id	sid	tid	token	lemma	pos
ejpam-6036	1	1	european	european	PROPN
ejpam-6036	1	2	journal	journal	PROPN
ejpam-6036	1	3	of	of	ADP
ejpam-6036	1	4	pure	pure	ADJ
ejpam-6036	1	5	and	and	CCONJ
ejpam-6036	1	6	applied	applied	ADJ
ejpam-6036	1	7	mathematics	mathematic	NOUN
ejpam-6036	1	8	2025	2025	NUM
ejpam-6036	1	9	,	,	PUNCT
ejpam-6036	1	10	vol	vol	NOUN
ejpam-6036	1	11	.	.	PROPN
ejpam-6036	1	12	18	18	NUM
ejpam-6036	1	13	,	,	PUNCT
ejpam-6036	1	14	issue	issue	NOUN
ejpam-6036	1	15	2	2	NUM
ejpam-6036	1	16	,	,	PUNCT
ejpam-6036	1	17	article	article	NOUN
ejpam-6036	1	18	number	number	NOUN
ejpam-6036	1	19	6036	6036	NUM
ejpam-6036	1	20	issn	issn	VERB
ejpam-6036	1	21	1307	1307	NUM
ejpam-6036	1	22	-	-	SYM
ejpam-6036	1	23	5543	5543	NUM
ejpam-6036	1	24	–	–	PUNCT
ejpam-6036	1	25	ejpam.com	ejpam.com	X
ejpam-6036	1	26	published	publish	VERB
ejpam-6036	1	27	by	by	ADP
ejpam-6036	1	28	new	new	PROPN
ejpam-6036	1	29	york	york	PROPN
ejpam-6036	1	30	business	business	PROPN
ejpam-6036	1	31	global	global	ADJ
ejpam-6036	1	32	characterizations	characterization	NOUN
ejpam-6036	1	33	of	of	ADP
ejpam-6036	1	34	weakly	weakly	ADJ
ejpam-6036	1	35	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	1	36	,	,	PUNCT
ejpam-6036	1	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	1	38	functions	function	NOUN
ejpam-6036	1	39	butsakorn	butsakorn	PROPN
ejpam-6036	1	40	kong	kong	PROPN
ejpam-6036	1	41	-	-	PUNCT
ejpam-6036	1	42	ied1	ied1	PROPN
ejpam-6036	1	43	,	,	PUNCT
ejpam-6036	1	44	supunnee	supunnee	PROPN
ejpam-6036	1	45	sompong2	sompong2	PROPN
ejpam-6036	1	46	,	,	PUNCT
ejpam-6036	1	47	chawalit	chawalit	VERB
ejpam-6036	1	48	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6036	1	49	1	1	NUM
ejpam-6036	1	50	mathematics	mathematic	NOUN
ejpam-6036	1	51	and	and	CCONJ
ejpam-6036	1	52	applied	apply	VERB
ejpam-6036	1	53	mathematics	mathematics	PROPN
ejpam-6036	1	54	research	research	NOUN
ejpam-6036	1	55	unit	unit	NOUN
ejpam-6036	1	56	,	,	PUNCT
ejpam-6036	1	57	department	department	NOUN
ejpam-6036	1	58	of	of	ADP
ejpam-6036	1	59	mathematics	mathematic	NOUN
ejpam-6036	1	60	,	,	PUNCT
ejpam-6036	1	61	faculty	faculty	NOUN
ejpam-6036	1	62	of	of	ADP
ejpam-6036	1	63	science	science	NOUN
ejpam-6036	1	64	,	,	PUNCT
ejpam-6036	1	65	mahasarakham	mahasarakham	PROPN
ejpam-6036	1	66	university	university	PROPN
ejpam-6036	1	67	,	,	PUNCT
ejpam-6036	1	68	maha	maha	PROPN
ejpam-6036	1	69	sarakham	sarakham	PROPN
ejpam-6036	1	70	,	,	PUNCT
ejpam-6036	1	71	44150	44150	NUM
ejpam-6036	1	72	,	,	PUNCT
ejpam-6036	1	73	thailand	thailand	PROPN
ejpam-6036	1	74	2	2	NUM
ejpam-6036	1	75	department	department	NOUN
ejpam-6036	1	76	of	of	ADP
ejpam-6036	1	77	mathematics	mathematic	NOUN
ejpam-6036	1	78	and	and	CCONJ
ejpam-6036	1	79	statistics	statistic	NOUN
ejpam-6036	1	80	,	,	PUNCT
ejpam-6036	1	81	faculty	faculty	NOUN
ejpam-6036	1	82	of	of	ADP
ejpam-6036	1	83	science	science	NOUN
ejpam-6036	1	84	and	and	CCONJ
ejpam-6036	1	85	technology	technology	NOUN
ejpam-6036	1	86	,	,	PUNCT
ejpam-6036	1	87	sakon	sakon	PROPN
ejpam-6036	1	88	nakhon	nakhon	PROPN
ejpam-6036	1	89	rajbhat	rajbhat	PROPN
ejpam-6036	1	90	university	university	PROPN
ejpam-6036	1	91	,	,	PUNCT
ejpam-6036	1	92	sakon	sakon	PROPN
ejpam-6036	1	93	nakhon	nakhon	PROPN
ejpam-6036	1	94	,	,	PUNCT
ejpam-6036	1	95	47000	47000	NUM
ejpam-6036	1	96	,	,	PUNCT
ejpam-6036	1	97	thailand	thailand	PROPN
ejpam-6036	1	98	abstract	abstract	NOUN
ejpam-6036	1	99	.	.	PUNCT
ejpam-6036	2	1	this	this	DET
ejpam-6036	2	2	paper	paper	NOUN
ejpam-6036	2	3	presents	present	VERB
ejpam-6036	2	4	a	a	DET
ejpam-6036	2	5	new	new	ADJ
ejpam-6036	2	6	class	class	NOUN
ejpam-6036	2	7	of	of	ADP
ejpam-6036	2	8	functions	function	NOUN
ejpam-6036	2	9	called	call	VERB
ejpam-6036	2	10	weakly	weakly	ADJ
ejpam-6036	2	11	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	2	12	,	,	PUNCT
ejpam-6036	2	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	2	14	functions	function	NOUN
ejpam-6036	2	15	.	.	PUNCT
ejpam-6036	3	1	moreover	moreover	ADV
ejpam-6036	3	2	,	,	PUNCT
ejpam-6036	3	3	several	several	ADJ
ejpam-6036	3	4	characterizations	characterization	NOUN
ejpam-6036	3	5	and	and	CCONJ
ejpam-6036	3	6	some	some	DET
ejpam-6036	3	7	properties	property	NOUN
ejpam-6036	3	8	concerning	concern	VERB
ejpam-6036	3	9	weakly	weakly	ADJ
ejpam-6036	3	10	contra(τ1	contra(τ1	NOUN
ejpam-6036	3	11	,	,	PUNCT
ejpam-6036	3	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	3	13	functions	function	NOUN
ejpam-6036	3	14	are	be	AUX
ejpam-6036	3	15	established	establish	VERB
ejpam-6036	3	16	.	.	PUNCT
ejpam-6036	4	1	2020	2020	NUM
ejpam-6036	4	2	mathematics	mathematics	PROPN
ejpam-6036	4	3	subject	subject	NOUN
ejpam-6036	4	4	classifications	classification	NOUN
ejpam-6036	4	5	:	:	PUNCT
ejpam-6036	4	6	54c08	54c08	NUM
ejpam-6036	4	7	,	,	PUNCT
ejpam-6036	4	8	54e55	54e55	NUM
ejpam-6036	4	9	key	key	ADJ
ejpam-6036	4	10	words	word	NOUN
ejpam-6036	4	11	and	and	CCONJ
ejpam-6036	4	12	phrases	phrase	NOUN
ejpam-6036	4	13	:	:	PUNCT
ejpam-6036	4	14	τ1τ2	τ1τ2	ADJ
ejpam-6036	4	15	-	-	ADJ
ejpam-6036	4	16	open	open	ADJ
ejpam-6036	4	17	set	set	NOUN
ejpam-6036	4	18	,	,	PUNCT
ejpam-6036	4	19	weakly	weakly	ADJ
ejpam-6036	4	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	4	21	,	,	PUNCT
ejpam-6036	4	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	4	23	function	function	NOUN
ejpam-6036	4	24	1	1	NUM
ejpam-6036	4	25	.	.	PUNCT
ejpam-6036	5	1	introduction	introduction	NOUN
ejpam-6036	5	2	it	it	PRON
ejpam-6036	5	3	is	be	AUX
ejpam-6036	5	4	well	well	ADV
ejpam-6036	5	5	-	-	PUNCT
ejpam-6036	5	6	known	know	VERB
ejpam-6036	5	7	that	that	SCONJ
ejpam-6036	5	8	the	the	DET
ejpam-6036	5	9	branch	branch	NOUN
ejpam-6036	5	10	of	of	ADP
ejpam-6036	5	11	mathematics	mathematic	NOUN
ejpam-6036	5	12	called	call	VERB
ejpam-6036	5	13	topology	topology	NOUN
ejpam-6036	5	14	is	be	AUX
ejpam-6036	5	15	concerned	concern	VERB
ejpam-6036	5	16	with	with	ADP
ejpam-6036	5	17	all	all	DET
ejpam-6036	5	18	questions	question	NOUN
ejpam-6036	5	19	directly	directly	ADV
ejpam-6036	5	20	or	or	CCONJ
ejpam-6036	5	21	indirectly	indirectly	ADV
ejpam-6036	5	22	related	relate	VERB
ejpam-6036	5	23	to	to	ADP
ejpam-6036	5	24	continuity	continuity	NOUN
ejpam-6036	5	25	.	.	PUNCT
ejpam-6036	6	1	stronger	strong	ADJ
ejpam-6036	6	2	and	and	CCONJ
ejpam-6036	6	3	weaker	weak	ADJ
ejpam-6036	6	4	forms	form	NOUN
ejpam-6036	6	5	of	of	ADP
ejpam-6036	6	6	open	open	ADJ
ejpam-6036	6	7	sets	set	NOUN
ejpam-6036	6	8	play	play	VERB
ejpam-6036	6	9	an	an	DET
ejpam-6036	6	10	important	important	ADJ
ejpam-6036	6	11	role	role	NOUN
ejpam-6036	6	12	in	in	ADP
ejpam-6036	6	13	the	the	DET
ejpam-6036	6	14	generalization	generalization	NOUN
ejpam-6036	6	15	of	of	ADP
ejpam-6036	6	16	different	different	ADJ
ejpam-6036	6	17	forms	form	NOUN
ejpam-6036	6	18	of	of	ADP
ejpam-6036	6	19	continuity	continuity	NOUN
ejpam-6036	6	20	.	.	PUNCT
ejpam-6036	7	1	using	use	VERB
ejpam-6036	7	2	different	different	ADJ
ejpam-6036	7	3	forms	form	NOUN
ejpam-6036	7	4	of	of	ADP
ejpam-6036	7	5	open	open	ADJ
ejpam-6036	7	6	sets	set	NOUN
ejpam-6036	7	7	,	,	PUNCT
ejpam-6036	7	8	many	many	ADJ
ejpam-6036	7	9	authors	author	NOUN
ejpam-6036	7	10	have	have	AUX
ejpam-6036	7	11	introduced	introduce	VERB
ejpam-6036	7	12	and	and	CCONJ
ejpam-6036	7	13	studied	study	VERB
ejpam-6036	7	14	various	various	ADJ
ejpam-6036	7	15	types	type	NOUN
ejpam-6036	7	16	of	of	ADP
ejpam-6036	7	17	continuity	continuity	NOUN
ejpam-6036	7	18	for	for	ADP
ejpam-6036	7	19	functions	function	NOUN
ejpam-6036	7	20	.	.	PUNCT
ejpam-6036	8	1	in	in	ADP
ejpam-6036	8	2	[	[	X
ejpam-6036	8	3	1	1	NUM
ejpam-6036	8	4	]	]	PUNCT
ejpam-6036	8	5	,	,	PUNCT
ejpam-6036	8	6	the	the	DET
ejpam-6036	8	7	present	present	ADJ
ejpam-6036	8	8	authors	author	NOUN
ejpam-6036	8	9	investigated	investigate	VERB
ejpam-6036	8	10	several	several	ADJ
ejpam-6036	8	11	characterizations	characterization	NOUN
ejpam-6036	8	12	of	of	ADP
ejpam-6036	8	13	(	(	PUNCT
ejpam-6036	8	14	λ	λ	PROPN
ejpam-6036	8	15	,	,	PUNCT
ejpam-6036	8	16	sp)-continuous	sp)-continuous	ADJ
ejpam-6036	8	17	functions	function	NOUN
ejpam-6036	8	18	by	by	ADP
ejpam-6036	8	19	utilizing	utilize	VERB
ejpam-6036	8	20	the	the	DET
ejpam-6036	8	21	notions	notion	NOUN
ejpam-6036	8	22	of	of	ADP
ejpam-6036	8	23	(	(	PUNCT
ejpam-6036	8	24	λ	λ	PROPN
ejpam-6036	8	25	,	,	PUNCT
ejpam-6036	8	26	sp)-open	sp)-open	ADJ
ejpam-6036	8	27	sets	set	NOUN
ejpam-6036	8	28	and	and	CCONJ
ejpam-6036	8	29	(	(	PUNCT
ejpam-6036	8	30	λ	λ	PROPN
ejpam-6036	8	31	,	,	PUNCT
ejpam-6036	8	32	sp)closed	sp)close	VERB
ejpam-6036	8	33	sets	set	NOUN
ejpam-6036	8	34	due	due	ADP
ejpam-6036	8	35	to	to	ADP
ejpam-6036	8	36	boonpok	boonpok	NOUN
ejpam-6036	8	37	and	and	CCONJ
ejpam-6036	8	38	khampakdee	khampakdee	NOUN
ejpam-6036	8	39	[	[	X
ejpam-6036	8	40	2	2	NUM
ejpam-6036	8	41	]	]	PUNCT
ejpam-6036	8	42	.	.	PUNCT
ejpam-6036	9	1	dungthaisong	dungthaisong	NOUN
ejpam-6036	9	2	et	et	PROPN
ejpam-6036	9	3	al	al	PROPN
ejpam-6036	9	4	.	.	PUNCT
ejpam-6036	10	1	[	[	X
ejpam-6036	10	2	3	3	NUM
ejpam-6036	10	3	]	]	PUNCT
ejpam-6036	10	4	introduced	introduce	VERB
ejpam-6036	10	5	and	and	CCONJ
ejpam-6036	10	6	investigated	investigate	VERB
ejpam-6036	10	7	the	the	DET
ejpam-6036	10	8	concept	concept	NOUN
ejpam-6036	10	9	of	of	ADP
ejpam-6036	10	10	g(m	g(m	ADJ
ejpam-6036	10	11	,	,	PUNCT
ejpam-6036	10	12	n)-continuous	n)-continuous	ADJ
ejpam-6036	10	13	functions	function	NOUN
ejpam-6036	10	14	.	.	PUNCT
ejpam-6036	11	1	duangphui	duangphui	NOUN
ejpam-6036	11	2	et	et	PROPN
ejpam-6036	11	3	al	al	PROPN
ejpam-6036	11	4	.	.	PUNCT
ejpam-6036	12	1	[	[	X
ejpam-6036	12	2	4	4	X
ejpam-6036	12	3	]	]	PUNCT
ejpam-6036	12	4	introduced	introduce	VERB
ejpam-6036	12	5	and	and	CCONJ
ejpam-6036	12	6	studied	study	VERB
ejpam-6036	12	7	the	the	DET
ejpam-6036	12	8	notion	notion	NOUN
ejpam-6036	12	9	of	of	ADP
ejpam-6036	12	10	(	(	PUNCT
ejpam-6036	12	11	µ	µ	NOUN
ejpam-6036	12	12	,	,	PUNCT
ejpam-6036	12	13	µ′)(m	µ′)(m	VERB
ejpam-6036	12	14	,	,	PUNCT
ejpam-6036	12	15	n)-continuous	n)-continuous	ADJ
ejpam-6036	12	16	functions	function	NOUN
ejpam-6036	12	17	.	.	PUNCT
ejpam-6036	13	1	furthermore	furthermore	ADV
ejpam-6036	13	2	,	,	PUNCT
ejpam-6036	13	3	several	several	ADJ
ejpam-6036	13	4	characterizations	characterization	NOUN
ejpam-6036	13	5	of	of	ADP
ejpam-6036	13	6	almost	almost	ADV
ejpam-6036	13	7	(	(	PUNCT
ejpam-6036	13	8	λ	λ	PROPN
ejpam-6036	13	9	,	,	PUNCT
ejpam-6036	13	10	p)-continuous	p)-continuous	ADJ
ejpam-6036	13	11	functions	function	NOUN
ejpam-6036	13	12	,	,	PUNCT
ejpam-6036	13	13	strongly	strongly	ADV
ejpam-6036	13	14	θ(λ	θ(λ	PROPN
ejpam-6036	13	15	,	,	PUNCT
ejpam-6036	13	16	p)-continuous	p)-continuous	ADJ
ejpam-6036	13	17	functions	function	NOUN
ejpam-6036	13	18	,	,	PUNCT
ejpam-6036	13	19	almost	almost	ADV
ejpam-6036	13	20	strongly	strongly	ADV
ejpam-6036	13	21	θ(λ	θ(λ	VERB
ejpam-6036	13	22	,	,	PUNCT
ejpam-6036	13	23	p)-continuous	p)-continuous	ADJ
ejpam-6036	13	24	functions	function	NOUN
ejpam-6036	13	25	,	,	PUNCT
ejpam-6036	13	26	θ(λ	θ(λ	PROPN
ejpam-6036	13	27	,	,	PUNCT
ejpam-6036	13	28	p)-continuous	p)-continuous	ADJ
ejpam-6036	13	29	functions	function	NOUN
ejpam-6036	13	30	,	,	PUNCT
ejpam-6036	13	31	weakly	weakly	ADJ
ejpam-6036	13	32	(	(	PUNCT
ejpam-6036	13	33	λ	λ	PROPN
ejpam-6036	13	34	,	,	PUNCT
ejpam-6036	13	35	b)-continuous	b)-continuous	ADJ
ejpam-6036	13	36	functions	function	NOUN
ejpam-6036	13	37	,	,	PUNCT
ejpam-6036	13	38	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-6036	13	39	functions	function	NOUN
ejpam-6036	13	40	,	,	PUNCT
ejpam-6036	13	41	(	(	PUNCT
ejpam-6036	13	42	λ	λ	NOUN
ejpam-6036	13	43	,	,	PUNCT
ejpam-6036	13	44	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-6036	13	45	functions	function	NOUN
ejpam-6036	13	46	,	,	PUNCT
ejpam-6036	13	47	⋆-continuous	⋆-continuous	ADJ
ejpam-6036	13	48	functions	function	NOUN
ejpam-6036	13	49	,	,	PUNCT
ejpam-6036	13	50	θ	θ	PROPN
ejpam-6036	13	51	-	-	ADJ
ejpam-6036	13	52	i	i	NOUN
ejpam-6036	13	53	-continuous	-continuous	ADJ
ejpam-6036	13	54	functions	function	NOUN
ejpam-6036	13	55	,	,	PUNCT
ejpam-6036	13	56	almost	almost	ADV
ejpam-6036	13	57	(	(	PUNCT
ejpam-6036	13	58	g	g	NOUN
ejpam-6036	13	59	,	,	PUNCT
ejpam-6036	13	60	m)-continuous	m)-continuous	ADJ
ejpam-6036	13	61	functions	function	NOUN
ejpam-6036	13	62	,	,	PUNCT
ejpam-6036	13	63	pairwise	pairwise	NOUN
ejpam-6036	13	64	almost	almost	ADV
ejpam-6036	13	65	m	m	VERB
ejpam-6036	13	66	-continuous	-continuous	ADJ
ejpam-6036	13	67	functions	function	NOUN
ejpam-6036	13	68	,	,	PUNCT
ejpam-6036	13	69	faintly	faintly	ADV
ejpam-6036	13	70	(	(	PUNCT
ejpam-6036	13	71	τ1	τ1	PROPN
ejpam-6036	13	72	,	,	PUNCT
ejpam-6036	13	73	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	13	74	functions	function	NOUN
ejpam-6036	13	75	,	,	PUNCT
ejpam-6036	13	76	δ(τ1	δ(τ1	NOUN
ejpam-6036	13	77	,	,	PUNCT
ejpam-6036	13	78	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	13	79	functions	function	NOUN
ejpam-6036	13	80	and	and	CCONJ
ejpam-6036	13	81	almost	almost	ADV
ejpam-6036	13	82	nearly	nearly	ADV
ejpam-6036	13	83	(	(	PUNCT
ejpam-6036	13	84	τ1	τ1	NOUN
ejpam-6036	13	85	,	,	PUNCT
ejpam-6036	13	86	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	13	87	functions	function	NOUN
ejpam-6036	13	88	were	be	AUX
ejpam-6036	13	89	presented	present	VERB
ejpam-6036	13	90	in	in	ADP
ejpam-6036	13	91	[	[	X
ejpam-6036	13	92	5	5	NUM
ejpam-6036	13	93	]	]	PUNCT
ejpam-6036	13	94	,	,	PUNCT
ejpam-6036	13	95	∗corresponding	∗corresponde	VERB
ejpam-6036	13	96	author	author	NOUN
ejpam-6036	13	97	.	.	PUNCT
ejpam-6036	14	1	doi	doi	NOUN
ejpam-6036	14	2	:	:	PUNCT
ejpam-6036	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6036	https://doi.org/10.29020/nybg.ejpam.v18i2.6036	NOUN
ejpam-6036	14	4	email	email	NOUN
ejpam-6036	14	5	addresses	address	VERB
ejpam-6036	14	6	:	:	PUNCT
ejpam-6036	14	7	butsakorn.k@msu.ac.th	butsakorn.k@msu.ac.th	ADP
ejpam-6036	14	8	(	(	PUNCT
ejpam-6036	14	9	b.	b.	PROPN
ejpam-6036	14	10	kong	kong	PROPN
ejpam-6036	14	11	-	-	PUNCT
ejpam-6036	14	12	ied	ied	PROPN
ejpam-6036	14	13	)	)	PUNCT
ejpam-6036	14	14	,	,	PUNCT
ejpam-6036	14	15	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-6036	14	16	(	(	PUNCT
ejpam-6036	14	17	s.	s.	PROPN
ejpam-6036	14	18	sompong	sompong	PROPN
ejpam-6036	14	19	)	)	PUNCT
ejpam-6036	14	20	,	,	PUNCT
ejpam-6036	15	1	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6036	15	2	(	(	PUNCT
ejpam-6036	15	3	c.	c.	PROPN
ejpam-6036	15	4	boonpok	boonpok	PROPN
ejpam-6036	15	5	)	)	PUNCT
ejpam-6036	15	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6036	15	7	1	1	NUM
ejpam-6036	15	8	copyright	copyright	NOUN
ejpam-6036	15	9	:	:	PUNCT
ejpam-6036	15	10	©	©	PROPN
ejpam-6036	15	11	2025	2025	NUM
ejpam-6036	15	12	the	the	DET
ejpam-6036	15	13	author(s	author(s	NOUN
ejpam-6036	15	14	)	)	PUNCT
ejpam-6036	15	15	.	.	PUNCT
ejpam-6036	16	1	(	(	PUNCT
ejpam-6036	16	2	cc	cc	NOUN
ejpam-6036	16	3	by	by	ADP
ejpam-6036	16	4	-	-	PUNCT
ejpam-6036	16	5	nc	nc	PROPN
ejpam-6036	16	6	4.0	4.0	NUM
ejpam-6036	16	7	)	)	PUNCT
ejpam-6036	16	8	b.	b.	PROPN
ejpam-6036	16	9	kong	kong	PROPN
ejpam-6036	16	10	-	-	PUNCT
ejpam-6036	16	11	ied	ied	PROPN
ejpam-6036	16	12	,	,	PUNCT
ejpam-6036	16	13	s.	s.	PROPN
ejpam-6036	16	14	sompong	sompong	PROPN
ejpam-6036	16	15	,	,	PUNCT
ejpam-6036	16	16	c.	c.	PROPN
ejpam-6036	16	17	boonpok	boonpok	PROPN
ejpam-6036	16	18	/	/	SYM
ejpam-6036	16	19	eur	eur	PROPN
ejpam-6036	16	20	.	.	PUNCT
ejpam-6036	17	1	j.	j.	PROPN
ejpam-6036	17	2	pure	pure	PROPN
ejpam-6036	17	3	appl	appl	PROPN
ejpam-6036	17	4	.	.	PROPN
ejpam-6036	17	5	math	math	PROPN
ejpam-6036	17	6	,	,	PUNCT
ejpam-6036	17	7	18	18	NUM
ejpam-6036	17	8	(	(	PUNCT
ejpam-6036	17	9	2	2	NUM
ejpam-6036	17	10	)	)	PUNCT
ejpam-6036	17	11	(	(	PUNCT
ejpam-6036	17	12	2025	2025	NUM
ejpam-6036	17	13	)	)	PUNCT
ejpam-6036	17	14	,	,	PUNCT
ejpam-6036	17	15	6036	6036	NUM
ejpam-6036	17	16	2	2	NUM
ejpam-6036	17	17	of	of	ADP
ejpam-6036	17	18	11	11	NUM
ejpam-6036	18	1	[	[	X
ejpam-6036	18	2	6	6	NUM
ejpam-6036	18	3	]	]	PUNCT
ejpam-6036	18	4	,	,	PUNCT
ejpam-6036	19	1	[	[	X
ejpam-6036	19	2	7	7	NUM
ejpam-6036	19	3	]	]	PUNCT
ejpam-6036	19	4	,	,	PUNCT
ejpam-6036	19	5	[	[	X
ejpam-6036	19	6	8	8	NUM
ejpam-6036	19	7	]	]	PUNCT
ejpam-6036	19	8	,	,	PUNCT
ejpam-6036	19	9	[	[	X
ejpam-6036	19	10	9	9	NUM
ejpam-6036	19	11	]	]	PUNCT
ejpam-6036	19	12	,	,	PUNCT
ejpam-6036	19	13	[	[	X
ejpam-6036	19	14	10	10	NUM
ejpam-6036	19	15	]	]	PUNCT
ejpam-6036	19	16	,	,	PUNCT
ejpam-6036	19	17	[	[	X
ejpam-6036	19	18	11	11	NUM
ejpam-6036	19	19	]	]	PUNCT
ejpam-6036	19	20	,	,	PUNCT
ejpam-6036	19	21	[	[	X
ejpam-6036	19	22	12	12	NUM
ejpam-6036	19	23	]	]	PUNCT
ejpam-6036	19	24	,	,	PUNCT
ejpam-6036	19	25	[	[	X
ejpam-6036	19	26	13	13	NUM
ejpam-6036	19	27	]	]	PUNCT
ejpam-6036	19	28	,	,	PUNCT
ejpam-6036	19	29	[	[	X
ejpam-6036	19	30	14	14	NUM
ejpam-6036	19	31	]	]	PUNCT
ejpam-6036	19	32	,	,	PUNCT
ejpam-6036	19	33	[	[	X
ejpam-6036	19	34	15	15	NUM
ejpam-6036	19	35	]	]	PUNCT
ejpam-6036	19	36	,	,	PUNCT
ejpam-6036	19	37	[	[	X
ejpam-6036	19	38	16	16	NUM
ejpam-6036	19	39	]	]	PUNCT
ejpam-6036	19	40	,	,	PUNCT
ejpam-6036	20	1	[	[	X
ejpam-6036	20	2	17	17	NUM
ejpam-6036	20	3	]	]	PUNCT
ejpam-6036	20	4	and	and	CCONJ
ejpam-6036	20	5	[	[	X
ejpam-6036	20	6	18	18	NUM
ejpam-6036	20	7	]	]	PUNCT
ejpam-6036	20	8	,	,	PUNCT
ejpam-6036	20	9	respectively	respectively	ADV
ejpam-6036	20	10	.	.	PUNCT
ejpam-6036	21	1	in	in	ADP
ejpam-6036	21	2	1996	1996	NUM
ejpam-6036	21	3	,	,	PUNCT
ejpam-6036	21	4	dontchev	dontchev	ADJ
ejpam-6036	21	5	[	[	X
ejpam-6036	21	6	19	19	NUM
ejpam-6036	21	7	]	]	PUNCT
ejpam-6036	21	8	introduced	introduce	VERB
ejpam-6036	21	9	the	the	DET
ejpam-6036	21	10	notion	notion	NOUN
ejpam-6036	21	11	of	of	ADP
ejpam-6036	21	12	contra	contra	ADJ
ejpam-6036	21	13	-	-	ADJ
ejpam-6036	21	14	continuous	continuous	ADJ
ejpam-6036	21	15	functions	function	NOUN
ejpam-6036	21	16	.	.	PUNCT
ejpam-6036	22	1	jafari	jafari	PROPN
ejpam-6036	22	2	and	and	CCONJ
ejpam-6036	22	3	noiri	noiri	ADV
ejpam-6036	23	1	[	[	X
ejpam-6036	23	2	20	20	NUM
ejpam-6036	23	3	]	]	PUNCT
ejpam-6036	23	4	introduced	introduce	VERB
ejpam-6036	23	5	and	and	CCONJ
ejpam-6036	23	6	investigated	investigate	VERB
ejpam-6036	23	7	the	the	DET
ejpam-6036	23	8	concept	concept	NOUN
ejpam-6036	23	9	of	of	ADP
ejpam-6036	23	10	contra	contra	ADJ
ejpam-6036	23	11	-	-	ADJ
ejpam-6036	23	12	precontinuous	precontinuous	ADJ
ejpam-6036	23	13	functions	function	NOUN
ejpam-6036	23	14	.	.	PUNCT
ejpam-6036	24	1	moreover	moreover	ADV
ejpam-6036	24	2	,	,	PUNCT
ejpam-6036	24	3	jafari	jafari	ADJ
ejpam-6036	24	4	and	and	CCONJ
ejpam-6036	24	5	noiri	noiri	ADV
ejpam-6036	25	1	[	[	X
ejpam-6036	25	2	21	21	NUM
ejpam-6036	25	3	]	]	PUNCT
ejpam-6036	25	4	introduced	introduce	VERB
ejpam-6036	25	5	and	and	CCONJ
ejpam-6036	25	6	studied	study	VERB
ejpam-6036	25	7	the	the	DET
ejpam-6036	25	8	notion	notion	NOUN
ejpam-6036	25	9	of	of	ADP
ejpam-6036	25	10	contra	contra	PROPN
ejpam-6036	25	11	-	-	ADJ
ejpam-6036	25	12	α	α	ADJ
ejpam-6036	25	13	-	-	ADJ
ejpam-6036	25	14	continuous	continuous	ADJ
ejpam-6036	25	15	functions	function	NOUN
ejpam-6036	25	16	.	.	PUNCT
ejpam-6036	26	1	in	in	ADP
ejpam-6036	26	2	1999	1999	NUM
ejpam-6036	26	3	,	,	PUNCT
ejpam-6036	26	4	dontchev	dontchev	NOUN
ejpam-6036	26	5	and	and	CCONJ
ejpam-6036	26	6	noiri	noiri	ADV
ejpam-6036	26	7	[	[	X
ejpam-6036	26	8	22	22	NUM
ejpam-6036	26	9	]	]	PUNCT
ejpam-6036	26	10	introduced	introduce	VERB
ejpam-6036	26	11	and	and	CCONJ
ejpam-6036	26	12	investigated	investigate	VERB
ejpam-6036	26	13	the	the	DET
ejpam-6036	26	14	concept	concept	NOUN
ejpam-6036	26	15	of	of	ADP
ejpam-6036	26	16	contra	contra	ADJ
ejpam-6036	26	17	-	-	ADJ
ejpam-6036	26	18	semicontinuous	semicontinuous	ADJ
ejpam-6036	26	19	functions	function	NOUN
ejpam-6036	26	20	.	.	PUNCT
ejpam-6036	27	1	caldas	caldas	PROPN
ejpam-6036	27	2	and	and	CCONJ
ejpam-6036	27	3	jafari	jafari	PROPN
ejpam-6036	27	4	[	[	X
ejpam-6036	27	5	23	23	NUM
ejpam-6036	27	6	]	]	PUNCT
ejpam-6036	27	7	studied	study	VERB
ejpam-6036	27	8	some	some	DET
ejpam-6036	27	9	properties	property	NOUN
ejpam-6036	27	10	of	of	ADP
ejpam-6036	27	11	contra	contra	PROPN
ejpam-6036	27	12	-	-	PUNCT
ejpam-6036	27	13	β	β	ADJ
ejpam-6036	27	14	-	-	ADJ
ejpam-6036	27	15	continuous	continuous	ADJ
ejpam-6036	27	16	functions	function	NOUN
ejpam-6036	27	17	.	.	PUNCT
ejpam-6036	28	1	in	in	ADP
ejpam-6036	28	2	2007	2007	NUM
ejpam-6036	28	3	,	,	PUNCT
ejpam-6036	28	4	baker	baker	PROPN
ejpam-6036	29	1	[	[	X
ejpam-6036	29	2	24	24	NUM
ejpam-6036	29	3	]	]	PUNCT
ejpam-6036	29	4	introduced	introduce	VERB
ejpam-6036	29	5	and	and	CCONJ
ejpam-6036	29	6	investigated	investigate	VERB
ejpam-6036	29	7	the	the	DET
ejpam-6036	29	8	notion	notion	NOUN
ejpam-6036	29	9	of	of	ADP
ejpam-6036	29	10	weakly	weakly	ADJ
ejpam-6036	29	11	contra	contra	ADJ
ejpam-6036	29	12	-	-	ADJ
ejpam-6036	29	13	continuous	continuous	ADJ
ejpam-6036	29	14	functions	function	NOUN
ejpam-6036	29	15	.	.	PUNCT
ejpam-6036	30	1	baker	baker	NOUN
ejpam-6036	31	1	[	[	X
ejpam-6036	31	2	25	25	NUM
ejpam-6036	31	3	]	]	PUNCT
ejpam-6036	31	4	introduced	introduce	VERB
ejpam-6036	31	5	and	and	CCONJ
ejpam-6036	31	6	studied	study	VERB
ejpam-6036	31	7	the	the	DET
ejpam-6036	31	8	concept	concept	NOUN
ejpam-6036	31	9	of	of	ADP
ejpam-6036	31	10	weakly	weakly	ADJ
ejpam-6036	31	11	contra	contra	PROPN
ejpam-6036	31	12	β	β	ADJ
ejpam-6036	31	13	-	-	ADJ
ejpam-6036	31	14	continuous	continuous	ADJ
ejpam-6036	31	15	functions	function	NOUN
ejpam-6036	31	16	.	.	PUNCT
ejpam-6036	32	1	noiri	noiri	PROPN
ejpam-6036	32	2	and	and	CCONJ
ejpam-6036	32	3	popa	popa	NOUN
ejpam-6036	33	1	[	[	X
ejpam-6036	33	2	26	26	NUM
ejpam-6036	33	3	]	]	PUNCT
ejpam-6036	33	4	introduced	introduce	VERB
ejpam-6036	33	5	the	the	DET
ejpam-6036	33	6	notion	notion	NOUN
ejpam-6036	33	7	of	of	ADP
ejpam-6036	33	8	contram	contram	NOUN
ejpam-6036	33	9	-	-	PUNCT
ejpam-6036	33	10	continuous	continuous	ADJ
ejpam-6036	33	11	functions	function	NOUN
ejpam-6036	33	12	as	as	ADP
ejpam-6036	33	13	functions	function	NOUN
ejpam-6036	33	14	from	from	ADP
ejpam-6036	33	15	a	a	DET
ejpam-6036	33	16	set	set	NOUN
ejpam-6036	33	17	satisfying	satisfy	VERB
ejpam-6036	33	18	some	some	DET
ejpam-6036	33	19	minimal	minimal	ADJ
ejpam-6036	33	20	conditions	condition	NOUN
ejpam-6036	33	21	into	into	ADP
ejpam-6036	33	22	a	a	DET
ejpam-6036	33	23	topological	topological	ADJ
ejpam-6036	33	24	space	space	NOUN
ejpam-6036	33	25	and	and	CCONJ
ejpam-6036	33	26	investigated	investigate	VERB
ejpam-6036	33	27	some	some	DET
ejpam-6036	33	28	characterizations	characterization	NOUN
ejpam-6036	33	29	and	and	CCONJ
ejpam-6036	33	30	the	the	DET
ejpam-6036	33	31	relationships	relationship	NOUN
ejpam-6036	33	32	between	between	ADP
ejpam-6036	33	33	contra	contra	PROPN
ejpam-6036	33	34	-	-	PROPN
ejpam-6036	33	35	m	m	NOUN
ejpam-6036	33	36	-	-	PUNCT
ejpam-6036	33	37	continuity	continuity	NOUN
ejpam-6036	33	38	and	and	CCONJ
ejpam-6036	33	39	other	other	ADJ
ejpam-6036	33	40	related	related	ADJ
ejpam-6036	33	41	generalized	generalized	ADJ
ejpam-6036	33	42	forms	form	NOUN
ejpam-6036	33	43	of	of	ADP
ejpam-6036	33	44	continuity	continuity	NOUN
ejpam-6036	33	45	.	.	PUNCT
ejpam-6036	34	1	in	in	ADP
ejpam-6036	34	2	2011	2011	NUM
ejpam-6036	34	3	,	,	PUNCT
ejpam-6036	34	4	noiri	noiri	ADV
ejpam-6036	34	5	and	and	CCONJ
ejpam-6036	34	6	popa	popa	NOUN
ejpam-6036	34	7	[	[	X
ejpam-6036	34	8	27	27	NUM
ejpam-6036	34	9	]	]	PUNCT
ejpam-6036	34	10	introduced	introduce	VERB
ejpam-6036	34	11	a	a	DET
ejpam-6036	34	12	new	new	ADJ
ejpam-6036	34	13	class	class	NOUN
ejpam-6036	34	14	of	of	ADP
ejpam-6036	34	15	functions	function	NOUN
ejpam-6036	34	16	called	call	VERB
ejpam-6036	34	17	weakly	weakly	ADJ
ejpam-6036	34	18	contra	contra	PROPN
ejpam-6036	34	19	-	-	ADJ
ejpam-6036	34	20	m	m	ADJ
ejpam-6036	34	21	-	-	ADJ
ejpam-6036	34	22	continuous	continuous	ADJ
ejpam-6036	34	23	functions	function	NOUN
ejpam-6036	34	24	as	as	ADP
ejpam-6036	34	25	functions	function	NOUN
ejpam-6036	34	26	from	from	ADP
ejpam-6036	34	27	a	a	DET
ejpam-6036	34	28	set	set	NOUN
ejpam-6036	34	29	satisfying	satisfy	VERB
ejpam-6036	34	30	some	some	DET
ejpam-6036	34	31	minimal	minimal	ADJ
ejpam-6036	34	32	conditions	condition	NOUN
ejpam-6036	34	33	into	into	ADP
ejpam-6036	34	34	a	a	DET
ejpam-6036	34	35	topological	topological	ADJ
ejpam-6036	34	36	space	space	NOUN
ejpam-6036	34	37	and	and	CCONJ
ejpam-6036	34	38	obtained	obtain	VERB
ejpam-6036	34	39	some	some	DET
ejpam-6036	34	40	characterizations	characterization	NOUN
ejpam-6036	34	41	and	and	CCONJ
ejpam-6036	34	42	several	several	ADJ
ejpam-6036	34	43	properties	property	NOUN
ejpam-6036	34	44	of	of	ADP
ejpam-6036	34	45	such	such	ADJ
ejpam-6036	34	46	functions	function	NOUN
ejpam-6036	34	47	.	.	PUNCT
ejpam-6036	35	1	it	it	PRON
ejpam-6036	35	2	turns	turn	VERB
ejpam-6036	35	3	out	out	ADP
ejpam-6036	35	4	that	that	SCONJ
ejpam-6036	35	5	the	the	DET
ejpam-6036	35	6	weak	weak	ADJ
ejpam-6036	35	7	contra	contra	PROPN
ejpam-6036	35	8	-	-	ADJ
ejpam-6036	35	9	m	m	NOUN
ejpam-6036	35	10	-	-	PUNCT
ejpam-6036	35	11	continuity	continuity	NOUN
ejpam-6036	35	12	is	be	AUX
ejpam-6036	35	13	a	a	DET
ejpam-6036	35	14	unified	unified	ADJ
ejpam-6036	35	15	form	form	NOUN
ejpam-6036	35	16	of	of	ADP
ejpam-6036	35	17	several	several	ADJ
ejpam-6036	35	18	modifications	modification	NOUN
ejpam-6036	35	19	of	of	ADP
ejpam-6036	35	20	weak	weak	ADJ
ejpam-6036	35	21	contracontinuity	contracontinuity	NOUN
ejpam-6036	35	22	due	due	ADP
ejpam-6036	35	23	to	to	ADP
ejpam-6036	35	24	baker	baker	PROPN
ejpam-6036	36	1	[	[	X
ejpam-6036	36	2	24	24	NUM
ejpam-6036	36	3	]	]	PUNCT
ejpam-6036	36	4	.	.	PUNCT
ejpam-6036	37	1	on	on	ADP
ejpam-6036	37	2	the	the	DET
ejpam-6036	37	3	other	other	ADJ
ejpam-6036	37	4	hand	hand	NOUN
ejpam-6036	37	5	,	,	PUNCT
ejpam-6036	37	6	the	the	DET
ejpam-6036	37	7	present	present	ADJ
ejpam-6036	37	8	authors	author	NOUN
ejpam-6036	37	9	introduced	introduce	VERB
ejpam-6036	37	10	and	and	CCONJ
ejpam-6036	37	11	studied	study	VERB
ejpam-6036	37	12	the	the	DET
ejpam-6036	37	13	concepts	concept	NOUN
ejpam-6036	37	14	of	of	ADP
ejpam-6036	37	15	(	(	PUNCT
ejpam-6036	37	16	τ1	τ1	PROPN
ejpam-6036	37	17	,	,	PUNCT
ejpam-6036	37	18	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	19	functions	function	NOUN
ejpam-6036	37	20	[	[	X
ejpam-6036	37	21	28	28	NUM
ejpam-6036	37	22	]	]	PUNCT
ejpam-6036	37	23	,	,	PUNCT
ejpam-6036	37	24	almost	almost	ADV
ejpam-6036	37	25	(	(	PUNCT
ejpam-6036	37	26	τ1	τ1	NOUN
ejpam-6036	37	27	,	,	PUNCT
ejpam-6036	37	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	29	functions	function	NOUN
ejpam-6036	37	30	[	[	X
ejpam-6036	37	31	29	29	NUM
ejpam-6036	37	32	]	]	PUNCT
ejpam-6036	37	33	,	,	PUNCT
ejpam-6036	37	34	weakly	weakly	ADJ
ejpam-6036	37	35	(	(	PUNCT
ejpam-6036	37	36	τ1	τ1	NOUN
ejpam-6036	37	37	,	,	PUNCT
ejpam-6036	37	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	39	functions	function	NOUN
ejpam-6036	37	40	[	[	X
ejpam-6036	37	41	30	30	NUM
ejpam-6036	37	42	]	]	PUNCT
ejpam-6036	37	43	,	,	PUNCT
ejpam-6036	37	44	quasi	quasi	NOUN
ejpam-6036	37	45	θ(τ1	θ(τ1	NOUN
ejpam-6036	37	46	,	,	PUNCT
ejpam-6036	37	47	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	48	functions	function	NOUN
ejpam-6036	37	49	[	[	X
ejpam-6036	37	50	31	31	NUM
ejpam-6036	37	51	]	]	PUNCT
ejpam-6036	37	52	,	,	PUNCT
ejpam-6036	37	53	almost	almost	ADV
ejpam-6036	37	54	quasi	quasi	NOUN
ejpam-6036	37	55	(	(	PUNCT
ejpam-6036	37	56	τ1	τ1	NOUN
ejpam-6036	37	57	,	,	PUNCT
ejpam-6036	37	58	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	59	functions	function	NOUN
ejpam-6036	37	60	[	[	X
ejpam-6036	37	61	32	32	NUM
ejpam-6036	37	62	]	]	PUNCT
ejpam-6036	37	63	,	,	PUNCT
ejpam-6036	37	64	weakly	weakly	ADJ
ejpam-6036	37	65	quasi	quasi	NOUN
ejpam-6036	37	66	(	(	PUNCT
ejpam-6036	37	67	τ1	τ1	PROPN
ejpam-6036	37	68	,	,	PUNCT
ejpam-6036	37	69	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	70	functions	function	NOUN
ejpam-6036	37	71	[	[	X
ejpam-6036	37	72	33	33	NUM
ejpam-6036	37	73	]	]	PUNCT
ejpam-6036	37	74	,	,	PUNCT
ejpam-6036	37	75	almost	almost	ADV
ejpam-6036	37	76	weakly	weakly	ADJ
ejpam-6036	37	77	(	(	PUNCT
ejpam-6036	37	78	τ1	τ1	NOUN
ejpam-6036	37	79	,	,	PUNCT
ejpam-6036	37	80	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	37	81	functions	function	NOUN
ejpam-6036	37	82	[	[	X
ejpam-6036	37	83	34	34	NUM
ejpam-6036	37	84	]	]	PUNCT
ejpam-6036	37	85	and	and	CCONJ
ejpam-6036	37	86	almost	almost	ADV
ejpam-6036	37	87	contra-(λ	contra-(λ	PROPN
ejpam-6036	37	88	,	,	PUNCT
ejpam-6036	37	89	sp)-continuous	sp)-continuous	ADJ
ejpam-6036	37	90	functions	function	NOUN
ejpam-6036	37	91	[	[	X
ejpam-6036	37	92	35	35	NUM
ejpam-6036	37	93	]	]	PUNCT
ejpam-6036	37	94	.	.	PUNCT
ejpam-6036	38	1	in	in	ADP
ejpam-6036	38	2	this	this	DET
ejpam-6036	38	3	paper	paper	NOUN
ejpam-6036	38	4	,	,	PUNCT
ejpam-6036	38	5	we	we	PRON
ejpam-6036	38	6	introduce	introduce	VERB
ejpam-6036	38	7	the	the	DET
ejpam-6036	38	8	concept	concept	NOUN
ejpam-6036	38	9	of	of	ADP
ejpam-6036	38	10	weakly	weakly	ADJ
ejpam-6036	38	11	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	38	12	,	,	PUNCT
ejpam-6036	38	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	38	14	functions	function	NOUN
ejpam-6036	38	15	.	.	PUNCT
ejpam-6036	39	1	we	we	PRON
ejpam-6036	39	2	also	also	ADV
ejpam-6036	39	3	investigate	investigate	VERB
ejpam-6036	39	4	some	some	DET
ejpam-6036	39	5	characterizations	characterization	NOUN
ejpam-6036	39	6	of	of	ADP
ejpam-6036	39	7	weakly	weakly	ADJ
ejpam-6036	39	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	39	9	,	,	PUNCT
ejpam-6036	39	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	39	11	functions	function	NOUN
ejpam-6036	39	12	.	.	PUNCT
ejpam-6036	40	1	2	2	X
ejpam-6036	40	2	.	.	NUM
ejpam-6036	40	3	preliminaries	preliminary	NOUN
ejpam-6036	40	4	throughout	throughout	ADP
ejpam-6036	40	5	the	the	DET
ejpam-6036	40	6	present	present	ADJ
ejpam-6036	40	7	paper	paper	NOUN
ejpam-6036	40	8	,	,	PUNCT
ejpam-6036	40	9	spaces	space	NOUN
ejpam-6036	40	10	(	(	PUNCT
ejpam-6036	40	11	x	x	NOUN
ejpam-6036	40	12	,	,	PUNCT
ejpam-6036	40	13	τ1	τ1	NOUN
ejpam-6036	40	14	,	,	PUNCT
ejpam-6036	40	15	τ2	τ2	NOUN
ejpam-6036	40	16	)	)	PUNCT
ejpam-6036	40	17	and	and	CCONJ
ejpam-6036	40	18	(	(	PUNCT
ejpam-6036	40	19	y	y	PROPN
ejpam-6036	40	20	,	,	PUNCT
ejpam-6036	40	21	σ1	σ1	PROPN
ejpam-6036	40	22	,	,	PUNCT
ejpam-6036	40	23	σ2	σ2	NOUN
ejpam-6036	40	24	)	)	PUNCT
ejpam-6036	40	25	(	(	PUNCT
ejpam-6036	40	26	or	or	CCONJ
ejpam-6036	40	27	simply	simply	ADV
ejpam-6036	40	28	x	x	X
ejpam-6036	40	29	and	and	CCONJ
ejpam-6036	40	30	y	y	PROPN
ejpam-6036	40	31	)	)	PUNCT
ejpam-6036	40	32	always	always	ADV
ejpam-6036	40	33	mean	mean	VERB
ejpam-6036	40	34	bitopological	bitopological	ADJ
ejpam-6036	40	35	spaces	space	NOUN
ejpam-6036	40	36	on	on	ADP
ejpam-6036	40	37	which	which	PRON
ejpam-6036	40	38	no	no	DET
ejpam-6036	40	39	separation	separation	NOUN
ejpam-6036	40	40	axioms	axiom	NOUN
ejpam-6036	40	41	are	be	AUX
ejpam-6036	40	42	assumed	assume	VERB
ejpam-6036	40	43	unless	unless	SCONJ
ejpam-6036	40	44	explicitly	explicitly	ADV
ejpam-6036	40	45	stated	state	VERB
ejpam-6036	40	46	.	.	PUNCT
ejpam-6036	41	1	let	let	VERB
ejpam-6036	41	2	a	a	DET
ejpam-6036	41	3	be	be	AUX
ejpam-6036	41	4	a	a	DET
ejpam-6036	41	5	subset	subset	NOUN
ejpam-6036	41	6	of	of	ADP
ejpam-6036	41	7	a	a	DET
ejpam-6036	41	8	bitopological	bitopological	ADJ
ejpam-6036	41	9	space	space	NOUN
ejpam-6036	41	10	(	(	PUNCT
ejpam-6036	41	11	x	x	NOUN
ejpam-6036	41	12	,	,	PUNCT
ejpam-6036	41	13	τ1	τ1	NOUN
ejpam-6036	41	14	,	,	PUNCT
ejpam-6036	41	15	τ2	τ2	NOUN
ejpam-6036	41	16	)	)	PUNCT
ejpam-6036	41	17	.	.	PUNCT
ejpam-6036	42	1	the	the	DET
ejpam-6036	42	2	closure	closure	NOUN
ejpam-6036	42	3	of	of	ADP
ejpam-6036	42	4	a	a	PRON
ejpam-6036	42	5	and	and	CCONJ
ejpam-6036	42	6	the	the	DET
ejpam-6036	42	7	interior	interior	NOUN
ejpam-6036	42	8	of	of	ADP
ejpam-6036	42	9	a	a	PRON
ejpam-6036	42	10	with	with	ADP
ejpam-6036	42	11	respect	respect	NOUN
ejpam-6036	42	12	to	to	ADP
ejpam-6036	42	13	τi	τi	PROPN
ejpam-6036	42	14	are	be	AUX
ejpam-6036	42	15	denoted	denote	VERB
ejpam-6036	42	16	by	by	ADP
ejpam-6036	42	17	τi	τi	NOUN
ejpam-6036	42	18	-	-	PUNCT
ejpam-6036	42	19	cl(a	cl(a	NUM
ejpam-6036	42	20	)	)	PUNCT
ejpam-6036	42	21	and	and	CCONJ
ejpam-6036	42	22	τi	τi	NOUN
ejpam-6036	42	23	-	-	PUNCT
ejpam-6036	42	24	int(a	int(a	NOUN
ejpam-6036	42	25	)	)	PUNCT
ejpam-6036	42	26	,	,	PUNCT
ejpam-6036	42	27	respectively	respectively	ADV
ejpam-6036	42	28	,	,	PUNCT
ejpam-6036	42	29	for	for	ADP
ejpam-6036	42	30	i	i	PROPN
ejpam-6036	42	31	=	=	SYM
ejpam-6036	42	32	1	1	NUM
ejpam-6036	42	33	,	,	PUNCT
ejpam-6036	42	34	2	2	NUM
ejpam-6036	42	35	.	.	X
ejpam-6036	42	36	a	a	DET
ejpam-6036	42	37	subset	subset	NOUN
ejpam-6036	42	38	a	a	PRON
ejpam-6036	42	39	of	of	ADP
ejpam-6036	42	40	a	a	DET
ejpam-6036	42	41	bitopological	bitopological	ADJ
ejpam-6036	42	42	space	space	NOUN
ejpam-6036	42	43	(	(	PUNCT
ejpam-6036	42	44	x	x	NOUN
ejpam-6036	42	45	,	,	PUNCT
ejpam-6036	42	46	τ1	τ1	NOUN
ejpam-6036	42	47	,	,	PUNCT
ejpam-6036	42	48	τ2	τ2	NOUN
ejpam-6036	42	49	)	)	PUNCT
ejpam-6036	42	50	is	be	AUX
ejpam-6036	42	51	called	call	VERB
ejpam-6036	42	52	τ1τ2	τ1τ2	VERB
ejpam-6036	42	53	-	-	ADJ
ejpam-6036	42	54	closed	closed	ADJ
ejpam-6036	42	55	[	[	X
ejpam-6036	42	56	36	36	NUM
ejpam-6036	42	57	]	]	X
ejpam-6036	42	58	if	if	SCONJ
ejpam-6036	42	59	a	a	DET
ejpam-6036	42	60	=	=	NOUN
ejpam-6036	42	61	τ1	τ1	NOUN
ejpam-6036	42	62	-	-	PUNCT
ejpam-6036	42	63	cl(τ2	cl(τ2	NOUN
ejpam-6036	42	64	-	-	PUNCT
ejpam-6036	42	65	cl(a	cl(a	NUM
ejpam-6036	42	66	)	)	PUNCT
ejpam-6036	42	67	)	)	PUNCT
ejpam-6036	42	68	.	.	PUNCT
ejpam-6036	43	1	the	the	DET
ejpam-6036	43	2	complement	complement	NOUN
ejpam-6036	43	3	of	of	ADP
ejpam-6036	43	4	a	a	DET
ejpam-6036	43	5	τ1τ2	τ1τ2	ADJ
ejpam-6036	43	6	-	-	ADJ
ejpam-6036	43	7	closed	closed	ADJ
ejpam-6036	43	8	set	set	NOUN
ejpam-6036	43	9	is	be	AUX
ejpam-6036	43	10	called	call	VERB
ejpam-6036	43	11	τ1τ2	τ1τ2	NOUN
ejpam-6036	43	12	-	-	ADJ
ejpam-6036	43	13	open	open	ADJ
ejpam-6036	43	14	.	.	PUNCT
ejpam-6036	44	1	the	the	DET
ejpam-6036	44	2	intersection	intersection	NOUN
ejpam-6036	44	3	of	of	ADP
ejpam-6036	44	4	all	all	DET
ejpam-6036	44	5	τ1τ2	τ1τ2	ADJ
ejpam-6036	44	6	-	-	ADJ
ejpam-6036	44	7	closed	closed	ADJ
ejpam-6036	44	8	sets	set	NOUN
ejpam-6036	44	9	of	of	ADP
ejpam-6036	44	10	x	x	PUNCT
ejpam-6036	44	11	containing	contain	VERB
ejpam-6036	44	12	a	a	PRON
ejpam-6036	44	13	is	be	AUX
ejpam-6036	44	14	called	call	VERB
ejpam-6036	44	15	the	the	DET
ejpam-6036	44	16	τ1τ2	τ1τ2	NOUN
ejpam-6036	44	17	-	-	NOUN
ejpam-6036	44	18	closure	closure	NOUN
ejpam-6036	44	19	[	[	X
ejpam-6036	44	20	36	36	NUM
ejpam-6036	44	21	]	]	PUNCT
ejpam-6036	44	22	of	of	ADP
ejpam-6036	44	23	a	a	PRON
ejpam-6036	44	24	and	and	CCONJ
ejpam-6036	44	25	is	be	AUX
ejpam-6036	44	26	denoted	denote	VERB
ejpam-6036	44	27	by	by	ADP
ejpam-6036	44	28	τ1τ2	τ1τ2	NOUN
ejpam-6036	44	29	-	-	NUM
ejpam-6036	44	30	cl(a	cl(a	NUM
ejpam-6036	44	31	)	)	PUNCT
ejpam-6036	44	32	.	.	PUNCT
ejpam-6036	45	1	the	the	DET
ejpam-6036	45	2	union	union	NOUN
ejpam-6036	45	3	of	of	ADP
ejpam-6036	45	4	all	all	DET
ejpam-6036	45	5	τ1τ2	τ1τ2	ADJ
ejpam-6036	45	6	-	-	ADJ
ejpam-6036	45	7	open	open	ADJ
ejpam-6036	45	8	sets	set	NOUN
ejpam-6036	45	9	of	of	ADP
ejpam-6036	45	10	x	x	PUNCT
ejpam-6036	45	11	contained	contain	VERB
ejpam-6036	45	12	in	in	ADP
ejpam-6036	45	13	a	a	PRON
ejpam-6036	45	14	is	be	AUX
ejpam-6036	45	15	called	call	VERB
ejpam-6036	45	16	the	the	DET
ejpam-6036	45	17	τ1τ2	τ1τ2	NOUN
ejpam-6036	45	18	-	-	ADJ
ejpam-6036	45	19	interior	interior	ADJ
ejpam-6036	45	20	[	[	X
ejpam-6036	45	21	36	36	NUM
ejpam-6036	45	22	]	]	PUNCT
ejpam-6036	45	23	of	of	ADP
ejpam-6036	45	24	a	a	PRON
ejpam-6036	45	25	and	and	CCONJ
ejpam-6036	45	26	is	be	AUX
ejpam-6036	45	27	denoted	denote	VERB
ejpam-6036	45	28	by	by	ADP
ejpam-6036	45	29	τ1τ2	τ1τ2	NOUN
ejpam-6036	45	30	-	-	ADJ
ejpam-6036	45	31	int(a	int(a	NOUN
ejpam-6036	45	32	)	)	PUNCT
ejpam-6036	45	33	.	.	PUNCT
ejpam-6036	46	1	lemma	lemma	PROPN
ejpam-6036	46	2	1	1	NUM
ejpam-6036	46	3	.	.	PUNCT
ejpam-6036	47	1	[	[	X
ejpam-6036	47	2	36	36	NUM
ejpam-6036	47	3	]	]	PUNCT
ejpam-6036	47	4	let	let	VERB
ejpam-6036	47	5	a	a	PRON
ejpam-6036	47	6	and	and	CCONJ
ejpam-6036	47	7	b	b	NOUN
ejpam-6036	47	8	be	be	AUX
ejpam-6036	47	9	subsets	subset	NOUN
ejpam-6036	47	10	of	of	ADP
ejpam-6036	47	11	a	a	DET
ejpam-6036	47	12	bitopological	bitopological	ADJ
ejpam-6036	47	13	space	space	NOUN
ejpam-6036	47	14	(	(	PUNCT
ejpam-6036	47	15	x	x	NOUN
ejpam-6036	47	16	,	,	PUNCT
ejpam-6036	47	17	τ1	τ1	NOUN
ejpam-6036	47	18	,	,	PUNCT
ejpam-6036	47	19	τ2	τ2	NOUN
ejpam-6036	47	20	)	)	PUNCT
ejpam-6036	47	21	.	.	PUNCT
ejpam-6036	48	1	for	for	ADP
ejpam-6036	48	2	the	the	DET
ejpam-6036	48	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-6036	48	4	,	,	PUNCT
ejpam-6036	48	5	the	the	DET
ejpam-6036	48	6	following	follow	VERB
ejpam-6036	48	7	properties	property	NOUN
ejpam-6036	48	8	hold	hold	VERB
ejpam-6036	48	9	:	:	PUNCT
ejpam-6036	48	10	(	(	PUNCT
ejpam-6036	48	11	1	1	X
ejpam-6036	48	12	)	)	PUNCT
ejpam-6036	48	13	a	a	DET
ejpam-6036	48	14	⊆	⊆	NUM
ejpam-6036	48	15	τ1τ2	τ1τ2	NOUN
ejpam-6036	48	16	-	-	NUM
ejpam-6036	48	17	cl(a	cl(a	NUM
ejpam-6036	48	18	)	)	PUNCT
ejpam-6036	48	19	and	and	CCONJ
ejpam-6036	48	20	τ1τ2	τ1τ2	NOUN
ejpam-6036	48	21	-	-	ADJ
ejpam-6036	48	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6036	48	23	-	-	PUNCT
ejpam-6036	48	24	cl(a	cl(a	NUM
ejpam-6036	48	25	)	)	PUNCT
ejpam-6036	48	26	)	)	PUNCT
ejpam-6036	49	1	=	=	PUNCT
ejpam-6036	49	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	49	3	-	-	NUM
ejpam-6036	49	4	cl(a	cl(a	NUM
ejpam-6036	49	5	)	)	PUNCT
ejpam-6036	49	6	.	.	PUNCT
ejpam-6036	50	1	(	(	PUNCT
ejpam-6036	50	2	2	2	X
ejpam-6036	50	3	)	)	PUNCT
ejpam-6036	50	4	if	if	SCONJ
ejpam-6036	50	5	a	a	DET
ejpam-6036	50	6	⊆	⊆	NUM
ejpam-6036	50	7	b	b	NOUN
ejpam-6036	50	8	,	,	PUNCT
ejpam-6036	50	9	then	then	ADV
ejpam-6036	50	10	τ1τ2	τ1τ2	NOUN
ejpam-6036	50	11	-	-	NUM
ejpam-6036	50	12	cl(a	cl(a	NUM
ejpam-6036	50	13	)	)	PUNCT
ejpam-6036	50	14	⊆	⊆	NUM
ejpam-6036	50	15	τ1τ2	τ1τ2	NOUN
ejpam-6036	50	16	-	-	NOUN
ejpam-6036	50	17	cl(b	cl(b	NOUN
ejpam-6036	50	18	)	)	PUNCT
ejpam-6036	50	19	.	.	PUNCT
ejpam-6036	51	1	(	(	PUNCT
ejpam-6036	51	2	3	3	X
ejpam-6036	51	3	)	)	PUNCT
ejpam-6036	51	4	τ1τ2	τ1τ2	NOUN
ejpam-6036	51	5	-	-	NUM
ejpam-6036	51	6	cl(a	cl(a	NUM
ejpam-6036	51	7	)	)	PUNCT
ejpam-6036	51	8	is	be	AUX
ejpam-6036	51	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	51	10	-	-	ADJ
ejpam-6036	51	11	closed	closed	ADJ
ejpam-6036	51	12	.	.	PUNCT
ejpam-6036	52	1	b.	b.	PROPN
ejpam-6036	52	2	kong	kong	PROPN
ejpam-6036	52	3	-	-	PUNCT
ejpam-6036	52	4	ied	ied	PROPN
ejpam-6036	52	5	,	,	PUNCT
ejpam-6036	52	6	s.	s.	PROPN
ejpam-6036	52	7	sompong	sompong	PROPN
ejpam-6036	52	8	,	,	PUNCT
ejpam-6036	52	9	c.	c.	PROPN
ejpam-6036	52	10	boonpok	boonpok	PROPN
ejpam-6036	52	11	/	/	SYM
ejpam-6036	52	12	eur	eur	PROPN
ejpam-6036	52	13	.	.	PUNCT
ejpam-6036	53	1	j.	j.	PROPN
ejpam-6036	53	2	pure	pure	PROPN
ejpam-6036	53	3	appl	appl	PROPN
ejpam-6036	53	4	.	.	PROPN
ejpam-6036	53	5	math	math	PROPN
ejpam-6036	53	6	,	,	PUNCT
ejpam-6036	53	7	18	18	NUM
ejpam-6036	53	8	(	(	PUNCT
ejpam-6036	53	9	2	2	NUM
ejpam-6036	53	10	)	)	PUNCT
ejpam-6036	53	11	(	(	PUNCT
ejpam-6036	53	12	2025	2025	NUM
ejpam-6036	53	13	)	)	PUNCT
ejpam-6036	53	14	,	,	PUNCT
ejpam-6036	53	15	6036	6036	NUM
ejpam-6036	53	16	3	3	NUM
ejpam-6036	53	17	of	of	ADP
ejpam-6036	53	18	11	11	NUM
ejpam-6036	53	19	(	(	PUNCT
ejpam-6036	53	20	4	4	NUM
ejpam-6036	53	21	)	)	PUNCT
ejpam-6036	53	22	a	a	PRON
ejpam-6036	53	23	is	be	AUX
ejpam-6036	53	24	τ1τ2	τ1τ2	NOUN
ejpam-6036	53	25	-	-	ADJ
ejpam-6036	53	26	closed	closed	ADJ
ejpam-6036	53	27	if	if	SCONJ
ejpam-6036	54	1	and	and	CCONJ
ejpam-6036	54	2	only	only	ADV
ejpam-6036	54	3	if	if	SCONJ
ejpam-6036	54	4	a	a	PRON
ejpam-6036	54	5	=	=	PUNCT
ejpam-6036	54	6	τ1τ2	τ1τ2	NOUN
ejpam-6036	54	7	-	-	NUM
ejpam-6036	54	8	cl(a	cl(a	NUM
ejpam-6036	54	9	)	)	PUNCT
ejpam-6036	54	10	.	.	PUNCT
ejpam-6036	55	1	(	(	PUNCT
ejpam-6036	55	2	5	5	X
ejpam-6036	55	3	)	)	PUNCT
ejpam-6036	55	4	τ1τ2	τ1τ2	NOUN
ejpam-6036	55	5	-	-	NOUN
ejpam-6036	55	6	cl(x	cl(x	X
ejpam-6036	55	7	−a	−a	NOUN
ejpam-6036	55	8	)	)	PUNCT
ejpam-6036	56	1	=	=	PUNCT
ejpam-6036	56	2	x	x	X
ejpam-6036	57	1	−	−	ADP
ejpam-6036	57	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	57	3	-	-	PUNCT
ejpam-6036	57	4	int(a	int(a	NOUN
ejpam-6036	57	5	)	)	PUNCT
ejpam-6036	57	6	.	.	PUNCT
ejpam-6036	58	1	a	a	DET
ejpam-6036	58	2	subseta	subseta	NOUN
ejpam-6036	58	3	of	of	ADP
ejpam-6036	58	4	a	a	DET
ejpam-6036	58	5	bitopological	bitopological	ADJ
ejpam-6036	58	6	space	space	NOUN
ejpam-6036	58	7	(	(	PUNCT
ejpam-6036	58	8	x	x	NOUN
ejpam-6036	58	9	,	,	PUNCT
ejpam-6036	58	10	τ1	τ1	NOUN
ejpam-6036	58	11	,	,	PUNCT
ejpam-6036	58	12	τ2	τ2	NOUN
ejpam-6036	58	13	)	)	PUNCT
ejpam-6036	58	14	is	be	AUX
ejpam-6036	58	15	called	call	VERB
ejpam-6036	58	16	(	(	PUNCT
ejpam-6036	58	17	τ1	τ1	NOUN
ejpam-6036	58	18	,	,	PUNCT
ejpam-6036	58	19	τ2)r	τ2)r	NOUN
ejpam-6036	58	20	-	-	PUNCT
ejpam-6036	58	21	open	open	NOUN
ejpam-6036	58	22	[	[	X
ejpam-6036	58	23	37	37	NUM
ejpam-6036	58	24	]	]	PUNCT
ejpam-6036	58	25	(	(	PUNCT
ejpam-6036	58	26	resp	resp	NOUN
ejpam-6036	58	27	.	.	PUNCT
ejpam-6036	59	1	(	(	PUNCT
ejpam-6036	59	2	τ1	τ1	NOUN
ejpam-6036	59	3	,	,	PUNCT
ejpam-6036	59	4	τ2)sopen	τ2)sopen	VERB
ejpam-6036	59	5	[	[	X
ejpam-6036	59	6	38	38	NUM
ejpam-6036	59	7	]	]	PUNCT
ejpam-6036	59	8	,	,	PUNCT
ejpam-6036	59	9	(	(	PUNCT
ejpam-6036	59	10	τ1	τ1	NOUN
ejpam-6036	59	11	,	,	PUNCT
ejpam-6036	59	12	τ2)p	τ2)p	NOUN
ejpam-6036	59	13	-	-	ADJ
ejpam-6036	59	14	open	open	ADJ
ejpam-6036	59	15	[	[	X
ejpam-6036	59	16	38	38	NUM
ejpam-6036	59	17	]	]	PUNCT
ejpam-6036	59	18	,	,	PUNCT
ejpam-6036	59	19	(	(	PUNCT
ejpam-6036	59	20	τ1	τ1	NOUN
ejpam-6036	59	21	,	,	PUNCT
ejpam-6036	59	22	τ2)β	τ2)β	ADJ
ejpam-6036	59	23	-	-	PUNCT
ejpam-6036	59	24	open	open	NOUN
ejpam-6036	60	1	[	[	X
ejpam-6036	60	2	38	38	NUM
ejpam-6036	60	3	]	]	SYM
ejpam-6036	60	4	)	)	PUNCT
ejpam-6036	60	5	if	if	SCONJ
ejpam-6036	60	6	a	a	DET
ejpam-6036	60	7	=	=	PUNCT
ejpam-6036	60	8	τ1τ2	τ1τ2	NOUN
ejpam-6036	60	9	-	-	NOUN
ejpam-6036	60	10	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6036	60	11	-	-	PUNCT
ejpam-6036	60	12	cl(a	cl(a	NUM
ejpam-6036	60	13	)	)	PUNCT
ejpam-6036	60	14	)	)	PUNCT
ejpam-6036	60	15	(	(	PUNCT
ejpam-6036	60	16	resp	resp	NOUN
ejpam-6036	60	17	.	.	PUNCT
ejpam-6036	61	1	a	a	DET
ejpam-6036	61	2	⊆	⊆	NUM
ejpam-6036	61	3	τ1τ2	τ1τ2	NOUN
ejpam-6036	61	4	-	-	ADJ
ejpam-6036	61	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6036	61	6	-	-	PUNCT
ejpam-6036	61	7	int(a	int(a	NOUN
ejpam-6036	61	8	)	)	PUNCT
ejpam-6036	61	9	)	)	PUNCT
ejpam-6036	61	10	,	,	PUNCT
ejpam-6036	61	11	a	a	DET
ejpam-6036	61	12	⊆	⊆	NUM
ejpam-6036	61	13	τ1τ2	τ1τ2	NOUN
ejpam-6036	61	14	-	-	NOUN
ejpam-6036	61	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6036	61	16	-	-	PUNCT
ejpam-6036	61	17	cl(a	cl(a	NUM
ejpam-6036	61	18	)	)	PUNCT
ejpam-6036	61	19	)	)	PUNCT
ejpam-6036	61	20	,	,	PUNCT
ejpam-6036	61	21	a	a	DET
ejpam-6036	61	22	⊆	⊆	NUM
ejpam-6036	61	23	τ1τ2	τ1τ2	NOUN
ejpam-6036	61	24	-	-	PUNCT
ejpam-6036	61	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6036	61	26	-	-	PUNCT
ejpam-6036	61	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6036	61	28	-	-	PUNCT
ejpam-6036	61	29	cl(a	cl(a	NUM
ejpam-6036	61	30	)	)	PUNCT
ejpam-6036	61	31	)	)	PUNCT
ejpam-6036	61	32	)	)	PUNCT
ejpam-6036	61	33	)	)	PUNCT
ejpam-6036	61	34	.	.	PUNCT
ejpam-6036	62	1	the	the	DET
ejpam-6036	62	2	complement	complement	NOUN
ejpam-6036	62	3	of	of	ADP
ejpam-6036	62	4	a	a	DET
ejpam-6036	62	5	(	(	PUNCT
ejpam-6036	62	6	τ1	τ1	NOUN
ejpam-6036	62	7	,	,	PUNCT
ejpam-6036	62	8	τ2)r	τ2)r	NOUN
ejpam-6036	62	9	-	-	PUNCT
ejpam-6036	62	10	open	open	ADJ
ejpam-6036	62	11	(	(	PUNCT
ejpam-6036	62	12	resp	resp	NOUN
ejpam-6036	62	13	.	.	PUNCT
ejpam-6036	63	1	(	(	PUNCT
ejpam-6036	63	2	τ1	τ1	NOUN
ejpam-6036	63	3	,	,	PUNCT
ejpam-6036	63	4	τ2)s	τ2)s	NOUN
ejpam-6036	63	5	-	-	PUNCT
ejpam-6036	63	6	open	open	ADJ
ejpam-6036	63	7	,	,	PUNCT
ejpam-6036	63	8	(	(	PUNCT
ejpam-6036	63	9	τ1	τ1	NOUN
ejpam-6036	63	10	,	,	PUNCT
ejpam-6036	63	11	τ2)p	τ2)p	NOUN
ejpam-6036	63	12	-	-	ADJ
ejpam-6036	63	13	open	open	ADJ
ejpam-6036	63	14	,	,	PUNCT
ejpam-6036	63	15	(	(	PUNCT
ejpam-6036	63	16	τ1	τ1	NOUN
ejpam-6036	63	17	,	,	PUNCT
ejpam-6036	63	18	τ2)β	τ2)β	ADJ
ejpam-6036	63	19	-	-	PUNCT
ejpam-6036	63	20	open	open	ADJ
ejpam-6036	63	21	)	)	PUNCT
ejpam-6036	63	22	set	set	NOUN
ejpam-6036	63	23	is	be	AUX
ejpam-6036	63	24	said	say	VERB
ejpam-6036	63	25	to	to	PART
ejpam-6036	63	26	be	be	AUX
ejpam-6036	63	27	(	(	PUNCT
ejpam-6036	63	28	τ1	τ1	NOUN
ejpam-6036	63	29	,	,	PUNCT
ejpam-6036	63	30	τ2)r	τ2)r	NOUN
ejpam-6036	63	31	-	-	PUNCT
ejpam-6036	63	32	closed	closed	ADJ
ejpam-6036	63	33	(	(	PUNCT
ejpam-6036	63	34	resp	resp	NOUN
ejpam-6036	63	35	.	.	PUNCT
ejpam-6036	64	1	(	(	PUNCT
ejpam-6036	64	2	τ1	τ1	NOUN
ejpam-6036	64	3	,	,	PUNCT
ejpam-6036	64	4	τ2)s	τ2)s	NOUN
ejpam-6036	64	5	-	-	PUNCT
ejpam-6036	64	6	closed	closed	ADJ
ejpam-6036	64	7	,	,	PUNCT
ejpam-6036	64	8	(	(	PUNCT
ejpam-6036	64	9	τ1	τ1	NOUN
ejpam-6036	64	10	,	,	PUNCT
ejpam-6036	64	11	τ2)p	τ2)p	NOUN
ejpam-6036	64	12	-	-	PUNCT
ejpam-6036	64	13	closed	closed	ADJ
ejpam-6036	64	14	,	,	PUNCT
ejpam-6036	64	15	(	(	PUNCT
ejpam-6036	64	16	τ1	τ1	NOUN
ejpam-6036	64	17	,	,	PUNCT
ejpam-6036	64	18	τ2)β	τ2)β	ADJ
ejpam-6036	64	19	-	-	PUNCT
ejpam-6036	64	20	closed	closed	ADJ
ejpam-6036	64	21	)	)	PUNCT
ejpam-6036	64	22	.	.	PUNCT
ejpam-6036	65	1	a	a	DET
ejpam-6036	65	2	subset	subset	NOUN
ejpam-6036	65	3	a	a	PRON
ejpam-6036	65	4	of	of	ADP
ejpam-6036	65	5	a	a	DET
ejpam-6036	65	6	bitopological	bitopological	ADJ
ejpam-6036	65	7	space	space	NOUN
ejpam-6036	65	8	(	(	PUNCT
ejpam-6036	65	9	x	x	NOUN
ejpam-6036	65	10	,	,	PUNCT
ejpam-6036	65	11	τ1	τ1	NOUN
ejpam-6036	65	12	,	,	PUNCT
ejpam-6036	65	13	τ2	τ2	NOUN
ejpam-6036	65	14	)	)	PUNCT
ejpam-6036	65	15	is	be	AUX
ejpam-6036	65	16	said	say	VERB
ejpam-6036	65	17	to	to	PART
ejpam-6036	65	18	be	be	AUX
ejpam-6036	65	19	α(τ1	α(τ1	NOUN
ejpam-6036	65	20	,	,	PUNCT
ejpam-6036	65	21	τ2)-open	τ2)-open	ADJ
ejpam-6036	65	22	[	[	X
ejpam-6036	65	23	39	39	NUM
ejpam-6036	65	24	]	]	PUNCT
ejpam-6036	65	25	if	if	SCONJ
ejpam-6036	65	26	a	a	DET
ejpam-6036	65	27	⊆	⊆	NUM
ejpam-6036	65	28	τ1τ2	τ1τ2	NOUN
ejpam-6036	65	29	-	-	PUNCT
ejpam-6036	65	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6036	65	31	-	-	PUNCT
ejpam-6036	65	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6036	65	33	-	-	PUNCT
ejpam-6036	65	34	int(a	int(a	NOUN
ejpam-6036	65	35	)	)	PUNCT
ejpam-6036	65	36	)	)	PUNCT
ejpam-6036	65	37	)	)	PUNCT
ejpam-6036	65	38	.	.	PUNCT
ejpam-6036	66	1	the	the	DET
ejpam-6036	66	2	complement	complement	NOUN
ejpam-6036	66	3	of	of	ADP
ejpam-6036	66	4	an	an	DET
ejpam-6036	66	5	α(τ1	α(τ1	NOUN
ejpam-6036	66	6	,	,	PUNCT
ejpam-6036	66	7	τ2)-open	τ2)-open	ADJ
ejpam-6036	66	8	set	set	NOUN
ejpam-6036	66	9	is	be	AUX
ejpam-6036	66	10	said	say	VERB
ejpam-6036	66	11	to	to	PART
ejpam-6036	66	12	be	be	AUX
ejpam-6036	66	13	α(τ1	α(τ1	NOUN
ejpam-6036	66	14	,	,	PUNCT
ejpam-6036	66	15	τ2)-closed	τ2)-close	VERB
ejpam-6036	66	16	.	.	PUNCT
ejpam-6036	67	1	let	let	VERB
ejpam-6036	67	2	a	a	DET
ejpam-6036	67	3	be	be	AUX
ejpam-6036	67	4	a	a	DET
ejpam-6036	67	5	subset	subset	NOUN
ejpam-6036	67	6	of	of	ADP
ejpam-6036	67	7	a	a	DET
ejpam-6036	67	8	bitopological	bitopological	ADJ
ejpam-6036	67	9	space	space	NOUN
ejpam-6036	67	10	(	(	PUNCT
ejpam-6036	67	11	x	x	NOUN
ejpam-6036	67	12	,	,	PUNCT
ejpam-6036	67	13	τ1	τ1	NOUN
ejpam-6036	67	14	,	,	PUNCT
ejpam-6036	67	15	τ2	τ2	NOUN
ejpam-6036	67	16	)	)	PUNCT
ejpam-6036	67	17	.	.	PUNCT
ejpam-6036	68	1	the	the	DET
ejpam-6036	68	2	set	set	NOUN
ejpam-6036	68	3	∩{g	∩{g	INTJ
ejpam-6036	68	4	|	|	ADV
ejpam-6036	68	5	a	a	DET
ejpam-6036	68	6	⊆	⊆	NUM
ejpam-6036	68	7	g	g	NOUN
ejpam-6036	68	8	and	and	CCONJ
ejpam-6036	68	9	g	g	PROPN
ejpam-6036	68	10	is	be	AUX
ejpam-6036	68	11	τ1τ2	τ1τ2	VERB
ejpam-6036	68	12	-	-	ADJ
ejpam-6036	68	13	open	open	ADJ
ejpam-6036	68	14	}	}	PUNCT
ejpam-6036	68	15	is	be	AUX
ejpam-6036	68	16	called	call	VERB
ejpam-6036	68	17	the	the	DET
ejpam-6036	68	18	τ1τ2	τ1τ2	NOUN
ejpam-6036	68	19	-	-	NOUN
ejpam-6036	68	20	kernel	kernel	NOUN
ejpam-6036	69	1	[	[	X
ejpam-6036	69	2	36	36	NUM
ejpam-6036	69	3	]	]	PUNCT
ejpam-6036	69	4	of	of	ADP
ejpam-6036	69	5	a	a	PRON
ejpam-6036	69	6	and	and	CCONJ
ejpam-6036	69	7	is	be	AUX
ejpam-6036	69	8	denoted	denote	VERB
ejpam-6036	69	9	by	by	ADP
ejpam-6036	69	10	τ1τ2	τ1τ2	NOUN
ejpam-6036	69	11	-	-	ADJ
ejpam-6036	69	12	ker(a	ker(a	ADJ
ejpam-6036	69	13	)	)	PUNCT
ejpam-6036	69	14	.	.	PUNCT
ejpam-6036	70	1	lemma	lemma	PROPN
ejpam-6036	70	2	2	2	NUM
ejpam-6036	70	3	.	.	PUNCT
ejpam-6036	71	1	[	[	X
ejpam-6036	71	2	36	36	NUM
ejpam-6036	71	3	]	]	PUNCT
ejpam-6036	71	4	for	for	ADP
ejpam-6036	71	5	subsets	subset	NOUN
ejpam-6036	71	6	a	a	DET
ejpam-6036	71	7	,	,	PUNCT
ejpam-6036	71	8	b	b	NOUN
ejpam-6036	71	9	of	of	ADP
ejpam-6036	71	10	a	a	DET
ejpam-6036	71	11	bitopological	bitopological	ADJ
ejpam-6036	71	12	space	space	NOUN
ejpam-6036	71	13	(	(	PUNCT
ejpam-6036	71	14	x	x	NOUN
ejpam-6036	71	15	,	,	PUNCT
ejpam-6036	71	16	τ1	τ1	NOUN
ejpam-6036	71	17	,	,	PUNCT
ejpam-6036	71	18	τ2	τ2	NOUN
ejpam-6036	71	19	)	)	PUNCT
ejpam-6036	71	20	,	,	PUNCT
ejpam-6036	71	21	the	the	DET
ejpam-6036	71	22	following	follow	VERB
ejpam-6036	71	23	properties	property	NOUN
ejpam-6036	71	24	hold	hold	VERB
ejpam-6036	71	25	:	:	PUNCT
ejpam-6036	71	26	(	(	PUNCT
ejpam-6036	71	27	1	1	X
ejpam-6036	71	28	)	)	PUNCT
ejpam-6036	71	29	a	a	DET
ejpam-6036	71	30	⊆	⊆	NUM
ejpam-6036	71	31	τ1τ2	τ1τ2	NOUN
ejpam-6036	71	32	-	-	ADJ
ejpam-6036	71	33	ker(a	ker(a	ADJ
ejpam-6036	71	34	)	)	PUNCT
ejpam-6036	71	35	.	.	PUNCT
ejpam-6036	72	1	(	(	PUNCT
ejpam-6036	72	2	2	2	X
ejpam-6036	72	3	)	)	PUNCT
ejpam-6036	72	4	if	if	SCONJ
ejpam-6036	72	5	a	a	DET
ejpam-6036	72	6	⊆	⊆	NUM
ejpam-6036	72	7	b	b	NOUN
ejpam-6036	72	8	,	,	PUNCT
ejpam-6036	72	9	then	then	ADV
ejpam-6036	72	10	τ1τ2	τ1τ2	NOUN
ejpam-6036	72	11	-	-	ADJ
ejpam-6036	72	12	ker(a	ker(a	ADJ
ejpam-6036	72	13	)	)	PUNCT
ejpam-6036	72	14	⊆	⊆	NUM
ejpam-6036	72	15	τ1τ2	τ1τ2	PROPN
ejpam-6036	72	16	-	-	ADJ
ejpam-6036	72	17	ker(b	ker(b	PROPN
ejpam-6036	72	18	)	)	PUNCT
ejpam-6036	72	19	.	.	PUNCT
ejpam-6036	73	1	(	(	PUNCT
ejpam-6036	73	2	3	3	X
ejpam-6036	73	3	)	)	PUNCT
ejpam-6036	73	4	if	if	SCONJ
ejpam-6036	73	5	a	a	PRON
ejpam-6036	73	6	is	be	AUX
ejpam-6036	73	7	τ1τ2	τ1τ2	NOUN
ejpam-6036	73	8	-	-	ADJ
ejpam-6036	73	9	open	open	ADJ
ejpam-6036	73	10	,	,	PUNCT
ejpam-6036	73	11	then	then	ADV
ejpam-6036	73	12	τ1τ2	τ1τ2	NOUN
ejpam-6036	73	13	-	-	ADJ
ejpam-6036	73	14	ker(a	ker(a	ADJ
ejpam-6036	73	15	)	)	PUNCT
ejpam-6036	73	16	=	=	SYM
ejpam-6036	73	17	a.	a.	NOUN
ejpam-6036	73	18	(	(	PUNCT
ejpam-6036	73	19	4	4	NUM
ejpam-6036	73	20	)	)	PUNCT
ejpam-6036	73	21	x	x	SYM
ejpam-6036	73	22	∈	∈	PROPN
ejpam-6036	73	23	τ1τ2	τ1τ2	NOUN
ejpam-6036	73	24	-	-	ADJ
ejpam-6036	73	25	ker(a	ker(a	ADJ
ejpam-6036	73	26	)	)	PUNCT
ejpam-6036	73	27	if	if	SCONJ
ejpam-6036	73	28	and	and	CCONJ
ejpam-6036	73	29	only	only	ADV
ejpam-6036	73	30	if	if	SCONJ
ejpam-6036	73	31	a	a	DET
ejpam-6036	73	32	∩h	∩h	ADJ
ejpam-6036	73	33	̸=	̸=	PROPN
ejpam-6036	73	34	∅	∅	NOUN
ejpam-6036	73	35	for	for	ADP
ejpam-6036	73	36	every	every	DET
ejpam-6036	73	37	τ1τ2	τ1τ2	ADJ
ejpam-6036	73	38	-	-	ADJ
ejpam-6036	73	39	closed	closed	ADJ
ejpam-6036	73	40	set	set	ADJ
ejpam-6036	73	41	h	h	NOUN
ejpam-6036	73	42	containing	contain	VERB
ejpam-6036	73	43	x.	x.	NOUN
ejpam-6036	73	44	let	let	VERB
ejpam-6036	73	45	a	a	PRON
ejpam-6036	73	46	be	be	AUX
ejpam-6036	73	47	a	a	DET
ejpam-6036	73	48	subset	subset	NOUN
ejpam-6036	73	49	of	of	ADP
ejpam-6036	73	50	a	a	DET
ejpam-6036	73	51	bitopological	bitopological	ADJ
ejpam-6036	73	52	space	space	NOUN
ejpam-6036	73	53	(	(	PUNCT
ejpam-6036	73	54	x	x	NOUN
ejpam-6036	73	55	,	,	PUNCT
ejpam-6036	73	56	τ1	τ1	NOUN
ejpam-6036	73	57	,	,	PUNCT
ejpam-6036	73	58	τ2	τ2	NOUN
ejpam-6036	73	59	)	)	PUNCT
ejpam-6036	73	60	.	.	PUNCT
ejpam-6036	74	1	the	the	DET
ejpam-6036	74	2	intersection	intersection	NOUN
ejpam-6036	74	3	of	of	ADP
ejpam-6036	74	4	all	all	DET
ejpam-6036	74	5	(	(	PUNCT
ejpam-6036	74	6	τ1	τ1	NOUN
ejpam-6036	74	7	,	,	PUNCT
ejpam-6036	74	8	τ2)pclosed	τ2)pclose	VERB
ejpam-6036	74	9	sets	set	NOUN
ejpam-6036	74	10	of	of	ADP
ejpam-6036	74	11	x	x	PUNCT
ejpam-6036	74	12	containing	contain	VERB
ejpam-6036	74	13	a	a	PRON
ejpam-6036	74	14	is	be	AUX
ejpam-6036	74	15	called	call	VERB
ejpam-6036	74	16	the	the	DET
ejpam-6036	74	17	(	(	PUNCT
ejpam-6036	74	18	τ1	τ1	NOUN
ejpam-6036	74	19	,	,	PUNCT
ejpam-6036	74	20	τ2)p	τ2)p	NOUN
ejpam-6036	74	21	-	-	NOUN
ejpam-6036	74	22	closure	closure	NOUN
ejpam-6036	74	23	[	[	X
ejpam-6036	74	24	40	40	NUM
ejpam-6036	74	25	]	]	PUNCT
ejpam-6036	74	26	of	of	ADP
ejpam-6036	74	27	a	a	PRON
ejpam-6036	74	28	and	and	CCONJ
ejpam-6036	74	29	is	be	AUX
ejpam-6036	74	30	denoted	denote	VERB
ejpam-6036	74	31	by	by	ADP
ejpam-6036	74	32	(	(	PUNCT
ejpam-6036	74	33	τ1	τ1	PROPN
ejpam-6036	74	34	,	,	PUNCT
ejpam-6036	74	35	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6036	74	36	)	)	PUNCT
ejpam-6036	74	37	.	.	PUNCT
ejpam-6036	75	1	the	the	DET
ejpam-6036	75	2	union	union	NOUN
ejpam-6036	75	3	of	of	ADP
ejpam-6036	75	4	all	all	DET
ejpam-6036	75	5	(	(	PUNCT
ejpam-6036	75	6	τ1	τ1	NOUN
ejpam-6036	75	7	,	,	PUNCT
ejpam-6036	75	8	τ2)p	τ2)p	ADJ
ejpam-6036	75	9	-	-	PUNCT
ejpam-6036	75	10	open	open	ADJ
ejpam-6036	75	11	sets	set	NOUN
ejpam-6036	75	12	of	of	ADP
ejpam-6036	75	13	x	x	PUNCT
ejpam-6036	75	14	contained	contain	VERB
ejpam-6036	75	15	in	in	ADP
ejpam-6036	75	16	a	a	PRON
ejpam-6036	75	17	is	be	AUX
ejpam-6036	75	18	called	call	VERB
ejpam-6036	75	19	the	the	DET
ejpam-6036	75	20	(	(	PUNCT
ejpam-6036	75	21	τ1	τ1	NOUN
ejpam-6036	75	22	,	,	PUNCT
ejpam-6036	75	23	τ2)p	τ2)p	ADJ
ejpam-6036	75	24	-	-	NOUN
ejpam-6036	75	25	interior	interior	ADJ
ejpam-6036	75	26	[	[	X
ejpam-6036	75	27	40	40	NUM
ejpam-6036	75	28	]	]	PUNCT
ejpam-6036	75	29	of	of	ADP
ejpam-6036	75	30	a	a	PRON
ejpam-6036	75	31	and	and	CCONJ
ejpam-6036	75	32	is	be	AUX
ejpam-6036	75	33	denoted	denote	VERB
ejpam-6036	75	34	by	by	ADP
ejpam-6036	75	35	(	(	PUNCT
ejpam-6036	75	36	τ1	τ1	NOUN
ejpam-6036	75	37	,	,	PUNCT
ejpam-6036	75	38	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6036	75	39	)	)	PUNCT
ejpam-6036	75	40	.	.	PUNCT
ejpam-6036	76	1	lemma	lemma	PROPN
ejpam-6036	76	2	3	3	X
ejpam-6036	76	3	.	.	X
ejpam-6036	77	1	for	for	ADP
ejpam-6036	77	2	a	a	DET
ejpam-6036	77	3	subset	subset	NOUN
ejpam-6036	77	4	a	a	PRON
ejpam-6036	77	5	of	of	ADP
ejpam-6036	77	6	a	a	DET
ejpam-6036	77	7	bitopological	bitopological	ADJ
ejpam-6036	77	8	space	space	NOUN
ejpam-6036	77	9	(	(	PUNCT
ejpam-6036	77	10	x	x	NOUN
ejpam-6036	77	11	,	,	PUNCT
ejpam-6036	77	12	τ1	τ1	NOUN
ejpam-6036	77	13	,	,	PUNCT
ejpam-6036	77	14	τ2	τ2	NOUN
ejpam-6036	77	15	)	)	PUNCT
ejpam-6036	77	16	,	,	PUNCT
ejpam-6036	77	17	the	the	DET
ejpam-6036	77	18	following	follow	VERB
ejpam-6036	77	19	properties	property	NOUN
ejpam-6036	77	20	hold	hold	VERB
ejpam-6036	77	21	:	:	PUNCT
ejpam-6036	77	22	(	(	PUNCT
ejpam-6036	77	23	1	1	X
ejpam-6036	77	24	)	)	PUNCT
ejpam-6036	77	25	(	(	PUNCT
ejpam-6036	77	26	τ1	τ1	NOUN
ejpam-6036	77	27	,	,	PUNCT
ejpam-6036	77	28	τ2)-pcl(a	τ2)-pcl(a	ADJ
ejpam-6036	77	29	)	)	PUNCT
ejpam-6036	77	30	=	=	PUNCT
ejpam-6036	78	1	τ1τ2	τ1τ2	NOUN
ejpam-6036	78	2	-	-	ADJ
ejpam-6036	78	3	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6036	78	4	-	-	PUNCT
ejpam-6036	78	5	int(a	int(a	NOUN
ejpam-6036	78	6	)	)	PUNCT
ejpam-6036	78	7	)	)	PUNCT
ejpam-6036	78	8	∪a	∪a	X
ejpam-6036	79	1	[	[	X
ejpam-6036	79	2	40	40	NUM
ejpam-6036	79	3	]	]	PUNCT
ejpam-6036	79	4	;	;	PUNCT
ejpam-6036	79	5	(	(	PUNCT
ejpam-6036	79	6	2	2	X
ejpam-6036	79	7	)	)	PUNCT
ejpam-6036	79	8	(	(	PUNCT
ejpam-6036	79	9	τ1	τ1	NOUN
ejpam-6036	79	10	,	,	PUNCT
ejpam-6036	79	11	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6036	79	12	)	)	PUNCT
ejpam-6036	79	13	=	=	PUNCT
ejpam-6036	80	1	τ1τ2	τ1τ2	NOUN
ejpam-6036	80	2	-	-	NOUN
ejpam-6036	80	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6036	80	4	-	-	PUNCT
ejpam-6036	80	5	cl(a	cl(a	NUM
ejpam-6036	80	6	)	)	PUNCT
ejpam-6036	80	7	)	)	PUNCT
ejpam-6036	81	1	∩a	∩a	PROPN
ejpam-6036	82	1	[	[	X
ejpam-6036	82	2	34	34	NUM
ejpam-6036	82	3	]	]	PUNCT
ejpam-6036	82	4	.	.	PUNCT
ejpam-6036	83	1	3	3	X
ejpam-6036	83	2	.	.	X
ejpam-6036	83	3	characterizations	characterization	NOUN
ejpam-6036	83	4	of	of	ADP
ejpam-6036	83	5	weakly	weakly	ADJ
ejpam-6036	83	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	83	7	,	,	PUNCT
ejpam-6036	83	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	83	9	functions	function	NOUN
ejpam-6036	83	10	in	in	ADP
ejpam-6036	83	11	this	this	DET
ejpam-6036	83	12	section	section	NOUN
ejpam-6036	83	13	,	,	PUNCT
ejpam-6036	83	14	we	we	PRON
ejpam-6036	83	15	introduce	introduce	VERB
ejpam-6036	83	16	the	the	DET
ejpam-6036	83	17	concept	concept	NOUN
ejpam-6036	83	18	of	of	ADP
ejpam-6036	83	19	weakly	weakly	ADJ
ejpam-6036	83	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	83	21	,	,	PUNCT
ejpam-6036	83	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	83	23	functions	function	NOUN
ejpam-6036	83	24	.	.	PUNCT
ejpam-6036	84	1	furthermore	furthermore	ADV
ejpam-6036	84	2	,	,	PUNCT
ejpam-6036	84	3	several	several	ADJ
ejpam-6036	84	4	characterizations	characterization	NOUN
ejpam-6036	84	5	of	of	ADP
ejpam-6036	84	6	weakly	weakly	ADJ
ejpam-6036	84	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	84	8	,	,	PUNCT
ejpam-6036	84	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	84	10	functions	function	NOUN
ejpam-6036	84	11	are	be	AUX
ejpam-6036	84	12	discussed	discuss	VERB
ejpam-6036	84	13	.	.	PUNCT
ejpam-6036	85	1	definition	definition	NOUN
ejpam-6036	85	2	1	1	NUM
ejpam-6036	85	3	.	.	PUNCT
ejpam-6036	86	1	a	a	DET
ejpam-6036	86	2	function	function	NOUN
ejpam-6036	86	3	f	f	NOUN
ejpam-6036	86	4	:	:	PUNCT
ejpam-6036	86	5	(	(	PUNCT
ejpam-6036	86	6	x	x	NOUN
ejpam-6036	86	7	,	,	PUNCT
ejpam-6036	86	8	τ1	τ1	NOUN
ejpam-6036	86	9	,	,	PUNCT
ejpam-6036	86	10	τ2	τ2	NOUN
ejpam-6036	86	11	)	)	PUNCT
ejpam-6036	86	12	→	→	SYM
ejpam-6036	86	13	(	(	PUNCT
ejpam-6036	86	14	y	y	PROPN
ejpam-6036	86	15	,	,	PUNCT
ejpam-6036	86	16	σ1	σ1	PROPN
ejpam-6036	86	17	,	,	PUNCT
ejpam-6036	86	18	σ2	σ2	PROPN
ejpam-6036	86	19	)	)	PUNCT
ejpam-6036	86	20	is	be	AUX
ejpam-6036	86	21	said	say	VERB
ejpam-6036	86	22	to	to	PART
ejpam-6036	86	23	be	be	AUX
ejpam-6036	86	24	weakly	weakly	ADJ
ejpam-6036	86	25	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	86	26	,	,	PUNCT
ejpam-6036	86	27	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	86	28	if	if	SCONJ
ejpam-6036	86	29	for	for	ADP
ejpam-6036	86	30	each	each	DET
ejpam-6036	86	31	σ1σ2	σ1σ2	VERB
ejpam-6036	86	32	-	-	ADJ
ejpam-6036	86	33	open	open	ADJ
ejpam-6036	86	34	set	set	NOUN
ejpam-6036	86	35	v	v	NOUN
ejpam-6036	86	36	of	of	ADP
ejpam-6036	86	37	y	y	PROPN
ejpam-6036	86	38	and	and	CCONJ
ejpam-6036	86	39	each	each	DET
ejpam-6036	86	40	σ1σ2	σ1σ2	VERB
ejpam-6036	86	41	-	-	PUNCT
ejpam-6036	86	42	closed	closed	ADJ
ejpam-6036	86	43	set	set	NOUN
ejpam-6036	86	44	k	k	PROPN
ejpam-6036	86	45	of	of	ADP
ejpam-6036	86	46	y	y	PRON
ejpam-6036	86	47	such	such	ADJ
ejpam-6036	86	48	that	that	SCONJ
ejpam-6036	86	49	k	k	PROPN
ejpam-6036	86	50	⊆	⊆	NUM
ejpam-6036	86	51	v	v	NOUN
ejpam-6036	86	52	,	,	PUNCT
ejpam-6036	86	53	τ1τ2	τ1τ2	NOUN
ejpam-6036	86	54	-	-	NOUN
ejpam-6036	86	55	cl(f	cl(f	NUM
ejpam-6036	86	56	−1(k	−1(k	NOUN
ejpam-6036	86	57	)	)	PUNCT
ejpam-6036	86	58	)	)	PUNCT
ejpam-6036	86	59	⊆	⊆	NUM
ejpam-6036	86	60	f−1(v	f−1(v	NOUN
ejpam-6036	86	61	)	)	PUNCT
ejpam-6036	86	62	.	.	PUNCT
ejpam-6036	87	1	b.	b.	PROPN
ejpam-6036	87	2	kong	kong	PROPN
ejpam-6036	87	3	-	-	PUNCT
ejpam-6036	87	4	ied	ied	PROPN
ejpam-6036	87	5	,	,	PUNCT
ejpam-6036	87	6	s.	s.	PROPN
ejpam-6036	87	7	sompong	sompong	PROPN
ejpam-6036	87	8	,	,	PUNCT
ejpam-6036	87	9	c.	c.	PROPN
ejpam-6036	87	10	boonpok	boonpok	PROPN
ejpam-6036	87	11	/	/	SYM
ejpam-6036	87	12	eur	eur	PROPN
ejpam-6036	87	13	.	.	PUNCT
ejpam-6036	88	1	j.	j.	PROPN
ejpam-6036	88	2	pure	pure	PROPN
ejpam-6036	88	3	appl	appl	PROPN
ejpam-6036	88	4	.	.	PROPN
ejpam-6036	88	5	math	math	PROPN
ejpam-6036	88	6	,	,	PUNCT
ejpam-6036	88	7	18	18	NUM
ejpam-6036	88	8	(	(	PUNCT
ejpam-6036	88	9	2	2	NUM
ejpam-6036	88	10	)	)	PUNCT
ejpam-6036	88	11	(	(	PUNCT
ejpam-6036	88	12	2025	2025	NUM
ejpam-6036	88	13	)	)	PUNCT
ejpam-6036	88	14	,	,	PUNCT
ejpam-6036	88	15	6036	6036	NUM
ejpam-6036	88	16	4	4	NUM
ejpam-6036	88	17	of	of	ADP
ejpam-6036	88	18	11	11	NUM
ejpam-6036	88	19	definition	definition	NOUN
ejpam-6036	88	20	2	2	NUM
ejpam-6036	88	21	.	.	PUNCT
ejpam-6036	89	1	[	[	X
ejpam-6036	89	2	41	41	NUM
ejpam-6036	89	3	]	]	PUNCT
ejpam-6036	89	4	a	a	DET
ejpam-6036	89	5	function	function	NOUN
ejpam-6036	89	6	f	f	NOUN
ejpam-6036	89	7	:	:	PUNCT
ejpam-6036	89	8	(	(	PUNCT
ejpam-6036	89	9	x	x	NOUN
ejpam-6036	89	10	,	,	PUNCT
ejpam-6036	89	11	τ1	τ1	NOUN
ejpam-6036	89	12	,	,	PUNCT
ejpam-6036	89	13	τ2	τ2	NOUN
ejpam-6036	89	14	)	)	PUNCT
ejpam-6036	89	15	→	→	SYM
ejpam-6036	89	16	(	(	PUNCT
ejpam-6036	89	17	y	y	PROPN
ejpam-6036	89	18	,	,	PUNCT
ejpam-6036	89	19	σ1	σ1	PROPN
ejpam-6036	89	20	,	,	PUNCT
ejpam-6036	89	21	σ2	σ2	PROPN
ejpam-6036	89	22	)	)	PUNCT
ejpam-6036	89	23	is	be	AUX
ejpam-6036	89	24	said	say	VERB
ejpam-6036	89	25	to	to	PART
ejpam-6036	89	26	be	be	AUX
ejpam-6036	89	27	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	89	28	,	,	PUNCT
ejpam-6036	89	29	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	89	30	if	if	SCONJ
ejpam-6036	89	31	f−1(v	f−1(v	PROPN
ejpam-6036	89	32	)	)	PUNCT
ejpam-6036	89	33	is	be	AUX
ejpam-6036	89	34	τ1τ2	τ1τ2	NOUN
ejpam-6036	89	35	-	-	ADJ
ejpam-6036	89	36	closed	closed	ADJ
ejpam-6036	89	37	in	in	ADP
ejpam-6036	89	38	x	x	PUNCT
ejpam-6036	89	39	for	for	ADP
ejpam-6036	89	40	every	every	DET
ejpam-6036	89	41	σ1σ2	σ1σ2	NOUN
ejpam-6036	89	42	-	-	ADJ
ejpam-6036	89	43	open	open	ADJ
ejpam-6036	89	44	set	set	NOUN
ejpam-6036	89	45	v	v	NOUN
ejpam-6036	89	46	of	of	ADP
ejpam-6036	89	47	y	y	PROPN
ejpam-6036	89	48	.	.	PUNCT
ejpam-6036	90	1	lemma	lemma	PROPN
ejpam-6036	90	2	4	4	NUM
ejpam-6036	90	3	.	.	PUNCT
ejpam-6036	91	1	[	[	X
ejpam-6036	91	2	41	41	NUM
ejpam-6036	91	3	]	]	PUNCT
ejpam-6036	91	4	for	for	ADP
ejpam-6036	91	5	a	a	DET
ejpam-6036	91	6	function	function	NOUN
ejpam-6036	91	7	f	f	NOUN
ejpam-6036	91	8	:	:	PUNCT
ejpam-6036	91	9	(	(	PUNCT
ejpam-6036	91	10	x	x	NOUN
ejpam-6036	91	11	,	,	PUNCT
ejpam-6036	91	12	τ1	τ1	NOUN
ejpam-6036	91	13	,	,	PUNCT
ejpam-6036	91	14	τ2	τ2	NOUN
ejpam-6036	91	15	)	)	PUNCT
ejpam-6036	91	16	→	→	SYM
ejpam-6036	91	17	(	(	PUNCT
ejpam-6036	91	18	y	y	PROPN
ejpam-6036	91	19	,	,	PUNCT
ejpam-6036	91	20	σ1	σ1	PROPN
ejpam-6036	91	21	,	,	PUNCT
ejpam-6036	91	22	σ2	σ2	NOUN
ejpam-6036	91	23	)	)	PUNCT
ejpam-6036	91	24	,	,	PUNCT
ejpam-6036	91	25	the	the	DET
ejpam-6036	91	26	following	follow	VERB
ejpam-6036	91	27	properties	property	NOUN
ejpam-6036	91	28	are	be	AUX
ejpam-6036	91	29	equivalent	equivalent	ADJ
ejpam-6036	91	30	:	:	PUNCT
ejpam-6036	91	31	(	(	PUNCT
ejpam-6036	91	32	1	1	X
ejpam-6036	91	33	)	)	PUNCT
ejpam-6036	91	34	f	f	PROPN
ejpam-6036	91	35	is	be	AUX
ejpam-6036	91	36	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	91	37	,	,	PUNCT
ejpam-6036	91	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	91	39	;	;	PUNCT
ejpam-6036	91	40	(	(	PUNCT
ejpam-6036	91	41	2	2	X
ejpam-6036	91	42	)	)	PUNCT
ejpam-6036	91	43	f−1(k	f−1(k	PROPN
ejpam-6036	91	44	)	)	PUNCT
ejpam-6036	91	45	is	be	AUX
ejpam-6036	91	46	τ1τ2	τ1τ2	NOUN
ejpam-6036	91	47	-	-	ADJ
ejpam-6036	91	48	open	open	ADJ
ejpam-6036	91	49	in	in	ADP
ejpam-6036	91	50	x	x	PUNCT
ejpam-6036	91	51	for	for	ADP
ejpam-6036	91	52	every	every	DET
ejpam-6036	91	53	σ1σ2	σ1σ2	NUM
ejpam-6036	91	54	-	-	PUNCT
ejpam-6036	91	55	closed	closed	ADJ
ejpam-6036	91	56	set	set	NOUN
ejpam-6036	91	57	k	k	PROPN
ejpam-6036	91	58	of	of	ADP
ejpam-6036	91	59	y	y	PROPN
ejpam-6036	91	60	;	;	PUNCT
ejpam-6036	91	61	(	(	PUNCT
ejpam-6036	91	62	3	3	X
ejpam-6036	91	63	)	)	PUNCT
ejpam-6036	91	64	for	for	ADP
ejpam-6036	91	65	each	each	DET
ejpam-6036	91	66	x	x	SYM
ejpam-6036	91	67	∈	∈	PROPN
ejpam-6036	91	68	x	x	X
ejpam-6036	91	69	and	and	CCONJ
ejpam-6036	91	70	each	each	PRON
ejpam-6036	91	71	σ1σ2	σ1σ2	VERB
ejpam-6036	91	72	-	-	PUNCT
ejpam-6036	91	73	closed	closed	ADJ
ejpam-6036	91	74	set	set	NOUN
ejpam-6036	91	75	k	k	PROPN
ejpam-6036	91	76	of	of	ADP
ejpam-6036	91	77	y	y	PROPN
ejpam-6036	91	78	containing	contain	VERB
ejpam-6036	91	79	f(x	f(x	PROPN
ejpam-6036	91	80	)	)	PUNCT
ejpam-6036	91	81	,	,	PUNCT
ejpam-6036	91	82	there	there	PRON
ejpam-6036	91	83	exists	exist	VERB
ejpam-6036	91	84	a	a	DET
ejpam-6036	91	85	τ1τ2	τ1τ2	NOUN
ejpam-6036	91	86	-	-	ADJ
ejpam-6036	91	87	open	open	ADJ
ejpam-6036	91	88	set	set	ADJ
ejpam-6036	91	89	u	u	NOUN
ejpam-6036	91	90	of	of	ADP
ejpam-6036	91	91	x	x	PUNCT
ejpam-6036	91	92	containing	contain	VERB
ejpam-6036	91	93	x	x	PUNCT
ejpam-6036	91	94	such	such	ADJ
ejpam-6036	91	95	that	that	DET
ejpam-6036	91	96	f(u	f(u	PROPN
ejpam-6036	91	97	)	)	PUNCT
ejpam-6036	91	98	⊆	⊆	NUM
ejpam-6036	91	99	k	k	NOUN
ejpam-6036	91	100	;	;	PUNCT
ejpam-6036	91	101	(	(	PUNCT
ejpam-6036	91	102	4	4	X
ejpam-6036	91	103	)	)	PUNCT
ejpam-6036	91	104	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6036	91	105	-	-	PUNCT
ejpam-6036	91	106	cl(a	cl(a	NUM
ejpam-6036	91	107	)	)	PUNCT
ejpam-6036	91	108	)	)	PUNCT
ejpam-6036	92	1	⊆	⊆	X
ejpam-6036	92	2	σ1σ2	σ1σ2	NUM
ejpam-6036	92	3	-	-	PUNCT
ejpam-6036	92	4	ker(f(a	ker(f(a	NOUN
ejpam-6036	92	5	)	)	PUNCT
ejpam-6036	92	6	)	)	PUNCT
ejpam-6036	92	7	for	for	ADP
ejpam-6036	92	8	every	every	DET
ejpam-6036	92	9	subset	subset	NOUN
ejpam-6036	92	10	a	a	PRON
ejpam-6036	92	11	of	of	ADP
ejpam-6036	92	12	x	x	PRON
ejpam-6036	92	13	;	;	PUNCT
ejpam-6036	92	14	(	(	PUNCT
ejpam-6036	92	15	5	5	X
ejpam-6036	92	16	)	)	PUNCT
ejpam-6036	92	17	τ1τ2	τ1τ2	NOUN
ejpam-6036	92	18	-	-	NOUN
ejpam-6036	92	19	cl(f	cl(f	NOUN
ejpam-6036	92	20	−1(b	−1(b	NOUN
ejpam-6036	92	21	)	)	PUNCT
ejpam-6036	92	22	)	)	PUNCT
ejpam-6036	93	1	⊆	⊆	NUM
ejpam-6036	93	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	93	3	-	-	PUNCT
ejpam-6036	93	4	ker(b	ker(b	PROPN
ejpam-6036	93	5	)	)	PUNCT
ejpam-6036	93	6	)	)	PUNCT
ejpam-6036	93	7	for	for	ADP
ejpam-6036	93	8	every	every	DET
ejpam-6036	93	9	subset	subset	NOUN
ejpam-6036	93	10	b	b	PROPN
ejpam-6036	93	11	of	of	ADP
ejpam-6036	93	12	y	y	PROPN
ejpam-6036	93	13	.	.	PUNCT
ejpam-6036	94	1	theorem	theorem	NOUN
ejpam-6036	94	2	1	1	NUM
ejpam-6036	94	3	.	.	PUNCT
ejpam-6036	95	1	if	if	SCONJ
ejpam-6036	95	2	a	a	DET
ejpam-6036	95	3	function	function	NOUN
ejpam-6036	95	4	f	f	X
ejpam-6036	95	5	:	:	PUNCT
ejpam-6036	95	6	(	(	PUNCT
ejpam-6036	95	7	x	x	NOUN
ejpam-6036	95	8	,	,	PUNCT
ejpam-6036	95	9	τ1	τ1	NOUN
ejpam-6036	95	10	,	,	PUNCT
ejpam-6036	95	11	τ2	τ2	NOUN
ejpam-6036	95	12	)	)	PUNCT
ejpam-6036	95	13	→	→	SYM
ejpam-6036	95	14	(	(	PUNCT
ejpam-6036	95	15	y	y	PROPN
ejpam-6036	95	16	,	,	PUNCT
ejpam-6036	95	17	σ1	σ1	PROPN
ejpam-6036	95	18	,	,	PUNCT
ejpam-6036	95	19	σ2	σ2	PROPN
ejpam-6036	95	20	)	)	PUNCT
ejpam-6036	95	21	is	be	AUX
ejpam-6036	95	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	95	23	,	,	PUNCT
ejpam-6036	95	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	95	25	,	,	PUNCT
ejpam-6036	95	26	then	then	ADV
ejpam-6036	95	27	f	f	PROPN
ejpam-6036	95	28	is	be	AUX
ejpam-6036	95	29	weakly	weakly	ADJ
ejpam-6036	95	30	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	95	31	,	,	PUNCT
ejpam-6036	95	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	95	33	.	.	PUNCT
ejpam-6036	96	1	proof	proof	NOUN
ejpam-6036	96	2	.	.	PUNCT
ejpam-6036	97	1	let	let	VERB
ejpam-6036	97	2	v	v	PART
ejpam-6036	97	3	be	be	AUX
ejpam-6036	97	4	any	any	DET
ejpam-6036	97	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	97	6	-	-	ADJ
ejpam-6036	97	7	open	open	ADJ
ejpam-6036	97	8	set	set	NOUN
ejpam-6036	97	9	of	of	ADP
ejpam-6036	97	10	y	y	PROPN
ejpam-6036	97	11	and	and	CCONJ
ejpam-6036	97	12	k	k	PROPN
ejpam-6036	97	13	be	be	AUX
ejpam-6036	97	14	any	any	DET
ejpam-6036	97	15	σ1σ2	σ1σ2	NUM
ejpam-6036	97	16	-	-	PUNCT
ejpam-6036	97	17	closed	closed	ADJ
ejpam-6036	97	18	set	set	NOUN
ejpam-6036	97	19	of	of	ADP
ejpam-6036	97	20	y	y	PRON
ejpam-6036	97	21	such	such	ADJ
ejpam-6036	97	22	that	that	SCONJ
ejpam-6036	97	23	k	k	PROPN
ejpam-6036	97	24	⊆	⊆	NUM
ejpam-6036	97	25	v	v	NOUN
ejpam-6036	97	26	.	.	PUNCT
ejpam-6036	98	1	since	since	SCONJ
ejpam-6036	98	2	f	f	PROPN
ejpam-6036	98	3	is	be	AUX
ejpam-6036	98	4	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	98	5	,	,	PUNCT
ejpam-6036	98	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	98	7	,	,	PUNCT
ejpam-6036	98	8	by	by	ADP
ejpam-6036	98	9	lemma	lemma	PROPN
ejpam-6036	98	10	4	4	NUM
ejpam-6036	98	11	we	we	PRON
ejpam-6036	98	12	have	have	VERB
ejpam-6036	98	13	f−1(v	f−1(v	PROPN
ejpam-6036	98	14	)	)	PUNCT
ejpam-6036	98	15	is	be	AUX
ejpam-6036	98	16	τ1τ2	τ1τ2	NOUN
ejpam-6036	98	17	-	-	ADJ
ejpam-6036	98	18	closed	closed	ADJ
ejpam-6036	98	19	in	in	ADP
ejpam-6036	98	20	x	x	X
ejpam-6036	98	21	and	and	CCONJ
ejpam-6036	98	22	hence	hence	ADV
ejpam-6036	98	23	τ1τ2	τ1τ2	NOUN
ejpam-6036	98	24	-	-	NOUN
ejpam-6036	98	25	cl(f	cl(f	NUM
ejpam-6036	98	26	−1(k	−1(k	NOUN
ejpam-6036	98	27	)	)	PUNCT
ejpam-6036	98	28	)	)	PUNCT
ejpam-6036	99	1	⊆	⊆	X
ejpam-6036	99	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	99	3	-	-	NOUN
ejpam-6036	99	4	cl(f	cl(f	PRON
ejpam-6036	99	5	−1(v	−1(v	NOUN
ejpam-6036	99	6	)	)	PUNCT
ejpam-6036	99	7	)	)	PUNCT
ejpam-6036	100	1	=	=	SYM
ejpam-6036	100	2	f−1(v	f−1(v	PROPN
ejpam-6036	100	3	)	)	PUNCT
ejpam-6036	100	4	.	.	PUNCT
ejpam-6036	101	1	this	this	PRON
ejpam-6036	101	2	shows	show	VERB
ejpam-6036	101	3	that	that	SCONJ
ejpam-6036	101	4	f	f	PROPN
ejpam-6036	101	5	is	be	AUX
ejpam-6036	101	6	weakly	weakly	ADJ
ejpam-6036	101	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	101	8	,	,	PUNCT
ejpam-6036	101	9	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6036	101	10	.	.	PUNCT
ejpam-6036	102	1	definition	definition	NOUN
ejpam-6036	102	2	3	3	NUM
ejpam-6036	102	3	.	.	PUNCT
ejpam-6036	103	1	[	[	X
ejpam-6036	103	2	28	28	NUM
ejpam-6036	103	3	]	]	X
ejpam-6036	103	4	a	a	DET
ejpam-6036	103	5	function	function	NOUN
ejpam-6036	103	6	f	f	NOUN
ejpam-6036	103	7	:	:	PUNCT
ejpam-6036	103	8	(	(	PUNCT
ejpam-6036	103	9	x	x	NOUN
ejpam-6036	103	10	,	,	PUNCT
ejpam-6036	103	11	τ1	τ1	NOUN
ejpam-6036	103	12	,	,	PUNCT
ejpam-6036	103	13	τ2	τ2	NOUN
ejpam-6036	103	14	)	)	PUNCT
ejpam-6036	103	15	→	→	SYM
ejpam-6036	103	16	(	(	PUNCT
ejpam-6036	103	17	y	y	PROPN
ejpam-6036	103	18	,	,	PUNCT
ejpam-6036	103	19	σ1	σ1	PROPN
ejpam-6036	103	20	,	,	PUNCT
ejpam-6036	103	21	σ2	σ2	PROPN
ejpam-6036	103	22	)	)	PUNCT
ejpam-6036	103	23	is	be	AUX
ejpam-6036	103	24	called	call	VERB
ejpam-6036	103	25	(	(	PUNCT
ejpam-6036	103	26	τ1	τ1	NOUN
ejpam-6036	103	27	,	,	PUNCT
ejpam-6036	103	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	103	29	at	at	ADP
ejpam-6036	103	30	a	a	DET
ejpam-6036	103	31	point	point	NOUN
ejpam-6036	103	32	x	x	SYM
ejpam-6036	103	33	∈	∈	NOUN
ejpam-6036	103	34	x	x	PUNCT
ejpam-6036	103	35	if	if	SCONJ
ejpam-6036	103	36	for	for	ADP
ejpam-6036	103	37	each	each	DET
ejpam-6036	103	38	σ1σ2	σ1σ2	VERB
ejpam-6036	103	39	-	-	ADJ
ejpam-6036	103	40	open	open	ADJ
ejpam-6036	103	41	set	set	NOUN
ejpam-6036	103	42	v	v	NOUN
ejpam-6036	103	43	of	of	ADP
ejpam-6036	103	44	y	y	NOUN
ejpam-6036	103	45	containing	contain	VERB
ejpam-6036	103	46	f(x	f(x	PROPN
ejpam-6036	103	47	)	)	PUNCT
ejpam-6036	103	48	,	,	PUNCT
ejpam-6036	103	49	there	there	PRON
ejpam-6036	103	50	exists	exist	VERB
ejpam-6036	103	51	a	a	DET
ejpam-6036	103	52	τ1τ2	τ1τ2	NOUN
ejpam-6036	103	53	-	-	ADJ
ejpam-6036	103	54	open	open	ADJ
ejpam-6036	103	55	set	set	ADJ
ejpam-6036	103	56	u	u	NOUN
ejpam-6036	103	57	of	of	ADP
ejpam-6036	103	58	x	x	PUNCT
ejpam-6036	103	59	containing	contain	VERB
ejpam-6036	103	60	x	x	PUNCT
ejpam-6036	103	61	such	such	ADJ
ejpam-6036	103	62	that	that	DET
ejpam-6036	103	63	f(u	f(u	PROPN
ejpam-6036	103	64	)	)	PUNCT
ejpam-6036	103	65	⊆	⊆	NUM
ejpam-6036	103	66	v	v	NOUN
ejpam-6036	103	67	.	.	PUNCT
ejpam-6036	104	1	a	a	DET
ejpam-6036	104	2	function	function	NOUN
ejpam-6036	104	3	f	f	NOUN
ejpam-6036	104	4	:	:	PUNCT
ejpam-6036	104	5	(	(	PUNCT
ejpam-6036	104	6	x	x	NOUN
ejpam-6036	104	7	,	,	PUNCT
ejpam-6036	104	8	τ1	τ1	NOUN
ejpam-6036	104	9	,	,	PUNCT
ejpam-6036	104	10	τ2	τ2	NOUN
ejpam-6036	104	11	)	)	PUNCT
ejpam-6036	104	12	→	→	SYM
ejpam-6036	104	13	(	(	PUNCT
ejpam-6036	104	14	y	y	PROPN
ejpam-6036	104	15	,	,	PUNCT
ejpam-6036	104	16	σ1	σ1	PROPN
ejpam-6036	104	17	,	,	PUNCT
ejpam-6036	104	18	σ2	σ2	PROPN
ejpam-6036	104	19	)	)	PUNCT
ejpam-6036	104	20	is	be	AUX
ejpam-6036	104	21	called	call	VERB
ejpam-6036	104	22	(	(	PUNCT
ejpam-6036	104	23	τ1	τ1	NOUN
ejpam-6036	104	24	,	,	PUNCT
ejpam-6036	104	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	104	26	if	if	SCONJ
ejpam-6036	104	27	f	f	PROPN
ejpam-6036	104	28	has	have	VERB
ejpam-6036	104	29	this	this	DET
ejpam-6036	104	30	property	property	NOUN
ejpam-6036	104	31	at	at	ADP
ejpam-6036	104	32	each	each	DET
ejpam-6036	104	33	point	point	NOUN
ejpam-6036	104	34	of	of	ADP
ejpam-6036	104	35	x.	x.	PROPN
ejpam-6036	104	36	lemma	lemma	PROPN
ejpam-6036	105	1	5	5	NUM
ejpam-6036	105	2	.	.	PUNCT
ejpam-6036	106	1	[	[	X
ejpam-6036	106	2	28	28	NUM
ejpam-6036	106	3	]	]	PUNCT
ejpam-6036	106	4	for	for	ADP
ejpam-6036	106	5	a	a	DET
ejpam-6036	106	6	function	function	NOUN
ejpam-6036	106	7	(	(	PUNCT
ejpam-6036	106	8	x	x	NOUN
ejpam-6036	106	9	,	,	PUNCT
ejpam-6036	106	10	τ1	τ1	NOUN
ejpam-6036	106	11	,	,	PUNCT
ejpam-6036	106	12	τ2	τ2	NOUN
ejpam-6036	106	13	)	)	PUNCT
ejpam-6036	106	14	→	→	SYM
ejpam-6036	106	15	(	(	PUNCT
ejpam-6036	106	16	y	y	PROPN
ejpam-6036	106	17	,	,	PUNCT
ejpam-6036	106	18	σ1	σ1	PROPN
ejpam-6036	106	19	,	,	PUNCT
ejpam-6036	106	20	σ2	σ2	NOUN
ejpam-6036	106	21	)	)	PUNCT
ejpam-6036	106	22	,	,	PUNCT
ejpam-6036	106	23	the	the	DET
ejpam-6036	106	24	following	follow	VERB
ejpam-6036	106	25	properties	property	NOUN
ejpam-6036	106	26	are	be	AUX
ejpam-6036	106	27	equivalent	equivalent	ADJ
ejpam-6036	106	28	:	:	PUNCT
ejpam-6036	106	29	(	(	PUNCT
ejpam-6036	106	30	1	1	X
ejpam-6036	106	31	)	)	PUNCT
ejpam-6036	106	32	f	f	PROPN
ejpam-6036	106	33	is	be	AUX
ejpam-6036	106	34	(	(	PUNCT
ejpam-6036	106	35	τ1	τ1	NOUN
ejpam-6036	106	36	,	,	PUNCT
ejpam-6036	106	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	106	38	;	;	PUNCT
ejpam-6036	106	39	(	(	PUNCT
ejpam-6036	106	40	2	2	X
ejpam-6036	106	41	)	)	PUNCT
ejpam-6036	106	42	f−1(v	f−1(v	NOUN
ejpam-6036	106	43	)	)	PUNCT
ejpam-6036	106	44	is	be	AUX
ejpam-6036	106	45	τ1τ2	τ1τ2	NOUN
ejpam-6036	106	46	-	-	ADJ
ejpam-6036	106	47	open	open	ADJ
ejpam-6036	106	48	in	in	ADP
ejpam-6036	106	49	x	x	PUNCT
ejpam-6036	106	50	for	for	ADP
ejpam-6036	106	51	every	every	DET
ejpam-6036	106	52	σ1σ2	σ1σ2	NOUN
ejpam-6036	106	53	-	-	ADJ
ejpam-6036	106	54	open	open	ADJ
ejpam-6036	106	55	set	set	NOUN
ejpam-6036	106	56	v	v	NOUN
ejpam-6036	106	57	of	of	ADP
ejpam-6036	106	58	y	y	PROPN
ejpam-6036	106	59	;	;	PUNCT
ejpam-6036	106	60	(	(	PUNCT
ejpam-6036	106	61	3	3	X
ejpam-6036	106	62	)	)	PUNCT
ejpam-6036	106	63	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6036	106	64	-	-	PUNCT
ejpam-6036	106	65	cl(a	cl(a	NUM
ejpam-6036	106	66	)	)	PUNCT
ejpam-6036	106	67	)	)	PUNCT
ejpam-6036	107	1	⊆	⊆	X
ejpam-6036	107	2	σ1σ2	σ1σ2	NUM
ejpam-6036	107	3	-	-	PUNCT
ejpam-6036	107	4	cl(f(a	cl(f(a	NOUN
ejpam-6036	107	5	)	)	PUNCT
ejpam-6036	107	6	)	)	PUNCT
ejpam-6036	107	7	for	for	ADP
ejpam-6036	107	8	every	every	DET
ejpam-6036	107	9	subset	subset	NOUN
ejpam-6036	107	10	a	a	PRON
ejpam-6036	107	11	of	of	ADP
ejpam-6036	107	12	x	x	PRON
ejpam-6036	107	13	;	;	PUNCT
ejpam-6036	107	14	(	(	PUNCT
ejpam-6036	107	15	4	4	X
ejpam-6036	107	16	)	)	PUNCT
ejpam-6036	107	17	τ1τ2	τ1τ2	NOUN
ejpam-6036	107	18	-	-	NOUN
ejpam-6036	107	19	cl(f	cl(f	NOUN
ejpam-6036	107	20	−1(b	−1(b	NOUN
ejpam-6036	107	21	)	)	PUNCT
ejpam-6036	107	22	)	)	PUNCT
ejpam-6036	108	1	⊆	⊆	NUM
ejpam-6036	108	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	108	3	-	-	PUNCT
ejpam-6036	108	4	cl(b	cl(b	NOUN
ejpam-6036	108	5	)	)	PUNCT
ejpam-6036	108	6	)	)	PUNCT
ejpam-6036	108	7	for	for	ADP
ejpam-6036	108	8	every	every	DET
ejpam-6036	108	9	subset	subset	NOUN
ejpam-6036	108	10	b	b	PROPN
ejpam-6036	108	11	of	of	ADP
ejpam-6036	108	12	y	y	PROPN
ejpam-6036	108	13	;	;	PUNCT
ejpam-6036	108	14	(	(	PUNCT
ejpam-6036	108	15	5	5	X
ejpam-6036	108	16	)	)	PUNCT
ejpam-6036	108	17	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	108	18	-	-	PUNCT
ejpam-6036	108	19	int(b	int(b	NOUN
ejpam-6036	108	20	)	)	PUNCT
ejpam-6036	108	21	)	)	PUNCT
ejpam-6036	109	1	⊆	⊆	X
ejpam-6036	109	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	109	3	-	-	NUM
ejpam-6036	109	4	int(f	int(f	NOUN
ejpam-6036	109	5	−1(b	−1(b	NOUN
ejpam-6036	109	6	)	)	PUNCT
ejpam-6036	109	7	)	)	PUNCT
ejpam-6036	109	8	for	for	ADP
ejpam-6036	109	9	every	every	DET
ejpam-6036	109	10	subset	subset	NOUN
ejpam-6036	109	11	b	b	PROPN
ejpam-6036	109	12	of	of	ADP
ejpam-6036	109	13	y	y	PROPN
ejpam-6036	109	14	;	;	PUNCT
ejpam-6036	109	15	(	(	PUNCT
ejpam-6036	109	16	6	6	X
ejpam-6036	109	17	)	)	PUNCT
ejpam-6036	109	18	f−1(k	f−1(k	PROPN
ejpam-6036	109	19	)	)	PUNCT
ejpam-6036	109	20	is	be	AUX
ejpam-6036	109	21	τ1τ2	τ1τ2	NOUN
ejpam-6036	109	22	-	-	ADJ
ejpam-6036	109	23	closed	closed	ADJ
ejpam-6036	109	24	in	in	ADP
ejpam-6036	109	25	x	x	PUNCT
ejpam-6036	109	26	for	for	ADP
ejpam-6036	109	27	every	every	DET
ejpam-6036	109	28	σ1σ2	σ1σ2	NUM
ejpam-6036	109	29	-	-	PUNCT
ejpam-6036	109	30	closed	closed	ADJ
ejpam-6036	109	31	set	set	NOUN
ejpam-6036	109	32	k	k	PROPN
ejpam-6036	109	33	of	of	ADP
ejpam-6036	109	34	y	y	PROPN
ejpam-6036	109	35	.	.	PUNCT
ejpam-6036	110	1	theorem	theorem	NOUN
ejpam-6036	110	2	2	2	NUM
ejpam-6036	110	3	.	.	PUNCT
ejpam-6036	111	1	if	if	SCONJ
ejpam-6036	111	2	a	a	DET
ejpam-6036	111	3	function	function	NOUN
ejpam-6036	111	4	f	f	X
ejpam-6036	111	5	:	:	PUNCT
ejpam-6036	111	6	(	(	PUNCT
ejpam-6036	111	7	x	x	NOUN
ejpam-6036	111	8	,	,	PUNCT
ejpam-6036	111	9	τ1	τ1	NOUN
ejpam-6036	111	10	,	,	PUNCT
ejpam-6036	111	11	τ2	τ2	NOUN
ejpam-6036	111	12	)	)	PUNCT
ejpam-6036	111	13	→	→	SYM
ejpam-6036	111	14	(	(	PUNCT
ejpam-6036	111	15	y	y	PROPN
ejpam-6036	111	16	,	,	PUNCT
ejpam-6036	111	17	σ1	σ1	PROPN
ejpam-6036	111	18	,	,	PUNCT
ejpam-6036	111	19	σ2	σ2	PROPN
ejpam-6036	111	20	)	)	PUNCT
ejpam-6036	111	21	is	be	AUX
ejpam-6036	111	22	(	(	PUNCT
ejpam-6036	111	23	τ1	τ1	NOUN
ejpam-6036	111	24	,	,	PUNCT
ejpam-6036	111	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	111	26	,	,	PUNCT
ejpam-6036	111	27	then	then	ADV
ejpam-6036	111	28	f	f	PROPN
ejpam-6036	111	29	is	be	AUX
ejpam-6036	111	30	weakly	weakly	ADJ
ejpam-6036	111	31	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	111	32	,	,	PUNCT
ejpam-6036	111	33	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6036	111	34	.	.	PUNCT
ejpam-6036	112	1	b.	b.	PROPN
ejpam-6036	112	2	kong	kong	PROPN
ejpam-6036	112	3	-	-	PUNCT
ejpam-6036	112	4	ied	ied	PROPN
ejpam-6036	112	5	,	,	PUNCT
ejpam-6036	112	6	s.	s.	PROPN
ejpam-6036	112	7	sompong	sompong	PROPN
ejpam-6036	112	8	,	,	PUNCT
ejpam-6036	112	9	c.	c.	PROPN
ejpam-6036	112	10	boonpok	boonpok	PROPN
ejpam-6036	112	11	/	/	SYM
ejpam-6036	112	12	eur	eur	PROPN
ejpam-6036	112	13	.	.	PUNCT
ejpam-6036	113	1	j.	j.	PROPN
ejpam-6036	113	2	pure	pure	PROPN
ejpam-6036	113	3	appl	appl	PROPN
ejpam-6036	113	4	.	.	PROPN
ejpam-6036	113	5	math	math	PROPN
ejpam-6036	113	6	,	,	PUNCT
ejpam-6036	113	7	18	18	NUM
ejpam-6036	113	8	(	(	PUNCT
ejpam-6036	113	9	2	2	NUM
ejpam-6036	113	10	)	)	PUNCT
ejpam-6036	113	11	(	(	PUNCT
ejpam-6036	113	12	2025	2025	NUM
ejpam-6036	113	13	)	)	PUNCT
ejpam-6036	113	14	,	,	PUNCT
ejpam-6036	113	15	6036	6036	NUM
ejpam-6036	113	16	5	5	NUM
ejpam-6036	113	17	of	of	ADP
ejpam-6036	113	18	11	11	NUM
ejpam-6036	113	19	proof	proof	NOUN
ejpam-6036	113	20	.	.	PUNCT
ejpam-6036	114	1	let	let	VERB
ejpam-6036	114	2	v	v	PART
ejpam-6036	114	3	be	be	AUX
ejpam-6036	114	4	any	any	DET
ejpam-6036	114	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	114	6	-	-	ADJ
ejpam-6036	114	7	open	open	ADJ
ejpam-6036	114	8	set	set	NOUN
ejpam-6036	114	9	of	of	ADP
ejpam-6036	114	10	y	y	PROPN
ejpam-6036	114	11	and	and	CCONJ
ejpam-6036	114	12	k	k	PROPN
ejpam-6036	114	13	be	be	AUX
ejpam-6036	114	14	any	any	DET
ejpam-6036	114	15	σ1σ2	σ1σ2	NUM
ejpam-6036	114	16	-	-	PUNCT
ejpam-6036	114	17	closed	closed	ADJ
ejpam-6036	114	18	set	set	NOUN
ejpam-6036	114	19	of	of	ADP
ejpam-6036	114	20	y	y	PRON
ejpam-6036	114	21	such	such	ADJ
ejpam-6036	114	22	that	that	SCONJ
ejpam-6036	114	23	k	k	PROPN
ejpam-6036	114	24	⊆	⊆	NUM
ejpam-6036	114	25	v	v	NOUN
ejpam-6036	114	26	.	.	PUNCT
ejpam-6036	115	1	since	since	SCONJ
ejpam-6036	115	2	f	f	PROPN
ejpam-6036	115	3	is	be	AUX
ejpam-6036	115	4	(	(	PUNCT
ejpam-6036	115	5	τ1	τ1	NOUN
ejpam-6036	115	6	,	,	PUNCT
ejpam-6036	115	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	115	8	,	,	PUNCT
ejpam-6036	115	9	by	by	ADP
ejpam-6036	115	10	lemma	lemma	PROPN
ejpam-6036	115	11	5	5	NUM
ejpam-6036	115	12	we	we	PRON
ejpam-6036	115	13	have	have	VERB
ejpam-6036	115	14	f−1(k	f−1(k	PROPN
ejpam-6036	115	15	)	)	PUNCT
ejpam-6036	115	16	is	be	AUX
ejpam-6036	115	17	τ1τ2	τ1τ2	VERB
ejpam-6036	115	18	-	-	ADJ
ejpam-6036	115	19	closed	closed	ADJ
ejpam-6036	115	20	inx	inx	NOUN
ejpam-6036	115	21	and	and	CCONJ
ejpam-6036	115	22	so	so	ADV
ejpam-6036	115	23	τ1τ2	τ1τ2	NOUN
ejpam-6036	115	24	-	-	NOUN
ejpam-6036	115	25	cl(f	cl(f	NUM
ejpam-6036	115	26	−1(k	−1(k	NOUN
ejpam-6036	115	27	)	)	PUNCT
ejpam-6036	115	28	)	)	PUNCT
ejpam-6036	116	1	=	=	SYM
ejpam-6036	116	2	f−1(k	f−1(k	PROPN
ejpam-6036	116	3	)	)	PUNCT
ejpam-6036	116	4	⊆	⊆	NUM
ejpam-6036	116	5	f−1(v	f−1(v	NOUN
ejpam-6036	116	6	)	)	PUNCT
ejpam-6036	116	7	.	.	PUNCT
ejpam-6036	117	1	thus	thus	ADV
ejpam-6036	117	2	,	,	PUNCT
ejpam-6036	117	3	f	f	PROPN
ejpam-6036	117	4	is	be	AUX
ejpam-6036	117	5	weakly	weakly	ADJ
ejpam-6036	117	6	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	117	7	,	,	PUNCT
ejpam-6036	117	8	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6036	117	9	.	.	PUNCT
ejpam-6036	118	1	definition	definition	NOUN
ejpam-6036	118	2	4	4	NUM
ejpam-6036	118	3	.	.	PUNCT
ejpam-6036	119	1	[	[	X
ejpam-6036	119	2	42	42	NUM
ejpam-6036	119	3	]	]	PUNCT
ejpam-6036	119	4	a	a	DET
ejpam-6036	119	5	function	function	NOUN
ejpam-6036	119	6	f	f	NOUN
ejpam-6036	119	7	:	:	PUNCT
ejpam-6036	119	8	(	(	PUNCT
ejpam-6036	119	9	x	x	NOUN
ejpam-6036	119	10	,	,	PUNCT
ejpam-6036	119	11	τ1	τ1	NOUN
ejpam-6036	119	12	,	,	PUNCT
ejpam-6036	119	13	τ2	τ2	NOUN
ejpam-6036	119	14	)	)	PUNCT
ejpam-6036	119	15	→	→	SYM
ejpam-6036	119	16	(	(	PUNCT
ejpam-6036	119	17	y	y	PROPN
ejpam-6036	119	18	,	,	PUNCT
ejpam-6036	119	19	σ1	σ1	PROPN
ejpam-6036	119	20	,	,	PUNCT
ejpam-6036	119	21	σ2	σ2	PROPN
ejpam-6036	119	22	)	)	PUNCT
ejpam-6036	119	23	is	be	AUX
ejpam-6036	119	24	said	say	VERB
ejpam-6036	119	25	to	to	PART
ejpam-6036	119	26	be	be	AUX
ejpam-6036	119	27	slightly	slightly	ADV
ejpam-6036	119	28	(	(	PUNCT
ejpam-6036	119	29	τ1	τ1	NOUN
ejpam-6036	119	30	,	,	PUNCT
ejpam-6036	119	31	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	119	32	if	if	SCONJ
ejpam-6036	119	33	for	for	ADP
ejpam-6036	119	34	each	each	DET
ejpam-6036	119	35	x	x	SYM
ejpam-6036	119	36	∈	∈	PROPN
ejpam-6036	119	37	x	x	X
ejpam-6036	119	38	and	and	CCONJ
ejpam-6036	119	39	each	each	DET
ejpam-6036	119	40	σ1σ2	σ1σ2	NUM
ejpam-6036	119	41	-	-	PUNCT
ejpam-6036	119	42	clopen	clopen	ADJ
ejpam-6036	119	43	set	set	NOUN
ejpam-6036	119	44	v	v	NOUN
ejpam-6036	119	45	of	of	ADP
ejpam-6036	119	46	y	y	NOUN
ejpam-6036	119	47	containing	contain	VERB
ejpam-6036	119	48	f(x	f(x	PROPN
ejpam-6036	119	49	)	)	PUNCT
ejpam-6036	119	50	,	,	PUNCT
ejpam-6036	119	51	there	there	PRON
ejpam-6036	119	52	exists	exist	VERB
ejpam-6036	119	53	a	a	DET
ejpam-6036	119	54	τ1τ2	τ1τ2	NOUN
ejpam-6036	119	55	-	-	ADJ
ejpam-6036	119	56	open	open	ADJ
ejpam-6036	119	57	set	set	ADJ
ejpam-6036	119	58	u	u	NOUN
ejpam-6036	119	59	of	of	ADP
ejpam-6036	119	60	x	x	PUNCT
ejpam-6036	119	61	containing	contain	VERB
ejpam-6036	119	62	x	x	PUNCT
ejpam-6036	119	63	such	such	ADJ
ejpam-6036	119	64	that	that	DET
ejpam-6036	119	65	f(u	f(u	PROPN
ejpam-6036	119	66	)	)	PUNCT
ejpam-6036	119	67	⊆	⊆	NUM
ejpam-6036	119	68	v	v	NOUN
ejpam-6036	119	69	.	.	PUNCT
ejpam-6036	120	1	lemma	lemma	PROPN
ejpam-6036	120	2	6	6	NUM
ejpam-6036	120	3	.	.	PUNCT
ejpam-6036	121	1	[	[	X
ejpam-6036	121	2	42	42	NUM
ejpam-6036	121	3	]	]	PUNCT
ejpam-6036	121	4	for	for	ADP
ejpam-6036	121	5	a	a	DET
ejpam-6036	121	6	function	function	NOUN
ejpam-6036	121	7	f	f	NOUN
ejpam-6036	121	8	:	:	PUNCT
ejpam-6036	121	9	(	(	PUNCT
ejpam-6036	121	10	x	x	NOUN
ejpam-6036	121	11	,	,	PUNCT
ejpam-6036	121	12	τ1	τ1	NOUN
ejpam-6036	121	13	,	,	PUNCT
ejpam-6036	121	14	τ2	τ2	NOUN
ejpam-6036	121	15	)	)	PUNCT
ejpam-6036	121	16	→	→	SYM
ejpam-6036	121	17	(	(	PUNCT
ejpam-6036	121	18	y	y	PROPN
ejpam-6036	121	19	,	,	PUNCT
ejpam-6036	121	20	σ1	σ1	PROPN
ejpam-6036	121	21	,	,	PUNCT
ejpam-6036	121	22	σ2	σ2	NOUN
ejpam-6036	121	23	)	)	PUNCT
ejpam-6036	121	24	,	,	PUNCT
ejpam-6036	121	25	the	the	DET
ejpam-6036	121	26	following	follow	VERB
ejpam-6036	121	27	properties	property	NOUN
ejpam-6036	121	28	are	be	AUX
ejpam-6036	121	29	equivalent	equivalent	ADJ
ejpam-6036	121	30	:	:	PUNCT
ejpam-6036	121	31	(	(	PUNCT
ejpam-6036	121	32	1	1	X
ejpam-6036	121	33	)	)	PUNCT
ejpam-6036	121	34	f	f	PROPN
ejpam-6036	121	35	is	be	AUX
ejpam-6036	121	36	slightly	slightly	ADV
ejpam-6036	121	37	(	(	PUNCT
ejpam-6036	121	38	τ1	τ1	NOUN
ejpam-6036	121	39	,	,	PUNCT
ejpam-6036	121	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	121	41	;	;	PUNCT
ejpam-6036	121	42	(	(	PUNCT
ejpam-6036	121	43	2	2	X
ejpam-6036	121	44	)	)	PUNCT
ejpam-6036	121	45	f−1(v	f−1(v	NOUN
ejpam-6036	121	46	)	)	PUNCT
ejpam-6036	121	47	is	be	AUX
ejpam-6036	121	48	τ1τ2	τ1τ2	NOUN
ejpam-6036	121	49	-	-	ADJ
ejpam-6036	121	50	open	open	ADJ
ejpam-6036	121	51	in	in	ADP
ejpam-6036	121	52	x	x	PUNCT
ejpam-6036	121	53	for	for	ADP
ejpam-6036	121	54	each	each	DET
ejpam-6036	121	55	σ1σ2	σ1σ2	NUM
ejpam-6036	121	56	-	-	PUNCT
ejpam-6036	121	57	clopen	clopen	ADJ
ejpam-6036	121	58	set	set	NOUN
ejpam-6036	121	59	v	v	NOUN
ejpam-6036	121	60	of	of	ADP
ejpam-6036	121	61	y	y	PROPN
ejpam-6036	121	62	;	;	PUNCT
ejpam-6036	121	63	(	(	PUNCT
ejpam-6036	121	64	3	3	X
ejpam-6036	121	65	)	)	PUNCT
ejpam-6036	121	66	f−1(v	f−1(v	NOUN
ejpam-6036	121	67	)	)	PUNCT
ejpam-6036	121	68	is	be	AUX
ejpam-6036	121	69	τ1τ2	τ1τ2	NOUN
ejpam-6036	121	70	-	-	ADJ
ejpam-6036	121	71	closed	closed	ADJ
ejpam-6036	121	72	in	in	ADP
ejpam-6036	121	73	x	x	PUNCT
ejpam-6036	121	74	for	for	ADP
ejpam-6036	121	75	each	each	DET
ejpam-6036	121	76	σ1σ2	σ1σ2	NUM
ejpam-6036	121	77	-	-	PUNCT
ejpam-6036	121	78	clopen	clopen	ADJ
ejpam-6036	121	79	set	set	NOUN
ejpam-6036	121	80	v	v	NOUN
ejpam-6036	121	81	of	of	ADP
ejpam-6036	121	82	y	y	PROPN
ejpam-6036	121	83	;	;	PUNCT
ejpam-6036	121	84	(	(	PUNCT
ejpam-6036	121	85	4	4	X
ejpam-6036	121	86	)	)	PUNCT
ejpam-6036	121	87	f−1(v	f−1(v	NOUN
ejpam-6036	121	88	)	)	PUNCT
ejpam-6036	121	89	is	be	AUX
ejpam-6036	121	90	τ1τ2	τ1τ2	NOUN
ejpam-6036	121	91	-	-	ADJ
ejpam-6036	121	92	clopen	clopen	ADJ
ejpam-6036	121	93	in	in	ADP
ejpam-6036	121	94	x	x	PUNCT
ejpam-6036	121	95	for	for	ADP
ejpam-6036	121	96	each	each	DET
ejpam-6036	121	97	σ1σ2	σ1σ2	NUM
ejpam-6036	121	98	-	-	PUNCT
ejpam-6036	121	99	clopen	clopen	ADJ
ejpam-6036	121	100	set	set	NOUN
ejpam-6036	121	101	v	v	NOUN
ejpam-6036	121	102	of	of	ADP
ejpam-6036	121	103	y	y	PROPN
ejpam-6036	121	104	.	.	PUNCT
ejpam-6036	122	1	theorem	theorem	VERB
ejpam-6036	122	2	3	3	X
ejpam-6036	122	3	.	.	PUNCT
ejpam-6036	123	1	if	if	SCONJ
ejpam-6036	123	2	a	a	DET
ejpam-6036	123	3	function	function	NOUN
ejpam-6036	123	4	f	f	X
ejpam-6036	123	5	:	:	PUNCT
ejpam-6036	123	6	(	(	PUNCT
ejpam-6036	123	7	x	x	NOUN
ejpam-6036	123	8	,	,	PUNCT
ejpam-6036	123	9	τ1	τ1	NOUN
ejpam-6036	123	10	,	,	PUNCT
ejpam-6036	123	11	τ2	τ2	NOUN
ejpam-6036	123	12	)	)	PUNCT
ejpam-6036	123	13	→	→	SYM
ejpam-6036	123	14	(	(	PUNCT
ejpam-6036	123	15	y	y	PROPN
ejpam-6036	123	16	,	,	PUNCT
ejpam-6036	123	17	σ1	σ1	PROPN
ejpam-6036	123	18	,	,	PUNCT
ejpam-6036	123	19	σ2	σ2	NOUN
ejpam-6036	123	20	)	)	PUNCT
ejpam-6036	123	21	is	be	AUX
ejpam-6036	123	22	weakly	weakly	ADJ
ejpam-6036	123	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	123	24	,	,	PUNCT
ejpam-6036	123	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	123	26	,	,	PUNCT
ejpam-6036	123	27	then	then	ADV
ejpam-6036	123	28	f	f	PROPN
ejpam-6036	123	29	is	be	AUX
ejpam-6036	123	30	slightly	slightly	ADV
ejpam-6036	123	31	(	(	PUNCT
ejpam-6036	123	32	τ1	τ1	NOUN
ejpam-6036	123	33	,	,	PUNCT
ejpam-6036	123	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	123	35	.	.	PUNCT
ejpam-6036	124	1	proof	proof	NOUN
ejpam-6036	124	2	.	.	PUNCT
ejpam-6036	125	1	let	let	VERB
ejpam-6036	125	2	v	v	PART
ejpam-6036	125	3	be	be	AUX
ejpam-6036	125	4	any	any	DET
ejpam-6036	125	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	125	6	-	-	PUNCT
ejpam-6036	125	7	clopen	clopen	ADJ
ejpam-6036	125	8	set	set	NOUN
ejpam-6036	125	9	of	of	ADP
ejpam-6036	125	10	y	y	PROPN
ejpam-6036	125	11	.	.	PUNCT
ejpam-6036	126	1	if	if	SCONJ
ejpam-6036	126	2	we	we	PRON
ejpam-6036	126	3	put	put	VERB
ejpam-6036	126	4	k	k	PROPN
ejpam-6036	126	5	=	=	PUNCT
ejpam-6036	126	6	v	v	PROPN
ejpam-6036	126	7	,	,	PUNCT
ejpam-6036	126	8	then	then	ADV
ejpam-6036	126	9	by	by	ADP
ejpam-6036	126	10	the	the	DET
ejpam-6036	126	11	weak	weak	ADJ
ejpam-6036	126	12	contra(τ1	contra(τ1	NOUN
ejpam-6036	126	13	,	,	PUNCT
ejpam-6036	126	14	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6036	126	15	we	we	PRON
ejpam-6036	126	16	have	have	VERB
ejpam-6036	126	17	τ1τ2	τ1τ2	NOUN
ejpam-6036	126	18	-	-	ADJ
ejpam-6036	126	19	cl(f	cl(f	PRON
ejpam-6036	126	20	−1(v	−1(v	NOUN
ejpam-6036	126	21	)	)	PUNCT
ejpam-6036	126	22	)	)	PUNCT
ejpam-6036	127	1	⊆	⊆	NUM
ejpam-6036	127	2	f−1(v	f−1(v	NOUN
ejpam-6036	127	3	)	)	PUNCT
ejpam-6036	127	4	and	and	CCONJ
ejpam-6036	127	5	hence	hence	ADV
ejpam-6036	127	6	f−1(v	f−1(v	PROPN
ejpam-6036	127	7	)	)	PUNCT
ejpam-6036	127	8	is	be	AUX
ejpam-6036	127	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	127	10	-	-	ADJ
ejpam-6036	127	11	closed	closed	ADJ
ejpam-6036	127	12	in	in	ADP
ejpam-6036	127	13	x.	x.	NOUN
ejpam-6036	127	14	it	it	PRON
ejpam-6036	127	15	follows	follow	VERB
ejpam-6036	127	16	from	from	ADP
ejpam-6036	127	17	lemma	lemma	PROPN
ejpam-6036	127	18	6	6	NUM
ejpam-6036	127	19	that	that	SCONJ
ejpam-6036	127	20	f	f	PROPN
ejpam-6036	127	21	is	be	AUX
ejpam-6036	127	22	slightly	slightly	ADV
ejpam-6036	127	23	(	(	PUNCT
ejpam-6036	127	24	τ1	τ1	NOUN
ejpam-6036	127	25	,	,	PUNCT
ejpam-6036	127	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	127	27	.	.	PUNCT
ejpam-6036	128	1	definition	definition	NOUN
ejpam-6036	128	2	5	5	NUM
ejpam-6036	128	3	.	.	PUNCT
ejpam-6036	129	1	[	[	X
ejpam-6036	129	2	30	30	NUM
ejpam-6036	129	3	]	]	X
ejpam-6036	129	4	a	a	DET
ejpam-6036	129	5	function	function	NOUN
ejpam-6036	129	6	f	f	NOUN
ejpam-6036	129	7	:	:	PUNCT
ejpam-6036	129	8	(	(	PUNCT
ejpam-6036	129	9	x	x	NOUN
ejpam-6036	129	10	,	,	PUNCT
ejpam-6036	129	11	τ1	τ1	NOUN
ejpam-6036	129	12	,	,	PUNCT
ejpam-6036	129	13	τ2	τ2	NOUN
ejpam-6036	129	14	)	)	PUNCT
ejpam-6036	129	15	→	→	SYM
ejpam-6036	129	16	(	(	PUNCT
ejpam-6036	129	17	y	y	PROPN
ejpam-6036	129	18	,	,	PUNCT
ejpam-6036	129	19	σ1	σ1	PROPN
ejpam-6036	129	20	,	,	PUNCT
ejpam-6036	129	21	σ2	σ2	PROPN
ejpam-6036	129	22	)	)	PUNCT
ejpam-6036	129	23	is	be	AUX
ejpam-6036	129	24	said	say	VERB
ejpam-6036	129	25	to	to	PART
ejpam-6036	129	26	be	be	AUX
ejpam-6036	129	27	weakly	weakly	ADJ
ejpam-6036	129	28	(	(	PUNCT
ejpam-6036	129	29	τ1	τ1	NOUN
ejpam-6036	129	30	,	,	PUNCT
ejpam-6036	129	31	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	129	32	at	at	ADP
ejpam-6036	129	33	a	a	DET
ejpam-6036	129	34	point	point	NOUN
ejpam-6036	129	35	x	x	SYM
ejpam-6036	129	36	∈	∈	NOUN
ejpam-6036	129	37	x	x	PUNCT
ejpam-6036	129	38	if	if	SCONJ
ejpam-6036	129	39	for	for	ADP
ejpam-6036	129	40	each	each	DET
ejpam-6036	129	41	σ1σ2	σ1σ2	VERB
ejpam-6036	129	42	-	-	ADJ
ejpam-6036	129	43	open	open	ADJ
ejpam-6036	129	44	set	set	NOUN
ejpam-6036	129	45	v	v	NOUN
ejpam-6036	129	46	of	of	ADP
ejpam-6036	129	47	y	y	NOUN
ejpam-6036	129	48	containing	contain	VERB
ejpam-6036	129	49	f(x	f(x	PROPN
ejpam-6036	129	50	)	)	PUNCT
ejpam-6036	129	51	,	,	PUNCT
ejpam-6036	129	52	there	there	PRON
ejpam-6036	129	53	exists	exist	VERB
ejpam-6036	129	54	a	a	DET
ejpam-6036	129	55	τ1τ2	τ1τ2	NOUN
ejpam-6036	129	56	-	-	ADJ
ejpam-6036	129	57	open	open	ADJ
ejpam-6036	129	58	set	set	ADJ
ejpam-6036	129	59	u	u	NOUN
ejpam-6036	129	60	of	of	ADP
ejpam-6036	129	61	x	x	PUNCT
ejpam-6036	129	62	containing	contain	VERB
ejpam-6036	129	63	x	x	PUNCT
ejpam-6036	129	64	such	such	ADJ
ejpam-6036	129	65	that	that	DET
ejpam-6036	129	66	f(u	f(u	PROPN
ejpam-6036	129	67	)	)	PUNCT
ejpam-6036	129	68	⊆	⊆	NUM
ejpam-6036	129	69	σ1σ2	σ1σ2	NOUN
ejpam-6036	129	70	-	-	NUM
ejpam-6036	129	71	cl(v	cl(v	NOUN
ejpam-6036	129	72	)	)	PUNCT
ejpam-6036	129	73	.	.	PUNCT
ejpam-6036	130	1	a	a	DET
ejpam-6036	130	2	function	function	NOUN
ejpam-6036	130	3	f	f	NOUN
ejpam-6036	130	4	:	:	PUNCT
ejpam-6036	130	5	(	(	PUNCT
ejpam-6036	130	6	x	x	NOUN
ejpam-6036	130	7	,	,	PUNCT
ejpam-6036	130	8	τ1	τ1	NOUN
ejpam-6036	130	9	,	,	PUNCT
ejpam-6036	130	10	τ2	τ2	NOUN
ejpam-6036	130	11	)	)	PUNCT
ejpam-6036	130	12	→	→	SYM
ejpam-6036	130	13	(	(	PUNCT
ejpam-6036	130	14	y	y	PROPN
ejpam-6036	130	15	,	,	PUNCT
ejpam-6036	130	16	σ1	σ1	PROPN
ejpam-6036	130	17	,	,	PUNCT
ejpam-6036	130	18	σ2	σ2	PROPN
ejpam-6036	130	19	)	)	PUNCT
ejpam-6036	130	20	is	be	AUX
ejpam-6036	130	21	said	say	VERB
ejpam-6036	130	22	to	to	PART
ejpam-6036	130	23	be	be	AUX
ejpam-6036	130	24	weakly	weakly	ADJ
ejpam-6036	130	25	(	(	PUNCT
ejpam-6036	130	26	τ1	τ1	NOUN
ejpam-6036	130	27	,	,	PUNCT
ejpam-6036	130	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	130	29	if	if	SCONJ
ejpam-6036	130	30	f	f	PROPN
ejpam-6036	130	31	has	have	VERB
ejpam-6036	130	32	this	this	DET
ejpam-6036	130	33	property	property	NOUN
ejpam-6036	130	34	at	at	ADP
ejpam-6036	130	35	each	each	DET
ejpam-6036	130	36	point	point	NOUN
ejpam-6036	130	37	of	of	ADP
ejpam-6036	130	38	x.	x.	NOUN
ejpam-6036	130	39	lemma	lemma	PROPN
ejpam-6036	130	40	7	7	NUM
ejpam-6036	130	41	.	.	PUNCT
ejpam-6036	131	1	[	[	X
ejpam-6036	131	2	30	30	NUM
ejpam-6036	131	3	]	]	PUNCT
ejpam-6036	131	4	for	for	ADP
ejpam-6036	131	5	a	a	DET
ejpam-6036	131	6	function	function	NOUN
ejpam-6036	131	7	(	(	PUNCT
ejpam-6036	131	8	x	x	NOUN
ejpam-6036	131	9	,	,	PUNCT
ejpam-6036	131	10	τ1	τ1	NOUN
ejpam-6036	131	11	,	,	PUNCT
ejpam-6036	131	12	τ2	τ2	NOUN
ejpam-6036	131	13	)	)	PUNCT
ejpam-6036	131	14	→	→	SYM
ejpam-6036	131	15	(	(	PUNCT
ejpam-6036	131	16	y	y	PROPN
ejpam-6036	131	17	,	,	PUNCT
ejpam-6036	131	18	σ1	σ1	PROPN
ejpam-6036	131	19	,	,	PUNCT
ejpam-6036	131	20	σ2	σ2	NOUN
ejpam-6036	131	21	)	)	PUNCT
ejpam-6036	131	22	,	,	PUNCT
ejpam-6036	131	23	the	the	DET
ejpam-6036	131	24	following	follow	VERB
ejpam-6036	131	25	properties	property	NOUN
ejpam-6036	131	26	are	be	AUX
ejpam-6036	131	27	equivalent	equivalent	ADJ
ejpam-6036	131	28	:	:	PUNCT
ejpam-6036	131	29	(	(	PUNCT
ejpam-6036	131	30	1	1	X
ejpam-6036	131	31	)	)	PUNCT
ejpam-6036	131	32	f	f	PROPN
ejpam-6036	131	33	is	be	AUX
ejpam-6036	131	34	weakly	weakly	ADJ
ejpam-6036	131	35	(	(	PUNCT
ejpam-6036	131	36	τ1	τ1	NOUN
ejpam-6036	131	37	,	,	PUNCT
ejpam-6036	131	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	131	39	;	;	PUNCT
ejpam-6036	131	40	(	(	PUNCT
ejpam-6036	131	41	2	2	X
ejpam-6036	131	42	)	)	PUNCT
ejpam-6036	131	43	f−1(v	f−1(v	NOUN
ejpam-6036	131	44	)	)	PUNCT
ejpam-6036	132	1	⊆	⊆	X
ejpam-6036	132	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	132	3	-	-	NUM
ejpam-6036	132	4	int(f	int(f	PRON
ejpam-6036	132	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	132	6	-	-	PUNCT
ejpam-6036	132	7	cl(v	cl(v	NOUN
ejpam-6036	132	8	)	)	PUNCT
ejpam-6036	132	9	)	)	PUNCT
ejpam-6036	132	10	)	)	PUNCT
ejpam-6036	132	11	for	for	ADP
ejpam-6036	132	12	every	every	DET
ejpam-6036	132	13	σ1σ2	σ1σ2	NOUN
ejpam-6036	132	14	-	-	ADJ
ejpam-6036	132	15	open	open	ADJ
ejpam-6036	132	16	set	set	NOUN
ejpam-6036	132	17	v	v	NOUN
ejpam-6036	132	18	of	of	ADP
ejpam-6036	132	19	y	y	PROPN
ejpam-6036	132	20	;	;	PUNCT
ejpam-6036	132	21	(	(	PUNCT
ejpam-6036	132	22	3	3	X
ejpam-6036	132	23	)	)	PUNCT
ejpam-6036	132	24	τ1τ2	τ1τ2	NOUN
ejpam-6036	132	25	-	-	NOUN
ejpam-6036	132	26	cl(f	cl(f	NOUN
ejpam-6036	132	27	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	132	28	-	-	PUNCT
ejpam-6036	132	29	int(k	int(k	NUM
ejpam-6036	132	30	)	)	PUNCT
ejpam-6036	132	31	)	)	PUNCT
ejpam-6036	132	32	)	)	PUNCT
ejpam-6036	133	1	⊆	⊆	NUM
ejpam-6036	133	2	f−1(k	f−1(k	PROPN
ejpam-6036	133	3	)	)	PUNCT
ejpam-6036	133	4	for	for	ADP
ejpam-6036	133	5	every	every	DET
ejpam-6036	133	6	σ1σ2	σ1σ2	NUM
ejpam-6036	133	7	-	-	PUNCT
ejpam-6036	133	8	closed	closed	ADJ
ejpam-6036	133	9	set	set	NOUN
ejpam-6036	133	10	k	k	PROPN
ejpam-6036	133	11	of	of	ADP
ejpam-6036	133	12	y	y	PROPN
ejpam-6036	133	13	;	;	PUNCT
ejpam-6036	133	14	(	(	PUNCT
ejpam-6036	133	15	4	4	X
ejpam-6036	133	16	)	)	PUNCT
ejpam-6036	133	17	τ1τ2	τ1τ2	NOUN
ejpam-6036	133	18	-	-	NOUN
ejpam-6036	133	19	cl(f	cl(f	NOUN
ejpam-6036	133	20	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	133	21	-	-	PUNCT
ejpam-6036	133	22	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6036	133	23	-	-	PUNCT
ejpam-6036	133	24	cl(b	cl(b	NOUN
ejpam-6036	133	25	)	)	PUNCT
ejpam-6036	133	26	)	)	PUNCT
ejpam-6036	133	27	)	)	PUNCT
ejpam-6036	133	28	)	)	PUNCT
ejpam-6036	134	1	⊆	⊆	NUM
ejpam-6036	134	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	134	3	-	-	PUNCT
ejpam-6036	134	4	cl(b	cl(b	NOUN
ejpam-6036	134	5	)	)	PUNCT
ejpam-6036	134	6	)	)	PUNCT
ejpam-6036	134	7	for	for	ADP
ejpam-6036	134	8	every	every	DET
ejpam-6036	134	9	subset	subset	NOUN
ejpam-6036	134	10	b	b	PROPN
ejpam-6036	134	11	of	of	ADP
ejpam-6036	134	12	y	y	PROPN
ejpam-6036	134	13	;	;	PUNCT
ejpam-6036	134	14	(	(	PUNCT
ejpam-6036	134	15	5	5	X
ejpam-6036	134	16	)	)	PUNCT
ejpam-6036	134	17	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	134	18	-	-	PUNCT
ejpam-6036	134	19	int(b	int(b	NOUN
ejpam-6036	134	20	)	)	PUNCT
ejpam-6036	134	21	)	)	PUNCT
ejpam-6036	135	1	⊆	⊆	X
ejpam-6036	135	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	135	3	-	-	NUM
ejpam-6036	135	4	int(f	int(f	VERB
ejpam-6036	135	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	135	6	-	-	PUNCT
ejpam-6036	135	7	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6036	135	8	-	-	PUNCT
ejpam-6036	135	9	int(b	int(b	NOUN
ejpam-6036	135	10	)	)	PUNCT
ejpam-6036	135	11	)	)	PUNCT
ejpam-6036	135	12	)	)	PUNCT
ejpam-6036	135	13	)	)	PUNCT
ejpam-6036	135	14	for	for	ADP
ejpam-6036	135	15	every	every	DET
ejpam-6036	135	16	subset	subset	NOUN
ejpam-6036	135	17	b	b	PROPN
ejpam-6036	135	18	of	of	ADP
ejpam-6036	135	19	y	y	PROPN
ejpam-6036	135	20	;	;	PUNCT
ejpam-6036	135	21	(	(	PUNCT
ejpam-6036	135	22	6	6	X
ejpam-6036	135	23	)	)	PUNCT
ejpam-6036	135	24	τ1τ2	τ1τ2	NOUN
ejpam-6036	135	25	-	-	NOUN
ejpam-6036	135	26	cl(f	cl(f	PRON
ejpam-6036	135	27	−1(v	−1(v	NOUN
ejpam-6036	135	28	)	)	PUNCT
ejpam-6036	135	29	)	)	PUNCT
ejpam-6036	136	1	⊆	⊆	NUM
ejpam-6036	136	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	136	3	-	-	PUNCT
ejpam-6036	136	4	cl(v	cl(v	NOUN
ejpam-6036	136	5	)	)	PUNCT
ejpam-6036	136	6	)	)	PUNCT
ejpam-6036	136	7	for	for	ADP
ejpam-6036	136	8	every	every	DET
ejpam-6036	136	9	σ1σ2	σ1σ2	NOUN
ejpam-6036	136	10	-	-	ADJ
ejpam-6036	136	11	open	open	ADJ
ejpam-6036	136	12	set	set	NOUN
ejpam-6036	136	13	v	v	NOUN
ejpam-6036	136	14	of	of	ADP
ejpam-6036	136	15	y	y	PROPN
ejpam-6036	136	16	.	.	PUNCT
ejpam-6036	137	1	definition	definition	NOUN
ejpam-6036	137	2	6	6	NUM
ejpam-6036	137	3	.	.	PUNCT
ejpam-6036	138	1	[	[	X
ejpam-6036	138	2	39	39	NUM
ejpam-6036	138	3	]	]	PUNCT
ejpam-6036	138	4	a	a	DET
ejpam-6036	138	5	bitopological	bitopological	ADJ
ejpam-6036	138	6	space	space	NOUN
ejpam-6036	138	7	(	(	PUNCT
ejpam-6036	138	8	x	x	NOUN
ejpam-6036	138	9	,	,	PUNCT
ejpam-6036	138	10	τ1	τ1	NOUN
ejpam-6036	138	11	,	,	PUNCT
ejpam-6036	138	12	τ2	τ2	NOUN
ejpam-6036	138	13	)	)	PUNCT
ejpam-6036	138	14	is	be	AUX
ejpam-6036	138	15	said	say	VERB
ejpam-6036	138	16	to	to	PART
ejpam-6036	138	17	be	be	AUX
ejpam-6036	138	18	(	(	PUNCT
ejpam-6036	138	19	τ1	τ1	NOUN
ejpam-6036	138	20	,	,	PUNCT
ejpam-6036	138	21	τ2)-extremally	τ2)-extremally	ADV
ejpam-6036	138	22	disconnected	disconnected	ADJ
ejpam-6036	138	23	if	if	SCONJ
ejpam-6036	138	24	the	the	DET
ejpam-6036	138	25	τ1τ2	τ1τ2	NOUN
ejpam-6036	138	26	-	-	NOUN
ejpam-6036	138	27	closure	closure	NOUN
ejpam-6036	138	28	of	of	ADP
ejpam-6036	138	29	every	every	DET
ejpam-6036	138	30	τ1τ2	τ1τ2	NOUN
ejpam-6036	138	31	-	-	ADJ
ejpam-6036	138	32	open	open	ADJ
ejpam-6036	138	33	set	set	ADJ
ejpam-6036	138	34	u	u	NOUN
ejpam-6036	138	35	of	of	ADP
ejpam-6036	138	36	x	x	SYM
ejpam-6036	138	37	is	be	AUX
ejpam-6036	138	38	τ1τ2	τ1τ2	VERB
ejpam-6036	138	39	-	-	ADJ
ejpam-6036	138	40	open	open	ADJ
ejpam-6036	138	41	.	.	PUNCT
ejpam-6036	139	1	b.	b.	PROPN
ejpam-6036	139	2	kong	kong	PROPN
ejpam-6036	139	3	-	-	PUNCT
ejpam-6036	139	4	ied	ied	PROPN
ejpam-6036	139	5	,	,	PUNCT
ejpam-6036	139	6	s.	s.	PROPN
ejpam-6036	139	7	sompong	sompong	PROPN
ejpam-6036	139	8	,	,	PUNCT
ejpam-6036	139	9	c.	c.	PROPN
ejpam-6036	139	10	boonpok	boonpok	PROPN
ejpam-6036	139	11	/	/	SYM
ejpam-6036	139	12	eur	eur	PROPN
ejpam-6036	139	13	.	.	PUNCT
ejpam-6036	140	1	j.	j.	PROPN
ejpam-6036	140	2	pure	pure	PROPN
ejpam-6036	140	3	appl	appl	PROPN
ejpam-6036	140	4	.	.	PROPN
ejpam-6036	140	5	math	math	PROPN
ejpam-6036	140	6	,	,	PUNCT
ejpam-6036	140	7	18	18	NUM
ejpam-6036	140	8	(	(	PUNCT
ejpam-6036	140	9	2	2	NUM
ejpam-6036	140	10	)	)	PUNCT
ejpam-6036	140	11	(	(	PUNCT
ejpam-6036	140	12	2025	2025	NUM
ejpam-6036	140	13	)	)	PUNCT
ejpam-6036	140	14	,	,	PUNCT
ejpam-6036	140	15	6036	6036	NUM
ejpam-6036	140	16	6	6	NUM
ejpam-6036	140	17	of	of	ADP
ejpam-6036	140	18	11	11	NUM
ejpam-6036	140	19	theorem	theorem	NOUN
ejpam-6036	140	20	4	4	NUM
ejpam-6036	140	21	.	.	PUNCT
ejpam-6036	141	1	if	if	SCONJ
ejpam-6036	141	2	f	f	PROPN
ejpam-6036	141	3	:	:	PUNCT
ejpam-6036	141	4	(	(	PUNCT
ejpam-6036	141	5	x	x	NOUN
ejpam-6036	141	6	,	,	PUNCT
ejpam-6036	141	7	τ1	τ1	NOUN
ejpam-6036	141	8	,	,	PUNCT
ejpam-6036	141	9	τ2	τ2	NOUN
ejpam-6036	141	10	)	)	PUNCT
ejpam-6036	141	11	→	→	SYM
ejpam-6036	141	12	(	(	PUNCT
ejpam-6036	141	13	y	y	PROPN
ejpam-6036	141	14	,	,	PUNCT
ejpam-6036	141	15	σ1	σ1	PROPN
ejpam-6036	141	16	,	,	PUNCT
ejpam-6036	141	17	σ2	σ2	NOUN
ejpam-6036	141	18	)	)	PUNCT
ejpam-6036	141	19	is	be	AUX
ejpam-6036	141	20	weakly	weakly	ADJ
ejpam-6036	141	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	141	22	,	,	PUNCT
ejpam-6036	141	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	141	24	and	and	CCONJ
ejpam-6036	141	25	(	(	PUNCT
ejpam-6036	141	26	y	y	PROPN
ejpam-6036	141	27	,	,	PUNCT
ejpam-6036	141	28	σ1	σ1	PROPN
ejpam-6036	141	29	,	,	PUNCT
ejpam-6036	141	30	σ2	σ2	PROPN
ejpam-6036	141	31	)	)	PUNCT
ejpam-6036	141	32	is	be	AUX
ejpam-6036	141	33	(	(	PUNCT
ejpam-6036	141	34	σ1	σ1	NOUN
ejpam-6036	141	35	,	,	PUNCT
ejpam-6036	141	36	σ2)-extremally	σ2)-extremally	ADV
ejpam-6036	141	37	disconnected	disconnect	VERB
ejpam-6036	141	38	,	,	PUNCT
ejpam-6036	141	39	then	then	ADV
ejpam-6036	141	40	f	f	PROPN
ejpam-6036	141	41	is	be	AUX
ejpam-6036	141	42	weakly	weakly	ADJ
ejpam-6036	141	43	(	(	PUNCT
ejpam-6036	141	44	τ1	τ1	NOUN
ejpam-6036	141	45	,	,	PUNCT
ejpam-6036	141	46	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	141	47	.	.	PUNCT
ejpam-6036	142	1	proof	proof	NOUN
ejpam-6036	142	2	.	.	PUNCT
ejpam-6036	143	1	let	let	VERB
ejpam-6036	143	2	v	v	PART
ejpam-6036	143	3	be	be	AUX
ejpam-6036	143	4	any	any	DET
ejpam-6036	143	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	143	6	-	-	ADJ
ejpam-6036	143	7	open	open	ADJ
ejpam-6036	143	8	set	set	NOUN
ejpam-6036	143	9	of	of	ADP
ejpam-6036	143	10	y	y	PROPN
ejpam-6036	143	11	.	.	PUNCT
ejpam-6036	144	1	since	since	SCONJ
ejpam-6036	144	2	(	(	PUNCT
ejpam-6036	144	3	y	y	PROPN
ejpam-6036	144	4	,	,	PUNCT
ejpam-6036	144	5	σ1	σ1	PROPN
ejpam-6036	144	6	,	,	PUNCT
ejpam-6036	144	7	σ2	σ2	PROPN
ejpam-6036	144	8	)	)	PUNCT
ejpam-6036	144	9	is	be	AUX
ejpam-6036	144	10	(	(	PUNCT
ejpam-6036	144	11	σ1	σ1	NOUN
ejpam-6036	144	12	,	,	PUNCT
ejpam-6036	144	13	σ2)-extremally	σ2)-extremally	ADV
ejpam-6036	144	14	disconnected	disconnect	VERB
ejpam-6036	144	15	,	,	PUNCT
ejpam-6036	144	16	σ1σ2	σ1σ2	NOUN
ejpam-6036	144	17	-	-	NUM
ejpam-6036	144	18	cl(v	cl(v	NOUN
ejpam-6036	144	19	)	)	PUNCT
ejpam-6036	144	20	is	be	AUX
ejpam-6036	144	21	σ1σ2	σ1σ2	NOUN
ejpam-6036	144	22	-	-	ADJ
ejpam-6036	144	23	open	open	ADJ
ejpam-6036	144	24	.	.	PUNCT
ejpam-6036	145	1	since	since	SCONJ
ejpam-6036	145	2	f	f	PROPN
ejpam-6036	145	3	weakly	weakly	ADJ
ejpam-6036	145	4	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	145	5	,	,	PUNCT
ejpam-6036	145	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	145	7	,	,	PUNCT
ejpam-6036	145	8	τ1τ2	τ1τ2	NOUN
ejpam-6036	145	9	-	-	NOUN
ejpam-6036	145	10	cl(f	cl(f	PRON
ejpam-6036	145	11	−1(v	−1(v	NOUN
ejpam-6036	145	12	)	)	PUNCT
ejpam-6036	145	13	)	)	PUNCT
ejpam-6036	146	1	⊆	⊆	X
ejpam-6036	146	2	τ1τ2	τ1τ2	NOUN
ejpam-6036	146	3	-	-	ADJ
ejpam-6036	146	4	cl(f	cl(f	NOUN
ejpam-6036	146	5	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	146	6	-	-	PUNCT
ejpam-6036	146	7	cl(v	cl(v	NOUN
ejpam-6036	146	8	)	)	PUNCT
ejpam-6036	146	9	)	)	PUNCT
ejpam-6036	146	10	)	)	PUNCT
ejpam-6036	146	11	⊆	⊆	NUM
ejpam-6036	146	12	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	146	13	-	-	PUNCT
ejpam-6036	146	14	cl(v	cl(v	NOUN
ejpam-6036	146	15	)	)	PUNCT
ejpam-6036	146	16	)	)	PUNCT
ejpam-6036	146	17	.	.	PUNCT
ejpam-6036	147	1	thus	thus	ADV
ejpam-6036	147	2	,	,	PUNCT
ejpam-6036	147	3	τ1τ2	τ1τ2	NOUN
ejpam-6036	147	4	-	-	NOUN
ejpam-6036	147	5	cl(f	cl(f	PRON
ejpam-6036	147	6	−1(v	−1(v	NOUN
ejpam-6036	147	7	)	)	PUNCT
ejpam-6036	147	8	)	)	PUNCT
ejpam-6036	147	9	⊆	⊆	NUM
ejpam-6036	147	10	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6036	147	11	-	-	PUNCT
ejpam-6036	147	12	cl(v	cl(v	NOUN
ejpam-6036	147	13	)	)	PUNCT
ejpam-6036	147	14	)	)	PUNCT
ejpam-6036	147	15	for	for	ADP
ejpam-6036	147	16	every	every	DET
ejpam-6036	147	17	σ1σ2	σ1σ2	NOUN
ejpam-6036	147	18	-	-	ADJ
ejpam-6036	147	19	open	open	ADJ
ejpam-6036	147	20	set	set	NOUN
ejpam-6036	147	21	v	v	NOUN
ejpam-6036	147	22	of	of	ADP
ejpam-6036	147	23	y	y	PROPN
ejpam-6036	147	24	.	.	PUNCT
ejpam-6036	148	1	it	it	PRON
ejpam-6036	148	2	follows	follow	VERB
ejpam-6036	148	3	from	from	ADP
ejpam-6036	148	4	lemma	lemma	PROPN
ejpam-6036	148	5	7	7	NUM
ejpam-6036	148	6	that	that	PRON
ejpam-6036	148	7	f	f	PROPN
ejpam-6036	148	8	is	be	AUX
ejpam-6036	148	9	weakly	weakly	ADJ
ejpam-6036	148	10	(	(	PUNCT
ejpam-6036	148	11	τ1	τ1	NOUN
ejpam-6036	148	12	,	,	PUNCT
ejpam-6036	148	13	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6036	148	14	.	.	PUNCT
ejpam-6036	149	1	recall	recall	VERB
ejpam-6036	149	2	that	that	SCONJ
ejpam-6036	149	3	a	a	DET
ejpam-6036	149	4	subset	subset	NOUN
ejpam-6036	149	5	a	a	PRON
ejpam-6036	149	6	of	of	ADP
ejpam-6036	149	7	a	a	DET
ejpam-6036	149	8	bitopological	bitopological	ADJ
ejpam-6036	149	9	space	space	NOUN
ejpam-6036	149	10	(	(	PUNCT
ejpam-6036	149	11	x	x	NOUN
ejpam-6036	149	12	,	,	PUNCT
ejpam-6036	149	13	τ1	τ1	NOUN
ejpam-6036	149	14	,	,	PUNCT
ejpam-6036	149	15	τ2	τ2	NOUN
ejpam-6036	149	16	)	)	PUNCT
ejpam-6036	149	17	is	be	AUX
ejpam-6036	149	18	said	say	VERB
ejpam-6036	149	19	to	to	PART
ejpam-6036	149	20	be	be	AUX
ejpam-6036	149	21	generalized	generalize	VERB
ejpam-6036	149	22	(	(	PUNCT
ejpam-6036	149	23	τ1	τ1	NOUN
ejpam-6036	149	24	,	,	PUNCT
ejpam-6036	149	25	τ2)-closed	τ2)-close	VERB
ejpam-6036	149	26	(	(	PUNCT
ejpam-6036	149	27	briefly	briefly	ADV
ejpam-6036	149	28	,	,	PUNCT
ejpam-6036	149	29	g-(τ1	g-(τ1	PROPN
ejpam-6036	149	30	,	,	PUNCT
ejpam-6036	149	31	τ2)-closed	τ2)-closed	ADJ
ejpam-6036	149	32	)	)	PUNCT
ejpam-6036	150	1	[	[	X
ejpam-6036	150	2	43	43	NUM
ejpam-6036	150	3	]	]	X
ejpam-6036	150	4	if	if	SCONJ
ejpam-6036	150	5	τ1τ2	τ1τ2	NOUN
ejpam-6036	150	6	-	-	NUM
ejpam-6036	150	7	cl(a	cl(a	NUM
ejpam-6036	150	8	)	)	PUNCT
ejpam-6036	150	9	⊆	⊆	NUM
ejpam-6036	150	10	u	u	NOUN
ejpam-6036	150	11	whenever	whenever	SCONJ
ejpam-6036	150	12	a	a	DET
ejpam-6036	150	13	⊆	⊆	NUM
ejpam-6036	150	14	u	u	NOUN
ejpam-6036	150	15	and	and	CCONJ
ejpam-6036	150	16	u	u	NOUN
ejpam-6036	150	17	is	be	AUX
ejpam-6036	150	18	τ1τ2	τ1τ2	VERB
ejpam-6036	150	19	-	-	ADJ
ejpam-6036	150	20	open	open	ADJ
ejpam-6036	150	21	.	.	PUNCT
ejpam-6036	151	1	definition	definition	NOUN
ejpam-6036	151	2	7	7	NUM
ejpam-6036	151	3	.	.	PUNCT
ejpam-6036	152	1	a	a	DET
ejpam-6036	152	2	function	function	NOUN
ejpam-6036	152	3	f	f	NOUN
ejpam-6036	152	4	:	:	PUNCT
ejpam-6036	152	5	(	(	PUNCT
ejpam-6036	152	6	x	x	NOUN
ejpam-6036	152	7	,	,	PUNCT
ejpam-6036	152	8	τ1	τ1	NOUN
ejpam-6036	152	9	,	,	PUNCT
ejpam-6036	152	10	τ2	τ2	NOUN
ejpam-6036	152	11	)	)	PUNCT
ejpam-6036	152	12	→	→	SYM
ejpam-6036	152	13	(	(	PUNCT
ejpam-6036	152	14	y	y	PROPN
ejpam-6036	152	15	,	,	PUNCT
ejpam-6036	152	16	σ1	σ1	PROPN
ejpam-6036	152	17	,	,	PUNCT
ejpam-6036	152	18	σ2	σ2	PROPN
ejpam-6036	152	19	)	)	PUNCT
ejpam-6036	152	20	is	be	AUX
ejpam-6036	152	21	said	say	VERB
ejpam-6036	152	22	to	to	PART
ejpam-6036	152	23	be	be	AUX
ejpam-6036	152	24	g-(τ1	g-(τ1	PROPN
ejpam-6036	152	25	,	,	PUNCT
ejpam-6036	152	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	152	27	if	if	SCONJ
ejpam-6036	152	28	f−1(k	f−1(k	NOUN
ejpam-6036	152	29	)	)	PUNCT
ejpam-6036	152	30	is	be	AUX
ejpam-6036	152	31	g-(τ1	g-(τ1	PROPN
ejpam-6036	152	32	,	,	PUNCT
ejpam-6036	152	33	τ2)-closed	τ2)-close	VERB
ejpam-6036	152	34	in	in	ADP
ejpam-6036	152	35	x	x	PUNCT
ejpam-6036	152	36	for	for	ADP
ejpam-6036	152	37	every	every	DET
ejpam-6036	152	38	σ1σ2	σ1σ2	NUM
ejpam-6036	152	39	-	-	PUNCT
ejpam-6036	152	40	closed	closed	ADJ
ejpam-6036	152	41	set	set	NOUN
ejpam-6036	152	42	k	k	PROPN
ejpam-6036	152	43	of	of	ADP
ejpam-6036	152	44	y	y	PROPN
ejpam-6036	152	45	.	.	PUNCT
ejpam-6036	153	1	definition	definition	NOUN
ejpam-6036	153	2	8	8	NUM
ejpam-6036	153	3	.	.	PUNCT
ejpam-6036	154	1	a	a	DET
ejpam-6036	154	2	function	function	NOUN
ejpam-6036	154	3	f	f	NOUN
ejpam-6036	154	4	:	:	PUNCT
ejpam-6036	154	5	(	(	PUNCT
ejpam-6036	154	6	x	x	NOUN
ejpam-6036	154	7	,	,	PUNCT
ejpam-6036	154	8	τ1	τ1	NOUN
ejpam-6036	154	9	,	,	PUNCT
ejpam-6036	154	10	τ2	τ2	NOUN
ejpam-6036	154	11	)	)	PUNCT
ejpam-6036	154	12	→	→	SYM
ejpam-6036	154	13	(	(	PUNCT
ejpam-6036	154	14	y	y	PROPN
ejpam-6036	154	15	,	,	PUNCT
ejpam-6036	154	16	σ1	σ1	PROPN
ejpam-6036	154	17	,	,	PUNCT
ejpam-6036	154	18	σ2	σ2	PROPN
ejpam-6036	154	19	)	)	PUNCT
ejpam-6036	154	20	is	be	AUX
ejpam-6036	154	21	said	say	VERB
ejpam-6036	154	22	to	to	PART
ejpam-6036	154	23	be	be	AUX
ejpam-6036	154	24	approximately	approximately	ADV
ejpam-6036	154	25	(	(	PUNCT
ejpam-6036	154	26	τ1	τ1	NOUN
ejpam-6036	154	27	,	,	PUNCT
ejpam-6036	154	28	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	154	29	if	if	SCONJ
ejpam-6036	154	30	τ1τ2	τ1τ2	NOUN
ejpam-6036	154	31	-	-	PUNCT
ejpam-6036	154	32	cl(k	cl(k	NOUN
ejpam-6036	154	33	)	)	PUNCT
ejpam-6036	155	1	⊆	⊆	NUM
ejpam-6036	155	2	f−1(v	f−1(v	NOUN
ejpam-6036	155	3	)	)	PUNCT
ejpam-6036	155	4	whenever	whenever	SCONJ
ejpam-6036	155	5	v	v	NOUN
ejpam-6036	155	6	is	be	AUX
ejpam-6036	155	7	σ1σ2	σ1σ2	NOUN
ejpam-6036	155	8	-	-	ADJ
ejpam-6036	155	9	open	open	ADJ
ejpam-6036	155	10	in	in	ADP
ejpam-6036	155	11	y	y	PROPN
ejpam-6036	155	12	and	and	CCONJ
ejpam-6036	155	13	k	k	PROPN
ejpam-6036	155	14	is	be	AUX
ejpam-6036	155	15	g-(τ1	g-(τ1	PROPN
ejpam-6036	155	16	,	,	PUNCT
ejpam-6036	155	17	τ2)closed	τ2)close	VERB
ejpam-6036	155	18	in	in	ADP
ejpam-6036	155	19	x	x	INTJ
ejpam-6036	155	20	such	such	ADJ
ejpam-6036	155	21	that	that	SCONJ
ejpam-6036	155	22	k	k	PROPN
ejpam-6036	155	23	⊆	⊆	NUM
ejpam-6036	155	24	f−1(v	f−1(v	NOUN
ejpam-6036	155	25	)	)	PUNCT
ejpam-6036	155	26	.	.	PUNCT
ejpam-6036	156	1	theorem	theorem	NOUN
ejpam-6036	156	2	5	5	NUM
ejpam-6036	156	3	.	.	PUNCT
ejpam-6036	157	1	if	if	SCONJ
ejpam-6036	157	2	f	f	PROPN
ejpam-6036	157	3	:	:	PUNCT
ejpam-6036	157	4	(	(	PUNCT
ejpam-6036	157	5	x	x	NOUN
ejpam-6036	157	6	,	,	PUNCT
ejpam-6036	157	7	τ1	τ1	NOUN
ejpam-6036	157	8	,	,	PUNCT
ejpam-6036	157	9	τ2	τ2	NOUN
ejpam-6036	157	10	)	)	PUNCT
ejpam-6036	157	11	→	→	SYM
ejpam-6036	157	12	(	(	PUNCT
ejpam-6036	157	13	y	y	PROPN
ejpam-6036	157	14	,	,	PUNCT
ejpam-6036	157	15	σ1	σ1	PROPN
ejpam-6036	157	16	,	,	PUNCT
ejpam-6036	157	17	σ2	σ2	PROPN
ejpam-6036	157	18	)	)	PUNCT
ejpam-6036	157	19	is	be	AUX
ejpam-6036	157	20	g-(τ1	g-(τ1	PROPN
ejpam-6036	157	21	,	,	PUNCT
ejpam-6036	157	22	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	157	23	and	and	CCONJ
ejpam-6036	157	24	approximately	approximately	ADV
ejpam-6036	157	25	(	(	PUNCT
ejpam-6036	157	26	τ1	τ1	NOUN
ejpam-6036	157	27	,	,	PUNCT
ejpam-6036	157	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	157	29	,	,	PUNCT
ejpam-6036	157	30	then	then	ADV
ejpam-6036	157	31	f	f	PROPN
ejpam-6036	157	32	is	be	AUX
ejpam-6036	157	33	weakly	weakly	ADJ
ejpam-6036	157	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	157	35	,	,	PUNCT
ejpam-6036	157	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	157	37	.	.	PUNCT
ejpam-6036	158	1	proof	proof	NOUN
ejpam-6036	158	2	.	.	PUNCT
ejpam-6036	159	1	let	let	VERB
ejpam-6036	159	2	v	v	PART
ejpam-6036	159	3	be	be	AUX
ejpam-6036	159	4	any	any	DET
ejpam-6036	159	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	159	6	-	-	ADJ
ejpam-6036	159	7	open	open	ADJ
ejpam-6036	159	8	set	set	NOUN
ejpam-6036	159	9	of	of	ADP
ejpam-6036	159	10	y	y	PROPN
ejpam-6036	159	11	and	and	CCONJ
ejpam-6036	159	12	k	k	PROPN
ejpam-6036	159	13	be	be	AUX
ejpam-6036	159	14	any	any	DET
ejpam-6036	159	15	σ1σ2	σ1σ2	NUM
ejpam-6036	159	16	-	-	PUNCT
ejpam-6036	159	17	closed	closed	ADJ
ejpam-6036	159	18	set	set	NOUN
ejpam-6036	159	19	of	of	ADP
ejpam-6036	159	20	y	y	PRON
ejpam-6036	159	21	such	such	ADJ
ejpam-6036	159	22	that	that	SCONJ
ejpam-6036	159	23	k	k	PROPN
ejpam-6036	159	24	⊆	⊆	NUM
ejpam-6036	159	25	v	v	NOUN
ejpam-6036	159	26	.	.	PUNCT
ejpam-6036	160	1	since	since	SCONJ
ejpam-6036	160	2	f	f	PROPN
ejpam-6036	160	3	is	be	AUX
ejpam-6036	160	4	g-(τ1	g-(τ1	PROPN
ejpam-6036	160	5	,	,	PUNCT
ejpam-6036	160	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	160	7	,	,	PUNCT
ejpam-6036	160	8	f−1(k	f−1(k	PROPN
ejpam-6036	160	9	)	)	PUNCT
ejpam-6036	160	10	is	be	AUX
ejpam-6036	160	11	g-(τ1	g-(τ1	PROPN
ejpam-6036	160	12	,	,	PUNCT
ejpam-6036	160	13	τ2)-closed	τ2)-close	VERB
ejpam-6036	160	14	in	in	ADP
ejpam-6036	160	15	x.	x.	NOUN
ejpam-6036	160	16	since	since	SCONJ
ejpam-6036	160	17	f−1(k	f−1(k	PROPN
ejpam-6036	160	18	)	)	PUNCT
ejpam-6036	160	19	⊆	⊆	NUM
ejpam-6036	160	20	f−1(v	f−1(v	NOUN
ejpam-6036	160	21	)	)	PUNCT
ejpam-6036	160	22	and	and	CCONJ
ejpam-6036	160	23	f	f	PROPN
ejpam-6036	160	24	is	be	AUX
ejpam-6036	160	25	approximately	approximately	ADV
ejpam-6036	160	26	(	(	PUNCT
ejpam-6036	160	27	τ1	τ1	NOUN
ejpam-6036	160	28	,	,	PUNCT
ejpam-6036	160	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	160	30	,	,	PUNCT
ejpam-6036	160	31	τ1τ2	τ1τ2	NOUN
ejpam-6036	160	32	-	-	NOUN
ejpam-6036	160	33	cl(k	cl(k	NOUN
ejpam-6036	160	34	)	)	PUNCT
ejpam-6036	160	35	⊆	⊆	NUM
ejpam-6036	160	36	f−1(v	f−1(v	NOUN
ejpam-6036	160	37	)	)	PUNCT
ejpam-6036	160	38	.	.	PUNCT
ejpam-6036	161	1	this	this	PRON
ejpam-6036	161	2	shows	show	VERB
ejpam-6036	161	3	that	that	SCONJ
ejpam-6036	161	4	f	f	PROPN
ejpam-6036	161	5	is	be	AUX
ejpam-6036	161	6	weakly	weakly	ADJ
ejpam-6036	161	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	161	8	,	,	PUNCT
ejpam-6036	161	9	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6036	161	10	.	.	PUNCT
ejpam-6036	162	1	theorem	theorem	VERB
ejpam-6036	162	2	6	6	NUM
ejpam-6036	162	3	.	.	PUNCT
ejpam-6036	163	1	if	if	SCONJ
ejpam-6036	163	2	f	f	PROPN
ejpam-6036	163	3	:	:	PUNCT
ejpam-6036	163	4	(	(	PUNCT
ejpam-6036	163	5	x	x	NOUN
ejpam-6036	163	6	,	,	PUNCT
ejpam-6036	163	7	τ1	τ1	NOUN
ejpam-6036	163	8	,	,	PUNCT
ejpam-6036	163	9	τ2	τ2	NOUN
ejpam-6036	163	10	)	)	PUNCT
ejpam-6036	163	11	→	→	SYM
ejpam-6036	163	12	(	(	PUNCT
ejpam-6036	163	13	y	y	PROPN
ejpam-6036	163	14	,	,	PUNCT
ejpam-6036	163	15	σ1	σ1	PROPN
ejpam-6036	163	16	,	,	PUNCT
ejpam-6036	163	17	σ2	σ2	NOUN
ejpam-6036	163	18	)	)	PUNCT
ejpam-6036	163	19	is	be	AUX
ejpam-6036	163	20	weakly	weakly	ADJ
ejpam-6036	163	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	163	22	,	,	PUNCT
ejpam-6036	163	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	163	24	and	and	CCONJ
ejpam-6036	163	25	f(k	f(k	VERB
ejpam-6036	163	26	)	)	PUNCT
ejpam-6036	163	27	is	be	AUX
ejpam-6036	163	28	σ1σ2	σ1σ2	NOUN
ejpam-6036	163	29	-	-	ADJ
ejpam-6036	163	30	closed	closed	ADJ
ejpam-6036	163	31	in	in	ADP
ejpam-6036	163	32	y	y	PROPN
ejpam-6036	163	33	for	for	ADP
ejpam-6036	163	34	every	every	DET
ejpam-6036	163	35	g-(τ1	g-(τ1	PROPN
ejpam-6036	163	36	,	,	PUNCT
ejpam-6036	164	1	τ2)-closed	τ2)-close	VERB
ejpam-6036	164	2	set	set	NOUN
ejpam-6036	164	3	k	k	PROPN
ejpam-6036	164	4	of	of	ADP
ejpam-6036	164	5	x	x	PROPN
ejpam-6036	164	6	,	,	PUNCT
ejpam-6036	164	7	then	then	ADV
ejpam-6036	164	8	f	f	PROPN
ejpam-6036	164	9	is	be	AUX
ejpam-6036	164	10	approximately	approximately	ADV
ejpam-6036	164	11	(	(	PUNCT
ejpam-6036	164	12	τ1	τ1	NOUN
ejpam-6036	164	13	,	,	PUNCT
ejpam-6036	164	14	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	164	15	.	.	PUNCT
ejpam-6036	165	1	proof	proof	NOUN
ejpam-6036	165	2	.	.	PUNCT
ejpam-6036	166	1	let	let	VERB
ejpam-6036	166	2	v	v	PART
ejpam-6036	166	3	be	be	AUX
ejpam-6036	166	4	any	any	DET
ejpam-6036	166	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	166	6	-	-	ADJ
ejpam-6036	166	7	open	open	ADJ
ejpam-6036	166	8	set	set	NOUN
ejpam-6036	166	9	of	of	ADP
ejpam-6036	166	10	y	y	PROPN
ejpam-6036	166	11	and	and	CCONJ
ejpam-6036	166	12	k	k	PROPN
ejpam-6036	166	13	be	be	AUX
ejpam-6036	166	14	any	any	DET
ejpam-6036	166	15	g-(τ1	g-(τ1	PROPN
ejpam-6036	166	16	,	,	PUNCT
ejpam-6036	166	17	τ2)-closed	τ2)-close	VERB
ejpam-6036	166	18	set	set	NOUN
ejpam-6036	166	19	of	of	ADP
ejpam-6036	166	20	x	x	PUNCT
ejpam-6036	166	21	such	such	ADJ
ejpam-6036	166	22	that	that	SCONJ
ejpam-6036	166	23	k	k	PROPN
ejpam-6036	166	24	⊆	⊆	NUM
ejpam-6036	166	25	f−1(v	f−1(v	NOUN
ejpam-6036	166	26	)	)	PUNCT
ejpam-6036	166	27	.	.	PUNCT
ejpam-6036	167	1	then	then	ADV
ejpam-6036	167	2	,	,	PUNCT
ejpam-6036	167	3	f(k	f(k	VERB
ejpam-6036	167	4	)	)	PUNCT
ejpam-6036	167	5	is	be	AUX
ejpam-6036	167	6	σ1σ2	σ1σ2	NOUN
ejpam-6036	167	7	-	-	PUNCT
ejpam-6036	167	8	closed	closed	ADJ
ejpam-6036	167	9	and	and	CCONJ
ejpam-6036	167	10	f(k	f(k	VERB
ejpam-6036	167	11	)	)	PUNCT
ejpam-6036	167	12	⊆	⊆	NUM
ejpam-6036	167	13	v	v	NOUN
ejpam-6036	167	14	.	.	PUNCT
ejpam-6036	168	1	since	since	SCONJ
ejpam-6036	168	2	f	f	PROPN
ejpam-6036	168	3	is	be	AUX
ejpam-6036	168	4	weakly	weakly	ADJ
ejpam-6036	168	5	contra(τ1	contra(τ1	NOUN
ejpam-6036	168	6	,	,	PUNCT
ejpam-6036	168	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	168	8	,	,	PUNCT
ejpam-6036	168	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	168	10	-	-	NOUN
ejpam-6036	168	11	cl(f	cl(f	NOUN
ejpam-6036	168	12	−1(f(k	−1(f(k	NOUN
ejpam-6036	168	13	)	)	PUNCT
ejpam-6036	168	14	)	)	PUNCT
ejpam-6036	168	15	)	)	PUNCT
ejpam-6036	169	1	⊆	⊆	NUM
ejpam-6036	169	2	f−1(v	f−1(v	NOUN
ejpam-6036	169	3	)	)	PUNCT
ejpam-6036	169	4	and	and	CCONJ
ejpam-6036	169	5	hence	hence	ADV
ejpam-6036	169	6	τ1τ2	τ1τ2	NOUN
ejpam-6036	169	7	-	-	PUNCT
ejpam-6036	169	8	cl(k	cl(k	NUM
ejpam-6036	169	9	)	)	PUNCT
ejpam-6036	169	10	⊆	⊆	NUM
ejpam-6036	169	11	f−1(v	f−1(v	NOUN
ejpam-6036	169	12	)	)	PUNCT
ejpam-6036	169	13	.	.	PUNCT
ejpam-6036	170	1	this	this	PRON
ejpam-6036	170	2	shows	show	VERB
ejpam-6036	170	3	that	that	SCONJ
ejpam-6036	170	4	f	f	PROPN
ejpam-6036	170	5	is	be	AUX
ejpam-6036	170	6	approximately	approximately	ADV
ejpam-6036	170	7	(	(	PUNCT
ejpam-6036	170	8	τ1	τ1	NOUN
ejpam-6036	170	9	,	,	PUNCT
ejpam-6036	170	10	τ2)-continuous	τ2)-continuous	PROPN
ejpam-6036	170	11	.	.	PUNCT
ejpam-6036	171	1	recall	recall	VERB
ejpam-6036	171	2	that	that	SCONJ
ejpam-6036	171	3	a	a	DET
ejpam-6036	171	4	bitopological	bitopological	ADJ
ejpam-6036	171	5	space	space	NOUN
ejpam-6036	171	6	(	(	PUNCT
ejpam-6036	171	7	x	x	NOUN
ejpam-6036	171	8	,	,	PUNCT
ejpam-6036	171	9	τ1	τ1	NOUN
ejpam-6036	171	10	,	,	PUNCT
ejpam-6036	171	11	τ2	τ2	NOUN
ejpam-6036	171	12	)	)	PUNCT
ejpam-6036	171	13	is	be	AUX
ejpam-6036	171	14	said	say	VERB
ejpam-6036	171	15	to	to	PART
ejpam-6036	171	16	be	be	AUX
ejpam-6036	171	17	τ1τ2	τ1τ2	NOUN
ejpam-6036	171	18	-	-	ADJ
ejpam-6036	171	19	compact	compact	ADJ
ejpam-6036	171	20	[	[	X
ejpam-6036	171	21	36	36	NUM
ejpam-6036	171	22	]	]	PUNCT
ejpam-6036	171	23	if	if	SCONJ
ejpam-6036	171	24	every	every	DET
ejpam-6036	171	25	cover	cover	NOUN
ejpam-6036	171	26	of	of	ADP
ejpam-6036	171	27	x	x	PUNCT
ejpam-6036	171	28	by	by	ADP
ejpam-6036	171	29	τ1τ2	τ1τ2	ADJ
ejpam-6036	171	30	-	-	ADJ
ejpam-6036	171	31	open	open	ADJ
ejpam-6036	171	32	sets	set	NOUN
ejpam-6036	171	33	of	of	ADP
ejpam-6036	171	34	x	x	PUNCT
ejpam-6036	171	35	has	have	VERB
ejpam-6036	171	36	a	a	DET
ejpam-6036	171	37	finite	finite	ADJ
ejpam-6036	171	38	subcover	subcover	PROPN
ejpam-6036	171	39	.	.	PUNCT
ejpam-6036	172	1	definition	definition	NOUN
ejpam-6036	172	2	9	9	NUM
ejpam-6036	172	3	.	.	PUNCT
ejpam-6036	173	1	[	[	X
ejpam-6036	173	2	41	41	NUM
ejpam-6036	173	3	]	]	PUNCT
ejpam-6036	173	4	a	a	DET
ejpam-6036	173	5	bitopological	bitopological	ADJ
ejpam-6036	173	6	space	space	NOUN
ejpam-6036	173	7	(	(	PUNCT
ejpam-6036	173	8	x	x	NOUN
ejpam-6036	173	9	,	,	PUNCT
ejpam-6036	173	10	τ1	τ1	NOUN
ejpam-6036	173	11	,	,	PUNCT
ejpam-6036	173	12	τ2	τ2	NOUN
ejpam-6036	173	13	)	)	PUNCT
ejpam-6036	173	14	is	be	AUX
ejpam-6036	173	15	said	say	VERB
ejpam-6036	173	16	to	to	PART
ejpam-6036	173	17	be	be	AUX
ejpam-6036	173	18	strongly	strongly	ADV
ejpam-6036	173	19	s	s	NOUN
ejpam-6036	173	20	-	-	PUNCT
ejpam-6036	173	21	τ1τ2	τ1τ2	ADJ
ejpam-6036	173	22	-	-	ADJ
ejpam-6036	173	23	closed	closed	ADJ
ejpam-6036	173	24	if	if	SCONJ
ejpam-6036	173	25	every	every	DET
ejpam-6036	173	26	cover	cover	NOUN
ejpam-6036	173	27	of	of	ADP
ejpam-6036	173	28	x	x	PUNCT
ejpam-6036	173	29	by	by	ADP
ejpam-6036	173	30	τ1τ2	τ1τ2	ADJ
ejpam-6036	173	31	-	-	ADJ
ejpam-6036	173	32	closed	closed	ADJ
ejpam-6036	173	33	sets	set	NOUN
ejpam-6036	173	34	of	of	ADP
ejpam-6036	173	35	x	x	PUNCT
ejpam-6036	173	36	has	have	VERB
ejpam-6036	173	37	a	a	DET
ejpam-6036	173	38	finite	finite	ADJ
ejpam-6036	173	39	subcover	subcover	PROPN
ejpam-6036	173	40	.	.	PUNCT
ejpam-6036	174	1	definition	definition	NOUN
ejpam-6036	174	2	10	10	NUM
ejpam-6036	174	3	.	.	PUNCT
ejpam-6036	175	1	a	a	DET
ejpam-6036	175	2	bitopological	bitopological	ADJ
ejpam-6036	175	3	space	space	NOUN
ejpam-6036	175	4	(	(	PUNCT
ejpam-6036	175	5	x	x	NOUN
ejpam-6036	175	6	,	,	PUNCT
ejpam-6036	175	7	τ1	τ1	NOUN
ejpam-6036	175	8	,	,	PUNCT
ejpam-6036	175	9	τ2	τ2	NOUN
ejpam-6036	175	10	)	)	PUNCT
ejpam-6036	175	11	is	be	AUX
ejpam-6036	175	12	called	call	VERB
ejpam-6036	175	13	a	a	DET
ejpam-6036	175	14	c	c	NOUN
ejpam-6036	175	15	-(τ1	-(τ1	X
ejpam-6036	175	16	,	,	PUNCT
ejpam-6036	175	17	τ2)-space	τ2)-space	X
ejpam-6036	175	18	if	if	SCONJ
ejpam-6036	175	19	for	for	ADP
ejpam-6036	175	20	every	every	DET
ejpam-6036	175	21	τ1τ2	τ1τ2	ADJ
ejpam-6036	175	22	-	-	ADJ
ejpam-6036	175	23	open	open	ADJ
ejpam-6036	175	24	set	set	ADJ
ejpam-6036	175	25	u	u	NOUN
ejpam-6036	175	26	of	of	ADP
ejpam-6036	175	27	x	x	PUNCT
ejpam-6036	175	28	and	and	CCONJ
ejpam-6036	175	29	each	each	DET
ejpam-6036	175	30	x	x	SYM
ejpam-6036	175	31	∈	∈	PROPN
ejpam-6036	175	32	u	u	NOUN
ejpam-6036	175	33	,	,	PUNCT
ejpam-6036	175	34	there	there	PRON
ejpam-6036	175	35	exists	exist	VERB
ejpam-6036	175	36	a	a	DET
ejpam-6036	175	37	τ1τ2	τ1τ2	ADJ
ejpam-6036	175	38	-	-	ADJ
ejpam-6036	175	39	closed	closed	ADJ
ejpam-6036	175	40	set	set	ADJ
ejpam-6036	175	41	f	f	PROPN
ejpam-6036	175	42	of	of	ADP
ejpam-6036	175	43	x	x	INTJ
ejpam-6036	176	1	such	such	ADJ
ejpam-6036	176	2	that	that	SCONJ
ejpam-6036	176	3	x	x	SYM
ejpam-6036	176	4	∈	∈	NOUN
ejpam-6036	176	5	f	f	PROPN
ejpam-6036	176	6	⊆	⊆	NUM
ejpam-6036	176	7	u	u	PROPN
ejpam-6036	176	8	.	.	PUNCT
ejpam-6036	176	9	b.	b.	PROPN
ejpam-6036	176	10	kong	kong	PROPN
ejpam-6036	176	11	-	-	PUNCT
ejpam-6036	176	12	ied	ied	PROPN
ejpam-6036	176	13	,	,	PUNCT
ejpam-6036	176	14	s.	s.	PROPN
ejpam-6036	176	15	sompong	sompong	PROPN
ejpam-6036	176	16	,	,	PUNCT
ejpam-6036	176	17	c.	c.	PROPN
ejpam-6036	176	18	boonpok	boonpok	PROPN
ejpam-6036	176	19	/	/	SYM
ejpam-6036	176	20	eur	eur	PROPN
ejpam-6036	176	21	.	.	PUNCT
ejpam-6036	177	1	j.	j.	PROPN
ejpam-6036	177	2	pure	pure	PROPN
ejpam-6036	177	3	appl	appl	PROPN
ejpam-6036	177	4	.	.	PROPN
ejpam-6036	177	5	math	math	PROPN
ejpam-6036	177	6	,	,	PUNCT
ejpam-6036	177	7	18	18	NUM
ejpam-6036	177	8	(	(	PUNCT
ejpam-6036	177	9	2	2	NUM
ejpam-6036	177	10	)	)	PUNCT
ejpam-6036	177	11	(	(	PUNCT
ejpam-6036	177	12	2025	2025	NUM
ejpam-6036	177	13	)	)	PUNCT
ejpam-6036	177	14	,	,	PUNCT
ejpam-6036	177	15	6036	6036	NUM
ejpam-6036	177	16	7	7	NUM
ejpam-6036	177	17	of	of	ADP
ejpam-6036	177	18	11	11	NUM
ejpam-6036	177	19	theorem	theorem	NOUN
ejpam-6036	177	20	7	7	NUM
ejpam-6036	177	21	.	.	PUNCT
ejpam-6036	178	1	let	let	VERB
ejpam-6036	178	2	f	f	NOUN
ejpam-6036	178	3	:	:	PUNCT
ejpam-6036	178	4	(	(	PUNCT
ejpam-6036	178	5	x	x	NOUN
ejpam-6036	178	6	,	,	PUNCT
ejpam-6036	178	7	τ1	τ1	NOUN
ejpam-6036	178	8	,	,	PUNCT
ejpam-6036	178	9	τ2	τ2	NOUN
ejpam-6036	178	10	)	)	PUNCT
ejpam-6036	178	11	→	→	SYM
ejpam-6036	178	12	(	(	PUNCT
ejpam-6036	178	13	y	y	PROPN
ejpam-6036	178	14	,	,	PUNCT
ejpam-6036	178	15	σ1	σ1	PROPN
ejpam-6036	178	16	,	,	PUNCT
ejpam-6036	178	17	σ2	σ2	PROPN
ejpam-6036	178	18	)	)	PUNCT
ejpam-6036	178	19	be	be	AUX
ejpam-6036	178	20	a	a	DET
ejpam-6036	178	21	weakly	weakly	ADJ
ejpam-6036	178	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	178	23	,	,	PUNCT
ejpam-6036	178	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	178	25	function	function	NOUN
ejpam-6036	178	26	and	and	CCONJ
ejpam-6036	178	27	(	(	PUNCT
ejpam-6036	178	28	y	y	PROPN
ejpam-6036	178	29	,	,	PUNCT
ejpam-6036	178	30	σ1	σ1	PROPN
ejpam-6036	178	31	,	,	PUNCT
ejpam-6036	178	32	σ2	σ2	PROPN
ejpam-6036	178	33	)	)	PUNCT
ejpam-6036	178	34	be	be	VERB
ejpam-6036	178	35	a	a	DET
ejpam-6036	178	36	c	c	NOUN
ejpam-6036	178	37	-(σ1	-(σ1	NOUN
ejpam-6036	178	38	,	,	PUNCT
ejpam-6036	178	39	σ2)-space	σ2)-space	NOUN
ejpam-6036	178	40	.	.	PUNCT
ejpam-6036	179	1	if	if	SCONJ
ejpam-6036	179	2	(	(	PUNCT
ejpam-6036	179	3	x	x	NOUN
ejpam-6036	179	4	,	,	PUNCT
ejpam-6036	179	5	τ1	τ1	NOUN
ejpam-6036	179	6	,	,	PUNCT
ejpam-6036	179	7	τ2	τ2	NOUN
ejpam-6036	179	8	)	)	PUNCT
ejpam-6036	179	9	is	be	AUX
ejpam-6036	179	10	strongly	strongly	ADV
ejpam-6036	179	11	s	s	NOUN
ejpam-6036	179	12	-	-	PUNCT
ejpam-6036	179	13	τ1τ2	τ1τ2	ADJ
ejpam-6036	179	14	-	-	ADJ
ejpam-6036	179	15	closed	closed	ADJ
ejpam-6036	179	16	,	,	PUNCT
ejpam-6036	179	17	then	then	ADV
ejpam-6036	179	18	f(x	f(x	PROPN
ejpam-6036	179	19	)	)	PUNCT
ejpam-6036	179	20	is	be	AUX
ejpam-6036	179	21	σ1σ2	σ1σ2	NOUN
ejpam-6036	179	22	-	-	ADJ
ejpam-6036	179	23	compact	compact	ADJ
ejpam-6036	179	24	.	.	PUNCT
ejpam-6036	180	1	proof	proof	NOUN
ejpam-6036	180	2	.	.	PUNCT
ejpam-6036	181	1	suppose	suppose	VERB
ejpam-6036	181	2	that	that	SCONJ
ejpam-6036	181	3	(	(	PUNCT
ejpam-6036	181	4	x	x	NOUN
ejpam-6036	181	5	,	,	PUNCT
ejpam-6036	181	6	τ1	τ1	NOUN
ejpam-6036	181	7	,	,	PUNCT
ejpam-6036	181	8	τ2	τ2	NOUN
ejpam-6036	181	9	)	)	PUNCT
ejpam-6036	181	10	is	be	AUX
ejpam-6036	181	11	strongly	strongly	ADV
ejpam-6036	181	12	s	s	NOUN
ejpam-6036	181	13	-	-	PUNCT
ejpam-6036	181	14	τ1τ2	τ1τ2	ADJ
ejpam-6036	181	15	-	-	ADJ
ejpam-6036	181	16	closed	closed	ADJ
ejpam-6036	181	17	.	.	PUNCT
ejpam-6036	182	1	let	let	VERB
ejpam-6036	182	2	{	{	PUNCT
ejpam-6036	182	3	vγ	vγ	NOUN
ejpam-6036	182	4	∈	∈	PROPN
ejpam-6036	182	5	∇	∇	X
ejpam-6036	182	6	}	}	PUNCT
ejpam-6036	182	7	be	be	AUX
ejpam-6036	182	8	any	any	DET
ejpam-6036	182	9	cover	cover	NOUN
ejpam-6036	182	10	of	of	ADP
ejpam-6036	182	11	f(x	f(x	NOUN
ejpam-6036	182	12	)	)	PUNCT
ejpam-6036	182	13	by	by	ADP
ejpam-6036	182	14	σ1σ2	σ1σ2	NOUN
ejpam-6036	182	15	-	-	PUNCT
ejpam-6036	182	16	open	open	ADJ
ejpam-6036	182	17	sets	set	NOUN
ejpam-6036	182	18	of	of	ADP
ejpam-6036	182	19	y	y	PROPN
ejpam-6036	182	20	.	.	PUNCT
ejpam-6036	183	1	for	for	ADP
ejpam-6036	183	2	each	each	DET
ejpam-6036	183	3	x	x	SYM
ejpam-6036	183	4	∈	∈	PROPN
ejpam-6036	183	5	x	x	NOUN
ejpam-6036	183	6	,	,	PUNCT
ejpam-6036	183	7	there	there	PRON
ejpam-6036	183	8	exists	exist	VERB
ejpam-6036	183	9	γ(x	γ(x	NOUN
ejpam-6036	183	10	)	)	PUNCT
ejpam-6036	183	11	∈	∈	PROPN
ejpam-6036	183	12	∇	∇	X
ejpam-6036	183	13	such	such	ADJ
ejpam-6036	183	14	that	that	SCONJ
ejpam-6036	183	15	f(x	f(x	PROPN
ejpam-6036	183	16	)	)	PUNCT
ejpam-6036	183	17	∈	∈	PROPN
ejpam-6036	183	18	vγ(x	vγ(x	NOUN
ejpam-6036	183	19	)	)	PUNCT
ejpam-6036	183	20	.	.	PUNCT
ejpam-6036	184	1	since	since	SCONJ
ejpam-6036	184	2	(	(	PUNCT
ejpam-6036	184	3	y	y	PROPN
ejpam-6036	184	4	,	,	PUNCT
ejpam-6036	184	5	σ1	σ1	PROPN
ejpam-6036	184	6	,	,	PUNCT
ejpam-6036	184	7	σ2	σ2	PROPN
ejpam-6036	184	8	)	)	PUNCT
ejpam-6036	184	9	be	be	VERB
ejpam-6036	184	10	a	a	DET
ejpam-6036	184	11	c	c	NOUN
ejpam-6036	184	12	-(σ1	-(σ1	NOUN
ejpam-6036	184	13	,	,	PUNCT
ejpam-6036	184	14	σ2)-space	σ2)-space	NOUN
ejpam-6036	184	15	,	,	PUNCT
ejpam-6036	184	16	there	there	PRON
ejpam-6036	184	17	exists	exist	VERB
ejpam-6036	184	18	a	a	DET
ejpam-6036	184	19	σ1σ2	σ1σ2	NUM
ejpam-6036	184	20	-	-	PUNCT
ejpam-6036	184	21	closed	closed	ADJ
ejpam-6036	184	22	set	set	NOUN
ejpam-6036	184	23	fγ(x	fγ(x	NOUN
ejpam-6036	184	24	)	)	PUNCT
ejpam-6036	184	25	of	of	ADP
ejpam-6036	184	26	y	y	PRON
ejpam-6036	184	27	such	such	ADJ
ejpam-6036	184	28	that	that	SCONJ
ejpam-6036	184	29	f(x	f(x	PROPN
ejpam-6036	184	30	)	)	PUNCT
ejpam-6036	184	31	∈	∈	PROPN
ejpam-6036	184	32	fγ(x	fγ(x	NOUN
ejpam-6036	184	33	)	)	PUNCT
ejpam-6036	184	34	⊆	⊆	NUM
ejpam-6036	184	35	vγ(x	vγ(x	NOUN
ejpam-6036	184	36	)	)	PUNCT
ejpam-6036	184	37	.	.	PUNCT
ejpam-6036	185	1	since	since	SCONJ
ejpam-6036	185	2	f	f	PROPN
ejpam-6036	185	3	is	be	AUX
ejpam-6036	185	4	weakly	weakly	ADJ
ejpam-6036	185	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	185	6	,	,	PUNCT
ejpam-6036	185	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	185	8	,	,	PUNCT
ejpam-6036	185	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	185	10	-	-	NOUN
ejpam-6036	185	11	cl(f	cl(f	NOUN
ejpam-6036	185	12	−1(fγ(x	−1(fγ(x	NOUN
ejpam-6036	185	13	)	)	PUNCT
ejpam-6036	185	14	)	)	PUNCT
ejpam-6036	185	15	)	)	PUNCT
ejpam-6036	186	1	⊆	⊆	NUM
ejpam-6036	186	2	f−1(vγ(x	f−1(vγ(x	NOUN
ejpam-6036	186	3	)	)	PUNCT
ejpam-6036	186	4	)	)	PUNCT
ejpam-6036	186	5	.	.	PUNCT
ejpam-6036	187	1	the	the	DET
ejpam-6036	187	2	family	family	NOUN
ejpam-6036	187	3	{	{	PUNCT
ejpam-6036	187	4	τ1τ2	τ1τ2	NOUN
ejpam-6036	187	5	-	-	ADJ
ejpam-6036	187	6	cl(f−1(fγ(x	cl(f−1(fγ(x	NOUN
ejpam-6036	187	7	)	)	PUNCT
ejpam-6036	187	8	)	)	PUNCT
ejpam-6036	187	9	)	)	PUNCT
ejpam-6036	188	1	|	|	ADV
ejpam-6036	188	2	x	x	SYM
ejpam-6036	188	3	∈	∈	NOUN
ejpam-6036	188	4	x	x	X
ejpam-6036	188	5	}	}	PUNCT
ejpam-6036	188	6	is	be	AUX
ejpam-6036	188	7	a	a	DET
ejpam-6036	188	8	τ1τ2closed	τ1τ2close	VERB
ejpam-6036	188	9	cover	cover	NOUN
ejpam-6036	188	10	of	of	ADP
ejpam-6036	188	11	x.	x.	NOUN
ejpam-6036	188	12	since	since	SCONJ
ejpam-6036	188	13	(	(	PUNCT
ejpam-6036	188	14	x	x	NOUN
ejpam-6036	188	15	,	,	PUNCT
ejpam-6036	188	16	τ1	τ1	NOUN
ejpam-6036	188	17	,	,	PUNCT
ejpam-6036	188	18	τ2	τ2	NOUN
ejpam-6036	188	19	)	)	PUNCT
ejpam-6036	188	20	is	be	AUX
ejpam-6036	188	21	strongly	strongly	ADV
ejpam-6036	188	22	s	s	NOUN
ejpam-6036	188	23	-	-	PUNCT
ejpam-6036	188	24	τ1τ2	τ1τ2	ADJ
ejpam-6036	188	25	-	-	ADJ
ejpam-6036	188	26	closed	closed	ADJ
ejpam-6036	188	27	,	,	PUNCT
ejpam-6036	188	28	there	there	PRON
ejpam-6036	188	29	exists	exist	VERB
ejpam-6036	188	30	a	a	DET
ejpam-6036	188	31	finite	finite	ADJ
ejpam-6036	188	32	number	number	NOUN
ejpam-6036	188	33	of	of	ADP
ejpam-6036	188	34	pints	pint	NOUN
ejpam-6036	188	35	,	,	PUNCT
ejpam-6036	188	36	say	say	INTJ
ejpam-6036	188	37	,	,	PUNCT
ejpam-6036	188	38	x1	x1	PROPN
ejpam-6036	188	39	,	,	PUNCT
ejpam-6036	188	40	x2	x2	PROPN
ejpam-6036	188	41	,	,	PUNCT
ejpam-6036	188	42	x3	x3	ADJ
ejpam-6036	188	43	,	,	PUNCT
ejpam-6036	188	44	...	...	PUNCT
ejpam-6036	188	45	,	,	PUNCT
ejpam-6036	188	46	xn	xn	PROPN
ejpam-6036	189	1	in	in	ADP
ejpam-6036	189	2	x	x	X
ejpam-6036	189	3	such	such	ADJ
ejpam-6036	189	4	that	that	SCONJ
ejpam-6036	189	5	x	x	X
ejpam-6036	189	6	=	=	PUNCT
ejpam-6036	189	7	∪{τ1τ2	∪{τ1τ2	ADJ
ejpam-6036	189	8	-	-	ADJ
ejpam-6036	189	9	cl(f−1(fγ(xk	cl(f−1(fγ(xk	NUM
ejpam-6036	189	10	)	)	PUNCT
ejpam-6036	189	11	)	)	PUNCT
ejpam-6036	189	12	)	)	PUNCT
ejpam-6036	190	1	|	|	ADV
ejpam-6036	190	2	xk	xk	PROPN
ejpam-6036	190	3	∈	∈	PROPN
ejpam-6036	190	4	x	x	X
ejpam-6036	190	5	;	;	PUNCT
ejpam-6036	190	6	1	1	NUM
ejpam-6036	190	7	≤	≤	NUM
ejpam-6036	190	8	k	k	X
ejpam-6036	190	9	≤	≤	PROPN
ejpam-6036	190	10	n	n	CCONJ
ejpam-6036	190	11	}	}	PUNCT
ejpam-6036	190	12	.	.	PUNCT
ejpam-6036	191	1	thus	thus	ADV
ejpam-6036	191	2	,	,	PUNCT
ejpam-6036	191	3	f(x	f(x	PROPN
ejpam-6036	191	4	)	)	PUNCT
ejpam-6036	191	5	=	=	PUNCT
ejpam-6036	192	1	∪{f(τ1τ2	∪{f(τ1τ2	NOUN
ejpam-6036	192	2	-	-	PUNCT
ejpam-6036	192	3	cl(f−1(fγ(xk	cl(f−1(fγ(xk	NUM
ejpam-6036	192	4	)	)	PUNCT
ejpam-6036	192	5	)	)	PUNCT
ejpam-6036	192	6	)	)	PUNCT
ejpam-6036	192	7	)	)	PUNCT
ejpam-6036	193	1	|	|	ADV
ejpam-6036	193	2	xk	xk	PROPN
ejpam-6036	193	3	∈	∈	PROPN
ejpam-6036	193	4	x	x	X
ejpam-6036	193	5	;	;	PUNCT
ejpam-6036	193	6	1	1	NUM
ejpam-6036	193	7	≤	≤	NUM
ejpam-6036	193	8	k	k	X
ejpam-6036	193	9	≤	≤	PROPN
ejpam-6036	193	10	n	n	CCONJ
ejpam-6036	193	11	}	}	PUNCT
ejpam-6036	193	12	⊆	⊆	NUM
ejpam-6036	193	13	∪{vγ(xk	∪{vγ(xk	NOUN
ejpam-6036	193	14	)	)	PUNCT
ejpam-6036	193	15	|	|	ADV
ejpam-6036	193	16	xk	xk	PROPN
ejpam-6036	193	17	∈	∈	PROPN
ejpam-6036	194	1	x	x	X
ejpam-6036	194	2	;	;	PUNCT
ejpam-6036	194	3	1	1	NUM
ejpam-6036	194	4	≤	≤	NUM
ejpam-6036	194	5	k	k	X
ejpam-6036	194	6	≤	≤	PROPN
ejpam-6036	194	7	n	n	CCONJ
ejpam-6036	194	8	}	}	PUNCT
ejpam-6036	194	9	.	.	PUNCT
ejpam-6036	195	1	this	this	PRON
ejpam-6036	195	2	shows	show	VERB
ejpam-6036	195	3	that	that	SCONJ
ejpam-6036	195	4	f(x	f(x	PROPN
ejpam-6036	195	5	)	)	PUNCT
ejpam-6036	195	6	is	be	AUX
ejpam-6036	195	7	σ1σ2	σ1σ2	NOUN
ejpam-6036	195	8	-	-	ADJ
ejpam-6036	195	9	compact	compact	ADJ
ejpam-6036	195	10	.	.	PUNCT
ejpam-6036	196	1	definition	definition	NOUN
ejpam-6036	196	2	11	11	NUM
ejpam-6036	196	3	.	.	PUNCT
ejpam-6036	197	1	[	[	X
ejpam-6036	197	2	44	44	NUM
ejpam-6036	197	3	]	]	PUNCT
ejpam-6036	197	4	a	a	DET
ejpam-6036	197	5	bitopological	bitopological	ADJ
ejpam-6036	197	6	space	space	NOUN
ejpam-6036	197	7	(	(	PUNCT
ejpam-6036	197	8	x	x	NOUN
ejpam-6036	197	9	,	,	PUNCT
ejpam-6036	197	10	τ1	τ1	NOUN
ejpam-6036	197	11	,	,	PUNCT
ejpam-6036	197	12	τ2	τ2	NOUN
ejpam-6036	197	13	)	)	PUNCT
ejpam-6036	197	14	is	be	AUX
ejpam-6036	197	15	said	say	VERB
ejpam-6036	197	16	to	to	PART
ejpam-6036	197	17	be	be	AUX
ejpam-6036	197	18	(	(	PUNCT
ejpam-6036	197	19	τ1	τ1	NOUN
ejpam-6036	197	20	,	,	PUNCT
ejpam-6036	197	21	τ2)-t1	τ2)-t1	VERB
ejpam-6036	197	22	if	if	SCONJ
ejpam-6036	197	23	for	for	ADP
ejpam-6036	197	24	any	any	DET
ejpam-6036	197	25	pair	pair	NOUN
ejpam-6036	197	26	of	of	ADP
ejpam-6036	197	27	distinct	distinct	ADJ
ejpam-6036	197	28	points	point	NOUN
ejpam-6036	197	29	x	x	X
ejpam-6036	197	30	,	,	PUNCT
ejpam-6036	197	31	y	y	PROPN
ejpam-6036	197	32	in	in	ADP
ejpam-6036	197	33	x	x	SYM
ejpam-6036	197	34	,	,	PUNCT
ejpam-6036	197	35	there	there	PRON
ejpam-6036	197	36	exist	exist	VERB
ejpam-6036	197	37	τ1τ2	τ1τ2	ADJ
ejpam-6036	197	38	-	-	ADJ
ejpam-6036	197	39	open	open	ADJ
ejpam-6036	197	40	sets	set	NOUN
ejpam-6036	197	41	u	u	NOUN
ejpam-6036	197	42	and	and	CCONJ
ejpam-6036	197	43	v	v	ADP
ejpam-6036	197	44	such	such	ADJ
ejpam-6036	197	45	that	that	SCONJ
ejpam-6036	197	46	x	x	SYM
ejpam-6036	197	47	∈	∈	PROPN
ejpam-6036	197	48	u	u	PROPN
ejpam-6036	197	49	,	,	PUNCT
ejpam-6036	197	50	y	y	PROPN
ejpam-6036	197	51	̸∈	̸∈	PROPN
ejpam-6036	197	52	u	u	PROPN
ejpam-6036	197	53	and	and	CCONJ
ejpam-6036	197	54	y	y	PROPN
ejpam-6036	197	55	∈	∈	PROPN
ejpam-6036	197	56	v	v	NOUN
ejpam-6036	197	57	,	,	PUNCT
ejpam-6036	197	58	x	x	PROPN
ejpam-6036	197	59	̸∈	̸∈	PROPN
ejpam-6036	197	60	v	v	PROPN
ejpam-6036	197	61	.	.	PUNCT
ejpam-6036	198	1	lemma	lemma	PROPN
ejpam-6036	198	2	8	8	NUM
ejpam-6036	198	3	.	.	PUNCT
ejpam-6036	199	1	[	[	X
ejpam-6036	199	2	44	44	NUM
ejpam-6036	199	3	]	]	PUNCT
ejpam-6036	199	4	for	for	ADP
ejpam-6036	199	5	a	a	DET
ejpam-6036	199	6	bitopological	bitopological	ADJ
ejpam-6036	199	7	space	space	NOUN
ejpam-6036	199	8	(	(	PUNCT
ejpam-6036	199	9	x	x	NOUN
ejpam-6036	199	10	,	,	PUNCT
ejpam-6036	199	11	τ1	τ1	NOUN
ejpam-6036	199	12	,	,	PUNCT
ejpam-6036	199	13	τ2	τ2	NOUN
ejpam-6036	199	14	)	)	PUNCT
ejpam-6036	199	15	,	,	PUNCT
ejpam-6036	199	16	the	the	DET
ejpam-6036	199	17	following	follow	VERB
ejpam-6036	199	18	properties	property	NOUN
ejpam-6036	199	19	are	be	AUX
ejpam-6036	199	20	equivalent	equivalent	ADJ
ejpam-6036	199	21	:	:	PUNCT
ejpam-6036	199	22	(	(	PUNCT
ejpam-6036	199	23	1	1	X
ejpam-6036	199	24	)	)	PUNCT
ejpam-6036	199	25	(	(	PUNCT
ejpam-6036	199	26	x	x	NOUN
ejpam-6036	199	27	,	,	PUNCT
ejpam-6036	199	28	τ1	τ1	NOUN
ejpam-6036	199	29	,	,	PUNCT
ejpam-6036	199	30	τ2	τ2	NOUN
ejpam-6036	199	31	)	)	PUNCT
ejpam-6036	199	32	is	be	AUX
ejpam-6036	199	33	(	(	PUNCT
ejpam-6036	199	34	τ1	τ1	NOUN
ejpam-6036	199	35	,	,	PUNCT
ejpam-6036	199	36	τ2)-t1	τ2)-t1	NOUN
ejpam-6036	199	37	;	;	PUNCT
ejpam-6036	199	38	(	(	PUNCT
ejpam-6036	199	39	2	2	X
ejpam-6036	199	40	)	)	PUNCT
ejpam-6036	199	41	for	for	ADP
ejpam-6036	199	42	each	each	DET
ejpam-6036	199	43	x	x	SYM
ejpam-6036	199	44	∈	∈	PROPN
ejpam-6036	199	45	x	x	NOUN
ejpam-6036	199	46	,	,	PUNCT
ejpam-6036	199	47	the	the	DET
ejpam-6036	199	48	singleton	singleton	NOUN
ejpam-6036	199	49	{	{	PUNCT
ejpam-6036	199	50	x	x	NOUN
ejpam-6036	199	51	}	}	PUNCT
ejpam-6036	199	52	is	be	AUX
ejpam-6036	199	53	τ1τ2	τ1τ2	NOUN
ejpam-6036	199	54	-	-	ADJ
ejpam-6036	199	55	closed	closed	ADJ
ejpam-6036	199	56	in	in	ADP
ejpam-6036	199	57	x	x	PRON
ejpam-6036	199	58	;	;	PUNCT
ejpam-6036	199	59	(	(	PUNCT
ejpam-6036	199	60	3	3	X
ejpam-6036	199	61	)	)	PUNCT
ejpam-6036	199	62	for	for	ADP
ejpam-6036	199	63	each	each	DET
ejpam-6036	199	64	x	x	SYM
ejpam-6036	199	65	∈	∈	PROPN
ejpam-6036	199	66	x	x	NOUN
ejpam-6036	199	67	,	,	PUNCT
ejpam-6036	199	68	the	the	DET
ejpam-6036	199	69	singleton	singleton	NOUN
ejpam-6036	199	70	{	{	PUNCT
ejpam-6036	199	71	x	x	NOUN
ejpam-6036	199	72	}	}	PUNCT
ejpam-6036	199	73	is	be	AUX
ejpam-6036	199	74	a	a	DET
ejpam-6036	199	75	λ(τ1,τ2)-set	λ(τ1,τ2)-set	PROPN
ejpam-6036	199	76	.	.	PUNCT
ejpam-6036	199	77	theorem	theorem	NOUN
ejpam-6036	199	78	8	8	NUM
ejpam-6036	199	79	.	.	PUNCT
ejpam-6036	200	1	if	if	SCONJ
ejpam-6036	200	2	f	f	PROPN
ejpam-6036	200	3	:	:	PUNCT
ejpam-6036	200	4	(	(	PUNCT
ejpam-6036	200	5	x	x	NOUN
ejpam-6036	200	6	,	,	PUNCT
ejpam-6036	200	7	τ1	τ1	NOUN
ejpam-6036	200	8	,	,	PUNCT
ejpam-6036	200	9	τ2	τ2	NOUN
ejpam-6036	200	10	)	)	PUNCT
ejpam-6036	200	11	→	→	SYM
ejpam-6036	200	12	(	(	PUNCT
ejpam-6036	200	13	y	y	PROPN
ejpam-6036	200	14	,	,	PUNCT
ejpam-6036	200	15	σ1	σ1	PROPN
ejpam-6036	200	16	,	,	PUNCT
ejpam-6036	200	17	σ2	σ2	PROPN
ejpam-6036	200	18	)	)	PUNCT
ejpam-6036	200	19	is	be	AUX
ejpam-6036	200	20	a	a	DET
ejpam-6036	200	21	weakly	weakly	ADJ
ejpam-6036	200	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	200	23	,	,	PUNCT
ejpam-6036	200	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	200	25	injection	injection	NOUN
ejpam-6036	200	26	and	and	CCONJ
ejpam-6036	200	27	(	(	PUNCT
ejpam-6036	200	28	y	y	PROPN
ejpam-6036	200	29	,	,	PUNCT
ejpam-6036	200	30	σ1	σ1	PROPN
ejpam-6036	200	31	,	,	PUNCT
ejpam-6036	200	32	σ2	σ2	PROPN
ejpam-6036	200	33	)	)	PUNCT
ejpam-6036	200	34	is	be	AUX
ejpam-6036	200	35	(	(	PUNCT
ejpam-6036	200	36	σ1	σ1	PROPN
ejpam-6036	200	37	,	,	PUNCT
ejpam-6036	200	38	σ2)-t1	σ2)-t1	NOUN
ejpam-6036	200	39	,	,	PUNCT
ejpam-6036	200	40	(	(	PUNCT
ejpam-6036	200	41	x	x	NOUN
ejpam-6036	200	42	,	,	PUNCT
ejpam-6036	200	43	τ1	τ1	NOUN
ejpam-6036	200	44	,	,	PUNCT
ejpam-6036	200	45	τ2	τ2	NOUN
ejpam-6036	200	46	)	)	PUNCT
ejpam-6036	200	47	is	be	AUX
ejpam-6036	200	48	(	(	PUNCT
ejpam-6036	200	49	τ1	τ1	NOUN
ejpam-6036	200	50	,	,	PUNCT
ejpam-6036	200	51	τ2)-t1	τ2)-t1	NOUN
ejpam-6036	200	52	.	.	PUNCT
ejpam-6036	201	1	proof	proof	NOUN
ejpam-6036	201	2	.	.	PUNCT
ejpam-6036	202	1	let	let	VERB
ejpam-6036	202	2	x	x	PUNCT
ejpam-6036	202	3	and	and	CCONJ
ejpam-6036	202	4	x′	x′	PROPN
ejpam-6036	202	5	be	be	AUX
ejpam-6036	202	6	any	any	DET
ejpam-6036	202	7	distinct	distinct	ADJ
ejpam-6036	202	8	points	point	NOUN
ejpam-6036	202	9	of	of	ADP
ejpam-6036	202	10	x.	x.	NOUN
ejpam-6036	202	11	since	since	SCONJ
ejpam-6036	202	12	f	f	PROPN
ejpam-6036	202	13	is	be	AUX
ejpam-6036	202	14	injective	injective	ADJ
ejpam-6036	202	15	,	,	PUNCT
ejpam-6036	202	16	f(x	f(x	PROPN
ejpam-6036	202	17	)	)	PUNCT
ejpam-6036	202	18	̸=	̸=	PROPN
ejpam-6036	202	19	f(x′	f(x′	NUM
ejpam-6036	202	20	)	)	PUNCT
ejpam-6036	202	21	.	.	PUNCT
ejpam-6036	203	1	moreover	moreover	ADV
ejpam-6036	203	2	,	,	PUNCT
ejpam-6036	203	3	since	since	SCONJ
ejpam-6036	203	4	(	(	PUNCT
ejpam-6036	203	5	y	y	PROPN
ejpam-6036	203	6	,	,	PUNCT
ejpam-6036	203	7	σ1	σ1	PROPN
ejpam-6036	203	8	,	,	PUNCT
ejpam-6036	203	9	σ2	σ2	PROPN
ejpam-6036	203	10	)	)	PUNCT
ejpam-6036	203	11	is	be	AUX
ejpam-6036	203	12	(	(	PUNCT
ejpam-6036	203	13	σ1	σ1	PROPN
ejpam-6036	203	14	,	,	PUNCT
ejpam-6036	203	15	σ2)-t1	σ2)-t1	PROPN
ejpam-6036	203	16	,	,	PUNCT
ejpam-6036	203	17	there	there	PRON
ejpam-6036	203	18	exists	exist	VERB
ejpam-6036	203	19	a	a	DET
ejpam-6036	203	20	σ1σ2	σ1σ2	NUM
ejpam-6036	203	21	-	-	ADJ
ejpam-6036	203	22	open	open	ADJ
ejpam-6036	203	23	set	set	NOUN
ejpam-6036	203	24	v	v	NOUN
ejpam-6036	203	25	of	of	ADP
ejpam-6036	203	26	y	y	PRON
ejpam-6036	203	27	such	such	ADJ
ejpam-6036	203	28	that	that	SCONJ
ejpam-6036	203	29	f(x	f(x	PROPN
ejpam-6036	203	30	)	)	PUNCT
ejpam-6036	203	31	∈	∈	PROPN
ejpam-6036	203	32	v	v	NOUN
ejpam-6036	203	33	and	and	CCONJ
ejpam-6036	203	34	f(x′	f(x′	NUM
ejpam-6036	203	35	)	)	PUNCT
ejpam-6036	203	36	̸∈	̸∈	PROPN
ejpam-6036	203	37	v	v	PROPN
ejpam-6036	203	38	.	.	PUNCT
ejpam-6036	204	1	by	by	ADP
ejpam-6036	204	2	lemma	lemma	PROPN
ejpam-6036	204	3	8	8	NUM
ejpam-6036	204	4	,	,	PUNCT
ejpam-6036	204	5	{	{	PUNCT
ejpam-6036	204	6	f(x	f(x	PROPN
ejpam-6036	204	7	)	)	PUNCT
ejpam-6036	204	8	}	}	PUNCT
ejpam-6036	204	9	is	be	AUX
ejpam-6036	204	10	σ1σ2	σ1σ2	NOUN
ejpam-6036	204	11	-	-	ADJ
ejpam-6036	204	12	closed	closed	ADJ
ejpam-6036	204	13	in	in	ADP
ejpam-6036	204	14	y	y	PROPN
ejpam-6036	204	15	.	.	PUNCT
ejpam-6036	205	1	since	since	SCONJ
ejpam-6036	205	2	f	f	PROPN
ejpam-6036	205	3	is	be	AUX
ejpam-6036	205	4	weakly	weakly	ADJ
ejpam-6036	205	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	205	6	,	,	PUNCT
ejpam-6036	205	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	205	8	,	,	PUNCT
ejpam-6036	205	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	205	10	-	-	NOUN
ejpam-6036	205	11	cl(f	cl(f	NUM
ejpam-6036	205	12	−1({f(x	−1({f(x	NUM
ejpam-6036	205	13	)	)	PUNCT
ejpam-6036	205	14	}	}	PUNCT
ejpam-6036	205	15	)	)	PUNCT
ejpam-6036	205	16	)	)	PUNCT
ejpam-6036	206	1	⊆	⊆	NUM
ejpam-6036	206	2	f−1(v	f−1(v	NOUN
ejpam-6036	206	3	)	)	PUNCT
ejpam-6036	206	4	.	.	PUNCT
ejpam-6036	207	1	since	since	SCONJ
ejpam-6036	207	2	x′	x′	PROPN
ejpam-6036	207	3	̸∈	̸∈	PROPN
ejpam-6036	207	4	f−1(v	f−1(v	PROPN
ejpam-6036	207	5	)	)	PUNCT
ejpam-6036	207	6	,	,	PUNCT
ejpam-6036	207	7	we	we	PRON
ejpam-6036	207	8	have	have	VERB
ejpam-6036	207	9	x′	x′	PROPN
ejpam-6036	207	10	̸∈	̸∈	PROPN
ejpam-6036	207	11	τ1τ2	τ1τ2	PROPN
ejpam-6036	207	12	-	-	PROPN
ejpam-6036	207	13	cl(f	cl(f	NUM
ejpam-6036	207	14	−1({f(x	−1({f(x	NUM
ejpam-6036	207	15	)	)	PUNCT
ejpam-6036	207	16	}	}	PUNCT
ejpam-6036	207	17	)	)	PUNCT
ejpam-6036	207	18	)	)	PUNCT
ejpam-6036	207	19	.	.	PUNCT
ejpam-6036	208	1	then	then	ADV
ejpam-6036	208	2	by	by	ADP
ejpam-6036	208	3	lemma	lemma	PROPN
ejpam-6036	208	4	1	1	NUM
ejpam-6036	208	5	,	,	PUNCT
ejpam-6036	208	6	τ1τ2	τ1τ2	NOUN
ejpam-6036	208	7	-	-	NOUN
ejpam-6036	208	8	cl(f	cl(f	NUM
ejpam-6036	208	9	−1({f(x	−1({f(x	NUM
ejpam-6036	208	10	)	)	PUNCT
ejpam-6036	208	11	}	}	PUNCT
ejpam-6036	208	12	)	)	PUNCT
ejpam-6036	208	13	)	)	PUNCT
ejpam-6036	208	14	is	be	AUX
ejpam-6036	208	15	τ1τ2	τ1τ2	NOUN
ejpam-6036	208	16	-	-	ADJ
ejpam-6036	208	17	closed	closed	ADJ
ejpam-6036	208	18	and	and	CCONJ
ejpam-6036	208	19	hence	hence	ADV
ejpam-6036	208	20	x	x	NOUN
ejpam-6036	208	21	−	−	ADP
ejpam-6036	208	22	τ1τ2	τ1τ2	NOUN
ejpam-6036	208	23	-	-	NOUN
ejpam-6036	208	24	cl(f	cl(f	NUM
ejpam-6036	208	25	−1({f(x	−1({f(x	NUM
ejpam-6036	208	26	)	)	PUNCT
ejpam-6036	208	27	}	}	PUNCT
ejpam-6036	208	28	)	)	PUNCT
ejpam-6036	208	29	)	)	PUNCT
ejpam-6036	209	1	is	be	AUX
ejpam-6036	209	2	a	a	DET
ejpam-6036	209	3	τ1τ2	τ1τ2	ADJ
ejpam-6036	209	4	-	-	ADJ
ejpam-6036	209	5	open	open	ADJ
ejpam-6036	209	6	set	set	NOUN
ejpam-6036	209	7	of	of	ADP
ejpam-6036	209	8	x	x	PUNCT
ejpam-6036	209	9	containing	contain	VERB
ejpam-6036	209	10	x′	x′	PROPN
ejpam-6036	209	11	but	but	CCONJ
ejpam-6036	209	12	not	not	PART
ejpam-6036	209	13	x.	x.	NOUN
ejpam-6036	209	14	this	this	PRON
ejpam-6036	209	15	shows	show	VERB
ejpam-6036	209	16	that	that	SCONJ
ejpam-6036	209	17	(	(	PUNCT
ejpam-6036	209	18	x	x	NOUN
ejpam-6036	209	19	,	,	PUNCT
ejpam-6036	209	20	τ1	τ1	NOUN
ejpam-6036	209	21	,	,	PUNCT
ejpam-6036	209	22	τ2	τ2	NOUN
ejpam-6036	209	23	)	)	PUNCT
ejpam-6036	209	24	is	be	AUX
ejpam-6036	209	25	(	(	PUNCT
ejpam-6036	209	26	τ1	τ1	NOUN
ejpam-6036	209	27	,	,	PUNCT
ejpam-6036	209	28	τ2)-t1	τ2)-t1	NOUN
ejpam-6036	209	29	.	.	PUNCT
ejpam-6036	210	1	definition	definition	NOUN
ejpam-6036	210	2	12	12	NUM
ejpam-6036	210	3	.	.	PUNCT
ejpam-6036	211	1	a	a	DET
ejpam-6036	211	2	function	function	NOUN
ejpam-6036	211	3	f	f	NOUN
ejpam-6036	211	4	:	:	PUNCT
ejpam-6036	211	5	(	(	PUNCT
ejpam-6036	211	6	x	x	NOUN
ejpam-6036	211	7	,	,	PUNCT
ejpam-6036	211	8	τ1	τ1	NOUN
ejpam-6036	211	9	,	,	PUNCT
ejpam-6036	211	10	τ2	τ2	NOUN
ejpam-6036	211	11	)	)	PUNCT
ejpam-6036	211	12	→	→	SYM
ejpam-6036	211	13	(	(	PUNCT
ejpam-6036	211	14	y	y	PROPN
ejpam-6036	211	15	,	,	PUNCT
ejpam-6036	211	16	σ1	σ1	PROPN
ejpam-6036	211	17	,	,	PUNCT
ejpam-6036	211	18	σ2	σ2	PROPN
ejpam-6036	211	19	)	)	PUNCT
ejpam-6036	211	20	is	be	AUX
ejpam-6036	211	21	said	say	VERB
ejpam-6036	211	22	to	to	PART
ejpam-6036	211	23	have	have	VERB
ejpam-6036	211	24	a	a	DET
ejpam-6036	211	25	contra	contra	PROPN
ejpam-6036	211	26	-	-	PUNCT
ejpam-6036	211	27	c	c	ADJ
ejpam-6036	211	28	-closed	-close	VERB
ejpam-6036	211	29	graph	graph	NOUN
ejpam-6036	211	30	if	if	SCONJ
ejpam-6036	211	31	for	for	ADP
ejpam-6036	211	32	each	each	DET
ejpam-6036	211	33	(	(	PUNCT
ejpam-6036	211	34	x	x	NOUN
ejpam-6036	211	35	,	,	PUNCT
ejpam-6036	211	36	y	y	NOUN
ejpam-6036	211	37	)	)	PUNCT
ejpam-6036	211	38	∈	∈	PROPN
ejpam-6036	211	39	(	(	PUNCT
ejpam-6036	211	40	x	x	SYM
ejpam-6036	211	41	×	×	PROPN
ejpam-6036	211	42	y	y	PROPN
ejpam-6036	211	43	)	)	PUNCT
ejpam-6036	211	44	−g(f	−g(f	NOUN
ejpam-6036	211	45	)	)	PUNCT
ejpam-6036	211	46	,	,	PUNCT
ejpam-6036	211	47	there	there	PRON
ejpam-6036	211	48	exist	exist	VERB
ejpam-6036	211	49	a	a	DET
ejpam-6036	211	50	τ1τ2	τ1τ2	ADJ
ejpam-6036	211	51	-	-	ADJ
ejpam-6036	211	52	closed	closed	ADJ
ejpam-6036	211	53	set	set	ADJ
ejpam-6036	211	54	f	f	PROPN
ejpam-6036	211	55	of	of	ADP
ejpam-6036	211	56	x	x	SYM
ejpam-6036	211	57	containing	contain	VERB
ejpam-6036	211	58	x	x	X
ejpam-6036	211	59	and	and	CCONJ
ejpam-6036	211	60	a	a	DET
ejpam-6036	211	61	σ1σ2	σ1σ2	NUM
ejpam-6036	211	62	-	-	PUNCT
ejpam-6036	211	63	closed	closed	ADJ
ejpam-6036	211	64	set	set	VERB
ejpam-6036	211	65	f	f	PROPN
ejpam-6036	211	66	′	′	NOUN
ejpam-6036	211	67	of	of	ADP
ejpam-6036	211	68	y	y	PROPN
ejpam-6036	211	69	containing	contain	VERB
ejpam-6036	211	70	y	y	PRON
ejpam-6036	211	71	such	such	ADJ
ejpam-6036	211	72	that	that	PRON
ejpam-6036	211	73	(	(	PUNCT
ejpam-6036	211	74	f	f	X
ejpam-6036	211	75	×	×	PROPN
ejpam-6036	211	76	f	f	PROPN
ejpam-6036	211	77	′	′	NOUN
ejpam-6036	211	78	)	)	PUNCT
ejpam-6036	211	79	∩g(f	∩g(f	PROPN
ejpam-6036	211	80	)	)	PUNCT
ejpam-6036	211	81	=	=	PUNCT
ejpam-6036	211	82	∅.	∅.	PROPN
ejpam-6036	211	83	b.	b.	PROPN
ejpam-6036	211	84	kong	kong	PROPN
ejpam-6036	211	85	-	-	PUNCT
ejpam-6036	211	86	ied	ied	PROPN
ejpam-6036	211	87	,	,	PUNCT
ejpam-6036	211	88	s.	s.	PROPN
ejpam-6036	211	89	sompong	sompong	PROPN
ejpam-6036	211	90	,	,	PUNCT
ejpam-6036	211	91	c.	c.	PROPN
ejpam-6036	211	92	boonpok	boonpok	PROPN
ejpam-6036	211	93	/	/	SYM
ejpam-6036	211	94	eur	eur	PROPN
ejpam-6036	211	95	.	.	PUNCT
ejpam-6036	212	1	j.	j.	PROPN
ejpam-6036	212	2	pure	pure	PROPN
ejpam-6036	212	3	appl	appl	PROPN
ejpam-6036	212	4	.	.	PROPN
ejpam-6036	212	5	math	math	PROPN
ejpam-6036	212	6	,	,	PUNCT
ejpam-6036	212	7	18	18	NUM
ejpam-6036	212	8	(	(	PUNCT
ejpam-6036	212	9	2	2	NUM
ejpam-6036	212	10	)	)	PUNCT
ejpam-6036	212	11	(	(	PUNCT
ejpam-6036	212	12	2025	2025	NUM
ejpam-6036	212	13	)	)	PUNCT
ejpam-6036	212	14	,	,	PUNCT
ejpam-6036	212	15	6036	6036	NUM
ejpam-6036	212	16	8	8	NUM
ejpam-6036	212	17	of	of	ADP
ejpam-6036	212	18	11	11	NUM
ejpam-6036	212	19	theorem	theorem	NOUN
ejpam-6036	212	20	9	9	NUM
ejpam-6036	212	21	.	.	PUNCT
ejpam-6036	213	1	if	if	SCONJ
ejpam-6036	213	2	f	f	PROPN
ejpam-6036	213	3	:	:	PUNCT
ejpam-6036	213	4	(	(	PUNCT
ejpam-6036	213	5	x	x	NOUN
ejpam-6036	213	6	,	,	PUNCT
ejpam-6036	213	7	τ1	τ1	NOUN
ejpam-6036	213	8	,	,	PUNCT
ejpam-6036	213	9	τ2	τ2	NOUN
ejpam-6036	213	10	)	)	PUNCT
ejpam-6036	213	11	→	→	SYM
ejpam-6036	213	12	(	(	PUNCT
ejpam-6036	213	13	y	y	PROPN
ejpam-6036	213	14	,	,	PUNCT
ejpam-6036	213	15	σ1	σ1	PROPN
ejpam-6036	213	16	,	,	PUNCT
ejpam-6036	213	17	σ2	σ2	NOUN
ejpam-6036	213	18	)	)	PUNCT
ejpam-6036	213	19	is	be	AUX
ejpam-6036	213	20	weakly	weakly	ADJ
ejpam-6036	213	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	213	22	,	,	PUNCT
ejpam-6036	213	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	213	24	and	and	CCONJ
ejpam-6036	213	25	(	(	PUNCT
ejpam-6036	213	26	y	y	PROPN
ejpam-6036	213	27	,	,	PUNCT
ejpam-6036	213	28	σ1	σ1	PROPN
ejpam-6036	213	29	,	,	PUNCT
ejpam-6036	213	30	σ2	σ2	PROPN
ejpam-6036	213	31	)	)	PUNCT
ejpam-6036	213	32	is	be	AUX
ejpam-6036	213	33	(	(	PUNCT
ejpam-6036	213	34	σ1	σ1	PROPN
ejpam-6036	213	35	,	,	PUNCT
ejpam-6036	213	36	σ2)-t1	σ2)-t1	NOUN
ejpam-6036	213	37	,	,	PUNCT
ejpam-6036	213	38	then	then	ADV
ejpam-6036	213	39	g(f	g(f	PROPN
ejpam-6036	213	40	)	)	PUNCT
ejpam-6036	213	41	is	be	AUX
ejpam-6036	213	42	contra	contra	PROPN
ejpam-6036	213	43	-	-	PROPN
ejpam-6036	213	44	c	c	NOUN
ejpam-6036	213	45	-closed	-close	VERB
ejpam-6036	213	46	.	.	PUNCT
ejpam-6036	214	1	proof	proof	NOUN
ejpam-6036	214	2	.	.	PUNCT
ejpam-6036	215	1	let	let	VERB
ejpam-6036	215	2	(	(	PUNCT
ejpam-6036	215	3	x	x	NOUN
ejpam-6036	215	4	,	,	PUNCT
ejpam-6036	215	5	y	y	NOUN
ejpam-6036	215	6	)	)	PUNCT
ejpam-6036	215	7	∈	∈	PROPN
ejpam-6036	215	8	(	(	PUNCT
ejpam-6036	215	9	x	x	SYM
ejpam-6036	215	10	×	×	PROPN
ejpam-6036	215	11	y	y	PROPN
ejpam-6036	215	12	)	)	PUNCT
ejpam-6036	216	1	−	−	PROPN
ejpam-6036	216	2	g(f	g(f	NOUN
ejpam-6036	216	3	)	)	PUNCT
ejpam-6036	216	4	.	.	PUNCT
ejpam-6036	217	1	then	then	ADV
ejpam-6036	217	2	,	,	PUNCT
ejpam-6036	217	3	y	y	PROPN
ejpam-6036	217	4	̸=	̸=	PROPN
ejpam-6036	217	5	f(x	f(x	PROPN
ejpam-6036	217	6	)	)	PUNCT
ejpam-6036	217	7	.	.	PUNCT
ejpam-6036	218	1	since	since	SCONJ
ejpam-6036	218	2	(	(	PUNCT
ejpam-6036	218	3	y	y	PROPN
ejpam-6036	218	4	,	,	PUNCT
ejpam-6036	218	5	σ1	σ1	PROPN
ejpam-6036	218	6	,	,	PUNCT
ejpam-6036	218	7	σ2	σ2	PROPN
ejpam-6036	218	8	)	)	PUNCT
ejpam-6036	218	9	is	be	AUX
ejpam-6036	218	10	(	(	PUNCT
ejpam-6036	218	11	σ1	σ1	PROPN
ejpam-6036	218	12	,	,	PUNCT
ejpam-6036	218	13	σ2)t1	σ2)t1	PROPN
ejpam-6036	218	14	,	,	PUNCT
ejpam-6036	218	15	there	there	PRON
ejpam-6036	218	16	exists	exist	VERB
ejpam-6036	218	17	a	a	DET
ejpam-6036	218	18	σ1σ2	σ1σ2	NUM
ejpam-6036	218	19	-	-	ADJ
ejpam-6036	218	20	open	open	ADJ
ejpam-6036	218	21	set	set	NOUN
ejpam-6036	218	22	v	v	NOUN
ejpam-6036	218	23	of	of	ADP
ejpam-6036	218	24	y	y	PRON
ejpam-6036	218	25	such	such	ADJ
ejpam-6036	218	26	that	that	SCONJ
ejpam-6036	218	27	y	y	PROPN
ejpam-6036	218	28	̸∈	̸∈	PROPN
ejpam-6036	218	29	v	v	PROPN
ejpam-6036	218	30	and	and	CCONJ
ejpam-6036	218	31	f(x	f(x	PROPN
ejpam-6036	218	32	)	)	PUNCT
ejpam-6036	218	33	̸∈	̸∈	PROPN
ejpam-6036	218	34	v	v	PROPN
ejpam-6036	218	35	.	.	PUNCT
ejpam-6036	219	1	by	by	ADP
ejpam-6036	219	2	lemma	lemma	PROPN
ejpam-6036	219	3	8	8	NUM
ejpam-6036	219	4	,	,	PUNCT
ejpam-6036	219	5	we	we	PRON
ejpam-6036	219	6	have	have	AUX
ejpam-6036	219	7	{	{	PUNCT
ejpam-6036	219	8	f(x	f(x	PROPN
ejpam-6036	219	9	)	)	PUNCT
ejpam-6036	219	10	}	}	PUNCT
ejpam-6036	219	11	is	be	AUX
ejpam-6036	219	12	σ1σ2	σ1σ2	NOUN
ejpam-6036	219	13	-	-	ADJ
ejpam-6036	219	14	closed	closed	ADJ
ejpam-6036	219	15	in	in	ADP
ejpam-6036	219	16	y	y	PROPN
ejpam-6036	219	17	.	.	PUNCT
ejpam-6036	220	1	since	since	SCONJ
ejpam-6036	220	2	f	f	PROPN
ejpam-6036	220	3	is	be	AUX
ejpam-6036	220	4	weakly	weakly	ADJ
ejpam-6036	220	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	220	6	,	,	PUNCT
ejpam-6036	220	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	220	8	,	,	PUNCT
ejpam-6036	220	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	220	10	-	-	NOUN
ejpam-6036	220	11	cl(f	cl(f	NUM
ejpam-6036	220	12	−1({f(x	−1({f(x	NUM
ejpam-6036	220	13	)	)	PUNCT
ejpam-6036	220	14	}	}	PUNCT
ejpam-6036	220	15	)	)	PUNCT
ejpam-6036	220	16	)	)	PUNCT
ejpam-6036	221	1	⊆	⊆	NUM
ejpam-6036	221	2	f−1(v	f−1(v	NOUN
ejpam-6036	221	3	)	)	PUNCT
ejpam-6036	221	4	and	and	CCONJ
ejpam-6036	221	5	hence	hence	ADV
ejpam-6036	221	6	(	(	PUNCT
ejpam-6036	221	7	x	x	X
ejpam-6036	221	8	,	,	PUNCT
ejpam-6036	221	9	y	y	NOUN
ejpam-6036	221	10	)	)	PUNCT
ejpam-6036	221	11	∈	∈	PROPN
ejpam-6036	221	12	τ1τ2	τ1τ2	PROPN
ejpam-6036	221	13	-	-	ADJ
ejpam-6036	221	14	cl(f	cl(f	NOUN
ejpam-6036	221	15	−1({f(x)}))×	−1({f(x)}))×	PROPN
ejpam-6036	221	16	(	(	PUNCT
ejpam-6036	221	17	y	y	PROPN
ejpam-6036	221	18	−	−	PROPN
ejpam-6036	221	19	v	v	NOUN
ejpam-6036	221	20	)	)	PUNCT
ejpam-6036	221	21	⊆	⊆	NUM
ejpam-6036	221	22	(	(	PUNCT
ejpam-6036	221	23	x	x	SYM
ejpam-6036	221	24	×	×	PROPN
ejpam-6036	221	25	y	y	PROPN
ejpam-6036	221	26	)	)	PUNCT
ejpam-6036	221	27	−g(f	−g(f	NOUN
ejpam-6036	221	28	)	)	PUNCT
ejpam-6036	221	29	.	.	PUNCT
ejpam-6036	222	1	this	this	PRON
ejpam-6036	222	2	shows	show	VERB
ejpam-6036	222	3	that	that	SCONJ
ejpam-6036	222	4	g(f	g(f	PROPN
ejpam-6036	222	5	)	)	PUNCT
ejpam-6036	222	6	is	be	AUX
ejpam-6036	222	7	contra	contra	PROPN
ejpam-6036	222	8	-	-	PROPN
ejpam-6036	222	9	c	c	NOUN
ejpam-6036	222	10	-closed	-close	VERB
ejpam-6036	222	11	.	.	PUNCT
ejpam-6036	223	1	definition	definition	NOUN
ejpam-6036	223	2	13	13	NUM
ejpam-6036	223	3	.	.	PUNCT
ejpam-6036	224	1	a	a	DET
ejpam-6036	224	2	function	function	NOUN
ejpam-6036	224	3	f	f	NOUN
ejpam-6036	224	4	:	:	PUNCT
ejpam-6036	224	5	(	(	PUNCT
ejpam-6036	224	6	x	x	NOUN
ejpam-6036	224	7	,	,	PUNCT
ejpam-6036	224	8	τ1	τ1	NOUN
ejpam-6036	224	9	,	,	PUNCT
ejpam-6036	224	10	τ2	τ2	NOUN
ejpam-6036	224	11	)	)	PUNCT
ejpam-6036	224	12	→	→	SYM
ejpam-6036	224	13	(	(	PUNCT
ejpam-6036	224	14	y	y	PROPN
ejpam-6036	224	15	,	,	PUNCT
ejpam-6036	224	16	σ1	σ1	PROPN
ejpam-6036	224	17	,	,	PUNCT
ejpam-6036	224	18	σ2	σ2	PROPN
ejpam-6036	224	19	)	)	PUNCT
ejpam-6036	224	20	is	be	AUX
ejpam-6036	224	21	said	say	VERB
ejpam-6036	224	22	to	to	PART
ejpam-6036	224	23	have	have	VERB
ejpam-6036	224	24	a	a	DET
ejpam-6036	224	25	contra	contra	PROPN
ejpam-6036	224	26	-	-	PUNCT
ejpam-6036	224	27	cr	cr	ADV
ejpam-6036	224	28	-	-	PUNCT
ejpam-6036	224	29	closed	close	VERB
ejpam-6036	224	30	graph	graph	NOUN
ejpam-6036	224	31	if	if	SCONJ
ejpam-6036	224	32	for	for	ADP
ejpam-6036	224	33	each	each	DET
ejpam-6036	224	34	(	(	PUNCT
ejpam-6036	224	35	x	x	NOUN
ejpam-6036	224	36	,	,	PUNCT
ejpam-6036	224	37	y	y	NOUN
ejpam-6036	224	38	)	)	PUNCT
ejpam-6036	224	39	∈	∈	PROPN
ejpam-6036	224	40	(	(	PUNCT
ejpam-6036	224	41	x	x	SYM
ejpam-6036	224	42	×	×	PROPN
ejpam-6036	224	43	y	y	PROPN
ejpam-6036	224	44	)	)	PUNCT
ejpam-6036	224	45	−g(f	−g(f	NOUN
ejpam-6036	224	46	)	)	PUNCT
ejpam-6036	224	47	,	,	PUNCT
ejpam-6036	224	48	there	there	PRON
ejpam-6036	224	49	exist	exist	VERB
ejpam-6036	224	50	a	a	DET
ejpam-6036	224	51	τ1τ2	τ1τ2	ADJ
ejpam-6036	224	52	-	-	ADJ
ejpam-6036	224	53	closed	closed	ADJ
ejpam-6036	224	54	set	set	ADJ
ejpam-6036	224	55	f	f	PROPN
ejpam-6036	224	56	of	of	ADP
ejpam-6036	224	57	x	x	SYM
ejpam-6036	224	58	containing	contain	VERB
ejpam-6036	224	59	x	x	PROPN
ejpam-6036	224	60	and	and	CCONJ
ejpam-6036	224	61	a	a	DET
ejpam-6036	224	62	(	(	PUNCT
ejpam-6036	224	63	σ1	σ1	NOUN
ejpam-6036	224	64	,	,	PUNCT
ejpam-6036	225	1	σ2)r	σ2)r	NOUN
ejpam-6036	225	2	-	-	PUNCT
ejpam-6036	225	3	closed	close	VERB
ejpam-6036	225	4	set	set	VERB
ejpam-6036	225	5	f	f	PROPN
ejpam-6036	226	1	′	′	NOUN
ejpam-6036	226	2	of	of	ADP
ejpam-6036	226	3	y	y	PROPN
ejpam-6036	226	4	containing	contain	VERB
ejpam-6036	226	5	y	y	PRON
ejpam-6036	226	6	such	such	ADJ
ejpam-6036	226	7	that	that	PRON
ejpam-6036	226	8	(	(	PUNCT
ejpam-6036	226	9	f	f	X
ejpam-6036	226	10	×	×	PROPN
ejpam-6036	226	11	f	f	PROPN
ejpam-6036	226	12	′	′	NOUN
ejpam-6036	226	13	)	)	PUNCT
ejpam-6036	226	14	∩g(f	∩g(f	PROPN
ejpam-6036	226	15	)	)	PUNCT
ejpam-6036	226	16	=	=	PUNCT
ejpam-6036	226	17	∅.	∅.	PRON
ejpam-6036	226	18	definition	definition	NOUN
ejpam-6036	226	19	14	14	NUM
ejpam-6036	226	20	.	.	PUNCT
ejpam-6036	227	1	[	[	X
ejpam-6036	227	2	45	45	NUM
ejpam-6036	227	3	]	]	PUNCT
ejpam-6036	227	4	a	a	DET
ejpam-6036	227	5	bitopological	bitopological	ADJ
ejpam-6036	227	6	space	space	NOUN
ejpam-6036	227	7	(	(	PUNCT
ejpam-6036	227	8	x	x	NOUN
ejpam-6036	227	9	,	,	PUNCT
ejpam-6036	227	10	τ1	τ1	NOUN
ejpam-6036	227	11	,	,	PUNCT
ejpam-6036	227	12	τ2	τ2	NOUN
ejpam-6036	227	13	)	)	PUNCT
ejpam-6036	227	14	is	be	AUX
ejpam-6036	227	15	said	say	VERB
ejpam-6036	227	16	to	to	PART
ejpam-6036	227	17	be	be	AUX
ejpam-6036	227	18	τ1τ2	τ1τ2	NOUN
ejpam-6036	227	19	-	-	ADJ
ejpam-6036	227	20	urysohn	urysohn	ADJ
ejpam-6036	227	21	if	if	SCONJ
ejpam-6036	227	22	for	for	ADP
ejpam-6036	227	23	each	each	DET
ejpam-6036	227	24	pair	pair	NOUN
ejpam-6036	227	25	of	of	ADP
ejpam-6036	227	26	distinct	distinct	ADJ
ejpam-6036	227	27	points	point	NOUN
ejpam-6036	227	28	x	x	PUNCT
ejpam-6036	227	29	and	and	CCONJ
ejpam-6036	227	30	y	y	PROPN
ejpam-6036	227	31	in	in	ADP
ejpam-6036	227	32	x	x	SYM
ejpam-6036	227	33	,	,	PUNCT
ejpam-6036	227	34	there	there	PRON
ejpam-6036	227	35	exist	exist	VERB
ejpam-6036	227	36	τ1τ2	τ1τ2	ADJ
ejpam-6036	227	37	-	-	ADJ
ejpam-6036	227	38	open	open	ADJ
ejpam-6036	227	39	sets	set	NOUN
ejpam-6036	227	40	u	u	NOUN
ejpam-6036	227	41	and	and	CCONJ
ejpam-6036	227	42	v	v	ADP
ejpam-6036	227	43	such	such	ADJ
ejpam-6036	227	44	that	that	SCONJ
ejpam-6036	227	45	x	x	SYM
ejpam-6036	227	46	∈	∈	PROPN
ejpam-6036	227	47	u	u	NOUN
ejpam-6036	227	48	,	,	PUNCT
ejpam-6036	227	49	y	y	PROPN
ejpam-6036	227	50	∈	∈	PROPN
ejpam-6036	227	51	v	v	NOUN
ejpam-6036	227	52	and	and	CCONJ
ejpam-6036	227	53	τ1τ2	τ1τ2	NOUN
ejpam-6036	227	54	-	-	NOUN
ejpam-6036	227	55	cl(u	cl(u	NOUN
ejpam-6036	227	56	)	)	PUNCT
ejpam-6036	227	57	∩	∩	NOUN
ejpam-6036	227	58	τ1τ2	τ1τ2	NOUN
ejpam-6036	227	59	-	-	NOUN
ejpam-6036	227	60	cl(v	cl(v	X
ejpam-6036	227	61	)	)	PUNCT
ejpam-6036	227	62	=	=	PUNCT
ejpam-6036	227	63	∅.	∅.	NOUN
ejpam-6036	227	64	theorem	theorem	VERB
ejpam-6036	227	65	10	10	NUM
ejpam-6036	227	66	.	.	PUNCT
ejpam-6036	228	1	if	if	SCONJ
ejpam-6036	228	2	f	f	PROPN
ejpam-6036	228	3	:	:	PUNCT
ejpam-6036	228	4	(	(	PUNCT
ejpam-6036	228	5	x	x	NOUN
ejpam-6036	228	6	,	,	PUNCT
ejpam-6036	228	7	τ1	τ1	NOUN
ejpam-6036	228	8	,	,	PUNCT
ejpam-6036	228	9	τ2	τ2	NOUN
ejpam-6036	228	10	)	)	PUNCT
ejpam-6036	228	11	→	→	SYM
ejpam-6036	228	12	(	(	PUNCT
ejpam-6036	228	13	y	y	PROPN
ejpam-6036	228	14	,	,	PUNCT
ejpam-6036	228	15	σ1	σ1	PROPN
ejpam-6036	228	16	,	,	PUNCT
ejpam-6036	228	17	σ2	σ2	NOUN
ejpam-6036	228	18	)	)	PUNCT
ejpam-6036	228	19	is	be	AUX
ejpam-6036	228	20	weakly	weakly	ADJ
ejpam-6036	228	21	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	228	22	,	,	PUNCT
ejpam-6036	228	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	228	24	and	and	CCONJ
ejpam-6036	228	25	(	(	PUNCT
ejpam-6036	228	26	y	y	PROPN
ejpam-6036	228	27	,	,	PUNCT
ejpam-6036	228	28	σ1	σ1	PROPN
ejpam-6036	228	29	,	,	PUNCT
ejpam-6036	228	30	σ2	σ2	PROPN
ejpam-6036	228	31	)	)	PUNCT
ejpam-6036	228	32	is	be	AUX
ejpam-6036	228	33	σ1σ2	σ1σ2	NOUN
ejpam-6036	228	34	-	-	PUNCT
ejpam-6036	228	35	urysohn	urysohn	ADJ
ejpam-6036	228	36	,	,	PUNCT
ejpam-6036	228	37	then	then	ADV
ejpam-6036	228	38	g(f	g(f	PROPN
ejpam-6036	228	39	)	)	PUNCT
ejpam-6036	228	40	is	be	AUX
ejpam-6036	228	41	contra	contra	PROPN
ejpam-6036	228	42	-	-	PUNCT
ejpam-6036	228	43	cr	cr	ADV
ejpam-6036	228	44	-	-	PUNCT
ejpam-6036	228	45	closed	closed	ADJ
ejpam-6036	228	46	.	.	PUNCT
ejpam-6036	229	1	proof	proof	NOUN
ejpam-6036	229	2	.	.	PUNCT
ejpam-6036	230	1	let	let	VERB
ejpam-6036	230	2	(	(	PUNCT
ejpam-6036	230	3	x	x	NOUN
ejpam-6036	230	4	,	,	PUNCT
ejpam-6036	230	5	y	y	NOUN
ejpam-6036	230	6	)	)	PUNCT
ejpam-6036	230	7	∈	∈	PROPN
ejpam-6036	230	8	(	(	PUNCT
ejpam-6036	230	9	x	x	SYM
ejpam-6036	230	10	×	×	PROPN
ejpam-6036	230	11	y	y	PROPN
ejpam-6036	230	12	)	)	PUNCT
ejpam-6036	231	1	−	−	PROPN
ejpam-6036	231	2	g(f	g(f	NOUN
ejpam-6036	231	3	)	)	PUNCT
ejpam-6036	231	4	.	.	PUNCT
ejpam-6036	232	1	then	then	ADV
ejpam-6036	232	2	,	,	PUNCT
ejpam-6036	232	3	y	y	PROPN
ejpam-6036	232	4	̸=	̸=	PROPN
ejpam-6036	232	5	f(x	f(x	PROPN
ejpam-6036	232	6	)	)	PUNCT
ejpam-6036	232	7	.	.	PUNCT
ejpam-6036	233	1	since	since	SCONJ
ejpam-6036	233	2	(	(	PUNCT
ejpam-6036	233	3	y	y	PROPN
ejpam-6036	233	4	,	,	PUNCT
ejpam-6036	233	5	σ1	σ1	PROPN
ejpam-6036	233	6	,	,	PUNCT
ejpam-6036	233	7	σ2	σ2	PROPN
ejpam-6036	233	8	)	)	PUNCT
ejpam-6036	233	9	is	be	AUX
ejpam-6036	233	10	σ1σ2urysohn	σ1σ2urysohn	NUM
ejpam-6036	233	11	,	,	PUNCT
ejpam-6036	233	12	there	there	PRON
ejpam-6036	233	13	exist	exist	VERB
ejpam-6036	233	14	σ1σ2	σ1σ2	NOUN
ejpam-6036	233	15	-	-	ADJ
ejpam-6036	233	16	open	open	ADJ
ejpam-6036	233	17	sets	set	NOUN
ejpam-6036	233	18	v	v	ADP
ejpam-6036	233	19	and	and	CCONJ
ejpam-6036	233	20	w	w	PROPN
ejpam-6036	233	21	of	of	ADP
ejpam-6036	233	22	y	y	PROPN
ejpam-6036	233	23	containing	contain	VERB
ejpam-6036	233	24	y	y	PROPN
ejpam-6036	233	25	and	and	CCONJ
ejpam-6036	233	26	f(x	f(x	PROPN
ejpam-6036	233	27	)	)	PUNCT
ejpam-6036	233	28	,	,	PUNCT
ejpam-6036	233	29	respectively	respectively	ADV
ejpam-6036	233	30	,	,	PUNCT
ejpam-6036	233	31	such	such	ADJ
ejpam-6036	233	32	that	that	SCONJ
ejpam-6036	233	33	σ1σ2	σ1σ2	NOUN
ejpam-6036	233	34	-	-	PUNCT
ejpam-6036	233	35	cl(v	cl(v	NOUN
ejpam-6036	233	36	)	)	PUNCT
ejpam-6036	233	37	∩	∩	NOUN
ejpam-6036	233	38	σ1σ2	σ1σ2	NOUN
ejpam-6036	233	39	-	-	NUM
ejpam-6036	233	40	cl(w	cl(w	NOUN
ejpam-6036	233	41	)	)	PUNCT
ejpam-6036	234	1	=	=	NOUN
ejpam-6036	234	2	∅	∅	NOUN
ejpam-6036	234	3	;	;	PUNCT
ejpam-6036	234	4	hence	hence	ADV
ejpam-6036	234	5	σ1σ2	σ1σ2	NOUN
ejpam-6036	234	6	-	-	NUM
ejpam-6036	234	7	cl(v	cl(v	NOUN
ejpam-6036	234	8	)	)	PUNCT
ejpam-6036	235	1	⊆	⊆	NUM
ejpam-6036	235	2	y	y	NOUN
ejpam-6036	235	3	−	−	PUNCT
ejpam-6036	235	4	σ1σ2	σ1σ2	NOUN
ejpam-6036	235	5	-	-	PUNCT
ejpam-6036	235	6	cl(w	cl(w	NOUN
ejpam-6036	235	7	)	)	PUNCT
ejpam-6036	235	8	.	.	PUNCT
ejpam-6036	236	1	since	since	SCONJ
ejpam-6036	236	2	f	f	PROPN
ejpam-6036	236	3	is	be	AUX
ejpam-6036	236	4	weakly	weakly	ADJ
ejpam-6036	236	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	236	6	,	,	PUNCT
ejpam-6036	236	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	236	8	,	,	PUNCT
ejpam-6036	236	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	236	10	-	-	ADJ
ejpam-6036	236	11	cl(f	cl(f	NOUN
ejpam-6036	236	12	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	236	13	-	-	PUNCT
ejpam-6036	236	14	cl(v	cl(v	NOUN
ejpam-6036	236	15	)	)	PUNCT
ejpam-6036	236	16	)	)	PUNCT
ejpam-6036	236	17	)	)	PUNCT
ejpam-6036	237	1	⊆	⊆	X
ejpam-6036	237	2	f−1(y	f−1(y	NOUN
ejpam-6036	237	3	−	−	PUNCT
ejpam-6036	237	4	σ1σ2	σ1σ2	NOUN
ejpam-6036	237	5	-	-	PUNCT
ejpam-6036	237	6	cl(w	cl(w	NOUN
ejpam-6036	237	7	)	)	PUNCT
ejpam-6036	237	8	)	)	PUNCT
ejpam-6036	237	9	.	.	PUNCT
ejpam-6036	238	1	thus	thus	ADV
ejpam-6036	238	2	,	,	PUNCT
ejpam-6036	238	3	(	(	PUNCT
ejpam-6036	238	4	x	x	X
ejpam-6036	238	5	,	,	PUNCT
ejpam-6036	238	6	y	y	NOUN
ejpam-6036	238	7	)	)	PUNCT
ejpam-6036	238	8	∈	∈	PROPN
ejpam-6036	238	9	τ1τ2	τ1τ2	NOUN
ejpam-6036	238	10	-	-	ADJ
ejpam-6036	238	11	cl(f	cl(f	NOUN
ejpam-6036	238	12	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6036	238	13	-	-	PUNCT
ejpam-6036	238	14	cl(v	cl(v	NOUN
ejpam-6036	238	15	)	)	PUNCT
ejpam-6036	238	16	)	)	PUNCT
ejpam-6036	238	17	)	)	PUNCT
ejpam-6036	239	1	×σ1σ2	×σ1σ2	NOUN
ejpam-6036	239	2	-	-	PUNCT
ejpam-6036	239	3	cl(w	cl(w	NOUN
ejpam-6036	239	4	)	)	PUNCT
ejpam-6036	239	5	⊆	⊆	NUM
ejpam-6036	239	6	(	(	PUNCT
ejpam-6036	239	7	x×y	x×y	PROPN
ejpam-6036	239	8	)	)	PUNCT
ejpam-6036	239	9	−g(f	−g(f	NOUN
ejpam-6036	239	10	)	)	PUNCT
ejpam-6036	239	11	and	and	CCONJ
ejpam-6036	239	12	hence	hence	ADV
ejpam-6036	239	13	g(f	g(f	PROPN
ejpam-6036	239	14	)	)	PUNCT
ejpam-6036	239	15	is	be	AUX
ejpam-6036	239	16	contra	contra	PROPN
ejpam-6036	239	17	-	-	PUNCT
ejpam-6036	239	18	cr	cr	NOUN
ejpam-6036	239	19	-	-	PUNCT
ejpam-6036	239	20	closed	closed	ADJ
ejpam-6036	239	21	.	.	PUNCT
ejpam-6036	240	1	acknowledgements	acknowledgement	NOUN
ejpam-6036	240	2	this	this	DET
ejpam-6036	240	3	research	research	NOUN
ejpam-6036	240	4	project	project	NOUN
ejpam-6036	240	5	was	be	AUX
ejpam-6036	240	6	financially	financially	ADV
ejpam-6036	240	7	supported	support	VERB
ejpam-6036	240	8	by	by	ADP
ejpam-6036	240	9	mahasarakham	mahasarakham	PROPN
ejpam-6036	240	10	university	university	PROPN
ejpam-6036	240	11	.	.	PUNCT
ejpam-6036	241	1	references	reference	NOUN
ejpam-6036	241	2	[	[	X
ejpam-6036	241	3	1	1	NUM
ejpam-6036	241	4	]	]	PUNCT
ejpam-6036	241	5	c.	c.	PROPN
ejpam-6036	241	6	viriyapong	viriyapong	PROPN
ejpam-6036	241	7	and	and	CCONJ
ejpam-6036	241	8	c.	c.	PROPN
ejpam-6036	241	9	boonpok	boonpok	PROPN
ejpam-6036	241	10	.	.	PUNCT
ejpam-6036	242	1	(	(	PUNCT
ejpam-6036	242	2	λ	λ	X
ejpam-6036	242	3	,	,	PUNCT
ejpam-6036	242	4	sp)-continuous	sp)-continuous	ADJ
ejpam-6036	242	5	functions	function	NOUN
ejpam-6036	242	6	.	.	PUNCT
ejpam-6036	243	1	wseas	wseas	VERB
ejpam-6036	243	2	transactions	transaction	NOUN
ejpam-6036	243	3	on	on	ADP
ejpam-6036	243	4	mathematics	mathematic	NOUN
ejpam-6036	243	5	,	,	PUNCT
ejpam-6036	243	6	21:380–385	21:380–385	NUM
ejpam-6036	243	7	,	,	PUNCT
ejpam-6036	243	8	2022	2022	NUM
ejpam-6036	243	9	.	.	PUNCT
ejpam-6036	244	1	[	[	X
ejpam-6036	244	2	2	2	NUM
ejpam-6036	244	3	]	]	PUNCT
ejpam-6036	244	4	c.	c.	PROPN
ejpam-6036	244	5	boonpok	boonpok	PROPN
ejpam-6036	244	6	and	and	CCONJ
ejpam-6036	244	7	j.	j.	PROPN
ejpam-6036	244	8	khampakdee	khampakdee	PROPN
ejpam-6036	244	9	.	.	PUNCT
ejpam-6036	245	1	(	(	PUNCT
ejpam-6036	245	2	λ	λ	NOUN
ejpam-6036	245	3	,	,	PUNCT
ejpam-6036	245	4	sp)-open	sp)-open	ADJ
ejpam-6036	245	5	sets	set	NOUN
ejpam-6036	245	6	in	in	ADP
ejpam-6036	245	7	topological	topological	ADJ
ejpam-6036	245	8	spaces	space	NOUN
ejpam-6036	245	9	.	.	PUNCT
ejpam-6036	246	1	european	european	ADJ
ejpam-6036	246	2	journal	journal	PROPN
ejpam-6036	246	3	of	of	ADP
ejpam-6036	246	4	pure	pure	ADJ
ejpam-6036	246	5	and	and	CCONJ
ejpam-6036	246	6	applied	applied	ADJ
ejpam-6036	246	7	mathematics	mathematic	NOUN
ejpam-6036	246	8	,	,	PUNCT
ejpam-6036	246	9	15(2):572–588	15(2):572–588	NUM
ejpam-6036	246	10	,	,	PUNCT
ejpam-6036	246	11	2022	2022	NUM
ejpam-6036	246	12	.	.	PUNCT
ejpam-6036	247	1	[	[	X
ejpam-6036	247	2	3	3	X
ejpam-6036	247	3	]	]	PUNCT
ejpam-6036	247	4	t.	t.	NOUN
ejpam-6036	247	5	dungthaisong	dungthaisong	PROPN
ejpam-6036	247	6	,	,	PUNCT
ejpam-6036	247	7	c.	c.	PROPN
ejpam-6036	247	8	boonpok	boonpok	PROPN
ejpam-6036	247	9	,	,	PUNCT
ejpam-6036	247	10	and	and	CCONJ
ejpam-6036	247	11	c.	c.	PROPN
ejpam-6036	247	12	viriyapong	viriyapong	PROPN
ejpam-6036	247	13	.	.	PUNCT
ejpam-6036	248	1	generalized	generalize	VERB
ejpam-6036	248	2	closed	close	VERB
ejpam-6036	248	3	sets	set	NOUN
ejpam-6036	248	4	in	in	ADP
ejpam-6036	248	5	bigeneralized	bigeneralize	VERB
ejpam-6036	248	6	topological	topological	ADJ
ejpam-6036	248	7	spaces	space	NOUN
ejpam-6036	248	8	.	.	PUNCT
ejpam-6036	249	1	international	international	ADJ
ejpam-6036	249	2	journal	journal	PROPN
ejpam-6036	249	3	of	of	ADP
ejpam-6036	249	4	mathematical	mathematical	ADJ
ejpam-6036	249	5	analysis	analysis	NOUN
ejpam-6036	249	6	,	,	PUNCT
ejpam-6036	249	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-6036	249	8	,	,	PUNCT
ejpam-6036	249	9	2011	2011	NUM
ejpam-6036	249	10	.	.	PUNCT
ejpam-6036	250	1	b.	b.	PROPN
ejpam-6036	250	2	kong	kong	PROPN
ejpam-6036	250	3	-	-	PUNCT
ejpam-6036	250	4	ied	ied	PROPN
ejpam-6036	250	5	,	,	PUNCT
ejpam-6036	250	6	s.	s.	PROPN
ejpam-6036	250	7	sompong	sompong	PROPN
ejpam-6036	250	8	,	,	PUNCT
ejpam-6036	250	9	c.	c.	PROPN
ejpam-6036	250	10	boonpok	boonpok	PROPN
ejpam-6036	250	11	/	/	SYM
ejpam-6036	250	12	eur	eur	PROPN
ejpam-6036	250	13	.	.	PUNCT
ejpam-6036	251	1	j.	j.	PROPN
ejpam-6036	251	2	pure	pure	PROPN
ejpam-6036	251	3	appl	appl	PROPN
ejpam-6036	251	4	.	.	PROPN
ejpam-6036	251	5	math	math	PROPN
ejpam-6036	251	6	,	,	PUNCT
ejpam-6036	251	7	18	18	NUM
ejpam-6036	251	8	(	(	PUNCT
ejpam-6036	251	9	2	2	NUM
ejpam-6036	251	10	)	)	PUNCT
ejpam-6036	251	11	(	(	PUNCT
ejpam-6036	251	12	2025	2025	NUM
ejpam-6036	251	13	)	)	PUNCT
ejpam-6036	251	14	,	,	PUNCT
ejpam-6036	251	15	6036	6036	NUM
ejpam-6036	251	16	9	9	NUM
ejpam-6036	251	17	of	of	ADP
ejpam-6036	251	18	11	11	NUM
ejpam-6036	251	19	[	[	SYM
ejpam-6036	251	20	4	4	NUM
ejpam-6036	251	21	]	]	PUNCT
ejpam-6036	251	22	t.	t.	PROPN
ejpam-6036	251	23	duangphui	duangphui	PROPN
ejpam-6036	251	24	,	,	PUNCT
ejpam-6036	251	25	c.	c.	PROPN
ejpam-6036	251	26	boonpok	boonpok	PROPN
ejpam-6036	251	27	,	,	PUNCT
ejpam-6036	251	28	and	and	CCONJ
ejpam-6036	251	29	c.	c.	PROPN
ejpam-6036	251	30	viriyapong	viriyapong	PROPN
ejpam-6036	251	31	.	.	PUNCT
ejpam-6036	252	1	continuous	continuous	ADJ
ejpam-6036	252	2	functions	function	NOUN
ejpam-6036	252	3	on	on	ADP
ejpam-6036	252	4	bigeneralized	bigeneralize	VERB
ejpam-6036	252	5	topological	topological	ADJ
ejpam-6036	252	6	spaces	space	NOUN
ejpam-6036	252	7	.	.	PUNCT
ejpam-6036	253	1	international	international	ADJ
ejpam-6036	253	2	journal	journal	PROPN
ejpam-6036	253	3	of	of	ADP
ejpam-6036	253	4	mathematical	mathematical	ADJ
ejpam-6036	253	5	analysis	analysis	NOUN
ejpam-6036	253	6	,	,	PUNCT
ejpam-6036	253	7	5(24):1165	5(24):1165	NUM
ejpam-6036	253	8	–	–	PUNCT
ejpam-6036	253	9	1174	1174	NUM
ejpam-6036	253	10	,	,	PUNCT
ejpam-6036	253	11	2011	2011	NUM
ejpam-6036	253	12	.	.	PUNCT
ejpam-6036	254	1	[	[	X
ejpam-6036	254	2	5	5	NUM
ejpam-6036	254	3	]	]	X
ejpam-6036	254	4	n.	n.	NOUN
ejpam-6036	254	5	srisarakham	srisarakham	PROPN
ejpam-6036	254	6	and	and	CCONJ
ejpam-6036	254	7	c.	c.	PROPN
ejpam-6036	254	8	boonpok	boonpok	PROPN
ejpam-6036	254	9	.	.	PUNCT
ejpam-6036	255	1	almost	almost	ADV
ejpam-6036	255	2	(	(	PUNCT
ejpam-6036	255	3	λ	λ	NOUN
ejpam-6036	255	4	,	,	PUNCT
ejpam-6036	255	5	p)-continuous	p)-continuous	ADJ
ejpam-6036	255	6	functions	function	NOUN
ejpam-6036	255	7	.	.	PUNCT
ejpam-6036	256	1	international	international	ADJ
ejpam-6036	256	2	journal	journal	PROPN
ejpam-6036	256	3	of	of	ADP
ejpam-6036	256	4	mathematics	mathematic	NOUN
ejpam-6036	256	5	and	and	CCONJ
ejpam-6036	256	6	computer	computer	NOUN
ejpam-6036	256	7	science	science	NOUN
ejpam-6036	256	8	,	,	PUNCT
ejpam-6036	256	9	18(2):255–259	18(2):255–259	NUM
ejpam-6036	256	10	,	,	PUNCT
ejpam-6036	256	11	2023	2023	NUM
ejpam-6036	256	12	.	.	PUNCT
ejpam-6036	257	1	[	[	X
ejpam-6036	257	2	6	6	NUM
ejpam-6036	257	3	]	]	PUNCT
ejpam-6036	257	4	m.	m.	NOUN
ejpam-6036	257	5	thongmoon	thongmoon	NOUN
ejpam-6036	257	6	and	and	CCONJ
ejpam-6036	257	7	c.	c.	PROPN
ejpam-6036	257	8	boonpok	boonpok	PROPN
ejpam-6036	257	9	.	.	PUNCT
ejpam-6036	258	1	strongly	strongly	ADV
ejpam-6036	258	2	θ(λ	θ(λ	PROPN
ejpam-6036	258	3	,	,	PUNCT
ejpam-6036	258	4	p)-continuous	p)-continuous	ADJ
ejpam-6036	258	5	functions	function	NOUN
ejpam-6036	258	6	.	.	PUNCT
ejpam-6036	259	1	international	international	ADJ
ejpam-6036	259	2	journal	journal	PROPN
ejpam-6036	259	3	of	of	ADP
ejpam-6036	259	4	mathematics	mathematic	NOUN
ejpam-6036	259	5	and	and	CCONJ
ejpam-6036	259	6	computer	computer	NOUN
ejpam-6036	259	7	science	science	NOUN
ejpam-6036	259	8	,	,	PUNCT
ejpam-6036	259	9	19(2):475–479	19(2):475–479	PROPN
ejpam-6036	259	10	,	,	PUNCT
ejpam-6036	259	11	2024	2024	NUM
ejpam-6036	259	12	.	.	PUNCT
ejpam-6036	260	1	[	[	X
ejpam-6036	260	2	7	7	X
ejpam-6036	260	3	]	]	X
ejpam-6036	260	4	c.	c.	PROPN
ejpam-6036	260	5	boonpok	boonpok	PROPN
ejpam-6036	260	6	and	and	CCONJ
ejpam-6036	260	7	j.	j.	PROPN
ejpam-6036	260	8	khampakdee	khampakdee	PROPN
ejpam-6036	260	9	.	.	PUNCT
ejpam-6036	261	1	almost	almost	ADV
ejpam-6036	261	2	strong	strong	ADJ
ejpam-6036	261	3	θ(λ	θ(λ	PROPN
ejpam-6036	261	4	,	,	PUNCT
ejpam-6036	261	5	p)-continuity	p)-continuity	NOUN
ejpam-6036	261	6	for	for	ADP
ejpam-6036	261	7	functions	function	NOUN
ejpam-6036	261	8	.	.	PUNCT
ejpam-6036	262	1	european	european	ADJ
ejpam-6036	262	2	journal	journal	PROPN
ejpam-6036	262	3	of	of	ADP
ejpam-6036	262	4	pure	pure	ADJ
ejpam-6036	262	5	and	and	CCONJ
ejpam-6036	262	6	applied	applied	ADJ
ejpam-6036	262	7	mathematics	mathematic	NOUN
ejpam-6036	262	8	,	,	PUNCT
ejpam-6036	262	9	17(1):300–309	17(1):300–309	PROPN
ejpam-6036	262	10	,	,	PUNCT
ejpam-6036	262	11	2024	2024	NUM
ejpam-6036	262	12	.	.	PUNCT
ejpam-6036	263	1	[	[	X
ejpam-6036	263	2	8	8	NUM
ejpam-6036	263	3	]	]	X
ejpam-6036	263	4	p.	p.	NOUN
ejpam-6036	263	5	pue	pue	NOUN
ejpam-6036	263	6	-	-	PUNCT
ejpam-6036	263	7	on	on	ADP
ejpam-6036	263	8	and	and	CCONJ
ejpam-6036	263	9	c.	c.	PROPN
ejpam-6036	263	10	boonpok	boonpok	PROPN
ejpam-6036	263	11	.	.	PUNCT
ejpam-6036	264	1	θ(λ	θ(λ	PROPN
ejpam-6036	264	2	,	,	PUNCT
ejpam-6036	264	3	p)-continuity	p)-continuity	NOUN
ejpam-6036	264	4	for	for	ADP
ejpam-6036	264	5	functions	function	NOUN
ejpam-6036	264	6	.	.	PUNCT
ejpam-6036	265	1	international	international	ADJ
ejpam-6036	265	2	journal	journal	NOUN
ejpam-6036	265	3	of	of	ADP
ejpam-6036	265	4	mathematics	mathematic	NOUN
ejpam-6036	265	5	and	and	CCONJ
ejpam-6036	265	6	computer	computer	NOUN
ejpam-6036	265	7	science	science	NOUN
ejpam-6036	265	8	,	,	PUNCT
ejpam-6036	265	9	19(2):491–495	19(2):491–495	NUM
ejpam-6036	265	10	,	,	PUNCT
ejpam-6036	265	11	2024	2024	NUM
ejpam-6036	265	12	.	.	PUNCT
ejpam-6036	266	1	[	[	X
ejpam-6036	266	2	9	9	NUM
ejpam-6036	266	3	]	]	PUNCT
ejpam-6036	266	4	c.	c.	NOUN
ejpam-6036	266	5	boonpok	boonpok	PROPN
ejpam-6036	266	6	and	and	CCONJ
ejpam-6036	266	7	n.	n.	PROPN
ejpam-6036	266	8	srisarakham	srisarakham	PROPN
ejpam-6036	266	9	.	.	PUNCT
ejpam-6036	267	1	weak	weak	ADJ
ejpam-6036	267	2	forms	form	NOUN
ejpam-6036	267	3	of	of	ADP
ejpam-6036	267	4	(	(	PUNCT
ejpam-6036	267	5	λ	λ	PROPN
ejpam-6036	267	6	,	,	PUNCT
ejpam-6036	267	7	b)-open	b)-open	VERB
ejpam-6036	267	8	sets	set	NOUN
ejpam-6036	267	9	and	and	CCONJ
ejpam-6036	267	10	weak	weak	ADJ
ejpam-6036	267	11	(	(	PUNCT
ejpam-6036	267	12	λ	λ	NOUN
ejpam-6036	267	13	,	,	PUNCT
ejpam-6036	267	14	b)continuity	b)continuity	NOUN
ejpam-6036	267	15	.	.	PUNCT
ejpam-6036	268	1	european	european	PROPN
ejpam-6036	268	2	journal	journal	PROPN
ejpam-6036	268	3	of	of	ADP
ejpam-6036	268	4	pure	pure	ADJ
ejpam-6036	268	5	and	and	CCONJ
ejpam-6036	268	6	applied	applied	ADJ
ejpam-6036	268	7	mathematics	mathematic	NOUN
ejpam-6036	268	8	,	,	PUNCT
ejpam-6036	268	9	16(1):29–43	16(1):29–43	NUM
ejpam-6036	268	10	,	,	PUNCT
ejpam-6036	268	11	2023	2023	NUM
ejpam-6036	268	12	.	.	PUNCT
ejpam-6036	269	1	[	[	X
ejpam-6036	269	2	10	10	NUM
ejpam-6036	269	3	]	]	X
ejpam-6036	269	4	c.	c.	PROPN
ejpam-6036	269	5	boonpok	boonpok	PROPN
ejpam-6036	269	6	.	.	PUNCT
ejpam-6036	270	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-6036	270	2	.	.	PUNCT
ejpam-6036	271	1	mathematica	mathematica	PROPN
ejpam-6036	271	2	,	,	PUNCT
ejpam-6036	271	3	65(1):31–42	65(1):31–42	NUM
ejpam-6036	271	4	,	,	PUNCT
ejpam-6036	271	5	2023	2023	NUM
ejpam-6036	271	6	.	.	PUNCT
ejpam-6036	272	1	[	[	X
ejpam-6036	272	2	11	11	NUM
ejpam-6036	272	3	]	]	PUNCT
ejpam-6036	272	4	c.	c.	PROPN
ejpam-6036	272	5	boonpok	boonpok	PROPN
ejpam-6036	272	6	.	.	PUNCT
ejpam-6036	273	1	on	on	ADP
ejpam-6036	273	2	some	some	DET
ejpam-6036	273	3	closed	closed	ADJ
ejpam-6036	273	4	sets	set	NOUN
ejpam-6036	273	5	and	and	CCONJ
ejpam-6036	273	6	low	low	ADJ
ejpam-6036	273	7	separation	separation	NOUN
ejpam-6036	273	8	axioms	axiom	NOUN
ejpam-6036	273	9	via	via	ADP
ejpam-6036	273	10	topological	topological	ADJ
ejpam-6036	273	11	ideals	ideal	NOUN
ejpam-6036	273	12	.	.	PUNCT
ejpam-6036	274	1	european	european	ADJ
ejpam-6036	274	2	journal	journal	PROPN
ejpam-6036	274	3	of	of	ADP
ejpam-6036	274	4	pure	pure	ADJ
ejpam-6036	274	5	and	and	CCONJ
ejpam-6036	274	6	applied	applied	ADJ
ejpam-6036	274	7	mathematics	mathematic	NOUN
ejpam-6036	274	8	,	,	PUNCT
ejpam-6036	274	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-6036	274	10	,	,	PUNCT
ejpam-6036	274	11	2022	2022	NUM
ejpam-6036	274	12	.	.	PUNCT
ejpam-6036	275	1	[	[	X
ejpam-6036	275	2	12	12	NUM
ejpam-6036	275	3	]	]	PUNCT
ejpam-6036	275	4	c.	c.	PROPN
ejpam-6036	275	5	boonpok	boonpok	PROPN
ejpam-6036	275	6	.	.	PUNCT
ejpam-6036	276	1	on	on	ADP
ejpam-6036	276	2	some	some	DET
ejpam-6036	276	3	spaces	space	NOUN
ejpam-6036	276	4	via	via	ADP
ejpam-6036	276	5	topological	topological	ADJ
ejpam-6036	276	6	ideals	ideal	NOUN
ejpam-6036	276	7	.	.	PUNCT
ejpam-6036	277	1	open	open	ADJ
ejpam-6036	277	2	mathematics	mathematic	NOUN
ejpam-6036	277	3	,	,	PUNCT
ejpam-6036	277	4	21:20230118	21:20230118	NUM
ejpam-6036	277	5	,	,	PUNCT
ejpam-6036	277	6	2023	2023	NUM
ejpam-6036	277	7	.	.	PUNCT
ejpam-6036	278	1	[	[	X
ejpam-6036	278	2	13	13	NUM
ejpam-6036	278	3	]	]	PUNCT
ejpam-6036	278	4	c.	c.	PROPN
ejpam-6036	278	5	boonpok	boonpok	PROPN
ejpam-6036	278	6	.	.	PUNCT
ejpam-6036	279	1	on	on	ADP
ejpam-6036	279	2	characterizations	characterization	NOUN
ejpam-6036	279	3	of	of	ADP
ejpam-6036	279	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-6036	279	5	ideal	ideal	ADJ
ejpam-6036	279	6	topological	topological	ADJ
ejpam-6036	279	7	spaces	space	NOUN
ejpam-6036	279	8	.	.	PUNCT
ejpam-6036	280	1	journal	journal	NOUN
ejpam-6036	280	2	of	of	ADP
ejpam-6036	280	3	mathematics	mathematic	NOUN
ejpam-6036	280	4	,	,	PUNCT
ejpam-6036	280	5	2020:9387601	2020:9387601	NUM
ejpam-6036	280	6	,	,	PUNCT
ejpam-6036	280	7	2020	2020	NUM
ejpam-6036	280	8	.	.	PUNCT
ejpam-6036	281	1	[	[	X
ejpam-6036	281	2	14	14	NUM
ejpam-6036	281	3	]	]	X
ejpam-6036	281	4	c.	c.	PROPN
ejpam-6036	281	5	boonpok	boonpok	PROPN
ejpam-6036	281	6	.	.	PUNCT
ejpam-6036	282	1	almost	almost	ADV
ejpam-6036	282	2	(	(	PUNCT
ejpam-6036	282	3	g	g	NOUN
ejpam-6036	282	4	,	,	PUNCT
ejpam-6036	282	5	m)-continuous	m)-continuous	ADJ
ejpam-6036	282	6	functions	function	NOUN
ejpam-6036	282	7	.	.	PUNCT
ejpam-6036	283	1	international	international	ADJ
ejpam-6036	283	2	journal	journal	PROPN
ejpam-6036	283	3	of	of	ADP
ejpam-6036	283	4	mathematical	mathematical	ADJ
ejpam-6036	283	5	analysis	analysis	NOUN
ejpam-6036	283	6	,	,	PUNCT
ejpam-6036	283	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-6036	283	8	,	,	PUNCT
ejpam-6036	283	9	2010	2010	NUM
ejpam-6036	283	10	.	.	PUNCT
ejpam-6036	284	1	[	[	X
ejpam-6036	284	2	15	15	NUM
ejpam-6036	284	3	]	]	X
ejpam-6036	284	4	c.	c.	PROPN
ejpam-6036	284	5	boonpok	boonpok	PROPN
ejpam-6036	284	6	.	.	PUNCT
ejpam-6036	285	1	m	m	VERB
ejpam-6036	285	2	-continuous	-continuous	ADJ
ejpam-6036	285	3	functions	function	NOUN
ejpam-6036	285	4	in	in	ADP
ejpam-6036	285	5	biminimal	biminimal	NOUN
ejpam-6036	285	6	structure	structure	NOUN
ejpam-6036	285	7	spaces	space	NOUN
ejpam-6036	285	8	.	.	PUNCT
ejpam-6036	286	1	far	far	PROPN
ejpam-6036	286	2	east	east	PROPN
ejpam-6036	286	3	journal	journal	PROPN
ejpam-6036	286	4	of	of	ADP
ejpam-6036	286	5	mathematical	mathematical	ADJ
ejpam-6036	286	6	sciences	science	NOUN
ejpam-6036	286	7	,	,	PUNCT
ejpam-6036	286	8	43(1):41–58	43(1):41–58	NUM
ejpam-6036	286	9	,	,	PUNCT
ejpam-6036	286	10	2010	2010	NUM
ejpam-6036	286	11	.	.	PUNCT
ejpam-6036	287	1	[	[	X
ejpam-6036	287	2	16	16	NUM
ejpam-6036	287	3	]	]	X
ejpam-6036	287	4	n.	n.	PROPN
ejpam-6036	287	5	srisarakham	srisarakham	PROPN
ejpam-6036	287	6	,	,	PUNCT
ejpam-6036	287	7	a.	a.	PROPN
ejpam-6036	287	8	sama	sama	PROPN
ejpam-6036	287	9	-	-	PUNCT
ejpam-6036	287	10	ae	ae	PROPN
ejpam-6036	287	11	,	,	PUNCT
ejpam-6036	287	12	and	and	CCONJ
ejpam-6036	287	13	c.	c.	PROPN
ejpam-6036	287	14	boonpok	boonpok	PROPN
ejpam-6036	287	15	.	.	PUNCT
ejpam-6036	288	1	characterizations	characterization	NOUN
ejpam-6036	288	2	of	of	ADP
ejpam-6036	288	3	faintly	faintly	ADV
ejpam-6036	288	4	(	(	PUNCT
ejpam-6036	288	5	τ1	τ1	PROPN
ejpam-6036	288	6	,	,	PUNCT
ejpam-6036	288	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	288	8	functions	function	NOUN
ejpam-6036	288	9	.	.	PUNCT
ejpam-6036	289	1	european	european	ADJ
ejpam-6036	289	2	journal	journal	PROPN
ejpam-6036	289	3	of	of	ADP
ejpam-6036	289	4	pure	pure	ADJ
ejpam-6036	289	5	and	and	CCONJ
ejpam-6036	289	6	applied	applied	ADJ
ejpam-6036	289	7	mathematics	mathematic	NOUN
ejpam-6036	289	8	,	,	PUNCT
ejpam-6036	289	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-6036	289	10	,	,	PUNCT
ejpam-6036	289	11	2024	2024	NUM
ejpam-6036	289	12	.	.	PUNCT
ejpam-6036	290	1	[	[	X
ejpam-6036	290	2	17	17	NUM
ejpam-6036	290	3	]	]	PUNCT
ejpam-6036	290	4	c.	c.	NOUN
ejpam-6036	290	5	prachanpol	prachanpol	NOUN
ejpam-6036	290	6	,	,	PUNCT
ejpam-6036	290	7	c.	c.	PROPN
ejpam-6036	290	8	boonpok	boonpok	PROPN
ejpam-6036	290	9	,	,	PUNCT
ejpam-6036	290	10	and	and	CCONJ
ejpam-6036	290	11	c.	c.	PROPN
ejpam-6036	290	12	viriyapong	viriyapong	PROPN
ejpam-6036	290	13	.	.	PUNCT
ejpam-6036	291	1	δ(τ1	δ(τ1	PROPN
ejpam-6036	291	2	,	,	PUNCT
ejpam-6036	291	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	291	4	functions	function	NOUN
ejpam-6036	291	5	.	.	PUNCT
ejpam-6036	292	1	european	european	ADJ
ejpam-6036	292	2	journal	journal	PROPN
ejpam-6036	292	3	of	of	ADP
ejpam-6036	292	4	pure	pure	ADJ
ejpam-6036	292	5	and	and	CCONJ
ejpam-6036	292	6	applied	applied	ADJ
ejpam-6036	292	7	mathematics	mathematic	NOUN
ejpam-6036	292	8	,	,	PUNCT
ejpam-6036	292	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-6036	292	10	,	,	PUNCT
ejpam-6036	292	11	2024	2024	NUM
ejpam-6036	292	12	.	.	PUNCT
ejpam-6036	293	1	[	[	X
ejpam-6036	293	2	18	18	NUM
ejpam-6036	293	3	]	]	X
ejpam-6036	293	4	b.	b.	PROPN
ejpam-6036	293	5	kong	kong	PROPN
ejpam-6036	293	6	-	-	PUNCT
ejpam-6036	293	7	ied	ied	PROPN
ejpam-6036	293	8	,	,	PUNCT
ejpam-6036	293	9	a.	a.	PROPN
ejpam-6036	293	10	sama	sama	PROPN
ejpam-6036	293	11	-	-	PUNCT
ejpam-6036	293	12	ae	ae	PROPN
ejpam-6036	293	13	,	,	PUNCT
ejpam-6036	293	14	and	and	CCONJ
ejpam-6036	293	15	c.	c.	PROPN
ejpam-6036	293	16	boonpok	boonpok	PROPN
ejpam-6036	293	17	.	.	PUNCT
ejpam-6036	294	1	almost	almost	ADV
ejpam-6036	294	2	nearly	nearly	ADV
ejpam-6036	294	3	(	(	PUNCT
ejpam-6036	294	4	τ1	τ1	NOUN
ejpam-6036	294	5	,	,	PUNCT
ejpam-6036	294	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	294	7	functions	function	NOUN
ejpam-6036	294	8	.	.	PUNCT
ejpam-6036	295	1	international	international	ADJ
ejpam-6036	295	2	journal	journal	NOUN
ejpam-6036	295	3	of	of	ADP
ejpam-6036	295	4	analysis	analysis	NOUN
ejpam-6036	295	5	and	and	CCONJ
ejpam-6036	295	6	applications	application	NOUN
ejpam-6036	295	7	,	,	PUNCT
ejpam-6036	295	8	23:14	23:14	NUM
ejpam-6036	295	9	,	,	PUNCT
ejpam-6036	295	10	2025	2025	NUM
ejpam-6036	295	11	.	.	PUNCT
ejpam-6036	296	1	[	[	X
ejpam-6036	296	2	19	19	NUM
ejpam-6036	296	3	]	]	PUNCT
ejpam-6036	296	4	j.	j.	PROPN
ejpam-6036	296	5	dontchev	dontchev	PROPN
ejpam-6036	296	6	.	.	PUNCT
ejpam-6036	297	1	contra	contra	ADJ
ejpam-6036	297	2	-	-	ADJ
ejpam-6036	297	3	continuous	continuous	ADJ
ejpam-6036	297	4	functions	function	NOUN
ejpam-6036	297	5	and	and	CCONJ
ejpam-6036	297	6	strongly	strongly	ADV
ejpam-6036	297	7	s	s	NOUN
ejpam-6036	297	8	-	-	PUNCT
ejpam-6036	297	9	closed	closed	ADJ
ejpam-6036	297	10	spaces	space	NOUN
ejpam-6036	297	11	.	.	PUNCT
ejpam-6036	298	1	international	international	ADJ
ejpam-6036	298	2	journal	journal	PROPN
ejpam-6036	298	3	of	of	ADP
ejpam-6036	298	4	mathematics	mathematics	PROPN
ejpam-6036	298	5	and	and	CCONJ
ejpam-6036	298	6	mathematical	mathematical	ADJ
ejpam-6036	298	7	sciences	science	NOUN
ejpam-6036	298	8	,	,	PUNCT
ejpam-6036	298	9	19:303–310	19:303–310	PROPN
ejpam-6036	298	10	,	,	PUNCT
ejpam-6036	298	11	1966	1966	NUM
ejpam-6036	298	12	.	.	PUNCT
ejpam-6036	299	1	[	[	X
ejpam-6036	299	2	20	20	NUM
ejpam-6036	299	3	]	]	PUNCT
ejpam-6036	299	4	s.	s.	PROPN
ejpam-6036	299	5	jafari	jafari	PROPN
ejpam-6036	299	6	and	and	CCONJ
ejpam-6036	299	7	t.	t.	PROPN
ejpam-6036	299	8	noiri	noiri	PROPN
ejpam-6036	299	9	.	.	PUNCT
ejpam-6036	300	1	on	on	ADP
ejpam-6036	300	2	contra	contra	ADJ
ejpam-6036	300	3	-	-	ADJ
ejpam-6036	300	4	precontinuous	precontinuous	ADJ
ejpam-6036	300	5	functions	function	NOUN
ejpam-6036	300	6	.	.	PUNCT
ejpam-6036	301	1	bulletin	bulletin	NOUN
ejpam-6036	301	2	of	of	ADP
ejpam-6036	301	3	the	the	DET
ejpam-6036	301	4	malaysian	malaysian	PROPN
ejpam-6036	301	5	mathematical	mathematical	PROPN
ejpam-6036	301	6	sciences	sciences	PROPN
ejpam-6036	301	7	society	society	NOUN
ejpam-6036	301	8	,	,	PUNCT
ejpam-6036	301	9	25:115–128	25:115–128	PROPN
ejpam-6036	301	10	,	,	PUNCT
ejpam-6036	301	11	2002	2002	NUM
ejpam-6036	301	12	.	.	PUNCT
ejpam-6036	302	1	[	[	X
ejpam-6036	302	2	21	21	NUM
ejpam-6036	302	3	]	]	X
ejpam-6036	302	4	s.	s.	PROPN
ejpam-6036	302	5	jafari	jafari	PROPN
ejpam-6036	302	6	and	and	CCONJ
ejpam-6036	302	7	t.	t.	PROPN
ejpam-6036	302	8	noiri	noiri	PROPN
ejpam-6036	302	9	.	.	PUNCT
ejpam-6036	303	1	contra	contra	PROPN
ejpam-6036	303	2	-	-	PUNCT
ejpam-6036	303	3	α	α	NUM
ejpam-6036	303	4	-	-	ADJ
ejpam-6036	303	5	continuous	continuous	ADJ
ejpam-6036	303	6	functions	function	NOUN
ejpam-6036	303	7	between	between	ADP
ejpam-6036	303	8	topological	topological	ADJ
ejpam-6036	303	9	spaces	space	NOUN
ejpam-6036	303	10	.	.	PUNCT
ejpam-6036	304	1	iranian	iranian	ADJ
ejpam-6036	304	2	international	international	PROPN
ejpam-6036	304	3	journal	journal	PROPN
ejpam-6036	304	4	of	of	ADP
ejpam-6036	304	5	science	science	NOUN
ejpam-6036	304	6	,	,	PUNCT
ejpam-6036	304	7	2:153–167	2:153–167	NUM
ejpam-6036	304	8	,	,	PUNCT
ejpam-6036	304	9	2001	2001	NUM
ejpam-6036	304	10	.	.	PUNCT
ejpam-6036	305	1	[	[	X
ejpam-6036	305	2	22	22	NUM
ejpam-6036	305	3	]	]	X
ejpam-6036	305	4	j.	j.	PROPN
ejpam-6036	305	5	dontchev	dontchev	PROPN
ejpam-6036	305	6	and	and	CCONJ
ejpam-6036	305	7	t.	t.	PROPN
ejpam-6036	305	8	noiri	noiri	PROPN
ejpam-6036	305	9	.	.	PUNCT
ejpam-6036	306	1	contra	contra	ADJ
ejpam-6036	306	2	-	-	ADJ
ejpam-6036	306	3	semicontinuous	semicontinuous	ADJ
ejpam-6036	306	4	functions	function	NOUN
ejpam-6036	306	5	.	.	PUNCT
ejpam-6036	307	1	mathematica	mathematica	PROPN
ejpam-6036	307	2	pannonica	pannonica	PROPN
ejpam-6036	307	3	,	,	PUNCT
ejpam-6036	307	4	10:159–168	10:159–168	NOUN
ejpam-6036	307	5	,	,	PUNCT
ejpam-6036	307	6	1999	1999	NUM
ejpam-6036	307	7	.	.	PUNCT
ejpam-6036	308	1	[	[	X
ejpam-6036	308	2	23	23	NUM
ejpam-6036	308	3	]	]	PUNCT
ejpam-6036	308	4	m.	m.	NOUN
ejpam-6036	308	5	caldas	caldas	PROPN
ejpam-6036	308	6	and	and	CCONJ
ejpam-6036	308	7	s.	s.	PROPN
ejpam-6036	308	8	jafari	jafari	PROPN
ejpam-6036	308	9	.	.	PUNCT
ejpam-6036	309	1	some	some	DET
ejpam-6036	309	2	properties	property	NOUN
ejpam-6036	309	3	of	of	ADP
ejpam-6036	309	4	contra	contra	PROPN
ejpam-6036	309	5	-	-	PUNCT
ejpam-6036	309	6	β	β	ADJ
ejpam-6036	309	7	-	-	ADJ
ejpam-6036	309	8	continuous	continuous	ADJ
ejpam-6036	309	9	functions	function	NOUN
ejpam-6036	309	10	.	.	PUNCT
ejpam-6036	310	1	memoirs	memoir	NOUN
ejpam-6036	310	2	of	of	ADP
ejpam-6036	310	3	the	the	DET
ejpam-6036	310	4	faculty	faculty	NOUN
ejpam-6036	310	5	of	of	ADP
ejpam-6036	310	6	science	science	NOUN
ejpam-6036	310	7	,	,	PUNCT
ejpam-6036	310	8	kochi	kochi	PROPN
ejpam-6036	310	9	university	university	PROPN
ejpam-6036	310	10	.	.	PUNCT
ejpam-6036	311	1	series	series	PROPN
ejpam-6036	311	2	a	a	PROPN
ejpam-6036	311	3	,	,	PUNCT
ejpam-6036	311	4	mathematics	mathematic	NOUN
ejpam-6036	311	5	,	,	PUNCT
ejpam-6036	311	6	22:19–28	22:19–28	NUM
ejpam-6036	311	7	,	,	PUNCT
ejpam-6036	311	8	2001	2001	NUM
ejpam-6036	311	9	.	.	PUNCT
ejpam-6036	312	1	[	[	X
ejpam-6036	312	2	24	24	NUM
ejpam-6036	312	3	]	]	PUNCT
ejpam-6036	312	4	c.	c.	PROPN
ejpam-6036	312	5	w.	w.	PROPN
ejpam-6036	312	6	baker	baker	PROPN
ejpam-6036	312	7	.	.	PUNCT
ejpam-6036	313	1	weakly	weakly	ADJ
ejpam-6036	313	2	contra	contra	ADJ
ejpam-6036	313	3	-	-	ADJ
ejpam-6036	313	4	continuous	continuous	ADJ
ejpam-6036	313	5	functions	function	NOUN
ejpam-6036	313	6	.	.	PUNCT
ejpam-6036	314	1	international	international	ADJ
ejpam-6036	314	2	journal	journal	NOUN
ejpam-6036	314	3	of	of	ADP
ejpam-6036	314	4	pure	pure	ADJ
ejpam-6036	314	5	and	and	CCONJ
ejpam-6036	314	6	applied	applied	ADJ
ejpam-6036	314	7	mathematics	mathematic	NOUN
ejpam-6036	314	8	,	,	PUNCT
ejpam-6036	314	9	40:265–271	40:265–271	PROPN
ejpam-6036	314	10	,	,	PUNCT
ejpam-6036	314	11	2007	2007	NUM
ejpam-6036	314	12	.	.	PUNCT
ejpam-6036	315	1	b.	b.	PROPN
ejpam-6036	315	2	kong	kong	PROPN
ejpam-6036	315	3	-	-	PUNCT
ejpam-6036	315	4	ied	ied	PROPN
ejpam-6036	315	5	,	,	PUNCT
ejpam-6036	315	6	s.	s.	PROPN
ejpam-6036	315	7	sompong	sompong	PROPN
ejpam-6036	315	8	,	,	PUNCT
ejpam-6036	315	9	c.	c.	PROPN
ejpam-6036	315	10	boonpok	boonpok	PROPN
ejpam-6036	315	11	/	/	SYM
ejpam-6036	315	12	eur	eur	PROPN
ejpam-6036	315	13	.	.	PUNCT
ejpam-6036	316	1	j.	j.	PROPN
ejpam-6036	316	2	pure	pure	PROPN
ejpam-6036	316	3	appl	appl	PROPN
ejpam-6036	316	4	.	.	PROPN
ejpam-6036	316	5	math	math	PROPN
ejpam-6036	316	6	,	,	PUNCT
ejpam-6036	316	7	18	18	NUM
ejpam-6036	316	8	(	(	PUNCT
ejpam-6036	316	9	2	2	NUM
ejpam-6036	316	10	)	)	PUNCT
ejpam-6036	316	11	(	(	PUNCT
ejpam-6036	316	12	2025	2025	NUM
ejpam-6036	316	13	)	)	PUNCT
ejpam-6036	316	14	,	,	PUNCT
ejpam-6036	316	15	6036	6036	NUM
ejpam-6036	316	16	10	10	NUM
ejpam-6036	316	17	of	of	ADP
ejpam-6036	316	18	11	11	NUM
ejpam-6036	316	19	[	[	X
ejpam-6036	316	20	25	25	NUM
ejpam-6036	316	21	]	]	PUNCT
ejpam-6036	316	22	c.	c.	PROPN
ejpam-6036	316	23	w.	w.	PROPN
ejpam-6036	316	24	baker	baker	PROPN
ejpam-6036	316	25	.	.	PUNCT
ejpam-6036	317	1	weakly	weakly	ADJ
ejpam-6036	317	2	contra	contra	PROPN
ejpam-6036	317	3	β	β	ADJ
ejpam-6036	317	4	-	-	ADJ
ejpam-6036	317	5	continuous	continuous	ADJ
ejpam-6036	317	6	functions	function	NOUN
ejpam-6036	317	7	and	and	CCONJ
ejpam-6036	317	8	sβ	sβ	NOUN
ejpam-6036	317	9	-	-	PUNCT
ejpam-6036	317	10	closed	closed	ADJ
ejpam-6036	317	11	spaces	space	NOUN
ejpam-6036	317	12	.	.	PUNCT
ejpam-6036	318	1	journal	journal	NOUN
ejpam-6036	318	2	of	of	ADP
ejpam-6036	318	3	pure	pure	ADJ
ejpam-6036	318	4	mathematics	mathematic	NOUN
ejpam-6036	318	5	,	,	PUNCT
ejpam-6036	318	6	24:31–38	24:31–38	PROPN
ejpam-6036	318	7	,	,	PUNCT
ejpam-6036	318	8	2007	2007	NUM
ejpam-6036	318	9	.	.	PUNCT
ejpam-6036	319	1	[	[	X
ejpam-6036	319	2	26	26	NUM
ejpam-6036	319	3	]	]	PUNCT
ejpam-6036	319	4	t.	t.	PROPN
ejpam-6036	319	5	noiri	noiri	PROPN
ejpam-6036	319	6	and	and	CCONJ
ejpam-6036	319	7	v.	v.	ADP
ejpam-6036	319	8	popa	popa	NOUN
ejpam-6036	319	9	.	.	PUNCT
ejpam-6036	320	1	a	a	DET
ejpam-6036	320	2	unified	unified	ADJ
ejpam-6036	320	3	theory	theory	NOUN
ejpam-6036	320	4	of	of	ADP
ejpam-6036	320	5	contra	contra	PROPN
ejpam-6036	320	6	-	-	NOUN
ejpam-6036	320	7	continuity	continuity	NOUN
ejpam-6036	320	8	for	for	ADP
ejpam-6036	320	9	functions	function	NOUN
ejpam-6036	320	10	.	.	PUNCT
ejpam-6036	321	1	annales	annales	PROPN
ejpam-6036	321	2	universitatis	universitatis	PROPN
ejpam-6036	321	3	scientiarum	scientiarum	PROPN
ejpam-6036	321	4	budapestinensis	budapestinensis	PROPN
ejpam-6036	321	5	de	de	PROPN
ejpam-6036	321	6	rolando	rolando	PROPN
ejpam-6036	321	7	eötvös	eötvös	PROPN
ejpam-6036	321	8	,	,	PUNCT
ejpam-6036	321	9	sectio	sectio	PROPN
ejpam-6036	321	10	mathematica	mathematica	PROPN
ejpam-6036	321	11	,	,	PUNCT
ejpam-6036	321	12	44:115–137	44:115–137	PROPN
ejpam-6036	321	13	,	,	PUNCT
ejpam-6036	321	14	2002	2002	NUM
ejpam-6036	321	15	.	.	PUNCT
ejpam-6036	322	1	[	[	X
ejpam-6036	322	2	27	27	NUM
ejpam-6036	322	3	]	]	PUNCT
ejpam-6036	322	4	t.	t.	PROPN
ejpam-6036	322	5	noiri	noiri	PROPN
ejpam-6036	322	6	and	and	CCONJ
ejpam-6036	322	7	v.	v.	ADP
ejpam-6036	322	8	popa	popa	NOUN
ejpam-6036	322	9	.	.	PUNCT
ejpam-6036	323	1	a	a	DET
ejpam-6036	323	2	unified	unified	ADJ
ejpam-6036	323	3	theory	theory	NOUN
ejpam-6036	323	4	of	of	ADP
ejpam-6036	323	5	weak	weak	ADJ
ejpam-6036	323	6	contra	contra	NOUN
ejpam-6036	323	7	-	-	NOUN
ejpam-6036	323	8	continuity	continuity	NOUN
ejpam-6036	323	9	.	.	PUNCT
ejpam-6036	324	1	acta	acta	PROPN
ejpam-6036	324	2	mathematica	mathematica	PROPN
ejpam-6036	324	3	hungarica	hungarica	PROPN
ejpam-6036	324	4	,	,	PUNCT
ejpam-6036	324	5	132:63–77	132:63–77	NUM
ejpam-6036	324	6	,	,	PUNCT
ejpam-6036	324	7	2011	2011	NUM
ejpam-6036	324	8	.	.	PUNCT
ejpam-6036	325	1	[	[	X
ejpam-6036	325	2	28	28	NUM
ejpam-6036	325	3	]	]	X
ejpam-6036	325	4	c.	c.	PROPN
ejpam-6036	325	5	boonpok	boonpok	PROPN
ejpam-6036	325	6	and	and	CCONJ
ejpam-6036	325	7	n.	n.	PROPN
ejpam-6036	325	8	srisarakham	srisarakham	PROPN
ejpam-6036	325	9	.	.	PUNCT
ejpam-6036	326	1	(	(	PUNCT
ejpam-6036	326	2	τ1	τ1	NOUN
ejpam-6036	326	3	,	,	PUNCT
ejpam-6036	326	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6036	326	5	for	for	ADP
ejpam-6036	326	6	functions	function	NOUN
ejpam-6036	326	7	.	.	PUNCT
ejpam-6036	327	1	asia	asia	PROPN
ejpam-6036	327	2	pacific	pacific	PROPN
ejpam-6036	327	3	journal	journal	PROPN
ejpam-6036	327	4	of	of	ADP
ejpam-6036	327	5	mathematics	mathematic	NOUN
ejpam-6036	327	6	,	,	PUNCT
ejpam-6036	327	7	11:21	11:21	NUM
ejpam-6036	327	8	,	,	PUNCT
ejpam-6036	327	9	2024	2024	NUM
ejpam-6036	327	10	.	.	PUNCT
ejpam-6036	328	1	[	[	X
ejpam-6036	328	2	29	29	NUM
ejpam-6036	328	3	]	]	X
ejpam-6036	328	4	c.	c.	PROPN
ejpam-6036	328	5	boonpok	boonpok	PROPN
ejpam-6036	328	6	and	and	CCONJ
ejpam-6036	328	7	p.	p.	NOUN
ejpam-6036	328	8	pue	pue	NOUN
ejpam-6036	328	9	-	-	PUNCT
ejpam-6036	328	10	on	on	ADP
ejpam-6036	328	11	.	.	PUNCT
ejpam-6036	329	1	characterizations	characterization	NOUN
ejpam-6036	329	2	of	of	ADP
ejpam-6036	329	3	almost	almost	ADV
ejpam-6036	329	4	(	(	PUNCT
ejpam-6036	329	5	τ1	τ1	NOUN
ejpam-6036	329	6	,	,	PUNCT
ejpam-6036	329	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	329	8	functions	function	NOUN
ejpam-6036	329	9	.	.	PUNCT
ejpam-6036	330	1	international	international	ADJ
ejpam-6036	330	2	journal	journal	NOUN
ejpam-6036	330	3	of	of	ADP
ejpam-6036	330	4	analysis	analysis	NOUN
ejpam-6036	330	5	and	and	CCONJ
ejpam-6036	330	6	applications	application	NOUN
ejpam-6036	330	7	,	,	PUNCT
ejpam-6036	330	8	22:33	22:33	NUM
ejpam-6036	330	9	,	,	PUNCT
ejpam-6036	330	10	2024	2024	NUM
ejpam-6036	330	11	.	.	PUNCT
ejpam-6036	331	1	[	[	X
ejpam-6036	331	2	30	30	NUM
ejpam-6036	331	3	]	]	X
ejpam-6036	331	4	c.	c.	PROPN
ejpam-6036	331	5	boonpok	boonpok	PROPN
ejpam-6036	331	6	and	and	CCONJ
ejpam-6036	331	7	c.	c.	PROPN
ejpam-6036	331	8	klanarong	klanarong	PROPN
ejpam-6036	331	9	.	.	PUNCT
ejpam-6036	332	1	on	on	ADP
ejpam-6036	332	2	weakly	weakly	ADJ
ejpam-6036	332	3	(	(	PUNCT
ejpam-6036	332	4	τ1	τ1	NOUN
ejpam-6036	332	5	,	,	PUNCT
ejpam-6036	332	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	332	7	functions	function	NOUN
ejpam-6036	332	8	.	.	PUNCT
ejpam-6036	333	1	european	european	ADJ
ejpam-6036	333	2	journal	journal	PROPN
ejpam-6036	333	3	of	of	ADP
ejpam-6036	333	4	pure	pure	ADJ
ejpam-6036	333	5	and	and	CCONJ
ejpam-6036	333	6	applied	applied	ADJ
ejpam-6036	333	7	mathematics	mathematic	NOUN
ejpam-6036	333	8	,	,	PUNCT
ejpam-6036	333	9	17(1):416–425	17(1):416–425	NUM
ejpam-6036	333	10	,	,	PUNCT
ejpam-6036	333	11	2024	2024	NUM
ejpam-6036	333	12	.	.	PUNCT
ejpam-6036	334	1	[	[	X
ejpam-6036	334	2	31	31	NUM
ejpam-6036	334	3	]	]	X
ejpam-6036	334	4	n.	n.	PROPN
ejpam-6036	334	5	srisarakham	srisarakham	PROPN
ejpam-6036	334	6	,	,	PUNCT
ejpam-6036	334	7	s.	s.	PROPN
ejpam-6036	334	8	sompong	sompong	PROPN
ejpam-6036	334	9	,	,	PUNCT
ejpam-6036	334	10	and	and	CCONJ
ejpam-6036	334	11	c.	c.	PROPN
ejpam-6036	334	12	boonpok	boonpok	PROPN
ejpam-6036	334	13	.	.	PUNCT
ejpam-6036	335	1	quasi	quasi	PROPN
ejpam-6036	335	2	θ(τ1	θ(τ1	PROPN
ejpam-6036	335	3	,	,	PUNCT
ejpam-6036	335	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	335	5	functions	function	NOUN
ejpam-6036	335	6	.	.	PUNCT
ejpam-6036	336	1	european	european	ADJ
ejpam-6036	336	2	journal	journal	PROPN
ejpam-6036	336	3	of	of	ADP
ejpam-6036	336	4	pure	pure	ADJ
ejpam-6036	336	5	and	and	CCONJ
ejpam-6036	336	6	applied	applied	ADJ
ejpam-6036	336	7	mathematics	mathematic	NOUN
ejpam-6036	336	8	,	,	PUNCT
ejpam-6036	336	9	18(1):5722	18(1):5722	NUM
ejpam-6036	336	10	,	,	PUNCT
ejpam-6036	336	11	2025	2025	NUM
ejpam-6036	336	12	.	.	PUNCT
ejpam-6036	337	1	[	[	X
ejpam-6036	337	2	32	32	NUM
ejpam-6036	337	3	]	]	PUNCT
ejpam-6036	337	4	b.	b.	PROPN
ejpam-6036	337	5	kong	kong	PROPN
ejpam-6036	337	6	-	-	PUNCT
ejpam-6036	337	7	ied	ied	PROPN
ejpam-6036	337	8	,	,	PUNCT
ejpam-6036	337	9	s.	s.	PROPN
ejpam-6036	337	10	sompong	sompong	PROPN
ejpam-6036	337	11	,	,	PUNCT
ejpam-6036	337	12	and	and	CCONJ
ejpam-6036	337	13	c.	c.	PROPN
ejpam-6036	337	14	boonpok	boonpok	PROPN
ejpam-6036	337	15	.	.	PUNCT
ejpam-6036	338	1	almost	almost	ADV
ejpam-6036	338	2	quasi	quasi	X
ejpam-6036	338	3	(	(	PUNCT
ejpam-6036	338	4	τ1	τ1	NOUN
ejpam-6036	338	5	,	,	PUNCT
ejpam-6036	338	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	338	7	functions	function	NOUN
ejpam-6036	338	8	.	.	PUNCT
ejpam-6036	339	1	asia	asia	PROPN
ejpam-6036	339	2	pacific	pacific	PROPN
ejpam-6036	339	3	journal	journal	PROPN
ejpam-6036	339	4	of	of	ADP
ejpam-6036	339	5	mathematics	mathematic	NOUN
ejpam-6036	339	6	,	,	PUNCT
ejpam-6036	339	7	11:64	11:64	NUM
ejpam-6036	339	8	,	,	PUNCT
ejpam-6036	339	9	2024	2024	NUM
ejpam-6036	339	10	.	.	PUNCT
ejpam-6036	340	1	[	[	X
ejpam-6036	340	2	33	33	NUM
ejpam-6036	340	3	]	]	PUNCT
ejpam-6036	340	4	m.	m.	NOUN
ejpam-6036	340	5	chiangpradit	chiangpradit	NOUN
ejpam-6036	340	6	,	,	PUNCT
ejpam-6036	340	7	s.	s.	PROPN
ejpam-6036	340	8	sompong	sompong	PROPN
ejpam-6036	340	9	,	,	PUNCT
ejpam-6036	340	10	and	and	CCONJ
ejpam-6036	340	11	c.	c.	PROPN
ejpam-6036	340	12	boonpok	boonpok	PROPN
ejpam-6036	340	13	.	.	PUNCT
ejpam-6036	341	1	weakly	weakly	ADJ
ejpam-6036	341	2	quasi	quasi	NOUN
ejpam-6036	341	3	(	(	PUNCT
ejpam-6036	341	4	τ1	τ1	PROPN
ejpam-6036	341	5	,	,	PUNCT
ejpam-6036	341	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	341	7	functions	function	NOUN
ejpam-6036	341	8	.	.	PUNCT
ejpam-6036	342	1	international	international	ADJ
ejpam-6036	342	2	journal	journal	NOUN
ejpam-6036	342	3	of	of	ADP
ejpam-6036	342	4	analysis	analysis	NOUN
ejpam-6036	342	5	and	and	CCONJ
ejpam-6036	342	6	applications	application	NOUN
ejpam-6036	342	7	,	,	PUNCT
ejpam-6036	342	8	22:125	22:125	NUM
ejpam-6036	342	9	,	,	PUNCT
ejpam-6036	342	10	2024	2024	NUM
ejpam-6036	342	11	.	.	PUNCT
ejpam-6036	343	1	[	[	X
ejpam-6036	343	2	34	34	NUM
ejpam-6036	343	3	]	]	X
ejpam-6036	343	4	j.	j.	PROPN
ejpam-6036	343	5	khampakdee	khampakdee	PROPN
ejpam-6036	343	6	,	,	PUNCT
ejpam-6036	343	7	s.	s.	PROPN
ejpam-6036	343	8	sompong	sompong	PROPN
ejpam-6036	343	9	,	,	PUNCT
ejpam-6036	343	10	and	and	CCONJ
ejpam-6036	343	11	c.	c.	PROPN
ejpam-6036	343	12	boonpok	boonpok	PROPN
ejpam-6036	343	13	.	.	PUNCT
ejpam-6036	344	1	almost	almost	ADV
ejpam-6036	344	2	weakly	weakly	ADJ
ejpam-6036	344	3	(	(	PUNCT
ejpam-6036	344	4	τ1	τ1	NOUN
ejpam-6036	344	5	,	,	PUNCT
ejpam-6036	344	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6036	344	7	functions	function	NOUN
ejpam-6036	344	8	.	.	PUNCT
ejpam-6036	345	1	european	european	ADJ
ejpam-6036	345	2	journal	journal	PROPN
ejpam-6036	345	3	of	of	ADP
ejpam-6036	345	4	pure	pure	ADJ
ejpam-6036	345	5	and	and	CCONJ
ejpam-6036	345	6	applied	applied	ADJ
ejpam-6036	345	7	mathematics	mathematic	NOUN
ejpam-6036	345	8	,	,	PUNCT
ejpam-6036	345	9	18(1):5721	18(1):5721	NUM
ejpam-6036	345	10	,	,	PUNCT
ejpam-6036	345	11	2025	2025	NUM
ejpam-6036	345	12	.	.	PUNCT
ejpam-6036	346	1	[	[	X
ejpam-6036	346	2	35	35	NUM
ejpam-6036	346	3	]	]	X
ejpam-6036	346	4	c.	c.	PROPN
ejpam-6036	346	5	boonpok	boonpok	PROPN
ejpam-6036	346	6	and	and	CCONJ
ejpam-6036	346	7	j.	j.	PROPN
ejpam-6036	346	8	khampakdee	khampakdee	PROPN
ejpam-6036	346	9	.	.	PUNCT
ejpam-6036	347	1	upper	upper	ADJ
ejpam-6036	347	2	and	and	CCONJ
ejpam-6036	347	3	lower	low	ADJ
ejpam-6036	347	4	almost	almost	ADV
ejpam-6036	347	5	contra-(λ	contra-(λ	PROPN
ejpam-6036	347	6	,	,	PUNCT
ejpam-6036	347	7	sp)-continuity	sp)-continuity	NOUN
ejpam-6036	347	8	.	.	PUNCT
ejpam-6036	348	1	european	european	PROPN
ejpam-6036	348	2	journal	journal	PROPN
ejpam-6036	348	3	of	of	ADP
ejpam-6036	348	4	pure	pure	ADJ
ejpam-6036	348	5	and	and	CCONJ
ejpam-6036	348	6	applied	applied	ADJ
ejpam-6036	348	7	mathematics	mathematic	NOUN
ejpam-6036	348	8	,	,	PUNCT
ejpam-6036	348	9	16(1):156–168	16(1):156–168	PROPN
ejpam-6036	348	10	,	,	PUNCT
ejpam-6036	348	11	2023	2023	NUM
ejpam-6036	348	12	.	.	PUNCT
ejpam-6036	349	1	[	[	X
ejpam-6036	349	2	36	36	NUM
ejpam-6036	349	3	]	]	X
ejpam-6036	349	4	c.	c.	PROPN
ejpam-6036	349	5	boonpok	boonpok	PROPN
ejpam-6036	349	6	,	,	PUNCT
ejpam-6036	349	7	c.	c.	PROPN
ejpam-6036	349	8	viriyapong	viriyapong	PROPN
ejpam-6036	349	9	,	,	PUNCT
ejpam-6036	349	10	and	and	CCONJ
ejpam-6036	349	11	m.	m.	NOUN
ejpam-6036	349	12	thongmoon	thongmoon	NOUN
ejpam-6036	349	13	.	.	PUNCT
ejpam-6036	350	1	on	on	ADP
ejpam-6036	350	2	upper	upper	ADJ
ejpam-6036	350	3	and	and	CCONJ
ejpam-6036	350	4	lower	low	ADJ
ejpam-6036	350	5	(	(	PUNCT
ejpam-6036	350	6	τ1	τ1	NOUN
ejpam-6036	350	7	,	,	PUNCT
ejpam-6036	350	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6036	350	9	multifunctions	multifunction	NOUN
ejpam-6036	350	10	.	.	PUNCT
ejpam-6036	351	1	journal	journal	PROPN
ejpam-6036	351	2	of	of	ADP
ejpam-6036	351	3	mathematics	mathematics	PROPN
ejpam-6036	351	4	and	and	CCONJ
ejpam-6036	351	5	computer	computer	NOUN
ejpam-6036	351	6	science	science	NOUN
ejpam-6036	351	7	,	,	PUNCT
ejpam-6036	351	8	18:282–293	18:282–293	NUM
ejpam-6036	351	9	,	,	PUNCT
ejpam-6036	351	10	2018	2018	NUM
ejpam-6036	351	11	.	.	PUNCT
ejpam-6036	352	1	[	[	X
ejpam-6036	352	2	37	37	NUM
ejpam-6036	352	3	]	]	X
ejpam-6036	352	4	c.	c.	PROPN
ejpam-6036	352	5	viriyapong	viriyapong	PROPN
ejpam-6036	352	6	and	and	CCONJ
ejpam-6036	352	7	c.	c.	PROPN
ejpam-6036	352	8	boonpok	boonpok	PROPN
ejpam-6036	352	9	.	.	PUNCT
ejpam-6036	353	1	(	(	PUNCT
ejpam-6036	353	2	τ1	τ1	NOUN
ejpam-6036	353	3	,	,	PUNCT
ejpam-6036	353	4	τ2)α	τ2)α	NOUN
ejpam-6036	353	5	-	-	PUNCT
ejpam-6036	353	6	continuity	continuity	NOUN
ejpam-6036	353	7	for	for	ADP
ejpam-6036	353	8	multifunctions	multifunction	NOUN
ejpam-6036	353	9	.	.	PUNCT
ejpam-6036	354	1	journal	journal	PROPN
ejpam-6036	354	2	of	of	ADP
ejpam-6036	354	3	mathematics	mathematic	NOUN
ejpam-6036	354	4	,	,	PUNCT
ejpam-6036	354	5	2020:6285763	2020:6285763	NUM
ejpam-6036	354	6	,	,	PUNCT
ejpam-6036	354	7	2020	2020	NUM
ejpam-6036	354	8	.	.	PUNCT
ejpam-6036	355	1	[	[	X
ejpam-6036	355	2	38	38	NUM
ejpam-6036	355	3	]	]	PUNCT
ejpam-6036	355	4	c.	c.	PROPN
ejpam-6036	355	5	boonpok	boonpok	PROPN
ejpam-6036	355	6	.	.	PUNCT
ejpam-6036	356	1	(	(	PUNCT
ejpam-6036	356	2	τ1	τ1	NOUN
ejpam-6036	356	3	,	,	PUNCT
ejpam-6036	356	4	τ2)δ	τ2)δ	ADJ
ejpam-6036	356	5	-	-	PUNCT
ejpam-6036	356	6	semicontinuous	semicontinuous	ADJ
ejpam-6036	356	7	multifunctions	multifunction	NOUN
ejpam-6036	356	8	.	.	PUNCT
ejpam-6036	357	1	heliyon	heliyon	NOUN
ejpam-6036	357	2	,	,	PUNCT
ejpam-6036	357	3	6	6	NUM
ejpam-6036	357	4	:	:	SYM
ejpam-6036	357	5	e05367	e05367	PROPN
ejpam-6036	357	6	,	,	PUNCT
ejpam-6036	357	7	2020	2020	NUM
ejpam-6036	357	8	.	.	PUNCT
ejpam-6036	358	1	[	[	X
ejpam-6036	358	2	39	39	NUM
ejpam-6036	358	3	]	]	X
ejpam-6036	358	4	n.	n.	PROPN
ejpam-6036	358	5	viriyapong	viriyapong	PROPN
ejpam-6036	358	6	,	,	PUNCT
ejpam-6036	358	7	s.	s.	PROPN
ejpam-6036	358	8	sompong	sompong	PROPN
ejpam-6036	358	9	,	,	PUNCT
ejpam-6036	358	10	and	and	CCONJ
ejpam-6036	358	11	c.	c.	PROPN
ejpam-6036	358	12	boonpok	boonpok	PROPN
ejpam-6036	358	13	.	.	PUNCT
ejpam-6036	359	1	(	(	PUNCT
ejpam-6036	359	2	τ1	τ1	NOUN
ejpam-6036	359	3	,	,	PUNCT
ejpam-6036	359	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6036	359	5	disconnectedness	disconnectedness	NOUN
ejpam-6036	359	6	in	in	ADP
ejpam-6036	359	7	bitopological	bitopological	ADJ
ejpam-6036	359	8	spaces	space	NOUN
ejpam-6036	359	9	.	.	PUNCT
ejpam-6036	360	1	international	international	ADJ
ejpam-6036	360	2	journal	journal	PROPN
ejpam-6036	360	3	of	of	ADP
ejpam-6036	360	4	mathematics	mathematic	NOUN
ejpam-6036	360	5	and	and	CCONJ
ejpam-6036	360	6	computer	computer	NOUN
ejpam-6036	360	7	science	science	NOUN
ejpam-6036	360	8	,	,	PUNCT
ejpam-6036	360	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6036	360	10	,	,	PUNCT
ejpam-6036	360	11	2024	2024	NUM
ejpam-6036	360	12	.	.	PUNCT
ejpam-6036	361	1	[	[	X
ejpam-6036	361	2	40	40	NUM
ejpam-6036	361	3	]	]	X
ejpam-6036	361	4	n.	n.	PROPN
ejpam-6036	361	5	viriyapong	viriyapong	PROPN
ejpam-6036	361	6	,	,	PUNCT
ejpam-6036	361	7	s.	s.	PROPN
ejpam-6036	361	8	sompong	sompong	PROPN
ejpam-6036	361	9	,	,	PUNCT
ejpam-6036	361	10	and	and	CCONJ
ejpam-6036	361	11	c.	c.	PROPN
ejpam-6036	361	12	boonpok	boonpok	PROPN
ejpam-6036	361	13	.	.	PUNCT
ejpam-6036	362	1	upper	upper	ADJ
ejpam-6036	362	2	and	and	CCONJ
ejpam-6036	362	3	lower	low	ADJ
ejpam-6036	362	4	s-(τ1	s-(τ1	NOUN
ejpam-6036	362	5	,	,	PUNCT
ejpam-6036	362	6	τ2)p	τ2)p	ADJ
ejpam-6036	362	7	-	-	PUNCT
ejpam-6036	362	8	continuous	continuous	ADJ
ejpam-6036	362	9	multifunctions	multifunction	NOUN
ejpam-6036	362	10	.	.	PUNCT
ejpam-6036	363	1	european	european	ADJ
ejpam-6036	363	2	journal	journal	PROPN
ejpam-6036	363	3	of	of	ADP
ejpam-6036	363	4	pure	pure	ADJ
ejpam-6036	363	5	and	and	CCONJ
ejpam-6036	363	6	applied	applied	ADJ
ejpam-6036	363	7	mathematics	mathematic	NOUN
ejpam-6036	363	8	,	,	PUNCT
ejpam-6036	363	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-6036	363	10	,	,	PUNCT
ejpam-6036	363	11	2024	2024	NUM
ejpam-6036	363	12	.	.	PUNCT
ejpam-6036	364	1	[	[	X
ejpam-6036	364	2	41	41	NUM
ejpam-6036	364	3	]	]	X
ejpam-6036	364	4	n.	n.	NOUN
ejpam-6036	364	5	chutiman	chutiman	NOUN
ejpam-6036	364	6	,	,	PUNCT
ejpam-6036	364	7	a.	a.	PROPN
ejpam-6036	364	8	sama	sama	PROPN
ejpam-6036	364	9	-	-	PUNCT
ejpam-6036	364	10	ae	ae	PROPN
ejpam-6036	364	11	,	,	PUNCT
ejpam-6036	364	12	and	and	CCONJ
ejpam-6036	364	13	c.	c.	PROPN
ejpam-6036	364	14	boonpok	boonpok	PROPN
ejpam-6036	364	15	.	.	PUNCT
ejpam-6036	365	1	characterizations	characterization	NOUN
ejpam-6036	365	2	of	of	ADP
ejpam-6036	365	3	contra-(τ1	contra-(τ1	NOUN
ejpam-6036	365	4	,	,	PUNCT
ejpam-6036	365	5	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	365	6	functions	function	NOUN
ejpam-6036	365	7	.	.	PUNCT
ejpam-6036	366	1	(	(	PUNCT
ejpam-6036	366	2	submitted	submit	VERB
ejpam-6036	366	3	)	)	PUNCT
ejpam-6036	366	4	.	.	PUNCT
ejpam-6036	367	1	[	[	X
ejpam-6036	367	2	42	42	NUM
ejpam-6036	367	3	]	]	X
ejpam-6036	367	4	n.	n.	PROPN
ejpam-6036	367	5	srisarakham	srisarakham	PROPN
ejpam-6036	367	6	,	,	PUNCT
ejpam-6036	367	7	s.	s.	PROPN
ejpam-6036	367	8	sompong	sompong	PROPN
ejpam-6036	367	9	,	,	PUNCT
ejpam-6036	367	10	and	and	CCONJ
ejpam-6036	367	11	c.	c.	PROPN
ejpam-6036	367	12	boonpok	boonpok	PROPN
ejpam-6036	367	13	.	.	PUNCT
ejpam-6036	368	1	slight	slight	ADJ
ejpam-6036	368	2	(	(	PUNCT
ejpam-6036	368	3	τ1	τ1	NOUN
ejpam-6036	368	4	,	,	PUNCT
ejpam-6036	368	5	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6036	368	6	for	for	ADP
ejpam-6036	368	7	functions	function	NOUN
ejpam-6036	368	8	.	.	PUNCT
ejpam-6036	369	1	international	international	ADJ
ejpam-6036	369	2	journal	journal	NOUN
ejpam-6036	369	3	of	of	ADP
ejpam-6036	369	4	mathematics	mathematic	NOUN
ejpam-6036	369	5	and	and	CCONJ
ejpam-6036	369	6	computer	computer	NOUN
ejpam-6036	369	7	science	science	NOUN
ejpam-6036	369	8	,	,	PUNCT
ejpam-6036	369	9	20(1):211–215	20(1):211–215	PROPN
ejpam-6036	369	10	,	,	PUNCT
ejpam-6036	369	11	2025	2025	NUM
ejpam-6036	369	12	.	.	PUNCT
ejpam-6036	370	1	[	[	X
ejpam-6036	370	2	43	43	NUM
ejpam-6036	370	3	]	]	X
ejpam-6036	370	4	c.	c.	PROPN
ejpam-6036	370	5	viriyapong	viriyapong	PROPN
ejpam-6036	370	6	,	,	PUNCT
ejpam-6036	370	7	s.	s.	PROPN
ejpam-6036	370	8	sompong	sompong	PROPN
ejpam-6036	370	9	,	,	PUNCT
ejpam-6036	370	10	and	and	CCONJ
ejpam-6036	370	11	c.	c.	PROPN
ejpam-6036	370	12	boonpok	boonpok	PROPN
ejpam-6036	370	13	.	.	PUNCT
ejpam-6036	371	1	generalized	generalize	VERB
ejpam-6036	371	2	(	(	PUNCT
ejpam-6036	371	3	τ1	τ1	NOUN
ejpam-6036	371	4	,	,	PUNCT
ejpam-6036	371	5	τ2)-closed	τ2)-close	VERB
ejpam-6036	371	6	sets	set	NOUN
ejpam-6036	371	7	in	in	ADP
ejpam-6036	371	8	bitopological	bitopological	ADJ
ejpam-6036	371	9	spaces	space	NOUN
ejpam-6036	371	10	.	.	PUNCT
ejpam-6036	372	1	international	international	ADJ
ejpam-6036	372	2	journal	journal	PROPN
ejpam-6036	372	3	of	of	ADP
ejpam-6036	372	4	mathematics	mathematic	NOUN
ejpam-6036	372	5	and	and	CCONJ
ejpam-6036	372	6	computer	computer	NOUN
ejpam-6036	372	7	science	science	NOUN
ejpam-6036	372	8	,	,	PUNCT
ejpam-6036	372	9	19(3):821–826	19(3):821–826	PROPN
ejpam-6036	372	10	,	,	PUNCT
ejpam-6036	372	11	2024	2024	NUM
ejpam-6036	372	12	.	.	PUNCT
ejpam-6036	373	1	[	[	X
ejpam-6036	373	2	44	44	NUM
ejpam-6036	373	3	]	]	PUNCT
ejpam-6036	373	4	m.	m.	NOUN
ejpam-6036	373	5	chiangpradit	chiangpradit	NOUN
ejpam-6036	373	6	,	,	PUNCT
ejpam-6036	373	7	s.	s.	PROPN
ejpam-6036	373	8	sompong	sompong	PROPN
ejpam-6036	373	9	,	,	PUNCT
ejpam-6036	373	10	and	and	CCONJ
ejpam-6036	373	11	c.	c.	PROPN
ejpam-6036	373	12	boonpok	boonpok	PROPN
ejpam-6036	373	13	.	.	PUNCT
ejpam-6036	374	1	λ(τ1,τ2)-sets	λ(τ1,τ2)-set	NOUN
ejpam-6036	374	2	and	and	CCONJ
ejpam-6036	374	3	related	relate	VERB
ejpam-6036	374	4	topological	topological	PROPN
ejpam-6036	374	5	b.	b.	PROPN
ejpam-6036	374	6	kong	kong	PROPN
ejpam-6036	374	7	-	-	PUNCT
ejpam-6036	374	8	ied	ied	PROPN
ejpam-6036	374	9	,	,	PUNCT
ejpam-6036	374	10	s.	s.	PROPN
ejpam-6036	374	11	sompong	sompong	PROPN
ejpam-6036	374	12	,	,	PUNCT
ejpam-6036	374	13	c.	c.	PROPN
ejpam-6036	374	14	boonpok	boonpok	PROPN
ejpam-6036	374	15	/	/	SYM
ejpam-6036	374	16	eur	eur	PROPN
ejpam-6036	374	17	.	.	PUNCT
ejpam-6036	375	1	j.	j.	PROPN
ejpam-6036	375	2	pure	pure	PROPN
ejpam-6036	375	3	appl	appl	PROPN
ejpam-6036	375	4	.	.	PROPN
ejpam-6036	375	5	math	math	PROPN
ejpam-6036	375	6	,	,	PUNCT
ejpam-6036	375	7	18	18	NUM
ejpam-6036	375	8	(	(	PUNCT
ejpam-6036	375	9	2	2	NUM
ejpam-6036	375	10	)	)	PUNCT
ejpam-6036	375	11	(	(	PUNCT
ejpam-6036	375	12	2025	2025	NUM
ejpam-6036	375	13	)	)	PUNCT
ejpam-6036	375	14	,	,	PUNCT
ejpam-6036	375	15	6036	6036	NUM
ejpam-6036	375	16	11	11	NUM
ejpam-6036	375	17	of	of	ADP
ejpam-6036	375	18	11	11	NUM
ejpam-6036	375	19	spaces	space	NOUN
ejpam-6036	375	20	.	.	PUNCT
ejpam-6036	376	1	asia	asia	PROPN
ejpam-6036	376	2	pacific	pacific	PROPN
ejpam-6036	376	3	journal	journal	PROPN
ejpam-6036	376	4	of	of	ADP
ejpam-6036	376	5	mathematics	mathematic	NOUN
ejpam-6036	376	6	,	,	PUNCT
ejpam-6036	376	7	11:49	11:49	NUM
ejpam-6036	376	8	,	,	PUNCT
ejpam-6036	376	9	2024	2024	NUM
ejpam-6036	376	10	.	.	PUNCT
ejpam-6036	377	1	[	[	X
ejpam-6036	377	2	45	45	NUM
ejpam-6036	377	3	]	]	X
ejpam-6036	377	4	p.	p.	NOUN
ejpam-6036	377	5	pue	pue	NOUN
ejpam-6036	377	6	-	-	PUNCT
ejpam-6036	377	7	on	on	ADP
ejpam-6036	377	8	,	,	PUNCT
ejpam-6036	377	9	a.	a.	PROPN
ejpam-6036	377	10	sama	sama	PROPN
ejpam-6036	377	11	-	-	PUNCT
ejpam-6036	377	12	ae	ae	PROPN
ejpam-6036	377	13	,	,	PUNCT
ejpam-6036	377	14	and	and	CCONJ
ejpam-6036	377	15	c.	c.	PROPN
ejpam-6036	377	16	boonpok	boonpok	PROPN
ejpam-6036	377	17	.	.	PUNCT
ejpam-6036	378	1	characterizations	characterization	NOUN
ejpam-6036	378	2	of	of	ADP
ejpam-6036	378	3	quasi	quasi	NOUN
ejpam-6036	378	4	θ(τ1	θ(τ1	NOUN
ejpam-6036	378	5	,	,	PUNCT
ejpam-6036	378	6	τ2)continuous	τ2)continuous	ADJ
ejpam-6036	378	7	multifunctions	multifunction	NOUN
ejpam-6036	378	8	.	.	PUNCT
ejpam-6036	379	1	international	international	ADJ
ejpam-6036	379	2	journal	journal	NOUN
ejpam-6036	379	3	of	of	ADP
ejpam-6036	379	4	analysis	analysis	NOUN
ejpam-6036	379	5	and	and	CCONJ
ejpam-6036	379	6	applications	application	NOUN
ejpam-6036	379	7	,	,	PUNCT
ejpam-6036	379	8	23:59	23:59	NUM
ejpam-6036	379	9	,	,	PUNCT
ejpam-6036	379	10	2025	2025	NUM
ejpam-6036	379	11	.	.	PUNCT