571	159	11	)	)	PUNCT
ejpam-6571	159	12	.	.	PUNCT
ejpam-6571	160	1	then	then	ADV
ejpam-6571	160	2	,	,	PUNCT
ejpam-6571	160	3	u	u	NOUN
ejpam-6571	160	4	is	be	AUX
ejpam-6571	160	5	semi	semi	ADJ
ejpam-6571	160	6	-	-	ADJ
ejpam-6571	160	7	i	i	PRON
ejpam-6571	160	8	⋆-open	⋆-open	VERB
ejpam-6571	160	9	in	in	ADP
ejpam-6571	160	10	x	x	X
ejpam-6571	160	11	and	and	CCONJ
ejpam-6571	160	12	by	by	ADP
ejpam-6571	160	13	lemma	lemma	PROPN
ejpam-6571	160	14	3	3	NUM
ejpam-6571	160	15	,	,	PUNCT
ejpam-6571	160	16	x	x	SYM
ejpam-6571	160	17	∈	∈	PROPN
ejpam-6571	160	18	u	u	NOUN
ejpam-6571	160	19	⊆	⊆	NUM
ejpam-6571	160	20	cl⋆(int⋆(u	cl⋆(int⋆(u	NOUN
ejpam-6571	160	21	)	)	PUNCT
ejpam-6571	160	22	)	)	PUNCT
ejpam-6571	160	23	⊆	⊆	NUM
ejpam-6571	160	24	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	160	25	,	,	PUNCT
ejpam-6571	160	26	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	160	27	)	)	PUNCT
ejpam-6571	160	28	)	)	PUNCT
ejpam-6571	160	29	)	)	PUNCT
ejpam-6571	160	30	)	)	PUNCT
ejpam-6571	160	31	.	.	PUNCT
ejpam-6571	161	1	(	(	PUNCT
ejpam-6571	161	2	4	4	X
ejpam-6571	161	3	)	)	PUNCT
ejpam-6571	161	4	⇒	⇒	NOUN
ejpam-6571	161	5	(	(	PUNCT
ejpam-6571	161	6	1	1	NUM
ejpam-6571	161	7	):	):	PUNCT
ejpam-6571	161	8	let	let	VERB
ejpam-6571	161	9	u	u	PRON
ejpam-6571	161	10	be	be	AUX
ejpam-6571	161	11	any	any	DET
ejpam-6571	161	12	⋆-open	⋆-open	ADJ
ejpam-6571	161	13	set	set	NOUN
ejpam-6571	161	14	of	of	ADP
ejpam-6571	161	15	x	x	PUNCT
ejpam-6571	161	16	containing	contain	VERB
ejpam-6571	161	17	x	x	X
ejpam-6571	161	18	and	and	CCONJ
ejpam-6571	161	19	v	v	AUX
ejpam-6571	161	20	be	be	AUX
ejpam-6571	161	21	any	any	DET
ejpam-6571	161	22	σ1σ2	σ1σ2	NOUN
ejpam-6571	161	23	-	-	ADJ
ejpam-6571	161	24	open	open	ADJ
ejpam-6571	161	25	set	set	NOUN
ejpam-6571	161	26	of	of	ADP
ejpam-6571	161	27	y	y	PRON
ejpam-6571	161	28	such	such	ADJ
ejpam-6571	161	29	that	that	SCONJ
ejpam-6571	161	30	f	f	PROPN
ejpam-6571	161	31	(	(	PUNCT
ejpam-6571	161	32	x	x	X
ejpam-6571	161	33	)	)	PUNCT
ejpam-6571	161	34	⊆	⊆	NUM
ejpam-6571	161	35	v	v	NOUN
ejpam-6571	161	36	.	.	PUNCT
ejpam-6571	162	1	thus	thus	ADV
ejpam-6571	162	2	by	by	ADP
ejpam-6571	162	3	(	(	PUNCT
ejpam-6571	162	4	4	4	NUM
ejpam-6571	162	5	)	)	PUNCT
ejpam-6571	162	6	,	,	PUNCT
ejpam-6571	162	7	x	x	PUNCT
ejpam-6571	162	8	∈	∈	NOUN
ejpam-6571	162	9	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	162	10	,	,	PUNCT
ejpam-6571	162	11	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	162	12	)	)	PUNCT
ejpam-6571	162	13	)	)	PUNCT
ejpam-6571	162	14	)	)	PUNCT
ejpam-6571	162	15	)	)	PUNCT
ejpam-6571	162	16	and	and	CCONJ
ejpam-6571	162	17	hence	hence	ADV
ejpam-6571	162	18	int⋆(f+((σ1	int⋆(f+((σ1	NUM
ejpam-6571	162	19	,	,	PUNCT
ejpam-6571	162	20	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	162	21	)	)	PUNCT
ejpam-6571	162	22	)	)	PUNCT
ejpam-6571	162	23	)	)	PUNCT
ejpam-6571	163	1	∩	∩	NOUN
ejpam-6571	163	2	u	u	PROPN
ejpam-6571	163	3	̸=	̸=	PROPN
ejpam-6571	163	4	∅.	∅.	ADV
ejpam-6571	163	5	put	put	VERB
ejpam-6571	163	6	w	w	NOUN
ejpam-6571	163	7	=	=	PUNCT
ejpam-6571	163	8	int⋆(f+((σ1	int⋆(f+((σ1	NOUN
ejpam-6571	163	9	,	,	PUNCT
ejpam-6571	163	10	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	163	11	)	)	PUNCT
ejpam-6571	163	12	)	)	PUNCT
ejpam-6571	163	13	)	)	PUNCT
ejpam-6571	164	1	∩	∩	NOUN
ejpam-6571	164	2	u	u	NOUN
ejpam-6571	164	3	.	.	PUNCT
ejpam-6571	165	1	then	then	ADV
ejpam-6571	165	2	,	,	PUNCT
ejpam-6571	165	3	we	we	PRON
ejpam-6571	165	4	have	have	VERB
ejpam-6571	165	5	w	w	PROPN
ejpam-6571	165	6	is	be	AUX
ejpam-6571	165	7	a	a	DET
ejpam-6571	165	8	nonempty	nonempty	ADJ
ejpam-6571	165	9	⋆-open	⋆-open	NOUN
ejpam-6571	165	10	set	set	NOUN
ejpam-6571	165	11	of	of	ADP
ejpam-6571	165	12	x	x	PUNCT
ejpam-6571	165	13	such	such	ADJ
ejpam-6571	165	14	that	that	SCONJ
ejpam-6571	165	15	w	w	ADP
ejpam-6571	165	16	⊆	⊆	NUM
ejpam-6571	165	17	u	u	NOUN
ejpam-6571	165	18	and	and	CCONJ
ejpam-6571	165	19	f	f	PROPN
ejpam-6571	165	20	(	(	PUNCT
ejpam-6571	165	21	w	w	PROPN
ejpam-6571	165	22	)	)	PUNCT
ejpam-6571	165	23	⊆	⊆	NUM
ejpam-6571	165	24	(	(	PUNCT
ejpam-6571	165	25	σ1	σ1	PROPN
ejpam-6571	165	26	,	,	PUNCT
ejpam-6571	165	27	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	165	28	)	)	PUNCT
ejpam-6571	165	29	.	.	PUNCT
ejpam-6571	166	1	this	this	PRON
ejpam-6571	166	2	shows	show	VERB
ejpam-6571	166	3	that	that	SCONJ
ejpam-6571	166	4	f	f	PROPN
ejpam-6571	166	5	is	be	AUX
ejpam-6571	166	6	upper	upper	ADJ
ejpam-6571	166	7	almost	almost	ADV
ejpam-6571	166	8	quasi	quasi	ADJ
ejpam-6571	166	9	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	166	10	,	,	PUNCT
ejpam-6571	166	11	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	166	12	at	at	ADP
ejpam-6571	166	13	x.	x.	NOUN
ejpam-6571	166	14	definition	definition	NOUN
ejpam-6571	166	15	2	2	NUM
ejpam-6571	166	16	.	.	PUNCT
ejpam-6571	166	17	a	a	DET
ejpam-6571	166	18	multifunction	multifunction	NOUN
ejpam-6571	167	1	f	f	NOUN
ejpam-6571	167	2	:	:	PUNCT
ejpam-6571	167	3	(	(	PUNCT
ejpam-6571	167	4	x	x	X
ejpam-6571	167	5	,	,	PUNCT
ejpam-6571	167	6	τ	τ	PROPN
ejpam-6571	167	7	,	,	PUNCT
ejpam-6571	167	8	i	i	NOUN
ejpam-6571	167	9	)	)	PUNCT
ejpam-6571	167	10	→	→	PUNCT
ejpam-6571	167	11	(	(	PUNCT
ejpam-6571	167	12	y	y	PROPN
ejpam-6571	167	13	,	,	PUNCT
ejpam-6571	167	14	σ1	σ1	PROPN
ejpam-6571	167	15	,	,	PUNCT
ejpam-6571	167	16	σ2	σ2	PROPN
ejpam-6571	167	17	)	)	PUNCT
ejpam-6571	167	18	is	be	AUX
ejpam-6571	167	19	said	say	VERB
ejpam-6571	167	20	to	to	PART
ejpam-6571	167	21	be	be	AUX
ejpam-6571	167	22	lower	low	ADJ
ejpam-6571	167	23	almost	almost	ADV
ejpam-6571	167	24	quasi	quasi	ADJ
ejpam-6571	167	25	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	167	26	,	,	PUNCT
ejpam-6571	167	27	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	167	28	at	at	ADP
ejpam-6571	167	29	a	a	DET
ejpam-6571	167	30	point	point	NOUN
ejpam-6571	167	31	x	x	SYM
ejpam-6571	167	32	∈	∈	NOUN
ejpam-6571	167	33	x	x	INTJ
ejpam-6571	167	34	if	if	SCONJ
ejpam-6571	167	35	for	for	ADP
ejpam-6571	167	36	every	every	DET
ejpam-6571	167	37	σ1σ2	σ1σ2	NOUN
ejpam-6571	167	38	-	-	ADJ
ejpam-6571	167	39	open	open	ADJ
ejpam-6571	167	40	set	set	NOUN
ejpam-6571	167	41	v	v	NOUN
ejpam-6571	167	42	of	of	ADP
ejpam-6571	167	43	y	y	PRON
ejpam-6571	167	44	such	such	ADJ
ejpam-6571	167	45	that	that	SCONJ
ejpam-6571	167	46	f	f	PROPN
ejpam-6571	167	47	(	(	PUNCT
ejpam-6571	167	48	x	x	NOUN
ejpam-6571	167	49	)	)	PUNCT
ejpam-6571	167	50	∩	∩	NOUN
ejpam-6571	167	51	v	v	ADP
ejpam-6571	167	52	̸=	̸=	PROPN
ejpam-6571	167	53	∅	∅	NOUN
ejpam-6571	167	54	and	and	CCONJ
ejpam-6571	167	55	each	each	DET
ejpam-6571	167	56	⋆-open	⋆-open	ADV
ejpam-6571	167	57	set	set	VERB
ejpam-6571	167	58	u	u	NOUN
ejpam-6571	167	59	of	of	ADP
ejpam-6571	167	60	x	x	SYM
ejpam-6571	167	61	containing	contain	VERB
ejpam-6571	167	62	x	x	PRON
ejpam-6571	167	63	,	,	PUNCT
ejpam-6571	167	64	there	there	PRON
ejpam-6571	167	65	exists	exist	VERB
ejpam-6571	167	66	a	a	DET
ejpam-6571	167	67	nonempty	nonempty	ADJ
ejpam-6571	167	68	⋆-open	⋆-open	NOUN
ejpam-6571	167	69	set	set	VERB
ejpam-6571	167	70	g	g	PROPN
ejpam-6571	167	71	such	such	ADJ
ejpam-6571	167	72	that	that	SCONJ
ejpam-6571	167	73	g	g	PROPN
ejpam-6571	167	74	⊆	⊆	NUM
ejpam-6571	167	75	u	u	PROPN
ejpam-6571	167	76	and	and	CCONJ
ejpam-6571	167	77	(	(	PUNCT
ejpam-6571	167	78	σ1	σ1	PROPN
ejpam-6571	167	79	,	,	PUNCT
ejpam-6571	167	80	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	167	81	)	)	PUNCT
ejpam-6571	167	82	∩	∩	PROPN
ejpam-6571	167	83	f	f	X
ejpam-6571	167	84	(	(	PUNCT
ejpam-6571	167	85	z	z	NOUN
ejpam-6571	167	86	)	)	PUNCT
ejpam-6571	167	87	̸=	̸=	NOUN
ejpam-6571	167	88	∅	∅	NOUN
ejpam-6571	167	89	for	for	ADP
ejpam-6571	167	90	each	each	DET
ejpam-6571	167	91	z	z	PROPN
ejpam-6571	167	92	∈	∈	PROPN
ejpam-6571	167	93	g.	g.	NOUN
ejpam-6571	167	94	a	a	DET
ejpam-6571	167	95	multifunction	multifunction	NOUN
ejpam-6571	168	1	f	f	NOUN
ejpam-6571	168	2	:	:	PUNCT
ejpam-6571	168	3	(	(	PUNCT
ejpam-6571	168	4	x	x	X
ejpam-6571	168	5	,	,	PUNCT
ejpam-6571	168	6	τ	τ	PROPN
ejpam-6571	168	7	,	,	PUNCT
ejpam-6571	168	8	i	i	NOUN
ejpam-6571	168	9	)	)	PUNCT
ejpam-6571	168	10	→	→	PUNCT
ejpam-6571	168	11	(	(	PUNCT
ejpam-6571	168	12	y	y	PROPN
ejpam-6571	168	13	,	,	PUNCT
ejpam-6571	168	14	σ1	σ1	PROPN
ejpam-6571	168	15	,	,	PUNCT
ejpam-6571	168	16	σ2	σ2	PROPN
ejpam-6571	168	17	)	)	PUNCT
ejpam-6571	168	18	is	be	AUX
ejpam-6571	168	19	said	say	VERB
ejpam-6571	168	20	to	to	PART
ejpam-6571	168	21	be	be	AUX
ejpam-6571	168	22	lower	low	ADJ
ejpam-6571	168	23	almost	almost	ADV
ejpam-6571	168	24	quasi	quasi	ADJ
ejpam-6571	168	25	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	168	26	,	,	PUNCT
ejpam-6571	168	27	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	168	28	if	if	SCONJ
ejpam-6571	168	29	f	f	PROPN
ejpam-6571	168	30	is	be	AUX
ejpam-6571	168	31	lower	low	ADJ
ejpam-6571	168	32	almost	almost	ADV
ejpam-6571	168	33	quasi	quasi	ADJ
ejpam-6571	168	34	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	168	35	,	,	PUNCT
ejpam-6571	168	36	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	168	37	at	at	ADP
ejpam-6571	168	38	each	each	DET
ejpam-6571	168	39	point	point	NOUN
ejpam-6571	168	40	x	x	PUNCT
ejpam-6571	168	41	of	of	ADP
ejpam-6571	168	42	x.	x.	PROPN
ejpam-6571	168	43	theorem	theorem	VERB
ejpam-6571	168	44	2	2	NUM
ejpam-6571	168	45	.	.	X
ejpam-6571	168	46	for	for	ADP
ejpam-6571	168	47	a	a	DET
ejpam-6571	168	48	multifunction	multifunction	NOUN
ejpam-6571	168	49	f	f	NOUN
ejpam-6571	168	50	:	:	PUNCT
ejpam-6571	168	51	(	(	PUNCT
ejpam-6571	168	52	x	x	X
ejpam-6571	168	53	,	,	PUNCT
ejpam-6571	168	54	τ	τ	PROPN
ejpam-6571	168	55	,	,	PUNCT
ejpam-6571	168	56	i	i	NOUN
ejpam-6571	168	57	)	)	PUNCT
ejpam-6571	168	58	→	→	PUNCT
ejpam-6571	168	59	(	(	PUNCT
ejpam-6571	168	60	y	y	PROPN
ejpam-6571	168	61	,	,	PUNCT
ejpam-6571	168	62	σ1	σ1	PROPN
ejpam-6571	168	63	,	,	PUNCT
ejpam-6571	168	64	σ2	σ2	NOUN
ejpam-6571	168	65	)	)	PUNCT
ejpam-6571	168	66	,	,	PUNCT
ejpam-6571	168	67	the	the	DET
ejpam-6571	168	68	following	follow	VERB
ejpam-6571	168	69	properties	property	NOUN
ejpam-6571	168	70	are	be	AUX
ejpam-6571	168	71	equivalent	equivalent	ADJ
ejpam-6571	168	72	:	:	PUNCT
ejpam-6571	168	73	(	(	PUNCT
ejpam-6571	168	74	1	1	X
ejpam-6571	168	75	)	)	PUNCT
ejpam-6571	168	76	f	f	PROPN
ejpam-6571	168	77	is	be	AUX
ejpam-6571	168	78	lower	low	ADJ
ejpam-6571	168	79	almost	almost	ADV
ejpam-6571	168	80	quasi	quasi	ADJ
ejpam-6571	168	81	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	168	82	,	,	PUNCT
ejpam-6571	168	83	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	168	84	at	at	ADP
ejpam-6571	168	85	x	x	X
ejpam-6571	168	86	∈	∈	PROPN
ejpam-6571	168	87	x	x	X
ejpam-6571	168	88	;	;	PUNCT
ejpam-6571	168	89	(	(	PUNCT
ejpam-6571	168	90	2	2	X
ejpam-6571	168	91	)	)	PUNCT
ejpam-6571	168	92	for	for	ADP
ejpam-6571	168	93	every	every	DET
ejpam-6571	168	94	σ1σ2	σ1σ2	NOUN
ejpam-6571	168	95	-	-	ADJ
ejpam-6571	168	96	open	open	ADJ
ejpam-6571	168	97	set	set	NOUN
ejpam-6571	168	98	v	v	NOUN
ejpam-6571	168	99	of	of	ADP
ejpam-6571	168	100	y	y	PRON
ejpam-6571	168	101	such	such	ADJ
ejpam-6571	168	102	that	that	SCONJ
ejpam-6571	168	103	f	f	PROPN
ejpam-6571	168	104	(	(	PUNCT
ejpam-6571	168	105	x)∩v	x)∩v	PROPN
ejpam-6571	168	106	̸=	̸=	PROPN
ejpam-6571	168	107	∅	∅	NOUN
ejpam-6571	168	108	,	,	PUNCT
ejpam-6571	168	109	there	there	PRON
ejpam-6571	168	110	exists	exist	VERB
ejpam-6571	168	111	a	a	DET
ejpam-6571	168	112	semi	semi	NOUN
ejpam-6571	168	113	-	-	ADJ
ejpam-6571	168	114	i	i	PRON
ejpam-6571	168	115	⋆-open	⋆-open	VERB
ejpam-6571	168	116	set	set	VERB
ejpam-6571	168	117	u	u	NOUN
ejpam-6571	168	118	of	of	ADP
ejpam-6571	168	119	x	x	PUNCT
ejpam-6571	168	120	containing	contain	VERB
ejpam-6571	168	121	x	x	PUNCT
ejpam-6571	168	122	such	such	ADJ
ejpam-6571	168	123	that	that	PRON
ejpam-6571	168	124	(	(	PUNCT
ejpam-6571	168	125	σ1	σ1	PROPN
ejpam-6571	168	126	,	,	PUNCT
ejpam-6571	168	127	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	168	128	)	)	PUNCT
ejpam-6571	168	129	∩	∩	PROPN
ejpam-6571	168	130	f	f	X
ejpam-6571	168	131	(	(	PUNCT
ejpam-6571	168	132	z	z	NOUN
ejpam-6571	168	133	)	)	PUNCT
ejpam-6571	168	134	̸=	̸=	NOUN
ejpam-6571	168	135	∅	∅	NOUN
ejpam-6571	168	136	for	for	ADP
ejpam-6571	168	137	every	every	DET
ejpam-6571	168	138	z	z	NOUN
ejpam-6571	168	139	∈	∈	PROPN
ejpam-6571	168	140	u	u	NOUN
ejpam-6571	168	141	;	;	PUNCT
ejpam-6571	168	142	(	(	PUNCT
ejpam-6571	168	143	3	3	X
ejpam-6571	168	144	)	)	PUNCT
ejpam-6571	168	145	x	x	SYM
ejpam-6571	168	146	∈	∈	NOUN
ejpam-6571	168	147	sint⋆(f−((σ1	sint⋆(f−((σ1	NOUN
ejpam-6571	168	148	,	,	PUNCT
ejpam-6571	168	149	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	168	150	)	)	PUNCT
ejpam-6571	168	151	)	)	PUNCT
ejpam-6571	168	152	)	)	PUNCT
ejpam-6571	168	153	for	for	ADP
ejpam-6571	168	154	every	every	DET
ejpam-6571	168	155	σ1σ2	σ1σ2	NOUN
ejpam-6571	168	156	-	-	ADJ
ejpam-6571	168	157	open	open	ADJ
ejpam-6571	168	158	set	set	NOUN
ejpam-6571	168	159	v	v	NOUN
ejpam-6571	168	160	of	of	ADP
ejpam-6571	168	161	y	y	PRON
ejpam-6571	168	162	such	such	ADJ
ejpam-6571	168	163	that	that	SCONJ
ejpam-6571	168	164	f	f	PROPN
ejpam-6571	168	165	(	(	PUNCT
ejpam-6571	168	166	x	x	NOUN
ejpam-6571	168	167	)	)	PUNCT
ejpam-6571	168	168	∩	∩	NOUN
ejpam-6571	168	169	v	v	ADP
ejpam-6571	168	170	̸=	̸=	PROPN
ejpam-6571	168	171	∅	∅	NOUN
ejpam-6571	168	172	;	;	PUNCT
ejpam-6571	168	173	m.	m.	NOUN
ejpam-6571	168	174	thongmoon	thongmoon	NOUN
ejpam-6571	168	175	,	,	PUNCT
ejpam-6571	168	176	a.	a.	PROPN
ejpam-6571	168	177	sama	sama	PROPN
ejpam-6571	168	178	-	-	PUNCT
ejpam-6571	168	179	ae	ae	PROPN
ejpam-6571	168	180	,	,	PUNCT
ejpam-6571	168	181	c.	c.	PROPN
ejpam-6571	168	182	boonpok	boonpok	PROPN
ejpam-6571	168	183	/	/	SYM
ejpam-6571	168	184	eur	eur	PROPN
ejpam-6571	168	185	.	.	PUNCT
ejpam-6571	169	1	j.	j.	PROPN
ejpam-6571	169	2	pure	pure	PROPN
ejpam-6571	169	3	appl	appl	PROPN
ejpam-6571	169	4	.	.	PROPN
ejpam-6571	169	5	math	math	PROPN
ejpam-6571	169	6	,	,	PUNCT
ejpam-6571	169	7	18	18	NUM
ejpam-6571	169	8	(	(	PUNCT
ejpam-6571	169	9	3	3	NUM
ejpam-6571	169	10	)	)	PUNCT
ejpam-6571	169	11	(	(	PUNCT
ejpam-6571	169	12	2025	2025	NUM
ejpam-6571	169	13	)	)	PUNCT
ejpam-6571	169	14	,	,	PUNCT
ejpam-6571	169	15	6571	6571	NUM
ejpam-6571	169	16	6	6	NUM
ejpam-6571	169	17	of	of	ADP
ejpam-6571	169	18	15	15	NUM
ejpam-6571	169	19	(	(	PUNCT
ejpam-6571	169	20	4	4	NUM
ejpam-6571	169	21	)	)	PUNCT
ejpam-6571	169	22	x	x	SYM
ejpam-6571	169	23	∈	∈	NOUN
ejpam-6571	169	24	cl⋆(int⋆(f−((σ1	cl⋆(int⋆(f−((σ1	NUM
ejpam-6571	169	25	,	,	PUNCT
ejpam-6571	169	26	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	169	27	)	)	PUNCT
ejpam-6571	169	28	)	)	PUNCT
ejpam-6571	169	29	)	)	PUNCT
ejpam-6571	169	30	)	)	PUNCT
ejpam-6571	170	1	for	for	ADP
ejpam-6571	170	2	every	every	DET
ejpam-6571	170	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	170	4	-	-	ADJ
ejpam-6571	170	5	open	open	ADJ
ejpam-6571	170	6	set	set	NOUN
ejpam-6571	170	7	v	v	NOUN
ejpam-6571	170	8	of	of	ADP
ejpam-6571	170	9	y	y	PRON
ejpam-6571	170	10	such	such	ADJ
ejpam-6571	170	11	that	that	SCONJ
ejpam-6571	170	12	f	f	PROPN
ejpam-6571	170	13	(	(	PUNCT
ejpam-6571	170	14	x	x	NOUN
ejpam-6571	170	15	)	)	PUNCT
ejpam-6571	170	16	∩	∩	NOUN
ejpam-6571	170	17	v	v	ADP
ejpam-6571	170	18	̸=	̸=	PROPN
ejpam-6571	170	19	∅.	∅.	ADP
ejpam-6571	170	20	proof	proof	NOUN
ejpam-6571	170	21	.	.	PUNCT
ejpam-6571	171	1	the	the	DET
ejpam-6571	171	2	proof	proof	NOUN
ejpam-6571	171	3	is	be	AUX
ejpam-6571	171	4	similar	similar	ADJ
ejpam-6571	171	5	to	to	ADP
ejpam-6571	171	6	that	that	PRON
ejpam-6571	171	7	of	of	ADP
ejpam-6571	171	8	theorem	theorem	ADJ
ejpam-6571	171	9	1	1	NUM
ejpam-6571	171	10	.	.	PUNCT
ejpam-6571	171	11	theorem	theorem	NOUN
ejpam-6571	171	12	3	3	NUM
ejpam-6571	171	13	.	.	X
ejpam-6571	171	14	for	for	ADP
ejpam-6571	171	15	a	a	DET
ejpam-6571	171	16	multifunction	multifunction	NOUN
ejpam-6571	171	17	f	f	NOUN
ejpam-6571	171	18	:	:	PUNCT
ejpam-6571	171	19	(	(	PUNCT
ejpam-6571	171	20	x	x	X
ejpam-6571	171	21	,	,	PUNCT
ejpam-6571	171	22	τ	τ	PROPN
ejpam-6571	171	23	,	,	PUNCT
ejpam-6571	171	24	i	i	NOUN
ejpam-6571	171	25	)	)	PUNCT
ejpam-6571	171	26	→	→	PUNCT
ejpam-6571	171	27	(	(	PUNCT
ejpam-6571	171	28	y	y	PROPN
ejpam-6571	171	29	,	,	PUNCT
ejpam-6571	171	30	σ1	σ1	PROPN
ejpam-6571	171	31	,	,	PUNCT
ejpam-6571	171	32	σ2	σ2	NOUN
ejpam-6571	171	33	)	)	PUNCT
ejpam-6571	171	34	,	,	PUNCT
ejpam-6571	171	35	the	the	DET
ejpam-6571	171	36	following	follow	VERB
ejpam-6571	171	37	properties	property	NOUN
ejpam-6571	171	38	are	be	AUX
ejpam-6571	171	39	equivalent	equivalent	ADJ
ejpam-6571	171	40	:	:	PUNCT
ejpam-6571	171	41	(	(	PUNCT
ejpam-6571	171	42	1	1	X
ejpam-6571	171	43	)	)	PUNCT
ejpam-6571	171	44	f	f	PROPN
ejpam-6571	171	45	is	be	AUX
ejpam-6571	171	46	upper	upper	ADJ
ejpam-6571	171	47	almost	almost	ADV
ejpam-6571	171	48	quasi	quasi	ADJ
ejpam-6571	171	49	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	171	50	,	,	PUNCT
ejpam-6571	171	51	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	171	52	;	;	PUNCT
ejpam-6571	171	53	(	(	PUNCT
ejpam-6571	171	54	2	2	X
ejpam-6571	171	55	)	)	PUNCT
ejpam-6571	171	56	for	for	ADP
ejpam-6571	171	57	each	each	DET
ejpam-6571	171	58	x	x	SYM
ejpam-6571	171	59	∈	∈	PROPN
ejpam-6571	171	60	x	x	X
ejpam-6571	171	61	and	and	CCONJ
ejpam-6571	171	62	every	every	DET
ejpam-6571	171	63	σ1σ2	σ1σ2	NUM
ejpam-6571	171	64	-	-	ADJ
ejpam-6571	171	65	open	open	ADJ
ejpam-6571	171	66	set	set	NOUN
ejpam-6571	171	67	v	v	NOUN
ejpam-6571	171	68	of	of	ADP
ejpam-6571	171	69	y	y	PRON
ejpam-6571	171	70	such	such	ADJ
ejpam-6571	171	71	that	that	SCONJ
ejpam-6571	171	72	f	f	PROPN
ejpam-6571	171	73	(	(	PUNCT
ejpam-6571	171	74	x	x	X
ejpam-6571	171	75	)	)	PUNCT
ejpam-6571	171	76	⊆	⊆	NUM
ejpam-6571	171	77	v	v	NOUN
ejpam-6571	171	78	,	,	PUNCT
ejpam-6571	171	79	there	there	PRON
ejpam-6571	171	80	exists	exist	VERB
ejpam-6571	171	81	a	a	DET
ejpam-6571	171	82	semi	semi	NOUN
ejpam-6571	171	83	-	-	ADJ
ejpam-6571	171	84	i	i	PRON
ejpam-6571	171	85	⋆-open	⋆-open	VERB
ejpam-6571	171	86	set	set	VERB
ejpam-6571	171	87	u	u	NOUN
ejpam-6571	171	88	of	of	ADP
ejpam-6571	171	89	x	x	PUNCT
ejpam-6571	171	90	containing	contain	VERB
ejpam-6571	171	91	x	x	PUNCT
ejpam-6571	171	92	such	such	ADJ
ejpam-6571	171	93	that	that	SCONJ
ejpam-6571	171	94	f	f	PROPN
ejpam-6571	171	95	(	(	PUNCT
ejpam-6571	171	96	u	u	NOUN
ejpam-6571	171	97	)	)	PUNCT
ejpam-6571	171	98	⊆	⊆	NUM
ejpam-6571	171	99	(	(	PUNCT
ejpam-6571	171	100	σ1	σ1	PROPN
ejpam-6571	171	101	,	,	PUNCT
ejpam-6571	171	102	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	171	103	)	)	PUNCT
ejpam-6571	171	104	;	;	PUNCT
ejpam-6571	171	105	(	(	PUNCT
ejpam-6571	171	106	3	3	X
ejpam-6571	171	107	)	)	PUNCT
ejpam-6571	171	108	f+(v	f+(v	NOUN
ejpam-6571	171	109	)	)	PUNCT
ejpam-6571	171	110	is	be	AUX
ejpam-6571	171	111	semi	semi	ADJ
ejpam-6571	171	112	-	-	ADJ
ejpam-6571	171	113	i	i	PRON
ejpam-6571	171	114	⋆-open	⋆-open	VERB
ejpam-6571	171	115	in	in	ADP
ejpam-6571	171	116	x	x	PUNCT
ejpam-6571	171	117	for	for	ADP
ejpam-6571	171	118	every	every	DET
ejpam-6571	171	119	(	(	PUNCT
ejpam-6571	171	120	σ1	σ1	PROPN
ejpam-6571	171	121	,	,	PUNCT
ejpam-6571	171	122	σ2)r	σ2)r	NOUN
ejpam-6571	171	123	-	-	PUNCT
ejpam-6571	171	124	open	open	ADJ
ejpam-6571	171	125	set	set	VERB
ejpam-6571	171	126	v	v	NOUN
ejpam-6571	171	127	of	of	ADP
ejpam-6571	171	128	y	y	PROPN
ejpam-6571	171	129	;	;	PUNCT
ejpam-6571	171	130	(	(	PUNCT
ejpam-6571	172	1	4	4	X
ejpam-6571	172	2	)	)	PUNCT
ejpam-6571	172	3	f+(v	f+(v	NOUN
ejpam-6571	172	4	)	)	PUNCT
ejpam-6571	173	1	⊆	⊆	NUM
ejpam-6571	173	2	sint⋆(f+((σ1	sint⋆(f+((σ1	NUM
ejpam-6571	173	3	,	,	PUNCT
ejpam-6571	173	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	173	5	)	)	PUNCT
ejpam-6571	173	6	)	)	PUNCT
ejpam-6571	173	7	)	)	PUNCT
ejpam-6571	174	1	for	for	ADP
ejpam-6571	174	2	every	every	DET
ejpam-6571	174	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	174	4	-	-	ADJ
ejpam-6571	174	5	open	open	ADJ
ejpam-6571	174	6	set	set	NOUN
ejpam-6571	174	7	v	v	NOUN
ejpam-6571	174	8	of	of	ADP
ejpam-6571	174	9	y	y	PROPN
ejpam-6571	174	10	;	;	PUNCT
ejpam-6571	174	11	(	(	PUNCT
ejpam-6571	174	12	5	5	X
ejpam-6571	174	13	)	)	PUNCT
ejpam-6571	174	14	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	174	15	-	-	PUNCT
ejpam-6571	174	16	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	174	17	-	-	PUNCT
ejpam-6571	174	18	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	174	19	-	-	PUNCT
ejpam-6571	174	20	cl(b	cl(b	NOUN
ejpam-6571	174	21	)	)	PUNCT
ejpam-6571	174	22	)	)	PUNCT
ejpam-6571	174	23	)	)	PUNCT
ejpam-6571	174	24	)	)	PUNCT
ejpam-6571	174	25	)	)	PUNCT
ejpam-6571	175	1	⊆	⊆	X
ejpam-6571	175	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6571	175	3	-	-	PUNCT
ejpam-6571	175	4	cl(b	cl(b	NOUN
ejpam-6571	175	5	)	)	PUNCT
ejpam-6571	175	6	)	)	PUNCT
ejpam-6571	176	1	for	for	ADP
ejpam-6571	176	2	every	every	DET
ejpam-6571	176	3	subset	subset	NOUN
ejpam-6571	176	4	b	b	PROPN
ejpam-6571	176	5	of	of	ADP
ejpam-6571	176	6	y	y	PROPN
ejpam-6571	176	7	;	;	PUNCT
ejpam-6571	176	8	(	(	PUNCT
ejpam-6571	176	9	6	6	NUM
ejpam-6571	176	10	)	)	PUNCT
ejpam-6571	176	11	f+(v	f+(v	NOUN
ejpam-6571	176	12	)	)	PUNCT
ejpam-6571	176	13	⊆	⊆	NUM
ejpam-6571	176	14	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	176	15	,	,	PUNCT
ejpam-6571	176	16	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	176	17	)	)	PUNCT
ejpam-6571	176	18	)	)	PUNCT
ejpam-6571	176	19	)	)	PUNCT
ejpam-6571	176	20	)	)	PUNCT
ejpam-6571	176	21	for	for	ADP
ejpam-6571	176	22	every	every	DET
ejpam-6571	176	23	σ1σ2	σ1σ2	NOUN
ejpam-6571	176	24	-	-	ADJ
ejpam-6571	176	25	open	open	ADJ
ejpam-6571	176	26	set	set	NOUN
ejpam-6571	176	27	v	v	NOUN
ejpam-6571	176	28	of	of	ADP
ejpam-6571	176	29	y	y	PROPN
ejpam-6571	176	30	.	.	PUNCT
ejpam-6571	177	1	proof	proof	NOUN
ejpam-6571	177	2	.	.	PUNCT
ejpam-6571	178	1	(	(	PUNCT
ejpam-6571	178	2	1	1	X
ejpam-6571	178	3	)	)	PUNCT
ejpam-6571	178	4	⇒	⇒	NOUN
ejpam-6571	178	5	(	(	PUNCT
ejpam-6571	178	6	2	2	NUM
ejpam-6571	178	7	):	):	PUNCT
ejpam-6571	178	8	it	it	PRON
ejpam-6571	178	9	follows	follow	VERB
ejpam-6571	178	10	from	from	ADP
ejpam-6571	178	11	theorem	theorem	ADJ
ejpam-6571	178	12	1	1	NUM
ejpam-6571	178	13	.	.	PUNCT
ejpam-6571	178	14	(	(	PUNCT
ejpam-6571	178	15	2	2	X
ejpam-6571	178	16	)	)	PUNCT
ejpam-6571	178	17	⇒	⇒	NOUN
ejpam-6571	178	18	(	(	PUNCT
ejpam-6571	178	19	3	3	NUM
ejpam-6571	178	20	):	):	PUNCT
ejpam-6571	178	21	let	let	VERB
ejpam-6571	178	22	v	v	PART
ejpam-6571	178	23	be	be	AUX
ejpam-6571	178	24	any	any	DET
ejpam-6571	178	25	(	(	PUNCT
ejpam-6571	178	26	σ1	σ1	NOUN
ejpam-6571	178	27	,	,	PUNCT
ejpam-6571	178	28	σ2)r	σ2)r	NOUN
ejpam-6571	178	29	-	-	PUNCT
ejpam-6571	178	30	open	open	ADJ
ejpam-6571	178	31	set	set	NOUN
ejpam-6571	178	32	of	of	ADP
ejpam-6571	178	33	y	y	PROPN
ejpam-6571	178	34	and	and	CCONJ
ejpam-6571	178	35	x	x	PROPN
ejpam-6571	178	36	∈	∈	PROPN
ejpam-6571	178	37	f+(v	f+(v	NOUN
ejpam-6571	178	38	)	)	PUNCT
ejpam-6571	178	39	.	.	PUNCT
ejpam-6571	179	1	then	then	ADV
ejpam-6571	179	2	,	,	PUNCT
ejpam-6571	179	3	f	f	PROPN
ejpam-6571	179	4	(	(	PUNCT
ejpam-6571	179	5	x	x	X
ejpam-6571	179	6	)	)	PUNCT
ejpam-6571	179	7	⊆	⊆	NUM
ejpam-6571	179	8	v	v	NOUN
ejpam-6571	179	9	and	and	CCONJ
ejpam-6571	179	10	there	there	PRON
ejpam-6571	179	11	exists	exist	VERB
ejpam-6571	179	12	a	a	DET
ejpam-6571	179	13	semi	semi	NOUN
ejpam-6571	179	14	-	-	ADJ
ejpam-6571	179	15	i	i	PRON
ejpam-6571	179	16	⋆-open	⋆-open	VERB
ejpam-6571	179	17	set	set	VERB
ejpam-6571	179	18	u	u	NOUN
ejpam-6571	179	19	of	of	ADP
ejpam-6571	179	20	x	x	PUNCT
ejpam-6571	179	21	containing	contain	VERB
ejpam-6571	179	22	x	x	PUNCT
ejpam-6571	179	23	such	such	ADJ
ejpam-6571	179	24	that	that	SCONJ
ejpam-6571	179	25	f	f	PROPN
ejpam-6571	179	26	(	(	PUNCT
ejpam-6571	179	27	u	u	NOUN
ejpam-6571	179	28	)	)	PUNCT
ejpam-6571	179	29	⊆	⊆	NUM
ejpam-6571	179	30	v	v	NOUN
ejpam-6571	179	31	.	.	PUNCT
ejpam-6571	180	1	thus	thus	ADV
ejpam-6571	180	2	,	,	PUNCT
ejpam-6571	180	3	x	x	PUNCT
ejpam-6571	180	4	∈	∈	PROPN
ejpam-6571	180	5	u	u	NOUN
ejpam-6571	180	6	⊆	⊆	NUM
ejpam-6571	180	7	f+(v	f+(v	NOUN
ejpam-6571	180	8	)	)	PUNCT
ejpam-6571	180	9	and	and	CCONJ
ejpam-6571	180	10	hence	hence	ADV
ejpam-6571	180	11	x	x	PART
ejpam-6571	180	12	∈	∈	PROPN
ejpam-6571	180	13	sint⋆(f+(v	sint⋆(f+(v	PROPN
ejpam-6571	180	14	)	)	PUNCT
ejpam-6571	180	15	)	)	PUNCT
ejpam-6571	180	16	.	.	PUNCT
ejpam-6571	181	1	therefore	therefore	ADV
ejpam-6571	181	2	,	,	PUNCT
ejpam-6571	181	3	f+(v	f+(v	PROPN
ejpam-6571	181	4	)	)	PUNCT
ejpam-6571	181	5	⊆	⊆	NUM
ejpam-6571	181	6	sint⋆(f+(v	sint⋆(f+(v	PROPN
ejpam-6571	181	7	)	)	PUNCT
ejpam-6571	181	8	)	)	PUNCT
ejpam-6571	181	9	.	.	PUNCT
ejpam-6571	182	1	this	this	PRON
ejpam-6571	182	2	shows	show	VERB
ejpam-6571	182	3	that	that	SCONJ
ejpam-6571	182	4	f+(v	f+(v	PROPN
ejpam-6571	182	5	)	)	PUNCT
ejpam-6571	182	6	is	be	AUX
ejpam-6571	182	7	semi	semi	ADJ
ejpam-6571	182	8	-	-	ADJ
ejpam-6571	182	9	i	i	PRON
ejpam-6571	182	10	⋆-open	⋆-open	VERB
ejpam-6571	182	11	in	in	ADP
ejpam-6571	182	12	x.	x.	PROPN
ejpam-6571	182	13	(	(	PUNCT
ejpam-6571	182	14	3	3	NUM
ejpam-6571	182	15	)	)	PUNCT
ejpam-6571	182	16	⇒	⇒	NOUN
ejpam-6571	182	17	(	(	PUNCT
ejpam-6571	182	18	4	4	NUM
ejpam-6571	182	19	):	):	PUNCT
ejpam-6571	182	20	let	let	VERB
ejpam-6571	182	21	v	v	PART
ejpam-6571	182	22	be	be	AUX
ejpam-6571	182	23	any	any	DET
ejpam-6571	182	24	σ1σ2	σ1σ2	NOUN
ejpam-6571	182	25	-	-	ADJ
ejpam-6571	182	26	open	open	ADJ
ejpam-6571	182	27	set	set	NOUN
ejpam-6571	182	28	of	of	ADP
ejpam-6571	182	29	y	y	PROPN
ejpam-6571	182	30	and	and	CCONJ
ejpam-6571	182	31	x	x	PROPN
ejpam-6571	182	32	∈	∈	PROPN
ejpam-6571	182	33	f+(v	f+(v	NOUN
ejpam-6571	182	34	)	)	PUNCT
ejpam-6571	182	35	.	.	PUNCT
ejpam-6571	183	1	then	then	ADV
ejpam-6571	183	2	,	,	PUNCT
ejpam-6571	183	3	we	we	PRON
ejpam-6571	183	4	have	have	VERB
ejpam-6571	183	5	f	f	PROPN
ejpam-6571	183	6	(	(	PUNCT
ejpam-6571	183	7	x	x	NOUN
ejpam-6571	183	8	)	)	PUNCT
ejpam-6571	183	9	⊆	⊆	NUM
ejpam-6571	183	10	v	v	ADP
ejpam-6571	183	11	⊆	⊆	NUM
ejpam-6571	183	12	(	(	PUNCT
ejpam-6571	183	13	σ1	σ1	PROPN
ejpam-6571	183	14	,	,	PUNCT
ejpam-6571	183	15	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	183	16	)	)	PUNCT
ejpam-6571	183	17	.	.	PUNCT
ejpam-6571	184	1	thus	thus	ADV
ejpam-6571	184	2	,	,	PUNCT
ejpam-6571	184	3	x	x	SYM
ejpam-6571	184	4	∈	∈	NOUN
ejpam-6571	184	5	f+((σ1	f+((σ1	NOUN
ejpam-6571	184	6	,	,	PUNCT
ejpam-6571	184	7	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	184	8	)	)	PUNCT
ejpam-6571	184	9	)	)	PUNCT
ejpam-6571	184	10	.	.	PUNCT
ejpam-6571	185	1	by	by	ADP
ejpam-6571	185	2	lemma	lemma	PROPN
ejpam-6571	185	3	2	2	NUM
ejpam-6571	185	4	,	,	PUNCT
ejpam-6571	185	5	we	we	PRON
ejpam-6571	185	6	have	have	AUX
ejpam-6571	185	7	(	(	PUNCT
ejpam-6571	185	8	σ1	σ1	NOUN
ejpam-6571	185	9	,	,	PUNCT
ejpam-6571	185	10	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	185	11	)	)	PUNCT
ejpam-6571	185	12	is	be	AUX
ejpam-6571	185	13	(	(	PUNCT
ejpam-6571	185	14	σ1	σ1	NOUN
ejpam-6571	185	15	,	,	PUNCT
ejpam-6571	185	16	σ2)r	σ2)r	NOUN
ejpam-6571	185	17	-	-	PUNCT
ejpam-6571	185	18	open	open	ADJ
ejpam-6571	185	19	in	in	ADP
ejpam-6571	185	20	y	y	PROPN
ejpam-6571	185	21	and	and	CCONJ
ejpam-6571	185	22	by	by	ADP
ejpam-6571	185	23	(	(	PUNCT
ejpam-6571	185	24	3	3	NUM
ejpam-6571	185	25	)	)	PUNCT
ejpam-6571	185	26	,	,	PUNCT
ejpam-6571	185	27	f+((σ1	f+((σ1	NOUN
ejpam-6571	185	28	,	,	PUNCT
ejpam-6571	185	29	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	185	30	)	)	PUNCT
ejpam-6571	185	31	)	)	PUNCT
ejpam-6571	185	32	is	be	AUX
ejpam-6571	185	33	semi	semi	ADJ
ejpam-6571	185	34	-	-	ADJ
ejpam-6571	185	35	i	i	PRON
ejpam-6571	185	36	⋆-open	⋆-open	VERB
ejpam-6571	185	37	in	in	ADP
ejpam-6571	185	38	x	x	SYM
ejpam-6571	185	39	and	and	CCONJ
ejpam-6571	185	40	x	x	SYM
ejpam-6571	185	41	∈	∈	NOUN
ejpam-6571	185	42	sint⋆(f+((σ1	sint⋆(f+((σ1	NOUN
ejpam-6571	185	43	,	,	PUNCT
ejpam-6571	185	44	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	185	45	)	)	PUNCT
ejpam-6571	185	46	)	)	PUNCT
ejpam-6571	185	47	)	)	PUNCT
ejpam-6571	185	48	.	.	PUNCT
ejpam-6571	186	1	thus	thus	ADV
ejpam-6571	186	2	,	,	PUNCT
ejpam-6571	186	3	f+(v	f+(v	PROPN
ejpam-6571	186	4	)	)	PUNCT
ejpam-6571	186	5	⊆	⊆	NUM
ejpam-6571	186	6	sint⋆(f+((σ1	sint⋆(f+((σ1	NUM
ejpam-6571	186	7	,	,	PUNCT
ejpam-6571	186	8	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	186	9	)	)	PUNCT
ejpam-6571	186	10	)	)	PUNCT
ejpam-6571	186	11	)	)	PUNCT
ejpam-6571	186	12	.	.	PUNCT
ejpam-6571	187	1	(	(	PUNCT
ejpam-6571	187	2	4	4	X
ejpam-6571	187	3	)	)	PUNCT
ejpam-6571	187	4	⇒	⇒	NOUN
ejpam-6571	187	5	(	(	PUNCT
ejpam-6571	187	6	5	5	NUM
ejpam-6571	187	7	):	):	PUNCT
ejpam-6571	187	8	let	let	VERB
ejpam-6571	187	9	b	b	X
ejpam-6571	187	10	be	be	AUX
ejpam-6571	187	11	any	any	DET
ejpam-6571	187	12	subset	subset	NOUN
ejpam-6571	187	13	of	of	ADP
ejpam-6571	187	14	y	y	PROPN
ejpam-6571	187	15	.	.	PUNCT
ejpam-6571	188	1	then	then	ADV
ejpam-6571	188	2	,	,	PUNCT
ejpam-6571	188	3	we	we	PRON
ejpam-6571	188	4	have	have	AUX
ejpam-6571	188	5	y	y	NOUN
ejpam-6571	188	6	−	−	VERB
ejpam-6571	188	7	σ1σ2	σ1σ2	NOUN
ejpam-6571	188	8	-	-	PUNCT
ejpam-6571	188	9	cl(b	cl(b	NOUN
ejpam-6571	188	10	)	)	PUNCT
ejpam-6571	188	11	is	be	AUX
ejpam-6571	188	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	188	13	-	-	ADJ
ejpam-6571	188	14	open	open	ADJ
ejpam-6571	188	15	in	in	ADP
ejpam-6571	188	16	y	y	PROPN
ejpam-6571	188	17	.	.	PUNCT
ejpam-6571	189	1	thus	thus	ADV
ejpam-6571	189	2	by	by	ADP
ejpam-6571	189	3	(	(	PUNCT
ejpam-6571	189	4	4	4	NUM
ejpam-6571	189	5	)	)	PUNCT
ejpam-6571	189	6	and	and	CCONJ
ejpam-6571	189	7	lemma	lemma	PROPN
ejpam-6571	189	8	2	2	NUM
ejpam-6571	189	9	,	,	PUNCT
ejpam-6571	189	10	we	we	PRON
ejpam-6571	189	11	have	have	VERB
ejpam-6571	189	12	x	x	NOUN
ejpam-6571	189	13	−	−	PUNCT
ejpam-6571	189	14	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6571	189	15	-	-	PUNCT
ejpam-6571	189	16	cl(b	cl(b	NOUN
ejpam-6571	189	17	)	)	PUNCT
ejpam-6571	189	18	)	)	PUNCT
ejpam-6571	190	1	=	=	PUNCT
ejpam-6571	191	1	f+(y	f+(y	NOUN
ejpam-6571	191	2	−	−	NUM
ejpam-6571	191	3	σ1σ2	σ1σ2	NUM
ejpam-6571	191	4	-	-	PUNCT
ejpam-6571	191	5	cl(b	cl(b	NOUN
ejpam-6571	191	6	)	)	PUNCT
ejpam-6571	191	7	)	)	PUNCT
ejpam-6571	192	1	⊆	⊆	NUM
ejpam-6571	192	2	sint⋆(f+((σ1	sint⋆(f+((σ1	NOUN
ejpam-6571	192	3	,	,	PUNCT
ejpam-6571	192	4	σ2)-scl(y	σ2)-scl(y	NOUN
ejpam-6571	192	5	−	−	NOUN
ejpam-6571	192	6	σ1σ2	σ1σ2	NOUN
ejpam-6571	192	7	-	-	NOUN
ejpam-6571	192	8	cl(b	cl(b	NOUN
ejpam-6571	192	9	)	)	PUNCT
ejpam-6571	192	10	)	)	PUNCT
ejpam-6571	192	11	)	)	PUNCT
ejpam-6571	192	12	)	)	PUNCT
ejpam-6571	193	1	=	=	PUNCT
ejpam-6571	193	2	sint⋆(x	sint⋆(x	NOUN
ejpam-6571	193	3	−	−	NOUN
ejpam-6571	193	4	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	193	5	-	-	PUNCT
ejpam-6571	193	6	cl(σ1σ1	cl(σ1σ1	VERB
ejpam-6571	193	7	-	-	PUNCT
ejpam-6571	193	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	193	9	-	-	PUNCT
ejpam-6571	193	10	cl(b	cl(b	NOUN
ejpam-6571	193	11	)	)	PUNCT
ejpam-6571	193	12	)	)	PUNCT
ejpam-6571	193	13	)	)	PUNCT
ejpam-6571	193	14	)	)	PUNCT
ejpam-6571	193	15	)	)	PUNCT
ejpam-6571	194	1	=	=	PUNCT
ejpam-6571	195	1	x	x	X
ejpam-6571	195	2	−	−	PRON
ejpam-6571	195	3	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	195	4	-	-	PUNCT
ejpam-6571	195	5	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	195	6	-	-	PUNCT
ejpam-6571	195	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	195	8	-	-	PUNCT
ejpam-6571	195	9	cl(b	cl(b	NOUN
ejpam-6571	195	10	)	)	PUNCT
ejpam-6571	195	11	)	)	PUNCT
ejpam-6571	195	12	)	)	PUNCT
ejpam-6571	195	13	)	)	PUNCT
ejpam-6571	195	14	)	)	PUNCT
ejpam-6571	195	15	and	and	CCONJ
ejpam-6571	195	16	hence	hence	ADV
ejpam-6571	195	17	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	ADV
ejpam-6571	195	18	-	-	PUNCT
ejpam-6571	195	19	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	195	20	-	-	PUNCT
ejpam-6571	195	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	195	22	-	-	PUNCT
ejpam-6571	195	23	cl(b	cl(b	NOUN
ejpam-6571	195	24	)	)	PUNCT
ejpam-6571	195	25	)	)	PUNCT
ejpam-6571	195	26	)	)	PUNCT
ejpam-6571	195	27	)	)	PUNCT
ejpam-6571	195	28	)	)	PUNCT
ejpam-6571	196	1	⊆	⊆	X
ejpam-6571	196	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6571	196	3	-	-	PUNCT
ejpam-6571	196	4	cl(b	cl(b	NOUN
ejpam-6571	196	5	)	)	PUNCT
ejpam-6571	196	6	)	)	PUNCT
ejpam-6571	196	7	.	.	PUNCT
ejpam-6571	197	1	(	(	PUNCT
ejpam-6571	197	2	5	5	X
ejpam-6571	197	3	)	)	PUNCT
ejpam-6571	197	4	⇒	⇒	NOUN
ejpam-6571	197	5	(	(	PUNCT
ejpam-6571	197	6	6	6	NUM
ejpam-6571	197	7	):	):	PUNCT
ejpam-6571	197	8	let	let	VERB
ejpam-6571	197	9	v	v	PART
ejpam-6571	197	10	be	be	AUX
ejpam-6571	197	11	any	any	DET
ejpam-6571	197	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	197	13	-	-	ADJ
ejpam-6571	197	14	open	open	ADJ
ejpam-6571	197	15	set	set	NOUN
ejpam-6571	197	16	of	of	ADP
ejpam-6571	197	17	y	y	PROPN
ejpam-6571	197	18	.	.	PUNCT
ejpam-6571	198	1	then	then	ADV
ejpam-6571	198	2	,	,	PUNCT
ejpam-6571	198	3	y	y	PROPN
ejpam-6571	198	4	−	−	PROPN
ejpam-6571	198	5	v	v	NOUN
ejpam-6571	198	6	is	be	AUX
ejpam-6571	198	7	σ1σ2	σ1σ2	NOUN
ejpam-6571	198	8	-	-	ADJ
ejpam-6571	198	9	closed	closed	ADJ
ejpam-6571	198	10	in	in	ADP
ejpam-6571	198	11	y	y	PROPN
ejpam-6571	198	12	.	.	PUNCT
ejpam-6571	199	1	by	by	ADP
ejpam-6571	199	2	(	(	PUNCT
ejpam-6571	199	3	5	5	NUM
ejpam-6571	199	4	)	)	PUNCT
ejpam-6571	199	5	and	and	CCONJ
ejpam-6571	199	6	lemma	lemma	PROPN
ejpam-6571	199	7	3	3	NUM
ejpam-6571	199	8	,	,	PUNCT
ejpam-6571	199	9	int⋆(cl⋆(f−(σ1σ2	int⋆(cl⋆(f−(σ1σ2	NUM
ejpam-6571	199	10	-	-	PUNCT
ejpam-6571	199	11	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	199	12	-	-	PUNCT
ejpam-6571	199	13	int(y	int(y	PROPN
ejpam-6571	199	14	−v	−v	NOUN
ejpam-6571	199	15	)	)	PUNCT
ejpam-6571	199	16	)	)	PUNCT
ejpam-6571	199	17	)	)	PUNCT
ejpam-6571	199	18	)	)	PUNCT
ejpam-6571	199	19	)	)	PUNCT
ejpam-6571	200	1	⊆	⊆	NUM
ejpam-6571	200	2	f−(y	f−(y	NOUN
ejpam-6571	200	3	−v	−v	NOUN
ejpam-6571	200	4	)	)	PUNCT
ejpam-6571	200	5	=	=	SYM
ejpam-6571	200	6	x−f+(v	x−f+(v	PROPN
ejpam-6571	200	7	)	)	PUNCT
ejpam-6571	200	8	.	.	PUNCT
ejpam-6571	201	1	moreover	moreover	ADV
ejpam-6571	201	2	,	,	PUNCT
ejpam-6571	201	3	we	we	PRON
ejpam-6571	201	4	have	have	VERB
ejpam-6571	201	5	int⋆(cl⋆(f−(σ1σ2	int⋆(cl⋆(f−(σ1σ2	VERB
ejpam-6571	201	6	-	-	PUNCT
ejpam-6571	201	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	201	8	-	-	PUNCT
ejpam-6571	201	9	int(y	int(y	PROPN
ejpam-6571	201	10	−	−	PROPN
ejpam-6571	201	11	v	v	NOUN
ejpam-6571	201	12	)	)	PUNCT
ejpam-6571	201	13	)	)	PUNCT
ejpam-6571	201	14	)	)	PUNCT
ejpam-6571	201	15	)	)	PUNCT
ejpam-6571	201	16	)	)	PUNCT
ejpam-6571	202	1	=	=	NOUN
ejpam-6571	202	2	int⋆(cl⋆(f−(y	int⋆(cl⋆(f−(y	NOUN
ejpam-6571	202	3	−	−	ADP
ejpam-6571	202	4	σ1σ2	σ1σ2	SYM
ejpam-6571	202	5	-	-	PUNCT
ejpam-6571	202	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	202	7	-	-	PUNCT
ejpam-6571	202	8	cl(v	cl(v	NOUN
ejpam-6571	202	9	)	)	PUNCT
ejpam-6571	202	10	)	)	PUNCT
ejpam-6571	202	11	)	)	PUNCT
ejpam-6571	202	12	)	)	PUNCT
ejpam-6571	202	13	)	)	PUNCT
ejpam-6571	202	14	m.	m.	NOUN
ejpam-6571	202	15	thongmoon	thongmoon	NOUN
ejpam-6571	202	16	,	,	PUNCT
ejpam-6571	202	17	a.	a.	PROPN
ejpam-6571	202	18	sama	sama	PROPN
ejpam-6571	202	19	-	-	PUNCT
ejpam-6571	202	20	ae	ae	PROPN
ejpam-6571	202	21	,	,	PUNCT
ejpam-6571	202	22	c.	c.	PROPN
ejpam-6571	202	23	boonpok	boonpok	PROPN
ejpam-6571	202	24	/	/	SYM
ejpam-6571	202	25	eur	eur	PROPN
ejpam-6571	202	26	.	.	PUNCT
ejpam-6571	203	1	j.	j.	PROPN
ejpam-6571	203	2	pure	pure	PROPN
ejpam-6571	203	3	appl	appl	PROPN
ejpam-6571	203	4	.	.	PROPN
ejpam-6571	203	5	math	math	PROPN
ejpam-6571	203	6	,	,	PUNCT
ejpam-6571	203	7	18	18	NUM
ejpam-6571	203	8	(	(	PUNCT
ejpam-6571	203	9	3	3	NUM
ejpam-6571	203	10	)	)	PUNCT
ejpam-6571	203	11	(	(	PUNCT
ejpam-6571	203	12	2025	2025	NUM
ejpam-6571	203	13	)	)	PUNCT
ejpam-6571	203	14	,	,	PUNCT
ejpam-6571	203	15	6571	6571	NUM
ejpam-6571	203	16	7	7	NUM
ejpam-6571	203	17	of	of	ADP
ejpam-6571	203	18	15	15	NUM
ejpam-6571	203	19	=	=	NOUN
ejpam-6571	203	20	int⋆(cl⋆(x	int⋆(cl⋆(x	PRON
ejpam-6571	203	21	−	−	NOUN
ejpam-6571	203	22	f+((σ1	f+((σ1	ADJ
ejpam-6571	203	23	,	,	PUNCT
ejpam-6571	203	24	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	203	25	)	)	PUNCT
ejpam-6571	203	26	)	)	PUNCT
ejpam-6571	203	27	)	)	PUNCT
ejpam-6571	203	28	)	)	PUNCT
ejpam-6571	204	1	=	=	PUNCT
ejpam-6571	204	2	x	x	X
ejpam-6571	204	3	−	−	PUNCT
ejpam-6571	204	4	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	204	5	,	,	PUNCT
ejpam-6571	204	6	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	204	7	)	)	PUNCT
ejpam-6571	204	8	)	)	PUNCT
ejpam-6571	204	9	)	)	PUNCT
ejpam-6571	204	10	)	)	PUNCT
ejpam-6571	204	11	.	.	PUNCT
ejpam-6571	205	1	thus	thus	ADV
ejpam-6571	205	2	,	,	PUNCT
ejpam-6571	205	3	f+(v	f+(v	PROPN
ejpam-6571	205	4	)	)	PUNCT
ejpam-6571	205	5	⊆	⊆	NUM
ejpam-6571	205	6	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	205	7	,	,	PUNCT
ejpam-6571	205	8	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	205	9	)	)	PUNCT
ejpam-6571	205	10	)	)	PUNCT
ejpam-6571	205	11	)	)	PUNCT
ejpam-6571	205	12	)	)	PUNCT
ejpam-6571	205	13	.	.	PUNCT
ejpam-6571	206	1	(	(	PUNCT
ejpam-6571	206	2	6	6	X
ejpam-6571	206	3	)	)	PUNCT
ejpam-6571	206	4	⇒	⇒	NOUN
ejpam-6571	206	5	(	(	PUNCT
ejpam-6571	206	6	1	1	NUM
ejpam-6571	206	7	):	):	PUNCT
ejpam-6571	206	8	let	let	VERB
ejpam-6571	206	9	x	x	PUNCT
ejpam-6571	206	10	∈	∈	PROPN
ejpam-6571	206	11	x	x	X
ejpam-6571	206	12	and	and	CCONJ
ejpam-6571	206	13	v	v	X
ejpam-6571	206	14	be	be	AUX
ejpam-6571	206	15	any	any	DET
ejpam-6571	206	16	σ1σ2	σ1σ2	NOUN
ejpam-6571	206	17	-	-	ADJ
ejpam-6571	206	18	open	open	ADJ
ejpam-6571	206	19	set	set	NOUN
ejpam-6571	206	20	of	of	ADP
ejpam-6571	206	21	y	y	PRON
ejpam-6571	206	22	such	such	ADJ
ejpam-6571	206	23	that	that	SCONJ
ejpam-6571	206	24	f	f	PROPN
ejpam-6571	206	25	(	(	PUNCT
ejpam-6571	206	26	x	x	X
ejpam-6571	206	27	)	)	PUNCT
ejpam-6571	206	28	⊆	⊆	NUM
ejpam-6571	206	29	v	v	NOUN
ejpam-6571	206	30	.	.	PUNCT
ejpam-6571	207	1	by	by	ADP
ejpam-6571	207	2	(	(	PUNCT
ejpam-6571	207	3	6	6	NUM
ejpam-6571	207	4	)	)	PUNCT
ejpam-6571	207	5	,	,	PUNCT
ejpam-6571	207	6	we	we	PRON
ejpam-6571	207	7	have	have	VERB
ejpam-6571	207	8	x	x	X
ejpam-6571	207	9	∈	∈	NOUN
ejpam-6571	207	10	f+(v	f+(v	NOUN
ejpam-6571	207	11	)	)	PUNCT
ejpam-6571	208	1	⊆	⊆	NUM
ejpam-6571	208	2	cl⋆(int⋆(f+((σ1	cl⋆(int⋆(f+((σ1	NOUN
ejpam-6571	208	3	,	,	PUNCT
ejpam-6571	208	4	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	208	5	)	)	PUNCT
ejpam-6571	208	6	)	)	PUNCT
ejpam-6571	208	7	)	)	PUNCT
ejpam-6571	208	8	)	)	PUNCT
ejpam-6571	208	9	and	and	CCONJ
ejpam-6571	208	10	by	by	ADP
ejpam-6571	208	11	lemma	lemma	PROPN
ejpam-6571	208	12	3	3	NUM
ejpam-6571	208	13	,	,	PUNCT
ejpam-6571	208	14	x	x	SYM
ejpam-6571	208	15	∈	∈	NOUN
ejpam-6571	208	16	f+(v	f+(v	NOUN
ejpam-6571	208	17	)	)	PUNCT
ejpam-6571	208	18	⊆	⊆	NUM
ejpam-6571	208	19	sint⋆(f+((σ1	sint⋆(f+((σ1	NUM
ejpam-6571	208	20	,	,	PUNCT
ejpam-6571	208	21	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	208	22	)	)	PUNCT
ejpam-6571	208	23	)	)	PUNCT
ejpam-6571	208	24	)	)	PUNCT
ejpam-6571	208	25	.	.	PUNCT
ejpam-6571	209	1	put	put	VERB
ejpam-6571	209	2	u	u	PRON
ejpam-6571	209	3	=	=	NOUN
ejpam-6571	209	4	sint⋆(f+((σ1	sint⋆(f+((σ1	X
ejpam-6571	209	5	,	,	PUNCT
ejpam-6571	209	6	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	209	7	)	)	PUNCT
ejpam-6571	209	8	)	)	PUNCT
ejpam-6571	209	9	)	)	PUNCT
ejpam-6571	209	10	.	.	PUNCT
ejpam-6571	210	1	then	then	ADV
ejpam-6571	210	2	,	,	PUNCT
ejpam-6571	210	3	u	u	NOUN
ejpam-6571	210	4	is	be	AUX
ejpam-6571	210	5	a	a	DET
ejpam-6571	210	6	semi	semi	ADJ
ejpam-6571	210	7	-	-	ADJ
ejpam-6571	210	8	i	i	PRON
ejpam-6571	210	9	⋆-open	⋆-open	VERB
ejpam-6571	210	10	set	set	VERB
ejpam-6571	210	11	of	of	ADP
ejpam-6571	210	12	x	x	PUNCT
ejpam-6571	210	13	containing	contain	VERB
ejpam-6571	210	14	x	x	PUNCT
ejpam-6571	210	15	such	such	ADJ
ejpam-6571	210	16	that	that	SCONJ
ejpam-6571	210	17	f	f	PROPN
ejpam-6571	210	18	(	(	PUNCT
ejpam-6571	210	19	u	u	NOUN
ejpam-6571	210	20	)	)	PUNCT
ejpam-6571	210	21	⊆	⊆	NUM
ejpam-6571	210	22	(	(	PUNCT
ejpam-6571	210	23	σ1	σ1	PROPN
ejpam-6571	210	24	,	,	PUNCT
ejpam-6571	210	25	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	210	26	)	)	PUNCT
ejpam-6571	210	27	.	.	PUNCT
ejpam-6571	211	1	this	this	PRON
ejpam-6571	211	2	shows	show	VERB
ejpam-6571	211	3	that	that	SCONJ
ejpam-6571	211	4	f	f	PROPN
ejpam-6571	211	5	is	be	AUX
ejpam-6571	211	6	upper	upper	ADJ
ejpam-6571	211	7	almost	almost	ADV
ejpam-6571	211	8	quasi	quasi	ADJ
ejpam-6571	211	9	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	211	10	,	,	PUNCT
ejpam-6571	211	11	σ2)continuous	σ2)continuous	ADJ
ejpam-6571	211	12	.	.	PUNCT
ejpam-6571	212	1	theorem	theorem	NOUN
ejpam-6571	212	2	4	4	NUM
ejpam-6571	212	3	.	.	X
ejpam-6571	212	4	for	for	ADP
ejpam-6571	212	5	a	a	DET
ejpam-6571	212	6	multifunction	multifunction	NOUN
ejpam-6571	213	1	f	f	NOUN
ejpam-6571	213	2	:	:	PUNCT
ejpam-6571	213	3	(	(	PUNCT
ejpam-6571	213	4	x	x	X
ejpam-6571	213	5	,	,	PUNCT
ejpam-6571	213	6	τ	τ	PROPN
ejpam-6571	213	7	,	,	PUNCT
ejpam-6571	213	8	i	i	NOUN
ejpam-6571	213	9	)	)	PUNCT
ejpam-6571	213	10	→	→	PUNCT
ejpam-6571	213	11	(	(	PUNCT
ejpam-6571	213	12	y	y	PROPN
ejpam-6571	213	13	,	,	PUNCT
ejpam-6571	213	14	σ1	σ1	PROPN
ejpam-6571	213	15	,	,	PUNCT
ejpam-6571	213	16	σ2	σ2	NOUN
ejpam-6571	213	17	)	)	PUNCT
ejpam-6571	213	18	,	,	PUNCT
ejpam-6571	213	19	the	the	DET
ejpam-6571	213	20	following	follow	VERB
ejpam-6571	213	21	properties	property	NOUN
ejpam-6571	213	22	are	be	AUX
ejpam-6571	213	23	equivalent	equivalent	ADJ
ejpam-6571	213	24	:	:	PUNCT
ejpam-6571	213	25	(	(	PUNCT
ejpam-6571	213	26	1	1	X
ejpam-6571	213	27	)	)	PUNCT
ejpam-6571	213	28	f	f	PROPN
ejpam-6571	213	29	is	be	AUX
ejpam-6571	213	30	lower	low	ADJ
ejpam-6571	213	31	almost	almost	ADV
ejpam-6571	213	32	quasi	quasi	ADJ
ejpam-6571	213	33	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	213	34	,	,	PUNCT
ejpam-6571	213	35	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	213	36	;	;	PUNCT
ejpam-6571	213	37	(	(	PUNCT
ejpam-6571	213	38	2	2	X
ejpam-6571	213	39	)	)	PUNCT
ejpam-6571	213	40	for	for	ADP
ejpam-6571	213	41	each	each	DET
ejpam-6571	213	42	x	x	SYM
ejpam-6571	213	43	∈	∈	PROPN
ejpam-6571	213	44	x	x	X
ejpam-6571	213	45	and	and	CCONJ
ejpam-6571	213	46	every	every	DET
ejpam-6571	213	47	σ1σ2	σ1σ2	NUM
ejpam-6571	213	48	-	-	ADJ
ejpam-6571	213	49	open	open	ADJ
ejpam-6571	213	50	set	set	NOUN
ejpam-6571	213	51	v	v	NOUN
ejpam-6571	213	52	of	of	ADP
ejpam-6571	213	53	y	y	PRON
ejpam-6571	213	54	such	such	ADJ
ejpam-6571	213	55	that	that	SCONJ
ejpam-6571	213	56	f	f	PROPN
ejpam-6571	213	57	(	(	PUNCT
ejpam-6571	213	58	x)∩v	x)∩v	PROPN
ejpam-6571	213	59	̸=	̸=	PROPN
ejpam-6571	213	60	∅	∅	NOUN
ejpam-6571	213	61	,	,	PUNCT
ejpam-6571	213	62	there	there	PRON
ejpam-6571	213	63	exists	exist	VERB
ejpam-6571	213	64	a	a	DET
ejpam-6571	213	65	semi	semi	NOUN
ejpam-6571	213	66	-	-	ADJ
ejpam-6571	213	67	i	i	PRON
ejpam-6571	213	68	⋆-open	⋆-open	VERB
ejpam-6571	213	69	set	set	VERB
ejpam-6571	213	70	u	u	NOUN
ejpam-6571	213	71	of	of	ADP
ejpam-6571	213	72	x	x	PUNCT
ejpam-6571	213	73	containing	contain	VERB
ejpam-6571	213	74	x	x	PUNCT
ejpam-6571	213	75	such	such	ADJ
ejpam-6571	213	76	that	that	PRON
ejpam-6571	213	77	(	(	PUNCT
ejpam-6571	213	78	σ1	σ1	PROPN
ejpam-6571	213	79	,	,	PUNCT
ejpam-6571	213	80	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	213	81	)	)	PUNCT
ejpam-6571	213	82	∩	∩	PROPN
ejpam-6571	213	83	f	f	X
ejpam-6571	213	84	(	(	PUNCT
ejpam-6571	213	85	z	z	NOUN
ejpam-6571	213	86	)	)	PUNCT
ejpam-6571	213	87	̸=	̸=	NOUN
ejpam-6571	213	88	∅	∅	NOUN
ejpam-6571	213	89	for	for	ADP
ejpam-6571	213	90	every	every	DET
ejpam-6571	213	91	z	z	NOUN
ejpam-6571	213	92	∈	∈	PROPN
ejpam-6571	213	93	u	u	NOUN
ejpam-6571	213	94	;	;	PUNCT
ejpam-6571	213	95	(	(	PUNCT
ejpam-6571	213	96	3	3	X
ejpam-6571	213	97	)	)	PUNCT
ejpam-6571	213	98	f−(v	f−(v	NOUN
ejpam-6571	213	99	)	)	PUNCT
ejpam-6571	213	100	is	be	AUX
ejpam-6571	213	101	semi	semi	ADJ
ejpam-6571	213	102	-	-	ADJ
ejpam-6571	213	103	i	i	PRON
ejpam-6571	213	104	⋆-open	⋆-open	VERB
ejpam-6571	213	105	in	in	ADP
ejpam-6571	213	106	x	x	PUNCT
ejpam-6571	213	107	for	for	ADP
ejpam-6571	213	108	every	every	DET
ejpam-6571	213	109	(	(	PUNCT
ejpam-6571	213	110	σ1	σ1	PROPN
ejpam-6571	213	111	,	,	PUNCT
ejpam-6571	213	112	σ2)r	σ2)r	NOUN
ejpam-6571	213	113	-	-	PUNCT
ejpam-6571	213	114	open	open	ADJ
ejpam-6571	213	115	set	set	VERB
ejpam-6571	213	116	v	v	NOUN
ejpam-6571	213	117	of	of	ADP
ejpam-6571	213	118	y	y	PROPN
ejpam-6571	213	119	;	;	PUNCT
ejpam-6571	213	120	(	(	PUNCT
ejpam-6571	213	121	4	4	X
ejpam-6571	213	122	)	)	PUNCT
ejpam-6571	213	123	f−(v	f−(v	ADJ
ejpam-6571	213	124	)	)	PUNCT
ejpam-6571	213	125	⊆	⊆	NUM
ejpam-6571	213	126	sint⋆(f−((σ1	sint⋆(f−((σ1	NOUN
ejpam-6571	213	127	,	,	PUNCT
ejpam-6571	213	128	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	213	129	)	)	PUNCT
ejpam-6571	213	130	)	)	PUNCT
ejpam-6571	213	131	)	)	PUNCT
ejpam-6571	214	1	for	for	ADP
ejpam-6571	214	2	every	every	DET
ejpam-6571	214	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	214	4	-	-	ADJ
ejpam-6571	214	5	open	open	ADJ
ejpam-6571	214	6	set	set	NOUN
ejpam-6571	214	7	v	v	NOUN
ejpam-6571	214	8	of	of	ADP
ejpam-6571	214	9	y	y	PROPN
ejpam-6571	214	10	;	;	PUNCT
ejpam-6571	214	11	(	(	PUNCT
ejpam-6571	214	12	5	5	X
ejpam-6571	214	13	)	)	PUNCT
ejpam-6571	214	14	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	214	15	-	-	PUNCT
ejpam-6571	214	16	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	214	17	-	-	PUNCT
ejpam-6571	214	18	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	214	19	-	-	PUNCT
ejpam-6571	214	20	cl(b	cl(b	NOUN
ejpam-6571	214	21	)	)	PUNCT
ejpam-6571	214	22	)	)	PUNCT
ejpam-6571	214	23	)	)	PUNCT
ejpam-6571	214	24	)	)	PUNCT
ejpam-6571	214	25	)	)	PUNCT
ejpam-6571	214	26	⊆	⊆	X
ejpam-6571	214	27	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	214	28	-	-	PUNCT
ejpam-6571	214	29	cl(b	cl(b	NOUN
ejpam-6571	214	30	)	)	PUNCT
ejpam-6571	214	31	)	)	PUNCT
ejpam-6571	214	32	for	for	ADP
ejpam-6571	214	33	every	every	DET
ejpam-6571	214	34	subset	subset	NOUN
ejpam-6571	214	35	b	b	PROPN
ejpam-6571	214	36	of	of	ADP
ejpam-6571	214	37	y	y	PROPN
ejpam-6571	214	38	;	;	PUNCT
ejpam-6571	214	39	(	(	PUNCT
ejpam-6571	214	40	6	6	X
ejpam-6571	214	41	)	)	PUNCT
ejpam-6571	214	42	f−(v	f−(v	NOUN
ejpam-6571	214	43	)	)	PUNCT
ejpam-6571	214	44	⊆	⊆	NUM
ejpam-6571	214	45	cl⋆(int⋆(f−((σ1	cl⋆(int⋆(f−((σ1	NUM
ejpam-6571	214	46	,	,	PUNCT
ejpam-6571	214	47	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6571	214	48	)	)	PUNCT
ejpam-6571	214	49	)	)	PUNCT
ejpam-6571	214	50	)	)	PUNCT
ejpam-6571	214	51	)	)	PUNCT
ejpam-6571	214	52	for	for	ADP
ejpam-6571	214	53	every	every	DET
ejpam-6571	214	54	σ1σ2	σ1σ2	NOUN
ejpam-6571	214	55	-	-	ADJ
ejpam-6571	214	56	open	open	ADJ
ejpam-6571	214	57	set	set	NOUN
ejpam-6571	214	58	v	v	NOUN
ejpam-6571	214	59	of	of	ADP
ejpam-6571	214	60	y	y	PROPN
ejpam-6571	214	61	.	.	PUNCT
ejpam-6571	215	1	proof	proof	NOUN
ejpam-6571	215	2	.	.	PUNCT
ejpam-6571	216	1	the	the	DET
ejpam-6571	216	2	proof	proof	NOUN
ejpam-6571	216	3	is	be	AUX
ejpam-6571	216	4	similar	similar	ADJ
ejpam-6571	216	5	to	to	ADP
ejpam-6571	216	6	that	that	PRON
ejpam-6571	216	7	of	of	ADP
ejpam-6571	216	8	theorem	theorem	ADJ
ejpam-6571	216	9	3	3	NUM
ejpam-6571	216	10	.	.	PUNCT
ejpam-6571	216	11	theorem	theorem	NOUN
ejpam-6571	216	12	5	5	NUM
ejpam-6571	216	13	.	.	X
ejpam-6571	216	14	for	for	ADP
ejpam-6571	216	15	a	a	DET
ejpam-6571	216	16	multifunction	multifunction	NOUN
ejpam-6571	216	17	f	f	NOUN
ejpam-6571	216	18	:	:	PUNCT
ejpam-6571	216	19	(	(	PUNCT
ejpam-6571	216	20	x	x	X
ejpam-6571	216	21	,	,	PUNCT
ejpam-6571	216	22	τ	τ	PROPN
ejpam-6571	216	23	,	,	PUNCT
ejpam-6571	216	24	i	i	NOUN
ejpam-6571	216	25	)	)	PUNCT
ejpam-6571	216	26	→	→	PUNCT
ejpam-6571	216	27	(	(	PUNCT
ejpam-6571	216	28	y	y	PROPN
ejpam-6571	216	29	,	,	PUNCT
ejpam-6571	216	30	σ1	σ1	PROPN
ejpam-6571	216	31	,	,	PUNCT
ejpam-6571	216	32	σ2	σ2	NOUN
ejpam-6571	216	33	)	)	PUNCT
ejpam-6571	216	34	,	,	PUNCT
ejpam-6571	216	35	the	the	DET
ejpam-6571	216	36	following	follow	VERB
ejpam-6571	216	37	properties	property	NOUN
ejpam-6571	216	38	are	be	AUX
ejpam-6571	216	39	equivalent	equivalent	ADJ
ejpam-6571	216	40	:	:	PUNCT
ejpam-6571	216	41	(	(	PUNCT
ejpam-6571	216	42	1	1	X
ejpam-6571	216	43	)	)	PUNCT
ejpam-6571	216	44	f	f	PROPN
ejpam-6571	216	45	is	be	AUX
ejpam-6571	216	46	upper	upper	ADJ
ejpam-6571	216	47	almost	almost	ADV
ejpam-6571	216	48	quasi	quasi	ADJ
ejpam-6571	216	49	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	216	50	,	,	PUNCT
ejpam-6571	216	51	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	216	52	;	;	PUNCT
ejpam-6571	216	53	(	(	PUNCT
ejpam-6571	216	54	2	2	NUM
ejpam-6571	216	55	)	)	PUNCT
ejpam-6571	216	56	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	216	57	)	)	PUNCT
ejpam-6571	216	58	)	)	PUNCT
ejpam-6571	217	1	⊆	⊆	X
ejpam-6571	217	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	217	3	-	-	PUNCT
ejpam-6571	217	4	cl(v	cl(v	NOUN
ejpam-6571	217	5	)	)	PUNCT
ejpam-6571	217	6	)	)	PUNCT
ejpam-6571	217	7	for	for	ADP
ejpam-6571	217	8	every	every	DET
ejpam-6571	217	9	(	(	PUNCT
ejpam-6571	217	10	σ1	σ1	PROPN
ejpam-6571	217	11	,	,	PUNCT
ejpam-6571	217	12	σ2)β	σ2)β	NOUN
ejpam-6571	217	13	-	-	PUNCT
ejpam-6571	217	14	open	open	NOUN
ejpam-6571	217	15	set	set	NOUN
ejpam-6571	217	16	v	v	NOUN
ejpam-6571	217	17	of	of	ADP
ejpam-6571	217	18	y	y	PROPN
ejpam-6571	217	19	;	;	PUNCT
ejpam-6571	217	20	(	(	PUNCT
ejpam-6571	217	21	3	3	X
ejpam-6571	217	22	)	)	PUNCT
ejpam-6571	217	23	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	217	24	)	)	PUNCT
ejpam-6571	217	25	)	)	PUNCT
ejpam-6571	218	1	⊆	⊆	X
ejpam-6571	218	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	218	3	-	-	PUNCT
ejpam-6571	218	4	cl(v	cl(v	NOUN
ejpam-6571	218	5	)	)	PUNCT
ejpam-6571	218	6	)	)	PUNCT
ejpam-6571	218	7	for	for	ADP
ejpam-6571	218	8	every	every	DET
ejpam-6571	218	9	(	(	PUNCT
ejpam-6571	218	10	σ1	σ1	PROPN
ejpam-6571	218	11	,	,	PUNCT
ejpam-6571	218	12	σ2)s	σ2)s	NOUN
ejpam-6571	218	13	-	-	PUNCT
ejpam-6571	218	14	open	open	NOUN
ejpam-6571	218	15	set	set	NOUN
ejpam-6571	218	16	v	v	NOUN
ejpam-6571	218	17	of	of	ADP
ejpam-6571	218	18	y	y	PROPN
ejpam-6571	218	19	;	;	PUNCT
ejpam-6571	218	20	(	(	PUNCT
ejpam-6571	218	21	4	4	X
ejpam-6571	218	22	)	)	PUNCT
ejpam-6571	218	23	f+(v	f+(v	NOUN
ejpam-6571	218	24	)	)	PUNCT
ejpam-6571	219	1	⊆	⊆	X
ejpam-6571	219	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NUM
ejpam-6571	219	3	-	-	PUNCT
ejpam-6571	219	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	219	5	-	-	PUNCT
ejpam-6571	219	6	cl(v	cl(v	NOUN
ejpam-6571	219	7	)	)	PUNCT
ejpam-6571	219	8	)	)	PUNCT
ejpam-6571	219	9	)	)	PUNCT
ejpam-6571	219	10	)	)	PUNCT
ejpam-6571	219	11	for	for	ADP
ejpam-6571	219	12	every	every	DET
ejpam-6571	219	13	(	(	PUNCT
ejpam-6571	219	14	σ1	σ1	PROPN
ejpam-6571	219	15	,	,	PUNCT
ejpam-6571	219	16	σ2)p	σ2)p	NOUN
ejpam-6571	219	17	-	-	PUNCT
ejpam-6571	219	18	open	open	NOUN
ejpam-6571	219	19	set	set	NOUN
ejpam-6571	219	20	v	v	NOUN
ejpam-6571	219	21	of	of	ADP
ejpam-6571	219	22	y	y	PROPN
ejpam-6571	219	23	.	.	PUNCT
ejpam-6571	220	1	proof	proof	NOUN
ejpam-6571	220	2	.	.	PUNCT
ejpam-6571	221	1	the	the	DET
ejpam-6571	221	2	proof	proof	NOUN
ejpam-6571	221	3	is	be	AUX
ejpam-6571	221	4	similar	similar	ADJ
ejpam-6571	221	5	to	to	ADP
ejpam-6571	221	6	that	that	PRON
ejpam-6571	221	7	of	of	ADP
ejpam-6571	221	8	theorem	theorem	ADJ
ejpam-6571	221	9	3	3	NUM
ejpam-6571	221	10	.	.	PUNCT
ejpam-6571	221	11	theorem	theorem	VERB
ejpam-6571	221	12	6	6	NUM
ejpam-6571	221	13	.	.	PUNCT
ejpam-6571	221	14	for	for	ADP
ejpam-6571	221	15	a	a	DET
ejpam-6571	221	16	multifunction	multifunction	NOUN
ejpam-6571	221	17	f	f	NOUN
ejpam-6571	221	18	:	:	PUNCT
ejpam-6571	221	19	(	(	PUNCT
ejpam-6571	221	20	x	x	X
ejpam-6571	221	21	,	,	PUNCT
ejpam-6571	221	22	τ	τ	PROPN
ejpam-6571	221	23	,	,	PUNCT
ejpam-6571	221	24	i	i	NOUN
ejpam-6571	221	25	)	)	PUNCT
ejpam-6571	221	26	→	→	PUNCT
ejpam-6571	221	27	(	(	PUNCT
ejpam-6571	221	28	y	y	PROPN
ejpam-6571	221	29	,	,	PUNCT
ejpam-6571	221	30	σ1	σ1	PROPN
ejpam-6571	221	31	,	,	PUNCT
ejpam-6571	221	32	σ2	σ2	NOUN
ejpam-6571	221	33	)	)	PUNCT
ejpam-6571	221	34	,	,	PUNCT
ejpam-6571	221	35	the	the	DET
ejpam-6571	221	36	following	follow	VERB
ejpam-6571	221	37	properties	property	NOUN
ejpam-6571	221	38	are	be	AUX
ejpam-6571	221	39	equivalent	equivalent	ADJ
ejpam-6571	221	40	:	:	PUNCT
ejpam-6571	221	41	m.	m.	NOUN
ejpam-6571	221	42	thongmoon	thongmoon	NOUN
ejpam-6571	221	43	,	,	PUNCT
ejpam-6571	221	44	a.	a.	PROPN
ejpam-6571	221	45	sama	sama	PROPN
ejpam-6571	221	46	-	-	PUNCT
ejpam-6571	221	47	ae	ae	PROPN
ejpam-6571	221	48	,	,	PUNCT
ejpam-6571	221	49	c.	c.	PROPN
ejpam-6571	221	50	boonpok	boonpok	PROPN
ejpam-6571	221	51	/	/	SYM
ejpam-6571	221	52	eur	eur	PROPN
ejpam-6571	221	53	.	.	PUNCT
ejpam-6571	222	1	j.	j.	PROPN
ejpam-6571	222	2	pure	pure	PROPN
ejpam-6571	222	3	appl	appl	PROPN
ejpam-6571	222	4	.	.	PROPN
ejpam-6571	222	5	math	math	PROPN
ejpam-6571	222	6	,	,	PUNCT
ejpam-6571	222	7	18	18	NUM
ejpam-6571	222	8	(	(	PUNCT
ejpam-6571	222	9	3	3	NUM
ejpam-6571	222	10	)	)	PUNCT
ejpam-6571	222	11	(	(	PUNCT
ejpam-6571	222	12	2025	2025	NUM
ejpam-6571	222	13	)	)	PUNCT
ejpam-6571	222	14	,	,	PUNCT
ejpam-6571	222	15	6571	6571	NUM
ejpam-6571	222	16	8	8	NUM
ejpam-6571	222	17	of	of	ADP
ejpam-6571	222	18	15	15	NUM
ejpam-6571	222	19	(	(	PUNCT
ejpam-6571	222	20	1	1	NUM
ejpam-6571	222	21	)	)	PUNCT
ejpam-6571	222	22	f	f	PROPN
ejpam-6571	222	23	is	be	AUX
ejpam-6571	222	24	lower	low	ADJ
ejpam-6571	222	25	almost	almost	ADV
ejpam-6571	222	26	quasi	quasi	ADJ
ejpam-6571	222	27	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	222	28	,	,	PUNCT
ejpam-6571	222	29	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	222	30	;	;	PUNCT
ejpam-6571	222	31	(	(	PUNCT
ejpam-6571	222	32	2	2	X
ejpam-6571	222	33	)	)	PUNCT
ejpam-6571	222	34	scl⋆(f+(v	scl⋆(f+(v	PROPN
ejpam-6571	222	35	)	)	PUNCT
ejpam-6571	222	36	)	)	PUNCT
ejpam-6571	223	1	⊆	⊆	NUM
ejpam-6571	223	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	223	3	-	-	PUNCT
ejpam-6571	223	4	cl(v	cl(v	NOUN
ejpam-6571	223	5	)	)	PUNCT
ejpam-6571	223	6	)	)	PUNCT
ejpam-6571	223	7	for	for	ADP
ejpam-6571	223	8	every	every	DET
ejpam-6571	223	9	(	(	PUNCT
ejpam-6571	223	10	σ1	σ1	PROPN
ejpam-6571	223	11	,	,	PUNCT
ejpam-6571	223	12	σ2)β	σ2)β	NOUN
ejpam-6571	223	13	-	-	PUNCT
ejpam-6571	223	14	open	open	NOUN
ejpam-6571	223	15	set	set	NOUN
ejpam-6571	223	16	v	v	NOUN
ejpam-6571	223	17	of	of	ADP
ejpam-6571	223	18	y	y	PROPN
ejpam-6571	223	19	;	;	PUNCT
ejpam-6571	223	20	(	(	PUNCT
ejpam-6571	223	21	3	3	X
ejpam-6571	223	22	)	)	PUNCT
ejpam-6571	223	23	scl⋆(f+(v	scl⋆(f+(v	PROPN
ejpam-6571	223	24	)	)	PUNCT
ejpam-6571	223	25	)	)	PUNCT
ejpam-6571	224	1	⊆	⊆	NUM
ejpam-6571	224	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	224	3	-	-	PUNCT
ejpam-6571	224	4	cl(v	cl(v	NOUN
ejpam-6571	224	5	)	)	PUNCT
ejpam-6571	224	6	)	)	PUNCT
ejpam-6571	224	7	for	for	SCONJ
ejpam-6571	224	8	every	every	DET
ejpam-6571	224	9	(	(	PUNCT
ejpam-6571	224	10	σ1	σ1	PROPN
ejpam-6571	224	11	,	,	PUNCT
ejpam-6571	224	12	σ2)s	σ2)s	NOUN
ejpam-6571	224	13	-	-	PUNCT
ejpam-6571	224	14	open	open	NOUN
ejpam-6571	224	15	set	set	NOUN
ejpam-6571	224	16	v	v	NOUN
ejpam-6571	224	17	of	of	ADP
ejpam-6571	224	18	y	y	PROPN
ejpam-6571	224	19	;	;	PUNCT
ejpam-6571	224	20	(	(	PUNCT
ejpam-6571	224	21	4	4	X
ejpam-6571	224	22	)	)	PUNCT
ejpam-6571	224	23	f−(v	f−(v	NOUN
ejpam-6571	224	24	)	)	PUNCT
ejpam-6571	224	25	⊆	⊆	NUM
ejpam-6571	224	26	sint⋆(f−(σ1σ2	sint⋆(f−(σ1σ2	NOUN
ejpam-6571	224	27	-	-	PUNCT
ejpam-6571	224	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	224	29	-	-	PUNCT
ejpam-6571	224	30	cl(v	cl(v	NOUN
ejpam-6571	224	31	)	)	PUNCT
ejpam-6571	224	32	)	)	PUNCT
ejpam-6571	224	33	)	)	PUNCT
ejpam-6571	224	34	)	)	PUNCT
ejpam-6571	224	35	for	for	ADP
ejpam-6571	224	36	every	every	DET
ejpam-6571	224	37	(	(	PUNCT
ejpam-6571	224	38	σ1	σ1	PROPN
ejpam-6571	224	39	,	,	PUNCT
ejpam-6571	224	40	σ2)p	σ2)p	NOUN
ejpam-6571	224	41	-	-	PUNCT
ejpam-6571	224	42	open	open	NOUN
ejpam-6571	224	43	set	set	NOUN
ejpam-6571	224	44	v	v	NOUN
ejpam-6571	224	45	of	of	ADP
ejpam-6571	224	46	y	y	PROPN
ejpam-6571	224	47	.	.	PUNCT
ejpam-6571	225	1	proof	proof	NOUN
ejpam-6571	225	2	.	.	PUNCT
ejpam-6571	226	1	the	the	DET
ejpam-6571	226	2	proof	proof	NOUN
ejpam-6571	226	3	is	be	AUX
ejpam-6571	226	4	similar	similar	ADJ
ejpam-6571	226	5	to	to	ADP
ejpam-6571	226	6	that	that	PRON
ejpam-6571	226	7	of	of	ADP
ejpam-6571	226	8	theorem	theorem	NOUN
ejpam-6571	226	9	5	5	NUM
ejpam-6571	226	10	.	.	NOUN
ejpam-6571	226	11	4	4	NUM
ejpam-6571	226	12	.	.	NOUN
ejpam-6571	226	13	upper	upper	ADJ
ejpam-6571	226	14	and	and	CCONJ
ejpam-6571	226	15	lower	low	ADJ
ejpam-6571	226	16	weakly	weakly	ADJ
ejpam-6571	226	17	quasi	quasi	NOUN
ejpam-6571	226	18	τ	τ	PROPN
ejpam-6571	226	19	⋆(σ1	⋆(σ1	PROPN
ejpam-6571	226	20	,	,	PUNCT
ejpam-6571	226	21	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	226	22	multifunctions	multifunction	NOUN
ejpam-6571	226	23	in	in	ADP
ejpam-6571	226	24	this	this	DET
ejpam-6571	226	25	section	section	NOUN
ejpam-6571	226	26	,	,	PUNCT
ejpam-6571	226	27	we	we	PRON
ejpam-6571	226	28	introduce	introduce	VERB
ejpam-6571	226	29	the	the	DET
ejpam-6571	226	30	concepts	concept	NOUN
ejpam-6571	226	31	of	of	ADP
ejpam-6571	226	32	upper	upper	ADJ
ejpam-6571	226	33	weakly	weakly	ADJ
ejpam-6571	226	34	quasi	quasi	NOUN
ejpam-6571	226	35	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	226	36	,	,	PUNCT
ejpam-6571	226	37	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	226	38	multifunctions	multifunction	NOUN
ejpam-6571	226	39	and	and	CCONJ
ejpam-6571	226	40	lower	low	ADJ
ejpam-6571	226	41	weakly	weakly	ADJ
ejpam-6571	226	42	quasi	quasi	NOUN
ejpam-6571	226	43	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	226	44	,	,	PUNCT
ejpam-6571	226	45	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	226	46	multifunctions	multifunction	NOUN
ejpam-6571	226	47	.	.	PUNCT
ejpam-6571	227	1	moreover	moreover	ADV
ejpam-6571	227	2	,	,	PUNCT
ejpam-6571	227	3	several	several	ADJ
ejpam-6571	227	4	characterizations	characterization	NOUN
ejpam-6571	227	5	of	of	ADP
ejpam-6571	227	6	upper	upper	ADJ
ejpam-6571	227	7	weakly	weakly	ADJ
ejpam-6571	227	8	quasi	quasi	NOUN
ejpam-6571	227	9	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	227	10	,	,	PUNCT
ejpam-6571	227	11	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	227	12	multifunctions	multifunction	NOUN
ejpam-6571	227	13	and	and	CCONJ
ejpam-6571	227	14	lower	low	ADJ
ejpam-6571	227	15	weakly	weakly	ADJ
ejpam-6571	227	16	quasi	quasi	NOUN
ejpam-6571	227	17	τ⋆(σ1	τ⋆(σ1	ADP
ejpam-6571	227	18	,	,	PUNCT
ejpam-6571	227	19	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	227	20	multifunctions	multifunction	NOUN
ejpam-6571	227	21	are	be	AUX
ejpam-6571	227	22	discussed	discuss	VERB
ejpam-6571	227	23	.	.	PUNCT
ejpam-6571	228	1	definition	definition	NOUN
ejpam-6571	228	2	3	3	NUM
ejpam-6571	228	3	.	.	PUNCT
ejpam-6571	229	1	a	a	DET
ejpam-6571	229	2	multifunction	multifunction	NOUN
ejpam-6571	229	3	f	f	NOUN
ejpam-6571	229	4	:	:	PUNCT
ejpam-6571	229	5	(	(	PUNCT
ejpam-6571	229	6	x	x	X
ejpam-6571	229	7	,	,	PUNCT
ejpam-6571	229	8	τ	τ	PROPN
ejpam-6571	229	9	,	,	PUNCT
ejpam-6571	229	10	i	i	NOUN
ejpam-6571	229	11	)	)	PUNCT
ejpam-6571	229	12	→	→	PUNCT
ejpam-6571	229	13	(	(	PUNCT
ejpam-6571	229	14	y	y	PROPN
ejpam-6571	229	15	,	,	PUNCT
ejpam-6571	229	16	σ1	σ1	PROPN
ejpam-6571	229	17	,	,	PUNCT
ejpam-6571	229	18	σ2	σ2	PROPN
ejpam-6571	229	19	)	)	PUNCT
ejpam-6571	229	20	is	be	AUX
ejpam-6571	229	21	said	say	VERB
ejpam-6571	229	22	to	to	PART
ejpam-6571	229	23	be	be	AUX
ejpam-6571	229	24	upper	upper	ADJ
ejpam-6571	229	25	weakly	weakly	ADJ
ejpam-6571	229	26	quasi	quasi	NOUN
ejpam-6571	229	27	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	229	28	,	,	PUNCT
ejpam-6571	229	29	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	229	30	at	at	ADP
ejpam-6571	229	31	a	a	DET
ejpam-6571	229	32	point	point	NOUN
ejpam-6571	229	33	x	x	SYM
ejpam-6571	229	34	∈	∈	NOUN
ejpam-6571	229	35	x	x	PUNCT
ejpam-6571	229	36	if	if	SCONJ
ejpam-6571	229	37	for	for	ADP
ejpam-6571	229	38	each	each	DET
ejpam-6571	229	39	σ1σ2	σ1σ2	VERB
ejpam-6571	229	40	-	-	ADJ
ejpam-6571	229	41	open	open	ADJ
ejpam-6571	229	42	set	set	NOUN
ejpam-6571	229	43	v	v	NOUN
ejpam-6571	229	44	of	of	ADP
ejpam-6571	229	45	y	y	PRON
ejpam-6571	229	46	such	such	ADJ
ejpam-6571	229	47	that	that	SCONJ
ejpam-6571	229	48	f	f	PROPN
ejpam-6571	229	49	(	(	PUNCT
ejpam-6571	229	50	x	x	X
ejpam-6571	229	51	)	)	PUNCT
ejpam-6571	229	52	⊆	⊆	NUM
ejpam-6571	229	53	v	v	NOUN
ejpam-6571	229	54	and	and	CCONJ
ejpam-6571	229	55	each	each	DET
ejpam-6571	229	56	⋆-open	⋆-open	ADV
ejpam-6571	229	57	set	set	VERB
ejpam-6571	229	58	u	u	NOUN
ejpam-6571	229	59	of	of	ADP
ejpam-6571	229	60	x	x	SYM
ejpam-6571	229	61	containing	contain	VERB
ejpam-6571	229	62	x	x	PRON
ejpam-6571	229	63	,	,	PUNCT
ejpam-6571	229	64	there	there	PRON
ejpam-6571	229	65	exists	exist	VERB
ejpam-6571	229	66	a	a	DET
ejpam-6571	229	67	nonempty	nonempty	ADJ
ejpam-6571	229	68	⋆-open	⋆-open	NOUN
ejpam-6571	229	69	set	set	VERB
ejpam-6571	229	70	g	g	PROPN
ejpam-6571	230	1	such	such	ADJ
ejpam-6571	230	2	that	that	SCONJ
ejpam-6571	230	3	g	g	PROPN
ejpam-6571	230	4	⊆	⊆	NUM
ejpam-6571	230	5	u	u	NOUN
ejpam-6571	230	6	and	and	CCONJ
ejpam-6571	230	7	f	f	PROPN
ejpam-6571	230	8	(	(	PUNCT
ejpam-6571	230	9	g	g	NOUN
ejpam-6571	230	10	)	)	PUNCT
ejpam-6571	230	11	⊆	⊆	NUM
ejpam-6571	230	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	230	13	-	-	NUM
ejpam-6571	230	14	cl(v	cl(v	NOUN
ejpam-6571	230	15	)	)	PUNCT
ejpam-6571	230	16	.	.	PUNCT
ejpam-6571	231	1	a	a	DET
ejpam-6571	231	2	multifunction	multifunction	NOUN
ejpam-6571	231	3	f	f	NOUN
ejpam-6571	231	4	:	:	PUNCT
ejpam-6571	231	5	(	(	PUNCT
ejpam-6571	231	6	x	x	X
ejpam-6571	231	7	,	,	PUNCT
ejpam-6571	231	8	τ	τ	PROPN
ejpam-6571	231	9	,	,	PUNCT
ejpam-6571	231	10	i	i	NOUN
ejpam-6571	231	11	)	)	PUNCT
ejpam-6571	231	12	→	→	PUNCT
ejpam-6571	231	13	(	(	PUNCT
ejpam-6571	231	14	y	y	PROPN
ejpam-6571	231	15	,	,	PUNCT
ejpam-6571	231	16	σ1	σ1	PROPN
ejpam-6571	231	17	,	,	PUNCT
ejpam-6571	231	18	σ2	σ2	PROPN
ejpam-6571	231	19	)	)	PUNCT
ejpam-6571	231	20	is	be	AUX
ejpam-6571	231	21	said	say	VERB
ejpam-6571	231	22	to	to	PART
ejpam-6571	231	23	be	be	AUX
ejpam-6571	231	24	upper	upper	ADJ
ejpam-6571	231	25	weakly	weakly	ADJ
ejpam-6571	231	26	quasi	quasi	NOUN
ejpam-6571	231	27	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	231	28	,	,	PUNCT
ejpam-6571	231	29	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	231	30	if	if	SCONJ
ejpam-6571	231	31	f	f	PROPN
ejpam-6571	231	32	is	be	AUX
ejpam-6571	231	33	upper	upper	ADJ
ejpam-6571	231	34	weakly	weakly	ADJ
ejpam-6571	231	35	quasi	quasi	NOUN
ejpam-6571	231	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	231	37	,	,	PUNCT
ejpam-6571	231	38	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	231	39	at	at	ADP
ejpam-6571	231	40	each	each	DET
ejpam-6571	231	41	point	point	NOUN
ejpam-6571	231	42	x	x	PUNCT
ejpam-6571	231	43	of	of	ADP
ejpam-6571	231	44	x.	x.	NOUN
ejpam-6571	231	45	remark	remark	PROPN
ejpam-6571	231	46	1	1	NUM
ejpam-6571	231	47	.	.	PUNCT
ejpam-6571	231	48	for	for	ADP
ejpam-6571	231	49	a	a	DET
ejpam-6571	231	50	multifunction	multifunction	NOUN
ejpam-6571	231	51	f	f	NOUN
ejpam-6571	231	52	:	:	PUNCT
ejpam-6571	231	53	(	(	PUNCT
ejpam-6571	231	54	x	x	X
ejpam-6571	231	55	,	,	PUNCT
ejpam-6571	231	56	τ	τ	PROPN
ejpam-6571	231	57	,	,	PUNCT
ejpam-6571	231	58	i	i	NOUN
ejpam-6571	231	59	)	)	PUNCT
ejpam-6571	231	60	→	→	PUNCT
ejpam-6571	231	61	(	(	PUNCT
ejpam-6571	231	62	y	y	PROPN
ejpam-6571	231	63	,	,	PUNCT
ejpam-6571	231	64	σ1	σ1	PROPN
ejpam-6571	231	65	,	,	PUNCT
ejpam-6571	231	66	σ2	σ2	NOUN
ejpam-6571	231	67	)	)	PUNCT
ejpam-6571	231	68	,	,	PUNCT
ejpam-6571	231	69	the	the	DET
ejpam-6571	231	70	following	follow	VERB
ejpam-6571	231	71	implication	implication	NOUN
ejpam-6571	231	72	holds	hold	VERB
ejpam-6571	231	73	:	:	PUNCT
ejpam-6571	231	74	upper	upper	ADJ
ejpam-6571	231	75	almost	almost	ADV
ejpam-6571	231	76	quasi	quasi	ADJ
ejpam-6571	231	77	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	231	78	,	,	PUNCT
ejpam-6571	231	79	σ2)-continuity	σ2)-continuity	NOUN
ejpam-6571	231	80	⇒	⇒	VERB
ejpam-6571	231	81	upper	upper	ADJ
ejpam-6571	231	82	weakly	weakly	ADJ
ejpam-6571	231	83	quasi	quasi	NOUN
ejpam-6571	231	84	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	231	85	,	,	PUNCT
ejpam-6571	231	86	σ2)-continuity	σ2)-continuity	NOUN
ejpam-6571	231	87	.	.	PUNCT
ejpam-6571	232	1	the	the	DET
ejpam-6571	232	2	converse	converse	NOUN
ejpam-6571	232	3	of	of	ADP
ejpam-6571	232	4	the	the	DET
ejpam-6571	232	5	implication	implication	NOUN
ejpam-6571	232	6	is	be	AUX
ejpam-6571	232	7	not	not	PART
ejpam-6571	232	8	true	true	ADJ
ejpam-6571	232	9	in	in	ADP
ejpam-6571	232	10	general	general	ADJ
ejpam-6571	232	11	.	.	PUNCT
ejpam-6571	233	1	we	we	PRON
ejpam-6571	233	2	give	give	VERB
ejpam-6571	233	3	an	an	DET
ejpam-6571	233	4	example	example	NOUN
ejpam-6571	233	5	for	for	ADP
ejpam-6571	233	6	the	the	DET
ejpam-6571	233	7	implication	implication	NOUN
ejpam-6571	233	8	as	as	SCONJ
ejpam-6571	233	9	follows	follow	VERB
ejpam-6571	233	10	.	.	PUNCT
ejpam-6571	233	11	example	example	NOUN
ejpam-6571	234	1	1	1	NUM
ejpam-6571	234	2	.	.	PUNCT
ejpam-6571	234	3	let	let	VERB
ejpam-6571	234	4	x	x	PUNCT
ejpam-6571	234	5	=	=	PRON
ejpam-6571	234	6	{	{	PUNCT
ejpam-6571	234	7	1	1	NUM
ejpam-6571	234	8	,	,	PUNCT
ejpam-6571	234	9	2	2	NUM
ejpam-6571	234	10	,	,	PUNCT
ejpam-6571	234	11	3	3	NUM
ejpam-6571	234	12	}	}	PUNCT
ejpam-6571	234	13	with	with	ADP
ejpam-6571	234	14	a	a	DET
ejpam-6571	234	15	topology	topology	NOUN
ejpam-6571	234	16	τ	τ	X
ejpam-6571	234	17	=	=	SYM
ejpam-6571	234	18	{	{	PUNCT
ejpam-6571	234	19	∅	∅	NOUN
ejpam-6571	234	20	,	,	PUNCT
ejpam-6571	234	21	{	{	PUNCT
ejpam-6571	234	22	1	1	NUM
ejpam-6571	234	23	}	}	PUNCT
ejpam-6571	234	24	,	,	PUNCT
ejpam-6571	234	25	{	{	PUNCT
ejpam-6571	234	26	2	2	NUM
ejpam-6571	234	27	,	,	PUNCT
ejpam-6571	234	28	3	3	NUM
ejpam-6571	234	29	}	}	PUNCT
ejpam-6571	234	30	,	,	PUNCT
ejpam-6571	234	31	x	x	NOUN
ejpam-6571	234	32	}	}	PUNCT
ejpam-6571	234	33	and	and	CCONJ
ejpam-6571	234	34	an	an	DET
ejpam-6571	234	35	ideal	ideal	NOUN
ejpam-6571	234	36	i	i	X
ejpam-6571	234	37	=	=	SYM
ejpam-6571	234	38	{	{	PUNCT
ejpam-6571	234	39	∅	∅	NOUN
ejpam-6571	234	40	,	,	PUNCT
ejpam-6571	234	41	{	{	PUNCT
ejpam-6571	234	42	1	1	NUM
ejpam-6571	234	43	}	}	PUNCT
ejpam-6571	234	44	}	}	PUNCT
ejpam-6571	234	45	.	.	PUNCT
ejpam-6571	235	1	let	let	VERB
ejpam-6571	235	2	y	y	PROPN
ejpam-6571	235	3	=	=	PUNCT
ejpam-6571	235	4	{	{	PUNCT
ejpam-6571	235	5	a	a	PRON
ejpam-6571	235	6	,	,	PUNCT
ejpam-6571	235	7	b	b	NOUN
ejpam-6571	235	8	,	,	PUNCT
ejpam-6571	235	9	c	c	NOUN
ejpam-6571	235	10	}	}	PUNCT
ejpam-6571	235	11	with	with	ADP
ejpam-6571	235	12	topologies	topology	NOUN
ejpam-6571	235	13	σ1	σ1	NOUN
ejpam-6571	235	14	=	=	SYM
ejpam-6571	235	15	{	{	PUNCT
ejpam-6571	235	16	∅	∅	NOUN
ejpam-6571	235	17	,	,	PUNCT
ejpam-6571	235	18	{	{	PUNCT
ejpam-6571	235	19	a	a	X
ejpam-6571	235	20	}	}	PUNCT
ejpam-6571	235	21	,	,	PUNCT
ejpam-6571	235	22	{	{	PUNCT
ejpam-6571	235	23	b	b	NOUN
ejpam-6571	235	24	}	}	PUNCT
ejpam-6571	235	25	,	,	PUNCT
ejpam-6571	235	26	{	{	PUNCT
ejpam-6571	235	27	a	a	DET
ejpam-6571	235	28	,	,	PUNCT
ejpam-6571	235	29	b	b	NOUN
ejpam-6571	235	30	}	}	PUNCT
ejpam-6571	235	31	,	,	PUNCT
ejpam-6571	235	32	{	{	PUNCT
ejpam-6571	235	33	a	a	X
ejpam-6571	235	34	,	,	PUNCT
ejpam-6571	235	35	c	c	NOUN
ejpam-6571	235	36	}	}	PUNCT
ejpam-6571	235	37	,	,	PUNCT
ejpam-6571	235	38	y	y	PROPN
ejpam-6571	235	39	}	}	PUNCT
ejpam-6571	235	40	and	and	CCONJ
ejpam-6571	235	41	σ2	σ2	PROPN
ejpam-6571	235	42	=	=	SYM
ejpam-6571	235	43	{	{	PUNCT
ejpam-6571	235	44	∅	∅	NOUN
ejpam-6571	235	45	,	,	PUNCT
ejpam-6571	235	46	{	{	PUNCT
ejpam-6571	235	47	a	a	X
ejpam-6571	235	48	}	}	PUNCT
ejpam-6571	235	49	,	,	PUNCT
ejpam-6571	235	50	{	{	PUNCT
ejpam-6571	235	51	b	b	NOUN
ejpam-6571	235	52	}	}	PUNCT
ejpam-6571	235	53	,	,	PUNCT
ejpam-6571	235	54	{	{	PUNCT
ejpam-6571	235	55	a	a	DET
ejpam-6571	235	56	,	,	PUNCT
ejpam-6571	235	57	b	b	NOUN
ejpam-6571	235	58	}	}	PUNCT
ejpam-6571	235	59	,	,	PUNCT
ejpam-6571	235	60	y	y	PROPN
ejpam-6571	235	61	}	}	PUNCT
ejpam-6571	235	62	.	.	PUNCT
ejpam-6571	236	1	a	a	DET
ejpam-6571	236	2	multifunction	multifunction	NOUN
ejpam-6571	236	3	f	f	NOUN
ejpam-6571	236	4	:	:	PUNCT
ejpam-6571	236	5	(	(	PUNCT
ejpam-6571	236	6	x	x	X
ejpam-6571	236	7	,	,	PUNCT
ejpam-6571	236	8	τ	τ	PROPN
ejpam-6571	236	9	,	,	PUNCT
ejpam-6571	236	10	i	i	NOUN
ejpam-6571	236	11	)	)	PUNCT
ejpam-6571	236	12	→	→	PUNCT
ejpam-6571	236	13	(	(	PUNCT
ejpam-6571	236	14	y	y	PROPN
ejpam-6571	236	15	,	,	PUNCT
ejpam-6571	236	16	σ1	σ1	PROPN
ejpam-6571	236	17	,	,	PUNCT
ejpam-6571	236	18	σ2	σ2	PROPN
ejpam-6571	236	19	)	)	PUNCT
ejpam-6571	236	20	is	be	AUX
ejpam-6571	236	21	defined	define	VERB
ejpam-6571	236	22	as	as	SCONJ
ejpam-6571	236	23	follows	follow	VERB
ejpam-6571	236	24	:	:	PUNCT
ejpam-6571	236	25	f	f	X
ejpam-6571	236	26	(	(	PUNCT
ejpam-6571	236	27	1	1	X
ejpam-6571	236	28	)	)	PUNCT
ejpam-6571	237	1	=	=	PRON
ejpam-6571	237	2	{	{	PUNCT
ejpam-6571	237	3	a	a	NOUN
ejpam-6571	237	4	}	}	PUNCT
ejpam-6571	237	5	,	,	PUNCT
ejpam-6571	237	6	f	f	PROPN
ejpam-6571	237	7	(	(	PUNCT
ejpam-6571	237	8	2	2	NUM
ejpam-6571	237	9	)	)	PUNCT
ejpam-6571	237	10	=	=	PRON
ejpam-6571	237	11	{	{	PUNCT
ejpam-6571	237	12	b	b	NOUN
ejpam-6571	237	13	}	}	PUNCT
ejpam-6571	237	14	and	and	CCONJ
ejpam-6571	237	15	f	f	PROPN
ejpam-6571	237	16	(	(	PUNCT
ejpam-6571	237	17	3	3	X
ejpam-6571	237	18	)	)	PUNCT
ejpam-6571	237	19	=	=	PRON
ejpam-6571	237	20	{	{	PUNCT
ejpam-6571	237	21	b	b	NOUN
ejpam-6571	237	22	,	,	PUNCT
ejpam-6571	237	23	c	c	NOUN
ejpam-6571	237	24	}	}	PUNCT
ejpam-6571	237	25	.	.	PUNCT
ejpam-6571	238	1	then	then	ADV
ejpam-6571	238	2	,	,	PUNCT
ejpam-6571	238	3	f	f	PROPN
ejpam-6571	238	4	is	be	AUX
ejpam-6571	238	5	upper	upper	ADJ
ejpam-6571	238	6	weakly	weakly	ADJ
ejpam-6571	238	7	quasi	quasi	NOUN
ejpam-6571	238	8	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	238	9	,	,	PUNCT
ejpam-6571	238	10	σ2)continuous	σ2)continuous	ADJ
ejpam-6571	238	11	but	but	CCONJ
ejpam-6571	238	12	f	f	PROPN
ejpam-6571	238	13	is	be	AUX
ejpam-6571	238	14	not	not	PART
ejpam-6571	238	15	upper	upper	ADJ
ejpam-6571	238	16	almost	almost	ADV
ejpam-6571	238	17	quasi	quasi	ADJ
ejpam-6571	238	18	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	238	19	,	,	PUNCT
ejpam-6571	238	20	σ2)-continuous	σ2)-continuous	PROPN
ejpam-6571	238	21	.	.	X
ejpam-6571	239	1	theorem	theorem	VERB
ejpam-6571	239	2	7	7	NUM
ejpam-6571	239	3	.	.	X
ejpam-6571	239	4	for	for	ADP
ejpam-6571	239	5	a	a	DET
ejpam-6571	239	6	multifunction	multifunction	NOUN
ejpam-6571	240	1	f	f	NOUN
ejpam-6571	240	2	:	:	PUNCT
ejpam-6571	240	3	(	(	PUNCT
ejpam-6571	240	4	x	x	X
ejpam-6571	240	5	,	,	PUNCT
ejpam-6571	240	6	τ	τ	PROPN
ejpam-6571	240	7	,	,	PUNCT
ejpam-6571	240	8	i	i	NOUN
ejpam-6571	240	9	)	)	PUNCT
ejpam-6571	240	10	→	→	PUNCT
ejpam-6571	240	11	(	(	PUNCT
ejpam-6571	240	12	y	y	PROPN
ejpam-6571	240	13	,	,	PUNCT
ejpam-6571	240	14	σ1	σ1	PROPN
ejpam-6571	240	15	,	,	PUNCT
ejpam-6571	240	16	σ2	σ2	NOUN
ejpam-6571	240	17	)	)	PUNCT
ejpam-6571	240	18	,	,	PUNCT
ejpam-6571	240	19	the	the	DET
ejpam-6571	240	20	following	follow	VERB
ejpam-6571	240	21	properties	property	NOUN
ejpam-6571	240	22	are	be	AUX
ejpam-6571	240	23	equivalent	equivalent	ADJ
ejpam-6571	240	24	:	:	PUNCT
ejpam-6571	240	25	(	(	PUNCT
ejpam-6571	240	26	1	1	X
ejpam-6571	240	27	)	)	PUNCT
ejpam-6571	240	28	f	f	PROPN
ejpam-6571	240	29	is	be	AUX
ejpam-6571	240	30	upper	upper	ADJ
ejpam-6571	240	31	weakly	weakly	ADJ
ejpam-6571	240	32	quasi	quasi	NOUN
ejpam-6571	240	33	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	240	34	,	,	PUNCT
ejpam-6571	240	35	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	240	36	;	;	PUNCT
ejpam-6571	240	37	(	(	PUNCT
ejpam-6571	240	38	2	2	X
ejpam-6571	240	39	)	)	PUNCT
ejpam-6571	240	40	for	for	ADP
ejpam-6571	240	41	each	each	DET
ejpam-6571	240	42	x	x	SYM
ejpam-6571	240	43	∈	∈	PROPN
ejpam-6571	240	44	x	x	X
ejpam-6571	240	45	and	and	CCONJ
ejpam-6571	240	46	every	every	DET
ejpam-6571	240	47	σ1σ2	σ1σ2	NUM
ejpam-6571	240	48	-	-	ADJ
ejpam-6571	240	49	open	open	ADJ
ejpam-6571	240	50	set	set	NOUN
ejpam-6571	240	51	v	v	NOUN
ejpam-6571	240	52	of	of	ADP
ejpam-6571	240	53	y	y	PRON
ejpam-6571	240	54	such	such	ADJ
ejpam-6571	240	55	that	that	SCONJ
ejpam-6571	240	56	f	f	PROPN
ejpam-6571	240	57	(	(	PUNCT
ejpam-6571	240	58	x	x	X
ejpam-6571	240	59	)	)	PUNCT
ejpam-6571	240	60	⊆	⊆	NUM
ejpam-6571	240	61	v	v	NOUN
ejpam-6571	240	62	,	,	PUNCT
ejpam-6571	240	63	there	there	PRON
ejpam-6571	240	64	exists	exist	VERB
ejpam-6571	240	65	a	a	DET
ejpam-6571	240	66	semi	semi	NOUN
ejpam-6571	240	67	-	-	ADJ
ejpam-6571	240	68	i	i	PRON
ejpam-6571	240	69	⋆-open	⋆-open	VERB
ejpam-6571	240	70	set	set	VERB
ejpam-6571	240	71	u	u	NOUN
ejpam-6571	240	72	of	of	ADP
ejpam-6571	240	73	x	x	PUNCT
ejpam-6571	240	74	containing	contain	VERB
ejpam-6571	240	75	x	x	PUNCT
ejpam-6571	240	76	such	such	ADJ
ejpam-6571	240	77	that	that	SCONJ
ejpam-6571	240	78	f	f	PROPN
ejpam-6571	240	79	(	(	PUNCT
ejpam-6571	240	80	u	u	NOUN
ejpam-6571	240	81	)	)	PUNCT
ejpam-6571	240	82	⊆	⊆	NUM
ejpam-6571	240	83	σ1σ2	σ1σ2	NOUN
ejpam-6571	240	84	-	-	NUM
ejpam-6571	240	85	cl(v	cl(v	NOUN
ejpam-6571	240	86	)	)	PUNCT
ejpam-6571	240	87	;	;	PUNCT
ejpam-6571	240	88	(	(	PUNCT
ejpam-6571	240	89	3	3	X
ejpam-6571	240	90	)	)	PUNCT
ejpam-6571	240	91	int⋆(cl⋆(f−(σ1σ2	int⋆(cl⋆(f−(σ1σ2	NUM
ejpam-6571	240	92	-	-	PUNCT
ejpam-6571	240	93	int(k	int(k	NOUN
ejpam-6571	240	94	)	)	PUNCT
ejpam-6571	240	95	)	)	PUNCT
ejpam-6571	240	96	)	)	PUNCT
ejpam-6571	240	97	)	)	PUNCT
ejpam-6571	241	1	⊆	⊆	X
ejpam-6571	241	2	f−(k	f−(k	PROPN
ejpam-6571	241	3	)	)	PUNCT
ejpam-6571	241	4	for	for	ADP
ejpam-6571	241	5	every	every	DET
ejpam-6571	241	6	σ1σ2	σ1σ2	NUM
ejpam-6571	241	7	-	-	PUNCT
ejpam-6571	241	8	closed	closed	ADJ
ejpam-6571	241	9	set	set	NOUN
ejpam-6571	241	10	k	k	PROPN
ejpam-6571	241	11	of	of	ADP
ejpam-6571	241	12	y	y	PROPN
ejpam-6571	241	13	;	;	PUNCT
ejpam-6571	241	14	m.	m.	NOUN
ejpam-6571	241	15	thongmoon	thongmoon	NOUN
ejpam-6571	241	16	,	,	PUNCT
ejpam-6571	241	17	a.	a.	PROPN
ejpam-6571	241	18	sama	sama	PROPN
ejpam-6571	241	19	-	-	PUNCT
ejpam-6571	241	20	ae	ae	PROPN
ejpam-6571	241	21	,	,	PUNCT
ejpam-6571	241	22	c.	c.	PROPN
ejpam-6571	241	23	boonpok	boonpok	PROPN
ejpam-6571	241	24	/	/	SYM
ejpam-6571	241	25	eur	eur	PROPN
ejpam-6571	241	26	.	.	PUNCT
ejpam-6571	242	1	j.	j.	PROPN
ejpam-6571	242	2	pure	pure	PROPN
ejpam-6571	242	3	appl	appl	PROPN
ejpam-6571	242	4	.	.	PROPN
ejpam-6571	242	5	math	math	PROPN
ejpam-6571	242	6	,	,	PUNCT
ejpam-6571	242	7	18	18	NUM
ejpam-6571	242	8	(	(	PUNCT
ejpam-6571	242	9	3	3	NUM
ejpam-6571	242	10	)	)	PUNCT
ejpam-6571	242	11	(	(	PUNCT
ejpam-6571	242	12	2025	2025	NUM
ejpam-6571	242	13	)	)	PUNCT
ejpam-6571	242	14	,	,	PUNCT
ejpam-6571	242	15	6571	6571	NUM
ejpam-6571	242	16	9	9	NUM
ejpam-6571	242	17	of	of	ADP
ejpam-6571	242	18	15	15	NUM
ejpam-6571	242	19	(	(	PUNCT
ejpam-6571	242	20	4	4	NUM
ejpam-6571	242	21	)	)	PUNCT
ejpam-6571	242	22	f+(v	f+(v	NOUN
ejpam-6571	242	23	)	)	PUNCT
ejpam-6571	243	1	⊆	⊆	X
ejpam-6571	243	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	243	3	-	-	PUNCT
ejpam-6571	243	4	cl(v	cl(v	NOUN
ejpam-6571	243	5	)	)	PUNCT
ejpam-6571	243	6	)	)	PUNCT
ejpam-6571	243	7	)	)	PUNCT
ejpam-6571	243	8	for	for	ADP
ejpam-6571	243	9	every	every	DET
ejpam-6571	243	10	σ1σ2	σ1σ2	NOUN
ejpam-6571	243	11	-	-	ADJ
ejpam-6571	243	12	open	open	ADJ
ejpam-6571	243	13	set	set	NOUN
ejpam-6571	243	14	v	v	NOUN
ejpam-6571	243	15	of	of	ADP
ejpam-6571	243	16	y	y	PROPN
ejpam-6571	243	17	;	;	PUNCT
ejpam-6571	243	18	(	(	PUNCT
ejpam-6571	243	19	5	5	NUM
ejpam-6571	243	20	)	)	PUNCT
ejpam-6571	243	21	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	243	22	)	)	PUNCT
ejpam-6571	243	23	)	)	PUNCT
ejpam-6571	244	1	⊆	⊆	X
ejpam-6571	244	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	244	3	-	-	PUNCT
ejpam-6571	244	4	cl(v	cl(v	NOUN
ejpam-6571	244	5	)	)	PUNCT
ejpam-6571	244	6	)	)	PUNCT
ejpam-6571	244	7	for	for	ADP
ejpam-6571	244	8	every	every	DET
ejpam-6571	244	9	σ1σ2	σ1σ2	NOUN
ejpam-6571	244	10	-	-	ADJ
ejpam-6571	244	11	open	open	ADJ
ejpam-6571	244	12	set	set	NOUN
ejpam-6571	244	13	v	v	NOUN
ejpam-6571	244	14	of	of	ADP
ejpam-6571	244	15	y	y	PROPN
ejpam-6571	244	16	.	.	PUNCT
ejpam-6571	245	1	proof	proof	NOUN
ejpam-6571	245	2	.	.	PUNCT
ejpam-6571	246	1	(	(	PUNCT
ejpam-6571	246	2	1	1	X
ejpam-6571	246	3	)	)	PUNCT
ejpam-6571	246	4	⇒	⇒	NOUN
ejpam-6571	246	5	(	(	PUNCT
ejpam-6571	246	6	2	2	NUM
ejpam-6571	246	7	):	):	PUNCT
ejpam-6571	246	8	let	let	VERB
ejpam-6571	246	9	u	u	PRON
ejpam-6571	246	10	(	(	PUNCT
ejpam-6571	246	11	x	x	NOUN
ejpam-6571	246	12	)	)	PUNCT
ejpam-6571	246	13	be	be	VERB
ejpam-6571	246	14	the	the	DET
ejpam-6571	246	15	family	family	NOUN
ejpam-6571	246	16	of	of	ADP
ejpam-6571	246	17	all	all	DET
ejpam-6571	246	18	⋆-open	⋆-open	ADJ
ejpam-6571	246	19	sets	set	NOUN
ejpam-6571	246	20	of	of	ADP
ejpam-6571	246	21	x	x	PUNCT
ejpam-6571	246	22	containing	contain	VERB
ejpam-6571	246	23	x.	x.	NOUN
ejpam-6571	246	24	let	let	VERB
ejpam-6571	246	25	v	v	PART
ejpam-6571	246	26	be	be	AUX
ejpam-6571	246	27	any	any	DET
ejpam-6571	246	28	σ1σ2	σ1σ2	NOUN
ejpam-6571	246	29	-	-	ADJ
ejpam-6571	246	30	open	open	ADJ
ejpam-6571	246	31	set	set	NOUN
ejpam-6571	246	32	of	of	ADP
ejpam-6571	246	33	y	y	PRON
ejpam-6571	246	34	such	such	ADJ
ejpam-6571	246	35	that	that	SCONJ
ejpam-6571	246	36	f	f	PROPN
ejpam-6571	246	37	(	(	PUNCT
ejpam-6571	246	38	x	x	X
ejpam-6571	246	39	)	)	PUNCT
ejpam-6571	246	40	⊆	⊆	NUM
ejpam-6571	246	41	v	v	NOUN
ejpam-6571	246	42	.	.	PUNCT
ejpam-6571	247	1	for	for	ADP
ejpam-6571	247	2	each	each	DET
ejpam-6571	247	3	h	h	NOUN
ejpam-6571	247	4	∈	∈	PROPN
ejpam-6571	247	5	u	u	NOUN
ejpam-6571	247	6	(	(	PUNCT
ejpam-6571	247	7	x	x	NOUN
ejpam-6571	247	8	)	)	PUNCT
ejpam-6571	247	9	,	,	PUNCT
ejpam-6571	247	10	there	there	PRON
ejpam-6571	247	11	exists	exist	VERB
ejpam-6571	247	12	a	a	DET
ejpam-6571	247	13	nonempty	nonempty	ADJ
ejpam-6571	247	14	⋆-open	⋆-open	NOUN
ejpam-6571	247	15	set	set	NOUN
ejpam-6571	247	16	gh	gh	PROPN
ejpam-6571	248	1	such	such	ADJ
ejpam-6571	248	2	that	that	SCONJ
ejpam-6571	248	3	gh	gh	PROPN
ejpam-6571	248	4	⊆	⊆	NUM
ejpam-6571	248	5	h	h	PROPN
ejpam-6571	248	6	and	and	CCONJ
ejpam-6571	248	7	f	f	PROPN
ejpam-6571	248	8	(	(	PUNCT
ejpam-6571	248	9	gh	gh	PROPN
ejpam-6571	248	10	)	)	PUNCT
ejpam-6571	248	11	⊆	⊆	NUM
ejpam-6571	248	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	248	13	-	-	NUM
ejpam-6571	248	14	cl(v	cl(v	NOUN
ejpam-6571	248	15	)	)	PUNCT
ejpam-6571	248	16	.	.	PUNCT
ejpam-6571	249	1	let	let	VERB
ejpam-6571	249	2	w	w	NOUN
ejpam-6571	249	3	=	=	PUNCT
ejpam-6571	249	4	∪{gh	∪{gh	NOUN
ejpam-6571	249	5	|	|	ADV
ejpam-6571	249	6	h	h	NOUN
ejpam-6571	249	7	∈	∈	PROPN
ejpam-6571	249	8	u	u	NOUN
ejpam-6571	249	9	(	(	PUNCT
ejpam-6571	249	10	x	x	NOUN
ejpam-6571	249	11	)	)	PUNCT
ejpam-6571	249	12	}	}	PUNCT
ejpam-6571	249	13	.	.	PUNCT
ejpam-6571	250	1	then	then	ADV
ejpam-6571	250	2	,	,	PUNCT
ejpam-6571	250	3	w	w	PROPN
ejpam-6571	250	4	is	be	AUX
ejpam-6571	250	5	⋆-open	⋆-open	ADJ
ejpam-6571	250	6	in	in	ADP
ejpam-6571	250	7	x	x	X
ejpam-6571	250	8	,	,	PUNCT
ejpam-6571	250	9	x	x	PROPN
ejpam-6571	250	10	∈	∈	PROPN
ejpam-6571	250	11	cl⋆(w	cl⋆(w	PROPN
ejpam-6571	250	12	)	)	PUNCT
ejpam-6571	250	13	and	and	CCONJ
ejpam-6571	250	14	f	f	PROPN
ejpam-6571	250	15	(	(	PUNCT
ejpam-6571	250	16	w	w	PROPN
ejpam-6571	250	17	)	)	PUNCT
ejpam-6571	250	18	⊆	⊆	NUM
ejpam-6571	250	19	σ1σ2	σ1σ2	NOUN
ejpam-6571	250	20	-	-	NUM
ejpam-6571	250	21	cl(v	cl(v	NOUN
ejpam-6571	250	22	)	)	PUNCT
ejpam-6571	250	23	.	.	PUNCT
ejpam-6571	251	1	put	put	VERB
ejpam-6571	251	2	u	u	NOUN
ejpam-6571	251	3	=	=	X
ejpam-6571	251	4	w	w	PROPN
ejpam-6571	251	5	∪{x	∪{x	NOUN
ejpam-6571	251	6	}	}	PUNCT
ejpam-6571	251	7	,	,	PUNCT
ejpam-6571	251	8	then	then	ADV
ejpam-6571	251	9	w	w	PROPN
ejpam-6571	251	10	⊆	⊆	NUM
ejpam-6571	251	11	u	u	NOUN
ejpam-6571	251	12	⊆	⊆	NUM
ejpam-6571	251	13	cl⋆(w	cl⋆(w	NOUN
ejpam-6571	251	14	)	)	PUNCT
ejpam-6571	251	15	.	.	PUNCT
ejpam-6571	252	1	thus	thus	ADV
ejpam-6571	252	2	,	,	PUNCT
ejpam-6571	252	3	u	u	NOUN
ejpam-6571	252	4	is	be	AUX
ejpam-6571	252	5	a	a	DET
ejpam-6571	252	6	semi	semi	ADJ
ejpam-6571	252	7	-	-	ADJ
ejpam-6571	252	8	i	i	PRON
ejpam-6571	252	9	⋆-open	⋆-open	VERB
ejpam-6571	252	10	set	set	VERB
ejpam-6571	252	11	of	of	ADP
ejpam-6571	252	12	x	x	PUNCT
ejpam-6571	252	13	containing	contain	VERB
ejpam-6571	252	14	x	x	PUNCT
ejpam-6571	252	15	such	such	ADJ
ejpam-6571	252	16	that	that	SCONJ
ejpam-6571	252	17	f	f	PROPN
ejpam-6571	252	18	(	(	PUNCT
ejpam-6571	252	19	u	u	NOUN
ejpam-6571	252	20	)	)	PUNCT
ejpam-6571	252	21	⊆	⊆	NUM
ejpam-6571	252	22	σ1σ2	σ1σ2	NOUN
ejpam-6571	252	23	-	-	NUM
ejpam-6571	252	24	cl(v	cl(v	NOUN
ejpam-6571	252	25	)	)	PUNCT
ejpam-6571	252	26	.	.	PUNCT
ejpam-6571	253	1	(	(	PUNCT
ejpam-6571	253	2	2	2	X
ejpam-6571	253	3	)	)	PUNCT
ejpam-6571	253	4	⇒	⇒	NOUN
ejpam-6571	253	5	(	(	PUNCT
ejpam-6571	253	6	4	4	NUM
ejpam-6571	253	7	):	):	PUNCT
ejpam-6571	253	8	let	let	VERB
ejpam-6571	253	9	v	v	PART
ejpam-6571	253	10	be	be	AUX
ejpam-6571	253	11	any	any	DET
ejpam-6571	253	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	253	13	-	-	ADJ
ejpam-6571	253	14	open	open	ADJ
ejpam-6571	253	15	set	set	NOUN
ejpam-6571	253	16	of	of	ADP
ejpam-6571	253	17	y	y	PROPN
ejpam-6571	253	18	and	and	CCONJ
ejpam-6571	253	19	x	x	PROPN
ejpam-6571	253	20	∈	∈	PROPN
ejpam-6571	253	21	f+(v	f+(v	NOUN
ejpam-6571	253	22	)	)	PUNCT
ejpam-6571	253	23	.	.	PUNCT
ejpam-6571	254	1	then	then	ADV
ejpam-6571	254	2	,	,	PUNCT
ejpam-6571	254	3	f	f	PROPN
ejpam-6571	254	4	(	(	PUNCT
ejpam-6571	254	5	x	x	X
ejpam-6571	254	6	)	)	PUNCT
ejpam-6571	254	7	⊆	⊆	NUM
ejpam-6571	254	8	v	v	NOUN
ejpam-6571	254	9	and	and	CCONJ
ejpam-6571	254	10	there	there	PRON
ejpam-6571	254	11	exists	exist	VERB
ejpam-6571	254	12	a	a	DET
ejpam-6571	254	13	semi	semi	NOUN
ejpam-6571	254	14	-	-	ADJ
ejpam-6571	254	15	i	i	PRON
ejpam-6571	254	16	⋆-open	⋆-open	VERB
ejpam-6571	254	17	set	set	VERB
ejpam-6571	254	18	u	u	NOUN
ejpam-6571	254	19	of	of	ADP
ejpam-6571	254	20	x	x	PUNCT
ejpam-6571	254	21	containing	contain	VERB
ejpam-6571	254	22	x	x	PUNCT
ejpam-6571	254	23	such	such	ADJ
ejpam-6571	254	24	that	that	SCONJ
ejpam-6571	254	25	f	f	PROPN
ejpam-6571	254	26	(	(	PUNCT
ejpam-6571	254	27	u	u	NOUN
ejpam-6571	254	28	)	)	PUNCT
ejpam-6571	254	29	⊆	⊆	NUM
ejpam-6571	254	30	σ1σ2	σ1σ2	NOUN
ejpam-6571	254	31	-	-	NUM
ejpam-6571	254	32	cl(v	cl(v	NOUN
ejpam-6571	254	33	)	)	PUNCT
ejpam-6571	254	34	.	.	PUNCT
ejpam-6571	255	1	thus	thus	ADV
ejpam-6571	255	2	,	,	PUNCT
ejpam-6571	255	3	x	x	PUNCT
ejpam-6571	255	4	∈	∈	PROPN
ejpam-6571	255	5	u	u	NOUN
ejpam-6571	255	6	⊆	⊆	NUM
ejpam-6571	255	7	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	255	8	-	-	PUNCT
ejpam-6571	255	9	cl(v	cl(v	NOUN
ejpam-6571	255	10	)	)	PUNCT
ejpam-6571	255	11	)	)	PUNCT
ejpam-6571	255	12	)	)	PUNCT
ejpam-6571	255	13	and	and	CCONJ
ejpam-6571	255	14	so	so	ADV
ejpam-6571	255	15	f+(v	f+(v	PROPN
ejpam-6571	255	16	)	)	PUNCT
ejpam-6571	256	1	⊆	⊆	X
ejpam-6571	256	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	256	3	-	-	PUNCT
ejpam-6571	256	4	cl(v	cl(v	NOUN
ejpam-6571	256	5	)	)	PUNCT
ejpam-6571	256	6	)	)	PUNCT
ejpam-6571	256	7	)	)	PUNCT
ejpam-6571	256	8	.	.	PUNCT
ejpam-6571	257	1	(	(	PUNCT
ejpam-6571	257	2	4	4	X
ejpam-6571	257	3	)	)	PUNCT
ejpam-6571	257	4	⇒	⇒	NOUN
ejpam-6571	257	5	(	(	PUNCT
ejpam-6571	257	6	5	5	NUM
ejpam-6571	257	7	):	):	PUNCT
ejpam-6571	257	8	let	let	VERB
ejpam-6571	257	9	v	v	PART
ejpam-6571	257	10	be	be	AUX
ejpam-6571	257	11	any	any	DET
ejpam-6571	257	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	257	13	-	-	ADJ
ejpam-6571	257	14	open	open	ADJ
ejpam-6571	257	15	set	set	NOUN
ejpam-6571	257	16	of	of	ADP
ejpam-6571	257	17	y	y	PROPN
ejpam-6571	257	18	.	.	PUNCT
ejpam-6571	258	1	then	then	ADV
ejpam-6571	258	2	by	by	ADP
ejpam-6571	258	3	(	(	PUNCT
ejpam-6571	258	4	4	4	NUM
ejpam-6571	258	5	)	)	PUNCT
ejpam-6571	258	6	,	,	PUNCT
ejpam-6571	258	7	we	we	PRON
ejpam-6571	258	8	have	have	VERB
ejpam-6571	258	9	x	x	NOUN
ejpam-6571	258	10	−	−	PUNCT
ejpam-6571	258	11	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	258	12	-	-	PUNCT
ejpam-6571	258	13	cl(v	cl(v	NOUN
ejpam-6571	258	14	)	)	PUNCT
ejpam-6571	258	15	)	)	PUNCT
ejpam-6571	259	1	=	=	PUNCT
ejpam-6571	260	1	f+(y	f+(y	NOUN
ejpam-6571	260	2	−	−	NUM
ejpam-6571	260	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	260	4	-	-	NUM
ejpam-6571	260	5	cl(v	cl(v	NOUN
ejpam-6571	260	6	)	)	PUNCT
ejpam-6571	260	7	)	)	PUNCT
ejpam-6571	261	1	⊆	⊆	X
ejpam-6571	261	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NUM
ejpam-6571	261	3	-	-	PUNCT
ejpam-6571	261	4	cl(y	cl(y	NOUN
ejpam-6571	261	5	−	−	NOUN
ejpam-6571	261	6	σ1σ2	σ1σ2	NOUN
ejpam-6571	261	7	-	-	NUM
ejpam-6571	261	8	cl(v	cl(v	NOUN
ejpam-6571	261	9	)	)	PUNCT
ejpam-6571	261	10	)	)	PUNCT
ejpam-6571	261	11	)	)	PUNCT
ejpam-6571	261	12	)	)	PUNCT
ejpam-6571	262	1	=	=	PUNCT
ejpam-6571	262	2	sint⋆(f+(y	sint⋆(f+(y	VERB
ejpam-6571	262	3	−	−	NOUN
ejpam-6571	262	4	σ1σ2	σ1σ2	NOUN
ejpam-6571	262	5	-	-	PUNCT
ejpam-6571	262	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	262	7	-	-	PUNCT
ejpam-6571	262	8	cl(v	cl(v	NOUN
ejpam-6571	262	9	)	)	PUNCT
ejpam-6571	262	10	)	)	PUNCT
ejpam-6571	262	11	)	)	PUNCT
ejpam-6571	262	12	)	)	PUNCT
ejpam-6571	263	1	⊆	⊆	X
ejpam-6571	263	2	sint⋆(f+(y	sint⋆(f+(y	NOUN
ejpam-6571	263	3	−	−	NOUN
ejpam-6571	263	4	v	v	NOUN
ejpam-6571	263	5	)	)	PUNCT
ejpam-6571	263	6	)	)	PUNCT
ejpam-6571	264	1	=	=	PUNCT
ejpam-6571	264	2	sint⋆(x	sint⋆(x	VERB
ejpam-6571	264	3	−	−	PROPN
ejpam-6571	264	4	f−(v	f−(v	NOUN
ejpam-6571	264	5	)	)	PUNCT
ejpam-6571	264	6	)	)	PUNCT
ejpam-6571	265	1	=	=	PUNCT
ejpam-6571	265	2	x	x	X
ejpam-6571	265	3	−	−	NOUN
ejpam-6571	265	4	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	265	5	)	)	PUNCT
ejpam-6571	265	6	)	)	PUNCT
ejpam-6571	265	7	and	and	CCONJ
ejpam-6571	265	8	hence	hence	ADV
ejpam-6571	265	9	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	265	10	)	)	PUNCT
ejpam-6571	265	11	)	)	PUNCT
ejpam-6571	266	1	⊆	⊆	X
ejpam-6571	266	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	266	3	-	-	PUNCT
ejpam-6571	266	4	cl(v	cl(v	NOUN
ejpam-6571	266	5	)	)	PUNCT
ejpam-6571	266	6	)	)	PUNCT
ejpam-6571	266	7	.	.	PUNCT
ejpam-6571	267	1	(	(	PUNCT
ejpam-6571	267	2	5	5	X
ejpam-6571	267	3	)	)	PUNCT
ejpam-6571	267	4	⇒	⇒	NOUN
ejpam-6571	267	5	(	(	PUNCT
ejpam-6571	267	6	3	3	NUM
ejpam-6571	267	7	):	):	PUNCT
ejpam-6571	267	8	let	let	VERB
ejpam-6571	267	9	k	k	PRON
ejpam-6571	267	10	be	be	AUX
ejpam-6571	267	11	any	any	DET
ejpam-6571	267	12	σ1σ2	σ1σ2	NUM
ejpam-6571	267	13	-	-	PUNCT
ejpam-6571	267	14	closed	closed	ADJ
ejpam-6571	267	15	set	set	NOUN
ejpam-6571	267	16	of	of	ADP
ejpam-6571	267	17	y	y	PROPN
ejpam-6571	267	18	.	.	PUNCT
ejpam-6571	268	1	by	by	ADP
ejpam-6571	268	2	(	(	PUNCT
ejpam-6571	268	3	5	5	NUM
ejpam-6571	268	4	)	)	PUNCT
ejpam-6571	268	5	and	and	CCONJ
ejpam-6571	268	6	lemma	lemma	PROPN
ejpam-6571	268	7	3	3	NUM
ejpam-6571	268	8	,	,	PUNCT
ejpam-6571	268	9	we	we	PRON
ejpam-6571	268	10	have	have	VERB
ejpam-6571	268	11	int⋆(cl⋆(f−(σ1σ2	int⋆(cl⋆(f−(σ1σ2	VERB
ejpam-6571	268	12	-	-	PUNCT
ejpam-6571	268	13	int(k	int(k	NOUN
ejpam-6571	268	14	)	)	PUNCT
ejpam-6571	268	15	)	)	PUNCT
ejpam-6571	268	16	)	)	PUNCT
ejpam-6571	268	17	)	)	PUNCT
ejpam-6571	269	1	⊆	⊆	X
ejpam-6571	269	2	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	269	3	-	-	PUNCT
ejpam-6571	269	4	int(k	int(k	NOUN
ejpam-6571	269	5	)	)	PUNCT
ejpam-6571	269	6	)	)	PUNCT
ejpam-6571	269	7	)	)	PUNCT
ejpam-6571	270	1	⊆	⊆	X
ejpam-6571	270	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6571	270	3	-	-	PUNCT
ejpam-6571	270	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	270	5	-	-	PUNCT
ejpam-6571	270	6	int(k	int(k	NOUN
ejpam-6571	270	7	)	)	PUNCT
ejpam-6571	270	8	)	)	PUNCT
ejpam-6571	270	9	)	)	PUNCT
ejpam-6571	271	1	⊆	⊆	X
ejpam-6571	271	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	271	3	-	-	PUNCT
ejpam-6571	271	4	cl(k	cl(k	NOUN
ejpam-6571	271	5	)	)	PUNCT
ejpam-6571	271	6	)	)	PUNCT
ejpam-6571	272	1	=	=	SYM
ejpam-6571	272	2	f−(k	f−(k	PROPN
ejpam-6571	272	3	)	)	PUNCT
ejpam-6571	272	4	.	.	PUNCT
ejpam-6571	273	1	(	(	PUNCT
ejpam-6571	273	2	3	3	X
ejpam-6571	273	3	)	)	PUNCT
ejpam-6571	273	4	⇒	⇒	NOUN
ejpam-6571	273	5	(	(	PUNCT
ejpam-6571	273	6	4	4	NUM
ejpam-6571	273	7	):	):	PUNCT
ejpam-6571	273	8	let	let	VERB
ejpam-6571	273	9	v	v	PART
ejpam-6571	273	10	be	be	AUX
ejpam-6571	273	11	any	any	DET
ejpam-6571	273	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	273	13	-	-	ADJ
ejpam-6571	273	14	open	open	ADJ
ejpam-6571	273	15	set	set	NOUN
ejpam-6571	273	16	of	of	ADP
ejpam-6571	273	17	y	y	PROPN
ejpam-6571	273	18	.	.	PUNCT
ejpam-6571	274	1	by	by	ADP
ejpam-6571	274	2	(	(	PUNCT
ejpam-6571	274	3	3	3	X
ejpam-6571	274	4	)	)	PUNCT
ejpam-6571	274	5	and	and	CCONJ
ejpam-6571	274	6	lemma	lemma	PROPN
ejpam-6571	274	7	3	3	NUM
ejpam-6571	274	8	,	,	PUNCT
ejpam-6571	274	9	x	x	PUNCT
ejpam-6571	274	10	−	−	NOUN
ejpam-6571	274	11	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	274	12	-	-	PUNCT
ejpam-6571	274	13	cl(v	cl(v	NOUN
ejpam-6571	274	14	)	)	PUNCT
ejpam-6571	274	15	)	)	PUNCT
ejpam-6571	274	16	)	)	PUNCT
ejpam-6571	275	1	=	=	NOUN
ejpam-6571	275	2	scl⋆(f−(y	scl⋆(f−(y	NOUN
ejpam-6571	276	1	−	−	ADP
ejpam-6571	276	2	σ1σ2	σ1σ2	NOUN
ejpam-6571	276	3	-	-	NUM
ejpam-6571	276	4	cl(v	cl(v	NOUN
ejpam-6571	276	5	)	)	PUNCT
ejpam-6571	276	6	)	)	PUNCT
ejpam-6571	276	7	)	)	PUNCT
ejpam-6571	277	1	⊆	⊆	X
ejpam-6571	277	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6571	277	3	-	-	PUNCT
ejpam-6571	277	4	cl(y	cl(y	NOUN
ejpam-6571	277	5	−	−	NOUN
ejpam-6571	277	6	σ1σ2	σ1σ2	NOUN
ejpam-6571	277	7	-	-	NUM
ejpam-6571	277	8	cl(v	cl(v	NOUN
ejpam-6571	277	9	)	)	PUNCT
ejpam-6571	277	10	)	)	PUNCT
ejpam-6571	277	11	)	)	PUNCT
ejpam-6571	278	1	=	=	PUNCT
ejpam-6571	278	2	f−(y	f−(y	NOUN
ejpam-6571	278	3	−	−	ADP
ejpam-6571	278	4	σ1σ2	σ1σ2	NOUN
ejpam-6571	278	5	-	-	PUNCT
ejpam-6571	278	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	278	7	-	-	PUNCT
ejpam-6571	278	8	cl(v	cl(v	NOUN
ejpam-6571	278	9	)	)	PUNCT
ejpam-6571	278	10	)	)	PUNCT
ejpam-6571	278	11	)	)	PUNCT
ejpam-6571	279	1	⊆	⊆	NUM
ejpam-6571	279	2	f−(y	f−(y	NOUN
ejpam-6571	279	3	−	−	NOUN
ejpam-6571	279	4	v	v	NOUN
ejpam-6571	279	5	)	)	PUNCT
ejpam-6571	279	6	=	=	PUNCT
ejpam-6571	279	7	x	x	X
ejpam-6571	279	8	−	−	PROPN
ejpam-6571	279	9	f+(v	f+(v	NOUN
ejpam-6571	279	10	)	)	PUNCT
ejpam-6571	279	11	and	and	CCONJ
ejpam-6571	279	12	so	so	ADV
ejpam-6571	279	13	f+(v	f+(v	PROPN
ejpam-6571	279	14	)	)	PUNCT
ejpam-6571	279	15	⊆	⊆	X
ejpam-6571	279	16	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	279	17	-	-	PUNCT
ejpam-6571	279	18	cl(v	cl(v	NOUN
ejpam-6571	279	19	)	)	PUNCT
ejpam-6571	279	20	)	)	PUNCT
ejpam-6571	279	21	)	)	PUNCT
ejpam-6571	279	22	.	.	PUNCT
ejpam-6571	280	1	(	(	PUNCT
ejpam-6571	280	2	4	4	X
ejpam-6571	280	3	)	)	PUNCT
ejpam-6571	280	4	⇒	⇒	NOUN
ejpam-6571	280	5	(	(	PUNCT
ejpam-6571	280	6	1	1	NUM
ejpam-6571	280	7	):	):	PUNCT
ejpam-6571	280	8	let	let	VERB
ejpam-6571	280	9	x	x	PUNCT
ejpam-6571	280	10	∈	∈	PROPN
ejpam-6571	280	11	x	x	X
ejpam-6571	280	12	and	and	CCONJ
ejpam-6571	280	13	v	v	X
ejpam-6571	280	14	be	be	AUX
ejpam-6571	280	15	any	any	DET
ejpam-6571	280	16	σ1σ2	σ1σ2	NOUN
ejpam-6571	280	17	-	-	ADJ
ejpam-6571	280	18	open	open	ADJ
ejpam-6571	280	19	set	set	NOUN
ejpam-6571	280	20	of	of	ADP
ejpam-6571	280	21	y	y	PRON
ejpam-6571	280	22	such	such	ADJ
ejpam-6571	280	23	that	that	SCONJ
ejpam-6571	280	24	f	f	PROPN
ejpam-6571	280	25	(	(	PUNCT
ejpam-6571	280	26	x	x	X
ejpam-6571	280	27	)	)	PUNCT
ejpam-6571	280	28	⊆	⊆	NUM
ejpam-6571	280	29	v	v	NOUN
ejpam-6571	280	30	.	.	PUNCT
ejpam-6571	281	1	thus	thus	ADV
ejpam-6571	281	2	by	by	ADP
ejpam-6571	281	3	(	(	PUNCT
ejpam-6571	281	4	4	4	NUM
ejpam-6571	281	5	)	)	PUNCT
ejpam-6571	281	6	,	,	PUNCT
ejpam-6571	281	7	we	we	PRON
ejpam-6571	281	8	have	have	VERB
ejpam-6571	281	9	f+(v	f+(v	NOUN
ejpam-6571	281	10	)	)	PUNCT
ejpam-6571	282	1	⊆	⊆	X
ejpam-6571	282	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	282	3	-	-	PUNCT
ejpam-6571	282	4	cl(v	cl(v	NOUN
ejpam-6571	282	5	)	)	PUNCT
ejpam-6571	282	6	)	)	PUNCT
ejpam-6571	282	7	)	)	PUNCT
ejpam-6571	282	8	.	.	PUNCT
ejpam-6571	283	1	put	put	VERB
ejpam-6571	283	2	u	u	NOUN
ejpam-6571	283	3	=	=	PUNCT
ejpam-6571	283	4	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	283	5	-	-	PUNCT
ejpam-6571	283	6	cl(v	cl(v	NOUN
ejpam-6571	283	7	)	)	PUNCT
ejpam-6571	283	8	)	)	PUNCT
ejpam-6571	283	9	)	)	PUNCT
ejpam-6571	283	10	,	,	PUNCT
ejpam-6571	283	11	then	then	ADV
ejpam-6571	283	12	u	u	NOUN
ejpam-6571	283	13	is	be	AUX
ejpam-6571	283	14	a	a	DET
ejpam-6571	283	15	semi	semi	ADJ
ejpam-6571	283	16	-	-	ADJ
ejpam-6571	283	17	i	i	PRON
ejpam-6571	283	18	⋆-open	⋆-open	VERB
ejpam-6571	283	19	set	set	VERB
ejpam-6571	283	20	of	of	ADP
ejpam-6571	283	21	x	x	PUNCT
ejpam-6571	283	22	containing	contain	VERB
ejpam-6571	283	23	x	x	PUNCT
ejpam-6571	283	24	such	such	ADJ
ejpam-6571	283	25	that	that	SCONJ
ejpam-6571	283	26	f	f	PROPN
ejpam-6571	283	27	(	(	PUNCT
ejpam-6571	283	28	u	u	NOUN
ejpam-6571	283	29	)	)	PUNCT
ejpam-6571	283	30	⊆	⊆	NUM
ejpam-6571	283	31	σ1σ2	σ1σ2	NOUN
ejpam-6571	283	32	-	-	NUM
ejpam-6571	283	33	cl(v	cl(v	NOUN
ejpam-6571	283	34	)	)	PUNCT
ejpam-6571	283	35	.	.	PUNCT
ejpam-6571	284	1	this	this	PRON
ejpam-6571	284	2	shows	show	VERB
ejpam-6571	284	3	that	that	SCONJ
ejpam-6571	284	4	f	f	PROPN
ejpam-6571	284	5	is	be	AUX
ejpam-6571	284	6	upper	upper	ADJ
ejpam-6571	284	7	weakly	weakly	ADJ
ejpam-6571	284	8	quasi	quasi	NOUN
ejpam-6571	284	9	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	284	10	,	,	PUNCT
ejpam-6571	284	11	σ2)-continuous	σ2)-continuous	PROPN
ejpam-6571	284	12	.	.	PROPN
ejpam-6571	284	13	m.	m.	NOUN
ejpam-6571	284	14	thongmoon	thongmoon	PROPN
ejpam-6571	284	15	,	,	PUNCT
ejpam-6571	284	16	a.	a.	PROPN
ejpam-6571	284	17	sama	sama	PROPN
ejpam-6571	284	18	-	-	PUNCT
ejpam-6571	284	19	ae	ae	PROPN
ejpam-6571	284	20	,	,	PUNCT
ejpam-6571	284	21	c.	c.	PROPN
ejpam-6571	284	22	boonpok	boonpok	PROPN
ejpam-6571	284	23	/	/	SYM
ejpam-6571	284	24	eur	eur	PROPN
ejpam-6571	284	25	.	.	PUNCT
ejpam-6571	285	1	j.	j.	PROPN
ejpam-6571	285	2	pure	pure	PROPN
ejpam-6571	285	3	appl	appl	PROPN
ejpam-6571	285	4	.	.	PROPN
ejpam-6571	285	5	math	math	PROPN
ejpam-6571	285	6	,	,	PUNCT
ejpam-6571	285	7	18	18	NUM
ejpam-6571	285	8	(	(	PUNCT
ejpam-6571	285	9	3	3	NUM
ejpam-6571	285	10	)	)	PUNCT
ejpam-6571	285	11	(	(	PUNCT
ejpam-6571	285	12	2025	2025	NUM
ejpam-6571	285	13	)	)	PUNCT
ejpam-6571	285	14	,	,	PUNCT
ejpam-6571	285	15	6571	6571	NUM
ejpam-6571	285	16	10	10	NUM
ejpam-6571	285	17	of	of	ADP
ejpam-6571	285	18	15	15	NUM
ejpam-6571	285	19	definition	definition	NOUN
ejpam-6571	285	20	4	4	NUM
ejpam-6571	285	21	.	.	PUNCT
ejpam-6571	286	1	a	a	DET
ejpam-6571	286	2	multifunction	multifunction	NOUN
ejpam-6571	286	3	f	f	NOUN
ejpam-6571	286	4	:	:	PUNCT
ejpam-6571	286	5	(	(	PUNCT
ejpam-6571	286	6	x	x	X
ejpam-6571	286	7	,	,	PUNCT
ejpam-6571	286	8	τ	τ	PROPN
ejpam-6571	286	9	,	,	PUNCT
ejpam-6571	286	10	i	i	NOUN
ejpam-6571	286	11	)	)	PUNCT
ejpam-6571	286	12	→	→	PUNCT
ejpam-6571	286	13	(	(	PUNCT
ejpam-6571	286	14	y	y	PROPN
ejpam-6571	286	15	,	,	PUNCT
ejpam-6571	286	16	σ1	σ1	PROPN
ejpam-6571	286	17	,	,	PUNCT
ejpam-6571	286	18	σ2	σ2	PROPN
ejpam-6571	286	19	)	)	PUNCT
ejpam-6571	286	20	is	be	AUX
ejpam-6571	286	21	said	say	VERB
ejpam-6571	286	22	to	to	PART
ejpam-6571	286	23	be	be	AUX
ejpam-6571	286	24	lower	low	ADJ
ejpam-6571	286	25	weakly	weakly	ADJ
ejpam-6571	286	26	quasi	quasi	NOUN
ejpam-6571	286	27	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	286	28	,	,	PUNCT
ejpam-6571	286	29	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	286	30	at	at	ADP
ejpam-6571	286	31	a	a	DET
ejpam-6571	286	32	point	point	NOUN
ejpam-6571	286	33	x	x	SYM
ejpam-6571	286	34	∈	∈	NOUN
ejpam-6571	286	35	x	x	PUNCT
ejpam-6571	286	36	if	if	SCONJ
ejpam-6571	286	37	for	for	ADP
ejpam-6571	286	38	each	each	DET
ejpam-6571	286	39	σ1σ2	σ1σ2	VERB
ejpam-6571	286	40	-	-	ADJ
ejpam-6571	286	41	open	open	ADJ
ejpam-6571	286	42	set	set	NOUN
ejpam-6571	286	43	v	v	NOUN
ejpam-6571	286	44	of	of	ADP
ejpam-6571	286	45	y	y	PRON
ejpam-6571	286	46	such	such	ADJ
ejpam-6571	286	47	that	that	SCONJ
ejpam-6571	286	48	f	f	PROPN
ejpam-6571	286	49	(	(	PUNCT
ejpam-6571	286	50	x	x	NOUN
ejpam-6571	286	51	)	)	PUNCT
ejpam-6571	286	52	∩	∩	NOUN
ejpam-6571	286	53	v	v	ADP
ejpam-6571	286	54	̸=	̸=	PROPN
ejpam-6571	286	55	∅	∅	NOUN
ejpam-6571	286	56	and	and	CCONJ
ejpam-6571	286	57	each	each	DET
ejpam-6571	286	58	⋆-open	⋆-open	ADV
ejpam-6571	286	59	set	set	VERB
ejpam-6571	286	60	u	u	NOUN
ejpam-6571	286	61	of	of	ADP
ejpam-6571	286	62	x	x	SYM
ejpam-6571	286	63	containing	contain	VERB
ejpam-6571	286	64	x	x	PRON
ejpam-6571	286	65	,	,	PUNCT
ejpam-6571	286	66	there	there	PRON
ejpam-6571	286	67	exists	exist	VERB
ejpam-6571	286	68	a	a	DET
ejpam-6571	286	69	nonempty	nonempty	ADJ
ejpam-6571	286	70	⋆-open	⋆-open	NOUN
ejpam-6571	286	71	set	set	VERB
ejpam-6571	286	72	g	g	PROPN
ejpam-6571	286	73	such	such	ADJ
ejpam-6571	286	74	that	that	SCONJ
ejpam-6571	286	75	g	g	PROPN
ejpam-6571	286	76	⊆	⊆	NUM
ejpam-6571	286	77	u	u	NOUN
ejpam-6571	286	78	and	and	CCONJ
ejpam-6571	286	79	σ1σ2	σ1σ2	NOUN
ejpam-6571	286	80	-	-	NUM
ejpam-6571	286	81	cl(v	cl(v	NOUN
ejpam-6571	286	82	)	)	PUNCT
ejpam-6571	286	83	∩	∩	PROPN
ejpam-6571	286	84	f	f	X
ejpam-6571	286	85	(	(	PUNCT
ejpam-6571	286	86	z	z	NOUN
ejpam-6571	286	87	)	)	PUNCT
ejpam-6571	286	88	̸=	̸=	NOUN
ejpam-6571	286	89	∅	∅	NOUN
ejpam-6571	286	90	for	for	ADP
ejpam-6571	286	91	each	each	DET
ejpam-6571	286	92	z	z	PROPN
ejpam-6571	286	93	∈	∈	PROPN
ejpam-6571	286	94	g.	g.	NOUN
ejpam-6571	286	95	a	a	DET
ejpam-6571	286	96	multifunction	multifunction	NOUN
ejpam-6571	287	1	f	f	NOUN
ejpam-6571	287	2	:	:	PUNCT
ejpam-6571	287	3	(	(	PUNCT
ejpam-6571	287	4	x	x	X
ejpam-6571	287	5	,	,	PUNCT
ejpam-6571	287	6	τ	τ	PROPN
ejpam-6571	287	7	,	,	PUNCT
ejpam-6571	287	8	i	i	NOUN
ejpam-6571	287	9	)	)	PUNCT
ejpam-6571	287	10	→	→	PUNCT
ejpam-6571	287	11	(	(	PUNCT
ejpam-6571	287	12	y	y	PROPN
ejpam-6571	287	13	,	,	PUNCT
ejpam-6571	287	14	σ1	σ1	PROPN
ejpam-6571	287	15	,	,	PUNCT
ejpam-6571	287	16	σ2	σ2	PROPN
ejpam-6571	287	17	)	)	PUNCT
ejpam-6571	287	18	is	be	AUX
ejpam-6571	287	19	said	say	VERB
ejpam-6571	287	20	to	to	PART
ejpam-6571	287	21	be	be	AUX
ejpam-6571	287	22	lower	low	ADJ
ejpam-6571	287	23	weakly	weakly	ADJ
ejpam-6571	287	24	quasi	quasi	NOUN
ejpam-6571	287	25	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	287	26	,	,	PUNCT
ejpam-6571	287	27	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	287	28	if	if	SCONJ
ejpam-6571	287	29	f	f	PROPN
ejpam-6571	287	30	is	be	AUX
ejpam-6571	287	31	lower	low	ADJ
ejpam-6571	287	32	weakly	weakly	ADJ
ejpam-6571	287	33	quasi	quasi	NOUN
ejpam-6571	287	34	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	287	35	,	,	PUNCT
ejpam-6571	287	36	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	287	37	at	at	ADP
ejpam-6571	287	38	each	each	DET
ejpam-6571	287	39	point	point	NOUN
ejpam-6571	287	40	x	x	PUNCT
ejpam-6571	287	41	of	of	ADP
ejpam-6571	287	42	x.	x.	PROPN
ejpam-6571	287	43	theorem	theorem	VERB
ejpam-6571	287	44	8	8	NUM
ejpam-6571	287	45	.	.	PUNCT
ejpam-6571	287	46	for	for	ADP
ejpam-6571	287	47	a	a	DET
ejpam-6571	287	48	multifunction	multifunction	NOUN
ejpam-6571	287	49	f	f	NOUN
ejpam-6571	287	50	:	:	PUNCT
ejpam-6571	287	51	(	(	PUNCT
ejpam-6571	287	52	x	x	X
ejpam-6571	287	53	,	,	PUNCT
ejpam-6571	287	54	τ	τ	PROPN
ejpam-6571	287	55	,	,	PUNCT
ejpam-6571	287	56	i	i	NOUN
ejpam-6571	287	57	)	)	PUNCT
ejpam-6571	287	58	→	→	PUNCT
ejpam-6571	287	59	(	(	PUNCT
ejpam-6571	287	60	y	y	PROPN
ejpam-6571	287	61	,	,	PUNCT
ejpam-6571	287	62	σ1	σ1	PROPN
ejpam-6571	287	63	,	,	PUNCT
ejpam-6571	287	64	σ2	σ2	NOUN
ejpam-6571	287	65	)	)	PUNCT
ejpam-6571	287	66	,	,	PUNCT
ejpam-6571	287	67	the	the	DET
ejpam-6571	287	68	following	follow	VERB
ejpam-6571	287	69	properties	property	NOUN
ejpam-6571	287	70	are	be	AUX
ejpam-6571	287	71	equivalent	equivalent	ADJ
ejpam-6571	287	72	:	:	PUNCT
ejpam-6571	287	73	(	(	PUNCT
ejpam-6571	287	74	1	1	X
ejpam-6571	287	75	)	)	PUNCT
ejpam-6571	287	76	f	f	PROPN
ejpam-6571	287	77	is	be	AUX
ejpam-6571	287	78	lower	low	ADJ
ejpam-6571	287	79	weakly	weakly	ADJ
ejpam-6571	287	80	quasi	quasi	ADJ
ejpam-6571	287	81	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	287	82	,	,	PUNCT
ejpam-6571	287	83	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	287	84	;	;	PUNCT
ejpam-6571	287	85	(	(	PUNCT
ejpam-6571	287	86	2	2	X
ejpam-6571	287	87	)	)	PUNCT
ejpam-6571	287	88	for	for	ADP
ejpam-6571	287	89	each	each	DET
ejpam-6571	287	90	x	x	SYM
ejpam-6571	287	91	∈	∈	PROPN
ejpam-6571	287	92	x	x	X
ejpam-6571	287	93	and	and	CCONJ
ejpam-6571	287	94	every	every	DET
ejpam-6571	287	95	σ1σ2	σ1σ2	NUM
ejpam-6571	287	96	-	-	ADJ
ejpam-6571	287	97	open	open	ADJ
ejpam-6571	287	98	set	set	NOUN
ejpam-6571	287	99	v	v	NOUN
ejpam-6571	287	100	of	of	ADP
ejpam-6571	287	101	y	y	PRON
ejpam-6571	287	102	such	such	ADJ
ejpam-6571	287	103	that	that	SCONJ
ejpam-6571	287	104	f	f	PROPN
ejpam-6571	287	105	(	(	PUNCT
ejpam-6571	287	106	x)∩v	x)∩v	PROPN
ejpam-6571	287	107	̸=	̸=	PROPN
ejpam-6571	287	108	∅	∅	NOUN
ejpam-6571	287	109	,	,	PUNCT
ejpam-6571	287	110	there	there	PRON
ejpam-6571	287	111	exists	exist	VERB
ejpam-6571	287	112	a	a	DET
ejpam-6571	287	113	semi	semi	NOUN
ejpam-6571	287	114	-	-	ADJ
ejpam-6571	287	115	i	i	PRON
ejpam-6571	287	116	⋆-open	⋆-open	VERB
ejpam-6571	287	117	set	set	VERB
ejpam-6571	287	118	u	u	NOUN
ejpam-6571	287	119	of	of	ADP
ejpam-6571	287	120	x	x	PUNCT
ejpam-6571	287	121	containing	contain	VERB
ejpam-6571	287	122	x	x	PUNCT
ejpam-6571	287	123	such	such	ADJ
ejpam-6571	288	1	that	that	SCONJ
ejpam-6571	288	2	σ1σ2	σ1σ2	NOUN
ejpam-6571	288	3	-	-	NUM
ejpam-6571	288	4	cl(v	cl(v	PUNCT
ejpam-6571	288	5	)	)	PUNCT
ejpam-6571	288	6	∩f	∩f	NOUN
ejpam-6571	288	7	(	(	PUNCT
ejpam-6571	288	8	z	z	X
ejpam-6571	288	9	)	)	PUNCT
ejpam-6571	288	10	̸=	̸=	NOUN
ejpam-6571	288	11	∅	∅	NOUN
ejpam-6571	288	12	for	for	ADP
ejpam-6571	288	13	every	every	DET
ejpam-6571	288	14	z	z	NOUN
ejpam-6571	288	15	∈	∈	PROPN
ejpam-6571	288	16	u	u	NOUN
ejpam-6571	288	17	;	;	PUNCT
ejpam-6571	288	18	(	(	PUNCT
ejpam-6571	288	19	3	3	X
ejpam-6571	288	20	)	)	PUNCT
ejpam-6571	288	21	int⋆(cl⋆(f+(σ1σ2	int⋆(cl⋆(f+(σ1σ2	NOUN
ejpam-6571	288	22	-	-	PUNCT
ejpam-6571	288	23	int(k	int(k	NOUN
ejpam-6571	288	24	)	)	PUNCT
ejpam-6571	288	25	)	)	PUNCT
ejpam-6571	288	26	)	)	PUNCT
ejpam-6571	288	27	)	)	PUNCT
ejpam-6571	288	28	⊆	⊆	NUM
ejpam-6571	288	29	f+(k	f+(k	NOUN
ejpam-6571	288	30	)	)	PUNCT
ejpam-6571	288	31	for	for	ADP
ejpam-6571	288	32	every	every	DET
ejpam-6571	288	33	σ1σ2	σ1σ2	NUM
ejpam-6571	288	34	-	-	PUNCT
ejpam-6571	288	35	closed	closed	ADJ
ejpam-6571	288	36	set	set	NOUN
ejpam-6571	288	37	k	k	PROPN
ejpam-6571	288	38	of	of	ADP
ejpam-6571	288	39	y	y	PROPN
ejpam-6571	288	40	;	;	PUNCT
ejpam-6571	288	41	(	(	PUNCT
ejpam-6571	288	42	4	4	X
ejpam-6571	288	43	)	)	PUNCT
ejpam-6571	288	44	f−(v	f−(v	NOUN
ejpam-6571	288	45	)	)	PUNCT
ejpam-6571	289	1	⊆	⊆	NUM
ejpam-6571	289	2	sint⋆(f−(σ1σ2	sint⋆(f−(σ1σ2	NOUN
ejpam-6571	289	3	-	-	PUNCT
ejpam-6571	289	4	cl(v	cl(v	NOUN
ejpam-6571	289	5	)	)	PUNCT
ejpam-6571	289	6	)	)	PUNCT
ejpam-6571	289	7	)	)	PUNCT
ejpam-6571	289	8	for	for	ADP
ejpam-6571	289	9	every	every	DET
ejpam-6571	289	10	σ1σ2	σ1σ2	NOUN
ejpam-6571	289	11	-	-	ADJ
ejpam-6571	289	12	open	open	ADJ
ejpam-6571	289	13	set	set	NOUN
ejpam-6571	289	14	v	v	NOUN
ejpam-6571	289	15	of	of	ADP
ejpam-6571	289	16	y	y	PROPN
ejpam-6571	289	17	;	;	PUNCT
ejpam-6571	289	18	(	(	PUNCT
ejpam-6571	289	19	5	5	X
ejpam-6571	289	20	)	)	PUNCT
ejpam-6571	289	21	scl⋆(f+(v	scl⋆(f+(v	PROPN
ejpam-6571	289	22	)	)	PUNCT
ejpam-6571	289	23	)	)	PUNCT
ejpam-6571	290	1	⊆	⊆	NUM
ejpam-6571	290	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	290	3	-	-	PUNCT
ejpam-6571	290	4	cl(v	cl(v	NOUN
ejpam-6571	290	5	)	)	PUNCT
ejpam-6571	290	6	)	)	PUNCT
ejpam-6571	290	7	for	for	ADP
ejpam-6571	290	8	every	every	DET
ejpam-6571	290	9	σ1σ2	σ1σ2	NOUN
ejpam-6571	290	10	-	-	ADJ
ejpam-6571	290	11	open	open	ADJ
ejpam-6571	290	12	set	set	NOUN
ejpam-6571	290	13	v	v	NOUN
ejpam-6571	290	14	of	of	ADP
ejpam-6571	290	15	y	y	PROPN
ejpam-6571	290	16	.	.	PUNCT
ejpam-6571	291	1	proof	proof	NOUN
ejpam-6571	291	2	.	.	PUNCT
ejpam-6571	292	1	the	the	DET
ejpam-6571	292	2	proof	proof	NOUN
ejpam-6571	292	3	is	be	AUX
ejpam-6571	292	4	similar	similar	ADJ
ejpam-6571	292	5	to	to	ADP
ejpam-6571	292	6	that	that	PRON
ejpam-6571	292	7	of	of	ADP
ejpam-6571	292	8	theorem	theorem	ADJ
ejpam-6571	292	9	7	7	NUM
ejpam-6571	292	10	.	.	PUNCT
ejpam-6571	292	11	theorem	theorem	NOUN
ejpam-6571	292	12	9	9	NUM
ejpam-6571	292	13	.	.	X
ejpam-6571	292	14	for	for	ADP
ejpam-6571	292	15	a	a	DET
ejpam-6571	292	16	multifunction	multifunction	NOUN
ejpam-6571	292	17	f	f	NOUN
ejpam-6571	292	18	:	:	PUNCT
ejpam-6571	292	19	(	(	PUNCT
ejpam-6571	292	20	x	x	X
ejpam-6571	292	21	,	,	PUNCT
ejpam-6571	292	22	τ	τ	PROPN
ejpam-6571	292	23	,	,	PUNCT
ejpam-6571	292	24	i	i	NOUN
ejpam-6571	292	25	)	)	PUNCT
ejpam-6571	292	26	→	→	PUNCT
ejpam-6571	292	27	(	(	PUNCT
ejpam-6571	292	28	y	y	PROPN
ejpam-6571	292	29	,	,	PUNCT
ejpam-6571	292	30	σ1	σ1	PROPN
ejpam-6571	292	31	,	,	PUNCT
ejpam-6571	292	32	σ2	σ2	NOUN
ejpam-6571	292	33	)	)	PUNCT
ejpam-6571	292	34	,	,	PUNCT
ejpam-6571	292	35	the	the	DET
ejpam-6571	292	36	following	follow	VERB
ejpam-6571	292	37	properties	property	NOUN
ejpam-6571	292	38	are	be	AUX
ejpam-6571	292	39	equivalent	equivalent	ADJ
ejpam-6571	292	40	:	:	PUNCT
ejpam-6571	292	41	(	(	PUNCT
ejpam-6571	292	42	1	1	X
ejpam-6571	292	43	)	)	PUNCT
ejpam-6571	292	44	f	f	PROPN
ejpam-6571	292	45	is	be	AUX
ejpam-6571	292	46	upper	upper	ADJ
ejpam-6571	292	47	weakly	weakly	ADJ
ejpam-6571	292	48	quasi	quasi	NOUN
ejpam-6571	292	49	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	292	50	,	,	PUNCT
ejpam-6571	292	51	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	292	52	;	;	PUNCT
ejpam-6571	292	53	(	(	PUNCT
ejpam-6571	292	54	2	2	X
ejpam-6571	292	55	)	)	PUNCT
ejpam-6571	292	56	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	292	57	-	-	PUNCT
ejpam-6571	292	58	int((σ1	int((σ1	NUM
ejpam-6571	292	59	,	,	PUNCT
ejpam-6571	292	60	σ2)θ	σ2)θ	ADJ
ejpam-6571	292	61	-	-	PUNCT
ejpam-6571	292	62	cl(b	cl(b	NOUN
ejpam-6571	292	63	)	)	PUNCT
ejpam-6571	292	64	)	)	PUNCT
ejpam-6571	292	65	)	)	PUNCT
ejpam-6571	292	66	)	)	PUNCT
ejpam-6571	293	1	⊆	⊆	NUM
ejpam-6571	293	2	f−((σ1	f−((σ1	NOUN
ejpam-6571	293	3	,	,	PUNCT
ejpam-6571	293	4	σ2)θ	σ2)θ	ADJ
ejpam-6571	293	5	-	-	PUNCT
ejpam-6571	293	6	cl(b	cl(b	NOUN
ejpam-6571	293	7	)	)	PUNCT
ejpam-6571	293	8	)	)	PUNCT
ejpam-6571	293	9	for	for	ADP
ejpam-6571	293	10	every	every	DET
ejpam-6571	293	11	subset	subset	NOUN
ejpam-6571	293	12	b	b	PROPN
ejpam-6571	293	13	of	of	ADP
ejpam-6571	293	14	y	y	PROPN
ejpam-6571	293	15	;	;	PUNCT
ejpam-6571	293	16	(	(	PUNCT
ejpam-6571	293	17	3	3	X
ejpam-6571	293	18	)	)	PUNCT
ejpam-6571	293	19	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	293	20	-	-	PUNCT
ejpam-6571	293	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	293	22	-	-	PUNCT
ejpam-6571	293	23	cl(b	cl(b	NOUN
ejpam-6571	293	24	)	)	PUNCT
ejpam-6571	293	25	)	)	PUNCT
ejpam-6571	293	26	)	)	PUNCT
ejpam-6571	293	27	)	)	PUNCT
ejpam-6571	294	1	⊆	⊆	NUM
ejpam-6571	294	2	f−((σ1	f−((σ1	NOUN
ejpam-6571	294	3	,	,	PUNCT
ejpam-6571	294	4	σ2)θ	σ2)θ	ADJ
ejpam-6571	294	5	-	-	PUNCT
ejpam-6571	294	6	cl(b	cl(b	NOUN
ejpam-6571	294	7	)	)	PUNCT
ejpam-6571	294	8	)	)	PUNCT
ejpam-6571	294	9	for	for	ADP
ejpam-6571	294	10	every	every	DET
ejpam-6571	294	11	subset	subset	NOUN
ejpam-6571	294	12	b	b	PROPN
ejpam-6571	294	13	of	of	ADP
ejpam-6571	294	14	y	y	PROPN
ejpam-6571	294	15	;	;	PUNCT
ejpam-6571	294	16	(	(	PUNCT
ejpam-6571	294	17	4	4	X
ejpam-6571	294	18	)	)	PUNCT
ejpam-6571	294	19	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	294	20	-	-	PUNCT
ejpam-6571	294	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	294	22	-	-	PUNCT
ejpam-6571	294	23	cl(v	cl(v	NOUN
ejpam-6571	294	24	)	)	PUNCT
ejpam-6571	294	25	)	)	PUNCT
ejpam-6571	294	26	)	)	PUNCT
ejpam-6571	294	27	)	)	PUNCT
ejpam-6571	295	1	⊆	⊆	X
ejpam-6571	295	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	295	3	-	-	PUNCT
ejpam-6571	295	4	cl(v	cl(v	NOUN
ejpam-6571	295	5	)	)	PUNCT
ejpam-6571	295	6	)	)	PUNCT
ejpam-6571	295	7	for	for	ADP
ejpam-6571	295	8	every	every	DET
ejpam-6571	295	9	σ1σ2	σ1σ2	NOUN
ejpam-6571	295	10	-	-	ADJ
ejpam-6571	295	11	open	open	ADJ
ejpam-6571	295	12	set	set	NOUN
ejpam-6571	295	13	v	v	NOUN
ejpam-6571	295	14	of	of	ADP
ejpam-6571	295	15	y	y	PROPN
ejpam-6571	295	16	;	;	PUNCT
ejpam-6571	295	17	(	(	PUNCT
ejpam-6571	295	18	5	5	X
ejpam-6571	295	19	)	)	PUNCT
ejpam-6571	295	20	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	295	21	-	-	PUNCT
ejpam-6571	295	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	295	23	-	-	PUNCT
ejpam-6571	295	24	cl(v	cl(v	NOUN
ejpam-6571	295	25	)	)	PUNCT
ejpam-6571	295	26	)	)	PUNCT
ejpam-6571	295	27	)	)	PUNCT
ejpam-6571	295	28	)	)	PUNCT
ejpam-6571	296	1	⊆	⊆	X
ejpam-6571	296	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	296	3	-	-	PUNCT
ejpam-6571	296	4	cl(v	cl(v	NOUN
ejpam-6571	296	5	)	)	PUNCT
ejpam-6571	296	6	)	)	PUNCT
ejpam-6571	296	7	for	for	ADP
ejpam-6571	296	8	every	every	DET
ejpam-6571	296	9	(	(	PUNCT
ejpam-6571	296	10	σ1	σ1	PROPN
ejpam-6571	296	11	,	,	PUNCT
ejpam-6571	296	12	σ2)p	σ2)p	NOUN
ejpam-6571	296	13	-	-	PUNCT
ejpam-6571	296	14	open	open	NOUN
ejpam-6571	296	15	set	set	NOUN
ejpam-6571	296	16	v	v	NOUN
ejpam-6571	296	17	of	of	ADP
ejpam-6571	296	18	y	y	PROPN
ejpam-6571	296	19	;	;	PUNCT
ejpam-6571	296	20	(	(	PUNCT
ejpam-6571	296	21	6	6	X
ejpam-6571	296	22	)	)	PUNCT
ejpam-6571	296	23	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	296	24	-	-	PUNCT
ejpam-6571	296	25	int(k	int(k	NOUN
ejpam-6571	296	26	)	)	PUNCT
ejpam-6571	296	27	)	)	PUNCT
ejpam-6571	296	28	)	)	PUNCT
ejpam-6571	297	1	⊆	⊆	X
ejpam-6571	297	2	f−(k	f−(k	PROPN
ejpam-6571	297	3	)	)	PUNCT
ejpam-6571	297	4	for	for	ADP
ejpam-6571	297	5	every	every	DET
ejpam-6571	297	6	(	(	PUNCT
ejpam-6571	297	7	σ1	σ1	PROPN
ejpam-6571	297	8	,	,	PUNCT
ejpam-6571	297	9	σ2)r	σ2)r	NOUN
ejpam-6571	297	10	-	-	PUNCT
ejpam-6571	297	11	closed	close	VERB
ejpam-6571	297	12	set	set	ADJ
ejpam-6571	297	13	k	k	PROPN
ejpam-6571	297	14	of	of	ADP
ejpam-6571	297	15	y	y	PROPN
ejpam-6571	297	16	.	.	PUNCT
ejpam-6571	298	1	proof	proof	NOUN
ejpam-6571	298	2	.	.	PUNCT
ejpam-6571	299	1	(	(	PUNCT
ejpam-6571	299	2	1	1	X
ejpam-6571	299	3	)	)	PUNCT
ejpam-6571	299	4	⇒	⇒	NOUN
ejpam-6571	299	5	(	(	PUNCT
ejpam-6571	299	6	2	2	NUM
ejpam-6571	299	7	):	):	PUNCT
ejpam-6571	299	8	let	let	VERB
ejpam-6571	299	9	b	b	X
ejpam-6571	299	10	be	be	AUX
ejpam-6571	299	11	any	any	DET
ejpam-6571	299	12	subset	subset	NOUN
ejpam-6571	299	13	of	of	ADP
ejpam-6571	299	14	y	y	PROPN
ejpam-6571	299	15	.	.	PUNCT
ejpam-6571	300	1	since	since	SCONJ
ejpam-6571	300	2	(	(	PUNCT
ejpam-6571	300	3	σ1	σ1	PROPN
ejpam-6571	300	4	,	,	PUNCT
ejpam-6571	300	5	σ2)θ	σ2)θ	NOUN
ejpam-6571	300	6	-	-	PUNCT
ejpam-6571	300	7	cl(b	cl(b	NOUN
ejpam-6571	300	8	)	)	PUNCT
ejpam-6571	300	9	is	be	AUX
ejpam-6571	300	10	σ1σ2	σ1σ2	NOUN
ejpam-6571	300	11	-	-	ADJ
ejpam-6571	300	12	closed	closed	ADJ
ejpam-6571	300	13	in	in	ADP
ejpam-6571	300	14	y	y	PROPN
ejpam-6571	300	15	,	,	PUNCT
ejpam-6571	300	16	by	by	ADP
ejpam-6571	300	17	theorem	theorem	NOUN
ejpam-6571	300	18	7	7	NUM
ejpam-6571	300	19	we	we	PRON
ejpam-6571	300	20	have	have	VERB
ejpam-6571	300	21	int⋆(cl⋆(f−(σ1σ2	int⋆(cl⋆(f−(σ1σ2	VERB
ejpam-6571	300	22	-	-	PUNCT
ejpam-6571	300	23	int((σ1	int((σ1	ADJ
ejpam-6571	300	24	,	,	PUNCT
ejpam-6571	300	25	σ2)θ	σ2)θ	ADJ
ejpam-6571	300	26	-	-	PUNCT
ejpam-6571	300	27	cl(b	cl(b	NOUN
ejpam-6571	300	28	)	)	PUNCT
ejpam-6571	300	29	)	)	PUNCT
ejpam-6571	300	30	)	)	PUNCT
ejpam-6571	300	31	)	)	PUNCT
ejpam-6571	300	32	)	)	PUNCT
ejpam-6571	301	1	⊆	⊆	NUM
ejpam-6571	301	2	f−((σ1	f−((σ1	NOUN
ejpam-6571	301	3	,	,	PUNCT
ejpam-6571	301	4	σ2)θ	σ2)θ	ADJ
ejpam-6571	301	5	-	-	PUNCT
ejpam-6571	301	6	cl(b	cl(b	NOUN
ejpam-6571	301	7	)	)	PUNCT
ejpam-6571	301	8	)	)	PUNCT
ejpam-6571	301	9	and	and	CCONJ
ejpam-6571	301	10	by	by	ADP
ejpam-6571	301	11	lemma	lemma	PROPN
ejpam-6571	301	12	3	3	NUM
ejpam-6571	301	13	,	,	PUNCT
ejpam-6571	301	14	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	301	15	-	-	PUNCT
ejpam-6571	301	16	int((σ1	int((σ1	NUM
ejpam-6571	301	17	,	,	PUNCT
ejpam-6571	301	18	σ2)θ	σ2)θ	ADJ
ejpam-6571	301	19	-	-	PUNCT
ejpam-6571	301	20	cl(b	cl(b	NOUN
ejpam-6571	301	21	)	)	PUNCT
ejpam-6571	301	22	)	)	PUNCT
ejpam-6571	301	23	)	)	PUNCT
ejpam-6571	301	24	)	)	PUNCT
ejpam-6571	302	1	⊆	⊆	NUM
ejpam-6571	302	2	f−((σ1	f−((σ1	NOUN
ejpam-6571	302	3	,	,	PUNCT
ejpam-6571	302	4	σ2)θ	σ2)θ	ADJ
ejpam-6571	302	5	-	-	PUNCT
ejpam-6571	302	6	cl(b	cl(b	NOUN
ejpam-6571	302	7	)	)	PUNCT
ejpam-6571	302	8	)	)	PUNCT
ejpam-6571	302	9	.	.	PUNCT
ejpam-6571	303	1	(	(	PUNCT
ejpam-6571	303	2	2	2	X
ejpam-6571	303	3	)	)	PUNCT
ejpam-6571	303	4	⇒	⇒	NOUN
ejpam-6571	303	5	(	(	PUNCT
ejpam-6571	303	6	3	3	NUM
ejpam-6571	303	7	):	):	PUNCT
ejpam-6571	303	8	this	this	PRON
ejpam-6571	303	9	is	be	AUX
ejpam-6571	303	10	obvious	obvious	ADJ
ejpam-6571	303	11	since	since	SCONJ
ejpam-6571	303	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	303	13	-	-	NOUN
ejpam-6571	303	14	cl(b	cl(b	NOUN
ejpam-6571	303	15	)	)	PUNCT
ejpam-6571	303	16	⊆	⊆	NUM
ejpam-6571	303	17	(	(	PUNCT
ejpam-6571	303	18	σ1	σ1	PROPN
ejpam-6571	303	19	,	,	PUNCT
ejpam-6571	303	20	σ2)θ	σ2)θ	NOUN
ejpam-6571	303	21	-	-	PUNCT
ejpam-6571	303	22	cl(b	cl(b	NOUN
ejpam-6571	303	23	)	)	PUNCT
ejpam-6571	303	24	for	for	ADP
ejpam-6571	303	25	every	every	DET
ejpam-6571	303	26	subset	subset	NOUN
ejpam-6571	303	27	b	b	PROPN
ejpam-6571	303	28	of	of	ADP
ejpam-6571	303	29	y	y	PROPN
ejpam-6571	303	30	.	.	PUNCT
ejpam-6571	304	1	(	(	PUNCT
ejpam-6571	304	2	3	3	X
ejpam-6571	304	3	)	)	PUNCT
ejpam-6571	304	4	⇒	⇒	NOUN
ejpam-6571	304	5	(	(	PUNCT
ejpam-6571	304	6	4	4	NUM
ejpam-6571	304	7	):	):	PUNCT
ejpam-6571	304	8	this	this	PRON
ejpam-6571	304	9	is	be	AUX
ejpam-6571	304	10	obvious	obvious	ADJ
ejpam-6571	304	11	since	since	SCONJ
ejpam-6571	304	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	304	13	-	-	NOUN
ejpam-6571	304	14	cl(v	cl(v	X
ejpam-6571	304	15	)	)	PUNCT
ejpam-6571	305	1	=	=	SYM
ejpam-6571	305	2	(	(	PUNCT
ejpam-6571	305	3	σ1	σ1	PROPN
ejpam-6571	305	4	,	,	PUNCT
ejpam-6571	305	5	σ2)θ	σ2)θ	NOUN
ejpam-6571	305	6	-	-	PUNCT
ejpam-6571	305	7	cl(v	cl(v	NOUN
ejpam-6571	305	8	)	)	PUNCT
ejpam-6571	305	9	for	for	ADP
ejpam-6571	305	10	every	every	DET
ejpam-6571	305	11	σ1σ2	σ1σ2	NOUN
ejpam-6571	305	12	-	-	ADJ
ejpam-6571	305	13	open	open	ADJ
ejpam-6571	305	14	set	set	NOUN
ejpam-6571	305	15	v	v	NOUN
ejpam-6571	305	16	of	of	ADP
ejpam-6571	305	17	y	y	PROPN
ejpam-6571	305	18	.	.	PUNCT
ejpam-6571	306	1	m.	m.	NOUN
ejpam-6571	306	2	thongmoon	thongmoon	PROPN
ejpam-6571	306	3	,	,	PUNCT
ejpam-6571	306	4	a.	a.	PROPN
ejpam-6571	306	5	sama	sama	PROPN
ejpam-6571	306	6	-	-	PUNCT
ejpam-6571	306	7	ae	ae	PROPN
ejpam-6571	306	8	,	,	PUNCT
ejpam-6571	306	9	c.	c.	PROPN
ejpam-6571	306	10	boonpok	boonpok	PROPN
ejpam-6571	306	11	/	/	SYM
ejpam-6571	306	12	eur	eur	PROPN
ejpam-6571	306	13	.	.	PUNCT
ejpam-6571	307	1	j.	j.	PROPN
ejpam-6571	307	2	pure	pure	PROPN
ejpam-6571	307	3	appl	appl	PROPN
ejpam-6571	307	4	.	.	PROPN
ejpam-6571	307	5	math	math	PROPN
ejpam-6571	307	6	,	,	PUNCT
ejpam-6571	307	7	18	18	NUM
ejpam-6571	307	8	(	(	PUNCT
ejpam-6571	307	9	3	3	NUM
ejpam-6571	307	10	)	)	PUNCT
ejpam-6571	307	11	(	(	PUNCT
ejpam-6571	307	12	2025	2025	NUM
ejpam-6571	307	13	)	)	PUNCT
ejpam-6571	307	14	,	,	PUNCT
ejpam-6571	307	15	6571	6571	NUM
ejpam-6571	307	16	11	11	NUM
ejpam-6571	307	17	of	of	ADP
ejpam-6571	307	18	15	15	NUM
ejpam-6571	307	19	(	(	PUNCT
ejpam-6571	307	20	4	4	NUM
ejpam-6571	307	21	)	)	PUNCT
ejpam-6571	307	22	⇒	⇒	NOUN
ejpam-6571	307	23	(	(	PUNCT
ejpam-6571	307	24	5	5	NUM
ejpam-6571	307	25	):	):	PUNCT
ejpam-6571	307	26	let	let	VERB
ejpam-6571	307	27	v	v	PART
ejpam-6571	307	28	be	be	AUX
ejpam-6571	307	29	any	any	DET
ejpam-6571	307	30	(	(	PUNCT
ejpam-6571	307	31	σ1	σ1	PROPN
ejpam-6571	307	32	,	,	PUNCT
ejpam-6571	307	33	σ2)p	σ2)p	NOUN
ejpam-6571	307	34	-	-	PUNCT
ejpam-6571	307	35	open	open	ADJ
ejpam-6571	307	36	set	set	NOUN
ejpam-6571	307	37	of	of	ADP
ejpam-6571	307	38	y	y	PROPN
ejpam-6571	307	39	.	.	PUNCT
ejpam-6571	308	1	then	then	ADV
ejpam-6571	308	2	,	,	PUNCT
ejpam-6571	308	3	v	v	ADP
ejpam-6571	308	4	⊆	⊆	NUM
ejpam-6571	308	5	σ1σ2	σ1σ2	NOUN
ejpam-6571	308	6	-	-	PUNCT
ejpam-6571	308	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	308	8	-	-	PUNCT
ejpam-6571	308	9	cl(v	cl(v	NOUN
ejpam-6571	308	10	)	)	PUNCT
ejpam-6571	308	11	)	)	PUNCT
ejpam-6571	308	12	and	and	CCONJ
ejpam-6571	308	13	σ1σ2	σ1σ2	NOUN
ejpam-6571	308	14	-	-	NUM
ejpam-6571	308	15	cl(v	cl(v	X
ejpam-6571	308	16	)	)	PUNCT
ejpam-6571	309	1	=	=	SYM
ejpam-6571	309	2	σ1σ2	σ1σ2	X
ejpam-6571	309	3	-	-	PUNCT
ejpam-6571	309	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	309	5	-	-	PUNCT
ejpam-6571	309	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	309	7	-	-	PUNCT
ejpam-6571	309	8	cl(v	cl(v	NOUN
ejpam-6571	309	9	)	)	PUNCT
ejpam-6571	309	10	)	)	PUNCT
ejpam-6571	309	11	)	)	PUNCT
ejpam-6571	309	12	.	.	PUNCT
ejpam-6571	310	1	now	now	ADV
ejpam-6571	310	2	,	,	PUNCT
ejpam-6571	310	3	put	put	VERB
ejpam-6571	310	4	g	g	NOUN
ejpam-6571	310	5	=	=	SYM
ejpam-6571	310	6	σ1σ2	σ1σ2	NOUN
ejpam-6571	310	7	-	-	PUNCT
ejpam-6571	310	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	310	9	-	-	PUNCT
ejpam-6571	310	10	cl(v	cl(v	NOUN
ejpam-6571	310	11	)	)	PUNCT
ejpam-6571	310	12	)	)	PUNCT
ejpam-6571	310	13	,	,	PUNCT
ejpam-6571	310	14	then	then	ADV
ejpam-6571	310	15	g	g	PROPN
ejpam-6571	310	16	is	be	AUX
ejpam-6571	310	17	σ1σ2	σ1σ2	NOUN
ejpam-6571	310	18	-	-	ADJ
ejpam-6571	310	19	open	open	ADJ
ejpam-6571	310	20	in	in	ADP
ejpam-6571	310	21	y	y	PROPN
ejpam-6571	310	22	and	and	CCONJ
ejpam-6571	310	23	σ1σ2	σ1σ2	NOUN
ejpam-6571	310	24	-	-	NUM
ejpam-6571	310	25	cl(g	cl(g	ADJ
ejpam-6571	310	26	)	)	PUNCT
ejpam-6571	310	27	=	=	PUNCT
ejpam-6571	310	28	σ1σ2	σ1σ2	NOUN
ejpam-6571	310	29	-	-	NUM
ejpam-6571	310	30	cl(v	cl(v	NOUN
ejpam-6571	310	31	)	)	PUNCT
ejpam-6571	310	32	.	.	PUNCT
ejpam-6571	311	1	thus	thus	ADV
ejpam-6571	311	2	by	by	ADP
ejpam-6571	311	3	(	(	PUNCT
ejpam-6571	311	4	4	4	NUM
ejpam-6571	311	5	)	)	PUNCT
ejpam-6571	311	6	,	,	PUNCT
ejpam-6571	311	7	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	311	8	-	-	PUNCT
ejpam-6571	311	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	311	10	-	-	PUNCT
ejpam-6571	311	11	cl(v	cl(v	NOUN
ejpam-6571	311	12	)	)	PUNCT
ejpam-6571	311	13	)	)	PUNCT
ejpam-6571	311	14	)	)	PUNCT
ejpam-6571	311	15	)	)	PUNCT
ejpam-6571	311	16	⊆	⊆	X
ejpam-6571	311	17	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	311	18	-	-	PUNCT
ejpam-6571	311	19	cl(v	cl(v	NOUN
ejpam-6571	311	20	)	)	PUNCT
ejpam-6571	311	21	)	)	PUNCT
ejpam-6571	311	22	.	.	PUNCT
ejpam-6571	312	1	(	(	PUNCT
ejpam-6571	312	2	5	5	X
ejpam-6571	312	3	)	)	PUNCT
ejpam-6571	312	4	⇒	⇒	NOUN
ejpam-6571	312	5	(	(	PUNCT
ejpam-6571	312	6	6	6	NUM
ejpam-6571	312	7	):	):	PUNCT
ejpam-6571	312	8	let	let	VERB
ejpam-6571	312	9	k	k	PRON
ejpam-6571	312	10	be	be	AUX
ejpam-6571	312	11	any	any	DET
ejpam-6571	312	12	(	(	PUNCT
ejpam-6571	312	13	σ1	σ1	NOUN
ejpam-6571	312	14	,	,	PUNCT
ejpam-6571	312	15	σ2)r	σ2)r	NOUN
ejpam-6571	312	16	-	-	PUNCT
ejpam-6571	312	17	closed	close	VERB
ejpam-6571	312	18	set	set	NOUN
ejpam-6571	312	19	of	of	ADP
ejpam-6571	312	20	y	y	PROPN
ejpam-6571	312	21	.	.	PUNCT
ejpam-6571	313	1	since	since	SCONJ
ejpam-6571	313	2	σ1σ2	σ1σ2	NOUN
ejpam-6571	313	3	-	-	SYM
ejpam-6571	313	4	int(k	int(k	NOUN
ejpam-6571	313	5	)	)	PUNCT
ejpam-6571	313	6	is	be	AUX
ejpam-6571	313	7	(	(	PUNCT
ejpam-6571	313	8	σ1	σ1	PROPN
ejpam-6571	313	9	,	,	PUNCT
ejpam-6571	313	10	σ2)p	σ2)p	NOUN
ejpam-6571	313	11	-	-	PUNCT
ejpam-6571	313	12	open	open	ADJ
ejpam-6571	313	13	in	in	ADP
ejpam-6571	313	14	y	y	PROPN
ejpam-6571	313	15	,	,	PUNCT
ejpam-6571	313	16	by	by	ADP
ejpam-6571	313	17	(	(	PUNCT
ejpam-6571	313	18	5	5	X
ejpam-6571	313	19	)	)	PUNCT
ejpam-6571	313	20	we	we	PRON
ejpam-6571	313	21	have	have	VERB
ejpam-6571	313	22	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	313	23	-	-	PUNCT
ejpam-6571	313	24	int(k	int(k	NOUN
ejpam-6571	313	25	)	)	PUNCT
ejpam-6571	313	26	)	)	PUNCT
ejpam-6571	313	27	)	)	PUNCT
ejpam-6571	314	1	=	=	PRON
ejpam-6571	314	2	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	VERB
ejpam-6571	314	3	-	-	PUNCT
ejpam-6571	314	4	int(σ1σ2	int(σ1σ2	ADV
ejpam-6571	314	5	-	-	PUNCT
ejpam-6571	314	6	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-6571	314	7	-	-	PUNCT
ejpam-6571	314	8	int(k	int(k	NOUN
ejpam-6571	314	9	)	)	PUNCT
ejpam-6571	314	10	)	)	PUNCT
ejpam-6571	314	11	)	)	PUNCT
ejpam-6571	314	12	)	)	PUNCT
ejpam-6571	314	13	)	)	PUNCT
ejpam-6571	315	1	⊆	⊆	X
ejpam-6571	315	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-6571	315	3	-	-	PUNCT
ejpam-6571	315	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	315	5	-	-	PUNCT
ejpam-6571	315	6	int(k	int(k	NOUN
ejpam-6571	315	7	)	)	PUNCT
ejpam-6571	315	8	)	)	PUNCT
ejpam-6571	315	9	)	)	PUNCT
ejpam-6571	316	1	=	=	SYM
ejpam-6571	316	2	f−(k	f−(k	PROPN
ejpam-6571	316	3	)	)	PUNCT
ejpam-6571	316	4	.	.	PUNCT
ejpam-6571	317	1	(	(	PUNCT
ejpam-6571	317	2	6	6	X
ejpam-6571	317	3	)	)	PUNCT
ejpam-6571	317	4	⇒	⇒	NOUN
ejpam-6571	317	5	(	(	PUNCT
ejpam-6571	317	6	1	1	NUM
ejpam-6571	317	7	):	):	PUNCT
ejpam-6571	317	8	let	let	VERB
ejpam-6571	317	9	v	v	PART
ejpam-6571	317	10	be	be	AUX
ejpam-6571	317	11	any	any	DET
ejpam-6571	317	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	317	13	-	-	ADJ
ejpam-6571	317	14	open	open	ADJ
ejpam-6571	317	15	set	set	NOUN
ejpam-6571	317	16	of	of	ADP
ejpam-6571	317	17	y	y	PROPN
ejpam-6571	317	18	.	.	PUNCT
ejpam-6571	318	1	then	then	ADV
ejpam-6571	318	2	,	,	PUNCT
ejpam-6571	318	3	σ1σ2	σ1σ2	NOUN
ejpam-6571	318	4	-	-	NUM
ejpam-6571	318	5	cl(v	cl(v	NOUN
ejpam-6571	318	6	)	)	PUNCT
ejpam-6571	318	7	is	be	AUX
ejpam-6571	318	8	(	(	PUNCT
ejpam-6571	318	9	σ1	σ1	NOUN
ejpam-6571	318	10	,	,	PUNCT
ejpam-6571	318	11	σ2)r	σ2)r	NOUN
ejpam-6571	318	12	-	-	PUNCT
ejpam-6571	318	13	closed	closed	ADJ
ejpam-6571	318	14	in	in	ADP
ejpam-6571	318	15	y	y	PROPN
ejpam-6571	318	16	and	and	CCONJ
ejpam-6571	318	17	by	by	ADP
ejpam-6571	318	18	(	(	PUNCT
ejpam-6571	318	19	6	6	NUM
ejpam-6571	318	20	)	)	PUNCT
ejpam-6571	318	21	,	,	PUNCT
ejpam-6571	318	22	scl⋆(f−(v	scl⋆(f−(v	PUNCT
ejpam-6571	318	23	)	)	PUNCT
ejpam-6571	318	24	)	)	PUNCT
ejpam-6571	319	1	⊆	⊆	X
ejpam-6571	319	2	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	319	3	-	-	PUNCT
ejpam-6571	319	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	319	5	-	-	PUNCT
ejpam-6571	319	6	cl(v	cl(v	NOUN
ejpam-6571	319	7	)	)	PUNCT
ejpam-6571	319	8	)	)	PUNCT
ejpam-6571	319	9	)	)	PUNCT
ejpam-6571	319	10	)	)	PUNCT
ejpam-6571	320	1	⊆	⊆	X
ejpam-6571	320	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	320	3	-	-	PUNCT
ejpam-6571	320	4	cl(v	cl(v	NOUN
ejpam-6571	320	5	)	)	PUNCT
ejpam-6571	320	6	)	)	PUNCT
ejpam-6571	320	7	.	.	PUNCT
ejpam-6571	321	1	it	it	PRON
ejpam-6571	321	2	follows	follow	VERB
ejpam-6571	321	3	from	from	ADP
ejpam-6571	321	4	theorem	theorem	ADJ
ejpam-6571	321	5	7	7	NUM
ejpam-6571	321	6	that	that	SCONJ
ejpam-6571	321	7	f	f	PROPN
ejpam-6571	321	8	is	be	AUX
ejpam-6571	321	9	upper	upper	ADJ
ejpam-6571	321	10	weakly	weakly	ADJ
ejpam-6571	321	11	quasi	quasi	NOUN
ejpam-6571	321	12	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	321	13	,	,	PUNCT
ejpam-6571	321	14	σ2)-continuous	σ2)-continuous	PROPN
ejpam-6571	321	15	.	.	X
ejpam-6571	321	16	theorem	theorem	NOUN
ejpam-6571	321	17	10	10	NUM
ejpam-6571	321	18	.	.	PUNCT
ejpam-6571	322	1	for	for	ADP
ejpam-6571	322	2	a	a	DET
ejpam-6571	322	3	multifunction	multifunction	NOUN
ejpam-6571	322	4	f	f	NOUN
ejpam-6571	322	5	:	:	PUNCT
ejpam-6571	322	6	(	(	PUNCT
ejpam-6571	322	7	x	x	X
ejpam-6571	322	8	,	,	PUNCT
ejpam-6571	322	9	τ	τ	PROPN
ejpam-6571	322	10	,	,	PUNCT
ejpam-6571	322	11	i	i	NOUN
ejpam-6571	322	12	)	)	PUNCT
ejpam-6571	322	13	→	→	PUNCT
ejpam-6571	322	14	(	(	PUNCT
ejpam-6571	322	15	y	y	PROPN
ejpam-6571	322	16	,	,	PUNCT
ejpam-6571	322	17	σ1	σ1	PROPN
ejpam-6571	322	18	,	,	PUNCT
ejpam-6571	322	19	σ2	σ2	NOUN
ejpam-6571	322	20	)	)	PUNCT
ejpam-6571	322	21	,	,	PUNCT
ejpam-6571	322	22	the	the	DET
ejpam-6571	322	23	following	follow	VERB
ejpam-6571	322	24	properties	property	NOUN
ejpam-6571	322	25	are	be	AUX
ejpam-6571	322	26	equivalent	equivalent	ADJ
ejpam-6571	322	27	:	:	PUNCT
ejpam-6571	322	28	(	(	PUNCT
ejpam-6571	322	29	1	1	X
ejpam-6571	322	30	)	)	PUNCT
ejpam-6571	322	31	f	f	PROPN
ejpam-6571	322	32	is	be	AUX
ejpam-6571	322	33	lower	low	ADJ
ejpam-6571	322	34	weakly	weakly	ADJ
ejpam-6571	322	35	quasi	quasi	ADJ
ejpam-6571	322	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	322	37	,	,	PUNCT
ejpam-6571	322	38	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	322	39	;	;	PUNCT
ejpam-6571	322	40	(	(	PUNCT
ejpam-6571	322	41	2	2	X
ejpam-6571	322	42	)	)	PUNCT
ejpam-6571	322	43	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	322	44	-	-	PUNCT
ejpam-6571	322	45	int((σ1	int((σ1	PROPN
ejpam-6571	322	46	,	,	PUNCT
ejpam-6571	322	47	σ2)θ	σ2)θ	ADJ
ejpam-6571	322	48	-	-	PUNCT
ejpam-6571	322	49	cl(b	cl(b	NOUN
ejpam-6571	322	50	)	)	PUNCT
ejpam-6571	322	51	)	)	PUNCT
ejpam-6571	322	52	)	)	PUNCT
ejpam-6571	322	53	)	)	PUNCT
ejpam-6571	323	1	⊆	⊆	NUM
ejpam-6571	323	2	f+((σ1	f+((σ1	NOUN
ejpam-6571	323	3	,	,	PUNCT
ejpam-6571	323	4	σ2)θ	σ2)θ	ADJ
ejpam-6571	323	5	-	-	PUNCT
ejpam-6571	323	6	cl(b	cl(b	NOUN
ejpam-6571	323	7	)	)	PUNCT
ejpam-6571	323	8	)	)	PUNCT
ejpam-6571	323	9	for	for	ADP
ejpam-6571	323	10	every	every	DET
ejpam-6571	323	11	subset	subset	NOUN
ejpam-6571	323	12	b	b	PROPN
ejpam-6571	323	13	of	of	ADP
ejpam-6571	323	14	y	y	PROPN
ejpam-6571	323	15	;	;	PUNCT
ejpam-6571	323	16	(	(	PUNCT
ejpam-6571	323	17	3	3	X
ejpam-6571	323	18	)	)	PUNCT
ejpam-6571	323	19	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	323	20	-	-	PUNCT
ejpam-6571	323	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	323	22	-	-	PUNCT
ejpam-6571	323	23	cl(b	cl(b	NOUN
ejpam-6571	323	24	)	)	PUNCT
ejpam-6571	323	25	)	)	PUNCT
ejpam-6571	323	26	)	)	PUNCT
ejpam-6571	323	27	)	)	PUNCT
ejpam-6571	324	1	⊆	⊆	NUM
ejpam-6571	324	2	f+((σ1	f+((σ1	NOUN
ejpam-6571	324	3	,	,	PUNCT
ejpam-6571	324	4	σ2)θ	σ2)θ	ADJ
ejpam-6571	324	5	-	-	PUNCT
ejpam-6571	324	6	cl(b	cl(b	NOUN
ejpam-6571	324	7	)	)	PUNCT
ejpam-6571	324	8	)	)	PUNCT
ejpam-6571	324	9	for	for	ADP
ejpam-6571	324	10	every	every	DET
ejpam-6571	324	11	subset	subset	NOUN
ejpam-6571	324	12	b	b	PROPN
ejpam-6571	324	13	of	of	ADP
ejpam-6571	324	14	y	y	PROPN
ejpam-6571	324	15	;	;	PUNCT
ejpam-6571	324	16	(	(	PUNCT
ejpam-6571	324	17	4	4	X
ejpam-6571	324	18	)	)	PUNCT
ejpam-6571	324	19	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	324	20	-	-	PUNCT
ejpam-6571	324	21	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	324	22	-	-	PUNCT
ejpam-6571	324	23	cl(v	cl(v	NOUN
ejpam-6571	324	24	)	)	PUNCT
ejpam-6571	324	25	)	)	PUNCT
ejpam-6571	324	26	)	)	PUNCT
ejpam-6571	324	27	)	)	PUNCT
ejpam-6571	325	1	⊆	⊆	X
ejpam-6571	325	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	325	3	-	-	PUNCT
ejpam-6571	325	4	cl(v	cl(v	NOUN
ejpam-6571	325	5	)	)	PUNCT
ejpam-6571	325	6	)	)	PUNCT
ejpam-6571	325	7	for	for	ADP
ejpam-6571	325	8	every	every	DET
ejpam-6571	325	9	σ1σ2	σ1σ2	NOUN
ejpam-6571	325	10	-	-	ADJ
ejpam-6571	325	11	open	open	ADJ
ejpam-6571	325	12	set	set	NOUN
ejpam-6571	325	13	v	v	NOUN
ejpam-6571	325	14	of	of	ADP
ejpam-6571	325	15	y	y	PROPN
ejpam-6571	325	16	;	;	PUNCT
ejpam-6571	325	17	(	(	PUNCT
ejpam-6571	325	18	5	5	X
ejpam-6571	325	19	)	)	PUNCT
ejpam-6571	325	20	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	325	21	-	-	PUNCT
ejpam-6571	325	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	325	23	-	-	PUNCT
ejpam-6571	325	24	cl(v	cl(v	NOUN
ejpam-6571	325	25	)	)	PUNCT
ejpam-6571	325	26	)	)	PUNCT
ejpam-6571	325	27	)	)	PUNCT
ejpam-6571	325	28	)	)	PUNCT
ejpam-6571	325	29	⊆	⊆	X
ejpam-6571	325	30	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	325	31	-	-	PUNCT
ejpam-6571	325	32	cl(v	cl(v	NOUN
ejpam-6571	325	33	)	)	PUNCT
ejpam-6571	325	34	)	)	PUNCT
ejpam-6571	325	35	for	for	ADP
ejpam-6571	325	36	every	every	DET
ejpam-6571	325	37	(	(	PUNCT
ejpam-6571	325	38	σ1	σ1	PROPN
ejpam-6571	325	39	,	,	PUNCT
ejpam-6571	325	40	σ2)p	σ2)p	NOUN
ejpam-6571	325	41	-	-	PUNCT
ejpam-6571	325	42	open	open	NOUN
ejpam-6571	325	43	set	set	NOUN
ejpam-6571	325	44	v	v	NOUN
ejpam-6571	325	45	of	of	ADP
ejpam-6571	325	46	y	y	PROPN
ejpam-6571	325	47	;	;	PUNCT
ejpam-6571	325	48	(	(	PUNCT
ejpam-6571	325	49	6	6	X
ejpam-6571	325	50	)	)	PUNCT
ejpam-6571	325	51	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	325	52	-	-	PUNCT
ejpam-6571	325	53	int(k	int(k	PROPN
ejpam-6571	325	54	)	)	PUNCT
ejpam-6571	325	55	)	)	PUNCT
ejpam-6571	325	56	)	)	PUNCT
ejpam-6571	325	57	⊆	⊆	NUM
ejpam-6571	325	58	f+(k	f+(k	NOUN
ejpam-6571	325	59	)	)	PUNCT
ejpam-6571	325	60	for	for	ADP
ejpam-6571	325	61	every	every	DET
ejpam-6571	325	62	(	(	PUNCT
ejpam-6571	325	63	σ1	σ1	PROPN
ejpam-6571	325	64	,	,	PUNCT
ejpam-6571	325	65	σ2)r	σ2)r	NOUN
ejpam-6571	325	66	-	-	PUNCT
ejpam-6571	325	67	closed	close	VERB
ejpam-6571	325	68	set	set	ADJ
ejpam-6571	325	69	k	k	PROPN
ejpam-6571	325	70	of	of	ADP
ejpam-6571	325	71	y	y	PROPN
ejpam-6571	325	72	.	.	PUNCT
ejpam-6571	326	1	proof	proof	NOUN
ejpam-6571	326	2	.	.	PUNCT
ejpam-6571	327	1	the	the	DET
ejpam-6571	327	2	proof	proof	NOUN
ejpam-6571	327	3	is	be	AUX
ejpam-6571	327	4	similar	similar	ADJ
ejpam-6571	327	5	to	to	ADP
ejpam-6571	327	6	that	that	PRON
ejpam-6571	327	7	of	of	ADP
ejpam-6571	327	8	theorem	theorem	ADJ
ejpam-6571	327	9	9	9	NUM
ejpam-6571	327	10	.	.	PUNCT
ejpam-6571	327	11	theorem	theorem	VERB
ejpam-6571	327	12	11	11	NUM
ejpam-6571	327	13	.	.	PUNCT
ejpam-6571	328	1	for	for	ADP
ejpam-6571	328	2	a	a	DET
ejpam-6571	328	3	multifunction	multifunction	NOUN
ejpam-6571	328	4	f	f	NOUN
ejpam-6571	328	5	:	:	PUNCT
ejpam-6571	328	6	(	(	PUNCT
ejpam-6571	328	7	x	x	X
ejpam-6571	328	8	,	,	PUNCT
ejpam-6571	328	9	τ	τ	PROPN
ejpam-6571	328	10	,	,	PUNCT
ejpam-6571	328	11	i	i	NOUN
ejpam-6571	328	12	)	)	PUNCT
ejpam-6571	328	13	→	→	PUNCT
ejpam-6571	328	14	(	(	PUNCT
ejpam-6571	328	15	y	y	PROPN
ejpam-6571	328	16	,	,	PUNCT
ejpam-6571	328	17	σ1	σ1	PROPN
ejpam-6571	328	18	,	,	PUNCT
ejpam-6571	328	19	σ2	σ2	NOUN
ejpam-6571	328	20	)	)	PUNCT
ejpam-6571	328	21	,	,	PUNCT
ejpam-6571	328	22	the	the	DET
ejpam-6571	328	23	following	follow	VERB
ejpam-6571	328	24	properties	property	NOUN
ejpam-6571	328	25	are	be	AUX
ejpam-6571	328	26	equivalent	equivalent	ADJ
ejpam-6571	328	27	:	:	PUNCT
ejpam-6571	328	28	(	(	PUNCT
ejpam-6571	328	29	1	1	X
ejpam-6571	328	30	)	)	PUNCT
ejpam-6571	328	31	f	f	PROPN
ejpam-6571	328	32	is	be	AUX
ejpam-6571	328	33	upper	upper	ADJ
ejpam-6571	328	34	weakly	weakly	ADJ
ejpam-6571	328	35	quasi	quasi	NOUN
ejpam-6571	328	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	328	37	,	,	PUNCT
ejpam-6571	328	38	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	328	39	;	;	PUNCT
ejpam-6571	328	40	(	(	PUNCT
ejpam-6571	328	41	2	2	X
ejpam-6571	328	42	)	)	PUNCT
ejpam-6571	328	43	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	328	44	-	-	PUNCT
ejpam-6571	328	45	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	328	46	-	-	PUNCT
ejpam-6571	328	47	cl(v	cl(v	NOUN
ejpam-6571	328	48	)	)	PUNCT
ejpam-6571	328	49	)	)	PUNCT
ejpam-6571	328	50	)	)	PUNCT
ejpam-6571	328	51	)	)	PUNCT
ejpam-6571	329	1	⊆	⊆	X
ejpam-6571	329	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	329	3	-	-	PUNCT
ejpam-6571	329	4	cl(v	cl(v	NOUN
ejpam-6571	329	5	)	)	PUNCT
ejpam-6571	329	6	)	)	PUNCT
ejpam-6571	329	7	for	for	ADP
ejpam-6571	329	8	every	every	DET
ejpam-6571	329	9	(	(	PUNCT
ejpam-6571	329	10	σ1	σ1	PROPN
ejpam-6571	329	11	,	,	PUNCT
ejpam-6571	329	12	σ2)β	σ2)β	NOUN
ejpam-6571	329	13	-	-	PUNCT
ejpam-6571	329	14	open	open	NOUN
ejpam-6571	329	15	set	set	NOUN
ejpam-6571	329	16	v	v	NOUN
ejpam-6571	329	17	of	of	ADP
ejpam-6571	329	18	y	y	PROPN
ejpam-6571	329	19	;	;	PUNCT
ejpam-6571	329	20	(	(	PUNCT
ejpam-6571	329	21	3	3	X
ejpam-6571	329	22	)	)	PUNCT
ejpam-6571	329	23	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	329	24	-	-	PUNCT
ejpam-6571	329	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	329	26	-	-	PUNCT
ejpam-6571	329	27	cl(v	cl(v	NOUN
ejpam-6571	329	28	)	)	PUNCT
ejpam-6571	329	29	)	)	PUNCT
ejpam-6571	329	30	)	)	PUNCT
ejpam-6571	329	31	)	)	PUNCT
ejpam-6571	330	1	⊆	⊆	X
ejpam-6571	330	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	330	3	-	-	PUNCT
ejpam-6571	330	4	cl(v	cl(v	NOUN
ejpam-6571	330	5	)	)	PUNCT
ejpam-6571	330	6	)	)	PUNCT
ejpam-6571	330	7	for	for	ADP
ejpam-6571	330	8	every	every	DET
ejpam-6571	330	9	(	(	PUNCT
ejpam-6571	330	10	σ1	σ1	PROPN
ejpam-6571	330	11	,	,	PUNCT
ejpam-6571	330	12	σ2)s	σ2)s	NOUN
ejpam-6571	330	13	-	-	PUNCT
ejpam-6571	330	14	open	open	NOUN
ejpam-6571	330	15	set	set	NOUN
ejpam-6571	330	16	v	v	NOUN
ejpam-6571	330	17	of	of	ADP
ejpam-6571	330	18	y	y	PROPN
ejpam-6571	330	19	;	;	PUNCT
ejpam-6571	330	20	(	(	PUNCT
ejpam-6571	330	21	4	4	X
ejpam-6571	330	22	)	)	PUNCT
ejpam-6571	330	23	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	330	24	-	-	PUNCT
ejpam-6571	330	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	330	26	-	-	PUNCT
ejpam-6571	330	27	cl(v	cl(v	NOUN
ejpam-6571	330	28	)	)	PUNCT
ejpam-6571	330	29	)	)	PUNCT
ejpam-6571	330	30	)	)	PUNCT
ejpam-6571	330	31	)	)	PUNCT
ejpam-6571	331	1	⊆	⊆	X
ejpam-6571	331	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	331	3	-	-	PUNCT
ejpam-6571	331	4	cl(v	cl(v	NOUN
ejpam-6571	331	5	)	)	PUNCT
ejpam-6571	331	6	)	)	PUNCT
ejpam-6571	331	7	for	for	ADP
ejpam-6571	331	8	every	every	DET
ejpam-6571	331	9	(	(	PUNCT
ejpam-6571	331	10	σ1	σ1	PROPN
ejpam-6571	331	11	,	,	PUNCT
ejpam-6571	331	12	σ2)p	σ2)p	NOUN
ejpam-6571	331	13	-	-	PUNCT
ejpam-6571	331	14	open	open	NOUN
ejpam-6571	331	15	set	set	NOUN
ejpam-6571	331	16	v	v	NOUN
ejpam-6571	331	17	of	of	ADP
ejpam-6571	331	18	y	y	PROPN
ejpam-6571	331	19	.	.	PUNCT
ejpam-6571	332	1	m.	m.	NOUN
ejpam-6571	332	2	thongmoon	thongmoon	PROPN
ejpam-6571	332	3	,	,	PUNCT
ejpam-6571	332	4	a.	a.	PROPN
ejpam-6571	332	5	sama	sama	PROPN
ejpam-6571	332	6	-	-	PUNCT
ejpam-6571	332	7	ae	ae	PROPN
ejpam-6571	332	8	,	,	PUNCT
ejpam-6571	332	9	c.	c.	PROPN
ejpam-6571	332	10	boonpok	boonpok	PROPN
ejpam-6571	332	11	/	/	SYM
ejpam-6571	332	12	eur	eur	PROPN
ejpam-6571	332	13	.	.	PUNCT
ejpam-6571	333	1	j.	j.	PROPN
ejpam-6571	333	2	pure	pure	PROPN
ejpam-6571	333	3	appl	appl	PROPN
ejpam-6571	333	4	.	.	PROPN
ejpam-6571	333	5	math	math	PROPN
ejpam-6571	333	6	,	,	PUNCT
ejpam-6571	333	7	18	18	NUM
ejpam-6571	333	8	(	(	PUNCT
ejpam-6571	333	9	3	3	NUM
ejpam-6571	333	10	)	)	PUNCT
ejpam-6571	333	11	(	(	PUNCT
ejpam-6571	333	12	2025	2025	NUM
ejpam-6571	333	13	)	)	PUNCT
ejpam-6571	333	14	,	,	PUNCT
ejpam-6571	333	15	6571	6571	NUM
ejpam-6571	333	16	12	12	NUM
ejpam-6571	333	17	of	of	ADP
ejpam-6571	333	18	15	15	NUM
ejpam-6571	333	19	proof	proof	NOUN
ejpam-6571	333	20	.	.	PUNCT
ejpam-6571	334	1	(	(	PUNCT
ejpam-6571	334	2	1	1	X
ejpam-6571	334	3	)	)	PUNCT
ejpam-6571	334	4	⇒	⇒	NOUN
ejpam-6571	334	5	(	(	PUNCT
ejpam-6571	334	6	2	2	NUM
ejpam-6571	334	7	):	):	PUNCT
ejpam-6571	334	8	let	let	VERB
ejpam-6571	334	9	v	v	PART
ejpam-6571	334	10	be	be	AUX
ejpam-6571	334	11	any	any	DET
ejpam-6571	334	12	(	(	PUNCT
ejpam-6571	334	13	σ1	σ1	PROPN
ejpam-6571	334	14	,	,	PUNCT
ejpam-6571	334	15	σ2)β	σ2)β	NOUN
ejpam-6571	334	16	-	-	PUNCT
ejpam-6571	334	17	open	open	ADJ
ejpam-6571	334	18	set	set	NOUN
ejpam-6571	334	19	of	of	ADP
ejpam-6571	334	20	y	y	PROPN
ejpam-6571	334	21	.	.	PUNCT
ejpam-6571	335	1	then	then	ADV
ejpam-6571	335	2	,	,	PUNCT
ejpam-6571	335	3	we	we	PRON
ejpam-6571	335	4	have	have	VERB
ejpam-6571	335	5	v	v	ADP
ejpam-6571	335	6	⊆	⊆	NUM
ejpam-6571	335	7	σ1σ2	σ1σ2	NOUN
ejpam-6571	335	8	-	-	PUNCT
ejpam-6571	335	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	335	10	-	-	PUNCT
ejpam-6571	335	11	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	335	12	-	-	PUNCT
ejpam-6571	335	13	cl(v	cl(v	NOUN
ejpam-6571	335	14	)	)	PUNCT
ejpam-6571	335	15	)	)	PUNCT
ejpam-6571	335	16	)	)	PUNCT
ejpam-6571	335	17	and	and	CCONJ
ejpam-6571	335	18	hence	hence	ADV
ejpam-6571	335	19	σ1σ2	σ1σ2	NOUN
ejpam-6571	335	20	-	-	NOUN
ejpam-6571	335	21	cl(v	cl(v	NOUN
ejpam-6571	335	22	)	)	PUNCT
ejpam-6571	336	1	=	=	SYM
ejpam-6571	336	2	σ1σ2	σ1σ2	X
ejpam-6571	336	3	-	-	PUNCT
ejpam-6571	336	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6571	336	5	-	-	PUNCT
ejpam-6571	336	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	336	7	-	-	PUNCT
ejpam-6571	336	8	cl(v	cl(v	NOUN
ejpam-6571	336	9	)	)	PUNCT
ejpam-6571	336	10	)	)	PUNCT
ejpam-6571	336	11	)	)	PUNCT
ejpam-6571	336	12	.	.	PUNCT
ejpam-6571	337	1	since	since	SCONJ
ejpam-6571	337	2	σ1σ2	σ1σ2	NOUN
ejpam-6571	337	3	-	-	NOUN
ejpam-6571	337	4	cl(v	cl(v	NOUN
ejpam-6571	337	5	)	)	PUNCT
ejpam-6571	337	6	is	be	AUX
ejpam-6571	337	7	(	(	PUNCT
ejpam-6571	337	8	σ1	σ1	PROPN
ejpam-6571	337	9	,	,	PUNCT
ejpam-6571	337	10	σ2)rclosed	σ2)rclose	VERB
ejpam-6571	337	11	in	in	ADP
ejpam-6571	337	12	y	y	PROPN
ejpam-6571	337	13	and	and	CCONJ
ejpam-6571	337	14	by	by	ADP
ejpam-6571	337	15	theorem	theorem	NOUN
ejpam-6571	337	16	9	9	NUM
ejpam-6571	337	17	,	,	PUNCT
ejpam-6571	337	18	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	NOUN
ejpam-6571	337	19	-	-	PUNCT
ejpam-6571	337	20	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	337	21	-	-	PUNCT
ejpam-6571	337	22	cl(v	cl(v	NOUN
ejpam-6571	337	23	)	)	PUNCT
ejpam-6571	337	24	)	)	PUNCT
ejpam-6571	337	25	)	)	PUNCT
ejpam-6571	337	26	)	)	PUNCT
ejpam-6571	338	1	⊆	⊆	X
ejpam-6571	338	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	338	3	-	-	PUNCT
ejpam-6571	338	4	cl(v	cl(v	NOUN
ejpam-6571	338	5	)	)	PUNCT
ejpam-6571	338	6	)	)	PUNCT
ejpam-6571	338	7	.	.	PUNCT
ejpam-6571	339	1	(	(	PUNCT
ejpam-6571	339	2	2	2	X
ejpam-6571	339	3	)	)	PUNCT
ejpam-6571	339	4	⇒	⇒	NOUN
ejpam-6571	339	5	(	(	PUNCT
ejpam-6571	339	6	3	3	NUM
ejpam-6571	339	7	):	):	PUNCT
ejpam-6571	339	8	this	this	PRON
ejpam-6571	339	9	is	be	AUX
ejpam-6571	339	10	obvious	obvious	ADJ
ejpam-6571	339	11	since	since	SCONJ
ejpam-6571	339	12	every	every	DET
ejpam-6571	339	13	(	(	PUNCT
ejpam-6571	339	14	σ1	σ1	PROPN
ejpam-6571	339	15	,	,	PUNCT
ejpam-6571	339	16	σ2)s	σ2)s	NOUN
ejpam-6571	339	17	-	-	PUNCT
ejpam-6571	339	18	open	open	ADJ
ejpam-6571	339	19	set	set	NOUN
ejpam-6571	339	20	is	be	AUX
ejpam-6571	339	21	(	(	PUNCT
ejpam-6571	339	22	σ1	σ1	PROPN
ejpam-6571	339	23	,	,	PUNCT
ejpam-6571	339	24	σ2)β	σ2)β	NOUN
ejpam-6571	339	25	-	-	PUNCT
ejpam-6571	339	26	open	open	ADJ
ejpam-6571	339	27	.	.	PUNCT
ejpam-6571	340	1	(	(	PUNCT
ejpam-6571	340	2	3	3	X
ejpam-6571	340	3	)	)	PUNCT
ejpam-6571	340	4	⇒	⇒	NOUN
ejpam-6571	340	5	(	(	PUNCT
ejpam-6571	340	6	4	4	NUM
ejpam-6571	340	7	):	):	PUNCT
ejpam-6571	340	8	for	for	ADP
ejpam-6571	340	9	any	any	DET
ejpam-6571	340	10	(	(	PUNCT
ejpam-6571	340	11	σ1	σ1	PROPN
ejpam-6571	340	12	,	,	PUNCT
ejpam-6571	340	13	σ2)p	σ2)p	NOUN
ejpam-6571	340	14	-	-	PUNCT
ejpam-6571	340	15	open	open	NOUN
ejpam-6571	340	16	set	set	NOUN
ejpam-6571	340	17	v	v	NOUN
ejpam-6571	340	18	of	of	ADP
ejpam-6571	340	19	y	y	PROPN
ejpam-6571	340	20	,	,	PUNCT
ejpam-6571	340	21	σ1σ2	σ1σ2	NOUN
ejpam-6571	340	22	-	-	NUM
ejpam-6571	340	23	cl(v	cl(v	NOUN
ejpam-6571	340	24	)	)	PUNCT
ejpam-6571	340	25	is	be	AUX
ejpam-6571	340	26	(	(	PUNCT
ejpam-6571	340	27	σ1	σ1	NOUN
ejpam-6571	340	28	,	,	PUNCT
ejpam-6571	340	29	σ2)r	σ2)r	NOUN
ejpam-6571	340	30	-	-	PUNCT
ejpam-6571	340	31	closed	closed	ADJ
ejpam-6571	340	32	and	and	CCONJ
ejpam-6571	340	33	σ1σ2	σ1σ2	NOUN
ejpam-6571	340	34	-	-	NUM
ejpam-6571	340	35	cl(v	cl(v	NOUN
ejpam-6571	340	36	)	)	PUNCT
ejpam-6571	340	37	is	be	AUX
ejpam-6571	340	38	(	(	PUNCT
ejpam-6571	340	39	σ1	σ1	PROPN
ejpam-6571	340	40	,	,	PUNCT
ejpam-6571	340	41	σ2)s	σ2)s	NOUN
ejpam-6571	340	42	-	-	PUNCT
ejpam-6571	340	43	open	open	ADJ
ejpam-6571	340	44	in	in	ADP
ejpam-6571	340	45	y	y	PROPN
ejpam-6571	340	46	.	.	PUNCT
ejpam-6571	341	1	(	(	PUNCT
ejpam-6571	341	2	4	4	X
ejpam-6571	341	3	)	)	PUNCT
ejpam-6571	341	4	⇒	⇒	NOUN
ejpam-6571	341	5	(	(	PUNCT
ejpam-6571	341	6	1	1	NUM
ejpam-6571	341	7	):	):	PUNCT
ejpam-6571	341	8	let	let	VERB
ejpam-6571	341	9	v	v	PART
ejpam-6571	341	10	be	be	AUX
ejpam-6571	341	11	any	any	DET
ejpam-6571	341	12	σ1σ2	σ1σ2	NOUN
ejpam-6571	341	13	-	-	ADJ
ejpam-6571	341	14	open	open	ADJ
ejpam-6571	341	15	set	set	NOUN
ejpam-6571	341	16	of	of	ADP
ejpam-6571	341	17	y	y	PROPN
ejpam-6571	341	18	.	.	PUNCT
ejpam-6571	342	1	then	then	ADV
ejpam-6571	342	2	,	,	PUNCT
ejpam-6571	342	3	v	v	NOUN
ejpam-6571	342	4	is	be	AUX
ejpam-6571	342	5	(	(	PUNCT
ejpam-6571	342	6	σ1	σ1	PROPN
ejpam-6571	342	7	,	,	PUNCT
ejpam-6571	342	8	σ2)p	σ2)p	NOUN
ejpam-6571	342	9	-	-	PUNCT
ejpam-6571	342	10	open	open	ADJ
ejpam-6571	342	11	in	in	ADP
ejpam-6571	342	12	y	y	PROPN
ejpam-6571	342	13	.	.	PUNCT
ejpam-6571	343	1	by	by	ADP
ejpam-6571	343	2	(	(	PUNCT
ejpam-6571	343	3	4	4	NUM
ejpam-6571	343	4	)	)	PUNCT
ejpam-6571	343	5	,	,	PUNCT
ejpam-6571	343	6	we	we	PRON
ejpam-6571	343	7	have	have	VERB
ejpam-6571	343	8	scl⋆(f−(σ1σ2	scl⋆(f−(σ1σ2	VERB
ejpam-6571	343	9	-	-	PUNCT
ejpam-6571	343	10	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	343	11	-	-	PUNCT
ejpam-6571	343	12	cl(v	cl(v	NOUN
ejpam-6571	343	13	)	)	PUNCT
ejpam-6571	343	14	)	)	PUNCT
ejpam-6571	343	15	)	)	PUNCT
ejpam-6571	343	16	)	)	PUNCT
ejpam-6571	344	1	⊆	⊆	X
ejpam-6571	344	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	344	3	-	-	PUNCT
ejpam-6571	344	4	cl(v	cl(v	NOUN
ejpam-6571	344	5	)	)	PUNCT
ejpam-6571	344	6	)	)	PUNCT
ejpam-6571	344	7	.	.	PUNCT
ejpam-6571	345	1	it	it	PRON
ejpam-6571	345	2	follows	follow	VERB
ejpam-6571	345	3	from	from	ADP
ejpam-6571	345	4	theorem	theorem	ADJ
ejpam-6571	345	5	9	9	NUM
ejpam-6571	345	6	that	that	SCONJ
ejpam-6571	345	7	f	f	PROPN
ejpam-6571	345	8	is	be	AUX
ejpam-6571	345	9	upper	upper	ADJ
ejpam-6571	345	10	weakly	weakly	ADJ
ejpam-6571	345	11	quasi	quasi	NOUN
ejpam-6571	345	12	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	345	13	,	,	PUNCT
ejpam-6571	345	14	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	345	15	.	.	X
ejpam-6571	345	16	theorem	theorem	NOUN
ejpam-6571	345	17	12	12	NUM
ejpam-6571	345	18	.	.	PUNCT
ejpam-6571	346	1	for	for	ADP
ejpam-6571	346	2	a	a	DET
ejpam-6571	346	3	multifunction	multifunction	NOUN
ejpam-6571	346	4	f	f	NOUN
ejpam-6571	346	5	:	:	PUNCT
ejpam-6571	346	6	(	(	PUNCT
ejpam-6571	346	7	x	x	X
ejpam-6571	346	8	,	,	PUNCT
ejpam-6571	346	9	τ	τ	PROPN
ejpam-6571	346	10	,	,	PUNCT
ejpam-6571	346	11	i	i	NOUN
ejpam-6571	346	12	)	)	PUNCT
ejpam-6571	346	13	→	→	PUNCT
ejpam-6571	346	14	(	(	PUNCT
ejpam-6571	346	15	y	y	PROPN
ejpam-6571	346	16	,	,	PUNCT
ejpam-6571	346	17	σ1	σ1	PROPN
ejpam-6571	346	18	,	,	PUNCT
ejpam-6571	346	19	σ2	σ2	NOUN
ejpam-6571	346	20	)	)	PUNCT
ejpam-6571	346	21	,	,	PUNCT
ejpam-6571	346	22	the	the	DET
ejpam-6571	346	23	following	follow	VERB
ejpam-6571	346	24	properties	property	NOUN
ejpam-6571	346	25	are	be	AUX
ejpam-6571	346	26	equivalent	equivalent	ADJ
ejpam-6571	346	27	:	:	PUNCT
ejpam-6571	346	28	(	(	PUNCT
ejpam-6571	346	29	1	1	X
ejpam-6571	346	30	)	)	PUNCT
ejpam-6571	346	31	f	f	PROPN
ejpam-6571	346	32	is	be	AUX
ejpam-6571	346	33	lower	low	ADJ
ejpam-6571	346	34	weakly	weakly	ADJ
ejpam-6571	346	35	quasi	quasi	ADJ
ejpam-6571	346	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	346	37	,	,	PUNCT
ejpam-6571	346	38	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	346	39	;	;	PUNCT
ejpam-6571	346	40	(	(	PUNCT
ejpam-6571	346	41	2	2	X
ejpam-6571	346	42	)	)	PUNCT
ejpam-6571	346	43	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	346	44	-	-	PUNCT
ejpam-6571	346	45	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	346	46	-	-	PUNCT
ejpam-6571	346	47	cl(v	cl(v	NOUN
ejpam-6571	346	48	)	)	PUNCT
ejpam-6571	346	49	)	)	PUNCT
ejpam-6571	346	50	)	)	PUNCT
ejpam-6571	346	51	)	)	PUNCT
ejpam-6571	347	1	⊆	⊆	X
ejpam-6571	347	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	347	3	-	-	PUNCT
ejpam-6571	347	4	cl(v	cl(v	NOUN
ejpam-6571	347	5	)	)	PUNCT
ejpam-6571	347	6	)	)	PUNCT
ejpam-6571	347	7	for	for	ADP
ejpam-6571	347	8	every	every	DET
ejpam-6571	347	9	(	(	PUNCT
ejpam-6571	347	10	σ1	σ1	PROPN
ejpam-6571	347	11	,	,	PUNCT
ejpam-6571	347	12	σ2)β	σ2)β	NOUN
ejpam-6571	347	13	-	-	PUNCT
ejpam-6571	347	14	open	open	NOUN
ejpam-6571	347	15	set	set	NOUN
ejpam-6571	347	16	v	v	NOUN
ejpam-6571	347	17	of	of	ADP
ejpam-6571	347	18	y	y	PROPN
ejpam-6571	347	19	;	;	PUNCT
ejpam-6571	347	20	(	(	PUNCT
ejpam-6571	347	21	3	3	X
ejpam-6571	347	22	)	)	PUNCT
ejpam-6571	347	23	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	347	24	-	-	PUNCT
ejpam-6571	347	25	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	347	26	-	-	PUNCT
ejpam-6571	347	27	cl(v	cl(v	NOUN
ejpam-6571	347	28	)	)	PUNCT
ejpam-6571	347	29	)	)	PUNCT
ejpam-6571	347	30	)	)	PUNCT
ejpam-6571	347	31	)	)	PUNCT
ejpam-6571	347	32	⊆	⊆	X
ejpam-6571	347	33	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	347	34	-	-	PUNCT
ejpam-6571	347	35	cl(v	cl(v	NOUN
ejpam-6571	347	36	)	)	PUNCT
ejpam-6571	347	37	)	)	PUNCT
ejpam-6571	347	38	for	for	SCONJ
ejpam-6571	347	39	every	every	DET
ejpam-6571	347	40	(	(	PUNCT
ejpam-6571	347	41	σ1	σ1	PROPN
ejpam-6571	347	42	,	,	PUNCT
ejpam-6571	347	43	σ2)s	σ2)s	NOUN
ejpam-6571	347	44	-	-	PUNCT
ejpam-6571	347	45	open	open	NOUN
ejpam-6571	347	46	set	set	NOUN
ejpam-6571	347	47	v	v	NOUN
ejpam-6571	347	48	of	of	ADP
ejpam-6571	347	49	y	y	PROPN
ejpam-6571	347	50	;	;	PUNCT
ejpam-6571	347	51	(	(	PUNCT
ejpam-6571	347	52	4	4	X
ejpam-6571	347	53	)	)	PUNCT
ejpam-6571	347	54	scl⋆(f+(σ1σ2	scl⋆(f+(σ1σ2	NOUN
ejpam-6571	347	55	-	-	PUNCT
ejpam-6571	347	56	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	347	57	-	-	PUNCT
ejpam-6571	347	58	cl(v	cl(v	NOUN
ejpam-6571	347	59	)	)	PUNCT
ejpam-6571	347	60	)	)	PUNCT
ejpam-6571	347	61	)	)	PUNCT
ejpam-6571	347	62	)	)	PUNCT
ejpam-6571	347	63	⊆	⊆	X
ejpam-6571	347	64	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	347	65	-	-	PUNCT
ejpam-6571	347	66	cl(v	cl(v	NOUN
ejpam-6571	347	67	)	)	PUNCT
ejpam-6571	347	68	)	)	PUNCT
ejpam-6571	347	69	for	for	ADP
ejpam-6571	347	70	every	every	DET
ejpam-6571	347	71	(	(	PUNCT
ejpam-6571	347	72	σ1	σ1	PROPN
ejpam-6571	347	73	,	,	PUNCT
ejpam-6571	347	74	σ2)p	σ2)p	NOUN
ejpam-6571	347	75	-	-	PUNCT
ejpam-6571	347	76	open	open	NOUN
ejpam-6571	347	77	set	set	NOUN
ejpam-6571	347	78	v	v	NOUN
ejpam-6571	347	79	of	of	ADP
ejpam-6571	347	80	y	y	PROPN
ejpam-6571	347	81	.	.	PUNCT
ejpam-6571	348	1	proof	proof	NOUN
ejpam-6571	348	2	.	.	PUNCT
ejpam-6571	349	1	the	the	DET
ejpam-6571	349	2	proof	proof	NOUN
ejpam-6571	349	3	is	be	AUX
ejpam-6571	349	4	similar	similar	ADJ
ejpam-6571	349	5	to	to	ADP
ejpam-6571	349	6	that	that	PRON
ejpam-6571	349	7	of	of	ADP
ejpam-6571	349	8	theorem	theorem	ADJ
ejpam-6571	349	9	11	11	NUM
ejpam-6571	349	10	.	.	PUNCT
ejpam-6571	350	1	theorem	theorem	VERB
ejpam-6571	350	2	13	13	NUM
ejpam-6571	350	3	.	.	PUNCT
ejpam-6571	351	1	for	for	ADP
ejpam-6571	351	2	a	a	DET
ejpam-6571	351	3	multifunction	multifunction	NOUN
ejpam-6571	351	4	f	f	NOUN
ejpam-6571	351	5	:	:	PUNCT
ejpam-6571	351	6	(	(	PUNCT
ejpam-6571	351	7	x	x	X
ejpam-6571	351	8	,	,	PUNCT
ejpam-6571	351	9	τ	τ	PROPN
ejpam-6571	351	10	,	,	PUNCT
ejpam-6571	351	11	i	i	NOUN
ejpam-6571	351	12	)	)	PUNCT
ejpam-6571	351	13	→	→	PUNCT
ejpam-6571	351	14	(	(	PUNCT
ejpam-6571	351	15	y	y	PROPN
ejpam-6571	351	16	,	,	PUNCT
ejpam-6571	351	17	σ1	σ1	PROPN
ejpam-6571	351	18	,	,	PUNCT
ejpam-6571	351	19	σ2	σ2	NOUN
ejpam-6571	351	20	)	)	PUNCT
ejpam-6571	351	21	,	,	PUNCT
ejpam-6571	351	22	the	the	DET
ejpam-6571	351	23	following	follow	VERB
ejpam-6571	351	24	properties	property	NOUN
ejpam-6571	351	25	are	be	AUX
ejpam-6571	351	26	equivalent	equivalent	ADJ
ejpam-6571	351	27	:	:	PUNCT
ejpam-6571	351	28	(	(	PUNCT
ejpam-6571	351	29	1	1	X
ejpam-6571	351	30	)	)	PUNCT
ejpam-6571	351	31	f	f	PROPN
ejpam-6571	351	32	is	be	AUX
ejpam-6571	351	33	upper	upper	ADJ
ejpam-6571	351	34	weakly	weakly	ADJ
ejpam-6571	351	35	quasi	quasi	NOUN
ejpam-6571	351	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	351	37	,	,	PUNCT
ejpam-6571	351	38	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	351	39	;	;	PUNCT
ejpam-6571	351	40	(	(	PUNCT
ejpam-6571	351	41	2	2	X
ejpam-6571	351	42	)	)	PUNCT
ejpam-6571	351	43	int⋆(cl⋆(f−(v	int⋆(cl⋆(f−(v	NOUN
ejpam-6571	351	44	)	)	PUNCT
ejpam-6571	351	45	)	)	PUNCT
ejpam-6571	351	46	)	)	PUNCT
ejpam-6571	352	1	⊆	⊆	X
ejpam-6571	352	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	352	3	-	-	PUNCT
ejpam-6571	352	4	cl(v	cl(v	NOUN
ejpam-6571	352	5	)	)	PUNCT
ejpam-6571	352	6	)	)	PUNCT
ejpam-6571	352	7	for	for	ADP
ejpam-6571	352	8	every	every	DET
ejpam-6571	352	9	(	(	PUNCT
ejpam-6571	352	10	σ1	σ1	PROPN
ejpam-6571	352	11	,	,	PUNCT
ejpam-6571	352	12	σ2)p	σ2)p	NOUN
ejpam-6571	352	13	-	-	PUNCT
ejpam-6571	352	14	open	open	NOUN
ejpam-6571	352	15	set	set	NOUN
ejpam-6571	352	16	v	v	NOUN
ejpam-6571	352	17	of	of	ADP
ejpam-6571	352	18	y	y	PROPN
ejpam-6571	352	19	;	;	PUNCT
ejpam-6571	352	20	(	(	PUNCT
ejpam-6571	352	21	3	3	X
ejpam-6571	352	22	)	)	PUNCT
ejpam-6571	352	23	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	352	24	)	)	PUNCT
ejpam-6571	352	25	)	)	PUNCT
ejpam-6571	353	1	⊆	⊆	X
ejpam-6571	353	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	353	3	-	-	PUNCT
ejpam-6571	353	4	cl(v	cl(v	NOUN
ejpam-6571	353	5	)	)	PUNCT
ejpam-6571	353	6	)	)	PUNCT
ejpam-6571	353	7	for	for	ADP
ejpam-6571	353	8	every	every	DET
ejpam-6571	353	9	(	(	PUNCT
ejpam-6571	353	10	σ1	σ1	PROPN
ejpam-6571	353	11	,	,	PUNCT
ejpam-6571	353	12	σ2)p	σ2)p	NOUN
ejpam-6571	353	13	-	-	PUNCT
ejpam-6571	353	14	open	open	NOUN
ejpam-6571	353	15	set	set	NOUN
ejpam-6571	353	16	v	v	NOUN
ejpam-6571	353	17	of	of	ADP
ejpam-6571	353	18	y	y	PROPN
ejpam-6571	353	19	;	;	PUNCT
ejpam-6571	353	20	(	(	PUNCT
ejpam-6571	353	21	4	4	X
ejpam-6571	353	22	)	)	PUNCT
ejpam-6571	353	23	f+(v	f+(v	NOUN
ejpam-6571	353	24	)	)	PUNCT
ejpam-6571	354	1	⊆	⊆	X
ejpam-6571	354	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	354	3	-	-	PUNCT
ejpam-6571	354	4	cl(v	cl(v	NOUN
ejpam-6571	354	5	)	)	PUNCT
ejpam-6571	354	6	)	)	PUNCT
ejpam-6571	354	7	)	)	PUNCT
ejpam-6571	354	8	for	for	ADP
ejpam-6571	354	9	every	every	DET
ejpam-6571	354	10	(	(	PUNCT
ejpam-6571	354	11	σ1	σ1	PROPN
ejpam-6571	354	12	,	,	PUNCT
ejpam-6571	354	13	σ2)p	σ2)p	NOUN
ejpam-6571	354	14	-	-	PUNCT
ejpam-6571	354	15	open	open	NOUN
ejpam-6571	354	16	set	set	NOUN
ejpam-6571	354	17	v	v	NOUN
ejpam-6571	354	18	of	of	ADP
ejpam-6571	354	19	y	y	PROPN
ejpam-6571	354	20	.	.	PUNCT
ejpam-6571	355	1	proof	proof	NOUN
ejpam-6571	355	2	.	.	PUNCT
ejpam-6571	356	1	(	(	PUNCT
ejpam-6571	356	2	1	1	X
ejpam-6571	356	3	)	)	PUNCT
ejpam-6571	356	4	⇒	⇒	NOUN
ejpam-6571	356	5	(	(	PUNCT
ejpam-6571	356	6	2	2	NUM
ejpam-6571	356	7	):	):	PUNCT
ejpam-6571	356	8	let	let	VERB
ejpam-6571	356	9	v	v	PART
ejpam-6571	356	10	be	be	AUX
ejpam-6571	356	11	any	any	DET
ejpam-6571	356	12	(	(	PUNCT
ejpam-6571	356	13	σ1	σ1	PROPN
ejpam-6571	356	14	,	,	PUNCT
ejpam-6571	356	15	σ2)p	σ2)p	NOUN
ejpam-6571	356	16	-	-	PUNCT
ejpam-6571	356	17	open	open	ADJ
ejpam-6571	356	18	set	set	NOUN
ejpam-6571	356	19	of	of	ADP
ejpam-6571	356	20	y	y	PROPN
ejpam-6571	356	21	.	.	PUNCT
ejpam-6571	357	1	since	since	SCONJ
ejpam-6571	357	2	f	f	PROPN
ejpam-6571	357	3	is	be	AUX
ejpam-6571	357	4	upper	upper	ADJ
ejpam-6571	357	5	weakly	weakly	ADJ
ejpam-6571	357	6	quasi	quasi	NOUN
ejpam-6571	357	7	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	357	8	,	,	PUNCT
ejpam-6571	357	9	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	357	10	,	,	PUNCT
ejpam-6571	357	11	by	by	ADP
ejpam-6571	357	12	lemma	lemma	PROPN
ejpam-6571	357	13	3	3	NUM
ejpam-6571	357	14	and	and	CCONJ
ejpam-6571	357	15	theorem	theorem	VERB
ejpam-6571	357	16	9	9	NUM
ejpam-6571	357	17	,	,	PUNCT
ejpam-6571	357	18	int⋆(cl⋆(f−(v	int⋆(cl⋆(f−(v	NOUN
ejpam-6571	357	19	)	)	PUNCT
ejpam-6571	357	20	)	)	PUNCT
ejpam-6571	357	21	)	)	PUNCT
ejpam-6571	358	1	⊆	⊆	X
ejpam-6571	358	2	int⋆(cl⋆(f−(σ1σ2	int⋆(cl⋆(f−(σ1σ2	NUM
ejpam-6571	358	3	-	-	PUNCT
ejpam-6571	358	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	358	5	-	-	PUNCT
ejpam-6571	358	6	cl(v	cl(v	NOUN
ejpam-6571	358	7	)	)	PUNCT
ejpam-6571	358	8	)	)	PUNCT
ejpam-6571	358	9	)	)	PUNCT
ejpam-6571	358	10	)	)	PUNCT
ejpam-6571	358	11	)	)	PUNCT
ejpam-6571	359	1	⊆	⊆	X
ejpam-6571	359	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	359	3	-	-	PUNCT
ejpam-6571	359	4	cl(v	cl(v	NOUN
ejpam-6571	359	5	)	)	PUNCT
ejpam-6571	359	6	)	)	PUNCT
ejpam-6571	359	7	.	.	PUNCT
ejpam-6571	360	1	(	(	PUNCT
ejpam-6571	360	2	2	2	X
ejpam-6571	360	3	)	)	PUNCT
ejpam-6571	360	4	⇒	⇒	NOUN
ejpam-6571	360	5	(	(	PUNCT
ejpam-6571	360	6	3	3	NUM
ejpam-6571	360	7	):	):	PUNCT
ejpam-6571	360	8	let	let	VERB
ejpam-6571	360	9	v	v	PART
ejpam-6571	360	10	be	be	AUX
ejpam-6571	360	11	any	any	DET
ejpam-6571	360	12	(	(	PUNCT
ejpam-6571	360	13	σ1	σ1	PROPN
ejpam-6571	360	14	,	,	PUNCT
ejpam-6571	360	15	σ2)p	σ2)p	NOUN
ejpam-6571	360	16	-	-	PUNCT
ejpam-6571	360	17	open	open	ADJ
ejpam-6571	360	18	set	set	NOUN
ejpam-6571	360	19	of	of	ADP
ejpam-6571	360	20	y	y	PROPN
ejpam-6571	360	21	.	.	PUNCT
ejpam-6571	361	1	by	by	ADP
ejpam-6571	361	2	(	(	PUNCT
ejpam-6571	361	3	2	2	NUM
ejpam-6571	361	4	)	)	PUNCT
ejpam-6571	361	5	and	and	CCONJ
ejpam-6571	361	6	lemma	lemma	PROPN
ejpam-6571	361	7	3	3	NUM
ejpam-6571	361	8	,	,	PUNCT
ejpam-6571	361	9	we	we	PRON
ejpam-6571	361	10	have	have	VERB
ejpam-6571	361	11	scl⋆(f−(v	scl⋆(f−(v	NUM
ejpam-6571	361	12	)	)	PUNCT
ejpam-6571	361	13	)	)	PUNCT
ejpam-6571	362	1	=	=	SYM
ejpam-6571	362	2	f−(v	f−(v	ADJ
ejpam-6571	362	3	)	)	PUNCT
ejpam-6571	362	4	∪	∪	NOUN
ejpam-6571	362	5	int⋆(cl⋆(f−(v	int⋆(cl⋆(f−(v	NOUN
ejpam-6571	362	6	)	)	PUNCT
ejpam-6571	362	7	)	)	PUNCT
ejpam-6571	362	8	)	)	PUNCT
ejpam-6571	363	1	⊆	⊆	X
ejpam-6571	363	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-6571	363	3	-	-	PUNCT
ejpam-6571	363	4	cl(v	cl(v	NOUN
ejpam-6571	363	5	)	)	PUNCT
ejpam-6571	363	6	)	)	PUNCT
ejpam-6571	363	7	.	.	PUNCT
ejpam-6571	364	1	m.	m.	NOUN
ejpam-6571	364	2	thongmoon	thongmoon	PROPN
ejpam-6571	364	3	,	,	PUNCT
ejpam-6571	364	4	a.	a.	PROPN
ejpam-6571	364	5	sama	sama	PROPN
ejpam-6571	364	6	-	-	PUNCT
ejpam-6571	364	7	ae	ae	PROPN
ejpam-6571	364	8	,	,	PUNCT
ejpam-6571	364	9	c.	c.	PROPN
ejpam-6571	364	10	boonpok	boonpok	PROPN
ejpam-6571	364	11	/	/	SYM
ejpam-6571	364	12	eur	eur	PROPN
ejpam-6571	364	13	.	.	PUNCT
ejpam-6571	365	1	j.	j.	PROPN
ejpam-6571	365	2	pure	pure	PROPN
ejpam-6571	365	3	appl	appl	PROPN
ejpam-6571	365	4	.	.	PROPN
ejpam-6571	365	5	math	math	PROPN
ejpam-6571	365	6	,	,	PUNCT
ejpam-6571	365	7	18	18	NUM
ejpam-6571	365	8	(	(	PUNCT
ejpam-6571	365	9	3	3	NUM
ejpam-6571	365	10	)	)	PUNCT
ejpam-6571	365	11	(	(	PUNCT
ejpam-6571	365	12	2025	2025	NUM
ejpam-6571	365	13	)	)	PUNCT
ejpam-6571	365	14	,	,	PUNCT
ejpam-6571	365	15	6571	6571	NUM
ejpam-6571	365	16	13	13	NUM
ejpam-6571	365	17	of	of	ADP
ejpam-6571	365	18	15	15	NUM
ejpam-6571	365	19	(	(	PUNCT
ejpam-6571	365	20	3	3	NUM
ejpam-6571	365	21	)	)	PUNCT
ejpam-6571	365	22	⇒	⇒	NOUN
ejpam-6571	365	23	(	(	PUNCT
ejpam-6571	365	24	4	4	NUM
ejpam-6571	365	25	):	):	PUNCT
ejpam-6571	365	26	let	let	VERB
ejpam-6571	365	27	v	v	PART
ejpam-6571	365	28	be	be	AUX
ejpam-6571	365	29	any	any	DET
ejpam-6571	365	30	(	(	PUNCT
ejpam-6571	365	31	σ1	σ1	PROPN
ejpam-6571	365	32	,	,	PUNCT
ejpam-6571	365	33	σ2)p	σ2)p	NOUN
ejpam-6571	365	34	-	-	PUNCT
ejpam-6571	365	35	open	open	ADJ
ejpam-6571	365	36	set	set	NOUN
ejpam-6571	365	37	of	of	ADP
ejpam-6571	365	38	y	y	PROPN
ejpam-6571	365	39	.	.	PUNCT
ejpam-6571	366	1	then	then	ADV
ejpam-6571	366	2	by	by	ADP
ejpam-6571	366	3	(	(	PUNCT
ejpam-6571	366	4	3	3	NUM
ejpam-6571	366	5	)	)	PUNCT
ejpam-6571	366	6	,	,	PUNCT
ejpam-6571	366	7	we	we	PRON
ejpam-6571	366	8	have	have	VERB
ejpam-6571	366	9	x	x	X
ejpam-6571	366	10	−	−	PUNCT
ejpam-6571	366	11	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	366	12	-	-	PUNCT
ejpam-6571	366	13	cl(v	cl(v	NOUN
ejpam-6571	366	14	)	)	PUNCT
ejpam-6571	366	15	)	)	PUNCT
ejpam-6571	366	16	)	)	PUNCT
ejpam-6571	367	1	=	=	PRON
ejpam-6571	367	2	scl⋆(x	scl⋆(x	VERB
ejpam-6571	367	3	−	−	ADP
ejpam-6571	367	4	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	367	5	-	-	PUNCT
ejpam-6571	367	6	cl(v	cl(v	NOUN
ejpam-6571	367	7	)	)	PUNCT
ejpam-6571	367	8	)	)	PUNCT
ejpam-6571	367	9	)	)	PUNCT
ejpam-6571	368	1	=	=	NOUN
ejpam-6571	368	2	scl⋆(f−(y	scl⋆(f−(y	NOUN
ejpam-6571	369	1	−	−	ADP
ejpam-6571	369	2	σ1σ2	σ1σ2	NOUN
ejpam-6571	369	3	-	-	NUM
ejpam-6571	369	4	cl(v	cl(v	NOUN
ejpam-6571	369	5	)	)	PUNCT
ejpam-6571	369	6	)	)	PUNCT
ejpam-6571	369	7	)	)	PUNCT
ejpam-6571	370	1	⊆	⊆	X
ejpam-6571	370	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-6571	370	3	-	-	PUNCT
ejpam-6571	370	4	cl(y	cl(y	NOUN
ejpam-6571	370	5	−	−	NOUN
ejpam-6571	370	6	σ1σ2	σ1σ2	NOUN
ejpam-6571	370	7	-	-	NUM
ejpam-6571	370	8	cl(v	cl(v	NOUN
ejpam-6571	370	9	)	)	PUNCT
ejpam-6571	370	10	)	)	PUNCT
ejpam-6571	370	11	)	)	PUNCT
ejpam-6571	371	1	=	=	PUNCT
ejpam-6571	371	2	x	x	X
ejpam-6571	371	3	−	−	ADP
ejpam-6571	371	4	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-6571	371	5	-	-	PUNCT
ejpam-6571	371	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6571	371	7	-	-	PUNCT
ejpam-6571	371	8	cl(v	cl(v	NOUN
ejpam-6571	371	9	)	)	PUNCT
ejpam-6571	371	10	)	)	PUNCT
ejpam-6571	371	11	)	)	PUNCT
ejpam-6571	372	1	⊆	⊆	NUM
ejpam-6571	372	2	x	x	SYM
ejpam-6571	372	3	−	−	NOUN
ejpam-6571	372	4	f+(v	f+(v	NOUN
ejpam-6571	372	5	)	)	PUNCT
ejpam-6571	372	6	and	and	CCONJ
ejpam-6571	372	7	hence	hence	ADV
ejpam-6571	372	8	f+(v	f+(v	NOUN
ejpam-6571	372	9	)	)	PUNCT
ejpam-6571	373	1	⊆	⊆	X
ejpam-6571	373	2	sint⋆(f+(σ1σ2	sint⋆(f+(σ1σ2	NOUN
ejpam-6571	373	3	-	-	PUNCT
ejpam-6571	373	4	cl(v	cl(v	NOUN
ejpam-6571	373	5	)	)	PUNCT
ejpam-6571	373	6	)	)	PUNCT
ejpam-6571	373	7	)	)	PUNCT
ejpam-6571	373	8	.	.	PUNCT
ejpam-6571	374	1	(	(	PUNCT
ejpam-6571	374	2	4	4	X
ejpam-6571	374	3	)	)	PUNCT
ejpam-6571	374	4	⇒	⇒	NOUN
ejpam-6571	374	5	(	(	PUNCT
ejpam-6571	374	6	1	1	NUM
ejpam-6571	374	7	):	):	PUNCT
ejpam-6571	374	8	since	since	SCONJ
ejpam-6571	374	9	every	every	DET
ejpam-6571	374	10	σ1σ2	σ1σ2	NUM
ejpam-6571	374	11	-	-	ADJ
ejpam-6571	374	12	open	open	ADJ
ejpam-6571	374	13	set	set	NOUN
ejpam-6571	374	14	is	be	AUX
ejpam-6571	374	15	(	(	PUNCT
ejpam-6571	374	16	σ1	σ1	PROPN
ejpam-6571	374	17	,	,	PUNCT
ejpam-6571	374	18	σ2)p	σ2)p	NOUN
ejpam-6571	374	19	-	-	PUNCT
ejpam-6571	374	20	open	open	ADJ
ejpam-6571	374	21	,	,	PUNCT
ejpam-6571	374	22	this	this	PRON
ejpam-6571	374	23	follows	follow	VERB
ejpam-6571	374	24	from	from	ADP
ejpam-6571	374	25	theorem	theorem	ADJ
ejpam-6571	374	26	7	7	NUM
ejpam-6571	374	27	.	.	PUNCT
ejpam-6571	374	28	theorem	theorem	VERB
ejpam-6571	374	29	14	14	NUM
ejpam-6571	374	30	.	.	PUNCT
ejpam-6571	375	1	for	for	ADP
ejpam-6571	375	2	a	a	DET
ejpam-6571	375	3	multifunction	multifunction	NOUN
ejpam-6571	375	4	f	f	NOUN
ejpam-6571	375	5	:	:	PUNCT
ejpam-6571	375	6	(	(	PUNCT
ejpam-6571	375	7	x	x	X
ejpam-6571	375	8	,	,	PUNCT
ejpam-6571	375	9	τ	τ	PROPN
ejpam-6571	375	10	,	,	PUNCT
ejpam-6571	375	11	i	i	NOUN
ejpam-6571	375	12	)	)	PUNCT
ejpam-6571	375	13	→	→	PUNCT
ejpam-6571	375	14	(	(	PUNCT
ejpam-6571	375	15	y	y	PROPN
ejpam-6571	375	16	,	,	PUNCT
ejpam-6571	375	17	σ1	σ1	PROPN
ejpam-6571	375	18	,	,	PUNCT
ejpam-6571	375	19	σ2	σ2	NOUN
ejpam-6571	375	20	)	)	PUNCT
ejpam-6571	375	21	,	,	PUNCT
ejpam-6571	375	22	the	the	DET
ejpam-6571	375	23	following	follow	VERB
ejpam-6571	375	24	properties	property	NOUN
ejpam-6571	375	25	are	be	AUX
ejpam-6571	375	26	equivalent	equivalent	ADJ
ejpam-6571	375	27	:	:	PUNCT
ejpam-6571	375	28	(	(	PUNCT
ejpam-6571	375	29	1	1	X
ejpam-6571	375	30	)	)	PUNCT
ejpam-6571	375	31	f	f	PROPN
ejpam-6571	375	32	is	be	AUX
ejpam-6571	375	33	lower	low	ADJ
ejpam-6571	375	34	weakly	weakly	ADJ
ejpam-6571	375	35	quasi	quasi	ADJ
ejpam-6571	375	36	τ⋆(σ1	τ⋆(σ1	ADV
ejpam-6571	375	37	,	,	PUNCT
ejpam-6571	375	38	σ2)-continuous	σ2)-continuous	ADJ
ejpam-6571	375	39	;	;	PUNCT
ejpam-6571	375	40	(	(	PUNCT
ejpam-6571	375	41	2	2	X
ejpam-6571	375	42	)	)	PUNCT
ejpam-6571	375	43	int⋆(cl⋆(f+(v	int⋆(cl⋆(f+(v	PROPN
ejpam-6571	375	44	)	)	PUNCT
ejpam-6571	375	45	)	)	PUNCT
ejpam-6571	375	46	)	)	PUNCT
ejpam-6571	376	1	⊆	⊆	X
ejpam-6571	376	2	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	376	3	-	-	PUNCT
ejpam-6571	376	4	cl(v	cl(v	NOUN
ejpam-6571	376	5	)	)	PUNCT
ejpam-6571	376	6	)	)	PUNCT
ejpam-6571	376	7	for	for	ADP
ejpam-6571	376	8	every	every	DET
ejpam-6571	376	9	(	(	PUNCT
ejpam-6571	376	10	σ1	σ1	PROPN
ejpam-6571	376	11	,	,	PUNCT
ejpam-6571	376	12	σ2)p	σ2)p	NOUN
ejpam-6571	376	13	-	-	PUNCT
ejpam-6571	376	14	open	open	NOUN
ejpam-6571	376	15	set	set	NOUN
ejpam-6571	376	16	v	v	NOUN
ejpam-6571	376	17	of	of	ADP
ejpam-6571	376	18	y	y	PROPN
ejpam-6571	376	19	;	;	PUNCT
ejpam-6571	376	20	(	(	PUNCT
ejpam-6571	376	21	3	3	X
ejpam-6571	376	22	)	)	PUNCT
ejpam-6571	376	23	scl⋆(f+(v	scl⋆(f+(v	PROPN
ejpam-6571	376	24	)	)	PUNCT
ejpam-6571	376	25	)	)	PUNCT
ejpam-6571	376	26	⊆	⊆	NUM
ejpam-6571	376	27	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-6571	376	28	-	-	PUNCT
ejpam-6571	376	29	cl(v	cl(v	NOUN
ejpam-6571	376	30	)	)	PUNCT
ejpam-6571	376	31	)	)	PUNCT
ejpam-6571	376	32	for	for	ADP
ejpam-6571	376	33	every	every	DET
ejpam-6571	376	34	(	(	PUNCT
ejpam-6571	376	35	σ1	σ1	PROPN
ejpam-6571	376	36	,	,	PUNCT
ejpam-6571	376	37	σ2)p	σ2)p	NOUN
ejpam-6571	376	38	-	-	PUNCT
ejpam-6571	376	39	open	open	NOUN
ejpam-6571	376	40	set	set	NOUN
ejpam-6571	376	41	v	v	NOUN
ejpam-6571	376	42	of	of	ADP
ejpam-6571	376	43	y	y	PROPN
ejpam-6571	376	44	;	;	PUNCT
ejpam-6571	376	45	(	(	PUNCT
ejpam-6571	376	46	4	4	X
ejpam-6571	376	47	)	)	PUNCT
ejpam-6571	376	48	f−(v	f−(v	NOUN
ejpam-6571	376	49	)	)	PUNCT
ejpam-6571	376	50	⊆	⊆	NUM
ejpam-6571	376	51	sint⋆(f−(σ1σ2	sint⋆(f−(σ1σ2	NOUN
ejpam-6571	376	52	-	-	PUNCT
ejpam-6571	376	53	cl(v	cl(v	NOUN
ejpam-6571	376	54	)	)	PUNCT
ejpam-6571	376	55	)	)	PUNCT
ejpam-6571	376	56	)	)	PUNCT
ejpam-6571	376	57	for	for	ADP
ejpam-6571	376	58	every	every	DET
ejpam-6571	376	59	(	(	PUNCT
ejpam-6571	376	60	σ1	σ1	PROPN
ejpam-6571	376	61	,	,	PUNCT
ejpam-6571	376	62	σ2)p	σ2)p	NOUN
ejpam-6571	376	63	-	-	PUNCT
ejpam-6571	376	64	open	open	NOUN
ejpam-6571	376	65	set	set	NOUN
ejpam-6571	376	66	v	v	NOUN
ejpam-6571	376	67	of	of	ADP
ejpam-6571	376	68	y	y	PROPN
ejpam-6571	376	69	.	.	PUNCT
ejpam-6571	377	1	proof	proof	NOUN
ejpam-6571	377	2	.	.	PUNCT
ejpam-6571	378	1	the	the	DET
ejpam-6571	378	2	proof	proof	NOUN
ejpam-6571	378	3	is	be	AUX
ejpam-6571	378	4	similar	similar	ADJ
ejpam-6571	378	5	to	to	ADP
ejpam-6571	378	6	that	that	PRON
ejpam-6571	378	7	of	of	ADP
ejpam-6571	378	8	theorem	theorem	ADJ
ejpam-6571	378	9	13	13	NUM
ejpam-6571	378	10	.	.	PUNCT
ejpam-6571	379	1	acknowledgements	acknowledgement	NOUN
ejpam-6571	379	2	this	this	DET
ejpam-6571	379	3	research	research	NOUN
ejpam-6571	379	4	project	project	NOUN
ejpam-6571	379	5	was	be	AUX
ejpam-6571	379	6	financially	financially	ADV
ejpam-6571	379	7	supported	support	VERB
ejpam-6571	379	8	by	by	ADP
ejpam-6571	379	9	mahasarakham	mahasarakham	PROPN
ejpam-6571	379	10	university	university	PROPN
ejpam-6571	379	11	.	.	PUNCT
ejpam-6571	380	1	references	reference	NOUN
ejpam-6571	380	2	[	[	X
ejpam-6571	380	3	1	1	X
ejpam-6571	380	4	]	]	PUNCT
ejpam-6571	380	5	s.	s.	PROPN
ejpam-6571	380	6	marcus	marcus	PROPN
ejpam-6571	380	7	.	.	PUNCT
ejpam-6571	381	1	sur	sur	PROPN
ejpam-6571	381	2	les	les	PROPN
ejpam-6571	381	3	fonctions	fonctions	PROPN
ejpam-6571	381	4	quasicontinues	quasicontinue	NOUN
ejpam-6571	381	5	au	au	ADP
ejpam-6571	381	6	sense	sense	NOUN
ejpam-6571	381	7	de	de	X
ejpam-6571	381	8	s.	s.	PROPN
ejpam-6571	381	9	kempisty	kempisty	PROPN
ejpam-6571	381	10	.	.	PUNCT
ejpam-6571	382	1	colloquium	colloquium	NOUN
ejpam-6571	382	2	mathematicum	mathematicum	PROPN
ejpam-6571	382	3	,	,	PUNCT
ejpam-6571	382	4	8:47–53	8:47–53	NUM
ejpam-6571	382	5	,	,	PUNCT
ejpam-6571	382	6	1961	1961	NUM
ejpam-6571	382	7	.	.	PUNCT
ejpam-6571	383	1	[	[	X
ejpam-6571	383	2	2	2	X
ejpam-6571	383	3	]	]	PUNCT
ejpam-6571	383	4	v.	v.	CCONJ
ejpam-6571	383	5	popa	popa	NOUN
ejpam-6571	383	6	.	.	PUNCT
ejpam-6571	384	1	on	on	ADP
ejpam-6571	384	2	the	the	DET
ejpam-6571	384	3	decomposition	decomposition	NOUN
ejpam-6571	384	4	of	of	ADP
ejpam-6571	384	5	the	the	DET
ejpam-6571	384	6	quasi	quasi	NOUN
ejpam-6571	384	7	-	-	NOUN
ejpam-6571	384	8	continuity	continuity	NOUN
ejpam-6571	384	9	in	in	ADP
ejpam-6571	384	10	topological	topological	ADJ
ejpam-6571	384	11	spaces	space	NOUN
ejpam-6571	384	12	(	(	PUNCT
ejpam-6571	384	13	romanian	romanian	ADJ
ejpam-6571	384	14	)	)	PUNCT
ejpam-6571	384	15	.	.	PUNCT
ejpam-6571	385	1	studii	studii	PROPN
ejpam-6571	385	2	şi	şi	PROPN
ejpam-6571	385	3	cercetǎri	cercetǎri	NOUN
ejpam-6571	385	4	de	de	X
ejpam-6571	385	5	matematicǎ	matematicǎ	NOUN
ejpam-6571	385	6	,	,	PUNCT
ejpam-6571	385	7	30:31–35	30:31–35	NUM
ejpam-6571	385	8	,	,	PUNCT
ejpam-6571	385	9	1978	1978	NUM
ejpam-6571	385	10	.	.	PUNCT
ejpam-6571	386	1	[	[	X
ejpam-6571	386	2	3	3	NUM
ejpam-6571	386	3	]	]	PUNCT
ejpam-6571	386	4	a.	a.	NOUN
ejpam-6571	386	5	neubrunnová.	neubrunnová.	PROPN
ejpam-6571	386	6	on	on	ADP
ejpam-6571	386	7	certain	certain	ADJ
ejpam-6571	386	8	generalizations	generalization	NOUN
ejpam-6571	386	9	of	of	ADP
ejpam-6571	386	10	the	the	DET
ejpam-6571	386	11	notion	notion	NOUN
ejpam-6571	386	12	of	of	ADP
ejpam-6571	386	13	continuity	continuity	NOUN
ejpam-6571	386	14	.	.	PUNCT
ejpam-6571	387	1	matematický	matematický	ADJ
ejpam-6571	387	2	c̆asopis	c̆asopis	PROPN
ejpam-6571	387	3	,	,	PUNCT
ejpam-6571	387	4	23:374–380	23:374–380	NUM
ejpam-6571	387	5	,	,	PUNCT
ejpam-6571	387	6	1973	1973	NUM
ejpam-6571	387	7	.	.	PUNCT
ejpam-6571	388	1	[	[	X
ejpam-6571	388	2	4	4	NUM
ejpam-6571	388	3	]	]	X
ejpam-6571	388	4	n.	n.	PROPN
ejpam-6571	388	5	levine	levine	PROPN
ejpam-6571	388	6	.	.	PUNCT
ejpam-6571	389	1	semi	semi	ADJ
ejpam-6571	389	2	-	-	ADJ
ejpam-6571	389	3	open	open	ADJ
ejpam-6571	389	4	sets	set	NOUN
ejpam-6571	389	5	and	and	CCONJ
ejpam-6571	389	6	semi	semi	ADJ
ejpam-6571	389	7	-	-	NOUN
ejpam-6571	389	8	continuity	continuity	NOUN
ejpam-6571	389	9	in	in	ADP
ejpam-6571	389	10	topological	topological	ADJ
ejpam-6571	389	11	spaces	space	NOUN
ejpam-6571	389	12	.	.	PUNCT
ejpam-6571	390	1	the	the	DET
ejpam-6571	390	2	american	american	PROPN
ejpam-6571	390	3	mathematical	mathematical	PROPN
ejpam-6571	390	4	monthly	monthly	ADV
ejpam-6571	390	5	,	,	PUNCT
ejpam-6571	390	6	70:36–41	70:36–41	NUM
ejpam-6571	390	7	,	,	PUNCT
ejpam-6571	390	8	1963	1963	NUM
ejpam-6571	390	9	.	.	PUNCT
ejpam-6571	391	1	[	[	X
ejpam-6571	391	2	5	5	X
ejpam-6571	391	3	]	]	PUNCT
ejpam-6571	391	4	v.	v.	CCONJ
ejpam-6571	391	5	popa	popa	NOUN
ejpam-6571	391	6	and	and	CCONJ
ejpam-6571	391	7	c.	c.	PROPN
ejpam-6571	391	8	stan	stan	PROPN
ejpam-6571	391	9	.	.	PUNCT
ejpam-6571	392	1	on	on	ADP
ejpam-6571	392	2	a	a	DET
ejpam-6571	392	3	decomposition	decomposition	NOUN
ejpam-6571	392	4	of	of	ADP
ejpam-6571	392	5	quasicontinuity	quasicontinuity	NOUN
ejpam-6571	392	6	in	in	ADP
ejpam-6571	392	7	topological	topological	ADJ
ejpam-6571	392	8	spaces	space	NOUN
ejpam-6571	392	9	.	.	PUNCT
ejpam-6571	393	1	studii	studii	PROPN
ejpam-6571	393	2	şi	şi	PROPN
ejpam-6571	393	3	cercetǎri	cercetǎri	PROPN
ejpam-6571	393	4	de	de	X
ejpam-6571	393	5	matematicǎ	matematicǎ	NOUN
ejpam-6571	393	6	,	,	PUNCT
ejpam-6571	393	7	25:41–43	25:41–43	NUM
ejpam-6571	393	8	,	,	PUNCT
ejpam-6571	393	9	1973	1973	NUM
ejpam-6571	393	10	.	.	PUNCT
ejpam-6571	394	1	[	[	X
ejpam-6571	394	2	6	6	NUM
ejpam-6571	394	3	]	]	X
ejpam-6571	394	4	n.	n.	PROPN
ejpam-6571	394	5	levine	levine	PROPN
ejpam-6571	394	6	.	.	PUNCT
ejpam-6571	395	1	a	a	DET
ejpam-6571	395	2	decomposition	decomposition	NOUN
ejpam-6571	395	3	of	of	ADP
ejpam-6571	395	4	continuity	continuity	NOUN
ejpam-6571	395	5	in	in	ADP
ejpam-6571	395	6	topological	topological	ADJ
ejpam-6571	395	7	spaces	space	NOUN
ejpam-6571	395	8	.	.	PUNCT
ejpam-6571	396	1	the	the	DET
ejpam-6571	396	2	american	american	PROPN
ejpam-6571	396	3	mathematical	mathematical	PROPN
ejpam-6571	396	4	monthly	monthly	ADV
ejpam-6571	396	5	,	,	PUNCT
ejpam-6571	396	6	68:44–46	68:44–46	NUM
ejpam-6571	396	7	,	,	PUNCT
ejpam-6571	396	8	1961	1961	NUM
ejpam-6571	396	9	.	.	PUNCT
ejpam-6571	397	1	[	[	X
ejpam-6571	397	2	7	7	X
ejpam-6571	397	3	]	]	PUNCT
ejpam-6571	397	4	t.	t.	PROPN
ejpam-6571	397	5	noiri	noiri	PROPN
ejpam-6571	397	6	.	.	PUNCT
ejpam-6571	398	1	properties	property	NOUN
ejpam-6571	398	2	of	of	ADP
ejpam-6571	398	3	some	some	DET
ejpam-6571	398	4	weak	weak	ADJ
ejpam-6571	398	5	forms	form	NOUN
ejpam-6571	398	6	of	of	ADP
ejpam-6571	398	7	continuity	continuity	NOUN
ejpam-6571	398	8	.	.	PUNCT
ejpam-6571	399	1	international	international	ADJ
ejpam-6571	399	2	journal	journal	PROPN
ejpam-6571	399	3	of	of	ADP
ejpam-6571	399	4	mathematica	mathematica	PROPN
ejpam-6571	399	5	and	and	CCONJ
ejpam-6571	399	6	mathematical	mathematical	ADJ
ejpam-6571	399	7	sciences	science	NOUN
ejpam-6571	399	8	,	,	PUNCT
ejpam-6571	399	9	10:97–111	10:97–111	NUM
ejpam-6571	399	10	,	,	PUNCT
ejpam-6571	399	11	1987	1987	NUM
ejpam-6571	399	12	.	.	PUNCT
ejpam-6571	400	1	m.	m.	NOUN
ejpam-6571	400	2	thongmoon	thongmoon	PROPN
ejpam-6571	400	3	,	,	PUNCT
ejpam-6571	400	4	a.	a.	PROPN
ejpam-6571	400	5	sama	sama	PROPN
ejpam-6571	400	6	-	-	PUNCT
ejpam-6571	400	7	ae	ae	PROPN
ejpam-6571	400	8	,	,	PUNCT
ejpam-6571	400	9	c.	c.	PROPN
ejpam-6571	400	10	boonpok	boonpok	PROPN
ejpam-6571	400	11	/	/	SYM
ejpam-6571	400	12	eur	eur	PROPN
ejpam-6571	400	13	.	.	PUNCT
ejpam-6571	401	1	j.	j.	PROPN
ejpam-6571	401	2	pure	pure	PROPN
ejpam-6571	401	3	appl	appl	PROPN
ejpam-6571	401	4	.	.	PROPN
ejpam-6571	401	5	math	math	PROPN
ejpam-6571	401	6	,	,	PUNCT
ejpam-6571	401	7	18	18	NUM
ejpam-6571	401	8	(	(	PUNCT
ejpam-6571	401	9	3	3	NUM
ejpam-6571	401	10	)	)	PUNCT
ejpam-6571	401	11	(	(	PUNCT
ejpam-6571	401	12	2025	2025	NUM
ejpam-6571	401	13	)	)	PUNCT
ejpam-6571	401	14	,	,	PUNCT
ejpam-6571	401	15	6571	6571	NUM
ejpam-6571	401	16	14	14	NUM
ejpam-6571	401	17	of	of	ADP
ejpam-6571	401	18	15	15	NUM
ejpam-6571	401	19	[	[	SYM
ejpam-6571	401	20	8	8	NUM
ejpam-6571	401	21	]	]	PUNCT
ejpam-6571	402	1	s.	s.	PROPN
ejpam-6571	402	2	p.	p.	PROPN
ejpam-6571	402	3	arya	arya	PROPN
ejpam-6571	402	4	and	and	CCONJ
ejpam-6571	402	5	m.	m.	PROPN
ejpam-6571	402	6	p.	p.	PROPN
ejpam-6571	402	7	bhamini	bhamini	PROPN
ejpam-6571	402	8	.	.	PUNCT
ejpam-6571	403	1	some	some	DET
ejpam-6571	403	2	weaker	weak	ADJ
ejpam-6571	403	3	forms	form	NOUN
ejpam-6571	403	4	of	of	ADP
ejpam-6571	403	5	semi	semi	ADJ
ejpam-6571	403	6	-	-	ADJ
ejpam-6571	403	7	continuous	continuous	ADJ
ejpam-6571	403	8	functions	function	NOUN
ejpam-6571	403	9	.	.	PUNCT
ejpam-6571	404	1	ganita	ganita	NOUN
ejpam-6571	404	2	,	,	PUNCT
ejpam-6571	404	3	33:124–134	33:124–134	NUM
ejpam-6571	404	4	,	,	PUNCT
ejpam-6571	404	5	1982	1982	NUM
ejpam-6571	404	6	.	.	PUNCT
ejpam-6571	405	1	[	[	X
ejpam-6571	405	2	9	9	NUM
ejpam-6571	405	3	]	]	PUNCT
ejpam-6571	405	4	a.	a.	NOUN
ejpam-6571	405	5	kar	kar	PROPN
ejpam-6571	405	6	and	and	CCONJ
ejpam-6571	405	7	p.	p.	PROPN
ejpam-6571	405	8	bhattacharyya	bhattacharyya	PROPN
ejpam-6571	405	9	.	.	PUNCT
ejpam-6571	406	1	weakly	weakly	ADJ
ejpam-6571	406	2	semi	semi	ADJ
ejpam-6571	406	3	-	-	ADJ
ejpam-6571	406	4	continuous	continuous	ADJ
ejpam-6571	406	5	functions	function	NOUN
ejpam-6571	406	6	.	.	PUNCT
ejpam-6571	407	1	the	the	DET
ejpam-6571	407	2	journal	journal	NOUN
ejpam-6571	407	3	of	of	ADP
ejpam-6571	407	4	the	the	DET
ejpam-6571	407	5	indian	indian	PROPN
ejpam-6571	407	6	academy	academy	PROPN
ejpam-6571	407	7	of	of	ADP
ejpam-6571	407	8	mathematics	mathematics	PROPN
ejpam-6571	407	9	,	,	PUNCT
ejpam-6571	407	10	8:83–93	8:83–93	NUM
ejpam-6571	407	11	,	,	PUNCT
ejpam-6571	407	12	1986	1986	NUM
ejpam-6571	407	13	.	.	PUNCT
ejpam-6571	408	1	[	[	X
ejpam-6571	408	2	10	10	NUM
ejpam-6571	408	3	]	]	X
ejpam-6571	408	4	d.	d.	PROPN
ejpam-6571	408	5	janković	janković	PROPN
ejpam-6571	408	6	and	and	CCONJ
ejpam-6571	408	7	t.	t.	PROPN
ejpam-6571	408	8	r.	r.	PROPN
ejpam-6571	408	9	hamlett	hamlett	PROPN
ejpam-6571	408	10	.	.	PUNCT
ejpam-6571	409	1	new	new	ADJ
ejpam-6571	409	2	topologies	topology	NOUN
ejpam-6571	409	3	from	from	ADP
ejpam-6571	409	4	old	old	ADJ
ejpam-6571	409	5	via	via	ADP
ejpam-6571	409	6	ideals	ideal	NOUN
ejpam-6571	409	7	.	.	PUNCT
ejpam-6571	410	1	the	the	DET
ejpam-6571	410	2	american	american	PROPN
ejpam-6571	410	3	mathematical	mathematical	PROPN
ejpam-6571	410	4	monthly	monthly	ADV
ejpam-6571	410	5	,	,	PUNCT
ejpam-6571	410	6	97:295–310	97:295–310	PROPN
ejpam-6571	410	7	,	,	PUNCT
ejpam-6571	410	8	1990	1990	NUM
ejpam-6571	410	9	.	.	PUNCT
ejpam-6571	411	1	[	[	X
ejpam-6571	411	2	11	11	NUM
ejpam-6571	411	3	]	]	PUNCT
ejpam-6571	411	4	m.	m.	NOUN
ejpam-6571	411	5	e.	e.	PROPN
ejpam-6571	411	6	abd	abd	PROPN
ejpam-6571	411	7	el	el	PROPN
ejpam-6571	411	8	-	-	PROPN
ejpam-6571	411	9	monsef	monsef	PROPN
ejpam-6571	411	10	,	,	PUNCT
ejpam-6571	411	11	e.	e.	PROPN
ejpam-6571	411	12	f.	f.	PROPN
ejpam-6571	411	13	lashien	lashien	PROPN
ejpam-6571	411	14	,	,	PUNCT
ejpam-6571	411	15	and	and	CCONJ
ejpam-6571	411	16	a.	a.	NOUN
ejpam-6571	411	17	a.	a.	NOUN
ejpam-6571	411	18	nasef	nasef	PROPN
ejpam-6571	411	19	.	.	PUNCT
ejpam-6571	412	1	on	on	ADP
ejpam-6571	412	2	i	i	PRON
ejpam-6571	412	3	-open	-open	PROPN
ejpam-6571	412	4	sets	set	NOUN
ejpam-6571	412	5	and	and	CCONJ
ejpam-6571	412	6	i	i	PRON
ejpam-6571	412	7	continuous	continuous	ADJ
ejpam-6571	412	8	functions	function	NOUN
ejpam-6571	412	9	.	.	PUNCT
ejpam-6571	413	1	kyungpook	kyungpook	PROPN
ejpam-6571	413	2	mathematical	mathematical	PROPN
ejpam-6571	413	3	journal	journal	PROPN
ejpam-6571	413	4	,	,	PUNCT
ejpam-6571	413	5	32:21–30	32:21–30	NUM
ejpam-6571	413	6	,	,	PUNCT
ejpam-6571	413	7	1992	1992	NUM
ejpam-6571	413	8	.	.	PUNCT
ejpam-6571	414	1	[	[	X
ejpam-6571	414	2	12	12	NUM
ejpam-6571	414	3	]	]	X
ejpam-6571	414	4	e.	e.	PROPN
ejpam-6571	414	5	hatir	hatir	PROPN
ejpam-6571	414	6	and	and	CCONJ
ejpam-6571	414	7	t.	t.	PROPN
ejpam-6571	414	8	noiri	noiri	PROPN
ejpam-6571	414	9	.	.	PUNCT
ejpam-6571	415	1	weakly	weakly	ADJ
ejpam-6571	415	2	pre	pre	ADJ
ejpam-6571	415	3	-	-	ADJ
ejpam-6571	415	4	i	i	PRON
ejpam-6571	415	5	-	-	PUNCT
ejpam-6571	415	6	open	open	ADJ
ejpam-6571	415	7	sets	set	NOUN
ejpam-6571	415	8	and	and	CCONJ
ejpam-6571	415	9	decomposition	decomposition	NOUN
ejpam-6571	415	10	of	of	ADP
ejpam-6571	415	11	continuity	continuity	NOUN
ejpam-6571	415	12	.	.	PUNCT
ejpam-6571	416	1	acta	acta	PROPN
ejpam-6571	416	2	mathematica	mathematica	PROPN
ejpam-6571	416	3	hungarica	hungarica	PROPN
ejpam-6571	416	4	,	,	PUNCT
ejpam-6571	416	5	106(3):227–238	106(3):227–238	NUM
ejpam-6571	416	6	,	,	PUNCT
ejpam-6571	416	7	2005	2005	NUM
ejpam-6571	416	8	.	.	PUNCT
ejpam-6571	417	1	[	[	X
ejpam-6571	417	2	13	13	NUM
ejpam-6571	417	3	]	]	X
ejpam-6571	417	4	e.	e.	PROPN
ejpam-6571	417	5	hatir	hatir	PROPN
ejpam-6571	417	6	and	and	CCONJ
ejpam-6571	417	7	t.	t.	PROPN
ejpam-6571	417	8	noiri	noiri	PROPN
ejpam-6571	417	9	.	.	PUNCT
ejpam-6571	418	1	on	on	ADP
ejpam-6571	418	2	decompositions	decomposition	NOUN
ejpam-6571	418	3	of	of	ADP
ejpam-6571	418	4	continuity	continuity	NOUN
ejpam-6571	418	5	via	via	ADP
ejpam-6571	418	6	idealization	idealization	NOUN
ejpam-6571	418	7	.	.	PUNCT
ejpam-6571	419	1	acta	acta	PROPN
ejpam-6571	419	2	mathematica	mathematica	PROPN
ejpam-6571	419	3	hungarica	hungarica	PROPN
ejpam-6571	419	4	,	,	PUNCT
ejpam-6571	419	5	96:341–349	96:341–349	PROPN
ejpam-6571	419	6	,	,	PUNCT
ejpam-6571	419	7	2002	2002	NUM
ejpam-6571	419	8	.	.	PUNCT
ejpam-6571	420	1	[	[	X
ejpam-6571	420	2	14	14	NUM
ejpam-6571	420	3	]	]	X
ejpam-6571	420	4	c.	c.	PROPN
ejpam-6571	420	5	boonpok	boonpok	PROPN
ejpam-6571	420	6	.	.	PUNCT
ejpam-6571	421	1	weak	weak	ADJ
ejpam-6571	421	2	quasi	quasi	ADJ
ejpam-6571	421	3	continuity	continuity	NOUN
ejpam-6571	421	4	for	for	ADP
ejpam-6571	421	5	multifunctions	multifunction	NOUN
ejpam-6571	421	6	in	in	ADP
ejpam-6571	421	7	ideal	ideal	ADJ
ejpam-6571	421	8	topological	topological	ADJ
ejpam-6571	421	9	spaces	space	NOUN
ejpam-6571	421	10	.	.	PUNCT
ejpam-6571	422	1	advances	advance	NOUN
ejpam-6571	422	2	in	in	ADP
ejpam-6571	422	3	mathematics	mathematic	NOUN
ejpam-6571	422	4	:	:	PUNCT
ejpam-6571	422	5	scientific	scientific	ADJ
ejpam-6571	422	6	journal	journal	NOUN
ejpam-6571	422	7	,	,	PUNCT
ejpam-6571	422	8	19(1):339–355	19(1):339–355	NUM
ejpam-6571	422	9	,	,	PUNCT
ejpam-6571	422	10	2020	2020	NUM
ejpam-6571	422	11	.	.	PUNCT
ejpam-6571	423	1	[	[	X
ejpam-6571	423	2	15	15	NUM
ejpam-6571	423	3	]	]	X
ejpam-6571	423	4	c.	c.	PROPN
ejpam-6571	423	5	boonpok	boonpok	PROPN
ejpam-6571	423	6	.	.	PUNCT
ejpam-6571	424	1	pı	pı	NOUN
ejpam-6571	424	2	-	-	NOUN
ejpam-6571	424	3	continuity	continuity	NOUN
ejpam-6571	424	4	and	and	CCONJ
ejpam-6571	424	5	weak	weak	ADJ
ejpam-6571	424	6	pı	pı	NOUN
ejpam-6571	424	7	-	-	NOUN
ejpam-6571	424	8	continuity	continuity	NOUN
ejpam-6571	424	9	.	.	PUNCT
ejpam-6571	425	1	carpathian	carpathian	ADJ
ejpam-6571	425	2	mathematical	mathematical	ADJ
ejpam-6571	425	3	publications	publication	NOUN
ejpam-6571	425	4	,	,	PUNCT
ejpam-6571	425	5	17(1):171–186	17(1):171–186	PROPN
ejpam-6571	425	6	,	,	PUNCT
ejpam-6571	425	7	2025	2025	NUM
ejpam-6571	425	8	.	.	PUNCT
ejpam-6571	426	1	[	[	X
ejpam-6571	426	2	16	16	NUM
ejpam-6571	426	3	]	]	X
ejpam-6571	426	4	p.	p.	NOUN
ejpam-6571	426	5	pue	pue	NOUN
ejpam-6571	426	6	-	-	PUNCT
ejpam-6571	426	7	on	on	ADP
ejpam-6571	426	8	,	,	PUNCT
ejpam-6571	426	9	s.	s.	PROPN
ejpam-6571	426	10	sompong	sompong	PROPN
ejpam-6571	426	11	,	,	PUNCT
ejpam-6571	426	12	and	and	CCONJ
ejpam-6571	426	13	c.	c.	PROPN
ejpam-6571	426	14	boonpok	boonpok	PROPN
ejpam-6571	426	15	.	.	PUNCT
ejpam-6571	427	1	upper	upper	ADJ
ejpam-6571	427	2	and	and	CCONJ
ejpam-6571	427	3	lower	low	ADJ
ejpam-6571	427	4	(	(	PUNCT
ejpam-6571	427	5	τ1	τ1	NOUN
ejpam-6571	427	6	,	,	PUNCT
ejpam-6571	427	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	427	8	multifunctions	multifunction	NOUN
ejpam-6571	427	9	.	.	PUNCT
ejpam-6571	428	1	international	international	ADJ
ejpam-6571	428	2	journal	journal	PROPN
ejpam-6571	428	3	of	of	ADP
ejpam-6571	428	4	mathematics	mathematic	NOUN
ejpam-6571	428	5	and	and	CCONJ
ejpam-6571	428	6	computer	computer	NOUN
ejpam-6571	428	7	science	science	NOUN
ejpam-6571	428	8	,	,	PUNCT
ejpam-6571	428	9	19(4):1305	19(4):1305	NUM
ejpam-6571	428	10	–	–	PUNCT
ejpam-6571	428	11	1310	1310	NUM
ejpam-6571	428	12	,	,	PUNCT
ejpam-6571	428	13	2024	2024	NUM
ejpam-6571	428	14	.	.	PUNCT
ejpam-6571	429	1	[	[	X
ejpam-6571	429	2	17	17	NUM
ejpam-6571	429	3	]	]	X
ejpam-6571	429	4	c.	c.	PROPN
ejpam-6571	429	5	klanarong	klanarong	PROPN
ejpam-6571	429	6	,	,	PUNCT
ejpam-6571	429	7	s.	s.	PROPN
ejpam-6571	429	8	sompong	sompong	PROPN
ejpam-6571	429	9	,	,	PUNCT
ejpam-6571	429	10	and	and	CCONJ
ejpam-6571	429	11	c.	c.	PROPN
ejpam-6571	429	12	boonpok	boonpok	PROPN
ejpam-6571	429	13	.	.	PUNCT
ejpam-6571	430	1	upper	upper	ADJ
ejpam-6571	430	2	and	and	CCONJ
ejpam-6571	430	3	lower	low	ADJ
ejpam-6571	430	4	almost	almost	ADV
ejpam-6571	430	5	(	(	PUNCT
ejpam-6571	430	6	τ1	τ1	NOUN
ejpam-6571	430	7	,	,	PUNCT
ejpam-6571	430	8	τ2)continuous	τ2)continuous	ADJ
ejpam-6571	430	9	multifunctions	multifunction	NOUN
ejpam-6571	430	10	.	.	PUNCT
ejpam-6571	431	1	european	european	ADJ
ejpam-6571	431	2	journal	journal	PROPN
ejpam-6571	431	3	of	of	ADP
ejpam-6571	431	4	pure	pure	ADJ
ejpam-6571	431	5	and	and	CCONJ
ejpam-6571	431	6	applied	applied	ADJ
ejpam-6571	431	7	mathematics	mathematic	NOUN
ejpam-6571	431	8	,	,	PUNCT
ejpam-6571	431	9	17(2):1244–1253	17(2):1244–1253	NUM
ejpam-6571	431	10	,	,	PUNCT
ejpam-6571	431	11	2024	2024	NUM
ejpam-6571	431	12	.	.	PUNCT
ejpam-6571	432	1	[	[	X
ejpam-6571	432	2	18	18	NUM
ejpam-6571	432	3	]	]	PUNCT
ejpam-6571	432	4	m.	m.	NOUN
ejpam-6571	432	5	thongmoon	thongmoon	NOUN
ejpam-6571	432	6	,	,	PUNCT
ejpam-6571	432	7	s.	s.	PROPN
ejpam-6571	432	8	sompong	sompong	PROPN
ejpam-6571	432	9	,	,	PUNCT
ejpam-6571	432	10	and	and	CCONJ
ejpam-6571	432	11	c.	c.	PROPN
ejpam-6571	432	12	boonpok	boonpok	PROPN
ejpam-6571	432	13	.	.	PUNCT
ejpam-6571	433	1	upper	upper	ADJ
ejpam-6571	433	2	and	and	CCONJ
ejpam-6571	433	3	lower	low	ADJ
ejpam-6571	433	4	weak	weak	ADJ
ejpam-6571	433	5	(	(	PUNCT
ejpam-6571	433	6	τ1	τ1	NOUN
ejpam-6571	433	7	,	,	PUNCT
ejpam-6571	433	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6571	433	9	.	.	PUNCT
ejpam-6571	434	1	european	european	PROPN
ejpam-6571	434	2	journal	journal	PROPN
ejpam-6571	434	3	of	of	ADP
ejpam-6571	434	4	pure	pure	ADJ
ejpam-6571	434	5	and	and	CCONJ
ejpam-6571	434	6	applied	applied	ADJ
ejpam-6571	434	7	mathematics	mathematic	NOUN
ejpam-6571	434	8	,	,	PUNCT
ejpam-6571	434	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-6571	434	10	,	,	PUNCT
ejpam-6571	434	11	2024	2024	NUM
ejpam-6571	434	12	.	.	PUNCT
ejpam-6571	435	1	[	[	X
ejpam-6571	435	2	19	19	NUM
ejpam-6571	435	3	]	]	PUNCT
ejpam-6571	435	4	m.	m.	NOUN
ejpam-6571	435	5	chiangpradit	chiangpradit	NOUN
ejpam-6571	435	6	,	,	PUNCT
ejpam-6571	435	7	s.	s.	PROPN
ejpam-6571	435	8	sompong	sompong	PROPN
ejpam-6571	435	9	,	,	PUNCT
ejpam-6571	435	10	and	and	CCONJ
ejpam-6571	435	11	c.	c.	PROPN
ejpam-6571	435	12	boonpok	boonpok	PROPN
ejpam-6571	435	13	.	.	PUNCT
ejpam-6571	436	1	upper	upper	ADJ
ejpam-6571	436	2	and	and	CCONJ
ejpam-6571	436	3	lower	low	ADJ
ejpam-6571	436	4	almost	almost	ADV
ejpam-6571	436	5	quasi	quasi	NOUN
ejpam-6571	436	6	(	(	PUNCT
ejpam-6571	436	7	τ1	τ1	NOUN
ejpam-6571	436	8	,	,	PUNCT
ejpam-6571	436	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6571	436	10	.	.	PUNCT
ejpam-6571	436	11	asia	asia	PROPN
ejpam-6571	436	12	pacific	pacific	PROPN
ejpam-6571	436	13	journal	journal	PROPN
ejpam-6571	436	14	of	of	ADP
ejpam-6571	436	15	mathematics	mathematic	NOUN
ejpam-6571	436	16	,	,	PUNCT
ejpam-6571	436	17	12:12	12:12	NUM
ejpam-6571	436	18	,	,	PUNCT
ejpam-6571	436	19	2025	2025	NUM
ejpam-6571	436	20	.	.	PUNCT
ejpam-6571	437	1	[	[	X
ejpam-6571	437	2	20	20	NUM
ejpam-6571	437	3	]	]	PUNCT
ejpam-6571	437	4	p.	p.	NOUN
ejpam-6571	437	5	pue	pue	NOUN
ejpam-6571	437	6	-	-	PUNCT
ejpam-6571	437	7	on	on	ADP
ejpam-6571	437	8	,	,	PUNCT
ejpam-6571	437	9	s.	s.	PROPN
ejpam-6571	437	10	sompong	sompong	PROPN
ejpam-6571	437	11	,	,	PUNCT
ejpam-6571	437	12	and	and	CCONJ
ejpam-6571	437	13	c.	c.	PROPN
ejpam-6571	437	14	boonpok	boonpok	PROPN
ejpam-6571	437	15	.	.	PUNCT
ejpam-6571	438	1	weakly	weakly	ADJ
ejpam-6571	438	2	quasi	quasi	NOUN
ejpam-6571	438	3	(	(	PUNCT
ejpam-6571	438	4	τ1	τ1	PROPN
ejpam-6571	438	5	,	,	PUNCT
ejpam-6571	438	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	438	7	multifunctions	multifunction	NOUN
ejpam-6571	438	8	.	.	PUNCT
ejpam-6571	439	1	european	european	ADJ
ejpam-6571	439	2	journal	journal	PROPN
ejpam-6571	439	3	of	of	ADP
ejpam-6571	439	4	pure	pure	ADJ
ejpam-6571	439	5	and	and	CCONJ
ejpam-6571	439	6	applied	applied	ADJ
ejpam-6571	439	7	mathematics	mathematic	NOUN
ejpam-6571	439	8	,	,	PUNCT
ejpam-6571	439	9	17(3):1553–1564	17(3):1553–1564	NUM
ejpam-6571	439	10	,	,	PUNCT
ejpam-6571	439	11	2024	2024	NUM
ejpam-6571	439	12	.	.	PUNCT
ejpam-6571	440	1	[	[	X
ejpam-6571	440	2	21	21	NUM
ejpam-6571	440	3	]	]	X
ejpam-6571	440	4	c.	c.	PROPN
ejpam-6571	440	5	boonpok	boonpok	PROPN
ejpam-6571	440	6	,	,	PUNCT
ejpam-6571	440	7	c.	c.	PROPN
ejpam-6571	440	8	viriyapong	viriyapong	PROPN
ejpam-6571	440	9	,	,	PUNCT
ejpam-6571	440	10	and	and	CCONJ
ejpam-6571	440	11	m.	m.	NOUN
ejpam-6571	440	12	thongmoon	thongmoon	NOUN
ejpam-6571	440	13	.	.	PUNCT
ejpam-6571	441	1	on	on	ADP
ejpam-6571	441	2	upper	upper	ADJ
ejpam-6571	441	3	and	and	CCONJ
ejpam-6571	441	4	lower	low	ADJ
ejpam-6571	441	5	(	(	PUNCT
ejpam-6571	441	6	τ1	τ1	NOUN
ejpam-6571	441	7	,	,	PUNCT
ejpam-6571	441	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6571	441	9	multifunctions	multifunction	NOUN
ejpam-6571	441	10	.	.	PUNCT
ejpam-6571	442	1	journal	journal	PROPN
ejpam-6571	442	2	of	of	ADP
ejpam-6571	442	3	mathematics	mathematics	PROPN
ejpam-6571	442	4	and	and	CCONJ
ejpam-6571	442	5	computer	computer	NOUN
ejpam-6571	442	6	science	science	NOUN
ejpam-6571	442	7	,	,	PUNCT
ejpam-6571	442	8	18:282–293	18:282–293	NUM
ejpam-6571	442	9	,	,	PUNCT
ejpam-6571	442	10	2018	2018	NUM
ejpam-6571	442	11	.	.	PUNCT
ejpam-6571	443	1	[	[	X
ejpam-6571	443	2	22	22	NUM
ejpam-6571	443	3	]	]	X
ejpam-6571	443	4	c.	c.	PROPN
ejpam-6571	443	5	viriyapong	viriyapong	PROPN
ejpam-6571	443	6	and	and	CCONJ
ejpam-6571	443	7	c.	c.	PROPN
ejpam-6571	443	8	boonpok	boonpok	PROPN
ejpam-6571	443	9	.	.	PUNCT
ejpam-6571	444	1	(	(	PUNCT
ejpam-6571	444	2	τ1	τ1	NOUN
ejpam-6571	444	3	,	,	PUNCT
ejpam-6571	444	4	τ2)α	τ2)α	NOUN
ejpam-6571	444	5	-	-	PUNCT
ejpam-6571	444	6	continuity	continuity	NOUN
ejpam-6571	444	7	for	for	ADP
ejpam-6571	444	8	multifunctions	multifunction	NOUN
ejpam-6571	444	9	.	.	PUNCT
ejpam-6571	445	1	journal	journal	PROPN
ejpam-6571	445	2	of	of	ADP
ejpam-6571	445	3	mathematics	mathematic	NOUN
ejpam-6571	445	4	,	,	PUNCT
ejpam-6571	445	5	2020:6285763	2020:6285763	NUM
ejpam-6571	445	6	,	,	PUNCT
ejpam-6571	445	7	2020	2020	NUM
ejpam-6571	445	8	.	.	PUNCT
ejpam-6571	446	1	[	[	X
ejpam-6571	446	2	23	23	NUM
ejpam-6571	446	3	]	]	X
ejpam-6571	446	4	c.	c.	PROPN
ejpam-6571	446	5	boonpok	boonpok	PROPN
ejpam-6571	446	6	.	.	PUNCT
ejpam-6571	447	1	(	(	PUNCT
ejpam-6571	447	2	τ1	τ1	NOUN
ejpam-6571	447	3	,	,	PUNCT
ejpam-6571	447	4	τ2)δ	τ2)δ	ADJ
ejpam-6571	447	5	-	-	PUNCT
ejpam-6571	447	6	semicontinuous	semicontinuous	ADJ
ejpam-6571	447	7	multifunctions	multifunction	NOUN
ejpam-6571	447	8	.	.	PUNCT
ejpam-6571	448	1	heliyon	heliyon	NOUN
ejpam-6571	448	2	,	,	PUNCT
ejpam-6571	448	3	6	6	NUM
ejpam-6571	448	4	:	:	SYM
ejpam-6571	448	5	e05367	e05367	PROPN
ejpam-6571	448	6	,	,	PUNCT
ejpam-6571	448	7	2020	2020	NUM
ejpam-6571	448	8	.	.	PUNCT
ejpam-6571	449	1	[	[	X
ejpam-6571	449	2	24	24	NUM
ejpam-6571	449	3	]	]	X
ejpam-6571	449	4	n.	n.	PROPN
ejpam-6571	449	5	viriyapong	viriyapong	PROPN
ejpam-6571	449	6	,	,	PUNCT
ejpam-6571	449	7	s.	s.	PROPN
ejpam-6571	449	8	sompong	sompong	PROPN
ejpam-6571	449	9	,	,	PUNCT
ejpam-6571	449	10	and	and	CCONJ
ejpam-6571	449	11	c.	c.	PROPN
ejpam-6571	449	12	boonpok	boonpok	PROPN
ejpam-6571	449	13	.	.	PUNCT
ejpam-6571	450	1	(	(	PUNCT
ejpam-6571	450	2	τ1	τ1	NOUN
ejpam-6571	450	3	,	,	PUNCT
ejpam-6571	450	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6571	450	5	disconnectedness	disconnectedness	NOUN
ejpam-6571	450	6	in	in	ADP
ejpam-6571	450	7	bitopological	bitopological	ADJ
ejpam-6571	450	8	spaces	space	NOUN
ejpam-6571	450	9	.	.	PUNCT
ejpam-6571	451	1	international	international	ADJ
ejpam-6571	451	2	journal	journal	PROPN
ejpam-6571	451	3	of	of	ADP
ejpam-6571	451	4	mathematics	mathematic	NOUN
ejpam-6571	451	5	and	and	CCONJ
ejpam-6571	451	6	computer	computer	NOUN
ejpam-6571	451	7	science	science	NOUN
ejpam-6571	451	8	,	,	PUNCT
ejpam-6571	451	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6571	451	10	,	,	PUNCT
ejpam-6571	451	11	2024	2024	NUM
ejpam-6571	451	12	.	.	PUNCT
ejpam-6571	452	1	[	[	X
ejpam-6571	452	2	25	25	NUM
ejpam-6571	452	3	]	]	X
ejpam-6571	452	4	n.	n.	PROPN
ejpam-6571	452	5	viriyapong	viriyapong	PROPN
ejpam-6571	452	6	,	,	PUNCT
ejpam-6571	452	7	s.	s.	PROPN
ejpam-6571	452	8	sompong	sompong	PROPN
ejpam-6571	452	9	,	,	PUNCT
ejpam-6571	452	10	and	and	CCONJ
ejpam-6571	452	11	c.	c.	PROPN
ejpam-6571	452	12	boonpok	boonpok	PROPN
ejpam-6571	452	13	.	.	PUNCT
ejpam-6571	453	1	upper	upper	ADJ
ejpam-6571	453	2	and	and	CCONJ
ejpam-6571	453	3	lower	low	ADJ
ejpam-6571	453	4	s-(τ1	s-(τ1	NOUN
ejpam-6571	453	5	,	,	PUNCT
ejpam-6571	453	6	τ2)p	τ2)p	ADJ
ejpam-6571	453	7	-	-	PUNCT
ejpam-6571	453	8	continuous	continuous	ADJ
ejpam-6571	453	9	multifunctions	multifunction	NOUN
ejpam-6571	453	10	.	.	PUNCT
ejpam-6571	454	1	european	european	ADJ
ejpam-6571	454	2	journal	journal	PROPN
ejpam-6571	454	3	of	of	ADP
ejpam-6571	454	4	pure	pure	ADJ
ejpam-6571	454	5	and	and	CCONJ
ejpam-6571	454	6	applied	applied	ADJ
ejpam-6571	454	7	mathematics	mathematic	NOUN
ejpam-6571	454	8	,	,	PUNCT
ejpam-6571	454	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-6571	454	10	,	,	PUNCT
ejpam-6571	454	11	2024	2024	NUM
ejpam-6571	454	12	.	.	PUNCT
ejpam-6571	455	1	[	[	X
ejpam-6571	455	2	26	26	NUM
ejpam-6571	455	3	]	]	X
ejpam-6571	455	4	c.	c.	PROPN
ejpam-6571	455	5	viriyapong	viriyapong	PROPN
ejpam-6571	455	6	,	,	PUNCT
ejpam-6571	455	7	s.	s.	PROPN
ejpam-6571	455	8	sompong	sompong	PROPN
ejpam-6571	455	9	,	,	PUNCT
ejpam-6571	455	10	and	and	CCONJ
ejpam-6571	455	11	c.	c.	PROPN
ejpam-6571	455	12	boonpok	boonpok	PROPN
ejpam-6571	455	13	.	.	PUNCT
ejpam-6571	456	1	upper	upper	ADJ
ejpam-6571	456	2	and	and	CCONJ
ejpam-6571	456	3	lower	low	ADJ
ejpam-6571	456	4	slight	slight	ADJ
ejpam-6571	456	5	α(τ1	α(τ1	NOUN
ejpam-6571	456	6	,	,	PUNCT
ejpam-6571	456	7	τ2)continuity	τ2)continuity	PROPN
ejpam-6571	456	8	.	.	PUNCT
ejpam-6571	457	1	european	european	PROPN
ejpam-6571	457	2	journal	journal	PROPN
ejpam-6571	457	3	of	of	ADP
ejpam-6571	457	4	pure	pure	ADJ
ejpam-6571	457	5	and	and	CCONJ
ejpam-6571	457	6	applied	applied	ADJ
ejpam-6571	457	7	mathematics	mathematic	NOUN
ejpam-6571	457	8	,	,	PUNCT
ejpam-6571	457	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-6571	457	10	,	,	PUNCT
ejpam-6571	457	11	m.	m.	NOUN
ejpam-6571	457	12	thongmoon	thongmoon	NOUN
ejpam-6571	457	13	,	,	PUNCT
ejpam-6571	457	14	a.	a.	PROPN
ejpam-6571	457	15	sama	sama	PROPN
ejpam-6571	457	16	-	-	PUNCT
ejpam-6571	457	17	ae	ae	PROPN
ejpam-6571	457	18	,	,	PUNCT
ejpam-6571	457	19	c.	c.	PROPN
ejpam-6571	457	20	boonpok	boonpok	PROPN
ejpam-6571	457	21	/	/	SYM
ejpam-6571	457	22	eur	eur	PROPN
ejpam-6571	457	23	.	.	PUNCT
ejpam-6571	458	1	j.	j.	PROPN
ejpam-6571	458	2	pure	pure	PROPN
ejpam-6571	458	3	appl	appl	PROPN
ejpam-6571	458	4	.	.	PROPN
ejpam-6571	458	5	math	math	PROPN
ejpam-6571	458	6	,	,	PUNCT
ejpam-6571	458	7	18	18	NUM
ejpam-6571	458	8	(	(	PUNCT
ejpam-6571	458	9	3	3	NUM
ejpam-6571	458	10	)	)	PUNCT
ejpam-6571	458	11	(	(	PUNCT
ejpam-6571	458	12	2025	2025	NUM
ejpam-6571	458	13	)	)	PUNCT
ejpam-6571	458	14	,	,	PUNCT
ejpam-6571	458	15	6571	6571	NUM
ejpam-6571	458	16	15	15	NUM
ejpam-6571	458	17	of	of	ADP
ejpam-6571	458	18	15	15	NUM
ejpam-6571	458	19	2024	2024	NUM
ejpam-6571	458	20	.	.	PUNCT
ejpam-6571	459	1	[	[	X
ejpam-6571	459	2	27	27	NUM
ejpam-6571	459	3	]	]	X
ejpam-6571	459	4	b.	b.	PROPN
ejpam-6571	459	5	kong	kong	PROPN
ejpam-6571	459	6	-	-	PUNCT
ejpam-6571	459	7	ied	ied	PROPN
ejpam-6571	459	8	,	,	PUNCT
ejpam-6571	459	9	s.	s.	PROPN
ejpam-6571	459	10	sompong	sompong	PROPN
ejpam-6571	459	11	,	,	PUNCT
ejpam-6571	459	12	and	and	CCONJ
ejpam-6571	459	13	c.	c.	PROPN
ejpam-6571	459	14	boonpok	boonpok	PROPN
ejpam-6571	459	15	.	.	PUNCT
ejpam-6571	460	1	almost	almost	ADV
ejpam-6571	460	2	quasi	quasi	X
ejpam-6571	460	3	(	(	PUNCT
ejpam-6571	460	4	τ1	τ1	NOUN
ejpam-6571	460	5	,	,	PUNCT
ejpam-6571	460	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	460	7	functions	function	NOUN
ejpam-6571	460	8	.	.	PUNCT
ejpam-6571	461	1	asia	asia	PROPN
ejpam-6571	461	2	pacific	pacific	PROPN
ejpam-6571	461	3	journal	journal	PROPN
ejpam-6571	461	4	of	of	ADP
ejpam-6571	461	5	mathematics	mathematic	NOUN
ejpam-6571	461	6	,	,	PUNCT
ejpam-6571	461	7	11:64	11:64	NUM
ejpam-6571	461	8	,	,	PUNCT
ejpam-6571	461	9	2024	2024	NUM
ejpam-6571	461	10	.	.	PUNCT
ejpam-6571	462	1	[	[	X
ejpam-6571	462	2	28	28	NUM
ejpam-6571	462	3	]	]	X
ejpam-6571	462	4	c.	c.	PROPN
ejpam-6571	462	5	boonpok	boonpok	PROPN
ejpam-6571	462	6	and	and	CCONJ
ejpam-6571	462	7	c.	c.	PROPN
ejpam-6571	462	8	khanarong	khanarong	PROPN
ejpam-6571	462	9	.	.	PUNCT
ejpam-6571	463	1	on	on	ADP
ejpam-6571	463	2	weakly	weakly	ADJ
ejpam-6571	463	3	(	(	PUNCT
ejpam-6571	463	4	τ1	τ1	NOUN
ejpam-6571	463	5	,	,	PUNCT
ejpam-6571	463	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6571	463	7	functions	function	NOUN
ejpam-6571	463	8	.	.	PUNCT
ejpam-6571	464	1	european	european	ADJ
ejpam-6571	464	2	journal	journal	PROPN
ejpam-6571	464	3	of	of	ADP
ejpam-6571	464	4	pure	pure	ADJ
ejpam-6571	464	5	and	and	CCONJ
ejpam-6571	464	6	applied	applied	ADJ
ejpam-6571	464	7	mathematics	mathematic	NOUN
ejpam-6571	464	8	,	,	PUNCT
ejpam-6571	464	9	17(1):416–425	17(1):416–425	NUM
ejpam-6571	464	10	,	,	PUNCT
ejpam-6571	464	11	2024	2024	NUM
ejpam-6571	464	12	.	.	PUNCT
ejpam-6571	465	1	[	[	X
ejpam-6571	465	2	29	29	NUM
ejpam-6571	465	3	]	]	PUNCT
ejpam-6571	465	4	k.	k.	PROPN
ejpam-6571	465	5	kuratowski	kuratowski	PROPN
ejpam-6571	465	6	.	.	PUNCT
ejpam-6571	466	1	topology	topology	PROPN
ejpam-6571	466	2	,	,	PUNCT
ejpam-6571	466	3	vol	vol	NOUN
ejpam-6571	466	4	.	.	PUNCT
ejpam-6571	466	5	i.	i.	PROPN
ejpam-6571	466	6	academic	academic	PROPN
ejpam-6571	466	7	press	press	PROPN
ejpam-6571	466	8	,	,	PUNCT
ejpam-6571	466	9	new	new	PROPN
ejpam-6571	466	10	york	york	PROPN
ejpam-6571	466	11	,	,	PUNCT
ejpam-6571	466	12	1966	1966	NUM
ejpam-6571	466	13	.	.	PUNCT
ejpam-6571	467	1	[	[	X
ejpam-6571	467	2	30	30	NUM
ejpam-6571	467	3	]	]	X
ejpam-6571	467	4	e.	e.	PROPN
ejpam-6571	467	5	ekici	ekici	PROPN
ejpam-6571	467	6	and	and	CCONJ
ejpam-6571	467	7	t.	t.	PROPN
ejpam-6571	467	8	noiri	noiri	PROPN
ejpam-6571	467	9	.	.	PUNCT
ejpam-6571	468	1	⋆-extremally	⋆-extremally	ADV
ejpam-6571	468	2	disconnected	disconnect	VERB
ejpam-6571	468	3	ideal	ideal	ADJ
ejpam-6571	468	4	topological	topological	ADJ
ejpam-6571	468	5	spaces	space	NOUN
ejpam-6571	468	6	.	.	PUNCT
ejpam-6571	469	1	acta	acta	PROPN
ejpam-6571	469	2	mathematica	mathematica	PROPN
ejpam-6571	469	3	hungarica	hungarica	PROPN
ejpam-6571	469	4	,	,	PUNCT
ejpam-6571	469	5	122:81–90	122:81–90	NUM
ejpam-6571	469	6	,	,	PUNCT
ejpam-6571	469	7	2009	2009	NUM
ejpam-6571	469	8	.	.	PUNCT