id	sid	tid	token	lemma	pos
ejpam-5395	1	1	european	european	PROPN
ejpam-5395	1	2	journal	journal	PROPN
ejpam-5395	1	3	of	of	ADP
ejpam-5395	1	4	pure	pure	ADJ
ejpam-5395	1	5	and	and	CCONJ
ejpam-5395	1	6	applied	apply	VERB
ejpam-5395	1	7	mathematics	mathematic	NOUN
ejpam-5395	1	8	vol	vol	NOUN
ejpam-5395	1	9	.	.	PROPN
ejpam-5395	2	1	17	17	NUM
ejpam-5395	2	2	,	,	PUNCT
ejpam-5395	2	3	no	no	INTJ
ejpam-5395	2	4	.	.	NOUN
ejpam-5395	2	5	4	4	NUM
ejpam-5395	2	6	,	,	PUNCT
ejpam-5395	2	7	2024	2024	NUM
ejpam-5395	2	8	,	,	PUNCT
ejpam-5395	2	9	2753	2753	NUM
ejpam-5395	2	10	-	-	SYM
ejpam-5395	2	11	2762	2762	NUM
ejpam-5395	2	12	issn	issn	PROPN
ejpam-5395	2	13	1307	1307	NUM
ejpam-5395	2	14	-	-	SYM
ejpam-5395	2	15	5543	5543	NUM
ejpam-5395	2	16	–	–	PUNCT
ejpam-5395	2	17	ejpam.com	ejpam.com	X
ejpam-5395	2	18	published	publish	VERB
ejpam-5395	2	19	by	by	ADP
ejpam-5395	2	20	new	new	PROPN
ejpam-5395	2	21	york	york	PROPN
ejpam-5395	2	22	business	business	PROPN
ejpam-5395	2	23	global	global	ADJ
ejpam-5395	2	24	characterizations	characterization	NOUN
ejpam-5395	2	25	of	of	ADP
ejpam-5395	2	26	faintly	faintly	ADV
ejpam-5395	2	27	(	(	PUNCT
ejpam-5395	2	28	τ1	τ1	PROPN
ejpam-5395	2	29	,	,	PUNCT
ejpam-5395	2	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	2	31	functions	function	NOUN
ejpam-5395	2	32	napassanan	napassanan	PROPN
ejpam-5395	2	33	srisarakham1	srisarakham1	PROPN
ejpam-5395	2	34	,	,	PUNCT
ejpam-5395	2	35	areeyuth	areeyuth	NOUN
ejpam-5395	2	36	sama	sama	NOUN
ejpam-5395	2	37	-	-	PUNCT
ejpam-5395	2	38	ae2	ae2	PROPN
ejpam-5395	2	39	,	,	PUNCT
ejpam-5395	2	40	chawalit	chawalit	VERB
ejpam-5395	2	41	boonpok1,∗	boonpok1,∗	NOUN
ejpam-5395	2	42	1	1	NUM
ejpam-5395	2	43	mathematics	mathematic	NOUN
ejpam-5395	2	44	and	and	CCONJ
ejpam-5395	2	45	applied	apply	VERB
ejpam-5395	2	46	mathematics	mathematics	PROPN
ejpam-5395	2	47	research	research	NOUN
ejpam-5395	2	48	unit	unit	NOUN
ejpam-5395	2	49	,	,	PUNCT
ejpam-5395	2	50	department	department	NOUN
ejpam-5395	2	51	of	of	ADP
ejpam-5395	2	52	mathematics	mathematic	NOUN
ejpam-5395	2	53	,	,	PUNCT
ejpam-5395	2	54	faculty	faculty	NOUN
ejpam-5395	2	55	of	of	ADP
ejpam-5395	2	56	science	science	NOUN
ejpam-5395	2	57	,	,	PUNCT
ejpam-5395	2	58	mahasarakham	mahasarakham	PROPN
ejpam-5395	2	59	university	university	PROPN
ejpam-5395	2	60	,	,	PUNCT
ejpam-5395	2	61	maha	maha	PROPN
ejpam-5395	2	62	sarakham	sarakham	PROPN
ejpam-5395	2	63	,	,	PUNCT
ejpam-5395	2	64	44150	44150	NUM
ejpam-5395	2	65	,	,	PUNCT
ejpam-5395	2	66	thailand	thailand	PROPN
ejpam-5395	2	67	2	2	NUM
ejpam-5395	2	68	department	department	NOUN
ejpam-5395	2	69	of	of	ADP
ejpam-5395	2	70	mathematics	mathematic	NOUN
ejpam-5395	2	71	and	and	CCONJ
ejpam-5395	2	72	computer	computer	NOUN
ejpam-5395	2	73	science	science	NOUN
ejpam-5395	2	74	,	,	PUNCT
ejpam-5395	2	75	faculty	faculty	NOUN
ejpam-5395	2	76	of	of	ADP
ejpam-5395	2	77	science	science	NOUN
ejpam-5395	2	78	and	and	CCONJ
ejpam-5395	2	79	technology	technology	NOUN
ejpam-5395	2	80	,	,	PUNCT
ejpam-5395	2	81	prince	prince	NOUN
ejpam-5395	2	82	of	of	ADP
ejpam-5395	2	83	songkla	songkla	PROPN
ejpam-5395	2	84	university	university	PROPN
ejpam-5395	2	85	,	,	PUNCT
ejpam-5395	2	86	pattani	pattani	NOUN
ejpam-5395	2	87	campus	campus	NOUN
ejpam-5395	2	88	,	,	PUNCT
ejpam-5395	2	89	pattani	pattani	NOUN
ejpam-5395	2	90	,	,	PUNCT
ejpam-5395	2	91	94000	94000	NUM
ejpam-5395	2	92	,	,	PUNCT
ejpam-5395	2	93	thailand	thailand	PROPN
ejpam-5395	2	94	abstract	abstract	PROPN
ejpam-5395	2	95	.	.	PUNCT
ejpam-5395	3	1	this	this	DET
ejpam-5395	3	2	paper	paper	NOUN
ejpam-5395	3	3	deals	deal	NOUN
ejpam-5395	3	4	with	with	ADP
ejpam-5395	3	5	the	the	DET
ejpam-5395	3	6	concept	concept	NOUN
ejpam-5395	3	7	of	of	ADP
ejpam-5395	3	8	faintly	faintly	ADV
ejpam-5395	3	9	(	(	PUNCT
ejpam-5395	3	10	τ1	τ1	PROPN
ejpam-5395	3	11	,	,	PUNCT
ejpam-5395	3	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	3	13	functions	function	NOUN
ejpam-5395	3	14	.	.	PUNCT
ejpam-5395	4	1	furthermore	furthermore	ADV
ejpam-5395	4	2	,	,	PUNCT
ejpam-5395	4	3	some	some	DET
ejpam-5395	4	4	characterizations	characterization	NOUN
ejpam-5395	4	5	of	of	ADP
ejpam-5395	4	6	faintly	faintly	ADV
ejpam-5395	4	7	(	(	PUNCT
ejpam-5395	4	8	τ1	τ1	PROPN
ejpam-5395	4	9	,	,	PUNCT
ejpam-5395	4	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	4	11	functions	function	NOUN
ejpam-5395	4	12	are	be	AUX
ejpam-5395	4	13	investigated	investigate	VERB
ejpam-5395	4	14	.	.	PUNCT
ejpam-5395	5	1	the	the	DET
ejpam-5395	5	2	relationships	relationship	NOUN
ejpam-5395	5	3	between	between	ADP
ejpam-5395	5	4	faint	faint	ADJ
ejpam-5395	5	5	(	(	PUNCT
ejpam-5395	5	6	τ1	τ1	NOUN
ejpam-5395	5	7	,	,	PUNCT
ejpam-5395	5	8	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	5	9	and	and	CCONJ
ejpam-5395	5	10	other	other	ADJ
ejpam-5395	5	11	forms	form	NOUN
ejpam-5395	5	12	of	of	ADP
ejpam-5395	5	13	(	(	PUNCT
ejpam-5395	5	14	τ1	τ1	NOUN
ejpam-5395	5	15	,	,	PUNCT
ejpam-5395	5	16	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	5	17	are	be	AUX
ejpam-5395	5	18	considered	consider	VERB
ejpam-5395	5	19	.	.	PUNCT
ejpam-5395	6	1	2020	2020	NUM
ejpam-5395	6	2	mathematics	mathematic	NOUN
ejpam-5395	6	3	subject	subject	NOUN
ejpam-5395	6	4	classifications	classification	NOUN
ejpam-5395	6	5	:	:	PUNCT
ejpam-5395	6	6	54c08	54c08	NUM
ejpam-5395	6	7	,	,	PUNCT
ejpam-5395	6	8	54e55	54e55	NUM
ejpam-5395	6	9	key	key	ADJ
ejpam-5395	6	10	words	word	NOUN
ejpam-5395	6	11	and	and	CCONJ
ejpam-5395	6	12	phrases	phrase	NOUN
ejpam-5395	6	13	:	:	PUNCT
ejpam-5395	6	14	(	(	PUNCT
ejpam-5395	6	15	τ1	τ1	NOUN
ejpam-5395	6	16	,	,	PUNCT
ejpam-5395	6	17	τ2)θ	τ2)θ	ADJ
ejpam-5395	6	18	-	-	PUNCT
ejpam-5395	6	19	open	open	ADJ
ejpam-5395	6	20	set	set	NOUN
ejpam-5395	6	21	,	,	PUNCT
ejpam-5395	6	22	(	(	PUNCT
ejpam-5395	6	23	τ1	τ1	NOUN
ejpam-5395	6	24	,	,	PUNCT
ejpam-5395	6	25	τ2)θ	τ2)θ	ADJ
ejpam-5395	6	26	-	-	PUNCT
ejpam-5395	6	27	closed	close	VERB
ejpam-5395	6	28	set	set	NOUN
ejpam-5395	6	29	,	,	PUNCT
ejpam-5395	6	30	faintly	faintly	ADV
ejpam-5395	6	31	(	(	PUNCT
ejpam-5395	6	32	τ1	τ1	PROPN
ejpam-5395	6	33	,	,	PUNCT
ejpam-5395	6	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	6	35	function	function	NOUN
ejpam-5395	6	36	1	1	NUM
ejpam-5395	6	37	.	.	PUNCT
ejpam-5395	6	38	introduction	introduction	NOUN
ejpam-5395	6	39	the	the	DET
ejpam-5395	6	40	field	field	NOUN
ejpam-5395	6	41	of	of	ADP
ejpam-5395	6	42	the	the	DET
ejpam-5395	6	43	mathematical	mathematical	ADJ
ejpam-5395	6	44	science	science	NOUN
ejpam-5395	6	45	which	which	PRON
ejpam-5395	6	46	goes	go	VERB
ejpam-5395	6	47	under	under	ADP
ejpam-5395	6	48	the	the	DET
ejpam-5395	6	49	name	name	NOUN
ejpam-5395	6	50	of	of	ADP
ejpam-5395	6	51	topology	topology	NOUN
ejpam-5395	6	52	is	be	AUX
ejpam-5395	6	53	concerned	concern	VERB
ejpam-5395	6	54	with	with	ADP
ejpam-5395	6	55	all	all	DET
ejpam-5395	6	56	questions	question	NOUN
ejpam-5395	6	57	directly	directly	ADV
ejpam-5395	6	58	or	or	CCONJ
ejpam-5395	6	59	indirectly	indirectly	ADV
ejpam-5395	6	60	related	relate	VERB
ejpam-5395	6	61	to	to	ADP
ejpam-5395	6	62	continuity	continuity	NOUN
ejpam-5395	6	63	.	.	PUNCT
ejpam-5395	7	1	semi	semi	ADJ
ejpam-5395	7	2	-	-	ADJ
ejpam-5395	7	3	open	open	ADJ
ejpam-5395	7	4	sets	set	NOUN
ejpam-5395	7	5	[	[	X
ejpam-5395	7	6	25	25	NUM
ejpam-5395	7	7	]	]	PUNCT
ejpam-5395	7	8	,	,	PUNCT
ejpam-5395	7	9	preopen	preopen	ADJ
ejpam-5395	7	10	sets	set	NOUN
ejpam-5395	7	11	[	[	X
ejpam-5395	7	12	27	27	NUM
ejpam-5395	7	13	]	]	PUNCT
ejpam-5395	7	14	,	,	PUNCT
ejpam-5395	7	15	α	α	X
ejpam-5395	7	16	-	-	ADJ
ejpam-5395	7	17	open	open	ADJ
ejpam-5395	7	18	sets	set	NOUN
ejpam-5395	7	19	[	[	X
ejpam-5395	7	20	29	29	NUM
ejpam-5395	7	21	]	]	PUNCT
ejpam-5395	7	22	,	,	PUNCT
ejpam-5395	7	23	β	β	X
ejpam-5395	7	24	-	-	ADJ
ejpam-5395	7	25	open	open	ADJ
ejpam-5395	7	26	sets	set	NOUN
ejpam-5395	7	27	[	[	X
ejpam-5395	7	28	22	22	NUM
ejpam-5395	7	29	]	]	PUNCT
ejpam-5395	7	30	and	and	CCONJ
ejpam-5395	7	31	θ	θ	ADJ
ejpam-5395	7	32	-	-	ADJ
ejpam-5395	7	33	open	open	ADJ
ejpam-5395	7	34	sets	set	NOUN
ejpam-5395	7	35	[	[	X
ejpam-5395	7	36	38	38	NUM
ejpam-5395	7	37	]	]	PUNCT
ejpam-5395	7	38	play	play	VERB
ejpam-5395	7	39	an	an	DET
ejpam-5395	7	40	important	important	ADJ
ejpam-5395	7	41	role	role	NOUN
ejpam-5395	7	42	in	in	ADP
ejpam-5395	7	43	researches	research	NOUN
ejpam-5395	7	44	of	of	ADP
ejpam-5395	7	45	generalizations	generalization	NOUN
ejpam-5395	7	46	of	of	ADP
ejpam-5395	7	47	continuity	continuity	NOUN
ejpam-5395	7	48	.	.	PUNCT
ejpam-5395	8	1	using	use	VERB
ejpam-5395	8	2	these	these	DET
ejpam-5395	8	3	sets	set	NOUN
ejpam-5395	8	4	several	several	ADJ
ejpam-5395	8	5	authors	author	NOUN
ejpam-5395	8	6	introduced	introduce	VERB
ejpam-5395	8	7	and	and	CCONJ
ejpam-5395	8	8	investigated	investigate	VERB
ejpam-5395	8	9	various	various	ADJ
ejpam-5395	8	10	types	type	NOUN
ejpam-5395	8	11	of	of	ADP
ejpam-5395	8	12	generalizations	generalization	NOUN
ejpam-5395	8	13	of	of	ADP
ejpam-5395	8	14	continuity	continuity	NOUN
ejpam-5395	8	15	in	in	ADP
ejpam-5395	8	16	topological	topological	ADJ
ejpam-5395	8	17	spaces	space	NOUN
ejpam-5395	8	18	.	.	PUNCT
ejpam-5395	9	1	viriyapong	viriyapong	PROPN
ejpam-5395	9	2	and	and	CCONJ
ejpam-5395	9	3	boonpok	boonpok	VERB
ejpam-5395	10	1	[	[	X
ejpam-5395	10	2	40	40	NUM
ejpam-5395	10	3	]	]	PUNCT
ejpam-5395	10	4	studied	study	VERB
ejpam-5395	10	5	some	some	DET
ejpam-5395	10	6	characterizations	characterization	NOUN
ejpam-5395	10	7	of	of	ADP
ejpam-5395	10	8	(	(	PUNCT
ejpam-5395	10	9	λ	λ	PROPN
ejpam-5395	10	10	,	,	PUNCT
ejpam-5395	10	11	sp)-continuous	sp)-continuous	ADJ
ejpam-5395	10	12	functions	function	NOUN
ejpam-5395	10	13	by	by	ADP
ejpam-5395	10	14	utilizing	utilize	VERB
ejpam-5395	10	15	the	the	DET
ejpam-5395	10	16	notions	notion	NOUN
ejpam-5395	10	17	of	of	ADP
ejpam-5395	10	18	(	(	PUNCT
ejpam-5395	10	19	λ	λ	PROPN
ejpam-5395	10	20	,	,	PUNCT
ejpam-5395	10	21	sp)-open	sp)-open	ADJ
ejpam-5395	10	22	sets	set	NOUN
ejpam-5395	10	23	and	and	CCONJ
ejpam-5395	10	24	(	(	PUNCT
ejpam-5395	10	25	λ	λ	PROPN
ejpam-5395	10	26	,	,	PUNCT
ejpam-5395	10	27	sp)-closed	sp)-close	VERB
ejpam-5395	10	28	sets	set	NOUN
ejpam-5395	10	29	due	due	ADP
ejpam-5395	10	30	to	to	ADP
ejpam-5395	10	31	boonpok	boonpok	NOUN
ejpam-5395	10	32	and	and	CCONJ
ejpam-5395	10	33	khampakdee	khampakdee	NOUN
ejpam-5395	10	34	[	[	X
ejpam-5395	10	35	8	8	NUM
ejpam-5395	10	36	]	]	PUNCT
ejpam-5395	10	37	.	.	PUNCT
ejpam-5395	11	1	dungthaisong	dungthaisong	NOUN
ejpam-5395	11	2	et	et	PROPN
ejpam-5395	11	3	al	al	PROPN
ejpam-5395	11	4	.	.	PUNCT
ejpam-5395	12	1	[	[	X
ejpam-5395	12	2	21	21	NUM
ejpam-5395	12	3	]	]	PUNCT
ejpam-5395	12	4	introduced	introduce	VERB
ejpam-5395	12	5	and	and	CCONJ
ejpam-5395	12	6	studied	study	VERB
ejpam-5395	12	7	the	the	DET
ejpam-5395	12	8	concept	concept	NOUN
ejpam-5395	12	9	of	of	ADP
ejpam-5395	12	10	g(m	g(m	ADJ
ejpam-5395	12	11	,	,	PUNCT
ejpam-5395	12	12	n)-continuous	n)-continuous	ADJ
ejpam-5395	12	13	functions	function	NOUN
ejpam-5395	12	14	.	.	PUNCT
ejpam-5395	13	1	duangphui	duangphui	NOUN
ejpam-5395	13	2	et	et	PROPN
ejpam-5395	13	3	al	al	PROPN
ejpam-5395	13	4	.	.	PUNCT
ejpam-5395	14	1	[	[	X
ejpam-5395	14	2	20	20	NUM
ejpam-5395	14	3	]	]	PUNCT
ejpam-5395	14	4	introduced	introduce	VERB
ejpam-5395	14	5	and	and	CCONJ
ejpam-5395	14	6	investigated	investigate	VERB
ejpam-5395	14	7	the	the	DET
ejpam-5395	14	8	notion	notion	NOUN
ejpam-5395	14	9	of	of	ADP
ejpam-5395	14	10	(	(	PUNCT
ejpam-5395	14	11	µ	µ	NOUN
ejpam-5395	14	12	,	,	PUNCT
ejpam-5395	14	13	µ′)(m	µ′)(m	VERB
ejpam-5395	14	14	,	,	PUNCT
ejpam-5395	14	15	n)-continuous	n)-continuous	ADJ
ejpam-5395	14	16	functions	function	NOUN
ejpam-5395	14	17	.	.	PUNCT
ejpam-5395	15	1	furthermore	furthermore	ADV
ejpam-5395	15	2	,	,	PUNCT
ejpam-5395	15	3	several	several	ADJ
ejpam-5395	15	4	characterizations	characterization	NOUN
ejpam-5395	15	5	of	of	ADP
ejpam-5395	15	6	almost	almost	ADV
ejpam-5395	15	7	(	(	PUNCT
ejpam-5395	15	8	λ	λ	PROPN
ejpam-5395	15	9	,	,	PUNCT
ejpam-5395	15	10	p)-continuous	p)-continuous	ADJ
ejpam-5395	15	11	functions	function	NOUN
ejpam-5395	15	12	,	,	PUNCT
ejpam-5395	15	13	strongly	strongly	ADV
ejpam-5395	15	14	θ(λ	θ(λ	PROPN
ejpam-5395	15	15	,	,	PUNCT
ejpam-5395	15	16	p)-continuous	p)-continuous	ADJ
ejpam-5395	15	17	functions	function	NOUN
ejpam-5395	15	18	,	,	PUNCT
ejpam-5395	15	19	almost	almost	ADV
ejpam-5395	15	20	strongly	strongly	ADV
ejpam-5395	15	21	θ(λ	θ(λ	VERB
ejpam-5395	15	22	,	,	PUNCT
ejpam-5395	15	23	p)continuous	p)continuous	ADJ
ejpam-5395	15	24	functions	function	NOUN
ejpam-5395	15	25	,	,	PUNCT
ejpam-5395	15	26	θ(λ	θ(λ	PROPN
ejpam-5395	15	27	,	,	PUNCT
ejpam-5395	15	28	p)-continuous	p)-continuous	ADJ
ejpam-5395	15	29	functions	function	NOUN
ejpam-5395	15	30	,	,	PUNCT
ejpam-5395	15	31	weakly	weakly	ADJ
ejpam-5395	15	32	(	(	PUNCT
ejpam-5395	15	33	λ	λ	PROPN
ejpam-5395	15	34	,	,	PUNCT
ejpam-5395	15	35	b)-continuous	b)-continuous	ADJ
ejpam-5395	15	36	functions	function	NOUN
ejpam-5395	15	37	,	,	PUNCT
ejpam-5395	15	38	∗corresponding	∗corresponde	VERB
ejpam-5395	15	39	author	author	NOUN
ejpam-5395	15	40	.	.	PUNCT
ejpam-5395	16	1	doi	doi	NOUN
ejpam-5395	16	2	:	:	PUNCT
ejpam-5395	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5395	https://doi.org/10.29020/nybg.ejpam.v17i4.5395	PROPN
ejpam-5395	16	4	email	email	NOUN
ejpam-5395	16	5	addresses	address	NOUN
ejpam-5395	16	6	:	:	PUNCT
ejpam-5395	16	7	napassanan.sri@msu.ac.th	napassanan.sri@msu.ac.th	PRON
ejpam-5395	16	8	(	(	PUNCT
ejpam-5395	16	9	n.	n.	NOUN
ejpam-5395	16	10	srisarakham	srisarakham	PROPN
ejpam-5395	16	11	)	)	PUNCT
ejpam-5395	16	12	,	,	PUNCT
ejpam-5395	16	13	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-5395	16	14	(	(	PUNCT
ejpam-5395	16	15	a.	a.	PROPN
ejpam-5395	16	16	sama	sama	PROPN
ejpam-5395	16	17	-	-	PUNCT
ejpam-5395	16	18	ae	ae	PROPN
ejpam-5395	16	19	)	)	PUNCT
ejpam-5395	16	20	,	,	PUNCT
ejpam-5395	16	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-5395	16	22	(	(	PUNCT
ejpam-5395	16	23	c.	c.	PROPN
ejpam-5395	16	24	boonpok	boonpok	PROPN
ejpam-5395	16	25	)	)	PUNCT
ejpam-5395	16	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5395	16	27	2753	2753	NUM
ejpam-5395	17	1	copyright	copyright	NOUN
ejpam-5395	17	2	:	:	PUNCT
ejpam-5395	17	3	©	©	PROPN
ejpam-5395	17	4	2024	2024	NUM
ejpam-5395	17	5	the	the	DET
ejpam-5395	17	6	author(s	author(s	NOUN
ejpam-5395	17	7	)	)	PUNCT
ejpam-5395	17	8	.	.	PUNCT
ejpam-5395	18	1	(	(	PUNCT
ejpam-5395	18	2	cc	cc	NOUN
ejpam-5395	18	3	by	by	ADP
ejpam-5395	18	4	-	-	PUNCT
ejpam-5395	18	5	nc	nc	PROPN
ejpam-5395	18	6	4.0	4.0	NUM
ejpam-5395	18	7	)	)	PUNCT
ejpam-5395	18	8	n.	n.	NOUN
ejpam-5395	18	9	srisarakham	srisarakham	PROPN
ejpam-5395	18	10	,	,	PUNCT
ejpam-5395	18	11	a.	a.	PROPN
ejpam-5395	18	12	sama	sama	PROPN
ejpam-5395	18	13	-	-	PUNCT
ejpam-5395	18	14	ae	ae	PROPN
ejpam-5395	18	15	,	,	PUNCT
ejpam-5395	18	16	c.	c.	PROPN
ejpam-5395	18	17	boonpok	boonpok	PROPN
ejpam-5395	18	18	/	/	SYM
ejpam-5395	18	19	eur	eur	PROPN
ejpam-5395	18	20	.	.	PUNCT
ejpam-5395	19	1	j.	j.	PROPN
ejpam-5395	19	2	pure	pure	PROPN
ejpam-5395	19	3	appl	appl	PROPN
ejpam-5395	19	4	.	.	PROPN
ejpam-5395	19	5	math	math	PROPN
ejpam-5395	19	6	,	,	PUNCT
ejpam-5395	19	7	17	17	NUM
ejpam-5395	19	8	(	(	PUNCT
ejpam-5395	19	9	4	4	NUM
ejpam-5395	19	10	)	)	PUNCT
ejpam-5395	19	11	(	(	PUNCT
ejpam-5395	19	12	2024	2024	NUM
ejpam-5395	19	13	)	)	PUNCT
ejpam-5395	19	14	,	,	PUNCT
ejpam-5395	19	15	2753	2753	NUM
ejpam-5395	19	16	-	-	SYM
ejpam-5395	19	17	2762	2762	NUM
ejpam-5395	19	18	2754	2754	NUM
ejpam-5395	19	19	(	(	PUNCT
ejpam-5395	19	20	λ	λ	NOUN
ejpam-5395	19	21	,	,	PUNCT
ejpam-5395	19	22	p(⋆))-continuous	p(⋆))-continuous	ADJ
ejpam-5395	19	23	functions	function	NOUN
ejpam-5395	19	24	,	,	PUNCT
ejpam-5395	19	25	θ(⋆)-precontinuous	θ(⋆)-precontinuous	ADJ
ejpam-5395	19	26	functions	function	NOUN
ejpam-5395	19	27	,	,	PUNCT
ejpam-5395	19	28	⋆-continuous	⋆-continuous	ADJ
ejpam-5395	19	29	functions	function	NOUN
ejpam-5395	19	30	,	,	PUNCT
ejpam-5395	19	31	θi	θi	ADP
ejpam-5395	19	32	-continuous	-continuous	ADJ
ejpam-5395	19	33	functions	function	NOUN
ejpam-5395	19	34	,	,	PUNCT
ejpam-5395	19	35	almost	almost	ADV
ejpam-5395	19	36	(	(	PUNCT
ejpam-5395	19	37	g	g	NOUN
ejpam-5395	19	38	,	,	PUNCT
ejpam-5395	19	39	m)-continuous	m)-continuous	ADJ
ejpam-5395	19	40	functions	function	NOUN
ejpam-5395	19	41	,	,	PUNCT
ejpam-5395	19	42	pairwise	pairwise	PROPN
ejpam-5395	19	43	m	m	PROPN
ejpam-5395	19	44	-continuous	-continuous	ADJ
ejpam-5395	19	45	functions	function	NOUN
ejpam-5395	19	46	,	,	PUNCT
ejpam-5395	19	47	almost	almost	ADV
ejpam-5395	19	48	quasi	quasi	NOUN
ejpam-5395	19	49	(	(	PUNCT
ejpam-5395	19	50	τ1	τ1	NOUN
ejpam-5395	19	51	,	,	PUNCT
ejpam-5395	19	52	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	19	53	functions	function	NOUN
ejpam-5395	19	54	and	and	CCONJ
ejpam-5395	19	55	weakly	weakly	ADJ
ejpam-5395	19	56	quasi	quasi	NOUN
ejpam-5395	19	57	(	(	PUNCT
ejpam-5395	19	58	τ1	τ1	PROPN
ejpam-5395	19	59	,	,	PUNCT
ejpam-5395	19	60	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	19	61	functions	function	NOUN
ejpam-5395	19	62	were	be	AUX
ejpam-5395	19	63	presented	present	VERB
ejpam-5395	19	64	in	in	ADP
ejpam-5395	19	65	[	[	X
ejpam-5395	19	66	35	35	NUM
ejpam-5395	19	67	]	]	PUNCT
ejpam-5395	19	68	,	,	PUNCT
ejpam-5395	19	69	[	[	X
ejpam-5395	19	70	37	37	NUM
ejpam-5395	19	71	]	]	PUNCT
ejpam-5395	19	72	,	,	PUNCT
ejpam-5395	19	73	[	[	X
ejpam-5395	19	74	9	9	NUM
ejpam-5395	19	75	]	]	PUNCT
ejpam-5395	19	76	,	,	PUNCT
ejpam-5395	19	77	[	[	X
ejpam-5395	19	78	33	33	NUM
ejpam-5395	19	79	]	]	PUNCT
ejpam-5395	19	80	,	,	PUNCT
ejpam-5395	19	81	[	[	X
ejpam-5395	19	82	12	12	NUM
ejpam-5395	19	83	]	]	PUNCT
ejpam-5395	19	84	,	,	PUNCT
ejpam-5395	19	85	[	[	X
ejpam-5395	19	86	5	5	NUM
ejpam-5395	19	87	]	]	PUNCT
ejpam-5395	19	88	,	,	PUNCT
ejpam-5395	19	89	[	[	X
ejpam-5395	19	90	7	7	NUM
ejpam-5395	19	91	]	]	PUNCT
ejpam-5395	19	92	,	,	PUNCT
ejpam-5395	19	93	[	[	X
ejpam-5395	19	94	6	6	NUM
ejpam-5395	19	95	]	]	PUNCT
ejpam-5395	19	96	,	,	PUNCT
ejpam-5395	19	97	[	[	X
ejpam-5395	19	98	3	3	NUM
ejpam-5395	19	99	]	]	PUNCT
ejpam-5395	19	100	,	,	PUNCT
ejpam-5395	19	101	[	[	X
ejpam-5395	19	102	1	1	NUM
ejpam-5395	19	103	]	]	PUNCT
ejpam-5395	19	104	,	,	PUNCT
ejpam-5395	19	105	[	[	X
ejpam-5395	19	106	2	2	NUM
ejpam-5395	19	107	]	]	PUNCT
ejpam-5395	19	108	,	,	PUNCT
ejpam-5395	19	109	[	[	X
ejpam-5395	19	110	24	24	NUM
ejpam-5395	19	111	]	]	PUNCT
ejpam-5395	19	112	and	and	CCONJ
ejpam-5395	19	113	[	[	X
ejpam-5395	19	114	17	17	NUM
ejpam-5395	19	115	]	]	PUNCT
ejpam-5395	19	116	,	,	PUNCT
ejpam-5395	19	117	respectively	respectively	ADV
ejpam-5395	19	118	.	.	PUNCT
ejpam-5395	20	1	long	long	ADJ
ejpam-5395	20	2	and	and	CCONJ
ejpam-5395	20	3	herrington	herrington	PROPN
ejpam-5395	21	1	[	[	X
ejpam-5395	21	2	26	26	NUM
ejpam-5395	21	3	]	]	PUNCT
ejpam-5395	21	4	introduced	introduce	VERB
ejpam-5395	21	5	the	the	DET
ejpam-5395	21	6	notion	notion	NOUN
ejpam-5395	21	7	of	of	ADP
ejpam-5395	21	8	faintly	faintly	ADV
ejpam-5395	21	9	continuous	continuous	ADJ
ejpam-5395	21	10	functions	function	NOUN
ejpam-5395	21	11	.	.	PUNCT
ejpam-5395	22	1	moreover	moreover	ADV
ejpam-5395	22	2	,	,	PUNCT
ejpam-5395	22	3	some	some	DET
ejpam-5395	22	4	characterizations	characterization	NOUN
ejpam-5395	22	5	of	of	ADP
ejpam-5395	22	6	faintly	faintly	ADV
ejpam-5395	22	7	continuous	continuous	ADJ
ejpam-5395	22	8	functions	function	NOUN
ejpam-5395	22	9	were	be	AUX
ejpam-5395	22	10	investigated	investigate	VERB
ejpam-5395	22	11	in	in	ADP
ejpam-5395	22	12	[	[	X
ejpam-5395	22	13	28	28	NUM
ejpam-5395	22	14	]	]	PUNCT
ejpam-5395	22	15	and	and	CCONJ
ejpam-5395	22	16	[	[	X
ejpam-5395	22	17	30	30	NUM
ejpam-5395	22	18	]	]	PUNCT
ejpam-5395	22	19	,	,	PUNCT
ejpam-5395	22	20	respectively	respectively	ADV
ejpam-5395	22	21	.	.	PUNCT
ejpam-5395	23	1	three	three	NUM
ejpam-5395	23	2	weak	weak	ADJ
ejpam-5395	23	3	forms	form	NOUN
ejpam-5395	23	4	of	of	ADP
ejpam-5395	23	5	faint	faint	ADJ
ejpam-5395	23	6	continuity	continuity	NOUN
ejpam-5395	23	7	were	be	AUX
ejpam-5395	23	8	introduced	introduce	VERB
ejpam-5395	23	9	by	by	ADP
ejpam-5395	23	10	noiri	noiri	PROPN
ejpam-5395	23	11	and	and	CCONJ
ejpam-5395	23	12	popa	popa	NOUN
ejpam-5395	24	1	[	[	X
ejpam-5395	24	2	31	31	NUM
ejpam-5395	24	3	]	]	PUNCT
ejpam-5395	24	4	.	.	PUNCT
ejpam-5395	25	1	nasef	nasef	PROPN
ejpam-5395	25	2	and	and	CCONJ
ejpam-5395	25	3	noiri	noiri	ADV
ejpam-5395	26	1	[	[	X
ejpam-5395	26	2	28	28	NUM
ejpam-5395	26	3	]	]	PUNCT
ejpam-5395	26	4	introduced	introduce	VERB
ejpam-5395	26	5	and	and	CCONJ
ejpam-5395	26	6	studied	study	VERB
ejpam-5395	26	7	three	three	NUM
ejpam-5395	26	8	strong	strong	ADJ
ejpam-5395	26	9	forms	form	NOUN
ejpam-5395	26	10	of	of	ADP
ejpam-5395	26	11	faint	faint	ADJ
ejpam-5395	26	12	continuity	continuity	NOUN
ejpam-5395	26	13	under	under	ADP
ejpam-5395	26	14	the	the	DET
ejpam-5395	26	15	names	name	NOUN
ejpam-5395	26	16	of	of	ADP
ejpam-5395	26	17	strongly	strongly	ADV
ejpam-5395	26	18	faint	faint	ADJ
ejpam-5395	26	19	semi	semi	ADJ
ejpam-5395	26	20	-	-	NOUN
ejpam-5395	26	21	continuity	continuity	ADJ
ejpam-5395	26	22	,	,	PUNCT
ejpam-5395	26	23	strongly	strongly	ADV
ejpam-5395	26	24	faint	faint	ADJ
ejpam-5395	26	25	precontinuity	precontinuity	NOUN
ejpam-5395	26	26	and	and	CCONJ
ejpam-5395	26	27	strongly	strongly	ADV
ejpam-5395	26	28	faint	faint	ADJ
ejpam-5395	26	29	β	β	NOUN
ejpam-5395	26	30	-	-	NOUN
ejpam-5395	26	31	continuity	continuity	NOUN
ejpam-5395	26	32	.	.	PUNCT
ejpam-5395	27	1	jafari	jafari	PROPN
ejpam-5395	27	2	and	and	CCONJ
ejpam-5395	27	3	noiri	noiri	ADV
ejpam-5395	27	4	[	[	X
ejpam-5395	27	5	23	23	NUM
ejpam-5395	27	6	]	]	PUNCT
ejpam-5395	27	7	introduced	introduce	VERB
ejpam-5395	27	8	and	and	CCONJ
ejpam-5395	27	9	investigated	investigate	VERB
ejpam-5395	27	10	the	the	DET
ejpam-5395	27	11	concept	concept	NOUN
ejpam-5395	27	12	of	of	ADP
ejpam-5395	27	13	faintly	faintly	ADV
ejpam-5395	27	14	α	α	NUM
ejpam-5395	27	15	-	-	ADJ
ejpam-5395	27	16	continuous	continuous	ADJ
ejpam-5395	27	17	functions	function	NOUN
ejpam-5395	27	18	.	.	PUNCT
ejpam-5395	28	1	chananan	chananan	PROPN
ejpam-5395	28	2	et	et	PROPN
ejpam-5395	28	3	al	al	PROPN
ejpam-5395	28	4	.	.	PUNCT
ejpam-5395	29	1	[	[	X
ejpam-5395	29	2	15	15	NUM
ejpam-5395	29	3	]	]	PUNCT
ejpam-5395	29	4	introduced	introduce	VERB
ejpam-5395	29	5	a	a	DET
ejpam-5395	29	6	new	new	ADJ
ejpam-5395	29	7	class	class	NOUN
ejpam-5395	29	8	of	of	ADP
ejpam-5395	29	9	functions	function	NOUN
ejpam-5395	29	10	,	,	PUNCT
ejpam-5395	29	11	called	call	VERB
ejpam-5395	29	12	faintly	faintly	ADV
ejpam-5395	29	13	(	(	PUNCT
ejpam-5395	29	14	m,µ)-continuous	m,µ)-continuous	ADJ
ejpam-5395	29	15	functions	function	NOUN
ejpam-5395	29	16	and	and	CCONJ
ejpam-5395	29	17	established	establish	VERB
ejpam-5395	29	18	the	the	DET
ejpam-5395	29	19	relationships	relationship	NOUN
ejpam-5395	29	20	between	between	ADP
ejpam-5395	29	21	faint	faint	ADJ
ejpam-5395	29	22	(	(	PUNCT
ejpam-5395	29	23	m,µ)-continuity	m,µ)-continuity	NOUN
ejpam-5395	29	24	and	and	CCONJ
ejpam-5395	29	25	other	other	ADJ
ejpam-5395	29	26	related	related	ADJ
ejpam-5395	29	27	generalized	generalized	ADJ
ejpam-5395	29	28	forms	form	NOUN
ejpam-5395	29	29	of	of	ADP
ejpam-5395	29	30	(	(	PUNCT
ejpam-5395	29	31	m,µ)-continuity	m,µ)-continuity	PROPN
ejpam-5395	29	32	.	.	PUNCT
ejpam-5395	30	1	noiri	noiri	PROPN
ejpam-5395	30	2	and	and	CCONJ
ejpam-5395	30	3	popa	popa	NOUN
ejpam-5395	31	1	[	[	X
ejpam-5395	31	2	32	32	NUM
ejpam-5395	31	3	]	]	PUNCT
ejpam-5395	31	4	introduced	introduce	VERB
ejpam-5395	31	5	the	the	DET
ejpam-5395	31	6	notion	notion	NOUN
ejpam-5395	31	7	of	of	ADP
ejpam-5395	31	8	faintly	faintly	ADV
ejpam-5395	31	9	m	m	ADJ
ejpam-5395	31	10	-	-	ADJ
ejpam-5395	31	11	continuous	continuous	ADJ
ejpam-5395	31	12	functions	function	NOUN
ejpam-5395	31	13	as	as	ADP
ejpam-5395	31	14	functions	function	NOUN
ejpam-5395	31	15	from	from	ADP
ejpam-5395	31	16	a	a	DET
ejpam-5395	31	17	set	set	NOUN
ejpam-5395	31	18	x	x	PUNCT
ejpam-5395	31	19	satisfying	satisfy	VERB
ejpam-5395	31	20	some	some	DET
ejpam-5395	31	21	minimal	minimal	ADJ
ejpam-5395	31	22	conditions	condition	NOUN
ejpam-5395	31	23	into	into	ADP
ejpam-5395	31	24	a	a	DET
ejpam-5395	31	25	topological	topological	ADJ
ejpam-5395	31	26	space	space	NOUN
ejpam-5395	31	27	and	and	CCONJ
ejpam-5395	31	28	investigated	investigate	VERB
ejpam-5395	31	29	several	several	ADJ
ejpam-5395	31	30	characterizations	characterization	NOUN
ejpam-5395	31	31	of	of	ADP
ejpam-5395	31	32	faintly	faintly	ADV
ejpam-5395	31	33	m	m	ADJ
ejpam-5395	31	34	-	-	ADJ
ejpam-5395	31	35	continuous	continuous	ADJ
ejpam-5395	31	36	functions	function	NOUN
ejpam-5395	31	37	.	.	PUNCT
ejpam-5395	32	1	pue	pue	NOUN
ejpam-5395	32	2	-	-	PUNCT
ejpam-5395	32	3	on	on	NOUN
ejpam-5395	32	4	et	et	PROPN
ejpam-5395	32	5	al	al	PROPN
ejpam-5395	32	6	.	.	PUNCT
ejpam-5395	33	1	[	[	X
ejpam-5395	33	2	34	34	NUM
ejpam-5395	33	3	]	]	PUNCT
ejpam-5395	33	4	introduced	introduce	VERB
ejpam-5395	33	5	the	the	DET
ejpam-5395	33	6	concept	concept	NOUN
ejpam-5395	33	7	of	of	ADP
ejpam-5395	33	8	faintly	faintly	ADV
ejpam-5395	33	9	(	(	PUNCT
ejpam-5395	33	10	τ1	τ1	PROPN
ejpam-5395	33	11	,	,	PUNCT
ejpam-5395	33	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	33	13	functions	function	NOUN
ejpam-5395	33	14	.	.	PUNCT
ejpam-5395	34	1	in	in	ADP
ejpam-5395	34	2	this	this	DET
ejpam-5395	34	3	paper	paper	NOUN
ejpam-5395	34	4	,	,	PUNCT
ejpam-5395	34	5	we	we	PRON
ejpam-5395	34	6	investigate	investigate	VERB
ejpam-5395	34	7	some	some	DET
ejpam-5395	34	8	characterizations	characterization	NOUN
ejpam-5395	34	9	of	of	ADP
ejpam-5395	34	10	faintly	faintly	ADV
ejpam-5395	34	11	(	(	PUNCT
ejpam-5395	34	12	τ1	τ1	PROPN
ejpam-5395	34	13	,	,	PUNCT
ejpam-5395	34	14	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	34	15	functions	function	NOUN
ejpam-5395	34	16	.	.	PUNCT
ejpam-5395	35	1	we	we	PRON
ejpam-5395	35	2	also	also	ADV
ejpam-5395	35	3	discuss	discuss	VERB
ejpam-5395	35	4	the	the	DET
ejpam-5395	35	5	relationships	relationship	NOUN
ejpam-5395	35	6	between	between	ADP
ejpam-5395	35	7	faintly	faintly	ADV
ejpam-5395	35	8	(	(	PUNCT
ejpam-5395	35	9	τ1	τ1	PROPN
ejpam-5395	35	10	,	,	PUNCT
ejpam-5395	35	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	35	12	functions	function	NOUN
ejpam-5395	35	13	and	and	CCONJ
ejpam-5395	35	14	other	other	ADJ
ejpam-5395	35	15	forms	form	NOUN
ejpam-5395	35	16	of	of	ADP
ejpam-5395	35	17	(	(	PUNCT
ejpam-5395	35	18	τ1	τ1	PROPN
ejpam-5395	35	19	,	,	PUNCT
ejpam-5395	35	20	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	35	21	functions	function	NOUN
ejpam-5395	35	22	.	.	PUNCT
ejpam-5395	36	1	2	2	X
ejpam-5395	36	2	.	.	NUM
ejpam-5395	36	3	preliminaries	preliminary	NOUN
ejpam-5395	36	4	throughout	throughout	ADP
ejpam-5395	36	5	the	the	DET
ejpam-5395	36	6	present	present	ADJ
ejpam-5395	36	7	paper	paper	NOUN
ejpam-5395	36	8	,	,	PUNCT
ejpam-5395	36	9	spaces	space	NOUN
ejpam-5395	36	10	(	(	PUNCT
ejpam-5395	36	11	x	x	NOUN
ejpam-5395	36	12	,	,	PUNCT
ejpam-5395	36	13	τ1	τ1	NOUN
ejpam-5395	36	14	,	,	PUNCT
ejpam-5395	36	15	τ2	τ2	NOUN
ejpam-5395	36	16	)	)	PUNCT
ejpam-5395	36	17	and	and	CCONJ
ejpam-5395	36	18	(	(	PUNCT
ejpam-5395	36	19	y	y	PROPN
ejpam-5395	36	20	,	,	PUNCT
ejpam-5395	36	21	σ1	σ1	PROPN
ejpam-5395	36	22	,	,	PUNCT
ejpam-5395	36	23	σ2	σ2	NOUN
ejpam-5395	36	24	)	)	PUNCT
ejpam-5395	36	25	(	(	PUNCT
ejpam-5395	36	26	or	or	CCONJ
ejpam-5395	36	27	simply	simply	ADV
ejpam-5395	36	28	x	x	X
ejpam-5395	36	29	and	and	CCONJ
ejpam-5395	36	30	y	y	PROPN
ejpam-5395	36	31	)	)	PUNCT
ejpam-5395	36	32	always	always	ADV
ejpam-5395	36	33	mean	mean	VERB
ejpam-5395	36	34	bitopological	bitopological	ADJ
ejpam-5395	36	35	spaces	space	NOUN
ejpam-5395	36	36	on	on	ADP
ejpam-5395	36	37	which	which	PRON
ejpam-5395	36	38	no	no	DET
ejpam-5395	36	39	separation	separation	NOUN
ejpam-5395	36	40	axioms	axiom	NOUN
ejpam-5395	36	41	are	be	AUX
ejpam-5395	36	42	assumed	assume	VERB
ejpam-5395	36	43	unless	unless	SCONJ
ejpam-5395	36	44	explicitly	explicitly	ADV
ejpam-5395	36	45	stated	state	VERB
ejpam-5395	36	46	.	.	PUNCT
ejpam-5395	37	1	let	let	VERB
ejpam-5395	37	2	a	a	DET
ejpam-5395	37	3	be	be	AUX
ejpam-5395	37	4	a	a	DET
ejpam-5395	37	5	subset	subset	NOUN
ejpam-5395	37	6	of	of	ADP
ejpam-5395	37	7	a	a	DET
ejpam-5395	37	8	bitopological	bitopological	ADJ
ejpam-5395	37	9	space	space	NOUN
ejpam-5395	37	10	(	(	PUNCT
ejpam-5395	37	11	x	x	NOUN
ejpam-5395	37	12	,	,	PUNCT
ejpam-5395	37	13	τ1	τ1	NOUN
ejpam-5395	37	14	,	,	PUNCT
ejpam-5395	37	15	τ2	τ2	NOUN
ejpam-5395	37	16	)	)	PUNCT
ejpam-5395	37	17	.	.	PUNCT
ejpam-5395	38	1	the	the	DET
ejpam-5395	38	2	closure	closure	NOUN
ejpam-5395	38	3	of	of	ADP
ejpam-5395	38	4	a	a	PRON
ejpam-5395	38	5	and	and	CCONJ
ejpam-5395	38	6	the	the	DET
ejpam-5395	38	7	interior	interior	NOUN
ejpam-5395	38	8	of	of	ADP
ejpam-5395	38	9	a	a	PRON
ejpam-5395	38	10	with	with	ADP
ejpam-5395	38	11	respect	respect	NOUN
ejpam-5395	38	12	to	to	ADP
ejpam-5395	38	13	τi	τi	PROPN
ejpam-5395	38	14	are	be	AUX
ejpam-5395	38	15	denoted	denote	VERB
ejpam-5395	38	16	by	by	ADP
ejpam-5395	38	17	τi	τi	NOUN
ejpam-5395	38	18	-	-	PUNCT
ejpam-5395	38	19	cl(a	cl(a	NUM
ejpam-5395	38	20	)	)	PUNCT
ejpam-5395	38	21	and	and	CCONJ
ejpam-5395	38	22	τi	τi	NOUN
ejpam-5395	38	23	-	-	PUNCT
ejpam-5395	38	24	int(a	int(a	NOUN
ejpam-5395	38	25	)	)	PUNCT
ejpam-5395	38	26	,	,	PUNCT
ejpam-5395	38	27	respectively	respectively	ADV
ejpam-5395	38	28	,	,	PUNCT
ejpam-5395	38	29	for	for	ADP
ejpam-5395	38	30	i	i	PROPN
ejpam-5395	38	31	=	=	SYM
ejpam-5395	38	32	1	1	NUM
ejpam-5395	38	33	,	,	PUNCT
ejpam-5395	38	34	2	2	NUM
ejpam-5395	38	35	.	.	X
ejpam-5395	38	36	a	a	DET
ejpam-5395	38	37	subset	subset	NOUN
ejpam-5395	38	38	a	a	PRON
ejpam-5395	38	39	of	of	ADP
ejpam-5395	38	40	a	a	DET
ejpam-5395	38	41	bitopological	bitopological	ADJ
ejpam-5395	38	42	space	space	NOUN
ejpam-5395	38	43	(	(	PUNCT
ejpam-5395	38	44	x	x	NOUN
ejpam-5395	38	45	,	,	PUNCT
ejpam-5395	38	46	τ1	τ1	NOUN
ejpam-5395	38	47	,	,	PUNCT
ejpam-5395	38	48	τ2	τ2	NOUN
ejpam-5395	38	49	)	)	PUNCT
ejpam-5395	38	50	is	be	AUX
ejpam-5395	38	51	called	call	VERB
ejpam-5395	38	52	τ1τ2	τ1τ2	VERB
ejpam-5395	38	53	-	-	ADJ
ejpam-5395	38	54	closed	closed	ADJ
ejpam-5395	38	55	[	[	X
ejpam-5395	38	56	14	14	NUM
ejpam-5395	38	57	]	]	X
ejpam-5395	38	58	if	if	SCONJ
ejpam-5395	38	59	a	a	DET
ejpam-5395	38	60	=	=	NOUN
ejpam-5395	38	61	τ1	τ1	NOUN
ejpam-5395	38	62	-	-	PUNCT
ejpam-5395	38	63	cl(τ2	cl(τ2	NOUN
ejpam-5395	38	64	-	-	PUNCT
ejpam-5395	38	65	cl(a	cl(a	NUM
ejpam-5395	38	66	)	)	PUNCT
ejpam-5395	38	67	)	)	PUNCT
ejpam-5395	38	68	.	.	PUNCT
ejpam-5395	39	1	the	the	DET
ejpam-5395	39	2	complement	complement	NOUN
ejpam-5395	39	3	of	of	ADP
ejpam-5395	39	4	a	a	DET
ejpam-5395	39	5	τ1τ2	τ1τ2	ADJ
ejpam-5395	39	6	-	-	ADJ
ejpam-5395	39	7	closed	closed	ADJ
ejpam-5395	39	8	set	set	NOUN
ejpam-5395	39	9	is	be	AUX
ejpam-5395	39	10	called	call	VERB
ejpam-5395	39	11	τ1τ2	τ1τ2	NOUN
ejpam-5395	39	12	-	-	ADJ
ejpam-5395	39	13	open	open	ADJ
ejpam-5395	39	14	.	.	PUNCT
ejpam-5395	40	1	a	a	DET
ejpam-5395	40	2	subset	subset	NOUN
ejpam-5395	40	3	a	a	PRON
ejpam-5395	40	4	of	of	ADP
ejpam-5395	40	5	a	a	DET
ejpam-5395	40	6	bitopological	bitopological	ADJ
ejpam-5395	40	7	space	space	NOUN
ejpam-5395	40	8	(	(	PUNCT
ejpam-5395	40	9	x	x	NOUN
ejpam-5395	40	10	,	,	PUNCT
ejpam-5395	40	11	τ1	τ1	NOUN
ejpam-5395	40	12	,	,	PUNCT
ejpam-5395	40	13	τ2	τ2	NOUN
ejpam-5395	40	14	)	)	PUNCT
ejpam-5395	40	15	is	be	AUX
ejpam-5395	40	16	said	say	VERB
ejpam-5395	40	17	to	to	PART
ejpam-5395	40	18	be	be	AUX
ejpam-5395	40	19	τ1τ2	τ1τ2	NOUN
ejpam-5395	40	20	-	-	ADJ
ejpam-5395	40	21	clopen	clopen	ADJ
ejpam-5395	40	22	[	[	X
ejpam-5395	40	23	14	14	NUM
ejpam-5395	40	24	]	]	X
ejpam-5395	40	25	if	if	SCONJ
ejpam-5395	40	26	a	a	PRON
ejpam-5395	40	27	is	be	AUX
ejpam-5395	40	28	both	both	PRON
ejpam-5395	40	29	τ1τ2	τ1τ2	ADJ
ejpam-5395	40	30	-	-	ADJ
ejpam-5395	40	31	open	open	ADJ
ejpam-5395	40	32	and	and	CCONJ
ejpam-5395	40	33	τ1τ2	τ1τ2	NOUN
ejpam-5395	40	34	-	-	ADJ
ejpam-5395	40	35	closed	closed	ADJ
ejpam-5395	40	36	.	.	PUNCT
ejpam-5395	41	1	let	let	VERB
ejpam-5395	41	2	a	a	DET
ejpam-5395	41	3	be	be	AUX
ejpam-5395	41	4	a	a	DET
ejpam-5395	41	5	subset	subset	NOUN
ejpam-5395	41	6	of	of	ADP
ejpam-5395	41	7	a	a	DET
ejpam-5395	41	8	bitopological	bitopological	ADJ
ejpam-5395	41	9	space	space	NOUN
ejpam-5395	41	10	(	(	PUNCT
ejpam-5395	41	11	x	x	NOUN
ejpam-5395	41	12	,	,	PUNCT
ejpam-5395	41	13	τ1	τ1	NOUN
ejpam-5395	41	14	,	,	PUNCT
ejpam-5395	41	15	τ2	τ2	NOUN
ejpam-5395	41	16	)	)	PUNCT
ejpam-5395	41	17	.	.	PUNCT
ejpam-5395	42	1	the	the	DET
ejpam-5395	42	2	intersection	intersection	NOUN
ejpam-5395	42	3	of	of	ADP
ejpam-5395	42	4	all	all	DET
ejpam-5395	42	5	τ1τ2	τ1τ2	ADJ
ejpam-5395	42	6	-	-	ADJ
ejpam-5395	42	7	closed	closed	ADJ
ejpam-5395	42	8	sets	set	NOUN
ejpam-5395	42	9	of	of	ADP
ejpam-5395	42	10	x	x	PUNCT
ejpam-5395	42	11	containing	contain	VERB
ejpam-5395	42	12	a	a	PRON
ejpam-5395	42	13	is	be	AUX
ejpam-5395	42	14	called	call	VERB
ejpam-5395	42	15	the	the	DET
ejpam-5395	42	16	τ1τ2	τ1τ2	NOUN
ejpam-5395	42	17	-	-	NOUN
ejpam-5395	42	18	closure	closure	NOUN
ejpam-5395	42	19	[	[	X
ejpam-5395	42	20	14	14	NUM
ejpam-5395	42	21	]	]	PUNCT
ejpam-5395	42	22	of	of	ADP
ejpam-5395	42	23	a	a	PRON
ejpam-5395	42	24	and	and	CCONJ
ejpam-5395	42	25	is	be	AUX
ejpam-5395	42	26	denoted	denote	VERB
ejpam-5395	42	27	by	by	ADP
ejpam-5395	42	28	τ1τ2	τ1τ2	NOUN
ejpam-5395	42	29	-	-	NUM
ejpam-5395	42	30	cl(a	cl(a	NUM
ejpam-5395	42	31	)	)	PUNCT
ejpam-5395	42	32	.	.	PUNCT
ejpam-5395	43	1	the	the	DET
ejpam-5395	43	2	union	union	NOUN
ejpam-5395	43	3	of	of	ADP
ejpam-5395	43	4	all	all	DET
ejpam-5395	43	5	τ1τ2	τ1τ2	ADJ
ejpam-5395	43	6	-	-	ADJ
ejpam-5395	43	7	open	open	ADJ
ejpam-5395	43	8	sets	set	NOUN
ejpam-5395	43	9	of	of	ADP
ejpam-5395	43	10	x	x	PUNCT
ejpam-5395	43	11	contained	contain	VERB
ejpam-5395	43	12	in	in	ADP
ejpam-5395	43	13	a	a	PRON
ejpam-5395	43	14	is	be	AUX
ejpam-5395	43	15	called	call	VERB
ejpam-5395	43	16	the	the	DET
ejpam-5395	43	17	τ1τ2	τ1τ2	NOUN
ejpam-5395	43	18	-	-	ADJ
ejpam-5395	43	19	interior	interior	ADJ
ejpam-5395	43	20	[	[	X
ejpam-5395	43	21	14	14	NUM
ejpam-5395	43	22	]	]	PUNCT
ejpam-5395	43	23	of	of	ADP
ejpam-5395	43	24	a	a	PRON
ejpam-5395	43	25	and	and	CCONJ
ejpam-5395	43	26	is	be	AUX
ejpam-5395	43	27	denoted	denote	VERB
ejpam-5395	43	28	by	by	ADP
ejpam-5395	43	29	τ1τ2	τ1τ2	NOUN
ejpam-5395	43	30	-	-	ADJ
ejpam-5395	43	31	int(a	int(a	NOUN
ejpam-5395	43	32	)	)	PUNCT
ejpam-5395	43	33	.	.	PUNCT
ejpam-5395	44	1	lemma	lemma	PROPN
ejpam-5395	44	2	1	1	NUM
ejpam-5395	44	3	.	.	PUNCT
ejpam-5395	45	1	[	[	X
ejpam-5395	45	2	14	14	NUM
ejpam-5395	45	3	]	]	PUNCT
ejpam-5395	45	4	let	let	VERB
ejpam-5395	45	5	a	a	PRON
ejpam-5395	45	6	and	and	CCONJ
ejpam-5395	45	7	b	b	NOUN
ejpam-5395	45	8	be	be	AUX
ejpam-5395	45	9	subsets	subset	NOUN
ejpam-5395	45	10	of	of	ADP
ejpam-5395	45	11	a	a	DET
ejpam-5395	45	12	bitopological	bitopological	ADJ
ejpam-5395	45	13	space	space	NOUN
ejpam-5395	45	14	(	(	PUNCT
ejpam-5395	45	15	x	x	NOUN
ejpam-5395	45	16	,	,	PUNCT
ejpam-5395	45	17	τ1	τ1	NOUN
ejpam-5395	45	18	,	,	PUNCT
ejpam-5395	45	19	τ2	τ2	NOUN
ejpam-5395	45	20	)	)	PUNCT
ejpam-5395	45	21	.	.	PUNCT
ejpam-5395	46	1	for	for	ADP
ejpam-5395	46	2	the	the	DET
ejpam-5395	46	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-5395	46	4	,	,	PUNCT
ejpam-5395	46	5	the	the	DET
ejpam-5395	46	6	following	follow	VERB
ejpam-5395	46	7	properties	property	NOUN
ejpam-5395	46	8	hold	hold	VERB
ejpam-5395	46	9	:	:	PUNCT
ejpam-5395	46	10	(	(	PUNCT
ejpam-5395	46	11	1	1	X
ejpam-5395	46	12	)	)	PUNCT
ejpam-5395	46	13	a	a	DET
ejpam-5395	46	14	⊆	⊆	NUM
ejpam-5395	46	15	τ1τ2	τ1τ2	NOUN
ejpam-5395	46	16	-	-	NUM
ejpam-5395	46	17	cl(a	cl(a	NUM
ejpam-5395	46	18	)	)	PUNCT
ejpam-5395	46	19	and	and	CCONJ
ejpam-5395	46	20	τ1τ2	τ1τ2	NOUN
ejpam-5395	46	21	-	-	ADJ
ejpam-5395	46	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5395	46	23	-	-	PUNCT
ejpam-5395	46	24	cl(a	cl(a	NUM
ejpam-5395	46	25	)	)	PUNCT
ejpam-5395	46	26	)	)	PUNCT
ejpam-5395	47	1	=	=	PUNCT
ejpam-5395	47	2	τ1τ2	τ1τ2	NOUN
ejpam-5395	47	3	-	-	NUM
ejpam-5395	47	4	cl(a	cl(a	NUM
ejpam-5395	47	5	)	)	PUNCT
ejpam-5395	47	6	.	.	PUNCT
ejpam-5395	48	1	(	(	PUNCT
ejpam-5395	48	2	2	2	X
ejpam-5395	48	3	)	)	PUNCT
ejpam-5395	48	4	if	if	SCONJ
ejpam-5395	48	5	a	a	DET
ejpam-5395	48	6	⊆	⊆	NUM
ejpam-5395	48	7	b	b	NOUN
ejpam-5395	48	8	,	,	PUNCT
ejpam-5395	48	9	then	then	ADV
ejpam-5395	48	10	τ1τ2	τ1τ2	NOUN
ejpam-5395	48	11	-	-	NUM
ejpam-5395	48	12	cl(a	cl(a	NUM
ejpam-5395	48	13	)	)	PUNCT
ejpam-5395	48	14	⊆	⊆	NUM
ejpam-5395	48	15	τ1τ2	τ1τ2	NOUN
ejpam-5395	48	16	-	-	NOUN
ejpam-5395	48	17	cl(b	cl(b	NOUN
ejpam-5395	48	18	)	)	PUNCT
ejpam-5395	48	19	.	.	PUNCT
ejpam-5395	49	1	(	(	PUNCT
ejpam-5395	49	2	3	3	X
ejpam-5395	49	3	)	)	PUNCT
ejpam-5395	49	4	τ1τ2	τ1τ2	NOUN
ejpam-5395	49	5	-	-	NUM
ejpam-5395	49	6	cl(a	cl(a	NUM
ejpam-5395	49	7	)	)	PUNCT
ejpam-5395	49	8	is	be	AUX
ejpam-5395	49	9	τ1τ2	τ1τ2	NOUN
ejpam-5395	49	10	-	-	ADJ
ejpam-5395	49	11	closed	closed	ADJ
ejpam-5395	49	12	.	.	PUNCT
ejpam-5395	50	1	(	(	PUNCT
ejpam-5395	50	2	4	4	X
ejpam-5395	50	3	)	)	PUNCT
ejpam-5395	50	4	a	a	PRON
ejpam-5395	50	5	is	be	AUX
ejpam-5395	50	6	τ1τ2	τ1τ2	NOUN
ejpam-5395	50	7	-	-	ADJ
ejpam-5395	50	8	closed	closed	ADJ
ejpam-5395	50	9	if	if	SCONJ
ejpam-5395	50	10	and	and	CCONJ
ejpam-5395	50	11	only	only	ADV
ejpam-5395	50	12	if	if	SCONJ
ejpam-5395	50	13	a	a	DET
ejpam-5395	50	14	=	=	PUNCT
ejpam-5395	50	15	τ1τ2	τ1τ2	NOUN
ejpam-5395	50	16	-	-	NUM
ejpam-5395	50	17	cl(a	cl(a	NUM
ejpam-5395	50	18	)	)	PUNCT
ejpam-5395	50	19	.	.	PUNCT
ejpam-5395	51	1	n.	n.	PROPN
ejpam-5395	51	2	srisarakham	srisarakham	PROPN
ejpam-5395	51	3	,	,	PUNCT
ejpam-5395	51	4	a.	a.	PROPN
ejpam-5395	51	5	sama	sama	PROPN
ejpam-5395	51	6	-	-	PUNCT
ejpam-5395	51	7	ae	ae	PROPN
ejpam-5395	51	8	,	,	PUNCT
ejpam-5395	51	9	c.	c.	PROPN
ejpam-5395	51	10	boonpok	boonpok	PROPN
ejpam-5395	51	11	/	/	SYM
ejpam-5395	51	12	eur	eur	PROPN
ejpam-5395	51	13	.	.	PUNCT
ejpam-5395	52	1	j.	j.	PROPN
ejpam-5395	52	2	pure	pure	PROPN
ejpam-5395	52	3	appl	appl	PROPN
ejpam-5395	52	4	.	.	PROPN
ejpam-5395	52	5	math	math	PROPN
ejpam-5395	52	6	,	,	PUNCT
ejpam-5395	52	7	17	17	NUM
ejpam-5395	52	8	(	(	PUNCT
ejpam-5395	52	9	4	4	NUM
ejpam-5395	52	10	)	)	PUNCT
ejpam-5395	52	11	(	(	PUNCT
ejpam-5395	52	12	2024	2024	NUM
ejpam-5395	52	13	)	)	PUNCT
ejpam-5395	52	14	,	,	PUNCT
ejpam-5395	52	15	2753	2753	NUM
ejpam-5395	52	16	-	-	SYM
ejpam-5395	52	17	2762	2762	NUM
ejpam-5395	52	18	2755	2755	NUM
ejpam-5395	52	19	(	(	PUNCT
ejpam-5395	52	20	5	5	NUM
ejpam-5395	52	21	)	)	PUNCT
ejpam-5395	52	22	τ1τ2	τ1τ2	NOUN
ejpam-5395	52	23	-	-	NOUN
ejpam-5395	52	24	cl(x	cl(x	X
ejpam-5395	52	25	−a	−a	NOUN
ejpam-5395	52	26	)	)	PUNCT
ejpam-5395	52	27	=	=	PUNCT
ejpam-5395	53	1	x	x	X
ejpam-5395	53	2	−	−	ADP
ejpam-5395	53	3	τ1τ2	τ1τ2	NOUN
ejpam-5395	53	4	-	-	PUNCT
ejpam-5395	53	5	int(a	int(a	NOUN
ejpam-5395	53	6	)	)	PUNCT
ejpam-5395	53	7	.	.	PUNCT
ejpam-5395	54	1	a	a	DET
ejpam-5395	54	2	subset	subset	NOUN
ejpam-5395	54	3	a	a	PRON
ejpam-5395	54	4	of	of	ADP
ejpam-5395	54	5	a	a	DET
ejpam-5395	54	6	bitopological	bitopological	ADJ
ejpam-5395	54	7	space	space	NOUN
ejpam-5395	54	8	(	(	PUNCT
ejpam-5395	54	9	x	x	NOUN
ejpam-5395	54	10	,	,	PUNCT
ejpam-5395	54	11	τ1	τ1	NOUN
ejpam-5395	54	12	,	,	PUNCT
ejpam-5395	54	13	τ2	τ2	NOUN
ejpam-5395	54	14	)	)	PUNCT
ejpam-5395	54	15	is	be	AUX
ejpam-5395	54	16	said	say	VERB
ejpam-5395	54	17	to	to	PART
ejpam-5395	54	18	be	be	AUX
ejpam-5395	54	19	(	(	PUNCT
ejpam-5395	54	20	τ1	τ1	NOUN
ejpam-5395	54	21	,	,	PUNCT
ejpam-5395	54	22	τ2)r	τ2)r	NOUN
ejpam-5395	54	23	-	-	PUNCT
ejpam-5395	54	24	open	open	NOUN
ejpam-5395	55	1	[	[	X
ejpam-5395	55	2	39	39	NUM
ejpam-5395	55	3	]	]	PUNCT
ejpam-5395	55	4	(	(	PUNCT
ejpam-5395	55	5	resp	resp	NOUN
ejpam-5395	55	6	.	.	PUNCT
ejpam-5395	56	1	(	(	PUNCT
ejpam-5395	56	2	τ1	τ1	NOUN
ejpam-5395	56	3	,	,	PUNCT
ejpam-5395	56	4	τ2)s	τ2)s	NOUN
ejpam-5395	56	5	-	-	PUNCT
ejpam-5395	56	6	open	open	ADJ
ejpam-5395	56	7	[	[	X
ejpam-5395	56	8	4	4	NUM
ejpam-5395	56	9	]	]	PUNCT
ejpam-5395	56	10	,	,	PUNCT
ejpam-5395	56	11	(	(	PUNCT
ejpam-5395	56	12	τ1	τ1	NOUN
ejpam-5395	56	13	,	,	PUNCT
ejpam-5395	56	14	τ2)p	τ2)p	NOUN
ejpam-5395	56	15	-	-	ADJ
ejpam-5395	56	16	open	open	ADJ
ejpam-5395	56	17	[	[	X
ejpam-5395	56	18	4	4	NUM
ejpam-5395	56	19	]	]	PUNCT
ejpam-5395	56	20	,	,	PUNCT
ejpam-5395	56	21	(	(	PUNCT
ejpam-5395	56	22	τ1	τ1	NOUN
ejpam-5395	56	23	,	,	PUNCT
ejpam-5395	56	24	τ2)β	τ2)β	ADJ
ejpam-5395	56	25	-	-	PUNCT
ejpam-5395	56	26	open	open	NOUN
ejpam-5395	56	27	[	[	X
ejpam-5395	56	28	4	4	NUM
ejpam-5395	56	29	]	]	PUNCT
ejpam-5395	56	30	)	)	PUNCT
ejpam-5395	56	31	if	if	SCONJ
ejpam-5395	56	32	a	a	DET
ejpam-5395	56	33	=	=	PUNCT
ejpam-5395	56	34	τ1τ2	τ1τ2	NOUN
ejpam-5395	56	35	-	-	NOUN
ejpam-5395	56	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5395	56	37	-	-	PUNCT
ejpam-5395	56	38	cl(a	cl(a	NUM
ejpam-5395	56	39	)	)	PUNCT
ejpam-5395	56	40	)	)	PUNCT
ejpam-5395	56	41	(	(	PUNCT
ejpam-5395	56	42	resp	resp	NOUN
ejpam-5395	56	43	.	.	PUNCT
ejpam-5395	57	1	a	a	DET
ejpam-5395	57	2	⊆	⊆	NUM
ejpam-5395	57	3	τ1τ2	τ1τ2	NOUN
ejpam-5395	57	4	-	-	ADJ
ejpam-5395	57	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5395	57	6	-	-	PUNCT
ejpam-5395	57	7	int(a	int(a	NOUN
ejpam-5395	57	8	)	)	PUNCT
ejpam-5395	57	9	)	)	PUNCT
ejpam-5395	57	10	,	,	PUNCT
ejpam-5395	57	11	a	a	DET
ejpam-5395	57	12	⊆	⊆	NUM
ejpam-5395	57	13	τ1τ2	τ1τ2	NOUN
ejpam-5395	57	14	-	-	NOUN
ejpam-5395	57	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5395	57	16	-	-	PUNCT
ejpam-5395	57	17	cl(a	cl(a	NUM
ejpam-5395	57	18	)	)	PUNCT
ejpam-5395	57	19	)	)	PUNCT
ejpam-5395	57	20	,	,	PUNCT
ejpam-5395	57	21	a	a	DET
ejpam-5395	57	22	⊆	⊆	NUM
ejpam-5395	57	23	τ1τ2	τ1τ2	NOUN
ejpam-5395	57	24	-	-	PUNCT
ejpam-5395	57	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5395	57	26	-	-	PUNCT
ejpam-5395	57	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5395	57	28	-	-	PUNCT
ejpam-5395	57	29	cl(a	cl(a	NUM
ejpam-5395	57	30	)	)	PUNCT
ejpam-5395	57	31	)	)	PUNCT
ejpam-5395	57	32	)	)	PUNCT
ejpam-5395	57	33	)	)	PUNCT
ejpam-5395	57	34	.	.	PUNCT
ejpam-5395	58	1	the	the	DET
ejpam-5395	58	2	complement	complement	NOUN
ejpam-5395	58	3	of	of	ADP
ejpam-5395	58	4	a	a	DET
ejpam-5395	58	5	(	(	PUNCT
ejpam-5395	58	6	τ1	τ1	NOUN
ejpam-5395	58	7	,	,	PUNCT
ejpam-5395	58	8	τ2)r	τ2)r	NOUN
ejpam-5395	58	9	-	-	PUNCT
ejpam-5395	58	10	open	open	ADJ
ejpam-5395	58	11	(	(	PUNCT
ejpam-5395	58	12	resp	resp	NOUN
ejpam-5395	58	13	.	.	PUNCT
ejpam-5395	59	1	(	(	PUNCT
ejpam-5395	59	2	τ1	τ1	NOUN
ejpam-5395	59	3	,	,	PUNCT
ejpam-5395	59	4	τ2)s	τ2)s	NOUN
ejpam-5395	59	5	-	-	PUNCT
ejpam-5395	59	6	open	open	ADJ
ejpam-5395	59	7	,	,	PUNCT
ejpam-5395	59	8	(	(	PUNCT
ejpam-5395	59	9	τ1	τ1	NOUN
ejpam-5395	59	10	,	,	PUNCT
ejpam-5395	59	11	τ2)p	τ2)p	NOUN
ejpam-5395	59	12	-	-	ADJ
ejpam-5395	59	13	open	open	ADJ
ejpam-5395	59	14	,	,	PUNCT
ejpam-5395	59	15	(	(	PUNCT
ejpam-5395	59	16	τ1	τ1	NOUN
ejpam-5395	59	17	,	,	PUNCT
ejpam-5395	59	18	τ2)β	τ2)β	ADJ
ejpam-5395	59	19	-	-	PUNCT
ejpam-5395	59	20	open	open	ADJ
ejpam-5395	59	21	)	)	PUNCT
ejpam-5395	59	22	set	set	NOUN
ejpam-5395	59	23	is	be	AUX
ejpam-5395	59	24	called	call	VERB
ejpam-5395	59	25	(	(	PUNCT
ejpam-5395	59	26	τ1	τ1	NOUN
ejpam-5395	59	27	,	,	PUNCT
ejpam-5395	59	28	τ2)r	τ2)r	NOUN
ejpam-5395	59	29	-	-	PUNCT
ejpam-5395	59	30	closed	closed	ADJ
ejpam-5395	59	31	(	(	PUNCT
ejpam-5395	59	32	resp	resp	NOUN
ejpam-5395	59	33	.	.	PUNCT
ejpam-5395	60	1	(	(	PUNCT
ejpam-5395	60	2	τ1	τ1	NOUN
ejpam-5395	60	3	,	,	PUNCT
ejpam-5395	60	4	τ2)s	τ2)s	NOUN
ejpam-5395	60	5	-	-	PUNCT
ejpam-5395	60	6	closed	closed	ADJ
ejpam-5395	60	7	,	,	PUNCT
ejpam-5395	60	8	(	(	PUNCT
ejpam-5395	60	9	τ1	τ1	NOUN
ejpam-5395	60	10	,	,	PUNCT
ejpam-5395	60	11	τ2)p	τ2)p	NOUN
ejpam-5395	60	12	-	-	PUNCT
ejpam-5395	60	13	closed	closed	ADJ
ejpam-5395	60	14	,	,	PUNCT
ejpam-5395	60	15	(	(	PUNCT
ejpam-5395	60	16	τ1	τ1	NOUN
ejpam-5395	60	17	,	,	PUNCT
ejpam-5395	60	18	τ2)β	τ2)β	ADJ
ejpam-5395	60	19	-	-	PUNCT
ejpam-5395	60	20	closed	closed	ADJ
ejpam-5395	60	21	)	)	PUNCT
ejpam-5395	60	22	.	.	PUNCT
ejpam-5395	61	1	a	a	DET
ejpam-5395	61	2	subset	subset	NOUN
ejpam-5395	61	3	a	a	PRON
ejpam-5395	61	4	of	of	ADP
ejpam-5395	61	5	a	a	DET
ejpam-5395	61	6	bitopological	bitopological	ADJ
ejpam-5395	61	7	space	space	NOUN
ejpam-5395	61	8	(	(	PUNCT
ejpam-5395	61	9	x	x	NOUN
ejpam-5395	61	10	,	,	PUNCT
ejpam-5395	61	11	τ1	τ1	NOUN
ejpam-5395	61	12	,	,	PUNCT
ejpam-5395	61	13	τ2	τ2	NOUN
ejpam-5395	61	14	)	)	PUNCT
ejpam-5395	61	15	is	be	AUX
ejpam-5395	61	16	said	say	VERB
ejpam-5395	61	17	to	to	PART
ejpam-5395	61	18	be	be	AUX
ejpam-5395	61	19	α(τ1	α(τ1	NOUN
ejpam-5395	61	20	,	,	PUNCT
ejpam-5395	61	21	τ2)-open	τ2)-open	ADJ
ejpam-5395	61	22	[	[	X
ejpam-5395	61	23	41	41	NUM
ejpam-5395	61	24	]	]	X
ejpam-5395	61	25	if	if	SCONJ
ejpam-5395	61	26	a	a	DET
ejpam-5395	61	27	⊆	⊆	NUM
ejpam-5395	61	28	τ1τ2	τ1τ2	NOUN
ejpam-5395	61	29	-	-	PUNCT
ejpam-5395	61	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-5395	61	31	-	-	PUNCT
ejpam-5395	61	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-5395	61	33	-	-	PUNCT
ejpam-5395	61	34	int(a	int(a	NOUN
ejpam-5395	61	35	)	)	PUNCT
ejpam-5395	61	36	)	)	PUNCT
ejpam-5395	61	37	)	)	PUNCT
ejpam-5395	61	38	.	.	PUNCT
ejpam-5395	62	1	the	the	DET
ejpam-5395	62	2	complement	complement	NOUN
ejpam-5395	62	3	of	of	ADP
ejpam-5395	62	4	an	an	DET
ejpam-5395	62	5	α(τ1	α(τ1	NOUN
ejpam-5395	62	6	,	,	PUNCT
ejpam-5395	62	7	τ2)-open	τ2)-open	ADJ
ejpam-5395	62	8	set	set	NOUN
ejpam-5395	62	9	is	be	AUX
ejpam-5395	62	10	said	say	VERB
ejpam-5395	62	11	to	to	PART
ejpam-5395	62	12	be	be	AUX
ejpam-5395	62	13	α(τ1	α(τ1	NOUN
ejpam-5395	62	14	,	,	PUNCT
ejpam-5395	62	15	τ2)-closed	τ2)-close	VERB
ejpam-5395	62	16	.	.	PUNCT
ejpam-5395	63	1	let	let	VERB
ejpam-5395	63	2	a	a	DET
ejpam-5395	63	3	be	be	AUX
ejpam-5395	63	4	a	a	DET
ejpam-5395	63	5	subset	subset	NOUN
ejpam-5395	63	6	of	of	ADP
ejpam-5395	63	7	a	a	DET
ejpam-5395	63	8	bitopological	bitopological	ADJ
ejpam-5395	63	9	space	space	NOUN
ejpam-5395	63	10	(	(	PUNCT
ejpam-5395	63	11	x	x	NOUN
ejpam-5395	63	12	,	,	PUNCT
ejpam-5395	63	13	τ1	τ1	NOUN
ejpam-5395	63	14	,	,	PUNCT
ejpam-5395	63	15	τ2	τ2	NOUN
ejpam-5395	63	16	)	)	PUNCT
ejpam-5395	63	17	.	.	PUNCT
ejpam-5395	64	1	a	a	DET
ejpam-5395	64	2	point	point	NOUN
ejpam-5395	64	3	x	x	X
ejpam-5395	64	4	∈	∈	NOUN
ejpam-5395	64	5	x	x	PUNCT
ejpam-5395	64	6	is	be	AUX
ejpam-5395	64	7	called	call	VERB
ejpam-5395	64	8	a	a	DET
ejpam-5395	64	9	(	(	PUNCT
ejpam-5395	64	10	τ1	τ1	NOUN
ejpam-5395	64	11	,	,	PUNCT
ejpam-5395	64	12	τ2)θ	τ2)θ	ADJ
ejpam-5395	64	13	-	-	PUNCT
ejpam-5395	64	14	cluster	cluster	NOUN
ejpam-5395	64	15	point	point	NOUN
ejpam-5395	64	16	[	[	X
ejpam-5395	64	17	39	39	NUM
ejpam-5395	64	18	]	]	PUNCT
ejpam-5395	64	19	of	of	ADP
ejpam-5395	64	20	a	a	DET
ejpam-5395	64	21	if	if	SCONJ
ejpam-5395	64	22	τ1τ2	τ1τ2	ADJ
ejpam-5395	64	23	-	-	ADJ
ejpam-5395	64	24	cl(u)∩a	cl(u)∩a	ADJ
ejpam-5395	64	25	̸=	̸=	PROPN
ejpam-5395	64	26	∅	∅	NOUN
ejpam-5395	64	27	for	for	ADP
ejpam-5395	64	28	every	every	DET
ejpam-5395	64	29	τ1τ2	τ1τ2	ADJ
ejpam-5395	64	30	-	-	ADJ
ejpam-5395	64	31	open	open	ADJ
ejpam-5395	64	32	set	set	ADJ
ejpam-5395	64	33	u	u	NOUN
ejpam-5395	64	34	of	of	ADP
ejpam-5395	64	35	x	x	SYM
ejpam-5395	64	36	containing	contain	VERB
ejpam-5395	64	37	x.	x.	NOUN
ejpam-5395	64	38	the	the	DET
ejpam-5395	64	39	set	set	NOUN
ejpam-5395	64	40	of	of	ADP
ejpam-5395	64	41	all	all	DET
ejpam-5395	64	42	(	(	PUNCT
ejpam-5395	64	43	τ1	τ1	NOUN
ejpam-5395	64	44	,	,	PUNCT
ejpam-5395	64	45	τ2)θ	τ2)θ	ADJ
ejpam-5395	64	46	-	-	PUNCT
ejpam-5395	64	47	cluster	cluster	NOUN
ejpam-5395	64	48	points	point	NOUN
ejpam-5395	64	49	of	of	ADP
ejpam-5395	64	50	a	a	PRON
ejpam-5395	64	51	is	be	AUX
ejpam-5395	64	52	called	call	VERB
ejpam-5395	64	53	the	the	DET
ejpam-5395	64	54	(	(	PUNCT
ejpam-5395	64	55	τ1	τ1	NOUN
ejpam-5395	64	56	,	,	PUNCT
ejpam-5395	64	57	τ2)θ	τ2)θ	ADJ
ejpam-5395	64	58	-	-	PUNCT
ejpam-5395	64	59	closure	closure	NOUN
ejpam-5395	64	60	[	[	X
ejpam-5395	64	61	39	39	NUM
ejpam-5395	64	62	]	]	PUNCT
ejpam-5395	64	63	of	of	ADP
ejpam-5395	64	64	a	a	PRON
ejpam-5395	64	65	and	and	CCONJ
ejpam-5395	64	66	is	be	AUX
ejpam-5395	64	67	denoted	denote	VERB
ejpam-5395	64	68	by	by	ADP
ejpam-5395	64	69	(	(	PUNCT
ejpam-5395	64	70	τ1	τ1	NOUN
ejpam-5395	64	71	,	,	PUNCT
ejpam-5395	64	72	τ2)θ	τ2)θ	NOUN
ejpam-5395	64	73	-	-	PUNCT
ejpam-5395	64	74	cl(a	cl(a	NUM
ejpam-5395	64	75	)	)	PUNCT
ejpam-5395	64	76	.	.	PUNCT
ejpam-5395	65	1	a	a	DET
ejpam-5395	65	2	subset	subset	NOUN
ejpam-5395	65	3	a	a	PRON
ejpam-5395	65	4	of	of	ADP
ejpam-5395	65	5	a	a	DET
ejpam-5395	65	6	bitopological	bitopological	ADJ
ejpam-5395	65	7	space	space	NOUN
ejpam-5395	65	8	(	(	PUNCT
ejpam-5395	65	9	x	x	NOUN
ejpam-5395	65	10	,	,	PUNCT
ejpam-5395	65	11	τ1	τ1	NOUN
ejpam-5395	65	12	,	,	PUNCT
ejpam-5395	65	13	τ2	τ2	NOUN
ejpam-5395	65	14	)	)	PUNCT
ejpam-5395	65	15	is	be	AUX
ejpam-5395	65	16	said	say	VERB
ejpam-5395	65	17	to	to	PART
ejpam-5395	65	18	be	be	AUX
ejpam-5395	65	19	(	(	PUNCT
ejpam-5395	65	20	τ1	τ1	NOUN
ejpam-5395	65	21	,	,	PUNCT
ejpam-5395	65	22	τ2)θ	τ2)θ	NOUN
ejpam-5395	65	23	-	-	PUNCT
ejpam-5395	65	24	closed	closed	ADJ
ejpam-5395	65	25	[	[	X
ejpam-5395	65	26	39	39	NUM
ejpam-5395	65	27	]	]	PUNCT
ejpam-5395	65	28	if	if	SCONJ
ejpam-5395	65	29	(	(	PUNCT
ejpam-5395	65	30	τ1	τ1	NOUN
ejpam-5395	65	31	,	,	PUNCT
ejpam-5395	65	32	τ2)θ	τ2)θ	NOUN
ejpam-5395	65	33	-	-	PUNCT
ejpam-5395	65	34	cl(a	cl(a	NUM
ejpam-5395	65	35	)	)	PUNCT
ejpam-5395	66	1	=	=	PUNCT
ejpam-5395	66	2	a.	a.	NOUN
ejpam-5395	66	3	the	the	DET
ejpam-5395	66	4	complement	complement	NOUN
ejpam-5395	66	5	of	of	ADP
ejpam-5395	66	6	a	a	DET
ejpam-5395	66	7	(	(	PUNCT
ejpam-5395	66	8	τ1	τ1	NOUN
ejpam-5395	66	9	,	,	PUNCT
ejpam-5395	66	10	τ2)θ	τ2)θ	ADJ
ejpam-5395	66	11	-	-	PUNCT
ejpam-5395	66	12	closed	close	VERB
ejpam-5395	66	13	set	set	NOUN
ejpam-5395	66	14	is	be	AUX
ejpam-5395	66	15	said	say	VERB
ejpam-5395	66	16	to	to	PART
ejpam-5395	66	17	be	be	AUX
ejpam-5395	66	18	(	(	PUNCT
ejpam-5395	66	19	τ1	τ1	NOUN
ejpam-5395	66	20	,	,	PUNCT
ejpam-5395	66	21	τ2)θ	τ2)θ	NOUN
ejpam-5395	66	22	-	-	PUNCT
ejpam-5395	66	23	open	open	ADJ
ejpam-5395	66	24	.	.	PUNCT
ejpam-5395	67	1	the	the	DET
ejpam-5395	67	2	union	union	NOUN
ejpam-5395	67	3	of	of	ADP
ejpam-5395	67	4	all	all	DET
ejpam-5395	67	5	(	(	PUNCT
ejpam-5395	67	6	τ1	τ1	NOUN
ejpam-5395	67	7	,	,	PUNCT
ejpam-5395	67	8	τ2)θ	τ2)θ	ADJ
ejpam-5395	67	9	-	-	PUNCT
ejpam-5395	67	10	open	open	ADJ
ejpam-5395	67	11	sets	set	NOUN
ejpam-5395	67	12	of	of	ADP
ejpam-5395	67	13	x	x	PUNCT
ejpam-5395	67	14	contained	contain	VERB
ejpam-5395	67	15	in	in	ADP
ejpam-5395	67	16	a	a	PRON
ejpam-5395	67	17	is	be	AUX
ejpam-5395	67	18	called	call	VERB
ejpam-5395	67	19	the	the	DET
ejpam-5395	67	20	(	(	PUNCT
ejpam-5395	67	21	τ1	τ1	NOUN
ejpam-5395	67	22	,	,	PUNCT
ejpam-5395	67	23	τ2)θ	τ2)θ	ADJ
ejpam-5395	67	24	-	-	PUNCT
ejpam-5395	67	25	interior	interior	NOUN
ejpam-5395	67	26	[	[	X
ejpam-5395	67	27	39	39	NUM
ejpam-5395	67	28	]	]	PUNCT
ejpam-5395	67	29	of	of	ADP
ejpam-5395	67	30	a	a	PRON
ejpam-5395	67	31	and	and	CCONJ
ejpam-5395	67	32	is	be	AUX
ejpam-5395	67	33	denoted	denote	VERB
ejpam-5395	67	34	by	by	ADP
ejpam-5395	67	35	(	(	PUNCT
ejpam-5395	67	36	τ1	τ1	NOUN
ejpam-5395	67	37	,	,	PUNCT
ejpam-5395	67	38	τ2)θ	τ2)θ	NOUN
ejpam-5395	67	39	-	-	PUNCT
ejpam-5395	67	40	int(a	int(a	NOUN
ejpam-5395	67	41	)	)	PUNCT
ejpam-5395	67	42	.	.	PUNCT
ejpam-5395	68	1	3	3	X
ejpam-5395	68	2	.	.	X
ejpam-5395	68	3	characterizations	characterization	NOUN
ejpam-5395	68	4	of	of	ADP
ejpam-5395	68	5	faintly	faintly	ADV
ejpam-5395	68	6	(	(	PUNCT
ejpam-5395	68	7	τ1	τ1	PROPN
ejpam-5395	68	8	,	,	PUNCT
ejpam-5395	68	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	68	10	functions	function	NOUN
ejpam-5395	68	11	in	in	ADP
ejpam-5395	68	12	this	this	DET
ejpam-5395	68	13	section	section	NOUN
ejpam-5395	68	14	,	,	PUNCT
ejpam-5395	68	15	we	we	PRON
ejpam-5395	68	16	investigate	investigate	VERB
ejpam-5395	68	17	several	several	ADJ
ejpam-5395	68	18	characterizations	characterization	NOUN
ejpam-5395	68	19	of	of	ADP
ejpam-5395	68	20	faintly	faintly	ADV
ejpam-5395	68	21	(	(	PUNCT
ejpam-5395	68	22	τ1	τ1	PROPN
ejpam-5395	68	23	,	,	PUNCT
ejpam-5395	68	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	68	25	functions	function	NOUN
ejpam-5395	68	26	.	.	PUNCT
ejpam-5395	69	1	definition	definition	NOUN
ejpam-5395	69	2	1	1	NUM
ejpam-5395	69	3	.	.	PUNCT
ejpam-5395	70	1	[	[	X
ejpam-5395	70	2	34	34	NUM
ejpam-5395	70	3	]	]	X
ejpam-5395	70	4	a	a	DET
ejpam-5395	70	5	function	function	NOUN
ejpam-5395	70	6	f	f	NOUN
ejpam-5395	70	7	:	:	PUNCT
ejpam-5395	70	8	(	(	PUNCT
ejpam-5395	70	9	x	x	NOUN
ejpam-5395	70	10	,	,	PUNCT
ejpam-5395	70	11	τ1	τ1	NOUN
ejpam-5395	70	12	,	,	PUNCT
ejpam-5395	70	13	τ2	τ2	NOUN
ejpam-5395	70	14	)	)	PUNCT
ejpam-5395	70	15	→	→	SYM
ejpam-5395	70	16	(	(	PUNCT
ejpam-5395	70	17	y	y	PROPN
ejpam-5395	70	18	,	,	PUNCT
ejpam-5395	70	19	σ1	σ1	PROPN
ejpam-5395	70	20	,	,	PUNCT
ejpam-5395	70	21	σ2	σ2	PROPN
ejpam-5395	70	22	)	)	PUNCT
ejpam-5395	70	23	is	be	AUX
ejpam-5395	70	24	called	call	VERB
ejpam-5395	70	25	faintly	faintly	ADV
ejpam-5395	70	26	(	(	PUNCT
ejpam-5395	70	27	τ1	τ1	NOUN
ejpam-5395	70	28	,	,	PUNCT
ejpam-5395	70	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	70	30	at	at	ADP
ejpam-5395	70	31	a	a	DET
ejpam-5395	70	32	point	point	NOUN
ejpam-5395	70	33	x	x	SYM
ejpam-5395	70	34	∈	∈	NOUN
ejpam-5395	70	35	x	x	INTJ
ejpam-5395	70	36	if	if	SCONJ
ejpam-5395	70	37	for	for	SCONJ
ejpam-5395	70	38	each	each	DET
ejpam-5395	70	39	(	(	PUNCT
ejpam-5395	70	40	σ1	σ1	PROPN
ejpam-5395	70	41	,	,	PUNCT
ejpam-5395	70	42	σ2)θ	σ2)θ	NOUN
ejpam-5395	70	43	-	-	PUNCT
ejpam-5395	70	44	open	open	ADJ
ejpam-5395	70	45	set	set	NOUN
ejpam-5395	70	46	v	v	NOUN
ejpam-5395	70	47	of	of	ADP
ejpam-5395	70	48	y	y	NOUN
ejpam-5395	70	49	containing	contain	VERB
ejpam-5395	70	50	f(x	f(x	PROPN
ejpam-5395	70	51	)	)	PUNCT
ejpam-5395	70	52	,	,	PUNCT
ejpam-5395	70	53	there	there	PRON
ejpam-5395	70	54	exists	exist	VERB
ejpam-5395	70	55	a	a	DET
ejpam-5395	70	56	τ1τ2open	τ1τ2open	ADJ
ejpam-5395	70	57	set	set	NOUN
ejpam-5395	70	58	u	u	NOUN
ejpam-5395	70	59	of	of	ADP
ejpam-5395	70	60	x	x	PUNCT
ejpam-5395	70	61	containing	contain	VERB
ejpam-5395	70	62	x	x	PUNCT
ejpam-5395	70	63	such	such	ADJ
ejpam-5395	70	64	that	that	DET
ejpam-5395	70	65	f(u	f(u	PROPN
ejpam-5395	70	66	)	)	PUNCT
ejpam-5395	70	67	⊆	⊆	NUM
ejpam-5395	70	68	v	v	NOUN
ejpam-5395	70	69	.	.	PUNCT
ejpam-5395	71	1	a	a	DET
ejpam-5395	71	2	function	function	NOUN
ejpam-5395	71	3	f	f	NOUN
ejpam-5395	71	4	:	:	PUNCT
ejpam-5395	71	5	(	(	PUNCT
ejpam-5395	71	6	x	x	NOUN
ejpam-5395	71	7	,	,	PUNCT
ejpam-5395	71	8	τ1	τ1	NOUN
ejpam-5395	71	9	,	,	PUNCT
ejpam-5395	71	10	τ2	τ2	NOUN
ejpam-5395	71	11	)	)	PUNCT
ejpam-5395	71	12	→	→	SYM
ejpam-5395	71	13	(	(	PUNCT
ejpam-5395	71	14	y	y	PROPN
ejpam-5395	71	15	,	,	PUNCT
ejpam-5395	71	16	σ1	σ1	PROPN
ejpam-5395	71	17	,	,	PUNCT
ejpam-5395	71	18	σ2	σ2	PROPN
ejpam-5395	71	19	)	)	PUNCT
ejpam-5395	71	20	is	be	AUX
ejpam-5395	71	21	called	call	VERB
ejpam-5395	71	22	faintly	faintly	ADV
ejpam-5395	71	23	(	(	PUNCT
ejpam-5395	71	24	τ1	τ1	NOUN
ejpam-5395	71	25	,	,	PUNCT
ejpam-5395	71	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	71	27	if	if	SCONJ
ejpam-5395	71	28	f	f	PROPN
ejpam-5395	71	29	has	have	VERB
ejpam-5395	71	30	this	this	DET
ejpam-5395	71	31	property	property	NOUN
ejpam-5395	71	32	at	at	ADP
ejpam-5395	71	33	every	every	DET
ejpam-5395	71	34	point	point	NOUN
ejpam-5395	71	35	of	of	ADP
ejpam-5395	71	36	x.	x.	NOUN
ejpam-5395	71	37	theorem	theorem	VERB
ejpam-5395	71	38	1	1	NUM
ejpam-5395	71	39	.	.	PUNCT
ejpam-5395	72	1	a	a	DET
ejpam-5395	72	2	function	function	NOUN
ejpam-5395	72	3	f	f	NOUN
ejpam-5395	72	4	:	:	PUNCT
ejpam-5395	72	5	(	(	PUNCT
ejpam-5395	72	6	x	x	NOUN
ejpam-5395	72	7	,	,	PUNCT
ejpam-5395	72	8	τ1	τ1	NOUN
ejpam-5395	72	9	,	,	PUNCT
ejpam-5395	72	10	τ2	τ2	NOUN
ejpam-5395	72	11	)	)	PUNCT
ejpam-5395	72	12	→	→	SYM
ejpam-5395	72	13	(	(	PUNCT
ejpam-5395	72	14	y	y	PROPN
ejpam-5395	72	15	,	,	PUNCT
ejpam-5395	72	16	σ1	σ1	PROPN
ejpam-5395	72	17	,	,	PUNCT
ejpam-5395	72	18	σ2	σ2	PROPN
ejpam-5395	72	19	)	)	PUNCT
ejpam-5395	72	20	is	be	AUX
ejpam-5395	72	21	faintly	faintly	ADV
ejpam-5395	72	22	(	(	PUNCT
ejpam-5395	72	23	τ1	τ1	NOUN
ejpam-5395	72	24	,	,	PUNCT
ejpam-5395	72	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	72	26	at	at	ADP
ejpam-5395	72	27	x	x	X
ejpam-5395	72	28	∈	∈	PROPN
ejpam-5395	72	29	x	x	SYM
ejpam-5395	72	30	if	if	SCONJ
ejpam-5395	72	31	and	and	CCONJ
ejpam-5395	72	32	only	only	ADV
ejpam-5395	72	33	if	if	SCONJ
ejpam-5395	72	34	for	for	ADP
ejpam-5395	72	35	each	each	DET
ejpam-5395	72	36	(	(	PUNCT
ejpam-5395	72	37	σ1	σ1	PROPN
ejpam-5395	72	38	,	,	PUNCT
ejpam-5395	72	39	σ2)θ	σ2)θ	NOUN
ejpam-5395	72	40	-	-	PUNCT
ejpam-5395	72	41	open	open	ADJ
ejpam-5395	72	42	set	set	NOUN
ejpam-5395	72	43	v	v	NOUN
ejpam-5395	72	44	of	of	ADP
ejpam-5395	72	45	y	y	NOUN
ejpam-5395	72	46	containing	contain	VERB
ejpam-5395	72	47	f(x	f(x	PROPN
ejpam-5395	72	48	)	)	PUNCT
ejpam-5395	72	49	,	,	PUNCT
ejpam-5395	72	50	x	x	PUNCT
ejpam-5395	72	51	∈	∈	PROPN
ejpam-5395	72	52	τ1τ2	τ1τ2	PUNCT
ejpam-5395	72	53	-	-	NUM
ejpam-5395	72	54	int(f	int(f	NOUN
ejpam-5395	72	55	−1(v	−1(v	NOUN
ejpam-5395	72	56	)	)	PUNCT
ejpam-5395	72	57	)	)	PUNCT
ejpam-5395	72	58	.	.	PUNCT
ejpam-5395	73	1	proof	proof	NOUN
ejpam-5395	73	2	.	.	PUNCT
ejpam-5395	74	1	let	let	VERB
ejpam-5395	74	2	x	x	PUNCT
ejpam-5395	74	3	∈	∈	PROPN
ejpam-5395	74	4	x	x	X
ejpam-5395	74	5	and	and	CCONJ
ejpam-5395	74	6	v	v	X
ejpam-5395	74	7	be	be	AUX
ejpam-5395	74	8	any	any	DET
ejpam-5395	74	9	(	(	PUNCT
ejpam-5395	74	10	σ1	σ1	PROPN
ejpam-5395	74	11	,	,	PUNCT
ejpam-5395	74	12	σ2)θ	σ2)θ	NOUN
ejpam-5395	74	13	-	-	PUNCT
ejpam-5395	74	14	open	open	ADJ
ejpam-5395	74	15	set	set	NOUN
ejpam-5395	74	16	of	of	ADP
ejpam-5395	74	17	y	y	PROPN
ejpam-5395	74	18	containing	contain	VERB
ejpam-5395	74	19	f(x	f(x	PROPN
ejpam-5395	74	20	)	)	PUNCT
ejpam-5395	74	21	.	.	PUNCT
ejpam-5395	75	1	then	then	ADV
ejpam-5395	75	2	,	,	PUNCT
ejpam-5395	75	3	there	there	PRON
ejpam-5395	75	4	exists	exist	VERB
ejpam-5395	75	5	a	a	DET
ejpam-5395	75	6	τ1τ2	τ1τ2	NOUN
ejpam-5395	75	7	-	-	ADJ
ejpam-5395	75	8	open	open	ADJ
ejpam-5395	75	9	set	set	ADJ
ejpam-5395	75	10	u	u	NOUN
ejpam-5395	75	11	of	of	ADP
ejpam-5395	75	12	x	x	PUNCT
ejpam-5395	75	13	containing	contain	VERB
ejpam-5395	75	14	x	x	PUNCT
ejpam-5395	75	15	such	such	ADJ
ejpam-5395	75	16	that	that	DET
ejpam-5395	75	17	f(u	f(u	PROPN
ejpam-5395	75	18	)	)	PUNCT
ejpam-5395	75	19	⊆	⊆	NUM
ejpam-5395	75	20	v	v	NOUN
ejpam-5395	75	21	.	.	PUNCT
ejpam-5395	76	1	thus	thus	ADV
ejpam-5395	76	2	x	x	X
ejpam-5395	76	3	∈	∈	PROPN
ejpam-5395	76	4	u	u	NOUN
ejpam-5395	76	5	⊆	⊆	NUM
ejpam-5395	76	6	f−1(v	f−1(v	NOUN
ejpam-5395	76	7	)	)	PUNCT
ejpam-5395	76	8	and	and	CCONJ
ejpam-5395	76	9	hence	hence	ADV
ejpam-5395	76	10	x	x	X
ejpam-5395	76	11	∈	∈	PRON
ejpam-5395	76	12	τ1τ2	τ1τ2	NOUN
ejpam-5395	76	13	-	-	NUM
ejpam-5395	76	14	int(f	int(f	NOUN
ejpam-5395	76	15	−1(v	−1(v	NOUN
ejpam-5395	76	16	)	)	PUNCT
ejpam-5395	76	17	)	)	PUNCT
ejpam-5395	76	18	.	.	PUNCT
ejpam-5395	77	1	conversely	conversely	ADV
ejpam-5395	77	2	,	,	PUNCT
ejpam-5395	77	3	let	let	VERB
ejpam-5395	77	4	v	v	PART
ejpam-5395	77	5	be	be	AUX
ejpam-5395	77	6	any	any	DET
ejpam-5395	77	7	(	(	PUNCT
ejpam-5395	77	8	σ1	σ1	PROPN
ejpam-5395	77	9	,	,	PUNCT
ejpam-5395	77	10	σ2)θ	σ2)θ	NOUN
ejpam-5395	77	11	-	-	PUNCT
ejpam-5395	77	12	open	open	ADJ
ejpam-5395	77	13	set	set	NOUN
ejpam-5395	77	14	of	of	ADP
ejpam-5395	77	15	y	y	PROPN
ejpam-5395	77	16	containing	contain	VERB
ejpam-5395	77	17	f(x	f(x	PROPN
ejpam-5395	77	18	)	)	PUNCT
ejpam-5395	77	19	.	.	PUNCT
ejpam-5395	78	1	by	by	ADP
ejpam-5395	78	2	the	the	DET
ejpam-5395	78	3	hypothesis	hypothesis	NOUN
ejpam-5395	78	4	,	,	PUNCT
ejpam-5395	78	5	x	x	X
ejpam-5395	78	6	∈	∈	PROPN
ejpam-5395	78	7	τ1τ2	τ1τ2	PUNCT
ejpam-5395	78	8	-	-	NUM
ejpam-5395	78	9	int(f	int(f	NOUN
ejpam-5395	78	10	−1(v	−1(v	NOUN
ejpam-5395	78	11	)	)	PUNCT
ejpam-5395	78	12	)	)	PUNCT
ejpam-5395	78	13	.	.	PUNCT
ejpam-5395	79	1	then	then	ADV
ejpam-5395	79	2	,	,	PUNCT
ejpam-5395	79	3	there	there	PRON
ejpam-5395	79	4	exists	exist	VERB
ejpam-5395	79	5	a	a	DET
ejpam-5395	79	6	τ1τ2	τ1τ2	NOUN
ejpam-5395	79	7	-	-	ADJ
ejpam-5395	79	8	open	open	ADJ
ejpam-5395	79	9	set	set	ADJ
ejpam-5395	79	10	u	u	NOUN
ejpam-5395	79	11	of	of	ADP
ejpam-5395	79	12	x	x	PUNCT
ejpam-5395	79	13	containing	contain	VERB
ejpam-5395	79	14	x	x	PUNCT
ejpam-5395	79	15	such	such	ADJ
ejpam-5395	79	16	that	that	SCONJ
ejpam-5395	79	17	u	u	PROPN
ejpam-5395	79	18	⊆	⊆	NUM
ejpam-5395	79	19	f−1(v	f−1(v	NOUN
ejpam-5395	79	20	)	)	PUNCT
ejpam-5395	79	21	;	;	PUNCT
ejpam-5395	79	22	hence	hence	ADV
ejpam-5395	79	23	f(u	f(u	PROPN
ejpam-5395	79	24	)	)	PUNCT
ejpam-5395	79	25	⊆	⊆	NUM
ejpam-5395	79	26	v	v	NOUN
ejpam-5395	79	27	.	.	PUNCT
ejpam-5395	80	1	this	this	PRON
ejpam-5395	80	2	shows	show	VERB
ejpam-5395	80	3	that	that	SCONJ
ejpam-5395	80	4	f	f	PROPN
ejpam-5395	80	5	is	be	AUX
ejpam-5395	80	6	faintly	faintly	ADV
ejpam-5395	80	7	(	(	PUNCT
ejpam-5395	80	8	τ1	τ1	NOUN
ejpam-5395	80	9	,	,	PUNCT
ejpam-5395	80	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	80	11	at	at	ADP
ejpam-5395	80	12	x	x	SYM
ejpam-5395	80	13	∈	∈	PROPN
ejpam-5395	80	14	x.	x.	NOUN
ejpam-5395	80	15	recall	recall	VERB
ejpam-5395	80	16	that	that	SCONJ
ejpam-5395	80	17	a	a	DET
ejpam-5395	80	18	bitopological	bitopological	ADJ
ejpam-5395	80	19	space	space	NOUN
ejpam-5395	80	20	(	(	PUNCT
ejpam-5395	80	21	x	x	NOUN
ejpam-5395	80	22	,	,	PUNCT
ejpam-5395	80	23	τ1	τ1	NOUN
ejpam-5395	80	24	,	,	PUNCT
ejpam-5395	80	25	τ2	τ2	NOUN
ejpam-5395	80	26	)	)	PUNCT
ejpam-5395	80	27	is	be	AUX
ejpam-5395	80	28	said	say	VERB
ejpam-5395	80	29	to	to	PART
ejpam-5395	80	30	be	be	AUX
ejpam-5395	80	31	(	(	PUNCT
ejpam-5395	80	32	τ1	τ1	NOUN
ejpam-5395	80	33	,	,	PUNCT
ejpam-5395	80	34	τ2)-t2	τ2)-t2	X
ejpam-5395	81	1	[	[	X
ejpam-5395	81	2	19	19	NUM
ejpam-5395	81	3	]	]	X
ejpam-5395	81	4	if	if	SCONJ
ejpam-5395	81	5	for	for	ADP
ejpam-5395	81	6	any	any	DET
ejpam-5395	81	7	pair	pair	NOUN
ejpam-5395	81	8	of	of	ADP
ejpam-5395	81	9	distinct	distinct	ADJ
ejpam-5395	81	10	points	point	NOUN
ejpam-5395	81	11	x	x	X
ejpam-5395	81	12	,	,	PUNCT
ejpam-5395	81	13	y	y	PROPN
ejpam-5395	81	14	in	in	ADP
ejpam-5395	81	15	x	x	SYM
ejpam-5395	81	16	,	,	PUNCT
ejpam-5395	81	17	there	there	PRON
ejpam-5395	81	18	exist	exist	VERB
ejpam-5395	81	19	disjoint	disjoint	ADJ
ejpam-5395	81	20	τ1τ2	τ1τ2	ADJ
ejpam-5395	81	21	-	-	ADJ
ejpam-5395	81	22	open	open	ADJ
ejpam-5395	81	23	sets	set	NOUN
ejpam-5395	81	24	u	u	NOUN
ejpam-5395	81	25	and	and	CCONJ
ejpam-5395	81	26	v	v	NOUN
ejpam-5395	81	27	of	of	ADP
ejpam-5395	81	28	x	x	PUNCT
ejpam-5395	81	29	containing	contain	VERB
ejpam-5395	81	30	x	x	PROPN
ejpam-5395	81	31	and	and	CCONJ
ejpam-5395	81	32	y	y	PROPN
ejpam-5395	81	33	,	,	PUNCT
ejpam-5395	81	34	respectively	respectively	ADV
ejpam-5395	81	35	.	.	PUNCT
ejpam-5395	82	1	definition	definition	NOUN
ejpam-5395	82	2	2	2	NUM
ejpam-5395	82	3	.	.	PUNCT
ejpam-5395	83	1	a	a	DET
ejpam-5395	83	2	bitopological	bitopological	ADJ
ejpam-5395	83	3	space	space	NOUN
ejpam-5395	83	4	(	(	PUNCT
ejpam-5395	83	5	x	x	NOUN
ejpam-5395	83	6	,	,	PUNCT
ejpam-5395	83	7	τ1	τ1	NOUN
ejpam-5395	83	8	,	,	PUNCT
ejpam-5395	83	9	τ2	τ2	NOUN
ejpam-5395	83	10	)	)	PUNCT
ejpam-5395	83	11	is	be	AUX
ejpam-5395	83	12	said	say	VERB
ejpam-5395	83	13	to	to	PART
ejpam-5395	83	14	be	be	AUX
ejpam-5395	83	15	(	(	PUNCT
ejpam-5395	83	16	τ1	τ1	NOUN
ejpam-5395	83	17	,	,	PUNCT
ejpam-5395	83	18	τ2)θ	τ2)θ	ADJ
ejpam-5395	83	19	-	-	PUNCT
ejpam-5395	83	20	t2	t2	NOUN
ejpam-5395	83	21	if	if	SCONJ
ejpam-5395	83	22	for	for	ADP
ejpam-5395	83	23	each	each	DET
ejpam-5395	83	24	distinct	distinct	ADJ
ejpam-5395	83	25	points	point	NOUN
ejpam-5395	83	26	x	x	NOUN
ejpam-5395	83	27	,	,	PUNCT
ejpam-5395	83	28	y	y	PROPN
ejpam-5395	83	29	∈	∈	PROPN
ejpam-5395	83	30	x	x	PRON
ejpam-5395	83	31	,	,	PUNCT
ejpam-5395	83	32	there	there	PRON
ejpam-5395	83	33	there	there	ADV
ejpam-5395	83	34	exist	exist	VERB
ejpam-5395	83	35	(	(	PUNCT
ejpam-5395	83	36	τ1	τ1	NOUN
ejpam-5395	83	37	,	,	PUNCT
ejpam-5395	83	38	τ2)θ	τ2)θ	ADJ
ejpam-5395	83	39	-	-	PUNCT
ejpam-5395	83	40	open	open	ADJ
ejpam-5395	83	41	sets	set	NOUN
ejpam-5395	83	42	u	u	NOUN
ejpam-5395	83	43	and	and	CCONJ
ejpam-5395	83	44	v	v	NOUN
ejpam-5395	83	45	of	of	ADP
ejpam-5395	83	46	x	x	PUNCT
ejpam-5395	83	47	containing	contain	VERB
ejpam-5395	83	48	x	x	PROPN
ejpam-5395	83	49	and	and	CCONJ
ejpam-5395	83	50	y	y	PROPN
ejpam-5395	83	51	,	,	PUNCT
ejpam-5395	83	52	respectively	respectively	ADV
ejpam-5395	83	53	,	,	PUNCT
ejpam-5395	83	54	such	such	ADJ
ejpam-5395	83	55	that	that	SCONJ
ejpam-5395	83	56	u	u	PROPN
ejpam-5395	83	57	∩	∩	NOUN
ejpam-5395	83	58	v	v	NOUN
ejpam-5395	83	59	=	=	PUNCT
ejpam-5395	83	60	∅.	∅.	NOUN
ejpam-5395	83	61	theorem	theorem	NOUN
ejpam-5395	83	62	2	2	NUM
ejpam-5395	83	63	.	.	PUNCT
ejpam-5395	84	1	if	if	SCONJ
ejpam-5395	84	2	f	f	PROPN
ejpam-5395	84	3	:	:	PUNCT
ejpam-5395	84	4	(	(	PUNCT
ejpam-5395	84	5	x	x	NOUN
ejpam-5395	84	6	,	,	PUNCT
ejpam-5395	84	7	τ1	τ1	NOUN
ejpam-5395	84	8	,	,	PUNCT
ejpam-5395	84	9	τ2	τ2	NOUN
ejpam-5395	84	10	)	)	PUNCT
ejpam-5395	84	11	→	→	SYM
ejpam-5395	84	12	(	(	PUNCT
ejpam-5395	84	13	y	y	PROPN
ejpam-5395	84	14	,	,	PUNCT
ejpam-5395	84	15	σ1	σ1	PROPN
ejpam-5395	84	16	,	,	PUNCT
ejpam-5395	84	17	σ2	σ2	PROPN
ejpam-5395	84	18	)	)	PUNCT
ejpam-5395	84	19	is	be	AUX
ejpam-5395	84	20	a	a	DET
ejpam-5395	84	21	faintly	faintly	ADV
ejpam-5395	84	22	(	(	PUNCT
ejpam-5395	84	23	τ1	τ1	NOUN
ejpam-5395	84	24	,	,	PUNCT
ejpam-5395	84	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	84	26	injection	injection	NOUN
ejpam-5395	84	27	and	and	CCONJ
ejpam-5395	84	28	(	(	PUNCT
ejpam-5395	84	29	y	y	PROPN
ejpam-5395	84	30	,	,	PUNCT
ejpam-5395	84	31	σ1	σ1	PROPN
ejpam-5395	84	32	,	,	PUNCT
ejpam-5395	84	33	σ2	σ2	PROPN
ejpam-5395	84	34	)	)	PUNCT
ejpam-5395	84	35	is	be	AUX
ejpam-5395	84	36	(	(	PUNCT
ejpam-5395	84	37	σ1	σ1	PROPN
ejpam-5395	84	38	,	,	PUNCT
ejpam-5395	84	39	σ2)θ	σ2)θ	NOUN
ejpam-5395	84	40	-	-	PUNCT
ejpam-5395	84	41	t2	t2	NOUN
ejpam-5395	84	42	,	,	PUNCT
ejpam-5395	84	43	then	then	ADV
ejpam-5395	84	44	(	(	PUNCT
ejpam-5395	84	45	x	x	NOUN
ejpam-5395	84	46	,	,	PUNCT
ejpam-5395	84	47	τ1	τ1	NOUN
ejpam-5395	84	48	,	,	PUNCT
ejpam-5395	84	49	τ2	τ2	NOUN
ejpam-5395	84	50	)	)	PUNCT
ejpam-5395	84	51	is	be	AUX
ejpam-5395	84	52	(	(	PUNCT
ejpam-5395	84	53	τ1	τ1	NOUN
ejpam-5395	84	54	,	,	PUNCT
ejpam-5395	84	55	τ2)-t2	τ2)-t2	PROPN
ejpam-5395	84	56	.	.	PUNCT
ejpam-5395	85	1	n.	n.	PROPN
ejpam-5395	85	2	srisarakham	srisarakham	PROPN
ejpam-5395	85	3	,	,	PUNCT
ejpam-5395	85	4	a.	a.	PROPN
ejpam-5395	85	5	sama	sama	PROPN
ejpam-5395	85	6	-	-	PUNCT
ejpam-5395	85	7	ae	ae	PROPN
ejpam-5395	85	8	,	,	PUNCT
ejpam-5395	85	9	c.	c.	PROPN
ejpam-5395	85	10	boonpok	boonpok	PROPN
ejpam-5395	85	11	/	/	SYM
ejpam-5395	85	12	eur	eur	PROPN
ejpam-5395	85	13	.	.	PUNCT
ejpam-5395	86	1	j.	j.	PROPN
ejpam-5395	86	2	pure	pure	PROPN
ejpam-5395	86	3	appl	appl	PROPN
ejpam-5395	86	4	.	.	PROPN
ejpam-5395	86	5	math	math	PROPN
ejpam-5395	86	6	,	,	PUNCT
ejpam-5395	86	7	17	17	NUM
ejpam-5395	86	8	(	(	PUNCT
ejpam-5395	86	9	4	4	NUM
ejpam-5395	86	10	)	)	PUNCT
ejpam-5395	86	11	(	(	PUNCT
ejpam-5395	86	12	2024	2024	NUM
ejpam-5395	86	13	)	)	PUNCT
ejpam-5395	86	14	,	,	PUNCT
ejpam-5395	86	15	2753	2753	NUM
ejpam-5395	86	16	-	-	SYM
ejpam-5395	86	17	2762	2762	NUM
ejpam-5395	86	18	2756	2756	NUM
ejpam-5395	86	19	proof	proof	NOUN
ejpam-5395	86	20	.	.	PUNCT
ejpam-5395	87	1	let	let	VERB
ejpam-5395	87	2	x	x	PRON
ejpam-5395	87	3	,	,	PUNCT
ejpam-5395	87	4	y	y	PROPN
ejpam-5395	87	5	be	be	VERB
ejpam-5395	87	6	any	any	DET
ejpam-5395	87	7	distinct	distinct	ADJ
ejpam-5395	87	8	points	point	NOUN
ejpam-5395	87	9	of	of	ADP
ejpam-5395	87	10	x.	x.	NOUN
ejpam-5395	87	11	then	then	ADV
ejpam-5395	87	12	f(x	f(x	PROPN
ejpam-5395	87	13	)	)	PUNCT
ejpam-5395	87	14	̸=	̸=	PROPN
ejpam-5395	87	15	f(y	f(y	NOUN
ejpam-5395	87	16	)	)	PUNCT
ejpam-5395	87	17	.	.	PUNCT
ejpam-5395	88	1	since	since	SCONJ
ejpam-5395	88	2	(	(	PUNCT
ejpam-5395	88	3	y	y	PROPN
ejpam-5395	88	4	,	,	PUNCT
ejpam-5395	88	5	σ1	σ1	PROPN
ejpam-5395	88	6	,	,	PUNCT
ejpam-5395	88	7	σ2	σ2	PROPN
ejpam-5395	88	8	)	)	PUNCT
ejpam-5395	88	9	is	be	AUX
ejpam-5395	88	10	(	(	PUNCT
ejpam-5395	88	11	σ1	σ1	PROPN
ejpam-5395	88	12	,	,	PUNCT
ejpam-5395	88	13	σ2)θ	σ2)θ	NOUN
ejpam-5395	88	14	-	-	PUNCT
ejpam-5395	88	15	t2	t2	NOUN
ejpam-5395	88	16	,	,	PUNCT
ejpam-5395	88	17	there	there	PRON
ejpam-5395	88	18	exist	exist	VERB
ejpam-5395	88	19	(	(	PUNCT
ejpam-5395	88	20	σ1	σ1	PROPN
ejpam-5395	88	21	,	,	PUNCT
ejpam-5395	88	22	σ2)θ	σ2)θ	ADJ
ejpam-5395	88	23	-	-	PUNCT
ejpam-5395	88	24	open	open	ADJ
ejpam-5395	88	25	sets	set	NOUN
ejpam-5395	88	26	u	u	NOUN
ejpam-5395	88	27	and	and	CCONJ
ejpam-5395	88	28	v	v	NOUN
ejpam-5395	88	29	of	of	ADP
ejpam-5395	88	30	y	y	NOUN
ejpam-5395	88	31	containing	contain	VERB
ejpam-5395	88	32	f(x	f(x	PROPN
ejpam-5395	88	33	)	)	PUNCT
ejpam-5395	88	34	and	and	CCONJ
ejpam-5395	88	35	f(y	f(y	NOUN
ejpam-5395	88	36	)	)	PUNCT
ejpam-5395	88	37	,	,	PUNCT
ejpam-5395	88	38	respectively	respectively	ADV
ejpam-5395	88	39	,	,	PUNCT
ejpam-5395	88	40	such	such	ADJ
ejpam-5395	88	41	that	that	SCONJ
ejpam-5395	88	42	u	u	PROPN
ejpam-5395	88	43	∩	∩	NOUN
ejpam-5395	88	44	v	v	NOUN
ejpam-5395	88	45	=	=	PUNCT
ejpam-5395	88	46	∅.	∅.	NOUN
ejpam-5395	88	47	since	since	SCONJ
ejpam-5395	88	48	f	f	PROPN
ejpam-5395	88	49	is	be	AUX
ejpam-5395	88	50	faintly	faintly	ADV
ejpam-5395	88	51	(	(	PUNCT
ejpam-5395	88	52	τ1	τ1	NOUN
ejpam-5395	88	53	,	,	PUNCT
ejpam-5395	88	54	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	88	55	,	,	PUNCT
ejpam-5395	88	56	there	there	PRON
ejpam-5395	88	57	exist	exist	VERB
ejpam-5395	88	58	τ1τ2open	τ1τ2open	NOUN
ejpam-5395	88	59	sets	set	VERB
ejpam-5395	88	60	g	g	NOUN
ejpam-5395	88	61	and	and	CCONJ
ejpam-5395	88	62	w	w	PROPN
ejpam-5395	88	63	of	of	ADP
ejpam-5395	88	64	x	x	PUNCT
ejpam-5395	88	65	containing	contain	VERB
ejpam-5395	88	66	x	x	PROPN
ejpam-5395	88	67	and	and	CCONJ
ejpam-5395	88	68	y	y	PROPN
ejpam-5395	88	69	,	,	PUNCT
ejpam-5395	88	70	respectively	respectively	ADV
ejpam-5395	88	71	,	,	PUNCT
ejpam-5395	88	72	such	such	ADJ
ejpam-5395	88	73	that	that	DET
ejpam-5395	88	74	f(g	f(g	NOUN
ejpam-5395	88	75	)	)	PUNCT
ejpam-5395	88	76	⊆	⊆	NUM
ejpam-5395	88	77	u	u	NOUN
ejpam-5395	88	78	and	and	CCONJ
ejpam-5395	88	79	f(w	f(w	PROPN
ejpam-5395	88	80	)	)	PUNCT
ejpam-5395	89	1	⊆	⊆	NUM
ejpam-5395	89	2	v	v	NOUN
ejpam-5395	89	3	.	.	PUNCT
ejpam-5395	90	1	this	this	PRON
ejpam-5395	90	2	implies	imply	VERB
ejpam-5395	90	3	that	that	SCONJ
ejpam-5395	90	4	g	g	PROPN
ejpam-5395	90	5	∩w	∩w	NOUN
ejpam-5395	90	6	=	=	PUNCT
ejpam-5395	90	7	∅.	∅.	VERB
ejpam-5395	90	8	thus	thus	ADV
ejpam-5395	90	9	,	,	PUNCT
ejpam-5395	90	10	(	(	PUNCT
ejpam-5395	90	11	x	x	NOUN
ejpam-5395	90	12	,	,	PUNCT
ejpam-5395	90	13	τ1	τ1	NOUN
ejpam-5395	90	14	,	,	PUNCT
ejpam-5395	90	15	τ2	τ2	NOUN
ejpam-5395	90	16	)	)	PUNCT
ejpam-5395	90	17	is	be	AUX
ejpam-5395	90	18	(	(	PUNCT
ejpam-5395	90	19	τ1	τ1	NOUN
ejpam-5395	90	20	,	,	PUNCT
ejpam-5395	90	21	τ2)-t2	τ2)-t2	PROPN
ejpam-5395	90	22	.	.	PUNCT
ejpam-5395	91	1	recall	recall	VERB
ejpam-5395	91	2	that	that	SCONJ
ejpam-5395	91	3	a	a	DET
ejpam-5395	91	4	bitopological	bitopological	ADJ
ejpam-5395	91	5	space	space	NOUN
ejpam-5395	91	6	(	(	PUNCT
ejpam-5395	91	7	x	x	NOUN
ejpam-5395	91	8	,	,	PUNCT
ejpam-5395	91	9	τ1	τ1	NOUN
ejpam-5395	91	10	,	,	PUNCT
ejpam-5395	91	11	τ2	τ2	NOUN
ejpam-5395	91	12	)	)	PUNCT
ejpam-5395	91	13	is	be	AUX
ejpam-5395	91	14	said	say	VERB
ejpam-5395	91	15	to	to	PART
ejpam-5395	91	16	be	be	AUX
ejpam-5395	91	17	τ1τ2	τ1τ2	NOUN
ejpam-5395	91	18	-	-	ADJ
ejpam-5395	91	19	compact	compact	ADJ
ejpam-5395	91	20	[	[	X
ejpam-5395	91	21	14	14	NUM
ejpam-5395	91	22	]	]	PUNCT
ejpam-5395	91	23	if	if	SCONJ
ejpam-5395	91	24	every	every	DET
ejpam-5395	91	25	cover	cover	NOUN
ejpam-5395	91	26	of	of	ADP
ejpam-5395	91	27	x	x	PUNCT
ejpam-5395	91	28	by	by	ADP
ejpam-5395	91	29	τ1τ2	τ1τ2	ADJ
ejpam-5395	91	30	-	-	ADJ
ejpam-5395	91	31	open	open	ADJ
ejpam-5395	91	32	sets	set	NOUN
ejpam-5395	91	33	of	of	ADP
ejpam-5395	91	34	x	x	PUNCT
ejpam-5395	91	35	has	have	VERB
ejpam-5395	91	36	a	a	DET
ejpam-5395	91	37	finite	finite	ADJ
ejpam-5395	91	38	subcover	subcover	PROPN
ejpam-5395	91	39	.	.	PUNCT
ejpam-5395	92	1	a	a	DET
ejpam-5395	92	2	subset	subset	NOUN
ejpam-5395	92	3	k	k	NOUN
ejpam-5395	92	4	of	of	ADP
ejpam-5395	92	5	x	x	PROPN
ejpam-5395	92	6	is	be	AUX
ejpam-5395	92	7	said	say	VERB
ejpam-5395	92	8	to	to	PART
ejpam-5395	92	9	be	be	AUX
ejpam-5395	92	10	τ1τ2	τ1τ2	ADJ
ejpam-5395	92	11	-	-	ADJ
ejpam-5395	92	12	compact	compact	ADJ
ejpam-5395	92	13	relative	relative	NOUN
ejpam-5395	92	14	to	to	ADP
ejpam-5395	92	15	(	(	PUNCT
ejpam-5395	92	16	x	x	NOUN
ejpam-5395	92	17	,	,	PUNCT
ejpam-5395	92	18	τ1	τ1	NOUN
ejpam-5395	92	19	,	,	PUNCT
ejpam-5395	92	20	τ2	τ2	NOUN
ejpam-5395	92	21	)	)	PUNCT
ejpam-5395	92	22	if	if	SCONJ
ejpam-5395	92	23	every	every	DET
ejpam-5395	92	24	cover	cover	NOUN
ejpam-5395	92	25	of	of	ADP
ejpam-5395	92	26	k	k	X
ejpam-5395	92	27	by	by	ADP
ejpam-5395	92	28	τ1τ2	τ1τ2	ADJ
ejpam-5395	92	29	-	-	ADJ
ejpam-5395	92	30	open	open	ADJ
ejpam-5395	92	31	sets	set	NOUN
ejpam-5395	92	32	of	of	ADP
ejpam-5395	92	33	x	x	PUNCT
ejpam-5395	92	34	has	have	VERB
ejpam-5395	92	35	a	a	DET
ejpam-5395	92	36	finite	finite	ADJ
ejpam-5395	92	37	subcover	subcover	PROPN
ejpam-5395	92	38	.	.	PUNCT
ejpam-5395	93	1	definition	definition	NOUN
ejpam-5395	93	2	3	3	NUM
ejpam-5395	93	3	.	.	PUNCT
ejpam-5395	94	1	a	a	DET
ejpam-5395	94	2	subset	subset	NOUN
ejpam-5395	94	3	k	k	NOUN
ejpam-5395	94	4	of	of	ADP
ejpam-5395	94	5	a	a	DET
ejpam-5395	94	6	bitopological	bitopological	ADJ
ejpam-5395	94	7	space	space	NOUN
ejpam-5395	94	8	(	(	PUNCT
ejpam-5395	94	9	x	x	NOUN
ejpam-5395	94	10	,	,	PUNCT
ejpam-5395	94	11	τ1	τ1	NOUN
ejpam-5395	94	12	,	,	PUNCT
ejpam-5395	94	13	τ2	τ2	NOUN
ejpam-5395	94	14	)	)	PUNCT
ejpam-5395	94	15	is	be	AUX
ejpam-5395	94	16	said	say	VERB
ejpam-5395	94	17	to	to	PART
ejpam-5395	94	18	be	be	AUX
ejpam-5395	94	19	(	(	PUNCT
ejpam-5395	94	20	τ1	τ1	NOUN
ejpam-5395	94	21	,	,	PUNCT
ejpam-5395	94	22	τ2)θ	τ2)θ	ADJ
ejpam-5395	94	23	-	-	PUNCT
ejpam-5395	94	24	compact	compact	ADJ
ejpam-5395	94	25	relative	relative	NOUN
ejpam-5395	94	26	to	to	ADP
ejpam-5395	94	27	(	(	PUNCT
ejpam-5395	94	28	x	x	NOUN
ejpam-5395	94	29	,	,	PUNCT
ejpam-5395	94	30	τ1	τ1	NOUN
ejpam-5395	94	31	,	,	PUNCT
ejpam-5395	94	32	τ2	τ2	NOUN
ejpam-5395	94	33	)	)	PUNCT
ejpam-5395	94	34	if	if	SCONJ
ejpam-5395	94	35	every	every	DET
ejpam-5395	94	36	cover	cover	NOUN
ejpam-5395	94	37	of	of	ADP
ejpam-5395	94	38	k	k	X
ejpam-5395	94	39	by	by	ADP
ejpam-5395	94	40	(	(	PUNCT
ejpam-5395	94	41	τ1	τ1	NOUN
ejpam-5395	94	42	,	,	PUNCT
ejpam-5395	94	43	τ2)θ	τ2)θ	ADJ
ejpam-5395	94	44	-	-	PUNCT
ejpam-5395	94	45	open	open	ADJ
ejpam-5395	94	46	sets	set	NOUN
ejpam-5395	94	47	of	of	ADP
ejpam-5395	94	48	x	x	PUNCT
ejpam-5395	94	49	has	have	VERB
ejpam-5395	94	50	a	a	DET
ejpam-5395	94	51	finite	finite	ADJ
ejpam-5395	94	52	subcover	subcover	PROPN
ejpam-5395	94	53	.	.	PUNCT
ejpam-5395	95	1	a	a	DET
ejpam-5395	95	2	bitopological	bitopological	ADJ
ejpam-5395	95	3	space	space	NOUN
ejpam-5395	95	4	(	(	PUNCT
ejpam-5395	95	5	x	x	NOUN
ejpam-5395	95	6	,	,	PUNCT
ejpam-5395	95	7	τ1	τ1	NOUN
ejpam-5395	95	8	,	,	PUNCT
ejpam-5395	95	9	τ2	τ2	NOUN
ejpam-5395	95	10	)	)	PUNCT
ejpam-5395	95	11	is	be	AUX
ejpam-5395	95	12	said	say	VERB
ejpam-5395	95	13	to	to	PART
ejpam-5395	95	14	be	be	AUX
ejpam-5395	95	15	(	(	PUNCT
ejpam-5395	95	16	τ1	τ1	NOUN
ejpam-5395	95	17	,	,	PUNCT
ejpam-5395	95	18	τ2)θ	τ2)θ	ADJ
ejpam-5395	95	19	-	-	PUNCT
ejpam-5395	95	20	compact	compact	ADJ
ejpam-5395	95	21	if	if	SCONJ
ejpam-5395	95	22	the	the	DET
ejpam-5395	95	23	set	set	NOUN
ejpam-5395	95	24	x	x	X
ejpam-5395	95	25	is	be	AUX
ejpam-5395	95	26	(	(	PUNCT
ejpam-5395	95	27	τ1	τ1	NOUN
ejpam-5395	95	28	,	,	PUNCT
ejpam-5395	95	29	τ2)θ	τ2)θ	ADJ
ejpam-5395	95	30	-	-	PUNCT
ejpam-5395	95	31	compact	compact	ADJ
ejpam-5395	95	32	relative	relative	NOUN
ejpam-5395	95	33	to	to	ADP
ejpam-5395	95	34	(	(	PUNCT
ejpam-5395	95	35	x	x	NOUN
ejpam-5395	95	36	,	,	PUNCT
ejpam-5395	95	37	τ1	τ1	NOUN
ejpam-5395	95	38	,	,	PUNCT
ejpam-5395	95	39	τ2	τ2	NOUN
ejpam-5395	95	40	)	)	PUNCT
ejpam-5395	95	41	.	.	PUNCT
ejpam-5395	96	1	theorem	theorem	NOUN
ejpam-5395	96	2	3	3	NUM
ejpam-5395	96	3	.	.	PUNCT
ejpam-5395	97	1	if	if	SCONJ
ejpam-5395	97	2	f	f	PROPN
ejpam-5395	97	3	:	:	PUNCT
ejpam-5395	97	4	(	(	PUNCT
ejpam-5395	97	5	x	x	NOUN
ejpam-5395	97	6	,	,	PUNCT
ejpam-5395	97	7	τ1	τ1	NOUN
ejpam-5395	97	8	,	,	PUNCT
ejpam-5395	97	9	τ2	τ2	NOUN
ejpam-5395	97	10	)	)	PUNCT
ejpam-5395	97	11	→	→	SYM
ejpam-5395	97	12	(	(	PUNCT
ejpam-5395	97	13	y	y	PROPN
ejpam-5395	97	14	,	,	PUNCT
ejpam-5395	97	15	σ1	σ1	PROPN
ejpam-5395	97	16	,	,	PUNCT
ejpam-5395	97	17	σ2	σ2	PROPN
ejpam-5395	97	18	)	)	PUNCT
ejpam-5395	97	19	is	be	AUX
ejpam-5395	97	20	a	a	DET
ejpam-5395	97	21	faintly	faintly	ADV
ejpam-5395	97	22	(	(	PUNCT
ejpam-5395	97	23	τ1	τ1	NOUN
ejpam-5395	97	24	,	,	PUNCT
ejpam-5395	97	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	97	26	function	function	NOUN
ejpam-5395	97	27	and	and	CCONJ
ejpam-5395	97	28	k	k	PROPN
ejpam-5395	97	29	is	be	AUX
ejpam-5395	97	30	τ1τ2	τ1τ2	ADJ
ejpam-5395	97	31	-	-	ADJ
ejpam-5395	97	32	compact	compact	ADJ
ejpam-5395	97	33	relative	relative	NOUN
ejpam-5395	97	34	to	to	ADP
ejpam-5395	97	35	(	(	PUNCT
ejpam-5395	97	36	x	x	NOUN
ejpam-5395	97	37	,	,	PUNCT
ejpam-5395	97	38	τ1	τ1	NOUN
ejpam-5395	97	39	,	,	PUNCT
ejpam-5395	97	40	τ2	τ2	NOUN
ejpam-5395	97	41	)	)	PUNCT
ejpam-5395	97	42	,	,	PUNCT
ejpam-5395	97	43	then	then	ADV
ejpam-5395	97	44	f(k	f(k	VERB
ejpam-5395	97	45	)	)	PUNCT
ejpam-5395	97	46	is	be	AUX
ejpam-5395	97	47	(	(	PUNCT
ejpam-5395	97	48	σ1	σ1	PROPN
ejpam-5395	97	49	,	,	PUNCT
ejpam-5395	97	50	σ2)θ	σ2)θ	ADJ
ejpam-5395	97	51	-	-	PUNCT
ejpam-5395	97	52	compact	compact	ADJ
ejpam-5395	97	53	relative	relative	NOUN
ejpam-5395	97	54	to	to	ADP
ejpam-5395	97	55	(	(	PUNCT
ejpam-5395	97	56	y	y	PROPN
ejpam-5395	97	57	,	,	PUNCT
ejpam-5395	97	58	σ1	σ1	PROPN
ejpam-5395	97	59	,	,	PUNCT
ejpam-5395	97	60	σ2	σ2	NOUN
ejpam-5395	97	61	)	)	PUNCT
ejpam-5395	97	62	.	.	PUNCT
ejpam-5395	98	1	proof	proof	NOUN
ejpam-5395	98	2	.	.	PUNCT
ejpam-5395	99	1	let	let	VERB
ejpam-5395	99	2	{	{	PUNCT
ejpam-5395	99	3	vγ	vγ	VERB
ejpam-5395	99	4	:	:	PUNCT
ejpam-5395	99	5	γ	γ	PROPN
ejpam-5395	99	6	∈	∈	PROPN
ejpam-5395	99	7	γ	γ	AUX
ejpam-5395	99	8	}	}	PUNCT
ejpam-5395	99	9	be	be	VERB
ejpam-5395	99	10	any	any	DET
ejpam-5395	99	11	cover	cover	NOUN
ejpam-5395	99	12	of	of	ADP
ejpam-5395	99	13	f(k	f(k	VERB
ejpam-5395	99	14	)	)	PUNCT
ejpam-5395	99	15	by	by	ADP
ejpam-5395	99	16	(	(	PUNCT
ejpam-5395	99	17	σ1	σ1	PROPN
ejpam-5395	99	18	,	,	PUNCT
ejpam-5395	99	19	σ2)θ	σ2)θ	ADJ
ejpam-5395	99	20	-	-	PUNCT
ejpam-5395	99	21	open	open	ADJ
ejpam-5395	99	22	sets	set	NOUN
ejpam-5395	99	23	of	of	ADP
ejpam-5395	99	24	y	y	PROPN
ejpam-5395	99	25	.	.	PUNCT
ejpam-5395	100	1	for	for	ADP
ejpam-5395	100	2	each	each	DET
ejpam-5395	100	3	x	x	SYM
ejpam-5395	100	4	∈	∈	PROPN
ejpam-5395	100	5	k	k	NOUN
ejpam-5395	100	6	,	,	PUNCT
ejpam-5395	100	7	there	there	PRON
ejpam-5395	100	8	exists	exist	VERB
ejpam-5395	100	9	γ(x	γ(x	NOUN
ejpam-5395	100	10	)	)	PUNCT
ejpam-5395	100	11	∈	∈	PROPN
ejpam-5395	100	12	γ	γ	NOUN
ejpam-5395	100	13	such	such	ADJ
ejpam-5395	100	14	that	that	SCONJ
ejpam-5395	100	15	f(x	f(x	PROPN
ejpam-5395	100	16	)	)	PUNCT
ejpam-5395	100	17	∈	∈	PROPN
ejpam-5395	100	18	vγ(x	vγ(x	NOUN
ejpam-5395	100	19	)	)	PUNCT
ejpam-5395	100	20	.	.	PUNCT
ejpam-5395	101	1	since	since	SCONJ
ejpam-5395	101	2	f	f	PROPN
ejpam-5395	101	3	is	be	AUX
ejpam-5395	101	4	faintly	faintly	ADV
ejpam-5395	101	5	(	(	PUNCT
ejpam-5395	101	6	τ1	τ1	NOUN
ejpam-5395	101	7	,	,	PUNCT
ejpam-5395	101	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	101	9	,	,	PUNCT
ejpam-5395	101	10	there	there	PRON
ejpam-5395	101	11	exist	exist	VERB
ejpam-5395	101	12	a	a	DET
ejpam-5395	101	13	τ1τ2	τ1τ2	ADJ
ejpam-5395	101	14	-	-	ADJ
ejpam-5395	101	15	open	open	ADJ
ejpam-5395	101	16	set	set	ADJ
ejpam-5395	101	17	u(x	u(x	NOUN
ejpam-5395	101	18	)	)	PUNCT
ejpam-5395	101	19	of	of	ADP
ejpam-5395	101	20	x	x	SYM
ejpam-5395	101	21	containing	contain	VERB
ejpam-5395	101	22	x	x	PUNCT
ejpam-5395	101	23	such	such	ADJ
ejpam-5395	101	24	that	that	SCONJ
ejpam-5395	101	25	f(u(x	f(u(x	PROPN
ejpam-5395	101	26	)	)	PUNCT
ejpam-5395	101	27	)	)	PUNCT
ejpam-5395	102	1	⊆	⊆	NUM
ejpam-5395	102	2	vγ(x	vγ(x	NOUN
ejpam-5395	102	3	)	)	PUNCT
ejpam-5395	102	4	.	.	PUNCT
ejpam-5395	103	1	the	the	DET
ejpam-5395	103	2	family	family	NOUN
ejpam-5395	103	3	{	{	PUNCT
ejpam-5395	103	4	u(x	u(x	PROPN
ejpam-5395	103	5	)	)	PUNCT
ejpam-5395	103	6	:	:	PUNCT
ejpam-5395	104	1	x	x	X
ejpam-5395	104	2	∈	∈	PROPN
ejpam-5395	104	3	k	k	NOUN
ejpam-5395	104	4	}	}	PUNCT
ejpam-5395	104	5	is	be	AUX
ejpam-5395	104	6	a	a	DET
ejpam-5395	104	7	cover	cover	NOUN
ejpam-5395	104	8	of	of	ADP
ejpam-5395	104	9	k	k	X
ejpam-5395	104	10	by	by	ADP
ejpam-5395	104	11	τ1τ2	τ1τ2	ADJ
ejpam-5395	104	12	-	-	ADJ
ejpam-5395	104	13	open	open	ADJ
ejpam-5395	104	14	sets	set	NOUN
ejpam-5395	104	15	of	of	ADP
ejpam-5395	104	16	x.	x.	NOUN
ejpam-5395	104	17	since	since	SCONJ
ejpam-5395	104	18	k	k	PROPN
ejpam-5395	104	19	is	be	AUX
ejpam-5395	104	20	τ1τ2	τ1τ2	ADJ
ejpam-5395	104	21	-	-	ADJ
ejpam-5395	104	22	compact	compact	ADJ
ejpam-5395	104	23	relative	relative	NOUN
ejpam-5395	104	24	to	to	ADP
ejpam-5395	104	25	(	(	PUNCT
ejpam-5395	104	26	x	x	NOUN
ejpam-5395	104	27	,	,	PUNCT
ejpam-5395	104	28	τ1	τ1	NOUN
ejpam-5395	104	29	,	,	PUNCT
ejpam-5395	104	30	τ2	τ2	NOUN
ejpam-5395	104	31	)	)	PUNCT
ejpam-5395	104	32	,	,	PUNCT
ejpam-5395	104	33	there	there	PRON
ejpam-5395	104	34	exists	exist	VERB
ejpam-5395	104	35	a	a	DET
ejpam-5395	104	36	finite	finite	ADJ
ejpam-5395	104	37	number	number	NOUN
ejpam-5395	104	38	of	of	ADP
ejpam-5395	104	39	points	point	NOUN
ejpam-5395	104	40	,	,	PUNCT
ejpam-5395	104	41	say	say	INTJ
ejpam-5395	104	42	,	,	PUNCT
ejpam-5395	104	43	x1	x1	PROPN
ejpam-5395	104	44	,	,	PUNCT
ejpam-5395	104	45	x2	x2	PROPN
ejpam-5395	104	46	,	,	PUNCT
ejpam-5395	104	47	x3	x3	ADJ
ejpam-5395	104	48	,	,	PUNCT
ejpam-5395	104	49	...	...	PUNCT
ejpam-5395	104	50	,	,	PUNCT
ejpam-5395	104	51	xn	xn	PROPN
ejpam-5395	105	1	in	in	ADP
ejpam-5395	105	2	k	k	PROPN
ejpam-5395	105	3	such	such	ADJ
ejpam-5395	105	4	that	that	SCONJ
ejpam-5395	105	5	k	k	PROPN
ejpam-5395	105	6	⊆	⊆	NUM
ejpam-5395	105	7	∪{u(xk	∪{u(xk	NUM
ejpam-5395	105	8	)	)	PUNCT
ejpam-5395	105	9	:	:	PUNCT
ejpam-5395	105	10	xk	xk	PROPN
ejpam-5395	105	11	∈	∈	PROPN
ejpam-5395	105	12	k	k	PROPN
ejpam-5395	105	13	,	,	PUNCT
ejpam-5395	105	14	1	1	NUM
ejpam-5395	105	15	≤	≤	NUM
ejpam-5395	105	16	k	k	X
ejpam-5395	105	17	≤	≤	PROPN
ejpam-5395	105	18	n	n	CCONJ
ejpam-5395	105	19	}	}	PUNCT
ejpam-5395	105	20	.	.	PUNCT
ejpam-5395	106	1	thus	thus	ADV
ejpam-5395	106	2	,	,	PUNCT
ejpam-5395	106	3	f(k	f(k	VERB
ejpam-5395	106	4	)	)	PUNCT
ejpam-5395	106	5	⊆	⊆	NUM
ejpam-5395	106	6	∪{f(u(xk	∪{f(u(xk	NUM
ejpam-5395	106	7	)	)	PUNCT
ejpam-5395	106	8	)	)	PUNCT
ejpam-5395	106	9	:	:	PUNCT
ejpam-5395	107	1	xk	xk	PROPN
ejpam-5395	107	2	∈	∈	PROPN
ejpam-5395	107	3	k	k	PROPN
ejpam-5395	107	4	,	,	PUNCT
ejpam-5395	107	5	1	1	NUM
ejpam-5395	107	6	≤	≤	NUM
ejpam-5395	107	7	k	k	X
ejpam-5395	107	8	≤	≤	PROPN
ejpam-5395	107	9	n	n	CCONJ
ejpam-5395	107	10	}	}	PUNCT
ejpam-5395	107	11	⊆	⊆	NUM
ejpam-5395	107	12	∪{vγ(xk	∪{vγ(xk	NUM
ejpam-5395	107	13	)	)	PUNCT
ejpam-5395	107	14	:	:	PUNCT
ejpam-5395	107	15	xk	xk	PROPN
ejpam-5395	107	16	∈	∈	PROPN
ejpam-5395	107	17	k	k	PROPN
ejpam-5395	107	18	,	,	PUNCT
ejpam-5395	107	19	1	1	NUM
ejpam-5395	107	20	≤	≤	NUM
ejpam-5395	107	21	k	k	X
ejpam-5395	107	22	≤	≤	PROPN
ejpam-5395	107	23	n	n	CCONJ
ejpam-5395	107	24	}	}	PUNCT
ejpam-5395	107	25	.	.	PUNCT
ejpam-5395	108	1	this	this	PRON
ejpam-5395	108	2	shows	show	VERB
ejpam-5395	108	3	that	that	SCONJ
ejpam-5395	108	4	f(k	f(k	VERB
ejpam-5395	108	5	)	)	PUNCT
ejpam-5395	108	6	is	be	AUX
ejpam-5395	108	7	(	(	PUNCT
ejpam-5395	108	8	σ1	σ1	PROPN
ejpam-5395	108	9	,	,	PUNCT
ejpam-5395	108	10	σ2)θ	σ2)θ	ADJ
ejpam-5395	108	11	-	-	PUNCT
ejpam-5395	108	12	compact	compact	ADJ
ejpam-5395	108	13	relative	relative	NOUN
ejpam-5395	108	14	to	to	ADP
ejpam-5395	108	15	(	(	PUNCT
ejpam-5395	108	16	y	y	PROPN
ejpam-5395	108	17	,	,	PUNCT
ejpam-5395	108	18	σ1	σ1	PROPN
ejpam-5395	108	19	,	,	PUNCT
ejpam-5395	108	20	σ2	σ2	PROPN
ejpam-5395	108	21	)	)	PUNCT
ejpam-5395	108	22	.	.	PUNCT
ejpam-5395	109	1	recall	recall	VERB
ejpam-5395	109	2	that	that	SCONJ
ejpam-5395	109	3	a	a	DET
ejpam-5395	109	4	bitopological	bitopological	ADJ
ejpam-5395	109	5	space	space	NOUN
ejpam-5395	109	6	(	(	PUNCT
ejpam-5395	109	7	x	x	NOUN
ejpam-5395	109	8	,	,	PUNCT
ejpam-5395	109	9	τ1	τ1	NOUN
ejpam-5395	109	10	,	,	PUNCT
ejpam-5395	109	11	τ2	τ2	NOUN
ejpam-5395	109	12	)	)	PUNCT
ejpam-5395	109	13	is	be	AUX
ejpam-5395	109	14	said	say	VERB
ejpam-5395	109	15	to	to	PART
ejpam-5395	109	16	be	be	AUX
ejpam-5395	109	17	τ1τ2	τ1τ2	NOUN
ejpam-5395	109	18	-	-	ADJ
ejpam-5395	109	19	connected	connected	ADJ
ejpam-5395	110	1	[	[	X
ejpam-5395	110	2	14	14	NUM
ejpam-5395	110	3	]	]	X
ejpam-5395	110	4	if	if	SCONJ
ejpam-5395	110	5	x	x	PRON
ejpam-5395	110	6	can	can	AUX
ejpam-5395	110	7	not	not	PART
ejpam-5395	110	8	be	be	AUX
ejpam-5395	110	9	written	write	VERB
ejpam-5395	110	10	as	as	ADP
ejpam-5395	110	11	the	the	DET
ejpam-5395	110	12	union	union	NOUN
ejpam-5395	110	13	of	of	ADP
ejpam-5395	110	14	two	two	NUM
ejpam-5395	110	15	disjoint	disjoint	NOUN
ejpam-5395	110	16	nonempty	nonempty	ADJ
ejpam-5395	110	17	τ1τ2	τ1τ2	ADJ
ejpam-5395	110	18	-	-	ADJ
ejpam-5395	110	19	open	open	ADJ
ejpam-5395	110	20	sets	set	NOUN
ejpam-5395	110	21	.	.	PUNCT
ejpam-5395	111	1	lemma	lemma	PROPN
ejpam-5395	111	2	2	2	NUM
ejpam-5395	111	3	.	.	PUNCT
ejpam-5395	112	1	[	[	X
ejpam-5395	112	2	34	34	NUM
ejpam-5395	112	3	]	]	PUNCT
ejpam-5395	112	4	for	for	ADP
ejpam-5395	112	5	a	a	DET
ejpam-5395	112	6	function	function	NOUN
ejpam-5395	112	7	f	f	NOUN
ejpam-5395	112	8	:	:	PUNCT
ejpam-5395	112	9	(	(	PUNCT
ejpam-5395	112	10	x	x	NOUN
ejpam-5395	112	11	,	,	PUNCT
ejpam-5395	112	12	τ1	τ1	NOUN
ejpam-5395	112	13	,	,	PUNCT
ejpam-5395	112	14	τ2	τ2	NOUN
ejpam-5395	112	15	)	)	PUNCT
ejpam-5395	112	16	→	→	SYM
ejpam-5395	112	17	(	(	PUNCT
ejpam-5395	112	18	y	y	PROPN
ejpam-5395	112	19	,	,	PUNCT
ejpam-5395	112	20	σ1	σ1	PROPN
ejpam-5395	112	21	,	,	PUNCT
ejpam-5395	112	22	σ2	σ2	NOUN
ejpam-5395	112	23	)	)	PUNCT
ejpam-5395	112	24	,	,	PUNCT
ejpam-5395	112	25	the	the	DET
ejpam-5395	112	26	following	follow	VERB
ejpam-5395	112	27	properties	property	NOUN
ejpam-5395	112	28	are	be	AUX
ejpam-5395	112	29	equivalent	equivalent	ADJ
ejpam-5395	112	30	:	:	PUNCT
ejpam-5395	112	31	(	(	PUNCT
ejpam-5395	112	32	1	1	X
ejpam-5395	112	33	)	)	PUNCT
ejpam-5395	112	34	f	f	PROPN
ejpam-5395	112	35	is	be	AUX
ejpam-5395	112	36	faintly	faintly	ADV
ejpam-5395	112	37	(	(	PUNCT
ejpam-5395	112	38	τ1	τ1	NOUN
ejpam-5395	112	39	,	,	PUNCT
ejpam-5395	112	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	112	41	;	;	PUNCT
ejpam-5395	112	42	(	(	PUNCT
ejpam-5395	112	43	2	2	X
ejpam-5395	112	44	)	)	PUNCT
ejpam-5395	112	45	f−1(v	f−1(v	NOUN
ejpam-5395	112	46	)	)	PUNCT
ejpam-5395	112	47	is	be	AUX
ejpam-5395	112	48	τ1τ2	τ1τ2	NOUN
ejpam-5395	112	49	-	-	ADJ
ejpam-5395	112	50	open	open	ADJ
ejpam-5395	112	51	in	in	ADP
ejpam-5395	112	52	x	x	PUNCT
ejpam-5395	112	53	for	for	ADP
ejpam-5395	112	54	each	each	DET
ejpam-5395	112	55	(	(	PUNCT
ejpam-5395	112	56	σ1	σ1	PROPN
ejpam-5395	112	57	,	,	PUNCT
ejpam-5395	112	58	σ2)θ	σ2)θ	NOUN
ejpam-5395	112	59	-	-	PUNCT
ejpam-5395	112	60	open	open	ADJ
ejpam-5395	112	61	set	set	NOUN
ejpam-5395	112	62	v	v	NOUN
ejpam-5395	112	63	of	of	ADP
ejpam-5395	112	64	y	y	PROPN
ejpam-5395	112	65	;	;	PUNCT
ejpam-5395	112	66	(	(	PUNCT
ejpam-5395	112	67	3	3	X
ejpam-5395	112	68	)	)	PUNCT
ejpam-5395	112	69	f−1(k	f−1(k	PROPN
ejpam-5395	112	70	)	)	PUNCT
ejpam-5395	112	71	is	be	AUX
ejpam-5395	112	72	τ1τ2	τ1τ2	NOUN
ejpam-5395	112	73	-	-	ADJ
ejpam-5395	112	74	closed	closed	ADJ
ejpam-5395	112	75	in	in	ADP
ejpam-5395	112	76	x	x	PUNCT
ejpam-5395	112	77	for	for	ADP
ejpam-5395	112	78	each	each	DET
ejpam-5395	112	79	(	(	PUNCT
ejpam-5395	112	80	σ1	σ1	PROPN
ejpam-5395	112	81	,	,	PUNCT
ejpam-5395	112	82	σ2)θ	σ2)θ	NOUN
ejpam-5395	112	83	-	-	PUNCT
ejpam-5395	112	84	closed	close	VERB
ejpam-5395	112	85	set	set	NOUN
ejpam-5395	112	86	k	k	PROPN
ejpam-5395	112	87	of	of	ADP
ejpam-5395	112	88	y	y	PROPN
ejpam-5395	112	89	;	;	PUNCT
ejpam-5395	112	90	(	(	PUNCT
ejpam-5395	112	91	4	4	X
ejpam-5395	112	92	)	)	PUNCT
ejpam-5395	112	93	for	for	ADP
ejpam-5395	112	94	each	each	DET
ejpam-5395	112	95	x	x	SYM
ejpam-5395	112	96	∈	∈	PROPN
ejpam-5395	112	97	x	x	X
ejpam-5395	112	98	and	and	CCONJ
ejpam-5395	112	99	for	for	ADP
ejpam-5395	112	100	each	each	DET
ejpam-5395	112	101	(	(	PUNCT
ejpam-5395	112	102	σ1	σ1	PROPN
ejpam-5395	112	103	,	,	PUNCT
ejpam-5395	112	104	σ2)θ	σ2)θ	NOUN
ejpam-5395	112	105	-	-	PUNCT
ejpam-5395	112	106	open	open	ADJ
ejpam-5395	112	107	set	set	NOUN
ejpam-5395	112	108	v	v	NOUN
ejpam-5395	112	109	of	of	ADP
ejpam-5395	112	110	y	y	NOUN
ejpam-5395	112	111	containing	contain	VERB
ejpam-5395	112	112	f(x	f(x	PROPN
ejpam-5395	112	113	)	)	PUNCT
ejpam-5395	112	114	,	,	PUNCT
ejpam-5395	112	115	there	there	PRON
ejpam-5395	112	116	exists	exist	VERB
ejpam-5395	112	117	a	a	DET
ejpam-5395	112	118	τ1τ2	τ1τ2	NOUN
ejpam-5395	112	119	-	-	ADJ
ejpam-5395	112	120	open	open	ADJ
ejpam-5395	112	121	set	set	ADJ
ejpam-5395	112	122	u	u	NOUN
ejpam-5395	112	123	of	of	ADP
ejpam-5395	112	124	x	x	PUNCT
ejpam-5395	112	125	containing	contain	VERB
ejpam-5395	112	126	x	x	PUNCT
ejpam-5395	112	127	such	such	ADJ
ejpam-5395	112	128	that	that	DET
ejpam-5395	112	129	f(u	f(u	PROPN
ejpam-5395	112	130	)	)	PUNCT
ejpam-5395	112	131	⊆	⊆	NUM
ejpam-5395	112	132	v	v	NOUN
ejpam-5395	112	133	.	.	PUNCT
ejpam-5395	113	1	theorem	theorem	ADJ
ejpam-5395	113	2	4	4	NUM
ejpam-5395	113	3	.	.	PUNCT
ejpam-5395	114	1	if	if	SCONJ
ejpam-5395	114	2	f	f	PROPN
ejpam-5395	114	3	:	:	PUNCT
ejpam-5395	114	4	(	(	PUNCT
ejpam-5395	114	5	x	x	NOUN
ejpam-5395	114	6	,	,	PUNCT
ejpam-5395	114	7	τ1	τ1	NOUN
ejpam-5395	114	8	,	,	PUNCT
ejpam-5395	114	9	τ2	τ2	NOUN
ejpam-5395	114	10	)	)	PUNCT
ejpam-5395	114	11	→	→	SYM
ejpam-5395	114	12	(	(	PUNCT
ejpam-5395	114	13	y	y	PROPN
ejpam-5395	114	14	,	,	PUNCT
ejpam-5395	114	15	σ1	σ1	PROPN
ejpam-5395	114	16	,	,	PUNCT
ejpam-5395	114	17	σ2	σ2	PROPN
ejpam-5395	114	18	)	)	PUNCT
ejpam-5395	114	19	is	be	AUX
ejpam-5395	114	20	a	a	DET
ejpam-5395	114	21	faintly	faintly	ADV
ejpam-5395	114	22	(	(	PUNCT
ejpam-5395	114	23	τ1	τ1	NOUN
ejpam-5395	114	24	,	,	PUNCT
ejpam-5395	114	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	114	26	surjection	surjection	NOUN
ejpam-5395	114	27	and	and	CCONJ
ejpam-5395	114	28	(	(	PUNCT
ejpam-5395	114	29	x	x	NOUN
ejpam-5395	114	30	,	,	PUNCT
ejpam-5395	114	31	τ1	τ1	NOUN
ejpam-5395	114	32	,	,	PUNCT
ejpam-5395	114	33	τ2	τ2	NOUN
ejpam-5395	114	34	)	)	PUNCT
ejpam-5395	114	35	is	be	AUX
ejpam-5395	114	36	τ1τ2	τ1τ2	NOUN
ejpam-5395	114	37	-	-	ADJ
ejpam-5395	114	38	connected	connected	ADJ
ejpam-5395	114	39	,	,	PUNCT
ejpam-5395	114	40	then	then	ADV
ejpam-5395	114	41	(	(	PUNCT
ejpam-5395	114	42	y	y	PROPN
ejpam-5395	114	43	,	,	PUNCT
ejpam-5395	114	44	σ1	σ1	PROPN
ejpam-5395	114	45	,	,	PUNCT
ejpam-5395	114	46	σ2	σ2	PROPN
ejpam-5395	114	47	)	)	PUNCT
ejpam-5395	114	48	is	be	AUX
ejpam-5395	114	49	σ1σ2	σ1σ2	NOUN
ejpam-5395	114	50	-	-	PUNCT
ejpam-5395	114	51	connected	connect	VERB
ejpam-5395	114	52	.	.	PUNCT
ejpam-5395	115	1	n.	n.	PROPN
ejpam-5395	115	2	srisarakham	srisarakham	PROPN
ejpam-5395	115	3	,	,	PUNCT
ejpam-5395	115	4	a.	a.	PROPN
ejpam-5395	115	5	sama	sama	PROPN
ejpam-5395	115	6	-	-	PUNCT
ejpam-5395	115	7	ae	ae	PROPN
ejpam-5395	115	8	,	,	PUNCT
ejpam-5395	115	9	c.	c.	PROPN
ejpam-5395	115	10	boonpok	boonpok	PROPN
ejpam-5395	115	11	/	/	SYM
ejpam-5395	115	12	eur	eur	PROPN
ejpam-5395	115	13	.	.	PUNCT
ejpam-5395	116	1	j.	j.	PROPN
ejpam-5395	116	2	pure	pure	PROPN
ejpam-5395	116	3	appl	appl	PROPN
ejpam-5395	116	4	.	.	PROPN
ejpam-5395	116	5	math	math	PROPN
ejpam-5395	116	6	,	,	PUNCT
ejpam-5395	116	7	17	17	NUM
ejpam-5395	116	8	(	(	PUNCT
ejpam-5395	116	9	4	4	NUM
ejpam-5395	116	10	)	)	PUNCT
ejpam-5395	116	11	(	(	PUNCT
ejpam-5395	116	12	2024	2024	NUM
ejpam-5395	116	13	)	)	PUNCT
ejpam-5395	116	14	,	,	PUNCT
ejpam-5395	116	15	2753	2753	NUM
ejpam-5395	116	16	-	-	SYM
ejpam-5395	116	17	2762	2762	NUM
ejpam-5395	116	18	2757	2757	NUM
ejpam-5395	116	19	proof	proof	NOUN
ejpam-5395	116	20	.	.	PUNCT
ejpam-5395	117	1	assume	assume	VERB
ejpam-5395	117	2	that	that	SCONJ
ejpam-5395	117	3	(	(	PUNCT
ejpam-5395	117	4	y	y	PROPN
ejpam-5395	117	5	,	,	PUNCT
ejpam-5395	117	6	σ1	σ1	PROPN
ejpam-5395	117	7	,	,	PUNCT
ejpam-5395	117	8	σ2	σ2	PROPN
ejpam-5395	117	9	)	)	PUNCT
ejpam-5395	117	10	is	be	AUX
ejpam-5395	117	11	not	not	PART
ejpam-5395	117	12	σ1σ2	σ1σ2	VERB
ejpam-5395	117	13	-	-	PUNCT
ejpam-5395	117	14	connected	connect	VERB
ejpam-5395	117	15	.	.	PUNCT
ejpam-5395	118	1	then	then	ADV
ejpam-5395	118	2	,	,	PUNCT
ejpam-5395	118	3	there	there	PRON
ejpam-5395	118	4	exist	exist	VERB
ejpam-5395	118	5	nonempty	nonempty	ADV
ejpam-5395	118	6	σ1σ2	σ1σ2	NOUN
ejpam-5395	118	7	-	-	ADJ
ejpam-5395	118	8	open	open	ADJ
ejpam-5395	118	9	sets	set	NOUN
ejpam-5395	118	10	v	v	ADP
ejpam-5395	118	11	andw	andw	NOUN
ejpam-5395	119	1	such	such	DET
ejpam-5395	119	2	that	that	DET
ejpam-5395	119	3	v	v	NOUN
ejpam-5395	119	4	∩w	∩w	NOUN
ejpam-5395	119	5	=	=	NOUN
ejpam-5395	119	6	∅	∅	NOUN
ejpam-5395	119	7	and	and	CCONJ
ejpam-5395	119	8	v	v	ADP
ejpam-5395	119	9	∪w	∪w	PROPN
ejpam-5395	119	10	=	=	SYM
ejpam-5395	119	11	y	y	PROPN
ejpam-5395	119	12	.	.	PUNCT
ejpam-5395	120	1	thus	thus	ADV
ejpam-5395	120	2	,	,	PUNCT
ejpam-5395	120	3	f−1(v	f−1(v	PROPN
ejpam-5395	120	4	)	)	PUNCT
ejpam-5395	120	5	∩f−1(w	∩f−1(w	X
ejpam-5395	120	6	)	)	PUNCT
ejpam-5395	121	1	=	=	NOUN
ejpam-5395	121	2	∅	∅	NOUN
ejpam-5395	121	3	and	and	CCONJ
ejpam-5395	121	4	f−1(v	f−1(v	NOUN
ejpam-5395	121	5	)	)	PUNCT
ejpam-5395	121	6	∪f−1(w	∪f−1(w	ADV
ejpam-5395	121	7	)	)	PUNCT
ejpam-5395	121	8	=	=	PUNCT
ejpam-5395	122	1	x.	x.	NOUN
ejpam-5395	122	2	since	since	SCONJ
ejpam-5395	122	3	f	f	PROPN
ejpam-5395	122	4	is	be	AUX
ejpam-5395	122	5	surjective	surjective	ADJ
ejpam-5395	122	6	,	,	PUNCT
ejpam-5395	122	7	f−1(v	f−1(v	PROPN
ejpam-5395	122	8	)	)	PUNCT
ejpam-5395	122	9	and	and	CCONJ
ejpam-5395	122	10	f−1(w	f−1(w	PROPN
ejpam-5395	122	11	)	)	PUNCT
ejpam-5395	122	12	are	be	AUX
ejpam-5395	122	13	nonempty	nonempty	ADJ
ejpam-5395	122	14	.	.	PUNCT
ejpam-5395	123	1	since	since	SCONJ
ejpam-5395	123	2	v	v	NOUN
ejpam-5395	123	3	and	and	CCONJ
ejpam-5395	123	4	w	w	NOUN
ejpam-5395	123	5	are	be	AUX
ejpam-5395	123	6	σ1σ2	σ1σ2	NOUN
ejpam-5395	123	7	-	-	ADJ
ejpam-5395	123	8	open	open	ADJ
ejpam-5395	123	9	and	and	CCONJ
ejpam-5395	123	10	σ1σ2	σ1σ2	NOUN
ejpam-5395	123	11	-	-	PUNCT
ejpam-5395	123	12	closed	closed	ADJ
ejpam-5395	123	13	,	,	PUNCT
ejpam-5395	123	14	we	we	PRON
ejpam-5395	123	15	have	have	VERB
ejpam-5395	123	16	v	v	NOUN
ejpam-5395	123	17	and	and	CCONJ
ejpam-5395	123	18	w	w	NOUN
ejpam-5395	123	19	are	be	AUX
ejpam-5395	123	20	(	(	PUNCT
ejpam-5395	123	21	σ1	σ1	NOUN
ejpam-5395	123	22	,	,	PUNCT
ejpam-5395	123	23	σ2)θ	σ2)θ	ADJ
ejpam-5395	123	24	-	-	PUNCT
ejpam-5395	123	25	open	open	ADJ
ejpam-5395	123	26	sets	set	NOUN
ejpam-5395	123	27	of	of	ADP
ejpam-5395	123	28	y	y	PROPN
ejpam-5395	123	29	.	.	PUNCT
ejpam-5395	124	1	since	since	SCONJ
ejpam-5395	124	2	f	f	PROPN
ejpam-5395	124	3	is	be	AUX
ejpam-5395	124	4	faintly	faintly	ADV
ejpam-5395	124	5	(	(	PUNCT
ejpam-5395	124	6	τ1	τ1	NOUN
ejpam-5395	124	7	,	,	PUNCT
ejpam-5395	124	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	124	9	,	,	PUNCT
ejpam-5395	124	10	by	by	ADP
ejpam-5395	124	11	lemma	lemma	PROPN
ejpam-5395	124	12	2	2	NUM
ejpam-5395	124	13	,	,	PUNCT
ejpam-5395	124	14	f−1(v	f−1(v	PROPN
ejpam-5395	124	15	)	)	PUNCT
ejpam-5395	124	16	and	and	CCONJ
ejpam-5395	124	17	f−1(w	f−1(w	PROPN
ejpam-5395	124	18	)	)	PUNCT
ejpam-5395	124	19	are	be	AUX
ejpam-5395	124	20	τ1τ2	τ1τ2	NOUN
ejpam-5395	124	21	-	-	ADJ
ejpam-5395	124	22	open	open	ADJ
ejpam-5395	124	23	in	in	ADP
ejpam-5395	124	24	x.	x.	NOUN
ejpam-5395	124	25	thus	thus	ADV
ejpam-5395	124	26	,	,	PUNCT
ejpam-5395	124	27	(	(	PUNCT
ejpam-5395	124	28	x	x	NOUN
ejpam-5395	124	29	,	,	PUNCT
ejpam-5395	124	30	τ1	τ1	NOUN
ejpam-5395	124	31	,	,	PUNCT
ejpam-5395	124	32	τ2	τ2	NOUN
ejpam-5395	124	33	)	)	PUNCT
ejpam-5395	124	34	is	be	AUX
ejpam-5395	124	35	not	not	PART
ejpam-5395	124	36	τ1τ2	τ1τ2	ADJ
ejpam-5395	124	37	-	-	VERB
ejpam-5395	124	38	connected	connected	ADJ
ejpam-5395	124	39	.	.	PUNCT
ejpam-5395	125	1	this	this	PRON
ejpam-5395	125	2	is	be	AUX
ejpam-5395	125	3	a	a	DET
ejpam-5395	125	4	contradiction	contradiction	NOUN
ejpam-5395	125	5	and	and	CCONJ
ejpam-5395	125	6	hence	hence	ADV
ejpam-5395	125	7	(	(	PUNCT
ejpam-5395	125	8	y	y	PROPN
ejpam-5395	125	9	,	,	PUNCT
ejpam-5395	125	10	σ1	σ1	PROPN
ejpam-5395	125	11	,	,	PUNCT
ejpam-5395	125	12	σ2	σ2	PROPN
ejpam-5395	125	13	)	)	PUNCT
ejpam-5395	125	14	is	be	AUX
ejpam-5395	125	15	σ1σ2	σ1σ2	NOUN
ejpam-5395	125	16	-	-	PUNCT
ejpam-5395	125	17	connected	connect	VERB
ejpam-5395	125	18	.	.	PUNCT
ejpam-5395	126	1	the	the	DET
ejpam-5395	126	2	τ1τ2	τ1τ2	NOUN
ejpam-5395	126	3	-	-	NOUN
ejpam-5395	126	4	frontier	frontier	NOUN
ejpam-5395	126	5	[	[	NOUN
ejpam-5395	126	6	13	13	NUM
ejpam-5395	126	7	]	]	PUNCT
ejpam-5395	126	8	of	of	ADP
ejpam-5395	126	9	a	a	DET
ejpam-5395	126	10	subset	subset	NOUN
ejpam-5395	126	11	a	a	PRON
ejpam-5395	126	12	of	of	ADP
ejpam-5395	126	13	a	a	DET
ejpam-5395	126	14	bitopological	bitopological	ADJ
ejpam-5395	126	15	space	space	NOUN
ejpam-5395	126	16	(	(	PUNCT
ejpam-5395	126	17	x	x	NOUN
ejpam-5395	126	18	,	,	PUNCT
ejpam-5395	126	19	τ1	τ1	NOUN
ejpam-5395	126	20	,	,	PUNCT
ejpam-5395	126	21	τ2	τ2	PROPN
ejpam-5395	126	22	)	)	PUNCT
ejpam-5395	126	23	,	,	PUNCT
ejpam-5395	126	24	denoted	denote	VERB
ejpam-5395	126	25	by	by	ADP
ejpam-5395	126	26	τ1τ2	τ1τ2	NOUN
ejpam-5395	126	27	-	-	ADJ
ejpam-5395	126	28	fr(a	fr(a	NUM
ejpam-5395	126	29	)	)	PUNCT
ejpam-5395	126	30	,	,	PUNCT
ejpam-5395	126	31	is	be	AUX
ejpam-5395	126	32	defined	define	VERB
ejpam-5395	126	33	by	by	ADP
ejpam-5395	126	34	τ1τ2	τ1τ2	NOUN
ejpam-5395	126	35	-	-	ADJ
ejpam-5395	126	36	fr(a	fr(a	ADJ
ejpam-5395	126	37	)	)	PUNCT
ejpam-5395	127	1	=	=	PUNCT
ejpam-5395	127	2	τ1τ2	τ1τ2	NOUN
ejpam-5395	127	3	-	-	NUM
ejpam-5395	127	4	cl(a	cl(a	NUM
ejpam-5395	127	5	)	)	PUNCT
ejpam-5395	127	6	∩	∩	NOUN
ejpam-5395	127	7	τ1τ2	τ1τ2	NOUN
ejpam-5395	127	8	-	-	ADJ
ejpam-5395	127	9	cl(x	cl(x	SYM
ejpam-5395	127	10	−a	−a	NOUN
ejpam-5395	127	11	)	)	PUNCT
ejpam-5395	127	12	=	=	PUNCT
ejpam-5395	128	1	τ1τ2	τ1τ2	ADJ
ejpam-5395	128	2	-	-	ADJ
ejpam-5395	128	3	cl(a)−	cl(a)−	ADJ
ejpam-5395	128	4	τ1τ2	τ1τ2	NOUN
ejpam-5395	128	5	-	-	ADJ
ejpam-5395	128	6	int(a	int(a	NOUN
ejpam-5395	128	7	)	)	PUNCT
ejpam-5395	128	8	.	.	PUNCT
ejpam-5395	129	1	theorem	theorem	NOUN
ejpam-5395	129	2	5	5	NUM
ejpam-5395	129	3	.	.	PUNCT
ejpam-5395	130	1	the	the	DET
ejpam-5395	130	2	set	set	NOUN
ejpam-5395	130	3	of	of	ADP
ejpam-5395	130	4	all	all	DET
ejpam-5395	130	5	points	point	NOUN
ejpam-5395	130	6	x	x	X
ejpam-5395	130	7	∈	∈	NOUN
ejpam-5395	130	8	x	x	PUNCT
ejpam-5395	130	9	at	at	ADP
ejpam-5395	130	10	which	which	PRON
ejpam-5395	130	11	a	a	DET
ejpam-5395	130	12	function	function	NOUN
ejpam-5395	130	13	f	f	NOUN
ejpam-5395	130	14	:	:	PUNCT
ejpam-5395	130	15	(	(	PUNCT
ejpam-5395	130	16	x	x	NOUN
ejpam-5395	130	17	,	,	PUNCT
ejpam-5395	130	18	τ1	τ1	NOUN
ejpam-5395	130	19	,	,	PUNCT
ejpam-5395	130	20	τ2	τ2	NOUN
ejpam-5395	130	21	)	)	PUNCT
ejpam-5395	130	22	→	→	SYM
ejpam-5395	130	23	(	(	PUNCT
ejpam-5395	130	24	y	y	PROPN
ejpam-5395	130	25	,	,	PUNCT
ejpam-5395	130	26	σ1	σ1	PROPN
ejpam-5395	130	27	,	,	PUNCT
ejpam-5395	130	28	σ2	σ2	PROPN
ejpam-5395	130	29	)	)	PUNCT
ejpam-5395	130	30	is	be	AUX
ejpam-5395	130	31	not	not	PART
ejpam-5395	130	32	faintly	faintly	ADV
ejpam-5395	130	33	(	(	PUNCT
ejpam-5395	130	34	τ1	τ1	NOUN
ejpam-5395	130	35	,	,	PUNCT
ejpam-5395	130	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	130	37	is	be	AUX
ejpam-5395	130	38	identical	identical	ADJ
ejpam-5395	130	39	with	with	ADP
ejpam-5395	130	40	the	the	DET
ejpam-5395	130	41	union	union	NOUN
ejpam-5395	130	42	of	of	ADP
ejpam-5395	130	43	the	the	DET
ejpam-5395	130	44	τ1τ2	τ1τ2	NOUN
ejpam-5395	130	45	-	-	NOUN
ejpam-5395	130	46	frontier	frontier	NOUN
ejpam-5395	130	47	of	of	ADP
ejpam-5395	130	48	the	the	DET
ejpam-5395	130	49	inverse	inverse	NOUN
ejpam-5395	130	50	images	image	NOUN
ejpam-5395	130	51	of	of	ADP
ejpam-5395	130	52	(	(	PUNCT
ejpam-5395	130	53	σ1	σ1	PROPN
ejpam-5395	130	54	,	,	PUNCT
ejpam-5395	130	55	σ2)θ	σ2)θ	ADJ
ejpam-5395	130	56	-	-	PUNCT
ejpam-5395	130	57	open	open	ADJ
ejpam-5395	130	58	sets	set	NOUN
ejpam-5395	130	59	of	of	ADP
ejpam-5395	130	60	y	y	NOUN
ejpam-5395	130	61	containing	contain	VERB
ejpam-5395	130	62	f(x	f(x	PROPN
ejpam-5395	130	63	)	)	PUNCT
ejpam-5395	130	64	.	.	PUNCT
ejpam-5395	131	1	proof	proof	NOUN
ejpam-5395	131	2	.	.	PUNCT
ejpam-5395	132	1	suppose	suppose	VERB
ejpam-5395	132	2	that	that	SCONJ
ejpam-5395	132	3	f	f	PROPN
ejpam-5395	132	4	is	be	AUX
ejpam-5395	132	5	not	not	PART
ejpam-5395	132	6	faintly	faintly	ADV
ejpam-5395	132	7	(	(	PUNCT
ejpam-5395	132	8	τ1	τ1	NOUN
ejpam-5395	132	9	,	,	PUNCT
ejpam-5395	132	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	132	11	at	at	ADP
ejpam-5395	132	12	x	x	SYM
ejpam-5395	132	13	∈	∈	PROPN
ejpam-5395	132	14	x.	x.	NOUN
ejpam-5395	132	15	then	then	ADV
ejpam-5395	132	16	,	,	PUNCT
ejpam-5395	132	17	there	there	PRON
ejpam-5395	132	18	exists	exist	VERB
ejpam-5395	132	19	a	a	DET
ejpam-5395	132	20	(	(	PUNCT
ejpam-5395	132	21	σ1	σ1	PROPN
ejpam-5395	132	22	,	,	PUNCT
ejpam-5395	132	23	σ2)θ	σ2)θ	NOUN
ejpam-5395	132	24	-	-	PUNCT
ejpam-5395	132	25	open	open	ADJ
ejpam-5395	132	26	set	set	NOUN
ejpam-5395	132	27	v	v	NOUN
ejpam-5395	132	28	of	of	ADP
ejpam-5395	132	29	y	y	NOUN
ejpam-5395	132	30	containing	contain	VERB
ejpam-5395	132	31	f(x	f(x	PROPN
ejpam-5395	132	32	)	)	PUNCT
ejpam-5395	132	33	such	such	ADJ
ejpam-5395	132	34	that	that	DET
ejpam-5395	132	35	f(u	f(u	PROPN
ejpam-5395	132	36	)	)	PUNCT
ejpam-5395	132	37	is	be	AUX
ejpam-5395	132	38	not	not	PART
ejpam-5395	132	39	contained	contain	VERB
ejpam-5395	132	40	in	in	ADP
ejpam-5395	132	41	v	v	NOUN
ejpam-5395	132	42	for	for	ADP
ejpam-5395	132	43	every	every	DET
ejpam-5395	132	44	τ1τ2	τ1τ2	ADJ
ejpam-5395	132	45	-	-	ADJ
ejpam-5395	132	46	open	open	ADJ
ejpam-5395	132	47	set	set	ADJ
ejpam-5395	132	48	u	u	NOUN
ejpam-5395	132	49	of	of	ADP
ejpam-5395	132	50	x	x	SYM
ejpam-5395	132	51	containing	contain	VERB
ejpam-5395	132	52	x.	x.	NOUN
ejpam-5395	132	53	then	then	ADV
ejpam-5395	132	54	,	,	PUNCT
ejpam-5395	132	55	u	u	NOUN
ejpam-5395	132	56	∩	∩	NOUN
ejpam-5395	132	57	(	(	PUNCT
ejpam-5395	132	58	x	x	SYM
ejpam-5395	132	59	−	−	PROPN
ejpam-5395	132	60	f−1(v	f−1(v	NOUN
ejpam-5395	132	61	)	)	PUNCT
ejpam-5395	132	62	)	)	PUNCT
ejpam-5395	133	1	̸=	̸=	NOUN
ejpam-5395	133	2	∅	∅	NOUN
ejpam-5395	133	3	for	for	ADP
ejpam-5395	133	4	every	every	DET
ejpam-5395	133	5	τ1τ2	τ1τ2	ADJ
ejpam-5395	133	6	-	-	ADJ
ejpam-5395	133	7	open	open	ADJ
ejpam-5395	133	8	set	set	ADJ
ejpam-5395	133	9	u	u	NOUN
ejpam-5395	133	10	of	of	ADP
ejpam-5395	133	11	x	x	SYM
ejpam-5395	133	12	containing	contain	VERB
ejpam-5395	133	13	x.	x.	NOUN
ejpam-5395	133	14	thus	thus	ADV
ejpam-5395	133	15	,	,	PUNCT
ejpam-5395	133	16	x	x	SYM
ejpam-5395	133	17	∈	∈	PROPN
ejpam-5395	133	18	τ1τ2	τ1τ2	NOUN
ejpam-5395	133	19	-	-	NOUN
ejpam-5395	133	20	cl(x	cl(x	SYM
ejpam-5395	133	21	−	−	PROPN
ejpam-5395	133	22	f−1(v	f−1(v	NOUN
ejpam-5395	133	23	)	)	PUNCT
ejpam-5395	133	24	)	)	PUNCT
ejpam-5395	133	25	.	.	PUNCT
ejpam-5395	134	1	on	on	ADP
ejpam-5395	134	2	the	the	DET
ejpam-5395	134	3	other	other	ADJ
ejpam-5395	134	4	hand	hand	NOUN
ejpam-5395	134	5	,	,	PUNCT
ejpam-5395	134	6	we	we	PRON
ejpam-5395	134	7	have	have	VERB
ejpam-5395	134	8	x	x	X
ejpam-5395	134	9	∈	∈	PROPN
ejpam-5395	134	10	f−1(v	f−1(v	NOUN
ejpam-5395	134	11	)	)	PUNCT
ejpam-5395	135	1	⊆	⊆	NUM
ejpam-5395	135	2	τ1τ2	τ1τ2	NOUN
ejpam-5395	135	3	-	-	NOUN
ejpam-5395	135	4	cl(f	cl(f	PRON
ejpam-5395	135	5	−1(v	−1(v	NOUN
ejpam-5395	135	6	)	)	PUNCT
ejpam-5395	135	7	)	)	PUNCT
ejpam-5395	135	8	and	and	CCONJ
ejpam-5395	135	9	hence	hence	ADV
ejpam-5395	135	10	x	x	X
ejpam-5395	135	11	∈	∈	PRON
ejpam-5395	135	12	τ1τ2	τ1τ2	NOUN
ejpam-5395	135	13	-	-	PUNCT
ejpam-5395	135	14	fr(a	fr(a	NUM
ejpam-5395	135	15	)	)	PUNCT
ejpam-5395	135	16	.	.	PUNCT
ejpam-5395	136	1	conversely	conversely	ADV
ejpam-5395	136	2	,	,	PUNCT
ejpam-5395	136	3	suppose	suppose	VERB
ejpam-5395	136	4	that	that	SCONJ
ejpam-5395	136	5	f	f	PROPN
ejpam-5395	136	6	is	be	AUX
ejpam-5395	136	7	faintly	faintly	ADV
ejpam-5395	136	8	(	(	PUNCT
ejpam-5395	136	9	τ1	τ1	NOUN
ejpam-5395	136	10	,	,	PUNCT
ejpam-5395	136	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	136	12	at	at	ADP
ejpam-5395	136	13	x	x	SYM
ejpam-5395	136	14	∈	∈	PROPN
ejpam-5395	136	15	x.	x.	NOUN
ejpam-5395	136	16	let	let	VERB
ejpam-5395	136	17	v	v	PART
ejpam-5395	136	18	be	be	AUX
ejpam-5395	136	19	any	any	DET
ejpam-5395	136	20	(	(	PUNCT
ejpam-5395	136	21	σ1	σ1	PROPN
ejpam-5395	136	22	,	,	PUNCT
ejpam-5395	136	23	σ2)θ	σ2)θ	NOUN
ejpam-5395	136	24	-	-	PUNCT
ejpam-5395	136	25	open	open	ADJ
ejpam-5395	136	26	set	set	NOUN
ejpam-5395	136	27	of	of	ADP
ejpam-5395	136	28	y	y	PROPN
ejpam-5395	136	29	containing	contain	VERB
ejpam-5395	136	30	f(x	f(x	PROPN
ejpam-5395	136	31	)	)	PUNCT
ejpam-5395	136	32	.	.	PUNCT
ejpam-5395	137	1	then	then	ADV
ejpam-5395	137	2	by	by	ADP
ejpam-5395	137	3	theorem	theorem	NOUN
ejpam-5395	137	4	1	1	NUM
ejpam-5395	137	5	,	,	PUNCT
ejpam-5395	137	6	x	x	SYM
ejpam-5395	137	7	∈	∈	PRON
ejpam-5395	137	8	τ1τ2	τ1τ2	PUNCT
ejpam-5395	137	9	-	-	NUM
ejpam-5395	137	10	int(f	int(f	NOUN
ejpam-5395	137	11	−1(v	−1(v	NOUN
ejpam-5395	137	12	)	)	PUNCT
ejpam-5395	137	13	)	)	PUNCT
ejpam-5395	137	14	.	.	PUNCT
ejpam-5395	138	1	thus	thus	ADV
ejpam-5395	138	2	,	,	PUNCT
ejpam-5395	138	3	x	x	PROPN
ejpam-5395	138	4	̸∈	̸∈	PROPN
ejpam-5395	138	5	τ1τ2	τ1τ2	PROPN
ejpam-5395	138	6	-	-	NOUN
ejpam-5395	138	7	fr(f	fr(f	PUNCT
ejpam-5395	138	8	−1(v	−1(v	NOUN
ejpam-5395	138	9	)	)	PUNCT
ejpam-5395	138	10	)	)	PUNCT
ejpam-5395	138	11	for	for	ADP
ejpam-5395	138	12	each	each	DET
ejpam-5395	138	13	(	(	PUNCT
ejpam-5395	138	14	σ1	σ1	PROPN
ejpam-5395	138	15	,	,	PUNCT
ejpam-5395	138	16	σ2)θ	σ2)θ	NOUN
ejpam-5395	138	17	-	-	PUNCT
ejpam-5395	138	18	open	open	ADJ
ejpam-5395	138	19	set	set	NOUN
ejpam-5395	138	20	v	v	NOUN
ejpam-5395	138	21	of	of	ADP
ejpam-5395	138	22	y	y	NOUN
ejpam-5395	138	23	containing	contain	VERB
ejpam-5395	138	24	f(x	f(x	PROPN
ejpam-5395	138	25	)	)	PUNCT
ejpam-5395	138	26	.	.	PUNCT
ejpam-5395	139	1	this	this	PRON
ejpam-5395	139	2	completes	complete	VERB
ejpam-5395	139	3	the	the	DET
ejpam-5395	139	4	proof	proof	NOUN
ejpam-5395	139	5	.	.	PUNCT
ejpam-5395	140	1	definition	definition	NOUN
ejpam-5395	140	2	4	4	NUM
ejpam-5395	140	3	.	.	PUNCT
ejpam-5395	141	1	[	[	X
ejpam-5395	141	2	36	36	NUM
ejpam-5395	141	3	]	]	PUNCT
ejpam-5395	141	4	a	a	DET
ejpam-5395	141	5	function	function	NOUN
ejpam-5395	141	6	f	f	NOUN
ejpam-5395	141	7	:	:	PUNCT
ejpam-5395	141	8	(	(	PUNCT
ejpam-5395	141	9	x	x	NOUN
ejpam-5395	141	10	,	,	PUNCT
ejpam-5395	141	11	τ1	τ1	NOUN
ejpam-5395	141	12	,	,	PUNCT
ejpam-5395	141	13	τ2	τ2	NOUN
ejpam-5395	141	14	)	)	PUNCT
ejpam-5395	141	15	→	→	SYM
ejpam-5395	141	16	(	(	PUNCT
ejpam-5395	141	17	y	y	PROPN
ejpam-5395	141	18	,	,	PUNCT
ejpam-5395	141	19	σ1	σ1	PROPN
ejpam-5395	141	20	,	,	PUNCT
ejpam-5395	141	21	σ2	σ2	PROPN
ejpam-5395	141	22	)	)	PUNCT
ejpam-5395	141	23	is	be	AUX
ejpam-5395	141	24	said	say	VERB
ejpam-5395	141	25	to	to	PART
ejpam-5395	141	26	be	be	AUX
ejpam-5395	141	27	slightly	slightly	ADV
ejpam-5395	141	28	(	(	PUNCT
ejpam-5395	141	29	τ1	τ1	NOUN
ejpam-5395	141	30	,	,	PUNCT
ejpam-5395	141	31	τ2)continuous	τ2)continuous	ADJ
ejpam-5395	141	32	if	if	SCONJ
ejpam-5395	141	33	for	for	ADP
ejpam-5395	141	34	each	each	DET
ejpam-5395	141	35	x	x	SYM
ejpam-5395	141	36	∈	∈	PROPN
ejpam-5395	141	37	x	x	X
ejpam-5395	141	38	and	and	CCONJ
ejpam-5395	141	39	each	each	DET
ejpam-5395	141	40	σ1σ2	σ1σ2	NUM
ejpam-5395	141	41	-	-	PUNCT
ejpam-5395	141	42	clopen	clopen	ADJ
ejpam-5395	141	43	set	set	NOUN
ejpam-5395	141	44	v	v	NOUN
ejpam-5395	141	45	of	of	ADP
ejpam-5395	141	46	y	y	NOUN
ejpam-5395	141	47	containing	contain	VERB
ejpam-5395	141	48	f(x	f(x	PROPN
ejpam-5395	141	49	)	)	PUNCT
ejpam-5395	141	50	,	,	PUNCT
ejpam-5395	141	51	there	there	PRON
ejpam-5395	141	52	exists	exist	VERB
ejpam-5395	141	53	a	a	DET
ejpam-5395	141	54	τ1τ2	τ1τ2	NOUN
ejpam-5395	141	55	-	-	ADJ
ejpam-5395	141	56	open	open	ADJ
ejpam-5395	141	57	set	set	ADJ
ejpam-5395	141	58	u	u	NOUN
ejpam-5395	141	59	of	of	ADP
ejpam-5395	141	60	x	x	PUNCT
ejpam-5395	141	61	containing	contain	VERB
ejpam-5395	141	62	x	x	PUNCT
ejpam-5395	141	63	such	such	ADJ
ejpam-5395	141	64	that	that	DET
ejpam-5395	141	65	f(u	f(u	PROPN
ejpam-5395	141	66	)	)	PUNCT
ejpam-5395	141	67	⊆	⊆	NUM
ejpam-5395	141	68	v	v	NOUN
ejpam-5395	141	69	.	.	PUNCT
ejpam-5395	142	1	theorem	theorem	NOUN
ejpam-5395	142	2	6	6	NUM
ejpam-5395	142	3	.	.	PUNCT
ejpam-5395	143	1	if	if	SCONJ
ejpam-5395	143	2	f	f	PROPN
ejpam-5395	143	3	:	:	PUNCT
ejpam-5395	143	4	(	(	PUNCT
ejpam-5395	143	5	x	x	NOUN
ejpam-5395	143	6	,	,	PUNCT
ejpam-5395	143	7	τ1	τ1	NOUN
ejpam-5395	143	8	,	,	PUNCT
ejpam-5395	143	9	τ2	τ2	NOUN
ejpam-5395	143	10	)	)	PUNCT
ejpam-5395	143	11	→	→	SYM
ejpam-5395	143	12	(	(	PUNCT
ejpam-5395	143	13	y	y	PROPN
ejpam-5395	143	14	,	,	PUNCT
ejpam-5395	143	15	σ1	σ1	PROPN
ejpam-5395	143	16	,	,	PUNCT
ejpam-5395	143	17	σ2	σ2	PROPN
ejpam-5395	143	18	)	)	PUNCT
ejpam-5395	143	19	is	be	AUX
ejpam-5395	143	20	faintly	faintly	ADV
ejpam-5395	143	21	(	(	PUNCT
ejpam-5395	143	22	τ1	τ1	NOUN
ejpam-5395	143	23	,	,	PUNCT
ejpam-5395	143	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	143	25	,	,	PUNCT
ejpam-5395	143	26	then	then	ADV
ejpam-5395	143	27	f	f	PROPN
ejpam-5395	143	28	is	be	AUX
ejpam-5395	143	29	slightly	slightly	ADV
ejpam-5395	143	30	(	(	PUNCT
ejpam-5395	143	31	τ1	τ1	NOUN
ejpam-5395	143	32	,	,	PUNCT
ejpam-5395	143	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	143	34	.	.	PUNCT
ejpam-5395	144	1	proof	proof	NOUN
ejpam-5395	144	2	.	.	PUNCT
ejpam-5395	145	1	let	let	VERB
ejpam-5395	145	2	x	x	PUNCT
ejpam-5395	145	3	∈	∈	PROPN
ejpam-5395	145	4	x	x	X
ejpam-5395	145	5	and	and	CCONJ
ejpam-5395	145	6	v	v	X
ejpam-5395	145	7	be	be	AUX
ejpam-5395	145	8	any	any	DET
ejpam-5395	145	9	σ1σ2	σ1σ2	NOUN
ejpam-5395	145	10	-	-	PUNCT
ejpam-5395	145	11	clopen	clopen	ADJ
ejpam-5395	145	12	set	set	NOUN
ejpam-5395	145	13	of	of	ADP
ejpam-5395	145	14	y	y	PROPN
ejpam-5395	145	15	containing	contain	VERB
ejpam-5395	145	16	f(x	f(x	PROPN
ejpam-5395	145	17	)	)	PUNCT
ejpam-5395	145	18	.	.	PUNCT
ejpam-5395	146	1	then	then	ADV
ejpam-5395	146	2	,	,	PUNCT
ejpam-5395	146	3	v	v	NOUN
ejpam-5395	146	4	is	be	AUX
ejpam-5395	146	5	(	(	PUNCT
ejpam-5395	146	6	σ1	σ1	PROPN
ejpam-5395	146	7	,	,	PUNCT
ejpam-5395	146	8	σ2)θ	σ2)θ	NOUN
ejpam-5395	146	9	-	-	PUNCT
ejpam-5395	146	10	open	open	ADJ
ejpam-5395	146	11	in	in	ADP
ejpam-5395	146	12	y	y	PROPN
ejpam-5395	146	13	.	.	PUNCT
ejpam-5395	147	1	since	since	SCONJ
ejpam-5395	147	2	f	f	PROPN
ejpam-5395	147	3	is	be	AUX
ejpam-5395	147	4	faintly	faintly	ADV
ejpam-5395	147	5	(	(	PUNCT
ejpam-5395	147	6	τ1	τ1	NOUN
ejpam-5395	147	7	,	,	PUNCT
ejpam-5395	147	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	147	9	,	,	PUNCT
ejpam-5395	147	10	there	there	PRON
ejpam-5395	147	11	exists	exist	VERB
ejpam-5395	147	12	a	a	DET
ejpam-5395	147	13	τ1τ2	τ1τ2	NOUN
ejpam-5395	147	14	-	-	ADJ
ejpam-5395	147	15	open	open	ADJ
ejpam-5395	147	16	set	set	ADJ
ejpam-5395	147	17	u	u	NOUN
ejpam-5395	147	18	of	of	ADP
ejpam-5395	147	19	x	x	PUNCT
ejpam-5395	147	20	containing	contain	VERB
ejpam-5395	147	21	x	x	PUNCT
ejpam-5395	147	22	such	such	ADJ
ejpam-5395	147	23	that	that	DET
ejpam-5395	147	24	f(u	f(u	PROPN
ejpam-5395	147	25	)	)	PUNCT
ejpam-5395	147	26	⊆	⊆	NUM
ejpam-5395	147	27	v	v	NOUN
ejpam-5395	147	28	.	.	PUNCT
ejpam-5395	148	1	this	this	PRON
ejpam-5395	148	2	shows	show	VERB
ejpam-5395	148	3	that	that	SCONJ
ejpam-5395	148	4	f	f	PROPN
ejpam-5395	148	5	is	be	AUX
ejpam-5395	148	6	slightly	slightly	ADV
ejpam-5395	148	7	(	(	PUNCT
ejpam-5395	148	8	τ1	τ1	NOUN
ejpam-5395	148	9	,	,	PUNCT
ejpam-5395	148	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	148	11	.	.	NOUN
ejpam-5395	149	1	4	4	NUM
ejpam-5395	149	2	.	.	X
ejpam-5395	149	3	on	on	ADP
ejpam-5395	149	4	faint	faint	ADJ
ejpam-5395	149	5	(	(	PUNCT
ejpam-5395	149	6	τ1	τ1	NOUN
ejpam-5395	149	7	,	,	PUNCT
ejpam-5395	149	8	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	149	9	and	and	CCONJ
ejpam-5395	149	10	other	other	ADJ
ejpam-5395	149	11	forms	form	NOUN
ejpam-5395	149	12	of	of	ADP
ejpam-5395	149	13	(	(	PUNCT
ejpam-5395	149	14	τ1	τ1	NOUN
ejpam-5395	149	15	,	,	PUNCT
ejpam-5395	149	16	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	149	17	in	in	ADP
ejpam-5395	149	18	this	this	DET
ejpam-5395	149	19	paper	paper	NOUN
ejpam-5395	149	20	,	,	PUNCT
ejpam-5395	149	21	we	we	PRON
ejpam-5395	149	22	investigate	investigate	VERB
ejpam-5395	149	23	the	the	DET
ejpam-5395	149	24	relationships	relationship	NOUN
ejpam-5395	149	25	between	between	ADP
ejpam-5395	149	26	faintly	faintly	ADV
ejpam-5395	149	27	(	(	PUNCT
ejpam-5395	149	28	τ1	τ1	PROPN
ejpam-5395	149	29	,	,	PUNCT
ejpam-5395	149	30	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	149	31	functions	function	NOUN
ejpam-5395	149	32	and	and	CCONJ
ejpam-5395	149	33	other	other	ADJ
ejpam-5395	149	34	forms	form	NOUN
ejpam-5395	149	35	of	of	ADP
ejpam-5395	149	36	(	(	PUNCT
ejpam-5395	149	37	τ1	τ1	PROPN
ejpam-5395	149	38	,	,	PUNCT
ejpam-5395	149	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	149	40	functions	function	NOUN
ejpam-5395	149	41	.	.	PUNCT
ejpam-5395	150	1	definition	definition	NOUN
ejpam-5395	150	2	5	5	NUM
ejpam-5395	150	3	.	.	PUNCT
ejpam-5395	151	1	[	[	X
ejpam-5395	151	2	10	10	NUM
ejpam-5395	151	3	]	]	X
ejpam-5395	151	4	a	a	DET
ejpam-5395	151	5	function	function	NOUN
ejpam-5395	151	6	f	f	NOUN
ejpam-5395	151	7	:	:	PUNCT
ejpam-5395	151	8	(	(	PUNCT
ejpam-5395	151	9	x	x	NOUN
ejpam-5395	151	10	,	,	PUNCT
ejpam-5395	151	11	τ1	τ1	NOUN
ejpam-5395	151	12	,	,	PUNCT
ejpam-5395	151	13	τ2	τ2	NOUN
ejpam-5395	151	14	)	)	PUNCT
ejpam-5395	151	15	→	→	SYM
ejpam-5395	151	16	(	(	PUNCT
ejpam-5395	151	17	y	y	PROPN
ejpam-5395	151	18	,	,	PUNCT
ejpam-5395	151	19	σ1	σ1	PROPN
ejpam-5395	151	20	,	,	PUNCT
ejpam-5395	151	21	σ2	σ2	PROPN
ejpam-5395	151	22	)	)	PUNCT
ejpam-5395	151	23	is	be	AUX
ejpam-5395	151	24	said	say	VERB
ejpam-5395	151	25	to	to	PART
ejpam-5395	151	26	be	be	AUX
ejpam-5395	151	27	weakly	weakly	ADJ
ejpam-5395	151	28	(	(	PUNCT
ejpam-5395	151	29	τ1	τ1	NOUN
ejpam-5395	151	30	,	,	PUNCT
ejpam-5395	151	31	τ2)continuous	τ2)continuous	ADJ
ejpam-5395	151	32	at	at	ADP
ejpam-5395	151	33	a	a	DET
ejpam-5395	151	34	point	point	NOUN
ejpam-5395	151	35	x	x	SYM
ejpam-5395	151	36	∈	∈	NOUN
ejpam-5395	151	37	x	x	PUNCT
ejpam-5395	151	38	if	if	SCONJ
ejpam-5395	151	39	for	for	ADP
ejpam-5395	151	40	each	each	DET
ejpam-5395	151	41	τ1τ2	τ1τ2	ADJ
ejpam-5395	151	42	-	-	ADJ
ejpam-5395	151	43	open	open	ADJ
ejpam-5395	151	44	set	set	VERB
ejpam-5395	151	45	v	v	NOUN
ejpam-5395	151	46	of	of	ADP
ejpam-5395	151	47	y	y	NOUN
ejpam-5395	151	48	containing	contain	VERB
ejpam-5395	151	49	f(x	f(x	PROPN
ejpam-5395	151	50	)	)	PUNCT
ejpam-5395	151	51	,	,	PUNCT
ejpam-5395	151	52	there	there	PRON
ejpam-5395	151	53	n.	n.	PROPN
ejpam-5395	151	54	srisarakham	srisarakham	PROPN
ejpam-5395	151	55	,	,	PUNCT
ejpam-5395	151	56	a.	a.	PROPN
ejpam-5395	151	57	sama	sama	PROPN
ejpam-5395	151	58	-	-	PUNCT
ejpam-5395	151	59	ae	ae	PROPN
ejpam-5395	151	60	,	,	PUNCT
ejpam-5395	151	61	c.	c.	PROPN
ejpam-5395	151	62	boonpok	boonpok	PROPN
ejpam-5395	151	63	/	/	SYM
ejpam-5395	151	64	eur	eur	PROPN
ejpam-5395	151	65	.	.	PUNCT
ejpam-5395	152	1	j.	j.	PROPN
ejpam-5395	152	2	pure	pure	PROPN
ejpam-5395	152	3	appl	appl	PROPN
ejpam-5395	152	4	.	.	PROPN
ejpam-5395	152	5	math	math	PROPN
ejpam-5395	152	6	,	,	PUNCT
ejpam-5395	152	7	17	17	NUM
ejpam-5395	152	8	(	(	PUNCT
ejpam-5395	152	9	4	4	NUM
ejpam-5395	152	10	)	)	PUNCT
ejpam-5395	152	11	(	(	PUNCT
ejpam-5395	152	12	2024	2024	NUM
ejpam-5395	152	13	)	)	PUNCT
ejpam-5395	152	14	,	,	PUNCT
ejpam-5395	152	15	2753	2753	NUM
ejpam-5395	152	16	-	-	SYM
ejpam-5395	152	17	2762	2762	NUM
ejpam-5395	152	18	2758	2758	NUM
ejpam-5395	152	19	exists	exist	VERB
ejpam-5395	152	20	a	a	DET
ejpam-5395	152	21	τ1τ2	τ1τ2	NOUN
ejpam-5395	152	22	-	-	ADJ
ejpam-5395	152	23	open	open	ADJ
ejpam-5395	152	24	set	set	ADJ
ejpam-5395	152	25	u	u	NOUN
ejpam-5395	152	26	of	of	ADP
ejpam-5395	152	27	x	x	PUNCT
ejpam-5395	152	28	containing	contain	VERB
ejpam-5395	152	29	x	x	PUNCT
ejpam-5395	152	30	such	such	ADJ
ejpam-5395	152	31	that	that	DET
ejpam-5395	152	32	f(u	f(u	PROPN
ejpam-5395	152	33	)	)	PUNCT
ejpam-5395	152	34	⊆	⊆	NUM
ejpam-5395	152	35	σ1σ2	σ1σ2	NOUN
ejpam-5395	152	36	-	-	NUM
ejpam-5395	152	37	cl(v	cl(v	NOUN
ejpam-5395	152	38	)	)	PUNCT
ejpam-5395	152	39	.	.	PUNCT
ejpam-5395	153	1	a	a	DET
ejpam-5395	153	2	function	function	NOUN
ejpam-5395	153	3	f	f	NOUN
ejpam-5395	153	4	:	:	PUNCT
ejpam-5395	153	5	(	(	PUNCT
ejpam-5395	153	6	x	x	NOUN
ejpam-5395	153	7	,	,	PUNCT
ejpam-5395	153	8	τ1	τ1	NOUN
ejpam-5395	153	9	,	,	PUNCT
ejpam-5395	153	10	τ2	τ2	NOUN
ejpam-5395	153	11	)	)	PUNCT
ejpam-5395	153	12	→	→	SYM
ejpam-5395	153	13	(	(	PUNCT
ejpam-5395	153	14	y	y	PROPN
ejpam-5395	153	15	,	,	PUNCT
ejpam-5395	153	16	σ1	σ1	PROPN
ejpam-5395	153	17	,	,	PUNCT
ejpam-5395	153	18	σ2	σ2	PROPN
ejpam-5395	153	19	)	)	PUNCT
ejpam-5395	153	20	is	be	AUX
ejpam-5395	153	21	said	say	VERB
ejpam-5395	153	22	to	to	PART
ejpam-5395	153	23	be	be	AUX
ejpam-5395	153	24	weakly	weakly	ADJ
ejpam-5395	153	25	(	(	PUNCT
ejpam-5395	153	26	τ1	τ1	NOUN
ejpam-5395	153	27	,	,	PUNCT
ejpam-5395	153	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	153	29	if	if	SCONJ
ejpam-5395	153	30	f	f	PROPN
ejpam-5395	153	31	has	have	VERB
ejpam-5395	153	32	this	this	DET
ejpam-5395	153	33	property	property	NOUN
ejpam-5395	153	34	at	at	ADP
ejpam-5395	153	35	each	each	DET
ejpam-5395	153	36	point	point	NOUN
ejpam-5395	153	37	of	of	ADP
ejpam-5395	153	38	x.	x.	NOUN
ejpam-5395	153	39	theorem	theorem	VERB
ejpam-5395	153	40	7	7	NUM
ejpam-5395	153	41	.	.	PUNCT
ejpam-5395	154	1	if	if	SCONJ
ejpam-5395	154	2	f	f	PROPN
ejpam-5395	154	3	:	:	PUNCT
ejpam-5395	154	4	(	(	PUNCT
ejpam-5395	154	5	x	x	NOUN
ejpam-5395	154	6	,	,	PUNCT
ejpam-5395	154	7	τ1	τ1	NOUN
ejpam-5395	154	8	,	,	PUNCT
ejpam-5395	154	9	τ2	τ2	NOUN
ejpam-5395	154	10	)	)	PUNCT
ejpam-5395	154	11	→	→	SYM
ejpam-5395	154	12	(	(	PUNCT
ejpam-5395	154	13	y	y	PROPN
ejpam-5395	154	14	,	,	PUNCT
ejpam-5395	154	15	σ1	σ1	PROPN
ejpam-5395	154	16	,	,	PUNCT
ejpam-5395	154	17	σ2	σ2	NOUN
ejpam-5395	154	18	)	)	PUNCT
ejpam-5395	154	19	is	be	AUX
ejpam-5395	154	20	weakly	weakly	ADJ
ejpam-5395	154	21	(	(	PUNCT
ejpam-5395	154	22	τ1	τ1	NOUN
ejpam-5395	154	23	,	,	PUNCT
ejpam-5395	154	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	154	25	,	,	PUNCT
ejpam-5395	154	26	then	then	ADV
ejpam-5395	154	27	f	f	PROPN
ejpam-5395	154	28	is	be	AUX
ejpam-5395	154	29	faintly	faintly	ADV
ejpam-5395	154	30	(	(	PUNCT
ejpam-5395	154	31	τ1	τ1	NOUN
ejpam-5395	154	32	,	,	PUNCT
ejpam-5395	154	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	154	34	.	.	PUNCT
ejpam-5395	155	1	proof	proof	NOUN
ejpam-5395	155	2	.	.	PUNCT
ejpam-5395	156	1	let	let	VERB
ejpam-5395	156	2	x	x	PUNCT
ejpam-5395	156	3	∈	∈	PROPN
ejpam-5395	156	4	x	x	X
ejpam-5395	156	5	and	and	CCONJ
ejpam-5395	156	6	v	v	X
ejpam-5395	156	7	be	be	AUX
ejpam-5395	156	8	any	any	DET
ejpam-5395	156	9	(	(	PUNCT
ejpam-5395	156	10	σ1	σ1	PROPN
ejpam-5395	156	11	,	,	PUNCT
ejpam-5395	156	12	σ2)θ	σ2)θ	NOUN
ejpam-5395	156	13	-	-	PUNCT
ejpam-5395	156	14	open	open	ADJ
ejpam-5395	156	15	set	set	NOUN
ejpam-5395	156	16	of	of	ADP
ejpam-5395	156	17	y	y	PROPN
ejpam-5395	156	18	containing	contain	VERB
ejpam-5395	156	19	f(x	f(x	PROPN
ejpam-5395	156	20	)	)	PUNCT
ejpam-5395	156	21	.	.	PUNCT
ejpam-5395	157	1	there	there	PRON
ejpam-5395	157	2	exists	exist	VERB
ejpam-5395	157	3	a	a	DET
ejpam-5395	157	4	σ1σ2	σ1σ2	NUM
ejpam-5395	157	5	-	-	ADJ
ejpam-5395	157	6	open	open	ADJ
ejpam-5395	157	7	set	set	NOUN
ejpam-5395	157	8	w	w	PROPN
ejpam-5395	157	9	of	of	ADP
ejpam-5395	157	10	y	y	PRON
ejpam-5395	157	11	such	such	ADJ
ejpam-5395	157	12	that	that	SCONJ
ejpam-5395	157	13	f(x	f(x	PROPN
ejpam-5395	157	14	)	)	PUNCT
ejpam-5395	157	15	∈	∈	PROPN
ejpam-5395	157	16	w	w	ADP
ejpam-5395	157	17	⊆	⊆	NUM
ejpam-5395	157	18	σ1σ2	σ1σ2	NOUN
ejpam-5395	157	19	-	-	PUNCT
ejpam-5395	157	20	cl(w	cl(w	NOUN
ejpam-5395	157	21	)	)	PUNCT
ejpam-5395	157	22	⊆	⊆	NUM
ejpam-5395	157	23	v	v	NOUN
ejpam-5395	157	24	.	.	PUNCT
ejpam-5395	158	1	since	since	SCONJ
ejpam-5395	158	2	f	f	PROPN
ejpam-5395	158	3	is	be	AUX
ejpam-5395	158	4	weakly	weakly	ADJ
ejpam-5395	158	5	(	(	PUNCT
ejpam-5395	158	6	τ1	τ1	NOUN
ejpam-5395	158	7	,	,	PUNCT
ejpam-5395	158	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	158	9	,	,	PUNCT
ejpam-5395	158	10	there	there	PRON
ejpam-5395	158	11	exists	exist	VERB
ejpam-5395	158	12	a	a	DET
ejpam-5395	158	13	τ1τ2	τ1τ2	NOUN
ejpam-5395	158	14	-	-	ADJ
ejpam-5395	158	15	open	open	ADJ
ejpam-5395	158	16	set	set	ADJ
ejpam-5395	158	17	u	u	NOUN
ejpam-5395	158	18	of	of	ADP
ejpam-5395	158	19	x	x	PUNCT
ejpam-5395	158	20	containing	contain	VERB
ejpam-5395	158	21	x	x	PUNCT
ejpam-5395	158	22	such	such	ADJ
ejpam-5395	158	23	that	that	DET
ejpam-5395	158	24	f(u	f(u	PROPN
ejpam-5395	158	25	)	)	PUNCT
ejpam-5395	159	1	⊆	⊆	NUM
ejpam-5395	159	2	σ1σ2	σ1σ2	NOUN
ejpam-5395	159	3	-	-	PUNCT
ejpam-5395	159	4	cl(w	cl(w	NOUN
ejpam-5395	159	5	)	)	PUNCT
ejpam-5395	159	6	⊆	⊆	NUM
ejpam-5395	159	7	v	v	NOUN
ejpam-5395	159	8	.	.	PUNCT
ejpam-5395	160	1	thus	thus	ADV
ejpam-5395	160	2	,	,	PUNCT
ejpam-5395	160	3	f	f	PROPN
ejpam-5395	160	4	is	be	AUX
ejpam-5395	160	5	faintly	faintly	ADV
ejpam-5395	160	6	(	(	PUNCT
ejpam-5395	160	7	τ1	τ1	NOUN
ejpam-5395	160	8	,	,	PUNCT
ejpam-5395	160	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	160	10	.	.	PUNCT
ejpam-5395	161	1	definition	definition	NOUN
ejpam-5395	161	2	6	6	NUM
ejpam-5395	161	3	.	.	PUNCT
ejpam-5395	162	1	[	[	X
ejpam-5395	162	2	13	13	NUM
ejpam-5395	162	3	]	]	PUNCT
ejpam-5395	162	4	a	a	DET
ejpam-5395	162	5	function	function	NOUN
ejpam-5395	162	6	f	f	NOUN
ejpam-5395	162	7	:	:	PUNCT
ejpam-5395	162	8	(	(	PUNCT
ejpam-5395	162	9	x	x	NOUN
ejpam-5395	162	10	,	,	PUNCT
ejpam-5395	162	11	τ1	τ1	NOUN
ejpam-5395	162	12	,	,	PUNCT
ejpam-5395	162	13	τ2	τ2	NOUN
ejpam-5395	162	14	)	)	PUNCT
ejpam-5395	162	15	→	→	SYM
ejpam-5395	162	16	(	(	PUNCT
ejpam-5395	162	17	y	y	PROPN
ejpam-5395	162	18	,	,	PUNCT
ejpam-5395	162	19	σ1	σ1	PROPN
ejpam-5395	162	20	,	,	PUNCT
ejpam-5395	162	21	σ2	σ2	PROPN
ejpam-5395	162	22	)	)	PUNCT
ejpam-5395	162	23	is	be	AUX
ejpam-5395	162	24	called	call	VERB
ejpam-5395	162	25	(	(	PUNCT
ejpam-5395	162	26	τ1	τ1	NOUN
ejpam-5395	162	27	,	,	PUNCT
ejpam-5395	162	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	162	29	at	at	ADP
ejpam-5395	162	30	a	a	DET
ejpam-5395	162	31	point	point	NOUN
ejpam-5395	162	32	x	x	SYM
ejpam-5395	162	33	∈	∈	NOUN
ejpam-5395	162	34	x	x	PUNCT
ejpam-5395	162	35	if	if	SCONJ
ejpam-5395	162	36	for	for	ADP
ejpam-5395	162	37	each	each	DET
ejpam-5395	162	38	σ1σ2	σ1σ2	VERB
ejpam-5395	162	39	-	-	ADJ
ejpam-5395	162	40	open	open	ADJ
ejpam-5395	162	41	set	set	NOUN
ejpam-5395	162	42	v	v	NOUN
ejpam-5395	162	43	of	of	ADP
ejpam-5395	162	44	y	y	NOUN
ejpam-5395	162	45	containing	contain	VERB
ejpam-5395	162	46	f(x	f(x	PROPN
ejpam-5395	162	47	)	)	PUNCT
ejpam-5395	162	48	,	,	PUNCT
ejpam-5395	162	49	there	there	PRON
ejpam-5395	162	50	exists	exist	VERB
ejpam-5395	162	51	a	a	DET
ejpam-5395	162	52	τ1τ2	τ1τ2	NOUN
ejpam-5395	162	53	-	-	ADJ
ejpam-5395	162	54	open	open	ADJ
ejpam-5395	162	55	set	set	ADJ
ejpam-5395	162	56	u	u	NOUN
ejpam-5395	162	57	of	of	ADP
ejpam-5395	162	58	x	x	PUNCT
ejpam-5395	162	59	containing	contain	VERB
ejpam-5395	162	60	x	x	PUNCT
ejpam-5395	162	61	such	such	ADJ
ejpam-5395	162	62	that	that	DET
ejpam-5395	162	63	f(u	f(u	PROPN
ejpam-5395	162	64	)	)	PUNCT
ejpam-5395	162	65	⊆	⊆	NUM
ejpam-5395	162	66	v	v	NOUN
ejpam-5395	162	67	.	.	PUNCT
ejpam-5395	163	1	a	a	DET
ejpam-5395	163	2	function	function	NOUN
ejpam-5395	163	3	f	f	NOUN
ejpam-5395	163	4	:	:	PUNCT
ejpam-5395	163	5	(	(	PUNCT
ejpam-5395	163	6	x	x	NOUN
ejpam-5395	163	7	,	,	PUNCT
ejpam-5395	163	8	τ1	τ1	NOUN
ejpam-5395	163	9	,	,	PUNCT
ejpam-5395	163	10	τ2	τ2	NOUN
ejpam-5395	163	11	)	)	PUNCT
ejpam-5395	163	12	→	→	SYM
ejpam-5395	163	13	(	(	PUNCT
ejpam-5395	163	14	y	y	PROPN
ejpam-5395	163	15	,	,	PUNCT
ejpam-5395	163	16	σ1	σ1	PROPN
ejpam-5395	163	17	,	,	PUNCT
ejpam-5395	163	18	σ2	σ2	PROPN
ejpam-5395	163	19	)	)	PUNCT
ejpam-5395	163	20	is	be	AUX
ejpam-5395	163	21	called	call	VERB
ejpam-5395	163	22	(	(	PUNCT
ejpam-5395	163	23	τ1	τ1	NOUN
ejpam-5395	163	24	,	,	PUNCT
ejpam-5395	163	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	163	26	if	if	SCONJ
ejpam-5395	163	27	f	f	PROPN
ejpam-5395	163	28	has	have	VERB
ejpam-5395	163	29	this	this	DET
ejpam-5395	163	30	property	property	NOUN
ejpam-5395	163	31	at	at	ADP
ejpam-5395	163	32	each	each	DET
ejpam-5395	163	33	point	point	NOUN
ejpam-5395	163	34	of	of	ADP
ejpam-5395	163	35	x.	x.	NOUN
ejpam-5395	163	36	recall	recall	VERB
ejpam-5395	163	37	that	that	SCONJ
ejpam-5395	163	38	a	a	DET
ejpam-5395	163	39	bitopological	bitopological	ADJ
ejpam-5395	163	40	space	space	NOUN
ejpam-5395	163	41	(	(	PUNCT
ejpam-5395	163	42	x	x	NOUN
ejpam-5395	163	43	,	,	PUNCT
ejpam-5395	163	44	τ1	τ1	NOUN
ejpam-5395	163	45	,	,	PUNCT
ejpam-5395	163	46	τ2	τ2	NOUN
ejpam-5395	163	47	)	)	PUNCT
ejpam-5395	163	48	is	be	AUX
ejpam-5395	163	49	said	say	VERB
ejpam-5395	163	50	to	to	PART
ejpam-5395	163	51	be	be	AUX
ejpam-5395	163	52	(	(	PUNCT
ejpam-5395	163	53	τ1	τ1	NOUN
ejpam-5395	163	54	,	,	PUNCT
ejpam-5395	163	55	τ2)-regular	τ2)-regular	ADJ
ejpam-5395	163	56	[	[	X
ejpam-5395	163	57	16	16	NUM
ejpam-5395	163	58	]	]	X
ejpam-5395	163	59	if	if	SCONJ
ejpam-5395	163	60	for	for	ADP
ejpam-5395	163	61	each	each	DET
ejpam-5395	163	62	τ1τ2	τ1τ2	ADJ
ejpam-5395	163	63	-	-	ADJ
ejpam-5395	163	64	closed	closed	ADJ
ejpam-5395	163	65	set	set	VERB
ejpam-5395	163	66	f	f	NOUN
ejpam-5395	163	67	and	and	CCONJ
ejpam-5395	163	68	each	each	DET
ejpam-5395	163	69	point	point	NOUN
ejpam-5395	163	70	x	x	X
ejpam-5395	163	71	∈	∈	NOUN
ejpam-5395	163	72	x	x	X
ejpam-5395	164	1	−	−	PROPN
ejpam-5395	164	2	f	f	NOUN
ejpam-5395	164	3	,	,	PUNCT
ejpam-5395	164	4	there	there	PRON
ejpam-5395	164	5	exist	exist	VERB
ejpam-5395	164	6	disjoint	disjoint	ADJ
ejpam-5395	164	7	τ1τ2	τ1τ2	ADJ
ejpam-5395	164	8	-	-	ADJ
ejpam-5395	164	9	open	open	ADJ
ejpam-5395	164	10	sets	set	NOUN
ejpam-5395	164	11	u	u	NOUN
ejpam-5395	164	12	and	and	CCONJ
ejpam-5395	164	13	v	v	ADP
ejpam-5395	164	14	such	such	ADJ
ejpam-5395	164	15	that	that	SCONJ
ejpam-5395	164	16	x	x	SYM
ejpam-5395	164	17	∈	∈	PROPN
ejpam-5395	164	18	u	u	NOUN
ejpam-5395	164	19	and	and	CCONJ
ejpam-5395	164	20	f	f	PROPN
ejpam-5395	164	21	⊆	⊆	NUM
ejpam-5395	164	22	v	v	NOUN
ejpam-5395	164	23	.	.	PUNCT
ejpam-5395	165	1	lemma	lemma	PROPN
ejpam-5395	165	2	3	3	X
ejpam-5395	165	3	.	.	PUNCT
ejpam-5395	166	1	[	[	X
ejpam-5395	166	2	13	13	NUM
ejpam-5395	166	3	]	]	PUNCT
ejpam-5395	166	4	for	for	ADP
ejpam-5395	166	5	a	a	DET
ejpam-5395	166	6	function	function	NOUN
ejpam-5395	166	7	(	(	PUNCT
ejpam-5395	166	8	x	x	NOUN
ejpam-5395	166	9	,	,	PUNCT
ejpam-5395	166	10	τ1	τ1	NOUN
ejpam-5395	166	11	,	,	PUNCT
ejpam-5395	166	12	τ2	τ2	NOUN
ejpam-5395	166	13	)	)	PUNCT
ejpam-5395	166	14	→	→	SYM
ejpam-5395	166	15	(	(	PUNCT
ejpam-5395	166	16	y	y	PROPN
ejpam-5395	166	17	,	,	PUNCT
ejpam-5395	166	18	σ1	σ1	PROPN
ejpam-5395	166	19	,	,	PUNCT
ejpam-5395	166	20	σ2	σ2	NOUN
ejpam-5395	166	21	)	)	PUNCT
ejpam-5395	166	22	,	,	PUNCT
ejpam-5395	166	23	the	the	DET
ejpam-5395	166	24	following	follow	VERB
ejpam-5395	166	25	properties	property	NOUN
ejpam-5395	166	26	are	be	AUX
ejpam-5395	166	27	equivalent	equivalent	ADJ
ejpam-5395	166	28	:	:	PUNCT
ejpam-5395	166	29	(	(	PUNCT
ejpam-5395	166	30	1	1	X
ejpam-5395	166	31	)	)	PUNCT
ejpam-5395	166	32	f	f	PROPN
ejpam-5395	166	33	is	be	AUX
ejpam-5395	166	34	(	(	PUNCT
ejpam-5395	166	35	τ1	τ1	NOUN
ejpam-5395	166	36	,	,	PUNCT
ejpam-5395	166	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	166	38	;	;	PUNCT
ejpam-5395	166	39	(	(	PUNCT
ejpam-5395	166	40	2	2	X
ejpam-5395	166	41	)	)	PUNCT
ejpam-5395	166	42	f−1(v	f−1(v	NOUN
ejpam-5395	166	43	)	)	PUNCT
ejpam-5395	166	44	is	be	AUX
ejpam-5395	166	45	τ1τ2	τ1τ2	NOUN
ejpam-5395	166	46	-	-	ADJ
ejpam-5395	166	47	open	open	ADJ
ejpam-5395	166	48	in	in	ADP
ejpam-5395	166	49	x	x	PUNCT
ejpam-5395	166	50	for	for	ADP
ejpam-5395	166	51	every	every	DET
ejpam-5395	166	52	σ1σ2	σ1σ2	NOUN
ejpam-5395	166	53	-	-	ADJ
ejpam-5395	166	54	open	open	ADJ
ejpam-5395	166	55	set	set	NOUN
ejpam-5395	166	56	v	v	NOUN
ejpam-5395	166	57	of	of	ADP
ejpam-5395	166	58	y	y	PROPN
ejpam-5395	166	59	;	;	PUNCT
ejpam-5395	166	60	(	(	PUNCT
ejpam-5395	166	61	3	3	X
ejpam-5395	166	62	)	)	PUNCT
ejpam-5395	166	63	f(τ1τ2	f(τ1τ2	NOUN
ejpam-5395	166	64	-	-	PUNCT
ejpam-5395	166	65	cl(a	cl(a	NUM
ejpam-5395	166	66	)	)	PUNCT
ejpam-5395	166	67	)	)	PUNCT
ejpam-5395	167	1	⊆	⊆	X
ejpam-5395	167	2	σ1σ2	σ1σ2	NUM
ejpam-5395	167	3	-	-	PUNCT
ejpam-5395	167	4	cl(f(a	cl(f(a	NOUN
ejpam-5395	167	5	)	)	PUNCT
ejpam-5395	167	6	)	)	PUNCT
ejpam-5395	167	7	for	for	ADP
ejpam-5395	167	8	every	every	DET
ejpam-5395	167	9	subset	subset	NOUN
ejpam-5395	167	10	a	a	PRON
ejpam-5395	167	11	of	of	ADP
ejpam-5395	167	12	x	x	PRON
ejpam-5395	167	13	;	;	PUNCT
ejpam-5395	167	14	(	(	PUNCT
ejpam-5395	167	15	4	4	X
ejpam-5395	167	16	)	)	PUNCT
ejpam-5395	167	17	τ1τ2	τ1τ2	NOUN
ejpam-5395	167	18	-	-	NOUN
ejpam-5395	167	19	cl(f	cl(f	NOUN
ejpam-5395	167	20	−1(b	−1(b	NOUN
ejpam-5395	167	21	)	)	PUNCT
ejpam-5395	167	22	)	)	PUNCT
ejpam-5395	168	1	⊆	⊆	NUM
ejpam-5395	168	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5395	168	3	-	-	PUNCT
ejpam-5395	168	4	cl(b	cl(b	NOUN
ejpam-5395	168	5	)	)	PUNCT
ejpam-5395	168	6	)	)	PUNCT
ejpam-5395	168	7	for	for	ADP
ejpam-5395	168	8	every	every	DET
ejpam-5395	168	9	subset	subset	NOUN
ejpam-5395	168	10	b	b	PROPN
ejpam-5395	168	11	of	of	ADP
ejpam-5395	168	12	y	y	PROPN
ejpam-5395	168	13	;	;	PUNCT
ejpam-5395	168	14	(	(	PUNCT
ejpam-5395	168	15	5	5	X
ejpam-5395	168	16	)	)	PUNCT
ejpam-5395	168	17	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-5395	168	18	-	-	PUNCT
ejpam-5395	168	19	int(b	int(b	NOUN
ejpam-5395	168	20	)	)	PUNCT
ejpam-5395	168	21	)	)	PUNCT
ejpam-5395	169	1	⊆	⊆	X
ejpam-5395	169	2	τ1τ2	τ1τ2	NOUN
ejpam-5395	169	3	-	-	NUM
ejpam-5395	169	4	int(f	int(f	NOUN
ejpam-5395	169	5	−1(b	−1(b	NOUN
ejpam-5395	169	6	)	)	PUNCT
ejpam-5395	169	7	)	)	PUNCT
ejpam-5395	169	8	for	for	ADP
ejpam-5395	169	9	every	every	DET
ejpam-5395	169	10	subset	subset	NOUN
ejpam-5395	169	11	b	b	PROPN
ejpam-5395	169	12	of	of	ADP
ejpam-5395	169	13	y	y	PROPN
ejpam-5395	169	14	;	;	PUNCT
ejpam-5395	169	15	(	(	PUNCT
ejpam-5395	169	16	6	6	X
ejpam-5395	169	17	)	)	PUNCT
ejpam-5395	169	18	f−1(k	f−1(k	PROPN
ejpam-5395	169	19	)	)	PUNCT
ejpam-5395	169	20	is	be	AUX
ejpam-5395	169	21	τ1τ2	τ1τ2	NOUN
ejpam-5395	169	22	-	-	ADJ
ejpam-5395	169	23	closed	closed	ADJ
ejpam-5395	169	24	in	in	ADP
ejpam-5395	169	25	x	x	PUNCT
ejpam-5395	169	26	for	for	ADP
ejpam-5395	169	27	every	every	DET
ejpam-5395	169	28	σ1σ2	σ1σ2	NUM
ejpam-5395	169	29	-	-	PUNCT
ejpam-5395	169	30	closed	closed	ADJ
ejpam-5395	169	31	set	set	NOUN
ejpam-5395	169	32	k	k	PROPN
ejpam-5395	169	33	of	of	ADP
ejpam-5395	169	34	y	y	PROPN
ejpam-5395	169	35	.	.	PUNCT
ejpam-5395	170	1	theorem	theorem	VERB
ejpam-5395	170	2	8	8	NUM
ejpam-5395	170	3	.	.	PUNCT
ejpam-5395	171	1	if	if	SCONJ
ejpam-5395	171	2	f	f	PROPN
ejpam-5395	171	3	:	:	PUNCT
ejpam-5395	171	4	(	(	PUNCT
ejpam-5395	171	5	x	x	NOUN
ejpam-5395	171	6	,	,	PUNCT
ejpam-5395	171	7	τ1	τ1	NOUN
ejpam-5395	171	8	,	,	PUNCT
ejpam-5395	171	9	τ2	τ2	NOUN
ejpam-5395	171	10	)	)	PUNCT
ejpam-5395	171	11	→	→	SYM
ejpam-5395	171	12	(	(	PUNCT
ejpam-5395	171	13	y	y	PROPN
ejpam-5395	171	14	,	,	PUNCT
ejpam-5395	171	15	σ1	σ1	PROPN
ejpam-5395	171	16	,	,	PUNCT
ejpam-5395	171	17	σ2	σ2	PROPN
ejpam-5395	171	18	)	)	PUNCT
ejpam-5395	171	19	is	be	AUX
ejpam-5395	171	20	faintly	faintly	ADV
ejpam-5395	171	21	(	(	PUNCT
ejpam-5395	171	22	τ1	τ1	NOUN
ejpam-5395	171	23	,	,	PUNCT
ejpam-5395	171	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	171	25	and	and	CCONJ
ejpam-5395	171	26	(	(	PUNCT
ejpam-5395	171	27	y	y	PROPN
ejpam-5395	171	28	,	,	PUNCT
ejpam-5395	171	29	σ1	σ1	PROPN
ejpam-5395	171	30	,	,	PUNCT
ejpam-5395	171	31	σ2	σ2	PROPN
ejpam-5395	171	32	)	)	PUNCT
ejpam-5395	171	33	is	be	AUX
ejpam-5395	171	34	a	a	DET
ejpam-5395	171	35	(	(	PUNCT
ejpam-5395	171	36	σ1	σ1	NOUN
ejpam-5395	171	37	,	,	PUNCT
ejpam-5395	171	38	σ2)-regular	σ2)-regular	ADJ
ejpam-5395	171	39	space	space	NOUN
ejpam-5395	171	40	,	,	PUNCT
ejpam-5395	171	41	then	then	ADV
ejpam-5395	171	42	f	f	PROPN
ejpam-5395	171	43	is	be	AUX
ejpam-5395	171	44	(	(	PUNCT
ejpam-5395	171	45	τ1	τ1	NOUN
ejpam-5395	171	46	,	,	PUNCT
ejpam-5395	171	47	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	171	48	.	.	PUNCT
ejpam-5395	172	1	proof	proof	NOUN
ejpam-5395	172	2	.	.	PUNCT
ejpam-5395	173	1	let	let	VERB
ejpam-5395	173	2	v	v	PART
ejpam-5395	173	3	be	be	AUX
ejpam-5395	173	4	any	any	DET
ejpam-5395	173	5	σ1σ2	σ1σ2	NOUN
ejpam-5395	173	6	-	-	ADJ
ejpam-5395	173	7	open	open	ADJ
ejpam-5395	173	8	set	set	NOUN
ejpam-5395	173	9	of	of	ADP
ejpam-5395	173	10	y	y	PROPN
ejpam-5395	173	11	.	.	PUNCT
ejpam-5395	174	1	since	since	SCONJ
ejpam-5395	174	2	(	(	PUNCT
ejpam-5395	174	3	y	y	PROPN
ejpam-5395	174	4	,	,	PUNCT
ejpam-5395	174	5	σ1	σ1	PROPN
ejpam-5395	174	6	,	,	PUNCT
ejpam-5395	174	7	σ2	σ2	PROPN
ejpam-5395	174	8	)	)	PUNCT
ejpam-5395	174	9	is	be	AUX
ejpam-5395	174	10	a	a	DET
ejpam-5395	174	11	(	(	PUNCT
ejpam-5395	174	12	σ1	σ1	NOUN
ejpam-5395	174	13	,	,	PUNCT
ejpam-5395	174	14	σ2)-regular	σ2)-regular	ADJ
ejpam-5395	174	15	space	space	NOUN
ejpam-5395	174	16	,	,	PUNCT
ejpam-5395	174	17	v	v	NOUN
ejpam-5395	174	18	is	be	AUX
ejpam-5395	174	19	(	(	PUNCT
ejpam-5395	174	20	σ1	σ1	PROPN
ejpam-5395	174	21	,	,	PUNCT
ejpam-5395	174	22	σ2)θ	σ2)θ	NOUN
ejpam-5395	174	23	-	-	PUNCT
ejpam-5395	174	24	open	open	ADJ
ejpam-5395	174	25	in	in	ADP
ejpam-5395	174	26	y	y	PROPN
ejpam-5395	174	27	.	.	PUNCT
ejpam-5395	175	1	since	since	SCONJ
ejpam-5395	175	2	f	f	PROPN
ejpam-5395	175	3	is	be	AUX
ejpam-5395	175	4	faintly	faintly	ADV
ejpam-5395	175	5	(	(	PUNCT
ejpam-5395	175	6	τ1	τ1	NOUN
ejpam-5395	175	7	,	,	PUNCT
ejpam-5395	175	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	175	9	,	,	PUNCT
ejpam-5395	175	10	by	by	ADP
ejpam-5395	175	11	lemma	lemma	PROPN
ejpam-5395	175	12	2	2	NUM
ejpam-5395	175	13	we	we	PRON
ejpam-5395	175	14	have	have	VERB
ejpam-5395	175	15	f−1(v	f−1(v	PROPN
ejpam-5395	175	16	)	)	PUNCT
ejpam-5395	175	17	is	be	AUX
ejpam-5395	175	18	τ1τ2	τ1τ2	NOUN
ejpam-5395	175	19	-	-	ADJ
ejpam-5395	175	20	open	open	ADJ
ejpam-5395	175	21	in	in	ADP
ejpam-5395	175	22	x	x	PUNCT
ejpam-5395	175	23	and	and	CCONJ
ejpam-5395	175	24	hence	hence	ADV
ejpam-5395	175	25	by	by	ADP
ejpam-5395	175	26	lemma	lemma	PROPN
ejpam-5395	175	27	3	3	NUM
ejpam-5395	175	28	,	,	PUNCT
ejpam-5395	175	29	f	f	PROPN
ejpam-5395	175	30	is	be	AUX
ejpam-5395	175	31	(	(	PUNCT
ejpam-5395	175	32	τ1	τ1	NOUN
ejpam-5395	175	33	,	,	PUNCT
ejpam-5395	175	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	175	35	.	.	PUNCT
ejpam-5395	176	1	definition	definition	NOUN
ejpam-5395	176	2	7	7	NUM
ejpam-5395	176	3	.	.	PUNCT
ejpam-5395	177	1	[	[	X
ejpam-5395	177	2	11	11	NUM
ejpam-5395	177	3	]	]	PUNCT
ejpam-5395	177	4	a	a	DET
ejpam-5395	177	5	function	function	NOUN
ejpam-5395	177	6	f	f	NOUN
ejpam-5395	177	7	:	:	PUNCT
ejpam-5395	177	8	(	(	PUNCT
ejpam-5395	177	9	x	x	NOUN
ejpam-5395	177	10	,	,	PUNCT
ejpam-5395	177	11	τ1	τ1	NOUN
ejpam-5395	177	12	,	,	PUNCT
ejpam-5395	177	13	τ2	τ2	NOUN
ejpam-5395	177	14	)	)	PUNCT
ejpam-5395	177	15	→	→	SYM
ejpam-5395	177	16	(	(	PUNCT
ejpam-5395	177	17	y	y	PROPN
ejpam-5395	177	18	,	,	PUNCT
ejpam-5395	177	19	σ1	σ1	PROPN
ejpam-5395	177	20	,	,	PUNCT
ejpam-5395	177	21	σ2	σ2	PROPN
ejpam-5395	177	22	)	)	PUNCT
ejpam-5395	177	23	is	be	AUX
ejpam-5395	177	24	said	say	VERB
ejpam-5395	177	25	to	to	PART
ejpam-5395	177	26	be	be	AUX
ejpam-5395	177	27	almost	almost	ADV
ejpam-5395	177	28	(	(	PUNCT
ejpam-5395	177	29	τ1	τ1	NOUN
ejpam-5395	177	30	,	,	PUNCT
ejpam-5395	177	31	τ2)continuous	τ2)continuous	ADJ
ejpam-5395	177	32	at	at	ADP
ejpam-5395	177	33	a	a	DET
ejpam-5395	177	34	point	point	NOUN
ejpam-5395	177	35	x	x	SYM
ejpam-5395	177	36	∈	∈	NOUN
ejpam-5395	177	37	x	x	PUNCT
ejpam-5395	177	38	if	if	SCONJ
ejpam-5395	177	39	for	for	ADP
ejpam-5395	177	40	each	each	DET
ejpam-5395	177	41	σ1σ2	σ1σ2	VERB
ejpam-5395	177	42	-	-	ADJ
ejpam-5395	177	43	open	open	ADJ
ejpam-5395	177	44	set	set	NOUN
ejpam-5395	177	45	v	v	NOUN
ejpam-5395	177	46	of	of	ADP
ejpam-5395	177	47	y	y	NOUN
ejpam-5395	177	48	containing	contain	VERB
ejpam-5395	177	49	f(x	f(x	PROPN
ejpam-5395	177	50	)	)	PUNCT
ejpam-5395	177	51	,	,	PUNCT
ejpam-5395	177	52	there	there	PRON
ejpam-5395	177	53	exists	exist	VERB
ejpam-5395	177	54	a	a	DET
ejpam-5395	177	55	τ1τ2	τ1τ2	NOUN
ejpam-5395	177	56	-	-	ADJ
ejpam-5395	177	57	open	open	ADJ
ejpam-5395	177	58	set	set	ADJ
ejpam-5395	177	59	u	u	NOUN
ejpam-5395	177	60	of	of	ADP
ejpam-5395	177	61	x	x	PUNCT
ejpam-5395	177	62	containing	contain	VERB
ejpam-5395	177	63	x	x	PUNCT
ejpam-5395	177	64	such	such	ADJ
ejpam-5395	177	65	that	that	DET
ejpam-5395	177	66	f(u	f(u	PROPN
ejpam-5395	177	67	)	)	PUNCT
ejpam-5395	177	68	⊆	⊆	NUM
ejpam-5395	177	69	σ1σ2	σ1σ2	X
ejpam-5395	177	70	-	-	PUNCT
ejpam-5395	177	71	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5395	177	72	-	-	PUNCT
ejpam-5395	177	73	cl(v	cl(v	NOUN
ejpam-5395	177	74	)	)	PUNCT
ejpam-5395	177	75	)	)	PUNCT
ejpam-5395	177	76	.	.	PUNCT
ejpam-5395	178	1	a	a	DET
ejpam-5395	178	2	function	function	NOUN
ejpam-5395	178	3	f	f	NOUN
ejpam-5395	178	4	:	:	PUNCT
ejpam-5395	178	5	(	(	PUNCT
ejpam-5395	178	6	x	x	NOUN
ejpam-5395	178	7	,	,	PUNCT
ejpam-5395	178	8	τ1	τ1	NOUN
ejpam-5395	178	9	,	,	PUNCT
ejpam-5395	178	10	τ2	τ2	NOUN
ejpam-5395	178	11	)	)	PUNCT
ejpam-5395	178	12	→	→	SYM
ejpam-5395	178	13	(	(	PUNCT
ejpam-5395	178	14	y	y	PROPN
ejpam-5395	178	15	,	,	PUNCT
ejpam-5395	178	16	σ1	σ1	PROPN
ejpam-5395	178	17	,	,	PUNCT
ejpam-5395	178	18	σ2	σ2	PROPN
ejpam-5395	178	19	)	)	PUNCT
ejpam-5395	178	20	is	be	AUX
ejpam-5395	178	21	said	say	VERB
ejpam-5395	178	22	to	to	PART
ejpam-5395	178	23	be	be	AUX
ejpam-5395	178	24	almost	almost	ADV
ejpam-5395	178	25	(	(	PUNCT
ejpam-5395	178	26	τ1	τ1	NOUN
ejpam-5395	178	27	,	,	PUNCT
ejpam-5395	178	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	178	29	if	if	SCONJ
ejpam-5395	178	30	f	f	PROPN
ejpam-5395	178	31	has	have	VERB
ejpam-5395	178	32	this	this	DET
ejpam-5395	178	33	property	property	NOUN
ejpam-5395	178	34	at	at	ADP
ejpam-5395	178	35	each	each	DET
ejpam-5395	178	36	point	point	NOUN
ejpam-5395	178	37	of	of	ADP
ejpam-5395	178	38	x.	x.	NOUN
ejpam-5395	178	39	references	reference	NOUN
ejpam-5395	178	40	2759	2759	NUM
ejpam-5395	178	41	lemma	lemma	PROPN
ejpam-5395	178	42	4	4	NUM
ejpam-5395	178	43	.	.	PUNCT
ejpam-5395	179	1	[	[	X
ejpam-5395	179	2	11	11	NUM
ejpam-5395	179	3	]	]	PUNCT
ejpam-5395	179	4	for	for	ADP
ejpam-5395	179	5	a	a	DET
ejpam-5395	179	6	function	function	NOUN
ejpam-5395	179	7	(	(	PUNCT
ejpam-5395	179	8	x	x	NOUN
ejpam-5395	179	9	,	,	PUNCT
ejpam-5395	179	10	τ1	τ1	NOUN
ejpam-5395	179	11	,	,	PUNCT
ejpam-5395	179	12	τ2	τ2	NOUN
ejpam-5395	179	13	)	)	PUNCT
ejpam-5395	179	14	→	→	SYM
ejpam-5395	179	15	(	(	PUNCT
ejpam-5395	179	16	y	y	PROPN
ejpam-5395	179	17	,	,	PUNCT
ejpam-5395	179	18	σ1	σ1	PROPN
ejpam-5395	179	19	,	,	PUNCT
ejpam-5395	179	20	σ2	σ2	NOUN
ejpam-5395	179	21	)	)	PUNCT
ejpam-5395	179	22	,	,	PUNCT
ejpam-5395	179	23	the	the	DET
ejpam-5395	179	24	following	follow	VERB
ejpam-5395	179	25	properties	property	NOUN
ejpam-5395	179	26	are	be	AUX
ejpam-5395	179	27	equivalent	equivalent	ADJ
ejpam-5395	179	28	:	:	PUNCT
ejpam-5395	179	29	(	(	PUNCT
ejpam-5395	179	30	1	1	X
ejpam-5395	179	31	)	)	PUNCT
ejpam-5395	179	32	f	f	NOUN
ejpam-5395	179	33	is	be	AUX
ejpam-5395	179	34	almost	almost	ADV
ejpam-5395	179	35	(	(	PUNCT
ejpam-5395	179	36	τ1	τ1	NOUN
ejpam-5395	179	37	,	,	PUNCT
ejpam-5395	179	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	179	39	at	at	ADP
ejpam-5395	179	40	x	x	X
ejpam-5395	179	41	∈	∈	PROPN
ejpam-5395	179	42	x	x	X
ejpam-5395	179	43	;	;	PUNCT
ejpam-5395	179	44	(	(	PUNCT
ejpam-5395	179	45	2	2	X
ejpam-5395	179	46	)	)	PUNCT
ejpam-5395	179	47	x	x	SYM
ejpam-5395	179	48	∈	∈	PRON
ejpam-5395	179	49	τ1τ2	τ1τ2	PUNCT
ejpam-5395	179	50	-	-	NUM
ejpam-5395	179	51	int(f	int(f	VERB
ejpam-5395	179	52	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-5395	179	53	-	-	PUNCT
ejpam-5395	179	54	int(σ1σ2	int(σ1σ2	NOUN
ejpam-5395	179	55	-	-	PUNCT
ejpam-5395	179	56	cl(v	cl(v	NOUN
ejpam-5395	179	57	)	)	PUNCT
ejpam-5395	179	58	)	)	PUNCT
ejpam-5395	179	59	)	)	PUNCT
ejpam-5395	179	60	)	)	PUNCT
ejpam-5395	180	1	for	for	ADP
ejpam-5395	180	2	every	every	DET
ejpam-5395	180	3	σ1σ2	σ1σ2	NOUN
ejpam-5395	180	4	-	-	ADJ
ejpam-5395	180	5	open	open	ADJ
ejpam-5395	180	6	set	set	NOUN
ejpam-5395	180	7	v	v	NOUN
ejpam-5395	180	8	of	of	ADP
ejpam-5395	180	9	y	y	NOUN
ejpam-5395	180	10	containing	contain	VERB
ejpam-5395	180	11	f(x	f(x	PROPN
ejpam-5395	180	12	)	)	PUNCT
ejpam-5395	180	13	;	;	PUNCT
ejpam-5395	180	14	(	(	PUNCT
ejpam-5395	180	15	3	3	X
ejpam-5395	180	16	)	)	PUNCT
ejpam-5395	180	17	x	x	SYM
ejpam-5395	180	18	∈	∈	PRON
ejpam-5395	180	19	τ1τ2	τ1τ2	NOUN
ejpam-5395	180	20	-	-	NUM
ejpam-5395	180	21	int(f	int(f	X
ejpam-5395	180	22	−1(v	−1(v	NOUN
ejpam-5395	180	23	)	)	PUNCT
ejpam-5395	180	24	)	)	PUNCT
ejpam-5395	180	25	for	for	ADP
ejpam-5395	180	26	every	every	DET
ejpam-5395	180	27	(	(	PUNCT
ejpam-5395	180	28	σ1	σ1	PROPN
ejpam-5395	180	29	,	,	PUNCT
ejpam-5395	180	30	σ2)r	σ2)r	NOUN
ejpam-5395	180	31	-	-	PUNCT
ejpam-5395	180	32	open	open	ADJ
ejpam-5395	180	33	set	set	VERB
ejpam-5395	180	34	v	v	NOUN
ejpam-5395	180	35	of	of	ADP
ejpam-5395	180	36	y	y	NOUN
ejpam-5395	180	37	containing	contain	VERB
ejpam-5395	180	38	f(x	f(x	PROPN
ejpam-5395	180	39	)	)	PUNCT
ejpam-5395	180	40	;	;	PUNCT
ejpam-5395	180	41	(	(	PUNCT
ejpam-5395	180	42	4	4	X
ejpam-5395	180	43	)	)	PUNCT
ejpam-5395	180	44	for	for	ADP
ejpam-5395	180	45	each	each	DET
ejpam-5395	180	46	(	(	PUNCT
ejpam-5395	180	47	σ1	σ1	PROPN
ejpam-5395	180	48	,	,	PUNCT
ejpam-5395	180	49	σ2)r	σ2)r	NOUN
ejpam-5395	180	50	-	-	PUNCT
ejpam-5395	180	51	open	open	ADJ
ejpam-5395	180	52	set	set	VERB
ejpam-5395	180	53	v	v	NOUN
ejpam-5395	180	54	of	of	ADP
ejpam-5395	180	55	y	y	NOUN
ejpam-5395	180	56	containing	contain	VERB
ejpam-5395	180	57	f(x	f(x	PROPN
ejpam-5395	180	58	)	)	PUNCT
ejpam-5395	180	59	,	,	PUNCT
ejpam-5395	180	60	there	there	PRON
ejpam-5395	180	61	exists	exist	VERB
ejpam-5395	180	62	a	a	DET
ejpam-5395	180	63	τ1τ2	τ1τ2	NOUN
ejpam-5395	180	64	-	-	ADJ
ejpam-5395	180	65	open	open	ADJ
ejpam-5395	180	66	set	set	ADJ
ejpam-5395	180	67	u	u	NOUN
ejpam-5395	180	68	of	of	ADP
ejpam-5395	180	69	x	x	PUNCT
ejpam-5395	180	70	containing	contain	VERB
ejpam-5395	180	71	x	x	PUNCT
ejpam-5395	180	72	such	such	ADJ
ejpam-5395	180	73	that	that	DET
ejpam-5395	180	74	f(u	f(u	PROPN
ejpam-5395	180	75	)	)	PUNCT
ejpam-5395	180	76	⊆	⊆	NUM
ejpam-5395	180	77	v	v	NOUN
ejpam-5395	180	78	.	.	PUNCT
ejpam-5395	181	1	recall	recall	VERB
ejpam-5395	181	2	that	that	SCONJ
ejpam-5395	181	3	a	a	DET
ejpam-5395	181	4	bitopological	bitopological	ADJ
ejpam-5395	181	5	space	space	NOUN
ejpam-5395	181	6	(	(	PUNCT
ejpam-5395	181	7	x	x	NOUN
ejpam-5395	181	8	,	,	PUNCT
ejpam-5395	181	9	τ1	τ1	NOUN
ejpam-5395	181	10	,	,	PUNCT
ejpam-5395	181	11	τ2	τ2	NOUN
ejpam-5395	181	12	)	)	PUNCT
ejpam-5395	181	13	is	be	AUX
ejpam-5395	181	14	said	say	VERB
ejpam-5395	181	15	to	to	PART
ejpam-5395	181	16	be	be	AUX
ejpam-5395	181	17	almost	almost	ADV
ejpam-5395	181	18	(	(	PUNCT
ejpam-5395	181	19	τ1	τ1	NOUN
ejpam-5395	181	20	,	,	PUNCT
ejpam-5395	182	1	τ2)-regular	τ2)-regular	ADJ
ejpam-5395	182	2	[	[	X
ejpam-5395	182	3	18	18	NUM
ejpam-5395	182	4	]	]	X
ejpam-5395	182	5	if	if	SCONJ
ejpam-5395	182	6	for	for	ADP
ejpam-5395	182	7	each	each	DET
ejpam-5395	182	8	(	(	PUNCT
ejpam-5395	182	9	τ1	τ1	NOUN
ejpam-5395	182	10	,	,	PUNCT
ejpam-5395	182	11	τ2)r	τ2)r	NOUN
ejpam-5395	182	12	-	-	PUNCT
ejpam-5395	182	13	closed	close	VERB
ejpam-5395	182	14	set	set	VERB
ejpam-5395	182	15	f	f	NOUN
ejpam-5395	182	16	and	and	CCONJ
ejpam-5395	182	17	each	each	DET
ejpam-5395	182	18	x	x	PROPN
ejpam-5395	182	19	̸∈	̸∈	PROPN
ejpam-5395	182	20	f	f	PROPN
ejpam-5395	182	21	,	,	PUNCT
ejpam-5395	182	22	there	there	PRON
ejpam-5395	182	23	exist	exist	VERB
ejpam-5395	182	24	disjoint	disjoint	ADJ
ejpam-5395	182	25	τ1τ2	τ1τ2	ADJ
ejpam-5395	182	26	-	-	ADJ
ejpam-5395	182	27	open	open	ADJ
ejpam-5395	182	28	sets	set	NOUN
ejpam-5395	182	29	u	u	NOUN
ejpam-5395	182	30	and	and	CCONJ
ejpam-5395	182	31	v	v	ADP
ejpam-5395	182	32	such	such	ADJ
ejpam-5395	182	33	that	that	SCONJ
ejpam-5395	182	34	x	x	SYM
ejpam-5395	182	35	∈	∈	PROPN
ejpam-5395	182	36	u	u	NOUN
ejpam-5395	182	37	and	and	CCONJ
ejpam-5395	182	38	f	f	PROPN
ejpam-5395	182	39	⊆	⊆	NUM
ejpam-5395	182	40	v	v	NOUN
ejpam-5395	182	41	.	.	PUNCT
ejpam-5395	183	1	lemma	lemma	PROPN
ejpam-5395	183	2	5	5	X
ejpam-5395	183	3	.	.	PUNCT
ejpam-5395	184	1	let	let	AUX
ejpam-5395	184	2	(	(	PUNCT
ejpam-5395	184	3	x	x	NOUN
ejpam-5395	184	4	,	,	PUNCT
ejpam-5395	184	5	τ1	τ1	NOUN
ejpam-5395	184	6	,	,	PUNCT
ejpam-5395	184	7	τ2	τ2	PROPN
ejpam-5395	184	8	)	)	PUNCT
ejpam-5395	184	9	be	be	VERB
ejpam-5395	184	10	an	an	DET
ejpam-5395	184	11	almost	almost	ADV
ejpam-5395	184	12	(	(	PUNCT
ejpam-5395	184	13	τ1	τ1	NOUN
ejpam-5395	184	14	,	,	PUNCT
ejpam-5395	184	15	τ2)-regular	τ2)-regular	ADJ
ejpam-5395	184	16	space	space	NOUN
ejpam-5395	184	17	.	.	PUNCT
ejpam-5395	185	1	then	then	ADV
ejpam-5395	185	2	,	,	PUNCT
ejpam-5395	185	3	every	every	DET
ejpam-5395	185	4	(	(	PUNCT
ejpam-5395	185	5	τ1	τ1	NOUN
ejpam-5395	185	6	,	,	PUNCT
ejpam-5395	185	7	τ2)r	τ2)r	ADJ
ejpam-5395	185	8	-	-	PUNCT
ejpam-5395	185	9	open	open	ADJ
ejpam-5395	185	10	set	set	NOUN
ejpam-5395	185	11	is	be	AUX
ejpam-5395	185	12	(	(	PUNCT
ejpam-5395	185	13	τ1	τ1	NOUN
ejpam-5395	185	14	,	,	PUNCT
ejpam-5395	185	15	τ2)θ	τ2)θ	ADJ
ejpam-5395	185	16	-	-	PUNCT
ejpam-5395	185	17	open	open	ADJ
ejpam-5395	185	18	.	.	PUNCT
ejpam-5395	186	1	theorem	theorem	NOUN
ejpam-5395	186	2	9	9	NUM
ejpam-5395	186	3	.	.	PUNCT
ejpam-5395	187	1	if	if	SCONJ
ejpam-5395	187	2	f	f	PROPN
ejpam-5395	187	3	:	:	PUNCT
ejpam-5395	187	4	(	(	PUNCT
ejpam-5395	187	5	x	x	NOUN
ejpam-5395	187	6	,	,	PUNCT
ejpam-5395	187	7	τ1	τ1	NOUN
ejpam-5395	187	8	,	,	PUNCT
ejpam-5395	187	9	τ2	τ2	NOUN
ejpam-5395	187	10	)	)	PUNCT
ejpam-5395	187	11	→	→	SYM
ejpam-5395	187	12	(	(	PUNCT
ejpam-5395	187	13	y	y	PROPN
ejpam-5395	187	14	,	,	PUNCT
ejpam-5395	187	15	σ1	σ1	PROPN
ejpam-5395	187	16	,	,	PUNCT
ejpam-5395	187	17	σ2	σ2	PROPN
ejpam-5395	187	18	)	)	PUNCT
ejpam-5395	187	19	is	be	AUX
ejpam-5395	187	20	faintly	faintly	ADV
ejpam-5395	187	21	(	(	PUNCT
ejpam-5395	187	22	τ1	τ1	NOUN
ejpam-5395	187	23	,	,	PUNCT
ejpam-5395	187	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	187	25	and	and	CCONJ
ejpam-5395	187	26	(	(	PUNCT
ejpam-5395	187	27	y	y	PROPN
ejpam-5395	187	28	,	,	PUNCT
ejpam-5395	187	29	σ1	σ1	PROPN
ejpam-5395	187	30	,	,	PUNCT
ejpam-5395	187	31	σ2	σ2	PROPN
ejpam-5395	187	32	)	)	PUNCT
ejpam-5395	187	33	is	be	AUX
ejpam-5395	187	34	almost	almost	ADV
ejpam-5395	187	35	(	(	PUNCT
ejpam-5395	187	36	σ1	σ1	NOUN
ejpam-5395	187	37	,	,	PUNCT
ejpam-5395	187	38	σ2)-regular	σ2)-regular	ADJ
ejpam-5395	187	39	,	,	PUNCT
ejpam-5395	187	40	then	then	ADV
ejpam-5395	187	41	f	f	PROPN
ejpam-5395	187	42	is	be	AUX
ejpam-5395	187	43	almost	almost	ADV
ejpam-5395	187	44	(	(	PUNCT
ejpam-5395	187	45	τ1	τ1	NOUN
ejpam-5395	187	46	,	,	PUNCT
ejpam-5395	187	47	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	187	48	.	.	PUNCT
ejpam-5395	188	1	proof	proof	NOUN
ejpam-5395	188	2	.	.	PUNCT
ejpam-5395	189	1	let	let	VERB
ejpam-5395	189	2	x	x	PUNCT
ejpam-5395	189	3	∈	∈	PROPN
ejpam-5395	189	4	x	x	X
ejpam-5395	189	5	and	and	CCONJ
ejpam-5395	189	6	v	v	X
ejpam-5395	189	7	be	be	AUX
ejpam-5395	189	8	any	any	DET
ejpam-5395	189	9	(	(	PUNCT
ejpam-5395	189	10	σ1	σ1	NOUN
ejpam-5395	189	11	,	,	PUNCT
ejpam-5395	189	12	σ2)r	σ2)r	NOUN
ejpam-5395	189	13	-	-	PUNCT
ejpam-5395	189	14	open	open	ADJ
ejpam-5395	189	15	set	set	NOUN
ejpam-5395	189	16	of	of	ADP
ejpam-5395	189	17	y	y	PROPN
ejpam-5395	189	18	containing	contain	VERB
ejpam-5395	189	19	f(x	f(x	PROPN
ejpam-5395	189	20	)	)	PUNCT
ejpam-5395	189	21	.	.	PUNCT
ejpam-5395	190	1	then	then	ADV
ejpam-5395	190	2	by	by	ADP
ejpam-5395	190	3	lemma	lemma	PROPN
ejpam-5395	190	4	5	5	NUM
ejpam-5395	190	5	,	,	PUNCT
ejpam-5395	190	6	v	v	NOUN
ejpam-5395	190	7	is	be	AUX
ejpam-5395	190	8	(	(	PUNCT
ejpam-5395	190	9	σ1	σ1	PROPN
ejpam-5395	190	10	,	,	PUNCT
ejpam-5395	190	11	σ2)θ	σ2)θ	NOUN
ejpam-5395	190	12	-	-	PUNCT
ejpam-5395	190	13	open	open	ADJ
ejpam-5395	190	14	in	in	ADP
ejpam-5395	190	15	y	y	PROPN
ejpam-5395	190	16	.	.	PUNCT
ejpam-5395	191	1	since	since	SCONJ
ejpam-5395	191	2	f	f	PROPN
ejpam-5395	191	3	is	be	AUX
ejpam-5395	191	4	faintly	faintly	ADV
ejpam-5395	191	5	(	(	PUNCT
ejpam-5395	191	6	τ1	τ1	NOUN
ejpam-5395	191	7	,	,	PUNCT
ejpam-5395	191	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	191	9	,	,	PUNCT
ejpam-5395	191	10	there	there	PRON
ejpam-5395	191	11	exists	exist	VERB
ejpam-5395	191	12	a	a	DET
ejpam-5395	191	13	τ1τ2	τ1τ2	NOUN
ejpam-5395	191	14	-	-	ADJ
ejpam-5395	191	15	open	open	ADJ
ejpam-5395	191	16	set	set	ADJ
ejpam-5395	191	17	u	u	NOUN
ejpam-5395	191	18	of	of	ADP
ejpam-5395	191	19	x	x	PUNCT
ejpam-5395	191	20	containing	contain	VERB
ejpam-5395	191	21	x	x	PUNCT
ejpam-5395	191	22	such	such	ADJ
ejpam-5395	191	23	that	that	DET
ejpam-5395	191	24	f(u	f(u	PROPN
ejpam-5395	191	25	)	)	PUNCT
ejpam-5395	191	26	⊆	⊆	NUM
ejpam-5395	191	27	v	v	NOUN
ejpam-5395	191	28	.	.	PUNCT
ejpam-5395	192	1	it	it	PRON
ejpam-5395	192	2	follows	follow	VERB
ejpam-5395	192	3	from	from	ADP
ejpam-5395	192	4	lemma	lemma	PROPN
ejpam-5395	192	5	4	4	NUM
ejpam-5395	192	6	that	that	PRON
ejpam-5395	192	7	f	f	PROPN
ejpam-5395	192	8	is	be	AUX
ejpam-5395	192	9	almost	almost	ADV
ejpam-5395	192	10	(	(	PUNCT
ejpam-5395	192	11	τ1	τ1	NOUN
ejpam-5395	192	12	,	,	PUNCT
ejpam-5395	192	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	192	14	.	.	PUNCT
ejpam-5395	193	1	acknowledgements	acknowledgement	NOUN
ejpam-5395	193	2	this	this	DET
ejpam-5395	193	3	research	research	NOUN
ejpam-5395	193	4	project	project	NOUN
ejpam-5395	193	5	was	be	AUX
ejpam-5395	193	6	financially	financially	ADV
ejpam-5395	193	7	supported	support	VERB
ejpam-5395	193	8	by	by	ADP
ejpam-5395	193	9	mahasarakham	mahasarakham	PROPN
ejpam-5395	193	10	university	university	PROPN
ejpam-5395	193	11	.	.	PUNCT
ejpam-5395	194	1	references	reference	NOUN
ejpam-5395	194	2	[	[	X
ejpam-5395	194	3	1	1	NUM
ejpam-5395	194	4	]	]	PUNCT
ejpam-5395	194	5	c.	c.	PROPN
ejpam-5395	194	6	boonpok	boonpok	PROPN
ejpam-5395	194	7	.	.	PUNCT
ejpam-5395	195	1	almost	almost	ADV
ejpam-5395	195	2	(	(	PUNCT
ejpam-5395	195	3	g	g	NOUN
ejpam-5395	195	4	,	,	PUNCT
ejpam-5395	195	5	m)-continuous	m)-continuous	ADJ
ejpam-5395	195	6	functions	function	NOUN
ejpam-5395	195	7	.	.	PUNCT
ejpam-5395	196	1	international	international	ADJ
ejpam-5395	196	2	journal	journal	PROPN
ejpam-5395	196	3	of	of	ADP
ejpam-5395	196	4	mathematical	mathematical	ADJ
ejpam-5395	196	5	analysis	analysis	NOUN
ejpam-5395	196	6	,	,	PUNCT
ejpam-5395	196	7	4(40):1957–1964	4(40):1957–1964	NUM
ejpam-5395	196	8	,	,	PUNCT
ejpam-5395	196	9	2010	2010	NUM
ejpam-5395	196	10	.	.	PUNCT
ejpam-5395	197	1	[	[	X
ejpam-5395	197	2	2	2	NUM
ejpam-5395	197	3	]	]	PUNCT
ejpam-5395	197	4	c.	c.	PROPN
ejpam-5395	197	5	boonpok	boonpok	PROPN
ejpam-5395	197	6	.	.	PUNCT
ejpam-5395	198	1	m	m	VERB
ejpam-5395	198	2	-continuous	-continuous	ADJ
ejpam-5395	198	3	functions	function	NOUN
ejpam-5395	198	4	in	in	ADP
ejpam-5395	198	5	biminimal	biminimal	NOUN
ejpam-5395	198	6	structure	structure	NOUN
ejpam-5395	198	7	spaces	space	NOUN
ejpam-5395	198	8	.	.	PUNCT
ejpam-5395	199	1	far	far	PROPN
ejpam-5395	199	2	east	east	PROPN
ejpam-5395	199	3	journal	journal	PROPN
ejpam-5395	199	4	of	of	ADP
ejpam-5395	199	5	mathematical	mathematical	ADJ
ejpam-5395	199	6	sciences	science	NOUN
ejpam-5395	199	7	,	,	PUNCT
ejpam-5395	199	8	43(1):41–58	43(1):41–58	NUM
ejpam-5395	199	9	,	,	PUNCT
ejpam-5395	199	10	2010	2010	NUM
ejpam-5395	199	11	.	.	PUNCT
ejpam-5395	200	1	[	[	X
ejpam-5395	200	2	3	3	X
ejpam-5395	200	3	]	]	PUNCT
ejpam-5395	200	4	c.	c.	PROPN
ejpam-5395	200	5	boonpok	boonpok	PROPN
ejpam-5395	200	6	.	.	PUNCT
ejpam-5395	201	1	on	on	ADP
ejpam-5395	201	2	characterizations	characterization	NOUN
ejpam-5395	201	3	of	of	ADP
ejpam-5395	201	4	⋆-hyperconnected	⋆-hyperconnecte	VERB
ejpam-5395	201	5	ideal	ideal	ADJ
ejpam-5395	201	6	topological	topological	ADJ
ejpam-5395	201	7	spaces	space	NOUN
ejpam-5395	201	8	.	.	PUNCT
ejpam-5395	202	1	journal	journal	NOUN
ejpam-5395	202	2	of	of	ADP
ejpam-5395	202	3	mathematics	mathematic	NOUN
ejpam-5395	202	4	,	,	PUNCT
ejpam-5395	202	5	2020:9387601	2020:9387601	NUM
ejpam-5395	202	6	,	,	PUNCT
ejpam-5395	202	7	2020	2020	NUM
ejpam-5395	202	8	.	.	PUNCT
ejpam-5395	203	1	[	[	X
ejpam-5395	203	2	4	4	NUM
ejpam-5395	203	3	]	]	PUNCT
ejpam-5395	203	4	c.	c.	PROPN
ejpam-5395	203	5	boonpok	boonpok	PROPN
ejpam-5395	203	6	.	.	PUNCT
ejpam-5395	204	1	(	(	PUNCT
ejpam-5395	204	2	τ1	τ1	NOUN
ejpam-5395	204	3	,	,	PUNCT
ejpam-5395	204	4	τ2)δ	τ2)δ	ADJ
ejpam-5395	204	5	-	-	PUNCT
ejpam-5395	204	6	semicontinuous	semicontinuous	ADJ
ejpam-5395	204	7	multifunctions	multifunction	NOUN
ejpam-5395	204	8	.	.	PUNCT
ejpam-5395	205	1	heliyon	heliyon	NOUN
ejpam-5395	205	2	,	,	PUNCT
ejpam-5395	205	3	6	6	NUM
ejpam-5395	205	4	:	:	SYM
ejpam-5395	205	5	e05367	e05367	PROPN
ejpam-5395	205	6	,	,	PUNCT
ejpam-5395	205	7	2020	2020	NUM
ejpam-5395	205	8	.	.	PUNCT
ejpam-5395	206	1	[	[	X
ejpam-5395	206	2	5	5	X
ejpam-5395	206	3	]	]	PUNCT
ejpam-5395	206	4	c.	c.	PROPN
ejpam-5395	206	5	boonpok	boonpok	PROPN
ejpam-5395	206	6	.	.	PUNCT
ejpam-5395	207	1	on	on	ADP
ejpam-5395	207	2	some	some	DET
ejpam-5395	207	3	closed	closed	ADJ
ejpam-5395	207	4	sets	set	NOUN
ejpam-5395	207	5	and	and	CCONJ
ejpam-5395	207	6	low	low	ADJ
ejpam-5395	207	7	separation	separation	NOUN
ejpam-5395	207	8	axioms	axiom	NOUN
ejpam-5395	207	9	via	via	ADP
ejpam-5395	207	10	topological	topological	ADJ
ejpam-5395	207	11	ideals	ideal	NOUN
ejpam-5395	207	12	.	.	PUNCT
ejpam-5395	208	1	european	european	ADJ
ejpam-5395	208	2	journal	journal	PROPN
ejpam-5395	208	3	of	of	ADP
ejpam-5395	208	4	pure	pure	ADJ
ejpam-5395	208	5	and	and	CCONJ
ejpam-5395	208	6	applied	applied	ADJ
ejpam-5395	208	7	mathematics	mathematic	NOUN
ejpam-5395	208	8	,	,	PUNCT
ejpam-5395	208	9	15(3):1023–1046	15(3):1023–1046	NUM
ejpam-5395	208	10	,	,	PUNCT
ejpam-5395	208	11	2022	2022	NUM
ejpam-5395	208	12	.	.	PUNCT
ejpam-5395	209	1	references	reference	NOUN
ejpam-5395	209	2	2760	2760	NUM
ejpam-5395	210	1	[	[	X
ejpam-5395	210	2	6	6	NUM
ejpam-5395	210	3	]	]	PUNCT
ejpam-5395	210	4	c.	c.	PROPN
ejpam-5395	210	5	boonpok	boonpok	PROPN
ejpam-5395	210	6	.	.	PUNCT
ejpam-5395	211	1	on	on	ADP
ejpam-5395	211	2	some	some	DET
ejpam-5395	211	3	spaces	space	NOUN
ejpam-5395	211	4	via	via	ADP
ejpam-5395	211	5	topological	topological	ADJ
ejpam-5395	211	6	ideals	ideal	NOUN
ejpam-5395	211	7	.	.	PUNCT
ejpam-5395	212	1	open	open	ADJ
ejpam-5395	212	2	mathematics	mathematic	NOUN
ejpam-5395	212	3	,	,	PUNCT
ejpam-5395	212	4	21:20230118	21:20230118	NUM
ejpam-5395	212	5	,	,	PUNCT
ejpam-5395	212	6	2023	2023	NUM
ejpam-5395	212	7	.	.	PUNCT
ejpam-5395	213	1	[	[	X
ejpam-5395	213	2	7	7	X
ejpam-5395	213	3	]	]	X
ejpam-5395	213	4	c.	c.	PROPN
ejpam-5395	213	5	boonpok	boonpok	PROPN
ejpam-5395	213	6	.	.	PUNCT
ejpam-5395	214	1	θ(⋆)-precontinuity	θ(⋆)-precontinuity	NOUN
ejpam-5395	214	2	.	.	PUNCT
ejpam-5395	215	1	mathematica	mathematica	PROPN
ejpam-5395	215	2	,	,	PUNCT
ejpam-5395	215	3	65(1):31–42	65(1):31–42	NUM
ejpam-5395	215	4	,	,	PUNCT
ejpam-5395	215	5	2023	2023	NUM
ejpam-5395	215	6	.	.	PUNCT
ejpam-5395	216	1	[	[	X
ejpam-5395	216	2	8	8	NUM
ejpam-5395	216	3	]	]	X
ejpam-5395	216	4	c.	c.	PROPN
ejpam-5395	216	5	boonpok	boonpok	PROPN
ejpam-5395	216	6	and	and	CCONJ
ejpam-5395	216	7	j.	j.	PROPN
ejpam-5395	216	8	khampakdee	khampakdee	PROPN
ejpam-5395	216	9	.	.	PUNCT
ejpam-5395	217	1	(	(	PUNCT
ejpam-5395	217	2	λ	λ	NOUN
ejpam-5395	217	3	,	,	PUNCT
ejpam-5395	217	4	sp)-open	sp)-open	ADJ
ejpam-5395	217	5	sets	set	NOUN
ejpam-5395	217	6	in	in	ADP
ejpam-5395	217	7	topological	topological	ADJ
ejpam-5395	217	8	spaces	space	NOUN
ejpam-5395	217	9	.	.	PUNCT
ejpam-5395	218	1	european	european	ADJ
ejpam-5395	218	2	journal	journal	PROPN
ejpam-5395	218	3	of	of	ADP
ejpam-5395	218	4	pure	pure	ADJ
ejpam-5395	218	5	and	and	CCONJ
ejpam-5395	218	6	applied	applied	ADJ
ejpam-5395	218	7	mathematics	mathematic	NOUN
ejpam-5395	218	8	,	,	PUNCT
ejpam-5395	218	9	15(2):572–588	15(2):572–588	NUM
ejpam-5395	218	10	,	,	PUNCT
ejpam-5395	218	11	2022	2022	NUM
ejpam-5395	218	12	.	.	PUNCT
ejpam-5395	219	1	[	[	X
ejpam-5395	219	2	9	9	NUM
ejpam-5395	219	3	]	]	PUNCT
ejpam-5395	219	4	c.	c.	NOUN
ejpam-5395	219	5	boonpok	boonpok	PROPN
ejpam-5395	219	6	and	and	CCONJ
ejpam-5395	219	7	j.	j.	PROPN
ejpam-5395	219	8	khampakdee	khampakdee	PROPN
ejpam-5395	219	9	.	.	PUNCT
ejpam-5395	220	1	almost	almost	ADV
ejpam-5395	220	2	strong	strong	ADJ
ejpam-5395	220	3	θ(λ	θ(λ	PROPN
ejpam-5395	220	4	,	,	PUNCT
ejpam-5395	220	5	p)-continuity	p)-continuity	NOUN
ejpam-5395	220	6	for	for	ADP
ejpam-5395	220	7	functions	function	NOUN
ejpam-5395	220	8	.	.	PUNCT
ejpam-5395	221	1	european	european	ADJ
ejpam-5395	221	2	journal	journal	PROPN
ejpam-5395	221	3	of	of	ADP
ejpam-5395	221	4	pure	pure	ADJ
ejpam-5395	221	5	and	and	CCONJ
ejpam-5395	221	6	applied	applied	ADJ
ejpam-5395	221	7	mathematics	mathematic	NOUN
ejpam-5395	221	8	,	,	PUNCT
ejpam-5395	221	9	17(1):300–309	17(1):300–309	PROPN
ejpam-5395	221	10	,	,	PUNCT
ejpam-5395	221	11	2024	2024	NUM
ejpam-5395	221	12	.	.	PUNCT
ejpam-5395	222	1	[	[	X
ejpam-5395	222	2	10	10	NUM
ejpam-5395	222	3	]	]	X
ejpam-5395	222	4	c.	c.	PROPN
ejpam-5395	222	5	boonpok	boonpok	PROPN
ejpam-5395	222	6	and	and	CCONJ
ejpam-5395	222	7	c.	c.	PROPN
ejpam-5395	222	8	klanarong	klanarong	PROPN
ejpam-5395	222	9	.	.	PUNCT
ejpam-5395	223	1	on	on	ADP
ejpam-5395	223	2	weakly	weakly	ADJ
ejpam-5395	223	3	(	(	PUNCT
ejpam-5395	223	4	τ1	τ1	NOUN
ejpam-5395	223	5	,	,	PUNCT
ejpam-5395	223	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	223	7	functions	function	NOUN
ejpam-5395	223	8	.	.	PUNCT
ejpam-5395	224	1	european	european	ADJ
ejpam-5395	224	2	journal	journal	PROPN
ejpam-5395	224	3	of	of	ADP
ejpam-5395	224	4	pure	pure	ADJ
ejpam-5395	224	5	and	and	CCONJ
ejpam-5395	224	6	applied	applied	ADJ
ejpam-5395	224	7	mathematics	mathematic	NOUN
ejpam-5395	224	8	,	,	PUNCT
ejpam-5395	224	9	17(1):416–425	17(1):416–425	NUM
ejpam-5395	224	10	,	,	PUNCT
ejpam-5395	224	11	2024	2024	NUM
ejpam-5395	224	12	.	.	PUNCT
ejpam-5395	225	1	[	[	X
ejpam-5395	225	2	11	11	NUM
ejpam-5395	225	3	]	]	X
ejpam-5395	225	4	c.	c.	PROPN
ejpam-5395	225	5	boonpok	boonpok	PROPN
ejpam-5395	225	6	and	and	CCONJ
ejpam-5395	225	7	p.	p.	NOUN
ejpam-5395	225	8	pue	pue	NOUN
ejpam-5395	225	9	-	-	PUNCT
ejpam-5395	225	10	on	on	ADP
ejpam-5395	225	11	.	.	PUNCT
ejpam-5395	226	1	characterizations	characterization	NOUN
ejpam-5395	226	2	of	of	ADP
ejpam-5395	226	3	almost	almost	ADV
ejpam-5395	226	4	(	(	PUNCT
ejpam-5395	226	5	τ1	τ1	NOUN
ejpam-5395	226	6	,	,	PUNCT
ejpam-5395	226	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	226	8	functions	function	NOUN
ejpam-5395	226	9	.	.	PUNCT
ejpam-5395	227	1	international	international	ADJ
ejpam-5395	227	2	journal	journal	NOUN
ejpam-5395	227	3	of	of	ADP
ejpam-5395	227	4	analysis	analysis	NOUN
ejpam-5395	227	5	and	and	CCONJ
ejpam-5395	227	6	applications	application	NOUN
ejpam-5395	227	7	,	,	PUNCT
ejpam-5395	227	8	22:33	22:33	NUM
ejpam-5395	227	9	,	,	PUNCT
ejpam-5395	227	10	2024	2024	NUM
ejpam-5395	227	11	.	.	PUNCT
ejpam-5395	228	1	[	[	X
ejpam-5395	228	2	12	12	NUM
ejpam-5395	228	3	]	]	X
ejpam-5395	228	4	c.	c.	PROPN
ejpam-5395	228	5	boonpok	boonpok	PROPN
ejpam-5395	228	6	and	and	CCONJ
ejpam-5395	228	7	n.	n.	PROPN
ejpam-5395	228	8	srisarakham	srisarakham	PROPN
ejpam-5395	228	9	.	.	PUNCT
ejpam-5395	229	1	weak	weak	ADJ
ejpam-5395	229	2	forms	form	NOUN
ejpam-5395	229	3	of	of	ADP
ejpam-5395	229	4	(	(	PUNCT
ejpam-5395	229	5	λ	λ	PROPN
ejpam-5395	229	6	,	,	PUNCT
ejpam-5395	229	7	b)-open	b)-open	VERB
ejpam-5395	229	8	sets	set	NOUN
ejpam-5395	229	9	and	and	CCONJ
ejpam-5395	229	10	weak	weak	ADJ
ejpam-5395	229	11	(	(	PUNCT
ejpam-5395	229	12	λ	λ	NOUN
ejpam-5395	229	13	,	,	PUNCT
ejpam-5395	229	14	b)continuity	b)continuity	NOUN
ejpam-5395	229	15	.	.	PUNCT
ejpam-5395	230	1	european	european	PROPN
ejpam-5395	230	2	journal	journal	PROPN
ejpam-5395	230	3	of	of	ADP
ejpam-5395	230	4	pure	pure	ADJ
ejpam-5395	230	5	and	and	CCONJ
ejpam-5395	230	6	applied	applied	ADJ
ejpam-5395	230	7	mathematics	mathematic	NOUN
ejpam-5395	230	8	,	,	PUNCT
ejpam-5395	230	9	16(1):29–43	16(1):29–43	NUM
ejpam-5395	230	10	,	,	PUNCT
ejpam-5395	230	11	2023	2023	NUM
ejpam-5395	230	12	.	.	PUNCT
ejpam-5395	231	1	[	[	X
ejpam-5395	231	2	13	13	NUM
ejpam-5395	231	3	]	]	PUNCT
ejpam-5395	231	4	c.	c.	PROPN
ejpam-5395	231	5	boonpok	boonpok	PROPN
ejpam-5395	231	6	and	and	CCONJ
ejpam-5395	231	7	n.	n.	PROPN
ejpam-5395	231	8	srisarakham	srisarakham	PROPN
ejpam-5395	231	9	.	.	PUNCT
ejpam-5395	232	1	(	(	PUNCT
ejpam-5395	232	2	τ1	τ1	NOUN
ejpam-5395	232	3	,	,	PUNCT
ejpam-5395	232	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	232	5	for	for	ADP
ejpam-5395	232	6	functions	function	NOUN
ejpam-5395	232	7	.	.	PUNCT
ejpam-5395	233	1	asia	asia	PROPN
ejpam-5395	233	2	pacific	pacific	PROPN
ejpam-5395	233	3	journal	journal	PROPN
ejpam-5395	233	4	of	of	ADP
ejpam-5395	233	5	mathematics	mathematic	NOUN
ejpam-5395	233	6	,	,	PUNCT
ejpam-5395	233	7	11:21	11:21	NUM
ejpam-5395	233	8	,	,	PUNCT
ejpam-5395	233	9	2024	2024	NUM
ejpam-5395	233	10	.	.	PUNCT
ejpam-5395	234	1	[	[	X
ejpam-5395	234	2	14	14	NUM
ejpam-5395	234	3	]	]	X
ejpam-5395	234	4	c.	c.	PROPN
ejpam-5395	234	5	boonpok	boonpok	PROPN
ejpam-5395	234	6	,	,	PUNCT
ejpam-5395	234	7	c.	c.	PROPN
ejpam-5395	234	8	viriyapong	viriyapong	PROPN
ejpam-5395	234	9	,	,	PUNCT
ejpam-5395	234	10	and	and	CCONJ
ejpam-5395	234	11	m.	m.	NOUN
ejpam-5395	234	12	thongmoon	thongmoon	NOUN
ejpam-5395	234	13	.	.	PUNCT
ejpam-5395	235	1	on	on	ADP
ejpam-5395	235	2	upper	upper	ADJ
ejpam-5395	235	3	and	and	CCONJ
ejpam-5395	235	4	lower	low	ADJ
ejpam-5395	235	5	(	(	PUNCT
ejpam-5395	235	6	τ1	τ1	NOUN
ejpam-5395	235	7	,	,	PUNCT
ejpam-5395	235	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-5395	235	9	multifunctions	multifunction	NOUN
ejpam-5395	235	10	.	.	PUNCT
ejpam-5395	236	1	journal	journal	PROPN
ejpam-5395	236	2	of	of	ADP
ejpam-5395	236	3	mathematics	mathematics	PROPN
ejpam-5395	236	4	and	and	CCONJ
ejpam-5395	236	5	computer	computer	NOUN
ejpam-5395	236	6	science	science	NOUN
ejpam-5395	236	7	,	,	PUNCT
ejpam-5395	236	8	18:282–293	18:282–293	NUM
ejpam-5395	236	9	,	,	PUNCT
ejpam-5395	236	10	2018	2018	NUM
ejpam-5395	236	11	.	.	PUNCT
ejpam-5395	237	1	[	[	X
ejpam-5395	237	2	15	15	NUM
ejpam-5395	237	3	]	]	X
ejpam-5395	237	4	p.	p.	NOUN
ejpam-5395	237	5	chanapan	chanapan	PROPN
ejpam-5395	237	6	,	,	PUNCT
ejpam-5395	237	7	c.	c.	PROPN
ejpam-5395	237	8	viriyapong	viriyapong	PROPN
ejpam-5395	237	9	,	,	PUNCT
ejpam-5395	237	10	and	and	CCONJ
ejpam-5395	237	11	c.	c.	PROPN
ejpam-5395	237	12	boonpok	boonpok	PROPN
ejpam-5395	237	13	.	.	PUNCT
ejpam-5395	238	1	faintly	faintly	ADV
ejpam-5395	238	2	(	(	PUNCT
ejpam-5395	238	3	m,µ)-continuous	m,µ)-continuous	ADJ
ejpam-5395	238	4	functions	function	NOUN
ejpam-5395	238	5	.	.	PUNCT
ejpam-5395	239	1	international	international	ADJ
ejpam-5395	239	2	journal	journal	PROPN
ejpam-5395	239	3	of	of	ADP
ejpam-5395	239	4	mathematical	mathematical	ADJ
ejpam-5395	239	5	analysis	analysis	NOUN
ejpam-5395	239	6	,	,	PUNCT
ejpam-5395	239	7	7(39):1919–1926	7(39):1919–1926	NUM
ejpam-5395	239	8	,	,	PUNCT
ejpam-5395	239	9	2013	2013	NUM
ejpam-5395	239	10	.	.	PUNCT
ejpam-5395	240	1	[	[	X
ejpam-5395	240	2	16	16	NUM
ejpam-5395	240	3	]	]	PUNCT
ejpam-5395	240	4	m.	m.	NOUN
ejpam-5395	240	5	chiangpradit	chiangpradit	NOUN
ejpam-5395	240	6	,	,	PUNCT
ejpam-5395	240	7	s.	s.	PROPN
ejpam-5395	240	8	sompong	sompong	PROPN
ejpam-5395	240	9	,	,	PUNCT
ejpam-5395	240	10	and	and	CCONJ
ejpam-5395	240	11	c.	c.	PROPN
ejpam-5395	240	12	boonpok	boonpok	PROPN
ejpam-5395	240	13	.	.	PUNCT
ejpam-5395	241	1	on	on	ADP
ejpam-5395	241	2	characterizations	characterization	NOUN
ejpam-5395	241	3	of	of	ADP
ejpam-5395	241	4	(	(	PUNCT
ejpam-5395	241	5	τ1	τ1	NOUN
ejpam-5395	241	6	,	,	PUNCT
ejpam-5395	241	7	τ2)regular	τ2)regular	ADJ
ejpam-5395	241	8	spaces	space	NOUN
ejpam-5395	241	9	.	.	PUNCT
ejpam-5395	242	1	international	international	ADJ
ejpam-5395	242	2	journal	journal	PROPN
ejpam-5395	242	3	of	of	ADP
ejpam-5395	242	4	mathematics	mathematic	NOUN
ejpam-5395	242	5	and	and	CCONJ
ejpam-5395	242	6	computer	computer	NOUN
ejpam-5395	242	7	science	science	NOUN
ejpam-5395	242	8	,	,	PUNCT
ejpam-5395	242	9	19(4):1329–1334	19(4):1329–1334	NUM
ejpam-5395	242	10	,	,	PUNCT
ejpam-5395	242	11	2024	2024	NUM
ejpam-5395	242	12	.	.	PUNCT
ejpam-5395	243	1	[	[	X
ejpam-5395	243	2	17	17	NUM
ejpam-5395	243	3	]	]	PUNCT
ejpam-5395	243	4	m.	m.	NOUN
ejpam-5395	243	5	chiangpradit	chiangpradit	NOUN
ejpam-5395	243	6	,	,	PUNCT
ejpam-5395	243	7	s.	s.	PROPN
ejpam-5395	243	8	sompong	sompong	PROPN
ejpam-5395	243	9	,	,	PUNCT
ejpam-5395	243	10	and	and	CCONJ
ejpam-5395	243	11	c.	c.	PROPN
ejpam-5395	243	12	boonpok	boonpok	PROPN
ejpam-5395	243	13	.	.	PUNCT
ejpam-5395	244	1	weakly	weakly	ADJ
ejpam-5395	244	2	quasi	quasi	NOUN
ejpam-5395	244	3	(	(	PUNCT
ejpam-5395	244	4	τ1	τ1	PROPN
ejpam-5395	244	5	,	,	PUNCT
ejpam-5395	244	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	244	7	functions	function	NOUN
ejpam-5395	244	8	.	.	PUNCT
ejpam-5395	245	1	international	international	ADJ
ejpam-5395	245	2	journal	journal	NOUN
ejpam-5395	245	3	of	of	ADP
ejpam-5395	245	4	analysis	analysis	NOUN
ejpam-5395	245	5	and	and	CCONJ
ejpam-5395	245	6	applications	application	NOUN
ejpam-5395	245	7	,	,	PUNCT
ejpam-5395	245	8	22:125	22:125	NUM
ejpam-5395	245	9	,	,	PUNCT
ejpam-5395	245	10	2024	2024	NUM
ejpam-5395	245	11	.	.	PUNCT
ejpam-5395	246	1	[	[	X
ejpam-5395	246	2	18	18	NUM
ejpam-5395	246	3	]	]	X
ejpam-5395	246	4	n.	n.	NOUN
ejpam-5395	246	5	chutiman	chutiman	NOUN
ejpam-5395	246	6	,	,	PUNCT
ejpam-5395	246	7	s.	s.	PROPN
ejpam-5395	246	8	sompong	sompong	PROPN
ejpam-5395	246	9	,	,	PUNCT
ejpam-5395	246	10	and	and	CCONJ
ejpam-5395	246	11	c.	c.	PROPN
ejpam-5395	246	12	boonpok	boonpok	PROPN
ejpam-5395	246	13	.	.	PUNCT
ejpam-5395	247	1	on	on	ADP
ejpam-5395	247	2	almost	almost	ADV
ejpam-5395	247	3	(	(	PUNCT
ejpam-5395	247	4	τ1	τ1	NOUN
ejpam-5395	247	5	,	,	PUNCT
ejpam-5395	247	6	τ2)-regular	τ2)-regular	ADJ
ejpam-5395	247	7	spaces	space	NOUN
ejpam-5395	247	8	.	.	PUNCT
ejpam-5395	248	1	international	international	ADJ
ejpam-5395	248	2	journal	journal	PROPN
ejpam-5395	248	3	of	of	ADP
ejpam-5395	248	4	mathematics	mathematic	NOUN
ejpam-5395	248	5	and	and	CCONJ
ejpam-5395	248	6	computer	computer	NOUN
ejpam-5395	248	7	science	science	NOUN
ejpam-5395	248	8	,	,	PUNCT
ejpam-5395	248	9	19(4):1363–1368	19(4):1363–1368	NUM
ejpam-5395	248	10	,	,	PUNCT
ejpam-5395	248	11	2024	2024	NUM
ejpam-5395	248	12	.	.	PUNCT
ejpam-5395	249	1	[	[	X
ejpam-5395	249	2	19	19	NUM
ejpam-5395	249	3	]	]	X
ejpam-5395	249	4	n.	n.	NOUN
ejpam-5395	249	5	chutiman	chutiman	NOUN
ejpam-5395	249	6	,	,	PUNCT
ejpam-5395	249	7	s.	s.	PROPN
ejpam-5395	249	8	sompong	sompong	PROPN
ejpam-5395	249	9	,	,	PUNCT
ejpam-5395	249	10	and	and	CCONJ
ejpam-5395	249	11	c.	c.	PROPN
ejpam-5395	249	12	boonpok	boonpok	PROPN
ejpam-5395	249	13	.	.	PUNCT
ejpam-5395	250	1	on	on	ADP
ejpam-5395	250	2	some	some	DET
ejpam-5395	250	3	separation	separation	NOUN
ejpam-5395	250	4	axioms	axiom	NOUN
ejpam-5395	250	5	in	in	ADP
ejpam-5395	250	6	bitopological	bitopological	ADJ
ejpam-5395	250	7	spaces	space	NOUN
ejpam-5395	250	8	.	.	PUNCT
ejpam-5395	251	1	asia	asia	PROPN
ejpam-5395	251	2	pacific	pacific	PROPN
ejpam-5395	251	3	journal	journal	PROPN
ejpam-5395	251	4	of	of	ADP
ejpam-5395	251	5	mathematics	mathematic	NOUN
ejpam-5395	251	6	,	,	PUNCT
ejpam-5395	251	7	11:41	11:41	NUM
ejpam-5395	251	8	,	,	PUNCT
ejpam-5395	251	9	2024	2024	NUM
ejpam-5395	251	10	.	.	PUNCT
ejpam-5395	252	1	[	[	X
ejpam-5395	252	2	20	20	NUM
ejpam-5395	252	3	]	]	PUNCT
ejpam-5395	252	4	t.	t.	PROPN
ejpam-5395	252	5	duangphui	duangphui	PROPN
ejpam-5395	252	6	,	,	PUNCT
ejpam-5395	252	7	c.	c.	PROPN
ejpam-5395	252	8	boonpok	boonpok	PROPN
ejpam-5395	252	9	,	,	PUNCT
ejpam-5395	252	10	and	and	CCONJ
ejpam-5395	252	11	c.	c.	PROPN
ejpam-5395	252	12	viriyapong	viriyapong	PROPN
ejpam-5395	252	13	.	.	PUNCT
ejpam-5395	253	1	continuous	continuous	ADJ
ejpam-5395	253	2	functions	function	NOUN
ejpam-5395	253	3	on	on	ADP
ejpam-5395	253	4	bigeneralized	bigeneralize	VERB
ejpam-5395	253	5	topological	topological	ADJ
ejpam-5395	253	6	spaces	space	NOUN
ejpam-5395	253	7	.	.	PUNCT
ejpam-5395	254	1	international	international	ADJ
ejpam-5395	254	2	journal	journal	PROPN
ejpam-5395	254	3	of	of	ADP
ejpam-5395	254	4	mathematical	mathematical	ADJ
ejpam-5395	254	5	analysis	analysis	NOUN
ejpam-5395	254	6	,	,	PUNCT
ejpam-5395	254	7	5(24):1165	5(24):1165	NUM
ejpam-5395	254	8	–	–	PUNCT
ejpam-5395	254	9	1174	1174	NUM
ejpam-5395	254	10	,	,	PUNCT
ejpam-5395	254	11	2011	2011	NUM
ejpam-5395	254	12	.	.	PUNCT
ejpam-5395	255	1	references	reference	NOUN
ejpam-5395	255	2	2761	2761	NUM
ejpam-5395	255	3	[	[	X
ejpam-5395	255	4	21	21	NUM
ejpam-5395	255	5	]	]	PUNCT
ejpam-5395	255	6	t.	t.	NOUN
ejpam-5395	255	7	dungthaisong	dungthaisong	PROPN
ejpam-5395	255	8	,	,	PUNCT
ejpam-5395	255	9	c.	c.	PROPN
ejpam-5395	255	10	boonpok	boonpok	PROPN
ejpam-5395	255	11	,	,	PUNCT
ejpam-5395	255	12	and	and	CCONJ
ejpam-5395	255	13	c.	c.	PROPN
ejpam-5395	255	14	viriyapong	viriyapong	PROPN
ejpam-5395	255	15	.	.	PUNCT
ejpam-5395	256	1	generalized	generalize	VERB
ejpam-5395	256	2	closed	close	VERB
ejpam-5395	256	3	sets	set	NOUN
ejpam-5395	256	4	in	in	ADP
ejpam-5395	256	5	bigeneralized	bigeneralize	VERB
ejpam-5395	256	6	topological	topological	ADJ
ejpam-5395	256	7	spaces	space	NOUN
ejpam-5395	256	8	.	.	PUNCT
ejpam-5395	257	1	international	international	ADJ
ejpam-5395	257	2	journal	journal	PROPN
ejpam-5395	257	3	of	of	ADP
ejpam-5395	257	4	mathematical	mathematical	ADJ
ejpam-5395	257	5	analysis	analysis	NOUN
ejpam-5395	257	6	,	,	PUNCT
ejpam-5395	257	7	5(24):1175–1184	5(24):1175–1184	NUM
ejpam-5395	257	8	,	,	PUNCT
ejpam-5395	257	9	2011	2011	NUM
ejpam-5395	257	10	.	.	PUNCT
ejpam-5395	258	1	[	[	X
ejpam-5395	258	2	22	22	NUM
ejpam-5395	258	3	]	]	PUNCT
ejpam-5395	258	4	m.	m.	NOUN
ejpam-5395	258	5	e.	e.	PROPN
ejpam-5395	258	6	abd	abd	PROPN
ejpam-5395	258	7	el	el	PROPN
ejpam-5395	258	8	-	-	PROPN
ejpam-5395	258	9	monsef	monsef	PROPN
ejpam-5395	258	10	,	,	PUNCT
ejpam-5395	258	11	s.	s.	PROPN
ejpam-5395	258	12	n.	n.	PROPN
ejpam-5395	258	13	el	el	PROPN
ejpam-5395	258	14	-	-	PROPN
ejpam-5395	258	15	deeb	deeb	PROPN
ejpam-5395	258	16	,	,	PUNCT
ejpam-5395	258	17	and	and	CCONJ
ejpam-5395	258	18	r.	r.	PROPN
ejpam-5395	258	19	a.	a.	PROPN
ejpam-5395	258	20	mahmoud	mahmoud	PROPN
ejpam-5395	258	21	.	.	PUNCT
ejpam-5395	259	1	β	β	X
ejpam-5395	259	2	-	-	ADJ
ejpam-5395	259	3	open	open	ADJ
ejpam-5395	259	4	sets	set	NOUN
ejpam-5395	259	5	and	and	CCONJ
ejpam-5395	259	6	βcontinuous	βcontinuous	ADJ
ejpam-5395	259	7	mappings	mapping	NOUN
ejpam-5395	259	8	.	.	PUNCT
ejpam-5395	260	1	bulletin	bulletin	NOUN
ejpam-5395	260	2	of	of	ADP
ejpam-5395	260	3	the	the	DET
ejpam-5395	260	4	faculty	faculty	NOUN
ejpam-5395	260	5	of	of	ADP
ejpam-5395	260	6	science	science	NOUN
ejpam-5395	260	7	.	.	PUNCT
ejpam-5395	261	1	assiut	assiut	PROPN
ejpam-5395	261	2	university	university	PROPN
ejpam-5395	261	3	,	,	PUNCT
ejpam-5395	261	4	12:77–90	12:77–90	NUM
ejpam-5395	261	5	,	,	PUNCT
ejpam-5395	261	6	1983	1983	NUM
ejpam-5395	261	7	.	.	PUNCT
ejpam-5395	262	1	[	[	X
ejpam-5395	262	2	23	23	NUM
ejpam-5395	262	3	]	]	X
ejpam-5395	262	4	s.	s.	PROPN
ejpam-5395	262	5	jafari	jafari	PROPN
ejpam-5395	262	6	and	and	CCONJ
ejpam-5395	262	7	t.	t.	PROPN
ejpam-5395	262	8	noiri	noiri	PROPN
ejpam-5395	262	9	.	.	PUNCT
ejpam-5395	263	1	on	on	ADP
ejpam-5395	263	2	faintly	faintly	ADV
ejpam-5395	263	3	α	α	NUM
ejpam-5395	263	4	-	-	ADJ
ejpam-5395	263	5	continuous	continuous	ADJ
ejpam-5395	263	6	functions	function	NOUN
ejpam-5395	263	7	.	.	PUNCT
ejpam-5395	264	1	indian	indian	ADJ
ejpam-5395	264	2	journal	journal	PROPN
ejpam-5395	264	3	of	of	ADP
ejpam-5395	264	4	mathematics	mathematics	PROPN
ejpam-5395	264	5	,	,	PUNCT
ejpam-5395	264	6	42:203–210	42:203–210	PROPN
ejpam-5395	264	7	,	,	PUNCT
ejpam-5395	264	8	2000	2000	NUM
ejpam-5395	264	9	.	.	PUNCT
ejpam-5395	265	1	[	[	X
ejpam-5395	265	2	24	24	NUM
ejpam-5395	265	3	]	]	PUNCT
ejpam-5395	265	4	b.	b.	PROPN
ejpam-5395	265	5	kong	kong	PROPN
ejpam-5395	265	6	-	-	PUNCT
ejpam-5395	265	7	ied	ied	PROPN
ejpam-5395	265	8	,	,	PUNCT
ejpam-5395	265	9	s.	s.	PROPN
ejpam-5395	265	10	sompong	sompong	PROPN
ejpam-5395	265	11	,	,	PUNCT
ejpam-5395	265	12	and	and	CCONJ
ejpam-5395	265	13	c.	c.	PROPN
ejpam-5395	265	14	boonpok	boonpok	PROPN
ejpam-5395	265	15	.	.	PUNCT
ejpam-5395	266	1	almost	almost	ADV
ejpam-5395	266	2	quasi	quasi	X
ejpam-5395	266	3	(	(	PUNCT
ejpam-5395	266	4	τ1	τ1	NOUN
ejpam-5395	266	5	,	,	PUNCT
ejpam-5395	266	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-5395	266	7	functions	function	NOUN
ejpam-5395	266	8	.	.	PUNCT
ejpam-5395	267	1	asia	asia	PROPN
ejpam-5395	267	2	pacific	pacific	PROPN
ejpam-5395	267	3	journal	journal	PROPN
ejpam-5395	267	4	of	of	ADP
ejpam-5395	267	5	mathematics	mathematic	NOUN
ejpam-5395	267	6	,	,	PUNCT
ejpam-5395	267	7	11:64	11:64	NUM
ejpam-5395	267	8	,	,	PUNCT
ejpam-5395	267	9	2024	2024	NUM
ejpam-5395	267	10	.	.	PUNCT
ejpam-5395	268	1	[	[	X
ejpam-5395	268	2	25	25	NUM
ejpam-5395	268	3	]	]	X
ejpam-5395	268	4	n.	n.	PROPN
ejpam-5395	268	5	levine	levine	PROPN
ejpam-5395	268	6	.	.	PUNCT
ejpam-5395	269	1	semi	semi	ADJ
ejpam-5395	269	2	-	-	ADJ
ejpam-5395	269	3	open	open	ADJ
ejpam-5395	269	4	sets	set	NOUN
ejpam-5395	269	5	and	and	CCONJ
ejpam-5395	269	6	semi	semi	ADJ
ejpam-5395	269	7	-	-	NOUN
ejpam-5395	269	8	continuity	continuity	NOUN
ejpam-5395	269	9	in	in	ADP
ejpam-5395	269	10	topological	topological	ADJ
ejpam-5395	269	11	spaces	space	NOUN
ejpam-5395	269	12	.	.	PUNCT
ejpam-5395	270	1	the	the	DET
ejpam-5395	270	2	american	american	PROPN
ejpam-5395	270	3	mathematical	mathematical	PROPN
ejpam-5395	270	4	monthly	monthly	ADV
ejpam-5395	270	5	,	,	PUNCT
ejpam-5395	270	6	70:36–41	70:36–41	NUM
ejpam-5395	270	7	,	,	PUNCT
ejpam-5395	270	8	1963	1963	NUM
ejpam-5395	270	9	.	.	PUNCT
ejpam-5395	271	1	[	[	X
ejpam-5395	271	2	26	26	NUM
ejpam-5395	271	3	]	]	PUNCT
ejpam-5395	272	1	p.	p.	NOUN
ejpam-5395	272	2	e.	e.	PROPN
ejpam-5395	273	1	long	long	PROPN
ejpam-5395	273	2	and	and	CCONJ
ejpam-5395	273	3	l.	l.	PROPN
ejpam-5395	273	4	l.	l.	PROPN
ejpam-5395	273	5	herrington	herrington	PROPN
ejpam-5395	273	6	.	.	PUNCT
ejpam-5395	274	1	the	the	DET
ejpam-5395	274	2	tθ	tθ	NOUN
ejpam-5395	274	3	-	-	PUNCT
ejpam-5395	274	4	topology	topology	NOUN
ejpam-5395	274	5	and	and	CCONJ
ejpam-5395	274	6	faintly	faintly	ADV
ejpam-5395	274	7	continuous	continuous	ADJ
ejpam-5395	274	8	functions	function	NOUN
ejpam-5395	274	9	.	.	PUNCT
ejpam-5395	275	1	kyungpook	kyungpook	PROPN
ejpam-5395	275	2	mathematical	mathematical	PROPN
ejpam-5395	275	3	journal	journal	PROPN
ejpam-5395	275	4	,	,	PUNCT
ejpam-5395	275	5	22:7–14	22:7–14	NUM
ejpam-5395	275	6	,	,	PUNCT
ejpam-5395	275	7	1982	1982	NUM
ejpam-5395	275	8	.	.	PUNCT
ejpam-5395	276	1	[	[	X
ejpam-5395	276	2	27	27	NUM
ejpam-5395	276	3	]	]	PUNCT
ejpam-5395	276	4	a.	a.	NOUN
ejpam-5395	276	5	s.	s.	PROPN
ejpam-5395	276	6	mashhour	mashhour	PROPN
ejpam-5395	276	7	,	,	PUNCT
ejpam-5395	276	8	m.	m.	PROPN
ejpam-5395	276	9	e.	e.	PROPN
ejpam-5395	276	10	abd	abd	PROPN
ejpam-5395	276	11	el	el	PROPN
ejpam-5395	276	12	-	-	PROPN
ejpam-5395	276	13	monsef	monsef	ADJ
ejpam-5395	276	14	,	,	PUNCT
ejpam-5395	276	15	and	and	CCONJ
ejpam-5395	276	16	s.	s.	PROPN
ejpam-5395	276	17	n.	n.	PROPN
ejpam-5395	276	18	el	el	PROPN
ejpam-5395	276	19	-	-	PROPN
ejpam-5395	276	20	deeb	deeb	PROPN
ejpam-5395	276	21	.	.	PUNCT
ejpam-5395	277	1	on	on	ADP
ejpam-5395	277	2	precontinuous	precontinuous	ADJ
ejpam-5395	277	3	and	and	CCONJ
ejpam-5395	277	4	weak	weak	ADJ
ejpam-5395	277	5	precontinuous	precontinuous	ADJ
ejpam-5395	277	6	mappings	mapping	NOUN
ejpam-5395	277	7	.	.	PUNCT
ejpam-5395	278	1	proceedings	proceeding	NOUN
ejpam-5395	278	2	of	of	ADP
ejpam-5395	278	3	the	the	DET
ejpam-5395	278	4	mathematical	mathematical	ADJ
ejpam-5395	278	5	and	and	CCONJ
ejpam-5395	278	6	physical	physical	ADJ
ejpam-5395	278	7	society	society	NOUN
ejpam-5395	278	8	of	of	ADP
ejpam-5395	278	9	egypt	egypt	PROPN
ejpam-5395	278	10	,	,	PUNCT
ejpam-5395	278	11	53:47–53	53:47–53	NUM
ejpam-5395	278	12	,	,	PUNCT
ejpam-5395	278	13	1982	1982	NUM
ejpam-5395	278	14	.	.	PUNCT
ejpam-5395	279	1	[	[	X
ejpam-5395	279	2	28	28	NUM
ejpam-5395	279	3	]	]	X
ejpam-5395	279	4	a.	a.	NOUN
ejpam-5395	279	5	a.	a.	NOUN
ejpam-5395	279	6	nasef	nasef	PROPN
ejpam-5395	279	7	and	and	CCONJ
ejpam-5395	279	8	t.	t.	PROPN
ejpam-5395	279	9	noiri	noiri	PROPN
ejpam-5395	279	10	.	.	PUNCT
ejpam-5395	280	1	strong	strong	ADJ
ejpam-5395	280	2	forms	form	NOUN
ejpam-5395	280	3	of	of	ADP
ejpam-5395	280	4	faint	faint	ADJ
ejpam-5395	280	5	continuity	continuity	NOUN
ejpam-5395	280	6	.	.	PUNCT
ejpam-5395	281	1	memoirs	memoir	NOUN
ejpam-5395	281	2	of	of	ADP
ejpam-5395	281	3	the	the	DET
ejpam-5395	281	4	faculty	faculty	NOUN
ejpam-5395	281	5	of	of	ADP
ejpam-5395	281	6	science	science	PROPN
ejpam-5395	281	7	kochi	kochi	PROPN
ejpam-5395	281	8	university	university	PROPN
ejpam-5395	281	9	series	series	NOUN
ejpam-5395	281	10	a	a	DET
ejpam-5395	281	11	mathematics	mathematic	NOUN
ejpam-5395	281	12	,	,	PUNCT
ejpam-5395	281	13	19:21–28	19:21–28	NUM
ejpam-5395	281	14	,	,	PUNCT
ejpam-5395	281	15	1998	1998	NUM
ejpam-5395	281	16	.	.	PUNCT
ejpam-5395	282	1	[	[	X
ejpam-5395	282	2	29	29	NUM
ejpam-5395	282	3	]	]	X
ejpam-5395	282	4	o.	o.	NOUN
ejpam-5395	282	5	nj̊astad	nj̊astad	NOUN
ejpam-5395	282	6	.	.	PUNCT
ejpam-5395	283	1	on	on	ADP
ejpam-5395	283	2	some	some	DET
ejpam-5395	283	3	classes	class	NOUN
ejpam-5395	283	4	of	of	ADP
ejpam-5395	283	5	nearly	nearly	ADV
ejpam-5395	283	6	open	open	ADJ
ejpam-5395	283	7	sets	set	NOUN
ejpam-5395	283	8	.	.	PUNCT
ejpam-5395	284	1	pasific	pasific	PROPN
ejpam-5395	284	2	journal	journal	PROPN
ejpam-5395	284	3	of	of	ADP
ejpam-5395	284	4	mathematics	mathematic	NOUN
ejpam-5395	284	5	,	,	PUNCT
ejpam-5395	284	6	15:961–970	15:961–970	PROPN
ejpam-5395	284	7	,	,	PUNCT
ejpam-5395	284	8	1965	1965	NUM
ejpam-5395	284	9	.	.	PUNCT
ejpam-5395	285	1	[	[	X
ejpam-5395	285	2	30	30	NUM
ejpam-5395	285	3	]	]	PUNCT
ejpam-5395	285	4	t.	t.	PROPN
ejpam-5395	285	5	noiri	noiri	PROPN
ejpam-5395	285	6	.	.	PUNCT
ejpam-5395	286	1	properties	property	NOUN
ejpam-5395	286	2	of	of	ADP
ejpam-5395	286	3	some	some	DET
ejpam-5395	286	4	weak	weak	ADJ
ejpam-5395	286	5	forms	form	NOUN
ejpam-5395	286	6	of	of	ADP
ejpam-5395	286	7	continuity	continuity	NOUN
ejpam-5395	286	8	.	.	PUNCT
ejpam-5395	287	1	international	international	ADJ
ejpam-5395	287	2	journal	journal	PROPN
ejpam-5395	287	3	of	of	ADP
ejpam-5395	287	4	mathematics	mathematics	PROPN
ejpam-5395	287	5	and	and	CCONJ
ejpam-5395	287	6	mathematical	mathematical	ADJ
ejpam-5395	287	7	sciences	science	NOUN
ejpam-5395	287	8	,	,	PUNCT
ejpam-5395	287	9	10:97–111	10:97–111	NUM
ejpam-5395	287	10	,	,	PUNCT
ejpam-5395	287	11	1987	1987	NUM
ejpam-5395	287	12	.	.	PUNCT
ejpam-5395	288	1	[	[	X
ejpam-5395	288	2	31	31	NUM
ejpam-5395	288	3	]	]	PUNCT
ejpam-5395	288	4	t.	t.	PROPN
ejpam-5395	288	5	noiri	noiri	PROPN
ejpam-5395	288	6	and	and	CCONJ
ejpam-5395	288	7	v.	v.	ADP
ejpam-5395	288	8	popa	popa	NOUN
ejpam-5395	288	9	.	.	PUNCT
ejpam-5395	289	1	weak	weak	ADJ
ejpam-5395	289	2	forms	form	NOUN
ejpam-5395	289	3	of	of	ADP
ejpam-5395	289	4	faint	faint	ADJ
ejpam-5395	289	5	continuity	continuity	NOUN
ejpam-5395	289	6	.	.	PUNCT
ejpam-5395	290	1	bulletin	bulletin	PROPN
ejpam-5395	290	2	mathématique	mathématique	PROPN
ejpam-5395	290	3	de	de	X
ejpam-5395	290	4	la	la	PROPN
ejpam-5395	290	5	société	société	PROPN
ejpam-5395	290	6	des	des	PROPN
ejpam-5395	290	7	sciences	science	NOUN
ejpam-5395	290	8	mathématiques	mathématiques	PROPN
ejpam-5395	290	9	de	de	X
ejpam-5395	290	10	la	la	X
ejpam-5395	290	11	république	république	PROPN
ejpam-5395	290	12	socialiste	socialiste	PROPN
ejpam-5395	290	13	de	de	PROPN
ejpam-5395	290	14	roumanie	roumanie	PROPN
ejpam-5395	290	15	,	,	PUNCT
ejpam-5395	290	16	34(82):263–270	34(82):263–270	NUM
ejpam-5395	290	17	,	,	PUNCT
ejpam-5395	290	18	1990	1990	NUM
ejpam-5395	290	19	.	.	PUNCT
ejpam-5395	291	1	[	[	X
ejpam-5395	291	2	32	32	NUM
ejpam-5395	291	3	]	]	PUNCT
ejpam-5395	291	4	t.	t.	PROPN
ejpam-5395	291	5	noiri	noiri	PROPN
ejpam-5395	291	6	and	and	CCONJ
ejpam-5395	291	7	v.	v.	ADP
ejpam-5395	291	8	popa	popa	NOUN
ejpam-5395	291	9	.	.	PUNCT
ejpam-5395	292	1	faintly	faintly	ADV
ejpam-5395	292	2	m	m	ADJ
ejpam-5395	292	3	-	-	ADJ
ejpam-5395	292	4	continuous	continuous	ADJ
ejpam-5395	292	5	functions	function	NOUN
ejpam-5395	292	6	.	.	PUNCT
ejpam-5395	293	1	chaos	chaos	NOUN
ejpam-5395	293	2	,	,	PUNCT
ejpam-5395	293	3	silitons	siliton	NOUN
ejpam-5395	293	4	&	&	CCONJ
ejpam-5395	293	5	fractals	fractal	NOUN
ejpam-5395	293	6	,	,	PUNCT
ejpam-5395	293	7	19:1147–1159	19:1147–1159	NUM
ejpam-5395	293	8	,	,	PUNCT
ejpam-5395	293	9	2004	2004	NUM
ejpam-5395	293	10	.	.	PUNCT
ejpam-5395	294	1	[	[	X
ejpam-5395	294	2	33	33	NUM
ejpam-5395	294	3	]	]	PUNCT
ejpam-5395	294	4	p.	p.	NOUN
ejpam-5395	294	5	pue	pue	NOUN
ejpam-5395	294	6	-	-	PUNCT
ejpam-5395	294	7	on	on	ADP
ejpam-5395	294	8	and	and	CCONJ
ejpam-5395	294	9	c.	c.	PROPN
ejpam-5395	294	10	boonpok	boonpok	PROPN
ejpam-5395	294	11	.	.	PUNCT
ejpam-5395	295	1	θ(λ	θ(λ	PROPN
ejpam-5395	295	2	,	,	PUNCT
ejpam-5395	295	3	p)-continuity	p)-continuity	NOUN
ejpam-5395	295	4	for	for	ADP
ejpam-5395	295	5	functions	function	NOUN
ejpam-5395	295	6	.	.	PUNCT
ejpam-5395	296	1	international	international	ADJ
ejpam-5395	296	2	journal	journal	NOUN
ejpam-5395	296	3	of	of	ADP
ejpam-5395	296	4	mathematics	mathematic	NOUN
ejpam-5395	296	5	and	and	CCONJ
ejpam-5395	296	6	computer	computer	NOUN
ejpam-5395	296	7	science	science	NOUN
ejpam-5395	296	8	,	,	PUNCT
ejpam-5395	296	9	19(2):491–495	19(2):491–495	NUM
ejpam-5395	296	10	,	,	PUNCT
ejpam-5395	296	11	2024	2024	NUM
ejpam-5395	296	12	.	.	PUNCT
ejpam-5395	297	1	[	[	X
ejpam-5395	297	2	34	34	NUM
ejpam-5395	297	3	]	]	X
ejpam-5395	297	4	p.	p.	NOUN
ejpam-5395	297	5	pue	pue	NOUN
ejpam-5395	297	6	-	-	PUNCT
ejpam-5395	297	7	on	on	ADP
ejpam-5395	297	8	,	,	PUNCT
ejpam-5395	297	9	a.	a.	PROPN
ejpam-5395	297	10	sama	sama	PROPN
ejpam-5395	297	11	-	-	PUNCT
ejpam-5395	297	12	ae	ae	PROPN
ejpam-5395	297	13	,	,	PUNCT
ejpam-5395	297	14	and	and	CCONJ
ejpam-5395	297	15	c.	c.	PROPN
ejpam-5395	297	16	boonpok	boonpok	PROPN
ejpam-5395	297	17	.	.	PUNCT
ejpam-5395	298	1	upper	upper	ADJ
ejpam-5395	298	2	and	and	CCONJ
ejpam-5395	298	3	lower	low	ADJ
ejpam-5395	298	4	faint	faint	ADJ
ejpam-5395	298	5	(	(	PUNCT
ejpam-5395	298	6	τ1	τ1	NOUN
ejpam-5395	298	7	,	,	PUNCT
ejpam-5395	298	8	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	298	9	.	.	PUNCT
ejpam-5395	299	1	international	international	ADJ
ejpam-5395	299	2	journal	journal	NOUN
ejpam-5395	299	3	of	of	ADP
ejpam-5395	299	4	analysis	analysis	NOUN
ejpam-5395	299	5	and	and	CCONJ
ejpam-5395	299	6	applications	application	NOUN
ejpam-5395	299	7	,	,	PUNCT
ejpam-5395	299	8	22:169	22:169	NUM
ejpam-5395	299	9	,	,	PUNCT
ejpam-5395	299	10	2024	2024	NUM
ejpam-5395	299	11	.	.	PUNCT
ejpam-5395	300	1	[	[	X
ejpam-5395	300	2	35	35	NUM
ejpam-5395	300	3	]	]	X
ejpam-5395	300	4	n.	n.	NOUN
ejpam-5395	300	5	srisarakham	srisarakham	PROPN
ejpam-5395	300	6	and	and	CCONJ
ejpam-5395	300	7	c.	c.	PROPN
ejpam-5395	300	8	boonpok	boonpok	PROPN
ejpam-5395	300	9	.	.	PUNCT
ejpam-5395	301	1	almost	almost	ADV
ejpam-5395	301	2	(	(	PUNCT
ejpam-5395	301	3	λ	λ	NOUN
ejpam-5395	301	4	,	,	PUNCT
ejpam-5395	301	5	p)-continuous	p)-continuous	ADJ
ejpam-5395	301	6	functions	function	NOUN
ejpam-5395	301	7	.	.	PUNCT
ejpam-5395	302	1	international	international	ADJ
ejpam-5395	302	2	journal	journal	PROPN
ejpam-5395	302	3	of	of	ADP
ejpam-5395	302	4	mathematics	mathematic	NOUN
ejpam-5395	302	5	and	and	CCONJ
ejpam-5395	302	6	computer	computer	NOUN
ejpam-5395	302	7	science	science	NOUN
ejpam-5395	302	8	,	,	PUNCT
ejpam-5395	302	9	18(2):255–259	18(2):255–259	NUM
ejpam-5395	302	10	,	,	PUNCT
ejpam-5395	302	11	2023	2023	NUM
ejpam-5395	302	12	.	.	PUNCT
ejpam-5395	303	1	references	reference	NOUN
ejpam-5395	303	2	2762	2762	NUM
ejpam-5395	303	3	[	[	SYM
ejpam-5395	303	4	36	36	NUM
ejpam-5395	303	5	]	]	X
ejpam-5395	303	6	n.	n.	PROPN
ejpam-5395	303	7	srisarakham	srisarakham	PROPN
ejpam-5395	303	8	,	,	PUNCT
ejpam-5395	303	9	s.	s.	PROPN
ejpam-5395	303	10	sompong	sompong	PROPN
ejpam-5395	303	11	,	,	PUNCT
ejpam-5395	303	12	and	and	CCONJ
ejpam-5395	303	13	c.	c.	PROPN
ejpam-5395	303	14	boonpok	boonpok	PROPN
ejpam-5395	303	15	.	.	PUNCT
ejpam-5395	304	1	slight	slight	ADJ
ejpam-5395	304	2	(	(	PUNCT
ejpam-5395	304	3	τ1	τ1	NOUN
ejpam-5395	304	4	,	,	PUNCT
ejpam-5395	304	5	τ2)-continuity	τ2)-continuity	NOUN
ejpam-5395	304	6	for	for	ADP
ejpam-5395	304	7	functions	function	NOUN
ejpam-5395	304	8	.	.	PUNCT
ejpam-5395	305	1	international	international	ADJ
ejpam-5395	305	2	journal	journal	NOUN
ejpam-5395	305	3	of	of	ADP
ejpam-5395	305	4	mathematics	mathematic	NOUN
ejpam-5395	305	5	and	and	CCONJ
ejpam-5395	305	6	computer	computer	NOUN
ejpam-5395	305	7	science	science	NOUN
ejpam-5395	305	8	,	,	PUNCT
ejpam-5395	305	9	20(1):211–215	20(1):211–215	PROPN
ejpam-5395	305	10	,	,	PUNCT
ejpam-5395	305	11	2025	2025	NUM
ejpam-5395	305	12	.	.	PUNCT
ejpam-5395	306	1	[	[	X
ejpam-5395	306	2	37	37	NUM
ejpam-5395	306	3	]	]	PUNCT
ejpam-5395	306	4	m.	m.	NOUN
ejpam-5395	306	5	thongmoon	thongmoon	NOUN
ejpam-5395	306	6	and	and	CCONJ
ejpam-5395	306	7	c.	c.	PROPN
ejpam-5395	306	8	boonpok	boonpok	PROPN
ejpam-5395	306	9	.	.	PUNCT
ejpam-5395	307	1	strongly	strongly	ADV
ejpam-5395	307	2	θ(λ	θ(λ	PROPN
ejpam-5395	307	3	,	,	PUNCT
ejpam-5395	307	4	p)-continuous	p)-continuous	ADJ
ejpam-5395	307	5	functions	function	NOUN
ejpam-5395	307	6	.	.	PUNCT
ejpam-5395	308	1	international	international	ADJ
ejpam-5395	308	2	journal	journal	PROPN
ejpam-5395	308	3	of	of	ADP
ejpam-5395	308	4	mathematics	mathematic	NOUN
ejpam-5395	308	5	and	and	CCONJ
ejpam-5395	308	6	computer	computer	NOUN
ejpam-5395	308	7	science	science	NOUN
ejpam-5395	308	8	,	,	PUNCT
ejpam-5395	308	9	19(2):475–479	19(2):475–479	PROPN
ejpam-5395	308	10	,	,	PUNCT
ejpam-5395	308	11	2024	2024	NUM
ejpam-5395	308	12	.	.	PUNCT
ejpam-5395	309	1	[	[	X
ejpam-5395	309	2	38	38	NUM
ejpam-5395	309	3	]	]	X
ejpam-5395	309	4	n.	n.	NOUN
ejpam-5395	309	5	v.	v.	ADP
ejpam-5395	309	6	veličko	veličko	PROPN
ejpam-5395	309	7	.	.	PUNCT
ejpam-5395	310	1	h	h	NOUN
ejpam-5395	310	2	-	-	PUNCT
ejpam-5395	310	3	closed	close	VERB
ejpam-5395	310	4	topological	topological	ADJ
ejpam-5395	310	5	spaces	space	NOUN
ejpam-5395	310	6	.	.	PUNCT
ejpam-5395	311	1	american	american	PROPN
ejpam-5395	311	2	mathematical	mathematical	ADJ
ejpam-5395	311	3	society	society	NOUN
ejpam-5395	311	4	translations	translation	NOUN
ejpam-5395	311	5	,	,	PUNCT
ejpam-5395	311	6	78(2):102–118	78(2):102–118	NUM
ejpam-5395	311	7	,	,	PUNCT
ejpam-5395	311	8	1968	1968	NUM
ejpam-5395	311	9	.	.	PUNCT
ejpam-5395	312	1	[	[	X
ejpam-5395	312	2	39	39	NUM
ejpam-5395	312	3	]	]	PUNCT
ejpam-5395	312	4	c.	c.	PROPN
ejpam-5395	312	5	viriyapong	viriyapong	PROPN
ejpam-5395	312	6	and	and	CCONJ
ejpam-5395	312	7	c.	c.	PROPN
ejpam-5395	312	8	boonpok	boonpok	PROPN
ejpam-5395	312	9	.	.	PUNCT
ejpam-5395	313	1	(	(	PUNCT
ejpam-5395	313	2	τ1	τ1	NOUN
ejpam-5395	313	3	,	,	PUNCT
ejpam-5395	313	4	τ2)α	τ2)α	NOUN
ejpam-5395	313	5	-	-	PUNCT
ejpam-5395	313	6	continuity	continuity	NOUN
ejpam-5395	313	7	for	for	ADP
ejpam-5395	313	8	multifunctions	multifunction	NOUN
ejpam-5395	313	9	.	.	PUNCT
ejpam-5395	314	1	journal	journal	PROPN
ejpam-5395	314	2	of	of	ADP
ejpam-5395	314	3	mathematics	mathematic	NOUN
ejpam-5395	314	4	,	,	PUNCT
ejpam-5395	314	5	2020:6285763	2020:6285763	NUM
ejpam-5395	314	6	,	,	PUNCT
ejpam-5395	314	7	2020	2020	NUM
ejpam-5395	314	8	.	.	PUNCT
ejpam-5395	315	1	[	[	X
ejpam-5395	315	2	40	40	NUM
ejpam-5395	315	3	]	]	PUNCT
ejpam-5395	315	4	c.	c.	PROPN
ejpam-5395	315	5	viriyapong	viriyapong	PROPN
ejpam-5395	315	6	and	and	CCONJ
ejpam-5395	315	7	c.	c.	PROPN
ejpam-5395	315	8	boonpok	boonpok	PROPN
ejpam-5395	315	9	.	.	PUNCT
ejpam-5395	316	1	(	(	PUNCT
ejpam-5395	316	2	λ	λ	X
ejpam-5395	316	3	,	,	PUNCT
ejpam-5395	316	4	sp)-continuous	sp)-continuous	ADJ
ejpam-5395	316	5	functions	function	NOUN
ejpam-5395	316	6	.	.	PUNCT
ejpam-5395	317	1	wseas	wseas	VERB
ejpam-5395	317	2	transactions	transaction	NOUN
ejpam-5395	317	3	on	on	ADP
ejpam-5395	317	4	mathematics	mathematic	NOUN
ejpam-5395	317	5	,	,	PUNCT
ejpam-5395	317	6	21:380–385	21:380–385	NUM
ejpam-5395	317	7	,	,	PUNCT
ejpam-5395	317	8	2022	2022	NUM
ejpam-5395	317	9	.	.	PUNCT
ejpam-5395	318	1	[	[	X
ejpam-5395	318	2	41	41	NUM
ejpam-5395	318	3	]	]	X
ejpam-5395	318	4	n.	n.	PROPN
ejpam-5395	318	5	viriyapong	viriyapong	PROPN
ejpam-5395	318	6	,	,	PUNCT
ejpam-5395	318	7	s.	s.	PROPN
ejpam-5395	318	8	sompong	sompong	PROPN
ejpam-5395	318	9	,	,	PUNCT
ejpam-5395	318	10	and	and	CCONJ
ejpam-5395	318	11	c.	c.	PROPN
ejpam-5395	318	12	boonpok	boonpok	PROPN
ejpam-5395	318	13	.	.	PUNCT
ejpam-5395	319	1	(	(	PUNCT
ejpam-5395	319	2	τ1	τ1	NOUN
ejpam-5395	319	3	,	,	PUNCT
ejpam-5395	319	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-5395	319	5	disconnectedness	disconnectedness	NOUN
ejpam-5395	319	6	in	in	ADP
ejpam-5395	319	7	bitopological	bitopological	ADJ
ejpam-5395	319	8	spaces	space	NOUN
ejpam-5395	319	9	.	.	PUNCT
ejpam-5395	320	1	international	international	ADJ
ejpam-5395	320	2	journal	journal	PROPN
ejpam-5395	320	3	of	of	ADP
ejpam-5395	320	4	mathematics	mathematic	NOUN
ejpam-5395	320	5	and	and	CCONJ
ejpam-5395	320	6	computer	computer	NOUN
ejpam-5395	320	7	science	science	NOUN
ejpam-5395	320	8	,	,	PUNCT
ejpam-5395	320	9	19(3):855–860	19(3):855–860	PROPN
ejpam-5395	320	10	,	,	PUNCT
ejpam-5395	320	11	2024	2024	NUM
ejpam-5395	320	12	.	.	PUNCT