id	sid	tid	token	lemma	pos
ejpam-5722	1	1	european	european	PROPN
ejpam-5722	1	2	journal	journal	PROPN
ejpam-5722	1	3	of	of	ADP
ejpam-5722	1	4	pure	pure	ADJ
ejpam-5722	1	5	and	and	CCONJ
ejpam-5722	1	6	applied	applied	ADJ
ejpam-5722	1	7	mathematics	mathematic	NOUN
ejpam-5722	1	8	2025	2025	NUM
ejpam-5722	1	9	,	,	PUNCT
ejpam-5722	1	10	vol	vol	NOUN
ejpam-5722	1	11	.	.	PROPN
ejpam-5722	1	12	18	18	NUM
ejpam-5722	1	13	,	,	PUNCT
ejpam-5722	1	14	issue	issue	NOUN
ejpam-5722	1	15	1	1	NUM
ejpam-5722	1	16	,	,	PUNCT
ejpam-5722	1	17	article	article	NOUN
ejpam-5722	1	18	number	number	NOUN
ejpam-5722	1	19	5722	5722	NUM
ejpam-5722	1	20	issn	issn	PROPN
ejpam-5722	1	21	1307	1307	NUM
ejpam-5722	1	22	-	-	SYM
ejpam-5722	1	23	5543	5543	NUM
ejpam-5722	1	24	–	–	PUNCT
ejpam-5722	1	25	ejpam.com	ejpam.com	X
ejpam-5722	1	26	published	publish	VERB
ejpam-5722	1	27	by	by	ADP
ejpam-5722	1	28	new	new	PROPN
ejpam-5722	1	29	york	york	PROPN
ejpam-5722	1	30	business	business	PROPN
ejpam-5722	1	31	global	global	PROPN
ejpam-5722	1	32	quasi	quasi	PROPN
ejpam-5722	1	33	θ(τ1	θ(τ1	PROPN
ejpam-5722	1	34	,	,	PUNCT
ejpam-5722	1	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	1	36	functions	function	NOUN
ejpam-5722	1	37	napassanan	napassanan	PROPN
ejpam-5722	1	38	srisarakham1	srisarakham1	PROPN
ejpam-5722	1	39	,	,	PUNCT
ejpam-5722	1	40	supunnee	supunnee	PROPN
ejpam-5722	1	41	sompong2	sompong2	PROPN
ejpam-5722	1	42	,	,	PUNCT
ejpam-5722	1	43	chawalit	chawalit	VERB
ejpam-5722	1	44	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5722	1	45	1	1	NUM
ejpam-5722	1	46	mathematics	mathematic	NOUN
ejpam-5722	1	47	and	and	CCONJ
ejpam-5722	1	48	applied	apply	VERB
ejpam-5722	1	49	mathematics	mathematics	PROPN
ejpam-5722	1	50	research	research	NOUN
ejpam-5722	1	51	unit	unit	NOUN
ejpam-5722	1	52	,	,	PUNCT
ejpam-5722	1	53	department	department	NOUN
ejpam-5722	1	54	of	of	ADP
ejpam-5722	1	55	mathematics	mathematic	NOUN
ejpam-5722	1	56	,	,	PUNCT
ejpam-5722	1	57	faculty	faculty	NOUN
ejpam-5722	1	58	of	of	ADP
ejpam-5722	1	59	science	science	NOUN
ejpam-5722	1	60	,	,	PUNCT
ejpam-5722	1	61	mahasarakham	mahasarakham	PROPN
ejpam-5722	1	62	university	university	PROPN
ejpam-5722	1	63	,	,	PUNCT
ejpam-5722	1	64	maha	maha	PROPN
ejpam-5722	1	65	sarakham	sarakham	PROPN
ejpam-5722	1	66	,	,	PUNCT
ejpam-5722	1	67	44150	44150	NUM
ejpam-5722	1	68	,	,	PUNCT
ejpam-5722	1	69	thailand	thailand	PROPN
ejpam-5722	1	70	2	2	NUM
ejpam-5722	1	71	department	department	NOUN
ejpam-5722	1	72	of	of	ADP
ejpam-5722	1	73	mathematics	mathematic	NOUN
ejpam-5722	1	74	and	and	CCONJ
ejpam-5722	1	75	statistics	statistic	NOUN
ejpam-5722	1	76	,	,	PUNCT
ejpam-5722	1	77	faculty	faculty	NOUN
ejpam-5722	1	78	of	of	ADP
ejpam-5722	1	79	science	science	NOUN
ejpam-5722	1	80	and	and	CCONJ
ejpam-5722	1	81	technology	technology	NOUN
ejpam-5722	1	82	,	,	PUNCT
ejpam-5722	1	83	sakon	sakon	PROPN
ejpam-5722	1	84	nakhon	nakhon	PROPN
ejpam-5722	1	85	rajbhat	rajbhat	PROPN
ejpam-5722	1	86	university	university	PROPN
ejpam-5722	1	87	,	,	PUNCT
ejpam-5722	1	88	sakon	sakon	PROPN
ejpam-5722	1	89	nakhon	nakhon	PROPN
ejpam-5722	1	90	,	,	PUNCT
ejpam-5722	1	91	47000	47000	NUM
ejpam-5722	1	92	,	,	PUNCT
ejpam-5722	1	93	thailand	thailand	PROPN
ejpam-5722	1	94	abstract	abstract	NOUN
ejpam-5722	1	95	.	.	PUNCT
ejpam-5722	2	1	our	our	PRON
ejpam-5722	2	2	main	main	ADJ
ejpam-5722	2	3	purpose	purpose	NOUN
ejpam-5722	2	4	is	be	AUX
ejpam-5722	2	5	to	to	PART
ejpam-5722	2	6	introduce	introduce	VERB
ejpam-5722	2	7	the	the	DET
ejpam-5722	2	8	concept	concept	NOUN
ejpam-5722	2	9	of	of	ADP
ejpam-5722	2	10	quasi	quasi	NOUN
ejpam-5722	2	11	θ(τ1	θ(τ1	NOUN
ejpam-5722	2	12	,	,	PUNCT
ejpam-5722	2	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	2	14	functions	function	NOUN
ejpam-5722	2	15	.	.	PUNCT
ejpam-5722	3	1	furthermore	furthermore	ADV
ejpam-5722	3	2	,	,	PUNCT
ejpam-5722	3	3	several	several	ADJ
ejpam-5722	3	4	characterizations	characterization	NOUN
ejpam-5722	3	5	and	and	CCONJ
ejpam-5722	3	6	some	some	DET
ejpam-5722	3	7	properties	property	NOUN
ejpam-5722	3	8	concerning	concern	VERB
ejpam-5722	3	9	quasi	quasi	NOUN
ejpam-5722	3	10	θ(τ1	θ(τ1	NOUN
ejpam-5722	3	11	,	,	PUNCT
ejpam-5722	3	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	3	13	functions	function	NOUN
ejpam-5722	3	14	are	be	AUX
ejpam-5722	3	15	investigated	investigate	VERB
ejpam-5722	3	16	.	.	PUNCT
ejpam-5722	4	1	2020	2020	NUM
ejpam-5722	4	2	mathematics	mathematic	NOUN
ejpam-5722	4	3	subject	subject	NOUN
ejpam-5722	4	4	classifications	classification	NOUN
ejpam-5722	4	5	:	:	PUNCT
ejpam-5722	4	6	54c08	54c08	NUM
ejpam-5722	4	7	,	,	PUNCT
ejpam-5722	4	8	54e55	54e55	NUM
ejpam-5722	4	9	key	key	ADJ
ejpam-5722	4	10	words	word	NOUN
ejpam-5722	4	11	and	and	CCONJ
ejpam-5722	4	12	phrases	phrase	NOUN
ejpam-5722	4	13	:	:	PUNCT
ejpam-5722	4	14	τ1τ2	τ1τ2	ADJ
ejpam-5722	4	15	-	-	ADJ
ejpam-5722	4	16	open	open	ADJ
ejpam-5722	4	17	set	set	NOUN
ejpam-5722	4	18	,	,	PUNCT
ejpam-5722	4	19	quasi	quasi	NOUN
ejpam-5722	4	20	θ(τ1	θ(τ1	NOUN
ejpam-5722	4	21	,	,	PUNCT
ejpam-5722	4	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	4	23	function	function	NOUN
ejpam-5722	4	24	1	1	NUM
ejpam-5722	4	25	.	.	PUNCT
ejpam-5722	4	26	introduction	introduction	NOUN
ejpam-5722	4	27	the	the	DET
ejpam-5722	4	28	notion	notion	NOUN
ejpam-5722	4	29	of	of	ADP
ejpam-5722	4	30	continuity	continuity	NOUN
ejpam-5722	4	31	is	be	AUX
ejpam-5722	4	32	an	an	DET
ejpam-5722	4	33	important	important	ADJ
ejpam-5722	4	34	concept	concept	NOUN
ejpam-5722	4	35	for	for	ADP
ejpam-5722	4	36	the	the	DET
ejpam-5722	4	37	study	study	NOUN
ejpam-5722	4	38	in	in	ADP
ejpam-5722	4	39	topological	topological	ADJ
ejpam-5722	4	40	spaces	space	NOUN
ejpam-5722	4	41	.	.	PUNCT
ejpam-5722	5	1	this	this	DET
ejpam-5722	5	2	concept	concept	NOUN
ejpam-5722	5	3	has	have	AUX
ejpam-5722	5	4	been	be	AUX
ejpam-5722	5	5	generalized	generalize	VERB
ejpam-5722	5	6	by	by	ADP
ejpam-5722	5	7	weaker	weak	ADJ
ejpam-5722	5	8	forms	form	NOUN
ejpam-5722	5	9	of	of	ADP
ejpam-5722	5	10	open	open	ADJ
ejpam-5722	5	11	sets	set	NOUN
ejpam-5722	5	12	such	such	ADJ
ejpam-5722	5	13	as	as	ADP
ejpam-5722	5	14	semi	semi	ADJ
ejpam-5722	5	15	-	-	ADJ
ejpam-5722	5	16	open	open	ADJ
ejpam-5722	5	17	sets	set	NOUN
ejpam-5722	5	18	[	[	X
ejpam-5722	5	19	23	23	NUM
ejpam-5722	5	20	]	]	PUNCT
ejpam-5722	5	21	,	,	PUNCT
ejpam-5722	5	22	preopen	preopen	ADJ
ejpam-5722	5	23	sets	set	NOUN
ejpam-5722	5	24	[	[	X
ejpam-5722	5	25	25	25	NUM
ejpam-5722	5	26	]	]	PUNCT
ejpam-5722	5	27	,	,	PUNCT
ejpam-5722	5	28	α	α	X
ejpam-5722	5	29	-	-	ADJ
ejpam-5722	5	30	open	open	ADJ
ejpam-5722	5	31	sets	set	NOUN
ejpam-5722	5	32	[	[	X
ejpam-5722	5	33	27	27	NUM
ejpam-5722	5	34	]	]	PUNCT
ejpam-5722	5	35	,	,	PUNCT
ejpam-5722	5	36	β	β	X
ejpam-5722	5	37	-	-	ADJ
ejpam-5722	5	38	open	open	ADJ
ejpam-5722	5	39	sets	set	NOUN
ejpam-5722	5	40	[	[	X
ejpam-5722	5	41	19	19	NUM
ejpam-5722	5	42	]	]	PUNCT
ejpam-5722	5	43	and	and	CCONJ
ejpam-5722	5	44	θ	θ	ADJ
ejpam-5722	5	45	-	-	ADJ
ejpam-5722	5	46	open	open	ADJ
ejpam-5722	5	47	sets	set	NOUN
ejpam-5722	5	48	[	[	X
ejpam-5722	5	49	42	42	NUM
ejpam-5722	5	50	]	]	PUNCT
ejpam-5722	5	51	.	.	PUNCT
ejpam-5722	6	1	levine	levine	PROPN
ejpam-5722	7	1	[	[	X
ejpam-5722	7	2	23	23	NUM
ejpam-5722	7	3	]	]	PUNCT
ejpam-5722	7	4	introduced	introduce	VERB
ejpam-5722	7	5	and	and	CCONJ
ejpam-5722	7	6	studied	study	VERB
ejpam-5722	7	7	the	the	DET
ejpam-5722	7	8	notion	notion	NOUN
ejpam-5722	7	9	of	of	ADP
ejpam-5722	7	10	semi	semi	ADJ
ejpam-5722	7	11	-	-	ADJ
ejpam-5722	7	12	continuous	continuous	ADJ
ejpam-5722	7	13	functions	function	NOUN
ejpam-5722	7	14	.	.	PUNCT
ejpam-5722	8	1	arya	arya	PROPN
ejpam-5722	8	2	and	and	CCONJ
ejpam-5722	8	3	bhamini	bhamini	PROPN
ejpam-5722	9	1	[	[	X
ejpam-5722	9	2	1	1	NUM
ejpam-5722	9	3	]	]	PUNCT
ejpam-5722	9	4	introduced	introduce	VERB
ejpam-5722	9	5	the	the	DET
ejpam-5722	9	6	concept	concept	NOUN
ejpam-5722	9	7	of	of	ADP
ejpam-5722	9	8	θ	θ	NOUN
ejpam-5722	9	9	-	-	PUNCT
ejpam-5722	9	10	semi	semi	NOUN
ejpam-5722	9	11	-	-	NOUN
ejpam-5722	9	12	continuity	continuity	NOUN
ejpam-5722	9	13	as	as	ADP
ejpam-5722	9	14	a	a	DET
ejpam-5722	9	15	generalization	generalization	NOUN
ejpam-5722	9	16	of	of	ADP
ejpam-5722	9	17	semi	semi	NOUN
ejpam-5722	9	18	-	-	NOUN
ejpam-5722	9	19	continuity	continuity	NOUN
ejpam-5722	9	20	.	.	PUNCT
ejpam-5722	10	1	noiri	noiri	PROPN
ejpam-5722	11	1	[	[	X
ejpam-5722	11	2	28	28	NUM
ejpam-5722	11	3	]	]	PUNCT
ejpam-5722	11	4	and	and	CCONJ
ejpam-5722	11	5	jafari	jafari	PROPN
ejpam-5722	11	6	and	and	CCONJ
ejpam-5722	11	7	noiri	noiri	ADV
ejpam-5722	11	8	[	[	X
ejpam-5722	11	9	20	20	NUM
ejpam-5722	11	10	]	]	PUNCT
ejpam-5722	11	11	have	have	AUX
ejpam-5722	11	12	further	far	ADV
ejpam-5722	11	13	investigated	investigate	VERB
ejpam-5722	11	14	some	some	DET
ejpam-5722	11	15	characterizations	characterization	NOUN
ejpam-5722	11	16	of	of	ADP
ejpam-5722	11	17	θ	θ	ADJ
ejpam-5722	11	18	-	-	PUNCT
ejpam-5722	11	19	semicontinuous	semicontinuous	ADJ
ejpam-5722	11	20	functions	function	NOUN
ejpam-5722	11	21	.	.	PUNCT
ejpam-5722	12	1	viriyapong	viriyapong	PROPN
ejpam-5722	12	2	and	and	CCONJ
ejpam-5722	12	3	boonpok	boonpok	VERB
ejpam-5722	13	1	[	[	X
ejpam-5722	13	2	44	44	NUM
ejpam-5722	13	3	]	]	PUNCT
ejpam-5722	13	4	investigated	investigate	VERB
ejpam-5722	13	5	some	some	DET
ejpam-5722	13	6	characterizations	characterization	NOUN
ejpam-5722	13	7	of	of	ADP
ejpam-5722	13	8	(	(	PUNCT
ejpam-5722	13	9	λ	λ	PROPN
ejpam-5722	13	10	,	,	PUNCT
ejpam-5722	13	11	sp)-continuous	sp)-continuous	ADJ
ejpam-5722	13	12	functions	function	NOUN
ejpam-5722	13	13	by	by	ADP
ejpam-5722	13	14	utilizing	utilize	VERB
ejpam-5722	13	15	the	the	DET
ejpam-5722	13	16	notions	notion	NOUN
ejpam-5722	13	17	of	of	ADP
ejpam-5722	13	18	(	(	PUNCT
ejpam-5722	13	19	λ	λ	PROPN
ejpam-5722	13	20	,	,	PUNCT
ejpam-5722	13	21	sp)-open	sp)-open	ADJ
ejpam-5722	13	22	sets	set	NOUN
ejpam-5722	13	23	and	and	CCONJ
ejpam-5722	13	24	(	(	PUNCT
ejpam-5722	13	25	λ	λ	PROPN
ejpam-5722	13	26	,	,	PUNCT
ejpam-5722	13	27	sp)closed	sp)close	VERB
ejpam-5722	13	28	sets	set	NOUN
ejpam-5722	13	29	due	due	ADP
ejpam-5722	13	30	to	to	ADP
ejpam-5722	13	31	boonpok	boonpok	NOUN
ejpam-5722	13	32	and	and	CCONJ
ejpam-5722	13	33	khampakdee	khampakdee	NOUN
ejpam-5722	13	34	[	[	X
ejpam-5722	13	35	9	9	NUM
ejpam-5722	13	36	]	]	PUNCT
ejpam-5722	13	37	.	.	PUNCT
ejpam-5722	14	1	dungthaisong	dungthaisong	NOUN
ejpam-5722	14	2	et	et	PROPN
ejpam-5722	14	3	al	al	PROPN
ejpam-5722	14	4	.	.	PUNCT
ejpam-5722	15	1	[	[	X
ejpam-5722	15	2	18	18	NUM
ejpam-5722	15	3	]	]	PUNCT
ejpam-5722	15	4	introduced	introduce	VERB
ejpam-5722	15	5	and	and	CCONJ
ejpam-5722	15	6	studied	study	VERB
ejpam-5722	15	7	the	the	DET
ejpam-5722	15	8	concept	concept	NOUN
ejpam-5722	15	9	of	of	ADP
ejpam-5722	15	10	g(m	g(m	ADJ
ejpam-5722	15	11	,	,	PUNCT
ejpam-5722	15	12	n)-continuous	n)-continuous	ADJ
ejpam-5722	15	13	functions	function	NOUN
ejpam-5722	15	14	.	.	PUNCT
ejpam-5722	16	1	duangphui	duangphui	NOUN
ejpam-5722	16	2	et	et	PROPN
ejpam-5722	16	3	al	al	PROPN
ejpam-5722	16	4	.	.	PUNCT
ejpam-5722	17	1	[	[	X
ejpam-5722	17	2	17	17	NUM
ejpam-5722	17	3	]	]	PUNCT
ejpam-5722	17	4	introduced	introduce	VERB
ejpam-5722	17	5	and	and	CCONJ
ejpam-5722	17	6	investigated	investigate	VERB
ejpam-5722	17	7	the	the	DET
ejpam-5722	17	8	notion	notion	NOUN
ejpam-5722	17	9	of	of	ADP
ejpam-5722	17	10	(	(	PUNCT
ejpam-5722	17	11	µ	µ	NOUN
ejpam-5722	17	12	,	,	PUNCT
ejpam-5722	17	13	µ′)(m	µ′)(m	VERB
ejpam-5722	17	14	,	,	PUNCT
ejpam-5722	17	15	n)-continuous	n)-continuous	ADJ
ejpam-5722	17	16	functions	function	NOUN
ejpam-5722	17	17	.	.	PUNCT
ejpam-5722	18	1	moreover	moreover	ADV
ejpam-5722	18	2	,	,	PUNCT
ejpam-5722	18	3	several	several	ADJ
ejpam-5722	18	4	characterizations	characterization	NOUN
ejpam-5722	18	5	of	of	ADP
ejpam-5722	18	6	almost	almost	ADV
ejpam-5722	18	7	(	(	PUNCT
ejpam-5722	18	8	λ	λ	PROPN
ejpam-5722	18	9	,	,	PUNCT
ejpam-5722	18	10	p)-continuous	p)-continuous	ADJ
ejpam-5722	18	11	functions	function	NOUN
ejpam-5722	18	12	,	,	PUNCT
ejpam-5722	18	13	strongly	strongly	ADV
ejpam-5722	18	14	θ(λ	θ(λ	PROPN
ejpam-5722	18	15	,	,	PUNCT
ejpam-5722	18	16	p)-continuous	p)-continuous	ADJ
ejpam-5722	18	17	functions	function	NOUN
ejpam-5722	18	18	,	,	PUNCT
ejpam-5722	18	19	almost	almost	ADV
ejpam-5722	18	20	strongly	strongly	ADV
ejpam-5722	18	21	θ(λ	θ(λ	VERB
ejpam-5722	18	22	,	,	PUNCT
ejpam-5722	18	23	p)-continuous	p)-continuous	ADJ
ejpam-5722	18	24	functions	function	NOUN
ejpam-5722	18	25	,	,	PUNCT
ejpam-5722	18	26	θ(λ	θ(λ	PROPN
ejpam-5722	18	27	,	,	PUNCT
ejpam-5722	18	28	p)-continuous	p)-continuous	ADJ
ejpam-5722	18	29	functions	function	NOUN
ejpam-5722	18	30	,	,	PUNCT
ejpam-5722	18	31	weakly	weakly	ADJ
ejpam-5722	18	32	(	(	PUNCT
ejpam-5722	18	33	λ	λ	PROPN
ejpam-5722	18	34	,	,	PUNCT
ejpam-5722	18	35	b)-continuous	b)-continuous	ADJ
ejpam-5722	18	36	functions	function	NOUN
ejpam-5722	18	37	,	,	PUNCT
ejpam-5722	18	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5722	18	39	functions	function	NOUN
ejpam-5722	18	40	,	,	PUNCT
ejpam-5722	18	41	(	(	PUNCT
ejpam-5722	18	42	λ	λ	NOUN
ejpam-5722	18	43	,	,	PUNCT
ejpam-5722	18	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5722	18	45	functions	function	NOUN
ejpam-5722	18	46	,	,	PUNCT
ejpam-5722	18	47	⋆-continuous	⋆-continuous	ADJ
ejpam-5722	18	48	functions	function	NOUN
ejpam-5722	18	49	,	,	PUNCT
ejpam-5722	18	50	θ	θ	PROPN
ejpam-5722	18	51	-	-	ADJ
ejpam-5722	18	52	i	i	NOUN
ejpam-5722	18	53	-continuous	-continuous	ADJ
ejpam-5722	18	54	functions	function	NOUN
ejpam-5722	18	55	,	,	PUNCT
ejpam-5722	18	56	almost	almost	ADV
ejpam-5722	18	57	(	(	PUNCT
ejpam-5722	18	58	g	g	NOUN
ejpam-5722	18	59	,	,	PUNCT
ejpam-5722	18	60	m)-continuous	m)-continuous	ADJ
ejpam-5722	18	61	functions	function	NOUN
ejpam-5722	18	62	,	,	PUNCT
ejpam-5722	18	63	pairwise	pairwise	NOUN
ejpam-5722	18	64	almost	almost	ADV
ejpam-5722	18	65	m	m	VERB
ejpam-5722	18	66	-continuous	-continuous	ADJ
ejpam-5722	18	67	functions	function	NOUN
ejpam-5722	18	68	,	,	PUNCT
ejpam-5722	18	69	(	(	PUNCT
ejpam-5722	18	70	τ1	τ1	NOUN
ejpam-5722	18	71	,	,	PUNCT
ejpam-5722	18	72	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	18	73	functions	function	NOUN
ejpam-5722	18	74	,	,	PUNCT
ejpam-5722	18	75	almost	almost	ADV
ejpam-5722	18	76	(	(	PUNCT
ejpam-5722	18	77	τ1	τ1	NOUN
ejpam-5722	18	78	,	,	PUNCT
ejpam-5722	18	79	τ2)continuous	τ2)continuous	ADJ
ejpam-5722	18	80	functions	function	NOUN
ejpam-5722	18	81	,	,	PUNCT
ejpam-5722	18	82	weakly	weakly	ADJ
ejpam-5722	18	83	(	(	PUNCT
ejpam-5722	18	84	τ1	τ1	NOUN
ejpam-5722	18	85	,	,	PUNCT
ejpam-5722	18	86	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	18	87	functions	function	NOUN
ejpam-5722	18	88	,	,	PUNCT
ejpam-5722	18	89	slightly	slightly	ADV
ejpam-5722	18	90	(	(	PUNCT
ejpam-5722	18	91	τ1	τ1	NOUN
ejpam-5722	18	92	,	,	PUNCT
ejpam-5722	18	93	τ2)s	τ2)s	NOUN
ejpam-5722	18	94	-	-	PUNCT
ejpam-5722	18	95	continuous	continuous	ADJ
ejpam-5722	18	96	∗corresponding	∗corresponding	NOUN
ejpam-5722	18	97	author	author	NOUN
ejpam-5722	18	98	.	.	PUNCT
ejpam-5722	19	1	doi	doi	NOUN
ejpam-5722	19	2	:	:	PUNCT
ejpam-5722	19	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5722	https://doi.org/10.29020/nybg.ejpam.v18i1.5722	DET
ejpam-5722	19	4	email	email	NOUN
ejpam-5722	19	5	addresses	address	VERB
ejpam-5722	19	6	:	:	PUNCT
ejpam-5722	19	7	napassanan.sri@msu.ac.th	napassanan.sri@msu.ac.th	PRON
ejpam-5722	19	8	(	(	PUNCT
ejpam-5722	19	9	n.	n.	NOUN
ejpam-5722	19	10	srisarakham	srisarakham	PROPN
ejpam-5722	19	11	)	)	PUNCT
ejpam-5722	19	12	,	,	PUNCT
ejpam-5722	19	13	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-5722	19	14	(	(	PUNCT
ejpam-5722	19	15	s.	s.	PROPN
ejpam-5722	19	16	sompong	sompong	PROPN
ejpam-5722	19	17	)	)	PUNCT
ejpam-5722	19	18	,	,	PUNCT
ejpam-5722	19	19	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5722	19	20	(	(	PUNCT
ejpam-5722	19	21	c.	c.	PROPN
ejpam-5722	19	22	boonpok	boonpok	PROPN
ejpam-5722	19	23	)	)	PUNCT
ejpam-5722	19	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5722	20	1	1	1	NUM
ejpam-5722	20	2	copyright	copyright	NOUN
ejpam-5722	20	3	:	:	PUNCT
ejpam-5722	20	4	©	©	PROPN
ejpam-5722	20	5	2025	2025	NUM
ejpam-5722	20	6	the	the	DET
ejpam-5722	20	7	author(s	author(s	NOUN
ejpam-5722	20	8	)	)	PUNCT
ejpam-5722	20	9	.	.	PUNCT
ejpam-5722	21	1	(	(	PUNCT
ejpam-5722	21	2	cc	cc	NOUN
ejpam-5722	21	3	by	by	ADP
ejpam-5722	21	4	-	-	PUNCT
ejpam-5722	21	5	nc	nc	PROPN
ejpam-5722	21	6	4.0	4.0	NUM
ejpam-5722	21	7	)	)	PUNCT
ejpam-5722	21	8	n.	n.	NOUN
ejpam-5722	21	9	srisarakham	srisarakham	PROPN
ejpam-5722	21	10	,	,	PUNCT
ejpam-5722	21	11	s.	s.	PROPN
ejpam-5722	21	12	sompong	sompong	PROPN
ejpam-5722	21	13	,	,	PUNCT
ejpam-5722	21	14	c.	c.	PROPN
ejpam-5722	21	15	boonpok	boonpok	PROPN
ejpam-5722	21	16	/	/	SYM
ejpam-5722	21	17	eur	eur	PROPN
ejpam-5722	21	18	.	.	PUNCT
ejpam-5722	22	1	j.	j.	PROPN
ejpam-5722	22	2	pure	pure	PROPN
ejpam-5722	22	3	appl	appl	PROPN
ejpam-5722	22	4	.	.	PROPN
ejpam-5722	22	5	math	math	PROPN
ejpam-5722	22	6	,	,	PUNCT
ejpam-5722	22	7	18	18	NUM
ejpam-5722	22	8	(	(	PUNCT
ejpam-5722	22	9	1	1	NUM
ejpam-5722	22	10	)	)	PUNCT
ejpam-5722	22	11	(	(	PUNCT
ejpam-5722	22	12	2025	2025	NUM
ejpam-5722	22	13	)	)	PUNCT
ejpam-5722	22	14	,	,	PUNCT
ejpam-5722	22	15	5722	5722	NUM
ejpam-5722	22	16	2	2	NUM
ejpam-5722	22	17	of	of	ADP
ejpam-5722	22	18	12	12	NUM
ejpam-5722	22	19	functions	function	NOUN
ejpam-5722	22	20	,	,	PUNCT
ejpam-5722	22	21	δ(τ1	δ(τ1	NOUN
ejpam-5722	22	22	,	,	PUNCT
ejpam-5722	22	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	22	24	functions	function	NOUN
ejpam-5722	22	25	,	,	PUNCT
ejpam-5722	22	26	faintly	faintly	ADV
ejpam-5722	22	27	(	(	PUNCT
ejpam-5722	22	28	τ1	τ1	PROPN
ejpam-5722	22	29	,	,	PUNCT
ejpam-5722	22	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	22	31	functions	function	NOUN
ejpam-5722	22	32	and	and	CCONJ
ejpam-5722	22	33	rarely	rarely	ADV
ejpam-5722	22	34	(	(	PUNCT
ejpam-5722	22	35	τ1	τ1	NOUN
ejpam-5722	22	36	,	,	PUNCT
ejpam-5722	22	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	22	38	functions	function	NOUN
ejpam-5722	22	39	were	be	AUX
ejpam-5722	22	40	presented	present	VERB
ejpam-5722	22	41	in	in	ADP
ejpam-5722	22	42	[	[	X
ejpam-5722	22	43	36	36	NUM
ejpam-5722	22	44	]	]	PUNCT
ejpam-5722	22	45	,	,	PUNCT
ejpam-5722	22	46	[	[	X
ejpam-5722	22	47	38	38	NUM
ejpam-5722	22	48	]	]	PUNCT
ejpam-5722	22	49	,	,	PUNCT
ejpam-5722	22	50	[	[	X
ejpam-5722	22	51	10	10	NUM
ejpam-5722	22	52	]	]	PUNCT
ejpam-5722	22	53	,	,	PUNCT
ejpam-5722	22	54	[	[	X
ejpam-5722	22	55	32	32	NUM
ejpam-5722	22	56	]	]	PUNCT
ejpam-5722	22	57	,	,	PUNCT
ejpam-5722	22	58	[	[	X
ejpam-5722	22	59	13	13	NUM
ejpam-5722	22	60	]	]	PUNCT
ejpam-5722	22	61	,	,	PUNCT
ejpam-5722	22	62	[	[	X
ejpam-5722	22	63	8	8	NUM
ejpam-5722	22	64	]	]	PUNCT
ejpam-5722	22	65	,	,	PUNCT
ejpam-5722	22	66	[	[	X
ejpam-5722	22	67	6	6	NUM
ejpam-5722	22	68	]	]	PUNCT
ejpam-5722	22	69	,	,	PUNCT
ejpam-5722	22	70	[	[	X
ejpam-5722	22	71	7	7	NUM
ejpam-5722	22	72	]	]	PUNCT
ejpam-5722	22	73	,	,	PUNCT
ejpam-5722	22	74	[	[	X
ejpam-5722	22	75	4	4	NUM
ejpam-5722	22	76	]	]	PUNCT
ejpam-5722	22	77	,	,	PUNCT
ejpam-5722	22	78	[	[	X
ejpam-5722	22	79	2	2	NUM
ejpam-5722	22	80	]	]	PUNCT
ejpam-5722	22	81	,	,	PUNCT
ejpam-5722	22	82	[	[	X
ejpam-5722	22	83	3	3	NUM
ejpam-5722	22	84	]	]	PUNCT
ejpam-5722	22	85	,	,	PUNCT
ejpam-5722	22	86	[	[	X
ejpam-5722	22	87	14	14	NUM
ejpam-5722	22	88	]	]	PUNCT
ejpam-5722	22	89	,	,	PUNCT
ejpam-5722	22	90	[	[	X
ejpam-5722	22	91	12	12	NUM
ejpam-5722	22	92	]	]	PUNCT
ejpam-5722	22	93	,	,	PUNCT
ejpam-5722	22	94	[	[	X
ejpam-5722	22	95	11	11	NUM
ejpam-5722	22	96	]	]	PUNCT
ejpam-5722	22	97	,	,	PUNCT
ejpam-5722	22	98	[	[	X
ejpam-5722	22	99	35	35	NUM
ejpam-5722	22	100	]	]	PUNCT
ejpam-5722	22	101	,	,	PUNCT
ejpam-5722	22	102	[	[	X
ejpam-5722	22	103	31	31	NUM
ejpam-5722	22	104	]	]	PUNCT
ejpam-5722	22	105	,	,	PUNCT
ejpam-5722	22	106	[	[	X
ejpam-5722	22	107	37	37	NUM
ejpam-5722	22	108	]	]	PUNCT
ejpam-5722	22	109	and	and	CCONJ
ejpam-5722	22	110	[	[	X
ejpam-5722	22	111	41	41	NUM
ejpam-5722	22	112	]	]	PUNCT
ejpam-5722	22	113	,	,	PUNCT
ejpam-5722	22	114	respectively	respectively	ADV
ejpam-5722	22	115	.	.	PUNCT
ejpam-5722	23	1	marcus	marcus	PROPN
ejpam-5722	24	1	[	[	X
ejpam-5722	24	2	24	24	NUM
ejpam-5722	24	3	]	]	PUNCT
ejpam-5722	24	4	introduced	introduce	VERB
ejpam-5722	24	5	and	and	CCONJ
ejpam-5722	24	6	investigated	investigate	VERB
ejpam-5722	24	7	the	the	DET
ejpam-5722	24	8	notion	notion	NOUN
ejpam-5722	24	9	of	of	ADP
ejpam-5722	24	10	quasi	quasi	ADJ
ejpam-5722	24	11	continuous	continuous	ADJ
ejpam-5722	24	12	functions	function	NOUN
ejpam-5722	24	13	.	.	PUNCT
ejpam-5722	25	1	popa	popa	NOUN
ejpam-5722	25	2	[	[	X
ejpam-5722	25	3	29	29	NUM
ejpam-5722	25	4	]	]	PUNCT
ejpam-5722	25	5	introduced	introduce	VERB
ejpam-5722	25	6	and	and	CCONJ
ejpam-5722	25	7	studied	study	VERB
ejpam-5722	25	8	the	the	DET
ejpam-5722	25	9	notion	notion	NOUN
ejpam-5722	25	10	of	of	ADP
ejpam-5722	25	11	almost	almost	ADV
ejpam-5722	25	12	quasi	quasi	ADJ
ejpam-5722	25	13	continuous	continuous	ADJ
ejpam-5722	25	14	functions	function	NOUN
ejpam-5722	25	15	.	.	PUNCT
ejpam-5722	26	1	neubrunnovaá	neubrunnovaá	PUNCT
ejpam-5722	27	1	[	[	X
ejpam-5722	27	2	26	26	NUM
ejpam-5722	27	3	]	]	PUNCT
ejpam-5722	27	4	showed	show	VERB
ejpam-5722	27	5	that	that	SCONJ
ejpam-5722	27	6	quasi	quasi	NOUN
ejpam-5722	27	7	continuity	continuity	NOUN
ejpam-5722	27	8	is	be	AUX
ejpam-5722	27	9	equivalent	equivalent	ADJ
ejpam-5722	27	10	to	to	ADP
ejpam-5722	27	11	semi	semi	ADJ
ejpam-5722	27	12	-	-	NOUN
ejpam-5722	27	13	continuity	continuity	NOUN
ejpam-5722	27	14	due	due	ADP
ejpam-5722	27	15	to	to	ADP
ejpam-5722	27	16	levine	levine	PROPN
ejpam-5722	27	17	[	[	X
ejpam-5722	27	18	23	23	NUM
ejpam-5722	27	19	]	]	PUNCT
ejpam-5722	27	20	.	.	PUNCT
ejpam-5722	28	1	popa	popa	NOUN
ejpam-5722	28	2	and	and	CCONJ
ejpam-5722	28	3	stan	stan	PROPN
ejpam-5722	29	1	[	[	X
ejpam-5722	29	2	30	30	NUM
ejpam-5722	29	3	]	]	PUNCT
ejpam-5722	29	4	introduced	introduce	VERB
ejpam-5722	29	5	and	and	CCONJ
ejpam-5722	29	6	investigated	investigate	VERB
ejpam-5722	29	7	the	the	DET
ejpam-5722	29	8	notion	notion	NOUN
ejpam-5722	29	9	of	of	ADP
ejpam-5722	29	10	weakly	weakly	ADJ
ejpam-5722	29	11	quasi	quasi	ADJ
ejpam-5722	29	12	continuous	continuous	ADJ
ejpam-5722	29	13	functions	function	NOUN
ejpam-5722	29	14	.	.	PUNCT
ejpam-5722	30	1	weak	weak	ADJ
ejpam-5722	30	2	quasi	quasi	NOUN
ejpam-5722	30	3	continuity	continuity	NOUN
ejpam-5722	30	4	is	be	AUX
ejpam-5722	30	5	implied	imply	VERB
ejpam-5722	30	6	by	by	ADP
ejpam-5722	30	7	quasi	quasi	NOUN
ejpam-5722	30	8	continuity	continuity	NOUN
ejpam-5722	30	9	and	and	CCONJ
ejpam-5722	30	10	weak	weak	ADJ
ejpam-5722	30	11	continuity	continuity	NOUN
ejpam-5722	30	12	[	[	X
ejpam-5722	30	13	22	22	NUM
ejpam-5722	30	14	]	]	PUNCT
ejpam-5722	30	15	which	which	PRON
ejpam-5722	30	16	are	be	AUX
ejpam-5722	30	17	independent	independent	ADJ
ejpam-5722	30	18	of	of	ADP
ejpam-5722	30	19	each	each	DET
ejpam-5722	30	20	other	other	ADJ
ejpam-5722	30	21	.	.	PUNCT
ejpam-5722	31	1	kong	kong	PROPN
ejpam-5722	31	2	-	-	PUNCT
ejpam-5722	31	3	ied	ied	PROPN
ejpam-5722	31	4	et	et	PROPN
ejpam-5722	31	5	al	al	PROPN
ejpam-5722	31	6	.	.	PUNCT
ejpam-5722	32	1	[	[	X
ejpam-5722	32	2	21	21	NUM
ejpam-5722	32	3	]	]	PUNCT
ejpam-5722	32	4	introduced	introduce	VERB
ejpam-5722	32	5	and	and	CCONJ
ejpam-5722	32	6	investigated	investigate	VERB
ejpam-5722	32	7	the	the	DET
ejpam-5722	32	8	concept	concept	NOUN
ejpam-5722	32	9	of	of	ADP
ejpam-5722	32	10	almost	almost	ADV
ejpam-5722	32	11	quasi	quasi	X
ejpam-5722	32	12	(	(	PUNCT
ejpam-5722	32	13	τ1	τ1	NOUN
ejpam-5722	32	14	,	,	PUNCT
ejpam-5722	32	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	32	16	functions	function	NOUN
ejpam-5722	32	17	.	.	PUNCT
ejpam-5722	33	1	chiangpradit	chiangpradit	NOUN
ejpam-5722	33	2	et	et	PROPN
ejpam-5722	33	3	al	al	PROPN
ejpam-5722	33	4	.	.	PUNCT
ejpam-5722	34	1	[	[	X
ejpam-5722	34	2	16	16	NUM
ejpam-5722	34	3	]	]	PUNCT
ejpam-5722	34	4	introduced	introduce	VERB
ejpam-5722	34	5	and	and	CCONJ
ejpam-5722	34	6	studied	study	VERB
ejpam-5722	34	7	the	the	DET
ejpam-5722	34	8	notion	notion	NOUN
ejpam-5722	34	9	of	of	ADP
ejpam-5722	34	10	weakly	weakly	ADJ
ejpam-5722	34	11	quasi	quasi	NOUN
ejpam-5722	34	12	(	(	PUNCT
ejpam-5722	34	13	τ1	τ1	PROPN
ejpam-5722	34	14	,	,	PUNCT
ejpam-5722	34	15	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	34	16	functions	function	NOUN
ejpam-5722	34	17	.	.	PUNCT
ejpam-5722	35	1	in	in	ADP
ejpam-5722	35	2	this	this	DET
ejpam-5722	35	3	paper	paper	NOUN
ejpam-5722	35	4	,	,	PUNCT
ejpam-5722	35	5	we	we	PRON
ejpam-5722	35	6	introduce	introduce	VERB
ejpam-5722	35	7	the	the	DET
ejpam-5722	35	8	notion	notion	NOUN
ejpam-5722	35	9	of	of	ADP
ejpam-5722	35	10	quasi	quasi	NOUN
ejpam-5722	35	11	θ(τ1	θ(τ1	NOUN
ejpam-5722	35	12	,	,	PUNCT
ejpam-5722	35	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	35	14	functions	function	NOUN
ejpam-5722	35	15	.	.	PUNCT
ejpam-5722	36	1	we	we	PRON
ejpam-5722	36	2	also	also	ADV
ejpam-5722	36	3	investigate	investigate	VERB
ejpam-5722	36	4	several	several	ADJ
ejpam-5722	36	5	characterizations	characterization	NOUN
ejpam-5722	36	6	of	of	ADP
ejpam-5722	36	7	quasi	quasi	NOUN
ejpam-5722	36	8	θ(τ1	θ(τ1	NOUN
ejpam-5722	36	9	,	,	PUNCT
ejpam-5722	36	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	36	11	functions	function	NOUN
ejpam-5722	36	12	.	.	PUNCT
ejpam-5722	37	1	2	2	X
ejpam-5722	37	2	.	.	NUM
ejpam-5722	37	3	preliminaries	preliminary	NOUN
ejpam-5722	37	4	throughout	throughout	ADP
ejpam-5722	37	5	the	the	DET
ejpam-5722	37	6	present	present	ADJ
ejpam-5722	37	7	paper	paper	NOUN
ejpam-5722	37	8	,	,	PUNCT
ejpam-5722	37	9	spaces	space	NOUN
ejpam-5722	37	10	(	(	PUNCT
ejpam-5722	37	11	x	x	NOUN
ejpam-5722	37	12	,	,	PUNCT
ejpam-5722	37	13	τ1	τ1	NOUN
ejpam-5722	37	14	,	,	PUNCT
ejpam-5722	37	15	τ2	τ2	NOUN
ejpam-5722	37	16	)	)	PUNCT
ejpam-5722	37	17	and	and	CCONJ
ejpam-5722	37	18	(	(	PUNCT
ejpam-5722	37	19	y	y	PROPN
ejpam-5722	37	20	,	,	PUNCT
ejpam-5722	37	21	σ1	σ1	PROPN
ejpam-5722	37	22	,	,	PUNCT
ejpam-5722	37	23	σ2	σ2	NOUN
ejpam-5722	37	24	)	)	PUNCT
ejpam-5722	37	25	(	(	PUNCT
ejpam-5722	37	26	or	or	CCONJ
ejpam-5722	37	27	simply	simply	ADV
ejpam-5722	37	28	x	x	X
ejpam-5722	37	29	and	and	CCONJ
ejpam-5722	37	30	y	y	PROPN
ejpam-5722	37	31	)	)	PUNCT
ejpam-5722	37	32	always	always	ADV
ejpam-5722	37	33	mean	mean	VERB
ejpam-5722	37	34	bitopological	bitopological	ADJ
ejpam-5722	37	35	spaces	space	NOUN
ejpam-5722	37	36	on	on	ADP
ejpam-5722	37	37	which	which	PRON
ejpam-5722	37	38	no	no	DET
ejpam-5722	37	39	separation	separation	NOUN
ejpam-5722	37	40	axioms	axiom	NOUN
ejpam-5722	37	41	are	be	AUX
ejpam-5722	37	42	assumed	assume	VERB
ejpam-5722	37	43	unless	unless	SCONJ
ejpam-5722	37	44	explicitly	explicitly	ADV
ejpam-5722	37	45	stated	state	VERB
ejpam-5722	37	46	.	.	PUNCT
ejpam-5722	38	1	let	let	VERB
ejpam-5722	38	2	a	a	DET
ejpam-5722	38	3	be	be	AUX
ejpam-5722	38	4	a	a	DET
ejpam-5722	38	5	subset	subset	NOUN
ejpam-5722	38	6	of	of	ADP
ejpam-5722	38	7	a	a	DET
ejpam-5722	38	8	bitopological	bitopological	ADJ
ejpam-5722	38	9	space	space	NOUN
ejpam-5722	38	10	(	(	PUNCT
ejpam-5722	38	11	x	x	NOUN
ejpam-5722	38	12	,	,	PUNCT
ejpam-5722	38	13	τ1	τ1	NOUN
ejpam-5722	38	14	,	,	PUNCT
ejpam-5722	38	15	τ2	τ2	NOUN
ejpam-5722	38	16	)	)	PUNCT
ejpam-5722	38	17	.	.	PUNCT
ejpam-5722	39	1	the	the	DET
ejpam-5722	39	2	closure	closure	NOUN
ejpam-5722	39	3	of	of	ADP
ejpam-5722	39	4	a	a	PRON
ejpam-5722	39	5	and	and	CCONJ
ejpam-5722	39	6	the	the	DET
ejpam-5722	39	7	interior	interior	NOUN
ejpam-5722	39	8	of	of	ADP
ejpam-5722	39	9	a	a	PRON
ejpam-5722	39	10	with	with	ADP
ejpam-5722	39	11	respect	respect	NOUN
ejpam-5722	39	12	to	to	ADP
ejpam-5722	39	13	τi	τi	PROPN
ejpam-5722	39	14	are	be	AUX
ejpam-5722	39	15	denoted	denote	VERB
ejpam-5722	39	16	by	by	ADP
ejpam-5722	39	17	τi	τi	NOUN
ejpam-5722	39	18	-	-	PUNCT
ejpam-5722	39	19	cl(a	cl(a	NUM
ejpam-5722	39	20	)	)	PUNCT
ejpam-5722	39	21	and	and	CCONJ
ejpam-5722	39	22	τi	τi	NOUN
ejpam-5722	39	23	-	-	PUNCT
ejpam-5722	39	24	int(a	int(a	NOUN
ejpam-5722	39	25	)	)	PUNCT
ejpam-5722	39	26	,	,	PUNCT
ejpam-5722	39	27	respectively	respectively	ADV
ejpam-5722	39	28	,	,	PUNCT
ejpam-5722	39	29	for	for	ADP
ejpam-5722	39	30	i	i	PROPN
ejpam-5722	39	31	=	=	SYM
ejpam-5722	39	32	1	1	NUM
ejpam-5722	39	33	,	,	PUNCT
ejpam-5722	39	34	2	2	NUM
ejpam-5722	39	35	.	.	X
ejpam-5722	39	36	a	a	DET
ejpam-5722	39	37	subset	subset	NOUN
ejpam-5722	39	38	a	a	PRON
ejpam-5722	39	39	of	of	ADP
ejpam-5722	39	40	a	a	DET
ejpam-5722	39	41	bitopological	bitopological	ADJ
ejpam-5722	39	42	space	space	NOUN
ejpam-5722	39	43	(	(	PUNCT
ejpam-5722	39	44	x	x	NOUN
ejpam-5722	39	45	,	,	PUNCT
ejpam-5722	39	46	τ1	τ1	NOUN
ejpam-5722	39	47	,	,	PUNCT
ejpam-5722	39	48	τ2	τ2	NOUN
ejpam-5722	39	49	)	)	PUNCT
ejpam-5722	39	50	is	be	AUX
ejpam-5722	39	51	called	call	VERB
ejpam-5722	39	52	τ1τ2	τ1τ2	VERB
ejpam-5722	39	53	-	-	ADJ
ejpam-5722	39	54	closed	closed	ADJ
ejpam-5722	39	55	[	[	X
ejpam-5722	39	56	15	15	NUM
ejpam-5722	39	57	]	]	X
ejpam-5722	39	58	if	if	SCONJ
ejpam-5722	39	59	a	a	DET
ejpam-5722	39	60	=	=	NOUN
ejpam-5722	39	61	τ1	τ1	NOUN
ejpam-5722	39	62	-	-	PUNCT
ejpam-5722	39	63	cl(τ2	cl(τ2	NOUN
ejpam-5722	39	64	-	-	PUNCT
ejpam-5722	39	65	cl(a	cl(a	NUM
ejpam-5722	39	66	)	)	PUNCT
ejpam-5722	39	67	)	)	PUNCT
ejpam-5722	39	68	.	.	PUNCT
ejpam-5722	40	1	the	the	DET
ejpam-5722	40	2	complement	complement	NOUN
ejpam-5722	40	3	of	of	ADP
ejpam-5722	40	4	a	a	DET
ejpam-5722	40	5	τ1τ2	τ1τ2	ADJ
ejpam-5722	40	6	-	-	ADJ
ejpam-5722	40	7	closed	closed	ADJ
ejpam-5722	40	8	set	set	NOUN
ejpam-5722	40	9	is	be	AUX
ejpam-5722	40	10	called	call	VERB
ejpam-5722	40	11	τ1τ2	τ1τ2	NOUN
ejpam-5722	40	12	-	-	ADJ
ejpam-5722	40	13	open	open	ADJ
ejpam-5722	40	14	.	.	PUNCT
ejpam-5722	41	1	let	let	VERB
ejpam-5722	41	2	a	a	DET
ejpam-5722	41	3	be	be	AUX
ejpam-5722	41	4	a	a	DET
ejpam-5722	41	5	subset	subset	NOUN
ejpam-5722	41	6	of	of	ADP
ejpam-5722	41	7	a	a	DET
ejpam-5722	41	8	bitopological	bitopological	ADJ
ejpam-5722	41	9	space	space	NOUN
ejpam-5722	41	10	(	(	PUNCT
ejpam-5722	41	11	x	x	NOUN
ejpam-5722	41	12	,	,	PUNCT
ejpam-5722	41	13	τ1	τ1	NOUN
ejpam-5722	41	14	,	,	PUNCT
ejpam-5722	41	15	τ2	τ2	NOUN
ejpam-5722	41	16	)	)	PUNCT
ejpam-5722	41	17	.	.	PUNCT
ejpam-5722	42	1	the	the	DET
ejpam-5722	42	2	intersection	intersection	NOUN
ejpam-5722	42	3	of	of	ADP
ejpam-5722	42	4	all	all	DET
ejpam-5722	42	5	τ1τ2	τ1τ2	ADJ
ejpam-5722	42	6	-	-	ADJ
ejpam-5722	42	7	closed	closed	ADJ
ejpam-5722	42	8	sets	set	NOUN
ejpam-5722	42	9	of	of	ADP
ejpam-5722	42	10	x	x	PUNCT
ejpam-5722	42	11	containing	contain	VERB
ejpam-5722	42	12	a	a	PRON
ejpam-5722	42	13	is	be	AUX
ejpam-5722	42	14	called	call	VERB
ejpam-5722	42	15	the	the	DET
ejpam-5722	42	16	τ1τ2	τ1τ2	NOUN
ejpam-5722	42	17	-	-	NOUN
ejpam-5722	42	18	closure	closure	NOUN
ejpam-5722	42	19	[	[	X
ejpam-5722	42	20	15	15	NUM
ejpam-5722	42	21	]	]	PUNCT
ejpam-5722	42	22	of	of	ADP
ejpam-5722	42	23	a	a	PRON
ejpam-5722	42	24	and	and	CCONJ
ejpam-5722	42	25	is	be	AUX
ejpam-5722	42	26	denoted	denote	VERB
ejpam-5722	42	27	by	by	ADP
ejpam-5722	42	28	τ1τ2	τ1τ2	NOUN
ejpam-5722	42	29	-	-	NUM
ejpam-5722	42	30	cl(a	cl(a	NUM
ejpam-5722	42	31	)	)	PUNCT
ejpam-5722	42	32	.	.	PUNCT
ejpam-5722	43	1	the	the	DET
ejpam-5722	43	2	union	union	NOUN
ejpam-5722	43	3	of	of	ADP
ejpam-5722	43	4	all	all	DET
ejpam-5722	43	5	τ1τ2	τ1τ2	ADJ
ejpam-5722	43	6	-	-	ADJ
ejpam-5722	43	7	open	open	ADJ
ejpam-5722	43	8	sets	set	NOUN
ejpam-5722	43	9	of	of	ADP
ejpam-5722	43	10	x	x	PUNCT
ejpam-5722	43	11	contained	contain	VERB
ejpam-5722	43	12	in	in	ADP
ejpam-5722	43	13	a	a	PRON
ejpam-5722	43	14	is	be	AUX
ejpam-5722	43	15	called	call	VERB
ejpam-5722	43	16	the	the	DET
ejpam-5722	43	17	τ1τ2	τ1τ2	NOUN
ejpam-5722	43	18	-	-	ADJ
ejpam-5722	43	19	interior	interior	ADJ
ejpam-5722	43	20	[	[	X
ejpam-5722	43	21	15	15	NUM
ejpam-5722	43	22	]	]	PUNCT
ejpam-5722	43	23	of	of	ADP
ejpam-5722	43	24	a	a	PRON
ejpam-5722	43	25	and	and	CCONJ
ejpam-5722	43	26	is	be	AUX
ejpam-5722	43	27	denoted	denote	VERB
ejpam-5722	43	28	by	by	ADP
ejpam-5722	43	29	τ1τ2	τ1τ2	NOUN
ejpam-5722	43	30	-	-	ADJ
ejpam-5722	43	31	int(a	int(a	NOUN
ejpam-5722	43	32	)	)	PUNCT
ejpam-5722	43	33	.	.	PUNCT
ejpam-5722	44	1	lemma	lemma	PROPN
ejpam-5722	44	2	1	1	NUM
ejpam-5722	44	3	.	.	PUNCT
ejpam-5722	45	1	[	[	X
ejpam-5722	45	2	15	15	NUM
ejpam-5722	45	3	]	]	PUNCT
ejpam-5722	45	4	let	let	VERB
ejpam-5722	45	5	a	a	PRON
ejpam-5722	45	6	and	and	CCONJ
ejpam-5722	45	7	b	b	NOUN
ejpam-5722	45	8	be	be	AUX
ejpam-5722	45	9	subsets	subset	NOUN
ejpam-5722	45	10	of	of	ADP
ejpam-5722	45	11	a	a	DET
ejpam-5722	45	12	bitopological	bitopological	ADJ
ejpam-5722	45	13	space	space	NOUN
ejpam-5722	45	14	(	(	PUNCT
ejpam-5722	45	15	x	x	NOUN
ejpam-5722	45	16	,	,	PUNCT
ejpam-5722	45	17	τ1	τ1	NOUN
ejpam-5722	45	18	,	,	PUNCT
ejpam-5722	45	19	τ2	τ2	NOUN
ejpam-5722	45	20	)	)	PUNCT
ejpam-5722	45	21	.	.	PUNCT
ejpam-5722	46	1	for	for	ADP
ejpam-5722	46	2	the	the	DET
ejpam-5722	46	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5722	46	4	,	,	PUNCT
ejpam-5722	46	5	the	the	DET
ejpam-5722	46	6	following	follow	VERB
ejpam-5722	46	7	properties	property	NOUN
ejpam-5722	46	8	hold	hold	VERB
ejpam-5722	46	9	:	:	PUNCT
ejpam-5722	46	10	(	(	PUNCT
ejpam-5722	46	11	1	1	X
ejpam-5722	46	12	)	)	PUNCT
ejpam-5722	46	13	a	a	DET
ejpam-5722	46	14	⊆	⊆	NUM
ejpam-5722	46	15	τ1τ2	τ1τ2	NOUN
ejpam-5722	46	16	-	-	NUM
ejpam-5722	46	17	cl(a	cl(a	NUM
ejpam-5722	46	18	)	)	PUNCT
ejpam-5722	46	19	and	and	CCONJ
ejpam-5722	46	20	τ1τ2	τ1τ2	NOUN
ejpam-5722	46	21	-	-	ADJ
ejpam-5722	46	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5722	46	23	-	-	PUNCT
ejpam-5722	46	24	cl(a	cl(a	NUM
ejpam-5722	46	25	)	)	PUNCT
ejpam-5722	46	26	)	)	PUNCT
ejpam-5722	47	1	=	=	PUNCT
ejpam-5722	47	2	τ1τ2	τ1τ2	NOUN
ejpam-5722	47	3	-	-	NUM
ejpam-5722	47	4	cl(a	cl(a	NUM
ejpam-5722	47	5	)	)	PUNCT
ejpam-5722	47	6	.	.	PUNCT
ejpam-5722	48	1	(	(	PUNCT
ejpam-5722	48	2	2	2	X
ejpam-5722	48	3	)	)	PUNCT
ejpam-5722	48	4	if	if	SCONJ
ejpam-5722	48	5	a	a	DET
ejpam-5722	48	6	⊆	⊆	NUM
ejpam-5722	48	7	b	b	NOUN
ejpam-5722	48	8	,	,	PUNCT
ejpam-5722	48	9	then	then	ADV
ejpam-5722	48	10	τ1τ2	τ1τ2	NOUN
ejpam-5722	48	11	-	-	NUM
ejpam-5722	48	12	cl(a	cl(a	NUM
ejpam-5722	48	13	)	)	PUNCT
ejpam-5722	48	14	⊆	⊆	NUM
ejpam-5722	48	15	τ1τ2	τ1τ2	NOUN
ejpam-5722	48	16	-	-	NOUN
ejpam-5722	48	17	cl(b	cl(b	NOUN
ejpam-5722	48	18	)	)	PUNCT
ejpam-5722	48	19	.	.	PUNCT
ejpam-5722	49	1	(	(	PUNCT
ejpam-5722	49	2	3	3	X
ejpam-5722	49	3	)	)	PUNCT
ejpam-5722	49	4	τ1τ2	τ1τ2	NOUN
ejpam-5722	49	5	-	-	NUM
ejpam-5722	49	6	cl(a	cl(a	NUM
ejpam-5722	49	7	)	)	PUNCT
ejpam-5722	49	8	is	be	AUX
ejpam-5722	49	9	τ1τ2	τ1τ2	NOUN
ejpam-5722	49	10	-	-	ADJ
ejpam-5722	49	11	closed	closed	ADJ
ejpam-5722	49	12	.	.	PUNCT
ejpam-5722	50	1	(	(	PUNCT
ejpam-5722	50	2	4	4	X
ejpam-5722	50	3	)	)	PUNCT
ejpam-5722	50	4	a	a	PRON
ejpam-5722	50	5	is	be	AUX
ejpam-5722	50	6	τ1τ2	τ1τ2	NOUN
ejpam-5722	50	7	-	-	ADJ
ejpam-5722	50	8	closed	closed	ADJ
ejpam-5722	50	9	if	if	SCONJ
ejpam-5722	50	10	and	and	CCONJ
ejpam-5722	50	11	only	only	ADV
ejpam-5722	50	12	if	if	SCONJ
ejpam-5722	50	13	a	a	DET
ejpam-5722	50	14	=	=	PUNCT
ejpam-5722	50	15	τ1τ2	τ1τ2	NOUN
ejpam-5722	50	16	-	-	NUM
ejpam-5722	50	17	cl(a	cl(a	NUM
ejpam-5722	50	18	)	)	PUNCT
ejpam-5722	50	19	.	.	PUNCT
ejpam-5722	51	1	(	(	PUNCT
ejpam-5722	51	2	5	5	X
ejpam-5722	51	3	)	)	PUNCT
ejpam-5722	51	4	τ1τ2	τ1τ2	NOUN
ejpam-5722	51	5	-	-	NOUN
ejpam-5722	51	6	cl(x	cl(x	X
ejpam-5722	51	7	−a	−a	NOUN
ejpam-5722	51	8	)	)	PUNCT
ejpam-5722	52	1	=	=	PUNCT
ejpam-5722	52	2	x	x	X
ejpam-5722	53	1	−	−	ADP
ejpam-5722	53	2	τ1τ2	τ1τ2	NOUN
ejpam-5722	53	3	-	-	PUNCT
ejpam-5722	53	4	int(a	int(a	NOUN
ejpam-5722	53	5	)	)	PUNCT
ejpam-5722	53	6	.	.	PUNCT
ejpam-5722	54	1	a	a	DET
ejpam-5722	54	2	subset	subset	NOUN
ejpam-5722	54	3	a	a	PRON
ejpam-5722	54	4	of	of	ADP
ejpam-5722	54	5	a	a	DET
ejpam-5722	54	6	bitopological	bitopological	ADJ
ejpam-5722	54	7	space	space	NOUN
ejpam-5722	54	8	(	(	PUNCT
ejpam-5722	54	9	x	x	NOUN
ejpam-5722	54	10	,	,	PUNCT
ejpam-5722	54	11	τ1	τ1	NOUN
ejpam-5722	54	12	,	,	PUNCT
ejpam-5722	54	13	τ2	τ2	NOUN
ejpam-5722	54	14	)	)	PUNCT
ejpam-5722	54	15	is	be	AUX
ejpam-5722	54	16	said	say	VERB
ejpam-5722	54	17	to	to	PART
ejpam-5722	54	18	be	be	AUX
ejpam-5722	54	19	τ1τ2	τ1τ2	NOUN
ejpam-5722	54	20	-	-	ADJ
ejpam-5722	54	21	clopen	clopen	ADJ
ejpam-5722	55	1	[	[	X
ejpam-5722	55	2	15	15	NUM
ejpam-5722	55	3	]	]	X
ejpam-5722	55	4	if	if	SCONJ
ejpam-5722	55	5	a	a	PRON
ejpam-5722	55	6	is	be	AUX
ejpam-5722	55	7	both	both	PRON
ejpam-5722	55	8	τ1τ2	τ1τ2	ADJ
ejpam-5722	55	9	-	-	ADJ
ejpam-5722	55	10	open	open	ADJ
ejpam-5722	55	11	and	and	CCONJ
ejpam-5722	55	12	τ1τ2	τ1τ2	NOUN
ejpam-5722	55	13	-	-	ADJ
ejpam-5722	55	14	closed	closed	ADJ
ejpam-5722	55	15	.	.	PUNCT
ejpam-5722	56	1	a	a	DET
ejpam-5722	56	2	subset	subset	NOUN
ejpam-5722	56	3	a	a	PRON
ejpam-5722	56	4	of	of	ADP
ejpam-5722	56	5	a	a	DET
ejpam-5722	56	6	bitopological	bitopological	ADJ
ejpam-5722	56	7	space	space	NOUN
ejpam-5722	56	8	(	(	PUNCT
ejpam-5722	56	9	x	x	NOUN
ejpam-5722	56	10	,	,	PUNCT
ejpam-5722	56	11	τ1	τ1	NOUN
ejpam-5722	56	12	,	,	PUNCT
ejpam-5722	56	13	τ2	τ2	NOUN
ejpam-5722	56	14	)	)	PUNCT
ejpam-5722	56	15	is	be	AUX
ejpam-5722	56	16	said	say	VERB
ejpam-5722	56	17	to	to	PART
ejpam-5722	56	18	be	be	AUX
ejpam-5722	56	19	(	(	PUNCT
ejpam-5722	56	20	τ1	τ1	NOUN
ejpam-5722	56	21	,	,	PUNCT
ejpam-5722	56	22	τ2)r	τ2)r	NOUN
ejpam-5722	56	23	-	-	PUNCT
ejpam-5722	56	24	open	open	NOUN
ejpam-5722	57	1	[	[	X
ejpam-5722	57	2	43	43	NUM
ejpam-5722	57	3	]	]	PUNCT
ejpam-5722	57	4	(	(	PUNCT
ejpam-5722	57	5	resp	resp	NOUN
ejpam-5722	57	6	.	.	PUNCT
ejpam-5722	58	1	(	(	PUNCT
ejpam-5722	58	2	τ1	τ1	NOUN
ejpam-5722	58	3	,	,	PUNCT
ejpam-5722	58	4	τ2)s	τ2)s	NOUN
ejpam-5722	58	5	-	-	PUNCT
ejpam-5722	58	6	open	open	ADJ
ejpam-5722	58	7	[	[	X
ejpam-5722	58	8	5	5	NUM
ejpam-5722	58	9	]	]	PUNCT
ejpam-5722	58	10	,	,	PUNCT
ejpam-5722	58	11	(	(	PUNCT
ejpam-5722	58	12	τ1	τ1	NOUN
ejpam-5722	58	13	,	,	PUNCT
ejpam-5722	58	14	τ2)p	τ2)p	NOUN
ejpam-5722	58	15	-	-	ADJ
ejpam-5722	58	16	open	open	ADJ
ejpam-5722	58	17	[	[	X
ejpam-5722	58	18	5	5	NUM
ejpam-5722	58	19	]	]	PUNCT
ejpam-5722	58	20	,	,	PUNCT
ejpam-5722	58	21	(	(	PUNCT
ejpam-5722	58	22	τ1	τ1	NOUN
ejpam-5722	58	23	,	,	PUNCT
ejpam-5722	58	24	τ2)β	τ2)β	ADJ
ejpam-5722	58	25	-	-	PUNCT
ejpam-5722	58	26	open	open	ADJ
ejpam-5722	58	27	[	[	X
ejpam-5722	58	28	5	5	NUM
ejpam-5722	58	29	]	]	PUNCT
ejpam-5722	58	30	)	)	PUNCT
ejpam-5722	58	31	if	if	SCONJ
ejpam-5722	58	32	a	a	DET
ejpam-5722	58	33	=	=	PUNCT
ejpam-5722	58	34	τ1τ2	τ1τ2	NOUN
ejpam-5722	58	35	-	-	NOUN
ejpam-5722	58	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5722	58	37	-	-	PUNCT
ejpam-5722	58	38	cl(a	cl(a	NUM
ejpam-5722	58	39	)	)	PUNCT
ejpam-5722	58	40	)	)	PUNCT
ejpam-5722	58	41	(	(	PUNCT
ejpam-5722	58	42	resp	resp	NOUN
ejpam-5722	58	43	.	.	PUNCT
ejpam-5722	59	1	a	a	DET
ejpam-5722	59	2	⊆	⊆	NUM
ejpam-5722	59	3	τ1τ2	τ1τ2	NOUN
ejpam-5722	59	4	-	-	ADJ
ejpam-5722	59	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5722	59	6	-	-	PUNCT
ejpam-5722	59	7	int(a	int(a	NOUN
ejpam-5722	59	8	)	)	PUNCT
ejpam-5722	59	9	)	)	PUNCT
ejpam-5722	59	10	,	,	PUNCT
ejpam-5722	59	11	a	a	DET
ejpam-5722	59	12	⊆	⊆	NUM
ejpam-5722	59	13	τ1τ2	τ1τ2	NOUN
ejpam-5722	59	14	-	-	NOUN
ejpam-5722	59	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5722	59	16	-	-	PUNCT
ejpam-5722	59	17	cl(a	cl(a	NUM
ejpam-5722	59	18	)	)	PUNCT
ejpam-5722	59	19	)	)	PUNCT
ejpam-5722	59	20	,	,	PUNCT
ejpam-5722	59	21	a	a	DET
ejpam-5722	59	22	⊆	⊆	NUM
ejpam-5722	59	23	τ1τ2	τ1τ2	NOUN
ejpam-5722	59	24	-	-	PUNCT
ejpam-5722	59	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5722	59	26	-	-	PUNCT
ejpam-5722	59	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5722	59	28	-	-	PUNCT
ejpam-5722	59	29	cl(a	cl(a	NUM
ejpam-5722	59	30	)	)	PUNCT
ejpam-5722	59	31	)	)	PUNCT
ejpam-5722	59	32	)	)	PUNCT
ejpam-5722	59	33	)	)	PUNCT
ejpam-5722	59	34	.	.	PUNCT
ejpam-5722	60	1	the	the	DET
ejpam-5722	60	2	complement	complement	NOUN
ejpam-5722	60	3	of	of	ADP
ejpam-5722	60	4	a	a	DET
ejpam-5722	60	5	(	(	PUNCT
ejpam-5722	60	6	τ1	τ1	NOUN
ejpam-5722	60	7	,	,	PUNCT
ejpam-5722	60	8	τ2)r	τ2)r	NOUN
ejpam-5722	60	9	-	-	PUNCT
ejpam-5722	60	10	open	open	ADJ
ejpam-5722	60	11	(	(	PUNCT
ejpam-5722	60	12	resp	resp	NOUN
ejpam-5722	60	13	.	.	PUNCT
ejpam-5722	61	1	(	(	PUNCT
ejpam-5722	61	2	τ1	τ1	NOUN
ejpam-5722	61	3	,	,	PUNCT
ejpam-5722	61	4	τ2)sopen	τ2)sopen	ADJ
ejpam-5722	61	5	,	,	PUNCT
ejpam-5722	61	6	(	(	PUNCT
ejpam-5722	61	7	τ1	τ1	NOUN
ejpam-5722	61	8	,	,	PUNCT
ejpam-5722	61	9	τ2)p	τ2)p	NOUN
ejpam-5722	61	10	-	-	ADJ
ejpam-5722	61	11	open	open	ADJ
ejpam-5722	61	12	,	,	PUNCT
ejpam-5722	61	13	(	(	PUNCT
ejpam-5722	61	14	τ1	τ1	NOUN
ejpam-5722	61	15	,	,	PUNCT
ejpam-5722	61	16	τ2)β	τ2)β	ADJ
ejpam-5722	61	17	-	-	PUNCT
ejpam-5722	61	18	open	open	ADJ
ejpam-5722	61	19	)	)	PUNCT
ejpam-5722	61	20	set	set	NOUN
ejpam-5722	61	21	is	be	AUX
ejpam-5722	61	22	called	call	VERB
ejpam-5722	61	23	(	(	PUNCT
ejpam-5722	61	24	τ1	τ1	NOUN
ejpam-5722	61	25	,	,	PUNCT
ejpam-5722	61	26	τ2)r	τ2)r	NOUN
ejpam-5722	61	27	-	-	PUNCT
ejpam-5722	61	28	closed	closed	ADJ
ejpam-5722	61	29	(	(	PUNCT
ejpam-5722	61	30	resp	resp	NOUN
ejpam-5722	61	31	.	.	PUNCT
ejpam-5722	62	1	(	(	PUNCT
ejpam-5722	62	2	τ1	τ1	NOUN
ejpam-5722	62	3	,	,	PUNCT
ejpam-5722	62	4	τ2)s	τ2)s	NOUN
ejpam-5722	62	5	-	-	PUNCT
ejpam-5722	62	6	closed	closed	ADJ
ejpam-5722	62	7	,	,	PUNCT
ejpam-5722	62	8	n.	n.	PROPN
ejpam-5722	62	9	srisarakham	srisarakham	PROPN
ejpam-5722	62	10	,	,	PUNCT
ejpam-5722	62	11	s.	s.	PROPN
ejpam-5722	62	12	sompong	sompong	PROPN
ejpam-5722	62	13	,	,	PUNCT
ejpam-5722	62	14	c.	c.	PROPN
ejpam-5722	62	15	boonpok	boonpok	PROPN
ejpam-5722	62	16	/	/	SYM
ejpam-5722	62	17	eur	eur	PROPN
ejpam-5722	62	18	.	.	PUNCT
ejpam-5722	63	1	j.	j.	PROPN
ejpam-5722	63	2	pure	pure	PROPN
ejpam-5722	63	3	appl	appl	PROPN
ejpam-5722	63	4	.	.	PROPN
ejpam-5722	63	5	math	math	PROPN
ejpam-5722	63	6	,	,	PUNCT
ejpam-5722	63	7	18	18	NUM
ejpam-5722	63	8	(	(	PUNCT
ejpam-5722	63	9	1	1	NUM
ejpam-5722	63	10	)	)	PUNCT
ejpam-5722	63	11	(	(	PUNCT
ejpam-5722	63	12	2025	2025	NUM
ejpam-5722	63	13	)	)	PUNCT
ejpam-5722	63	14	,	,	PUNCT
ejpam-5722	63	15	5722	5722	NUM
ejpam-5722	63	16	3	3	NUM
ejpam-5722	63	17	of	of	ADP
ejpam-5722	63	18	12	12	NUM
ejpam-5722	63	19	(	(	PUNCT
ejpam-5722	63	20	τ1	τ1	NOUN
ejpam-5722	63	21	,	,	PUNCT
ejpam-5722	63	22	τ2)p	τ2)p	NOUN
ejpam-5722	63	23	-	-	PUNCT
ejpam-5722	63	24	closed	closed	ADJ
ejpam-5722	63	25	,	,	PUNCT
ejpam-5722	63	26	(	(	PUNCT
ejpam-5722	63	27	τ1	τ1	NOUN
ejpam-5722	63	28	,	,	PUNCT
ejpam-5722	63	29	τ2)β	τ2)β	ADJ
ejpam-5722	63	30	-	-	PUNCT
ejpam-5722	63	31	closed	closed	ADJ
ejpam-5722	63	32	)	)	PUNCT
ejpam-5722	63	33	.	.	PUNCT
ejpam-5722	64	1	a	a	DET
ejpam-5722	64	2	subset	subset	NOUN
ejpam-5722	64	3	a	a	PRON
ejpam-5722	64	4	of	of	ADP
ejpam-5722	64	5	a	a	DET
ejpam-5722	64	6	bitopological	bitopological	ADJ
ejpam-5722	64	7	space	space	NOUN
ejpam-5722	64	8	(	(	PUNCT
ejpam-5722	64	9	x	x	NOUN
ejpam-5722	64	10	,	,	PUNCT
ejpam-5722	64	11	τ1	τ1	NOUN
ejpam-5722	64	12	,	,	PUNCT
ejpam-5722	64	13	τ2	τ2	NOUN
ejpam-5722	64	14	)	)	PUNCT
ejpam-5722	64	15	is	be	AUX
ejpam-5722	64	16	said	say	VERB
ejpam-5722	64	17	to	to	PART
ejpam-5722	64	18	be	be	AUX
ejpam-5722	64	19	α(τ1	α(τ1	NOUN
ejpam-5722	64	20	,	,	PUNCT
ejpam-5722	64	21	τ2)-open	τ2)-open	ADJ
ejpam-5722	65	1	[	[	X
ejpam-5722	65	2	45	45	NUM
ejpam-5722	65	3	]	]	PUNCT
ejpam-5722	65	4	if	if	SCONJ
ejpam-5722	65	5	a	a	DET
ejpam-5722	65	6	⊆	⊆	NUM
ejpam-5722	65	7	τ1τ2	τ1τ2	NOUN
ejpam-5722	65	8	-	-	PUNCT
ejpam-5722	65	9	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5722	65	10	-	-	PUNCT
ejpam-5722	65	11	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5722	65	12	-	-	PUNCT
ejpam-5722	65	13	int(a	int(a	NOUN
ejpam-5722	65	14	)	)	PUNCT
ejpam-5722	65	15	)	)	PUNCT
ejpam-5722	65	16	)	)	PUNCT
ejpam-5722	65	17	.	.	PUNCT
ejpam-5722	66	1	the	the	DET
ejpam-5722	66	2	complement	complement	NOUN
ejpam-5722	66	3	of	of	ADP
ejpam-5722	66	4	an	an	DET
ejpam-5722	66	5	α(τ1	α(τ1	NOUN
ejpam-5722	66	6	,	,	PUNCT
ejpam-5722	66	7	τ2)-open	τ2)-open	ADJ
ejpam-5722	66	8	set	set	NOUN
ejpam-5722	66	9	is	be	AUX
ejpam-5722	66	10	said	say	VERB
ejpam-5722	66	11	to	to	PART
ejpam-5722	66	12	be	be	AUX
ejpam-5722	66	13	α(τ1	α(τ1	NOUN
ejpam-5722	66	14	,	,	PUNCT
ejpam-5722	66	15	τ2)-closed	τ2)-close	VERB
ejpam-5722	66	16	.	.	PUNCT
ejpam-5722	67	1	let	let	VERB
ejpam-5722	67	2	a	a	DET
ejpam-5722	67	3	be	be	AUX
ejpam-5722	67	4	a	a	DET
ejpam-5722	67	5	subset	subset	NOUN
ejpam-5722	67	6	of	of	ADP
ejpam-5722	67	7	a	a	DET
ejpam-5722	67	8	bitopological	bitopological	ADJ
ejpam-5722	67	9	space	space	NOUN
ejpam-5722	67	10	(	(	PUNCT
ejpam-5722	67	11	x	x	NOUN
ejpam-5722	67	12	,	,	PUNCT
ejpam-5722	67	13	τ1	τ1	NOUN
ejpam-5722	67	14	,	,	PUNCT
ejpam-5722	67	15	τ2	τ2	NOUN
ejpam-5722	67	16	)	)	PUNCT
ejpam-5722	67	17	.	.	PUNCT
ejpam-5722	68	1	a	a	DET
ejpam-5722	68	2	point	point	NOUN
ejpam-5722	68	3	x	x	X
ejpam-5722	68	4	∈	∈	NOUN
ejpam-5722	68	5	x	x	PUNCT
ejpam-5722	68	6	is	be	AUX
ejpam-5722	68	7	called	call	VERB
ejpam-5722	68	8	a	a	DET
ejpam-5722	68	9	(	(	PUNCT
ejpam-5722	68	10	τ1	τ1	NOUN
ejpam-5722	68	11	,	,	PUNCT
ejpam-5722	68	12	τ2)θ	τ2)θ	ADJ
ejpam-5722	68	13	-	-	PUNCT
ejpam-5722	68	14	cluster	cluster	NOUN
ejpam-5722	68	15	point	point	NOUN
ejpam-5722	68	16	[	[	X
ejpam-5722	68	17	43	43	NUM
ejpam-5722	68	18	]	]	PUNCT
ejpam-5722	68	19	of	of	ADP
ejpam-5722	68	20	a	a	DET
ejpam-5722	68	21	if	if	SCONJ
ejpam-5722	68	22	τ1τ2	τ1τ2	ADJ
ejpam-5722	68	23	-	-	ADJ
ejpam-5722	68	24	cl(u)∩a	cl(u)∩a	ADJ
ejpam-5722	68	25	̸=	̸=	PROPN
ejpam-5722	68	26	∅	∅	NOUN
ejpam-5722	68	27	for	for	ADP
ejpam-5722	68	28	every	every	DET
ejpam-5722	68	29	τ1τ2	τ1τ2	ADJ
ejpam-5722	68	30	-	-	ADJ
ejpam-5722	68	31	open	open	ADJ
ejpam-5722	68	32	set	set	NOUN
ejpam-5722	68	33	u	u	NOUN
ejpam-5722	68	34	containing	contain	VERB
ejpam-5722	68	35	x.	x.	NOUN
ejpam-5722	68	36	the	the	DET
ejpam-5722	68	37	set	set	NOUN
ejpam-5722	68	38	of	of	ADP
ejpam-5722	68	39	all	all	DET
ejpam-5722	68	40	(	(	PUNCT
ejpam-5722	68	41	τ1	τ1	NOUN
ejpam-5722	68	42	,	,	PUNCT
ejpam-5722	68	43	τ2)θ	τ2)θ	ADJ
ejpam-5722	68	44	-	-	PUNCT
ejpam-5722	68	45	cluster	cluster	NOUN
ejpam-5722	68	46	points	point	NOUN
ejpam-5722	68	47	of	of	ADP
ejpam-5722	68	48	a	a	PRON
ejpam-5722	68	49	is	be	AUX
ejpam-5722	68	50	called	call	VERB
ejpam-5722	68	51	the	the	DET
ejpam-5722	68	52	(	(	PUNCT
ejpam-5722	68	53	τ1	τ1	NOUN
ejpam-5722	68	54	,	,	PUNCT
ejpam-5722	68	55	τ2)θ	τ2)θ	ADJ
ejpam-5722	68	56	-	-	PUNCT
ejpam-5722	68	57	closure	closure	NOUN
ejpam-5722	68	58	[	[	X
ejpam-5722	68	59	43	43	NUM
ejpam-5722	68	60	]	]	PUNCT
ejpam-5722	68	61	of	of	ADP
ejpam-5722	68	62	a	a	PRON
ejpam-5722	68	63	and	and	CCONJ
ejpam-5722	68	64	is	be	AUX
ejpam-5722	68	65	denoted	denote	VERB
ejpam-5722	68	66	by	by	ADP
ejpam-5722	68	67	(	(	PUNCT
ejpam-5722	68	68	τ1	τ1	NOUN
ejpam-5722	68	69	,	,	PUNCT
ejpam-5722	68	70	τ2)θ	τ2)θ	NOUN
ejpam-5722	68	71	-	-	PUNCT
ejpam-5722	68	72	cl(a	cl(a	NUM
ejpam-5722	68	73	)	)	PUNCT
ejpam-5722	68	74	.	.	PUNCT
ejpam-5722	69	1	a	a	DET
ejpam-5722	69	2	subset	subset	NOUN
ejpam-5722	69	3	a	a	PRON
ejpam-5722	69	4	of	of	ADP
ejpam-5722	69	5	a	a	DET
ejpam-5722	69	6	bitopological	bitopological	ADJ
ejpam-5722	69	7	space	space	NOUN
ejpam-5722	69	8	(	(	PUNCT
ejpam-5722	69	9	x	x	NOUN
ejpam-5722	69	10	,	,	PUNCT
ejpam-5722	69	11	τ1	τ1	NOUN
ejpam-5722	69	12	,	,	PUNCT
ejpam-5722	69	13	τ2	τ2	NOUN
ejpam-5722	69	14	)	)	PUNCT
ejpam-5722	69	15	is	be	AUX
ejpam-5722	69	16	said	say	VERB
ejpam-5722	69	17	to	to	PART
ejpam-5722	69	18	be	be	AUX
ejpam-5722	69	19	(	(	PUNCT
ejpam-5722	69	20	τ1	τ1	NOUN
ejpam-5722	69	21	,	,	PUNCT
ejpam-5722	69	22	τ2)θ	τ2)θ	NOUN
ejpam-5722	69	23	-	-	PUNCT
ejpam-5722	69	24	closed	closed	ADJ
ejpam-5722	70	1	[	[	X
ejpam-5722	70	2	43	43	NUM
ejpam-5722	70	3	]	]	X
ejpam-5722	70	4	if	if	SCONJ
ejpam-5722	70	5	(	(	PUNCT
ejpam-5722	70	6	τ1	τ1	NOUN
ejpam-5722	70	7	,	,	PUNCT
ejpam-5722	70	8	τ2)θ	τ2)θ	NOUN
ejpam-5722	70	9	-	-	PUNCT
ejpam-5722	70	10	cl(a	cl(a	NUM
ejpam-5722	70	11	)	)	PUNCT
ejpam-5722	70	12	=	=	PUNCT
ejpam-5722	70	13	a.	a.	NOUN
ejpam-5722	70	14	the	the	DET
ejpam-5722	70	15	complement	complement	NOUN
ejpam-5722	70	16	of	of	ADP
ejpam-5722	70	17	a	a	DET
ejpam-5722	70	18	(	(	PUNCT
ejpam-5722	70	19	τ1	τ1	NOUN
ejpam-5722	70	20	,	,	PUNCT
ejpam-5722	70	21	τ2)θ	τ2)θ	ADJ
ejpam-5722	70	22	-	-	PUNCT
ejpam-5722	70	23	closed	close	VERB
ejpam-5722	70	24	set	set	NOUN
ejpam-5722	70	25	is	be	AUX
ejpam-5722	70	26	said	say	VERB
ejpam-5722	70	27	to	to	PART
ejpam-5722	70	28	be	be	AUX
ejpam-5722	70	29	(	(	PUNCT
ejpam-5722	70	30	τ1	τ1	NOUN
ejpam-5722	70	31	,	,	PUNCT
ejpam-5722	70	32	τ2)θ	τ2)θ	NOUN
ejpam-5722	70	33	-	-	PUNCT
ejpam-5722	70	34	open	open	ADJ
ejpam-5722	70	35	.	.	PUNCT
ejpam-5722	71	1	the	the	DET
ejpam-5722	71	2	union	union	NOUN
ejpam-5722	71	3	of	of	ADP
ejpam-5722	71	4	all	all	DET
ejpam-5722	71	5	(	(	PUNCT
ejpam-5722	71	6	τ1	τ1	NOUN
ejpam-5722	71	7	,	,	PUNCT
ejpam-5722	71	8	τ2)θopen	τ2)θopen	PROPN
ejpam-5722	71	9	sets	set	NOUN
ejpam-5722	71	10	of	of	ADP
ejpam-5722	71	11	x	x	PUNCT
ejpam-5722	71	12	contained	contain	VERB
ejpam-5722	71	13	in	in	ADP
ejpam-5722	71	14	a	a	PRON
ejpam-5722	71	15	is	be	AUX
ejpam-5722	71	16	called	call	VERB
ejpam-5722	71	17	the	the	DET
ejpam-5722	71	18	(	(	PUNCT
ejpam-5722	71	19	τ1	τ1	NOUN
ejpam-5722	71	20	,	,	PUNCT
ejpam-5722	71	21	τ2)θ	τ2)θ	ADJ
ejpam-5722	71	22	-	-	PUNCT
ejpam-5722	71	23	interior	interior	NOUN
ejpam-5722	71	24	[	[	X
ejpam-5722	71	25	43	43	NUM
ejpam-5722	71	26	]	]	PUNCT
ejpam-5722	71	27	of	of	ADP
ejpam-5722	71	28	a	a	PRON
ejpam-5722	71	29	and	and	CCONJ
ejpam-5722	71	30	is	be	AUX
ejpam-5722	71	31	denoted	denote	VERB
ejpam-5722	71	32	by	by	ADP
ejpam-5722	71	33	(	(	PUNCT
ejpam-5722	71	34	τ1	τ1	NOUN
ejpam-5722	71	35	,	,	PUNCT
ejpam-5722	71	36	τ2)θ	τ2)θ	NOUN
ejpam-5722	71	37	-	-	PUNCT
ejpam-5722	71	38	int(a	int(a	NOUN
ejpam-5722	71	39	)	)	PUNCT
ejpam-5722	71	40	.	.	PUNCT
ejpam-5722	72	1	lemma	lemma	PROPN
ejpam-5722	72	2	2	2	NUM
ejpam-5722	72	3	.	.	PUNCT
ejpam-5722	73	1	[	[	X
ejpam-5722	73	2	43	43	NUM
ejpam-5722	73	3	]	]	PUNCT
ejpam-5722	73	4	for	for	ADP
ejpam-5722	73	5	a	a	DET
ejpam-5722	73	6	subset	subset	NOUN
ejpam-5722	73	7	a	a	PRON
ejpam-5722	73	8	of	of	ADP
ejpam-5722	73	9	a	a	DET
ejpam-5722	73	10	bitopological	bitopological	ADJ
ejpam-5722	73	11	space	space	NOUN
ejpam-5722	73	12	(	(	PUNCT
ejpam-5722	73	13	x	x	NOUN
ejpam-5722	73	14	,	,	PUNCT
ejpam-5722	73	15	τ1	τ1	NOUN
ejpam-5722	73	16	,	,	PUNCT
ejpam-5722	73	17	τ2	τ2	NOUN
ejpam-5722	73	18	)	)	PUNCT
ejpam-5722	73	19	,	,	PUNCT
ejpam-5722	73	20	the	the	DET
ejpam-5722	73	21	following	follow	VERB
ejpam-5722	73	22	properties	property	NOUN
ejpam-5722	73	23	hold	hold	VERB
ejpam-5722	73	24	:	:	PUNCT
ejpam-5722	73	25	(	(	PUNCT
ejpam-5722	73	26	1	1	X
ejpam-5722	73	27	)	)	PUNCT
ejpam-5722	73	28	if	if	SCONJ
ejpam-5722	73	29	a	a	PRON
ejpam-5722	73	30	is	be	AUX
ejpam-5722	73	31	τ1τ2	τ1τ2	NOUN
ejpam-5722	73	32	-	-	ADJ
ejpam-5722	73	33	open	open	ADJ
ejpam-5722	73	34	in	in	ADP
ejpam-5722	73	35	x	x	NOUN
ejpam-5722	73	36	,	,	PUNCT
ejpam-5722	73	37	then	then	ADV
ejpam-5722	73	38	τ1τ2	τ1τ2	NOUN
ejpam-5722	73	39	-	-	NUM
ejpam-5722	73	40	cl(a	cl(a	NUM
ejpam-5722	73	41	)	)	PUNCT
ejpam-5722	73	42	=	=	PUNCT
ejpam-5722	73	43	(	(	PUNCT
ejpam-5722	73	44	τ1	τ1	NOUN
ejpam-5722	73	45	,	,	PUNCT
ejpam-5722	73	46	τ2)θ	τ2)θ	NOUN
ejpam-5722	73	47	-	-	PUNCT
ejpam-5722	73	48	cl(a	cl(a	NUM
ejpam-5722	73	49	)	)	PUNCT
ejpam-5722	73	50	.	.	PUNCT
ejpam-5722	74	1	(	(	PUNCT
ejpam-5722	74	2	2	2	X
ejpam-5722	74	3	)	)	PUNCT
ejpam-5722	74	4	(	(	PUNCT
ejpam-5722	74	5	τ1	τ1	NOUN
ejpam-5722	74	6	,	,	PUNCT
ejpam-5722	74	7	τ2)θ	τ2)θ	NOUN
ejpam-5722	74	8	-	-	PUNCT
ejpam-5722	74	9	cl(a	cl(a	NUM
ejpam-5722	74	10	)	)	PUNCT
ejpam-5722	74	11	is	be	AUX
ejpam-5722	74	12	τ1τ2	τ1τ2	NOUN
ejpam-5722	74	13	-	-	ADJ
ejpam-5722	74	14	closed	closed	ADJ
ejpam-5722	74	15	in	in	ADP
ejpam-5722	74	16	x.	x.	NOUN
ejpam-5722	74	17	let	let	VERB
ejpam-5722	74	18	a	a	PRON
ejpam-5722	74	19	be	be	AUX
ejpam-5722	74	20	a	a	DET
ejpam-5722	74	21	subset	subset	NOUN
ejpam-5722	74	22	of	of	ADP
ejpam-5722	74	23	a	a	DET
ejpam-5722	74	24	bitopological	bitopological	ADJ
ejpam-5722	74	25	space	space	NOUN
ejpam-5722	74	26	(	(	PUNCT
ejpam-5722	74	27	x	x	NOUN
ejpam-5722	74	28	,	,	PUNCT
ejpam-5722	74	29	τ1	τ1	NOUN
ejpam-5722	74	30	,	,	PUNCT
ejpam-5722	74	31	τ2	τ2	NOUN
ejpam-5722	74	32	)	)	PUNCT
ejpam-5722	74	33	.	.	PUNCT
ejpam-5722	75	1	a	a	DET
ejpam-5722	75	2	point	point	NOUN
ejpam-5722	75	3	x	x	X
ejpam-5722	75	4	∈	∈	NOUN
ejpam-5722	75	5	x	x	PUNCT
ejpam-5722	75	6	is	be	AUX
ejpam-5722	75	7	called	call	VERB
ejpam-5722	75	8	a	a	DET
ejpam-5722	75	9	θ(τ1	θ(τ1	NOUN
ejpam-5722	75	10	,	,	PUNCT
ejpam-5722	75	11	τ2)s	τ2)s	NOUN
ejpam-5722	75	12	-	-	PUNCT
ejpam-5722	75	13	cluster	cluster	NOUN
ejpam-5722	75	14	point	point	NOUN
ejpam-5722	75	15	of	of	ADP
ejpam-5722	75	16	a	a	DET
ejpam-5722	75	17	if	if	NOUN
ejpam-5722	75	18	(	(	PUNCT
ejpam-5722	75	19	τ1	τ1	NOUN
ejpam-5722	75	20	,	,	PUNCT
ejpam-5722	75	21	τ2)-scl(u	τ2)-scl(u	ADJ
ejpam-5722	75	22	)	)	PUNCT
ejpam-5722	75	23	∩	∩	NOUN
ejpam-5722	75	24	a	a	DET
ejpam-5722	75	25	̸=	̸=	PROPN
ejpam-5722	75	26	∅	∅	NOUN
ejpam-5722	75	27	for	for	ADP
ejpam-5722	75	28	every	every	DET
ejpam-5722	75	29	(	(	PUNCT
ejpam-5722	75	30	τ1	τ1	NOUN
ejpam-5722	75	31	,	,	PUNCT
ejpam-5722	75	32	τ2)s	τ2)s	NOUN
ejpam-5722	75	33	-	-	PUNCT
ejpam-5722	75	34	open	open	ADJ
ejpam-5722	75	35	set	set	NOUN
ejpam-5722	75	36	u	u	NOUN
ejpam-5722	75	37	containing	contain	VERB
ejpam-5722	75	38	x.	x.	NOUN
ejpam-5722	75	39	the	the	DET
ejpam-5722	75	40	set	set	NOUN
ejpam-5722	75	41	of	of	ADP
ejpam-5722	75	42	all	all	DET
ejpam-5722	75	43	θ(τ1	θ(τ1	NOUN
ejpam-5722	75	44	,	,	PUNCT
ejpam-5722	75	45	τ2)s	τ2)s	ADJ
ejpam-5722	75	46	-	-	PUNCT
ejpam-5722	75	47	cluster	cluster	NOUN
ejpam-5722	75	48	points	point	NOUN
ejpam-5722	75	49	of	of	ADP
ejpam-5722	75	50	a	a	PRON
ejpam-5722	75	51	is	be	AUX
ejpam-5722	75	52	called	call	VERB
ejpam-5722	75	53	the	the	DET
ejpam-5722	75	54	θ(τ1	θ(τ1	NOUN
ejpam-5722	75	55	,	,	PUNCT
ejpam-5722	75	56	τ2)s	τ2)s	NOUN
ejpam-5722	75	57	-	-	PUNCT
ejpam-5722	75	58	closure	closure	NOUN
ejpam-5722	75	59	of	of	ADP
ejpam-5722	75	60	a	a	PRON
ejpam-5722	75	61	and	and	CCONJ
ejpam-5722	75	62	is	be	AUX
ejpam-5722	75	63	denoted	denote	VERB
ejpam-5722	75	64	by	by	ADP
ejpam-5722	75	65	θ(τ1	θ(τ1	NOUN
ejpam-5722	75	66	,	,	PUNCT
ejpam-5722	75	67	τ2)-scl(a	τ2)-scl(a	PROPN
ejpam-5722	75	68	)	)	PUNCT
ejpam-5722	75	69	.	.	PUNCT
ejpam-5722	76	1	a	a	DET
ejpam-5722	76	2	subset	subset	NOUN
ejpam-5722	76	3	a	a	PRON
ejpam-5722	76	4	of	of	ADP
ejpam-5722	76	5	a	a	DET
ejpam-5722	76	6	bitopological	bitopological	ADJ
ejpam-5722	76	7	space	space	NOUN
ejpam-5722	76	8	(	(	PUNCT
ejpam-5722	76	9	x	x	NOUN
ejpam-5722	76	10	,	,	PUNCT
ejpam-5722	76	11	τ1	τ1	NOUN
ejpam-5722	76	12	,	,	PUNCT
ejpam-5722	76	13	τ2	τ2	NOUN
ejpam-5722	76	14	)	)	PUNCT
ejpam-5722	76	15	is	be	AUX
ejpam-5722	76	16	said	say	VERB
ejpam-5722	76	17	to	to	PART
ejpam-5722	76	18	be	be	AUX
ejpam-5722	76	19	θ(τ1	θ(τ1	NOUN
ejpam-5722	76	20	,	,	PUNCT
ejpam-5722	76	21	τ2)s	τ2)s	NOUN
ejpam-5722	76	22	-	-	PUNCT
ejpam-5722	76	23	closed	close	VERB
ejpam-5722	76	24	if	if	SCONJ
ejpam-5722	76	25	θ(τ1	θ(τ1	NOUN
ejpam-5722	76	26	,	,	PUNCT
ejpam-5722	76	27	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-5722	76	28	)	)	PUNCT
ejpam-5722	76	29	=	=	VERB
ejpam-5722	77	1	a.	a.	NOUN
ejpam-5722	77	2	the	the	DET
ejpam-5722	77	3	complement	complement	NOUN
ejpam-5722	77	4	of	of	ADP
ejpam-5722	77	5	a	a	DET
ejpam-5722	77	6	θ(τ1	θ(τ1	NOUN
ejpam-5722	77	7	,	,	PUNCT
ejpam-5722	77	8	τ2)s	τ2)s	NOUN
ejpam-5722	77	9	-	-	PUNCT
ejpam-5722	77	10	closed	close	VERB
ejpam-5722	77	11	set	set	NOUN
ejpam-5722	77	12	is	be	AUX
ejpam-5722	77	13	said	say	VERB
ejpam-5722	77	14	to	to	PART
ejpam-5722	77	15	be	be	AUX
ejpam-5722	77	16	θ(τ1	θ(τ1	NOUN
ejpam-5722	77	17	,	,	PUNCT
ejpam-5722	77	18	τ2)s	τ2)s	NOUN
ejpam-5722	77	19	-	-	PUNCT
ejpam-5722	77	20	open	open	ADJ
ejpam-5722	77	21	.	.	PUNCT
ejpam-5722	78	1	the	the	DET
ejpam-5722	78	2	union	union	NOUN
ejpam-5722	78	3	of	of	ADP
ejpam-5722	78	4	all	all	DET
ejpam-5722	78	5	θ(τ1	θ(τ1	NOUN
ejpam-5722	78	6	,	,	PUNCT
ejpam-5722	78	7	τ2)s	τ2)s	NOUN
ejpam-5722	78	8	-	-	PUNCT
ejpam-5722	78	9	open	open	ADJ
ejpam-5722	78	10	sets	set	NOUN
ejpam-5722	78	11	of	of	ADP
ejpam-5722	78	12	x	x	PUNCT
ejpam-5722	78	13	contained	contain	VERB
ejpam-5722	78	14	in	in	ADP
ejpam-5722	78	15	a	a	PRON
ejpam-5722	78	16	is	be	AUX
ejpam-5722	78	17	called	call	VERB
ejpam-5722	78	18	the	the	DET
ejpam-5722	78	19	θ(τ1	θ(τ1	NOUN
ejpam-5722	78	20	,	,	PUNCT
ejpam-5722	78	21	τ2)s	τ2)s	NOUN
ejpam-5722	78	22	-	-	NOUN
ejpam-5722	78	23	interior	interior	NOUN
ejpam-5722	78	24	of	of	ADP
ejpam-5722	78	25	a	a	PRON
ejpam-5722	78	26	and	and	CCONJ
ejpam-5722	78	27	is	be	AUX
ejpam-5722	78	28	denoted	denote	VERB
ejpam-5722	78	29	by	by	ADP
ejpam-5722	78	30	θ(τ1	θ(τ1	NOUN
ejpam-5722	78	31	,	,	PUNCT
ejpam-5722	78	32	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-5722	78	33	)	)	PUNCT
ejpam-5722	78	34	.	.	PUNCT
ejpam-5722	79	1	3	3	X
ejpam-5722	79	2	.	.	X
ejpam-5722	79	3	quasi	quasi	PROPN
ejpam-5722	79	4	θ(τ1	θ(τ1	PROPN
ejpam-5722	79	5	,	,	PUNCT
ejpam-5722	79	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	79	7	functions	function	NOUN
ejpam-5722	79	8	in	in	ADP
ejpam-5722	79	9	this	this	DET
ejpam-5722	79	10	section	section	NOUN
ejpam-5722	79	11	,	,	PUNCT
ejpam-5722	79	12	we	we	PRON
ejpam-5722	79	13	introduce	introduce	VERB
ejpam-5722	79	14	the	the	DET
ejpam-5722	79	15	notion	notion	NOUN
ejpam-5722	79	16	of	of	ADP
ejpam-5722	79	17	quasi	quasi	NOUN
ejpam-5722	79	18	θ(τ1	θ(τ1	NOUN
ejpam-5722	79	19	,	,	PUNCT
ejpam-5722	79	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	79	21	functions	function	NOUN
ejpam-5722	79	22	.	.	PUNCT
ejpam-5722	80	1	moreover	moreover	ADV
ejpam-5722	80	2	,	,	PUNCT
ejpam-5722	80	3	some	some	DET
ejpam-5722	80	4	characterizations	characterization	NOUN
ejpam-5722	80	5	of	of	ADP
ejpam-5722	80	6	quasi	quasi	NOUN
ejpam-5722	80	7	θ(τ1	θ(τ1	NOUN
ejpam-5722	80	8	,	,	PUNCT
ejpam-5722	80	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	80	10	functions	function	NOUN
ejpam-5722	80	11	are	be	AUX
ejpam-5722	80	12	discussed	discuss	VERB
ejpam-5722	80	13	.	.	PUNCT
ejpam-5722	81	1	definition	definition	NOUN
ejpam-5722	81	2	1	1	NUM
ejpam-5722	81	3	.	.	PUNCT
ejpam-5722	82	1	a	a	DET
ejpam-5722	82	2	function	function	NOUN
ejpam-5722	82	3	f	f	NOUN
ejpam-5722	82	4	:	:	PUNCT
ejpam-5722	82	5	(	(	PUNCT
ejpam-5722	82	6	x	x	NOUN
ejpam-5722	82	7	,	,	PUNCT
ejpam-5722	82	8	τ1	τ1	NOUN
ejpam-5722	82	9	,	,	PUNCT
ejpam-5722	82	10	τ2	τ2	NOUN
ejpam-5722	82	11	)	)	PUNCT
ejpam-5722	82	12	→	→	SYM
ejpam-5722	82	13	(	(	PUNCT
ejpam-5722	82	14	y	y	PROPN
ejpam-5722	82	15	,	,	PUNCT
ejpam-5722	82	16	σ1	σ1	PROPN
ejpam-5722	82	17	,	,	PUNCT
ejpam-5722	82	18	σ2	σ2	PROPN
ejpam-5722	82	19	)	)	PUNCT
ejpam-5722	82	20	is	be	AUX
ejpam-5722	82	21	said	say	VERB
ejpam-5722	82	22	to	to	PART
ejpam-5722	82	23	be	be	AUX
ejpam-5722	82	24	quasi	quasi	NOUN
ejpam-5722	82	25	θ(τ1	θ(τ1	NOUN
ejpam-5722	82	26	,	,	PUNCT
ejpam-5722	82	27	τ2)continuous	τ2)continuous	ADJ
ejpam-5722	82	28	if	if	SCONJ
ejpam-5722	82	29	for	for	ADP
ejpam-5722	82	30	each	each	DET
ejpam-5722	82	31	x	x	SYM
ejpam-5722	82	32	∈	∈	PROPN
ejpam-5722	82	33	x	x	X
ejpam-5722	82	34	and	and	CCONJ
ejpam-5722	82	35	each	each	DET
ejpam-5722	82	36	σ1σ2	σ1σ2	VERB
ejpam-5722	82	37	-	-	ADJ
ejpam-5722	82	38	open	open	ADJ
ejpam-5722	82	39	set	set	NOUN
ejpam-5722	82	40	v	v	NOUN
ejpam-5722	82	41	of	of	ADP
ejpam-5722	82	42	y	y	NOUN
ejpam-5722	82	43	containing	contain	VERB
ejpam-5722	82	44	f(x	f(x	PROPN
ejpam-5722	82	45	)	)	PUNCT
ejpam-5722	82	46	,	,	PUNCT
ejpam-5722	82	47	there	there	PRON
ejpam-5722	82	48	exists	exist	VERB
ejpam-5722	82	49	a	a	DET
ejpam-5722	82	50	(	(	PUNCT
ejpam-5722	82	51	τ1	τ1	NOUN
ejpam-5722	82	52	,	,	PUNCT
ejpam-5722	82	53	τ2)s	τ2)s	NOUN
ejpam-5722	82	54	-	-	PUNCT
ejpam-5722	82	55	open	open	ADJ
ejpam-5722	82	56	set	set	NOUN
ejpam-5722	82	57	u	u	NOUN
ejpam-5722	82	58	of	of	ADP
ejpam-5722	82	59	x	x	PUNCT
ejpam-5722	82	60	containing	contain	VERB
ejpam-5722	82	61	x	x	PUNCT
ejpam-5722	82	62	such	such	ADJ
ejpam-5722	82	63	that	that	DET
ejpam-5722	82	64	f((τ1	f((τ1	PROPN
ejpam-5722	82	65	,	,	PUNCT
ejpam-5722	82	66	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	82	67	)	)	PUNCT
ejpam-5722	82	68	)	)	PUNCT
ejpam-5722	83	1	⊆	⊆	X
ejpam-5722	83	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	83	3	-	-	NUM
ejpam-5722	83	4	cl(v	cl(v	NOUN
ejpam-5722	83	5	)	)	PUNCT
ejpam-5722	83	6	.	.	PUNCT
ejpam-5722	84	1	theorem	theorem	NOUN
ejpam-5722	84	2	1	1	NUM
ejpam-5722	84	3	.	.	X
ejpam-5722	84	4	for	for	ADP
ejpam-5722	84	5	a	a	DET
ejpam-5722	84	6	function	function	NOUN
ejpam-5722	84	7	f	f	NOUN
ejpam-5722	84	8	:	:	PUNCT
ejpam-5722	84	9	(	(	PUNCT
ejpam-5722	84	10	x	x	NOUN
ejpam-5722	84	11	,	,	PUNCT
ejpam-5722	84	12	τ1	τ1	NOUN
ejpam-5722	84	13	,	,	PUNCT
ejpam-5722	84	14	τ2	τ2	NOUN
ejpam-5722	84	15	)	)	PUNCT
ejpam-5722	84	16	→	→	SYM
ejpam-5722	84	17	(	(	PUNCT
ejpam-5722	84	18	y	y	PROPN
ejpam-5722	84	19	,	,	PUNCT
ejpam-5722	84	20	σ1	σ1	PROPN
ejpam-5722	84	21	,	,	PUNCT
ejpam-5722	84	22	σ2	σ2	NOUN
ejpam-5722	84	23	)	)	PUNCT
ejpam-5722	84	24	,	,	PUNCT
ejpam-5722	84	25	the	the	DET
ejpam-5722	84	26	following	follow	VERB
ejpam-5722	84	27	properties	property	NOUN
ejpam-5722	84	28	are	be	AUX
ejpam-5722	84	29	equivalent	equivalent	ADJ
ejpam-5722	84	30	:	:	PUNCT
ejpam-5722	84	31	(	(	PUNCT
ejpam-5722	84	32	1	1	X
ejpam-5722	84	33	)	)	PUNCT
ejpam-5722	84	34	f	f	PROPN
ejpam-5722	84	35	is	be	AUX
ejpam-5722	84	36	quasi	quasi	NOUN
ejpam-5722	84	37	θ(τ1	θ(τ1	NOUN
ejpam-5722	84	38	,	,	PUNCT
ejpam-5722	84	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	84	40	;	;	PUNCT
ejpam-5722	84	41	(	(	PUNCT
ejpam-5722	84	42	2	2	X
ejpam-5722	84	43	)	)	PUNCT
ejpam-5722	84	44	θ(τ1	θ(τ1	NOUN
ejpam-5722	84	45	,	,	PUNCT
ejpam-5722	84	46	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	84	47	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	84	48	-	-	PUNCT
ejpam-5722	84	49	int((σ1	int((σ1	NUM
ejpam-5722	84	50	,	,	PUNCT
ejpam-5722	84	51	σ2)θ	σ2)θ	ADJ
ejpam-5722	84	52	-	-	PUNCT
ejpam-5722	84	53	cl(b	cl(b	NOUN
ejpam-5722	84	54	)	)	PUNCT
ejpam-5722	84	55	)	)	PUNCT
ejpam-5722	84	56	)	)	PUNCT
ejpam-5722	84	57	)	)	PUNCT
ejpam-5722	85	1	⊆	⊆	NUM
ejpam-5722	85	2	f−1((σ1	f−1((σ1	NOUN
ejpam-5722	85	3	,	,	PUNCT
ejpam-5722	85	4	σ2)θ	σ2)θ	NOUN
ejpam-5722	85	5	-	-	PUNCT
ejpam-5722	85	6	cl(b	cl(b	NOUN
ejpam-5722	85	7	)	)	PUNCT
ejpam-5722	85	8	)	)	PUNCT
ejpam-5722	85	9	for	for	ADP
ejpam-5722	85	10	every	every	DET
ejpam-5722	85	11	subset	subset	NOUN
ejpam-5722	85	12	b	b	PROPN
ejpam-5722	85	13	of	of	ADP
ejpam-5722	85	14	y	y	PROPN
ejpam-5722	85	15	;	;	PUNCT
ejpam-5722	85	16	(	(	PUNCT
ejpam-5722	85	17	3	3	X
ejpam-5722	85	18	)	)	PUNCT
ejpam-5722	85	19	θ(τ1	θ(τ1	NOUN
ejpam-5722	85	20	,	,	PUNCT
ejpam-5722	85	21	τ2)-scl(f	τ2)-scl(f	ADV
ejpam-5722	85	22	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	85	23	-	-	PUNCT
ejpam-5722	85	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	85	25	-	-	PUNCT
ejpam-5722	85	26	cl(v	cl(v	NOUN
ejpam-5722	85	27	)	)	PUNCT
ejpam-5722	85	28	)	)	PUNCT
ejpam-5722	85	29	)	)	PUNCT
ejpam-5722	85	30	)	)	PUNCT
ejpam-5722	86	1	⊆	⊆	NUM
ejpam-5722	86	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	86	3	-	-	PUNCT
ejpam-5722	86	4	cl(v	cl(v	NOUN
ejpam-5722	86	5	)	)	PUNCT
ejpam-5722	86	6	)	)	PUNCT
ejpam-5722	86	7	for	for	ADP
ejpam-5722	86	8	every	every	DET
ejpam-5722	86	9	σ1σ2	σ1σ2	NOUN
ejpam-5722	86	10	-	-	ADJ
ejpam-5722	86	11	open	open	ADJ
ejpam-5722	86	12	set	set	NOUN
ejpam-5722	86	13	v	v	NOUN
ejpam-5722	86	14	of	of	ADP
ejpam-5722	86	15	y	y	PROPN
ejpam-5722	86	16	;	;	PUNCT
ejpam-5722	86	17	(	(	PUNCT
ejpam-5722	86	18	4	4	X
ejpam-5722	86	19	)	)	PUNCT
ejpam-5722	86	20	θ(τ1	θ(τ1	NOUN
ejpam-5722	86	21	,	,	PUNCT
ejpam-5722	86	22	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	86	23	−1(σ1σ2	−1(σ1σ2	PROPN
ejpam-5722	86	24	-	-	PUNCT
ejpam-5722	86	25	int(k	int(k	NUM
ejpam-5722	86	26	)	)	PUNCT
ejpam-5722	86	27	)	)	PUNCT
ejpam-5722	86	28	)	)	PUNCT
ejpam-5722	87	1	⊆	⊆	NUM
ejpam-5722	87	2	f−1(k	f−1(k	PROPN
ejpam-5722	87	3	)	)	PUNCT
ejpam-5722	87	4	for	for	ADP
ejpam-5722	87	5	every	every	DET
ejpam-5722	87	6	(	(	PUNCT
ejpam-5722	87	7	σ1	σ1	PROPN
ejpam-5722	87	8	,	,	PUNCT
ejpam-5722	87	9	σ2)r	σ2)r	NOUN
ejpam-5722	87	10	-	-	PUNCT
ejpam-5722	87	11	closed	close	VERB
ejpam-5722	87	12	set	set	ADJ
ejpam-5722	87	13	k	k	PROPN
ejpam-5722	87	14	of	of	ADP
ejpam-5722	87	15	y	y	PROPN
ejpam-5722	87	16	;	;	PUNCT
ejpam-5722	87	17	n.	n.	PROPN
ejpam-5722	87	18	srisarakham	srisarakham	PROPN
ejpam-5722	87	19	,	,	PUNCT
ejpam-5722	87	20	s.	s.	PROPN
ejpam-5722	87	21	sompong	sompong	PROPN
ejpam-5722	87	22	,	,	PUNCT
ejpam-5722	87	23	c.	c.	PROPN
ejpam-5722	87	24	boonpok	boonpok	PROPN
ejpam-5722	87	25	/	/	SYM
ejpam-5722	87	26	eur	eur	PROPN
ejpam-5722	87	27	.	.	PUNCT
ejpam-5722	88	1	j.	j.	PROPN
ejpam-5722	88	2	pure	pure	PROPN
ejpam-5722	88	3	appl	appl	PROPN
ejpam-5722	88	4	.	.	PROPN
ejpam-5722	88	5	math	math	PROPN
ejpam-5722	88	6	,	,	PUNCT
ejpam-5722	88	7	18	18	NUM
ejpam-5722	88	8	(	(	PUNCT
ejpam-5722	88	9	1	1	NUM
ejpam-5722	88	10	)	)	PUNCT
ejpam-5722	88	11	(	(	PUNCT
ejpam-5722	88	12	2025	2025	NUM
ejpam-5722	88	13	)	)	PUNCT
ejpam-5722	88	14	,	,	PUNCT
ejpam-5722	88	15	5722	5722	NUM
ejpam-5722	88	16	4	4	NUM
ejpam-5722	88	17	of	of	ADP
ejpam-5722	88	18	12	12	NUM
ejpam-5722	88	19	(	(	PUNCT
ejpam-5722	88	20	5	5	NUM
ejpam-5722	88	21	)	)	PUNCT
ejpam-5722	88	22	f−1(v	f−1(v	NOUN
ejpam-5722	88	23	)	)	PUNCT
ejpam-5722	89	1	⊆	⊆	NUM
ejpam-5722	89	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	89	3	,	,	PUNCT
ejpam-5722	89	4	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	89	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	89	6	-	-	PUNCT
ejpam-5722	89	7	cl(v	cl(v	NOUN
ejpam-5722	89	8	)	)	PUNCT
ejpam-5722	89	9	)	)	PUNCT
ejpam-5722	89	10	)	)	PUNCT
ejpam-5722	90	1	for	for	ADP
ejpam-5722	90	2	every	every	DET
ejpam-5722	90	3	σ1σ2	σ1σ2	NOUN
ejpam-5722	90	4	-	-	ADJ
ejpam-5722	90	5	open	open	ADJ
ejpam-5722	90	6	set	set	NOUN
ejpam-5722	90	7	v	v	NOUN
ejpam-5722	90	8	of	of	ADP
ejpam-5722	90	9	y	y	PROPN
ejpam-5722	90	10	;	;	PUNCT
ejpam-5722	90	11	(	(	PUNCT
ejpam-5722	90	12	6	6	NUM
ejpam-5722	90	13	)	)	PUNCT
ejpam-5722	90	14	θ(τ1	θ(τ1	NOUN
ejpam-5722	90	15	,	,	PUNCT
ejpam-5722	90	16	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	90	17	−1(σ1σ2	−1(σ1σ2	PROPN
ejpam-5722	90	18	-	-	PUNCT
ejpam-5722	90	19	int(k	int(k	NUM
ejpam-5722	90	20	)	)	PUNCT
ejpam-5722	90	21	)	)	PUNCT
ejpam-5722	90	22	)	)	PUNCT
ejpam-5722	91	1	⊆	⊆	NUM
ejpam-5722	91	2	f−1(k	f−1(k	PROPN
ejpam-5722	91	3	)	)	PUNCT
ejpam-5722	91	4	for	for	ADP
ejpam-5722	91	5	every	every	DET
ejpam-5722	91	6	σ1σ2	σ1σ2	NUM
ejpam-5722	91	7	-	-	PUNCT
ejpam-5722	91	8	closed	closed	ADJ
ejpam-5722	91	9	set	set	NOUN
ejpam-5722	91	10	k	k	PROPN
ejpam-5722	91	11	of	of	ADP
ejpam-5722	91	12	y	y	PROPN
ejpam-5722	91	13	;	;	PUNCT
ejpam-5722	91	14	(	(	PUNCT
ejpam-5722	91	15	7	7	X
ejpam-5722	91	16	)	)	PUNCT
ejpam-5722	91	17	θ(τ1	θ(τ1	NOUN
ejpam-5722	91	18	,	,	PUNCT
ejpam-5722	91	19	τ2)-scl(f	τ2)-scl(f	ADV
ejpam-5722	91	20	−1(v	−1(v	PROPN
ejpam-5722	91	21	)	)	PUNCT
ejpam-5722	91	22	)	)	PUNCT
ejpam-5722	92	1	⊆	⊆	NUM
ejpam-5722	92	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	92	3	-	-	PUNCT
ejpam-5722	92	4	cl(v	cl(v	NOUN
ejpam-5722	92	5	)	)	PUNCT
ejpam-5722	92	6	)	)	PUNCT
ejpam-5722	92	7	for	for	ADP
ejpam-5722	92	8	every	every	DET
ejpam-5722	92	9	σ1σ2	σ1σ2	NOUN
ejpam-5722	92	10	-	-	ADJ
ejpam-5722	92	11	open	open	ADJ
ejpam-5722	92	12	set	set	NOUN
ejpam-5722	92	13	v	v	NOUN
ejpam-5722	92	14	of	of	ADP
ejpam-5722	92	15	y	y	PROPN
ejpam-5722	92	16	.	.	PUNCT
ejpam-5722	93	1	proof	proof	NOUN
ejpam-5722	93	2	.	.	PUNCT
ejpam-5722	94	1	(	(	PUNCT
ejpam-5722	94	2	1	1	X
ejpam-5722	94	3	)	)	PUNCT
ejpam-5722	94	4	⇒	⇒	NOUN
ejpam-5722	94	5	(	(	PUNCT
ejpam-5722	94	6	2	2	NUM
ejpam-5722	94	7	):	):	PUNCT
ejpam-5722	94	8	let	let	VERB
ejpam-5722	94	9	b	b	X
ejpam-5722	94	10	be	be	AUX
ejpam-5722	94	11	any	any	DET
ejpam-5722	94	12	subset	subset	NOUN
ejpam-5722	94	13	of	of	ADP
ejpam-5722	94	14	y	y	PROPN
ejpam-5722	94	15	.	.	PUNCT
ejpam-5722	94	16	suppose	suppose	VERB
ejpam-5722	94	17	that	that	SCONJ
ejpam-5722	94	18	x	x	PRON
ejpam-5722	94	19	̸∈	̸∈	PROPN
ejpam-5722	94	20	f−1((σ1	f−1((σ1	NOUN
ejpam-5722	94	21	,	,	PUNCT
ejpam-5722	94	22	σ2)θ	σ2)θ	NOUN
ejpam-5722	94	23	-	-	PUNCT
ejpam-5722	94	24	cl(b	cl(b	NOUN
ejpam-5722	94	25	)	)	PUNCT
ejpam-5722	94	26	)	)	PUNCT
ejpam-5722	94	27	.	.	PUNCT
ejpam-5722	95	1	then	then	ADV
ejpam-5722	95	2	,	,	PUNCT
ejpam-5722	95	3	x	x	PUNCT
ejpam-5722	95	4	∈	∈	NOUN
ejpam-5722	95	5	x−f−1((σ1	x−f−1((σ1	NOUN
ejpam-5722	95	6	,	,	PUNCT
ejpam-5722	95	7	σ2)θ	σ2)θ	ADJ
ejpam-5722	95	8	-	-	PUNCT
ejpam-5722	95	9	cl(b	cl(b	NOUN
ejpam-5722	95	10	)	)	PUNCT
ejpam-5722	95	11	)	)	PUNCT
ejpam-5722	95	12	and	and	CCONJ
ejpam-5722	95	13	f(x	f(x	PROPN
ejpam-5722	95	14	)	)	PUNCT
ejpam-5722	95	15	∈	∈	PROPN
ejpam-5722	95	16	y	y	NOUN
ejpam-5722	95	17	−(σ1	−(σ1	PROPN
ejpam-5722	95	18	,	,	PUNCT
ejpam-5722	95	19	σ2)θ	σ2)θ	ADJ
ejpam-5722	95	20	-	-	PUNCT
ejpam-5722	95	21	cl(b	cl(b	NOUN
ejpam-5722	95	22	)	)	PUNCT
ejpam-5722	95	23	.	.	PUNCT
ejpam-5722	96	1	since	since	SCONJ
ejpam-5722	96	2	(	(	PUNCT
ejpam-5722	96	3	σ1	σ1	PROPN
ejpam-5722	96	4	,	,	PUNCT
ejpam-5722	96	5	σ2)θ	σ2)θ	NOUN
ejpam-5722	96	6	-	-	PUNCT
ejpam-5722	96	7	cl(b	cl(b	NOUN
ejpam-5722	96	8	)	)	PUNCT
ejpam-5722	96	9	is	be	AUX
ejpam-5722	96	10	σ1σ2	σ1σ2	NOUN
ejpam-5722	96	11	-	-	ADJ
ejpam-5722	96	12	closed	closed	ADJ
ejpam-5722	96	13	in	in	ADP
ejpam-5722	96	14	y	y	PROPN
ejpam-5722	96	15	,	,	PUNCT
ejpam-5722	96	16	there	there	PRON
ejpam-5722	96	17	exists	exist	VERB
ejpam-5722	96	18	a	a	DET
ejpam-5722	96	19	(	(	PUNCT
ejpam-5722	96	20	τ1	τ1	NOUN
ejpam-5722	96	21	,	,	PUNCT
ejpam-5722	96	22	τ2)s	τ2)s	NOUN
ejpam-5722	96	23	-	-	PUNCT
ejpam-5722	96	24	open	open	ADJ
ejpam-5722	96	25	set	set	NOUN
ejpam-5722	96	26	u	u	NOUN
ejpam-5722	96	27	of	of	ADP
ejpam-5722	96	28	x	x	PUNCT
ejpam-5722	96	29	containing	contain	VERB
ejpam-5722	96	30	x	x	PUNCT
ejpam-5722	96	31	such	such	ADJ
ejpam-5722	96	32	that	that	DET
ejpam-5722	96	33	f((τ1	f((τ1	PROPN
ejpam-5722	96	34	,	,	PUNCT
ejpam-5722	96	35	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	96	36	)	)	PUNCT
ejpam-5722	96	37	)	)	PUNCT
ejpam-5722	97	1	⊆	⊆	X
ejpam-5722	97	2	σ1σ2	σ1σ2	NUM
ejpam-5722	97	3	-	-	PUNCT
ejpam-5722	97	4	cl(y	cl(y	NOUN
ejpam-5722	97	5	−	−	PROPN
ejpam-5722	97	6	(	(	PUNCT
ejpam-5722	97	7	σ1	σ1	PROPN
ejpam-5722	97	8	,	,	PUNCT
ejpam-5722	97	9	σ2)θ	σ2)θ	NOUN
ejpam-5722	97	10	-	-	PUNCT
ejpam-5722	97	11	cl(b	cl(b	NOUN
ejpam-5722	97	12	)	)	PUNCT
ejpam-5722	97	13	)	)	PUNCT
ejpam-5722	98	1	=	=	PUNCT
ejpam-5722	98	2	y	y	PROPN
ejpam-5722	98	3	−σ1σ2	−σ1σ2	PROPN
ejpam-5722	98	4	-	-	PUNCT
ejpam-5722	98	5	int((σ1	int((σ1	PROPN
ejpam-5722	98	6	,	,	PUNCT
ejpam-5722	98	7	σ2)θ	σ2)θ	ADJ
ejpam-5722	98	8	-	-	PUNCT
ejpam-5722	98	9	cl(b	cl(b	NOUN
ejpam-5722	98	10	)	)	PUNCT
ejpam-5722	98	11	)	)	PUNCT
ejpam-5722	98	12	.	.	PUNCT
ejpam-5722	99	1	thus	thus	ADV
ejpam-5722	99	2	,	,	PUNCT
ejpam-5722	99	3	we	we	PRON
ejpam-5722	99	4	have	have	AUX
ejpam-5722	99	5	f((τ1	f((τ1	NOUN
ejpam-5722	99	6	,	,	PUNCT
ejpam-5722	99	7	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	99	8	)	)	PUNCT
ejpam-5722	99	9	)	)	PUNCT
ejpam-5722	100	1	∩	∩	NOUN
ejpam-5722	100	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	100	3	-	-	PUNCT
ejpam-5722	100	4	int((σ1	int((σ1	ADJ
ejpam-5722	100	5	,	,	PUNCT
ejpam-5722	100	6	σ2)θ	σ2)θ	ADJ
ejpam-5722	100	7	-	-	PUNCT
ejpam-5722	100	8	cl(b	cl(b	NOUN
ejpam-5722	100	9	)	)	PUNCT
ejpam-5722	100	10	)	)	PUNCT
ejpam-5722	101	1	=	=	PUNCT
ejpam-5722	101	2	∅	∅	NOUN
ejpam-5722	101	3	and	and	CCONJ
ejpam-5722	101	4	(	(	PUNCT
ejpam-5722	101	5	τ1	τ1	NOUN
ejpam-5722	101	6	,	,	PUNCT
ejpam-5722	101	7	τ2)-scl(u	τ2)-scl(u	ADJ
ejpam-5722	101	8	)	)	PUNCT
ejpam-5722	101	9	∩	∩	NOUN
ejpam-5722	101	10	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	101	11	-	-	PUNCT
ejpam-5722	101	12	int((σ1	int((σ1	NUM
ejpam-5722	101	13	,	,	PUNCT
ejpam-5722	101	14	σ2)θ	σ2)θ	ADJ
ejpam-5722	101	15	-	-	PUNCT
ejpam-5722	101	16	cl(b	cl(b	NOUN
ejpam-5722	101	17	)	)	PUNCT
ejpam-5722	101	18	)	)	PUNCT
ejpam-5722	101	19	)	)	PUNCT
ejpam-5722	102	1	=	=	PUNCT
ejpam-5722	102	2	∅.	∅.	ADP
ejpam-5722	102	3	this	this	PRON
ejpam-5722	102	4	shows	show	VERB
ejpam-5722	102	5	that	that	SCONJ
ejpam-5722	102	6	x	x	PROPN
ejpam-5722	102	7	̸∈	̸∈	PROPN
ejpam-5722	102	8	θ(τ1	θ(τ1	VERB
ejpam-5722	102	9	,	,	PUNCT
ejpam-5722	102	10	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	102	11	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	102	12	-	-	PUNCT
ejpam-5722	102	13	int((σ1	int((σ1	NUM
ejpam-5722	102	14	,	,	PUNCT
ejpam-5722	102	15	σ2)θ	σ2)θ	ADJ
ejpam-5722	102	16	-	-	PUNCT
ejpam-5722	102	17	cl(b	cl(b	NOUN
ejpam-5722	102	18	)	)	PUNCT
ejpam-5722	102	19	)	)	PUNCT
ejpam-5722	102	20	)	)	PUNCT
ejpam-5722	102	21	)	)	PUNCT
ejpam-5722	102	22	.	.	PUNCT
ejpam-5722	103	1	thus	thus	ADV
ejpam-5722	103	2	,	,	PUNCT
ejpam-5722	103	3	θ(τ1	θ(τ1	NOUN
ejpam-5722	103	4	,	,	PUNCT
ejpam-5722	103	5	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	103	6	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	103	7	-	-	PUNCT
ejpam-5722	103	8	int((σ1	int((σ1	NUM
ejpam-5722	103	9	,	,	PUNCT
ejpam-5722	103	10	σ2)θ	σ2)θ	ADJ
ejpam-5722	103	11	-	-	PUNCT
ejpam-5722	103	12	cl(b	cl(b	NOUN
ejpam-5722	103	13	)	)	PUNCT
ejpam-5722	103	14	)	)	PUNCT
ejpam-5722	103	15	)	)	PUNCT
ejpam-5722	103	16	)	)	PUNCT
ejpam-5722	104	1	⊆	⊆	NUM
ejpam-5722	104	2	f−1((σ1	f−1((σ1	NOUN
ejpam-5722	104	3	,	,	PUNCT
ejpam-5722	104	4	σ2)θ	σ2)θ	NOUN
ejpam-5722	104	5	-	-	PUNCT
ejpam-5722	104	6	cl(b	cl(b	NOUN
ejpam-5722	104	7	)	)	PUNCT
ejpam-5722	104	8	)	)	PUNCT
ejpam-5722	104	9	.	.	PUNCT
ejpam-5722	105	1	(	(	PUNCT
ejpam-5722	105	2	2	2	X
ejpam-5722	105	3	)	)	PUNCT
ejpam-5722	105	4	⇒	⇒	NOUN
ejpam-5722	105	5	(	(	PUNCT
ejpam-5722	105	6	3	3	NUM
ejpam-5722	105	7	):	):	PUNCT
ejpam-5722	105	8	this	this	PRON
ejpam-5722	105	9	is	be	AUX
ejpam-5722	105	10	obvious	obvious	ADJ
ejpam-5722	105	11	since	since	SCONJ
ejpam-5722	105	12	σ1σ2	σ1σ2	NOUN
ejpam-5722	105	13	-	-	NOUN
ejpam-5722	105	14	cl(v	cl(v	X
ejpam-5722	105	15	)	)	PUNCT
ejpam-5722	106	1	=	=	SYM
ejpam-5722	106	2	(	(	PUNCT
ejpam-5722	106	3	σ1	σ1	PROPN
ejpam-5722	106	4	,	,	PUNCT
ejpam-5722	106	5	σ2)θ	σ2)θ	NOUN
ejpam-5722	106	6	-	-	PUNCT
ejpam-5722	106	7	cl(v	cl(v	NOUN
ejpam-5722	106	8	)	)	PUNCT
ejpam-5722	106	9	for	for	ADP
ejpam-5722	106	10	every	every	DET
ejpam-5722	106	11	σ1σ2	σ1σ2	NOUN
ejpam-5722	106	12	-	-	ADJ
ejpam-5722	106	13	open	open	ADJ
ejpam-5722	106	14	set	set	NOUN
ejpam-5722	106	15	v	v	NOUN
ejpam-5722	106	16	of	of	ADP
ejpam-5722	106	17	y	y	PROPN
ejpam-5722	106	18	.	.	PUNCT
ejpam-5722	107	1	(	(	PUNCT
ejpam-5722	107	2	3	3	X
ejpam-5722	107	3	)	)	PUNCT
ejpam-5722	107	4	⇒	⇒	NOUN
ejpam-5722	107	5	(	(	PUNCT
ejpam-5722	107	6	4	4	NUM
ejpam-5722	107	7	):	):	PUNCT
ejpam-5722	107	8	let	let	VERB
ejpam-5722	107	9	k	k	PRON
ejpam-5722	107	10	be	be	AUX
ejpam-5722	107	11	any	any	DET
ejpam-5722	107	12	(	(	PUNCT
ejpam-5722	107	13	σ1	σ1	NOUN
ejpam-5722	107	14	,	,	PUNCT
ejpam-5722	107	15	σ2)r	σ2)r	NOUN
ejpam-5722	107	16	-	-	PUNCT
ejpam-5722	107	17	closed	close	VERB
ejpam-5722	107	18	set	set	NOUN
ejpam-5722	107	19	of	of	ADP
ejpam-5722	107	20	y	y	PROPN
ejpam-5722	107	21	.	.	PUNCT
ejpam-5722	108	1	by	by	ADP
ejpam-5722	108	2	(	(	PUNCT
ejpam-5722	108	3	3	3	NUM
ejpam-5722	108	4	)	)	PUNCT
ejpam-5722	108	5	,	,	PUNCT
ejpam-5722	108	6	we	we	PRON
ejpam-5722	108	7	have	have	VERB
ejpam-5722	108	8	θ(τ1	θ(τ1	NOUN
ejpam-5722	108	9	,	,	PUNCT
ejpam-5722	108	10	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	108	11	−1(σ1σ2	−1(σ1σ2	PROPN
ejpam-5722	108	12	-	-	PUNCT
ejpam-5722	108	13	int(k	int(k	NUM
ejpam-5722	108	14	)	)	PUNCT
ejpam-5722	108	15	)	)	PUNCT
ejpam-5722	108	16	)	)	PUNCT
ejpam-5722	109	1	=	=	SYM
ejpam-5722	109	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	109	3	,	,	PUNCT
ejpam-5722	109	4	τ2)-scl(f	τ2)-scl(f	ADJ
ejpam-5722	109	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	109	6	-	-	PUNCT
ejpam-5722	109	7	int(σ1σ2	int(σ1σ2	ADV
ejpam-5722	109	8	-	-	PUNCT
ejpam-5722	109	9	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5722	109	10	-	-	PUNCT
ejpam-5722	109	11	int(k	int(k	NOUN
ejpam-5722	109	12	)	)	PUNCT
ejpam-5722	109	13	)	)	PUNCT
ejpam-5722	109	14	)	)	PUNCT
ejpam-5722	109	15	)	)	PUNCT
ejpam-5722	109	16	)	)	PUNCT
ejpam-5722	110	1	⊆	⊆	NUM
ejpam-5722	110	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	110	3	-	-	PUNCT
ejpam-5722	110	4	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-5722	110	5	-	-	PUNCT
ejpam-5722	110	6	int(k	int(k	NOUN
ejpam-5722	110	7	)	)	PUNCT
ejpam-5722	110	8	)	)	PUNCT
ejpam-5722	110	9	)	)	PUNCT
ejpam-5722	111	1	=	=	PUNCT
ejpam-5722	111	2	f−1(k	f−1(k	PROPN
ejpam-5722	111	3	)	)	PUNCT
ejpam-5722	111	4	.	.	PUNCT
ejpam-5722	112	1	(	(	PUNCT
ejpam-5722	112	2	4	4	X
ejpam-5722	112	3	)	)	PUNCT
ejpam-5722	112	4	⇒	⇒	NOUN
ejpam-5722	112	5	(	(	PUNCT
ejpam-5722	112	6	5	5	NUM
ejpam-5722	112	7	):	):	PUNCT
ejpam-5722	112	8	let	let	VERB
ejpam-5722	112	9	v	v	PART
ejpam-5722	112	10	be	be	AUX
ejpam-5722	112	11	any	any	DET
ejpam-5722	112	12	σ1σ2	σ1σ2	NOUN
ejpam-5722	112	13	-	-	ADJ
ejpam-5722	112	14	open	open	ADJ
ejpam-5722	112	15	set	set	NOUN
ejpam-5722	112	16	of	of	ADP
ejpam-5722	112	17	y	y	PROPN
ejpam-5722	112	18	.	.	PUNCT
ejpam-5722	113	1	then	then	ADV
ejpam-5722	113	2	,	,	PUNCT
ejpam-5722	113	3	we	we	PRON
ejpam-5722	113	4	have	have	VERB
ejpam-5722	113	5	x	x	PART
ejpam-5722	113	6	−	−	NOUN
ejpam-5722	113	7	θ(τ1	θ(τ1	NOUN
ejpam-5722	113	8	,	,	PUNCT
ejpam-5722	113	9	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	113	10	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	113	11	-	-	PUNCT
ejpam-5722	113	12	cl(v	cl(v	NOUN
ejpam-5722	113	13	)	)	PUNCT
ejpam-5722	113	14	)	)	PUNCT
ejpam-5722	113	15	)	)	PUNCT
ejpam-5722	114	1	=	=	SYM
ejpam-5722	114	2	θ(τ1	θ(τ1	PROPN
ejpam-5722	114	3	,	,	PUNCT
ejpam-5722	114	4	τ2)-scl(x	τ2)-scl(x	PROPN
ejpam-5722	114	5	−	−	PROPN
ejpam-5722	114	6	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	114	7	-	-	PUNCT
ejpam-5722	114	8	cl(v	cl(v	NOUN
ejpam-5722	114	9	)	)	PUNCT
ejpam-5722	114	10	)	)	PUNCT
ejpam-5722	114	11	)	)	PUNCT
ejpam-5722	115	1	=	=	SYM
ejpam-5722	115	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	115	3	,	,	PUNCT
ejpam-5722	115	4	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5722	115	5	−1(y	−1(y	PUNCT
ejpam-5722	116	1	−	−	ADP
ejpam-5722	116	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	116	3	-	-	NUM
ejpam-5722	116	4	cl(v	cl(v	NOUN
ejpam-5722	116	5	)	)	PUNCT
ejpam-5722	116	6	)	)	PUNCT
ejpam-5722	116	7	)	)	PUNCT
ejpam-5722	116	8	,	,	PUNCT
ejpam-5722	116	9	y	y	PROPN
ejpam-5722	116	10	−	−	NUM
ejpam-5722	116	11	σ1σ2	σ1σ2	NOUN
ejpam-5722	116	12	-	-	NUM
ejpam-5722	116	13	cl(v	cl(v	X
ejpam-5722	116	14	)	)	PUNCT
ejpam-5722	116	15	=	=	SYM
ejpam-5722	116	16	σ1σ2	σ1σ2	X
ejpam-5722	116	17	-	-	PUNCT
ejpam-5722	116	18	int(y	int(y	ADJ
ejpam-5722	116	19	−	−	NOUN
ejpam-5722	116	20	σ1σ2	σ1σ2	NOUN
ejpam-5722	116	21	-	-	NUM
ejpam-5722	116	22	cl(v	cl(v	NOUN
ejpam-5722	116	23	)	)	PUNCT
ejpam-5722	116	24	)	)	PUNCT
ejpam-5722	117	1	⊆	⊆	X
ejpam-5722	117	2	σ1σ2	σ1σ2	X
ejpam-5722	117	3	-	-	PUNCT
ejpam-5722	117	4	int(y	int(y	ADJ
ejpam-5722	117	5	−	−	NOUN
ejpam-5722	117	6	σ1σ2	σ1σ2	NOUN
ejpam-5722	117	7	-	-	PUNCT
ejpam-5722	117	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	117	9	-	-	PUNCT
ejpam-5722	117	10	cl(v	cl(v	NOUN
ejpam-5722	117	11	)	)	PUNCT
ejpam-5722	117	12	)	)	PUNCT
ejpam-5722	117	13	)	)	PUNCT
ejpam-5722	117	14	and	and	CCONJ
ejpam-5722	117	15	y	y	PROPN
ejpam-5722	117	16	−	−	PROPN
ejpam-5722	117	17	σ1σ2	σ1σ2	ADV
ejpam-5722	117	18	-	-	PUNCT
ejpam-5722	117	19	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	117	20	-	-	PUNCT
ejpam-5722	117	21	cl(v	cl(v	NOUN
ejpam-5722	117	22	)	)	PUNCT
ejpam-5722	117	23	)	)	PUNCT
ejpam-5722	117	24	is	be	AUX
ejpam-5722	117	25	(	(	PUNCT
ejpam-5722	117	26	σ1	σ1	NOUN
ejpam-5722	117	27	,	,	PUNCT
ejpam-5722	117	28	σ2)r	σ2)r	NOUN
ejpam-5722	117	29	-	-	PUNCT
ejpam-5722	117	30	closed	closed	ADJ
ejpam-5722	117	31	in	in	ADP
ejpam-5722	117	32	y	y	PROPN
ejpam-5722	117	33	.	.	PUNCT
ejpam-5722	118	1	thus	thus	ADV
ejpam-5722	118	2	by	by	ADP
ejpam-5722	118	3	(	(	PUNCT
ejpam-5722	118	4	4	4	NUM
ejpam-5722	118	5	)	)	PUNCT
ejpam-5722	118	6	,	,	PUNCT
ejpam-5722	118	7	θ(τ1	θ(τ1	VERB
ejpam-5722	118	8	,	,	PUNCT
ejpam-5722	118	9	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5722	118	10	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	118	11	-	-	PUNCT
ejpam-5722	118	12	int(y	int(y	PROPN
ejpam-5722	118	13	−	−	NOUN
ejpam-5722	118	14	σ1σ2	σ1σ2	NOUN
ejpam-5722	118	15	-	-	PUNCT
ejpam-5722	118	16	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	118	17	-	-	PUNCT
ejpam-5722	118	18	cl(v	cl(v	NOUN
ejpam-5722	118	19	)	)	PUNCT
ejpam-5722	118	20	)	)	PUNCT
ejpam-5722	118	21	)	)	PUNCT
ejpam-5722	118	22	)	)	PUNCT
ejpam-5722	118	23	)	)	PUNCT
ejpam-5722	119	1	⊆	⊆	X
ejpam-5722	119	2	f−1(y	f−1(y	NOUN
ejpam-5722	119	3	−	−	PUNCT
ejpam-5722	119	4	σ1σ2	σ1σ2	SYM
ejpam-5722	119	5	-	-	PUNCT
ejpam-5722	119	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	119	7	-	-	PUNCT
ejpam-5722	119	8	cl(v	cl(v	NOUN
ejpam-5722	119	9	)	)	PUNCT
ejpam-5722	119	10	)	)	PUNCT
ejpam-5722	119	11	)	)	PUNCT
ejpam-5722	120	1	=	=	PUNCT
ejpam-5722	120	2	x	x	X
ejpam-5722	120	3	−	−	PRON
ejpam-5722	120	4	f−1(σ1σ2	f−1(σ1σ2	VERB
ejpam-5722	120	5	-	-	PUNCT
ejpam-5722	120	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	120	7	-	-	PUNCT
ejpam-5722	120	8	cl(v	cl(v	NOUN
ejpam-5722	120	9	)	)	PUNCT
ejpam-5722	120	10	)	)	PUNCT
ejpam-5722	120	11	)	)	PUNCT
ejpam-5722	121	1	⊆	⊆	NUM
ejpam-5722	121	2	x	x	SYM
ejpam-5722	121	3	−	−	PROPN
ejpam-5722	121	4	f−1(v	f−1(v	PROPN
ejpam-5722	121	5	)	)	PUNCT
ejpam-5722	121	6	and	and	CCONJ
ejpam-5722	121	7	hence	hence	ADV
ejpam-5722	121	8	f−1(v	f−1(v	NOUN
ejpam-5722	121	9	)	)	PUNCT
ejpam-5722	122	1	⊆	⊆	NUM
ejpam-5722	122	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	122	3	,	,	PUNCT
ejpam-5722	122	4	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	122	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	122	6	-	-	PUNCT
ejpam-5722	122	7	cl(v	cl(v	NOUN
ejpam-5722	122	8	)	)	PUNCT
ejpam-5722	122	9	)	)	PUNCT
ejpam-5722	122	10	)	)	PUNCT
ejpam-5722	122	11	.	.	PUNCT
ejpam-5722	123	1	(	(	PUNCT
ejpam-5722	123	2	5	5	X
ejpam-5722	123	3	)	)	PUNCT
ejpam-5722	123	4	⇒	⇒	NOUN
ejpam-5722	123	5	(	(	PUNCT
ejpam-5722	123	6	6	6	NUM
ejpam-5722	123	7	):	):	PUNCT
ejpam-5722	123	8	let	let	VERB
ejpam-5722	123	9	k	k	PRON
ejpam-5722	123	10	be	be	AUX
ejpam-5722	123	11	any	any	DET
ejpam-5722	123	12	σ1σ2	σ1σ2	NUM
ejpam-5722	123	13	-	-	PUNCT
ejpam-5722	123	14	closed	closed	ADJ
ejpam-5722	123	15	set	set	NOUN
ejpam-5722	123	16	of	of	ADP
ejpam-5722	123	17	y	y	PROPN
ejpam-5722	123	18	.	.	PUNCT
ejpam-5722	124	1	then	then	ADV
ejpam-5722	124	2	by	by	ADP
ejpam-5722	124	3	(	(	PUNCT
ejpam-5722	124	4	5	5	NUM
ejpam-5722	124	5	)	)	PUNCT
ejpam-5722	124	6	,	,	PUNCT
ejpam-5722	124	7	we	we	PRON
ejpam-5722	124	8	have	have	VERB
ejpam-5722	124	9	x	x	X
ejpam-5722	124	10	−	−	PROPN
ejpam-5722	124	11	f−1(k	f−1(k	PROPN
ejpam-5722	124	12	)	)	PUNCT
ejpam-5722	125	1	=	=	SYM
ejpam-5722	125	2	f−1(y	f−1(y	PROPN
ejpam-5722	125	3	−k	−k	PROPN
ejpam-5722	125	4	)	)	PUNCT
ejpam-5722	125	5	⊆	⊆	NUM
ejpam-5722	125	6	θ(τ1	θ(τ1	NOUN
ejpam-5722	125	7	,	,	PUNCT
ejpam-5722	125	8	τ2)-sint(f	τ2)-sint(f	ADP
ejpam-5722	125	9	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	125	10	-	-	PUNCT
ejpam-5722	125	11	cl(y	cl(y	NOUN
ejpam-5722	125	12	−k	−k	NOUN
ejpam-5722	125	13	)	)	PUNCT
ejpam-5722	125	14	)	)	PUNCT
ejpam-5722	125	15	)	)	PUNCT
ejpam-5722	126	1	=	=	SYM
ejpam-5722	126	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	126	3	,	,	PUNCT
ejpam-5722	126	4	τ2)-sint(f	τ2)-sint(f	ADP
ejpam-5722	126	5	−1(y	−1(y	PUNCT
ejpam-5722	126	6	−	−	ADP
ejpam-5722	126	7	σ1σ2	σ1σ2	NUM
ejpam-5722	126	8	-	-	PUNCT
ejpam-5722	126	9	int(k	int(k	NOUN
ejpam-5722	126	10	)	)	PUNCT
ejpam-5722	126	11	)	)	PUNCT
ejpam-5722	126	12	)	)	PUNCT
ejpam-5722	127	1	n.	n.	PROPN
ejpam-5722	127	2	srisarakham	srisarakham	PROPN
ejpam-5722	127	3	,	,	PUNCT
ejpam-5722	127	4	s.	s.	PROPN
ejpam-5722	127	5	sompong	sompong	PROPN
ejpam-5722	127	6	,	,	PUNCT
ejpam-5722	127	7	c.	c.	PROPN
ejpam-5722	127	8	boonpok	boonpok	PROPN
ejpam-5722	127	9	/	/	SYM
ejpam-5722	127	10	eur	eur	PROPN
ejpam-5722	127	11	.	.	PUNCT
ejpam-5722	128	1	j.	j.	PROPN
ejpam-5722	128	2	pure	pure	PROPN
ejpam-5722	128	3	appl	appl	PROPN
ejpam-5722	128	4	.	.	PROPN
ejpam-5722	128	5	math	math	PROPN
ejpam-5722	128	6	,	,	PUNCT
ejpam-5722	128	7	18	18	NUM
ejpam-5722	128	8	(	(	PUNCT
ejpam-5722	128	9	1	1	NUM
ejpam-5722	128	10	)	)	PUNCT
ejpam-5722	128	11	(	(	PUNCT
ejpam-5722	128	12	2025	2025	NUM
ejpam-5722	128	13	)	)	PUNCT
ejpam-5722	128	14	,	,	PUNCT
ejpam-5722	128	15	5722	5722	NUM
ejpam-5722	128	16	5	5	NUM
ejpam-5722	128	17	of	of	ADP
ejpam-5722	128	18	12	12	NUM
ejpam-5722	128	19	=	=	SYM
ejpam-5722	128	20	θ(τ1	θ(τ1	NOUN
ejpam-5722	128	21	,	,	PUNCT
ejpam-5722	128	22	τ2)-sint(x	τ2)-sint(x	PUNCT
ejpam-5722	128	23	−	−	NOUN
ejpam-5722	128	24	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	128	25	-	-	PUNCT
ejpam-5722	128	26	int(k	int(k	NOUN
ejpam-5722	128	27	)	)	PUNCT
ejpam-5722	128	28	)	)	PUNCT
ejpam-5722	128	29	)	)	PUNCT
ejpam-5722	129	1	=	=	PUNCT
ejpam-5722	129	2	x	x	SYM
ejpam-5722	129	3	−	−	NOUN
ejpam-5722	129	4	θ(τ1	θ(τ1	NOUN
ejpam-5722	129	5	,	,	PUNCT
ejpam-5722	129	6	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	129	7	−1(σ1σ2	−1(σ1σ2	PROPN
ejpam-5722	129	8	-	-	PUNCT
ejpam-5722	129	9	int(k	int(k	NUM
ejpam-5722	129	10	)	)	PUNCT
ejpam-5722	129	11	)	)	PUNCT
ejpam-5722	129	12	)	)	PUNCT
ejpam-5722	129	13	.	.	PUNCT
ejpam-5722	130	1	thus	thus	ADV
ejpam-5722	130	2	,	,	PUNCT
ejpam-5722	130	3	θ(τ1	θ(τ1	NOUN
ejpam-5722	130	4	,	,	PUNCT
ejpam-5722	130	5	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	130	6	−1(σ1σ2	−1(σ1σ2	PROPN
ejpam-5722	130	7	-	-	PUNCT
ejpam-5722	130	8	int(k	int(k	NUM
ejpam-5722	130	9	)	)	PUNCT
ejpam-5722	130	10	)	)	PUNCT
ejpam-5722	130	11	)	)	PUNCT
ejpam-5722	131	1	⊆	⊆	NUM
ejpam-5722	131	2	f−1(k	f−1(k	NOUN
ejpam-5722	131	3	)	)	PUNCT
ejpam-5722	131	4	.	.	PUNCT
ejpam-5722	132	1	(	(	PUNCT
ejpam-5722	132	2	6	6	X
ejpam-5722	132	3	)	)	PUNCT
ejpam-5722	132	4	⇒	⇒	NOUN
ejpam-5722	132	5	(	(	PUNCT
ejpam-5722	132	6	7	7	NUM
ejpam-5722	132	7	):	):	PUNCT
ejpam-5722	132	8	let	let	VERB
ejpam-5722	132	9	v	v	PART
ejpam-5722	132	10	be	be	AUX
ejpam-5722	132	11	any	any	DET
ejpam-5722	132	12	σ1σ2	σ1σ2	NUM
ejpam-5722	132	13	-	-	PUNCT
ejpam-5722	132	14	closed	closed	ADJ
ejpam-5722	132	15	set	set	NOUN
ejpam-5722	132	16	of	of	ADP
ejpam-5722	132	17	y	y	PROPN
ejpam-5722	132	18	.	.	PUNCT
ejpam-5722	133	1	then	then	ADV
ejpam-5722	133	2	,	,	PUNCT
ejpam-5722	133	3	we	we	PRON
ejpam-5722	133	4	have	have	VERB
ejpam-5722	133	5	σ1σ2	σ1σ2	NOUN
ejpam-5722	133	6	-	-	NUM
ejpam-5722	133	7	cl(v	cl(v	NOUN
ejpam-5722	133	8	)	)	PUNCT
ejpam-5722	133	9	is	be	AUX
ejpam-5722	133	10	σ1σ2	σ1σ2	NOUN
ejpam-5722	133	11	-	-	ADJ
ejpam-5722	133	12	closed	closed	ADJ
ejpam-5722	133	13	in	in	ADP
ejpam-5722	133	14	y	y	PROPN
ejpam-5722	133	15	and	and	CCONJ
ejpam-5722	133	16	by	by	ADP
ejpam-5722	133	17	(	(	PUNCT
ejpam-5722	133	18	6	6	NUM
ejpam-5722	133	19	)	)	PUNCT
ejpam-5722	133	20	,	,	PUNCT
ejpam-5722	133	21	θ(τ1	θ(τ1	VERB
ejpam-5722	133	22	,	,	PUNCT
ejpam-5722	133	23	τ2)-scl(f	τ2)-scl(f	ADJ
ejpam-5722	133	24	−1(v	−1(v	PROPN
ejpam-5722	133	25	)	)	PUNCT
ejpam-5722	133	26	)	)	PUNCT
ejpam-5722	134	1	⊆	⊆	NUM
ejpam-5722	134	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	134	3	,	,	PUNCT
ejpam-5722	134	4	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	134	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	134	6	-	-	PUNCT
ejpam-5722	134	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	134	8	-	-	PUNCT
ejpam-5722	134	9	cl(v	cl(v	NOUN
ejpam-5722	134	10	)	)	PUNCT
ejpam-5722	134	11	)	)	PUNCT
ejpam-5722	134	12	)	)	PUNCT
ejpam-5722	134	13	)	)	PUNCT
ejpam-5722	135	1	⊆	⊆	NUM
ejpam-5722	135	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	135	3	-	-	PUNCT
ejpam-5722	135	4	cl(v	cl(v	NOUN
ejpam-5722	135	5	)	)	PUNCT
ejpam-5722	135	6	)	)	PUNCT
ejpam-5722	135	7	.	.	PUNCT
ejpam-5722	136	1	(	(	PUNCT
ejpam-5722	136	2	7	7	X
ejpam-5722	136	3	)	)	PUNCT
ejpam-5722	136	4	⇒	⇒	NOUN
ejpam-5722	136	5	(	(	PUNCT
ejpam-5722	136	6	1	1	NUM
ejpam-5722	136	7	):	):	PUNCT
ejpam-5722	136	8	let	let	VERB
ejpam-5722	136	9	x	x	PUNCT
ejpam-5722	136	10	∈	∈	PROPN
ejpam-5722	136	11	x	x	X
ejpam-5722	136	12	and	and	CCONJ
ejpam-5722	136	13	v	v	X
ejpam-5722	136	14	be	be	AUX
ejpam-5722	136	15	any	any	DET
ejpam-5722	136	16	σ1σ2	σ1σ2	NOUN
ejpam-5722	136	17	-	-	ADJ
ejpam-5722	136	18	open	open	ADJ
ejpam-5722	136	19	set	set	NOUN
ejpam-5722	136	20	of	of	ADP
ejpam-5722	136	21	y	y	PROPN
ejpam-5722	136	22	containing	contain	VERB
ejpam-5722	136	23	f(x	f(x	PROPN
ejpam-5722	136	24	)	)	PUNCT
ejpam-5722	136	25	.	.	PUNCT
ejpam-5722	137	1	then	then	ADV
ejpam-5722	137	2	,	,	PUNCT
ejpam-5722	137	3	σ1σ2	σ1σ2	NOUN
ejpam-5722	137	4	-	-	PUNCT
ejpam-5722	137	5	cl(y	cl(y	NOUN
ejpam-5722	137	6	−	−	NOUN
ejpam-5722	137	7	σ1σ2	σ1σ2	NOUN
ejpam-5722	137	8	-	-	NUM
ejpam-5722	137	9	cl(v	cl(v	NOUN
ejpam-5722	137	10	)	)	PUNCT
ejpam-5722	137	11	)	)	PUNCT
ejpam-5722	138	1	∩	∩	PROPN
ejpam-5722	138	2	f(x	f(x	PROPN
ejpam-5722	138	3	)	)	PUNCT
ejpam-5722	138	4	=	=	NOUN
ejpam-5722	138	5	∅	∅	NOUN
ejpam-5722	138	6	and	and	CCONJ
ejpam-5722	138	7	x	x	PART
ejpam-5722	138	8	̸∈	̸∈	PROPN
ejpam-5722	138	9	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	138	10	-	-	PUNCT
ejpam-5722	138	11	cl(y	cl(y	NOUN
ejpam-5722	138	12	−	−	NOUN
ejpam-5722	138	13	σ1σ2	σ1σ2	NOUN
ejpam-5722	138	14	-	-	NUM
ejpam-5722	138	15	cl(v	cl(v	NOUN
ejpam-5722	138	16	)	)	PUNCT
ejpam-5722	138	17	)	)	PUNCT
ejpam-5722	138	18	)	)	PUNCT
ejpam-5722	138	19	.	.	PUNCT
ejpam-5722	139	1	it	it	PRON
ejpam-5722	139	2	follows	follow	VERB
ejpam-5722	139	3	from	from	ADP
ejpam-5722	139	4	(	(	PUNCT
ejpam-5722	139	5	7	7	NUM
ejpam-5722	139	6	)	)	PUNCT
ejpam-5722	139	7	that	that	PRON
ejpam-5722	139	8	x	x	SYM
ejpam-5722	139	9	̸∈	̸∈	PROPN
ejpam-5722	139	10	θ(τ1	θ(τ1	VERB
ejpam-5722	139	11	,	,	PUNCT
ejpam-5722	140	1	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	140	2	−1(y	−1(y	PUNCT
ejpam-5722	141	1	−	−	ADP
ejpam-5722	141	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	141	3	-	-	NUM
ejpam-5722	141	4	cl(v	cl(v	NOUN
ejpam-5722	141	5	)	)	PUNCT
ejpam-5722	141	6	)	)	PUNCT
ejpam-5722	141	7	)	)	PUNCT
ejpam-5722	141	8	.	.	PUNCT
ejpam-5722	142	1	then	then	ADV
ejpam-5722	142	2	,	,	PUNCT
ejpam-5722	142	3	there	there	PRON
ejpam-5722	142	4	exists	exist	VERB
ejpam-5722	142	5	a	a	DET
ejpam-5722	142	6	(	(	PUNCT
ejpam-5722	142	7	τ1	τ1	NOUN
ejpam-5722	142	8	,	,	PUNCT
ejpam-5722	142	9	τ2)s	τ2)s	NOUN
ejpam-5722	142	10	-	-	PUNCT
ejpam-5722	142	11	open	open	ADJ
ejpam-5722	142	12	set	set	NOUN
ejpam-5722	142	13	u	u	NOUN
ejpam-5722	142	14	of	of	ADP
ejpam-5722	142	15	x	x	PUNCT
ejpam-5722	142	16	containing	contain	VERB
ejpam-5722	142	17	x	x	PUNCT
ejpam-5722	142	18	such	such	ADJ
ejpam-5722	142	19	that	that	SCONJ
ejpam-5722	142	20	(	(	PUNCT
ejpam-5722	142	21	τ1	τ1	NOUN
ejpam-5722	142	22	,	,	PUNCT
ejpam-5722	142	23	τ2)-scl(u	τ2)-scl(u	ADJ
ejpam-5722	142	24	)	)	PUNCT
ejpam-5722	142	25	∩	∩	PROPN
ejpam-5722	142	26	f−1(y	f−1(y	NOUN
ejpam-5722	142	27	−	−	NUM
ejpam-5722	142	28	σ1σ2	σ1σ2	NOUN
ejpam-5722	142	29	-	-	NUM
ejpam-5722	142	30	cl(v	cl(v	NOUN
ejpam-5722	142	31	)	)	PUNCT
ejpam-5722	142	32	)	)	PUNCT
ejpam-5722	143	1	=	=	NOUN
ejpam-5722	143	2	∅	∅	NOUN
ejpam-5722	143	3	;	;	PUNCT
ejpam-5722	143	4	hence	hence	ADV
ejpam-5722	143	5	f((τ1	f((τ1	VERB
ejpam-5722	143	6	,	,	PUNCT
ejpam-5722	143	7	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	143	8	)	)	PUNCT
ejpam-5722	143	9	)	)	PUNCT
ejpam-5722	144	1	⊆	⊆	X
ejpam-5722	144	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	144	3	-	-	NUM
ejpam-5722	144	4	cl(v	cl(v	NOUN
ejpam-5722	144	5	)	)	PUNCT
ejpam-5722	144	6	.	.	PUNCT
ejpam-5722	145	1	this	this	PRON
ejpam-5722	145	2	shows	show	VERB
ejpam-5722	145	3	that	that	SCONJ
ejpam-5722	145	4	f	f	PROPN
ejpam-5722	145	5	is	be	AUX
ejpam-5722	145	6	quasi	quasi	NOUN
ejpam-5722	145	7	θ(τ1	θ(τ1	NOUN
ejpam-5722	145	8	,	,	PUNCT
ejpam-5722	145	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	145	10	.	.	PUNCT
ejpam-5722	146	1	definition	definition	NOUN
ejpam-5722	146	2	2	2	NUM
ejpam-5722	146	3	.	.	PUNCT
ejpam-5722	147	1	[	[	X
ejpam-5722	147	2	21	21	NUM
ejpam-5722	147	3	]	]	X
ejpam-5722	147	4	a	a	DET
ejpam-5722	147	5	function	function	NOUN
ejpam-5722	147	6	f	f	NOUN
ejpam-5722	147	7	:	:	PUNCT
ejpam-5722	147	8	(	(	PUNCT
ejpam-5722	147	9	x	x	NOUN
ejpam-5722	147	10	,	,	PUNCT
ejpam-5722	147	11	τ1	τ1	NOUN
ejpam-5722	147	12	,	,	PUNCT
ejpam-5722	147	13	τ2	τ2	NOUN
ejpam-5722	147	14	)	)	PUNCT
ejpam-5722	147	15	→	→	SYM
ejpam-5722	147	16	(	(	PUNCT
ejpam-5722	147	17	y	y	PROPN
ejpam-5722	147	18	,	,	PUNCT
ejpam-5722	147	19	σ1	σ1	PROPN
ejpam-5722	147	20	,	,	PUNCT
ejpam-5722	147	21	σ2	σ2	PROPN
ejpam-5722	147	22	)	)	PUNCT
ejpam-5722	147	23	is	be	AUX
ejpam-5722	147	24	said	say	VERB
ejpam-5722	147	25	to	to	PART
ejpam-5722	147	26	be	be	AUX
ejpam-5722	147	27	almost	almost	ADV
ejpam-5722	147	28	quasi	quasi	ADJ
ejpam-5722	147	29	(	(	PUNCT
ejpam-5722	147	30	τ1	τ1	NOUN
ejpam-5722	147	31	,	,	PUNCT
ejpam-5722	147	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	147	33	at	at	ADP
ejpam-5722	147	34	a	a	DET
ejpam-5722	147	35	point	point	NOUN
ejpam-5722	147	36	x	x	SYM
ejpam-5722	147	37	∈	∈	NOUN
ejpam-5722	147	38	x	x	INTJ
ejpam-5722	147	39	if	if	SCONJ
ejpam-5722	147	40	for	for	ADP
ejpam-5722	147	41	every	every	DET
ejpam-5722	147	42	σ1σ2	σ1σ2	NOUN
ejpam-5722	147	43	-	-	ADJ
ejpam-5722	147	44	open	open	ADJ
ejpam-5722	147	45	set	set	NOUN
ejpam-5722	147	46	v	v	NOUN
ejpam-5722	147	47	of	of	ADP
ejpam-5722	147	48	y	y	NOUN
ejpam-5722	147	49	containing	contain	VERB
ejpam-5722	147	50	f(x	f(x	PROPN
ejpam-5722	147	51	)	)	PUNCT
ejpam-5722	147	52	and	and	CCONJ
ejpam-5722	147	53	each	each	DET
ejpam-5722	147	54	τ1τ2	τ1τ2	ADJ
ejpam-5722	147	55	-	-	ADJ
ejpam-5722	147	56	open	open	ADJ
ejpam-5722	147	57	set	set	ADJ
ejpam-5722	147	58	u	u	NOUN
ejpam-5722	147	59	of	of	ADP
ejpam-5722	147	60	x	x	PUNCT
ejpam-5722	147	61	containing	contain	VERB
ejpam-5722	147	62	x	x	PRON
ejpam-5722	147	63	,	,	PUNCT
ejpam-5722	147	64	there	there	PRON
ejpam-5722	147	65	exists	exist	VERB
ejpam-5722	147	66	a	a	DET
ejpam-5722	147	67	nonempty	nonempty	ADJ
ejpam-5722	147	68	τ1τ2	τ1τ2	NOUN
ejpam-5722	147	69	-	-	ADJ
ejpam-5722	147	70	open	open	ADJ
ejpam-5722	147	71	set	set	NOUN
ejpam-5722	147	72	g	g	PROPN
ejpam-5722	147	73	such	such	ADJ
ejpam-5722	147	74	that	that	SCONJ
ejpam-5722	147	75	g	g	PROPN
ejpam-5722	147	76	⊆	⊆	NUM
ejpam-5722	147	77	u	u	NOUN
ejpam-5722	147	78	,	,	PUNCT
ejpam-5722	147	79	f(g	f(g	PROPN
ejpam-5722	147	80	)	)	PUNCT
ejpam-5722	147	81	⊆	⊆	NUM
ejpam-5722	147	82	(	(	PUNCT
ejpam-5722	147	83	σ1	σ1	PROPN
ejpam-5722	147	84	,	,	PUNCT
ejpam-5722	147	85	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5722	147	86	)	)	PUNCT
ejpam-5722	147	87	.	.	PUNCT
ejpam-5722	148	1	a	a	DET
ejpam-5722	148	2	function	function	NOUN
ejpam-5722	148	3	f	f	NOUN
ejpam-5722	148	4	:	:	PUNCT
ejpam-5722	148	5	(	(	PUNCT
ejpam-5722	148	6	x	x	NOUN
ejpam-5722	148	7	,	,	PUNCT
ejpam-5722	148	8	τ1	τ1	NOUN
ejpam-5722	148	9	,	,	PUNCT
ejpam-5722	148	10	τ2	τ2	NOUN
ejpam-5722	148	11	)	)	PUNCT
ejpam-5722	148	12	→	→	SYM
ejpam-5722	148	13	(	(	PUNCT
ejpam-5722	148	14	y	y	PROPN
ejpam-5722	148	15	,	,	PUNCT
ejpam-5722	148	16	σ1	σ1	PROPN
ejpam-5722	148	17	,	,	PUNCT
ejpam-5722	148	18	σ2	σ2	PROPN
ejpam-5722	148	19	)	)	PUNCT
ejpam-5722	148	20	is	be	AUX
ejpam-5722	148	21	said	say	VERB
ejpam-5722	148	22	to	to	PART
ejpam-5722	148	23	be	be	AUX
ejpam-5722	148	24	almost	almost	ADV
ejpam-5722	148	25	quasi	quasi	ADJ
ejpam-5722	148	26	(	(	PUNCT
ejpam-5722	148	27	τ1	τ1	NOUN
ejpam-5722	148	28	,	,	PUNCT
ejpam-5722	148	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	148	30	if	if	SCONJ
ejpam-5722	148	31	f	f	PROPN
ejpam-5722	148	32	is	be	AUX
ejpam-5722	148	33	almost	almost	ADV
ejpam-5722	148	34	quasi	quasi	ADJ
ejpam-5722	148	35	(	(	PUNCT
ejpam-5722	148	36	τ1	τ1	NOUN
ejpam-5722	148	37	,	,	PUNCT
ejpam-5722	148	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	148	39	at	at	ADP
ejpam-5722	148	40	each	each	DET
ejpam-5722	148	41	point	point	NOUN
ejpam-5722	148	42	of	of	ADP
ejpam-5722	148	43	x.	x.	PROPN
ejpam-5722	148	44	lemma	lemma	PROPN
ejpam-5722	149	1	3	3	X
ejpam-5722	149	2	.	.	PUNCT
ejpam-5722	150	1	[	[	X
ejpam-5722	150	2	21	21	NUM
ejpam-5722	150	3	]	]	PUNCT
ejpam-5722	150	4	for	for	ADP
ejpam-5722	150	5	a	a	DET
ejpam-5722	150	6	function	function	NOUN
ejpam-5722	150	7	f	f	NOUN
ejpam-5722	150	8	:	:	PUNCT
ejpam-5722	150	9	(	(	PUNCT
ejpam-5722	150	10	x	x	NOUN
ejpam-5722	150	11	,	,	PUNCT
ejpam-5722	150	12	τ1	τ1	NOUN
ejpam-5722	150	13	,	,	PUNCT
ejpam-5722	150	14	τ2	τ2	NOUN
ejpam-5722	150	15	)	)	PUNCT
ejpam-5722	150	16	→	→	SYM
ejpam-5722	150	17	(	(	PUNCT
ejpam-5722	150	18	y	y	PROPN
ejpam-5722	150	19	,	,	PUNCT
ejpam-5722	150	20	σ1	σ1	PROPN
ejpam-5722	150	21	,	,	PUNCT
ejpam-5722	150	22	σ2	σ2	NOUN
ejpam-5722	150	23	)	)	PUNCT
ejpam-5722	150	24	,	,	PUNCT
ejpam-5722	150	25	the	the	DET
ejpam-5722	150	26	following	follow	VERB
ejpam-5722	150	27	properties	property	NOUN
ejpam-5722	150	28	are	be	AUX
ejpam-5722	150	29	equivalent	equivalent	ADJ
ejpam-5722	150	30	:	:	PUNCT
ejpam-5722	150	31	(	(	PUNCT
ejpam-5722	150	32	1	1	X
ejpam-5722	150	33	)	)	PUNCT
ejpam-5722	150	34	f	f	NOUN
ejpam-5722	150	35	is	be	AUX
ejpam-5722	150	36	almost	almost	ADV
ejpam-5722	150	37	quasi	quasi	ADJ
ejpam-5722	150	38	(	(	PUNCT
ejpam-5722	150	39	τ1	τ1	NOUN
ejpam-5722	150	40	,	,	PUNCT
ejpam-5722	150	41	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	150	42	;	;	PUNCT
ejpam-5722	150	43	(	(	PUNCT
ejpam-5722	150	44	2	2	X
ejpam-5722	150	45	)	)	PUNCT
ejpam-5722	150	46	for	for	ADP
ejpam-5722	150	47	each	each	DET
ejpam-5722	150	48	x	x	SYM
ejpam-5722	150	49	∈	∈	PROPN
ejpam-5722	150	50	x	x	X
ejpam-5722	150	51	and	and	CCONJ
ejpam-5722	150	52	every	every	DET
ejpam-5722	150	53	σ1σ2	σ1σ2	NUM
ejpam-5722	150	54	-	-	ADJ
ejpam-5722	150	55	open	open	ADJ
ejpam-5722	150	56	set	set	NOUN
ejpam-5722	150	57	v	v	NOUN
ejpam-5722	150	58	of	of	ADP
ejpam-5722	150	59	y	y	NOUN
ejpam-5722	150	60	containing	contain	VERB
ejpam-5722	150	61	f(x	f(x	PROPN
ejpam-5722	150	62	)	)	PUNCT
ejpam-5722	150	63	,	,	PUNCT
ejpam-5722	150	64	there	there	PRON
ejpam-5722	150	65	exists	exist	VERB
ejpam-5722	150	66	a	a	DET
ejpam-5722	150	67	(	(	PUNCT
ejpam-5722	150	68	τ1	τ1	NOUN
ejpam-5722	150	69	,	,	PUNCT
ejpam-5722	150	70	τ2)s	τ2)s	NOUN
ejpam-5722	150	71	-	-	PUNCT
ejpam-5722	150	72	open	open	ADJ
ejpam-5722	150	73	set	set	NOUN
ejpam-5722	150	74	u	u	NOUN
ejpam-5722	150	75	of	of	ADP
ejpam-5722	150	76	x	x	PUNCT
ejpam-5722	150	77	containing	contain	VERB
ejpam-5722	150	78	x	x	PUNCT
ejpam-5722	150	79	such	such	ADJ
ejpam-5722	150	80	that	that	DET
ejpam-5722	150	81	f(u	f(u	PROPN
ejpam-5722	150	82	)	)	PUNCT
ejpam-5722	150	83	⊆	⊆	NUM
ejpam-5722	150	84	(	(	PUNCT
ejpam-5722	150	85	σ1	σ1	PROPN
ejpam-5722	150	86	,	,	PUNCT
ejpam-5722	150	87	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5722	150	88	)	)	PUNCT
ejpam-5722	150	89	;	;	PUNCT
ejpam-5722	150	90	(	(	PUNCT
ejpam-5722	150	91	3	3	X
ejpam-5722	150	92	)	)	PUNCT
ejpam-5722	150	93	f−1(v	f−1(v	NOUN
ejpam-5722	150	94	)	)	PUNCT
ejpam-5722	150	95	is	be	AUX
ejpam-5722	150	96	(	(	PUNCT
ejpam-5722	150	97	τ1	τ1	NOUN
ejpam-5722	150	98	,	,	PUNCT
ejpam-5722	150	99	τ2)s	τ2)s	NOUN
ejpam-5722	150	100	-	-	PUNCT
ejpam-5722	150	101	open	open	ADJ
ejpam-5722	150	102	in	in	ADP
ejpam-5722	150	103	x	x	PUNCT
ejpam-5722	150	104	for	for	ADP
ejpam-5722	150	105	every	every	DET
ejpam-5722	150	106	(	(	PUNCT
ejpam-5722	150	107	σ1	σ1	PROPN
ejpam-5722	150	108	,	,	PUNCT
ejpam-5722	150	109	σ2)r	σ2)r	NOUN
ejpam-5722	150	110	-	-	PUNCT
ejpam-5722	150	111	open	open	ADJ
ejpam-5722	150	112	set	set	VERB
ejpam-5722	150	113	v	v	NOUN
ejpam-5722	150	114	of	of	ADP
ejpam-5722	150	115	y	y	PROPN
ejpam-5722	150	116	;	;	PUNCT
ejpam-5722	150	117	(	(	PUNCT
ejpam-5722	150	118	4	4	X
ejpam-5722	150	119	)	)	PUNCT
ejpam-5722	150	120	f−1(v	f−1(v	NOUN
ejpam-5722	150	121	)	)	PUNCT
ejpam-5722	151	1	⊆	⊆	NUM
ejpam-5722	151	2	(	(	PUNCT
ejpam-5722	151	3	τ1	τ1	NOUN
ejpam-5722	151	4	,	,	PUNCT
ejpam-5722	151	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5722	151	6	−1((σ1	−1((σ1	NOUN
ejpam-5722	151	7	,	,	PUNCT
ejpam-5722	151	8	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5722	151	9	)	)	PUNCT
ejpam-5722	151	10	)	)	PUNCT
ejpam-5722	151	11	)	)	PUNCT
ejpam-5722	152	1	for	for	ADP
ejpam-5722	152	2	every	every	DET
ejpam-5722	152	3	σ1σ2	σ1σ2	NOUN
ejpam-5722	152	4	-	-	ADJ
ejpam-5722	152	5	open	open	ADJ
ejpam-5722	152	6	set	set	NOUN
ejpam-5722	152	7	v	v	NOUN
ejpam-5722	152	8	of	of	ADP
ejpam-5722	152	9	y	y	PROPN
ejpam-5722	152	10	;	;	PUNCT
ejpam-5722	152	11	(	(	PUNCT
ejpam-5722	152	12	5	5	X
ejpam-5722	152	13	)	)	PUNCT
ejpam-5722	152	14	(	(	PUNCT
ejpam-5722	152	15	τ1	τ1	NOUN
ejpam-5722	152	16	,	,	PUNCT
ejpam-5722	152	17	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	152	18	−1(σ1σ2	−1(σ1σ2	ADV
ejpam-5722	152	19	-	-	PUNCT
ejpam-5722	152	20	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5722	152	21	-	-	PUNCT
ejpam-5722	152	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	152	23	-	-	PUNCT
ejpam-5722	152	24	cl(b	cl(b	NOUN
ejpam-5722	152	25	)	)	PUNCT
ejpam-5722	152	26	)	)	PUNCT
ejpam-5722	152	27	)	)	PUNCT
ejpam-5722	152	28	)	)	PUNCT
ejpam-5722	152	29	)	)	PUNCT
ejpam-5722	153	1	⊆	⊆	NUM
ejpam-5722	153	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	153	3	-	-	PUNCT
ejpam-5722	153	4	cl(b	cl(b	NOUN
ejpam-5722	153	5	)	)	PUNCT
ejpam-5722	153	6	)	)	PUNCT
ejpam-5722	153	7	for	for	ADP
ejpam-5722	153	8	every	every	DET
ejpam-5722	153	9	subset	subset	NOUN
ejpam-5722	153	10	b	b	PROPN
ejpam-5722	153	11	of	of	ADP
ejpam-5722	153	12	y	y	PROPN
ejpam-5722	153	13	;	;	PUNCT
ejpam-5722	153	14	(	(	PUNCT
ejpam-5722	153	15	6	6	X
ejpam-5722	153	16	)	)	PUNCT
ejpam-5722	153	17	f−1(v	f−1(v	NOUN
ejpam-5722	153	18	)	)	PUNCT
ejpam-5722	153	19	⊆	⊆	X
ejpam-5722	153	20	τ1τ2	τ1τ2	NOUN
ejpam-5722	153	21	-	-	NUM
ejpam-5722	153	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5722	153	23	-	-	PUNCT
ejpam-5722	153	24	int(f	int(f	VERB
ejpam-5722	153	25	−1((σ1	−1((σ1	NOUN
ejpam-5722	153	26	,	,	PUNCT
ejpam-5722	153	27	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-5722	153	28	)	)	PUNCT
ejpam-5722	153	29	)	)	PUNCT
ejpam-5722	153	30	)	)	PUNCT
ejpam-5722	153	31	)	)	PUNCT
ejpam-5722	154	1	for	for	ADP
ejpam-5722	154	2	every	every	DET
ejpam-5722	154	3	σ1σ2	σ1σ2	NOUN
ejpam-5722	154	4	-	-	ADJ
ejpam-5722	154	5	open	open	ADJ
ejpam-5722	154	6	set	set	NOUN
ejpam-5722	154	7	v	v	NOUN
ejpam-5722	154	8	of	of	ADP
ejpam-5722	154	9	y	y	PROPN
ejpam-5722	154	10	.	.	PUNCT
ejpam-5722	155	1	definition	definition	NOUN
ejpam-5722	155	2	3	3	NUM
ejpam-5722	155	3	.	.	PUNCT
ejpam-5722	156	1	[	[	X
ejpam-5722	156	2	16	16	NUM
ejpam-5722	156	3	]	]	PUNCT
ejpam-5722	156	4	a	a	DET
ejpam-5722	156	5	function	function	NOUN
ejpam-5722	156	6	f	f	NOUN
ejpam-5722	156	7	:	:	PUNCT
ejpam-5722	156	8	(	(	PUNCT
ejpam-5722	156	9	x	x	NOUN
ejpam-5722	156	10	,	,	PUNCT
ejpam-5722	156	11	τ1	τ1	NOUN
ejpam-5722	156	12	,	,	PUNCT
ejpam-5722	156	13	τ2	τ2	NOUN
ejpam-5722	156	14	)	)	PUNCT
ejpam-5722	156	15	→	→	SYM
ejpam-5722	156	16	(	(	PUNCT
ejpam-5722	156	17	y	y	PROPN
ejpam-5722	156	18	,	,	PUNCT
ejpam-5722	156	19	σ1	σ1	PROPN
ejpam-5722	156	20	,	,	PUNCT
ejpam-5722	156	21	σ2	σ2	PROPN
ejpam-5722	156	22	)	)	PUNCT
ejpam-5722	156	23	is	be	AUX
ejpam-5722	156	24	said	say	VERB
ejpam-5722	156	25	to	to	PART
ejpam-5722	156	26	be	be	AUX
ejpam-5722	156	27	weakly	weakly	ADJ
ejpam-5722	156	28	quasi	quasi	NOUN
ejpam-5722	156	29	(	(	PUNCT
ejpam-5722	156	30	τ1	τ1	NOUN
ejpam-5722	156	31	,	,	PUNCT
ejpam-5722	156	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	156	33	at	at	ADP
ejpam-5722	156	34	a	a	DET
ejpam-5722	156	35	point	point	NOUN
ejpam-5722	156	36	x	x	SYM
ejpam-5722	156	37	∈	∈	NOUN
ejpam-5722	156	38	x	x	PUNCT
ejpam-5722	156	39	if	if	SCONJ
ejpam-5722	156	40	for	for	ADP
ejpam-5722	156	41	each	each	DET
ejpam-5722	156	42	σ1σ2	σ1σ2	VERB
ejpam-5722	156	43	-	-	ADJ
ejpam-5722	156	44	open	open	ADJ
ejpam-5722	156	45	set	set	NOUN
ejpam-5722	156	46	v	v	NOUN
ejpam-5722	156	47	of	of	ADP
ejpam-5722	156	48	y	y	NOUN
ejpam-5722	156	49	containing	contain	VERB
ejpam-5722	156	50	f(x	f(x	PROPN
ejpam-5722	156	51	)	)	PUNCT
ejpam-5722	156	52	and	and	CCONJ
ejpam-5722	156	53	each	each	DET
ejpam-5722	156	54	τ1τ2	τ1τ2	ADJ
ejpam-5722	156	55	-	-	ADJ
ejpam-5722	156	56	open	open	ADJ
ejpam-5722	156	57	set	set	ADJ
ejpam-5722	156	58	u	u	NOUN
ejpam-5722	156	59	of	of	ADP
ejpam-5722	156	60	x	x	PUNCT
ejpam-5722	156	61	containing	contain	VERB
ejpam-5722	156	62	x	x	PRON
ejpam-5722	156	63	,	,	PUNCT
ejpam-5722	156	64	there	there	PRON
ejpam-5722	156	65	exists	exist	VERB
ejpam-5722	156	66	a	a	DET
ejpam-5722	156	67	nonempty	nonempty	ADJ
ejpam-5722	156	68	τ1τ2	τ1τ2	NOUN
ejpam-5722	156	69	-	-	ADJ
ejpam-5722	156	70	open	open	ADJ
ejpam-5722	156	71	set	set	NOUN
ejpam-5722	156	72	g	g	PROPN
ejpam-5722	157	1	such	such	ADJ
ejpam-5722	157	2	that	that	SCONJ
ejpam-5722	157	3	g	g	PROPN
ejpam-5722	157	4	⊆	⊆	NUM
ejpam-5722	157	5	u	u	NOUN
ejpam-5722	157	6	,	,	PUNCT
ejpam-5722	157	7	f(g	f(g	PROPN
ejpam-5722	157	8	)	)	PUNCT
ejpam-5722	157	9	⊆	⊆	NUM
ejpam-5722	157	10	σ1σ2	σ1σ2	NOUN
ejpam-5722	157	11	-	-	NUM
ejpam-5722	157	12	cl(v	cl(v	NOUN
ejpam-5722	157	13	)	)	PUNCT
ejpam-5722	157	14	.	.	PUNCT
ejpam-5722	158	1	a	a	DET
ejpam-5722	158	2	function	function	NOUN
ejpam-5722	158	3	f	f	NOUN
ejpam-5722	158	4	:	:	PUNCT
ejpam-5722	158	5	(	(	PUNCT
ejpam-5722	158	6	x	x	NOUN
ejpam-5722	158	7	,	,	PUNCT
ejpam-5722	158	8	τ1	τ1	NOUN
ejpam-5722	158	9	,	,	PUNCT
ejpam-5722	158	10	τ2	τ2	NOUN
ejpam-5722	158	11	)	)	PUNCT
ejpam-5722	158	12	→	→	SYM
ejpam-5722	158	13	(	(	PUNCT
ejpam-5722	158	14	y	y	PROPN
ejpam-5722	158	15	,	,	PUNCT
ejpam-5722	158	16	σ1	σ1	PROPN
ejpam-5722	158	17	,	,	PUNCT
ejpam-5722	158	18	σ2	σ2	PROPN
ejpam-5722	158	19	)	)	PUNCT
ejpam-5722	158	20	is	be	AUX
ejpam-5722	158	21	said	say	VERB
ejpam-5722	158	22	to	to	PART
ejpam-5722	158	23	be	be	AUX
ejpam-5722	158	24	weakly	weakly	ADJ
ejpam-5722	158	25	quasi	quasi	NOUN
ejpam-5722	158	26	(	(	PUNCT
ejpam-5722	158	27	τ1	τ1	NOUN
ejpam-5722	158	28	,	,	PUNCT
ejpam-5722	158	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	158	30	if	if	SCONJ
ejpam-5722	158	31	f	f	PROPN
ejpam-5722	158	32	is	be	AUX
ejpam-5722	158	33	weakly	weakly	ADJ
ejpam-5722	158	34	quasi	quasi	NOUN
ejpam-5722	158	35	(	(	PUNCT
ejpam-5722	158	36	τ1	τ1	NOUN
ejpam-5722	158	37	,	,	PUNCT
ejpam-5722	158	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	158	39	at	at	ADP
ejpam-5722	158	40	each	each	DET
ejpam-5722	158	41	point	point	NOUN
ejpam-5722	158	42	of	of	ADP
ejpam-5722	158	43	x.	x.	PROPN
ejpam-5722	158	44	n.	n.	PROPN
ejpam-5722	158	45	srisarakham	srisarakham	PROPN
ejpam-5722	158	46	,	,	PUNCT
ejpam-5722	158	47	s.	s.	PROPN
ejpam-5722	158	48	sompong	sompong	PROPN
ejpam-5722	158	49	,	,	PUNCT
ejpam-5722	158	50	c.	c.	PROPN
ejpam-5722	158	51	boonpok	boonpok	PROPN
ejpam-5722	158	52	/	/	SYM
ejpam-5722	158	53	eur	eur	PROPN
ejpam-5722	158	54	.	.	PUNCT
ejpam-5722	159	1	j.	j.	PROPN
ejpam-5722	159	2	pure	pure	PROPN
ejpam-5722	159	3	appl	appl	PROPN
ejpam-5722	159	4	.	.	PROPN
ejpam-5722	159	5	math	math	PROPN
ejpam-5722	159	6	,	,	PUNCT
ejpam-5722	159	7	18	18	NUM
ejpam-5722	159	8	(	(	PUNCT
ejpam-5722	159	9	1	1	NUM
ejpam-5722	159	10	)	)	PUNCT
ejpam-5722	159	11	(	(	PUNCT
ejpam-5722	159	12	2025	2025	NUM
ejpam-5722	159	13	)	)	PUNCT
ejpam-5722	159	14	,	,	PUNCT
ejpam-5722	159	15	5722	5722	NUM
ejpam-5722	159	16	6	6	NUM
ejpam-5722	159	17	of	of	ADP
ejpam-5722	159	18	12	12	NUM
ejpam-5722	159	19	lemma	lemma	PROPN
ejpam-5722	159	20	4	4	NUM
ejpam-5722	159	21	.	.	PUNCT
ejpam-5722	160	1	[	[	X
ejpam-5722	160	2	16	16	NUM
ejpam-5722	160	3	]	]	PUNCT
ejpam-5722	160	4	for	for	ADP
ejpam-5722	160	5	a	a	DET
ejpam-5722	160	6	function	function	NOUN
ejpam-5722	160	7	f	f	NOUN
ejpam-5722	160	8	:	:	PUNCT
ejpam-5722	160	9	(	(	PUNCT
ejpam-5722	160	10	x	x	NOUN
ejpam-5722	160	11	,	,	PUNCT
ejpam-5722	160	12	τ1	τ1	NOUN
ejpam-5722	160	13	,	,	PUNCT
ejpam-5722	160	14	τ2	τ2	NOUN
ejpam-5722	160	15	)	)	PUNCT
ejpam-5722	160	16	→	→	SYM
ejpam-5722	160	17	(	(	PUNCT
ejpam-5722	160	18	y	y	PROPN
ejpam-5722	160	19	,	,	PUNCT
ejpam-5722	160	20	σ1	σ1	PROPN
ejpam-5722	160	21	,	,	PUNCT
ejpam-5722	160	22	σ2	σ2	NOUN
ejpam-5722	160	23	)	)	PUNCT
ejpam-5722	160	24	,	,	PUNCT
ejpam-5722	160	25	the	the	DET
ejpam-5722	160	26	following	follow	VERB
ejpam-5722	160	27	properties	property	NOUN
ejpam-5722	160	28	are	be	AUX
ejpam-5722	160	29	equivalent	equivalent	ADJ
ejpam-5722	160	30	:	:	PUNCT
ejpam-5722	160	31	(	(	PUNCT
ejpam-5722	160	32	1	1	X
ejpam-5722	160	33	)	)	PUNCT
ejpam-5722	160	34	f	f	PROPN
ejpam-5722	160	35	is	be	AUX
ejpam-5722	160	36	weakly	weakly	ADJ
ejpam-5722	160	37	quasi	quasi	NOUN
ejpam-5722	160	38	(	(	PUNCT
ejpam-5722	160	39	τ1	τ1	NOUN
ejpam-5722	160	40	,	,	PUNCT
ejpam-5722	160	41	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	160	42	;	;	PUNCT
ejpam-5722	160	43	(	(	PUNCT
ejpam-5722	160	44	2	2	X
ejpam-5722	160	45	)	)	PUNCT
ejpam-5722	160	46	for	for	ADP
ejpam-5722	160	47	each	each	DET
ejpam-5722	160	48	x	x	SYM
ejpam-5722	160	49	∈	∈	PROPN
ejpam-5722	160	50	x	x	X
ejpam-5722	160	51	and	and	CCONJ
ejpam-5722	160	52	each	each	DET
ejpam-5722	160	53	σ1σ2	σ1σ2	VERB
ejpam-5722	160	54	-	-	ADJ
ejpam-5722	160	55	open	open	ADJ
ejpam-5722	160	56	set	set	NOUN
ejpam-5722	160	57	v	v	NOUN
ejpam-5722	160	58	of	of	ADP
ejpam-5722	160	59	y	y	NOUN
ejpam-5722	160	60	containing	contain	VERB
ejpam-5722	160	61	f(x	f(x	PROPN
ejpam-5722	160	62	)	)	PUNCT
ejpam-5722	160	63	,	,	PUNCT
ejpam-5722	160	64	there	there	PRON
ejpam-5722	160	65	exists	exist	VERB
ejpam-5722	160	66	a	a	DET
ejpam-5722	160	67	(	(	PUNCT
ejpam-5722	160	68	τ1	τ1	NOUN
ejpam-5722	160	69	,	,	PUNCT
ejpam-5722	160	70	τ2)s	τ2)s	NOUN
ejpam-5722	160	71	-	-	PUNCT
ejpam-5722	160	72	open	open	ADJ
ejpam-5722	160	73	set	set	NOUN
ejpam-5722	160	74	u	u	NOUN
ejpam-5722	160	75	of	of	ADP
ejpam-5722	160	76	x	x	PUNCT
ejpam-5722	160	77	containing	contain	VERB
ejpam-5722	160	78	x	x	PUNCT
ejpam-5722	160	79	such	such	ADJ
ejpam-5722	160	80	that	that	DET
ejpam-5722	160	81	f(u	f(u	PROPN
ejpam-5722	160	82	)	)	PUNCT
ejpam-5722	160	83	⊆	⊆	NUM
ejpam-5722	160	84	σ1σ2	σ1σ2	NOUN
ejpam-5722	160	85	-	-	NUM
ejpam-5722	160	86	cl(v	cl(v	NOUN
ejpam-5722	160	87	)	)	PUNCT
ejpam-5722	160	88	;	;	PUNCT
ejpam-5722	160	89	(	(	PUNCT
ejpam-5722	160	90	3	3	X
ejpam-5722	160	91	)	)	PUNCT
ejpam-5722	160	92	τ1τ2	τ1τ2	NOUN
ejpam-5722	160	93	-	-	NOUN
ejpam-5722	160	94	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5722	160	95	-	-	PUNCT
ejpam-5722	160	96	cl(f	cl(f	NOUN
ejpam-5722	160	97	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	160	98	-	-	PUNCT
ejpam-5722	160	99	int(k	int(k	NUM
ejpam-5722	160	100	)	)	PUNCT
ejpam-5722	160	101	)	)	PUNCT
ejpam-5722	160	102	)	)	PUNCT
ejpam-5722	160	103	)	)	PUNCT
ejpam-5722	161	1	⊆	⊆	NUM
ejpam-5722	161	2	f−1(k	f−1(k	PROPN
ejpam-5722	161	3	)	)	PUNCT
ejpam-5722	161	4	for	for	ADP
ejpam-5722	161	5	every	every	DET
ejpam-5722	161	6	σ1σ2	σ1σ2	NUM
ejpam-5722	161	7	-	-	PUNCT
ejpam-5722	161	8	closed	closed	ADJ
ejpam-5722	161	9	set	set	NOUN
ejpam-5722	161	10	k	k	PROPN
ejpam-5722	161	11	of	of	ADP
ejpam-5722	161	12	y	y	PROPN
ejpam-5722	161	13	;	;	PUNCT
ejpam-5722	161	14	(	(	PUNCT
ejpam-5722	161	15	4	4	X
ejpam-5722	161	16	)	)	PUNCT
ejpam-5722	161	17	f−1(v	f−1(v	NOUN
ejpam-5722	161	18	)	)	PUNCT
ejpam-5722	162	1	⊆	⊆	NUM
ejpam-5722	162	2	(	(	PUNCT
ejpam-5722	162	3	τ1	τ1	NOUN
ejpam-5722	162	4	,	,	PUNCT
ejpam-5722	162	5	τ2)-sint(f	τ2)-sint(f	PUNCT
ejpam-5722	162	6	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	162	7	-	-	PUNCT
ejpam-5722	162	8	cl(v	cl(v	NOUN
ejpam-5722	162	9	)	)	PUNCT
ejpam-5722	162	10	)	)	PUNCT
ejpam-5722	162	11	)	)	PUNCT
ejpam-5722	162	12	for	for	ADP
ejpam-5722	162	13	every	every	DET
ejpam-5722	162	14	σ1σ2	σ1σ2	NOUN
ejpam-5722	162	15	-	-	ADJ
ejpam-5722	162	16	open	open	ADJ
ejpam-5722	162	17	set	set	NOUN
ejpam-5722	162	18	v	v	NOUN
ejpam-5722	162	19	of	of	ADP
ejpam-5722	162	20	y	y	PROPN
ejpam-5722	162	21	;	;	PUNCT
ejpam-5722	162	22	(	(	PUNCT
ejpam-5722	162	23	5	5	X
ejpam-5722	162	24	)	)	PUNCT
ejpam-5722	162	25	(	(	PUNCT
ejpam-5722	162	26	τ1	τ1	NOUN
ejpam-5722	162	27	,	,	PUNCT
ejpam-5722	162	28	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	162	29	−1(v	−1(v	PROPN
ejpam-5722	162	30	)	)	PUNCT
ejpam-5722	162	31	)	)	PUNCT
ejpam-5722	163	1	⊆	⊆	NUM
ejpam-5722	163	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	163	3	-	-	PUNCT
ejpam-5722	163	4	cl(v	cl(v	NOUN
ejpam-5722	163	5	)	)	PUNCT
ejpam-5722	163	6	)	)	PUNCT
ejpam-5722	163	7	for	for	ADP
ejpam-5722	163	8	every	every	DET
ejpam-5722	163	9	σ1σ2	σ1σ2	NOUN
ejpam-5722	163	10	-	-	ADJ
ejpam-5722	163	11	open	open	ADJ
ejpam-5722	163	12	set	set	NOUN
ejpam-5722	163	13	v	v	NOUN
ejpam-5722	163	14	of	of	ADP
ejpam-5722	163	15	y	y	PROPN
ejpam-5722	163	16	.	.	PUNCT
ejpam-5722	164	1	theorem	theorem	NOUN
ejpam-5722	164	2	2	2	NUM
ejpam-5722	164	3	.	.	PUNCT
ejpam-5722	165	1	if	if	SCONJ
ejpam-5722	165	2	a	a	DET
ejpam-5722	165	3	function	function	NOUN
ejpam-5722	165	4	f	f	X
ejpam-5722	165	5	:	:	PUNCT
ejpam-5722	165	6	(	(	PUNCT
ejpam-5722	165	7	x	x	NOUN
ejpam-5722	165	8	,	,	PUNCT
ejpam-5722	165	9	τ1	τ1	NOUN
ejpam-5722	165	10	,	,	PUNCT
ejpam-5722	165	11	τ2	τ2	NOUN
ejpam-5722	165	12	)	)	PUNCT
ejpam-5722	165	13	→	→	SYM
ejpam-5722	165	14	(	(	PUNCT
ejpam-5722	165	15	y	y	PROPN
ejpam-5722	165	16	,	,	PUNCT
ejpam-5722	165	17	σ1	σ1	PROPN
ejpam-5722	165	18	,	,	PUNCT
ejpam-5722	165	19	σ2	σ2	NOUN
ejpam-5722	165	20	)	)	PUNCT
ejpam-5722	165	21	is	be	AUX
ejpam-5722	165	22	weakly	weakly	ADJ
ejpam-5722	165	23	quasi	quasi	NOUN
ejpam-5722	165	24	(	(	PUNCT
ejpam-5722	165	25	τ1	τ1	PROPN
ejpam-5722	165	26	,	,	PUNCT
ejpam-5722	165	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	165	28	and	and	CCONJ
ejpam-5722	165	29	almost	almost	ADV
ejpam-5722	165	30	quasi	quasi	NOUN
ejpam-5722	165	31	(	(	PUNCT
ejpam-5722	165	32	τ1	τ1	NOUN
ejpam-5722	165	33	,	,	PUNCT
ejpam-5722	165	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	165	35	,	,	PUNCT
ejpam-5722	165	36	then	then	ADV
ejpam-5722	165	37	f	f	PROPN
ejpam-5722	165	38	is	be	AUX
ejpam-5722	165	39	quasi	quasi	NOUN
ejpam-5722	165	40	θ(τ1	θ(τ1	NOUN
ejpam-5722	165	41	,	,	PUNCT
ejpam-5722	165	42	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	165	43	.	.	PUNCT
ejpam-5722	166	1	proof	proof	NOUN
ejpam-5722	166	2	.	.	PUNCT
ejpam-5722	167	1	let	let	VERB
ejpam-5722	167	2	x	x	PUNCT
ejpam-5722	167	3	∈	∈	PROPN
ejpam-5722	167	4	x	x	X
ejpam-5722	167	5	and	and	CCONJ
ejpam-5722	167	6	v	v	X
ejpam-5722	167	7	be	be	AUX
ejpam-5722	167	8	any	any	DET
ejpam-5722	167	9	σ1σ2	σ1σ2	NOUN
ejpam-5722	167	10	-	-	ADJ
ejpam-5722	167	11	open	open	ADJ
ejpam-5722	167	12	set	set	NOUN
ejpam-5722	167	13	of	of	ADP
ejpam-5722	167	14	y	y	PROPN
ejpam-5722	167	15	containing	contain	VERB
ejpam-5722	167	16	f(x	f(x	PROPN
ejpam-5722	167	17	)	)	PUNCT
ejpam-5722	167	18	.	.	PUNCT
ejpam-5722	168	1	since	since	SCONJ
ejpam-5722	168	2	f	f	PROPN
ejpam-5722	168	3	is	be	AUX
ejpam-5722	168	4	weakly	weakly	ADJ
ejpam-5722	168	5	quasi	quasi	NOUN
ejpam-5722	168	6	(	(	PUNCT
ejpam-5722	168	7	τ1	τ1	NOUN
ejpam-5722	168	8	,	,	PUNCT
ejpam-5722	168	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	168	10	,	,	PUNCT
ejpam-5722	168	11	by	by	ADP
ejpam-5722	168	12	lemma	lemma	PROPN
ejpam-5722	168	13	4	4	NUM
ejpam-5722	168	14	,	,	PUNCT
ejpam-5722	168	15	there	there	PRON
ejpam-5722	168	16	exists	exist	VERB
ejpam-5722	168	17	a	a	DET
ejpam-5722	168	18	(	(	PUNCT
ejpam-5722	168	19	τ1	τ1	NOUN
ejpam-5722	168	20	,	,	PUNCT
ejpam-5722	168	21	τ2)s	τ2)s	NOUN
ejpam-5722	168	22	-	-	PUNCT
ejpam-5722	168	23	open	open	ADJ
ejpam-5722	168	24	set	set	NOUN
ejpam-5722	168	25	u	u	NOUN
ejpam-5722	168	26	of	of	ADP
ejpam-5722	168	27	x	x	PUNCT
ejpam-5722	168	28	containing	contain	VERB
ejpam-5722	168	29	x	x	PUNCT
ejpam-5722	168	30	such	such	ADJ
ejpam-5722	168	31	that	that	DET
ejpam-5722	168	32	f(u	f(u	PROPN
ejpam-5722	168	33	)	)	PUNCT
ejpam-5722	168	34	⊆	⊆	NUM
ejpam-5722	168	35	σ1σ2	σ1σ2	NOUN
ejpam-5722	168	36	-	-	NUM
ejpam-5722	168	37	cl(v	cl(v	NOUN
ejpam-5722	168	38	)	)	PUNCT
ejpam-5722	168	39	and	and	CCONJ
ejpam-5722	168	40	hence	hence	ADV
ejpam-5722	168	41	u	u	NOUN
ejpam-5722	168	42	⊆	⊆	NUM
ejpam-5722	168	43	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	168	44	-	-	PUNCT
ejpam-5722	168	45	cl(v	cl(v	NOUN
ejpam-5722	168	46	)	)	PUNCT
ejpam-5722	168	47	)	)	PUNCT
ejpam-5722	168	48	.	.	PUNCT
ejpam-5722	169	1	since	since	SCONJ
ejpam-5722	169	2	f	f	PROPN
ejpam-5722	169	3	is	be	AUX
ejpam-5722	169	4	almost	almost	ADV
ejpam-5722	169	5	quasi	quasi	NOUN
ejpam-5722	169	6	(	(	PUNCT
ejpam-5722	169	7	τ1	τ1	NOUN
ejpam-5722	169	8	,	,	PUNCT
ejpam-5722	169	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	169	10	and	and	CCONJ
ejpam-5722	169	11	σ1σ2	σ1σ2	NOUN
ejpam-5722	169	12	-	-	NUM
ejpam-5722	169	13	cl(v	cl(v	NOUN
ejpam-5722	169	14	)	)	PUNCT
ejpam-5722	169	15	is	be	AUX
ejpam-5722	169	16	a	a	DET
ejpam-5722	169	17	(	(	PUNCT
ejpam-5722	169	18	σ1	σ1	NOUN
ejpam-5722	169	19	,	,	PUNCT
ejpam-5722	169	20	σ2)r	σ2)r	NOUN
ejpam-5722	169	21	-	-	PUNCT
ejpam-5722	169	22	closed	close	VERB
ejpam-5722	169	23	set	set	NOUN
ejpam-5722	169	24	of	of	ADP
ejpam-5722	169	25	y	y	PROPN
ejpam-5722	169	26	,	,	PUNCT
ejpam-5722	169	27	by	by	ADP
ejpam-5722	169	28	lemma	lemma	PROPN
ejpam-5722	169	29	3	3	NUM
ejpam-5722	169	30	we	we	PRON
ejpam-5722	169	31	have	have	AUX
ejpam-5722	169	32	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	169	33	-	-	PUNCT
ejpam-5722	169	34	cl(v	cl(v	NOUN
ejpam-5722	169	35	)	)	PUNCT
ejpam-5722	169	36	)	)	PUNCT
ejpam-5722	170	1	is	be	AUX
ejpam-5722	170	2	(	(	PUNCT
ejpam-5722	170	3	τ1	τ1	NOUN
ejpam-5722	170	4	,	,	PUNCT
ejpam-5722	170	5	τ2)s	τ2)s	NOUN
ejpam-5722	170	6	-	-	PUNCT
ejpam-5722	170	7	closed	close	VERB
ejpam-5722	170	8	in	in	ADP
ejpam-5722	170	9	x.	x.	NOUN
ejpam-5722	170	10	thus	thus	ADV
ejpam-5722	170	11	,	,	PUNCT
ejpam-5722	170	12	(	(	PUNCT
ejpam-5722	170	13	τ1	τ1	NOUN
ejpam-5722	170	14	,	,	PUNCT
ejpam-5722	170	15	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	170	16	)	)	PUNCT
ejpam-5722	170	17	⊆	⊆	NUM
ejpam-5722	170	18	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	170	19	-	-	PUNCT
ejpam-5722	170	20	cl(v	cl(v	NOUN
ejpam-5722	170	21	)	)	PUNCT
ejpam-5722	170	22	)	)	PUNCT
ejpam-5722	170	23	and	and	CCONJ
ejpam-5722	170	24	hence	hence	ADV
ejpam-5722	170	25	f((τ1	f((τ1	VERB
ejpam-5722	170	26	,	,	PUNCT
ejpam-5722	170	27	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	170	28	)	)	PUNCT
ejpam-5722	170	29	)	)	PUNCT
ejpam-5722	171	1	⊆	⊆	X
ejpam-5722	171	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	171	3	-	-	NUM
ejpam-5722	171	4	cl(v	cl(v	NOUN
ejpam-5722	171	5	)	)	PUNCT
ejpam-5722	171	6	.	.	PUNCT
ejpam-5722	172	1	this	this	PRON
ejpam-5722	172	2	shows	show	VERB
ejpam-5722	172	3	that	that	SCONJ
ejpam-5722	172	4	f	f	PROPN
ejpam-5722	172	5	is	be	AUX
ejpam-5722	172	6	quasi	quasi	NOUN
ejpam-5722	172	7	θ(τ1	θ(τ1	NOUN
ejpam-5722	172	8	,	,	PUNCT
ejpam-5722	172	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	172	10	.	.	PUNCT
ejpam-5722	173	1	definition	definition	NOUN
ejpam-5722	173	2	4	4	NUM
ejpam-5722	173	3	.	.	PUNCT
ejpam-5722	174	1	[	[	X
ejpam-5722	174	2	39	39	NUM
ejpam-5722	174	3	]	]	PUNCT
ejpam-5722	174	4	a	a	DET
ejpam-5722	174	5	bitopological	bitopological	ADJ
ejpam-5722	174	6	space	space	NOUN
ejpam-5722	174	7	(	(	PUNCT
ejpam-5722	174	8	x	x	NOUN
ejpam-5722	174	9	,	,	PUNCT
ejpam-5722	174	10	τ1	τ1	NOUN
ejpam-5722	174	11	,	,	PUNCT
ejpam-5722	174	12	τ2	τ2	NOUN
ejpam-5722	174	13	)	)	PUNCT
ejpam-5722	174	14	is	be	AUX
ejpam-5722	174	15	said	say	VERB
ejpam-5722	174	16	to	to	PART
ejpam-5722	174	17	be	be	AUX
ejpam-5722	174	18	(	(	PUNCT
ejpam-5722	174	19	τ1	τ1	NOUN
ejpam-5722	174	20	,	,	PUNCT
ejpam-5722	174	21	τ2)s	τ2)s	NOUN
ejpam-5722	174	22	-	-	PUNCT
ejpam-5722	174	23	regular	regular	ADJ
ejpam-5722	174	24	if	if	SCONJ
ejpam-5722	174	25	for	for	ADP
ejpam-5722	174	26	each	each	DET
ejpam-5722	174	27	(	(	PUNCT
ejpam-5722	174	28	τ1	τ1	NOUN
ejpam-5722	174	29	,	,	PUNCT
ejpam-5722	174	30	τ2)s	τ2)s	NOUN
ejpam-5722	174	31	-	-	PUNCT
ejpam-5722	174	32	closed	close	VERB
ejpam-5722	174	33	set	set	ADJ
ejpam-5722	174	34	f	f	PROPN
ejpam-5722	174	35	of	of	ADP
ejpam-5722	174	36	x	x	INTJ
ejpam-5722	174	37	and	and	CCONJ
ejpam-5722	174	38	each	each	DET
ejpam-5722	174	39	x	x	X
ejpam-5722	174	40	̸∈	̸∈	PROPN
ejpam-5722	174	41	f	f	PROPN
ejpam-5722	174	42	,	,	PUNCT
ejpam-5722	174	43	there	there	PRON
ejpam-5722	174	44	exist	exist	VERB
ejpam-5722	174	45	disjoint	disjoint	NOUN
ejpam-5722	174	46	(	(	PUNCT
ejpam-5722	174	47	τ1	τ1	NOUN
ejpam-5722	174	48	,	,	PUNCT
ejpam-5722	174	49	τ2)s	τ2)s	NOUN
ejpam-5722	174	50	-	-	PUNCT
ejpam-5722	174	51	open	open	ADJ
ejpam-5722	174	52	sets	set	NOUN
ejpam-5722	174	53	v	v	ADP
ejpam-5722	174	54	and	and	CCONJ
ejpam-5722	174	55	v	v	ADP
ejpam-5722	174	56	such	such	ADJ
ejpam-5722	174	57	that	that	SCONJ
ejpam-5722	174	58	x	x	SYM
ejpam-5722	174	59	∈	∈	PROPN
ejpam-5722	174	60	u	u	NOUN
ejpam-5722	174	61	and	and	CCONJ
ejpam-5722	174	62	f	f	PROPN
ejpam-5722	174	63	⊆	⊆	NUM
ejpam-5722	174	64	v	v	NOUN
ejpam-5722	174	65	.	.	PUNCT
ejpam-5722	175	1	lemma	lemma	PROPN
ejpam-5722	175	2	5	5	NUM
ejpam-5722	175	3	.	.	PUNCT
ejpam-5722	176	1	[	[	X
ejpam-5722	176	2	39	39	NUM
ejpam-5722	176	3	]	]	PUNCT
ejpam-5722	176	4	a	a	DET
ejpam-5722	176	5	bitopological	bitopological	ADJ
ejpam-5722	176	6	space	space	NOUN
ejpam-5722	176	7	(	(	PUNCT
ejpam-5722	176	8	x	x	NOUN
ejpam-5722	176	9	,	,	PUNCT
ejpam-5722	176	10	τ1	τ1	NOUN
ejpam-5722	176	11	,	,	PUNCT
ejpam-5722	176	12	τ2	τ2	NOUN
ejpam-5722	176	13	)	)	PUNCT
ejpam-5722	176	14	is	be	AUX
ejpam-5722	176	15	(	(	PUNCT
ejpam-5722	176	16	τ1	τ1	NOUN
ejpam-5722	176	17	,	,	PUNCT
ejpam-5722	176	18	τ2)s	τ2)s	NOUN
ejpam-5722	176	19	-	-	PUNCT
ejpam-5722	176	20	regular	regular	ADJ
ejpam-5722	176	21	if	if	SCONJ
ejpam-5722	176	22	and	and	CCONJ
ejpam-5722	176	23	only	only	ADV
ejpam-5722	176	24	if	if	SCONJ
ejpam-5722	176	25	for	for	ADP
ejpam-5722	176	26	each	each	DET
ejpam-5722	176	27	x	x	SYM
ejpam-5722	176	28	∈	∈	PROPN
ejpam-5722	176	29	x	x	X
ejpam-5722	176	30	and	and	CCONJ
ejpam-5722	176	31	each	each	DET
ejpam-5722	176	32	(	(	PUNCT
ejpam-5722	176	33	τ1	τ1	NOUN
ejpam-5722	176	34	,	,	PUNCT
ejpam-5722	176	35	τ2)s	τ2)s	NOUN
ejpam-5722	176	36	-	-	PUNCT
ejpam-5722	176	37	open	open	ADJ
ejpam-5722	176	38	set	set	NOUN
ejpam-5722	176	39	u	u	NOUN
ejpam-5722	176	40	containing	contain	VERB
ejpam-5722	176	41	x	x	PRON
ejpam-5722	176	42	,	,	PUNCT
ejpam-5722	176	43	there	there	PRON
ejpam-5722	176	44	exists	exist	VERB
ejpam-5722	176	45	a	a	DET
ejpam-5722	176	46	(	(	PUNCT
ejpam-5722	176	47	τ1	τ1	NOUN
ejpam-5722	176	48	,	,	PUNCT
ejpam-5722	176	49	τ2)s	τ2)s	NOUN
ejpam-5722	176	50	-	-	PUNCT
ejpam-5722	176	51	open	open	NOUN
ejpam-5722	176	52	set	set	VERB
ejpam-5722	176	53	v	v	ADP
ejpam-5722	177	1	such	such	ADJ
ejpam-5722	177	2	that	that	SCONJ
ejpam-5722	177	3	x	x	SYM
ejpam-5722	177	4	∈	∈	NOUN
ejpam-5722	177	5	v	v	ADP
ejpam-5722	177	6	⊆	⊆	NUM
ejpam-5722	177	7	(	(	PUNCT
ejpam-5722	177	8	τ1	τ1	NOUN
ejpam-5722	177	9	,	,	PUNCT
ejpam-5722	177	10	τ2)-scl(v	τ2)-scl(v	NOUN
ejpam-5722	177	11	)	)	PUNCT
ejpam-5722	177	12	⊆	⊆	NUM
ejpam-5722	177	13	u	u	NOUN
ejpam-5722	177	14	.	.	PUNCT
ejpam-5722	177	15	theorem	theorem	NOUN
ejpam-5722	177	16	3	3	X
ejpam-5722	177	17	.	.	PUNCT
ejpam-5722	178	1	if	if	SCONJ
ejpam-5722	178	2	a	a	DET
ejpam-5722	178	3	function	function	NOUN
ejpam-5722	178	4	f	f	X
ejpam-5722	178	5	:	:	PUNCT
ejpam-5722	178	6	(	(	PUNCT
ejpam-5722	178	7	x	x	NOUN
ejpam-5722	178	8	,	,	PUNCT
ejpam-5722	178	9	τ1	τ1	NOUN
ejpam-5722	178	10	,	,	PUNCT
ejpam-5722	178	11	τ2	τ2	NOUN
ejpam-5722	178	12	)	)	PUNCT
ejpam-5722	178	13	→	→	SYM
ejpam-5722	178	14	(	(	PUNCT
ejpam-5722	178	15	y	y	PROPN
ejpam-5722	178	16	,	,	PUNCT
ejpam-5722	178	17	σ1	σ1	PROPN
ejpam-5722	178	18	,	,	PUNCT
ejpam-5722	178	19	σ2	σ2	NOUN
ejpam-5722	178	20	)	)	PUNCT
ejpam-5722	178	21	is	be	AUX
ejpam-5722	178	22	weakly	weakly	ADJ
ejpam-5722	178	23	quasi	quasi	NOUN
ejpam-5722	178	24	(	(	PUNCT
ejpam-5722	178	25	τ1	τ1	PROPN
ejpam-5722	178	26	,	,	PUNCT
ejpam-5722	178	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	178	28	and	and	CCONJ
ejpam-5722	178	29	(	(	PUNCT
ejpam-5722	178	30	x	x	NOUN
ejpam-5722	178	31	,	,	PUNCT
ejpam-5722	178	32	τ1	τ1	NOUN
ejpam-5722	178	33	,	,	PUNCT
ejpam-5722	178	34	τ2	τ2	NOUN
ejpam-5722	178	35	)	)	PUNCT
ejpam-5722	178	36	is	be	AUX
ejpam-5722	178	37	(	(	PUNCT
ejpam-5722	178	38	τ1	τ1	NOUN
ejpam-5722	178	39	,	,	PUNCT
ejpam-5722	178	40	τ2)s	τ2)s	NOUN
ejpam-5722	178	41	-	-	PUNCT
ejpam-5722	178	42	regular	regular	ADJ
ejpam-5722	178	43	,	,	PUNCT
ejpam-5722	178	44	then	then	ADV
ejpam-5722	178	45	f	f	PROPN
ejpam-5722	178	46	is	be	AUX
ejpam-5722	178	47	quasi	quasi	NOUN
ejpam-5722	178	48	θ(τ1	θ(τ1	NOUN
ejpam-5722	178	49	,	,	PUNCT
ejpam-5722	178	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	178	51	.	.	PUNCT
ejpam-5722	179	1	proof	proof	NOUN
ejpam-5722	179	2	.	.	PUNCT
ejpam-5722	180	1	let	let	VERB
ejpam-5722	180	2	x	x	PUNCT
ejpam-5722	180	3	∈	∈	PROPN
ejpam-5722	180	4	x	x	X
ejpam-5722	180	5	and	and	CCONJ
ejpam-5722	180	6	v	v	X
ejpam-5722	180	7	be	be	AUX
ejpam-5722	180	8	any	any	DET
ejpam-5722	180	9	σ1σ2	σ1σ2	NOUN
ejpam-5722	180	10	-	-	ADJ
ejpam-5722	180	11	open	open	ADJ
ejpam-5722	180	12	set	set	NOUN
ejpam-5722	180	13	of	of	ADP
ejpam-5722	180	14	y	y	PROPN
ejpam-5722	180	15	containing	contain	VERB
ejpam-5722	180	16	f(x	f(x	PROPN
ejpam-5722	180	17	)	)	PUNCT
ejpam-5722	180	18	.	.	PUNCT
ejpam-5722	181	1	since	since	SCONJ
ejpam-5722	181	2	f	f	PROPN
ejpam-5722	181	3	is	be	AUX
ejpam-5722	181	4	weakly	weakly	ADJ
ejpam-5722	181	5	quasi	quasi	NOUN
ejpam-5722	181	6	(	(	PUNCT
ejpam-5722	181	7	τ1	τ1	NOUN
ejpam-5722	181	8	,	,	PUNCT
ejpam-5722	181	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	181	10	,	,	PUNCT
ejpam-5722	181	11	by	by	ADP
ejpam-5722	181	12	lemma	lemma	PROPN
ejpam-5722	181	13	4	4	NUM
ejpam-5722	181	14	,	,	PUNCT
ejpam-5722	181	15	there	there	PRON
ejpam-5722	181	16	exists	exist	VERB
ejpam-5722	181	17	a	a	DET
ejpam-5722	181	18	(	(	PUNCT
ejpam-5722	181	19	τ1	τ1	NOUN
ejpam-5722	181	20	,	,	PUNCT
ejpam-5722	181	21	τ2)s	τ2)s	NOUN
ejpam-5722	181	22	-	-	PUNCT
ejpam-5722	181	23	open	open	ADJ
ejpam-5722	181	24	set	set	NOUN
ejpam-5722	181	25	u	u	NOUN
ejpam-5722	181	26	of	of	ADP
ejpam-5722	181	27	x	x	PUNCT
ejpam-5722	181	28	containing	contain	VERB
ejpam-5722	181	29	x	x	PUNCT
ejpam-5722	181	30	such	such	ADJ
ejpam-5722	181	31	that	that	DET
ejpam-5722	181	32	f(u	f(u	PROPN
ejpam-5722	181	33	)	)	PUNCT
ejpam-5722	181	34	⊆	⊆	NUM
ejpam-5722	181	35	σ1σ2	σ1σ2	NOUN
ejpam-5722	181	36	-	-	NUM
ejpam-5722	181	37	cl(v	cl(v	NOUN
ejpam-5722	181	38	)	)	PUNCT
ejpam-5722	181	39	.	.	PUNCT
ejpam-5722	182	1	by	by	ADP
ejpam-5722	182	2	lemma	lemma	PROPN
ejpam-5722	182	3	5	5	NUM
ejpam-5722	182	4	,	,	PUNCT
ejpam-5722	182	5	there	there	PRON
ejpam-5722	182	6	exists	exist	VERB
ejpam-5722	182	7	a	a	DET
ejpam-5722	182	8	(	(	PUNCT
ejpam-5722	182	9	τ1	τ1	NOUN
ejpam-5722	182	10	,	,	PUNCT
ejpam-5722	182	11	τ2)s	τ2)s	NOUN
ejpam-5722	182	12	-	-	PUNCT
ejpam-5722	182	13	open	open	ADJ
ejpam-5722	182	14	set	set	NOUN
ejpam-5722	182	15	w	w	ADP
ejpam-5722	182	16	such	such	ADJ
ejpam-5722	182	17	that	that	SCONJ
ejpam-5722	182	18	x	x	SYM
ejpam-5722	182	19	∈	∈	PROPN
ejpam-5722	182	20	w	w	ADP
ejpam-5722	182	21	⊆	⊆	NUM
ejpam-5722	182	22	(	(	PUNCT
ejpam-5722	182	23	τ1	τ1	NOUN
ejpam-5722	182	24	,	,	PUNCT
ejpam-5722	182	25	τ2)-scl(w	τ2)-scl(w	NOUN
ejpam-5722	182	26	)	)	PUNCT
ejpam-5722	182	27	⊆	⊆	NUM
ejpam-5722	182	28	u	u	NOUN
ejpam-5722	182	29	.	.	PUNCT
ejpam-5722	183	1	thus	thus	ADV
ejpam-5722	183	2	,	,	PUNCT
ejpam-5722	183	3	f((τ1	f((τ1	PROPN
ejpam-5722	183	4	,	,	PUNCT
ejpam-5722	183	5	τ2)-scl(w	τ2)-scl(w	NOUN
ejpam-5722	183	6	)	)	PUNCT
ejpam-5722	184	1	⊆	⊆	NUM
ejpam-5722	184	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	184	3	-	-	NUM
ejpam-5722	184	4	cl(v	cl(v	NOUN
ejpam-5722	184	5	)	)	PUNCT
ejpam-5722	184	6	and	and	CCONJ
ejpam-5722	184	7	hence	hence	ADV
ejpam-5722	184	8	f	f	PROPN
ejpam-5722	184	9	is	be	AUX
ejpam-5722	184	10	quasi	quasi	NOUN
ejpam-5722	184	11	θ(τ1	θ(τ1	NOUN
ejpam-5722	184	12	,	,	PUNCT
ejpam-5722	184	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	184	14	.	.	PUNCT
ejpam-5722	185	1	theorem	theorem	NOUN
ejpam-5722	185	2	4	4	NUM
ejpam-5722	185	3	.	.	X
ejpam-5722	185	4	for	for	ADP
ejpam-5722	185	5	a	a	DET
ejpam-5722	185	6	function	function	NOUN
ejpam-5722	185	7	f	f	NOUN
ejpam-5722	185	8	:	:	PUNCT
ejpam-5722	185	9	(	(	PUNCT
ejpam-5722	185	10	x	x	NOUN
ejpam-5722	185	11	,	,	PUNCT
ejpam-5722	185	12	τ1	τ1	NOUN
ejpam-5722	185	13	,	,	PUNCT
ejpam-5722	185	14	τ2	τ2	NOUN
ejpam-5722	185	15	)	)	PUNCT
ejpam-5722	185	16	→	→	SYM
ejpam-5722	185	17	(	(	PUNCT
ejpam-5722	185	18	y	y	PROPN
ejpam-5722	185	19	,	,	PUNCT
ejpam-5722	185	20	σ1	σ1	PROPN
ejpam-5722	185	21	,	,	PUNCT
ejpam-5722	185	22	σ2	σ2	NOUN
ejpam-5722	185	23	)	)	PUNCT
ejpam-5722	185	24	,	,	PUNCT
ejpam-5722	185	25	the	the	DET
ejpam-5722	185	26	following	follow	VERB
ejpam-5722	185	27	properties	property	NOUN
ejpam-5722	185	28	are	be	AUX
ejpam-5722	185	29	equivalent	equivalent	ADJ
ejpam-5722	185	30	:	:	PUNCT
ejpam-5722	185	31	(	(	PUNCT
ejpam-5722	185	32	1	1	X
ejpam-5722	185	33	)	)	PUNCT
ejpam-5722	185	34	f	f	PROPN
ejpam-5722	185	35	is	be	AUX
ejpam-5722	185	36	quasi	quasi	NOUN
ejpam-5722	185	37	θ(τ1	θ(τ1	NOUN
ejpam-5722	185	38	,	,	PUNCT
ejpam-5722	185	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	185	40	;	;	PUNCT
ejpam-5722	185	41	(	(	PUNCT
ejpam-5722	185	42	2	2	X
ejpam-5722	185	43	)	)	PUNCT
ejpam-5722	185	44	θ(τ1	θ(τ1	NOUN
ejpam-5722	185	45	,	,	PUNCT
ejpam-5722	185	46	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5722	185	47	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	185	48	-	-	PUNCT
ejpam-5722	185	49	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	185	50	-	-	PUNCT
ejpam-5722	185	51	cl(v	cl(v	NOUN
ejpam-5722	185	52	)	)	PUNCT
ejpam-5722	185	53	)	)	PUNCT
ejpam-5722	185	54	)	)	PUNCT
ejpam-5722	185	55	)	)	PUNCT
ejpam-5722	186	1	⊆	⊆	NUM
ejpam-5722	186	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	186	3	-	-	PUNCT
ejpam-5722	186	4	cl(v	cl(v	NOUN
ejpam-5722	186	5	)	)	PUNCT
ejpam-5722	186	6	)	)	PUNCT
ejpam-5722	186	7	for	for	ADP
ejpam-5722	186	8	every	every	DET
ejpam-5722	186	9	(	(	PUNCT
ejpam-5722	186	10	σ1	σ1	PROPN
ejpam-5722	186	11	,	,	PUNCT
ejpam-5722	186	12	σ2)βopen	σ2)βopen	PROPN
ejpam-5722	186	13	set	set	VERB
ejpam-5722	186	14	v	v	NOUN
ejpam-5722	186	15	of	of	ADP
ejpam-5722	186	16	y	y	PROPN
ejpam-5722	186	17	;	;	PUNCT
ejpam-5722	186	18	n.	n.	PROPN
ejpam-5722	186	19	srisarakham	srisarakham	PROPN
ejpam-5722	186	20	,	,	PUNCT
ejpam-5722	186	21	s.	s.	PROPN
ejpam-5722	186	22	sompong	sompong	PROPN
ejpam-5722	186	23	,	,	PUNCT
ejpam-5722	186	24	c.	c.	PROPN
ejpam-5722	186	25	boonpok	boonpok	PROPN
ejpam-5722	186	26	/	/	SYM
ejpam-5722	186	27	eur	eur	PROPN
ejpam-5722	186	28	.	.	PUNCT
ejpam-5722	187	1	j.	j.	PROPN
ejpam-5722	187	2	pure	pure	PROPN
ejpam-5722	187	3	appl	appl	PROPN
ejpam-5722	187	4	.	.	PROPN
ejpam-5722	187	5	math	math	PROPN
ejpam-5722	187	6	,	,	PUNCT
ejpam-5722	187	7	18	18	NUM
ejpam-5722	187	8	(	(	PUNCT
ejpam-5722	187	9	1	1	NUM
ejpam-5722	187	10	)	)	PUNCT
ejpam-5722	187	11	(	(	PUNCT
ejpam-5722	187	12	2025	2025	NUM
ejpam-5722	187	13	)	)	PUNCT
ejpam-5722	187	14	,	,	PUNCT
ejpam-5722	187	15	5722	5722	NUM
ejpam-5722	187	16	7	7	NUM
ejpam-5722	187	17	of	of	ADP
ejpam-5722	187	18	12	12	NUM
ejpam-5722	187	19	(	(	PUNCT
ejpam-5722	187	20	3	3	NUM
ejpam-5722	187	21	)	)	PUNCT
ejpam-5722	187	22	θ(τ1	θ(τ1	NOUN
ejpam-5722	187	23	,	,	PUNCT
ejpam-5722	187	24	τ2)-scl(f	τ2)-scl(f	ADV
ejpam-5722	187	25	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	187	26	-	-	PUNCT
ejpam-5722	187	27	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	187	28	-	-	PUNCT
ejpam-5722	187	29	cl(v	cl(v	NOUN
ejpam-5722	187	30	)	)	PUNCT
ejpam-5722	187	31	)	)	PUNCT
ejpam-5722	187	32	)	)	PUNCT
ejpam-5722	187	33	)	)	PUNCT
ejpam-5722	188	1	⊆	⊆	NUM
ejpam-5722	188	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	188	3	-	-	PUNCT
ejpam-5722	188	4	cl(v	cl(v	NOUN
ejpam-5722	188	5	)	)	PUNCT
ejpam-5722	188	6	)	)	PUNCT
ejpam-5722	188	7	for	for	ADP
ejpam-5722	188	8	every	every	DET
ejpam-5722	188	9	(	(	PUNCT
ejpam-5722	188	10	σ1	σ1	PROPN
ejpam-5722	188	11	,	,	PUNCT
ejpam-5722	188	12	σ2)s	σ2)s	NOUN
ejpam-5722	188	13	-	-	PUNCT
ejpam-5722	188	14	open	open	NOUN
ejpam-5722	188	15	set	set	NOUN
ejpam-5722	188	16	v	v	NOUN
ejpam-5722	188	17	of	of	ADP
ejpam-5722	188	18	y	y	PROPN
ejpam-5722	188	19	.	.	PUNCT
ejpam-5722	189	1	proof	proof	NOUN
ejpam-5722	189	2	.	.	PUNCT
ejpam-5722	190	1	(	(	PUNCT
ejpam-5722	190	2	1	1	X
ejpam-5722	190	3	)	)	PUNCT
ejpam-5722	190	4	⇒	⇒	NOUN
ejpam-5722	190	5	(	(	PUNCT
ejpam-5722	190	6	2	2	NUM
ejpam-5722	190	7	):	):	PUNCT
ejpam-5722	190	8	let	let	VERB
ejpam-5722	190	9	v	v	PART
ejpam-5722	190	10	be	be	AUX
ejpam-5722	190	11	any	any	DET
ejpam-5722	190	12	(	(	PUNCT
ejpam-5722	190	13	σ1	σ1	PROPN
ejpam-5722	190	14	,	,	PUNCT
ejpam-5722	190	15	σ2)β	σ2)β	NOUN
ejpam-5722	190	16	-	-	PUNCT
ejpam-5722	190	17	open	open	ADJ
ejpam-5722	190	18	set	set	NOUN
ejpam-5722	190	19	of	of	ADP
ejpam-5722	190	20	y	y	PROPN
ejpam-5722	190	21	.	.	PUNCT
ejpam-5722	191	1	then	then	ADV
ejpam-5722	191	2	,	,	PUNCT
ejpam-5722	191	3	v	v	ADP
ejpam-5722	191	4	⊆	⊆	NUM
ejpam-5722	191	5	σ1σ2	σ1σ2	NOUN
ejpam-5722	191	6	-	-	PUNCT
ejpam-5722	191	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5722	191	8	-	-	PUNCT
ejpam-5722	191	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	191	10	-	-	PUNCT
ejpam-5722	191	11	cl(v	cl(v	NOUN
ejpam-5722	191	12	)	)	PUNCT
ejpam-5722	191	13	)	)	PUNCT
ejpam-5722	191	14	)	)	PUNCT
ejpam-5722	191	15	and	and	CCONJ
ejpam-5722	191	16	hence	hence	ADV
ejpam-5722	191	17	σ1σ2	σ1σ2	NOUN
ejpam-5722	191	18	-	-	NOUN
ejpam-5722	191	19	cl(v	cl(v	NOUN
ejpam-5722	191	20	)	)	PUNCT
ejpam-5722	192	1	=	=	SYM
ejpam-5722	192	2	σ1σ2	σ1σ2	X
ejpam-5722	192	3	-	-	PUNCT
ejpam-5722	192	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5722	192	5	-	-	PUNCT
ejpam-5722	192	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	192	7	-	-	PUNCT
ejpam-5722	192	8	cl(v	cl(v	NOUN
ejpam-5722	192	9	)	)	PUNCT
ejpam-5722	192	10	)	)	PUNCT
ejpam-5722	192	11	)	)	PUNCT
ejpam-5722	192	12	.	.	PUNCT
ejpam-5722	193	1	since	since	SCONJ
ejpam-5722	193	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	193	3	-	-	NOUN
ejpam-5722	193	4	cl(v	cl(v	NOUN
ejpam-5722	193	5	)	)	PUNCT
ejpam-5722	193	6	is	be	AUX
ejpam-5722	193	7	(	(	PUNCT
ejpam-5722	193	8	σ1	σ1	PROPN
ejpam-5722	193	9	,	,	PUNCT
ejpam-5722	193	10	σ2)rclosed	σ2)rclose	VERB
ejpam-5722	193	11	in	in	ADP
ejpam-5722	193	12	y	y	PROPN
ejpam-5722	193	13	,	,	PUNCT
ejpam-5722	193	14	by	by	ADP
ejpam-5722	193	15	theorem	theorem	NOUN
ejpam-5722	193	16	1	1	NUM
ejpam-5722	193	17	we	we	PRON
ejpam-5722	193	18	have	have	AUX
ejpam-5722	193	19	θ(τ1	θ(τ1	NOUN
ejpam-5722	193	20	,	,	PUNCT
ejpam-5722	193	21	τ2)-scl(f	τ2)-scl(f	ADJ
ejpam-5722	193	22	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	193	23	-	-	PUNCT
ejpam-5722	193	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	193	25	-	-	PUNCT
ejpam-5722	193	26	cl(v	cl(v	NOUN
ejpam-5722	193	27	)	)	PUNCT
ejpam-5722	193	28	)	)	PUNCT
ejpam-5722	193	29	)	)	PUNCT
ejpam-5722	193	30	)	)	PUNCT
ejpam-5722	194	1	⊆	⊆	NUM
ejpam-5722	194	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	194	3	-	-	PUNCT
ejpam-5722	194	4	cl(v	cl(v	NOUN
ejpam-5722	194	5	)	)	PUNCT
ejpam-5722	194	6	)	)	PUNCT
ejpam-5722	194	7	.	.	PUNCT
ejpam-5722	195	1	(	(	PUNCT
ejpam-5722	195	2	2	2	X
ejpam-5722	195	3	)	)	PUNCT
ejpam-5722	195	4	⇒	⇒	NOUN
ejpam-5722	195	5	(	(	PUNCT
ejpam-5722	195	6	3	3	NUM
ejpam-5722	195	7	):	):	PUNCT
ejpam-5722	195	8	the	the	DET
ejpam-5722	195	9	proof	proof	NOUN
ejpam-5722	195	10	is	be	AUX
ejpam-5722	195	11	obvious	obvious	ADJ
ejpam-5722	195	12	.	.	PUNCT
ejpam-5722	196	1	(	(	PUNCT
ejpam-5722	196	2	3	3	X
ejpam-5722	196	3	)	)	PUNCT
ejpam-5722	196	4	⇒	⇒	NOUN
ejpam-5722	196	5	(	(	PUNCT
ejpam-5722	196	6	1	1	NUM
ejpam-5722	196	7	):	):	PUNCT
ejpam-5722	196	8	let	let	VERB
ejpam-5722	196	9	v	v	PART
ejpam-5722	196	10	be	be	AUX
ejpam-5722	196	11	any	any	DET
ejpam-5722	196	12	σ1σ2	σ1σ2	NOUN
ejpam-5722	196	13	-	-	ADJ
ejpam-5722	196	14	open	open	ADJ
ejpam-5722	196	15	set	set	NOUN
ejpam-5722	196	16	of	of	ADP
ejpam-5722	196	17	y	y	PROPN
ejpam-5722	196	18	.	.	PUNCT
ejpam-5722	197	1	then	then	ADV
ejpam-5722	197	2	,	,	PUNCT
ejpam-5722	197	3	v	v	NOUN
ejpam-5722	197	4	is	be	AUX
ejpam-5722	197	5	(	(	PUNCT
ejpam-5722	197	6	σ1	σ1	PROPN
ejpam-5722	197	7	,	,	PUNCT
ejpam-5722	197	8	σ2)s	σ2)s	NOUN
ejpam-5722	197	9	-	-	PUNCT
ejpam-5722	197	10	open	open	ADJ
ejpam-5722	197	11	in	in	ADP
ejpam-5722	197	12	y	y	PROPN
ejpam-5722	197	13	and	and	CCONJ
ejpam-5722	197	14	by	by	ADP
ejpam-5722	197	15	(	(	PUNCT
ejpam-5722	197	16	3	3	NUM
ejpam-5722	197	17	)	)	PUNCT
ejpam-5722	197	18	,	,	PUNCT
ejpam-5722	197	19	θ(τ1	θ(τ1	VERB
ejpam-5722	197	20	,	,	PUNCT
ejpam-5722	197	21	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	197	22	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	197	23	-	-	PUNCT
ejpam-5722	197	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	197	25	-	-	PUNCT
ejpam-5722	197	26	cl(v	cl(v	NOUN
ejpam-5722	197	27	)	)	PUNCT
ejpam-5722	197	28	)	)	PUNCT
ejpam-5722	197	29	)	)	PUNCT
ejpam-5722	197	30	)	)	PUNCT
ejpam-5722	198	1	⊆	⊆	NUM
ejpam-5722	198	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	198	3	-	-	PUNCT
ejpam-5722	198	4	cl(v	cl(v	NOUN
ejpam-5722	198	5	)	)	PUNCT
ejpam-5722	198	6	)	)	PUNCT
ejpam-5722	198	7	.	.	PUNCT
ejpam-5722	199	1	thus	thus	ADV
ejpam-5722	199	2	by	by	ADP
ejpam-5722	199	3	theorem	theorem	NOUN
ejpam-5722	199	4	1	1	NUM
ejpam-5722	199	5	,	,	PUNCT
ejpam-5722	199	6	f	f	PROPN
ejpam-5722	199	7	is	be	AUX
ejpam-5722	199	8	quasi	quasi	NOUN
ejpam-5722	199	9	θ(τ1	θ(τ1	NOUN
ejpam-5722	199	10	,	,	PUNCT
ejpam-5722	199	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	199	12	.	.	PUNCT
ejpam-5722	200	1	theorem	theorem	NOUN
ejpam-5722	200	2	5	5	NUM
ejpam-5722	200	3	.	.	X
ejpam-5722	200	4	for	for	ADP
ejpam-5722	200	5	a	a	DET
ejpam-5722	200	6	function	function	NOUN
ejpam-5722	200	7	f	f	NOUN
ejpam-5722	200	8	:	:	PUNCT
ejpam-5722	200	9	(	(	PUNCT
ejpam-5722	200	10	x	x	NOUN
ejpam-5722	200	11	,	,	PUNCT
ejpam-5722	200	12	τ1	τ1	NOUN
ejpam-5722	200	13	,	,	PUNCT
ejpam-5722	200	14	τ2	τ2	NOUN
ejpam-5722	200	15	)	)	PUNCT
ejpam-5722	200	16	→	→	SYM
ejpam-5722	200	17	(	(	PUNCT
ejpam-5722	200	18	y	y	PROPN
ejpam-5722	200	19	,	,	PUNCT
ejpam-5722	200	20	σ1	σ1	PROPN
ejpam-5722	200	21	,	,	PUNCT
ejpam-5722	200	22	σ2	σ2	NOUN
ejpam-5722	200	23	)	)	PUNCT
ejpam-5722	200	24	,	,	PUNCT
ejpam-5722	200	25	the	the	DET
ejpam-5722	200	26	following	follow	VERB
ejpam-5722	200	27	properties	property	NOUN
ejpam-5722	200	28	are	be	AUX
ejpam-5722	200	29	equivalent	equivalent	ADJ
ejpam-5722	200	30	:	:	PUNCT
ejpam-5722	200	31	(	(	PUNCT
ejpam-5722	200	32	1	1	X
ejpam-5722	200	33	)	)	PUNCT
ejpam-5722	200	34	f	f	PROPN
ejpam-5722	200	35	is	be	AUX
ejpam-5722	200	36	quasi	quasi	NOUN
ejpam-5722	200	37	θ(τ1	θ(τ1	NOUN
ejpam-5722	200	38	,	,	PUNCT
ejpam-5722	200	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	200	40	;	;	PUNCT
ejpam-5722	200	41	(	(	PUNCT
ejpam-5722	200	42	2	2	X
ejpam-5722	200	43	)	)	PUNCT
ejpam-5722	200	44	θ(τ1	θ(τ1	NOUN
ejpam-5722	200	45	,	,	PUNCT
ejpam-5722	200	46	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5722	200	47	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	200	48	-	-	PUNCT
ejpam-5722	200	49	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	200	50	-	-	PUNCT
ejpam-5722	200	51	cl(v	cl(v	NOUN
ejpam-5722	200	52	)	)	PUNCT
ejpam-5722	200	53	)	)	PUNCT
ejpam-5722	200	54	)	)	PUNCT
ejpam-5722	200	55	)	)	PUNCT
ejpam-5722	201	1	⊆	⊆	NUM
ejpam-5722	201	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	201	3	-	-	PUNCT
ejpam-5722	201	4	cl(v	cl(v	NOUN
ejpam-5722	201	5	)	)	PUNCT
ejpam-5722	201	6	)	)	PUNCT
ejpam-5722	201	7	for	for	ADP
ejpam-5722	201	8	every	every	DET
ejpam-5722	201	9	(	(	PUNCT
ejpam-5722	201	10	σ1	σ1	PROPN
ejpam-5722	201	11	,	,	PUNCT
ejpam-5722	201	12	σ2)p	σ2)p	NOUN
ejpam-5722	201	13	-	-	PUNCT
ejpam-5722	201	14	open	open	NOUN
ejpam-5722	201	15	set	set	NOUN
ejpam-5722	201	16	v	v	NOUN
ejpam-5722	201	17	of	of	ADP
ejpam-5722	201	18	y	y	PROPN
ejpam-5722	201	19	;	;	PUNCT
ejpam-5722	201	20	(	(	PUNCT
ejpam-5722	201	21	3	3	X
ejpam-5722	201	22	)	)	PUNCT
ejpam-5722	201	23	θ(τ1	θ(τ1	NOUN
ejpam-5722	201	24	,	,	PUNCT
ejpam-5722	201	25	τ2)-scl(f	τ2)-scl(f	ADV
ejpam-5722	201	26	−1(v	−1(v	PROPN
ejpam-5722	201	27	)	)	PUNCT
ejpam-5722	201	28	)	)	PUNCT
ejpam-5722	202	1	⊆	⊆	NUM
ejpam-5722	202	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	202	3	-	-	PUNCT
ejpam-5722	202	4	cl(v	cl(v	NOUN
ejpam-5722	202	5	)	)	PUNCT
ejpam-5722	202	6	)	)	PUNCT
ejpam-5722	202	7	for	for	ADP
ejpam-5722	202	8	every	every	DET
ejpam-5722	202	9	(	(	PUNCT
ejpam-5722	202	10	σ1	σ1	PROPN
ejpam-5722	202	11	,	,	PUNCT
ejpam-5722	202	12	σ2)p	σ2)p	NOUN
ejpam-5722	202	13	-	-	PUNCT
ejpam-5722	202	14	open	open	NOUN
ejpam-5722	202	15	set	set	NOUN
ejpam-5722	202	16	v	v	NOUN
ejpam-5722	202	17	of	of	ADP
ejpam-5722	202	18	y	y	PROPN
ejpam-5722	202	19	;	;	PUNCT
ejpam-5722	202	20	(	(	PUNCT
ejpam-5722	202	21	4	4	X
ejpam-5722	202	22	)	)	PUNCT
ejpam-5722	202	23	f−1(v	f−1(v	NOUN
ejpam-5722	202	24	)	)	PUNCT
ejpam-5722	203	1	⊆	⊆	NUM
ejpam-5722	203	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	203	3	,	,	PUNCT
ejpam-5722	203	4	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	203	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	203	6	-	-	PUNCT
ejpam-5722	203	7	cl(v	cl(v	NOUN
ejpam-5722	203	8	)	)	PUNCT
ejpam-5722	203	9	)	)	PUNCT
ejpam-5722	203	10	)	)	PUNCT
ejpam-5722	204	1	for	for	ADP
ejpam-5722	204	2	every	every	DET
ejpam-5722	204	3	(	(	PUNCT
ejpam-5722	204	4	σ1	σ1	PROPN
ejpam-5722	204	5	,	,	PUNCT
ejpam-5722	204	6	σ2)p	σ2)p	NOUN
ejpam-5722	204	7	-	-	PUNCT
ejpam-5722	204	8	open	open	NOUN
ejpam-5722	204	9	set	set	NOUN
ejpam-5722	204	10	v	v	NOUN
ejpam-5722	204	11	of	of	ADP
ejpam-5722	204	12	y	y	PROPN
ejpam-5722	204	13	.	.	PUNCT
ejpam-5722	205	1	proof	proof	NOUN
ejpam-5722	205	2	.	.	PUNCT
ejpam-5722	206	1	(	(	PUNCT
ejpam-5722	206	2	1	1	X
ejpam-5722	206	3	)	)	PUNCT
ejpam-5722	206	4	⇒	⇒	NOUN
ejpam-5722	206	5	(	(	PUNCT
ejpam-5722	206	6	2	2	NUM
ejpam-5722	206	7	):	):	PUNCT
ejpam-5722	206	8	let	let	VERB
ejpam-5722	206	9	v	v	PART
ejpam-5722	206	10	be	be	AUX
ejpam-5722	206	11	any	any	DET
ejpam-5722	206	12	(	(	PUNCT
ejpam-5722	206	13	σ1	σ1	PROPN
ejpam-5722	206	14	,	,	PUNCT
ejpam-5722	206	15	σ2)p	σ2)p	NOUN
ejpam-5722	206	16	-	-	PUNCT
ejpam-5722	206	17	open	open	ADJ
ejpam-5722	206	18	set	set	NOUN
ejpam-5722	206	19	of	of	ADP
ejpam-5722	206	20	y	y	PROPN
ejpam-5722	206	21	.	.	PUNCT
ejpam-5722	207	1	since	since	SCONJ
ejpam-5722	207	2	σ1σ2	σ1σ2	ADV
ejpam-5722	207	3	-	-	PUNCT
ejpam-5722	207	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	207	5	-	-	PUNCT
ejpam-5722	207	6	cl(v	cl(v	NOUN
ejpam-5722	207	7	)	)	PUNCT
ejpam-5722	207	8	)	)	PUNCT
ejpam-5722	207	9	is	be	AUX
ejpam-5722	207	10	a	a	DET
ejpam-5722	207	11	σ1σ2	σ1σ2	NUM
ejpam-5722	207	12	-	-	ADJ
ejpam-5722	207	13	open	open	ADJ
ejpam-5722	207	14	set	set	NOUN
ejpam-5722	207	15	of	of	ADP
ejpam-5722	207	16	y	y	PROPN
ejpam-5722	207	17	,	,	PUNCT
ejpam-5722	207	18	by	by	ADP
ejpam-5722	207	19	theorem	theorem	NOUN
ejpam-5722	207	20	4	4	NUM
ejpam-5722	207	21	we	we	PRON
ejpam-5722	207	22	have	have	AUX
ejpam-5722	207	23	θ(τ1	θ(τ1	NOUN
ejpam-5722	207	24	,	,	PUNCT
ejpam-5722	208	1	τ2)-scl(f	τ2)-scl(f	ADJ
ejpam-5722	208	2	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	208	3	-	-	PUNCT
ejpam-5722	208	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	208	5	-	-	PUNCT
ejpam-5722	208	6	cl(v	cl(v	NOUN
ejpam-5722	208	7	)	)	PUNCT
ejpam-5722	208	8	)	)	PUNCT
ejpam-5722	208	9	)	)	PUNCT
ejpam-5722	208	10	)	)	PUNCT
ejpam-5722	209	1	⊆	⊆	NUM
ejpam-5722	209	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	209	3	-	-	PUNCT
ejpam-5722	209	4	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-5722	209	5	-	-	PUNCT
ejpam-5722	209	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	209	7	-	-	PUNCT
ejpam-5722	209	8	cl(v	cl(v	NOUN
ejpam-5722	209	9	)	)	PUNCT
ejpam-5722	209	10	)	)	PUNCT
ejpam-5722	209	11	)	)	PUNCT
ejpam-5722	209	12	)	)	PUNCT
ejpam-5722	210	1	=	=	PRON
ejpam-5722	210	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	210	3	-	-	PUNCT
ejpam-5722	210	4	cl(v	cl(v	NOUN
ejpam-5722	210	5	)	)	PUNCT
ejpam-5722	210	6	)	)	PUNCT
ejpam-5722	210	7	.	.	PUNCT
ejpam-5722	211	1	(	(	PUNCT
ejpam-5722	211	2	2	2	X
ejpam-5722	211	3	)	)	PUNCT
ejpam-5722	211	4	⇒	⇒	NOUN
ejpam-5722	211	5	(	(	PUNCT
ejpam-5722	211	6	3	3	NUM
ejpam-5722	211	7	):	):	PUNCT
ejpam-5722	211	8	let	let	VERB
ejpam-5722	211	9	v	v	PART
ejpam-5722	211	10	be	be	AUX
ejpam-5722	211	11	any	any	DET
ejpam-5722	211	12	(	(	PUNCT
ejpam-5722	211	13	σ1	σ1	PROPN
ejpam-5722	211	14	,	,	PUNCT
ejpam-5722	211	15	σ2)p	σ2)p	NOUN
ejpam-5722	211	16	-	-	PUNCT
ejpam-5722	211	17	open	open	ADJ
ejpam-5722	211	18	set	set	NOUN
ejpam-5722	211	19	of	of	ADP
ejpam-5722	211	20	y	y	PROPN
ejpam-5722	211	21	.	.	PUNCT
ejpam-5722	212	1	then	then	ADV
ejpam-5722	212	2	,	,	PUNCT
ejpam-5722	212	3	v	v	ADP
ejpam-5722	212	4	⊆	⊆	NUM
ejpam-5722	212	5	σ1σ2	σ1σ2	NOUN
ejpam-5722	212	6	-	-	PUNCT
ejpam-5722	212	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	212	8	-	-	PUNCT
ejpam-5722	212	9	cl(v	cl(v	NOUN
ejpam-5722	212	10	)	)	PUNCT
ejpam-5722	212	11	)	)	PUNCT
ejpam-5722	212	12	and	and	CCONJ
ejpam-5722	212	13	by	by	ADP
ejpam-5722	212	14	(	(	PUNCT
ejpam-5722	212	15	2	2	NUM
ejpam-5722	212	16	)	)	PUNCT
ejpam-5722	212	17	,	,	PUNCT
ejpam-5722	212	18	θ(τ1	θ(τ1	VERB
ejpam-5722	212	19	,	,	PUNCT
ejpam-5722	212	20	τ2)-scl(f	τ2)-scl(f	ADJ
ejpam-5722	212	21	−1(v	−1(v	PROPN
ejpam-5722	212	22	)	)	PUNCT
ejpam-5722	212	23	)	)	PUNCT
ejpam-5722	213	1	⊆	⊆	NUM
ejpam-5722	213	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	213	3	,	,	PUNCT
ejpam-5722	213	4	τ2)-scl(f	τ2)-scl(f	PROPN
ejpam-5722	213	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	213	6	-	-	PUNCT
ejpam-5722	213	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	213	8	-	-	PUNCT
ejpam-5722	213	9	cl(v	cl(v	NOUN
ejpam-5722	213	10	)	)	PUNCT
ejpam-5722	213	11	)	)	PUNCT
ejpam-5722	213	12	)	)	PUNCT
ejpam-5722	213	13	)	)	PUNCT
ejpam-5722	214	1	⊆	⊆	NUM
ejpam-5722	214	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	214	3	-	-	PUNCT
ejpam-5722	214	4	cl(v	cl(v	NOUN
ejpam-5722	214	5	)	)	PUNCT
ejpam-5722	214	6	)	)	PUNCT
ejpam-5722	214	7	.	.	PUNCT
ejpam-5722	215	1	(	(	PUNCT
ejpam-5722	215	2	3	3	X
ejpam-5722	215	3	)	)	PUNCT
ejpam-5722	215	4	⇒	⇒	NOUN
ejpam-5722	215	5	(	(	PUNCT
ejpam-5722	215	6	4	4	NUM
ejpam-5722	215	7	):	):	PUNCT
ejpam-5722	215	8	let	let	VERB
ejpam-5722	215	9	v	v	PART
ejpam-5722	215	10	be	be	AUX
ejpam-5722	215	11	any	any	DET
ejpam-5722	215	12	(	(	PUNCT
ejpam-5722	215	13	σ1	σ1	PROPN
ejpam-5722	215	14	,	,	PUNCT
ejpam-5722	215	15	σ2)p	σ2)p	NOUN
ejpam-5722	215	16	-	-	PUNCT
ejpam-5722	215	17	open	open	ADJ
ejpam-5722	215	18	set	set	NOUN
ejpam-5722	215	19	of	of	ADP
ejpam-5722	215	20	y	y	PROPN
ejpam-5722	215	21	.	.	PUNCT
ejpam-5722	216	1	then	then	ADV
ejpam-5722	216	2	by	by	ADP
ejpam-5722	216	3	(	(	PUNCT
ejpam-5722	216	4	3	3	NUM
ejpam-5722	216	5	)	)	PUNCT
ejpam-5722	216	6	,	,	PUNCT
ejpam-5722	216	7	we	we	PRON
ejpam-5722	216	8	have	have	VERB
ejpam-5722	216	9	x	x	PART
ejpam-5722	216	10	−	−	NOUN
ejpam-5722	216	11	θ(τ1	θ(τ1	NOUN
ejpam-5722	216	12	,	,	PUNCT
ejpam-5722	216	13	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	216	14	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	216	15	-	-	PUNCT
ejpam-5722	216	16	cl(v	cl(v	NOUN
ejpam-5722	216	17	)	)	PUNCT
ejpam-5722	216	18	)	)	PUNCT
ejpam-5722	216	19	)	)	PUNCT
ejpam-5722	217	1	=	=	SYM
ejpam-5722	217	2	θ(τ1	θ(τ1	PROPN
ejpam-5722	217	3	,	,	PUNCT
ejpam-5722	217	4	τ2)-scl(x	τ2)-scl(x	PROPN
ejpam-5722	217	5	−	−	PROPN
ejpam-5722	217	6	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	217	7	-	-	PUNCT
ejpam-5722	217	8	cl(v	cl(v	NOUN
ejpam-5722	217	9	)	)	PUNCT
ejpam-5722	217	10	)	)	PUNCT
ejpam-5722	217	11	)	)	PUNCT
ejpam-5722	218	1	=	=	SYM
ejpam-5722	218	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	218	3	,	,	PUNCT
ejpam-5722	218	4	τ2)-scl(f	τ2)-scl(f	NOUN
ejpam-5722	218	5	−1(y	−1(y	PUNCT
ejpam-5722	219	1	−	−	ADP
ejpam-5722	219	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	219	3	-	-	NUM
ejpam-5722	219	4	cl(v	cl(v	NOUN
ejpam-5722	219	5	)	)	PUNCT
ejpam-5722	219	6	)	)	PUNCT
ejpam-5722	219	7	)	)	PUNCT
ejpam-5722	220	1	⊆	⊆	NUM
ejpam-5722	220	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5722	220	3	-	-	PUNCT
ejpam-5722	220	4	cl(y	cl(y	NOUN
ejpam-5722	220	5	−	−	NOUN
ejpam-5722	220	6	σ1σ2	σ1σ2	NOUN
ejpam-5722	220	7	-	-	NUM
ejpam-5722	220	8	cl(v	cl(v	NOUN
ejpam-5722	220	9	)	)	PUNCT
ejpam-5722	220	10	)	)	PUNCT
ejpam-5722	220	11	)	)	PUNCT
ejpam-5722	221	1	n.	n.	PROPN
ejpam-5722	221	2	srisarakham	srisarakham	PROPN
ejpam-5722	221	3	,	,	PUNCT
ejpam-5722	221	4	s.	s.	PROPN
ejpam-5722	221	5	sompong	sompong	PROPN
ejpam-5722	221	6	,	,	PUNCT
ejpam-5722	221	7	c.	c.	PROPN
ejpam-5722	221	8	boonpok	boonpok	PROPN
ejpam-5722	221	9	/	/	SYM
ejpam-5722	221	10	eur	eur	PROPN
ejpam-5722	221	11	.	.	PUNCT
ejpam-5722	222	1	j.	j.	PROPN
ejpam-5722	222	2	pure	pure	PROPN
ejpam-5722	222	3	appl	appl	PROPN
ejpam-5722	222	4	.	.	PROPN
ejpam-5722	222	5	math	math	PROPN
ejpam-5722	222	6	,	,	PUNCT
ejpam-5722	222	7	18	18	NUM
ejpam-5722	222	8	(	(	PUNCT
ejpam-5722	222	9	1	1	NUM
ejpam-5722	222	10	)	)	PUNCT
ejpam-5722	222	11	(	(	PUNCT
ejpam-5722	222	12	2025	2025	NUM
ejpam-5722	222	13	)	)	PUNCT
ejpam-5722	222	14	,	,	PUNCT
ejpam-5722	222	15	5722	5722	NUM
ejpam-5722	222	16	8	8	NUM
ejpam-5722	222	17	of	of	ADP
ejpam-5722	222	18	12	12	NUM
ejpam-5722	222	19	=	=	SYM
ejpam-5722	222	20	x	x	SYM
ejpam-5722	222	21	−	−	PRON
ejpam-5722	222	22	f−1(σ1σ2	f−1(σ1σ2	VERB
ejpam-5722	222	23	-	-	PUNCT
ejpam-5722	222	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5722	222	25	-	-	PUNCT
ejpam-5722	222	26	cl(v	cl(v	NOUN
ejpam-5722	222	27	)	)	PUNCT
ejpam-5722	222	28	)	)	PUNCT
ejpam-5722	222	29	)	)	PUNCT
ejpam-5722	223	1	⊆	⊆	NUM
ejpam-5722	223	2	x	x	SYM
ejpam-5722	223	3	−	−	PROPN
ejpam-5722	223	4	f−1(v	f−1(v	PROPN
ejpam-5722	223	5	)	)	PUNCT
ejpam-5722	223	6	and	and	CCONJ
ejpam-5722	223	7	hence	hence	ADV
ejpam-5722	223	8	f−1(v	f−1(v	NOUN
ejpam-5722	223	9	)	)	PUNCT
ejpam-5722	224	1	⊆	⊆	NUM
ejpam-5722	224	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	224	3	,	,	PUNCT
ejpam-5722	224	4	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	224	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	224	6	-	-	PUNCT
ejpam-5722	224	7	cl(v	cl(v	NOUN
ejpam-5722	224	8	)	)	PUNCT
ejpam-5722	224	9	)	)	PUNCT
ejpam-5722	224	10	)	)	PUNCT
ejpam-5722	224	11	.	.	PUNCT
ejpam-5722	225	1	(	(	PUNCT
ejpam-5722	225	2	4	4	X
ejpam-5722	225	3	)	)	PUNCT
ejpam-5722	225	4	⇒	⇒	NOUN
ejpam-5722	225	5	(	(	PUNCT
ejpam-5722	225	6	1	1	NUM
ejpam-5722	225	7	):	):	PUNCT
ejpam-5722	225	8	let	let	VERB
ejpam-5722	225	9	v	v	PART
ejpam-5722	225	10	be	be	AUX
ejpam-5722	225	11	any	any	DET
ejpam-5722	225	12	σ1σ2	σ1σ2	NOUN
ejpam-5722	225	13	-	-	ADJ
ejpam-5722	225	14	open	open	ADJ
ejpam-5722	225	15	set	set	NOUN
ejpam-5722	225	16	of	of	ADP
ejpam-5722	225	17	y	y	PROPN
ejpam-5722	225	18	.	.	PUNCT
ejpam-5722	226	1	then	then	ADV
ejpam-5722	226	2	,	,	PUNCT
ejpam-5722	226	3	v	v	NOUN
ejpam-5722	226	4	is	be	AUX
ejpam-5722	226	5	(	(	PUNCT
ejpam-5722	226	6	σ1	σ1	PROPN
ejpam-5722	226	7	,	,	PUNCT
ejpam-5722	226	8	σ2)p	σ2)p	NOUN
ejpam-5722	226	9	-	-	PUNCT
ejpam-5722	226	10	open	open	ADJ
ejpam-5722	226	11	in	in	ADP
ejpam-5722	226	12	y	y	PROPN
ejpam-5722	226	13	and	and	CCONJ
ejpam-5722	226	14	by	by	ADP
ejpam-5722	226	15	(	(	PUNCT
ejpam-5722	226	16	4	4	NUM
ejpam-5722	226	17	)	)	PUNCT
ejpam-5722	226	18	,	,	PUNCT
ejpam-5722	226	19	we	we	PRON
ejpam-5722	226	20	have	have	AUX
ejpam-5722	226	21	f−1(v	f−1(v	NOUN
ejpam-5722	226	22	)	)	PUNCT
ejpam-5722	227	1	⊆	⊆	NUM
ejpam-5722	227	2	θ(τ1	θ(τ1	NOUN
ejpam-5722	227	3	,	,	PUNCT
ejpam-5722	227	4	τ2)-sint(f	τ2)-sint(f	PROPN
ejpam-5722	227	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5722	227	6	-	-	PUNCT
ejpam-5722	227	7	cl(v	cl(v	NOUN
ejpam-5722	227	8	)	)	PUNCT
ejpam-5722	227	9	)	)	PUNCT
ejpam-5722	227	10	)	)	PUNCT
ejpam-5722	227	11	.	.	PUNCT
ejpam-5722	228	1	by	by	ADP
ejpam-5722	228	2	theorem	theorem	NOUN
ejpam-5722	228	3	1	1	NUM
ejpam-5722	228	4	,	,	PUNCT
ejpam-5722	228	5	f	f	PROPN
ejpam-5722	228	6	is	be	AUX
ejpam-5722	228	7	quasi	quasi	NOUN
ejpam-5722	228	8	θ(τ1	θ(τ1	NOUN
ejpam-5722	228	9	,	,	PUNCT
ejpam-5722	228	10	τ2)-continuous	τ2)-continuous	PROPN
ejpam-5722	228	11	.	.	PUNCT
ejpam-5722	229	1	recall	recall	VERB
ejpam-5722	229	2	that	that	SCONJ
ejpam-5722	229	3	a	a	DET
ejpam-5722	229	4	bitopological	bitopological	ADJ
ejpam-5722	229	5	space	space	NOUN
ejpam-5722	229	6	(	(	PUNCT
ejpam-5722	229	7	x	x	NOUN
ejpam-5722	229	8	,	,	PUNCT
ejpam-5722	229	9	τ1	τ1	NOUN
ejpam-5722	229	10	,	,	PUNCT
ejpam-5722	229	11	τ2	τ2	NOUN
ejpam-5722	229	12	)	)	PUNCT
ejpam-5722	229	13	is	be	AUX
ejpam-5722	229	14	said	say	VERB
ejpam-5722	229	15	to	to	PART
ejpam-5722	229	16	be	be	AUX
ejpam-5722	229	17	quasi	quasi	X
ejpam-5722	229	18	(	(	PUNCT
ejpam-5722	229	19	τ1	τ1	NOUN
ejpam-5722	229	20	,	,	PUNCT
ejpam-5722	229	21	τ2)-h	τ2)-h	PUNCT
ejpam-5722	229	22	-closed	-closed	ADJ
ejpam-5722	229	23	[	[	X
ejpam-5722	229	24	40	40	NUM
ejpam-5722	229	25	]	]	PUNCT
ejpam-5722	229	26	if	if	SCONJ
ejpam-5722	229	27	every	every	DET
ejpam-5722	229	28	τ1τ2	τ1τ2	ADJ
ejpam-5722	229	29	-	-	ADJ
ejpam-5722	229	30	open	open	ADJ
ejpam-5722	229	31	cover	cover	NOUN
ejpam-5722	229	32	{	{	PUNCT
ejpam-5722	229	33	uγ	uγ	ADV
ejpam-5722	229	34	|	|	ADV
ejpam-5722	229	35	γ	γ	X
ejpam-5722	229	36	∈	∈	PROPN
ejpam-5722	229	37	γ	γ	X
ejpam-5722	229	38	}	}	PUNCT
ejpam-5722	229	39	,	,	PUNCT
ejpam-5722	229	40	there	there	PRON
ejpam-5722	229	41	exists	exist	VERB
ejpam-5722	229	42	a	a	DET
ejpam-5722	229	43	finite	finite	NOUN
ejpam-5722	229	44	subset	subset	NOUN
ejpam-5722	229	45	γ0	γ0	NOUN
ejpam-5722	229	46	of	of	ADP
ejpam-5722	229	47	γ	γ	NOUN
ejpam-5722	229	48	such	such	ADJ
ejpam-5722	229	49	that	that	SCONJ
ejpam-5722	229	50	x	x	X
ejpam-5722	230	1	=	=	PUNCT
ejpam-5722	230	2	∪{τ1τ2	∪{τ1τ2	NOUN
ejpam-5722	230	3	-	-	NOUN
ejpam-5722	230	4	cl(uγ	cl(uγ	NOUN
ejpam-5722	230	5	)	)	PUNCT
ejpam-5722	230	6	|	|	ADV
ejpam-5722	230	7	γ	γ	PROPN
ejpam-5722	230	8	∈	∈	PROPN
ejpam-5722	230	9	γ0	γ0	PROPN
ejpam-5722	230	10	}	}	PUNCT
ejpam-5722	230	11	.	.	PUNCT
ejpam-5722	231	1	a	a	DET
ejpam-5722	231	2	subset	subset	NOUN
ejpam-5722	231	3	k	k	NOUN
ejpam-5722	231	4	of	of	ADP
ejpam-5722	231	5	a	a	DET
ejpam-5722	231	6	bitopological	bitopological	ADJ
ejpam-5722	231	7	space	space	NOUN
ejpam-5722	231	8	(	(	PUNCT
ejpam-5722	231	9	x	x	NOUN
ejpam-5722	231	10	,	,	PUNCT
ejpam-5722	231	11	τ1	τ1	NOUN
ejpam-5722	231	12	,	,	PUNCT
ejpam-5722	231	13	τ2	τ2	NOUN
ejpam-5722	231	14	)	)	PUNCT
ejpam-5722	231	15	is	be	AUX
ejpam-5722	231	16	said	say	VERB
ejpam-5722	231	17	to	to	PART
ejpam-5722	231	18	be	be	AUX
ejpam-5722	231	19	quasi	quasi	X
ejpam-5722	231	20	(	(	PUNCT
ejpam-5722	231	21	τ1	τ1	NOUN
ejpam-5722	231	22	,	,	PUNCT
ejpam-5722	231	23	τ2)-h	τ2)-h	NOUN
ejpam-5722	231	24	-closed	-close	VERB
ejpam-5722	231	25	relative	relative	ADJ
ejpam-5722	231	26	to	to	ADP
ejpam-5722	231	27	x	x	PRON
ejpam-5722	231	28	if	if	SCONJ
ejpam-5722	231	29	for	for	ADP
ejpam-5722	231	30	any	any	DET
ejpam-5722	231	31	cover	cover	NOUN
ejpam-5722	231	32	{	{	PUNCT
ejpam-5722	231	33	vγ	vγ	NOUN
ejpam-5722	231	34	|	|	ADV
ejpam-5722	231	35	γ	γ	PROPN
ejpam-5722	231	36	∈	∈	PROPN
ejpam-5722	231	37	γ	γ	X
ejpam-5722	231	38	}	}	PUNCT
ejpam-5722	231	39	by	by	ADP
ejpam-5722	231	40	τ1τ2	τ1τ2	ADJ
ejpam-5722	231	41	-	-	ADJ
ejpam-5722	231	42	open	open	ADJ
ejpam-5722	231	43	sets	set	NOUN
ejpam-5722	231	44	of	of	ADP
ejpam-5722	231	45	x	x	NOUN
ejpam-5722	231	46	,	,	PUNCT
ejpam-5722	231	47	there	there	PRON
ejpam-5722	231	48	exists	exist	VERB
ejpam-5722	231	49	a	a	DET
ejpam-5722	231	50	finite	finite	NOUN
ejpam-5722	231	51	subset	subset	NOUN
ejpam-5722	231	52	γ0	γ0	NOUN
ejpam-5722	231	53	of	of	ADP
ejpam-5722	231	54	γ	γ	PRON
ejpam-5722	231	55	such	such	ADJ
ejpam-5722	231	56	that	that	SCONJ
ejpam-5722	231	57	k	k	PROPN
ejpam-5722	231	58	⊆	⊆	NUM
ejpam-5722	231	59	∪{τ1τ2	∪{τ1τ2	ADJ
ejpam-5722	231	60	-	-	ADJ
ejpam-5722	231	61	cl(vγ	cl(vγ	ADJ
ejpam-5722	231	62	)	)	PUNCT
ejpam-5722	231	63	|	|	ADV
ejpam-5722	231	64	γ	γ	PROPN
ejpam-5722	231	65	∈	∈	PROPN
ejpam-5722	231	66	γ0	γ0	PROPN
ejpam-5722	231	67	}	}	PUNCT
ejpam-5722	231	68	.	.	PUNCT
ejpam-5722	232	1	a	a	DET
ejpam-5722	232	2	bitopological	bitopological	ADJ
ejpam-5722	232	3	space	space	NOUN
ejpam-5722	232	4	(	(	PUNCT
ejpam-5722	232	5	x	x	NOUN
ejpam-5722	232	6	,	,	PUNCT
ejpam-5722	232	7	τ1	τ1	NOUN
ejpam-5722	232	8	,	,	PUNCT
ejpam-5722	232	9	τ2	τ2	NOUN
ejpam-5722	232	10	)	)	PUNCT
ejpam-5722	232	11	is	be	AUX
ejpam-5722	232	12	called	call	VERB
ejpam-5722	232	13	s-(τ1	s-(τ1	PROPN
ejpam-5722	232	14	,	,	PUNCT
ejpam-5722	232	15	τ2)-closed	τ2)-close	VERB
ejpam-5722	232	16	[	[	X
ejpam-5722	232	17	33	33	NUM
ejpam-5722	232	18	]	]	PUNCT
ejpam-5722	232	19	if	if	SCONJ
ejpam-5722	232	20	every	every	DET
ejpam-5722	232	21	(	(	PUNCT
ejpam-5722	232	22	τ1	τ1	NOUN
ejpam-5722	232	23	,	,	PUNCT
ejpam-5722	232	24	τ2)s	τ2)s	NOUN
ejpam-5722	232	25	-	-	PUNCT
ejpam-5722	232	26	open	open	ADJ
ejpam-5722	232	27	cover	cover	NOUN
ejpam-5722	232	28	{	{	PUNCT
ejpam-5722	232	29	uγ	uγ	ADV
ejpam-5722	232	30	|	|	ADV
ejpam-5722	232	31	γ	γ	X
ejpam-5722	232	32	∈	∈	PROPN
ejpam-5722	232	33	γ	γ	X
ejpam-5722	232	34	}	}	PUNCT
ejpam-5722	232	35	,	,	PUNCT
ejpam-5722	232	36	there	there	PRON
ejpam-5722	232	37	exists	exist	VERB
ejpam-5722	232	38	a	a	DET
ejpam-5722	232	39	finite	finite	NOUN
ejpam-5722	232	40	subset	subset	NOUN
ejpam-5722	232	41	γ0	γ0	NOUN
ejpam-5722	232	42	of	of	ADP
ejpam-5722	232	43	γ	γ	NOUN
ejpam-5722	232	44	such	such	ADJ
ejpam-5722	232	45	that	that	SCONJ
ejpam-5722	232	46	x	x	X
ejpam-5722	232	47	=	=	SYM
ejpam-5722	232	48	∪{(τ1	∪{(τ1	PROPN
ejpam-5722	232	49	,	,	PUNCT
ejpam-5722	232	50	τ2)-scl(uγ	τ2)-scl(uγ	NOUN
ejpam-5722	232	51	)	)	PUNCT
ejpam-5722	233	1	|	|	ADV
ejpam-5722	233	2	γ	γ	PROPN
ejpam-5722	233	3	∈	∈	PROPN
ejpam-5722	233	4	γ0	γ0	PROPN
ejpam-5722	233	5	}	}	PUNCT
ejpam-5722	233	6	.	.	PUNCT
ejpam-5722	234	1	a	a	DET
ejpam-5722	234	2	subset	subset	NOUN
ejpam-5722	234	3	k	k	NOUN
ejpam-5722	234	4	of	of	ADP
ejpam-5722	234	5	a	a	DET
ejpam-5722	234	6	bitopological	bitopological	ADJ
ejpam-5722	234	7	space	space	NOUN
ejpam-5722	234	8	(	(	PUNCT
ejpam-5722	234	9	x	x	NOUN
ejpam-5722	234	10	,	,	PUNCT
ejpam-5722	234	11	τ1	τ1	NOUN
ejpam-5722	234	12	,	,	PUNCT
ejpam-5722	234	13	τ2	τ2	NOUN
ejpam-5722	234	14	)	)	PUNCT
ejpam-5722	234	15	is	be	AUX
ejpam-5722	234	16	said	say	VERB
ejpam-5722	234	17	to	to	PART
ejpam-5722	234	18	be	be	AUX
ejpam-5722	234	19	s-(τ1	s-(τ1	PROPN
ejpam-5722	234	20	,	,	PUNCT
ejpam-5722	234	21	τ2)-closed	τ2)-close	VERB
ejpam-5722	234	22	relative	relative	ADJ
ejpam-5722	234	23	to	to	ADP
ejpam-5722	234	24	x	x	PRON
ejpam-5722	234	25	if	if	SCONJ
ejpam-5722	234	26	for	for	ADP
ejpam-5722	234	27	any	any	DET
ejpam-5722	234	28	cover	cover	NOUN
ejpam-5722	234	29	{	{	PUNCT
ejpam-5722	234	30	vγ	vγ	NOUN
ejpam-5722	234	31	|	|	ADV
ejpam-5722	234	32	γ	γ	PROPN
ejpam-5722	234	33	∈	∈	PROPN
ejpam-5722	234	34	γ	γ	X
ejpam-5722	234	35	}	}	PUNCT
ejpam-5722	234	36	by	by	ADP
ejpam-5722	234	37	(	(	PUNCT
ejpam-5722	234	38	τ1	τ1	NOUN
ejpam-5722	234	39	,	,	PUNCT
ejpam-5722	234	40	τ2)s	τ2)s	NOUN
ejpam-5722	234	41	-	-	PUNCT
ejpam-5722	234	42	open	open	ADJ
ejpam-5722	234	43	sets	set	NOUN
ejpam-5722	234	44	of	of	ADP
ejpam-5722	234	45	x	x	NOUN
ejpam-5722	234	46	,	,	PUNCT
ejpam-5722	234	47	there	there	PRON
ejpam-5722	234	48	exists	exist	VERB
ejpam-5722	234	49	a	a	DET
ejpam-5722	234	50	finite	finite	NOUN
ejpam-5722	234	51	subset	subset	NOUN
ejpam-5722	234	52	γ0	γ0	NOUN
ejpam-5722	234	53	of	of	ADP
ejpam-5722	234	54	γ	γ	PRON
ejpam-5722	234	55	such	such	ADJ
ejpam-5722	234	56	that	that	SCONJ
ejpam-5722	234	57	k	k	PROPN
ejpam-5722	234	58	⊆	⊆	NUM
ejpam-5722	234	59	∪{(τ1	∪{(τ1	PROPN
ejpam-5722	234	60	,	,	PUNCT
ejpam-5722	234	61	τ2)-scl(vγ	τ2)-scl(vγ	PROPN
ejpam-5722	234	62	)	)	PUNCT
ejpam-5722	234	63	|	|	ADV
ejpam-5722	234	64	γ	γ	PROPN
ejpam-5722	234	65	∈	∈	PROPN
ejpam-5722	234	66	γ0	γ0	PROPN
ejpam-5722	234	67	}	}	PUNCT
ejpam-5722	234	68	.	.	PUNCT
ejpam-5722	235	1	theorem	theorem	NOUN
ejpam-5722	235	2	6	6	NUM
ejpam-5722	235	3	.	.	PUNCT
ejpam-5722	236	1	if	if	SCONJ
ejpam-5722	236	2	f	f	PROPN
ejpam-5722	236	3	:	:	PUNCT
ejpam-5722	236	4	(	(	PUNCT
ejpam-5722	236	5	x	x	NOUN
ejpam-5722	236	6	,	,	PUNCT
ejpam-5722	236	7	τ1	τ1	NOUN
ejpam-5722	236	8	,	,	PUNCT
ejpam-5722	236	9	τ2	τ2	NOUN
ejpam-5722	236	10	)	)	PUNCT
ejpam-5722	236	11	→	→	SYM
ejpam-5722	236	12	(	(	PUNCT
ejpam-5722	236	13	y	y	PROPN
ejpam-5722	236	14	,	,	PUNCT
ejpam-5722	236	15	σ1	σ1	PROPN
ejpam-5722	236	16	,	,	PUNCT
ejpam-5722	236	17	σ2	σ2	PROPN
ejpam-5722	236	18	)	)	PUNCT
ejpam-5722	236	19	is	be	AUX
ejpam-5722	236	20	quasi	quasi	NOUN
ejpam-5722	236	21	θ(τ1	θ(τ1	NOUN
ejpam-5722	236	22	,	,	PUNCT
ejpam-5722	236	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	236	24	and	and	CCONJ
ejpam-5722	236	25	k	k	PROPN
ejpam-5722	236	26	is	be	AUX
ejpam-5722	236	27	s(τ1	s(τ1	NOUN
ejpam-5722	236	28	,	,	PUNCT
ejpam-5722	236	29	τ2)-closed	τ2)-close	VERB
ejpam-5722	236	30	relative	relative	ADJ
ejpam-5722	236	31	to	to	ADP
ejpam-5722	236	32	x	x	PRON
ejpam-5722	236	33	,	,	PUNCT
ejpam-5722	236	34	then	then	ADV
ejpam-5722	236	35	f(k	f(k	VERB
ejpam-5722	236	36	)	)	PUNCT
ejpam-5722	236	37	is	be	AUX
ejpam-5722	236	38	quasi	quasi	X
ejpam-5722	236	39	(	(	PUNCT
ejpam-5722	236	40	σ1	σ1	PROPN
ejpam-5722	236	41	,	,	PUNCT
ejpam-5722	236	42	σ2)-h	σ2)-h	PROPN
ejpam-5722	236	43	-closed	-closed	ADJ
ejpam-5722	236	44	relative	relative	ADJ
ejpam-5722	236	45	to	to	ADP
ejpam-5722	236	46	y	y	PROPN
ejpam-5722	236	47	.	.	PUNCT
ejpam-5722	237	1	proof	proof	NOUN
ejpam-5722	237	2	.	.	PUNCT
ejpam-5722	238	1	let	let	VERB
ejpam-5722	238	2	{	{	PUNCT
ejpam-5722	238	3	vγ	vγ	VERB
ejpam-5722	238	4	|	|	ADV
ejpam-5722	238	5	γ	γ	PROPN
ejpam-5722	238	6	∈	∈	PROPN
ejpam-5722	238	7	γ	γ	AUX
ejpam-5722	238	8	}	}	PUNCT
ejpam-5722	238	9	be	be	AUX
ejpam-5722	238	10	a	a	DET
ejpam-5722	238	11	cover	cover	NOUN
ejpam-5722	238	12	of	of	ADP
ejpam-5722	238	13	f(k	f(k	VERB
ejpam-5722	238	14	)	)	PUNCT
ejpam-5722	238	15	by	by	ADP
ejpam-5722	238	16	σ1σ2	σ1σ2	NOUN
ejpam-5722	238	17	-	-	PUNCT
ejpam-5722	238	18	open	open	ADJ
ejpam-5722	238	19	sets	set	NOUN
ejpam-5722	238	20	in	in	ADP
ejpam-5722	238	21	y	y	PROPN
ejpam-5722	238	22	.	.	PUNCT
ejpam-5722	239	1	for	for	ADP
ejpam-5722	239	2	each	each	DET
ejpam-5722	239	3	k	k	PROPN
ejpam-5722	239	4	∈	∈	PROPN
ejpam-5722	239	5	k	k	NOUN
ejpam-5722	239	6	,	,	PUNCT
ejpam-5722	239	7	there	there	PRON
ejpam-5722	239	8	exists	exist	VERB
ejpam-5722	239	9	γ(k	γ(k	PROPN
ejpam-5722	239	10	)	)	PUNCT
ejpam-5722	240	1	∈	∈	PROPN
ejpam-5722	240	2	γ	γ	NOUN
ejpam-5722	240	3	such	such	ADJ
ejpam-5722	240	4	that	that	SCONJ
ejpam-5722	240	5	f(k	f(k	ADJ
ejpam-5722	240	6	)	)	PUNCT
ejpam-5722	240	7	∈	∈	PROPN
ejpam-5722	240	8	vγ(k	vγ(k	NOUN
ejpam-5722	240	9	)	)	PUNCT
ejpam-5722	240	10	.	.	PUNCT
ejpam-5722	241	1	since	since	SCONJ
ejpam-5722	241	2	f	f	PROPN
ejpam-5722	241	3	is	be	AUX
ejpam-5722	241	4	quasi	quasi	NOUN
ejpam-5722	241	5	θ(τ1	θ(τ1	NOUN
ejpam-5722	241	6	,	,	PUNCT
ejpam-5722	241	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	241	8	,	,	PUNCT
ejpam-5722	241	9	there	there	PRON
ejpam-5722	241	10	exists	exist	VERB
ejpam-5722	241	11	a	a	DET
ejpam-5722	241	12	(	(	PUNCT
ejpam-5722	241	13	τ1	τ1	NOUN
ejpam-5722	241	14	,	,	PUNCT
ejpam-5722	241	15	τ2)s	τ2)s	NOUN
ejpam-5722	241	16	-	-	PUNCT
ejpam-5722	241	17	open	open	ADJ
ejpam-5722	241	18	set	set	ADJ
ejpam-5722	241	19	uk	uk	PROPN
ejpam-5722	241	20	of	of	ADP
ejpam-5722	241	21	x	x	PUNCT
ejpam-5722	241	22	containing	contain	VERB
ejpam-5722	241	23	k	k	PROPN
ejpam-5722	241	24	such	such	ADJ
ejpam-5722	241	25	that	that	DET
ejpam-5722	241	26	f((τ1	f((τ1	PROPN
ejpam-5722	241	27	,	,	PUNCT
ejpam-5722	241	28	τ2)-scl(uk	τ2)-scl(uk	ADJ
ejpam-5722	241	29	)	)	PUNCT
ejpam-5722	241	30	)	)	PUNCT
ejpam-5722	242	1	⊆	⊆	X
ejpam-5722	242	2	σ1σ2	σ1σ2	NUM
ejpam-5722	242	3	-	-	PUNCT
ejpam-5722	242	4	cl(vγ(k	cl(vγ(k	NOUN
ejpam-5722	242	5	)	)	PUNCT
ejpam-5722	242	6	)	)	PUNCT
ejpam-5722	242	7	.	.	PUNCT
ejpam-5722	243	1	since	since	SCONJ
ejpam-5722	243	2	{	{	PUNCT
ejpam-5722	243	3	uk	uk	PROPN
ejpam-5722	243	4	|	|	ADV
ejpam-5722	243	5	k	k	PROPN
ejpam-5722	243	6	∈	∈	PROPN
ejpam-5722	243	7	k	k	AUX
ejpam-5722	243	8	}	}	PUNCT
ejpam-5722	243	9	is	be	AUX
ejpam-5722	243	10	a	a	DET
ejpam-5722	243	11	cover	cover	NOUN
ejpam-5722	243	12	of	of	ADP
ejpam-5722	243	13	k	k	X
ejpam-5722	243	14	by	by	ADP
ejpam-5722	243	15	(	(	PUNCT
ejpam-5722	243	16	τ1	τ1	NOUN
ejpam-5722	243	17	,	,	PUNCT
ejpam-5722	243	18	τ2)s	τ2)s	NOUN
ejpam-5722	243	19	-	-	PUNCT
ejpam-5722	243	20	open	open	ADJ
ejpam-5722	243	21	sets	set	NOUN
ejpam-5722	243	22	in	in	ADP
ejpam-5722	243	23	x	x	NOUN
ejpam-5722	243	24	,	,	PUNCT
ejpam-5722	243	25	there	there	PRON
ejpam-5722	243	26	exists	exist	VERB
ejpam-5722	243	27	a	a	DET
ejpam-5722	243	28	finite	finite	NOUN
ejpam-5722	243	29	subset	subset	VERB
ejpam-5722	243	30	k0	k0	PROPN
ejpam-5722	243	31	of	of	ADP
ejpam-5722	243	32	k	k	PROPN
ejpam-5722	243	33	such	such	ADJ
ejpam-5722	243	34	that	that	SCONJ
ejpam-5722	243	35	k	k	PROPN
ejpam-5722	243	36	⊆	⊆	NUM
ejpam-5722	243	37	∪{uk	∪{uk	PROPN
ejpam-5722	243	38	|	|	NOUN
ejpam-5722	243	39	k	k	PROPN
ejpam-5722	243	40	∈	∈	PROPN
ejpam-5722	243	41	k0	k0	PROPN
ejpam-5722	243	42	}	}	PUNCT
ejpam-5722	243	43	.	.	PUNCT
ejpam-5722	244	1	thus	thus	ADV
ejpam-5722	244	2	,	,	PUNCT
ejpam-5722	244	3	f(k	f(k	VERB
ejpam-5722	244	4	)	)	PUNCT
ejpam-5722	244	5	⊆	⊆	NUM
ejpam-5722	244	6	∪{f((τ1	∪{f((τ1	NOUN
ejpam-5722	244	7	,	,	PUNCT
ejpam-5722	244	8	τ2)-scl(uk	τ2)-scl(uk	ADJ
ejpam-5722	244	9	)	)	PUNCT
ejpam-5722	244	10	)	)	PUNCT
ejpam-5722	245	1	|	|	ADV
ejpam-5722	245	2	k	k	PROPN
ejpam-5722	245	3	∈	∈	PROPN
ejpam-5722	245	4	k0	k0	PROPN
ejpam-5722	245	5	}	}	PUNCT
ejpam-5722	245	6	⊆	⊆	NUM
ejpam-5722	245	7	∪{σ1σ2	∪{σ1σ2	NOUN
ejpam-5722	245	8	-	-	PUNCT
ejpam-5722	245	9	cl(vγ(k	cl(vγ(k	NOUN
ejpam-5722	245	10	)	)	PUNCT
ejpam-5722	245	11	)	)	PUNCT
ejpam-5722	246	1	|	|	ADV
ejpam-5722	246	2	k	k	PROPN
ejpam-5722	246	3	∈	∈	PROPN
ejpam-5722	246	4	k0	k0	PROPN
ejpam-5722	246	5	}	}	PUNCT
ejpam-5722	246	6	.	.	PUNCT
ejpam-5722	247	1	this	this	PRON
ejpam-5722	247	2	shows	show	VERB
ejpam-5722	247	3	that	that	SCONJ
ejpam-5722	247	4	f(k	f(k	VERB
ejpam-5722	247	5	)	)	PUNCT
ejpam-5722	247	6	is	be	AUX
ejpam-5722	247	7	quasi	quasi	X
ejpam-5722	247	8	(	(	PUNCT
ejpam-5722	247	9	σ1	σ1	PROPN
ejpam-5722	247	10	,	,	PUNCT
ejpam-5722	247	11	σ2)-h	σ2)-h	PROPN
ejpam-5722	247	12	-closed	-closed	ADJ
ejpam-5722	247	13	relative	relative	ADJ
ejpam-5722	247	14	to	to	ADP
ejpam-5722	247	15	y	y	PROPN
ejpam-5722	247	16	.	.	PUNCT
ejpam-5722	248	1	corollary	corollary	ADJ
ejpam-5722	248	2	1	1	NUM
ejpam-5722	248	3	.	.	PUNCT
ejpam-5722	249	1	if	if	SCONJ
ejpam-5722	249	2	f	f	PROPN
ejpam-5722	249	3	:	:	PUNCT
ejpam-5722	249	4	(	(	PUNCT
ejpam-5722	249	5	x	x	NOUN
ejpam-5722	249	6	,	,	PUNCT
ejpam-5722	249	7	τ1	τ1	NOUN
ejpam-5722	249	8	,	,	PUNCT
ejpam-5722	249	9	τ2	τ2	NOUN
ejpam-5722	249	10	)	)	PUNCT
ejpam-5722	249	11	→	→	SYM
ejpam-5722	249	12	(	(	PUNCT
ejpam-5722	249	13	y	y	PROPN
ejpam-5722	249	14	,	,	PUNCT
ejpam-5722	249	15	σ1	σ1	PROPN
ejpam-5722	249	16	,	,	PUNCT
ejpam-5722	249	17	σ2	σ2	PROPN
ejpam-5722	249	18	)	)	PUNCT
ejpam-5722	249	19	is	be	AUX
ejpam-5722	249	20	a	a	DET
ejpam-5722	249	21	quasi	quasi	NOUN
ejpam-5722	249	22	θ(τ1	θ(τ1	NOUN
ejpam-5722	249	23	,	,	PUNCT
ejpam-5722	249	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	249	25	surjection	surjection	NOUN
ejpam-5722	249	26	and	and	CCONJ
ejpam-5722	249	27	(	(	PUNCT
ejpam-5722	249	28	x	x	NOUN
ejpam-5722	249	29	,	,	PUNCT
ejpam-5722	249	30	τ1	τ1	NOUN
ejpam-5722	249	31	,	,	PUNCT
ejpam-5722	249	32	τ2	τ2	NOUN
ejpam-5722	249	33	)	)	PUNCT
ejpam-5722	249	34	is	be	AUX
ejpam-5722	249	35	s-(τ1	s-(τ1	PROPN
ejpam-5722	249	36	,	,	PUNCT
ejpam-5722	249	37	τ2)-closed	τ2)-closed	ADJ
ejpam-5722	249	38	,	,	PUNCT
ejpam-5722	249	39	then	then	ADV
ejpam-5722	249	40	(	(	PUNCT
ejpam-5722	249	41	y	y	PROPN
ejpam-5722	249	42	,	,	PUNCT
ejpam-5722	249	43	σ1	σ1	PROPN
ejpam-5722	249	44	,	,	PUNCT
ejpam-5722	249	45	σ2	σ2	PROPN
ejpam-5722	249	46	)	)	PUNCT
ejpam-5722	249	47	is	be	AUX
ejpam-5722	249	48	quasi	quasi	X
ejpam-5722	249	49	(	(	PUNCT
ejpam-5722	249	50	σ1	σ1	PROPN
ejpam-5722	249	51	,	,	PUNCT
ejpam-5722	249	52	σ2)-h	σ2)-h	PROPN
ejpam-5722	249	53	-closed	-closed	ADJ
ejpam-5722	249	54	.	.	PUNCT
ejpam-5722	250	1	definition	definition	NOUN
ejpam-5722	250	2	5	5	NUM
ejpam-5722	250	3	.	.	PUNCT
ejpam-5722	251	1	[	[	X
ejpam-5722	251	2	34	34	NUM
ejpam-5722	251	3	]	]	PUNCT
ejpam-5722	251	4	a	a	DET
ejpam-5722	251	5	bitopological	bitopological	ADJ
ejpam-5722	251	6	space	space	NOUN
ejpam-5722	251	7	(	(	PUNCT
ejpam-5722	251	8	x	x	NOUN
ejpam-5722	251	9	,	,	PUNCT
ejpam-5722	251	10	τ1	τ1	NOUN
ejpam-5722	251	11	,	,	PUNCT
ejpam-5722	251	12	τ2	τ2	NOUN
ejpam-5722	251	13	)	)	PUNCT
ejpam-5722	251	14	is	be	AUX
ejpam-5722	251	15	said	say	VERB
ejpam-5722	251	16	to	to	PART
ejpam-5722	251	17	be	be	AUX
ejpam-5722	251	18	τ1τ2	τ1τ2	NOUN
ejpam-5722	251	19	-	-	ADJ
ejpam-5722	251	20	urysohn	urysohn	ADJ
ejpam-5722	251	21	if	if	SCONJ
ejpam-5722	251	22	for	for	ADP
ejpam-5722	251	23	each	each	DET
ejpam-5722	251	24	pair	pair	NOUN
ejpam-5722	251	25	of	of	ADP
ejpam-5722	251	26	distinct	distinct	ADJ
ejpam-5722	251	27	points	point	NOUN
ejpam-5722	251	28	x	x	PUNCT
ejpam-5722	251	29	and	and	CCONJ
ejpam-5722	251	30	y	y	PROPN
ejpam-5722	251	31	in	in	ADP
ejpam-5722	251	32	x	x	SYM
ejpam-5722	251	33	,	,	PUNCT
ejpam-5722	251	34	there	there	PRON
ejpam-5722	251	35	exist	exist	VERB
ejpam-5722	251	36	τ1τ2	τ1τ2	ADJ
ejpam-5722	251	37	-	-	ADJ
ejpam-5722	251	38	open	open	ADJ
ejpam-5722	251	39	sets	set	NOUN
ejpam-5722	251	40	u	u	NOUN
ejpam-5722	251	41	and	and	CCONJ
ejpam-5722	251	42	v	v	ADP
ejpam-5722	251	43	such	such	ADJ
ejpam-5722	251	44	that	that	SCONJ
ejpam-5722	251	45	x	x	SYM
ejpam-5722	251	46	∈	∈	PROPN
ejpam-5722	251	47	u	u	NOUN
ejpam-5722	251	48	,	,	PUNCT
ejpam-5722	251	49	y	y	PROPN
ejpam-5722	251	50	∈	∈	PROPN
ejpam-5722	251	51	v	v	NOUN
ejpam-5722	251	52	and	and	CCONJ
ejpam-5722	251	53	τ1τ2	τ1τ2	NOUN
ejpam-5722	251	54	-	-	NOUN
ejpam-5722	251	55	cl(u	cl(u	NOUN
ejpam-5722	251	56	)	)	PUNCT
ejpam-5722	251	57	∩	∩	NOUN
ejpam-5722	251	58	τ1τ2	τ1τ2	NOUN
ejpam-5722	251	59	-	-	NOUN
ejpam-5722	251	60	cl(v	cl(v	X
ejpam-5722	251	61	)	)	PUNCT
ejpam-5722	251	62	=	=	PUNCT
ejpam-5722	251	63	∅.	∅.	PRON
ejpam-5722	251	64	definition	definition	NOUN
ejpam-5722	251	65	6	6	NUM
ejpam-5722	251	66	.	.	PUNCT
ejpam-5722	252	1	a	a	DET
ejpam-5722	252	2	bitopological	bitopological	ADJ
ejpam-5722	252	3	space	space	NOUN
ejpam-5722	252	4	(	(	PUNCT
ejpam-5722	252	5	x	x	NOUN
ejpam-5722	252	6	,	,	PUNCT
ejpam-5722	252	7	τ1	τ1	NOUN
ejpam-5722	252	8	,	,	PUNCT
ejpam-5722	252	9	τ2	τ2	NOUN
ejpam-5722	252	10	)	)	PUNCT
ejpam-5722	252	11	is	be	AUX
ejpam-5722	252	12	called	call	VERB
ejpam-5722	252	13	(	(	PUNCT
ejpam-5722	252	14	τ1	τ1	NOUN
ejpam-5722	252	15	,	,	PUNCT
ejpam-5722	252	16	τ2)s	τ2)s	NOUN
ejpam-5722	252	17	-	-	PUNCT
ejpam-5722	252	18	hausdorff	hausdorff	NOUN
ejpam-5722	252	19	if	if	SCONJ
ejpam-5722	252	20	for	for	ADP
ejpam-5722	252	21	each	each	DET
ejpam-5722	252	22	pair	pair	NOUN
ejpam-5722	252	23	of	of	ADP
ejpam-5722	252	24	distinct	distinct	ADJ
ejpam-5722	252	25	points	point	NOUN
ejpam-5722	252	26	x	x	PUNCT
ejpam-5722	252	27	and	and	CCONJ
ejpam-5722	252	28	y	y	PROPN
ejpam-5722	252	29	in	in	ADP
ejpam-5722	252	30	x	x	SYM
ejpam-5722	252	31	,	,	PUNCT
ejpam-5722	252	32	there	there	PRON
ejpam-5722	252	33	exist	exist	VERB
ejpam-5722	252	34	(	(	PUNCT
ejpam-5722	252	35	τ1	τ1	NOUN
ejpam-5722	252	36	,	,	PUNCT
ejpam-5722	252	37	τ2)s	τ2)s	NOUN
ejpam-5722	252	38	-	-	PUNCT
ejpam-5722	252	39	open	open	ADJ
ejpam-5722	252	40	sets	set	VERB
ejpam-5722	252	41	u	u	NOUN
ejpam-5722	252	42	and	and	CCONJ
ejpam-5722	252	43	v	v	ADP
ejpam-5722	252	44	such	such	ADJ
ejpam-5722	252	45	that	that	SCONJ
ejpam-5722	252	46	x	x	SYM
ejpam-5722	252	47	∈	∈	PROPN
ejpam-5722	252	48	u	u	NOUN
ejpam-5722	252	49	,	,	PUNCT
ejpam-5722	252	50	y	y	PROPN
ejpam-5722	252	51	∈	∈	PROPN
ejpam-5722	252	52	v	v	NOUN
ejpam-5722	252	53	and	and	CCONJ
ejpam-5722	252	54	u	u	NOUN
ejpam-5722	252	55	∩	∩	NOUN
ejpam-5722	252	56	v	v	NOUN
ejpam-5722	252	57	=	=	PUNCT
ejpam-5722	252	58	∅.	∅.	PROPN
ejpam-5722	252	59	n.	n.	PROPN
ejpam-5722	252	60	srisarakham	srisarakham	PROPN
ejpam-5722	252	61	,	,	PUNCT
ejpam-5722	252	62	s.	s.	PROPN
ejpam-5722	252	63	sompong	sompong	PROPN
ejpam-5722	252	64	,	,	PUNCT
ejpam-5722	252	65	c.	c.	PROPN
ejpam-5722	252	66	boonpok	boonpok	PROPN
ejpam-5722	252	67	/	/	SYM
ejpam-5722	252	68	eur	eur	PROPN
ejpam-5722	252	69	.	.	PUNCT
ejpam-5722	253	1	j.	j.	PROPN
ejpam-5722	253	2	pure	pure	PROPN
ejpam-5722	253	3	appl	appl	PROPN
ejpam-5722	253	4	.	.	PROPN
ejpam-5722	253	5	math	math	PROPN
ejpam-5722	253	6	,	,	PUNCT
ejpam-5722	253	7	18	18	NUM
ejpam-5722	253	8	(	(	PUNCT
ejpam-5722	253	9	1	1	NUM
ejpam-5722	253	10	)	)	PUNCT
ejpam-5722	253	11	(	(	PUNCT
ejpam-5722	253	12	2025	2025	NUM
ejpam-5722	253	13	)	)	PUNCT
ejpam-5722	253	14	,	,	PUNCT
ejpam-5722	253	15	5722	5722	NUM
ejpam-5722	253	16	9	9	NUM
ejpam-5722	253	17	of	of	ADP
ejpam-5722	253	18	12	12	NUM
ejpam-5722	253	19	lemma	lemma	PROPN
ejpam-5722	253	20	6	6	NUM
ejpam-5722	253	21	.	.	PUNCT
ejpam-5722	254	1	a	a	DET
ejpam-5722	254	2	bitopological	bitopological	ADJ
ejpam-5722	254	3	space	space	NOUN
ejpam-5722	254	4	(	(	PUNCT
ejpam-5722	254	5	x	x	NOUN
ejpam-5722	254	6	,	,	PUNCT
ejpam-5722	254	7	τ1	τ1	NOUN
ejpam-5722	254	8	,	,	PUNCT
ejpam-5722	254	9	τ2	τ2	NOUN
ejpam-5722	254	10	)	)	PUNCT
ejpam-5722	254	11	is	be	AUX
ejpam-5722	254	12	(	(	PUNCT
ejpam-5722	254	13	τ1	τ1	NOUN
ejpam-5722	254	14	,	,	PUNCT
ejpam-5722	254	15	τ2)s	τ2)s	NOUN
ejpam-5722	254	16	-	-	PUNCT
ejpam-5722	254	17	hausdorff	hausdorff	NOUN
ejpam-5722	254	18	if	if	SCONJ
ejpam-5722	254	19	and	and	CCONJ
ejpam-5722	254	20	only	only	ADV
ejpam-5722	254	21	if	if	SCONJ
ejpam-5722	254	22	for	for	ADP
ejpam-5722	254	23	each	each	DET
ejpam-5722	254	24	pair	pair	NOUN
ejpam-5722	254	25	of	of	ADP
ejpam-5722	254	26	distinct	distinct	ADJ
ejpam-5722	254	27	points	point	NOUN
ejpam-5722	254	28	x	x	PUNCT
ejpam-5722	254	29	and	and	CCONJ
ejpam-5722	254	30	y	y	PROPN
ejpam-5722	254	31	in	in	ADP
ejpam-5722	254	32	x	x	SYM
ejpam-5722	254	33	,	,	PUNCT
ejpam-5722	254	34	there	there	PRON
ejpam-5722	254	35	exist	exist	VERB
ejpam-5722	254	36	(	(	PUNCT
ejpam-5722	254	37	τ1	τ1	NOUN
ejpam-5722	254	38	,	,	PUNCT
ejpam-5722	254	39	τ2)s	τ2)s	NOUN
ejpam-5722	254	40	-	-	PUNCT
ejpam-5722	254	41	open	open	ADJ
ejpam-5722	254	42	sets	set	VERB
ejpam-5722	254	43	u	u	NOUN
ejpam-5722	254	44	and	and	CCONJ
ejpam-5722	254	45	v	v	ADP
ejpam-5722	254	46	such	such	ADJ
ejpam-5722	254	47	that	that	SCONJ
ejpam-5722	254	48	x	x	SYM
ejpam-5722	254	49	∈	∈	PROPN
ejpam-5722	254	50	u	u	NOUN
ejpam-5722	254	51	,	,	PUNCT
ejpam-5722	254	52	y	y	PROPN
ejpam-5722	254	53	∈	∈	PROPN
ejpam-5722	254	54	v	v	PROPN
ejpam-5722	254	55	and	and	CCONJ
ejpam-5722	254	56	(	(	PUNCT
ejpam-5722	254	57	τ1	τ1	NOUN
ejpam-5722	254	58	,	,	PUNCT
ejpam-5722	254	59	τ2)-scl(u	τ2)-scl(u	ADJ
ejpam-5722	254	60	)	)	PUNCT
ejpam-5722	254	61	∩	∩	NOUN
ejpam-5722	254	62	(	(	PUNCT
ejpam-5722	254	63	τ1	τ1	NOUN
ejpam-5722	254	64	,	,	PUNCT
ejpam-5722	254	65	τ2)-scl(v	τ2)-scl(v	NOUN
ejpam-5722	254	66	)	)	PUNCT
ejpam-5722	255	1	=	=	PUNCT
ejpam-5722	255	2	∅.	∅.	NOUN
ejpam-5722	255	3	theorem	theorem	VERB
ejpam-5722	255	4	7	7	NUM
ejpam-5722	255	5	.	.	PUNCT
ejpam-5722	256	1	if	if	SCONJ
ejpam-5722	256	2	f	f	PROPN
ejpam-5722	256	3	:	:	PUNCT
ejpam-5722	256	4	(	(	PUNCT
ejpam-5722	256	5	x	x	NOUN
ejpam-5722	256	6	,	,	PUNCT
ejpam-5722	256	7	τ1	τ1	NOUN
ejpam-5722	256	8	,	,	PUNCT
ejpam-5722	256	9	τ2	τ2	NOUN
ejpam-5722	256	10	)	)	PUNCT
ejpam-5722	256	11	→	→	SYM
ejpam-5722	256	12	(	(	PUNCT
ejpam-5722	256	13	y	y	PROPN
ejpam-5722	256	14	,	,	PUNCT
ejpam-5722	256	15	σ1	σ1	PROPN
ejpam-5722	256	16	,	,	PUNCT
ejpam-5722	256	17	σ2	σ2	PROPN
ejpam-5722	256	18	)	)	PUNCT
ejpam-5722	256	19	is	be	AUX
ejpam-5722	256	20	a	a	DET
ejpam-5722	256	21	quasi	quasi	NOUN
ejpam-5722	256	22	θ(τ1	θ(τ1	NOUN
ejpam-5722	256	23	,	,	PUNCT
ejpam-5722	256	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	256	25	injection	injection	NOUN
ejpam-5722	256	26	and	and	CCONJ
ejpam-5722	256	27	(	(	PUNCT
ejpam-5722	256	28	y	y	PROPN
ejpam-5722	256	29	,	,	PUNCT
ejpam-5722	256	30	σ1	σ1	PROPN
ejpam-5722	256	31	,	,	PUNCT
ejpam-5722	256	32	σ2	σ2	PROPN
ejpam-5722	256	33	)	)	PUNCT
ejpam-5722	256	34	is	be	AUX
ejpam-5722	256	35	σ1σ2	σ1σ2	NOUN
ejpam-5722	256	36	-	-	PUNCT
ejpam-5722	256	37	urysohn	urysohn	ADJ
ejpam-5722	256	38	,	,	PUNCT
ejpam-5722	256	39	then	then	ADV
ejpam-5722	256	40	(	(	PUNCT
ejpam-5722	256	41	x	x	NOUN
ejpam-5722	256	42	,	,	PUNCT
ejpam-5722	256	43	τ1	τ1	NOUN
ejpam-5722	256	44	,	,	PUNCT
ejpam-5722	256	45	τ2	τ2	NOUN
ejpam-5722	256	46	)	)	PUNCT
ejpam-5722	256	47	is	be	AUX
ejpam-5722	256	48	(	(	PUNCT
ejpam-5722	256	49	τ1	τ1	NOUN
ejpam-5722	256	50	,	,	PUNCT
ejpam-5722	256	51	τ2)s	τ2)s	NOUN
ejpam-5722	256	52	-	-	PUNCT
ejpam-5722	256	53	hausdorff	hausdorff	NOUN
ejpam-5722	256	54	.	.	PUNCT
ejpam-5722	257	1	proof	proof	NOUN
ejpam-5722	257	2	.	.	PUNCT
ejpam-5722	258	1	since	since	SCONJ
ejpam-5722	258	2	f	f	PROPN
ejpam-5722	258	3	is	be	AUX
ejpam-5722	258	4	injective	injective	ADJ
ejpam-5722	258	5	,	,	PUNCT
ejpam-5722	258	6	then	then	ADV
ejpam-5722	258	7	f(x	f(x	PROPN
ejpam-5722	258	8	)	)	PUNCT
ejpam-5722	258	9	̸=	̸=	PROPN
ejpam-5722	258	10	f(y	f(y	NOUN
ejpam-5722	258	11	)	)	PUNCT
ejpam-5722	258	12	for	for	ADP
ejpam-5722	258	13	any	any	DET
ejpam-5722	258	14	distinct	distinct	ADJ
ejpam-5722	258	15	points	point	NOUN
ejpam-5722	258	16	x	x	PUNCT
ejpam-5722	258	17	and	and	CCONJ
ejpam-5722	258	18	y	y	PROPN
ejpam-5722	258	19	in	in	ADP
ejpam-5722	258	20	x.	x.	NOUN
ejpam-5722	258	21	since	since	SCONJ
ejpam-5722	258	22	(	(	PUNCT
ejpam-5722	258	23	y	y	PROPN
ejpam-5722	258	24	,	,	PUNCT
ejpam-5722	258	25	σ1	σ1	PROPN
ejpam-5722	258	26	,	,	PUNCT
ejpam-5722	258	27	σ2	σ2	PROPN
ejpam-5722	258	28	)	)	PUNCT
ejpam-5722	258	29	is	be	AUX
ejpam-5722	258	30	σ1σ2	σ1σ2	NOUN
ejpam-5722	258	31	-	-	PUNCT
ejpam-5722	258	32	urysohn	urysohn	ADJ
ejpam-5722	258	33	,	,	PUNCT
ejpam-5722	258	34	there	there	PRON
ejpam-5722	258	35	exist	exist	VERB
ejpam-5722	258	36	σ1σ2	σ1σ2	NOUN
ejpam-5722	258	37	-	-	ADJ
ejpam-5722	258	38	open	open	ADJ
ejpam-5722	258	39	sets	set	NOUN
ejpam-5722	258	40	v	v	ADP
ejpam-5722	258	41	and	and	CCONJ
ejpam-5722	258	42	v	v	ADP
ejpam-5722	258	43	′	′	NUM
ejpam-5722	258	44	of	of	ADP
ejpam-5722	258	45	y	y	PRON
ejpam-5722	258	46	such	such	ADJ
ejpam-5722	258	47	that	that	SCONJ
ejpam-5722	258	48	f(x	f(x	PROPN
ejpam-5722	258	49	)	)	PUNCT
ejpam-5722	258	50	∈	∈	PROPN
ejpam-5722	258	51	v	v	NOUN
ejpam-5722	258	52	,	,	PUNCT
ejpam-5722	258	53	f(y	f(y	NOUN
ejpam-5722	258	54	)	)	PUNCT
ejpam-5722	258	55	∈	∈	PROPN
ejpam-5722	258	56	v	v	ADP
ejpam-5722	258	57	′	′	NUM
ejpam-5722	258	58	and	and	CCONJ
ejpam-5722	258	59	σ1σ2	σ1σ2	NOUN
ejpam-5722	258	60	-	-	NUM
ejpam-5722	258	61	cl(v	cl(v	NOUN
ejpam-5722	258	62	)	)	PUNCT
ejpam-5722	258	63	∩	∩	NOUN
ejpam-5722	258	64	σ1σ2	σ1σ2	NOUN
ejpam-5722	258	65	-	-	PUNCT
ejpam-5722	258	66	cl(v	cl(v	PRON
ejpam-5722	258	67	′	′	NOUN
ejpam-5722	258	68	)	)	PUNCT
ejpam-5722	259	1	=	=	PUNCT
ejpam-5722	259	2	∅.	∅.	NOUN
ejpam-5722	259	3	since	since	SCONJ
ejpam-5722	259	4	f	f	PROPN
ejpam-5722	259	5	is	be	AUX
ejpam-5722	259	6	quasi	quasi	NOUN
ejpam-5722	259	7	θ(τ1	θ(τ1	NOUN
ejpam-5722	259	8	,	,	PUNCT
ejpam-5722	259	9	τ2)continuous	τ2)continuous	ADJ
ejpam-5722	259	10	,	,	PUNCT
ejpam-5722	259	11	there	there	PRON
ejpam-5722	259	12	exist	exist	VERB
ejpam-5722	259	13	(	(	PUNCT
ejpam-5722	259	14	τ1	τ1	NOUN
ejpam-5722	259	15	,	,	PUNCT
ejpam-5722	259	16	τ2)s	τ2)s	NOUN
ejpam-5722	259	17	-	-	PUNCT
ejpam-5722	259	18	open	open	ADJ
ejpam-5722	259	19	sets	set	VERB
ejpam-5722	259	20	u	u	NOUN
ejpam-5722	259	21	and	and	CCONJ
ejpam-5722	259	22	u	u	NOUN
ejpam-5722	259	23	′	′	NOUN
ejpam-5722	259	24	of	of	ADP
ejpam-5722	259	25	x	x	PUNCT
ejpam-5722	259	26	containing	contain	VERB
ejpam-5722	259	27	x	x	PROPN
ejpam-5722	259	28	and	and	CCONJ
ejpam-5722	259	29	y	y	PROPN
ejpam-5722	259	30	,	,	PUNCT
ejpam-5722	259	31	respectively	respectively	ADV
ejpam-5722	259	32	,	,	PUNCT
ejpam-5722	259	33	such	such	ADJ
ejpam-5722	259	34	that	that	SCONJ
ejpam-5722	259	35	f((τ1	f((τ1	PROPN
ejpam-5722	259	36	,	,	PUNCT
ejpam-5722	259	37	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	259	38	)	)	PUNCT
ejpam-5722	259	39	)	)	PUNCT
ejpam-5722	260	1	⊆	⊆	X
ejpam-5722	260	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	260	3	-	-	NUM
ejpam-5722	260	4	cl(v	cl(v	X
ejpam-5722	260	5	)	)	PUNCT
ejpam-5722	260	6	and	and	CCONJ
ejpam-5722	260	7	f((τ1	f((τ1	PROPN
ejpam-5722	260	8	,	,	PUNCT
ejpam-5722	260	9	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	260	10	′	′	NUM
ejpam-5722	260	11	)	)	PUNCT
ejpam-5722	260	12	)	)	PUNCT
ejpam-5722	261	1	⊆	⊆	X
ejpam-5722	261	2	σ1σ2	σ1σ2	NUM
ejpam-5722	261	3	-	-	PUNCT
ejpam-5722	261	4	cl(v	cl(v	PRON
ejpam-5722	261	5	′	′	NOUN
ejpam-5722	261	6	)	)	PUNCT
ejpam-5722	261	7	.	.	PUNCT
ejpam-5722	262	1	this	this	PRON
ejpam-5722	262	2	implies	imply	VERB
ejpam-5722	262	3	that	that	SCONJ
ejpam-5722	262	4	(	(	PUNCT
ejpam-5722	262	5	τ1	τ1	NOUN
ejpam-5722	262	6	,	,	PUNCT
ejpam-5722	262	7	τ2)-scl(u)∩(τ1	τ2)-scl(u)∩(τ1	NOUN
ejpam-5722	262	8	,	,	PUNCT
ejpam-5722	262	9	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	262	10	′	′	NUM
ejpam-5722	262	11	)	)	PUNCT
ejpam-5722	263	1	=	=	NOUN
ejpam-5722	263	2	∅.	∅.	VERB
ejpam-5722	263	3	thus	thus	ADV
ejpam-5722	263	4	by	by	ADP
ejpam-5722	263	5	lemma	lemma	PROPN
ejpam-5722	263	6	6	6	NUM
ejpam-5722	263	7	,	,	PUNCT
ejpam-5722	263	8	(	(	PUNCT
ejpam-5722	263	9	x	x	NOUN
ejpam-5722	263	10	,	,	PUNCT
ejpam-5722	263	11	τ1	τ1	NOUN
ejpam-5722	263	12	,	,	PUNCT
ejpam-5722	263	13	τ2	τ2	NOUN
ejpam-5722	263	14	)	)	PUNCT
ejpam-5722	263	15	is	be	AUX
ejpam-5722	263	16	(	(	PUNCT
ejpam-5722	263	17	τ1	τ1	NOUN
ejpam-5722	263	18	,	,	PUNCT
ejpam-5722	263	19	τ2)shausdorff	τ2)shausdorff	NOUN
ejpam-5722	263	20	.	.	PUNCT
ejpam-5722	264	1	definition	definition	NOUN
ejpam-5722	264	2	7	7	NUM
ejpam-5722	264	3	.	.	PUNCT
ejpam-5722	264	4	for	for	ADP
ejpam-5722	264	5	a	a	DET
ejpam-5722	264	6	function	function	NOUN
ejpam-5722	264	7	f	f	NOUN
ejpam-5722	264	8	:	:	PUNCT
ejpam-5722	264	9	(	(	PUNCT
ejpam-5722	264	10	x	x	NOUN
ejpam-5722	264	11	,	,	PUNCT
ejpam-5722	264	12	τ1	τ1	NOUN
ejpam-5722	264	13	,	,	PUNCT
ejpam-5722	264	14	τ2	τ2	NOUN
ejpam-5722	264	15	)	)	PUNCT
ejpam-5722	264	16	→	→	SYM
ejpam-5722	264	17	(	(	PUNCT
ejpam-5722	264	18	y	y	PROPN
ejpam-5722	264	19	,	,	PUNCT
ejpam-5722	264	20	σ1	σ1	PROPN
ejpam-5722	264	21	,	,	PUNCT
ejpam-5722	264	22	σ2	σ2	NOUN
ejpam-5722	264	23	)	)	PUNCT
ejpam-5722	264	24	,	,	PUNCT
ejpam-5722	264	25	the	the	DET
ejpam-5722	264	26	graph	graph	NOUN
ejpam-5722	264	27	g(f	g(f	NOUN
ejpam-5722	264	28	)	)	PUNCT
ejpam-5722	265	1	=	=	PRON
ejpam-5722	265	2	{	{	PUNCT
ejpam-5722	265	3	(	(	PUNCT
ejpam-5722	265	4	x	x	NOUN
ejpam-5722	265	5	,	,	PUNCT
ejpam-5722	265	6	f(x	f(x	PROPN
ejpam-5722	265	7	)	)	PUNCT
ejpam-5722	265	8	)	)	PUNCT
ejpam-5722	266	1	|	|	ADV
ejpam-5722	266	2	x	x	SYM
ejpam-5722	266	3	∈	∈	NOUN
ejpam-5722	266	4	x	x	X
ejpam-5722	266	5	}	}	PUNCT
ejpam-5722	266	6	is	be	AUX
ejpam-5722	266	7	said	say	VERB
ejpam-5722	266	8	to	to	PART
ejpam-5722	266	9	be	be	AUX
ejpam-5722	266	10	strong	strong	ADJ
ejpam-5722	266	11	(	(	PUNCT
ejpam-5722	266	12	τ1	τ1	NOUN
ejpam-5722	266	13	,	,	PUNCT
ejpam-5722	266	14	τ2)s	τ2)s	NOUN
ejpam-5722	266	15	-	-	PUNCT
ejpam-5722	266	16	closed	closed	ADJ
ejpam-5722	266	17	if	if	SCONJ
ejpam-5722	266	18	for	for	ADP
ejpam-5722	266	19	each	each	DET
ejpam-5722	266	20	(	(	PUNCT
ejpam-5722	266	21	x	x	NOUN
ejpam-5722	266	22	,	,	PUNCT
ejpam-5722	266	23	y	y	NOUN
ejpam-5722	266	24	)	)	PUNCT
ejpam-5722	266	25	∈	∈	PROPN
ejpam-5722	266	26	(	(	PUNCT
ejpam-5722	266	27	x	x	SYM
ejpam-5722	266	28	×	×	PROPN
ejpam-5722	266	29	y	y	PROPN
ejpam-5722	266	30	)	)	PUNCT
ejpam-5722	267	1	−	−	PROPN
ejpam-5722	267	2	g(f	g(f	NOUN
ejpam-5722	267	3	)	)	PUNCT
ejpam-5722	267	4	,	,	PUNCT
ejpam-5722	267	5	there	there	PRON
ejpam-5722	267	6	exist	exist	VERB
ejpam-5722	267	7	a	a	DET
ejpam-5722	267	8	(	(	PUNCT
ejpam-5722	267	9	τ1	τ1	NOUN
ejpam-5722	267	10	,	,	PUNCT
ejpam-5722	267	11	τ2)s	τ2)s	NOUN
ejpam-5722	267	12	-	-	PUNCT
ejpam-5722	267	13	open	open	ADJ
ejpam-5722	267	14	set	set	NOUN
ejpam-5722	267	15	u	u	NOUN
ejpam-5722	267	16	of	of	ADP
ejpam-5722	267	17	x	x	PUNCT
ejpam-5722	267	18	containing	contain	VERB
ejpam-5722	267	19	x	x	X
ejpam-5722	267	20	and	and	CCONJ
ejpam-5722	267	21	a	a	DET
ejpam-5722	267	22	σ1σ2	σ1σ2	NUM
ejpam-5722	267	23	-	-	ADJ
ejpam-5722	267	24	open	open	ADJ
ejpam-5722	267	25	set	set	NOUN
ejpam-5722	267	26	v	v	NOUN
ejpam-5722	267	27	of	of	ADP
ejpam-5722	267	28	y	y	PROPN
ejpam-5722	267	29	containing	contain	VERB
ejpam-5722	267	30	y	y	PRON
ejpam-5722	267	31	such	such	ADJ
ejpam-5722	267	32	that	that	SCONJ
ejpam-5722	267	33	[	[	X
ejpam-5722	267	34	(	(	PUNCT
ejpam-5722	267	35	τ1	τ1	NOUN
ejpam-5722	267	36	,	,	PUNCT
ejpam-5722	267	37	τ2)-scl(u)×	τ2)-scl(u)×	PRON
ejpam-5722	267	38	σ1σ2	σ1σ2	NOUN
ejpam-5722	267	39	-	-	NUM
ejpam-5722	267	40	cl(v	cl(v	NOUN
ejpam-5722	267	41	)	)	PUNCT
ejpam-5722	267	42	]	]	PUNCT
ejpam-5722	268	1	∩g(f	∩g(f	PROPN
ejpam-5722	268	2	)	)	PUNCT
ejpam-5722	268	3	=	=	PUNCT
ejpam-5722	268	4	∅.	∅.	PRON
ejpam-5722	268	5	lemma	lemma	PROPN
ejpam-5722	268	6	7	7	NUM
ejpam-5722	268	7	.	.	PUNCT
ejpam-5722	269	1	a	a	DET
ejpam-5722	269	2	function	function	NOUN
ejpam-5722	269	3	f	f	NOUN
ejpam-5722	269	4	:	:	PUNCT
ejpam-5722	269	5	(	(	PUNCT
ejpam-5722	269	6	x	x	NOUN
ejpam-5722	269	7	,	,	PUNCT
ejpam-5722	269	8	τ1	τ1	NOUN
ejpam-5722	269	9	,	,	PUNCT
ejpam-5722	269	10	τ2	τ2	NOUN
ejpam-5722	269	11	)	)	PUNCT
ejpam-5722	269	12	→	→	SYM
ejpam-5722	269	13	(	(	PUNCT
ejpam-5722	269	14	y	y	PROPN
ejpam-5722	269	15	,	,	PUNCT
ejpam-5722	269	16	σ1	σ1	PROPN
ejpam-5722	269	17	,	,	PUNCT
ejpam-5722	269	18	σ2	σ2	NOUN
ejpam-5722	269	19	)	)	PUNCT
ejpam-5722	269	20	has	have	VERB
ejpam-5722	269	21	a	a	DET
ejpam-5722	269	22	strong	strong	ADJ
ejpam-5722	269	23	(	(	PUNCT
ejpam-5722	269	24	τ1	τ1	NOUN
ejpam-5722	269	25	,	,	PUNCT
ejpam-5722	269	26	τ2)s	τ2)s	NOUN
ejpam-5722	269	27	-	-	PUNCT
ejpam-5722	269	28	closed	closed	ADJ
ejpam-5722	269	29	graph	graph	NOUN
ejpam-5722	269	30	if	if	SCONJ
ejpam-5722	270	1	and	and	CCONJ
ejpam-5722	270	2	only	only	ADV
ejpam-5722	270	3	if	if	SCONJ
ejpam-5722	270	4	for	for	ADP
ejpam-5722	270	5	each	each	DET
ejpam-5722	270	6	(	(	PUNCT
ejpam-5722	270	7	x	x	NOUN
ejpam-5722	270	8	,	,	PUNCT
ejpam-5722	270	9	y	y	NOUN
ejpam-5722	270	10	)	)	PUNCT
ejpam-5722	270	11	∈	∈	PROPN
ejpam-5722	270	12	(	(	PUNCT
ejpam-5722	270	13	x×y	x×y	PROPN
ejpam-5722	270	14	)	)	PUNCT
ejpam-5722	270	15	−g(f	−g(f	NOUN
ejpam-5722	270	16	)	)	PUNCT
ejpam-5722	270	17	,	,	PUNCT
ejpam-5722	270	18	there	there	PRON
ejpam-5722	270	19	exist	exist	VERB
ejpam-5722	270	20	a	a	DET
ejpam-5722	270	21	(	(	PUNCT
ejpam-5722	270	22	τ1	τ1	NOUN
ejpam-5722	270	23	,	,	PUNCT
ejpam-5722	270	24	τ2)s	τ2)s	NOUN
ejpam-5722	270	25	-	-	PUNCT
ejpam-5722	270	26	open	open	ADJ
ejpam-5722	270	27	set	set	NOUN
ejpam-5722	270	28	u	u	NOUN
ejpam-5722	270	29	of	of	ADP
ejpam-5722	270	30	x	x	PUNCT
ejpam-5722	270	31	containing	contain	VERB
ejpam-5722	270	32	x	x	X
ejpam-5722	270	33	and	and	CCONJ
ejpam-5722	270	34	a	a	DET
ejpam-5722	270	35	σ1σ2	σ1σ2	NUM
ejpam-5722	270	36	-	-	ADJ
ejpam-5722	270	37	open	open	ADJ
ejpam-5722	270	38	set	set	NOUN
ejpam-5722	270	39	v	v	NOUN
ejpam-5722	270	40	of	of	ADP
ejpam-5722	270	41	y	y	PROPN
ejpam-5722	270	42	containing	contain	VERB
ejpam-5722	270	43	y	y	PRON
ejpam-5722	270	44	such	such	ADJ
ejpam-5722	270	45	that	that	SCONJ
ejpam-5722	270	46	f((τ1	f((τ1	PROPN
ejpam-5722	270	47	,	,	PUNCT
ejpam-5722	270	48	τ2)-scl(u))∩σ1σ2	τ2)-scl(u))∩σ1σ2	NOUN
ejpam-5722	270	49	-	-	NOUN
ejpam-5722	270	50	cl(v	cl(v	X
ejpam-5722	270	51	)	)	PUNCT
ejpam-5722	271	1	=	=	PUNCT
ejpam-5722	271	2	∅.	∅.	NOUN
ejpam-5722	271	3	theorem	theorem	VERB
ejpam-5722	271	4	8	8	NUM
ejpam-5722	271	5	.	.	PUNCT
ejpam-5722	272	1	if	if	SCONJ
ejpam-5722	272	2	f	f	PROPN
ejpam-5722	272	3	:	:	PUNCT
ejpam-5722	272	4	(	(	PUNCT
ejpam-5722	272	5	x	x	NOUN
ejpam-5722	272	6	,	,	PUNCT
ejpam-5722	272	7	τ1	τ1	NOUN
ejpam-5722	272	8	,	,	PUNCT
ejpam-5722	272	9	τ2	τ2	NOUN
ejpam-5722	272	10	)	)	PUNCT
ejpam-5722	272	11	→	→	SYM
ejpam-5722	272	12	(	(	PUNCT
ejpam-5722	272	13	y	y	PROPN
ejpam-5722	272	14	,	,	PUNCT
ejpam-5722	272	15	σ1	σ1	PROPN
ejpam-5722	272	16	,	,	PUNCT
ejpam-5722	272	17	σ2	σ2	PROPN
ejpam-5722	272	18	)	)	PUNCT
ejpam-5722	272	19	is	be	AUX
ejpam-5722	272	20	quasi	quasi	NOUN
ejpam-5722	272	21	θ(τ1	θ(τ1	NOUN
ejpam-5722	272	22	,	,	PUNCT
ejpam-5722	272	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	272	24	and	and	CCONJ
ejpam-5722	272	25	(	(	PUNCT
ejpam-5722	272	26	y	y	PROPN
ejpam-5722	272	27	,	,	PUNCT
ejpam-5722	272	28	σ1	σ1	PROPN
ejpam-5722	272	29	,	,	PUNCT
ejpam-5722	272	30	σ2	σ2	PROPN
ejpam-5722	272	31	)	)	PUNCT
ejpam-5722	272	32	is	be	AUX
ejpam-5722	272	33	σ1σ2	σ1σ2	NOUN
ejpam-5722	272	34	-	-	PUNCT
ejpam-5722	272	35	urysohn	urysohn	ADJ
ejpam-5722	272	36	,	,	PUNCT
ejpam-5722	272	37	then	then	ADV
ejpam-5722	272	38	g(f	g(f	PROPN
ejpam-5722	272	39	)	)	PUNCT
ejpam-5722	273	1	is	be	AUX
ejpam-5722	273	2	strong	strong	ADJ
ejpam-5722	273	3	(	(	PUNCT
ejpam-5722	273	4	τ1	τ1	NOUN
ejpam-5722	273	5	,	,	PUNCT
ejpam-5722	273	6	τ2)s	τ2)s	NOUN
ejpam-5722	273	7	-	-	PUNCT
ejpam-5722	273	8	closed	closed	ADJ
ejpam-5722	273	9	.	.	PUNCT
ejpam-5722	274	1	proof	proof	NOUN
ejpam-5722	274	2	.	.	PUNCT
ejpam-5722	275	1	suppose	suppose	VERB
ejpam-5722	275	2	that	that	SCONJ
ejpam-5722	275	3	(	(	PUNCT
ejpam-5722	275	4	x	x	X
ejpam-5722	275	5	,	,	PUNCT
ejpam-5722	275	6	y	y	NOUN
ejpam-5722	275	7	)	)	PUNCT
ejpam-5722	275	8	∈	∈	PROPN
ejpam-5722	275	9	(	(	PUNCT
ejpam-5722	275	10	x×y	x×y	PROPN
ejpam-5722	275	11	)	)	PUNCT
ejpam-5722	275	12	−g(f	−g(f	NOUN
ejpam-5722	275	13	)	)	PUNCT
ejpam-5722	275	14	.	.	PUNCT
ejpam-5722	276	1	then	then	ADV
ejpam-5722	276	2	,	,	PUNCT
ejpam-5722	276	3	y	y	PROPN
ejpam-5722	276	4	̸=	̸=	PROPN
ejpam-5722	276	5	f(x	f(x	PROPN
ejpam-5722	276	6	)	)	PUNCT
ejpam-5722	276	7	.	.	PUNCT
ejpam-5722	277	1	since	since	SCONJ
ejpam-5722	277	2	(	(	PUNCT
ejpam-5722	277	3	y	y	PROPN
ejpam-5722	277	4	,	,	PUNCT
ejpam-5722	277	5	σ1	σ1	PROPN
ejpam-5722	277	6	,	,	PUNCT
ejpam-5722	277	7	σ2	σ2	PROPN
ejpam-5722	277	8	)	)	PUNCT
ejpam-5722	277	9	is	be	AUX
ejpam-5722	277	10	σ1σ2urysohn	σ1σ2urysohn	NUM
ejpam-5722	277	11	,	,	PUNCT
ejpam-5722	277	12	there	there	PRON
ejpam-5722	277	13	there	there	ADV
ejpam-5722	277	14	exist	exist	VERB
ejpam-5722	277	15	σ1σ2	σ1σ2	NOUN
ejpam-5722	277	16	-	-	ADJ
ejpam-5722	277	17	open	open	ADJ
ejpam-5722	277	18	sets	set	NOUN
ejpam-5722	277	19	v	v	ADP
ejpam-5722	277	20	and	and	CCONJ
ejpam-5722	277	21	w	w	PROPN
ejpam-5722	277	22	of	of	ADP
ejpam-5722	277	23	y	y	PROPN
ejpam-5722	277	24	containing	contain	VERB
ejpam-5722	277	25	y	y	PROPN
ejpam-5722	277	26	and	and	CCONJ
ejpam-5722	277	27	f(x	f(x	PROPN
ejpam-5722	277	28	)	)	PUNCT
ejpam-5722	277	29	,	,	PUNCT
ejpam-5722	277	30	respectively	respectively	ADV
ejpam-5722	277	31	,	,	PUNCT
ejpam-5722	277	32	such	such	ADJ
ejpam-5722	277	33	that	that	SCONJ
ejpam-5722	277	34	σ1σ2	σ1σ2	NOUN
ejpam-5722	277	35	-	-	NUM
ejpam-5722	277	36	cl(v	cl(v	NOUN
ejpam-5722	277	37	)	)	PUNCT
ejpam-5722	277	38	∩σ1σ2	∩σ1σ2	NOUN
ejpam-5722	277	39	-	-	NUM
ejpam-5722	277	40	cl(w	cl(w	NOUN
ejpam-5722	277	41	)	)	PUNCT
ejpam-5722	278	1	=	=	PUNCT
ejpam-5722	278	2	∅.	∅.	NOUN
ejpam-5722	278	3	since	since	SCONJ
ejpam-5722	278	4	f	f	PROPN
ejpam-5722	278	5	is	be	AUX
ejpam-5722	278	6	quasi	quasi	NOUN
ejpam-5722	278	7	θ(τ1	θ(τ1	NOUN
ejpam-5722	278	8	,	,	PUNCT
ejpam-5722	278	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	278	10	,	,	PUNCT
ejpam-5722	278	11	there	there	PRON
ejpam-5722	278	12	exists	exist	VERB
ejpam-5722	278	13	a	a	DET
ejpam-5722	278	14	(	(	PUNCT
ejpam-5722	278	15	τ1	τ1	NOUN
ejpam-5722	278	16	,	,	PUNCT
ejpam-5722	278	17	τ2)s	τ2)s	NOUN
ejpam-5722	278	18	-	-	PUNCT
ejpam-5722	278	19	open	open	ADJ
ejpam-5722	278	20	set	set	NOUN
ejpam-5722	278	21	u	u	NOUN
ejpam-5722	278	22	of	of	ADP
ejpam-5722	278	23	x	x	PUNCT
ejpam-5722	278	24	containing	contain	VERB
ejpam-5722	278	25	x	x	PUNCT
ejpam-5722	278	26	such	such	ADJ
ejpam-5722	278	27	that	that	DET
ejpam-5722	278	28	f((τ1	f((τ1	PROPN
ejpam-5722	278	29	,	,	PUNCT
ejpam-5722	278	30	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	278	31	)	)	PUNCT
ejpam-5722	278	32	)	)	PUNCT
ejpam-5722	279	1	⊆	⊆	X
ejpam-5722	279	2	σ1σ2	σ1σ2	NOUN
ejpam-5722	279	3	-	-	PUNCT
ejpam-5722	279	4	cl(w	cl(w	NOUN
ejpam-5722	279	5	)	)	PUNCT
ejpam-5722	279	6	.	.	PUNCT
ejpam-5722	280	1	this	this	PRON
ejpam-5722	280	2	implies	imply	VERB
ejpam-5722	280	3	that	that	SCONJ
ejpam-5722	280	4	f((τ1	f((τ1	PROPN
ejpam-5722	280	5	,	,	PUNCT
ejpam-5722	280	6	τ2)-scl(u	τ2)-scl(u	NOUN
ejpam-5722	280	7	)	)	PUNCT
ejpam-5722	280	8	)	)	PUNCT
ejpam-5722	280	9	∩	∩	NOUN
ejpam-5722	280	10	σ1σ2	σ1σ2	NOUN
ejpam-5722	280	11	-	-	NUM
ejpam-5722	280	12	cl(v	cl(v	X
ejpam-5722	280	13	)	)	PUNCT
ejpam-5722	280	14	=	=	NOUN
ejpam-5722	280	15	∅	∅	NOUN
ejpam-5722	280	16	and	and	CCONJ
ejpam-5722	280	17	by	by	ADP
ejpam-5722	280	18	lemma	lemma	PROPN
ejpam-5722	280	19	7	7	NUM
ejpam-5722	280	20	,	,	PUNCT
ejpam-5722	280	21	g(f	g(f	PROPN
ejpam-5722	280	22	)	)	PUNCT
ejpam-5722	280	23	is	be	AUX
ejpam-5722	280	24	strong	strong	ADJ
ejpam-5722	280	25	(	(	PUNCT
ejpam-5722	280	26	τ1	τ1	NOUN
ejpam-5722	280	27	,	,	PUNCT
ejpam-5722	280	28	τ2)s	τ2)s	NOUN
ejpam-5722	280	29	-	-	PUNCT
ejpam-5722	280	30	closed	closed	ADJ
ejpam-5722	280	31	.	.	PUNCT
ejpam-5722	281	1	acknowledgements	acknowledgement	NOUN
ejpam-5722	281	2	this	this	DET
ejpam-5722	281	3	research	research	NOUN
ejpam-5722	281	4	project	project	NOUN
ejpam-5722	281	5	was	be	AUX
ejpam-5722	281	6	financially	financially	ADV
ejpam-5722	281	7	supported	support	VERB
ejpam-5722	281	8	by	by	ADP
ejpam-5722	281	9	mahasarakham	mahasarakham	PROPN
ejpam-5722	281	10	university	university	PROPN
ejpam-5722	281	11	.	.	PUNCT
ejpam-5722	282	1	references	reference	NOUN
ejpam-5722	282	2	[	[	X
ejpam-5722	282	3	1	1	X
ejpam-5722	282	4	]	]	PUNCT
ejpam-5722	282	5	s.	s.	PROPN
ejpam-5722	282	6	p.	p.	PROPN
ejpam-5722	282	7	arya	arya	PROPN
ejpam-5722	282	8	and	and	CCONJ
ejpam-5722	282	9	m.	m.	PROPN
ejpam-5722	282	10	p.	p.	PROPN
ejpam-5722	282	11	bhamini	bhamini	PROPN
ejpam-5722	282	12	.	.	PUNCT
ejpam-5722	283	1	some	some	DET
ejpam-5722	283	2	weaker	weak	ADJ
ejpam-5722	283	3	forms	form	NOUN
ejpam-5722	283	4	of	of	ADP
ejpam-5722	283	5	semi	semi	ADJ
ejpam-5722	283	6	-	-	ADJ
ejpam-5722	283	7	continuous	continuous	ADJ
ejpam-5722	283	8	functions	function	NOUN
ejpam-5722	283	9	.	.	PUNCT
ejpam-5722	284	1	ganita	ganita	NOUN
ejpam-5722	284	2	,	,	PUNCT
ejpam-5722	284	3	33:124–134	33:124–134	NUM
ejpam-5722	284	4	,	,	PUNCT
ejpam-5722	284	5	1982	1982	NUM
ejpam-5722	284	6	.	.	PUNCT
ejpam-5722	285	1	n.	n.	PROPN
ejpam-5722	285	2	srisarakham	srisarakham	PROPN
ejpam-5722	285	3	,	,	PUNCT
ejpam-5722	285	4	s.	s.	PROPN
ejpam-5722	285	5	sompong	sompong	PROPN
ejpam-5722	285	6	,	,	PUNCT
ejpam-5722	285	7	c.	c.	PROPN
ejpam-5722	285	8	boonpok	boonpok	PROPN
ejpam-5722	285	9	/	/	SYM
ejpam-5722	285	10	eur	eur	PROPN
ejpam-5722	285	11	.	.	PUNCT
ejpam-5722	286	1	j.	j.	PROPN
ejpam-5722	286	2	pure	pure	PROPN
ejpam-5722	286	3	appl	appl	PROPN
ejpam-5722	286	4	.	.	PROPN
ejpam-5722	286	5	math	math	PROPN
ejpam-5722	286	6	,	,	PUNCT
ejpam-5722	286	7	18	18	NUM
ejpam-5722	286	8	(	(	PUNCT
ejpam-5722	286	9	1	1	NUM
ejpam-5722	286	10	)	)	PUNCT
ejpam-5722	286	11	(	(	PUNCT
ejpam-5722	286	12	2025	2025	NUM
ejpam-5722	286	13	)	)	PUNCT
ejpam-5722	286	14	,	,	PUNCT
ejpam-5722	286	15	5722	5722	NUM
ejpam-5722	286	16	10	10	NUM
ejpam-5722	286	17	of	of	ADP
ejpam-5722	286	18	12	12	NUM
ejpam-5722	286	19	[	[	SYM
ejpam-5722	286	20	2	2	NUM
ejpam-5722	286	21	]	]	PUNCT
ejpam-5722	286	22	c.	c.	PROPN
ejpam-5722	286	23	boonpok	boonpok	PROPN
ejpam-5722	286	24	.	.	PUNCT
ejpam-5722	287	1	almost	almost	ADV
ejpam-5722	287	2	(	(	PUNCT
ejpam-5722	287	3	g	g	NOUN
ejpam-5722	287	4	,	,	PUNCT
ejpam-5722	287	5	m)-continuous	m)-continuous	ADJ
ejpam-5722	287	6	functions	function	NOUN
ejpam-5722	287	7	.	.	PUNCT
ejpam-5722	288	1	international	international	ADJ
ejpam-5722	288	2	journal	journal	PROPN
ejpam-5722	288	3	of	of	ADP
ejpam-5722	288	4	mathematical	mathematical	ADJ
ejpam-5722	288	5	analysis	analysis	NOUN
ejpam-5722	288	6	,	,	PUNCT
ejpam-5722	288	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5722	288	8	,	,	PUNCT
ejpam-5722	288	9	2010	2010	NUM
ejpam-5722	288	10	.	.	PUNCT
ejpam-5722	289	1	[	[	X
ejpam-5722	289	2	3	3	X
ejpam-5722	289	3	]	]	PUNCT
ejpam-5722	289	4	c.	c.	PROPN
ejpam-5722	289	5	boonpok	boonpok	PROPN
ejpam-5722	289	6	.	.	PUNCT
ejpam-5722	290	1	m	m	VERB
ejpam-5722	290	2	-continuous	-continuous	ADJ
ejpam-5722	290	3	functions	function	NOUN
ejpam-5722	290	4	in	in	ADP
ejpam-5722	290	5	biminimal	biminimal	NOUN
ejpam-5722	290	6	structure	structure	NOUN
ejpam-5722	290	7	spaces	space	NOUN
ejpam-5722	290	8	.	.	PUNCT
ejpam-5722	291	1	far	far	PROPN
ejpam-5722	291	2	east	east	PROPN
ejpam-5722	291	3	journal	journal	PROPN
ejpam-5722	291	4	of	of	ADP
ejpam-5722	291	5	mathematical	mathematical	ADJ
ejpam-5722	291	6	sciences	science	NOUN
ejpam-5722	291	7	,	,	PUNCT
ejpam-5722	291	8	43(1):41–58	43(1):41–58	NUM
ejpam-5722	291	9	,	,	PUNCT
ejpam-5722	291	10	2010	2010	NUM
ejpam-5722	291	11	.	.	PUNCT
ejpam-5722	292	1	[	[	X
ejpam-5722	292	2	4	4	NUM
ejpam-5722	292	3	]	]	PUNCT
ejpam-5722	292	4	c.	c.	PROPN
ejpam-5722	292	5	boonpok	boonpok	PROPN
ejpam-5722	292	6	.	.	PUNCT
ejpam-5722	293	1	on	on	ADP
ejpam-5722	293	2	characterizations	characterization	NOUN
ejpam-5722	293	3	of	of	ADP
ejpam-5722	293	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5722	293	5	ideal	ideal	ADJ
ejpam-5722	293	6	topological	topological	ADJ
ejpam-5722	293	7	spaces	space	NOUN
ejpam-5722	293	8	.	.	PUNCT
ejpam-5722	294	1	journal	journal	NOUN
ejpam-5722	294	2	of	of	ADP
ejpam-5722	294	3	mathematics	mathematic	NOUN
ejpam-5722	294	4	,	,	PUNCT
ejpam-5722	294	5	2020:9387601	2020:9387601	NUM
ejpam-5722	294	6	,	,	PUNCT
ejpam-5722	294	7	2020	2020	NUM
ejpam-5722	294	8	.	.	PUNCT
ejpam-5722	295	1	[	[	X
ejpam-5722	295	2	5	5	X
ejpam-5722	295	3	]	]	PUNCT
ejpam-5722	295	4	c.	c.	PROPN
ejpam-5722	295	5	boonpok	boonpok	PROPN
ejpam-5722	295	6	.	.	PUNCT
ejpam-5722	296	1	(	(	PUNCT
ejpam-5722	296	2	τ1	τ1	NOUN
ejpam-5722	296	3	,	,	PUNCT
ejpam-5722	296	4	τ2)δ	τ2)δ	ADJ
ejpam-5722	296	5	-	-	PUNCT
ejpam-5722	296	6	semicontinuous	semicontinuous	ADJ
ejpam-5722	296	7	multifunctions	multifunction	NOUN
ejpam-5722	296	8	.	.	PUNCT
ejpam-5722	297	1	heliyon	heliyon	NOUN
ejpam-5722	297	2	,	,	PUNCT
ejpam-5722	297	3	6	6	NUM
ejpam-5722	297	4	:	:	SYM
ejpam-5722	297	5	e05367	e05367	PROPN
ejpam-5722	297	6	,	,	PUNCT
ejpam-5722	297	7	2020	2020	NUM
ejpam-5722	297	8	.	.	PUNCT
ejpam-5722	298	1	[	[	X
ejpam-5722	298	2	6	6	NUM
ejpam-5722	298	3	]	]	PUNCT
ejpam-5722	298	4	c.	c.	PROPN
ejpam-5722	298	5	boonpok	boonpok	PROPN
ejpam-5722	298	6	.	.	PUNCT
ejpam-5722	299	1	on	on	ADP
ejpam-5722	299	2	some	some	DET
ejpam-5722	299	3	closed	closed	ADJ
ejpam-5722	299	4	sets	set	NOUN
ejpam-5722	299	5	and	and	CCONJ
ejpam-5722	299	6	low	low	ADJ
ejpam-5722	299	7	separation	separation	NOUN
ejpam-5722	299	8	axioms	axiom	NOUN
ejpam-5722	299	9	via	via	ADP
ejpam-5722	299	10	topological	topological	ADJ
ejpam-5722	299	11	ideals	ideal	NOUN
ejpam-5722	299	12	.	.	PUNCT
ejpam-5722	300	1	european	european	ADJ
ejpam-5722	300	2	journal	journal	PROPN
ejpam-5722	300	3	of	of	ADP
ejpam-5722	300	4	pure	pure	ADJ
ejpam-5722	300	5	and	and	CCONJ
ejpam-5722	300	6	applied	applied	ADJ
ejpam-5722	300	7	mathematics	mathematic	NOUN
ejpam-5722	300	8	,	,	PUNCT
ejpam-5722	300	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5722	300	10	,	,	PUNCT
ejpam-5722	300	11	2022	2022	NUM
ejpam-5722	300	12	.	.	PUNCT
ejpam-5722	301	1	[	[	X
ejpam-5722	301	2	7	7	X
ejpam-5722	301	3	]	]	X
ejpam-5722	301	4	c.	c.	PROPN
ejpam-5722	301	5	boonpok	boonpok	PROPN
ejpam-5722	301	6	.	.	PUNCT
ejpam-5722	302	1	on	on	ADP
ejpam-5722	302	2	some	some	DET
ejpam-5722	302	3	spaces	space	NOUN
ejpam-5722	302	4	via	via	ADP
ejpam-5722	302	5	topological	topological	ADJ
ejpam-5722	302	6	ideals	ideal	NOUN
ejpam-5722	302	7	.	.	PUNCT
ejpam-5722	303	1	open	open	ADJ
ejpam-5722	303	2	mathematics	mathematic	NOUN
ejpam-5722	303	3	,	,	PUNCT
ejpam-5722	303	4	21:20230118	21:20230118	NUM
ejpam-5722	303	5	,	,	PUNCT
ejpam-5722	303	6	2023	2023	NUM
ejpam-5722	303	7	.	.	PUNCT
ejpam-5722	304	1	[	[	X
ejpam-5722	304	2	8	8	NUM
ejpam-5722	304	3	]	]	X
ejpam-5722	304	4	c.	c.	PROPN
ejpam-5722	304	5	boonpok	boonpok	PROPN
ejpam-5722	304	6	.	.	PUNCT
ejpam-5722	305	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5722	305	2	.	.	PUNCT
ejpam-5722	306	1	mathematica	mathematica	PROPN
ejpam-5722	306	2	,	,	PUNCT
ejpam-5722	306	3	65(1):31–42	65(1):31–42	NUM
ejpam-5722	306	4	,	,	PUNCT
ejpam-5722	306	5	2023	2023	NUM
ejpam-5722	306	6	.	.	PUNCT
ejpam-5722	307	1	[	[	X
ejpam-5722	307	2	9	9	NUM
ejpam-5722	307	3	]	]	PUNCT
ejpam-5722	307	4	c.	c.	NOUN
ejpam-5722	307	5	boonpok	boonpok	PROPN
ejpam-5722	307	6	and	and	CCONJ
ejpam-5722	307	7	j.	j.	PROPN
ejpam-5722	307	8	khampakdee	khampakdee	PROPN
ejpam-5722	307	9	.	.	PUNCT
ejpam-5722	308	1	(	(	PUNCT
ejpam-5722	308	2	λ	λ	NOUN
ejpam-5722	308	3	,	,	PUNCT
ejpam-5722	308	4	sp)-open	sp)-open	ADJ
ejpam-5722	308	5	sets	set	NOUN
ejpam-5722	308	6	in	in	ADP
ejpam-5722	308	7	topological	topological	ADJ
ejpam-5722	308	8	spaces	space	NOUN
ejpam-5722	308	9	.	.	PUNCT
ejpam-5722	309	1	european	european	ADJ
ejpam-5722	309	2	journal	journal	PROPN
ejpam-5722	309	3	of	of	ADP
ejpam-5722	309	4	pure	pure	ADJ
ejpam-5722	309	5	and	and	CCONJ
ejpam-5722	309	6	applied	applied	ADJ
ejpam-5722	309	7	mathematics	mathematic	NOUN
ejpam-5722	309	8	,	,	PUNCT
ejpam-5722	309	9	15(2):572–588	15(2):572–588	NUM
ejpam-5722	309	10	,	,	PUNCT
ejpam-5722	309	11	2022	2022	NUM
ejpam-5722	309	12	.	.	PUNCT
ejpam-5722	310	1	[	[	X
ejpam-5722	310	2	10	10	NUM
ejpam-5722	310	3	]	]	X
ejpam-5722	310	4	c.	c.	PROPN
ejpam-5722	310	5	boonpok	boonpok	PROPN
ejpam-5722	310	6	and	and	CCONJ
ejpam-5722	310	7	j.	j.	PROPN
ejpam-5722	310	8	khampakdee	khampakdee	PROPN
ejpam-5722	310	9	.	.	PUNCT
ejpam-5722	311	1	almost	almost	ADV
ejpam-5722	311	2	strong	strong	ADJ
ejpam-5722	311	3	θ(λ	θ(λ	PROPN
ejpam-5722	311	4	,	,	PUNCT
ejpam-5722	311	5	p)-continuity	p)-continuity	NOUN
ejpam-5722	311	6	for	for	ADP
ejpam-5722	311	7	functions	function	NOUN
ejpam-5722	311	8	.	.	PUNCT
ejpam-5722	312	1	european	european	ADJ
ejpam-5722	312	2	journal	journal	PROPN
ejpam-5722	312	3	of	of	ADP
ejpam-5722	312	4	pure	pure	ADJ
ejpam-5722	312	5	and	and	CCONJ
ejpam-5722	312	6	applied	applied	ADJ
ejpam-5722	312	7	mathematics	mathematic	NOUN
ejpam-5722	312	8	,	,	PUNCT
ejpam-5722	312	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5722	312	10	,	,	PUNCT
ejpam-5722	312	11	2024	2024	NUM
ejpam-5722	312	12	.	.	PUNCT
ejpam-5722	313	1	[	[	X
ejpam-5722	313	2	11	11	NUM
ejpam-5722	313	3	]	]	X
ejpam-5722	313	4	c.	c.	PROPN
ejpam-5722	313	5	boonpok	boonpok	PROPN
ejpam-5722	313	6	and	and	CCONJ
ejpam-5722	313	7	c.	c.	PROPN
ejpam-5722	313	8	klanarong	klanarong	PROPN
ejpam-5722	313	9	.	.	PUNCT
ejpam-5722	314	1	on	on	ADP
ejpam-5722	314	2	weakly	weakly	ADJ
ejpam-5722	314	3	(	(	PUNCT
ejpam-5722	314	4	τ1	τ1	NOUN
ejpam-5722	314	5	,	,	PUNCT
ejpam-5722	314	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	314	7	functions	function	NOUN
ejpam-5722	314	8	.	.	PUNCT
ejpam-5722	315	1	european	european	ADJ
ejpam-5722	315	2	journal	journal	PROPN
ejpam-5722	315	3	of	of	ADP
ejpam-5722	315	4	pure	pure	ADJ
ejpam-5722	315	5	and	and	CCONJ
ejpam-5722	315	6	applied	applied	ADJ
ejpam-5722	315	7	mathematics	mathematic	NOUN
ejpam-5722	315	8	,	,	PUNCT
ejpam-5722	315	9	17(1):416–425	17(1):416–425	NUM
ejpam-5722	315	10	,	,	PUNCT
ejpam-5722	315	11	2024	2024	NUM
ejpam-5722	315	12	.	.	PUNCT
ejpam-5722	316	1	[	[	X
ejpam-5722	316	2	12	12	NUM
ejpam-5722	316	3	]	]	X
ejpam-5722	316	4	c.	c.	PROPN
ejpam-5722	316	5	boonpok	boonpok	PROPN
ejpam-5722	316	6	and	and	CCONJ
ejpam-5722	316	7	p.	p.	NOUN
ejpam-5722	316	8	pue	pue	NOUN
ejpam-5722	316	9	-	-	PUNCT
ejpam-5722	316	10	on	on	ADP
ejpam-5722	316	11	.	.	PUNCT
ejpam-5722	317	1	characterizations	characterization	NOUN
ejpam-5722	317	2	of	of	ADP
ejpam-5722	317	3	almost	almost	ADV
ejpam-5722	317	4	(	(	PUNCT
ejpam-5722	317	5	τ1	τ1	NOUN
ejpam-5722	317	6	,	,	PUNCT
ejpam-5722	317	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	317	8	functions	function	NOUN
ejpam-5722	317	9	.	.	PUNCT
ejpam-5722	318	1	international	international	ADJ
ejpam-5722	318	2	journal	journal	NOUN
ejpam-5722	318	3	of	of	ADP
ejpam-5722	318	4	analysis	analysis	NOUN
ejpam-5722	318	5	and	and	CCONJ
ejpam-5722	318	6	applications	application	NOUN
ejpam-5722	318	7	,	,	PUNCT
ejpam-5722	318	8	22:33	22:33	NUM
ejpam-5722	318	9	,	,	PUNCT
ejpam-5722	318	10	2024	2024	NUM
ejpam-5722	318	11	.	.	PUNCT
ejpam-5722	319	1	[	[	X
ejpam-5722	319	2	13	13	NUM
ejpam-5722	319	3	]	]	PUNCT
ejpam-5722	319	4	c.	c.	PROPN
ejpam-5722	319	5	boonpok	boonpok	PROPN
ejpam-5722	319	6	and	and	CCONJ
ejpam-5722	319	7	n.	n.	PROPN
ejpam-5722	319	8	srisarakham	srisarakham	PROPN
ejpam-5722	319	9	.	.	PUNCT
ejpam-5722	320	1	weak	weak	ADJ
ejpam-5722	320	2	forms	form	NOUN
ejpam-5722	320	3	of	of	ADP
ejpam-5722	320	4	(	(	PUNCT
ejpam-5722	320	5	λ	λ	PROPN
ejpam-5722	320	6	,	,	PUNCT
ejpam-5722	320	7	b)-open	b)-open	VERB
ejpam-5722	320	8	sets	set	NOUN
ejpam-5722	320	9	and	and	CCONJ
ejpam-5722	320	10	weak	weak	ADJ
ejpam-5722	320	11	(	(	PUNCT
ejpam-5722	320	12	λ	λ	NOUN
ejpam-5722	320	13	,	,	PUNCT
ejpam-5722	320	14	b)continuity	b)continuity	NOUN
ejpam-5722	320	15	.	.	PUNCT
ejpam-5722	321	1	european	european	PROPN
ejpam-5722	321	2	journal	journal	PROPN
ejpam-5722	321	3	of	of	ADP
ejpam-5722	321	4	pure	pure	ADJ
ejpam-5722	321	5	and	and	CCONJ
ejpam-5722	321	6	applied	applied	ADJ
ejpam-5722	321	7	mathematics	mathematic	NOUN
ejpam-5722	321	8	,	,	PUNCT
ejpam-5722	321	9	16(1):29–43	16(1):29–43	NUM
ejpam-5722	321	10	,	,	PUNCT
ejpam-5722	321	11	2023	2023	NUM
ejpam-5722	321	12	.	.	PUNCT
ejpam-5722	322	1	[	[	X
ejpam-5722	322	2	14	14	NUM
ejpam-5722	322	3	]	]	X
ejpam-5722	322	4	c.	c.	PROPN
ejpam-5722	322	5	boonpok	boonpok	PROPN
ejpam-5722	322	6	and	and	CCONJ
ejpam-5722	322	7	n.	n.	PROPN
ejpam-5722	322	8	srisarakham	srisarakham	PROPN
ejpam-5722	322	9	.	.	PUNCT
ejpam-5722	323	1	(	(	PUNCT
ejpam-5722	323	2	τ1	τ1	NOUN
ejpam-5722	323	3	,	,	PUNCT
ejpam-5722	323	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5722	323	5	for	for	ADP
ejpam-5722	323	6	functions	function	NOUN
ejpam-5722	323	7	.	.	PUNCT
ejpam-5722	324	1	asia	asia	PROPN
ejpam-5722	324	2	pacific	pacific	PROPN
ejpam-5722	324	3	journal	journal	PROPN
ejpam-5722	324	4	of	of	ADP
ejpam-5722	324	5	mathematics	mathematic	NOUN
ejpam-5722	324	6	,	,	PUNCT
ejpam-5722	324	7	11:21	11:21	NUM
ejpam-5722	324	8	,	,	PUNCT
ejpam-5722	324	9	2024	2024	NUM
ejpam-5722	324	10	.	.	PUNCT
ejpam-5722	325	1	[	[	X
ejpam-5722	325	2	15	15	NUM
ejpam-5722	325	3	]	]	X
ejpam-5722	325	4	c.	c.	PROPN
ejpam-5722	325	5	boonpok	boonpok	PROPN
ejpam-5722	325	6	,	,	PUNCT
ejpam-5722	325	7	c.	c.	PROPN
ejpam-5722	325	8	viriyapong	viriyapong	PROPN
ejpam-5722	325	9	,	,	PUNCT
ejpam-5722	325	10	and	and	CCONJ
ejpam-5722	325	11	m.	m.	NOUN
ejpam-5722	325	12	thongmoon	thongmoon	NOUN
ejpam-5722	325	13	.	.	PUNCT
ejpam-5722	326	1	on	on	ADP
ejpam-5722	326	2	upper	upper	ADJ
ejpam-5722	326	3	and	and	CCONJ
ejpam-5722	326	4	lower	low	ADJ
ejpam-5722	326	5	(	(	PUNCT
ejpam-5722	326	6	τ1	τ1	NOUN
ejpam-5722	326	7	,	,	PUNCT
ejpam-5722	326	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5722	326	9	multifunctions	multifunction	NOUN
ejpam-5722	326	10	.	.	PUNCT
ejpam-5722	327	1	journal	journal	PROPN
ejpam-5722	327	2	of	of	ADP
ejpam-5722	327	3	mathematics	mathematics	PROPN
ejpam-5722	327	4	and	and	CCONJ
ejpam-5722	327	5	computer	computer	NOUN
ejpam-5722	327	6	science	science	NOUN
ejpam-5722	327	7	,	,	PUNCT
ejpam-5722	327	8	18:282–293	18:282–293	NUM
ejpam-5722	327	9	,	,	PUNCT
ejpam-5722	327	10	2018	2018	NUM
ejpam-5722	327	11	.	.	PUNCT
ejpam-5722	328	1	[	[	X
ejpam-5722	328	2	16	16	NUM
ejpam-5722	328	3	]	]	PUNCT
ejpam-5722	328	4	m.	m.	NOUN
ejpam-5722	328	5	chiangpradit	chiangpradit	NOUN
ejpam-5722	328	6	,	,	PUNCT
ejpam-5722	328	7	s.	s.	PROPN
ejpam-5722	328	8	sompong	sompong	PROPN
ejpam-5722	328	9	,	,	PUNCT
ejpam-5722	328	10	and	and	CCONJ
ejpam-5722	328	11	c.	c.	PROPN
ejpam-5722	328	12	boonpok	boonpok	PROPN
ejpam-5722	328	13	.	.	PUNCT
ejpam-5722	329	1	weakly	weakly	ADJ
ejpam-5722	329	2	quasi	quasi	NOUN
ejpam-5722	329	3	(	(	PUNCT
ejpam-5722	329	4	τ1	τ1	PROPN
ejpam-5722	329	5	,	,	PUNCT
ejpam-5722	329	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	329	7	functions	function	NOUN
ejpam-5722	329	8	.	.	PUNCT
ejpam-5722	330	1	international	international	ADJ
ejpam-5722	330	2	journal	journal	NOUN
ejpam-5722	330	3	of	of	ADP
ejpam-5722	330	4	analysis	analysis	NOUN
ejpam-5722	330	5	and	and	CCONJ
ejpam-5722	330	6	applications	application	NOUN
ejpam-5722	330	7	,	,	PUNCT
ejpam-5722	330	8	22:125	22:125	NUM
ejpam-5722	330	9	,	,	PUNCT
ejpam-5722	330	10	2024	2024	NUM
ejpam-5722	330	11	.	.	PUNCT
ejpam-5722	331	1	[	[	X
ejpam-5722	331	2	17	17	NUM
ejpam-5722	331	3	]	]	PUNCT
ejpam-5722	331	4	t.	t.	PROPN
ejpam-5722	331	5	duangphui	duangphui	PROPN
ejpam-5722	331	6	,	,	PUNCT
ejpam-5722	331	7	c.	c.	PROPN
ejpam-5722	331	8	boonpok	boonpok	PROPN
ejpam-5722	331	9	,	,	PUNCT
ejpam-5722	331	10	and	and	CCONJ
ejpam-5722	331	11	c.	c.	PROPN
ejpam-5722	331	12	viriyapong	viriyapong	PROPN
ejpam-5722	331	13	.	.	PUNCT
ejpam-5722	332	1	continuous	continuous	ADJ
ejpam-5722	332	2	functions	function	NOUN
ejpam-5722	332	3	on	on	ADP
ejpam-5722	332	4	bigeneralized	bigeneralize	VERB
ejpam-5722	332	5	topological	topological	ADJ
ejpam-5722	332	6	spaces	space	NOUN
ejpam-5722	332	7	.	.	PUNCT
ejpam-5722	333	1	international	international	ADJ
ejpam-5722	333	2	journal	journal	PROPN
ejpam-5722	333	3	of	of	ADP
ejpam-5722	333	4	mathematical	mathematical	ADJ
ejpam-5722	333	5	analysis	analysis	NOUN
ejpam-5722	333	6	,	,	PUNCT
ejpam-5722	333	7	5(24):1165	5(24):1165	NUM
ejpam-5722	333	8	–	–	PUNCT
ejpam-5722	333	9	1174	1174	NUM
ejpam-5722	333	10	,	,	PUNCT
ejpam-5722	333	11	2011	2011	NUM
ejpam-5722	333	12	.	.	PUNCT
ejpam-5722	334	1	[	[	X
ejpam-5722	334	2	18	18	NUM
ejpam-5722	334	3	]	]	PUNCT
ejpam-5722	334	4	t.	t.	NOUN
ejpam-5722	334	5	dungthaisong	dungthaisong	PROPN
ejpam-5722	334	6	,	,	PUNCT
ejpam-5722	334	7	c.	c.	PROPN
ejpam-5722	334	8	boonpok	boonpok	PROPN
ejpam-5722	334	9	,	,	PUNCT
ejpam-5722	334	10	and	and	CCONJ
ejpam-5722	334	11	c.	c.	PROPN
ejpam-5722	334	12	viriyapong	viriyapong	PROPN
ejpam-5722	334	13	.	.	PUNCT
ejpam-5722	335	1	generalized	generalize	VERB
ejpam-5722	335	2	closed	close	VERB
ejpam-5722	335	3	sets	set	NOUN
ejpam-5722	335	4	in	in	ADP
ejpam-5722	335	5	bigeneralized	bigeneralize	VERB
ejpam-5722	335	6	topological	topological	ADJ
ejpam-5722	335	7	spaces	space	NOUN
ejpam-5722	335	8	.	.	PUNCT
ejpam-5722	336	1	international	international	ADJ
ejpam-5722	336	2	journal	journal	PROPN
ejpam-5722	336	3	of	of	ADP
ejpam-5722	336	4	mathematical	mathematical	ADJ
ejpam-5722	336	5	analysis	analysis	NOUN
ejpam-5722	336	6	,	,	PUNCT
ejpam-5722	336	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5722	336	8	,	,	PUNCT
ejpam-5722	336	9	2011	2011	NUM
ejpam-5722	336	10	.	.	PUNCT
ejpam-5722	337	1	[	[	X
ejpam-5722	337	2	19	19	NUM
ejpam-5722	337	3	]	]	PUNCT
ejpam-5722	337	4	m.	m.	NOUN
ejpam-5722	337	5	e.	e.	PROPN
ejpam-5722	337	6	abd	abd	PROPN
ejpam-5722	338	1	el	el	PROPN
ejpam-5722	338	2	-	-	PROPN
ejpam-5722	338	3	monsef	monsef	PROPN
ejpam-5722	338	4	,	,	PUNCT
ejpam-5722	338	5	s.	s.	PROPN
ejpam-5722	338	6	n.	n.	PROPN
ejpam-5722	338	7	el	el	PROPN
ejpam-5722	338	8	-	-	PROPN
ejpam-5722	338	9	deeb	deeb	PROPN
ejpam-5722	338	10	,	,	PUNCT
ejpam-5722	338	11	and	and	CCONJ
ejpam-5722	338	12	r.	r.	PROPN
ejpam-5722	338	13	a.	a.	PROPN
ejpam-5722	338	14	mahmoud	mahmoud	PROPN
ejpam-5722	338	15	.	.	PUNCT
ejpam-5722	339	1	β	β	X
ejpam-5722	339	2	-	-	ADJ
ejpam-5722	339	3	open	open	ADJ
ejpam-5722	339	4	sets	set	NOUN
ejpam-5722	339	5	and	and	CCONJ
ejpam-5722	339	6	βcontinuous	βcontinuous	ADJ
ejpam-5722	339	7	mappings	mapping	NOUN
ejpam-5722	339	8	.	.	PUNCT
ejpam-5722	340	1	bulletin	bulletin	NOUN
ejpam-5722	340	2	of	of	ADP
ejpam-5722	340	3	the	the	DET
ejpam-5722	340	4	faculty	faculty	NOUN
ejpam-5722	340	5	of	of	ADP
ejpam-5722	340	6	science	science	NOUN
ejpam-5722	340	7	,	,	PUNCT
ejpam-5722	340	8	assiut	assiut	NOUN
ejpam-5722	340	9	university	university	NOUN
ejpam-5722	340	10	,	,	PUNCT
ejpam-5722	340	11	12:77–90	12:77–90	NUM
ejpam-5722	340	12	,	,	PUNCT
ejpam-5722	340	13	1983	1983	NUM
ejpam-5722	340	14	.	.	PUNCT
ejpam-5722	341	1	[	[	X
ejpam-5722	341	2	20	20	NUM
ejpam-5722	341	3	]	]	PUNCT
ejpam-5722	341	4	s.	s.	PROPN
ejpam-5722	341	5	jafari	jafari	PROPN
ejpam-5722	341	6	and	and	CCONJ
ejpam-5722	341	7	t.	t.	PROPN
ejpam-5722	341	8	noiri	noiri	PROPN
ejpam-5722	341	9	.	.	PUNCT
ejpam-5722	342	1	properties	property	NOUN
ejpam-5722	342	2	of	of	ADP
ejpam-5722	342	3	θ	θ	ADJ
ejpam-5722	342	4	-	-	ADJ
ejpam-5722	342	5	continuous	continuous	ADJ
ejpam-5722	342	6	functions	function	NOUN
ejpam-5722	342	7	.	.	PUNCT
ejpam-5722	343	1	journal	journal	PROPN
ejpam-5722	343	2	of	of	ADP
ejpam-5722	343	3	institute	institute	PROPN
ejpam-5722	343	4	of	of	ADP
ejpam-5722	343	5	mathematics	mathematics	PROPN
ejpam-5722	343	6	and	and	CCONJ
ejpam-5722	343	7	computer	computer	NOUN
ejpam-5722	343	8	science	science	NOUN
ejpam-5722	343	9	,	,	PUNCT
ejpam-5722	343	10	mathematics	mathematics	NOUN
ejpam-5722	343	11	series	series	NOUN
ejpam-5722	343	12	,	,	PUNCT
ejpam-5722	343	13	13:123–128	13:123–128	NUM
ejpam-5722	343	14	,	,	PUNCT
ejpam-5722	343	15	2000	2000	NUM
ejpam-5722	343	16	.	.	PUNCT
ejpam-5722	344	1	[	[	X
ejpam-5722	344	2	21	21	NUM
ejpam-5722	344	3	]	]	X
ejpam-5722	344	4	b.	b.	PROPN
ejpam-5722	344	5	kong	kong	PROPN
ejpam-5722	344	6	-	-	PUNCT
ejpam-5722	344	7	ied	ied	PROPN
ejpam-5722	344	8	,	,	PUNCT
ejpam-5722	344	9	s.	s.	PROPN
ejpam-5722	344	10	sompong	sompong	PROPN
ejpam-5722	344	11	,	,	PUNCT
ejpam-5722	344	12	and	and	CCONJ
ejpam-5722	344	13	c.	c.	PROPN
ejpam-5722	344	14	boonpok	boonpok	PROPN
ejpam-5722	344	15	.	.	PUNCT
ejpam-5722	345	1	almost	almost	ADV
ejpam-5722	345	2	quasi	quasi	X
ejpam-5722	345	3	(	(	PUNCT
ejpam-5722	345	4	τ1	τ1	NOUN
ejpam-5722	345	5	,	,	PUNCT
ejpam-5722	345	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	345	7	functions	function	NOUN
ejpam-5722	345	8	.	.	PUNCT
ejpam-5722	346	1	asia	asia	PROPN
ejpam-5722	346	2	pacific	pacific	PROPN
ejpam-5722	346	3	journal	journal	PROPN
ejpam-5722	346	4	of	of	ADP
ejpam-5722	346	5	mathematics	mathematic	NOUN
ejpam-5722	346	6	,	,	PUNCT
ejpam-5722	346	7	11:64	11:64	NUM
ejpam-5722	346	8	,	,	PUNCT
ejpam-5722	346	9	2024	2024	NUM
ejpam-5722	346	10	.	.	PUNCT
ejpam-5722	347	1	[	[	X
ejpam-5722	347	2	22	22	NUM
ejpam-5722	347	3	]	]	X
ejpam-5722	347	4	n.	n.	PROPN
ejpam-5722	347	5	levine	levine	PROPN
ejpam-5722	347	6	.	.	PUNCT
ejpam-5722	348	1	a	a	DET
ejpam-5722	348	2	decomposition	decomposition	NOUN
ejpam-5722	348	3	of	of	ADP
ejpam-5722	348	4	continuity	continuity	NOUN
ejpam-5722	348	5	in	in	ADP
ejpam-5722	348	6	topological	topological	ADJ
ejpam-5722	348	7	spaces	space	NOUN
ejpam-5722	348	8	.	.	PUNCT
ejpam-5722	349	1	the	the	DET
ejpam-5722	349	2	american	american	PROPN
ejpam-5722	349	3	mathn	mathn	PROPN
ejpam-5722	349	4	.	.	PUNCT
ejpam-5722	350	1	srisarakham	srisarakham	PROPN
ejpam-5722	350	2	,	,	PUNCT
ejpam-5722	350	3	s.	s.	PROPN
ejpam-5722	350	4	sompong	sompong	PROPN
ejpam-5722	350	5	,	,	PUNCT
ejpam-5722	350	6	c.	c.	PROPN
ejpam-5722	350	7	boonpok	boonpok	PROPN
ejpam-5722	350	8	/	/	SYM
ejpam-5722	350	9	eur	eur	PROPN
ejpam-5722	350	10	.	.	PUNCT
ejpam-5722	351	1	j.	j.	PROPN
ejpam-5722	351	2	pure	pure	PROPN
ejpam-5722	351	3	appl	appl	PROPN
ejpam-5722	351	4	.	.	PROPN
ejpam-5722	351	5	math	math	PROPN
ejpam-5722	351	6	,	,	PUNCT
ejpam-5722	351	7	18	18	NUM
ejpam-5722	351	8	(	(	PUNCT
ejpam-5722	351	9	1	1	NUM
ejpam-5722	351	10	)	)	PUNCT
ejpam-5722	351	11	(	(	PUNCT
ejpam-5722	351	12	2025	2025	NUM
ejpam-5722	351	13	)	)	PUNCT
ejpam-5722	351	14	,	,	PUNCT
ejpam-5722	351	15	5722	5722	NUM
ejpam-5722	351	16	11	11	NUM
ejpam-5722	351	17	of	of	ADP
ejpam-5722	351	18	12	12	NUM
ejpam-5722	351	19	ematical	ematical	ADJ
ejpam-5722	351	20	monthly	monthly	ADJ
ejpam-5722	351	21	,	,	PUNCT
ejpam-5722	351	22	60:44–46	60:44–46	NUM
ejpam-5722	351	23	,	,	PUNCT
ejpam-5722	351	24	1961	1961	NUM
ejpam-5722	351	25	.	.	PUNCT
ejpam-5722	352	1	[	[	X
ejpam-5722	352	2	23	23	NUM
ejpam-5722	352	3	]	]	X
ejpam-5722	352	4	n.	n.	PROPN
ejpam-5722	352	5	levine	levine	PROPN
ejpam-5722	352	6	.	.	PUNCT
ejpam-5722	353	1	semi	semi	ADJ
ejpam-5722	353	2	-	-	ADJ
ejpam-5722	353	3	open	open	ADJ
ejpam-5722	353	4	sets	set	NOUN
ejpam-5722	353	5	and	and	CCONJ
ejpam-5722	353	6	semi	semi	ADJ
ejpam-5722	353	7	-	-	NOUN
ejpam-5722	353	8	continuity	continuity	NOUN
ejpam-5722	353	9	in	in	ADP
ejpam-5722	353	10	topological	topological	ADJ
ejpam-5722	353	11	spaces	space	NOUN
ejpam-5722	353	12	.	.	PUNCT
ejpam-5722	354	1	the	the	DET
ejpam-5722	354	2	american	american	PROPN
ejpam-5722	354	3	mathematical	mathematical	PROPN
ejpam-5722	354	4	monthly	monthly	ADV
ejpam-5722	354	5	,	,	PUNCT
ejpam-5722	354	6	70:36–41	70:36–41	NUM
ejpam-5722	354	7	,	,	PUNCT
ejpam-5722	354	8	1963	1963	NUM
ejpam-5722	354	9	.	.	PUNCT
ejpam-5722	355	1	[	[	X
ejpam-5722	355	2	24	24	NUM
ejpam-5722	355	3	]	]	X
ejpam-5722	355	4	s.	s.	PROPN
ejpam-5722	355	5	marcus	marcus	PROPN
ejpam-5722	355	6	.	.	PUNCT
ejpam-5722	356	1	sur	sur	PROPN
ejpam-5722	356	2	les	les	PROPN
ejpam-5722	356	3	fonctions	fonctions	PROPN
ejpam-5722	356	4	quasicontinues	quasicontinue	NOUN
ejpam-5722	356	5	au	au	PROPN
ejpam-5722	356	6	sens	sens	X
ejpam-5722	356	7	de	de	PROPN
ejpam-5722	356	8	s.	s.	PROPN
ejpam-5722	356	9	kempisty	kempisty	PROPN
ejpam-5722	356	10	.	.	PUNCT
ejpam-5722	357	1	colloquium	colloquium	NOUN
ejpam-5722	357	2	mathematicum	mathematicum	PROPN
ejpam-5722	357	3	,	,	PUNCT
ejpam-5722	357	4	8:47–53	8:47–53	NUM
ejpam-5722	357	5	,	,	PUNCT
ejpam-5722	357	6	1961	1961	NUM
ejpam-5722	357	7	.	.	PUNCT
ejpam-5722	358	1	[	[	X
ejpam-5722	358	2	25	25	NUM
ejpam-5722	358	3	]	]	PUNCT
ejpam-5722	358	4	a.	a.	NOUN
ejpam-5722	358	5	s.	s.	PROPN
ejpam-5722	358	6	mashhour	mashhour	PROPN
ejpam-5722	358	7	,	,	PUNCT
ejpam-5722	358	8	m.	m.	PROPN
ejpam-5722	358	9	e.	e.	PROPN
ejpam-5722	358	10	abd	abd	PROPN
ejpam-5722	359	1	el	el	PROPN
ejpam-5722	359	2	-	-	PROPN
ejpam-5722	359	3	monsef	monsef	ADJ
ejpam-5722	359	4	,	,	PUNCT
ejpam-5722	359	5	and	and	CCONJ
ejpam-5722	359	6	s.	s.	PROPN
ejpam-5722	359	7	n.	n.	PROPN
ejpam-5722	359	8	el	el	PROPN
ejpam-5722	359	9	-	-	PROPN
ejpam-5722	359	10	deeb	deeb	PROPN
ejpam-5722	359	11	.	.	PUNCT
ejpam-5722	360	1	on	on	ADP
ejpam-5722	360	2	precontinuous	precontinuous	ADJ
ejpam-5722	360	3	and	and	CCONJ
ejpam-5722	360	4	weak	weak	ADJ
ejpam-5722	360	5	precontinuous	precontinuous	ADJ
ejpam-5722	360	6	mappings	mapping	NOUN
ejpam-5722	360	7	.	.	PUNCT
ejpam-5722	361	1	proceedings	proceeding	NOUN
ejpam-5722	361	2	of	of	ADP
ejpam-5722	361	3	the	the	DET
ejpam-5722	361	4	mathematical	mathematical	ADJ
ejpam-5722	361	5	and	and	CCONJ
ejpam-5722	361	6	physical	physical	ADJ
ejpam-5722	361	7	society	society	NOUN
ejpam-5722	361	8	of	of	ADP
ejpam-5722	361	9	egypt	egypt	PROPN
ejpam-5722	361	10	,	,	PUNCT
ejpam-5722	361	11	53:47–53	53:47–53	NUM
ejpam-5722	361	12	,	,	PUNCT
ejpam-5722	361	13	1982	1982	NUM
ejpam-5722	361	14	.	.	PUNCT
ejpam-5722	362	1	[	[	X
ejpam-5722	362	2	26	26	NUM
ejpam-5722	362	3	]	]	PUNCT
ejpam-5722	362	4	a.	a.	NOUN
ejpam-5722	362	5	neubrunnová.	neubrunnová.	PROPN
ejpam-5722	362	6	on	on	ADP
ejpam-5722	362	7	certain	certain	ADJ
ejpam-5722	362	8	generalizations	generalization	NOUN
ejpam-5722	362	9	of	of	ADP
ejpam-5722	362	10	the	the	DET
ejpam-5722	362	11	notion	notion	NOUN
ejpam-5722	362	12	of	of	ADP
ejpam-5722	362	13	continuity	continuity	NOUN
ejpam-5722	362	14	.	.	PUNCT
ejpam-5722	363	1	matematický	matematický	ADJ
ejpam-5722	363	2	časopis	časopis	PROPN
ejpam-5722	363	3	,	,	PUNCT
ejpam-5722	363	4	23:374–380	23:374–380	NUM
ejpam-5722	363	5	,	,	PUNCT
ejpam-5722	363	6	1973	1973	NUM
ejpam-5722	363	7	.	.	PUNCT
ejpam-5722	364	1	[	[	X
ejpam-5722	364	2	27	27	NUM
ejpam-5722	364	3	]	]	X
ejpam-5722	364	4	o.	o.	NOUN
ejpam-5722	364	5	nj̊astad	nj̊astad	NOUN
ejpam-5722	364	6	.	.	PUNCT
ejpam-5722	365	1	on	on	ADP
ejpam-5722	365	2	some	some	DET
ejpam-5722	365	3	classes	class	NOUN
ejpam-5722	365	4	of	of	ADP
ejpam-5722	365	5	nearly	nearly	ADV
ejpam-5722	365	6	open	open	ADJ
ejpam-5722	365	7	sets	set	NOUN
ejpam-5722	365	8	.	.	PUNCT
ejpam-5722	366	1	pacific	pacific	PROPN
ejpam-5722	366	2	journal	journal	PROPN
ejpam-5722	366	3	of	of	ADP
ejpam-5722	366	4	mathematics	mathematic	NOUN
ejpam-5722	366	5	,	,	PUNCT
ejpam-5722	366	6	15:961–970	15:961–970	PROPN
ejpam-5722	366	7	,	,	PUNCT
ejpam-5722	366	8	1965	1965	NUM
ejpam-5722	366	9	.	.	PUNCT
ejpam-5722	367	1	[	[	X
ejpam-5722	367	2	28	28	NUM
ejpam-5722	367	3	]	]	X
ejpam-5722	367	4	t.	t.	PROPN
ejpam-5722	367	5	noiri	noiri	PROPN
ejpam-5722	367	6	.	.	PUNCT
ejpam-5722	368	1	on	on	ADP
ejpam-5722	368	2	θ	θ	ADJ
ejpam-5722	368	3	-	-	ADJ
ejpam-5722	368	4	continuous	continuous	ADJ
ejpam-5722	368	5	functions	function	NOUN
ejpam-5722	368	6	.	.	PUNCT
ejpam-5722	369	1	indian	indian	ADJ
ejpam-5722	369	2	journal	journal	PROPN
ejpam-5722	369	3	of	of	ADP
ejpam-5722	369	4	pure	pure	ADJ
ejpam-5722	369	5	and	and	CCONJ
ejpam-5722	369	6	applied	applied	ADJ
ejpam-5722	369	7	mathematics	mathematic	NOUN
ejpam-5722	369	8	,	,	PUNCT
ejpam-5722	369	9	21:410–415	21:410–415	NUM
ejpam-5722	369	10	,	,	PUNCT
ejpam-5722	369	11	1990	1990	NUM
ejpam-5722	369	12	.	.	PUNCT
ejpam-5722	370	1	[	[	X
ejpam-5722	370	2	29	29	NUM
ejpam-5722	370	3	]	]	PUNCT
ejpam-5722	370	4	v.	v.	CCONJ
ejpam-5722	370	5	popa	popa	NOUN
ejpam-5722	370	6	.	.	PUNCT
ejpam-5722	371	1	on	on	ADP
ejpam-5722	371	2	the	the	DET
ejpam-5722	371	3	decompositions	decomposition	NOUN
ejpam-5722	371	4	of	of	ADP
ejpam-5722	371	5	the	the	DET
ejpam-5722	371	6	quasicontinuity	quasicontinuity	NOUN
ejpam-5722	371	7	in	in	ADP
ejpam-5722	371	8	topological	topological	ADJ
ejpam-5722	371	9	spaces	space	NOUN
ejpam-5722	371	10	.	.	PUNCT
ejpam-5722	372	1	studii	studii	PROPN
ejpam-5722	372	2	şi	şi	PROPN
ejpam-5722	372	3	cercetǎri	cercetǎri	NOUN
ejpam-5722	372	4	matematicǎ	matematicǎ	VERB
ejpam-5722	372	5	,	,	PUNCT
ejpam-5722	372	6	30:31–35	30:31–35	NUM
ejpam-5722	372	7	,	,	PUNCT
ejpam-5722	372	8	1978	1978	NUM
ejpam-5722	372	9	.	.	PUNCT
ejpam-5722	373	1	[	[	X
ejpam-5722	373	2	30	30	NUM
ejpam-5722	373	3	]	]	X
ejpam-5722	373	4	v.	v.	CCONJ
ejpam-5722	373	5	popa	popa	NOUN
ejpam-5722	373	6	and	and	CCONJ
ejpam-5722	373	7	c.	c.	PROPN
ejpam-5722	373	8	stan	stan	PROPN
ejpam-5722	373	9	.	.	PUNCT
ejpam-5722	374	1	on	on	ADP
ejpam-5722	374	2	a	a	DET
ejpam-5722	374	3	decomposition	decomposition	NOUN
ejpam-5722	374	4	of	of	ADP
ejpam-5722	374	5	quasicontinuity	quasicontinuity	NOUN
ejpam-5722	374	6	in	in	ADP
ejpam-5722	374	7	topological	topological	ADJ
ejpam-5722	374	8	spaces	space	NOUN
ejpam-5722	374	9	.	.	PUNCT
ejpam-5722	375	1	studii	studii	PROPN
ejpam-5722	375	2	şi	şi	PROPN
ejpam-5722	375	3	cercetǎri	cercetǎri	NOUN
ejpam-5722	375	4	matematicǎ	matematicǎ	VERB
ejpam-5722	375	5	,	,	PUNCT
ejpam-5722	375	6	25:41–43	25:41–43	NUM
ejpam-5722	375	7	,	,	PUNCT
ejpam-5722	375	8	1973	1973	NUM
ejpam-5722	375	9	.	.	PUNCT
ejpam-5722	376	1	[	[	X
ejpam-5722	376	2	31	31	NUM
ejpam-5722	376	3	]	]	PUNCT
ejpam-5722	376	4	c.	c.	NOUN
ejpam-5722	376	5	prachanpol	prachanpol	NOUN
ejpam-5722	376	6	,	,	PUNCT
ejpam-5722	376	7	c.	c.	PROPN
ejpam-5722	376	8	boonpok	boonpok	PROPN
ejpam-5722	376	9	,	,	PUNCT
ejpam-5722	376	10	and	and	CCONJ
ejpam-5722	376	11	c.	c.	PROPN
ejpam-5722	376	12	viriyapong	viriyapong	PROPN
ejpam-5722	376	13	.	.	PUNCT
ejpam-5722	377	1	δ(τ1	δ(τ1	PROPN
ejpam-5722	377	2	,	,	PUNCT
ejpam-5722	377	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	377	4	functions	function	NOUN
ejpam-5722	377	5	.	.	PUNCT
ejpam-5722	378	1	european	european	ADJ
ejpam-5722	378	2	journal	journal	PROPN
ejpam-5722	378	3	of	of	ADP
ejpam-5722	378	4	pure	pure	ADJ
ejpam-5722	378	5	and	and	CCONJ
ejpam-5722	378	6	applied	applied	ADJ
ejpam-5722	378	7	mathematics	mathematic	NOUN
ejpam-5722	378	8	,	,	PUNCT
ejpam-5722	378	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-5722	378	10	,	,	PUNCT
ejpam-5722	378	11	2024	2024	NUM
ejpam-5722	378	12	.	.	PUNCT
ejpam-5722	379	1	[	[	X
ejpam-5722	379	2	32	32	NUM
ejpam-5722	379	3	]	]	PUNCT
ejpam-5722	379	4	p.	p.	NOUN
ejpam-5722	379	5	pue	pue	NOUN
ejpam-5722	379	6	-	-	PUNCT
ejpam-5722	379	7	on	on	ADP
ejpam-5722	379	8	and	and	CCONJ
ejpam-5722	379	9	c.	c.	PROPN
ejpam-5722	379	10	boonpok	boonpok	PROPN
ejpam-5722	379	11	.	.	PUNCT
ejpam-5722	380	1	θ(λ	θ(λ	PROPN
ejpam-5722	380	2	,	,	PUNCT
ejpam-5722	380	3	p)-continuity	p)-continuity	NOUN
ejpam-5722	380	4	for	for	ADP
ejpam-5722	380	5	functions	function	NOUN
ejpam-5722	380	6	.	.	PUNCT
ejpam-5722	381	1	international	international	ADJ
ejpam-5722	381	2	journal	journal	NOUN
ejpam-5722	381	3	of	of	ADP
ejpam-5722	381	4	mathematics	mathematic	NOUN
ejpam-5722	381	5	and	and	CCONJ
ejpam-5722	381	6	computer	computer	NOUN
ejpam-5722	381	7	science	science	NOUN
ejpam-5722	381	8	,	,	PUNCT
ejpam-5722	381	9	19(2):491–495	19(2):491–495	NUM
ejpam-5722	381	10	,	,	PUNCT
ejpam-5722	381	11	2024	2024	NUM
ejpam-5722	381	12	.	.	PUNCT
ejpam-5722	382	1	[	[	X
ejpam-5722	382	2	33	33	NUM
ejpam-5722	382	3	]	]	PUNCT
ejpam-5722	382	4	p.	p.	NOUN
ejpam-5722	382	5	pue	pue	NOUN
ejpam-5722	382	6	-	-	PUNCT
ejpam-5722	382	7	on	on	ADP
ejpam-5722	382	8	,	,	PUNCT
ejpam-5722	382	9	a.	a.	PROPN
ejpam-5722	382	10	sama	sama	PROPN
ejpam-5722	382	11	-	-	PUNCT
ejpam-5722	382	12	ae	ae	PROPN
ejpam-5722	382	13	,	,	PUNCT
ejpam-5722	382	14	and	and	CCONJ
ejpam-5722	382	15	c.	c.	PROPN
ejpam-5722	382	16	boonpok	boonpok	PROPN
ejpam-5722	382	17	.	.	PUNCT
ejpam-5722	383	1	quasi	quasi	PROPN
ejpam-5722	383	2	θ(τ1	θ(τ1	PROPN
ejpam-5722	383	3	,	,	PUNCT
ejpam-5722	383	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5722	383	5	for	for	ADP
ejpam-5722	383	6	multifunctions	multifunction	NOUN
ejpam-5722	383	7	.	.	PUNCT
ejpam-5722	384	1	(	(	PUNCT
ejpam-5722	384	2	accepted	accept	VERB
ejpam-5722	384	3	)	)	PUNCT
ejpam-5722	384	4	.	.	PUNCT
ejpam-5722	385	1	[	[	X
ejpam-5722	385	2	34	34	NUM
ejpam-5722	385	3	]	]	X
ejpam-5722	385	4	p.	p.	NOUN
ejpam-5722	385	5	pue	pue	NOUN
ejpam-5722	385	6	-	-	PUNCT
ejpam-5722	385	7	on	on	ADP
ejpam-5722	385	8	,	,	PUNCT
ejpam-5722	385	9	a.	a.	PROPN
ejpam-5722	385	10	sama	sama	PROPN
ejpam-5722	385	11	-	-	PUNCT
ejpam-5722	385	12	ae	ae	PROPN
ejpam-5722	385	13	,	,	PUNCT
ejpam-5722	385	14	and	and	CCONJ
ejpam-5722	385	15	c.	c.	PROPN
ejpam-5722	385	16	boonpok	boonpok	PROPN
ejpam-5722	385	17	.	.	PUNCT
ejpam-5722	386	1	characterizations	characterization	NOUN
ejpam-5722	386	2	of	of	ADP
ejpam-5722	386	3	quasi	quasi	NOUN
ejpam-5722	386	4	θ(τ1	θ(τ1	NOUN
ejpam-5722	386	5	,	,	PUNCT
ejpam-5722	386	6	τ2)continuous	τ2)continuous	ADJ
ejpam-5722	386	7	multifunctions	multifunction	NOUN
ejpam-5722	386	8	.	.	PUNCT
ejpam-5722	387	1	(	(	PUNCT
ejpam-5722	387	2	submitted	submit	VERB
ejpam-5722	387	3	)	)	PUNCT
ejpam-5722	387	4	.	.	PUNCT
ejpam-5722	388	1	[	[	X
ejpam-5722	388	2	35	35	NUM
ejpam-5722	388	3	]	]	X
ejpam-5722	388	4	p.	p.	NOUN
ejpam-5722	388	5	pue	pue	NOUN
ejpam-5722	388	6	-	-	PUNCT
ejpam-5722	388	7	on	on	ADP
ejpam-5722	388	8	,	,	PUNCT
ejpam-5722	388	9	s.	s.	PROPN
ejpam-5722	388	10	sompong	sompong	PROPN
ejpam-5722	388	11	,	,	PUNCT
ejpam-5722	388	12	and	and	CCONJ
ejpam-5722	388	13	c.	c.	PROPN
ejpam-5722	388	14	boonpok	boonpok	PROPN
ejpam-5722	388	15	.	.	PUNCT
ejpam-5722	389	1	slightly	slightly	ADV
ejpam-5722	389	2	(	(	PUNCT
ejpam-5722	389	3	τ1	τ1	NOUN
ejpam-5722	389	4	,	,	PUNCT
ejpam-5722	389	5	τ2)s	τ2)s	ADJ
ejpam-5722	389	6	-	-	PUNCT
ejpam-5722	389	7	continuous	continuous	ADJ
ejpam-5722	389	8	functions	function	NOUN
ejpam-5722	389	9	.	.	PUNCT
ejpam-5722	390	1	international	international	ADJ
ejpam-5722	390	2	journal	journal	NOUN
ejpam-5722	390	3	of	of	ADP
ejpam-5722	390	4	mathematics	mathematic	NOUN
ejpam-5722	390	5	and	and	CCONJ
ejpam-5722	390	6	computer	computer	NOUN
ejpam-5722	390	7	science	science	NOUN
ejpam-5722	390	8	,	,	PUNCT
ejpam-5722	390	9	20(1):217–221	20(1):217–221	PROPN
ejpam-5722	390	10	,	,	PUNCT
ejpam-5722	390	11	2025	2025	NUM
ejpam-5722	390	12	.	.	PUNCT
ejpam-5722	391	1	[	[	X
ejpam-5722	391	2	36	36	NUM
ejpam-5722	391	3	]	]	X
ejpam-5722	391	4	n.	n.	PROPN
ejpam-5722	391	5	srisarakham	srisarakham	PROPN
ejpam-5722	391	6	and	and	CCONJ
ejpam-5722	391	7	c.	c.	PROPN
ejpam-5722	391	8	boonpok	boonpok	PROPN
ejpam-5722	391	9	.	.	PUNCT
ejpam-5722	392	1	almost	almost	ADV
ejpam-5722	392	2	(	(	PUNCT
ejpam-5722	392	3	λ	λ	NOUN
ejpam-5722	392	4	,	,	PUNCT
ejpam-5722	392	5	p)-continuous	p)-continuous	ADJ
ejpam-5722	392	6	functions	function	NOUN
ejpam-5722	392	7	.	.	PUNCT
ejpam-5722	393	1	international	international	ADJ
ejpam-5722	393	2	journal	journal	PROPN
ejpam-5722	393	3	of	of	ADP
ejpam-5722	393	4	mathematics	mathematic	NOUN
ejpam-5722	393	5	and	and	CCONJ
ejpam-5722	393	6	computer	computer	NOUN
ejpam-5722	393	7	science	science	NOUN
ejpam-5722	393	8	,	,	PUNCT
ejpam-5722	393	9	18(2):255–259	18(2):255–259	NUM
ejpam-5722	393	10	,	,	PUNCT
ejpam-5722	393	11	2023	2023	NUM
ejpam-5722	393	12	.	.	PUNCT
ejpam-5722	394	1	[	[	X
ejpam-5722	394	2	37	37	NUM
ejpam-5722	394	3	]	]	X
ejpam-5722	394	4	n.	n.	NOUN
ejpam-5722	394	5	srisarakham	srisarakham	PROPN
ejpam-5722	394	6	,	,	PUNCT
ejpam-5722	394	7	a.	a.	PROPN
ejpam-5722	394	8	sama	sama	PROPN
ejpam-5722	394	9	-	-	PUNCT
ejpam-5722	394	10	ae	ae	PROPN
ejpam-5722	394	11	,	,	PUNCT
ejpam-5722	394	12	and	and	CCONJ
ejpam-5722	394	13	c.	c.	PROPN
ejpam-5722	394	14	boonpok	boonpok	PROPN
ejpam-5722	394	15	.	.	PUNCT
ejpam-5722	395	1	characterizations	characterization	NOUN
ejpam-5722	395	2	of	of	ADP
ejpam-5722	395	3	faintly	faintly	ADV
ejpam-5722	395	4	(	(	PUNCT
ejpam-5722	395	5	τ1	τ1	PROPN
ejpam-5722	395	6	,	,	PUNCT
ejpam-5722	395	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	395	8	functions	function	NOUN
ejpam-5722	395	9	.	.	PUNCT
ejpam-5722	396	1	european	european	ADJ
ejpam-5722	396	2	journal	journal	PROPN
ejpam-5722	396	3	of	of	ADP
ejpam-5722	396	4	pure	pure	ADJ
ejpam-5722	396	5	and	and	CCONJ
ejpam-5722	396	6	applied	applied	ADJ
ejpam-5722	396	7	mathematics	mathematic	NOUN
ejpam-5722	396	8	,	,	PUNCT
ejpam-5722	396	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-5722	396	10	,	,	PUNCT
ejpam-5722	396	11	2024	2024	NUM
ejpam-5722	396	12	.	.	PUNCT
ejpam-5722	397	1	[	[	X
ejpam-5722	397	2	38	38	NUM
ejpam-5722	397	3	]	]	PUNCT
ejpam-5722	397	4	m.	m.	NOUN
ejpam-5722	397	5	thongmoon	thongmoon	NOUN
ejpam-5722	397	6	and	and	CCONJ
ejpam-5722	397	7	c.	c.	PROPN
ejpam-5722	397	8	boonpok	boonpok	PROPN
ejpam-5722	397	9	.	.	PUNCT
ejpam-5722	398	1	strongly	strongly	ADV
ejpam-5722	398	2	θ(λ	θ(λ	PROPN
ejpam-5722	398	3	,	,	PUNCT
ejpam-5722	398	4	p)-continuous	p)-continuous	ADJ
ejpam-5722	398	5	functions	function	NOUN
ejpam-5722	398	6	.	.	PUNCT
ejpam-5722	399	1	international	international	ADJ
ejpam-5722	399	2	journal	journal	PROPN
ejpam-5722	399	3	of	of	ADP
ejpam-5722	399	4	mathematics	mathematic	NOUN
ejpam-5722	399	5	and	and	CCONJ
ejpam-5722	399	6	computer	computer	NOUN
ejpam-5722	399	7	science	science	NOUN
ejpam-5722	399	8	,	,	PUNCT
ejpam-5722	399	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5722	399	10	,	,	PUNCT
ejpam-5722	399	11	2024	2024	NUM
ejpam-5722	399	12	.	.	PUNCT
ejpam-5722	400	1	[	[	X
ejpam-5722	400	2	39	39	NUM
ejpam-5722	400	3	]	]	PUNCT
ejpam-5722	400	4	m.	m.	NOUN
ejpam-5722	400	5	thongmoon	thongmoon	NOUN
ejpam-5722	400	6	,	,	PUNCT
ejpam-5722	400	7	s.	s.	PROPN
ejpam-5722	400	8	sompong	sompong	PROPN
ejpam-5722	400	9	,	,	PUNCT
ejpam-5722	400	10	and	and	CCONJ
ejpam-5722	400	11	c.	c.	PROPN
ejpam-5722	400	12	boonpok	boonpok	PROPN
ejpam-5722	400	13	.	.	PUNCT
ejpam-5722	401	1	(	(	PUNCT
ejpam-5722	401	2	τ1	τ1	NOUN
ejpam-5722	401	3	,	,	PUNCT
ejpam-5722	401	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	401	5	multifunctions	multifunction	NOUN
ejpam-5722	401	6	and	and	CCONJ
ejpam-5722	401	7	τ1τ2	τ1τ2	NOUN
ejpam-5722	401	8	-	-	ADJ
ejpam-5722	401	9	δ	δ	NOUN
ejpam-5722	401	10	-	-	ADJ
ejpam-5722	401	11	open	open	ADJ
ejpam-5722	401	12	sets	set	NOUN
ejpam-5722	401	13	.	.	PUNCT
ejpam-5722	402	1	international	international	ADJ
ejpam-5722	402	2	journal	journal	NOUN
ejpam-5722	402	3	of	of	ADP
ejpam-5722	402	4	mathematics	mathematic	NOUN
ejpam-5722	402	5	and	and	CCONJ
ejpam-5722	402	6	computer	computer	NOUN
ejpam-5722	402	7	science	science	NOUN
ejpam-5722	402	8	,	,	PUNCT
ejpam-5722	402	9	19(4):1369–1375	19(4):1369–1375	NUM
ejpam-5722	402	10	,	,	PUNCT
ejpam-5722	402	11	2024	2024	NUM
ejpam-5722	402	12	.	.	PUNCT
ejpam-5722	403	1	[	[	X
ejpam-5722	403	2	40	40	NUM
ejpam-5722	403	3	]	]	PUNCT
ejpam-5722	403	4	m.	m.	NOUN
ejpam-5722	403	5	thongmoon	thongmoon	NOUN
ejpam-5722	403	6	,	,	PUNCT
ejpam-5722	403	7	s.	s.	PROPN
ejpam-5722	403	8	sompong	sompong	PROPN
ejpam-5722	403	9	,	,	PUNCT
ejpam-5722	403	10	and	and	CCONJ
ejpam-5722	403	11	c.	c.	PROPN
ejpam-5722	403	12	boonpok	boonpok	PROPN
ejpam-5722	403	13	.	.	PUNCT
ejpam-5722	404	1	upper	upper	ADJ
ejpam-5722	404	2	and	and	CCONJ
ejpam-5722	404	3	lower	low	ADJ
ejpam-5722	404	4	weak	weak	ADJ
ejpam-5722	404	5	(	(	PUNCT
ejpam-5722	404	6	τ1	τ1	NOUN
ejpam-5722	404	7	,	,	PUNCT
ejpam-5722	404	8	τ2)continuity	τ2)continuity	PROPN
ejpam-5722	404	9	.	.	PUNCT
ejpam-5722	405	1	european	european	PROPN
ejpam-5722	405	2	journal	journal	PROPN
ejpam-5722	405	3	of	of	ADP
ejpam-5722	405	4	pure	pure	ADJ
ejpam-5722	405	5	and	and	CCONJ
ejpam-5722	405	6	applied	applied	ADJ
ejpam-5722	405	7	mathematics	mathematic	NOUN
ejpam-5722	405	8	,	,	PUNCT
ejpam-5722	405	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-5722	405	10	,	,	PUNCT
ejpam-5722	405	11	2024	2024	NUM
ejpam-5722	405	12	.	.	PUNCT
ejpam-5722	406	1	[	[	X
ejpam-5722	406	2	41	41	NUM
ejpam-5722	406	3	]	]	PUNCT
ejpam-5722	406	4	m.	m.	NOUN
ejpam-5722	406	5	thongmoon	thongmoon	NOUN
ejpam-5722	406	6	,	,	PUNCT
ejpam-5722	406	7	s.	s.	PROPN
ejpam-5722	406	8	sompong	sompong	PROPN
ejpam-5722	406	9	,	,	PUNCT
ejpam-5722	406	10	and	and	CCONJ
ejpam-5722	406	11	c.	c.	PROPN
ejpam-5722	406	12	boonpok	boonpok	PROPN
ejpam-5722	406	13	.	.	PUNCT
ejpam-5722	407	1	rarely	rarely	ADV
ejpam-5722	407	2	(	(	PUNCT
ejpam-5722	407	3	τ1	τ1	NOUN
ejpam-5722	407	4	,	,	PUNCT
ejpam-5722	407	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5722	407	6	functions	function	NOUN
ejpam-5722	407	7	.	.	PUNCT
ejpam-5722	408	1	international	international	ADJ
ejpam-5722	408	2	journal	journal	NOUN
ejpam-5722	408	3	of	of	ADP
ejpam-5722	408	4	mathematics	mathematic	NOUN
ejpam-5722	408	5	and	and	CCONJ
ejpam-5722	408	6	computer	computer	NOUN
ejpam-5722	408	7	science	science	NOUN
ejpam-5722	408	8	,	,	PUNCT
ejpam-5722	408	9	20(1):423–427	20(1):423–427	NUM
ejpam-5722	408	10	,	,	PUNCT
ejpam-5722	408	11	2025	2025	NUM
ejpam-5722	408	12	.	.	PUNCT
ejpam-5722	409	1	n.	n.	PROPN
ejpam-5722	409	2	srisarakham	srisarakham	PROPN
ejpam-5722	409	3	,	,	PUNCT
ejpam-5722	409	4	s.	s.	PROPN
ejpam-5722	409	5	sompong	sompong	PROPN
ejpam-5722	409	6	,	,	PUNCT
ejpam-5722	409	7	c.	c.	PROPN
ejpam-5722	409	8	boonpok	boonpok	PROPN
ejpam-5722	409	9	/	/	SYM
ejpam-5722	409	10	eur	eur	PROPN
ejpam-5722	409	11	.	.	PUNCT
ejpam-5722	410	1	j.	j.	PROPN
ejpam-5722	410	2	pure	pure	PROPN
ejpam-5722	410	3	appl	appl	PROPN
ejpam-5722	410	4	.	.	PROPN
ejpam-5722	410	5	math	math	PROPN
ejpam-5722	410	6	,	,	PUNCT
ejpam-5722	410	7	18	18	NUM
ejpam-5722	410	8	(	(	PUNCT
ejpam-5722	410	9	1	1	NUM
ejpam-5722	410	10	)	)	PUNCT
ejpam-5722	410	11	(	(	PUNCT
ejpam-5722	410	12	2025	2025	NUM
ejpam-5722	410	13	)	)	PUNCT
ejpam-5722	410	14	,	,	PUNCT
ejpam-5722	410	15	5722	5722	NUM
ejpam-5722	410	16	12	12	NUM
ejpam-5722	410	17	of	of	ADP
ejpam-5722	410	18	12	12	NUM
ejpam-5722	410	19	[	[	SYM
ejpam-5722	410	20	42	42	NUM
ejpam-5722	410	21	]	]	X
ejpam-5722	410	22	n.	n.	PROPN
ejpam-5722	410	23	v.	v.	ADP
ejpam-5722	410	24	veličko	veličko	PROPN
ejpam-5722	410	25	.	.	PUNCT
ejpam-5722	411	1	h	h	NOUN
ejpam-5722	411	2	-	-	PUNCT
ejpam-5722	411	3	closed	close	VERB
ejpam-5722	411	4	topological	topological	ADJ
ejpam-5722	411	5	spaces	space	NOUN
ejpam-5722	411	6	.	.	PUNCT
ejpam-5722	412	1	american	american	PROPN
ejpam-5722	412	2	mathematical	mathematical	ADJ
ejpam-5722	412	3	society	society	NOUN
ejpam-5722	412	4	translations	translation	NOUN
ejpam-5722	412	5	,	,	PUNCT
ejpam-5722	412	6	78(2):102–118	78(2):102–118	NUM
ejpam-5722	412	7	,	,	PUNCT
ejpam-5722	412	8	1968	1968	NUM
ejpam-5722	412	9	.	.	PUNCT
ejpam-5722	413	1	[	[	X
ejpam-5722	413	2	43	43	NUM
ejpam-5722	413	3	]	]	X
ejpam-5722	413	4	c.	c.	PROPN
ejpam-5722	413	5	viriyapong	viriyapong	PROPN
ejpam-5722	413	6	and	and	CCONJ
ejpam-5722	413	7	c.	c.	PROPN
ejpam-5722	413	8	boonpok	boonpok	PROPN
ejpam-5722	413	9	.	.	PUNCT
ejpam-5722	414	1	(	(	PUNCT
ejpam-5722	414	2	τ1	τ1	NOUN
ejpam-5722	414	3	,	,	PUNCT
ejpam-5722	414	4	τ2)α	τ2)α	NOUN
ejpam-5722	414	5	-	-	PUNCT
ejpam-5722	414	6	continuity	continuity	NOUN
ejpam-5722	414	7	for	for	ADP
ejpam-5722	414	8	multifunctions	multifunction	NOUN
ejpam-5722	414	9	.	.	PUNCT
ejpam-5722	415	1	journal	journal	PROPN
ejpam-5722	415	2	of	of	ADP
ejpam-5722	415	3	mathematics	mathematic	NOUN
ejpam-5722	415	4	,	,	PUNCT
ejpam-5722	415	5	2020:6285763	2020:6285763	NUM
ejpam-5722	415	6	,	,	PUNCT
ejpam-5722	415	7	2020	2020	NUM
ejpam-5722	415	8	.	.	PUNCT
ejpam-5722	416	1	[	[	X
ejpam-5722	416	2	44	44	NUM
ejpam-5722	416	3	]	]	PUNCT
ejpam-5722	416	4	c.	c.	PROPN
ejpam-5722	416	5	viriyapong	viriyapong	PROPN
ejpam-5722	416	6	and	and	CCONJ
ejpam-5722	416	7	c.	c.	PROPN
ejpam-5722	416	8	boonpok	boonpok	PROPN
ejpam-5722	416	9	.	.	PUNCT
ejpam-5722	417	1	(	(	PUNCT
ejpam-5722	417	2	λ	λ	X
ejpam-5722	417	3	,	,	PUNCT
ejpam-5722	417	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5722	417	5	functions	function	NOUN
ejpam-5722	417	6	.	.	PUNCT
ejpam-5722	418	1	wseas	wseas	VERB
ejpam-5722	418	2	transactions	transaction	NOUN
ejpam-5722	418	3	on	on	ADP
ejpam-5722	418	4	mathematics	mathematic	NOUN
ejpam-5722	418	5	,	,	PUNCT
ejpam-5722	418	6	21:380–385	21:380–385	NUM
ejpam-5722	418	7	,	,	PUNCT
ejpam-5722	418	8	2022	2022	NUM
ejpam-5722	418	9	.	.	PUNCT
ejpam-5722	419	1	[	[	X
ejpam-5722	419	2	45	45	NUM
ejpam-5722	419	3	]	]	X
ejpam-5722	419	4	n.	n.	PROPN
ejpam-5722	419	5	viriyapong	viriyapong	PROPN
ejpam-5722	419	6	,	,	PUNCT
ejpam-5722	419	7	s.	s.	PROPN
ejpam-5722	419	8	sompong	sompong	PROPN
ejpam-5722	419	9	,	,	PUNCT
ejpam-5722	419	10	and	and	CCONJ
ejpam-5722	419	11	c.	c.	PROPN
ejpam-5722	419	12	boonpok	boonpok	PROPN
ejpam-5722	419	13	.	.	PUNCT
ejpam-5722	420	1	(	(	PUNCT
ejpam-5722	420	2	τ1	τ1	NOUN
ejpam-5722	420	3	,	,	PUNCT
ejpam-5722	420	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5722	420	5	disconnectedness	disconnectedness	NOUN
ejpam-5722	420	6	in	in	ADP
ejpam-5722	420	7	bitopological	bitopological	ADJ
ejpam-5722	420	8	spaces	space	NOUN
ejpam-5722	420	9	.	.	PUNCT
ejpam-5722	421	1	international	international	ADJ
ejpam-5722	421	2	journal	journal	PROPN
ejpam-5722	421	3	of	of	ADP
ejpam-5722	421	4	mathematics	mathematic	NOUN
ejpam-5722	421	5	and	and	CCONJ
ejpam-5722	421	6	computer	computer	NOUN
ejpam-5722	421	7	science	science	NOUN
ejpam-5722	421	8	,	,	PUNCT
ejpam-5722	421	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5722	421	10	,	,	PUNCT
ejpam-5722	421	11	2024	2024	NUM
ejpam-5722	421	12	.	.	PUNCT