id	sid	tid	token	lemma	pos
ejpam-5191	1	1	european	european	PROPN
ejpam-5191	1	2	journal	journal	PROPN
ejpam-5191	1	3	of	of	ADP
ejpam-5191	1	4	pure	pure	ADJ
ejpam-5191	1	5	and	and	CCONJ
ejpam-5191	1	6	applied	apply	VERB
ejpam-5191	1	7	mathematics	mathematic	NOUN
ejpam-5191	1	8	vol	vol	NOUN
ejpam-5191	1	9	.	.	PROPN
ejpam-5191	2	1	17	17	NUM
ejpam-5191	2	2	,	,	PUNCT
ejpam-5191	2	3	no	no	INTJ
ejpam-5191	2	4	.	.	NOUN
ejpam-5191	2	5	3	3	NUM
ejpam-5191	2	6	,	,	PUNCT
ejpam-5191	2	7	2024	2024	NUM
ejpam-5191	2	8	,	,	PUNCT
ejpam-5191	2	9	1553	1553	NUM
ejpam-5191	2	10	-	-	SYM
ejpam-5191	2	11	1564	1564	NUM
ejpam-5191	2	12	issn	issn	PROPN
ejpam-5191	2	13	1307	1307	NUM
ejpam-5191	2	14	-	-	SYM
ejpam-5191	2	15	5543	5543	NUM
ejpam-5191	2	16	–	–	PUNCT
ejpam-5191	3	1	ejpam.com	ejpam.com	X
ejpam-5191	3	2	published	publish	VERB
ejpam-5191	3	3	by	by	ADP
ejpam-5191	3	4	new	new	PROPN
ejpam-5191	3	5	york	york	PROPN
ejpam-5191	3	6	business	business	PROPN
ejpam-5191	3	7	global	global	ADJ
ejpam-5191	3	8	weakly	weakly	ADJ
ejpam-5191	3	9	quasi	quasi	NOUN
ejpam-5191	3	10	(	(	PUNCT
ejpam-5191	3	11	τ1	τ1	PROPN
ejpam-5191	3	12	,	,	PUNCT
ejpam-5191	3	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	3	14	multifunctions	multifunction	NOUN
ejpam-5191	3	15	prapart	prapart	VERB
ejpam-5191	3	16	pue	pue	PROPN
ejpam-5191	3	17	-	-	PUNCT
ejpam-5191	3	18	on1	on1	PROPN
ejpam-5191	3	19	,	,	PUNCT
ejpam-5191	3	20	supannee	supannee	PROPN
ejpam-5191	3	21	sompong2	sompong2	PROPN
ejpam-5191	3	22	,	,	PUNCT
ejpam-5191	3	23	chawalit	chawalit	VERB
ejpam-5191	3	24	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5191	3	25	1	1	NUM
ejpam-5191	3	26	mathematics	mathematic	NOUN
ejpam-5191	3	27	and	and	CCONJ
ejpam-5191	3	28	applied	apply	VERB
ejpam-5191	3	29	mathematics	mathematics	PROPN
ejpam-5191	3	30	research	research	NOUN
ejpam-5191	3	31	unit	unit	NOUN
ejpam-5191	3	32	,	,	PUNCT
ejpam-5191	3	33	department	department	NOUN
ejpam-5191	3	34	of	of	ADP
ejpam-5191	3	35	mathematics	mathematic	NOUN
ejpam-5191	3	36	,	,	PUNCT
ejpam-5191	3	37	faculty	faculty	NOUN
ejpam-5191	3	38	of	of	ADP
ejpam-5191	3	39	science	science	NOUN
ejpam-5191	3	40	,	,	PUNCT
ejpam-5191	3	41	mahasarakham	mahasarakham	PROPN
ejpam-5191	3	42	university	university	PROPN
ejpam-5191	3	43	,	,	PUNCT
ejpam-5191	3	44	maha	maha	PROPN
ejpam-5191	3	45	sarakham	sarakham	PROPN
ejpam-5191	3	46	,	,	PUNCT
ejpam-5191	3	47	44150	44150	NUM
ejpam-5191	3	48	,	,	PUNCT
ejpam-5191	3	49	thailand	thailand	PROPN
ejpam-5191	3	50	2	2	NUM
ejpam-5191	3	51	department	department	NOUN
ejpam-5191	3	52	of	of	ADP
ejpam-5191	3	53	mathematics	mathematic	NOUN
ejpam-5191	3	54	and	and	CCONJ
ejpam-5191	3	55	statistics	statistic	NOUN
ejpam-5191	3	56	,	,	PUNCT
ejpam-5191	3	57	faculty	faculty	NOUN
ejpam-5191	3	58	of	of	ADP
ejpam-5191	3	59	science	science	NOUN
ejpam-5191	3	60	and	and	CCONJ
ejpam-5191	3	61	technology	technology	NOUN
ejpam-5191	3	62	,	,	PUNCT
ejpam-5191	3	63	sakon	sakon	PROPN
ejpam-5191	3	64	nakhon	nakhon	PROPN
ejpam-5191	3	65	rajbhat	rajbhat	PROPN
ejpam-5191	3	66	university	university	PROPN
ejpam-5191	3	67	,	,	PUNCT
ejpam-5191	3	68	sakon	sakon	PROPN
ejpam-5191	3	69	nakhon	nakhon	PROPN
ejpam-5191	3	70	,	,	PUNCT
ejpam-5191	3	71	47000	47000	NUM
ejpam-5191	3	72	,	,	PUNCT
ejpam-5191	3	73	thailand	thailand	PROPN
ejpam-5191	3	74	abstract	abstract	NOUN
ejpam-5191	3	75	.	.	PUNCT
ejpam-5191	4	1	our	our	PRON
ejpam-5191	4	2	main	main	ADJ
ejpam-5191	4	3	purpose	purpose	NOUN
ejpam-5191	4	4	is	be	AUX
ejpam-5191	4	5	to	to	PART
ejpam-5191	4	6	introduce	introduce	VERB
ejpam-5191	4	7	the	the	DET
ejpam-5191	4	8	notion	notion	NOUN
ejpam-5191	4	9	of	of	ADP
ejpam-5191	4	10	weakly	weakly	ADJ
ejpam-5191	4	11	quasi	quasi	NOUN
ejpam-5191	4	12	(	(	PUNCT
ejpam-5191	4	13	τ1	τ1	PROPN
ejpam-5191	4	14	,	,	PUNCT
ejpam-5191	4	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	4	16	multifunctions	multifunction	NOUN
ejpam-5191	4	17	.	.	PUNCT
ejpam-5191	5	1	furthermore	furthermore	ADV
ejpam-5191	5	2	,	,	PUNCT
ejpam-5191	5	3	several	several	ADJ
ejpam-5191	5	4	characterizations	characterization	NOUN
ejpam-5191	5	5	of	of	ADP
ejpam-5191	5	6	weakly	weakly	ADJ
ejpam-5191	5	7	quasi	quasi	NOUN
ejpam-5191	5	8	(	(	PUNCT
ejpam-5191	5	9	τ1	τ1	PROPN
ejpam-5191	5	10	,	,	PUNCT
ejpam-5191	5	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	5	12	multifunctions	multifunction	NOUN
ejpam-5191	5	13	are	be	AUX
ejpam-5191	5	14	established	establish	VERB
ejpam-5191	5	15	.	.	PUNCT
ejpam-5191	6	1	2020	2020	NUM
ejpam-5191	6	2	mathematics	mathematics	PROPN
ejpam-5191	6	3	subject	subject	NOUN
ejpam-5191	6	4	classifications	classification	NOUN
ejpam-5191	6	5	:	:	PUNCT
ejpam-5191	6	6	54c08	54c08	NUM
ejpam-5191	6	7	,	,	PUNCT
ejpam-5191	6	8	54c60	54c60	NUM
ejpam-5191	6	9	,	,	PUNCT
ejpam-5191	6	10	54e55	54e55	NUM
ejpam-5191	6	11	key	key	ADJ
ejpam-5191	6	12	words	word	NOUN
ejpam-5191	6	13	and	and	CCONJ
ejpam-5191	6	14	phrases	phrase	NOUN
ejpam-5191	6	15	:	:	PUNCT
ejpam-5191	6	16	τ1τ2	τ1τ2	ADJ
ejpam-5191	6	17	-	-	ADJ
ejpam-5191	6	18	open	open	ADJ
ejpam-5191	6	19	set	set	NOUN
ejpam-5191	6	20	,	,	PUNCT
ejpam-5191	6	21	weakly	weakly	ADJ
ejpam-5191	6	22	quasi	quasi	NOUN
ejpam-5191	6	23	(	(	PUNCT
ejpam-5191	6	24	τ1	τ1	PROPN
ejpam-5191	6	25	,	,	PUNCT
ejpam-5191	6	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	6	27	multifunction	multifunction	NOUN
ejpam-5191	6	28	1	1	NUM
ejpam-5191	6	29	.	.	PUNCT
ejpam-5191	6	30	introduction	introduction	NOUN
ejpam-5191	6	31	the	the	DET
ejpam-5191	6	32	concept	concept	NOUN
ejpam-5191	6	33	of	of	ADP
ejpam-5191	6	34	quasi	quasi	ADJ
ejpam-5191	6	35	continuous	continuous	ADJ
ejpam-5191	6	36	functions	function	NOUN
ejpam-5191	6	37	was	be	AUX
ejpam-5191	6	38	introduced	introduce	VERB
ejpam-5191	6	39	by	by	ADP
ejpam-5191	6	40	marcus	marcus	PROPN
ejpam-5191	7	1	[	[	X
ejpam-5191	7	2	28	28	NUM
ejpam-5191	7	3	]	]	PUNCT
ejpam-5191	7	4	.	.	PUNCT
ejpam-5191	8	1	popa	popa	NOUN
ejpam-5191	8	2	[	[	X
ejpam-5191	8	3	33	33	NUM
ejpam-5191	8	4	]	]	PUNCT
ejpam-5191	8	5	introduced	introduce	VERB
ejpam-5191	8	6	and	and	CCONJ
ejpam-5191	8	7	investigated	investigate	VERB
ejpam-5191	8	8	the	the	DET
ejpam-5191	8	9	notion	notion	NOUN
ejpam-5191	8	10	of	of	ADP
ejpam-5191	8	11	almost	almost	ADV
ejpam-5191	8	12	quasi	quasi	ADJ
ejpam-5191	8	13	continuous	continuous	ADJ
ejpam-5191	8	14	functions	function	NOUN
ejpam-5191	8	15	.	.	PUNCT
ejpam-5191	9	1	neubrunnovaá	neubrunnovaá	PUNCT
ejpam-5191	10	1	[	[	X
ejpam-5191	10	2	29	29	NUM
ejpam-5191	10	3	]	]	PUNCT
ejpam-5191	10	4	showed	show	VERB
ejpam-5191	10	5	that	that	SCONJ
ejpam-5191	10	6	quasi	quasi	NOUN
ejpam-5191	10	7	continuity	continuity	NOUN
ejpam-5191	10	8	is	be	AUX
ejpam-5191	10	9	equivalent	equivalent	ADJ
ejpam-5191	10	10	to	to	ADP
ejpam-5191	10	11	semi	semi	ADJ
ejpam-5191	10	12	-	-	NOUN
ejpam-5191	10	13	continuity	continuity	NOUN
ejpam-5191	10	14	due	due	ADP
ejpam-5191	10	15	to	to	ADP
ejpam-5191	10	16	levine	levine	PROPN
ejpam-5191	10	17	[	[	X
ejpam-5191	10	18	27	27	NUM
ejpam-5191	10	19	]	]	PUNCT
ejpam-5191	10	20	.	.	PUNCT
ejpam-5191	11	1	popa	popa	NOUN
ejpam-5191	11	2	and	and	CCONJ
ejpam-5191	11	3	stan	stan	PROPN
ejpam-5191	12	1	[	[	X
ejpam-5191	12	2	36	36	NUM
ejpam-5191	12	3	]	]	PUNCT
ejpam-5191	12	4	introduced	introduce	VERB
ejpam-5191	12	5	and	and	CCONJ
ejpam-5191	12	6	studied	study	VERB
ejpam-5191	12	7	the	the	DET
ejpam-5191	12	8	notion	notion	NOUN
ejpam-5191	12	9	of	of	ADP
ejpam-5191	12	10	weakly	weakly	ADJ
ejpam-5191	12	11	quasi	quasi	ADJ
ejpam-5191	12	12	continuous	continuous	ADJ
ejpam-5191	12	13	functions	function	NOUN
ejpam-5191	12	14	.	.	PUNCT
ejpam-5191	13	1	weak	weak	ADJ
ejpam-5191	13	2	quasi	quasi	NOUN
ejpam-5191	13	3	continuity	continuity	NOUN
ejpam-5191	13	4	is	be	AUX
ejpam-5191	13	5	implied	imply	VERB
ejpam-5191	13	6	by	by	ADP
ejpam-5191	13	7	quasi	quasi	NOUN
ejpam-5191	13	8	continuity	continuity	NOUN
ejpam-5191	13	9	and	and	CCONJ
ejpam-5191	13	10	weak	weak	ADJ
ejpam-5191	13	11	continuity	continuity	NOUN
ejpam-5191	13	12	[	[	X
ejpam-5191	13	13	26	26	NUM
ejpam-5191	13	14	]	]	PUNCT
ejpam-5191	13	15	which	which	PRON
ejpam-5191	13	16	are	be	AUX
ejpam-5191	13	17	independent	independent	ADJ
ejpam-5191	13	18	of	of	ADP
ejpam-5191	13	19	each	each	DET
ejpam-5191	13	20	other	other	ADJ
ejpam-5191	13	21	.	.	PUNCT
ejpam-5191	14	1	it	it	PRON
ejpam-5191	14	2	is	be	AUX
ejpam-5191	14	3	shown	show	VERB
ejpam-5191	14	4	in	in	ADP
ejpam-5191	14	5	[	[	X
ejpam-5191	14	6	30	30	NUM
ejpam-5191	14	7	]	]	PUNCT
ejpam-5191	14	8	that	that	SCONJ
ejpam-5191	14	9	weak	weak	ADJ
ejpam-5191	14	10	quasi	quasi	NOUN
ejpam-5191	14	11	continuity	continuity	NOUN
ejpam-5191	14	12	is	be	AUX
ejpam-5191	14	13	equivalent	equivalent	ADJ
ejpam-5191	14	14	to	to	AUX
ejpam-5191	14	15	weak	weak	ADJ
ejpam-5191	14	16	semi	semi	ADJ
ejpam-5191	14	17	-	-	NOUN
ejpam-5191	14	18	continuity	continuity	NOUN
ejpam-5191	14	19	due	due	ADP
ejpam-5191	14	20	to	to	ADP
ejpam-5191	14	21	arya	arya	PROPN
ejpam-5191	14	22	and	and	CCONJ
ejpam-5191	14	23	bhamini	bhamini	PROPN
ejpam-5191	15	1	[	[	X
ejpam-5191	15	2	1	1	NUM
ejpam-5191	15	3	]	]	PUNCT
ejpam-5191	15	4	and	and	CCONJ
ejpam-5191	15	5	kar	kar	NOUN
ejpam-5191	15	6	and	and	CCONJ
ejpam-5191	15	7	bhattacharyya	bhattacharyya	ADJ
ejpam-5191	16	1	[	[	X
ejpam-5191	16	2	24	24	NUM
ejpam-5191	16	3	]	]	PUNCT
ejpam-5191	16	4	.	.	PUNCT
ejpam-5191	17	1	duangphui	duangphui	NOUN
ejpam-5191	17	2	et	et	PROPN
ejpam-5191	17	3	al	al	PROPN
ejpam-5191	17	4	.	.	PUNCT
ejpam-5191	18	1	[	[	X
ejpam-5191	18	2	23	23	NUM
ejpam-5191	18	3	]	]	PUNCT
ejpam-5191	18	4	introduced	introduce	VERB
ejpam-5191	18	5	and	and	CCONJ
ejpam-5191	18	6	investigated	investigate	VERB
ejpam-5191	18	7	the	the	DET
ejpam-5191	18	8	notion	notion	NOUN
ejpam-5191	18	9	of	of	ADP
ejpam-5191	18	10	weakly	weakly	ADJ
ejpam-5191	18	11	(	(	PUNCT
ejpam-5191	18	12	µ	µ	NOUN
ejpam-5191	18	13	,	,	PUNCT
ejpam-5191	18	14	µ′)(m	µ′)(m	VERB
ejpam-5191	18	15	,	,	PUNCT
ejpam-5191	18	16	n)-continuous	n)-continuous	ADJ
ejpam-5191	18	17	functions	function	NOUN
ejpam-5191	18	18	.	.	PUNCT
ejpam-5191	19	1	moreover	moreover	ADV
ejpam-5191	19	2	,	,	PUNCT
ejpam-5191	19	3	some	some	DET
ejpam-5191	19	4	characterizations	characterization	NOUN
ejpam-5191	19	5	of	of	ADP
ejpam-5191	19	6	almost	almost	ADV
ejpam-5191	19	7	(	(	PUNCT
ejpam-5191	19	8	λ	λ	PROPN
ejpam-5191	19	9	,	,	PUNCT
ejpam-5191	19	10	p)-continuous	p)-continuous	ADJ
ejpam-5191	19	11	functions	function	NOUN
ejpam-5191	19	12	,	,	PUNCT
ejpam-5191	19	13	strongly	strongly	ADV
ejpam-5191	19	14	θ(λ	θ(λ	PROPN
ejpam-5191	19	15	,	,	PUNCT
ejpam-5191	19	16	p)-continuous	p)-continuous	ADJ
ejpam-5191	19	17	functions	function	NOUN
ejpam-5191	19	18	,	,	PUNCT
ejpam-5191	19	19	almost	almost	ADV
ejpam-5191	19	20	strongly	strongly	ADV
ejpam-5191	19	21	θ(λ	θ(λ	VERB
ejpam-5191	19	22	,	,	PUNCT
ejpam-5191	19	23	p)-continuous	p)-continuous	ADJ
ejpam-5191	19	24	functions	function	NOUN
ejpam-5191	19	25	,	,	PUNCT
ejpam-5191	19	26	θ(λ	θ(λ	PROPN
ejpam-5191	19	27	,	,	PUNCT
ejpam-5191	19	28	p)-continuous	p)-continuous	ADJ
ejpam-5191	19	29	functions	function	NOUN
ejpam-5191	19	30	,	,	PUNCT
ejpam-5191	19	31	weakly	weakly	ADJ
ejpam-5191	19	32	(	(	PUNCT
ejpam-5191	19	33	λ	λ	PROPN
ejpam-5191	19	34	,	,	PUNCT
ejpam-5191	19	35	b)-continuous	b)-continuous	ADJ
ejpam-5191	19	36	functions	function	NOUN
ejpam-5191	19	37	,	,	PUNCT
ejpam-5191	19	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5191	19	39	functions	function	NOUN
ejpam-5191	19	40	,	,	PUNCT
ejpam-5191	19	41	⋆-continuous	⋆-continuous	ADJ
ejpam-5191	19	42	functions	function	NOUN
ejpam-5191	19	43	,	,	PUNCT
ejpam-5191	19	44	θ	θ	PROPN
ejpam-5191	19	45	-	-	ADJ
ejpam-5191	19	46	i	i	NOUN
ejpam-5191	19	47	-continuous	-continuous	ADJ
ejpam-5191	19	48	functions	function	NOUN
ejpam-5191	19	49	,	,	PUNCT
ejpam-5191	19	50	almost	almost	ADV
ejpam-5191	19	51	(	(	PUNCT
ejpam-5191	19	52	g	g	NOUN
ejpam-5191	19	53	,	,	PUNCT
ejpam-5191	19	54	m)-continuous	m)-continuous	ADJ
ejpam-5191	19	55	functions	function	NOUN
ejpam-5191	19	56	,	,	PUNCT
ejpam-5191	19	57	(	(	PUNCT
ejpam-5191	19	58	λ	λ	NOUN
ejpam-5191	19	59	,	,	PUNCT
ejpam-5191	19	60	sp)-continuous	sp)-continuous	ADJ
ejpam-5191	19	61	functions	function	NOUN
ejpam-5191	19	62	,	,	PUNCT
ejpam-5191	19	63	δp(λ	δp(λ	NOUN
ejpam-5191	19	64	,	,	PUNCT
ejpam-5191	19	65	s)-continuous	s)-continuous	ADJ
ejpam-5191	19	66	functions	function	NOUN
ejpam-5191	19	67	,	,	PUNCT
ejpam-5191	19	68	(	(	PUNCT
ejpam-5191	19	69	λ	λ	NOUN
ejpam-5191	19	70	,	,	PUNCT
ejpam-5191	19	71	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5191	19	72	functions	function	NOUN
ejpam-5191	19	73	,	,	PUNCT
ejpam-5191	19	74	pairwise	pairwise	VERB
ejpam-5191	19	75	weakly	weakly	ADJ
ejpam-5191	19	76	m	m	VERB
ejpam-5191	19	77	-continuous	-continuous	ADJ
ejpam-5191	19	78	functions	function	NOUN
ejpam-5191	19	79	,	,	PUNCT
ejpam-5191	19	80	(	(	PUNCT
ejpam-5191	19	81	τ1	τ1	NOUN
ejpam-5191	19	82	,	,	PUNCT
ejpam-5191	19	83	τ2)continuous	τ2)continuous	ADJ
ejpam-5191	19	84	functions	function	NOUN
ejpam-5191	19	85	,	,	PUNCT
ejpam-5191	19	86	almost	almost	ADV
ejpam-5191	19	87	(	(	PUNCT
ejpam-5191	19	88	τ1	τ1	NOUN
ejpam-5191	19	89	,	,	PUNCT
ejpam-5191	19	90	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	19	91	functions	function	NOUN
ejpam-5191	19	92	and	and	CCONJ
ejpam-5191	19	93	weakly	weakly	ADJ
ejpam-5191	19	94	(	(	PUNCT
ejpam-5191	19	95	τ1	τ1	NOUN
ejpam-5191	19	96	,	,	PUNCT
ejpam-5191	19	97	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	19	98	functions	function	NOUN
ejpam-5191	19	99	were	be	AUX
ejpam-5191	19	100	presented	present	VERB
ejpam-5191	19	101	in	in	ADP
ejpam-5191	19	102	[	[	X
ejpam-5191	19	103	38	38	NUM
ejpam-5191	19	104	]	]	PUNCT
ejpam-5191	19	105	,	,	PUNCT
ejpam-5191	19	106	[	[	X
ejpam-5191	19	107	40	40	NUM
ejpam-5191	19	108	]	]	PUNCT
ejpam-5191	19	109	,	,	PUNCT
ejpam-5191	19	110	[	[	X
ejpam-5191	19	111	12	12	NUM
ejpam-5191	19	112	]	]	PUNCT
ejpam-5191	19	113	,	,	PUNCT
ejpam-5191	19	114	[	[	X
ejpam-5191	19	115	37	37	NUM
ejpam-5191	19	116	]	]	PUNCT
ejpam-5191	19	117	,	,	PUNCT
ejpam-5191	19	118	[	[	X
ejpam-5191	19	119	18	18	NUM
ejpam-5191	19	120	]	]	PUNCT
ejpam-5191	19	121	,	,	PUNCT
ejpam-5191	19	122	[	[	X
ejpam-5191	19	123	11	11	NUM
ejpam-5191	19	124	]	]	PUNCT
ejpam-5191	19	125	,	,	PUNCT
ejpam-5191	19	126	[	[	X
ejpam-5191	19	127	10	10	NUM
ejpam-5191	19	128	]	]	PUNCT
ejpam-5191	19	129	,	,	PUNCT
ejpam-5191	19	130	[	[	X
ejpam-5191	19	131	6	6	NUM
ejpam-5191	19	132	]	]	PUNCT
ejpam-5191	19	133	,	,	PUNCT
ejpam-5191	19	134	[	[	X
ejpam-5191	19	135	3	3	NUM
ejpam-5191	19	136	]	]	PUNCT
ejpam-5191	19	137	,	,	PUNCT
ejpam-5191	19	138	[	[	X
ejpam-5191	19	139	43	43	NUM
ejpam-5191	19	140	]	]	PUNCT
ejpam-5191	19	141	,	,	PUNCT
ejpam-5191	19	142	[	[	X
ejpam-5191	19	143	39	39	NUM
ejpam-5191	19	144	]	]	PUNCT
ejpam-5191	19	145	,	,	PUNCT
ejpam-5191	20	1	[	[	X
ejpam-5191	20	2	9	9	NUM
ejpam-5191	20	3	]	]	PUNCT
ejpam-5191	20	4	,	,	PUNCT
ejpam-5191	20	5	[	[	X
ejpam-5191	20	6	4	4	NUM
ejpam-5191	20	7	]	]	PUNCT
ejpam-5191	20	8	,	,	PUNCT
ejpam-5191	20	9	[	[	X
ejpam-5191	20	10	19	19	NUM
ejpam-5191	20	11	]	]	PUNCT
ejpam-5191	20	12	,	,	PUNCT
ejpam-5191	20	13	[	[	X
ejpam-5191	20	14	17	17	NUM
ejpam-5191	20	15	]	]	PUNCT
ejpam-5191	20	16	and	and	CCONJ
ejpam-5191	21	1	[	[	X
ejpam-5191	21	2	13	13	NUM
ejpam-5191	21	3	]	]	PUNCT
ejpam-5191	21	4	,	,	PUNCT
ejpam-5191	21	5	respectively	respectively	ADV
ejpam-5191	21	6	.	.	PUNCT
ejpam-5191	21	7	∗corresponding	∗corresponde	VERB
ejpam-5191	21	8	author	author	NOUN
ejpam-5191	21	9	.	.	PUNCT
ejpam-5191	22	1	doi	doi	NOUN
ejpam-5191	22	2	:	:	PUNCT
ejpam-5191	22	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5191	https://doi.org/10.29020/nybg.ejpam.v17i3.5191	NOUN
ejpam-5191	22	4	email	email	NOUN
ejpam-5191	22	5	addresses	address	VERB
ejpam-5191	22	6	:	:	PUNCT
ejpam-5191	22	7	prapart.p@msu.ac.th	prapart.p@msu.ac.th	PROPN
ejpam-5191	22	8	(	(	PUNCT
ejpam-5191	22	9	p.	p.	NOUN
ejpam-5191	22	10	pue	pue	NOUN
ejpam-5191	22	11	-	-	PUNCT
ejpam-5191	22	12	on	on	ADP
ejpam-5191	22	13	)	)	PUNCT
ejpam-5191	22	14	,	,	PUNCT
ejpam-5191	22	15	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-5191	22	16	(	(	PUNCT
ejpam-5191	22	17	s.	s.	PROPN
ejpam-5191	22	18	sompong	sompong	PROPN
ejpam-5191	22	19	)	)	PUNCT
ejpam-5191	22	20	,	,	PUNCT
ejpam-5191	22	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5191	22	22	(	(	PUNCT
ejpam-5191	22	23	c.	c.	PROPN
ejpam-5191	22	24	boonpok	boonpok	PROPN
ejpam-5191	22	25	)	)	PUNCT
ejpam-5191	22	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5191	22	27	1553	1553	NUM
ejpam-5191	23	1	©	©	ADP
ejpam-5191	23	2	2024	2024	NUM
ejpam-5191	23	3	ejpam	ejpam	NOUN
ejpam-5191	23	4	all	all	DET
ejpam-5191	23	5	rights	right	NOUN
ejpam-5191	23	6	reserved	reserve	VERB
ejpam-5191	23	7	.	.	PUNCT
ejpam-5191	24	1	p.	p.	NOUN
ejpam-5191	24	2	pue	pue	NOUN
ejpam-5191	24	3	-	-	PUNCT
ejpam-5191	24	4	on	on	ADP
ejpam-5191	24	5	,	,	PUNCT
ejpam-5191	24	6	s.	s.	PROPN
ejpam-5191	24	7	sompong	sompong	PROPN
ejpam-5191	24	8	,	,	PUNCT
ejpam-5191	24	9	c.	c.	PROPN
ejpam-5191	24	10	boonpok	boonpok	PROPN
ejpam-5191	24	11	/	/	SYM
ejpam-5191	24	12	eur	eur	PROPN
ejpam-5191	24	13	.	.	PUNCT
ejpam-5191	25	1	j.	j.	PROPN
ejpam-5191	25	2	pure	pure	PROPN
ejpam-5191	25	3	appl	appl	PROPN
ejpam-5191	25	4	.	.	PROPN
ejpam-5191	25	5	math	math	PROPN
ejpam-5191	25	6	,	,	PUNCT
ejpam-5191	25	7	17	17	NUM
ejpam-5191	25	8	(	(	PUNCT
ejpam-5191	25	9	3	3	NUM
ejpam-5191	25	10	)	)	PUNCT
ejpam-5191	25	11	(	(	PUNCT
ejpam-5191	25	12	2024	2024	NUM
ejpam-5191	25	13	)	)	PUNCT
ejpam-5191	25	14	,	,	PUNCT
ejpam-5191	25	15	1553	1553	NUM
ejpam-5191	25	16	-	-	SYM
ejpam-5191	25	17	1564	1564	NUM
ejpam-5191	25	18	1554	1554	NUM
ejpam-5191	25	19	the	the	DET
ejpam-5191	25	20	concept	concept	NOUN
ejpam-5191	25	21	of	of	ADP
ejpam-5191	25	22	almost	almost	ADV
ejpam-5191	25	23	quasi	quasi	ADJ
ejpam-5191	25	24	continuous	continuous	ADJ
ejpam-5191	25	25	multifunctions	multifunction	NOUN
ejpam-5191	25	26	was	be	AUX
ejpam-5191	25	27	introduced	introduce	VERB
ejpam-5191	25	28	by	by	ADP
ejpam-5191	25	29	popa	popa	NOUN
ejpam-5191	25	30	and	and	CCONJ
ejpam-5191	25	31	noiri	noiri	ADV
ejpam-5191	25	32	[	[	X
ejpam-5191	25	33	35	35	NUM
ejpam-5191	25	34	]	]	PUNCT
ejpam-5191	25	35	.	.	PUNCT
ejpam-5191	26	1	noiri	noiri	PROPN
ejpam-5191	26	2	and	and	CCONJ
ejpam-5191	26	3	popa	popa	NOUN
ejpam-5191	27	1	[	[	X
ejpam-5191	27	2	31	31	NUM
ejpam-5191	27	3	]	]	PUNCT
ejpam-5191	27	4	introduced	introduce	VERB
ejpam-5191	27	5	and	and	CCONJ
ejpam-5191	27	6	studied	study	VERB
ejpam-5191	27	7	the	the	DET
ejpam-5191	27	8	notion	notion	NOUN
ejpam-5191	27	9	of	of	ADP
ejpam-5191	27	10	weakly	weakly	ADJ
ejpam-5191	27	11	quasi	quasi	ADJ
ejpam-5191	27	12	continuous	continuous	ADJ
ejpam-5191	27	13	multifunctions	multifunction	NOUN
ejpam-5191	27	14	.	.	PUNCT
ejpam-5191	28	1	several	several	ADJ
ejpam-5191	28	2	characterizations	characterization	NOUN
ejpam-5191	28	3	of	of	ADP
ejpam-5191	28	4	weakly	weakly	ADJ
ejpam-5191	28	5	quasi	quasi	ADJ
ejpam-5191	28	6	continuous	continuous	ADJ
ejpam-5191	28	7	multifunctions	multifunction	NOUN
ejpam-5191	28	8	have	have	AUX
ejpam-5191	28	9	been	be	AUX
ejpam-5191	28	10	obtained	obtain	VERB
ejpam-5191	28	11	in	in	ADP
ejpam-5191	28	12	[	[	X
ejpam-5191	28	13	35	35	NUM
ejpam-5191	28	14	]	]	PUNCT
ejpam-5191	28	15	.	.	PUNCT
ejpam-5191	29	1	popa	popa	NOUN
ejpam-5191	29	2	and	and	CCONJ
ejpam-5191	29	3	noiri	noiri	ADV
ejpam-5191	30	1	[	[	X
ejpam-5191	30	2	34	34	NUM
ejpam-5191	30	3	]	]	PUNCT
ejpam-5191	30	4	introduced	introduce	VERB
ejpam-5191	30	5	and	and	CCONJ
ejpam-5191	30	6	investigated	investigate	VERB
ejpam-5191	30	7	the	the	DET
ejpam-5191	30	8	concepts	concept	NOUN
ejpam-5191	30	9	of	of	ADP
ejpam-5191	30	10	upper	upper	ADJ
ejpam-5191	30	11	and	and	CCONJ
ejpam-5191	30	12	lower	low	ADJ
ejpam-5191	30	13	θ	θ	ADJ
ejpam-5191	30	14	-	-	ADJ
ejpam-5191	30	15	quasi	quasi	ADJ
ejpam-5191	30	16	continuous	continuous	ADJ
ejpam-5191	30	17	multifunctions	multifunction	NOUN
ejpam-5191	30	18	.	.	PUNCT
ejpam-5191	31	1	in	in	ADP
ejpam-5191	31	2	particular	particular	ADJ
ejpam-5191	31	3	,	,	PUNCT
ejpam-5191	31	4	some	some	DET
ejpam-5191	31	5	characterizations	characterization	NOUN
ejpam-5191	31	6	of	of	ADP
ejpam-5191	31	7	upper	upper	ADJ
ejpam-5191	31	8	and	and	CCONJ
ejpam-5191	31	9	lower	low	ADJ
ejpam-5191	31	10	θ	θ	ADJ
ejpam-5191	31	11	-	-	ADJ
ejpam-5191	31	12	quasi	quasi	ADJ
ejpam-5191	31	13	continuous	continuous	ADJ
ejpam-5191	31	14	multifunctions	multifunction	NOUN
ejpam-5191	31	15	were	be	AUX
ejpam-5191	31	16	established	establish	VERB
ejpam-5191	31	17	in	in	ADP
ejpam-5191	31	18	[	[	X
ejpam-5191	31	19	32	32	NUM
ejpam-5191	31	20	]	]	PUNCT
ejpam-5191	31	21	.	.	PUNCT
ejpam-5191	32	1	in	in	ADP
ejpam-5191	32	2	[	[	X
ejpam-5191	32	3	8	8	NUM
ejpam-5191	32	4	]	]	PUNCT
ejpam-5191	32	5	,	,	PUNCT
ejpam-5191	32	6	the	the	DET
ejpam-5191	32	7	present	present	ADJ
ejpam-5191	32	8	author	author	NOUN
ejpam-5191	32	9	introduced	introduce	VERB
ejpam-5191	32	10	and	and	CCONJ
ejpam-5191	32	11	studied	study	VERB
ejpam-5191	32	12	the	the	DET
ejpam-5191	32	13	concepts	concept	NOUN
ejpam-5191	32	14	of	of	ADP
ejpam-5191	32	15	almost	almost	ADV
ejpam-5191	32	16	quasi	quasi	ADJ
ejpam-5191	32	17	⋆-continuous	⋆-continuous	ADJ
ejpam-5191	32	18	multifunctions	multifunction	NOUN
ejpam-5191	32	19	and	and	CCONJ
ejpam-5191	32	20	weakly	weakly	ADJ
ejpam-5191	32	21	quasi	quasi	ADJ
ejpam-5191	32	22	⋆-continuous	⋆-continuous	ADJ
ejpam-5191	32	23	multifunctions	multifunction	NOUN
ejpam-5191	32	24	.	.	PUNCT
ejpam-5191	33	1	laprom	laprom	ADP
ejpam-5191	33	2	et	et	PROPN
ejpam-5191	33	3	al	al	PROPN
ejpam-5191	33	4	.	.	PUNCT
ejpam-5191	34	1	[	[	X
ejpam-5191	34	2	25	25	NUM
ejpam-5191	34	3	]	]	PUNCT
ejpam-5191	34	4	introduced	introduce	VERB
ejpam-5191	34	5	and	and	CCONJ
ejpam-5191	34	6	investigated	investigate	VERB
ejpam-5191	34	7	the	the	DET
ejpam-5191	34	8	notion	notion	NOUN
ejpam-5191	34	9	of	of	ADP
ejpam-5191	34	10	almost	almost	ADV
ejpam-5191	34	11	β(τ1	β(τ1	NOUN
ejpam-5191	34	12	,	,	PUNCT
ejpam-5191	34	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	34	14	multifunctions	multifunction	NOUN
ejpam-5191	34	15	.	.	PUNCT
ejpam-5191	35	1	viriyapong	viriyapong	PROPN
ejpam-5191	35	2	and	and	CCONJ
ejpam-5191	35	3	boonpok	boonpok	VERB
ejpam-5191	36	1	[	[	X
ejpam-5191	36	2	42	42	NUM
ejpam-5191	36	3	]	]	PUNCT
ejpam-5191	36	4	introduced	introduce	VERB
ejpam-5191	36	5	and	and	CCONJ
ejpam-5191	36	6	studied	study	VERB
ejpam-5191	36	7	the	the	DET
ejpam-5191	36	8	concept	concept	NOUN
ejpam-5191	36	9	of	of	ADP
ejpam-5191	36	10	weakly	weakly	ADJ
ejpam-5191	36	11	(	(	PUNCT
ejpam-5191	36	12	τ1	τ1	NOUN
ejpam-5191	36	13	,	,	PUNCT
ejpam-5191	36	14	τ2)α	τ2)α	ADJ
ejpam-5191	36	15	-	-	PUNCT
ejpam-5191	36	16	continuous	continuous	ADJ
ejpam-5191	36	17	multifunctions	multifunction	NOUN
ejpam-5191	36	18	.	.	PUNCT
ejpam-5191	37	1	furthermore	furthermore	ADV
ejpam-5191	37	2	,	,	PUNCT
ejpam-5191	37	3	several	several	ADJ
ejpam-5191	37	4	characterizations	characterization	NOUN
ejpam-5191	37	5	of	of	ADP
ejpam-5191	37	6	weakly	weakly	ADJ
ejpam-5191	37	7	(	(	PUNCT
ejpam-5191	37	8	τ1	τ1	NOUN
ejpam-5191	37	9	,	,	PUNCT
ejpam-5191	37	10	τ2)δ	τ2)δ	ADJ
ejpam-5191	37	11	-	-	PUNCT
ejpam-5191	37	12	semicontinuous	semicontinuous	ADJ
ejpam-5191	37	13	multifunctions	multifunction	NOUN
ejpam-5191	37	14	,	,	PUNCT
ejpam-5191	37	15	almost	almost	ADV
ejpam-5191	37	16	weakly	weakly	ADJ
ejpam-5191	37	17	(	(	PUNCT
ejpam-5191	37	18	τ1	τ1	NOUN
ejpam-5191	37	19	,	,	PUNCT
ejpam-5191	37	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	37	21	multifunctions	multifunction	NOUN
ejpam-5191	37	22	,	,	PUNCT
ejpam-5191	37	23	almost	almost	ADV
ejpam-5191	37	24	weakly	weakly	ADJ
ejpam-5191	37	25	⋆-continuous	⋆-continuous	ADJ
ejpam-5191	37	26	multifunctions	multifunction	NOUN
ejpam-5191	37	27	,	,	PUNCT
ejpam-5191	37	28	weakly	weakly	ADJ
ejpam-5191	37	29	⋆-continuous	⋆-continuous	ADJ
ejpam-5191	37	30	multifunctions	multifunction	NOUN
ejpam-5191	37	31	,	,	PUNCT
ejpam-5191	37	32	weakly	weakly	ADJ
ejpam-5191	37	33	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5191	37	34	multifunctions	multifunction	NOUN
ejpam-5191	37	35	,	,	PUNCT
ejpam-5191	37	36	weakly	weakly	ADJ
ejpam-5191	37	37	ı⋆-continuous	ı⋆-continuous	ADJ
ejpam-5191	37	38	multifunctions	multifunction	NOUN
ejpam-5191	37	39	,	,	PUNCT
ejpam-5191	37	40	weakly	weakly	ADJ
ejpam-5191	37	41	quasi	quasi	NOUN
ejpam-5191	37	42	(	(	PUNCT
ejpam-5191	37	43	λ	λ	PROPN
ejpam-5191	37	44	,	,	PUNCT
ejpam-5191	37	45	sp)-continuous	sp)-continuous	ADJ
ejpam-5191	37	46	multifunctions	multifunction	NOUN
ejpam-5191	37	47	,	,	PUNCT
ejpam-5191	37	48	weakly	weakly	ADJ
ejpam-5191	37	49	(	(	PUNCT
ejpam-5191	37	50	λ	λ	NOUN
ejpam-5191	37	51	,	,	PUNCT
ejpam-5191	37	52	sp)-continuous	sp)-continuous	ADJ
ejpam-5191	37	53	multifunctions	multifunction	NOUN
ejpam-5191	37	54	and	and	CCONJ
ejpam-5191	37	55	weakly	weakly	ADJ
ejpam-5191	37	56	(	(	PUNCT
ejpam-5191	37	57	τ1	τ1	NOUN
ejpam-5191	37	58	,	,	PUNCT
ejpam-5191	37	59	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	37	60	multifunctions	multifunction	NOUN
ejpam-5191	37	61	were	be	AUX
ejpam-5191	37	62	investigated	investigate	VERB
ejpam-5191	37	63	in	in	ADP
ejpam-5191	37	64	[	[	X
ejpam-5191	37	65	7	7	NUM
ejpam-5191	37	66	]	]	PUNCT
ejpam-5191	37	67	,	,	PUNCT
ejpam-5191	37	68	[	[	X
ejpam-5191	37	69	21	21	NUM
ejpam-5191	37	70	]	]	PUNCT
ejpam-5191	37	71	,	,	PUNCT
ejpam-5191	37	72	[	[	X
ejpam-5191	37	73	20	20	NUM
ejpam-5191	37	74	]	]	PUNCT
ejpam-5191	37	75	,	,	PUNCT
ejpam-5191	37	76	[	[	X
ejpam-5191	37	77	5	5	NUM
ejpam-5191	37	78	]	]	PUNCT
ejpam-5191	37	79	,	,	PUNCT
ejpam-5191	37	80	[	[	X
ejpam-5191	37	81	15	15	NUM
ejpam-5191	37	82	]	]	PUNCT
ejpam-5191	37	83	,	,	PUNCT
ejpam-5191	37	84	[	[	X
ejpam-5191	37	85	14	14	NUM
ejpam-5191	37	86	]	]	PUNCT
ejpam-5191	37	87	,	,	PUNCT
ejpam-5191	37	88	[	[	X
ejpam-5191	37	89	44	44	NUM
ejpam-5191	37	90	]	]	PUNCT
ejpam-5191	37	91	,	,	PUNCT
ejpam-5191	37	92	[	[	X
ejpam-5191	37	93	16	16	NUM
ejpam-5191	37	94	]	]	PUNCT
ejpam-5191	37	95	and	and	CCONJ
ejpam-5191	37	96	[	[	X
ejpam-5191	37	97	41	41	NUM
ejpam-5191	37	98	]	]	PUNCT
ejpam-5191	37	99	,	,	PUNCT
ejpam-5191	37	100	respectively	respectively	ADV
ejpam-5191	37	101	.	.	PUNCT
ejpam-5191	38	1	in	in	ADP
ejpam-5191	38	2	this	this	DET
ejpam-5191	38	3	paper	paper	NOUN
ejpam-5191	38	4	,	,	PUNCT
ejpam-5191	38	5	we	we	PRON
ejpam-5191	38	6	introduce	introduce	VERB
ejpam-5191	38	7	the	the	DET
ejpam-5191	38	8	concept	concept	NOUN
ejpam-5191	38	9	of	of	ADP
ejpam-5191	38	10	weakly	weakly	ADJ
ejpam-5191	38	11	quasi	quasi	NOUN
ejpam-5191	38	12	(	(	PUNCT
ejpam-5191	38	13	τ1	τ1	PROPN
ejpam-5191	38	14	,	,	PUNCT
ejpam-5191	38	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	38	16	multifunctions	multifunction	NOUN
ejpam-5191	38	17	.	.	PUNCT
ejpam-5191	39	1	moreover	moreover	ADV
ejpam-5191	39	2	,	,	PUNCT
ejpam-5191	39	3	some	some	DET
ejpam-5191	39	4	characterizations	characterization	NOUN
ejpam-5191	39	5	of	of	ADP
ejpam-5191	39	6	weakly	weakly	ADJ
ejpam-5191	39	7	quasi	quasi	NOUN
ejpam-5191	39	8	(	(	PUNCT
ejpam-5191	39	9	τ1	τ1	PROPN
ejpam-5191	39	10	,	,	PUNCT
ejpam-5191	39	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	39	12	multifunctions	multifunction	NOUN
ejpam-5191	39	13	are	be	AUX
ejpam-5191	39	14	discussed	discuss	VERB
ejpam-5191	39	15	.	.	PUNCT
ejpam-5191	40	1	2	2	X
ejpam-5191	40	2	.	.	X
ejpam-5191	40	3	preliminaries	preliminary	NOUN
ejpam-5191	40	4	throughout	throughout	ADP
ejpam-5191	40	5	the	the	DET
ejpam-5191	40	6	present	present	ADJ
ejpam-5191	40	7	paper	paper	NOUN
ejpam-5191	40	8	,	,	PUNCT
ejpam-5191	40	9	spaces	space	NOUN
ejpam-5191	40	10	(	(	PUNCT
ejpam-5191	40	11	x	x	NOUN
ejpam-5191	40	12	,	,	PUNCT
ejpam-5191	40	13	τ1	τ1	NOUN
ejpam-5191	40	14	,	,	PUNCT
ejpam-5191	40	15	τ2	τ2	NOUN
ejpam-5191	40	16	)	)	PUNCT
ejpam-5191	40	17	and	and	CCONJ
ejpam-5191	40	18	(	(	PUNCT
ejpam-5191	40	19	y	y	PROPN
ejpam-5191	40	20	,	,	PUNCT
ejpam-5191	40	21	σ1	σ1	PROPN
ejpam-5191	40	22	,	,	PUNCT
ejpam-5191	40	23	σ2	σ2	NOUN
ejpam-5191	40	24	)	)	PUNCT
ejpam-5191	40	25	(	(	PUNCT
ejpam-5191	40	26	or	or	CCONJ
ejpam-5191	40	27	simply	simply	ADV
ejpam-5191	40	28	x	x	X
ejpam-5191	40	29	and	and	CCONJ
ejpam-5191	40	30	y	y	PROPN
ejpam-5191	40	31	)	)	PUNCT
ejpam-5191	40	32	always	always	ADV
ejpam-5191	40	33	mean	mean	VERB
ejpam-5191	40	34	bitopological	bitopological	ADJ
ejpam-5191	40	35	spaces	space	NOUN
ejpam-5191	40	36	on	on	ADP
ejpam-5191	40	37	which	which	PRON
ejpam-5191	40	38	no	no	DET
ejpam-5191	40	39	separation	separation	NOUN
ejpam-5191	40	40	axioms	axiom	NOUN
ejpam-5191	40	41	are	be	AUX
ejpam-5191	40	42	assumed	assume	VERB
ejpam-5191	40	43	unless	unless	SCONJ
ejpam-5191	40	44	explicitly	explicitly	ADV
ejpam-5191	40	45	stated	state	VERB
ejpam-5191	40	46	.	.	PUNCT
ejpam-5191	41	1	let	let	VERB
ejpam-5191	41	2	a	a	DET
ejpam-5191	41	3	be	be	AUX
ejpam-5191	41	4	a	a	DET
ejpam-5191	41	5	subset	subset	NOUN
ejpam-5191	41	6	of	of	ADP
ejpam-5191	41	7	a	a	DET
ejpam-5191	41	8	bitopological	bitopological	ADJ
ejpam-5191	41	9	space	space	NOUN
ejpam-5191	41	10	(	(	PUNCT
ejpam-5191	41	11	x	x	NOUN
ejpam-5191	41	12	,	,	PUNCT
ejpam-5191	41	13	τ1	τ1	NOUN
ejpam-5191	41	14	,	,	PUNCT
ejpam-5191	41	15	τ2	τ2	NOUN
ejpam-5191	41	16	)	)	PUNCT
ejpam-5191	41	17	.	.	PUNCT
ejpam-5191	42	1	the	the	DET
ejpam-5191	42	2	closure	closure	NOUN
ejpam-5191	42	3	of	of	ADP
ejpam-5191	42	4	a	a	PRON
ejpam-5191	42	5	and	and	CCONJ
ejpam-5191	42	6	the	the	DET
ejpam-5191	42	7	interior	interior	NOUN
ejpam-5191	42	8	of	of	ADP
ejpam-5191	42	9	a	a	PRON
ejpam-5191	42	10	with	with	ADP
ejpam-5191	42	11	respect	respect	NOUN
ejpam-5191	42	12	to	to	ADP
ejpam-5191	42	13	τi	τi	PROPN
ejpam-5191	42	14	are	be	AUX
ejpam-5191	42	15	denoted	denote	VERB
ejpam-5191	42	16	by	by	ADP
ejpam-5191	42	17	τi	τi	NOUN
ejpam-5191	42	18	-	-	PUNCT
ejpam-5191	42	19	cl(a	cl(a	NUM
ejpam-5191	42	20	)	)	PUNCT
ejpam-5191	42	21	and	and	CCONJ
ejpam-5191	42	22	τi	τi	NOUN
ejpam-5191	42	23	-	-	PUNCT
ejpam-5191	42	24	int(a	int(a	NOUN
ejpam-5191	42	25	)	)	PUNCT
ejpam-5191	42	26	,	,	PUNCT
ejpam-5191	42	27	respectively	respectively	ADV
ejpam-5191	42	28	,	,	PUNCT
ejpam-5191	42	29	for	for	ADP
ejpam-5191	42	30	i	i	PROPN
ejpam-5191	42	31	=	=	SYM
ejpam-5191	42	32	1	1	NUM
ejpam-5191	42	33	,	,	PUNCT
ejpam-5191	42	34	2	2	NUM
ejpam-5191	42	35	.	.	X
ejpam-5191	42	36	a	a	DET
ejpam-5191	42	37	subset	subset	NOUN
ejpam-5191	42	38	a	a	PRON
ejpam-5191	42	39	of	of	ADP
ejpam-5191	42	40	a	a	DET
ejpam-5191	42	41	bitopological	bitopological	ADJ
ejpam-5191	42	42	space	space	NOUN
ejpam-5191	42	43	(	(	PUNCT
ejpam-5191	42	44	x	x	NOUN
ejpam-5191	42	45	,	,	PUNCT
ejpam-5191	42	46	τ1	τ1	NOUN
ejpam-5191	42	47	,	,	PUNCT
ejpam-5191	42	48	τ2	τ2	NOUN
ejpam-5191	42	49	)	)	PUNCT
ejpam-5191	42	50	is	be	AUX
ejpam-5191	42	51	called	call	VERB
ejpam-5191	42	52	τ1τ2	τ1τ2	VERB
ejpam-5191	42	53	-	-	ADJ
ejpam-5191	42	54	closed	closed	ADJ
ejpam-5191	42	55	[	[	X
ejpam-5191	42	56	22	22	NUM
ejpam-5191	42	57	]	]	PUNCT
ejpam-5191	42	58	if	if	SCONJ
ejpam-5191	42	59	a	a	DET
ejpam-5191	42	60	=	=	NOUN
ejpam-5191	42	61	τ1	τ1	NOUN
ejpam-5191	42	62	-	-	PUNCT
ejpam-5191	42	63	cl(τ2	cl(τ2	NOUN
ejpam-5191	42	64	-	-	PUNCT
ejpam-5191	42	65	cl(a	cl(a	NUM
ejpam-5191	42	66	)	)	PUNCT
ejpam-5191	42	67	)	)	PUNCT
ejpam-5191	42	68	.	.	PUNCT
ejpam-5191	43	1	the	the	DET
ejpam-5191	43	2	complement	complement	NOUN
ejpam-5191	43	3	of	of	ADP
ejpam-5191	43	4	a	a	DET
ejpam-5191	43	5	τ1τ2	τ1τ2	ADJ
ejpam-5191	43	6	-	-	ADJ
ejpam-5191	43	7	closed	closed	ADJ
ejpam-5191	43	8	set	set	NOUN
ejpam-5191	43	9	is	be	AUX
ejpam-5191	43	10	called	call	VERB
ejpam-5191	43	11	τ1τ2	τ1τ2	NOUN
ejpam-5191	43	12	-	-	ADJ
ejpam-5191	43	13	open	open	ADJ
ejpam-5191	43	14	.	.	PUNCT
ejpam-5191	44	1	let	let	VERB
ejpam-5191	44	2	a	a	DET
ejpam-5191	44	3	be	be	AUX
ejpam-5191	44	4	a	a	DET
ejpam-5191	44	5	subset	subset	NOUN
ejpam-5191	44	6	of	of	ADP
ejpam-5191	44	7	a	a	DET
ejpam-5191	44	8	bitopological	bitopological	ADJ
ejpam-5191	44	9	space	space	NOUN
ejpam-5191	44	10	(	(	PUNCT
ejpam-5191	44	11	x	x	NOUN
ejpam-5191	44	12	,	,	PUNCT
ejpam-5191	44	13	τ1	τ1	NOUN
ejpam-5191	44	14	,	,	PUNCT
ejpam-5191	44	15	τ2	τ2	NOUN
ejpam-5191	44	16	)	)	PUNCT
ejpam-5191	44	17	.	.	PUNCT
ejpam-5191	45	1	the	the	DET
ejpam-5191	45	2	intersection	intersection	NOUN
ejpam-5191	45	3	of	of	ADP
ejpam-5191	45	4	all	all	DET
ejpam-5191	45	5	τ1τ2	τ1τ2	ADJ
ejpam-5191	45	6	-	-	ADJ
ejpam-5191	45	7	closed	closed	ADJ
ejpam-5191	45	8	sets	set	NOUN
ejpam-5191	45	9	of	of	ADP
ejpam-5191	45	10	x	x	PUNCT
ejpam-5191	45	11	containing	contain	VERB
ejpam-5191	45	12	a	a	PRON
ejpam-5191	45	13	is	be	AUX
ejpam-5191	45	14	called	call	VERB
ejpam-5191	45	15	the	the	DET
ejpam-5191	45	16	τ1τ2	τ1τ2	NOUN
ejpam-5191	45	17	-	-	NOUN
ejpam-5191	45	18	closure	closure	NOUN
ejpam-5191	45	19	[	[	X
ejpam-5191	45	20	22	22	NUM
ejpam-5191	45	21	]	]	PUNCT
ejpam-5191	45	22	of	of	ADP
ejpam-5191	45	23	a	a	PRON
ejpam-5191	45	24	and	and	CCONJ
ejpam-5191	45	25	is	be	AUX
ejpam-5191	45	26	denoted	denote	VERB
ejpam-5191	45	27	by	by	ADP
ejpam-5191	45	28	τ1τ2	τ1τ2	NOUN
ejpam-5191	45	29	-	-	NUM
ejpam-5191	45	30	cl(a	cl(a	NUM
ejpam-5191	45	31	)	)	PUNCT
ejpam-5191	45	32	.	.	PUNCT
ejpam-5191	46	1	the	the	DET
ejpam-5191	46	2	union	union	NOUN
ejpam-5191	46	3	of	of	ADP
ejpam-5191	46	4	all	all	DET
ejpam-5191	46	5	τ1τ2	τ1τ2	ADJ
ejpam-5191	46	6	-	-	ADJ
ejpam-5191	46	7	open	open	ADJ
ejpam-5191	46	8	sets	set	NOUN
ejpam-5191	46	9	of	of	ADP
ejpam-5191	46	10	x	x	PUNCT
ejpam-5191	46	11	contained	contain	VERB
ejpam-5191	46	12	in	in	ADP
ejpam-5191	46	13	a	a	PRON
ejpam-5191	46	14	is	be	AUX
ejpam-5191	46	15	called	call	VERB
ejpam-5191	46	16	the	the	DET
ejpam-5191	46	17	τ1τ2	τ1τ2	NOUN
ejpam-5191	46	18	-	-	ADJ
ejpam-5191	46	19	interior	interior	ADJ
ejpam-5191	46	20	[	[	X
ejpam-5191	46	21	22	22	NUM
ejpam-5191	46	22	]	]	PUNCT
ejpam-5191	46	23	of	of	ADP
ejpam-5191	46	24	a	a	PRON
ejpam-5191	46	25	and	and	CCONJ
ejpam-5191	46	26	is	be	AUX
ejpam-5191	46	27	denoted	denote	VERB
ejpam-5191	46	28	by	by	ADP
ejpam-5191	46	29	τ1τ2	τ1τ2	NOUN
ejpam-5191	46	30	-	-	ADJ
ejpam-5191	46	31	int(a	int(a	NOUN
ejpam-5191	46	32	)	)	PUNCT
ejpam-5191	46	33	.	.	PUNCT
ejpam-5191	47	1	lemma	lemma	PROPN
ejpam-5191	47	2	1	1	NUM
ejpam-5191	47	3	.	.	PUNCT
ejpam-5191	48	1	[	[	X
ejpam-5191	48	2	22	22	NUM
ejpam-5191	48	3	]	]	PUNCT
ejpam-5191	48	4	let	let	VERB
ejpam-5191	48	5	a	a	PRON
ejpam-5191	48	6	and	and	CCONJ
ejpam-5191	48	7	b	b	NOUN
ejpam-5191	48	8	be	be	AUX
ejpam-5191	48	9	subsets	subset	NOUN
ejpam-5191	48	10	of	of	ADP
ejpam-5191	48	11	a	a	DET
ejpam-5191	48	12	bitopological	bitopological	ADJ
ejpam-5191	48	13	space	space	NOUN
ejpam-5191	48	14	(	(	PUNCT
ejpam-5191	48	15	x	x	NOUN
ejpam-5191	48	16	,	,	PUNCT
ejpam-5191	48	17	τ1	τ1	NOUN
ejpam-5191	48	18	,	,	PUNCT
ejpam-5191	48	19	τ2	τ2	NOUN
ejpam-5191	48	20	)	)	PUNCT
ejpam-5191	48	21	.	.	PUNCT
ejpam-5191	49	1	for	for	ADP
ejpam-5191	49	2	the	the	DET
ejpam-5191	49	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5191	49	4	,	,	PUNCT
ejpam-5191	49	5	the	the	DET
ejpam-5191	49	6	following	follow	VERB
ejpam-5191	49	7	properties	property	NOUN
ejpam-5191	49	8	hold	hold	VERB
ejpam-5191	49	9	:	:	PUNCT
ejpam-5191	49	10	(	(	PUNCT
ejpam-5191	49	11	1	1	X
ejpam-5191	49	12	)	)	PUNCT
ejpam-5191	49	13	a	a	DET
ejpam-5191	49	14	⊆	⊆	NUM
ejpam-5191	49	15	τ1τ2	τ1τ2	NOUN
ejpam-5191	49	16	-	-	NUM
ejpam-5191	49	17	cl(a	cl(a	NUM
ejpam-5191	49	18	)	)	PUNCT
ejpam-5191	49	19	and	and	CCONJ
ejpam-5191	49	20	τ1τ2	τ1τ2	NOUN
ejpam-5191	49	21	-	-	NUM
ejpam-5191	49	22	cl(τ1τ2cl(a	cl(τ1τ2cl(a	NUM
ejpam-5191	49	23	)	)	PUNCT
ejpam-5191	49	24	)	)	PUNCT
ejpam-5191	50	1	=	=	PUNCT
ejpam-5191	50	2	τ1τ2	τ1τ2	NOUN
ejpam-5191	50	3	-	-	NUM
ejpam-5191	50	4	cl(a	cl(a	NUM
ejpam-5191	50	5	)	)	PUNCT
ejpam-5191	50	6	.	.	PUNCT
ejpam-5191	51	1	(	(	PUNCT
ejpam-5191	51	2	2	2	X
ejpam-5191	51	3	)	)	PUNCT
ejpam-5191	51	4	if	if	SCONJ
ejpam-5191	51	5	a	a	DET
ejpam-5191	51	6	⊆	⊆	NUM
ejpam-5191	51	7	b	b	NOUN
ejpam-5191	51	8	,	,	PUNCT
ejpam-5191	51	9	then	then	ADV
ejpam-5191	51	10	τ1τ2cl(a	τ1τ2cl(a	NUM
ejpam-5191	51	11	)	)	PUNCT
ejpam-5191	51	12	⊆	⊆	NUM
ejpam-5191	51	13	τ1τ2	τ1τ2	NOUN
ejpam-5191	51	14	-	-	NOUN
ejpam-5191	51	15	cl(b	cl(b	NOUN
ejpam-5191	51	16	)	)	PUNCT
ejpam-5191	51	17	.	.	PUNCT
ejpam-5191	52	1	(	(	PUNCT
ejpam-5191	52	2	3	3	X
ejpam-5191	52	3	)	)	PUNCT
ejpam-5191	52	4	τ1τ2	τ1τ2	NOUN
ejpam-5191	52	5	-	-	NUM
ejpam-5191	52	6	cl(a	cl(a	NUM
ejpam-5191	52	7	)	)	PUNCT
ejpam-5191	52	8	is	be	AUX
ejpam-5191	52	9	τ1τ2	τ1τ2	NOUN
ejpam-5191	52	10	-	-	ADJ
ejpam-5191	52	11	closed	closed	ADJ
ejpam-5191	52	12	.	.	PUNCT
ejpam-5191	53	1	(	(	PUNCT
ejpam-5191	53	2	4	4	X
ejpam-5191	53	3	)	)	PUNCT
ejpam-5191	53	4	a	a	PRON
ejpam-5191	53	5	is	be	AUX
ejpam-5191	53	6	τ1τ2	τ1τ2	NOUN
ejpam-5191	53	7	-	-	ADJ
ejpam-5191	53	8	closed	closed	ADJ
ejpam-5191	53	9	if	if	SCONJ
ejpam-5191	53	10	and	and	CCONJ
ejpam-5191	53	11	only	only	ADV
ejpam-5191	53	12	if	if	SCONJ
ejpam-5191	53	13	a	a	DET
ejpam-5191	53	14	=	=	PUNCT
ejpam-5191	53	15	τ1τ2	τ1τ2	NOUN
ejpam-5191	53	16	-	-	NUM
ejpam-5191	53	17	cl(a	cl(a	NUM
ejpam-5191	53	18	)	)	PUNCT
ejpam-5191	53	19	.	.	PUNCT
ejpam-5191	54	1	(	(	PUNCT
ejpam-5191	54	2	5	5	X
ejpam-5191	54	3	)	)	PUNCT
ejpam-5191	54	4	τ1τ2	τ1τ2	NOUN
ejpam-5191	54	5	-	-	NOUN
ejpam-5191	54	6	cl(x	cl(x	X
ejpam-5191	54	7	−a	−a	NOUN
ejpam-5191	54	8	)	)	PUNCT
ejpam-5191	55	1	=	=	PUNCT
ejpam-5191	55	2	x	x	X
ejpam-5191	56	1	−	−	ADP
ejpam-5191	56	2	τ1τ2	τ1τ2	NOUN
ejpam-5191	56	3	-	-	PUNCT
ejpam-5191	56	4	int(a	int(a	NOUN
ejpam-5191	56	5	)	)	PUNCT
ejpam-5191	56	6	.	.	PUNCT
ejpam-5191	57	1	p.	p.	NOUN
ejpam-5191	57	2	pue	pue	NOUN
ejpam-5191	57	3	-	-	PUNCT
ejpam-5191	57	4	on	on	ADP
ejpam-5191	57	5	,	,	PUNCT
ejpam-5191	57	6	s.	s.	PROPN
ejpam-5191	57	7	sompong	sompong	PROPN
ejpam-5191	57	8	,	,	PUNCT
ejpam-5191	57	9	c.	c.	PROPN
ejpam-5191	57	10	boonpok	boonpok	PROPN
ejpam-5191	57	11	/	/	SYM
ejpam-5191	57	12	eur	eur	PROPN
ejpam-5191	57	13	.	.	PUNCT
ejpam-5191	58	1	j.	j.	PROPN
ejpam-5191	58	2	pure	pure	PROPN
ejpam-5191	58	3	appl	appl	PROPN
ejpam-5191	58	4	.	.	PROPN
ejpam-5191	58	5	math	math	PROPN
ejpam-5191	58	6	,	,	PUNCT
ejpam-5191	58	7	17	17	NUM
ejpam-5191	58	8	(	(	PUNCT
ejpam-5191	58	9	3	3	NUM
ejpam-5191	58	10	)	)	PUNCT
ejpam-5191	58	11	(	(	PUNCT
ejpam-5191	58	12	2024	2024	NUM
ejpam-5191	58	13	)	)	PUNCT
ejpam-5191	58	14	,	,	PUNCT
ejpam-5191	58	15	1553	1553	NUM
ejpam-5191	58	16	-	-	SYM
ejpam-5191	58	17	1564	1564	NUM
ejpam-5191	58	18	1555	1555	NUM
ejpam-5191	58	19	a	a	DET
ejpam-5191	58	20	subseta	subseta	NOUN
ejpam-5191	58	21	of	of	ADP
ejpam-5191	58	22	a	a	DET
ejpam-5191	58	23	bitopological	bitopological	ADJ
ejpam-5191	58	24	space	space	NOUN
ejpam-5191	58	25	(	(	PUNCT
ejpam-5191	58	26	x	x	NOUN
ejpam-5191	58	27	,	,	PUNCT
ejpam-5191	58	28	τ1	τ1	NOUN
ejpam-5191	58	29	,	,	PUNCT
ejpam-5191	58	30	τ2	τ2	NOUN
ejpam-5191	58	31	)	)	PUNCT
ejpam-5191	58	32	is	be	AUX
ejpam-5191	58	33	called	call	VERB
ejpam-5191	58	34	(	(	PUNCT
ejpam-5191	58	35	τ1	τ1	NOUN
ejpam-5191	58	36	,	,	PUNCT
ejpam-5191	58	37	τ2)r	τ2)r	NOUN
ejpam-5191	58	38	-	-	PUNCT
ejpam-5191	58	39	open	open	ADJ
ejpam-5191	59	1	[	[	X
ejpam-5191	59	2	42	42	NUM
ejpam-5191	59	3	]	]	PUNCT
ejpam-5191	59	4	(	(	PUNCT
ejpam-5191	59	5	resp	resp	NOUN
ejpam-5191	59	6	.	.	PUNCT
ejpam-5191	60	1	(	(	PUNCT
ejpam-5191	60	2	τ1	τ1	NOUN
ejpam-5191	60	3	,	,	PUNCT
ejpam-5191	60	4	τ2)sopen	τ2)sopen	VERB
ejpam-5191	60	5	[	[	X
ejpam-5191	60	6	7	7	NUM
ejpam-5191	60	7	]	]	PUNCT
ejpam-5191	60	8	,	,	PUNCT
ejpam-5191	60	9	(	(	PUNCT
ejpam-5191	60	10	τ1	τ1	NOUN
ejpam-5191	60	11	,	,	PUNCT
ejpam-5191	60	12	τ2)p	τ2)p	NOUN
ejpam-5191	60	13	-	-	ADJ
ejpam-5191	60	14	open	open	ADJ
ejpam-5191	60	15	[	[	X
ejpam-5191	60	16	7	7	NUM
ejpam-5191	60	17	]	]	PUNCT
ejpam-5191	60	18	,	,	PUNCT
ejpam-5191	60	19	(	(	PUNCT
ejpam-5191	60	20	τ1	τ1	NOUN
ejpam-5191	60	21	,	,	PUNCT
ejpam-5191	60	22	τ2)β	τ2)β	ADJ
ejpam-5191	60	23	-	-	PUNCT
ejpam-5191	60	24	open	open	NOUN
ejpam-5191	61	1	[	[	X
ejpam-5191	61	2	7	7	NUM
ejpam-5191	61	3	]	]	NUM
ejpam-5191	61	4	,	,	PUNCT
ejpam-5191	61	5	α(τ1	α(τ1	NOUN
ejpam-5191	61	6	,	,	PUNCT
ejpam-5191	61	7	τ2)-open	τ2)-open	ADJ
ejpam-5191	61	8	[	[	X
ejpam-5191	61	9	45	45	NUM
ejpam-5191	61	10	]	]	PUNCT
ejpam-5191	61	11	)	)	PUNCT
ejpam-5191	62	1	ifa	ifa	PROPN
ejpam-5191	62	2	=	=	PUNCT
ejpam-5191	62	3	τ1τ2	τ1τ2	NOUN
ejpam-5191	62	4	-	-	NOUN
ejpam-5191	62	5	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	62	6	-	-	PUNCT
ejpam-5191	62	7	cl(a	cl(a	NUM
ejpam-5191	62	8	)	)	PUNCT
ejpam-5191	62	9	)	)	PUNCT
ejpam-5191	62	10	(	(	PUNCT
ejpam-5191	62	11	resp	resp	NOUN
ejpam-5191	62	12	.	.	PUNCT
ejpam-5191	63	1	a	a	DET
ejpam-5191	63	2	⊆	⊆	NUM
ejpam-5191	63	3	τ1τ2	τ1τ2	NOUN
ejpam-5191	63	4	-	-	ADJ
ejpam-5191	63	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5191	63	6	-	-	PUNCT
ejpam-5191	63	7	int(a	int(a	NOUN
ejpam-5191	63	8	)	)	PUNCT
ejpam-5191	63	9	)	)	PUNCT
ejpam-5191	63	10	,	,	PUNCT
ejpam-5191	63	11	a	a	DET
ejpam-5191	63	12	⊆	⊆	NUM
ejpam-5191	63	13	τ1τ2	τ1τ2	NOUN
ejpam-5191	63	14	-	-	NOUN
ejpam-5191	63	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	63	16	-	-	PUNCT
ejpam-5191	63	17	cl(a	cl(a	NUM
ejpam-5191	63	18	)	)	PUNCT
ejpam-5191	63	19	)	)	PUNCT
ejpam-5191	63	20	,	,	PUNCT
ejpam-5191	63	21	a	a	DET
ejpam-5191	63	22	⊆	⊆	NUM
ejpam-5191	63	23	τ1τ2	τ1τ2	NOUN
ejpam-5191	63	24	-	-	PUNCT
ejpam-5191	63	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5191	63	26	-	-	PUNCT
ejpam-5191	63	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	63	28	-	-	PUNCT
ejpam-5191	63	29	cl(a	cl(a	NUM
ejpam-5191	63	30	)	)	PUNCT
ejpam-5191	63	31	)	)	PUNCT
ejpam-5191	63	32	)	)	PUNCT
ejpam-5191	63	33	,	,	PUNCT
ejpam-5191	63	34	a	a	DET
ejpam-5191	63	35	⊆	⊆	NUM
ejpam-5191	63	36	τ1τ2	τ1τ2	NOUN
ejpam-5191	63	37	-	-	PUNCT
ejpam-5191	63	38	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	63	39	-	-	PUNCT
ejpam-5191	63	40	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5191	63	41	-	-	PUNCT
ejpam-5191	63	42	int(a	int(a	NOUN
ejpam-5191	63	43	)	)	PUNCT
ejpam-5191	63	44	)	)	PUNCT
ejpam-5191	63	45	)	)	PUNCT
ejpam-5191	63	46	)	)	PUNCT
ejpam-5191	63	47	.	.	PUNCT
ejpam-5191	64	1	the	the	DET
ejpam-5191	64	2	complement	complement	NOUN
ejpam-5191	64	3	of	of	ADP
ejpam-5191	64	4	a	a	DET
ejpam-5191	64	5	(	(	PUNCT
ejpam-5191	64	6	τ1	τ1	NOUN
ejpam-5191	64	7	,	,	PUNCT
ejpam-5191	64	8	τ2)r	τ2)r	NOUN
ejpam-5191	64	9	-	-	PUNCT
ejpam-5191	64	10	open	open	ADJ
ejpam-5191	64	11	(	(	PUNCT
ejpam-5191	64	12	resp	resp	NOUN
ejpam-5191	64	13	.	.	PUNCT
ejpam-5191	65	1	(	(	PUNCT
ejpam-5191	65	2	τ1	τ1	NOUN
ejpam-5191	65	3	,	,	PUNCT
ejpam-5191	65	4	τ2)sopen	τ2)sopen	ADJ
ejpam-5191	65	5	,	,	PUNCT
ejpam-5191	65	6	(	(	PUNCT
ejpam-5191	65	7	τ1	τ1	NOUN
ejpam-5191	65	8	,	,	PUNCT
ejpam-5191	65	9	τ2)p	τ2)p	NOUN
ejpam-5191	65	10	-	-	ADJ
ejpam-5191	65	11	open	open	ADJ
ejpam-5191	65	12	,	,	PUNCT
ejpam-5191	65	13	(	(	PUNCT
ejpam-5191	65	14	τ1	τ1	NOUN
ejpam-5191	65	15	,	,	PUNCT
ejpam-5191	65	16	τ2)β	τ2)β	ADJ
ejpam-5191	65	17	-	-	PUNCT
ejpam-5191	65	18	open	open	ADJ
ejpam-5191	65	19	,	,	PUNCT
ejpam-5191	65	20	α(τ1	α(τ1	NOUN
ejpam-5191	65	21	,	,	PUNCT
ejpam-5191	65	22	τ2)-open	τ2)-open	ADJ
ejpam-5191	65	23	)	)	PUNCT
ejpam-5191	65	24	set	set	NOUN
ejpam-5191	65	25	is	be	AUX
ejpam-5191	65	26	called	call	VERB
ejpam-5191	65	27	(	(	PUNCT
ejpam-5191	65	28	τ1	τ1	NOUN
ejpam-5191	65	29	,	,	PUNCT
ejpam-5191	65	30	τ2)r	τ2)r	NOUN
ejpam-5191	65	31	-	-	PUNCT
ejpam-5191	65	32	closed	closed	ADJ
ejpam-5191	65	33	(	(	PUNCT
ejpam-5191	65	34	resp	resp	NOUN
ejpam-5191	65	35	.	.	PUNCT
ejpam-5191	66	1	(	(	PUNCT
ejpam-5191	66	2	τ1	τ1	NOUN
ejpam-5191	66	3	,	,	PUNCT
ejpam-5191	66	4	τ2)s	τ2)s	NOUN
ejpam-5191	66	5	-	-	PUNCT
ejpam-5191	66	6	closed	closed	ADJ
ejpam-5191	66	7	,	,	PUNCT
ejpam-5191	66	8	(	(	PUNCT
ejpam-5191	66	9	τ1	τ1	NOUN
ejpam-5191	66	10	,	,	PUNCT
ejpam-5191	66	11	τ2)p	τ2)p	NOUN
ejpam-5191	66	12	-	-	PUNCT
ejpam-5191	66	13	closed	closed	ADJ
ejpam-5191	66	14	,	,	PUNCT
ejpam-5191	66	15	(	(	PUNCT
ejpam-5191	66	16	τ1	τ1	NOUN
ejpam-5191	66	17	,	,	PUNCT
ejpam-5191	66	18	τ2)β	τ2)β	ADJ
ejpam-5191	66	19	-	-	PUNCT
ejpam-5191	66	20	closed	closed	ADJ
ejpam-5191	66	21	,	,	PUNCT
ejpam-5191	66	22	α(τ1	α(τ1	NOUN
ejpam-5191	66	23	,	,	PUNCT
ejpam-5191	66	24	τ2)-closed	τ2)-closed	ADJ
ejpam-5191	66	25	)	)	PUNCT
ejpam-5191	66	26	.	.	PUNCT
ejpam-5191	67	1	let	let	VERB
ejpam-5191	67	2	a	a	DET
ejpam-5191	67	3	be	be	AUX
ejpam-5191	67	4	a	a	DET
ejpam-5191	67	5	subset	subset	NOUN
ejpam-5191	67	6	of	of	ADP
ejpam-5191	67	7	a	a	DET
ejpam-5191	67	8	bitopological	bitopological	ADJ
ejpam-5191	67	9	space	space	NOUN
ejpam-5191	67	10	(	(	PUNCT
ejpam-5191	67	11	x	x	NOUN
ejpam-5191	67	12	,	,	PUNCT
ejpam-5191	67	13	τ1	τ1	NOUN
ejpam-5191	67	14	,	,	PUNCT
ejpam-5191	67	15	τ2	τ2	NOUN
ejpam-5191	67	16	)	)	PUNCT
ejpam-5191	67	17	.	.	PUNCT
ejpam-5191	68	1	the	the	DET
ejpam-5191	68	2	intersection	intersection	NOUN
ejpam-5191	68	3	of	of	ADP
ejpam-5191	68	4	all	all	DET
ejpam-5191	68	5	(	(	PUNCT
ejpam-5191	68	6	τ1	τ1	NOUN
ejpam-5191	68	7	,	,	PUNCT
ejpam-5191	68	8	τ2)s	τ2)s	NOUN
ejpam-5191	68	9	-	-	PUNCT
ejpam-5191	68	10	closed	close	VERB
ejpam-5191	68	11	sets	set	NOUN
ejpam-5191	68	12	of	of	ADP
ejpam-5191	68	13	x	x	PUNCT
ejpam-5191	68	14	containing	contain	VERB
ejpam-5191	68	15	a	a	PRON
ejpam-5191	68	16	is	be	AUX
ejpam-5191	68	17	called	call	VERB
ejpam-5191	68	18	the	the	DET
ejpam-5191	68	19	(	(	PUNCT
ejpam-5191	68	20	τ1	τ1	NOUN
ejpam-5191	68	21	,	,	PUNCT
ejpam-5191	68	22	τ2)s	τ2)s	NOUN
ejpam-5191	68	23	-	-	PUNCT
ejpam-5191	68	24	closure	closure	NOUN
ejpam-5191	68	25	[	[	X
ejpam-5191	68	26	7	7	NUM
ejpam-5191	68	27	]	]	PUNCT
ejpam-5191	68	28	of	of	ADP
ejpam-5191	68	29	a	a	PRON
ejpam-5191	68	30	and	and	CCONJ
ejpam-5191	68	31	is	be	AUX
ejpam-5191	68	32	denoted	denote	VERB
ejpam-5191	68	33	by	by	ADP
ejpam-5191	68	34	(	(	PUNCT
ejpam-5191	68	35	τ1	τ1	NOUN
ejpam-5191	68	36	,	,	PUNCT
ejpam-5191	68	37	τ2)-scl(a	τ2)-scl(a	PROPN
ejpam-5191	68	38	)	)	PUNCT
ejpam-5191	68	39	.	.	PUNCT
ejpam-5191	69	1	the	the	DET
ejpam-5191	69	2	union	union	NOUN
ejpam-5191	69	3	of	of	ADP
ejpam-5191	69	4	all	all	DET
ejpam-5191	69	5	(	(	PUNCT
ejpam-5191	69	6	τ1	τ1	NOUN
ejpam-5191	69	7	,	,	PUNCT
ejpam-5191	69	8	τ2)s	τ2)s	NOUN
ejpam-5191	69	9	-	-	PUNCT
ejpam-5191	69	10	open	open	ADJ
ejpam-5191	69	11	sets	set	NOUN
ejpam-5191	69	12	of	of	ADP
ejpam-5191	69	13	x	x	PUNCT
ejpam-5191	69	14	contained	contain	VERB
ejpam-5191	69	15	in	in	ADP
ejpam-5191	69	16	a	a	PRON
ejpam-5191	69	17	is	be	AUX
ejpam-5191	69	18	called	call	VERB
ejpam-5191	69	19	the	the	DET
ejpam-5191	69	20	(	(	PUNCT
ejpam-5191	69	21	τ1	τ1	NOUN
ejpam-5191	69	22	,	,	PUNCT
ejpam-5191	69	23	τ2)s	τ2)s	NOUN
ejpam-5191	69	24	-	-	NOUN
ejpam-5191	69	25	interior	interior	ADJ
ejpam-5191	69	26	[	[	X
ejpam-5191	69	27	7	7	NUM
ejpam-5191	69	28	]	]	PUNCT
ejpam-5191	69	29	of	of	ADP
ejpam-5191	69	30	a	a	PRON
ejpam-5191	69	31	and	and	CCONJ
ejpam-5191	69	32	is	be	AUX
ejpam-5191	69	33	denoted	denote	VERB
ejpam-5191	69	34	by	by	ADP
ejpam-5191	69	35	(	(	PUNCT
ejpam-5191	69	36	τ1	τ1	NOUN
ejpam-5191	69	37	,	,	PUNCT
ejpam-5191	69	38	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5191	69	39	)	)	PUNCT
ejpam-5191	69	40	.	.	PUNCT
ejpam-5191	70	1	lemma	lemma	PROPN
ejpam-5191	70	2	2	2	NUM
ejpam-5191	70	3	.	.	X
ejpam-5191	71	1	for	for	ADP
ejpam-5191	71	2	a	a	DET
ejpam-5191	71	3	subset	subset	NOUN
ejpam-5191	71	4	a	a	PRON
ejpam-5191	71	5	of	of	ADP
ejpam-5191	71	6	a	a	DET
ejpam-5191	71	7	bitopological	bitopological	ADJ
ejpam-5191	71	8	space	space	NOUN
ejpam-5191	71	9	(	(	PUNCT
ejpam-5191	71	10	x	x	NOUN
ejpam-5191	71	11	,	,	PUNCT
ejpam-5191	71	12	τ1	τ1	NOUN
ejpam-5191	71	13	,	,	PUNCT
ejpam-5191	71	14	τ2	τ2	NOUN
ejpam-5191	71	15	)	)	PUNCT
ejpam-5191	71	16	,	,	PUNCT
ejpam-5191	71	17	the	the	DET
ejpam-5191	71	18	following	follow	VERB
ejpam-5191	71	19	properties	property	NOUN
ejpam-5191	71	20	hold	hold	VERB
ejpam-5191	71	21	:	:	PUNCT
ejpam-5191	71	22	(	(	PUNCT
ejpam-5191	71	23	1	1	X
ejpam-5191	71	24	)	)	PUNCT
ejpam-5191	71	25	(	(	PUNCT
ejpam-5191	71	26	τ1	τ1	NOUN
ejpam-5191	71	27	,	,	PUNCT
ejpam-5191	71	28	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5191	71	29	)	)	PUNCT
ejpam-5191	71	30	=	=	PUNCT
ejpam-5191	72	1	τ1τ2	τ1τ2	NOUN
ejpam-5191	72	2	-	-	NOUN
ejpam-5191	72	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	72	4	-	-	PUNCT
ejpam-5191	72	5	cl(a	cl(a	NUM
ejpam-5191	72	6	)	)	PUNCT
ejpam-5191	72	7	)	)	PUNCT
ejpam-5191	72	8	∪a	∪a	X
ejpam-5191	73	1	[	[	X
ejpam-5191	73	2	21	21	NUM
ejpam-5191	73	3	]	]	X
ejpam-5191	73	4	;	;	PUNCT
ejpam-5191	73	5	(	(	PUNCT
ejpam-5191	73	6	2	2	X
ejpam-5191	73	7	)	)	PUNCT
ejpam-5191	73	8	(	(	PUNCT
ejpam-5191	73	9	τ1	τ1	NOUN
ejpam-5191	73	10	,	,	PUNCT
ejpam-5191	73	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5191	73	12	)	)	PUNCT
ejpam-5191	74	1	=	=	PUNCT
ejpam-5191	74	2	τ1τ2	τ1τ2	NOUN
ejpam-5191	74	3	-	-	ADJ
ejpam-5191	74	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5191	74	5	-	-	PUNCT
ejpam-5191	74	6	int(a	int(a	NOUN
ejpam-5191	74	7	)	)	PUNCT
ejpam-5191	74	8	)	)	PUNCT
ejpam-5191	75	1	∩a	∩a	PROPN
ejpam-5191	75	2	.	.	PUNCT
ejpam-5191	76	1	let	let	VERB
ejpam-5191	76	2	a	a	DET
ejpam-5191	76	3	be	be	AUX
ejpam-5191	76	4	a	a	DET
ejpam-5191	76	5	subset	subset	NOUN
ejpam-5191	76	6	of	of	ADP
ejpam-5191	76	7	a	a	DET
ejpam-5191	76	8	bitopological	bitopological	ADJ
ejpam-5191	76	9	space	space	NOUN
ejpam-5191	76	10	(	(	PUNCT
ejpam-5191	76	11	x	x	NOUN
ejpam-5191	76	12	,	,	PUNCT
ejpam-5191	76	13	τ1	τ1	NOUN
ejpam-5191	76	14	,	,	PUNCT
ejpam-5191	76	15	τ2	τ2	NOUN
ejpam-5191	76	16	)	)	PUNCT
ejpam-5191	76	17	.	.	PUNCT
ejpam-5191	77	1	a	a	DET
ejpam-5191	77	2	point	point	NOUN
ejpam-5191	77	3	x	x	X
ejpam-5191	77	4	∈	∈	NOUN
ejpam-5191	77	5	x	x	PUNCT
ejpam-5191	77	6	is	be	AUX
ejpam-5191	77	7	called	call	VERB
ejpam-5191	77	8	a	a	DET
ejpam-5191	77	9	(	(	PUNCT
ejpam-5191	77	10	τ1	τ1	NOUN
ejpam-5191	77	11	,	,	PUNCT
ejpam-5191	77	12	τ2)θ	τ2)θ	ADJ
ejpam-5191	77	13	-	-	PUNCT
ejpam-5191	77	14	cluster	cluster	NOUN
ejpam-5191	77	15	point	point	NOUN
ejpam-5191	77	16	[	[	X
ejpam-5191	77	17	42	42	NUM
ejpam-5191	77	18	]	]	PUNCT
ejpam-5191	77	19	of	of	ADP
ejpam-5191	77	20	a	a	DET
ejpam-5191	77	21	if	if	SCONJ
ejpam-5191	77	22	τ1τ2	τ1τ2	ADJ
ejpam-5191	77	23	-	-	ADJ
ejpam-5191	77	24	cl(u)∩a	cl(u)∩a	ADJ
ejpam-5191	77	25	̸=	̸=	PROPN
ejpam-5191	77	26	∅	∅	NOUN
ejpam-5191	77	27	for	for	ADP
ejpam-5191	77	28	every	every	DET
ejpam-5191	77	29	τ1τ2	τ1τ2	ADJ
ejpam-5191	77	30	-	-	ADJ
ejpam-5191	77	31	open	open	ADJ
ejpam-5191	77	32	set	set	NOUN
ejpam-5191	77	33	u	u	NOUN
ejpam-5191	77	34	containing	contain	VERB
ejpam-5191	77	35	x.	x.	NOUN
ejpam-5191	77	36	the	the	DET
ejpam-5191	77	37	set	set	NOUN
ejpam-5191	77	38	of	of	ADP
ejpam-5191	77	39	all	all	DET
ejpam-5191	77	40	(	(	PUNCT
ejpam-5191	77	41	τ1	τ1	NOUN
ejpam-5191	77	42	,	,	PUNCT
ejpam-5191	77	43	τ2)θ	τ2)θ	ADJ
ejpam-5191	77	44	-	-	PUNCT
ejpam-5191	77	45	cluster	cluster	NOUN
ejpam-5191	77	46	points	point	NOUN
ejpam-5191	77	47	of	of	ADP
ejpam-5191	77	48	a	a	PRON
ejpam-5191	77	49	is	be	AUX
ejpam-5191	77	50	called	call	VERB
ejpam-5191	77	51	the	the	DET
ejpam-5191	77	52	(	(	PUNCT
ejpam-5191	77	53	τ1	τ1	NOUN
ejpam-5191	77	54	,	,	PUNCT
ejpam-5191	77	55	τ2)θ	τ2)θ	ADJ
ejpam-5191	77	56	-	-	PUNCT
ejpam-5191	77	57	closure	closure	NOUN
ejpam-5191	77	58	[	[	X
ejpam-5191	77	59	42	42	NUM
ejpam-5191	77	60	]	]	PUNCT
ejpam-5191	77	61	of	of	ADP
ejpam-5191	77	62	a	a	PRON
ejpam-5191	77	63	and	and	CCONJ
ejpam-5191	77	64	is	be	AUX
ejpam-5191	77	65	denoted	denote	VERB
ejpam-5191	77	66	by	by	ADP
ejpam-5191	77	67	(	(	PUNCT
ejpam-5191	77	68	τ1	τ1	NOUN
ejpam-5191	77	69	,	,	PUNCT
ejpam-5191	77	70	τ2)θ	τ2)θ	NOUN
ejpam-5191	77	71	-	-	PUNCT
ejpam-5191	77	72	cl(a	cl(a	NUM
ejpam-5191	77	73	)	)	PUNCT
ejpam-5191	77	74	.	.	PUNCT
ejpam-5191	78	1	a	a	DET
ejpam-5191	78	2	subset	subset	NOUN
ejpam-5191	78	3	a	a	PRON
ejpam-5191	78	4	of	of	ADP
ejpam-5191	78	5	a	a	DET
ejpam-5191	78	6	bitopological	bitopological	ADJ
ejpam-5191	78	7	space	space	NOUN
ejpam-5191	78	8	(	(	PUNCT
ejpam-5191	78	9	x	x	NOUN
ejpam-5191	78	10	,	,	PUNCT
ejpam-5191	78	11	τ1	τ1	NOUN
ejpam-5191	78	12	,	,	PUNCT
ejpam-5191	78	13	τ2	τ2	NOUN
ejpam-5191	78	14	)	)	PUNCT
ejpam-5191	78	15	is	be	AUX
ejpam-5191	78	16	said	say	VERB
ejpam-5191	78	17	to	to	PART
ejpam-5191	78	18	be	be	AUX
ejpam-5191	78	19	(	(	PUNCT
ejpam-5191	78	20	τ1	τ1	NOUN
ejpam-5191	78	21	,	,	PUNCT
ejpam-5191	78	22	τ2)θ	τ2)θ	NOUN
ejpam-5191	78	23	-	-	PUNCT
ejpam-5191	78	24	closed	closed	ADJ
ejpam-5191	78	25	[	[	X
ejpam-5191	78	26	42	42	NUM
ejpam-5191	78	27	]	]	PUNCT
ejpam-5191	78	28	if	if	SCONJ
ejpam-5191	78	29	(	(	PUNCT
ejpam-5191	78	30	τ1	τ1	NOUN
ejpam-5191	78	31	,	,	PUNCT
ejpam-5191	78	32	τ2)θ	τ2)θ	NOUN
ejpam-5191	78	33	-	-	PUNCT
ejpam-5191	78	34	cl(a	cl(a	NUM
ejpam-5191	78	35	)	)	PUNCT
ejpam-5191	79	1	=	=	PUNCT
ejpam-5191	79	2	a.	a.	NOUN
ejpam-5191	79	3	the	the	DET
ejpam-5191	79	4	complement	complement	NOUN
ejpam-5191	79	5	of	of	ADP
ejpam-5191	79	6	a	a	DET
ejpam-5191	79	7	(	(	PUNCT
ejpam-5191	79	8	τ1	τ1	NOUN
ejpam-5191	79	9	,	,	PUNCT
ejpam-5191	79	10	τ2)θ	τ2)θ	ADJ
ejpam-5191	79	11	-	-	PUNCT
ejpam-5191	79	12	closed	close	VERB
ejpam-5191	79	13	set	set	NOUN
ejpam-5191	79	14	is	be	AUX
ejpam-5191	79	15	said	say	VERB
ejpam-5191	79	16	to	to	PART
ejpam-5191	79	17	be	be	AUX
ejpam-5191	79	18	(	(	PUNCT
ejpam-5191	79	19	τ1	τ1	NOUN
ejpam-5191	79	20	,	,	PUNCT
ejpam-5191	79	21	τ2)θ	τ2)θ	NOUN
ejpam-5191	79	22	-	-	PUNCT
ejpam-5191	79	23	open	open	ADJ
ejpam-5191	79	24	.	.	PUNCT
ejpam-5191	80	1	the	the	DET
ejpam-5191	80	2	union	union	NOUN
ejpam-5191	80	3	of	of	ADP
ejpam-5191	80	4	all	all	DET
ejpam-5191	80	5	(	(	PUNCT
ejpam-5191	80	6	τ1	τ1	NOUN
ejpam-5191	80	7	,	,	PUNCT
ejpam-5191	80	8	τ2)θ	τ2)θ	ADJ
ejpam-5191	80	9	-	-	PUNCT
ejpam-5191	80	10	open	open	ADJ
ejpam-5191	80	11	sets	set	NOUN
ejpam-5191	80	12	of	of	ADP
ejpam-5191	80	13	x	x	PUNCT
ejpam-5191	80	14	contained	contain	VERB
ejpam-5191	80	15	in	in	ADP
ejpam-5191	80	16	a	a	PRON
ejpam-5191	80	17	is	be	AUX
ejpam-5191	80	18	called	call	VERB
ejpam-5191	80	19	the	the	DET
ejpam-5191	80	20	(	(	PUNCT
ejpam-5191	80	21	τ1	τ1	NOUN
ejpam-5191	80	22	,	,	PUNCT
ejpam-5191	80	23	τ2)θ	τ2)θ	ADJ
ejpam-5191	80	24	-	-	PUNCT
ejpam-5191	80	25	interior	interior	NOUN
ejpam-5191	80	26	[	[	X
ejpam-5191	80	27	42	42	NUM
ejpam-5191	80	28	]	]	PUNCT
ejpam-5191	80	29	of	of	ADP
ejpam-5191	80	30	a	a	PRON
ejpam-5191	80	31	and	and	CCONJ
ejpam-5191	80	32	is	be	AUX
ejpam-5191	80	33	denoted	denote	VERB
ejpam-5191	80	34	by	by	ADP
ejpam-5191	80	35	(	(	PUNCT
ejpam-5191	80	36	τ1	τ1	NOUN
ejpam-5191	80	37	,	,	PUNCT
ejpam-5191	80	38	τ2)θ	τ2)θ	NOUN
ejpam-5191	80	39	-	-	PUNCT
ejpam-5191	80	40	int(a	int(a	NOUN
ejpam-5191	80	41	)	)	PUNCT
ejpam-5191	80	42	.	.	PUNCT
ejpam-5191	81	1	lemma	lemma	PROPN
ejpam-5191	81	2	3	3	X
ejpam-5191	81	3	.	.	PUNCT
ejpam-5191	82	1	[	[	X
ejpam-5191	82	2	42	42	NUM
ejpam-5191	82	3	]	]	PUNCT
ejpam-5191	82	4	for	for	ADP
ejpam-5191	82	5	a	a	DET
ejpam-5191	82	6	subset	subset	NOUN
ejpam-5191	82	7	a	a	PRON
ejpam-5191	82	8	of	of	ADP
ejpam-5191	82	9	a	a	DET
ejpam-5191	82	10	bitopological	bitopological	ADJ
ejpam-5191	82	11	space	space	NOUN
ejpam-5191	82	12	(	(	PUNCT
ejpam-5191	82	13	x	x	NOUN
ejpam-5191	82	14	,	,	PUNCT
ejpam-5191	82	15	τ1	τ1	NOUN
ejpam-5191	82	16	,	,	PUNCT
ejpam-5191	82	17	τ2	τ2	NOUN
ejpam-5191	82	18	)	)	PUNCT
ejpam-5191	82	19	,	,	PUNCT
ejpam-5191	82	20	the	the	DET
ejpam-5191	82	21	following	follow	VERB
ejpam-5191	82	22	properties	property	NOUN
ejpam-5191	82	23	hold	hold	VERB
ejpam-5191	82	24	:	:	PUNCT
ejpam-5191	82	25	(	(	PUNCT
ejpam-5191	82	26	1	1	X
ejpam-5191	82	27	)	)	PUNCT
ejpam-5191	82	28	if	if	SCONJ
ejpam-5191	82	29	a	a	PRON
ejpam-5191	82	30	is	be	AUX
ejpam-5191	82	31	τ1τ2	τ1τ2	NOUN
ejpam-5191	82	32	-	-	ADJ
ejpam-5191	82	33	open	open	ADJ
ejpam-5191	82	34	in	in	ADP
ejpam-5191	82	35	x	x	NOUN
ejpam-5191	82	36	,	,	PUNCT
ejpam-5191	82	37	then	then	ADV
ejpam-5191	82	38	τ1τ2	τ1τ2	NOUN
ejpam-5191	82	39	-	-	NUM
ejpam-5191	82	40	cl(a	cl(a	NUM
ejpam-5191	82	41	)	)	PUNCT
ejpam-5191	82	42	=	=	PUNCT
ejpam-5191	82	43	(	(	PUNCT
ejpam-5191	82	44	τ1	τ1	NOUN
ejpam-5191	82	45	,	,	PUNCT
ejpam-5191	82	46	τ2)θ	τ2)θ	NOUN
ejpam-5191	82	47	-	-	PUNCT
ejpam-5191	82	48	cl(a	cl(a	NUM
ejpam-5191	82	49	)	)	PUNCT
ejpam-5191	82	50	.	.	PUNCT
ejpam-5191	83	1	(	(	PUNCT
ejpam-5191	83	2	2	2	X
ejpam-5191	83	3	)	)	PUNCT
ejpam-5191	83	4	(	(	PUNCT
ejpam-5191	83	5	τ1	τ1	NOUN
ejpam-5191	83	6	,	,	PUNCT
ejpam-5191	83	7	τ2)θ	τ2)θ	NOUN
ejpam-5191	83	8	-	-	PUNCT
ejpam-5191	83	9	cl(a	cl(a	NUM
ejpam-5191	83	10	)	)	PUNCT
ejpam-5191	83	11	is	be	AUX
ejpam-5191	83	12	τ1τ2	τ1τ2	NOUN
ejpam-5191	83	13	-	-	ADJ
ejpam-5191	83	14	closed	closed	ADJ
ejpam-5191	83	15	in	in	ADP
ejpam-5191	83	16	x.	x.	NOUN
ejpam-5191	83	17	by	by	ADP
ejpam-5191	83	18	a	a	DET
ejpam-5191	83	19	multifunction	multifunction	NOUN
ejpam-5191	83	20	f	f	NOUN
ejpam-5191	83	21	:	:	PUNCT
ejpam-5191	83	22	x	x	X
ejpam-5191	83	23	→	→	SYM
ejpam-5191	83	24	y	y	PROPN
ejpam-5191	83	25	,	,	PUNCT
ejpam-5191	83	26	we	we	PRON
ejpam-5191	83	27	mean	mean	VERB
ejpam-5191	83	28	a	a	DET
ejpam-5191	83	29	point	point	NOUN
ejpam-5191	83	30	-	-	PUNCT
ejpam-5191	83	31	to	to	ADP
ejpam-5191	83	32	-	-	PUNCT
ejpam-5191	83	33	set	set	VERB
ejpam-5191	83	34	correspondence	correspondence	NOUN
ejpam-5191	83	35	from	from	ADP
ejpam-5191	83	36	x	x	PUNCT
ejpam-5191	83	37	into	into	ADP
ejpam-5191	83	38	y	y	PROPN
ejpam-5191	83	39	,	,	PUNCT
ejpam-5191	83	40	and	and	CCONJ
ejpam-5191	83	41	we	we	PRON
ejpam-5191	83	42	always	always	ADV
ejpam-5191	83	43	assume	assume	VERB
ejpam-5191	84	1	that	that	SCONJ
ejpam-5191	84	2	f	f	PROPN
ejpam-5191	84	3	(	(	PUNCT
ejpam-5191	84	4	x	x	X
ejpam-5191	84	5	)	)	PUNCT
ejpam-5191	84	6	̸=	̸=	NOUN
ejpam-5191	84	7	∅	∅	NOUN
ejpam-5191	84	8	for	for	ADP
ejpam-5191	84	9	all	all	PRON
ejpam-5191	84	10	x	x	SYM
ejpam-5191	84	11	∈	∈	ADJ
ejpam-5191	84	12	x.	x.	NOUN
ejpam-5191	84	13	for	for	ADP
ejpam-5191	84	14	a	a	DET
ejpam-5191	84	15	multifunction	multifunction	NOUN
ejpam-5191	84	16	f	f	NOUN
ejpam-5191	84	17	:	:	PUNCT
ejpam-5191	84	18	x	x	X
ejpam-5191	84	19	→	→	SYM
ejpam-5191	84	20	y	y	PROPN
ejpam-5191	84	21	,	,	PUNCT
ejpam-5191	84	22	following	follow	VERB
ejpam-5191	84	23	[	[	X
ejpam-5191	84	24	2	2	X
ejpam-5191	84	25	]	]	PUNCT
ejpam-5191	84	26	we	we	PRON
ejpam-5191	84	27	shall	shall	AUX
ejpam-5191	84	28	denote	denote	VERB
ejpam-5191	84	29	the	the	DET
ejpam-5191	84	30	upper	upper	ADJ
ejpam-5191	84	31	and	and	CCONJ
ejpam-5191	84	32	lower	low	ADJ
ejpam-5191	84	33	inverse	inverse	NOUN
ejpam-5191	84	34	of	of	ADP
ejpam-5191	84	35	a	a	DET
ejpam-5191	84	36	set	set	NOUN
ejpam-5191	84	37	b	b	PROPN
ejpam-5191	84	38	of	of	ADP
ejpam-5191	84	39	y	y	PROPN
ejpam-5191	84	40	by	by	ADP
ejpam-5191	84	41	f+(b	f+(b	NOUN
ejpam-5191	84	42	)	)	PUNCT
ejpam-5191	84	43	and	and	CCONJ
ejpam-5191	84	44	f−(b	f−(b	NOUN
ejpam-5191	84	45	)	)	PUNCT
ejpam-5191	84	46	,	,	PUNCT
ejpam-5191	84	47	respectively	respectively	ADV
ejpam-5191	84	48	,	,	PUNCT
ejpam-5191	84	49	that	that	ADV
ejpam-5191	84	50	is	is	ADV
ejpam-5191	84	51	,	,	PUNCT
ejpam-5191	84	52	f+(b	f+(b	NOUN
ejpam-5191	84	53	)	)	PUNCT
ejpam-5191	84	54	=	=	PRON
ejpam-5191	85	1	{	{	PUNCT
ejpam-5191	85	2	x	x	PUNCT
ejpam-5191	85	3	∈	∈	PROPN
ejpam-5191	85	4	x	x	INTJ
ejpam-5191	86	1	|	|	NOUN
ejpam-5191	86	2	f	f	X
ejpam-5191	86	3	(	(	PUNCT
ejpam-5191	86	4	x	x	NOUN
ejpam-5191	86	5	)	)	PUNCT
ejpam-5191	86	6	⊆	⊆	NUM
ejpam-5191	86	7	b	b	NOUN
ejpam-5191	86	8	}	}	PUNCT
ejpam-5191	86	9	and	and	CCONJ
ejpam-5191	86	10	f−(b	f−(b	PROPN
ejpam-5191	86	11	)	)	PUNCT
ejpam-5191	86	12	=	=	PRON
ejpam-5191	87	1	{	{	PUNCT
ejpam-5191	87	2	x	x	PUNCT
ejpam-5191	87	3	∈	∈	PROPN
ejpam-5191	87	4	x	x	INTJ
ejpam-5191	88	1	|	|	NOUN
ejpam-5191	88	2	f	f	X
ejpam-5191	88	3	(	(	PUNCT
ejpam-5191	88	4	x	x	NOUN
ejpam-5191	88	5	)	)	PUNCT
ejpam-5191	88	6	∩b	∩b	NOUN
ejpam-5191	88	7	̸=	̸=	PROPN
ejpam-5191	88	8	∅	∅	NOUN
ejpam-5191	88	9	}	}	PUNCT
ejpam-5191	88	10	.	.	PUNCT
ejpam-5191	89	1	in	in	ADP
ejpam-5191	89	2	particular	particular	ADJ
ejpam-5191	89	3	,	,	PUNCT
ejpam-5191	89	4	f−(y	f−(y	NOUN
ejpam-5191	89	5	)	)	PUNCT
ejpam-5191	89	6	=	=	SYM
ejpam-5191	90	1	{	{	PUNCT
ejpam-5191	90	2	x	x	PUNCT
ejpam-5191	90	3	∈	∈	PROPN
ejpam-5191	90	4	x	x	INTJ
ejpam-5191	91	1	|	|	ADV
ejpam-5191	91	2	y	y	PROPN
ejpam-5191	91	3	∈	∈	PROPN
ejpam-5191	91	4	f	f	X
ejpam-5191	91	5	(	(	PUNCT
ejpam-5191	91	6	x	x	NOUN
ejpam-5191	91	7	)	)	PUNCT
ejpam-5191	91	8	}	}	PUNCT
ejpam-5191	91	9	for	for	ADP
ejpam-5191	91	10	each	each	DET
ejpam-5191	91	11	point	point	NOUN
ejpam-5191	91	12	y	y	PROPN
ejpam-5191	91	13	∈	∈	PROPN
ejpam-5191	91	14	y	y	PROPN
ejpam-5191	91	15	.	.	PUNCT
ejpam-5191	92	1	for	for	ADP
ejpam-5191	92	2	each	each	PRON
ejpam-5191	92	3	a	a	DET
ejpam-5191	92	4	⊆	⊆	NUM
ejpam-5191	92	5	x	x	SYM
ejpam-5191	92	6	,	,	PUNCT
ejpam-5191	92	7	f	f	PROPN
ejpam-5191	92	8	(	(	PUNCT
ejpam-5191	92	9	a	a	NOUN
ejpam-5191	92	10	)	)	PUNCT
ejpam-5191	92	11	=	=	SYM
ejpam-5191	92	12	∪x∈af	∪x∈af	NOUN
ejpam-5191	92	13	(	(	PUNCT
ejpam-5191	92	14	x	x	NOUN
ejpam-5191	92	15	)	)	PUNCT
ejpam-5191	92	16	.	.	PUNCT
ejpam-5191	93	1	let	let	VERB
ejpam-5191	93	2	p(x	p(x	PROPN
ejpam-5191	93	3	)	)	PUNCT
ejpam-5191	93	4	be	be	AUX
ejpam-5191	93	5	the	the	DET
ejpam-5191	93	6	collection	collection	NOUN
ejpam-5191	93	7	of	of	ADP
ejpam-5191	93	8	all	all	DET
ejpam-5191	93	9	nonempty	nonempty	ADJ
ejpam-5191	93	10	subsets	subset	NOUN
ejpam-5191	93	11	of	of	ADP
ejpam-5191	93	12	x.	x.	NOUN
ejpam-5191	93	13	for	for	ADP
ejpam-5191	93	14	any	any	DET
ejpam-5191	93	15	τ1τ2	τ1τ2	ADJ
ejpam-5191	93	16	-	-	ADJ
ejpam-5191	93	17	open	open	ADJ
ejpam-5191	93	18	set	set	VERB
ejpam-5191	93	19	v	v	NOUN
ejpam-5191	93	20	of	of	ADP
ejpam-5191	93	21	a	a	DET
ejpam-5191	93	22	bitopological	bitopological	ADJ
ejpam-5191	93	23	space	space	NOUN
ejpam-5191	93	24	(	(	PUNCT
ejpam-5191	93	25	x	x	NOUN
ejpam-5191	93	26	,	,	PUNCT
ejpam-5191	93	27	τ1	τ1	NOUN
ejpam-5191	93	28	,	,	PUNCT
ejpam-5191	93	29	τ2	τ2	NOUN
ejpam-5191	93	30	)	)	PUNCT
ejpam-5191	93	31	,	,	PUNCT
ejpam-5191	93	32	we	we	PRON
ejpam-5191	93	33	denote	denote	VERB
ejpam-5191	93	34	v	v	ADP
ejpam-5191	93	35	+	+	NOUN
ejpam-5191	93	36	=	=	SYM
ejpam-5191	93	37	{	{	PUNCT
ejpam-5191	93	38	b	b	PROPN
ejpam-5191	93	39	∈	∈	PROPN
ejpam-5191	93	40	p(x	p(x	NOUN
ejpam-5191	93	41	)	)	PUNCT
ejpam-5191	94	1	|	|	ADV
ejpam-5191	94	2	b	b	NOUN
ejpam-5191	94	3	⊆	⊆	NUM
ejpam-5191	94	4	v	v	NOUN
ejpam-5191	94	5	}	}	PUNCT
ejpam-5191	94	6	and	and	CCONJ
ejpam-5191	94	7	v	v	ADP
ejpam-5191	94	8	−	−	PROPN
ejpam-5191	94	9	=	=	PUNCT
ejpam-5191	94	10	{	{	PUNCT
ejpam-5191	94	11	b	b	PROPN
ejpam-5191	94	12	∈	∈	PROPN
ejpam-5191	94	13	p(x	p(x	NOUN
ejpam-5191	94	14	)	)	PUNCT
ejpam-5191	94	15	|	|	ADV
ejpam-5191	94	16	b	b	NOUN
ejpam-5191	94	17	∩	∩	NOUN
ejpam-5191	94	18	v	v	ADP
ejpam-5191	94	19	̸=	̸=	PROPN
ejpam-5191	94	20	∅	∅	NOUN
ejpam-5191	94	21	}	}	PUNCT
ejpam-5191	94	22	.	.	PUNCT
ejpam-5191	95	1	p.	p.	NOUN
ejpam-5191	95	2	pue	pue	NOUN
ejpam-5191	95	3	-	-	PUNCT
ejpam-5191	95	4	on	on	ADP
ejpam-5191	95	5	,	,	PUNCT
ejpam-5191	95	6	s.	s.	PROPN
ejpam-5191	95	7	sompong	sompong	PROPN
ejpam-5191	95	8	,	,	PUNCT
ejpam-5191	95	9	c.	c.	PROPN
ejpam-5191	95	10	boonpok	boonpok	PROPN
ejpam-5191	95	11	/	/	SYM
ejpam-5191	95	12	eur	eur	PROPN
ejpam-5191	95	13	.	.	PUNCT
ejpam-5191	96	1	j.	j.	PROPN
ejpam-5191	96	2	pure	pure	PROPN
ejpam-5191	96	3	appl	appl	PROPN
ejpam-5191	96	4	.	.	PROPN
ejpam-5191	96	5	math	math	PROPN
ejpam-5191	96	6	,	,	PUNCT
ejpam-5191	96	7	17	17	NUM
ejpam-5191	96	8	(	(	PUNCT
ejpam-5191	96	9	3	3	NUM
ejpam-5191	96	10	)	)	PUNCT
ejpam-5191	96	11	(	(	PUNCT
ejpam-5191	96	12	2024	2024	NUM
ejpam-5191	96	13	)	)	PUNCT
ejpam-5191	96	14	,	,	PUNCT
ejpam-5191	96	15	1553	1553	NUM
ejpam-5191	96	16	-	-	SYM
ejpam-5191	96	17	1564	1564	NUM
ejpam-5191	96	18	1556	1556	NUM
ejpam-5191	96	19	3	3	NUM
ejpam-5191	96	20	.	.	PUNCT
ejpam-5191	96	21	weakly	weakly	ADJ
ejpam-5191	96	22	quasi	quasi	NOUN
ejpam-5191	96	23	(	(	PUNCT
ejpam-5191	96	24	τ1	τ1	PROPN
ejpam-5191	96	25	,	,	PUNCT
ejpam-5191	96	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	96	27	multifunctions	multifunction	NOUN
ejpam-5191	96	28	in	in	ADP
ejpam-5191	96	29	this	this	DET
ejpam-5191	96	30	section	section	NOUN
ejpam-5191	96	31	,	,	PUNCT
ejpam-5191	96	32	we	we	PRON
ejpam-5191	96	33	introduce	introduce	VERB
ejpam-5191	96	34	the	the	DET
ejpam-5191	96	35	concept	concept	NOUN
ejpam-5191	96	36	of	of	ADP
ejpam-5191	96	37	weakly	weakly	ADJ
ejpam-5191	96	38	quasi	quasi	NOUN
ejpam-5191	96	39	(	(	PUNCT
ejpam-5191	96	40	τ1	τ1	PROPN
ejpam-5191	96	41	,	,	PUNCT
ejpam-5191	96	42	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	96	43	multifunctions	multifunction	NOUN
ejpam-5191	96	44	.	.	PUNCT
ejpam-5191	97	1	moreover	moreover	ADV
ejpam-5191	97	2	,	,	PUNCT
ejpam-5191	97	3	some	some	DET
ejpam-5191	97	4	characterizations	characterization	NOUN
ejpam-5191	97	5	of	of	ADP
ejpam-5191	97	6	weakly	weakly	ADJ
ejpam-5191	97	7	quasi	quasi	NOUN
ejpam-5191	97	8	(	(	PUNCT
ejpam-5191	97	9	τ1	τ1	PROPN
ejpam-5191	97	10	,	,	PUNCT
ejpam-5191	97	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	97	12	multifunctions	multifunction	NOUN
ejpam-5191	97	13	are	be	AUX
ejpam-5191	97	14	discussed	discuss	VERB
ejpam-5191	97	15	.	.	PUNCT
ejpam-5191	98	1	definition	definition	NOUN
ejpam-5191	98	2	1	1	NUM
ejpam-5191	98	3	.	.	PUNCT
ejpam-5191	99	1	a	a	DET
ejpam-5191	99	2	multifunction	multifunction	NOUN
ejpam-5191	99	3	f	f	NOUN
ejpam-5191	99	4	:	:	PUNCT
ejpam-5191	99	5	(	(	PUNCT
ejpam-5191	99	6	x	x	NOUN
ejpam-5191	99	7	,	,	PUNCT
ejpam-5191	99	8	τ1	τ1	NOUN
ejpam-5191	99	9	,	,	PUNCT
ejpam-5191	99	10	τ2	τ2	NOUN
ejpam-5191	99	11	)	)	PUNCT
ejpam-5191	99	12	→	→	SYM
ejpam-5191	99	13	(	(	PUNCT
ejpam-5191	99	14	y	y	PROPN
ejpam-5191	99	15	,	,	PUNCT
ejpam-5191	99	16	σ1	σ1	PROPN
ejpam-5191	99	17	,	,	PUNCT
ejpam-5191	99	18	σ2	σ2	PROPN
ejpam-5191	99	19	)	)	PUNCT
ejpam-5191	99	20	is	be	AUX
ejpam-5191	99	21	said	say	VERB
ejpam-5191	99	22	to	to	PART
ejpam-5191	99	23	be	be	AUX
ejpam-5191	99	24	weakly	weakly	ADJ
ejpam-5191	99	25	quasi	quasi	NOUN
ejpam-5191	99	26	(	(	PUNCT
ejpam-5191	99	27	τ1	τ1	NOUN
ejpam-5191	99	28	,	,	PUNCT
ejpam-5191	99	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	99	30	at	at	ADP
ejpam-5191	99	31	a	a	DET
ejpam-5191	99	32	point	point	NOUN
ejpam-5191	99	33	x	x	SYM
ejpam-5191	99	34	∈	∈	NOUN
ejpam-5191	99	35	x	x	PUNCT
ejpam-5191	99	36	if	if	SCONJ
ejpam-5191	99	37	for	for	ADP
ejpam-5191	99	38	each	each	DET
ejpam-5191	99	39	σ1σ2	σ1σ2	VERB
ejpam-5191	99	40	-	-	ADJ
ejpam-5191	99	41	open	open	ADJ
ejpam-5191	99	42	sets	set	NOUN
ejpam-5191	99	43	v1	v1	NOUN
ejpam-5191	99	44	,	,	PUNCT
ejpam-5191	99	45	v2	v2	PROPN
ejpam-5191	99	46	of	of	ADP
ejpam-5191	99	47	y	y	PRON
ejpam-5191	99	48	such	such	ADJ
ejpam-5191	99	49	that	that	SCONJ
ejpam-5191	99	50	f	f	PROPN
ejpam-5191	99	51	(	(	PUNCT
ejpam-5191	99	52	x	x	X
ejpam-5191	99	53	)	)	PUNCT
ejpam-5191	99	54	∈	∈	NOUN
ejpam-5191	99	55	v	v	ADP
ejpam-5191	99	56	+	+	CCONJ
ejpam-5191	99	57	1	1	NUM
ejpam-5191	99	58	∩	∩	NOUN
ejpam-5191	99	59	v	v	ADP
ejpam-5191	99	60	−	−	PROPN
ejpam-5191	99	61	2	2	NUM
ejpam-5191	99	62	and	and	CCONJ
ejpam-5191	99	63	each	each	DET
ejpam-5191	99	64	τ1τ2	τ1τ2	ADJ
ejpam-5191	99	65	-	-	ADJ
ejpam-5191	99	66	open	open	ADJ
ejpam-5191	99	67	set	set	ADJ
ejpam-5191	99	68	u	u	NOUN
ejpam-5191	99	69	of	of	ADP
ejpam-5191	99	70	x	x	PUNCT
ejpam-5191	99	71	containing	contain	VERB
ejpam-5191	99	72	x	x	PRON
ejpam-5191	99	73	,	,	PUNCT
ejpam-5191	99	74	there	there	PRON
ejpam-5191	99	75	exists	exist	VERB
ejpam-5191	99	76	a	a	DET
ejpam-5191	99	77	nonempty	nonempty	ADJ
ejpam-5191	99	78	τ1τ2	τ1τ2	NOUN
ejpam-5191	99	79	-	-	ADJ
ejpam-5191	99	80	open	open	ADJ
ejpam-5191	99	81	set	set	NOUN
ejpam-5191	99	82	g	g	PROPN
ejpam-5191	99	83	such	such	ADJ
ejpam-5191	99	84	that	that	SCONJ
ejpam-5191	99	85	g	g	PROPN
ejpam-5191	99	86	⊆	⊆	NUM
ejpam-5191	99	87	u	u	NOUN
ejpam-5191	99	88	,	,	PUNCT
ejpam-5191	99	89	f	f	PROPN
ejpam-5191	99	90	(	(	PUNCT
ejpam-5191	99	91	g	g	NOUN
ejpam-5191	99	92	)	)	PUNCT
ejpam-5191	99	93	⊆	⊆	NUM
ejpam-5191	99	94	σ1σ2	σ1σ2	NOUN
ejpam-5191	99	95	-	-	PUNCT
ejpam-5191	99	96	cl(v1	cl(v1	X
ejpam-5191	99	97	)	)	PUNCT
ejpam-5191	99	98	and	and	CCONJ
ejpam-5191	99	99	σ1σ2	σ1σ2	NOUN
ejpam-5191	99	100	-	-	PUNCT
ejpam-5191	99	101	cl(v2	cl(v2	NOUN
ejpam-5191	99	102	)	)	PUNCT
ejpam-5191	99	103	∩	∩	PROPN
ejpam-5191	99	104	f	f	X
ejpam-5191	99	105	(	(	PUNCT
ejpam-5191	99	106	z	z	NOUN
ejpam-5191	99	107	)	)	PUNCT
ejpam-5191	99	108	̸=	̸=	NOUN
ejpam-5191	99	109	∅	∅	NOUN
ejpam-5191	99	110	for	for	ADP
ejpam-5191	99	111	every	every	DET
ejpam-5191	99	112	z	z	PROPN
ejpam-5191	99	113	∈	∈	PROPN
ejpam-5191	99	114	g.	g.	NOUN
ejpam-5191	99	115	a	a	DET
ejpam-5191	99	116	multifunction	multifunction	NOUN
ejpam-5191	100	1	f	f	NOUN
ejpam-5191	100	2	:	:	PUNCT
ejpam-5191	100	3	(	(	PUNCT
ejpam-5191	100	4	x	x	NOUN
ejpam-5191	100	5	,	,	PUNCT
ejpam-5191	100	6	τ1	τ1	NOUN
ejpam-5191	100	7	,	,	PUNCT
ejpam-5191	100	8	τ2	τ2	NOUN
ejpam-5191	100	9	)	)	PUNCT
ejpam-5191	100	10	→	→	SYM
ejpam-5191	100	11	(	(	PUNCT
ejpam-5191	100	12	y	y	PROPN
ejpam-5191	100	13	,	,	PUNCT
ejpam-5191	100	14	σ1	σ1	PROPN
ejpam-5191	100	15	,	,	PUNCT
ejpam-5191	100	16	σ2	σ2	PROPN
ejpam-5191	100	17	)	)	PUNCT
ejpam-5191	100	18	is	be	AUX
ejpam-5191	100	19	said	say	VERB
ejpam-5191	100	20	to	to	PART
ejpam-5191	100	21	be	be	AUX
ejpam-5191	100	22	weakly	weakly	ADJ
ejpam-5191	100	23	quasi	quasi	NOUN
ejpam-5191	100	24	(	(	PUNCT
ejpam-5191	100	25	τ1	τ1	NOUN
ejpam-5191	100	26	,	,	PUNCT
ejpam-5191	100	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	100	28	if	if	SCONJ
ejpam-5191	100	29	f	f	PROPN
ejpam-5191	100	30	is	be	AUX
ejpam-5191	100	31	weakly	weakly	ADJ
ejpam-5191	100	32	quasi	quasi	NOUN
ejpam-5191	100	33	(	(	PUNCT
ejpam-5191	100	34	τ1	τ1	NOUN
ejpam-5191	100	35	,	,	PUNCT
ejpam-5191	100	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	100	37	at	at	ADP
ejpam-5191	100	38	each	each	DET
ejpam-5191	100	39	point	point	NOUN
ejpam-5191	100	40	of	of	ADP
ejpam-5191	100	41	x.	x.	NOUN
ejpam-5191	100	42	theorem	theorem	VERB
ejpam-5191	100	43	1	1	NUM
ejpam-5191	100	44	.	.	X
ejpam-5191	100	45	for	for	ADP
ejpam-5191	100	46	a	a	DET
ejpam-5191	100	47	multifunction	multifunction	NOUN
ejpam-5191	100	48	f	f	NOUN
ejpam-5191	100	49	:	:	PUNCT
ejpam-5191	100	50	(	(	PUNCT
ejpam-5191	100	51	x	x	NOUN
ejpam-5191	100	52	,	,	PUNCT
ejpam-5191	100	53	τ1	τ1	NOUN
ejpam-5191	100	54	,	,	PUNCT
ejpam-5191	100	55	τ2	τ2	NOUN
ejpam-5191	100	56	)	)	PUNCT
ejpam-5191	100	57	→	→	SYM
ejpam-5191	100	58	(	(	PUNCT
ejpam-5191	100	59	y	y	PROPN
ejpam-5191	100	60	,	,	PUNCT
ejpam-5191	100	61	σ1	σ1	PROPN
ejpam-5191	100	62	,	,	PUNCT
ejpam-5191	100	63	σ2	σ2	NOUN
ejpam-5191	100	64	)	)	PUNCT
ejpam-5191	100	65	,	,	PUNCT
ejpam-5191	100	66	the	the	DET
ejpam-5191	100	67	following	follow	VERB
ejpam-5191	100	68	properties	property	NOUN
ejpam-5191	100	69	are	be	AUX
ejpam-5191	100	70	equivalent	equivalent	ADJ
ejpam-5191	100	71	:	:	PUNCT
ejpam-5191	100	72	(	(	PUNCT
ejpam-5191	100	73	1	1	X
ejpam-5191	100	74	)	)	PUNCT
ejpam-5191	100	75	f	f	PROPN
ejpam-5191	100	76	is	be	AUX
ejpam-5191	100	77	weakly	weakly	ADJ
ejpam-5191	100	78	quasi	quasi	NOUN
ejpam-5191	100	79	(	(	PUNCT
ejpam-5191	100	80	τ1	τ1	NOUN
ejpam-5191	100	81	,	,	PUNCT
ejpam-5191	100	82	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	100	83	;	;	PUNCT
ejpam-5191	100	84	(	(	PUNCT
ejpam-5191	100	85	2	2	X
ejpam-5191	100	86	)	)	PUNCT
ejpam-5191	100	87	for	for	ADP
ejpam-5191	100	88	each	each	DET
ejpam-5191	100	89	x	x	SYM
ejpam-5191	100	90	∈	∈	PROPN
ejpam-5191	100	91	x	x	X
ejpam-5191	100	92	and	and	CCONJ
ejpam-5191	100	93	every	every	DET
ejpam-5191	100	94	σ1σ2	σ1σ2	VERB
ejpam-5191	100	95	-	-	ADJ
ejpam-5191	100	96	open	open	ADJ
ejpam-5191	100	97	sets	set	NOUN
ejpam-5191	100	98	v1	v1	NOUN
ejpam-5191	100	99	,	,	PUNCT
ejpam-5191	100	100	v2	v2	PROPN
ejpam-5191	100	101	of	of	ADP
ejpam-5191	100	102	y	y	PRON
ejpam-5191	100	103	such	such	ADJ
ejpam-5191	100	104	that	that	SCONJ
ejpam-5191	100	105	f	f	PROPN
ejpam-5191	100	106	(	(	PUNCT
ejpam-5191	100	107	x	x	X
ejpam-5191	100	108	)	)	PUNCT
ejpam-5191	100	109	∈	∈	NOUN
ejpam-5191	100	110	v	v	ADP
ejpam-5191	100	111	+	+	CCONJ
ejpam-5191	100	112	1	1	NUM
ejpam-5191	100	113	∩	∩	NOUN
ejpam-5191	100	114	v	v	ADP
ejpam-5191	100	115	−	−	PROPN
ejpam-5191	100	116	2	2	NUM
ejpam-5191	100	117	,	,	PUNCT
ejpam-5191	100	118	there	there	PRON
ejpam-5191	100	119	exists	exist	VERB
ejpam-5191	100	120	a	a	DET
ejpam-5191	100	121	(	(	PUNCT
ejpam-5191	100	122	τ1	τ1	NOUN
ejpam-5191	100	123	,	,	PUNCT
ejpam-5191	100	124	τ2)s	τ2)s	NOUN
ejpam-5191	100	125	-	-	PUNCT
ejpam-5191	100	126	open	open	ADJ
ejpam-5191	100	127	set	set	NOUN
ejpam-5191	100	128	of	of	ADP
ejpam-5191	100	129	x	x	PUNCT
ejpam-5191	100	130	containing	contain	VERB
ejpam-5191	100	131	x	x	PUNCT
ejpam-5191	100	132	such	such	ADJ
ejpam-5191	100	133	that	that	SCONJ
ejpam-5191	100	134	f	f	PROPN
ejpam-5191	100	135	(	(	PUNCT
ejpam-5191	100	136	u	u	NOUN
ejpam-5191	100	137	)	)	PUNCT
ejpam-5191	100	138	⊆	⊆	NUM
ejpam-5191	100	139	σ1σ2	σ1σ2	NOUN
ejpam-5191	100	140	-	-	PUNCT
ejpam-5191	100	141	cl(v1	cl(v1	X
ejpam-5191	100	142	)	)	PUNCT
ejpam-5191	100	143	and	and	CCONJ
ejpam-5191	100	144	σ1σ2	σ1σ2	NOUN
ejpam-5191	100	145	-	-	PUNCT
ejpam-5191	100	146	cl(v2	cl(v2	NOUN
ejpam-5191	100	147	)	)	PUNCT
ejpam-5191	100	148	∩	∩	PROPN
ejpam-5191	100	149	f	f	X
ejpam-5191	100	150	(	(	PUNCT
ejpam-5191	100	151	z	z	NOUN
ejpam-5191	100	152	)	)	PUNCT
ejpam-5191	100	153	̸=	̸=	NOUN
ejpam-5191	100	154	∅	∅	NOUN
ejpam-5191	100	155	for	for	ADP
ejpam-5191	100	156	every	every	DET
ejpam-5191	100	157	z	z	NOUN
ejpam-5191	100	158	∈	∈	PROPN
ejpam-5191	100	159	u	u	NOUN
ejpam-5191	100	160	;	;	PUNCT
ejpam-5191	100	161	(	(	PUNCT
ejpam-5191	100	162	3	3	X
ejpam-5191	100	163	)	)	PUNCT
ejpam-5191	100	164	τ1τ2	τ1τ2	NOUN
ejpam-5191	100	165	-	-	NOUN
ejpam-5191	100	166	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	100	167	-	-	PUNCT
ejpam-5191	100	168	cl(f	cl(f	NOUN
ejpam-5191	100	169	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	100	170	-	-	PUNCT
ejpam-5191	100	171	int(k1	int(k1	PROPN
ejpam-5191	100	172	)	)	PUNCT
ejpam-5191	100	173	)	)	PUNCT
ejpam-5191	100	174	∪	∪	ADP
ejpam-5191	100	175	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	100	176	-	-	PUNCT
ejpam-5191	100	177	int(k2	int(k2	NOUN
ejpam-5191	100	178	)	)	PUNCT
ejpam-5191	100	179	)	)	PUNCT
ejpam-5191	100	180	)	)	PUNCT
ejpam-5191	100	181	)	)	PUNCT
ejpam-5191	101	1	⊆	⊆	NUM
ejpam-5191	101	2	f−(k1	f−(k1	NOUN
ejpam-5191	101	3	)	)	PUNCT
ejpam-5191	101	4	∪	∪	ADP
ejpam-5191	101	5	f+(k2	f+(k2	NOUN
ejpam-5191	101	6	)	)	PUNCT
ejpam-5191	101	7	for	for	ADP
ejpam-5191	101	8	every	every	DET
ejpam-5191	101	9	σ1σ2	σ1σ2	NUM
ejpam-5191	101	10	-	-	PUNCT
ejpam-5191	101	11	closed	closed	ADJ
ejpam-5191	101	12	sets	set	NOUN
ejpam-5191	101	13	k1,k2	k1,k2	PROPN
ejpam-5191	101	14	of	of	ADP
ejpam-5191	101	15	y	y	PROPN
ejpam-5191	101	16	;	;	PUNCT
ejpam-5191	101	17	(	(	PUNCT
ejpam-5191	101	18	4	4	X
ejpam-5191	101	19	)	)	PUNCT
ejpam-5191	101	20	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5191	101	21	)	)	PUNCT
ejpam-5191	101	22	⊆	⊆	NUM
ejpam-5191	101	23	(	(	PUNCT
ejpam-5191	101	24	τ1	τ1	NOUN
ejpam-5191	101	25	,	,	PUNCT
ejpam-5191	101	26	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	101	27	+	+	ADJ
ejpam-5191	101	28	(	(	PUNCT
ejpam-5191	101	29	σ1σ2	σ1σ2	X
ejpam-5191	101	30	-	-	PUNCT
ejpam-5191	101	31	cl(v1))∩f−(σ1σ2	cl(v1))∩f−(σ1σ2	NOUN
ejpam-5191	101	32	-	-	PUNCT
ejpam-5191	101	33	cl(v2	cl(v2	NOUN
ejpam-5191	101	34	)	)	PUNCT
ejpam-5191	101	35	)	)	PUNCT
ejpam-5191	101	36	)	)	PUNCT
ejpam-5191	102	1	for	for	ADP
ejpam-5191	102	2	every	every	DET
ejpam-5191	102	3	σ1σ2open	σ1σ2open	NUM
ejpam-5191	102	4	sets	set	NOUN
ejpam-5191	102	5	v1	v1	NOUN
ejpam-5191	102	6	,	,	PUNCT
ejpam-5191	102	7	v2	v2	PROPN
ejpam-5191	102	8	of	of	ADP
ejpam-5191	102	9	y	y	PROPN
ejpam-5191	102	10	;	;	PUNCT
ejpam-5191	102	11	(	(	PUNCT
ejpam-5191	102	12	5	5	X
ejpam-5191	102	13	)	)	PUNCT
ejpam-5191	102	14	(	(	PUNCT
ejpam-5191	102	15	τ1	τ1	PROPN
ejpam-5191	102	16	,	,	PUNCT
ejpam-5191	102	17	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	102	18	−(v1)∪f+(v2	−(v1)∪f+(v2	PROPN
ejpam-5191	102	19	)	)	PUNCT
ejpam-5191	102	20	)	)	PUNCT
ejpam-5191	103	1	⊆	⊆	X
ejpam-5191	103	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	103	3	-	-	PUNCT
ejpam-5191	103	4	cl(v1))∪f+(σ1σ2	cl(v1))∪f+(σ1σ2	NOUN
ejpam-5191	103	5	-	-	NOUN
ejpam-5191	103	6	cl(v2	cl(v2	NOUN
ejpam-5191	103	7	)	)	PUNCT
ejpam-5191	103	8	)	)	PUNCT
ejpam-5191	103	9	for	for	ADP
ejpam-5191	103	10	every	every	DET
ejpam-5191	103	11	σ1σ2open	σ1σ2open	NUM
ejpam-5191	103	12	sets	set	NOUN
ejpam-5191	103	13	v1	v1	NOUN
ejpam-5191	103	14	,	,	PUNCT
ejpam-5191	103	15	v2	v2	PROPN
ejpam-5191	103	16	of	of	ADP
ejpam-5191	103	17	y	y	PROPN
ejpam-5191	103	18	.	.	PUNCT
ejpam-5191	104	1	proof	proof	NOUN
ejpam-5191	104	2	.	.	PUNCT
ejpam-5191	105	1	(	(	PUNCT
ejpam-5191	105	2	1	1	X
ejpam-5191	105	3	)	)	PUNCT
ejpam-5191	105	4	⇒	⇒	NOUN
ejpam-5191	105	5	(	(	PUNCT
ejpam-5191	105	6	2	2	NUM
ejpam-5191	105	7	):	):	PUNCT
ejpam-5191	105	8	let	let	VERB
ejpam-5191	105	9	u	u	PRON
ejpam-5191	105	10	(	(	PUNCT
ejpam-5191	105	11	x	x	X
ejpam-5191	105	12	)	)	PUNCT
ejpam-5191	105	13	the	the	DET
ejpam-5191	105	14	family	family	NOUN
ejpam-5191	105	15	of	of	ADP
ejpam-5191	105	16	all	all	DET
ejpam-5191	105	17	τ1τ2	τ1τ2	ADJ
ejpam-5191	105	18	-	-	ADJ
ejpam-5191	105	19	open	open	ADJ
ejpam-5191	105	20	sets	set	NOUN
ejpam-5191	105	21	of	of	ADP
ejpam-5191	105	22	x	x	PUNCT
ejpam-5191	105	23	containing	contain	VERB
ejpam-5191	105	24	x.	x.	NOUN
ejpam-5191	105	25	let	let	VERB
ejpam-5191	105	26	v1	v1	NOUN
ejpam-5191	105	27	,	,	PUNCT
ejpam-5191	105	28	v2	v2	PROPN
ejpam-5191	105	29	be	be	AUX
ejpam-5191	105	30	any	any	DET
ejpam-5191	105	31	σ1σ2	σ1σ2	NOUN
ejpam-5191	105	32	-	-	PUNCT
ejpam-5191	105	33	open	open	ADJ
ejpam-5191	105	34	sets	set	NOUN
ejpam-5191	105	35	of	of	ADP
ejpam-5191	105	36	y	y	PRON
ejpam-5191	105	37	such	such	ADJ
ejpam-5191	105	38	that	that	SCONJ
ejpam-5191	105	39	f	f	PROPN
ejpam-5191	105	40	(	(	PUNCT
ejpam-5191	105	41	x	x	X
ejpam-5191	105	42	)	)	PUNCT
ejpam-5191	105	43	∈	∈	NOUN
ejpam-5191	105	44	v	v	ADP
ejpam-5191	105	45	+	+	CCONJ
ejpam-5191	105	46	1	1	NUM
ejpam-5191	105	47	∩	∩	NOUN
ejpam-5191	105	48	v	v	ADP
ejpam-5191	105	49	−	−	PROPN
ejpam-5191	105	50	2	2	NUM
ejpam-5191	105	51	.	.	PUNCT
ejpam-5191	106	1	for	for	ADP
ejpam-5191	106	2	each	each	DET
ejpam-5191	106	3	h	h	NOUN
ejpam-5191	106	4	∈	∈	PROPN
ejpam-5191	106	5	u	u	NOUN
ejpam-5191	106	6	(	(	PUNCT
ejpam-5191	106	7	x	x	NOUN
ejpam-5191	106	8	)	)	PUNCT
ejpam-5191	106	9	,	,	PUNCT
ejpam-5191	106	10	there	there	PRON
ejpam-5191	106	11	exists	exist	VERB
ejpam-5191	106	12	a	a	DET
ejpam-5191	106	13	nonempty	nonempty	ADJ
ejpam-5191	106	14	τ1τ2	τ1τ2	NOUN
ejpam-5191	106	15	-	-	ADJ
ejpam-5191	106	16	open	open	ADJ
ejpam-5191	106	17	set	set	NOUN
ejpam-5191	106	18	gh	gh	PROPN
ejpam-5191	107	1	such	such	ADJ
ejpam-5191	107	2	that	that	SCONJ
ejpam-5191	107	3	gh	gh	PROPN
ejpam-5191	107	4	⊆	⊆	NUM
ejpam-5191	107	5	h	h	NOUN
ejpam-5191	107	6	,	,	PUNCT
ejpam-5191	107	7	f	f	PROPN
ejpam-5191	107	8	(	(	PUNCT
ejpam-5191	107	9	gh	gh	PROPN
ejpam-5191	107	10	)	)	PUNCT
ejpam-5191	107	11	⊆	⊆	NUM
ejpam-5191	107	12	σ1σ2	σ1σ2	NOUN
ejpam-5191	107	13	-	-	PUNCT
ejpam-5191	107	14	cl(v1	cl(v1	X
ejpam-5191	107	15	)	)	PUNCT
ejpam-5191	107	16	and	and	CCONJ
ejpam-5191	107	17	σ1σ2	σ1σ2	NOUN
ejpam-5191	107	18	-	-	PUNCT
ejpam-5191	107	19	cl(v2	cl(v2	NOUN
ejpam-5191	107	20	)	)	PUNCT
ejpam-5191	107	21	∩	∩	PROPN
ejpam-5191	107	22	f	f	PROPN
ejpam-5191	107	23	(	(	PUNCT
ejpam-5191	107	24	y	y	NOUN
ejpam-5191	107	25	)	)	PUNCT
ejpam-5191	107	26	̸=	̸=	NOUN
ejpam-5191	107	27	∅	∅	NOUN
ejpam-5191	107	28	for	for	ADP
ejpam-5191	107	29	each	each	DET
ejpam-5191	107	30	y	y	PROPN
ejpam-5191	107	31	∈	∈	PROPN
ejpam-5191	107	32	gh	gh	PROPN
ejpam-5191	107	33	.	.	PUNCT
ejpam-5191	108	1	let	let	VERB
ejpam-5191	108	2	w	w	NOUN
ejpam-5191	108	3	=	=	PUNCT
ejpam-5191	108	4	∪{gh	∪{gh	NOUN
ejpam-5191	109	1	|	|	ADV
ejpam-5191	109	2	h	h	NOUN
ejpam-5191	109	3	∈	∈	PROPN
ejpam-5191	109	4	u	u	NOUN
ejpam-5191	109	5	(	(	PUNCT
ejpam-5191	109	6	x	x	NOUN
ejpam-5191	109	7	)	)	PUNCT
ejpam-5191	109	8	}	}	PUNCT
ejpam-5191	109	9	.	.	PUNCT
ejpam-5191	110	1	then	then	ADV
ejpam-5191	110	2	,	,	PUNCT
ejpam-5191	110	3	w	w	PROPN
ejpam-5191	110	4	is	be	AUX
ejpam-5191	110	5	τ1τ2	τ1τ2	NOUN
ejpam-5191	110	6	-	-	ADJ
ejpam-5191	110	7	open	open	ADJ
ejpam-5191	110	8	in	in	ADP
ejpam-5191	110	9	x	x	X
ejpam-5191	110	10	,	,	PUNCT
ejpam-5191	110	11	x	x	SYM
ejpam-5191	110	12	∈	∈	PROPN
ejpam-5191	110	13	τ1τ2	τ1τ2	NOUN
ejpam-5191	110	14	-	-	NOUN
ejpam-5191	110	15	cl(w	cl(w	NOUN
ejpam-5191	110	16	)	)	PUNCT
ejpam-5191	110	17	,	,	PUNCT
ejpam-5191	110	18	f	f	PROPN
ejpam-5191	110	19	(	(	PUNCT
ejpam-5191	110	20	w	w	PROPN
ejpam-5191	110	21	)	)	PUNCT
ejpam-5191	110	22	⊆	⊆	NUM
ejpam-5191	110	23	σ1σ2	σ1σ2	NOUN
ejpam-5191	110	24	-	-	PUNCT
ejpam-5191	110	25	cl(v1	cl(v1	X
ejpam-5191	110	26	)	)	PUNCT
ejpam-5191	110	27	and	and	CCONJ
ejpam-5191	110	28	σ1σ2	σ1σ2	NOUN
ejpam-5191	110	29	-	-	PUNCT
ejpam-5191	110	30	cl(v2	cl(v2	NOUN
ejpam-5191	110	31	)	)	PUNCT
ejpam-5191	110	32	∩	∩	PROPN
ejpam-5191	110	33	f	f	PROPN
ejpam-5191	110	34	(	(	PUNCT
ejpam-5191	110	35	w	w	NOUN
ejpam-5191	110	36	)	)	PUNCT
ejpam-5191	110	37	̸=	̸=	NOUN
ejpam-5191	110	38	∅	∅	NOUN
ejpam-5191	110	39	for	for	ADP
ejpam-5191	110	40	every	every	DET
ejpam-5191	110	41	w	w	PROPN
ejpam-5191	110	42	∈	∈	PROPN
ejpam-5191	110	43	w	w	PROPN
ejpam-5191	110	44	.	.	PUNCT
ejpam-5191	111	1	put	put	VERB
ejpam-5191	111	2	u	u	NOUN
ejpam-5191	112	1	=	=	NOUN
ejpam-5191	112	2	w	w	NOUN
ejpam-5191	112	3	∪	∪	X
ejpam-5191	112	4	{	{	PUNCT
ejpam-5191	112	5	x	x	NOUN
ejpam-5191	112	6	}	}	PUNCT
ejpam-5191	112	7	,	,	PUNCT
ejpam-5191	112	8	then	then	ADV
ejpam-5191	112	9	w	w	PROPN
ejpam-5191	112	10	⊆	⊆	NUM
ejpam-5191	112	11	u	u	NOUN
ejpam-5191	112	12	⊆	⊆	NUM
ejpam-5191	112	13	τ1τ2	τ1τ2	NOUN
ejpam-5191	112	14	-	-	NOUN
ejpam-5191	112	15	cl(w	cl(w	NOUN
ejpam-5191	112	16	)	)	PUNCT
ejpam-5191	112	17	.	.	PUNCT
ejpam-5191	113	1	thus	thus	ADV
ejpam-5191	113	2	,	,	PUNCT
ejpam-5191	113	3	u	u	NOUN
ejpam-5191	113	4	is	be	AUX
ejpam-5191	113	5	a	a	DET
ejpam-5191	113	6	(	(	PUNCT
ejpam-5191	113	7	τ1	τ1	NOUN
ejpam-5191	113	8	,	,	PUNCT
ejpam-5191	113	9	τ2)s	τ2)s	NOUN
ejpam-5191	113	10	-	-	PUNCT
ejpam-5191	113	11	open	open	ADJ
ejpam-5191	113	12	set	set	NOUN
ejpam-5191	113	13	of	of	ADP
ejpam-5191	113	14	x	x	PUNCT
ejpam-5191	113	15	containing	contain	VERB
ejpam-5191	113	16	x	x	PUNCT
ejpam-5191	113	17	such	such	ADJ
ejpam-5191	113	18	that	that	SCONJ
ejpam-5191	113	19	f	f	PROPN
ejpam-5191	113	20	(	(	PUNCT
ejpam-5191	113	21	u	u	NOUN
ejpam-5191	113	22	)	)	PUNCT
ejpam-5191	113	23	⊆	⊆	NUM
ejpam-5191	113	24	σ1σ2	σ1σ2	NOUN
ejpam-5191	113	25	-	-	PUNCT
ejpam-5191	113	26	cl(v1	cl(v1	X
ejpam-5191	113	27	)	)	PUNCT
ejpam-5191	113	28	and	and	CCONJ
ejpam-5191	113	29	σ1σ2	σ1σ2	PROPN
ejpam-5191	113	30	-	-	ADJ
ejpam-5191	113	31	cl(v2)∩f	cl(v2)∩f	ADJ
ejpam-5191	113	32	(	(	PUNCT
ejpam-5191	113	33	z	z	NOUN
ejpam-5191	113	34	)	)	PUNCT
ejpam-5191	113	35	̸=	̸=	NOUN
ejpam-5191	113	36	∅	∅	NOUN
ejpam-5191	113	37	for	for	ADP
ejpam-5191	113	38	every	every	DET
ejpam-5191	113	39	z	z	NOUN
ejpam-5191	113	40	∈	∈	PROPN
ejpam-5191	113	41	u	u	NOUN
ejpam-5191	113	42	.	.	PUNCT
ejpam-5191	114	1	(	(	PUNCT
ejpam-5191	114	2	2	2	X
ejpam-5191	114	3	)	)	PUNCT
ejpam-5191	114	4	⇒	⇒	NOUN
ejpam-5191	114	5	(	(	PUNCT
ejpam-5191	114	6	4	4	NUM
ejpam-5191	114	7	):	):	PUNCT
ejpam-5191	114	8	let	let	VERB
ejpam-5191	114	9	v1	v1	NOUN
ejpam-5191	114	10	,	,	PUNCT
ejpam-5191	114	11	v2	v2	PROPN
ejpam-5191	114	12	be	be	AUX
ejpam-5191	114	13	any	any	DET
ejpam-5191	114	14	σ1σ2	σ1σ2	NOUN
ejpam-5191	114	15	-	-	PUNCT
ejpam-5191	114	16	open	open	ADJ
ejpam-5191	114	17	sets	set	NOUN
ejpam-5191	114	18	of	of	ADP
ejpam-5191	114	19	y	y	PROPN
ejpam-5191	114	20	and	and	CCONJ
ejpam-5191	114	21	x	x	PUNCT
ejpam-5191	114	22	∈	∈	NOUN
ejpam-5191	114	23	f+(v1	f+(v1	NOUN
ejpam-5191	114	24	)	)	PUNCT
ejpam-5191	114	25	∩	∩	NOUN
ejpam-5191	114	26	f−(v2	f−(v2	NUM
ejpam-5191	114	27	)	)	PUNCT
ejpam-5191	114	28	.	.	PUNCT
ejpam-5191	115	1	then	then	ADV
ejpam-5191	115	2	,	,	PUNCT
ejpam-5191	115	3	f	f	PROPN
ejpam-5191	115	4	(	(	PUNCT
ejpam-5191	115	5	x	x	X
ejpam-5191	115	6	)	)	PUNCT
ejpam-5191	115	7	∈	∈	NOUN
ejpam-5191	115	8	v	v	ADP
ejpam-5191	115	9	+	+	CCONJ
ejpam-5191	115	10	1	1	NUM
ejpam-5191	115	11	∩	∩	NOUN
ejpam-5191	115	12	v	v	ADP
ejpam-5191	115	13	−	−	PROPN
ejpam-5191	115	14	2	2	NUM
ejpam-5191	115	15	and	and	CCONJ
ejpam-5191	115	16	there	there	PRON
ejpam-5191	115	17	exists	exist	VERB
ejpam-5191	115	18	a	a	DET
ejpam-5191	115	19	(	(	PUNCT
ejpam-5191	115	20	τ1	τ1	NOUN
ejpam-5191	115	21	,	,	PUNCT
ejpam-5191	115	22	τ2)s	τ2)s	NOUN
ejpam-5191	115	23	-	-	PUNCT
ejpam-5191	115	24	open	open	ADJ
ejpam-5191	115	25	set	set	NOUN
ejpam-5191	115	26	u	u	NOUN
ejpam-5191	115	27	of	of	ADP
ejpam-5191	115	28	x	x	PUNCT
ejpam-5191	115	29	containing	contain	VERB
ejpam-5191	115	30	x	x	PUNCT
ejpam-5191	115	31	such	such	ADJ
ejpam-5191	115	32	that	that	SCONJ
ejpam-5191	115	33	f	f	PROPN
ejpam-5191	115	34	(	(	PUNCT
ejpam-5191	115	35	u	u	NOUN
ejpam-5191	115	36	)	)	PUNCT
ejpam-5191	115	37	⊆	⊆	NUM
ejpam-5191	115	38	σ1σ2	σ1σ2	NOUN
ejpam-5191	115	39	-	-	PUNCT
ejpam-5191	115	40	cl(v1	cl(v1	X
ejpam-5191	115	41	)	)	PUNCT
ejpam-5191	115	42	and	and	CCONJ
ejpam-5191	115	43	σ1σ2	σ1σ2	NOUN
ejpam-5191	115	44	-	-	PUNCT
ejpam-5191	115	45	cl(v2	cl(v2	NOUN
ejpam-5191	115	46	)	)	PUNCT
ejpam-5191	115	47	∩	∩	PROPN
ejpam-5191	115	48	f	f	X
ejpam-5191	115	49	(	(	PUNCT
ejpam-5191	115	50	z	z	NOUN
ejpam-5191	115	51	)	)	PUNCT
ejpam-5191	115	52	̸=	̸=	NOUN
ejpam-5191	115	53	∅	∅	NOUN
ejpam-5191	115	54	for	for	ADP
ejpam-5191	115	55	each	each	DET
ejpam-5191	115	56	z	z	NOUN
ejpam-5191	115	57	∈	∈	PROPN
ejpam-5191	115	58	u	u	NOUN
ejpam-5191	115	59	.	.	PUNCT
ejpam-5191	116	1	thus	thus	ADV
ejpam-5191	116	2	,	,	PUNCT
ejpam-5191	116	3	x	x	PUNCT
ejpam-5191	116	4	∈	∈	PROPN
ejpam-5191	116	5	u	u	NOUN
ejpam-5191	116	6	⊆	⊆	NUM
ejpam-5191	116	7	(	(	PUNCT
ejpam-5191	116	8	τ1	τ1	NOUN
ejpam-5191	116	9	,	,	PUNCT
ejpam-5191	116	10	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	117	1	+	+	ADJ
ejpam-5191	117	2	(	(	PUNCT
ejpam-5191	117	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	117	4	-	-	PUNCT
ejpam-5191	117	5	cl(v1	cl(v1	NOUN
ejpam-5191	117	6	)	)	PUNCT
ejpam-5191	117	7	)	)	PUNCT
ejpam-5191	117	8	∩	∩	ADJ
ejpam-5191	117	9	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	117	10	-	-	PUNCT
ejpam-5191	117	11	cl(v2	cl(v2	NOUN
ejpam-5191	117	12	)	)	PUNCT
ejpam-5191	117	13	)	)	PUNCT
ejpam-5191	117	14	)	)	PUNCT
ejpam-5191	117	15	and	and	CCONJ
ejpam-5191	117	16	so	so	ADV
ejpam-5191	117	17	f+(v1	f+(v1	ADJ
ejpam-5191	117	18	)	)	PUNCT
ejpam-5191	117	19	∩	∩	NOUN
ejpam-5191	117	20	f−(v2	f−(v2	X
ejpam-5191	117	21	)	)	PUNCT
ejpam-5191	117	22	⊆	⊆	NUM
ejpam-5191	117	23	(	(	PUNCT
ejpam-5191	117	24	τ1	τ1	NOUN
ejpam-5191	117	25	,	,	PUNCT
ejpam-5191	117	26	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	118	1	+	+	ADJ
ejpam-5191	118	2	(	(	PUNCT
ejpam-5191	118	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	118	4	-	-	PUNCT
ejpam-5191	118	5	cl(v1	cl(v1	NOUN
ejpam-5191	118	6	)	)	PUNCT
ejpam-5191	118	7	)	)	PUNCT
ejpam-5191	118	8	∩	∩	ADJ
ejpam-5191	118	9	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	118	10	-	-	PUNCT
ejpam-5191	118	11	cl(v2	cl(v2	NOUN
ejpam-5191	118	12	)	)	PUNCT
ejpam-5191	118	13	)	)	PUNCT
ejpam-5191	118	14	)	)	PUNCT
ejpam-5191	118	15	.	.	PUNCT
ejpam-5191	119	1	p.	p.	NOUN
ejpam-5191	119	2	pue	pue	NOUN
ejpam-5191	119	3	-	-	PUNCT
ejpam-5191	119	4	on	on	ADP
ejpam-5191	119	5	,	,	PUNCT
ejpam-5191	119	6	s.	s.	PROPN
ejpam-5191	119	7	sompong	sompong	PROPN
ejpam-5191	119	8	,	,	PUNCT
ejpam-5191	119	9	c.	c.	PROPN
ejpam-5191	119	10	boonpok	boonpok	PROPN
ejpam-5191	119	11	/	/	SYM
ejpam-5191	119	12	eur	eur	PROPN
ejpam-5191	119	13	.	.	PUNCT
ejpam-5191	120	1	j.	j.	PROPN
ejpam-5191	120	2	pure	pure	PROPN
ejpam-5191	120	3	appl	appl	PROPN
ejpam-5191	120	4	.	.	PROPN
ejpam-5191	120	5	math	math	PROPN
ejpam-5191	120	6	,	,	PUNCT
ejpam-5191	120	7	17	17	NUM
ejpam-5191	120	8	(	(	PUNCT
ejpam-5191	120	9	3	3	NUM
ejpam-5191	120	10	)	)	PUNCT
ejpam-5191	120	11	(	(	PUNCT
ejpam-5191	120	12	2024	2024	NUM
ejpam-5191	120	13	)	)	PUNCT
ejpam-5191	120	14	,	,	PUNCT
ejpam-5191	120	15	1553	1553	NUM
ejpam-5191	120	16	-	-	SYM
ejpam-5191	120	17	1564	1564	NUM
ejpam-5191	120	18	1557	1557	NUM
ejpam-5191	120	19	(	(	PUNCT
ejpam-5191	120	20	4	4	NUM
ejpam-5191	120	21	)	)	PUNCT
ejpam-5191	120	22	⇒	⇒	NOUN
ejpam-5191	120	23	(	(	PUNCT
ejpam-5191	120	24	5	5	NUM
ejpam-5191	120	25	):	):	PUNCT
ejpam-5191	120	26	let	let	VERB
ejpam-5191	120	27	v1	v1	NOUN
ejpam-5191	120	28	,	,	PUNCT
ejpam-5191	120	29	v2	v2	PROPN
ejpam-5191	120	30	be	be	AUX
ejpam-5191	120	31	any	any	DET
ejpam-5191	120	32	σ1σ2	σ1σ2	NOUN
ejpam-5191	120	33	-	-	PUNCT
ejpam-5191	120	34	open	open	ADJ
ejpam-5191	120	35	sets	set	NOUN
ejpam-5191	120	36	of	of	ADP
ejpam-5191	120	37	y	y	PROPN
ejpam-5191	120	38	.	.	PUNCT
ejpam-5191	121	1	then	then	ADV
ejpam-5191	121	2	by	by	ADP
ejpam-5191	121	3	(	(	PUNCT
ejpam-5191	121	4	4	4	NUM
ejpam-5191	121	5	)	)	PUNCT
ejpam-5191	121	6	,	,	PUNCT
ejpam-5191	121	7	we	we	PRON
ejpam-5191	121	8	have	have	VERB
ejpam-5191	121	9	x	x	X
ejpam-5191	121	10	−	−	X
ejpam-5191	121	11	(	(	PUNCT
ejpam-5191	121	12	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	121	13	-	-	PUNCT
ejpam-5191	121	14	cl(v1	cl(v1	NOUN
ejpam-5191	121	15	)	)	PUNCT
ejpam-5191	121	16	)	)	PUNCT
ejpam-5191	121	17	∪	∪	ADP
ejpam-5191	121	18	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	121	19	-	-	PUNCT
ejpam-5191	121	20	cl(v2	cl(v2	NOUN
ejpam-5191	121	21	)	)	PUNCT
ejpam-5191	121	22	)	)	PUNCT
ejpam-5191	121	23	)	)	PUNCT
ejpam-5191	122	1	=	=	PUNCT
ejpam-5191	122	2	(	(	PUNCT
ejpam-5191	122	3	x	x	X
ejpam-5191	122	4	−	−	NOUN
ejpam-5191	122	5	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	122	6	-	-	PUNCT
ejpam-5191	122	7	cl(v1	cl(v1	NOUN
ejpam-5191	122	8	)	)	PUNCT
ejpam-5191	122	9	)	)	PUNCT
ejpam-5191	122	10	)	)	PUNCT
ejpam-5191	122	11	∩	∩	NOUN
ejpam-5191	122	12	(	(	PUNCT
ejpam-5191	122	13	x	x	SYM
ejpam-5191	122	14	−	−	PRON
ejpam-5191	122	15	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	122	16	-	-	PUNCT
ejpam-5191	122	17	cl(v2	cl(v2	NOUN
ejpam-5191	122	18	)	)	PUNCT
ejpam-5191	122	19	)	)	PUNCT
ejpam-5191	122	20	)	)	PUNCT
ejpam-5191	123	1	=	=	PUNCT
ejpam-5191	124	1	f+(y	f+(y	NOUN
ejpam-5191	124	2	−	−	NUM
ejpam-5191	124	3	σ1σ2	σ1σ2	NUM
ejpam-5191	124	4	-	-	PUNCT
ejpam-5191	124	5	cl(v1	cl(v1	NOUN
ejpam-5191	124	6	)	)	PUNCT
ejpam-5191	124	7	)	)	PUNCT
ejpam-5191	125	1	∩	∩	NOUN
ejpam-5191	125	2	f−(y	f−(y	NOUN
ejpam-5191	125	3	−	−	NUM
ejpam-5191	125	4	σ1σ2	σ1σ2	NOUN
ejpam-5191	125	5	-	-	NOUN
ejpam-5191	125	6	cl(v2	cl(v2	NOUN
ejpam-5191	125	7	)	)	PUNCT
ejpam-5191	125	8	)	)	PUNCT
ejpam-5191	126	1	⊆	⊆	NUM
ejpam-5191	126	2	(	(	PUNCT
ejpam-5191	126	3	τ1	τ1	NOUN
ejpam-5191	126	4	,	,	PUNCT
ejpam-5191	126	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	126	6	+	+	ADJ
ejpam-5191	126	7	(	(	PUNCT
ejpam-5191	126	8	σ1σ2	σ1σ2	NUM
ejpam-5191	126	9	-	-	PUNCT
ejpam-5191	126	10	cl(y	cl(y	NOUN
ejpam-5191	126	11	−	−	NOUN
ejpam-5191	126	12	σ1σ2	σ1σ2	NOUN
ejpam-5191	126	13	-	-	PUNCT
ejpam-5191	126	14	cl(v1	cl(v1	NOUN
ejpam-5191	126	15	)	)	PUNCT
ejpam-5191	126	16	)	)	PUNCT
ejpam-5191	126	17	)	)	PUNCT
ejpam-5191	126	18	∩	∩	ADJ
ejpam-5191	126	19	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	126	20	-	-	PUNCT
ejpam-5191	126	21	cl(y	cl(y	NOUN
ejpam-5191	126	22	−	−	NOUN
ejpam-5191	126	23	σ1σ2	σ1σ2	NOUN
ejpam-5191	126	24	-	-	NOUN
ejpam-5191	126	25	cl(v2	cl(v2	NOUN
ejpam-5191	126	26	)	)	PUNCT
ejpam-5191	126	27	)	)	PUNCT
ejpam-5191	126	28	)	)	PUNCT
ejpam-5191	126	29	)	)	PUNCT
ejpam-5191	127	1	=	=	PRON
ejpam-5191	127	2	(	(	PUNCT
ejpam-5191	127	3	τ1	τ1	NOUN
ejpam-5191	127	4	,	,	PUNCT
ejpam-5191	127	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	128	1	+	+	ADJ
ejpam-5191	128	2	(	(	PUNCT
ejpam-5191	128	3	y	y	PROPN
ejpam-5191	128	4	−	−	PROPN
ejpam-5191	128	5	σ1σ2	σ1σ2	NUM
ejpam-5191	128	6	-	-	PUNCT
ejpam-5191	128	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	128	8	-	-	PUNCT
ejpam-5191	128	9	cl(v1	cl(v1	NOUN
ejpam-5191	128	10	)	)	PUNCT
ejpam-5191	128	11	)	)	PUNCT
ejpam-5191	128	12	)	)	PUNCT
ejpam-5191	129	1	∩	∩	NOUN
ejpam-5191	129	2	f−(y	f−(y	NOUN
ejpam-5191	129	3	−	−	NUM
ejpam-5191	129	4	σ1σ2	σ1σ2	NOUN
ejpam-5191	129	5	-	-	PUNCT
ejpam-5191	129	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	129	7	-	-	PUNCT
ejpam-5191	129	8	cl(v2	cl(v2	NOUN
ejpam-5191	129	9	)	)	PUNCT
ejpam-5191	129	10	)	)	PUNCT
ejpam-5191	129	11	)	)	PUNCT
ejpam-5191	129	12	)	)	PUNCT
ejpam-5191	130	1	⊆	⊆	X
ejpam-5191	130	2	(	(	PUNCT
ejpam-5191	130	3	τ1	τ1	NOUN
ejpam-5191	130	4	,	,	PUNCT
ejpam-5191	130	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	130	6	+	+	ADJ
ejpam-5191	130	7	(	(	PUNCT
ejpam-5191	130	8	y	y	PROPN
ejpam-5191	130	9	−	−	PROPN
ejpam-5191	130	10	v1	v1	PROPN
ejpam-5191	130	11	)	)	PUNCT
ejpam-5191	130	12	∩	∩	NOUN
ejpam-5191	130	13	f−(y	f−(y	NOUN
ejpam-5191	130	14	−	−	PROPN
ejpam-5191	130	15	v2	v2	NOUN
ejpam-5191	130	16	)	)	PUNCT
ejpam-5191	130	17	)	)	PUNCT
ejpam-5191	131	1	=	=	PRON
ejpam-5191	131	2	(	(	PUNCT
ejpam-5191	131	3	τ1	τ1	PROPN
ejpam-5191	131	4	,	,	PUNCT
ejpam-5191	131	5	τ2)-sint((x	τ2)-sint((x	ADJ
ejpam-5191	131	6	−	−	NOUN
ejpam-5191	131	7	f−(v1	f−(v1	NOUN
ejpam-5191	131	8	)	)	PUNCT
ejpam-5191	131	9	)	)	PUNCT
ejpam-5191	131	10	∩	∩	NOUN
ejpam-5191	131	11	(	(	PUNCT
ejpam-5191	131	12	x	x	SYM
ejpam-5191	131	13	−	−	NOUN
ejpam-5191	131	14	f+(v2	f+(v2	NOUN
ejpam-5191	131	15	)	)	PUNCT
ejpam-5191	131	16	)	)	PUNCT
ejpam-5191	131	17	)	)	PUNCT
ejpam-5191	132	1	=	=	PRON
ejpam-5191	132	2	(	(	PUNCT
ejpam-5191	132	3	τ1	τ1	NOUN
ejpam-5191	132	4	,	,	PUNCT
ejpam-5191	132	5	τ2)-sint(x	τ2)-sint(x	PUNCT
ejpam-5191	132	6	−	−	PROPN
ejpam-5191	132	7	(	(	PUNCT
ejpam-5191	132	8	f−(v1	f−(v1	NOUN
ejpam-5191	132	9	)	)	PUNCT
ejpam-5191	132	10	∪	∪	NOUN
ejpam-5191	132	11	f+(v2	f+(v2	NOUN
ejpam-5191	132	12	)	)	PUNCT
ejpam-5191	132	13	)	)	PUNCT
ejpam-5191	132	14	)	)	PUNCT
ejpam-5191	133	1	=	=	PUNCT
ejpam-5191	133	2	x	x	X
ejpam-5191	133	3	−	−	PROPN
ejpam-5191	133	4	(	(	PUNCT
ejpam-5191	133	5	τ1	τ1	PROPN
ejpam-5191	133	6	,	,	PUNCT
ejpam-5191	133	7	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	133	8	−(v1	−(v1	NUM
ejpam-5191	133	9	)	)	PUNCT
ejpam-5191	133	10	∪	∪	ADP
ejpam-5191	133	11	f+(v2	f+(v2	NOUN
ejpam-5191	133	12	)	)	PUNCT
ejpam-5191	133	13	)	)	PUNCT
ejpam-5191	133	14	and	and	CCONJ
ejpam-5191	133	15	hence	hence	ADV
ejpam-5191	133	16	(	(	PUNCT
ejpam-5191	133	17	τ1	τ1	PROPN
ejpam-5191	133	18	,	,	PUNCT
ejpam-5191	133	19	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	133	20	−(v1	−(v1	NUM
ejpam-5191	133	21	)	)	PUNCT
ejpam-5191	133	22	∪	∪	ADP
ejpam-5191	133	23	f+(v2	f+(v2	NOUN
ejpam-5191	133	24	)	)	PUNCT
ejpam-5191	133	25	)	)	PUNCT
ejpam-5191	133	26	⊆	⊆	X
ejpam-5191	133	27	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	133	28	-	-	PUNCT
ejpam-5191	133	29	cl(v1	cl(v1	NOUN
ejpam-5191	133	30	)	)	PUNCT
ejpam-5191	133	31	)	)	PUNCT
ejpam-5191	133	32	∪	∪	ADP
ejpam-5191	133	33	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	133	34	-	-	PUNCT
ejpam-5191	133	35	cl(v2	cl(v2	NOUN
ejpam-5191	133	36	)	)	PUNCT
ejpam-5191	133	37	)	)	PUNCT
ejpam-5191	133	38	.	.	PUNCT
ejpam-5191	134	1	(	(	PUNCT
ejpam-5191	134	2	5	5	X
ejpam-5191	134	3	)	)	PUNCT
ejpam-5191	134	4	⇒	⇒	NOUN
ejpam-5191	134	5	(	(	PUNCT
ejpam-5191	134	6	3	3	NUM
ejpam-5191	134	7	):	):	PUNCT
ejpam-5191	134	8	let	let	VERB
ejpam-5191	134	9	k1,k2	k1,k2	PROPN
ejpam-5191	134	10	be	be	AUX
ejpam-5191	134	11	any	any	DET
ejpam-5191	134	12	σ1σ2	σ1σ2	NUM
ejpam-5191	134	13	-	-	PUNCT
ejpam-5191	134	14	closed	closed	ADJ
ejpam-5191	134	15	sets	set	NOUN
ejpam-5191	134	16	of	of	ADP
ejpam-5191	134	17	y	y	PROPN
ejpam-5191	134	18	.	.	PUNCT
ejpam-5191	135	1	by	by	ADP
ejpam-5191	135	2	(	(	PUNCT
ejpam-5191	135	3	5	5	NUM
ejpam-5191	135	4	)	)	PUNCT
ejpam-5191	135	5	and	and	CCONJ
ejpam-5191	135	6	lemma	lemma	PROPN
ejpam-5191	135	7	2	2	NUM
ejpam-5191	135	8	,	,	PUNCT
ejpam-5191	135	9	τ1τ2	τ1τ2	NOUN
ejpam-5191	135	10	-	-	NOUN
ejpam-5191	135	11	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	135	12	-	-	PUNCT
ejpam-5191	135	13	cl(f	cl(f	NOUN
ejpam-5191	135	14	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	135	15	-	-	PUNCT
ejpam-5191	135	16	int(k1	int(k1	PROPN
ejpam-5191	135	17	)	)	PUNCT
ejpam-5191	135	18	)	)	PUNCT
ejpam-5191	135	19	∪	∪	ADP
ejpam-5191	135	20	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	135	21	-	-	PUNCT
ejpam-5191	135	22	int(k2	int(k2	NOUN
ejpam-5191	135	23	)	)	PUNCT
ejpam-5191	135	24	)	)	PUNCT
ejpam-5191	135	25	)	)	PUNCT
ejpam-5191	135	26	)	)	PUNCT
ejpam-5191	136	1	⊆	⊆	X
ejpam-5191	136	2	(	(	PUNCT
ejpam-5191	136	3	τ1	τ1	NOUN
ejpam-5191	136	4	,	,	PUNCT
ejpam-5191	136	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	136	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	136	7	-	-	PUNCT
ejpam-5191	136	8	int(k1	int(k1	PROPN
ejpam-5191	136	9	)	)	PUNCT
ejpam-5191	136	10	)	)	PUNCT
ejpam-5191	136	11	∪	∪	ADP
ejpam-5191	136	12	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	136	13	-	-	PUNCT
ejpam-5191	136	14	int(k2	int(k2	NOUN
ejpam-5191	136	15	)	)	PUNCT
ejpam-5191	136	16	)	)	PUNCT
ejpam-5191	136	17	)	)	PUNCT
ejpam-5191	137	1	⊆	⊆	X
ejpam-5191	137	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	137	3	-	-	PUNCT
ejpam-5191	137	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5191	137	5	-	-	PUNCT
ejpam-5191	137	6	int(k1	int(k1	PROPN
ejpam-5191	137	7	)	)	PUNCT
ejpam-5191	137	8	)	)	PUNCT
ejpam-5191	137	9	)	)	PUNCT
ejpam-5191	137	10	∪	∪	ADP
ejpam-5191	137	11	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	137	12	-	-	PUNCT
ejpam-5191	137	13	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5191	137	14	-	-	PUNCT
ejpam-5191	137	15	int(k2	int(k2	NOUN
ejpam-5191	137	16	)	)	PUNCT
ejpam-5191	137	17	)	)	PUNCT
ejpam-5191	137	18	)	)	PUNCT
ejpam-5191	138	1	⊆	⊆	X
ejpam-5191	138	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5191	138	3	-	-	PUNCT
ejpam-5191	138	4	cl(k1	cl(k1	NOUN
ejpam-5191	138	5	)	)	PUNCT
ejpam-5191	138	6	)	)	PUNCT
ejpam-5191	138	7	∪	∪	ADP
ejpam-5191	138	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	138	9	-	-	PUNCT
ejpam-5191	138	10	cl(k2	cl(k2	NOUN
ejpam-5191	138	11	)	)	PUNCT
ejpam-5191	138	12	)	)	PUNCT
ejpam-5191	139	1	=	=	SYM
ejpam-5191	139	2	f−(k1	f−(k1	X
ejpam-5191	139	3	)	)	PUNCT
ejpam-5191	139	4	∪	∪	ADP
ejpam-5191	139	5	f+(k2	f+(k2	NOUN
ejpam-5191	139	6	)	)	PUNCT
ejpam-5191	139	7	.	.	PUNCT
ejpam-5191	140	1	(	(	PUNCT
ejpam-5191	140	2	3	3	X
ejpam-5191	140	3	)	)	PUNCT
ejpam-5191	140	4	⇒	⇒	NOUN
ejpam-5191	140	5	(	(	PUNCT
ejpam-5191	140	6	4	4	NUM
ejpam-5191	140	7	):	):	PUNCT
ejpam-5191	140	8	let	let	VERB
ejpam-5191	140	9	v1	v1	NOUN
ejpam-5191	140	10	,	,	PUNCT
ejpam-5191	140	11	v2	v2	PROPN
ejpam-5191	140	12	be	be	AUX
ejpam-5191	140	13	any	any	DET
ejpam-5191	140	14	σ1σ2	σ1σ2	NOUN
ejpam-5191	140	15	-	-	PUNCT
ejpam-5191	140	16	open	open	ADJ
ejpam-5191	140	17	sets	set	NOUN
ejpam-5191	140	18	of	of	ADP
ejpam-5191	140	19	y	y	PROPN
ejpam-5191	140	20	.	.	PUNCT
ejpam-5191	141	1	by	by	ADP
ejpam-5191	141	2	(	(	PUNCT
ejpam-5191	141	3	3	3	X
ejpam-5191	141	4	)	)	PUNCT
ejpam-5191	141	5	and	and	CCONJ
ejpam-5191	141	6	lemma	lemma	PROPN
ejpam-5191	141	7	2	2	NUM
ejpam-5191	141	8	,	,	PUNCT
ejpam-5191	141	9	x	x	PRON
ejpam-5191	141	10	−	−	PROPN
ejpam-5191	141	11	(	(	PUNCT
ejpam-5191	141	12	τ1	τ1	NOUN
ejpam-5191	141	13	,	,	PUNCT
ejpam-5191	141	14	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	141	15	+	+	ADJ
ejpam-5191	141	16	(	(	PUNCT
ejpam-5191	141	17	σ1σ2	σ1σ2	NOUN
ejpam-5191	141	18	-	-	PUNCT
ejpam-5191	141	19	cl(v1	cl(v1	NOUN
ejpam-5191	141	20	)	)	PUNCT
ejpam-5191	141	21	)	)	PUNCT
ejpam-5191	141	22	∩	∩	ADJ
ejpam-5191	141	23	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	141	24	-	-	PUNCT
ejpam-5191	141	25	cl(v2	cl(v2	NOUN
ejpam-5191	141	26	)	)	PUNCT
ejpam-5191	141	27	)	)	PUNCT
ejpam-5191	141	28	)	)	PUNCT
ejpam-5191	142	1	=	=	PRON
ejpam-5191	142	2	(	(	PUNCT
ejpam-5191	142	3	τ1	τ1	PROPN
ejpam-5191	142	4	,	,	PUNCT
ejpam-5191	142	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	143	1	−(y	−(y	NOUN
ejpam-5191	143	2	−	−	NOUN
ejpam-5191	143	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	143	4	-	-	PUNCT
ejpam-5191	143	5	cl(v1	cl(v1	NOUN
ejpam-5191	143	6	)	)	PUNCT
ejpam-5191	143	7	)	)	PUNCT
ejpam-5191	143	8	∪	∪	ADP
ejpam-5191	143	9	f+(y	f+(y	NUM
ejpam-5191	143	10	−	−	PROPN
ejpam-5191	143	11	σ1σ2	σ1σ2	NUM
ejpam-5191	143	12	-	-	NOUN
ejpam-5191	143	13	cl(v2	cl(v2	NOUN
ejpam-5191	143	14	)	)	PUNCT
ejpam-5191	143	15	)	)	PUNCT
ejpam-5191	143	16	)	)	PUNCT
ejpam-5191	144	1	⊆	⊆	X
ejpam-5191	144	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5191	144	3	-	-	PUNCT
ejpam-5191	144	4	cl(y	cl(y	NOUN
ejpam-5191	144	5	−	−	NOUN
ejpam-5191	144	6	σ1σ2	σ1σ2	NOUN
ejpam-5191	144	7	-	-	PUNCT
ejpam-5191	144	8	cl(v1	cl(v1	NOUN
ejpam-5191	144	9	)	)	PUNCT
ejpam-5191	144	10	)	)	PUNCT
ejpam-5191	144	11	)	)	PUNCT
ejpam-5191	144	12	∪	∪	ADP
ejpam-5191	144	13	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	144	14	-	-	PUNCT
ejpam-5191	144	15	cl(y	cl(y	NOUN
ejpam-5191	144	16	−	−	NOUN
ejpam-5191	144	17	σ1σ2	σ1σ2	NOUN
ejpam-5191	144	18	-	-	NOUN
ejpam-5191	144	19	cl(v2	cl(v2	NOUN
ejpam-5191	144	20	)	)	PUNCT
ejpam-5191	144	21	)	)	PUNCT
ejpam-5191	144	22	)	)	PUNCT
ejpam-5191	145	1	=	=	PUNCT
ejpam-5191	145	2	f−(y	f−(y	NOUN
ejpam-5191	145	3	−	−	ADP
ejpam-5191	145	4	σ1σ2	σ1σ2	NOUN
ejpam-5191	145	5	-	-	PUNCT
ejpam-5191	145	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	145	7	-	-	PUNCT
ejpam-5191	145	8	cl(v1	cl(v1	NOUN
ejpam-5191	145	9	)	)	PUNCT
ejpam-5191	145	10	)	)	PUNCT
ejpam-5191	145	11	)	)	PUNCT
ejpam-5191	145	12	∪	∪	ADP
ejpam-5191	145	13	f+(y	f+(y	NUM
ejpam-5191	145	14	−	−	PROPN
ejpam-5191	145	15	σ1σ2	σ1σ2	SYM
ejpam-5191	145	16	-	-	PUNCT
ejpam-5191	145	17	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	145	18	-	-	PUNCT
ejpam-5191	145	19	cl(v2	cl(v2	NOUN
ejpam-5191	145	20	)	)	PUNCT
ejpam-5191	145	21	)	)	PUNCT
ejpam-5191	145	22	)	)	PUNCT
ejpam-5191	146	1	⊆	⊆	NUM
ejpam-5191	146	2	f−(y	f−(y	NOUN
ejpam-5191	146	3	−	−	NOUN
ejpam-5191	146	4	v1	v1	NOUN
ejpam-5191	146	5	)	)	PUNCT
ejpam-5191	146	6	∪	∪	NOUN
ejpam-5191	146	7	f+(y	f+(y	ADP
ejpam-5191	146	8	−	−	PROPN
ejpam-5191	146	9	v2	v2	PROPN
ejpam-5191	146	10	)	)	PUNCT
ejpam-5191	146	11	=	=	SYM
ejpam-5191	146	12	(	(	PUNCT
ejpam-5191	146	13	x	x	SYM
ejpam-5191	146	14	−	−	NOUN
ejpam-5191	146	15	f+(v1	f+(v1	NOUN
ejpam-5191	146	16	)	)	PUNCT
ejpam-5191	146	17	)	)	PUNCT
ejpam-5191	146	18	∪	∪	ADP
ejpam-5191	146	19	(	(	PUNCT
ejpam-5191	146	20	x	x	NOUN
ejpam-5191	146	21	−	−	NOUN
ejpam-5191	146	22	f−(v2	f−(v2	NUM
ejpam-5191	146	23	)	)	PUNCT
ejpam-5191	146	24	)	)	PUNCT
ejpam-5191	147	1	=	=	PUNCT
ejpam-5191	147	2	x	x	X
ejpam-5191	147	3	−	−	PROPN
ejpam-5191	147	4	(	(	PUNCT
ejpam-5191	147	5	f+(v1	f+(v1	NOUN
ejpam-5191	147	6	)	)	PUNCT
ejpam-5191	147	7	∩	∩	NOUN
ejpam-5191	147	8	f−(v2	f−(v2	NUM
ejpam-5191	147	9	)	)	PUNCT
ejpam-5191	147	10	)	)	PUNCT
ejpam-5191	147	11	and	and	CCONJ
ejpam-5191	147	12	hence	hence	ADV
ejpam-5191	147	13	f+(v1	f+(v1	ADJ
ejpam-5191	147	14	)	)	PUNCT
ejpam-5191	147	15	∩	∩	NOUN
ejpam-5191	147	16	f−(v2	f−(v2	X
ejpam-5191	147	17	)	)	PUNCT
ejpam-5191	147	18	⊆	⊆	NUM
ejpam-5191	147	19	(	(	PUNCT
ejpam-5191	147	20	τ1	τ1	NOUN
ejpam-5191	147	21	,	,	PUNCT
ejpam-5191	147	22	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	148	1	+	+	ADJ
ejpam-5191	148	2	(	(	PUNCT
ejpam-5191	148	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	148	4	-	-	PUNCT
ejpam-5191	148	5	cl(v1	cl(v1	NOUN
ejpam-5191	148	6	)	)	PUNCT
ejpam-5191	148	7	)	)	PUNCT
ejpam-5191	148	8	∩	∩	ADJ
ejpam-5191	148	9	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	148	10	-	-	PUNCT
ejpam-5191	148	11	cl(v2	cl(v2	NOUN
ejpam-5191	148	12	)	)	PUNCT
ejpam-5191	148	13	)	)	PUNCT
ejpam-5191	148	14	)	)	PUNCT
ejpam-5191	148	15	.	.	PUNCT
ejpam-5191	149	1	(	(	PUNCT
ejpam-5191	149	2	4	4	X
ejpam-5191	149	3	)	)	PUNCT
ejpam-5191	149	4	⇒	⇒	NOUN
ejpam-5191	149	5	(	(	PUNCT
ejpam-5191	149	6	1	1	NUM
ejpam-5191	149	7	):	):	PUNCT
ejpam-5191	149	8	let	let	VERB
ejpam-5191	149	9	x	x	PUNCT
ejpam-5191	149	10	∈	∈	PROPN
ejpam-5191	149	11	x	x	X
ejpam-5191	149	12	and	and	CCONJ
ejpam-5191	149	13	v1	v1	NOUN
ejpam-5191	149	14	,	,	PUNCT
ejpam-5191	149	15	v2	v2	PROPN
ejpam-5191	149	16	be	be	AUX
ejpam-5191	149	17	any	any	DET
ejpam-5191	149	18	σ1σ2	σ1σ2	NOUN
ejpam-5191	149	19	-	-	PUNCT
ejpam-5191	149	20	open	open	ADJ
ejpam-5191	149	21	sets	set	NOUN
ejpam-5191	149	22	of	of	ADP
ejpam-5191	149	23	y	y	PRON
ejpam-5191	149	24	such	such	ADJ
ejpam-5191	149	25	that	that	SCONJ
ejpam-5191	149	26	f	f	PROPN
ejpam-5191	149	27	(	(	PUNCT
ejpam-5191	149	28	x	x	X
ejpam-5191	149	29	)	)	PUNCT
ejpam-5191	149	30	∈	∈	NOUN
ejpam-5191	149	31	v	v	ADP
ejpam-5191	149	32	+	+	CCONJ
ejpam-5191	149	33	1	1	NUM
ejpam-5191	149	34	∩v	∩v	NOUN
ejpam-5191	149	35	−	−	PROPN
ejpam-5191	149	36	2	2	NUM
ejpam-5191	149	37	.	.	PUNCT
ejpam-5191	150	1	by	by	ADP
ejpam-5191	150	2	(	(	PUNCT
ejpam-5191	150	3	4	4	NUM
ejpam-5191	150	4	)	)	PUNCT
ejpam-5191	150	5	,	,	PUNCT
ejpam-5191	150	6	we	we	PRON
ejpam-5191	150	7	have	have	VERB
ejpam-5191	150	8	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5191	150	9	)	)	PUNCT
ejpam-5191	150	10	⊆	⊆	NUM
ejpam-5191	150	11	(	(	PUNCT
ejpam-5191	150	12	τ1	τ1	NOUN
ejpam-5191	150	13	,	,	PUNCT
ejpam-5191	150	14	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	151	1	+	+	ADJ
ejpam-5191	151	2	(	(	PUNCT
ejpam-5191	151	3	σ1σ2	σ1σ2	X
ejpam-5191	151	4	-	-	PUNCT
ejpam-5191	151	5	cl(v1))∩f−(σ1σ2	cl(v1))∩f−(σ1σ2	NOUN
ejpam-5191	151	6	-	-	PUNCT
ejpam-5191	151	7	cl(v2	cl(v2	NOUN
ejpam-5191	151	8	)	)	PUNCT
ejpam-5191	151	9	)	)	PUNCT
ejpam-5191	151	10	)	)	PUNCT
ejpam-5191	151	11	.	.	PUNCT
ejpam-5191	152	1	put	put	VERB
ejpam-5191	152	2	u	u	NOUN
ejpam-5191	152	3	=	=	PUNCT
ejpam-5191	152	4	(	(	PUNCT
ejpam-5191	152	5	τ1	τ1	NOUN
ejpam-5191	152	6	,	,	PUNCT
ejpam-5191	152	7	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	153	1	+	+	ADJ
ejpam-5191	153	2	(	(	PUNCT
ejpam-5191	153	3	σ1σ2	σ1σ2	X
ejpam-5191	153	4	-	-	PUNCT
ejpam-5191	153	5	cl(v1))∩f−(σ1σ2	cl(v1))∩f−(σ1σ2	NOUN
ejpam-5191	153	6	-	-	PUNCT
ejpam-5191	153	7	cl(v2	cl(v2	NOUN
ejpam-5191	153	8	)	)	PUNCT
ejpam-5191	153	9	)	)	PUNCT
ejpam-5191	153	10	)	)	PUNCT
ejpam-5191	153	11	.	.	PUNCT
ejpam-5191	154	1	then	then	ADV
ejpam-5191	154	2	,	,	PUNCT
ejpam-5191	154	3	u	u	NOUN
ejpam-5191	154	4	is	be	AUX
ejpam-5191	154	5	(	(	PUNCT
ejpam-5191	154	6	τ1	τ1	NOUN
ejpam-5191	154	7	,	,	PUNCT
ejpam-5191	154	8	τ2)s	τ2)s	NOUN
ejpam-5191	154	9	-	-	PUNCT
ejpam-5191	154	10	open	open	ADJ
ejpam-5191	154	11	set	set	NOUN
ejpam-5191	154	12	of	of	ADP
ejpam-5191	154	13	x	x	PUNCT
ejpam-5191	154	14	containing	contain	VERB
ejpam-5191	154	15	x	x	PUNCT
ejpam-5191	154	16	such	such	ADJ
ejpam-5191	154	17	that	that	SCONJ
ejpam-5191	154	18	f	f	PROPN
ejpam-5191	154	19	(	(	PUNCT
ejpam-5191	154	20	u	u	NOUN
ejpam-5191	154	21	)	)	PUNCT
ejpam-5191	154	22	⊆	⊆	NUM
ejpam-5191	154	23	σ1σ2	σ1σ2	NOUN
ejpam-5191	154	24	-	-	PUNCT
ejpam-5191	154	25	cl(v1	cl(v1	X
ejpam-5191	154	26	)	)	PUNCT
ejpam-5191	154	27	and	and	CCONJ
ejpam-5191	154	28	σ1σ2	σ1σ2	NOUN
ejpam-5191	154	29	-	-	PUNCT
ejpam-5191	154	30	cl(v2	cl(v2	NOUN
ejpam-5191	154	31	)	)	PUNCT
ejpam-5191	154	32	∩	∩	PROPN
ejpam-5191	154	33	f	f	X
ejpam-5191	154	34	(	(	PUNCT
ejpam-5191	154	35	z	z	NOUN
ejpam-5191	154	36	)	)	PUNCT
ejpam-5191	154	37	̸=	̸=	NOUN
ejpam-5191	154	38	∅	∅	NOUN
ejpam-5191	154	39	for	for	ADP
ejpam-5191	154	40	every	every	DET
ejpam-5191	154	41	z	z	NOUN
ejpam-5191	154	42	∈	∈	PROPN
ejpam-5191	154	43	u	u	NOUN
ejpam-5191	154	44	.	.	PUNCT
ejpam-5191	155	1	this	this	PRON
ejpam-5191	155	2	shows	show	VERB
ejpam-5191	155	3	that	that	SCONJ
ejpam-5191	155	4	f	f	PROPN
ejpam-5191	155	5	is	be	AUX
ejpam-5191	155	6	weakly	weakly	ADJ
ejpam-5191	155	7	quasi	quasi	NOUN
ejpam-5191	155	8	(	(	PUNCT
ejpam-5191	155	9	τ1	τ1	NOUN
ejpam-5191	155	10	,	,	PUNCT
ejpam-5191	155	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	155	12	.	.	PUNCT
ejpam-5191	156	1	theorem	theorem	NOUN
ejpam-5191	156	2	2	2	NUM
ejpam-5191	156	3	.	.	X
ejpam-5191	156	4	for	for	ADP
ejpam-5191	156	5	a	a	DET
ejpam-5191	156	6	multifunction	multifunction	NOUN
ejpam-5191	157	1	f	f	NOUN
ejpam-5191	157	2	:	:	PUNCT
ejpam-5191	157	3	(	(	PUNCT
ejpam-5191	157	4	x	x	NOUN
ejpam-5191	157	5	,	,	PUNCT
ejpam-5191	157	6	τ1	τ1	NOUN
ejpam-5191	157	7	,	,	PUNCT
ejpam-5191	157	8	τ2	τ2	NOUN
ejpam-5191	157	9	)	)	PUNCT
ejpam-5191	157	10	→	→	SYM
ejpam-5191	157	11	(	(	PUNCT
ejpam-5191	157	12	y	y	PROPN
ejpam-5191	157	13	,	,	PUNCT
ejpam-5191	157	14	σ1	σ1	PROPN
ejpam-5191	157	15	,	,	PUNCT
ejpam-5191	157	16	σ2	σ2	NOUN
ejpam-5191	157	17	)	)	PUNCT
ejpam-5191	157	18	,	,	PUNCT
ejpam-5191	157	19	the	the	DET
ejpam-5191	157	20	following	follow	VERB
ejpam-5191	157	21	properties	property	NOUN
ejpam-5191	157	22	are	be	AUX
ejpam-5191	157	23	equivalent	equivalent	ADJ
ejpam-5191	157	24	:	:	PUNCT
ejpam-5191	157	25	p.	p.	NOUN
ejpam-5191	157	26	pue	pue	NOUN
ejpam-5191	157	27	-	-	PUNCT
ejpam-5191	157	28	on	on	ADP
ejpam-5191	157	29	,	,	PUNCT
ejpam-5191	157	30	s.	s.	PROPN
ejpam-5191	157	31	sompong	sompong	PROPN
ejpam-5191	157	32	,	,	PUNCT
ejpam-5191	157	33	c.	c.	PROPN
ejpam-5191	157	34	boonpok	boonpok	PROPN
ejpam-5191	157	35	/	/	SYM
ejpam-5191	157	36	eur	eur	PROPN
ejpam-5191	157	37	.	.	PUNCT
ejpam-5191	158	1	j.	j.	PROPN
ejpam-5191	158	2	pure	pure	PROPN
ejpam-5191	158	3	appl	appl	PROPN
ejpam-5191	158	4	.	.	PROPN
ejpam-5191	158	5	math	math	PROPN
ejpam-5191	158	6	,	,	PUNCT
ejpam-5191	158	7	17	17	NUM
ejpam-5191	158	8	(	(	PUNCT
ejpam-5191	158	9	3	3	NUM
ejpam-5191	158	10	)	)	PUNCT
ejpam-5191	158	11	(	(	PUNCT
ejpam-5191	158	12	2024	2024	NUM
ejpam-5191	158	13	)	)	PUNCT
ejpam-5191	158	14	,	,	PUNCT
ejpam-5191	158	15	1553	1553	NUM
ejpam-5191	158	16	-	-	SYM
ejpam-5191	158	17	1564	1564	NUM
ejpam-5191	158	18	1558	1558	NUM
ejpam-5191	158	19	(	(	PUNCT
ejpam-5191	158	20	1	1	X
ejpam-5191	158	21	)	)	PUNCT
ejpam-5191	158	22	f	f	PROPN
ejpam-5191	158	23	is	be	AUX
ejpam-5191	158	24	weakly	weakly	ADJ
ejpam-5191	158	25	quasi	quasi	NOUN
ejpam-5191	158	26	(	(	PUNCT
ejpam-5191	158	27	τ1	τ1	NOUN
ejpam-5191	158	28	,	,	PUNCT
ejpam-5191	158	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	158	30	;	;	PUNCT
ejpam-5191	158	31	(	(	PUNCT
ejpam-5191	158	32	2	2	X
ejpam-5191	158	33	)	)	PUNCT
ejpam-5191	158	34	(	(	PUNCT
ejpam-5191	158	35	τ1	τ1	NOUN
ejpam-5191	158	36	,	,	PUNCT
ejpam-5191	158	37	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	158	38	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	158	39	-	-	PUNCT
ejpam-5191	158	40	int((σ1	int((σ1	ADJ
ejpam-5191	158	41	,	,	PUNCT
ejpam-5191	158	42	σ2)θ	σ2)θ	NOUN
ejpam-5191	158	43	-	-	PUNCT
ejpam-5191	158	44	cl(b1	cl(b1	NOUN
ejpam-5191	158	45	)	)	PUNCT
ejpam-5191	158	46	)	)	PUNCT
ejpam-5191	158	47	)	)	PUNCT
ejpam-5191	158	48	∪	∪	ADP
ejpam-5191	158	49	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	158	50	-	-	PUNCT
ejpam-5191	158	51	int((σ1	int((σ1	ADJ
ejpam-5191	158	52	,	,	PUNCT
ejpam-5191	158	53	σ2)θ	σ2)θ	NOUN
ejpam-5191	158	54	-	-	PUNCT
ejpam-5191	158	55	cl(b2	cl(b2	NOUN
ejpam-5191	158	56	)	)	PUNCT
ejpam-5191	158	57	)	)	PUNCT
ejpam-5191	158	58	)	)	PUNCT
ejpam-5191	158	59	)	)	PUNCT
ejpam-5191	159	1	⊆	⊆	NUM
ejpam-5191	159	2	f−((σ1	f−((σ1	NOUN
ejpam-5191	159	3	,	,	PUNCT
ejpam-5191	159	4	σ2)θ	σ2)θ	NOUN
ejpam-5191	159	5	-	-	PUNCT
ejpam-5191	159	6	cl(b1	cl(b1	NOUN
ejpam-5191	159	7	)	)	PUNCT
ejpam-5191	159	8	)	)	PUNCT
ejpam-5191	159	9	∪	∪	ADP
ejpam-5191	159	10	f+((σ1	f+((σ1	NOUN
ejpam-5191	159	11	,	,	PUNCT
ejpam-5191	159	12	σ2)θ	σ2)θ	ADJ
ejpam-5191	159	13	-	-	PUNCT
ejpam-5191	159	14	cl(b2	cl(b2	NOUN
ejpam-5191	159	15	)	)	PUNCT
ejpam-5191	159	16	)	)	PUNCT
ejpam-5191	159	17	for	for	ADP
ejpam-5191	159	18	every	every	DET
ejpam-5191	159	19	subsets	subset	NOUN
ejpam-5191	159	20	b1	b1	NOUN
ejpam-5191	159	21	,	,	PUNCT
ejpam-5191	159	22	b2	b2	NOUN
ejpam-5191	159	23	of	of	ADP
ejpam-5191	159	24	y	y	PROPN
ejpam-5191	159	25	;	;	PUNCT
ejpam-5191	159	26	(	(	PUNCT
ejpam-5191	159	27	3	3	X
ejpam-5191	159	28	)	)	PUNCT
ejpam-5191	159	29	(	(	PUNCT
ejpam-5191	159	30	τ1	τ1	NOUN
ejpam-5191	159	31	,	,	PUNCT
ejpam-5191	159	32	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	159	33	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	159	34	-	-	PUNCT
ejpam-5191	159	35	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	159	36	-	-	PUNCT
ejpam-5191	159	37	cl(b1	cl(b1	NOUN
ejpam-5191	159	38	)	)	PUNCT
ejpam-5191	159	39	)	)	PUNCT
ejpam-5191	159	40	)	)	PUNCT
ejpam-5191	159	41	∪	∪	ADP
ejpam-5191	159	42	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	159	43	-	-	PUNCT
ejpam-5191	159	44	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	159	45	-	-	PUNCT
ejpam-5191	159	46	cl(b2	cl(b2	NOUN
ejpam-5191	159	47	)	)	PUNCT
ejpam-5191	159	48	)	)	PUNCT
ejpam-5191	159	49	)	)	PUNCT
ejpam-5191	159	50	)	)	PUNCT
ejpam-5191	160	1	⊆	⊆	NUM
ejpam-5191	160	2	f−((σ1	f−((σ1	NOUN
ejpam-5191	160	3	,	,	PUNCT
ejpam-5191	160	4	σ2)θ	σ2)θ	NOUN
ejpam-5191	160	5	-	-	PUNCT
ejpam-5191	160	6	cl(b1	cl(b1	NOUN
ejpam-5191	160	7	)	)	PUNCT
ejpam-5191	160	8	)	)	PUNCT
ejpam-5191	160	9	∪	∪	ADP
ejpam-5191	160	10	f+((σ1	f+((σ1	NOUN
ejpam-5191	160	11	,	,	PUNCT
ejpam-5191	160	12	σ2)θ	σ2)θ	ADJ
ejpam-5191	160	13	-	-	PUNCT
ejpam-5191	160	14	cl(b2	cl(b2	NOUN
ejpam-5191	160	15	)	)	PUNCT
ejpam-5191	160	16	)	)	PUNCT
ejpam-5191	160	17	for	for	ADP
ejpam-5191	160	18	every	every	DET
ejpam-5191	160	19	subsets	subset	NOUN
ejpam-5191	160	20	b1	b1	NOUN
ejpam-5191	160	21	,	,	PUNCT
ejpam-5191	160	22	b2	b2	NOUN
ejpam-5191	160	23	of	of	ADP
ejpam-5191	160	24	y	y	PROPN
ejpam-5191	160	25	;	;	PUNCT
ejpam-5191	160	26	(	(	PUNCT
ejpam-5191	160	27	4	4	X
ejpam-5191	160	28	)	)	PUNCT
ejpam-5191	160	29	(	(	PUNCT
ejpam-5191	160	30	τ1	τ1	NOUN
ejpam-5191	160	31	,	,	PUNCT
ejpam-5191	160	32	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	160	33	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	160	34	-	-	PUNCT
ejpam-5191	160	35	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	160	36	-	-	PUNCT
ejpam-5191	160	37	cl(v1	cl(v1	NOUN
ejpam-5191	160	38	)	)	PUNCT
ejpam-5191	160	39	)	)	PUNCT
ejpam-5191	160	40	)	)	PUNCT
ejpam-5191	160	41	∪	∪	ADP
ejpam-5191	160	42	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	160	43	-	-	PUNCT
ejpam-5191	160	44	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	160	45	-	-	PUNCT
ejpam-5191	160	46	cl(v2	cl(v2	NOUN
ejpam-5191	160	47	)	)	PUNCT
ejpam-5191	160	48	)	)	PUNCT
ejpam-5191	160	49	)	)	PUNCT
ejpam-5191	160	50	)	)	PUNCT
ejpam-5191	161	1	⊆	⊆	X
ejpam-5191	161	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	161	3	-	-	PUNCT
ejpam-5191	161	4	cl(v1	cl(v1	NOUN
ejpam-5191	161	5	)	)	PUNCT
ejpam-5191	161	6	)	)	PUNCT
ejpam-5191	161	7	∪	∪	ADP
ejpam-5191	161	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	161	9	-	-	PUNCT
ejpam-5191	161	10	cl(v2	cl(v2	NOUN
ejpam-5191	161	11	)	)	PUNCT
ejpam-5191	161	12	)	)	PUNCT
ejpam-5191	161	13	for	for	ADP
ejpam-5191	161	14	every	every	DET
ejpam-5191	161	15	σ1σ2	σ1σ2	NUM
ejpam-5191	161	16	-	-	ADJ
ejpam-5191	161	17	open	open	ADJ
ejpam-5191	161	18	sets	set	NOUN
ejpam-5191	161	19	v1	v1	NOUN
ejpam-5191	161	20	,	,	PUNCT
ejpam-5191	161	21	v2	v2	PROPN
ejpam-5191	161	22	of	of	ADP
ejpam-5191	161	23	y	y	PROPN
ejpam-5191	161	24	;	;	PUNCT
ejpam-5191	161	25	(	(	PUNCT
ejpam-5191	161	26	5	5	X
ejpam-5191	161	27	)	)	PUNCT
ejpam-5191	161	28	(	(	PUNCT
ejpam-5191	161	29	τ1	τ1	NOUN
ejpam-5191	161	30	,	,	PUNCT
ejpam-5191	161	31	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	161	32	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	161	33	-	-	PUNCT
ejpam-5191	161	34	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	161	35	-	-	PUNCT
ejpam-5191	161	36	cl(v1	cl(v1	NOUN
ejpam-5191	161	37	)	)	PUNCT
ejpam-5191	161	38	)	)	PUNCT
ejpam-5191	161	39	)	)	PUNCT
ejpam-5191	161	40	∪	∪	ADP
ejpam-5191	161	41	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	161	42	-	-	PUNCT
ejpam-5191	161	43	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	161	44	-	-	PUNCT
ejpam-5191	161	45	cl(v2	cl(v2	NOUN
ejpam-5191	161	46	)	)	PUNCT
ejpam-5191	161	47	)	)	PUNCT
ejpam-5191	161	48	)	)	PUNCT
ejpam-5191	161	49	)	)	PUNCT
ejpam-5191	162	1	⊆	⊆	X
ejpam-5191	162	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	162	3	-	-	PUNCT
ejpam-5191	162	4	cl(v1	cl(v1	NOUN
ejpam-5191	162	5	)	)	PUNCT
ejpam-5191	162	6	)	)	PUNCT
ejpam-5191	162	7	∪	∪	ADP
ejpam-5191	162	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	162	9	-	-	PUNCT
ejpam-5191	162	10	cl(v2	cl(v2	NOUN
ejpam-5191	162	11	)	)	PUNCT
ejpam-5191	162	12	)	)	PUNCT
ejpam-5191	162	13	for	for	ADP
ejpam-5191	162	14	every	every	DET
ejpam-5191	162	15	(	(	PUNCT
ejpam-5191	162	16	σ1	σ1	PROPN
ejpam-5191	162	17	,	,	PUNCT
ejpam-5191	162	18	σ2)p	σ2)p	NOUN
ejpam-5191	162	19	-	-	PUNCT
ejpam-5191	162	20	open	open	ADJ
ejpam-5191	162	21	sets	set	NOUN
ejpam-5191	162	22	v1	v1	NOUN
ejpam-5191	162	23	,	,	PUNCT
ejpam-5191	162	24	v2	v2	PROPN
ejpam-5191	162	25	of	of	ADP
ejpam-5191	162	26	y	y	PROPN
ejpam-5191	162	27	;	;	PUNCT
ejpam-5191	162	28	(	(	PUNCT
ejpam-5191	162	29	6	6	NUM
ejpam-5191	162	30	)	)	PUNCT
ejpam-5191	162	31	(	(	PUNCT
ejpam-5191	162	32	τ1	τ1	NOUN
ejpam-5191	162	33	,	,	PUNCT
ejpam-5191	162	34	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	162	35	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	162	36	-	-	PUNCT
ejpam-5191	162	37	int(k1	int(k1	PROPN
ejpam-5191	162	38	)	)	PUNCT
ejpam-5191	162	39	)	)	PUNCT
ejpam-5191	162	40	∪	∪	ADP
ejpam-5191	162	41	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	162	42	-	-	PUNCT
ejpam-5191	162	43	int(k2	int(k2	NOUN
ejpam-5191	162	44	)	)	PUNCT
ejpam-5191	162	45	)	)	PUNCT
ejpam-5191	162	46	)	)	PUNCT
ejpam-5191	163	1	⊆	⊆	NUM
ejpam-5191	163	2	f−(k1	f−(k1	NOUN
ejpam-5191	163	3	)	)	PUNCT
ejpam-5191	163	4	∪	∪	ADP
ejpam-5191	163	5	f+(k2	f+(k2	NOUN
ejpam-5191	163	6	)	)	PUNCT
ejpam-5191	163	7	for	for	ADP
ejpam-5191	163	8	every	every	DET
ejpam-5191	163	9	(	(	PUNCT
ejpam-5191	163	10	σ1	σ1	PROPN
ejpam-5191	163	11	,	,	PUNCT
ejpam-5191	163	12	σ2)r	σ2)r	NOUN
ejpam-5191	163	13	-	-	PUNCT
ejpam-5191	163	14	closed	close	VERB
ejpam-5191	163	15	sets	set	NOUN
ejpam-5191	163	16	k1,k2	k1,k2	PROPN
ejpam-5191	163	17	of	of	ADP
ejpam-5191	163	18	y	y	PROPN
ejpam-5191	163	19	.	.	PUNCT
ejpam-5191	164	1	proof	proof	NOUN
ejpam-5191	164	2	.	.	PUNCT
ejpam-5191	165	1	(	(	PUNCT
ejpam-5191	165	2	1	1	X
ejpam-5191	165	3	)	)	PUNCT
ejpam-5191	165	4	⇒	⇒	NOUN
ejpam-5191	165	5	(	(	PUNCT
ejpam-5191	165	6	2	2	NUM
ejpam-5191	165	7	):	):	PUNCT
ejpam-5191	165	8	let	let	VERB
ejpam-5191	165	9	b1	b1	NOUN
ejpam-5191	165	10	,	,	PUNCT
ejpam-5191	165	11	b2	b2	NOUN
ejpam-5191	165	12	be	be	VERB
ejpam-5191	165	13	any	any	DET
ejpam-5191	165	14	subsets	subset	NOUN
ejpam-5191	165	15	of	of	ADP
ejpam-5191	165	16	y	y	PROPN
ejpam-5191	165	17	.	.	PUNCT
ejpam-5191	166	1	since	since	SCONJ
ejpam-5191	166	2	(	(	PUNCT
ejpam-5191	166	3	σ1	σ1	PROPN
ejpam-5191	166	4	,	,	PUNCT
ejpam-5191	166	5	σ2)θ	σ2)θ	NOUN
ejpam-5191	166	6	-	-	PUNCT
ejpam-5191	166	7	cl(b1	cl(b1	NOUN
ejpam-5191	166	8	)	)	PUNCT
ejpam-5191	166	9	and	and	CCONJ
ejpam-5191	166	10	(	(	PUNCT
ejpam-5191	166	11	σ1	σ1	PROPN
ejpam-5191	166	12	,	,	PUNCT
ejpam-5191	166	13	σ2)θ	σ2)θ	NOUN
ejpam-5191	166	14	-	-	PUNCT
ejpam-5191	166	15	cl(b2	cl(b2	NOUN
ejpam-5191	166	16	)	)	PUNCT
ejpam-5191	166	17	are	be	AUX
ejpam-5191	166	18	σ1σ2	σ1σ2	NOUN
ejpam-5191	166	19	-	-	ADJ
ejpam-5191	166	20	closed	closed	ADJ
ejpam-5191	166	21	in	in	ADP
ejpam-5191	166	22	y	y	PROPN
ejpam-5191	166	23	,	,	PUNCT
ejpam-5191	166	24	by	by	ADP
ejpam-5191	166	25	theorem	theorem	NOUN
ejpam-5191	166	26	1	1	NUM
ejpam-5191	166	27	τ1τ2	τ1τ2	NOUN
ejpam-5191	166	28	-	-	NOUN
ejpam-5191	166	29	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	166	30	-	-	PUNCT
ejpam-5191	166	31	cl(f	cl(f	NOUN
ejpam-5191	166	32	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	166	33	-	-	PUNCT
ejpam-5191	166	34	int((σ1	int((σ1	ADJ
ejpam-5191	166	35	,	,	PUNCT
ejpam-5191	166	36	σ2)θ	σ2)θ	NOUN
ejpam-5191	166	37	-	-	PUNCT
ejpam-5191	166	38	cl(b1	cl(b1	NOUN
ejpam-5191	166	39	)	)	PUNCT
ejpam-5191	166	40	)	)	PUNCT
ejpam-5191	166	41	)	)	PUNCT
ejpam-5191	166	42	∪	∪	ADP
ejpam-5191	166	43	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	166	44	-	-	PUNCT
ejpam-5191	166	45	int((σ1	int((σ1	ADJ
ejpam-5191	166	46	,	,	PUNCT
ejpam-5191	166	47	σ2)θ	σ2)θ	NOUN
ejpam-5191	166	48	-	-	PUNCT
ejpam-5191	166	49	cl(b2	cl(b2	NOUN
ejpam-5191	166	50	)	)	PUNCT
ejpam-5191	166	51	)	)	PUNCT
ejpam-5191	166	52	)	)	PUNCT
ejpam-5191	166	53	)	)	PUNCT
ejpam-5191	166	54	)	)	PUNCT
ejpam-5191	167	1	⊆	⊆	NUM
ejpam-5191	167	2	f−((σ1	f−((σ1	NOUN
ejpam-5191	167	3	,	,	PUNCT
ejpam-5191	167	4	σ2)θ	σ2)θ	NOUN
ejpam-5191	167	5	-	-	PUNCT
ejpam-5191	167	6	cl(b1	cl(b1	NOUN
ejpam-5191	167	7	)	)	PUNCT
ejpam-5191	167	8	)	)	PUNCT
ejpam-5191	167	9	∪	∪	ADP
ejpam-5191	167	10	f+((σ1	f+((σ1	NOUN
ejpam-5191	167	11	,	,	PUNCT
ejpam-5191	167	12	σ2)θ	σ2)θ	ADJ
ejpam-5191	167	13	-	-	PUNCT
ejpam-5191	167	14	cl(b2	cl(b2	NOUN
ejpam-5191	167	15	)	)	PUNCT
ejpam-5191	167	16	)	)	PUNCT
ejpam-5191	167	17	and	and	CCONJ
ejpam-5191	167	18	by	by	ADP
ejpam-5191	167	19	lemma	lemma	PROPN
ejpam-5191	167	20	2	2	NUM
ejpam-5191	167	21	,	,	PUNCT
ejpam-5191	167	22	we	we	PRON
ejpam-5191	167	23	have	have	VERB
ejpam-5191	167	24	(	(	PUNCT
ejpam-5191	167	25	τ1	τ1	NOUN
ejpam-5191	167	26	,	,	PUNCT
ejpam-5191	167	27	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	167	28	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	167	29	-	-	PUNCT
ejpam-5191	167	30	int((σ1	int((σ1	ADJ
ejpam-5191	167	31	,	,	PUNCT
ejpam-5191	167	32	σ2)θ	σ2)θ	NOUN
ejpam-5191	167	33	-	-	PUNCT
ejpam-5191	167	34	cl(b1	cl(b1	NOUN
ejpam-5191	167	35	)	)	PUNCT
ejpam-5191	167	36	)	)	PUNCT
ejpam-5191	167	37	)	)	PUNCT
ejpam-5191	167	38	∪	∪	ADP
ejpam-5191	167	39	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	167	40	-	-	PUNCT
ejpam-5191	167	41	int((σ1	int((σ1	ADJ
ejpam-5191	167	42	,	,	PUNCT
ejpam-5191	167	43	σ2)θ	σ2)θ	NOUN
ejpam-5191	167	44	-	-	PUNCT
ejpam-5191	167	45	cl(b2	cl(b2	NOUN
ejpam-5191	167	46	)	)	PUNCT
ejpam-5191	167	47	)	)	PUNCT
ejpam-5191	167	48	)	)	PUNCT
ejpam-5191	167	49	)	)	PUNCT
ejpam-5191	168	1	⊆	⊆	NUM
ejpam-5191	168	2	f−((σ1	f−((σ1	NOUN
ejpam-5191	168	3	,	,	PUNCT
ejpam-5191	168	4	σ2)θ	σ2)θ	NOUN
ejpam-5191	168	5	-	-	PUNCT
ejpam-5191	168	6	cl(b1	cl(b1	NOUN
ejpam-5191	168	7	)	)	PUNCT
ejpam-5191	168	8	)	)	PUNCT
ejpam-5191	168	9	∪	∪	ADP
ejpam-5191	168	10	f+((σ1	f+((σ1	NOUN
ejpam-5191	168	11	,	,	PUNCT
ejpam-5191	168	12	σ2)θ	σ2)θ	ADJ
ejpam-5191	168	13	-	-	PUNCT
ejpam-5191	168	14	cl(b2	cl(b2	NOUN
ejpam-5191	168	15	)	)	PUNCT
ejpam-5191	168	16	)	)	PUNCT
ejpam-5191	168	17	.	.	PUNCT
ejpam-5191	169	1	p.	p.	NOUN
ejpam-5191	169	2	pue	pue	NOUN
ejpam-5191	169	3	-	-	PUNCT
ejpam-5191	169	4	on	on	ADP
ejpam-5191	169	5	,	,	PUNCT
ejpam-5191	169	6	s.	s.	PROPN
ejpam-5191	169	7	sompong	sompong	PROPN
ejpam-5191	169	8	,	,	PUNCT
ejpam-5191	169	9	c.	c.	PROPN
ejpam-5191	169	10	boonpok	boonpok	PROPN
ejpam-5191	169	11	/	/	SYM
ejpam-5191	169	12	eur	eur	PROPN
ejpam-5191	169	13	.	.	PUNCT
ejpam-5191	170	1	j.	j.	PROPN
ejpam-5191	170	2	pure	pure	PROPN
ejpam-5191	170	3	appl	appl	PROPN
ejpam-5191	170	4	.	.	PROPN
ejpam-5191	170	5	math	math	PROPN
ejpam-5191	170	6	,	,	PUNCT
ejpam-5191	170	7	17	17	NUM
ejpam-5191	170	8	(	(	PUNCT
ejpam-5191	170	9	3	3	NUM
ejpam-5191	170	10	)	)	PUNCT
ejpam-5191	170	11	(	(	PUNCT
ejpam-5191	170	12	2024	2024	NUM
ejpam-5191	170	13	)	)	PUNCT
ejpam-5191	170	14	,	,	PUNCT
ejpam-5191	170	15	1553	1553	NUM
ejpam-5191	170	16	-	-	SYM
ejpam-5191	170	17	1564	1564	NUM
ejpam-5191	170	18	1559	1559	NUM
ejpam-5191	170	19	(	(	PUNCT
ejpam-5191	170	20	2	2	NUM
ejpam-5191	170	21	)	)	PUNCT
ejpam-5191	170	22	⇒	⇒	NOUN
ejpam-5191	170	23	(	(	PUNCT
ejpam-5191	170	24	3	3	NUM
ejpam-5191	170	25	):	):	PUNCT
ejpam-5191	170	26	this	this	PRON
ejpam-5191	170	27	is	be	AUX
ejpam-5191	170	28	obvious	obvious	ADJ
ejpam-5191	170	29	since	since	SCONJ
ejpam-5191	170	30	σ1σ2	σ1σ2	NOUN
ejpam-5191	170	31	-	-	NOUN
ejpam-5191	170	32	cl(b	cl(b	NOUN
ejpam-5191	170	33	)	)	PUNCT
ejpam-5191	170	34	⊆	⊆	NUM
ejpam-5191	170	35	(	(	PUNCT
ejpam-5191	170	36	σ1	σ1	PROPN
ejpam-5191	170	37	,	,	PUNCT
ejpam-5191	170	38	σ2)θ	σ2)θ	NOUN
ejpam-5191	170	39	-	-	PUNCT
ejpam-5191	170	40	cl(b	cl(b	NOUN
ejpam-5191	170	41	)	)	PUNCT
ejpam-5191	170	42	for	for	ADP
ejpam-5191	170	43	every	every	DET
ejpam-5191	170	44	subset	subset	NOUN
ejpam-5191	170	45	b	b	PROPN
ejpam-5191	170	46	of	of	ADP
ejpam-5191	170	47	y	y	PROPN
ejpam-5191	170	48	.	.	PUNCT
ejpam-5191	171	1	(	(	PUNCT
ejpam-5191	171	2	3	3	X
ejpam-5191	171	3	)	)	PUNCT
ejpam-5191	171	4	⇒	⇒	NOUN
ejpam-5191	171	5	(	(	PUNCT
ejpam-5191	171	6	4	4	NUM
ejpam-5191	171	7	):	):	PUNCT
ejpam-5191	171	8	this	this	PRON
ejpam-5191	171	9	is	be	AUX
ejpam-5191	171	10	obvious	obvious	ADJ
ejpam-5191	171	11	since	since	SCONJ
ejpam-5191	171	12	σ1σ2	σ1σ2	NOUN
ejpam-5191	171	13	-	-	NOUN
ejpam-5191	171	14	cl(v	cl(v	X
ejpam-5191	171	15	)	)	PUNCT
ejpam-5191	172	1	=	=	SYM
ejpam-5191	172	2	(	(	PUNCT
ejpam-5191	172	3	σ1	σ1	PROPN
ejpam-5191	172	4	,	,	PUNCT
ejpam-5191	172	5	σ2)θ	σ2)θ	NOUN
ejpam-5191	172	6	-	-	PUNCT
ejpam-5191	172	7	cl(v	cl(v	NOUN
ejpam-5191	172	8	)	)	PUNCT
ejpam-5191	172	9	for	for	ADP
ejpam-5191	172	10	every	every	DET
ejpam-5191	172	11	σ1σ2	σ1σ2	NOUN
ejpam-5191	172	12	-	-	ADJ
ejpam-5191	172	13	open	open	ADJ
ejpam-5191	172	14	set	set	NOUN
ejpam-5191	172	15	v	v	NOUN
ejpam-5191	172	16	of	of	ADP
ejpam-5191	172	17	y	y	PROPN
ejpam-5191	172	18	.	.	PUNCT
ejpam-5191	173	1	(	(	PUNCT
ejpam-5191	173	2	4	4	X
ejpam-5191	173	3	)	)	PUNCT
ejpam-5191	173	4	⇒	⇒	NOUN
ejpam-5191	173	5	(	(	PUNCT
ejpam-5191	173	6	5	5	NUM
ejpam-5191	173	7	):	):	PUNCT
ejpam-5191	173	8	let	let	VERB
ejpam-5191	173	9	v1	v1	NOUN
ejpam-5191	173	10	,	,	PUNCT
ejpam-5191	173	11	v2	v2	PROPN
ejpam-5191	173	12	be	be	VERB
ejpam-5191	173	13	any	any	DET
ejpam-5191	173	14	(	(	PUNCT
ejpam-5191	173	15	σ1	σ1	PROPN
ejpam-5191	173	16	,	,	PUNCT
ejpam-5191	173	17	σ2)p	σ2)p	NOUN
ejpam-5191	173	18	-	-	PUNCT
ejpam-5191	173	19	open	open	ADJ
ejpam-5191	173	20	sets	set	NOUN
ejpam-5191	173	21	of	of	ADP
ejpam-5191	173	22	y	y	PROPN
ejpam-5191	173	23	.	.	PUNCT
ejpam-5191	174	1	then	then	ADV
ejpam-5191	174	2	,	,	PUNCT
ejpam-5191	174	3	we	we	PRON
ejpam-5191	174	4	have	have	VERB
ejpam-5191	174	5	vi	vi	NUM
ejpam-5191	174	6	⊆	⊆	NUM
ejpam-5191	174	7	σ1σ2	σ1σ2	NOUN
ejpam-5191	174	8	-	-	PUNCT
ejpam-5191	174	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	174	10	-	-	PUNCT
ejpam-5191	174	11	cl(vi	cl(vi	NOUN
ejpam-5191	174	12	)	)	PUNCT
ejpam-5191	174	13	)	)	PUNCT
ejpam-5191	174	14	and	and	CCONJ
ejpam-5191	174	15	σ1σ2	σ1σ2	NOUN
ejpam-5191	174	16	-	-	PUNCT
ejpam-5191	174	17	cl(vi	cl(vi	NOUN
ejpam-5191	174	18	)	)	PUNCT
ejpam-5191	174	19	=	=	SYM
ejpam-5191	174	20	σ1σ2	σ1σ2	X
ejpam-5191	174	21	-	-	PUNCT
ejpam-5191	174	22	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5191	174	23	-	-	PUNCT
ejpam-5191	174	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	174	25	-	-	PUNCT
ejpam-5191	174	26	cl(vi	cl(vi	NOUN
ejpam-5191	174	27	)	)	PUNCT
ejpam-5191	174	28	)	)	PUNCT
ejpam-5191	174	29	)	)	PUNCT
ejpam-5191	175	1	for	for	ADP
ejpam-5191	175	2	i	i	PROPN
ejpam-5191	175	3	=	=	SYM
ejpam-5191	175	4	1	1	NUM
ejpam-5191	175	5	,	,	PUNCT
ejpam-5191	175	6	2	2	NUM
ejpam-5191	175	7	.	.	PUNCT
ejpam-5191	175	8	now	now	ADV
ejpam-5191	175	9	,	,	PUNCT
ejpam-5191	175	10	put	put	VERB
ejpam-5191	175	11	gi	gi	NOUN
ejpam-5191	175	12	=	=	SYM
ejpam-5191	175	13	σ1σ2	σ1σ2	NOUN
ejpam-5191	175	14	-	-	PUNCT
ejpam-5191	175	15	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	175	16	-	-	PUNCT
ejpam-5191	175	17	cl(vi	cl(vi	NOUN
ejpam-5191	175	18	)	)	PUNCT
ejpam-5191	175	19	)	)	PUNCT
ejpam-5191	175	20	,	,	PUNCT
ejpam-5191	175	21	then	then	ADV
ejpam-5191	175	22	gi	gi	PROPN
ejpam-5191	175	23	is	be	AUX
ejpam-5191	175	24	σ1σ2	σ1σ2	NOUN
ejpam-5191	175	25	-	-	ADJ
ejpam-5191	175	26	open	open	ADJ
ejpam-5191	175	27	in	in	ADP
ejpam-5191	175	28	y	y	PROPN
ejpam-5191	175	29	and	and	CCONJ
ejpam-5191	175	30	σ1σ2	σ1σ2	NOUN
ejpam-5191	175	31	-	-	ADJ
ejpam-5191	175	32	cl(gi	cl(gi	NOUN
ejpam-5191	175	33	)	)	PUNCT
ejpam-5191	176	1	=	=	PUNCT
ejpam-5191	176	2	σ1σ2	σ1σ2	X
ejpam-5191	176	3	-	-	PUNCT
ejpam-5191	176	4	cl(vi	cl(vi	NOUN
ejpam-5191	176	5	)	)	PUNCT
ejpam-5191	176	6	.	.	PUNCT
ejpam-5191	177	1	thus	thus	ADV
ejpam-5191	177	2	,	,	PUNCT
ejpam-5191	177	3	by	by	ADP
ejpam-5191	177	4	(	(	PUNCT
ejpam-5191	177	5	4	4	NUM
ejpam-5191	177	6	)	)	PUNCT
ejpam-5191	177	7	,	,	PUNCT
ejpam-5191	177	8	(	(	PUNCT
ejpam-5191	177	9	τ1	τ1	NOUN
ejpam-5191	177	10	,	,	PUNCT
ejpam-5191	177	11	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	177	12	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	177	13	-	-	PUNCT
ejpam-5191	177	14	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	177	15	-	-	PUNCT
ejpam-5191	177	16	cl(v1	cl(v1	NOUN
ejpam-5191	177	17	)	)	PUNCT
ejpam-5191	177	18	)	)	PUNCT
ejpam-5191	177	19	)	)	PUNCT
ejpam-5191	177	20	∪	∪	ADP
ejpam-5191	177	21	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	177	22	-	-	PUNCT
ejpam-5191	177	23	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	177	24	-	-	PUNCT
ejpam-5191	177	25	cl(v2	cl(v2	NOUN
ejpam-5191	177	26	)	)	PUNCT
ejpam-5191	177	27	)	)	PUNCT
ejpam-5191	177	28	)	)	PUNCT
ejpam-5191	177	29	)	)	PUNCT
ejpam-5191	177	30	⊆	⊆	X
ejpam-5191	177	31	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	177	32	-	-	PUNCT
ejpam-5191	177	33	cl(v1	cl(v1	NOUN
ejpam-5191	177	34	)	)	PUNCT
ejpam-5191	177	35	)	)	PUNCT
ejpam-5191	177	36	∪	∪	ADP
ejpam-5191	177	37	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	177	38	-	-	PUNCT
ejpam-5191	177	39	cl(v2	cl(v2	NOUN
ejpam-5191	177	40	)	)	PUNCT
ejpam-5191	177	41	)	)	PUNCT
ejpam-5191	177	42	.	.	PUNCT
ejpam-5191	178	1	(	(	PUNCT
ejpam-5191	178	2	5	5	X
ejpam-5191	178	3	)	)	PUNCT
ejpam-5191	178	4	⇒	⇒	NOUN
ejpam-5191	178	5	(	(	PUNCT
ejpam-5191	178	6	6	6	NUM
ejpam-5191	178	7	):	):	PUNCT
ejpam-5191	178	8	let	let	VERB
ejpam-5191	178	9	k1,k2	k1,k2	PROPN
ejpam-5191	178	10	be	be	AUX
ejpam-5191	178	11	any	any	DET
ejpam-5191	178	12	(	(	PUNCT
ejpam-5191	178	13	σ1	σ1	NOUN
ejpam-5191	178	14	,	,	PUNCT
ejpam-5191	178	15	σ2)r	σ2)r	NOUN
ejpam-5191	178	16	-	-	PUNCT
ejpam-5191	178	17	closed	close	VERB
ejpam-5191	178	18	sets	set	NOUN
ejpam-5191	178	19	of	of	ADP
ejpam-5191	178	20	y	y	PROPN
ejpam-5191	178	21	.	.	PUNCT
ejpam-5191	179	1	since	since	SCONJ
ejpam-5191	179	2	σ1σ2	σ1σ2	NOUN
ejpam-5191	179	3	-	-	PUNCT
ejpam-5191	179	4	int(k1	int(k1	PROPN
ejpam-5191	179	5	)	)	PUNCT
ejpam-5191	179	6	and	and	CCONJ
ejpam-5191	179	7	σ1σ2	σ1σ2	NOUN
ejpam-5191	179	8	-	-	PUNCT
ejpam-5191	179	9	int(k2	int(k2	NOUN
ejpam-5191	179	10	)	)	PUNCT
ejpam-5191	179	11	are	be	AUX
ejpam-5191	179	12	(	(	PUNCT
ejpam-5191	179	13	σ1	σ1	PROPN
ejpam-5191	179	14	,	,	PUNCT
ejpam-5191	179	15	σ2)p	σ2)p	NOUN
ejpam-5191	179	16	-	-	PUNCT
ejpam-5191	179	17	open	open	ADJ
ejpam-5191	179	18	in	in	ADP
ejpam-5191	179	19	y	y	PROPN
ejpam-5191	179	20	,	,	PUNCT
ejpam-5191	179	21	by	by	ADP
ejpam-5191	179	22	(	(	PUNCT
ejpam-5191	179	23	5	5	NUM
ejpam-5191	179	24	)	)	PUNCT
ejpam-5191	179	25	,	,	PUNCT
ejpam-5191	179	26	we	we	PRON
ejpam-5191	179	27	have	have	AUX
ejpam-5191	179	28	(	(	PUNCT
ejpam-5191	179	29	τ1	τ1	NOUN
ejpam-5191	179	30	,	,	PUNCT
ejpam-5191	179	31	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	179	32	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	179	33	-	-	PUNCT
ejpam-5191	179	34	int(k1	int(k1	PROPN
ejpam-5191	179	35	)	)	PUNCT
ejpam-5191	179	36	)	)	PUNCT
ejpam-5191	179	37	∪	∪	ADP
ejpam-5191	179	38	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	179	39	-	-	PUNCT
ejpam-5191	179	40	int(k2	int(k2	NOUN
ejpam-5191	179	41	)	)	PUNCT
ejpam-5191	179	42	)	)	PUNCT
ejpam-5191	179	43	)	)	PUNCT
ejpam-5191	180	1	=	=	PRON
ejpam-5191	180	2	(	(	PUNCT
ejpam-5191	180	3	τ1	τ1	PROPN
ejpam-5191	180	4	,	,	PUNCT
ejpam-5191	180	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	180	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	180	7	-	-	PUNCT
ejpam-5191	180	8	int(σ1σ2	int(σ1σ2	ADV
ejpam-5191	180	9	-	-	PUNCT
ejpam-5191	180	10	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5191	180	11	-	-	PUNCT
ejpam-5191	180	12	int(k1	int(k1	PROPN
ejpam-5191	180	13	)	)	PUNCT
ejpam-5191	180	14	)	)	PUNCT
ejpam-5191	180	15	)	)	PUNCT
ejpam-5191	180	16	)	)	PUNCT
ejpam-5191	180	17	∪	∪	ADP
ejpam-5191	180	18	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	180	19	-	-	PUNCT
ejpam-5191	180	20	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	180	21	-	-	PUNCT
ejpam-5191	180	22	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5191	180	23	-	-	PUNCT
ejpam-5191	180	24	int(k2	int(k2	NOUN
ejpam-5191	180	25	)	)	PUNCT
ejpam-5191	180	26	)	)	PUNCT
ejpam-5191	180	27	)	)	PUNCT
ejpam-5191	180	28	)	)	PUNCT
ejpam-5191	180	29	)	)	PUNCT
ejpam-5191	181	1	⊆	⊆	X
ejpam-5191	181	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	181	3	-	-	PUNCT
ejpam-5191	181	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5191	181	5	-	-	PUNCT
ejpam-5191	181	6	int(k1	int(k1	PROPN
ejpam-5191	181	7	)	)	PUNCT
ejpam-5191	181	8	)	)	PUNCT
ejpam-5191	181	9	)	)	PUNCT
ejpam-5191	181	10	∪	∪	ADP
ejpam-5191	181	11	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	181	12	-	-	PUNCT
ejpam-5191	181	13	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5191	181	14	-	-	PUNCT
ejpam-5191	181	15	int(k2	int(k2	NOUN
ejpam-5191	181	16	)	)	PUNCT
ejpam-5191	181	17	)	)	PUNCT
ejpam-5191	181	18	)	)	PUNCT
ejpam-5191	182	1	=	=	PUNCT
ejpam-5191	182	2	f−(k1	f−(k1	X
ejpam-5191	182	3	)	)	PUNCT
ejpam-5191	182	4	∪	∪	ADP
ejpam-5191	182	5	f+(k2	f+(k2	NOUN
ejpam-5191	182	6	)	)	PUNCT
ejpam-5191	182	7	.	.	PUNCT
ejpam-5191	183	1	(	(	PUNCT
ejpam-5191	183	2	6	6	X
ejpam-5191	183	3	)	)	PUNCT
ejpam-5191	183	4	⇒	⇒	NOUN
ejpam-5191	183	5	(	(	PUNCT
ejpam-5191	183	6	1	1	NUM
ejpam-5191	183	7	):	):	PUNCT
ejpam-5191	183	8	let	let	VERB
ejpam-5191	183	9	v1	v1	NOUN
ejpam-5191	183	10	,	,	PUNCT
ejpam-5191	183	11	v2	v2	PROPN
ejpam-5191	183	12	be	be	AUX
ejpam-5191	183	13	any	any	DET
ejpam-5191	183	14	σ1σ2	σ1σ2	NOUN
ejpam-5191	183	15	-	-	PUNCT
ejpam-5191	183	16	open	open	ADJ
ejpam-5191	183	17	sets	set	NOUN
ejpam-5191	183	18	of	of	ADP
ejpam-5191	183	19	y	y	PROPN
ejpam-5191	183	20	.	.	PUNCT
ejpam-5191	184	1	then	then	ADV
ejpam-5191	184	2	,	,	PUNCT
ejpam-5191	184	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	184	4	-	-	PUNCT
ejpam-5191	184	5	cl(v1	cl(v1	X
ejpam-5191	184	6	)	)	PUNCT
ejpam-5191	184	7	and	and	CCONJ
ejpam-5191	184	8	σ1σ2	σ1σ2	NOUN
ejpam-5191	184	9	-	-	NOUN
ejpam-5191	184	10	cl(v2	cl(v2	NOUN
ejpam-5191	184	11	)	)	PUNCT
ejpam-5191	184	12	are	be	AUX
ejpam-5191	184	13	(	(	PUNCT
ejpam-5191	184	14	σ1	σ1	NOUN
ejpam-5191	184	15	,	,	PUNCT
ejpam-5191	184	16	σ2)r	σ2)r	NOUN
ejpam-5191	184	17	-	-	PUNCT
ejpam-5191	184	18	closed	closed	ADJ
ejpam-5191	184	19	in	in	ADP
ejpam-5191	184	20	y	y	PROPN
ejpam-5191	184	21	.	.	PUNCT
ejpam-5191	185	1	thus	thus	ADV
ejpam-5191	185	2	by	by	ADP
ejpam-5191	185	3	(	(	PUNCT
ejpam-5191	185	4	6	6	NUM
ejpam-5191	185	5	)	)	PUNCT
ejpam-5191	185	6	,	,	PUNCT
ejpam-5191	185	7	(	(	PUNCT
ejpam-5191	185	8	τ1	τ1	NOUN
ejpam-5191	185	9	,	,	PUNCT
ejpam-5191	185	10	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	185	11	−(v1	−(v1	NUM
ejpam-5191	185	12	)	)	PUNCT
ejpam-5191	185	13	∪	∪	ADP
ejpam-5191	185	14	f+(v2	f+(v2	NOUN
ejpam-5191	185	15	)	)	PUNCT
ejpam-5191	185	16	)	)	PUNCT
ejpam-5191	186	1	⊆	⊆	NUM
ejpam-5191	186	2	(	(	PUNCT
ejpam-5191	186	3	τ1	τ1	NOUN
ejpam-5191	186	4	,	,	PUNCT
ejpam-5191	186	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	186	6	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	186	7	-	-	PUNCT
ejpam-5191	186	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	186	9	-	-	PUNCT
ejpam-5191	186	10	cl(v1	cl(v1	NOUN
ejpam-5191	186	11	)	)	PUNCT
ejpam-5191	186	12	)	)	PUNCT
ejpam-5191	186	13	)	)	PUNCT
ejpam-5191	186	14	∪	∪	ADP
ejpam-5191	186	15	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	186	16	-	-	PUNCT
ejpam-5191	186	17	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	186	18	-	-	PUNCT
ejpam-5191	186	19	cl(v2	cl(v2	NOUN
ejpam-5191	186	20	)	)	PUNCT
ejpam-5191	186	21	)	)	PUNCT
ejpam-5191	186	22	)	)	PUNCT
ejpam-5191	186	23	)	)	PUNCT
ejpam-5191	187	1	⊆	⊆	X
ejpam-5191	187	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	187	3	-	-	PUNCT
ejpam-5191	187	4	cl(v1	cl(v1	NOUN
ejpam-5191	187	5	)	)	PUNCT
ejpam-5191	187	6	)	)	PUNCT
ejpam-5191	187	7	∪	∪	ADP
ejpam-5191	187	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	187	9	-	-	PUNCT
ejpam-5191	187	10	cl(v2	cl(v2	NOUN
ejpam-5191	187	11	)	)	PUNCT
ejpam-5191	187	12	)	)	PUNCT
ejpam-5191	187	13	.	.	PUNCT
ejpam-5191	188	1	it	it	PRON
ejpam-5191	188	2	follows	follow	VERB
ejpam-5191	188	3	from	from	ADP
ejpam-5191	188	4	theorem	theorem	ADJ
ejpam-5191	188	5	1	1	NUM
ejpam-5191	188	6	that	that	SCONJ
ejpam-5191	188	7	f	f	PROPN
ejpam-5191	188	8	is	be	AUX
ejpam-5191	188	9	weakly	weakly	ADJ
ejpam-5191	188	10	quasi	quasi	NOUN
ejpam-5191	188	11	(	(	PUNCT
ejpam-5191	188	12	τ1	τ1	NOUN
ejpam-5191	188	13	,	,	PUNCT
ejpam-5191	188	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	188	15	.	.	PUNCT
ejpam-5191	189	1	theorem	theorem	NOUN
ejpam-5191	189	2	3	3	NUM
ejpam-5191	189	3	.	.	X
ejpam-5191	189	4	for	for	ADP
ejpam-5191	189	5	a	a	DET
ejpam-5191	189	6	multifunction	multifunction	NOUN
ejpam-5191	190	1	f	f	NOUN
ejpam-5191	190	2	:	:	PUNCT
ejpam-5191	190	3	(	(	PUNCT
ejpam-5191	190	4	x	x	NOUN
ejpam-5191	190	5	,	,	PUNCT
ejpam-5191	190	6	τ1	τ1	NOUN
ejpam-5191	190	7	,	,	PUNCT
ejpam-5191	190	8	τ2	τ2	NOUN
ejpam-5191	190	9	)	)	PUNCT
ejpam-5191	190	10	→	→	SYM
ejpam-5191	190	11	(	(	PUNCT
ejpam-5191	190	12	y	y	PROPN
ejpam-5191	190	13	,	,	PUNCT
ejpam-5191	190	14	σ1	σ1	PROPN
ejpam-5191	190	15	,	,	PUNCT
ejpam-5191	190	16	σ2	σ2	NOUN
ejpam-5191	190	17	)	)	PUNCT
ejpam-5191	190	18	,	,	PUNCT
ejpam-5191	190	19	the	the	DET
ejpam-5191	190	20	following	follow	VERB
ejpam-5191	190	21	properties	property	NOUN
ejpam-5191	190	22	are	be	AUX
ejpam-5191	190	23	equivalent	equivalent	ADJ
ejpam-5191	190	24	:	:	PUNCT
ejpam-5191	190	25	(	(	PUNCT
ejpam-5191	190	26	1	1	X
ejpam-5191	190	27	)	)	PUNCT
ejpam-5191	190	28	f	f	PROPN
ejpam-5191	190	29	is	be	AUX
ejpam-5191	190	30	weakly	weakly	ADJ
ejpam-5191	190	31	quasi	quasi	NOUN
ejpam-5191	190	32	(	(	PUNCT
ejpam-5191	190	33	τ1	τ1	NOUN
ejpam-5191	190	34	,	,	PUNCT
ejpam-5191	190	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	190	36	;	;	PUNCT
ejpam-5191	190	37	(	(	PUNCT
ejpam-5191	190	38	2	2	X
ejpam-5191	190	39	)	)	PUNCT
ejpam-5191	190	40	(	(	PUNCT
ejpam-5191	190	41	τ1	τ1	NOUN
ejpam-5191	190	42	,	,	PUNCT
ejpam-5191	190	43	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	190	44	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	190	45	-	-	PUNCT
ejpam-5191	190	46	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	190	47	-	-	PUNCT
ejpam-5191	190	48	cl(v1	cl(v1	NOUN
ejpam-5191	190	49	)	)	PUNCT
ejpam-5191	190	50	)	)	PUNCT
ejpam-5191	190	51	)	)	PUNCT
ejpam-5191	190	52	∪	∪	ADP
ejpam-5191	190	53	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	190	54	-	-	PUNCT
ejpam-5191	190	55	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	190	56	-	-	PUNCT
ejpam-5191	190	57	cl(v2	cl(v2	NOUN
ejpam-5191	190	58	)	)	PUNCT
ejpam-5191	190	59	)	)	PUNCT
ejpam-5191	190	60	)	)	PUNCT
ejpam-5191	190	61	)	)	PUNCT
ejpam-5191	191	1	⊆	⊆	X
ejpam-5191	191	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	191	3	-	-	PUNCT
ejpam-5191	191	4	cl(v1	cl(v1	NOUN
ejpam-5191	191	5	)	)	PUNCT
ejpam-5191	191	6	)	)	PUNCT
ejpam-5191	191	7	∪	∪	ADP
ejpam-5191	191	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	191	9	-	-	PUNCT
ejpam-5191	191	10	cl(v2	cl(v2	NOUN
ejpam-5191	191	11	)	)	PUNCT
ejpam-5191	191	12	)	)	PUNCT
ejpam-5191	191	13	for	for	ADP
ejpam-5191	191	14	every	every	DET
ejpam-5191	191	15	(	(	PUNCT
ejpam-5191	191	16	σ1	σ1	PROPN
ejpam-5191	191	17	,	,	PUNCT
ejpam-5191	191	18	σ2)β	σ2)β	NOUN
ejpam-5191	191	19	-	-	PUNCT
ejpam-5191	191	20	open	open	ADJ
ejpam-5191	191	21	sets	set	NOUN
ejpam-5191	191	22	v1	v1	NOUN
ejpam-5191	191	23	,	,	PUNCT
ejpam-5191	191	24	v2	v2	PROPN
ejpam-5191	191	25	of	of	ADP
ejpam-5191	191	26	y	y	PROPN
ejpam-5191	191	27	;	;	PUNCT
ejpam-5191	191	28	p.	p.	NOUN
ejpam-5191	191	29	pue	pue	PROPN
ejpam-5191	191	30	-	-	PUNCT
ejpam-5191	191	31	on	on	ADP
ejpam-5191	191	32	,	,	PUNCT
ejpam-5191	191	33	s.	s.	PROPN
ejpam-5191	191	34	sompong	sompong	PROPN
ejpam-5191	191	35	,	,	PUNCT
ejpam-5191	191	36	c.	c.	PROPN
ejpam-5191	191	37	boonpok	boonpok	PROPN
ejpam-5191	191	38	/	/	SYM
ejpam-5191	191	39	eur	eur	PROPN
ejpam-5191	191	40	.	.	PUNCT
ejpam-5191	192	1	j.	j.	PROPN
ejpam-5191	192	2	pure	pure	PROPN
ejpam-5191	192	3	appl	appl	PROPN
ejpam-5191	192	4	.	.	PROPN
ejpam-5191	192	5	math	math	PROPN
ejpam-5191	192	6	,	,	PUNCT
ejpam-5191	192	7	17	17	NUM
ejpam-5191	192	8	(	(	PUNCT
ejpam-5191	192	9	3	3	NUM
ejpam-5191	192	10	)	)	PUNCT
ejpam-5191	192	11	(	(	PUNCT
ejpam-5191	192	12	2024	2024	NUM
ejpam-5191	192	13	)	)	PUNCT
ejpam-5191	192	14	,	,	PUNCT
ejpam-5191	192	15	1553	1553	NUM
ejpam-5191	192	16	-	-	SYM
ejpam-5191	192	17	1564	1564	NUM
ejpam-5191	192	18	1560	1560	NUM
ejpam-5191	192	19	(	(	PUNCT
ejpam-5191	192	20	3	3	NUM
ejpam-5191	192	21	)	)	PUNCT
ejpam-5191	192	22	(	(	PUNCT
ejpam-5191	192	23	τ1	τ1	NOUN
ejpam-5191	192	24	,	,	PUNCT
ejpam-5191	192	25	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	192	26	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	192	27	-	-	PUNCT
ejpam-5191	192	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	192	29	-	-	PUNCT
ejpam-5191	192	30	cl(v1	cl(v1	NOUN
ejpam-5191	192	31	)	)	PUNCT
ejpam-5191	192	32	)	)	PUNCT
ejpam-5191	192	33	)	)	PUNCT
ejpam-5191	192	34	∪	∪	ADP
ejpam-5191	192	35	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	192	36	-	-	PUNCT
ejpam-5191	192	37	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	192	38	-	-	PUNCT
ejpam-5191	192	39	cl(v2	cl(v2	NOUN
ejpam-5191	192	40	)	)	PUNCT
ejpam-5191	192	41	)	)	PUNCT
ejpam-5191	192	42	)	)	PUNCT
ejpam-5191	192	43	)	)	PUNCT
ejpam-5191	193	1	⊆	⊆	X
ejpam-5191	193	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	193	3	-	-	PUNCT
ejpam-5191	193	4	cl(v1	cl(v1	NOUN
ejpam-5191	193	5	)	)	PUNCT
ejpam-5191	193	6	)	)	PUNCT
ejpam-5191	193	7	∪	∪	ADP
ejpam-5191	193	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	193	9	-	-	PUNCT
ejpam-5191	193	10	cl(v2	cl(v2	NOUN
ejpam-5191	193	11	)	)	PUNCT
ejpam-5191	193	12	)	)	PUNCT
ejpam-5191	193	13	for	for	ADP
ejpam-5191	193	14	every	every	DET
ejpam-5191	193	15	(	(	PUNCT
ejpam-5191	193	16	σ1	σ1	PROPN
ejpam-5191	193	17	,	,	PUNCT
ejpam-5191	193	18	σ2)s	σ2)s	NOUN
ejpam-5191	193	19	-	-	PUNCT
ejpam-5191	193	20	open	open	ADJ
ejpam-5191	193	21	sets	set	NOUN
ejpam-5191	193	22	v1	v1	NOUN
ejpam-5191	193	23	,	,	PUNCT
ejpam-5191	193	24	v2	v2	PROPN
ejpam-5191	193	25	of	of	ADP
ejpam-5191	193	26	y	y	PROPN
ejpam-5191	193	27	;	;	PUNCT
ejpam-5191	193	28	(	(	PUNCT
ejpam-5191	193	29	4	4	X
ejpam-5191	193	30	)	)	PUNCT
ejpam-5191	193	31	(	(	PUNCT
ejpam-5191	193	32	τ1	τ1	NOUN
ejpam-5191	193	33	,	,	PUNCT
ejpam-5191	193	34	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	193	35	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	193	36	-	-	PUNCT
ejpam-5191	193	37	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	193	38	-	-	PUNCT
ejpam-5191	193	39	cl(v1	cl(v1	NOUN
ejpam-5191	193	40	)	)	PUNCT
ejpam-5191	193	41	)	)	PUNCT
ejpam-5191	193	42	)	)	PUNCT
ejpam-5191	193	43	∪	∪	ADP
ejpam-5191	193	44	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	193	45	-	-	PUNCT
ejpam-5191	193	46	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	193	47	-	-	PUNCT
ejpam-5191	193	48	cl(v2	cl(v2	NOUN
ejpam-5191	193	49	)	)	PUNCT
ejpam-5191	193	50	)	)	PUNCT
ejpam-5191	193	51	)	)	PUNCT
ejpam-5191	193	52	)	)	PUNCT
ejpam-5191	194	1	⊆	⊆	X
ejpam-5191	194	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	194	3	-	-	PUNCT
ejpam-5191	194	4	cl(v1	cl(v1	NOUN
ejpam-5191	194	5	)	)	PUNCT
ejpam-5191	194	6	)	)	PUNCT
ejpam-5191	194	7	∪	∪	ADP
ejpam-5191	194	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	194	9	-	-	PUNCT
ejpam-5191	194	10	cl(v2	cl(v2	NOUN
ejpam-5191	194	11	)	)	PUNCT
ejpam-5191	194	12	)	)	PUNCT
ejpam-5191	194	13	for	for	ADP
ejpam-5191	194	14	every	every	DET
ejpam-5191	194	15	(	(	PUNCT
ejpam-5191	194	16	σ1	σ1	PROPN
ejpam-5191	194	17	,	,	PUNCT
ejpam-5191	194	18	σ2)p	σ2)p	NOUN
ejpam-5191	194	19	-	-	PUNCT
ejpam-5191	194	20	open	open	ADJ
ejpam-5191	194	21	sets	set	NOUN
ejpam-5191	194	22	v1	v1	NOUN
ejpam-5191	194	23	,	,	PUNCT
ejpam-5191	194	24	v2	v2	PROPN
ejpam-5191	194	25	of	of	ADP
ejpam-5191	194	26	y	y	PROPN
ejpam-5191	194	27	.	.	PUNCT
ejpam-5191	195	1	proof	proof	NOUN
ejpam-5191	195	2	.	.	PUNCT
ejpam-5191	196	1	(	(	PUNCT
ejpam-5191	196	2	1	1	X
ejpam-5191	196	3	)	)	PUNCT
ejpam-5191	196	4	⇒	⇒	NOUN
ejpam-5191	196	5	(	(	PUNCT
ejpam-5191	196	6	2	2	NUM
ejpam-5191	196	7	):	):	PUNCT
ejpam-5191	196	8	let	let	VERB
ejpam-5191	196	9	v1	v1	NOUN
ejpam-5191	196	10	,	,	PUNCT
ejpam-5191	196	11	v2	v2	PROPN
ejpam-5191	196	12	be	be	VERB
ejpam-5191	196	13	any	any	DET
ejpam-5191	196	14	(	(	PUNCT
ejpam-5191	196	15	σ1	σ1	PROPN
ejpam-5191	196	16	,	,	PUNCT
ejpam-5191	196	17	σ2)β	σ2)β	NOUN
ejpam-5191	196	18	-	-	PUNCT
ejpam-5191	196	19	open	open	ADJ
ejpam-5191	196	20	sets	set	NOUN
ejpam-5191	196	21	of	of	ADP
ejpam-5191	196	22	y	y	PROPN
ejpam-5191	196	23	.	.	PUNCT
ejpam-5191	197	1	then	then	ADV
ejpam-5191	197	2	,	,	PUNCT
ejpam-5191	197	3	we	we	PRON
ejpam-5191	197	4	have	have	VERB
ejpam-5191	197	5	vi	vi	NUM
ejpam-5191	197	6	⊆	⊆	NUM
ejpam-5191	197	7	σ1σ2	σ1σ2	NOUN
ejpam-5191	197	8	-	-	PUNCT
ejpam-5191	197	9	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5191	197	10	-	-	PUNCT
ejpam-5191	197	11	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	197	12	-	-	PUNCT
ejpam-5191	197	13	cl(vi	cl(vi	NOUN
ejpam-5191	197	14	)	)	PUNCT
ejpam-5191	197	15	)	)	PUNCT
ejpam-5191	197	16	)	)	PUNCT
ejpam-5191	197	17	and	and	CCONJ
ejpam-5191	197	18	hence	hence	ADV
ejpam-5191	197	19	σ1σ2	σ1σ2	NOUN
ejpam-5191	197	20	-	-	PUNCT
ejpam-5191	197	21	cl(vi	cl(vi	NOUN
ejpam-5191	197	22	)	)	PUNCT
ejpam-5191	197	23	=	=	SYM
ejpam-5191	197	24	σ1σ2	σ1σ2	X
ejpam-5191	197	25	-	-	PUNCT
ejpam-5191	197	26	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5191	197	27	-	-	PUNCT
ejpam-5191	197	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	197	29	-	-	PUNCT
ejpam-5191	197	30	cl(vi	cl(vi	NOUN
ejpam-5191	197	31	)	)	PUNCT
ejpam-5191	197	32	)	)	PUNCT
ejpam-5191	197	33	)	)	PUNCT
ejpam-5191	198	1	for	for	ADP
ejpam-5191	198	2	i	i	PROPN
ejpam-5191	198	3	=	=	SYM
ejpam-5191	198	4	1	1	NUM
ejpam-5191	198	5	,	,	PUNCT
ejpam-5191	198	6	2	2	NUM
ejpam-5191	198	7	.	.	PUNCT
ejpam-5191	198	8	since	since	SCONJ
ejpam-5191	198	9	σ1σ2	σ1σ2	NOUN
ejpam-5191	198	10	-	-	PUNCT
ejpam-5191	198	11	cl(v1	cl(v1	X
ejpam-5191	198	12	)	)	PUNCT
ejpam-5191	198	13	and	and	CCONJ
ejpam-5191	198	14	σ1σ2	σ1σ2	NOUN
ejpam-5191	198	15	-	-	NOUN
ejpam-5191	198	16	cl(v2	cl(v2	NOUN
ejpam-5191	198	17	)	)	PUNCT
ejpam-5191	198	18	are	be	AUX
ejpam-5191	198	19	(	(	PUNCT
ejpam-5191	198	20	σ1	σ1	NOUN
ejpam-5191	198	21	,	,	PUNCT
ejpam-5191	198	22	σ2)r	σ2)r	NOUN
ejpam-5191	198	23	-	-	PUNCT
ejpam-5191	198	24	closed	close	VERB
ejpam-5191	198	25	sets	set	NOUN
ejpam-5191	198	26	,	,	PUNCT
ejpam-5191	198	27	by	by	ADP
ejpam-5191	198	28	theorem	theorem	NOUN
ejpam-5191	198	29	2	2	NUM
ejpam-5191	198	30	(	(	PUNCT
ejpam-5191	198	31	τ1	τ1	NOUN
ejpam-5191	198	32	,	,	PUNCT
ejpam-5191	198	33	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	198	34	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	198	35	-	-	PUNCT
ejpam-5191	198	36	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	198	37	-	-	PUNCT
ejpam-5191	198	38	cl(v1	cl(v1	NOUN
ejpam-5191	198	39	)	)	PUNCT
ejpam-5191	198	40	)	)	PUNCT
ejpam-5191	198	41	)	)	PUNCT
ejpam-5191	198	42	∪	∪	ADP
ejpam-5191	198	43	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	198	44	-	-	PUNCT
ejpam-5191	198	45	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	198	46	-	-	PUNCT
ejpam-5191	198	47	cl(v2	cl(v2	NOUN
ejpam-5191	198	48	)	)	PUNCT
ejpam-5191	198	49	)	)	PUNCT
ejpam-5191	198	50	)	)	PUNCT
ejpam-5191	198	51	)	)	PUNCT
ejpam-5191	199	1	⊆	⊆	X
ejpam-5191	199	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	199	3	-	-	PUNCT
ejpam-5191	199	4	cl(v1	cl(v1	NOUN
ejpam-5191	199	5	)	)	PUNCT
ejpam-5191	199	6	)	)	PUNCT
ejpam-5191	199	7	∪	∪	ADP
ejpam-5191	199	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	199	9	-	-	PUNCT
ejpam-5191	199	10	cl(v2	cl(v2	NOUN
ejpam-5191	199	11	)	)	PUNCT
ejpam-5191	199	12	)	)	PUNCT
ejpam-5191	199	13	.	.	PUNCT
ejpam-5191	200	1	(	(	PUNCT
ejpam-5191	200	2	2	2	X
ejpam-5191	200	3	)	)	PUNCT
ejpam-5191	200	4	⇒	⇒	NOUN
ejpam-5191	200	5	(	(	PUNCT
ejpam-5191	200	6	3	3	NUM
ejpam-5191	200	7	):	):	PUNCT
ejpam-5191	200	8	this	this	PRON
ejpam-5191	200	9	is	be	AUX
ejpam-5191	200	10	obvious	obvious	ADJ
ejpam-5191	200	11	since	since	SCONJ
ejpam-5191	200	12	every	every	DET
ejpam-5191	200	13	(	(	PUNCT
ejpam-5191	200	14	σ1	σ1	PROPN
ejpam-5191	200	15	,	,	PUNCT
ejpam-5191	200	16	σ2)s	σ2)s	NOUN
ejpam-5191	200	17	-	-	PUNCT
ejpam-5191	200	18	open	open	ADJ
ejpam-5191	200	19	set	set	NOUN
ejpam-5191	200	20	is	be	AUX
ejpam-5191	200	21	(	(	PUNCT
ejpam-5191	200	22	σ1	σ1	PROPN
ejpam-5191	200	23	,	,	PUNCT
ejpam-5191	200	24	σ2)β	σ2)β	NOUN
ejpam-5191	200	25	-	-	PUNCT
ejpam-5191	200	26	open	open	ADJ
ejpam-5191	200	27	.	.	PUNCT
ejpam-5191	201	1	(	(	PUNCT
ejpam-5191	201	2	3	3	X
ejpam-5191	201	3	)	)	PUNCT
ejpam-5191	201	4	⇒	⇒	NOUN
ejpam-5191	201	5	(	(	PUNCT
ejpam-5191	201	6	4	4	NUM
ejpam-5191	201	7	):	):	PUNCT
ejpam-5191	201	8	for	for	ADP
ejpam-5191	201	9	any	any	DET
ejpam-5191	201	10	(	(	PUNCT
ejpam-5191	201	11	σ1	σ1	PROPN
ejpam-5191	201	12	,	,	PUNCT
ejpam-5191	201	13	σ2)p	σ2)p	NOUN
ejpam-5191	201	14	-	-	PUNCT
ejpam-5191	201	15	open	open	NOUN
ejpam-5191	201	16	set	set	NOUN
ejpam-5191	201	17	v	v	NOUN
ejpam-5191	201	18	of	of	ADP
ejpam-5191	201	19	y	y	PROPN
ejpam-5191	201	20	,	,	PUNCT
ejpam-5191	201	21	σ1σ2	σ1σ2	NOUN
ejpam-5191	201	22	-	-	NUM
ejpam-5191	201	23	cl(v	cl(v	NOUN
ejpam-5191	201	24	)	)	PUNCT
ejpam-5191	201	25	is	be	AUX
ejpam-5191	201	26	(	(	PUNCT
ejpam-5191	201	27	σ1	σ1	NOUN
ejpam-5191	201	28	,	,	PUNCT
ejpam-5191	201	29	σ2)r	σ2)r	NOUN
ejpam-5191	201	30	-	-	PUNCT
ejpam-5191	201	31	closed	closed	ADJ
ejpam-5191	201	32	and	and	CCONJ
ejpam-5191	201	33	σ1σ2	σ1σ2	NOUN
ejpam-5191	201	34	-	-	NUM
ejpam-5191	201	35	cl(v	cl(v	NOUN
ejpam-5191	201	36	)	)	PUNCT
ejpam-5191	201	37	is	be	AUX
ejpam-5191	201	38	(	(	PUNCT
ejpam-5191	201	39	σ1	σ1	PROPN
ejpam-5191	201	40	,	,	PUNCT
ejpam-5191	201	41	σ2)s	σ2)s	NOUN
ejpam-5191	201	42	-	-	PUNCT
ejpam-5191	201	43	open	open	ADJ
ejpam-5191	201	44	in	in	ADP
ejpam-5191	201	45	y	y	PROPN
ejpam-5191	201	46	.	.	PUNCT
ejpam-5191	202	1	(	(	PUNCT
ejpam-5191	202	2	4	4	X
ejpam-5191	202	3	)	)	PUNCT
ejpam-5191	202	4	⇒	⇒	NOUN
ejpam-5191	202	5	(	(	PUNCT
ejpam-5191	202	6	1	1	NUM
ejpam-5191	202	7	):	):	PUNCT
ejpam-5191	202	8	let	let	VERB
ejpam-5191	202	9	v1	v1	NOUN
ejpam-5191	202	10	,	,	PUNCT
ejpam-5191	202	11	v2	v2	PROPN
ejpam-5191	202	12	be	be	AUX
ejpam-5191	202	13	any	any	DET
ejpam-5191	202	14	σ1σ2	σ1σ2	NOUN
ejpam-5191	202	15	-	-	PUNCT
ejpam-5191	202	16	open	open	ADJ
ejpam-5191	202	17	sets	set	NOUN
ejpam-5191	202	18	of	of	ADP
ejpam-5191	202	19	y	y	PROPN
ejpam-5191	202	20	.	.	PUNCT
ejpam-5191	203	1	then	then	ADV
ejpam-5191	203	2	,	,	PUNCT
ejpam-5191	203	3	v1	v1	VERB
ejpam-5191	203	4	and	and	CCONJ
ejpam-5191	203	5	v2	v2	PROPN
ejpam-5191	203	6	are	be	AUX
ejpam-5191	203	7	(	(	PUNCT
ejpam-5191	203	8	σ1	σ1	PROPN
ejpam-5191	203	9	,	,	PUNCT
ejpam-5191	203	10	σ2)ppreopen	σ2)ppreopen	ADJ
ejpam-5191	203	11	in	in	ADP
ejpam-5191	203	12	y	y	PROPN
ejpam-5191	203	13	.	.	PUNCT
ejpam-5191	204	1	by	by	ADP
ejpam-5191	204	2	(	(	PUNCT
ejpam-5191	204	3	4	4	NUM
ejpam-5191	204	4	)	)	PUNCT
ejpam-5191	204	5	,	,	PUNCT
ejpam-5191	204	6	we	we	PRON
ejpam-5191	204	7	have	have	VERB
ejpam-5191	204	8	(	(	PUNCT
ejpam-5191	204	9	τ1	τ1	NOUN
ejpam-5191	204	10	,	,	PUNCT
ejpam-5191	204	11	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	204	12	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	204	13	-	-	PUNCT
ejpam-5191	204	14	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	204	15	-	-	PUNCT
ejpam-5191	204	16	cl(v1	cl(v1	NOUN
ejpam-5191	204	17	)	)	PUNCT
ejpam-5191	204	18	)	)	PUNCT
ejpam-5191	204	19	)	)	PUNCT
ejpam-5191	205	1	∪	∪	ADP
ejpam-5191	205	2	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	205	3	-	-	PUNCT
ejpam-5191	205	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	205	5	-	-	PUNCT
ejpam-5191	205	6	cl(v2	cl(v2	NOUN
ejpam-5191	205	7	)	)	PUNCT
ejpam-5191	205	8	)	)	PUNCT
ejpam-5191	205	9	)	)	PUNCT
ejpam-5191	205	10	)	)	PUNCT
ejpam-5191	206	1	⊆	⊆	X
ejpam-5191	206	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	206	3	-	-	PUNCT
ejpam-5191	206	4	cl(v1	cl(v1	NOUN
ejpam-5191	206	5	)	)	PUNCT
ejpam-5191	206	6	)	)	PUNCT
ejpam-5191	206	7	∪	∪	ADP
ejpam-5191	206	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	206	9	-	-	PUNCT
ejpam-5191	206	10	cl(v2	cl(v2	NOUN
ejpam-5191	206	11	)	)	PUNCT
ejpam-5191	206	12	)	)	PUNCT
ejpam-5191	206	13	.	.	PUNCT
ejpam-5191	207	1	it	it	PRON
ejpam-5191	207	2	follows	follow	VERB
ejpam-5191	207	3	from	from	ADP
ejpam-5191	207	4	theorem	theorem	ADJ
ejpam-5191	207	5	2	2	NUM
ejpam-5191	207	6	that	that	PRON
ejpam-5191	207	7	f	f	PROPN
ejpam-5191	207	8	is	be	AUX
ejpam-5191	207	9	weakly	weakly	ADJ
ejpam-5191	207	10	quasi	quasi	NOUN
ejpam-5191	207	11	(	(	PUNCT
ejpam-5191	207	12	τ1	τ1	NOUN
ejpam-5191	207	13	,	,	PUNCT
ejpam-5191	207	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	207	15	.	.	PUNCT
ejpam-5191	208	1	theorem	theorem	NOUN
ejpam-5191	208	2	4	4	NUM
ejpam-5191	208	3	.	.	X
ejpam-5191	208	4	for	for	ADP
ejpam-5191	208	5	a	a	DET
ejpam-5191	208	6	multifunction	multifunction	NOUN
ejpam-5191	209	1	f	f	NOUN
ejpam-5191	209	2	:	:	PUNCT
ejpam-5191	209	3	(	(	PUNCT
ejpam-5191	209	4	x	x	NOUN
ejpam-5191	209	5	,	,	PUNCT
ejpam-5191	209	6	τ1	τ1	NOUN
ejpam-5191	209	7	,	,	PUNCT
ejpam-5191	209	8	τ2	τ2	NOUN
ejpam-5191	209	9	)	)	PUNCT
ejpam-5191	209	10	→	→	SYM
ejpam-5191	209	11	(	(	PUNCT
ejpam-5191	209	12	y	y	PROPN
ejpam-5191	209	13	,	,	PUNCT
ejpam-5191	209	14	σ1	σ1	PROPN
ejpam-5191	209	15	,	,	PUNCT
ejpam-5191	209	16	σ2	σ2	NOUN
ejpam-5191	209	17	)	)	PUNCT
ejpam-5191	209	18	,	,	PUNCT
ejpam-5191	209	19	the	the	DET
ejpam-5191	209	20	following	follow	VERB
ejpam-5191	209	21	properties	property	NOUN
ejpam-5191	209	22	are	be	AUX
ejpam-5191	209	23	equivalent	equivalent	ADJ
ejpam-5191	209	24	:	:	PUNCT
ejpam-5191	209	25	(	(	PUNCT
ejpam-5191	209	26	1	1	X
ejpam-5191	209	27	)	)	PUNCT
ejpam-5191	209	28	f	f	PROPN
ejpam-5191	209	29	is	be	AUX
ejpam-5191	209	30	weakly	weakly	ADJ
ejpam-5191	209	31	quasi	quasi	NOUN
ejpam-5191	209	32	(	(	PUNCT
ejpam-5191	209	33	τ1	τ1	NOUN
ejpam-5191	209	34	,	,	PUNCT
ejpam-5191	209	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	209	36	;	;	PUNCT
ejpam-5191	209	37	(	(	PUNCT
ejpam-5191	209	38	2	2	X
ejpam-5191	209	39	)	)	PUNCT
ejpam-5191	209	40	τ1τ2	τ1τ2	NOUN
ejpam-5191	209	41	-	-	NOUN
ejpam-5191	209	42	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	209	43	-	-	PUNCT
ejpam-5191	209	44	cl(f	cl(f	NOUN
ejpam-5191	209	45	−(v1)∪f+(v2	−(v1)∪f+(v2	PROPN
ejpam-5191	209	46	)	)	PUNCT
ejpam-5191	209	47	)	)	PUNCT
ejpam-5191	209	48	)	)	PUNCT
ejpam-5191	210	1	⊆	⊆	X
ejpam-5191	210	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	210	3	-	-	PUNCT
ejpam-5191	210	4	cl(v1))∪f+(σ1σ2	cl(v1))∪f+(σ1σ2	NOUN
ejpam-5191	210	5	-	-	NOUN
ejpam-5191	210	6	cl(v2	cl(v2	NOUN
ejpam-5191	210	7	)	)	PUNCT
ejpam-5191	210	8	)	)	PUNCT
ejpam-5191	210	9	for	for	ADP
ejpam-5191	210	10	every	every	DET
ejpam-5191	210	11	(	(	PUNCT
ejpam-5191	210	12	σ1	σ1	PROPN
ejpam-5191	210	13	,	,	PUNCT
ejpam-5191	210	14	σ2)p	σ2)p	NOUN
ejpam-5191	210	15	-	-	PUNCT
ejpam-5191	210	16	open	open	ADJ
ejpam-5191	210	17	sets	set	NOUN
ejpam-5191	210	18	v1	v1	NOUN
ejpam-5191	210	19	,	,	PUNCT
ejpam-5191	210	20	v2	v2	PROPN
ejpam-5191	210	21	of	of	ADP
ejpam-5191	210	22	y	y	PROPN
ejpam-5191	210	23	;	;	PUNCT
ejpam-5191	210	24	(	(	PUNCT
ejpam-5191	210	25	3	3	X
ejpam-5191	210	26	)	)	PUNCT
ejpam-5191	210	27	(	(	PUNCT
ejpam-5191	210	28	τ1	τ1	PROPN
ejpam-5191	210	29	,	,	PUNCT
ejpam-5191	210	30	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	210	31	−(v1)∪f+(v2	−(v1)∪f+(v2	PROPN
ejpam-5191	210	32	)	)	PUNCT
ejpam-5191	210	33	)	)	PUNCT
ejpam-5191	211	1	⊆	⊆	X
ejpam-5191	211	2	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	211	3	-	-	PUNCT
ejpam-5191	211	4	cl(v1))∪f+(σ1σ2	cl(v1))∪f+(σ1σ2	NOUN
ejpam-5191	211	5	-	-	NOUN
ejpam-5191	211	6	cl(v2	cl(v2	NOUN
ejpam-5191	211	7	)	)	PUNCT
ejpam-5191	211	8	)	)	PUNCT
ejpam-5191	211	9	for	for	ADP
ejpam-5191	211	10	every	every	DET
ejpam-5191	211	11	(	(	PUNCT
ejpam-5191	211	12	σ1	σ1	PROPN
ejpam-5191	211	13	,	,	PUNCT
ejpam-5191	211	14	σ2)popen	σ2)popen	PROPN
ejpam-5191	211	15	sets	set	NOUN
ejpam-5191	211	16	v1	v1	NOUN
ejpam-5191	211	17	,	,	PUNCT
ejpam-5191	211	18	v2	v2	PROPN
ejpam-5191	211	19	of	of	ADP
ejpam-5191	211	20	y	y	PROPN
ejpam-5191	211	21	;	;	PUNCT
ejpam-5191	211	22	(	(	PUNCT
ejpam-5191	211	23	4	4	X
ejpam-5191	211	24	)	)	PUNCT
ejpam-5191	211	25	f+(v1)∩f−(v2	f+(v1)∩f−(v2	NOUN
ejpam-5191	211	26	)	)	PUNCT
ejpam-5191	211	27	⊆	⊆	NUM
ejpam-5191	211	28	(	(	PUNCT
ejpam-5191	211	29	τ1	τ1	NOUN
ejpam-5191	211	30	,	,	PUNCT
ejpam-5191	211	31	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	211	32	+	+	ADJ
ejpam-5191	211	33	(	(	PUNCT
ejpam-5191	211	34	σ1σ2	σ1σ2	X
ejpam-5191	211	35	-	-	PUNCT
ejpam-5191	211	36	cl(v1))∩f−(σ1σ2	cl(v1))∩f−(σ1σ2	NOUN
ejpam-5191	211	37	-	-	PUNCT
ejpam-5191	211	38	cl(v2	cl(v2	NOUN
ejpam-5191	211	39	)	)	PUNCT
ejpam-5191	211	40	)	)	PUNCT
ejpam-5191	211	41	)	)	PUNCT
ejpam-5191	212	1	for	for	ADP
ejpam-5191	212	2	every	every	DET
ejpam-5191	212	3	(	(	PUNCT
ejpam-5191	212	4	σ1	σ1	PROPN
ejpam-5191	212	5	,	,	PUNCT
ejpam-5191	212	6	σ2)popen	σ2)popen	PROPN
ejpam-5191	212	7	sets	set	NOUN
ejpam-5191	212	8	v1	v1	NOUN
ejpam-5191	212	9	,	,	PUNCT
ejpam-5191	212	10	v2	v2	PROPN
ejpam-5191	212	11	of	of	ADP
ejpam-5191	212	12	y	y	PROPN
ejpam-5191	212	13	.	.	PUNCT
ejpam-5191	213	1	references	reference	NOUN
ejpam-5191	213	2	1561	1561	NUM
ejpam-5191	213	3	proof	proof	NOUN
ejpam-5191	213	4	.	.	PUNCT
ejpam-5191	214	1	(	(	PUNCT
ejpam-5191	214	2	1	1	X
ejpam-5191	214	3	)	)	PUNCT
ejpam-5191	214	4	⇒	⇒	NOUN
ejpam-5191	214	5	(	(	PUNCT
ejpam-5191	214	6	2	2	NUM
ejpam-5191	214	7	):	):	PUNCT
ejpam-5191	214	8	let	let	VERB
ejpam-5191	214	9	v1	v1	NOUN
ejpam-5191	214	10	,	,	PUNCT
ejpam-5191	214	11	v2	v2	PROPN
ejpam-5191	214	12	be	be	VERB
ejpam-5191	214	13	any	any	DET
ejpam-5191	214	14	(	(	PUNCT
ejpam-5191	214	15	σ1	σ1	PROPN
ejpam-5191	214	16	,	,	PUNCT
ejpam-5191	214	17	σ2)p	σ2)p	NOUN
ejpam-5191	214	18	-	-	PUNCT
ejpam-5191	214	19	open	open	ADJ
ejpam-5191	214	20	sets	set	NOUN
ejpam-5191	214	21	of	of	ADP
ejpam-5191	214	22	y	y	PROPN
ejpam-5191	214	23	.	.	PUNCT
ejpam-5191	215	1	since	since	SCONJ
ejpam-5191	215	2	f	f	PROPN
ejpam-5191	215	3	is	be	AUX
ejpam-5191	215	4	weakly	weakly	ADJ
ejpam-5191	215	5	quasi	quasi	NOUN
ejpam-5191	215	6	(	(	PUNCT
ejpam-5191	215	7	τ1	τ1	NOUN
ejpam-5191	215	8	,	,	PUNCT
ejpam-5191	215	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	215	10	,	,	PUNCT
ejpam-5191	215	11	by	by	ADP
ejpam-5191	215	12	theorem	theorem	NOUN
ejpam-5191	215	13	2	2	NUM
ejpam-5191	215	14	τ1τ2	τ1τ2	NOUN
ejpam-5191	215	15	-	-	NOUN
ejpam-5191	215	16	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	215	17	-	-	PUNCT
ejpam-5191	215	18	cl(f	cl(f	NOUN
ejpam-5191	215	19	−(v1	−(v1	NUM
ejpam-5191	215	20	)	)	PUNCT
ejpam-5191	215	21	∪	∪	ADP
ejpam-5191	215	22	f+(v2	f+(v2	NOUN
ejpam-5191	215	23	)	)	PUNCT
ejpam-5191	215	24	)	)	PUNCT
ejpam-5191	215	25	)	)	PUNCT
ejpam-5191	216	1	⊆	⊆	X
ejpam-5191	216	2	τ1τ2	τ1τ2	NOUN
ejpam-5191	216	3	-	-	NOUN
ejpam-5191	216	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	216	5	-	-	PUNCT
ejpam-5191	216	6	cl(f	cl(f	NOUN
ejpam-5191	216	7	−(σ1σ2	−(σ1σ2	NOUN
ejpam-5191	216	8	-	-	PUNCT
ejpam-5191	216	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	216	10	-	-	PUNCT
ejpam-5191	216	11	cl(v1	cl(v1	NOUN
ejpam-5191	216	12	)	)	PUNCT
ejpam-5191	216	13	)	)	PUNCT
ejpam-5191	216	14	)	)	PUNCT
ejpam-5191	216	15	∪	∪	ADP
ejpam-5191	216	16	f+(σ1σ2	f+(σ1σ2	ADV
ejpam-5191	216	17	-	-	PUNCT
ejpam-5191	216	18	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	216	19	-	-	PUNCT
ejpam-5191	216	20	cl(v2	cl(v2	NOUN
ejpam-5191	216	21	)	)	PUNCT
ejpam-5191	216	22	)	)	PUNCT
ejpam-5191	216	23	)	)	PUNCT
ejpam-5191	216	24	)	)	PUNCT
ejpam-5191	216	25	)	)	PUNCT
ejpam-5191	217	1	⊆	⊆	X
ejpam-5191	217	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	217	3	-	-	PUNCT
ejpam-5191	217	4	cl(v1	cl(v1	NOUN
ejpam-5191	217	5	)	)	PUNCT
ejpam-5191	217	6	)	)	PUNCT
ejpam-5191	217	7	∪	∪	ADP
ejpam-5191	217	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	217	9	-	-	PUNCT
ejpam-5191	217	10	cl(v2	cl(v2	NOUN
ejpam-5191	217	11	)	)	PUNCT
ejpam-5191	217	12	)	)	PUNCT
ejpam-5191	217	13	.	.	PUNCT
ejpam-5191	218	1	(	(	PUNCT
ejpam-5191	218	2	2	2	X
ejpam-5191	218	3	)	)	PUNCT
ejpam-5191	218	4	⇒	⇒	NOUN
ejpam-5191	218	5	(	(	PUNCT
ejpam-5191	218	6	3	3	NUM
ejpam-5191	218	7	):	):	PUNCT
ejpam-5191	218	8	let	let	VERB
ejpam-5191	218	9	v1	v1	NOUN
ejpam-5191	218	10	,	,	PUNCT
ejpam-5191	218	11	v2	v2	PROPN
ejpam-5191	218	12	be	be	VERB
ejpam-5191	218	13	any	any	DET
ejpam-5191	218	14	(	(	PUNCT
ejpam-5191	218	15	σ1	σ1	PROPN
ejpam-5191	218	16	,	,	PUNCT
ejpam-5191	218	17	σ2)p	σ2)p	NOUN
ejpam-5191	218	18	-	-	PUNCT
ejpam-5191	218	19	open	open	ADJ
ejpam-5191	218	20	sets	set	NOUN
ejpam-5191	218	21	of	of	ADP
ejpam-5191	218	22	y	y	PROPN
ejpam-5191	218	23	.	.	PUNCT
ejpam-5191	219	1	by	by	ADP
ejpam-5191	219	2	(	(	PUNCT
ejpam-5191	219	3	2	2	NUM
ejpam-5191	219	4	)	)	PUNCT
ejpam-5191	219	5	and	and	CCONJ
ejpam-5191	219	6	lemma	lemma	PROPN
ejpam-5191	219	7	2	2	NUM
ejpam-5191	219	8	,	,	PUNCT
ejpam-5191	219	9	we	we	PRON
ejpam-5191	219	10	have	have	VERB
ejpam-5191	219	11	(	(	PUNCT
ejpam-5191	219	12	τ1	τ1	NOUN
ejpam-5191	219	13	,	,	PUNCT
ejpam-5191	219	14	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	219	15	−(v1	−(v1	NUM
ejpam-5191	219	16	)	)	PUNCT
ejpam-5191	219	17	∪	∪	ADP
ejpam-5191	219	18	f+(v2	f+(v2	NOUN
ejpam-5191	219	19	)	)	PUNCT
ejpam-5191	219	20	)	)	PUNCT
ejpam-5191	220	1	=	=	PRON
ejpam-5191	220	2	(	(	PUNCT
ejpam-5191	220	3	f−(v1	f−(v1	NOUN
ejpam-5191	220	4	)	)	PUNCT
ejpam-5191	220	5	∪	∪	NOUN
ejpam-5191	220	6	f+(v2	f+(v2	NOUN
ejpam-5191	220	7	)	)	PUNCT
ejpam-5191	220	8	)	)	PUNCT
ejpam-5191	220	9	∪	∪	ADP
ejpam-5191	220	10	τ1τ2	τ1τ2	NOUN
ejpam-5191	220	11	-	-	NOUN
ejpam-5191	220	12	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5191	220	13	-	-	PUNCT
ejpam-5191	220	14	cl(f	cl(f	NOUN
ejpam-5191	220	15	−(v1	−(v1	NUM
ejpam-5191	220	16	)	)	PUNCT
ejpam-5191	220	17	∪	∪	ADP
ejpam-5191	220	18	f+(v2	f+(v2	NOUN
ejpam-5191	220	19	)	)	PUNCT
ejpam-5191	220	20	)	)	PUNCT
ejpam-5191	220	21	)	)	PUNCT
ejpam-5191	221	1	⊆	⊆	X
ejpam-5191	221	2	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	221	3	-	-	PUNCT
ejpam-5191	221	4	cl(v1	cl(v1	NOUN
ejpam-5191	221	5	)	)	PUNCT
ejpam-5191	221	6	)	)	PUNCT
ejpam-5191	221	7	∪	∪	ADP
ejpam-5191	221	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	221	9	-	-	PUNCT
ejpam-5191	221	10	cl(v2	cl(v2	NOUN
ejpam-5191	221	11	)	)	PUNCT
ejpam-5191	221	12	)	)	PUNCT
ejpam-5191	221	13	.	.	PUNCT
ejpam-5191	222	1	(	(	PUNCT
ejpam-5191	222	2	3	3	X
ejpam-5191	222	3	)	)	PUNCT
ejpam-5191	222	4	⇒	⇒	NOUN
ejpam-5191	222	5	(	(	PUNCT
ejpam-5191	222	6	4	4	NUM
ejpam-5191	222	7	):	):	PUNCT
ejpam-5191	222	8	let	let	VERB
ejpam-5191	222	9	v1	v1	NOUN
ejpam-5191	222	10	,	,	PUNCT
ejpam-5191	222	11	v2	v2	PROPN
ejpam-5191	222	12	be	be	VERB
ejpam-5191	222	13	any	any	DET
ejpam-5191	222	14	(	(	PUNCT
ejpam-5191	222	15	σ1	σ1	PROPN
ejpam-5191	222	16	,	,	PUNCT
ejpam-5191	222	17	σ2)p	σ2)p	NOUN
ejpam-5191	222	18	-	-	PUNCT
ejpam-5191	222	19	open	open	ADJ
ejpam-5191	222	20	sets	set	NOUN
ejpam-5191	222	21	of	of	ADP
ejpam-5191	222	22	y	y	PROPN
ejpam-5191	222	23	.	.	PUNCT
ejpam-5191	223	1	then	then	ADV
ejpam-5191	223	2	by	by	ADP
ejpam-5191	223	3	(	(	PUNCT
ejpam-5191	223	4	3	3	NUM
ejpam-5191	223	5	)	)	PUNCT
ejpam-5191	223	6	,	,	PUNCT
ejpam-5191	223	7	we	we	PRON
ejpam-5191	223	8	have	have	VERB
ejpam-5191	223	9	x	x	X
ejpam-5191	223	10	−	−	PROPN
ejpam-5191	223	11	(	(	PUNCT
ejpam-5191	223	12	τ1	τ1	NOUN
ejpam-5191	223	13	,	,	PUNCT
ejpam-5191	223	14	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	224	1	+	+	ADJ
ejpam-5191	224	2	(	(	PUNCT
ejpam-5191	224	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	224	4	-	-	PUNCT
ejpam-5191	224	5	cl(v1	cl(v1	NOUN
ejpam-5191	224	6	)	)	PUNCT
ejpam-5191	224	7	)	)	PUNCT
ejpam-5191	224	8	∩	∩	ADJ
ejpam-5191	224	9	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	224	10	-	-	PUNCT
ejpam-5191	224	11	cl(v2	cl(v2	NOUN
ejpam-5191	224	12	)	)	PUNCT
ejpam-5191	224	13	)	)	PUNCT
ejpam-5191	224	14	)	)	PUNCT
ejpam-5191	225	1	=	=	PRON
ejpam-5191	225	2	(	(	PUNCT
ejpam-5191	225	3	τ1	τ1	PROPN
ejpam-5191	225	4	,	,	PUNCT
ejpam-5191	225	5	τ2)-scl(x	τ2)-scl(x	NOUN
ejpam-5191	225	6	−	−	PROPN
ejpam-5191	225	7	(	(	PUNCT
ejpam-5191	225	8	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	225	9	-	-	PUNCT
ejpam-5191	225	10	cl(v1	cl(v1	NOUN
ejpam-5191	225	11	)	)	PUNCT
ejpam-5191	225	12	)	)	PUNCT
ejpam-5191	225	13	∩	∩	ADJ
ejpam-5191	225	14	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	225	15	-	-	PUNCT
ejpam-5191	225	16	cl(v2	cl(v2	NOUN
ejpam-5191	225	17	)	)	PUNCT
ejpam-5191	225	18	)	)	PUNCT
ejpam-5191	225	19	)	)	PUNCT
ejpam-5191	225	20	)	)	PUNCT
ejpam-5191	226	1	=	=	PRON
ejpam-5191	226	2	(	(	PUNCT
ejpam-5191	226	3	τ1	τ1	NOUN
ejpam-5191	226	4	,	,	PUNCT
ejpam-5191	226	5	τ2)-scl((x	τ2)-scl((x	NOUN
ejpam-5191	226	6	−	−	NOUN
ejpam-5191	226	7	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	226	8	-	-	PUNCT
ejpam-5191	226	9	cl(v1	cl(v1	NOUN
ejpam-5191	226	10	)	)	PUNCT
ejpam-5191	226	11	)	)	PUNCT
ejpam-5191	226	12	)	)	PUNCT
ejpam-5191	227	1	∪	∪	ADP
ejpam-5191	227	2	(	(	PUNCT
ejpam-5191	227	3	x	x	SYM
ejpam-5191	227	4	−	−	NOUN
ejpam-5191	227	5	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	227	6	-	-	PUNCT
ejpam-5191	227	7	cl(v2	cl(v2	NOUN
ejpam-5191	227	8	)	)	PUNCT
ejpam-5191	227	9	)	)	PUNCT
ejpam-5191	227	10	)	)	PUNCT
ejpam-5191	227	11	)	)	PUNCT
ejpam-5191	228	1	=	=	PRON
ejpam-5191	228	2	(	(	PUNCT
ejpam-5191	228	3	τ1	τ1	PROPN
ejpam-5191	228	4	,	,	PUNCT
ejpam-5191	228	5	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5191	229	1	−(y	−(y	NOUN
ejpam-5191	229	2	−	−	NOUN
ejpam-5191	229	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	229	4	-	-	PUNCT
ejpam-5191	229	5	cl(v1	cl(v1	NOUN
ejpam-5191	229	6	)	)	PUNCT
ejpam-5191	229	7	)	)	PUNCT
ejpam-5191	229	8	∪	∪	ADP
ejpam-5191	229	9	f+(y	f+(y	NUM
ejpam-5191	229	10	−	−	PROPN
ejpam-5191	229	11	σ1σ2	σ1σ2	NUM
ejpam-5191	229	12	-	-	NOUN
ejpam-5191	229	13	cl(v2	cl(v2	NOUN
ejpam-5191	229	14	)	)	PUNCT
ejpam-5191	229	15	)	)	PUNCT
ejpam-5191	229	16	)	)	PUNCT
ejpam-5191	230	1	⊆	⊆	X
ejpam-5191	230	2	f−(σ1σ2	f−(σ1σ2	ADJ
ejpam-5191	230	3	-	-	PUNCT
ejpam-5191	230	4	cl(y	cl(y	NOUN
ejpam-5191	230	5	−	−	NOUN
ejpam-5191	230	6	σ1σ2	σ1σ2	NOUN
ejpam-5191	230	7	-	-	PUNCT
ejpam-5191	230	8	cl(v1	cl(v1	NOUN
ejpam-5191	230	9	)	)	PUNCT
ejpam-5191	230	10	)	)	PUNCT
ejpam-5191	230	11	)	)	PUNCT
ejpam-5191	230	12	∪	∪	ADP
ejpam-5191	230	13	f+(σ1σ2	f+(σ1σ2	NOUN
ejpam-5191	230	14	-	-	PUNCT
ejpam-5191	230	15	cl(y	cl(y	NOUN
ejpam-5191	230	16	−	−	NOUN
ejpam-5191	230	17	σ1σ2	σ1σ2	NOUN
ejpam-5191	230	18	-	-	NOUN
ejpam-5191	230	19	cl(v2	cl(v2	NOUN
ejpam-5191	230	20	)	)	PUNCT
ejpam-5191	230	21	)	)	PUNCT
ejpam-5191	230	22	)	)	PUNCT
ejpam-5191	231	1	=	=	PUNCT
ejpam-5191	231	2	(	(	PUNCT
ejpam-5191	231	3	x	x	X
ejpam-5191	231	4	−	−	PRON
ejpam-5191	231	5	f+(σ1σ2	f+(σ1σ2	ADJ
ejpam-5191	231	6	-	-	PUNCT
ejpam-5191	231	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	231	8	-	-	PUNCT
ejpam-5191	231	9	cl(v1	cl(v1	NOUN
ejpam-5191	231	10	)	)	PUNCT
ejpam-5191	231	11	)	)	PUNCT
ejpam-5191	231	12	)	)	PUNCT
ejpam-5191	231	13	)	)	PUNCT
ejpam-5191	232	1	∪	∪	ADV
ejpam-5191	232	2	(	(	PUNCT
ejpam-5191	232	3	x	x	SYM
ejpam-5191	232	4	−	−	NOUN
ejpam-5191	232	5	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	232	6	-	-	PUNCT
ejpam-5191	232	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	232	8	-	-	PUNCT
ejpam-5191	232	9	cl(v2	cl(v2	NOUN
ejpam-5191	232	10	)	)	PUNCT
ejpam-5191	232	11	)	)	PUNCT
ejpam-5191	232	12	)	)	PUNCT
ejpam-5191	232	13	)	)	PUNCT
ejpam-5191	233	1	=	=	PUNCT
ejpam-5191	233	2	x	x	X
ejpam-5191	233	3	−	−	PROPN
ejpam-5191	233	4	(	(	PUNCT
ejpam-5191	233	5	f+(σ1σ2	f+(σ1σ2	VERB
ejpam-5191	233	6	-	-	PUNCT
ejpam-5191	233	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	233	8	-	-	PUNCT
ejpam-5191	233	9	cl(v1	cl(v1	NOUN
ejpam-5191	233	10	)	)	PUNCT
ejpam-5191	233	11	)	)	PUNCT
ejpam-5191	233	12	)	)	PUNCT
ejpam-5191	233	13	∩	∩	NOUN
ejpam-5191	233	14	f−(σ1σ2	f−(σ1σ2	ADV
ejpam-5191	233	15	-	-	PUNCT
ejpam-5191	233	16	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5191	233	17	-	-	PUNCT
ejpam-5191	233	18	cl(v2	cl(v2	NOUN
ejpam-5191	233	19	)	)	PUNCT
ejpam-5191	233	20	)	)	PUNCT
ejpam-5191	233	21	)	)	PUNCT
ejpam-5191	233	22	)	)	PUNCT
ejpam-5191	234	1	⊆	⊆	NUM
ejpam-5191	234	2	x	x	SYM
ejpam-5191	234	3	−	−	PROPN
ejpam-5191	234	4	(	(	PUNCT
ejpam-5191	234	5	f+(v1	f+(v1	NOUN
ejpam-5191	234	6	)	)	PUNCT
ejpam-5191	234	7	∩	∩	NOUN
ejpam-5191	234	8	f−(v2	f−(v2	NUM
ejpam-5191	234	9	)	)	PUNCT
ejpam-5191	234	10	)	)	PUNCT
ejpam-5191	234	11	and	and	CCONJ
ejpam-5191	234	12	hence	hence	ADV
ejpam-5191	234	13	f+(v1	f+(v1	ADJ
ejpam-5191	234	14	)	)	PUNCT
ejpam-5191	234	15	∩	∩	NOUN
ejpam-5191	234	16	f−(v2	f−(v2	X
ejpam-5191	234	17	)	)	PUNCT
ejpam-5191	234	18	⊆	⊆	NUM
ejpam-5191	234	19	(	(	PUNCT
ejpam-5191	234	20	τ1	τ1	NOUN
ejpam-5191	234	21	,	,	PUNCT
ejpam-5191	234	22	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5191	235	1	+	+	ADJ
ejpam-5191	235	2	(	(	PUNCT
ejpam-5191	235	3	σ1σ2	σ1σ2	NOUN
ejpam-5191	235	4	-	-	PUNCT
ejpam-5191	235	5	cl(v1	cl(v1	NOUN
ejpam-5191	235	6	)	)	PUNCT
ejpam-5191	235	7	)	)	PUNCT
ejpam-5191	235	8	∩	∩	ADJ
ejpam-5191	235	9	f−(σ1σ2	f−(σ1σ2	NOUN
ejpam-5191	235	10	-	-	PUNCT
ejpam-5191	235	11	cl(v2	cl(v2	NOUN
ejpam-5191	235	12	)	)	PUNCT
ejpam-5191	235	13	)	)	PUNCT
ejpam-5191	235	14	)	)	PUNCT
ejpam-5191	235	15	.	.	PUNCT
ejpam-5191	236	1	(	(	PUNCT
ejpam-5191	236	2	4	4	X
ejpam-5191	236	3	)	)	PUNCT
ejpam-5191	236	4	⇒	⇒	NOUN
ejpam-5191	236	5	(	(	PUNCT
ejpam-5191	236	6	1	1	NUM
ejpam-5191	236	7	):	):	PUNCT
ejpam-5191	236	8	since	since	SCONJ
ejpam-5191	236	9	every	every	DET
ejpam-5191	236	10	σ1σ2	σ1σ2	NUM
ejpam-5191	236	11	-	-	ADJ
ejpam-5191	236	12	open	open	ADJ
ejpam-5191	236	13	set	set	NOUN
ejpam-5191	236	14	is	be	AUX
ejpam-5191	236	15	(	(	PUNCT
ejpam-5191	236	16	σ1	σ1	PROPN
ejpam-5191	236	17	,	,	PUNCT
ejpam-5191	236	18	σ2)p	σ2)p	NOUN
ejpam-5191	236	19	-	-	PUNCT
ejpam-5191	236	20	open	open	ADJ
ejpam-5191	236	21	,	,	PUNCT
ejpam-5191	236	22	this	this	PRON
ejpam-5191	236	23	follows	follow	VERB
ejpam-5191	236	24	from	from	ADP
ejpam-5191	236	25	theorem	theorem	ADJ
ejpam-5191	236	26	1	1	NUM
ejpam-5191	236	27	.	.	PUNCT
ejpam-5191	237	1	acknowledgements	acknowledgement	NOUN
ejpam-5191	237	2	this	this	DET
ejpam-5191	237	3	research	research	NOUN
ejpam-5191	237	4	project	project	NOUN
ejpam-5191	237	5	was	be	AUX
ejpam-5191	237	6	financially	financially	ADV
ejpam-5191	237	7	supported	support	VERB
ejpam-5191	237	8	by	by	ADP
ejpam-5191	237	9	mahasarakham	mahasarakham	PROPN
ejpam-5191	237	10	university	university	PROPN
ejpam-5191	237	11	.	.	PUNCT
ejpam-5191	238	1	references	reference	NOUN
ejpam-5191	238	2	[	[	X
ejpam-5191	238	3	1	1	X
ejpam-5191	238	4	]	]	PUNCT
ejpam-5191	238	5	s.	s.	PROPN
ejpam-5191	238	6	p.	p.	PROPN
ejpam-5191	238	7	arya	arya	PROPN
ejpam-5191	238	8	and	and	CCONJ
ejpam-5191	238	9	m.	m.	PROPN
ejpam-5191	238	10	p.	p.	PROPN
ejpam-5191	238	11	bhamini	bhamini	PROPN
ejpam-5191	238	12	.	.	PUNCT
ejpam-5191	239	1	some	some	DET
ejpam-5191	239	2	weaker	weak	ADJ
ejpam-5191	239	3	forms	form	NOUN
ejpam-5191	239	4	of	of	ADP
ejpam-5191	239	5	semi	semi	ADJ
ejpam-5191	239	6	-	-	ADJ
ejpam-5191	239	7	continuous	continuous	ADJ
ejpam-5191	239	8	functions	function	NOUN
ejpam-5191	239	9	.	.	PUNCT
ejpam-5191	240	1	ganita	ganita	NOUN
ejpam-5191	240	2	,	,	PUNCT
ejpam-5191	240	3	33:124–134	33:124–134	NUM
ejpam-5191	240	4	,	,	PUNCT
ejpam-5191	240	5	1982	1982	NUM
ejpam-5191	240	6	.	.	PUNCT
ejpam-5191	241	1	[	[	X
ejpam-5191	241	2	2	2	NUM
ejpam-5191	241	3	]	]	PUNCT
ejpam-5191	241	4	c.	c.	PROPN
ejpam-5191	241	5	berge	berge	PROPN
ejpam-5191	241	6	.	.	PUNCT
ejpam-5191	241	7	espaces	espace	VERB
ejpam-5191	241	8	topologiques	topologique	NOUN
ejpam-5191	241	9	fonctions	fonction	NOUN
ejpam-5191	241	10	multivoques	multivoque	NOUN
ejpam-5191	241	11	.	.	PUNCT
ejpam-5191	242	1	dunod	dunod	PROPN
ejpam-5191	242	2	,	,	PUNCT
ejpam-5191	242	3	paris	paris	PROPN
ejpam-5191	242	4	,	,	PUNCT
ejpam-5191	242	5	1959	1959	NUM
ejpam-5191	242	6	.	.	PUNCT
ejpam-5191	243	1	[	[	X
ejpam-5191	243	2	3	3	X
ejpam-5191	243	3	]	]	PUNCT
ejpam-5191	243	4	c.	c.	PROPN
ejpam-5191	243	5	boonpok	boonpok	PROPN
ejpam-5191	243	6	.	.	PUNCT
ejpam-5191	244	1	almost	almost	ADV
ejpam-5191	244	2	(	(	PUNCT
ejpam-5191	244	3	g	g	NOUN
ejpam-5191	244	4	,	,	PUNCT
ejpam-5191	244	5	m)-continuous	m)-continuous	ADJ
ejpam-5191	244	6	functions	function	NOUN
ejpam-5191	244	7	.	.	PUNCT
ejpam-5191	245	1	international	international	ADJ
ejpam-5191	245	2	journal	journal	PROPN
ejpam-5191	245	3	of	of	ADP
ejpam-5191	245	4	mathematical	mathematical	ADJ
ejpam-5191	245	5	analysis	analysis	NOUN
ejpam-5191	245	6	,	,	PUNCT
ejpam-5191	245	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5191	245	8	,	,	PUNCT
ejpam-5191	245	9	2010	2010	NUM
ejpam-5191	245	10	.	.	PUNCT
ejpam-5191	246	1	[	[	X
ejpam-5191	246	2	4	4	NUM
ejpam-5191	246	3	]	]	PUNCT
ejpam-5191	246	4	c.	c.	PROPN
ejpam-5191	246	5	boonpok	boonpok	PROPN
ejpam-5191	246	6	.	.	PUNCT
ejpam-5191	247	1	m	m	VERB
ejpam-5191	247	2	-continuous	-continuous	ADJ
ejpam-5191	247	3	functions	function	NOUN
ejpam-5191	247	4	in	in	ADP
ejpam-5191	247	5	biminimal	biminimal	NOUN
ejpam-5191	247	6	structure	structure	NOUN
ejpam-5191	247	7	spaces	space	NOUN
ejpam-5191	247	8	.	.	PUNCT
ejpam-5191	248	1	far	far	PROPN
ejpam-5191	248	2	east	east	PROPN
ejpam-5191	248	3	journal	journal	PROPN
ejpam-5191	248	4	of	of	ADP
ejpam-5191	248	5	mathematical	mathematical	ADJ
ejpam-5191	248	6	sciences	science	NOUN
ejpam-5191	248	7	,	,	PUNCT
ejpam-5191	248	8	43(1):41–58	43(1):41–58	NUM
ejpam-5191	248	9	,	,	PUNCT
ejpam-5191	248	10	2010	2010	NUM
ejpam-5191	248	11	.	.	PUNCT
ejpam-5191	249	1	references	reference	NOUN
ejpam-5191	249	2	1562	1562	NUM
ejpam-5191	249	3	[	[	X
ejpam-5191	249	4	5	5	NUM
ejpam-5191	249	5	]	]	PUNCT
ejpam-5191	249	6	c.	c.	PROPN
ejpam-5191	249	7	boonpok	boonpok	PROPN
ejpam-5191	249	8	.	.	PUNCT
ejpam-5191	250	1	on	on	ADP
ejpam-5191	250	2	continuous	continuous	ADJ
ejpam-5191	250	3	multifunctions	multifunction	NOUN
ejpam-5191	250	4	in	in	ADP
ejpam-5191	250	5	ideal	ideal	ADJ
ejpam-5191	250	6	topological	topological	ADJ
ejpam-5191	250	7	spaces	space	NOUN
ejpam-5191	250	8	.	.	PUNCT
ejpam-5191	251	1	lobachevskii	lobachevskii	PROPN
ejpam-5191	251	2	journal	journal	PROPN
ejpam-5191	251	3	of	of	ADP
ejpam-5191	251	4	mathematics	mathematic	NOUN
ejpam-5191	251	5	,	,	PUNCT
ejpam-5191	251	6	40(1):24–35	40(1):24–35	NUM
ejpam-5191	251	7	,	,	PUNCT
ejpam-5191	251	8	2019	2019	NUM
ejpam-5191	251	9	.	.	PUNCT
ejpam-5191	252	1	[	[	X
ejpam-5191	252	2	6	6	NUM
ejpam-5191	252	3	]	]	PUNCT
ejpam-5191	252	4	c.	c.	PROPN
ejpam-5191	252	5	boonpok	boonpok	PROPN
ejpam-5191	252	6	.	.	PUNCT
ejpam-5191	253	1	on	on	ADP
ejpam-5191	253	2	characterizations	characterization	NOUN
ejpam-5191	253	3	of	of	ADP
ejpam-5191	253	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5191	253	5	ideal	ideal	ADJ
ejpam-5191	253	6	topological	topological	ADJ
ejpam-5191	253	7	spaces	space	NOUN
ejpam-5191	253	8	.	.	PUNCT
ejpam-5191	254	1	journal	journal	NOUN
ejpam-5191	254	2	of	of	ADP
ejpam-5191	254	3	mathematics	mathematic	NOUN
ejpam-5191	254	4	,	,	PUNCT
ejpam-5191	254	5	2020:9387601	2020:9387601	NUM
ejpam-5191	254	6	,	,	PUNCT
ejpam-5191	254	7	2020	2020	NUM
ejpam-5191	254	8	.	.	PUNCT
ejpam-5191	255	1	[	[	X
ejpam-5191	255	2	7	7	X
ejpam-5191	255	3	]	]	X
ejpam-5191	255	4	c.	c.	PROPN
ejpam-5191	255	5	boonpok	boonpok	PROPN
ejpam-5191	255	6	.	.	PUNCT
ejpam-5191	256	1	(	(	PUNCT
ejpam-5191	256	2	τ1	τ1	NOUN
ejpam-5191	256	3	,	,	PUNCT
ejpam-5191	256	4	τ2)δ	τ2)δ	ADJ
ejpam-5191	256	5	-	-	PUNCT
ejpam-5191	256	6	semicontinuous	semicontinuous	ADJ
ejpam-5191	256	7	multifunctions	multifunction	NOUN
ejpam-5191	256	8	.	.	PUNCT
ejpam-5191	257	1	heliyon	heliyon	NOUN
ejpam-5191	257	2	,	,	PUNCT
ejpam-5191	257	3	6	6	NUM
ejpam-5191	257	4	:	:	SYM
ejpam-5191	257	5	e05367	e05367	PROPN
ejpam-5191	257	6	,	,	PUNCT
ejpam-5191	257	7	2020	2020	NUM
ejpam-5191	257	8	.	.	PUNCT
ejpam-5191	258	1	[	[	X
ejpam-5191	258	2	8	8	NUM
ejpam-5191	258	3	]	]	X
ejpam-5191	258	4	c.	c.	PROPN
ejpam-5191	258	5	boonpok	boonpok	PROPN
ejpam-5191	258	6	.	.	PUNCT
ejpam-5191	259	1	weak	weak	ADJ
ejpam-5191	259	2	quasi	quasi	ADJ
ejpam-5191	259	3	continuity	continuity	NOUN
ejpam-5191	259	4	for	for	ADP
ejpam-5191	259	5	multifunctions	multifunction	NOUN
ejpam-5191	259	6	in	in	ADP
ejpam-5191	259	7	ideal	ideal	ADJ
ejpam-5191	259	8	topological	topological	ADJ
ejpam-5191	259	9	spaces	space	NOUN
ejpam-5191	259	10	.	.	PUNCT
ejpam-5191	260	1	advances	advance	NOUN
ejpam-5191	260	2	in	in	ADP
ejpam-5191	260	3	mathematics	mathematic	NOUN
ejpam-5191	260	4	:	:	PUNCT
ejpam-5191	260	5	scientific	scientific	ADJ
ejpam-5191	260	6	journal	journal	NOUN
ejpam-5191	260	7	,	,	PUNCT
ejpam-5191	260	8	9(1):339–355	9(1):339–355	NUM
ejpam-5191	260	9	,	,	PUNCT
ejpam-5191	260	10	2020	2020	NUM
ejpam-5191	260	11	.	.	PUNCT
ejpam-5191	261	1	[	[	X
ejpam-5191	261	2	9	9	NUM
ejpam-5191	261	3	]	]	PUNCT
ejpam-5191	261	4	c.	c.	PROPN
ejpam-5191	261	5	boonpok	boonpok	PROPN
ejpam-5191	261	6	.	.	PUNCT
ejpam-5191	262	1	on	on	ADP
ejpam-5191	262	2	some	some	DET
ejpam-5191	262	3	closed	closed	ADJ
ejpam-5191	262	4	sets	set	NOUN
ejpam-5191	262	5	and	and	CCONJ
ejpam-5191	262	6	low	low	ADJ
ejpam-5191	262	7	separation	separation	NOUN
ejpam-5191	262	8	axioms	axiom	NOUN
ejpam-5191	262	9	via	via	ADP
ejpam-5191	262	10	topological	topological	ADJ
ejpam-5191	262	11	spaces	space	NOUN
ejpam-5191	262	12	.	.	PUNCT
ejpam-5191	263	1	european	european	ADJ
ejpam-5191	263	2	journal	journal	PROPN
ejpam-5191	263	3	of	of	ADP
ejpam-5191	263	4	pure	pure	ADJ
ejpam-5191	263	5	and	and	CCONJ
ejpam-5191	263	6	applied	applied	ADJ
ejpam-5191	263	7	mathematics	mathematic	NOUN
ejpam-5191	263	8	,	,	PUNCT
ejpam-5191	263	9	15(3):300–309	15(3):300–309	NOUN
ejpam-5191	263	10	,	,	PUNCT
ejpam-5191	263	11	2022	2022	NUM
ejpam-5191	263	12	.	.	PUNCT
ejpam-5191	264	1	[	[	X
ejpam-5191	264	2	10	10	NUM
ejpam-5191	264	3	]	]	X
ejpam-5191	264	4	c.	c.	PROPN
ejpam-5191	264	5	boonpok	boonpok	PROPN
ejpam-5191	264	6	.	.	PUNCT
ejpam-5191	265	1	on	on	ADP
ejpam-5191	265	2	some	some	DET
ejpam-5191	265	3	spaces	space	NOUN
ejpam-5191	265	4	via	via	ADP
ejpam-5191	265	5	topological	topological	ADJ
ejpam-5191	265	6	ideals	ideal	NOUN
ejpam-5191	265	7	.	.	PUNCT
ejpam-5191	266	1	open	open	ADJ
ejpam-5191	266	2	mathematics	mathematic	NOUN
ejpam-5191	266	3	,	,	PUNCT
ejpam-5191	266	4	21:20230118	21:20230118	NUM
ejpam-5191	266	5	,	,	PUNCT
ejpam-5191	266	6	2023	2023	NUM
ejpam-5191	266	7	.	.	PUNCT
ejpam-5191	267	1	[	[	X
ejpam-5191	267	2	11	11	NUM
ejpam-5191	267	3	]	]	PUNCT
ejpam-5191	267	4	c.	c.	PROPN
ejpam-5191	267	5	boonpok	boonpok	PROPN
ejpam-5191	267	6	.	.	PUNCT
ejpam-5191	268	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5191	268	2	.	.	PUNCT
ejpam-5191	269	1	mathematica	mathematica	PROPN
ejpam-5191	269	2	,	,	PUNCT
ejpam-5191	269	3	65(1):31–42	65(1):31–42	NUM
ejpam-5191	269	4	,	,	PUNCT
ejpam-5191	269	5	2023	2023	NUM
ejpam-5191	269	6	.	.	PUNCT
ejpam-5191	270	1	[	[	X
ejpam-5191	270	2	12	12	NUM
ejpam-5191	270	3	]	]	X
ejpam-5191	270	4	c.	c.	PROPN
ejpam-5191	270	5	boonpok	boonpok	PROPN
ejpam-5191	270	6	and	and	CCONJ
ejpam-5191	270	7	j.	j.	PROPN
ejpam-5191	270	8	khampakdee	khampakdee	PROPN
ejpam-5191	270	9	.	.	PUNCT
ejpam-5191	271	1	almost	almost	ADV
ejpam-5191	271	2	strong	strong	ADJ
ejpam-5191	271	3	θ(λ	θ(λ	PROPN
ejpam-5191	271	4	,	,	PUNCT
ejpam-5191	271	5	p)-continuity	p)-continuity	NOUN
ejpam-5191	271	6	for	for	ADP
ejpam-5191	271	7	functions	function	NOUN
ejpam-5191	271	8	.	.	PUNCT
ejpam-5191	272	1	european	european	ADJ
ejpam-5191	272	2	journal	journal	PROPN
ejpam-5191	272	3	of	of	ADP
ejpam-5191	272	4	pure	pure	ADJ
ejpam-5191	272	5	and	and	CCONJ
ejpam-5191	272	6	applied	applied	ADJ
ejpam-5191	272	7	mathematics	mathematic	NOUN
ejpam-5191	272	8	,	,	PUNCT
ejpam-5191	272	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5191	272	10	,	,	PUNCT
ejpam-5191	272	11	2024	2024	NUM
ejpam-5191	272	12	.	.	PUNCT
ejpam-5191	273	1	[	[	X
ejpam-5191	273	2	13	13	NUM
ejpam-5191	273	3	]	]	PUNCT
ejpam-5191	273	4	c.	c.	PROPN
ejpam-5191	273	5	boonpok	boonpok	PROPN
ejpam-5191	273	6	and	and	CCONJ
ejpam-5191	273	7	c.	c.	PROPN
ejpam-5191	273	8	klanarong	klanarong	PROPN
ejpam-5191	273	9	.	.	PUNCT
ejpam-5191	274	1	on	on	ADP
ejpam-5191	274	2	weakly	weakly	ADJ
ejpam-5191	274	3	(	(	PUNCT
ejpam-5191	274	4	τ1	τ1	NOUN
ejpam-5191	274	5	,	,	PUNCT
ejpam-5191	274	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	274	7	functions	function	NOUN
ejpam-5191	274	8	.	.	PUNCT
ejpam-5191	275	1	european	european	ADJ
ejpam-5191	275	2	journal	journal	PROPN
ejpam-5191	275	3	of	of	ADP
ejpam-5191	275	4	pure	pure	ADJ
ejpam-5191	275	5	and	and	CCONJ
ejpam-5191	275	6	applied	applied	ADJ
ejpam-5191	275	7	mathematics	mathematic	NOUN
ejpam-5191	275	8	,	,	PUNCT
ejpam-5191	275	9	17(1):416–425	17(1):416–425	NUM
ejpam-5191	275	10	,	,	PUNCT
ejpam-5191	275	11	2024	2024	NUM
ejpam-5191	275	12	.	.	PUNCT
ejpam-5191	276	1	[	[	X
ejpam-5191	276	2	14	14	NUM
ejpam-5191	276	3	]	]	X
ejpam-5191	276	4	c.	c.	PROPN
ejpam-5191	276	5	boonpok	boonpok	PROPN
ejpam-5191	276	6	and	and	CCONJ
ejpam-5191	276	7	p.	p.	NOUN
ejpam-5191	276	8	pue	pue	NOUN
ejpam-5191	276	9	-	-	PUNCT
ejpam-5191	276	10	on	on	ADP
ejpam-5191	276	11	.	.	PUNCT
ejpam-5191	277	1	continuity	continuity	NOUN
ejpam-5191	277	2	for	for	ADP
ejpam-5191	277	3	multifunctions	multifunction	NOUN
ejpam-5191	277	4	in	in	ADP
ejpam-5191	277	5	ideal	ideal	ADJ
ejpam-5191	277	6	topological	topological	ADJ
ejpam-5191	277	7	spaces	space	NOUN
ejpam-5191	277	8	.	.	PUNCT
ejpam-5191	278	1	wseas	wseas	VERB
ejpam-5191	278	2	transactions	transaction	NOUN
ejpam-5191	278	3	on	on	ADP
ejpam-5191	278	4	mathematics	mathematic	NOUN
ejpam-5191	278	5	,	,	PUNCT
ejpam-5191	278	6	19:624–631	19:624–631	NUM
ejpam-5191	278	7	,	,	PUNCT
ejpam-5191	278	8	2020	2020	NUM
ejpam-5191	278	9	.	.	PUNCT
ejpam-5191	279	1	[	[	X
ejpam-5191	279	2	15	15	NUM
ejpam-5191	279	3	]	]	X
ejpam-5191	279	4	c.	c.	PROPN
ejpam-5191	279	5	boonpok	boonpok	PROPN
ejpam-5191	279	6	and	and	CCONJ
ejpam-5191	279	7	p.	p.	NOUN
ejpam-5191	279	8	pue	pue	NOUN
ejpam-5191	279	9	-	-	PUNCT
ejpam-5191	279	10	on	on	ADP
ejpam-5191	279	11	.	.	PUNCT
ejpam-5191	280	1	upper	upper	ADJ
ejpam-5191	280	2	and	and	CCONJ
ejpam-5191	280	3	lower	low	ADJ
ejpam-5191	280	4	weakly	weakly	ADJ
ejpam-5191	280	5	α-⋆-continuous	α-⋆-continuous	ADJ
ejpam-5191	280	6	multifunctions	multifunction	NOUN
ejpam-5191	280	7	.	.	PUNCT
ejpam-5191	281	1	international	international	ADJ
ejpam-5191	281	2	journal	journal	NOUN
ejpam-5191	281	3	of	of	ADP
ejpam-5191	281	4	analysis	analysis	NOUN
ejpam-5191	281	5	and	and	CCONJ
ejpam-5191	281	6	applications	application	NOUN
ejpam-5191	281	7	,	,	PUNCT
ejpam-5191	281	8	21:90	21:90	NUM
ejpam-5191	281	9	,	,	PUNCT
ejpam-5191	281	10	2023	2023	NUM
ejpam-5191	281	11	.	.	PUNCT
ejpam-5191	282	1	[	[	X
ejpam-5191	282	2	16	16	NUM
ejpam-5191	282	3	]	]	X
ejpam-5191	282	4	c.	c.	PROPN
ejpam-5191	282	5	boonpok	boonpok	PROPN
ejpam-5191	282	6	and	and	CCONJ
ejpam-5191	282	7	p.	p.	NOUN
ejpam-5191	282	8	pue	pue	NOUN
ejpam-5191	282	9	-	-	PUNCT
ejpam-5191	282	10	on	on	ADP
ejpam-5191	282	11	.	.	PUNCT
ejpam-5191	283	1	upper	upper	ADJ
ejpam-5191	283	2	and	and	CCONJ
ejpam-5191	283	3	lower	low	ADJ
ejpam-5191	283	4	weakly	weakly	ADJ
ejpam-5191	283	5	(	(	PUNCT
ejpam-5191	283	6	λ	λ	NOUN
ejpam-5191	283	7	,	,	PUNCT
ejpam-5191	283	8	sp)-continuous	sp)-continuous	ADJ
ejpam-5191	283	9	multifunctions	multifunction	NOUN
ejpam-5191	283	10	.	.	PUNCT
ejpam-5191	284	1	european	european	PROPN
ejpam-5191	284	2	journal	journal	PROPN
ejpam-5191	284	3	of	of	ADP
ejpam-5191	284	4	pure	pure	ADJ
ejpam-5191	284	5	and	and	CCONJ
ejpam-5191	284	6	applied	applied	ADJ
ejpam-5191	284	7	mathematics	mathematic	NOUN
ejpam-5191	284	8	,	,	PUNCT
ejpam-5191	284	9	16(2):1047–1058	16(2):1047–1058	NUM
ejpam-5191	284	10	,	,	PUNCT
ejpam-5191	284	11	2023	2023	NUM
ejpam-5191	284	12	.	.	PUNCT
ejpam-5191	285	1	[	[	X
ejpam-5191	285	2	17	17	NUM
ejpam-5191	285	3	]	]	X
ejpam-5191	285	4	c.	c.	PROPN
ejpam-5191	285	5	boonpok	boonpok	PROPN
ejpam-5191	285	6	and	and	CCONJ
ejpam-5191	285	7	p.	p.	NOUN
ejpam-5191	285	8	pue	pue	NOUN
ejpam-5191	285	9	-	-	PUNCT
ejpam-5191	285	10	on	on	ADP
ejpam-5191	285	11	.	.	PUNCT
ejpam-5191	286	1	characterizations	characterization	NOUN
ejpam-5191	286	2	of	of	ADP
ejpam-5191	286	3	almost	almost	ADV
ejpam-5191	286	4	(	(	PUNCT
ejpam-5191	286	5	τ1	τ1	NOUN
ejpam-5191	286	6	,	,	PUNCT
ejpam-5191	286	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	286	8	functions	function	NOUN
ejpam-5191	286	9	.	.	PUNCT
ejpam-5191	287	1	international	international	ADJ
ejpam-5191	287	2	journal	journal	NOUN
ejpam-5191	287	3	of	of	ADP
ejpam-5191	287	4	analysis	analysis	NOUN
ejpam-5191	287	5	and	and	CCONJ
ejpam-5191	287	6	applications	application	NOUN
ejpam-5191	287	7	,	,	PUNCT
ejpam-5191	287	8	22:33	22:33	NUM
ejpam-5191	287	9	,	,	PUNCT
ejpam-5191	287	10	2024	2024	NUM
ejpam-5191	287	11	.	.	PUNCT
ejpam-5191	288	1	[	[	X
ejpam-5191	288	2	18	18	NUM
ejpam-5191	288	3	]	]	PUNCT
ejpam-5191	288	4	c.	c.	PROPN
ejpam-5191	288	5	boonpok	boonpok	PROPN
ejpam-5191	288	6	and	and	CCONJ
ejpam-5191	288	7	n.	n.	PROPN
ejpam-5191	288	8	srisarakham	srisarakham	PROPN
ejpam-5191	288	9	.	.	PUNCT
ejpam-5191	289	1	weak	weak	ADJ
ejpam-5191	289	2	forms	form	NOUN
ejpam-5191	289	3	of	of	ADP
ejpam-5191	289	4	(	(	PUNCT
ejpam-5191	289	5	λ	λ	PROPN
ejpam-5191	289	6	,	,	PUNCT
ejpam-5191	289	7	b)-open	b)-open	VERB
ejpam-5191	289	8	sets	set	NOUN
ejpam-5191	289	9	and	and	CCONJ
ejpam-5191	289	10	weak	weak	ADJ
ejpam-5191	289	11	(	(	PUNCT
ejpam-5191	289	12	λ	λ	NOUN
ejpam-5191	289	13	,	,	PUNCT
ejpam-5191	289	14	b)continuity	b)continuity	NOUN
ejpam-5191	289	15	.	.	PUNCT
ejpam-5191	290	1	european	european	PROPN
ejpam-5191	290	2	journal	journal	PROPN
ejpam-5191	290	3	of	of	ADP
ejpam-5191	290	4	pure	pure	ADJ
ejpam-5191	290	5	and	and	CCONJ
ejpam-5191	290	6	applied	applied	ADJ
ejpam-5191	290	7	mathematics	mathematic	NOUN
ejpam-5191	290	8	,	,	PUNCT
ejpam-5191	290	9	16(1):29–43	16(1):29–43	NUM
ejpam-5191	290	10	,	,	PUNCT
ejpam-5191	290	11	2023	2023	NUM
ejpam-5191	290	12	.	.	PUNCT
ejpam-5191	291	1	[	[	X
ejpam-5191	291	2	19	19	NUM
ejpam-5191	291	3	]	]	X
ejpam-5191	291	4	c.	c.	PROPN
ejpam-5191	291	5	boonpok	boonpok	PROPN
ejpam-5191	291	6	and	and	CCONJ
ejpam-5191	291	7	n.	n.	PROPN
ejpam-5191	291	8	srisarakham	srisarakham	PROPN
ejpam-5191	291	9	.	.	PUNCT
ejpam-5191	292	1	(	(	PUNCT
ejpam-5191	292	2	τ1	τ1	NOUN
ejpam-5191	292	3	,	,	PUNCT
ejpam-5191	292	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5191	292	5	for	for	ADP
ejpam-5191	292	6	functions	function	NOUN
ejpam-5191	292	7	.	.	PUNCT
ejpam-5191	293	1	asia	asia	PROPN
ejpam-5191	293	2	pacific	pacific	PROPN
ejpam-5191	293	3	journal	journal	PROPN
ejpam-5191	293	4	of	of	ADP
ejpam-5191	293	5	mathematics	mathematic	NOUN
ejpam-5191	293	6	,	,	PUNCT
ejpam-5191	293	7	11:21	11:21	NUM
ejpam-5191	293	8	,	,	PUNCT
ejpam-5191	293	9	2024	2024	NUM
ejpam-5191	293	10	.	.	PUNCT
ejpam-5191	294	1	[	[	X
ejpam-5191	294	2	20	20	NUM
ejpam-5191	294	3	]	]	PUNCT
ejpam-5191	294	4	c.	c.	PROPN
ejpam-5191	294	5	boonpok	boonpok	PROPN
ejpam-5191	294	6	and	and	CCONJ
ejpam-5191	294	7	c.	c.	PROPN
ejpam-5191	294	8	viriyapong	viriyapong	PROPN
ejpam-5191	294	9	.	.	PUNCT
ejpam-5191	295	1	almost	almost	ADV
ejpam-5191	295	2	weak	weak	ADJ
ejpam-5191	295	3	continuity	continuity	NOUN
ejpam-5191	295	4	for	for	ADP
ejpam-5191	295	5	multifunctions	multifunction	NOUN
ejpam-5191	295	6	in	in	ADP
ejpam-5191	295	7	ideal	ideal	ADJ
ejpam-5191	295	8	topological	topological	ADJ
ejpam-5191	295	9	spaces	space	NOUN
ejpam-5191	295	10	.	.	PUNCT
ejpam-5191	296	1	wseas	wseas	VERB
ejpam-5191	296	2	transactions	transaction	NOUN
ejpam-5191	296	3	on	on	ADP
ejpam-5191	296	4	mathematics	mathematic	NOUN
ejpam-5191	296	5	,	,	PUNCT
ejpam-5191	296	6	19:367–372	19:367–372	PROPN
ejpam-5191	296	7	,	,	PUNCT
ejpam-5191	296	8	2020	2020	NUM
ejpam-5191	296	9	.	.	PUNCT
ejpam-5191	297	1	[	[	X
ejpam-5191	297	2	21	21	NUM
ejpam-5191	297	3	]	]	X
ejpam-5191	297	4	c.	c.	PROPN
ejpam-5191	297	5	boonpok	boonpok	PROPN
ejpam-5191	297	6	and	and	CCONJ
ejpam-5191	297	7	c.	c.	PROPN
ejpam-5191	297	8	viriyapong	viriyapong	PROPN
ejpam-5191	297	9	.	.	PUNCT
ejpam-5191	298	1	upper	upper	ADJ
ejpam-5191	298	2	and	and	CCONJ
ejpam-5191	298	3	lower	low	ADJ
ejpam-5191	298	4	almost	almost	ADV
ejpam-5191	298	5	weak	weak	ADJ
ejpam-5191	298	6	(	(	PUNCT
ejpam-5191	298	7	τ1	τ1	NOUN
ejpam-5191	298	8	,	,	PUNCT
ejpam-5191	298	9	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5191	298	10	.	.	PUNCT
ejpam-5191	299	1	european	european	PROPN
ejpam-5191	299	2	journal	journal	PROPN
ejpam-5191	299	3	of	of	ADP
ejpam-5191	299	4	pure	pure	ADJ
ejpam-5191	299	5	and	and	CCONJ
ejpam-5191	299	6	applied	applied	ADJ
ejpam-5191	299	7	mathematics	mathematic	NOUN
ejpam-5191	299	8	,	,	PUNCT
ejpam-5191	299	9	14(4):1212–1225	14(4):1212–1225	NUM
ejpam-5191	299	10	,	,	PUNCT
ejpam-5191	299	11	2021	2021	NUM
ejpam-5191	299	12	.	.	PUNCT
ejpam-5191	300	1	references	reference	NOUN
ejpam-5191	300	2	1563	1563	NUM
ejpam-5191	301	1	[	[	X
ejpam-5191	301	2	22	22	NUM
ejpam-5191	301	3	]	]	PUNCT
ejpam-5191	301	4	c.	c.	PROPN
ejpam-5191	301	5	boonpok	boonpok	PROPN
ejpam-5191	301	6	,	,	PUNCT
ejpam-5191	301	7	c.	c.	PROPN
ejpam-5191	301	8	viriyapong	viriyapong	PROPN
ejpam-5191	301	9	,	,	PUNCT
ejpam-5191	301	10	and	and	CCONJ
ejpam-5191	301	11	m.	m.	NOUN
ejpam-5191	301	12	thongmoon	thongmoon	NOUN
ejpam-5191	301	13	.	.	PUNCT
ejpam-5191	302	1	on	on	ADP
ejpam-5191	302	2	upper	upper	ADJ
ejpam-5191	302	3	and	and	CCONJ
ejpam-5191	302	4	lower	low	ADJ
ejpam-5191	302	5	(	(	PUNCT
ejpam-5191	302	6	τ1	τ1	NOUN
ejpam-5191	302	7	,	,	PUNCT
ejpam-5191	302	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5191	302	9	multifunctions	multifunction	NOUN
ejpam-5191	302	10	.	.	PUNCT
ejpam-5191	303	1	journal	journal	PROPN
ejpam-5191	303	2	of	of	ADP
ejpam-5191	303	3	mathematics	mathematics	PROPN
ejpam-5191	303	4	and	and	CCONJ
ejpam-5191	303	5	computer	computer	NOUN
ejpam-5191	303	6	science	science	NOUN
ejpam-5191	303	7	,	,	PUNCT
ejpam-5191	303	8	18:282–293	18:282–293	NUM
ejpam-5191	303	9	,	,	PUNCT
ejpam-5191	303	10	2018	2018	NUM
ejpam-5191	303	11	.	.	PUNCT
ejpam-5191	304	1	[	[	X
ejpam-5191	304	2	23	23	NUM
ejpam-5191	304	3	]	]	PUNCT
ejpam-5191	304	4	t.	t.	PROPN
ejpam-5191	304	5	duangphui	duangphui	PROPN
ejpam-5191	304	6	,	,	PUNCT
ejpam-5191	304	7	c.	c.	PROPN
ejpam-5191	304	8	boonpok	boonpok	PROPN
ejpam-5191	304	9	,	,	PUNCT
ejpam-5191	304	10	and	and	CCONJ
ejpam-5191	304	11	c.	c.	PROPN
ejpam-5191	304	12	viriyapong	viriyapong	PROPN
ejpam-5191	304	13	.	.	PUNCT
ejpam-5191	305	1	continuous	continuous	ADJ
ejpam-5191	305	2	functions	function	NOUN
ejpam-5191	305	3	on	on	ADP
ejpam-5191	305	4	bigeneralized	bigeneralize	VERB
ejpam-5191	305	5	topological	topological	ADJ
ejpam-5191	305	6	spaces	space	NOUN
ejpam-5191	305	7	.	.	PUNCT
ejpam-5191	306	1	international	international	ADJ
ejpam-5191	306	2	journal	journal	PROPN
ejpam-5191	306	3	of	of	ADP
ejpam-5191	306	4	mathematical	mathematical	ADJ
ejpam-5191	306	5	analysis	analysis	NOUN
ejpam-5191	306	6	,	,	PUNCT
ejpam-5191	306	7	5(24):1165	5(24):1165	NUM
ejpam-5191	306	8	–	–	PUNCT
ejpam-5191	306	9	1174	1174	NUM
ejpam-5191	306	10	,	,	PUNCT
ejpam-5191	306	11	2011	2011	NUM
ejpam-5191	306	12	.	.	PUNCT
ejpam-5191	307	1	[	[	X
ejpam-5191	307	2	24	24	NUM
ejpam-5191	307	3	]	]	PUNCT
ejpam-5191	307	4	a.	a.	NOUN
ejpam-5191	307	5	kar	kar	PROPN
ejpam-5191	307	6	and	and	CCONJ
ejpam-5191	307	7	p.	p.	PROPN
ejpam-5191	307	8	bhattacharyya	bhattacharyya	PROPN
ejpam-5191	307	9	.	.	PUNCT
ejpam-5191	308	1	weakly	weakly	ADJ
ejpam-5191	308	2	semi	semi	ADJ
ejpam-5191	308	3	-	-	ADJ
ejpam-5191	308	4	continuous	continuous	ADJ
ejpam-5191	308	5	functions	function	NOUN
ejpam-5191	308	6	.	.	PUNCT
ejpam-5191	309	1	the	the	DET
ejpam-5191	309	2	journal	journal	PROPN
ejpam-5191	309	3	of	of	ADP
ejpam-5191	309	4	indian	indian	PROPN
ejpam-5191	309	5	academy	academy	PROPN
ejpam-5191	309	6	of	of	ADP
ejpam-5191	309	7	mathematics	mathematics	PROPN
ejpam-5191	309	8	,	,	PUNCT
ejpam-5191	309	9	8:83–93	8:83–93	NUM
ejpam-5191	309	10	,	,	PUNCT
ejpam-5191	309	11	1986	1986	NUM
ejpam-5191	309	12	.	.	PUNCT
ejpam-5191	310	1	[	[	X
ejpam-5191	310	2	25	25	NUM
ejpam-5191	310	3	]	]	PUNCT
ejpam-5191	310	4	k.	k.	PROPN
ejpam-5191	310	5	laprom	laprom	PROPN
ejpam-5191	310	6	,	,	PUNCT
ejpam-5191	310	7	c.	c.	PROPN
ejpam-5191	310	8	boonpok	boonpok	PROPN
ejpam-5191	310	9	,	,	PUNCT
ejpam-5191	310	10	and	and	CCONJ
ejpam-5191	310	11	c.	c.	PROPN
ejpam-5191	310	12	viriyapong	viriyapong	PROPN
ejpam-5191	310	13	.	.	PUNCT
ejpam-5191	311	1	β(τ1	β(τ1	PROPN
ejpam-5191	311	2	,	,	PUNCT
ejpam-5191	311	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5191	311	4	multifunctions	multifunction	NOUN
ejpam-5191	311	5	on	on	ADP
ejpam-5191	311	6	bitopological	bitopological	ADJ
ejpam-5191	311	7	spaces	space	NOUN
ejpam-5191	311	8	.	.	PUNCT
ejpam-5191	312	1	journal	journal	NOUN
ejpam-5191	312	2	of	of	ADP
ejpam-5191	312	3	mathematics	mathematic	NOUN
ejpam-5191	312	4	,	,	PUNCT
ejpam-5191	312	5	2020:4020971	2020:4020971	NUM
ejpam-5191	312	6	,	,	PUNCT
ejpam-5191	312	7	2020	2020	NUM
ejpam-5191	312	8	.	.	PUNCT
ejpam-5191	313	1	[	[	X
ejpam-5191	313	2	26	26	NUM
ejpam-5191	313	3	]	]	X
ejpam-5191	313	4	n.	n.	PROPN
ejpam-5191	313	5	levine	levine	PROPN
ejpam-5191	313	6	.	.	PUNCT
ejpam-5191	314	1	a	a	DET
ejpam-5191	314	2	decomposition	decomposition	NOUN
ejpam-5191	314	3	of	of	ADP
ejpam-5191	314	4	continuity	continuity	NOUN
ejpam-5191	314	5	in	in	ADP
ejpam-5191	314	6	topological	topological	ADJ
ejpam-5191	314	7	spaces	space	NOUN
ejpam-5191	314	8	.	.	PUNCT
ejpam-5191	315	1	the	the	DET
ejpam-5191	315	2	american	american	PROPN
ejpam-5191	315	3	mathematical	mathematical	PROPN
ejpam-5191	315	4	monthly	monthly	ADV
ejpam-5191	315	5	,	,	PUNCT
ejpam-5191	315	6	68:44–46	68:44–46	NUM
ejpam-5191	315	7	,	,	PUNCT
ejpam-5191	315	8	1961	1961	NUM
ejpam-5191	315	9	.	.	PUNCT
ejpam-5191	316	1	[	[	X
ejpam-5191	316	2	27	27	NUM
ejpam-5191	316	3	]	]	X
ejpam-5191	316	4	n.	n.	PROPN
ejpam-5191	316	5	levine	levine	PROPN
ejpam-5191	316	6	.	.	PUNCT
ejpam-5191	317	1	semi	semi	ADJ
ejpam-5191	317	2	-	-	ADJ
ejpam-5191	317	3	open	open	ADJ
ejpam-5191	317	4	sets	set	NOUN
ejpam-5191	317	5	and	and	CCONJ
ejpam-5191	317	6	semi	semi	ADJ
ejpam-5191	317	7	-	-	NOUN
ejpam-5191	317	8	continuity	continuity	NOUN
ejpam-5191	317	9	in	in	ADP
ejpam-5191	317	10	topological	topological	ADJ
ejpam-5191	317	11	spaces	space	NOUN
ejpam-5191	317	12	.	.	PUNCT
ejpam-5191	318	1	the	the	DET
ejpam-5191	318	2	american	american	PROPN
ejpam-5191	318	3	mathematical	mathematical	PROPN
ejpam-5191	318	4	monthly	monthly	ADV
ejpam-5191	318	5	,	,	PUNCT
ejpam-5191	318	6	70:36–41	70:36–41	NUM
ejpam-5191	318	7	,	,	PUNCT
ejpam-5191	318	8	1963	1963	NUM
ejpam-5191	318	9	.	.	PUNCT
ejpam-5191	319	1	[	[	X
ejpam-5191	319	2	28	28	NUM
ejpam-5191	319	3	]	]	X
ejpam-5191	319	4	s.	s.	PROPN
ejpam-5191	319	5	marcus	marcus	PROPN
ejpam-5191	319	6	.	.	PUNCT
ejpam-5191	320	1	sur	sur	PROPN
ejpam-5191	320	2	les	les	PROPN
ejpam-5191	320	3	fonctions	fonctions	PROPN
ejpam-5191	320	4	quasicontinues	quasicontinue	NOUN
ejpam-5191	320	5	au	au	ADP
ejpam-5191	320	6	sense	sense	NOUN
ejpam-5191	320	7	de	de	X
ejpam-5191	320	8	s.	s.	PROPN
ejpam-5191	320	9	kempisty	kempisty	PROPN
ejpam-5191	320	10	.	.	PUNCT
ejpam-5191	321	1	colloquium	colloquium	NOUN
ejpam-5191	321	2	mathematicum	mathematicum	PROPN
ejpam-5191	321	3	,	,	PUNCT
ejpam-5191	321	4	8:47–53	8:47–53	NUM
ejpam-5191	321	5	,	,	PUNCT
ejpam-5191	321	6	1961	1961	NUM
ejpam-5191	321	7	.	.	PUNCT
ejpam-5191	322	1	[	[	X
ejpam-5191	322	2	29	29	NUM
ejpam-5191	322	3	]	]	PUNCT
ejpam-5191	322	4	a.	a.	NOUN
ejpam-5191	322	5	neubrunnová.	neubrunnová.	PROPN
ejpam-5191	322	6	on	on	ADP
ejpam-5191	322	7	certain	certain	ADJ
ejpam-5191	322	8	generalizations	generalization	NOUN
ejpam-5191	322	9	of	of	ADP
ejpam-5191	322	10	the	the	DET
ejpam-5191	322	11	notion	notion	NOUN
ejpam-5191	322	12	of	of	ADP
ejpam-5191	322	13	continuity	continuity	NOUN
ejpam-5191	322	14	.	.	PUNCT
ejpam-5191	323	1	matematički	matematički	PROPN
ejpam-5191	324	1	časopis	časopis	PROPN
ejpam-5191	324	2	,	,	PUNCT
ejpam-5191	324	3	23:374–380	23:374–380	NUM
ejpam-5191	324	4	,	,	PUNCT
ejpam-5191	324	5	1973	1973	NUM
ejpam-5191	324	6	.	.	PUNCT
ejpam-5191	325	1	[	[	X
ejpam-5191	325	2	30	30	NUM
ejpam-5191	325	3	]	]	PUNCT
ejpam-5191	325	4	t.	t.	PROPN
ejpam-5191	325	5	noiri	noiri	PROPN
ejpam-5191	325	6	.	.	PUNCT
ejpam-5191	326	1	properties	property	NOUN
ejpam-5191	326	2	of	of	ADP
ejpam-5191	326	3	some	some	DET
ejpam-5191	326	4	weak	weak	ADJ
ejpam-5191	326	5	forms	form	NOUN
ejpam-5191	326	6	of	of	ADP
ejpam-5191	326	7	continuity	continuity	NOUN
ejpam-5191	326	8	.	.	PUNCT
ejpam-5191	327	1	international	international	ADJ
ejpam-5191	327	2	journal	journal	PROPN
ejpam-5191	327	3	of	of	ADP
ejpam-5191	327	4	mathematics	mathematics	PROPN
ejpam-5191	327	5	and	and	CCONJ
ejpam-5191	327	6	mathematical	mathematical	ADJ
ejpam-5191	327	7	sciences	science	NOUN
ejpam-5191	327	8	,	,	PUNCT
ejpam-5191	327	9	10:97–111	10:97–111	NUM
ejpam-5191	327	10	,	,	PUNCT
ejpam-5191	327	11	1987	1987	NUM
ejpam-5191	327	12	.	.	PUNCT
ejpam-5191	328	1	[	[	X
ejpam-5191	328	2	31	31	NUM
ejpam-5191	328	3	]	]	PUNCT
ejpam-5191	328	4	t.	t.	PROPN
ejpam-5191	328	5	noiri	noiri	PROPN
ejpam-5191	328	6	and	and	CCONJ
ejpam-5191	328	7	v.	v.	ADP
ejpam-5191	328	8	popa	popa	NOUN
ejpam-5191	328	9	.	.	PUNCT
ejpam-5191	329	1	weakly	weakly	ADJ
ejpam-5191	329	2	quasi	quasi	ADJ
ejpam-5191	329	3	continuous	continuous	ADJ
ejpam-5191	329	4	multifunctions	multifunction	NOUN
ejpam-5191	329	5	.	.	PUNCT
ejpam-5191	330	1	analele	analele	PROPN
ejpam-5191	330	2	universităţii	universităţii	AUX
ejpam-5191	330	3	din	din	VERB
ejpam-5191	330	4	timişoara	timişoara	PROPN
ejpam-5191	330	5	.	.	PROPN
ejpam-5191	330	6	seria	seria	PROPN
ejpam-5191	330	7	matematică-informatică	matematică-informatică	PROPN
ejpam-5191	330	8	,	,	PUNCT
ejpam-5191	330	9	26:33–38	26:33–38	NUM
ejpam-5191	330	10	,	,	PUNCT
ejpam-5191	330	11	1988	1988	NUM
ejpam-5191	330	12	.	.	PUNCT
ejpam-5191	331	1	[	[	X
ejpam-5191	331	2	32	32	NUM
ejpam-5191	331	3	]	]	PUNCT
ejpam-5191	331	4	t.	t.	PROPN
ejpam-5191	331	5	noiri	noiri	PROPN
ejpam-5191	331	6	and	and	CCONJ
ejpam-5191	331	7	v.	v.	ADP
ejpam-5191	331	8	popa	popa	NOUN
ejpam-5191	331	9	.	.	PUNCT
ejpam-5191	332	1	some	some	DET
ejpam-5191	332	2	properties	property	NOUN
ejpam-5191	332	3	of	of	ADP
ejpam-5191	332	4	upper	upper	ADJ
ejpam-5191	332	5	and	and	CCONJ
ejpam-5191	332	6	lower	low	ADJ
ejpam-5191	332	7	θ	θ	ADJ
ejpam-5191	332	8	-	-	ADJ
ejpam-5191	332	9	quasi	quasi	ADJ
ejpam-5191	332	10	continuous	continuous	ADJ
ejpam-5191	332	11	multifunctions	multifunction	NOUN
ejpam-5191	332	12	.	.	PUNCT
ejpam-5191	333	1	demonstratio	demonstratio	PROPN
ejpam-5191	333	2	mathematica	mathematica	PROPN
ejpam-5191	333	3	,	,	PUNCT
ejpam-5191	333	4	38(1):223–234	38(1):223–234	PROPN
ejpam-5191	333	5	,	,	PUNCT
ejpam-5191	333	6	2005	2005	NUM
ejpam-5191	333	7	.	.	PUNCT
ejpam-5191	334	1	[	[	X
ejpam-5191	334	2	33	33	NUM
ejpam-5191	334	3	]	]	X
ejpam-5191	334	4	v.	v.	CCONJ
ejpam-5191	334	5	popa	popa	NOUN
ejpam-5191	334	6	.	.	PUNCT
ejpam-5191	335	1	on	on	ADP
ejpam-5191	335	2	a	a	DET
ejpam-5191	335	3	decomposition	decomposition	NOUN
ejpam-5191	335	4	of	of	ADP
ejpam-5191	335	5	quasicontinuity	quasicontinuity	NOUN
ejpam-5191	335	6	in	in	ADP
ejpam-5191	335	7	topological	topological	ADJ
ejpam-5191	335	8	spaces	space	NOUN
ejpam-5191	335	9	.	.	PUNCT
ejpam-5191	336	1	studii	studii	PROPN
ejpam-5191	336	2	şi	şi	PROPN
ejpam-5191	336	3	cercetări	cercetări	PROPN
ejpam-5191	336	4	de	de	X
ejpam-5191	336	5	matematicaă	matematicaă	PROPN
ejpam-5191	336	6	,	,	PUNCT
ejpam-5191	336	7	30:31–35	30:31–35	NUM
ejpam-5191	336	8	,	,	PUNCT
ejpam-5191	336	9	1978	1978	NUM
ejpam-5191	336	10	.	.	PUNCT
ejpam-5191	337	1	[	[	X
ejpam-5191	337	2	34	34	NUM
ejpam-5191	337	3	]	]	PUNCT
ejpam-5191	337	4	v.	v.	CCONJ
ejpam-5191	337	5	popa	popa	NOUN
ejpam-5191	337	6	and	and	CCONJ
ejpam-5191	337	7	t.	t.	PROPN
ejpam-5191	337	8	noiri	noiri	PROPN
ejpam-5191	337	9	.	.	PUNCT
ejpam-5191	338	1	on	on	ADP
ejpam-5191	338	2	θ	θ	ADJ
ejpam-5191	338	3	-	-	ADJ
ejpam-5191	338	4	quasi	quasi	ADJ
ejpam-5191	338	5	continuous	continuous	ADJ
ejpam-5191	338	6	multifunctions	multifunction	NOUN
ejpam-5191	338	7	.	.	PUNCT
ejpam-5191	339	1	demonstratio	demonstratio	PROPN
ejpam-5191	339	2	mathematica	mathematica	PROPN
ejpam-5191	339	3	,	,	PUNCT
ejpam-5191	339	4	28:111–122	28:111–122	PROPN
ejpam-5191	339	5	,	,	PUNCT
ejpam-5191	339	6	1995	1995	NUM
ejpam-5191	339	7	.	.	PUNCT
ejpam-5191	340	1	[	[	X
ejpam-5191	340	2	35	35	NUM
ejpam-5191	340	3	]	]	PUNCT
ejpam-5191	340	4	v.	v.	CCONJ
ejpam-5191	340	5	popa	popa	NOUN
ejpam-5191	340	6	and	and	CCONJ
ejpam-5191	340	7	t.	t.	NOUN
ejpam-5191	340	8	noiri	noiri	PROPN
ejpam-5191	340	9	.	.	PUNCT
ejpam-5191	341	1	almost	almost	ADV
ejpam-5191	341	2	quasi	quasi	VERB
ejpam-5191	341	3	continuous	continuous	ADJ
ejpam-5191	341	4	multifunctions	multifunction	NOUN
ejpam-5191	341	5	.	.	PUNCT
ejpam-5191	342	1	tatra	tatra	PROPN
ejpam-5191	342	2	mountains	mountains	PROPN
ejpam-5191	342	3	mathematical	mathematical	ADJ
ejpam-5191	342	4	publications	publication	NOUN
ejpam-5191	342	5	,	,	PUNCT
ejpam-5191	342	6	14:81–90	14:81–90	PROPN
ejpam-5191	342	7	,	,	PUNCT
ejpam-5191	342	8	1998	1998	NUM
ejpam-5191	342	9	.	.	PUNCT
ejpam-5191	343	1	[	[	X
ejpam-5191	343	2	36	36	NUM
ejpam-5191	343	3	]	]	X
ejpam-5191	343	4	v.	v.	CCONJ
ejpam-5191	343	5	popa	popa	NOUN
ejpam-5191	343	6	and	and	CCONJ
ejpam-5191	343	7	c.	c.	PROPN
ejpam-5191	343	8	stan	stan	PROPN
ejpam-5191	343	9	.	.	PUNCT
ejpam-5191	344	1	on	on	ADP
ejpam-5191	344	2	a	a	DET
ejpam-5191	344	3	decomposition	decomposition	NOUN
ejpam-5191	344	4	of	of	ADP
ejpam-5191	344	5	quasicontinuity	quasicontinuity	NOUN
ejpam-5191	344	6	in	in	ADP
ejpam-5191	344	7	topological	topological	ADJ
ejpam-5191	344	8	spaces	space	NOUN
ejpam-5191	344	9	.	.	PUNCT
ejpam-5191	345	1	studii	studii	PROPN
ejpam-5191	345	2	şi	şi	PROPN
ejpam-5191	345	3	cercetări	cercetări	PROPN
ejpam-5191	345	4	de	de	X
ejpam-5191	345	5	matematicaă	matematicaă	PROPN
ejpam-5191	345	6	,	,	PUNCT
ejpam-5191	345	7	25:41–43	25:41–43	NUM
ejpam-5191	345	8	,	,	PUNCT
ejpam-5191	345	9	1973	1973	NUM
ejpam-5191	345	10	.	.	PUNCT
ejpam-5191	346	1	[	[	X
ejpam-5191	346	2	37	37	NUM
ejpam-5191	346	3	]	]	X
ejpam-5191	346	4	p.	p.	NOUN
ejpam-5191	346	5	pue	pue	NOUN
ejpam-5191	346	6	-	-	PUNCT
ejpam-5191	346	7	on	on	ADP
ejpam-5191	346	8	and	and	CCONJ
ejpam-5191	346	9	c.	c.	PROPN
ejpam-5191	346	10	boonpok	boonpok	PROPN
ejpam-5191	346	11	.	.	PUNCT
ejpam-5191	347	1	θ(λ	θ(λ	PROPN
ejpam-5191	347	2	,	,	PUNCT
ejpam-5191	347	3	p)-continuity	p)-continuity	NOUN
ejpam-5191	347	4	for	for	ADP
ejpam-5191	347	5	functions	function	NOUN
ejpam-5191	347	6	.	.	PUNCT
ejpam-5191	348	1	international	international	ADJ
ejpam-5191	348	2	journal	journal	NOUN
ejpam-5191	348	3	of	of	ADP
ejpam-5191	348	4	mathematics	mathematic	NOUN
ejpam-5191	348	5	and	and	CCONJ
ejpam-5191	348	6	computer	computer	NOUN
ejpam-5191	348	7	science	science	NOUN
ejpam-5191	348	8	,	,	PUNCT
ejpam-5191	348	9	19(2):491–495	19(2):491–495	NUM
ejpam-5191	348	10	,	,	PUNCT
ejpam-5191	348	11	2024	2024	NUM
ejpam-5191	348	12	.	.	PUNCT
ejpam-5191	349	1	references	reference	NOUN
ejpam-5191	349	2	1564	1564	NUM
ejpam-5191	349	3	[	[	X
ejpam-5191	349	4	38	38	NUM
ejpam-5191	349	5	]	]	X
ejpam-5191	349	6	n.	n.	NOUN
ejpam-5191	349	7	srisarakham	srisarakham	PROPN
ejpam-5191	349	8	and	and	CCONJ
ejpam-5191	349	9	c.	c.	PROPN
ejpam-5191	349	10	boonpok	boonpok	PROPN
ejpam-5191	349	11	.	.	PUNCT
ejpam-5191	350	1	almost	almost	ADV
ejpam-5191	350	2	(	(	PUNCT
ejpam-5191	350	3	λ	λ	NOUN
ejpam-5191	350	4	,	,	PUNCT
ejpam-5191	350	5	p)-continuous	p)-continuous	ADJ
ejpam-5191	350	6	functions	function	NOUN
ejpam-5191	350	7	.	.	PUNCT
ejpam-5191	351	1	international	international	ADJ
ejpam-5191	351	2	journal	journal	PROPN
ejpam-5191	351	3	of	of	ADP
ejpam-5191	351	4	mathematics	mathematic	NOUN
ejpam-5191	351	5	and	and	CCONJ
ejpam-5191	351	6	computer	computer	NOUN
ejpam-5191	351	7	science	science	NOUN
ejpam-5191	351	8	,	,	PUNCT
ejpam-5191	351	9	18(2):255–259	18(2):255–259	NUM
ejpam-5191	351	10	,	,	PUNCT
ejpam-5191	351	11	2023	2023	NUM
ejpam-5191	351	12	.	.	PUNCT
ejpam-5191	352	1	[	[	X
ejpam-5191	352	2	39	39	NUM
ejpam-5191	352	3	]	]	X
ejpam-5191	352	4	n.	n.	NOUN
ejpam-5191	352	5	srisarakham	srisarakham	PROPN
ejpam-5191	352	6	and	and	CCONJ
ejpam-5191	352	7	c.	c.	PROPN
ejpam-5191	352	8	boonpok	boonpok	PROPN
ejpam-5191	352	9	.	.	PUNCT
ejpam-5191	353	1	on	on	ADP
ejpam-5191	353	2	characterizations	characterization	NOUN
ejpam-5191	353	3	of	of	ADP
ejpam-5191	353	4	δp(λ	δp(λ	NOUN
ejpam-5191	353	5	,	,	PUNCT
ejpam-5191	353	6	s)-d1	s)-d1	NOUN
ejpam-5191	353	7	spaces	space	NOUN
ejpam-5191	353	8	.	.	PUNCT
ejpam-5191	354	1	international	international	ADJ
ejpam-5191	354	2	journal	journal	PROPN
ejpam-5191	354	3	of	of	ADP
ejpam-5191	354	4	mathematics	mathematic	NOUN
ejpam-5191	354	5	and	and	CCONJ
ejpam-5191	354	6	computer	computer	NOUN
ejpam-5191	354	7	science	science	NOUN
ejpam-5191	354	8	,	,	PUNCT
ejpam-5191	354	9	18(4):743–747	18(4):743–747	PROPN
ejpam-5191	354	10	,	,	PUNCT
ejpam-5191	354	11	2023	2023	NUM
ejpam-5191	354	12	.	.	PUNCT
ejpam-5191	355	1	[	[	X
ejpam-5191	355	2	40	40	NUM
ejpam-5191	355	3	]	]	PUNCT
ejpam-5191	355	4	m.	m.	NOUN
ejpam-5191	355	5	thongmoon	thongmoon	NOUN
ejpam-5191	355	6	and	and	CCONJ
ejpam-5191	355	7	c.	c.	PROPN
ejpam-5191	355	8	boonpok	boonpok	PROPN
ejpam-5191	355	9	.	.	PUNCT
ejpam-5191	356	1	strongly	strongly	ADV
ejpam-5191	356	2	θ(λ	θ(λ	PROPN
ejpam-5191	356	3	,	,	PUNCT
ejpam-5191	356	4	p)-continuous	p)-continuous	ADJ
ejpam-5191	356	5	functions	function	NOUN
ejpam-5191	356	6	.	.	PUNCT
ejpam-5191	357	1	international	international	ADJ
ejpam-5191	357	2	journal	journal	PROPN
ejpam-5191	357	3	of	of	ADP
ejpam-5191	357	4	mathematics	mathematic	NOUN
ejpam-5191	357	5	and	and	CCONJ
ejpam-5191	357	6	computer	computer	NOUN
ejpam-5191	357	7	science	science	NOUN
ejpam-5191	357	8	,	,	PUNCT
ejpam-5191	357	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5191	357	10	,	,	PUNCT
ejpam-5191	357	11	2024	2024	NUM
ejpam-5191	357	12	.	.	PUNCT
ejpam-5191	358	1	[	[	X
ejpam-5191	358	2	41	41	NUM
ejpam-5191	358	3	]	]	PUNCT
ejpam-5191	358	4	m.	m.	NOUN
ejpam-5191	358	5	thongmoon	thongmoon	NOUN
ejpam-5191	358	6	,	,	PUNCT
ejpam-5191	358	7	s.	s.	PROPN
ejpam-5191	358	8	sompong	sompong	PROPN
ejpam-5191	358	9	,	,	PUNCT
ejpam-5191	358	10	and	and	CCONJ
ejpam-5191	358	11	c.	c.	PROPN
ejpam-5191	358	12	boonpok	boonpok	PROPN
ejpam-5191	358	13	.	.	PUNCT
ejpam-5191	359	1	upper	upper	ADJ
ejpam-5191	359	2	and	and	CCONJ
ejpam-5191	359	3	lower	low	ADJ
ejpam-5191	359	4	weak	weak	ADJ
ejpam-5191	359	5	(	(	PUNCT
ejpam-5191	359	6	τ1	τ1	NOUN
ejpam-5191	359	7	,	,	PUNCT
ejpam-5191	359	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5191	359	9	.	.	PUNCT
ejpam-5191	360	1	(	(	PUNCT
ejpam-5191	360	2	accepted	accept	VERB
ejpam-5191	360	3	)	)	PUNCT
ejpam-5191	360	4	.	.	PUNCT
ejpam-5191	361	1	[	[	X
ejpam-5191	361	2	42	42	NUM
ejpam-5191	361	3	]	]	X
ejpam-5191	361	4	c.	c.	PROPN
ejpam-5191	361	5	viriyapong	viriyapong	PROPN
ejpam-5191	361	6	and	and	CCONJ
ejpam-5191	361	7	c.	c.	PROPN
ejpam-5191	361	8	boonpok	boonpok	PROPN
ejpam-5191	361	9	.	.	PUNCT
ejpam-5191	362	1	(	(	PUNCT
ejpam-5191	362	2	τ1	τ1	NOUN
ejpam-5191	362	3	,	,	PUNCT
ejpam-5191	362	4	τ2)α	τ2)α	NOUN
ejpam-5191	362	5	-	-	PUNCT
ejpam-5191	362	6	continuity	continuity	NOUN
ejpam-5191	362	7	for	for	ADP
ejpam-5191	362	8	multifunctions	multifunction	NOUN
ejpam-5191	362	9	.	.	PUNCT
ejpam-5191	363	1	journal	journal	PROPN
ejpam-5191	363	2	of	of	ADP
ejpam-5191	363	3	mathematics	mathematic	NOUN
ejpam-5191	363	4	,	,	PUNCT
ejpam-5191	363	5	2020:6285763	2020:6285763	NUM
ejpam-5191	363	6	,	,	PUNCT
ejpam-5191	363	7	2020	2020	NUM
ejpam-5191	363	8	.	.	PUNCT
ejpam-5191	364	1	[	[	X
ejpam-5191	364	2	43	43	NUM
ejpam-5191	364	3	]	]	X
ejpam-5191	364	4	c.	c.	PROPN
ejpam-5191	364	5	viriyapong	viriyapong	PROPN
ejpam-5191	364	6	and	and	CCONJ
ejpam-5191	364	7	c.	c.	PROPN
ejpam-5191	364	8	boonpok	boonpok	PROPN
ejpam-5191	364	9	.	.	PUNCT
ejpam-5191	365	1	(	(	PUNCT
ejpam-5191	365	2	λ	λ	X
ejpam-5191	365	3	,	,	PUNCT
ejpam-5191	365	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5191	365	5	functions	function	NOUN
ejpam-5191	365	6	.	.	PUNCT
ejpam-5191	366	1	wseas	wseas	VERB
ejpam-5191	366	2	transactions	transaction	NOUN
ejpam-5191	366	3	on	on	ADP
ejpam-5191	366	4	mathematics	mathematic	NOUN
ejpam-5191	366	5	,	,	PUNCT
ejpam-5191	366	6	21:380–385	21:380–385	NUM
ejpam-5191	366	7	,	,	PUNCT
ejpam-5191	366	8	2022	2022	NUM
ejpam-5191	366	9	.	.	PUNCT
ejpam-5191	367	1	[	[	X
ejpam-5191	367	2	44	44	NUM
ejpam-5191	367	3	]	]	PUNCT
ejpam-5191	367	4	c.	c.	PROPN
ejpam-5191	367	5	viriyapong	viriyapong	PROPN
ejpam-5191	367	6	and	and	CCONJ
ejpam-5191	367	7	c.	c.	PROPN
ejpam-5191	367	8	boonpok	boonpok	PROPN
ejpam-5191	367	9	.	.	PUNCT
ejpam-5191	368	1	weak	weak	ADJ
ejpam-5191	368	2	quasi	quasi	NOUN
ejpam-5191	368	3	(	(	PUNCT
ejpam-5191	368	4	λ	λ	PROPN
ejpam-5191	368	5	,	,	PUNCT
ejpam-5191	368	6	sp)-continuity	sp)-continuity	NOUN
ejpam-5191	368	7	for	for	ADP
ejpam-5191	368	8	multifunctions	multifunction	NOUN
ejpam-5191	368	9	.	.	PUNCT
ejpam-5191	369	1	international	international	ADJ
ejpam-5191	369	2	journal	journal	PROPN
ejpam-5191	369	3	of	of	ADP
ejpam-5191	369	4	mathematics	mathematic	NOUN
ejpam-5191	369	5	and	and	CCONJ
ejpam-5191	369	6	computer	computer	NOUN
ejpam-5191	369	7	science	science	NOUN
ejpam-5191	369	8	,	,	PUNCT
ejpam-5191	369	9	17(3):1201–1209	17(3):1201–1209	NUM
ejpam-5191	369	10	,	,	PUNCT
ejpam-5191	369	11	2022	2022	NUM
ejpam-5191	369	12	.	.	PUNCT
ejpam-5191	370	1	[	[	X
ejpam-5191	370	2	45	45	NUM
ejpam-5191	370	3	]	]	X
ejpam-5191	370	4	n.	n.	PROPN
ejpam-5191	370	5	viriyapong	viriyapong	PROPN
ejpam-5191	370	6	,	,	PUNCT
ejpam-5191	370	7	s.	s.	PROPN
ejpam-5191	370	8	sompong	sompong	PROPN
ejpam-5191	370	9	,	,	PUNCT
ejpam-5191	370	10	and	and	CCONJ
ejpam-5191	370	11	c.	c.	PROPN
ejpam-5191	370	12	boonpok	boonpok	PROPN
ejpam-5191	370	13	.	.	PUNCT
ejpam-5191	371	1	(	(	PUNCT
ejpam-5191	371	2	τ1	τ1	NOUN
ejpam-5191	371	3	,	,	PUNCT
ejpam-5191	371	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5191	371	5	disconnectedness	disconnectedness	NOUN
ejpam-5191	371	6	in	in	ADP
ejpam-5191	371	7	bitopological	bitopological	ADJ
ejpam-5191	371	8	spaces	space	NOUN
ejpam-5191	371	9	.	.	PUNCT
ejpam-5191	372	1	international	international	ADJ
ejpam-5191	372	2	journal	journal	PROPN
ejpam-5191	372	3	of	of	ADP
ejpam-5191	372	4	mathematics	mathematic	NOUN
ejpam-5191	372	5	and	and	CCONJ
ejpam-5191	372	6	computer	computer	NOUN
ejpam-5191	372	7	science	science	NOUN
ejpam-5191	372	8	,	,	PUNCT
ejpam-5191	372	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5191	372	10	,	,	PUNCT
ejpam-5191	372	11	2024	2024	NUM
ejpam-5191	372	12	.	.	PUNCT