id	sid	tid	token	lemma	pos
ejpam-6017	1	1	european	european	PROPN
ejpam-6017	1	2	journal	journal	PROPN
ejpam-6017	1	3	of	of	ADP
ejpam-6017	1	4	pure	pure	ADJ
ejpam-6017	1	5	and	and	CCONJ
ejpam-6017	1	6	applied	applied	ADJ
ejpam-6017	1	7	mathematics	mathematic	NOUN
ejpam-6017	1	8	2025	2025	NUM
ejpam-6017	1	9	,	,	PUNCT
ejpam-6017	1	10	vol	vol	NOUN
ejpam-6017	1	11	.	.	PROPN
ejpam-6017	1	12	18	18	NUM
ejpam-6017	1	13	,	,	PUNCT
ejpam-6017	1	14	issue	issue	NOUN
ejpam-6017	1	15	2	2	NUM
ejpam-6017	1	16	,	,	PUNCT
ejpam-6017	1	17	article	article	NOUN
ejpam-6017	1	18	number	number	NOUN
ejpam-6017	1	19	6017	6017	NUM
ejpam-6017	1	20	issn	issn	VERB
ejpam-6017	1	21	1307	1307	NUM
ejpam-6017	1	22	-	-	SYM
ejpam-6017	1	23	5543	5543	NUM
ejpam-6017	1	24	–	–	PUNCT
ejpam-6017	1	25	ejpam.com	ejpam.com	X
ejpam-6017	1	26	published	publish	VERB
ejpam-6017	1	27	by	by	ADP
ejpam-6017	1	28	new	new	PROPN
ejpam-6017	1	29	york	york	PROPN
ejpam-6017	1	30	business	business	PROPN
ejpam-6017	1	31	global	global	PROPN
ejpam-6017	1	32	on	on	ADP
ejpam-6017	1	33	strongly	strongly	ADV
ejpam-6017	1	34	θ(τ1	θ(τ1	NOUN
ejpam-6017	1	35	,	,	PUNCT
ejpam-6017	1	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	1	37	functions	function	NOUN
ejpam-6017	1	38	prapart	prapart	VERB
ejpam-6017	1	39	pue	pue	PROPN
ejpam-6017	1	40	-	-	PUNCT
ejpam-6017	1	41	on1	on1	PROPN
ejpam-6017	1	42	,	,	PUNCT
ejpam-6017	1	43	supunnee	supunnee	PROPN
ejpam-6017	1	44	sompong2	sompong2	PROPN
ejpam-6017	1	45	,	,	PUNCT
ejpam-6017	1	46	chawalit	chawalit	VERB
ejpam-6017	1	47	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6017	1	48	1	1	NUM
ejpam-6017	1	49	mathematics	mathematic	NOUN
ejpam-6017	1	50	and	and	CCONJ
ejpam-6017	1	51	applied	apply	VERB
ejpam-6017	1	52	mathematics	mathematics	PROPN
ejpam-6017	1	53	research	research	NOUN
ejpam-6017	1	54	unit	unit	NOUN
ejpam-6017	1	55	,	,	PUNCT
ejpam-6017	1	56	department	department	NOUN
ejpam-6017	1	57	of	of	ADP
ejpam-6017	1	58	mathematics	mathematic	NOUN
ejpam-6017	1	59	,	,	PUNCT
ejpam-6017	1	60	faculty	faculty	NOUN
ejpam-6017	1	61	of	of	ADP
ejpam-6017	1	62	science	science	NOUN
ejpam-6017	1	63	,	,	PUNCT
ejpam-6017	1	64	mahasarakham	mahasarakham	PROPN
ejpam-6017	1	65	university	university	PROPN
ejpam-6017	1	66	,	,	PUNCT
ejpam-6017	1	67	maha	maha	PROPN
ejpam-6017	1	68	sarakham	sarakham	PROPN
ejpam-6017	1	69	,	,	PUNCT
ejpam-6017	1	70	44150	44150	NUM
ejpam-6017	1	71	,	,	PUNCT
ejpam-6017	1	72	thailand	thailand	PROPN
ejpam-6017	1	73	2	2	NUM
ejpam-6017	1	74	department	department	NOUN
ejpam-6017	1	75	of	of	ADP
ejpam-6017	1	76	mathematics	mathematic	NOUN
ejpam-6017	1	77	and	and	CCONJ
ejpam-6017	1	78	statistics	statistic	NOUN
ejpam-6017	1	79	,	,	PUNCT
ejpam-6017	1	80	faculty	faculty	NOUN
ejpam-6017	1	81	of	of	ADP
ejpam-6017	1	82	science	science	NOUN
ejpam-6017	1	83	and	and	CCONJ
ejpam-6017	1	84	technology	technology	NOUN
ejpam-6017	1	85	,	,	PUNCT
ejpam-6017	1	86	sakon	sakon	PROPN
ejpam-6017	1	87	nakhon	nakhon	PROPN
ejpam-6017	1	88	rajbhat	rajbhat	PROPN
ejpam-6017	1	89	university	university	PROPN
ejpam-6017	1	90	,	,	PUNCT
ejpam-6017	1	91	sakon	sakon	PROPN
ejpam-6017	1	92	nakhon	nakhon	PROPN
ejpam-6017	1	93	,	,	PUNCT
ejpam-6017	1	94	47000	47000	NUM
ejpam-6017	1	95	,	,	PUNCT
ejpam-6017	1	96	thailand	thailand	PROPN
ejpam-6017	1	97	abstract	abstract	NOUN
ejpam-6017	1	98	.	.	PUNCT
ejpam-6017	2	1	this	this	DET
ejpam-6017	2	2	paper	paper	NOUN
ejpam-6017	2	3	deals	deal	NOUN
ejpam-6017	2	4	with	with	ADP
ejpam-6017	2	5	the	the	DET
ejpam-6017	2	6	concept	concept	NOUN
ejpam-6017	2	7	of	of	ADP
ejpam-6017	2	8	strongly	strongly	ADV
ejpam-6017	2	9	θ(τ1	θ(τ1	NOUN
ejpam-6017	2	10	,	,	PUNCT
ejpam-6017	2	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	2	12	functions	function	NOUN
ejpam-6017	2	13	.	.	PUNCT
ejpam-6017	3	1	furthermore	furthermore	ADV
ejpam-6017	3	2	,	,	PUNCT
ejpam-6017	3	3	some	some	DET
ejpam-6017	3	4	characterizations	characterization	NOUN
ejpam-6017	3	5	and	and	CCONJ
ejpam-6017	3	6	several	several	ADJ
ejpam-6017	3	7	properties	property	NOUN
ejpam-6017	3	8	concerning	concern	VERB
ejpam-6017	3	9	strongly	strongly	ADV
ejpam-6017	3	10	θ(τ1	θ(τ1	NOUN
ejpam-6017	3	11	,	,	PUNCT
ejpam-6017	3	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	3	13	functions	function	NOUN
ejpam-6017	3	14	are	be	AUX
ejpam-6017	3	15	considered	consider	VERB
ejpam-6017	3	16	.	.	PUNCT
ejpam-6017	4	1	2020	2020	NUM
ejpam-6017	4	2	mathematics	mathematic	NOUN
ejpam-6017	4	3	subject	subject	NOUN
ejpam-6017	4	4	classifications	classification	NOUN
ejpam-6017	4	5	:	:	PUNCT
ejpam-6017	4	6	54c08	54c08	NUM
ejpam-6017	4	7	;	;	PUNCT
ejpam-6017	4	8	54e55	54e55	NUM
ejpam-6017	4	9	key	key	ADJ
ejpam-6017	4	10	words	word	NOUN
ejpam-6017	4	11	and	and	CCONJ
ejpam-6017	4	12	phrases	phrase	NOUN
ejpam-6017	4	13	:	:	PUNCT
ejpam-6017	4	14	(	(	PUNCT
ejpam-6017	4	15	τ1	τ1	NOUN
ejpam-6017	4	16	,	,	PUNCT
ejpam-6017	4	17	τ2)θ	τ2)θ	ADJ
ejpam-6017	4	18	-	-	PUNCT
ejpam-6017	4	19	open	open	ADJ
ejpam-6017	4	20	set	set	NOUN
ejpam-6017	4	21	,	,	PUNCT
ejpam-6017	4	22	strongly	strongly	ADV
ejpam-6017	4	23	θ(τ1	θ(τ1	VERB
ejpam-6017	4	24	,	,	PUNCT
ejpam-6017	4	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	4	26	function	function	NOUN
ejpam-6017	4	27	1	1	NUM
ejpam-6017	4	28	.	.	PUNCT
ejpam-6017	4	29	introduction	introduction	NOUN
ejpam-6017	4	30	in	in	ADP
ejpam-6017	4	31	1941	1941	NUM
ejpam-6017	4	32	,	,	PUNCT
ejpam-6017	4	33	fomin	fomin	VERB
ejpam-6017	5	1	[	[	X
ejpam-6017	5	2	1	1	X
ejpam-6017	5	3	]	]	PUNCT
ejpam-6017	5	4	introduced	introduce	VERB
ejpam-6017	5	5	the	the	DET
ejpam-6017	5	6	concept	concept	NOUN
ejpam-6017	5	7	of	of	ADP
ejpam-6017	5	8	θ	θ	ADJ
ejpam-6017	5	9	-	-	ADJ
ejpam-6017	5	10	continuous	continuous	ADJ
ejpam-6017	5	11	functions	function	NOUN
ejpam-6017	5	12	.	.	PUNCT
ejpam-6017	6	1	noiri	noiri	ADV
ejpam-6017	7	1	[	[	X
ejpam-6017	7	2	2	2	X
ejpam-6017	7	3	]	]	PUNCT
ejpam-6017	7	4	studied	study	VERB
ejpam-6017	7	5	some	some	DET
ejpam-6017	7	6	properties	property	NOUN
ejpam-6017	7	7	of	of	ADP
ejpam-6017	7	8	θ	θ	ADJ
ejpam-6017	7	9	-	-	ADJ
ejpam-6017	7	10	continuous	continuous	ADJ
ejpam-6017	7	11	functions	function	NOUN
ejpam-6017	7	12	.	.	PUNCT
ejpam-6017	8	1	popa	popa	NOUN
ejpam-6017	9	1	[	[	X
ejpam-6017	9	2	3	3	NUM
ejpam-6017	9	3	]	]	PUNCT
ejpam-6017	9	4	investigated	investigate	VERB
ejpam-6017	9	5	several	several	ADJ
ejpam-6017	9	6	characterizations	characterization	NOUN
ejpam-6017	9	7	of	of	ADP
ejpam-6017	9	8	θ	θ	ADJ
ejpam-6017	9	9	-	-	ADJ
ejpam-6017	9	10	continuous	continuous	ADJ
ejpam-6017	9	11	functions	function	NOUN
ejpam-6017	9	12	.	.	PUNCT
ejpam-6017	10	1	arya	arya	PROPN
ejpam-6017	10	2	and	and	CCONJ
ejpam-6017	10	3	bhamini	bhamini	PROPN
ejpam-6017	11	1	[	[	X
ejpam-6017	11	2	4	4	NUM
ejpam-6017	11	3	]	]	PUNCT
ejpam-6017	11	4	introduced	introduce	VERB
ejpam-6017	11	5	the	the	DET
ejpam-6017	11	6	notion	notion	NOUN
ejpam-6017	11	7	of	of	ADP
ejpam-6017	11	8	θsemi	θsemi	ADJ
ejpam-6017	11	9	-	-	PUNCT
ejpam-6017	11	10	continuous	continuous	ADJ
ejpam-6017	11	11	functions	function	NOUN
ejpam-6017	11	12	.	.	PUNCT
ejpam-6017	12	1	jafari	jafari	PROPN
ejpam-6017	12	2	and	and	CCONJ
ejpam-6017	12	3	noiri	noiri	ADV
ejpam-6017	13	1	[	[	X
ejpam-6017	13	2	5	5	NUM
ejpam-6017	13	3	]	]	PUNCT
ejpam-6017	13	4	investigated	investigate	VERB
ejpam-6017	13	5	several	several	ADJ
ejpam-6017	13	6	characterizations	characterization	NOUN
ejpam-6017	13	7	of	of	ADP
ejpam-6017	13	8	θ	θ	NOUN
ejpam-6017	13	9	-	-	PUNCT
ejpam-6017	13	10	semi	semi	ADJ
ejpam-6017	13	11	-	-	ADJ
ejpam-6017	13	12	continuous	continuous	ADJ
ejpam-6017	13	13	functions	function	NOUN
ejpam-6017	13	14	.	.	PUNCT
ejpam-6017	14	1	noiri	noiri	ADV
ejpam-6017	15	1	[	[	X
ejpam-6017	15	2	6	6	NUM
ejpam-6017	15	3	]	]	PUNCT
ejpam-6017	15	4	introduced	introduce	VERB
ejpam-6017	15	5	and	and	CCONJ
ejpam-6017	15	6	investigated	investigate	VERB
ejpam-6017	15	7	the	the	DET
ejpam-6017	15	8	concept	concept	NOUN
ejpam-6017	15	9	of	of	ADP
ejpam-6017	15	10	θprecontinuous	θprecontinuous	ADJ
ejpam-6017	15	11	functions	function	NOUN
ejpam-6017	15	12	.	.	PUNCT
ejpam-6017	16	1	in	in	ADP
ejpam-6017	16	2	1981	1981	NUM
ejpam-6017	16	3	,	,	PUNCT
ejpam-6017	16	4	long	long	ADJ
ejpam-6017	16	5	and	and	CCONJ
ejpam-6017	16	6	herrington	herrington	PROPN
ejpam-6017	17	1	[	[	X
ejpam-6017	17	2	7	7	NUM
ejpam-6017	17	3	]	]	PUNCT
ejpam-6017	17	4	investigated	investigate	VERB
ejpam-6017	17	5	some	some	DET
ejpam-6017	17	6	characterizations	characterization	NOUN
ejpam-6017	17	7	of	of	ADP
ejpam-6017	17	8	strongly	strongly	ADV
ejpam-6017	17	9	θ	θ	ADJ
ejpam-6017	17	10	-	-	ADJ
ejpam-6017	17	11	continuous	continuous	ADJ
ejpam-6017	17	12	functions	function	NOUN
ejpam-6017	17	13	.	.	PUNCT
ejpam-6017	18	1	jafari	jafari	PROPN
ejpam-6017	18	2	and	and	CCONJ
ejpam-6017	18	3	noiri	noiri	ADV
ejpam-6017	19	1	[	[	X
ejpam-6017	19	2	8	8	NUM
ejpam-6017	19	3	]	]	PUNCT
ejpam-6017	19	4	introduced	introduce	VERB
ejpam-6017	19	5	and	and	CCONJ
ejpam-6017	19	6	investigated	investigate	VERB
ejpam-6017	19	7	the	the	DET
ejpam-6017	19	8	concept	concept	NOUN
ejpam-6017	19	9	of	of	ADP
ejpam-6017	19	10	strongly	strongly	ADV
ejpam-6017	19	11	θ	θ	NOUN
ejpam-6017	19	12	-	-	PUNCT
ejpam-6017	19	13	semi	semi	ADJ
ejpam-6017	19	14	-	-	ADJ
ejpam-6017	19	15	continuous	continuous	ADJ
ejpam-6017	19	16	functions	function	NOUN
ejpam-6017	19	17	.	.	PUNCT
ejpam-6017	20	1	noiri	noiri	ADV
ejpam-6017	21	1	[	[	X
ejpam-6017	21	2	9	9	NUM
ejpam-6017	21	3	]	]	PUNCT
ejpam-6017	21	4	introduced	introduce	VERB
ejpam-6017	21	5	and	and	CCONJ
ejpam-6017	21	6	studied	study	VERB
ejpam-6017	21	7	the	the	DET
ejpam-6017	21	8	notion	notion	NOUN
ejpam-6017	21	9	of	of	ADP
ejpam-6017	21	10	strongly	strongly	ADV
ejpam-6017	21	11	θ	θ	ADJ
ejpam-6017	21	12	-	-	ADJ
ejpam-6017	21	13	precontinuous	precontinuous	ADJ
ejpam-6017	21	14	functions	function	NOUN
ejpam-6017	21	15	.	.	PUNCT
ejpam-6017	22	1	noiri	noiri	PROPN
ejpam-6017	22	2	and	and	CCONJ
ejpam-6017	22	3	popa	popa	NOUN
ejpam-6017	22	4	[	[	X
ejpam-6017	22	5	10	10	NUM
ejpam-6017	22	6	]	]	PUNCT
ejpam-6017	22	7	introduced	introduce	VERB
ejpam-6017	22	8	and	and	CCONJ
ejpam-6017	22	9	investigated	investigate	VERB
ejpam-6017	22	10	the	the	DET
ejpam-6017	22	11	concept	concept	NOUN
ejpam-6017	22	12	of	of	ADP
ejpam-6017	22	13	strongly	strongly	ADV
ejpam-6017	22	14	θ	θ	NOUN
ejpam-6017	22	15	-	-	PUNCT
ejpam-6017	22	16	β	β	ADJ
ejpam-6017	22	17	-	-	ADJ
ejpam-6017	22	18	continuous	continuous	ADJ
ejpam-6017	22	19	functions	function	NOUN
ejpam-6017	22	20	.	.	PUNCT
ejpam-6017	23	1	on	on	ADP
ejpam-6017	23	2	the	the	DET
ejpam-6017	23	3	other	other	ADJ
ejpam-6017	23	4	hand	hand	NOUN
ejpam-6017	23	5	,	,	PUNCT
ejpam-6017	23	6	di	di	NOUN
ejpam-6017	23	7	maio	maio	PROPN
ejpam-6017	23	8	and	and	CCONJ
ejpam-6017	23	9	noiri	noiri	ADV
ejpam-6017	23	10	[	[	X
ejpam-6017	23	11	11	11	NUM
ejpam-6017	23	12	]	]	PUNCT
ejpam-6017	23	13	introduced	introduce	VERB
ejpam-6017	23	14	the	the	DET
ejpam-6017	23	15	concept	concept	NOUN
ejpam-6017	23	16	of	of	ADP
ejpam-6017	23	17	strongly	strongly	ADV
ejpam-6017	23	18	irresolute	irresolute	ADJ
ejpam-6017	23	19	functions	function	NOUN
ejpam-6017	23	20	.	.	PUNCT
ejpam-6017	24	1	pal	pal	NOUN
ejpam-6017	24	2	and	and	CCONJ
ejpam-6017	24	3	bhattacharyya	bhattacharyya	ADJ
ejpam-6017	25	1	[	[	X
ejpam-6017	25	2	12	12	NUM
ejpam-6017	25	3	]	]	PUNCT
ejpam-6017	25	4	introduced	introduce	VERB
ejpam-6017	25	5	and	and	CCONJ
ejpam-6017	25	6	investigated	investigate	VERB
ejpam-6017	25	7	the	the	DET
ejpam-6017	25	8	notion	notion	NOUN
ejpam-6017	25	9	of	of	ADP
ejpam-6017	25	10	strongly	strongly	ADV
ejpam-6017	25	11	preirresolute	preirresolute	ADJ
ejpam-6017	25	12	functions	function	NOUN
ejpam-6017	25	13	.	.	PUNCT
ejpam-6017	26	1	noiri	noiri	PROPN
ejpam-6017	27	1	[	[	X
ejpam-6017	27	2	13	13	NUM
ejpam-6017	27	3	]	]	PUNCT
ejpam-6017	27	4	investigated	investigate	VERB
ejpam-6017	27	5	several	several	ADJ
ejpam-6017	27	6	characterizations	characterization	NOUN
ejpam-6017	27	7	of	of	ADP
ejpam-6017	27	8	strongly	strongly	ADV
ejpam-6017	27	9	β	β	ADJ
ejpam-6017	27	10	-	-	PUNCT
ejpam-6017	27	11	irresolute	irresolute	ADJ
ejpam-6017	27	12	functions	function	NOUN
ejpam-6017	27	13	.	.	PUNCT
ejpam-6017	28	1	jafari	jafari	PROPN
ejpam-6017	28	2	and	and	CCONJ
ejpam-6017	28	3	noiri	noiri	ADV
ejpam-6017	29	1	[	[	X
ejpam-6017	29	2	14	14	NUM
ejpam-6017	29	3	]	]	PUNCT
ejpam-6017	29	4	studied	study	VERB
ejpam-6017	29	5	some	some	DET
ejpam-6017	29	6	characterizations	characterization	NOUN
ejpam-6017	29	7	of	of	ADP
ejpam-6017	29	8	strongly	strongly	ADV
ejpam-6017	29	9	sober	sober	ADJ
ejpam-6017	29	10	θ	θ	ADJ
ejpam-6017	29	11	-	-	ADJ
ejpam-6017	29	12	continuous	continuous	ADJ
ejpam-6017	29	13	functions	function	NOUN
ejpam-6017	29	14	.	.	PUNCT
ejpam-6017	30	1	these	these	DET
ejpam-6017	30	2	classes	class	NOUN
ejpam-6017	30	3	of	of	ADP
ejpam-6017	30	4	functions	function	NOUN
ejpam-6017	30	5	have	have	VERB
ejpam-6017	30	6	characterizations	characterization	NOUN
ejpam-6017	30	7	similar	similar	ADJ
ejpam-6017	30	8	to	to	ADP
ejpam-6017	30	9	the	the	DET
ejpam-6017	30	10	class	class	NOUN
ejpam-6017	30	11	of	of	ADP
ejpam-6017	30	12	strongly	strongly	ADV
ejpam-6017	30	13	θ	θ	ADJ
ejpam-6017	30	14	-	-	ADJ
ejpam-6017	30	15	continuous	continuous	ADJ
ejpam-6017	30	16	functions	function	NOUN
ejpam-6017	30	17	.	.	PUNCT
ejpam-6017	31	1	in	in	ADP
ejpam-6017	31	2	2005	2005	NUM
ejpam-6017	31	3	,	,	PUNCT
ejpam-6017	31	4	noiri	noiri	ADV
ejpam-6017	31	5	and	and	CCONJ
ejpam-6017	31	6	popa	popa	NOUN
ejpam-6017	31	7	[	[	X
ejpam-6017	31	8	15	15	NUM
ejpam-6017	31	9	]	]	PUNCT
ejpam-6017	31	10	introduced	introduce	VERB
ejpam-6017	31	11	a	a	DET
ejpam-6017	31	12	new	new	ADJ
ejpam-6017	31	13	class	class	NOUN
ejpam-6017	31	14	of	of	ADP
ejpam-6017	31	15	functions	function	NOUN
ejpam-6017	31	16	called	call	VERB
ejpam-6017	31	17	strongly	strongly	ADV
ejpam-6017	31	18	θ	θ	PROPN
ejpam-6017	31	19	-	-	ADJ
ejpam-6017	31	20	m	m	VERB
ejpam-6017	31	21	-continuous	-continuous	ADJ
ejpam-6017	31	22	functions	function	NOUN
ejpam-6017	31	23	as	as	ADP
ejpam-6017	31	24	functions	function	NOUN
ejpam-6017	31	25	defined	define	VERB
ejpam-6017	31	26	between	between	ADP
ejpam-6017	31	27	sets	set	NOUN
ejpam-6017	31	28	satisfying	satisfy	VERB
ejpam-6017	31	29	∗corresponding	∗corresponde	VERB
ejpam-6017	31	30	author	author	NOUN
ejpam-6017	31	31	.	.	PUNCT
ejpam-6017	32	1	doi	doi	NOUN
ejpam-6017	32	2	:	:	PUNCT
ejpam-6017	32	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6017	https://doi.org/10.29020/nybg.ejpam.v18i2.6017	ADP
ejpam-6017	32	4	email	email	NOUN
ejpam-6017	32	5	addresses	address	NOUN
ejpam-6017	32	6	:	:	PUNCT
ejpam-6017	32	7	prapart.p@msu.ac.th	prapart.p@msu.ac.th	PROPN
ejpam-6017	32	8	(	(	PUNCT
ejpam-6017	32	9	p.	p.	NOUN
ejpam-6017	32	10	pue	pue	NOUN
ejpam-6017	32	11	-	-	PUNCT
ejpam-6017	32	12	on	on	ADP
ejpam-6017	32	13	)	)	PUNCT
ejpam-6017	32	14	,	,	PUNCT
ejpam-6017	32	15	s−sompong@snru.ac.th	s−sompong@snru.ac.th	PRON
ejpam-6017	32	16	(	(	PUNCT
ejpam-6017	32	17	s.	s.	PROPN
ejpam-6017	32	18	sompong	sompong	PROPN
ejpam-6017	32	19	)	)	PUNCT
ejpam-6017	32	20	,	,	PUNCT
ejpam-6017	32	21	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6017	32	22	(	(	PUNCT
ejpam-6017	32	23	c.	c.	PROPN
ejpam-6017	32	24	boonpok	boonpok	PROPN
ejpam-6017	32	25	)	)	PUNCT
ejpam-6017	32	26	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6017	33	1	1	1	NUM
ejpam-6017	33	2	copyright	copyright	NOUN
ejpam-6017	33	3	:	:	PUNCT
ejpam-6017	33	4	©	©	PROPN
ejpam-6017	33	5	2025	2025	NUM
ejpam-6017	33	6	the	the	DET
ejpam-6017	33	7	author(s	author(s	NOUN
ejpam-6017	33	8	)	)	PUNCT
ejpam-6017	33	9	.	.	PUNCT
ejpam-6017	34	1	(	(	PUNCT
ejpam-6017	34	2	cc	cc	NOUN
ejpam-6017	34	3	by	by	ADP
ejpam-6017	34	4	-	-	PUNCT
ejpam-6017	34	5	nc	nc	PROPN
ejpam-6017	34	6	4.0	4.0	NUM
ejpam-6017	34	7	)	)	PUNCT
ejpam-6017	34	8	p.	p.	NOUN
ejpam-6017	34	9	pue	pue	NOUN
ejpam-6017	34	10	-	-	PUNCT
ejpam-6017	34	11	on	on	ADP
ejpam-6017	34	12	,	,	PUNCT
ejpam-6017	34	13	s.	s.	PROPN
ejpam-6017	34	14	sompong	sompong	PROPN
ejpam-6017	34	15	,	,	PUNCT
ejpam-6017	34	16	c.	c.	PROPN
ejpam-6017	34	17	boonpok	boonpok	PROPN
ejpam-6017	34	18	/	/	SYM
ejpam-6017	34	19	eur	eur	PROPN
ejpam-6017	34	20	.	.	PUNCT
ejpam-6017	35	1	j.	j.	PROPN
ejpam-6017	35	2	pure	pure	PROPN
ejpam-6017	35	3	appl	appl	PROPN
ejpam-6017	35	4	.	.	PROPN
ejpam-6017	35	5	math	math	PROPN
ejpam-6017	35	6	,	,	PUNCT
ejpam-6017	35	7	18	18	NUM
ejpam-6017	35	8	(	(	PUNCT
ejpam-6017	35	9	2	2	NUM
ejpam-6017	35	10	)	)	PUNCT
ejpam-6017	35	11	(	(	PUNCT
ejpam-6017	35	12	2025	2025	NUM
ejpam-6017	35	13	)	)	PUNCT
ejpam-6017	35	14	,	,	PUNCT
ejpam-6017	35	15	6017	6017	NUM
ejpam-6017	35	16	2	2	NUM
ejpam-6017	35	17	of	of	ADP
ejpam-6017	35	18	11	11	NUM
ejpam-6017	35	19	some	some	DET
ejpam-6017	35	20	minimal	minimal	ADJ
ejpam-6017	35	21	conditions	condition	NOUN
ejpam-6017	35	22	and	and	CCONJ
ejpam-6017	35	23	obtained	obtain	VERB
ejpam-6017	35	24	several	several	ADJ
ejpam-6017	35	25	characterizations	characterization	NOUN
ejpam-6017	35	26	and	and	CCONJ
ejpam-6017	35	27	some	some	DET
ejpam-6017	35	28	properties	property	NOUN
ejpam-6017	35	29	of	of	ADP
ejpam-6017	35	30	such	such	ADJ
ejpam-6017	35	31	functions	function	NOUN
ejpam-6017	35	32	.	.	PUNCT
ejpam-6017	36	1	furthermore	furthermore	ADV
ejpam-6017	36	2	,	,	PUNCT
ejpam-6017	36	3	the	the	DET
ejpam-6017	36	4	present	present	ADJ
ejpam-6017	36	5	authors	author	NOUN
ejpam-6017	36	6	[	[	X
ejpam-6017	36	7	15	15	NUM
ejpam-6017	36	8	]	]	PUNCT
ejpam-6017	36	9	defined	define	VERB
ejpam-6017	36	10	and	and	CCONJ
ejpam-6017	36	11	studied	study	VERB
ejpam-6017	36	12	the	the	DET
ejpam-6017	36	13	notions	notion	NOUN
ejpam-6017	36	14	of	of	ADP
ejpam-6017	36	15	strongly	strongly	ADV
ejpam-6017	36	16	θ	θ	NOUN
ejpam-6017	36	17	-	-	PUNCT
ejpam-6017	36	18	m	m	PUNCT
ejpam-6017	36	19	-closed	-close	VERB
ejpam-6017	36	20	graphs	graph	NOUN
ejpam-6017	36	21	and	and	CCONJ
ejpam-6017	36	22	m	m	NOUN
ejpam-6017	36	23	-	-	ADJ
ejpam-6017	36	24	closed	closed	ADJ
ejpam-6017	36	25	spaces	space	NOUN
ejpam-6017	36	26	.	.	PUNCT
ejpam-6017	37	1	thongmoon	thongmoon	NOUN
ejpam-6017	37	2	and	and	CCONJ
ejpam-6017	37	3	boonpok	boonpok	VERB
ejpam-6017	37	4	[	[	X
ejpam-6017	37	5	16	16	NUM
ejpam-6017	37	6	]	]	PUNCT
ejpam-6017	37	7	introduced	introduce	VERB
ejpam-6017	37	8	and	and	CCONJ
ejpam-6017	37	9	studied	study	VERB
ejpam-6017	37	10	the	the	DET
ejpam-6017	37	11	notion	notion	NOUN
ejpam-6017	37	12	of	of	ADP
ejpam-6017	37	13	strongly	strongly	ADV
ejpam-6017	37	14	θ(λ	θ(λ	ADJ
ejpam-6017	37	15	,	,	PUNCT
ejpam-6017	37	16	p)-continuous	p)-continuous	ADJ
ejpam-6017	37	17	functions	function	NOUN
ejpam-6017	37	18	.	.	PUNCT
ejpam-6017	38	1	quite	quite	ADV
ejpam-6017	38	2	recently	recently	ADV
ejpam-6017	38	3	,	,	PUNCT
ejpam-6017	38	4	the	the	DET
ejpam-6017	38	5	present	present	ADJ
ejpam-6017	38	6	authors	author	NOUN
ejpam-6017	38	7	[	[	X
ejpam-6017	38	8	17	17	NUM
ejpam-6017	38	9	]	]	PUNCT
ejpam-6017	38	10	introduced	introduce	VERB
ejpam-6017	38	11	and	and	CCONJ
ejpam-6017	38	12	investigated	investigate	VERB
ejpam-6017	38	13	the	the	DET
ejpam-6017	38	14	notion	notion	NOUN
ejpam-6017	38	15	of	of	ADP
ejpam-6017	38	16	almost	almost	ADV
ejpam-6017	38	17	strongly	strongly	ADV
ejpam-6017	38	18	θ(λ	θ(λ	VERB
ejpam-6017	38	19	,	,	PUNCT
ejpam-6017	38	20	p)continuous	p)continuous	ADJ
ejpam-6017	38	21	functions	function	NOUN
ejpam-6017	38	22	.	.	PUNCT
ejpam-6017	39	1	moreover	moreover	ADV
ejpam-6017	39	2	,	,	PUNCT
ejpam-6017	39	3	several	several	ADJ
ejpam-6017	39	4	characterizations	characterization	NOUN
ejpam-6017	39	5	of	of	ADP
ejpam-6017	39	6	(	(	PUNCT
ejpam-6017	39	7	τ1	τ1	PROPN
ejpam-6017	39	8	,	,	PUNCT
ejpam-6017	39	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	10	functions	function	NOUN
ejpam-6017	39	11	,	,	PUNCT
ejpam-6017	39	12	almost	almost	ADV
ejpam-6017	39	13	(	(	PUNCT
ejpam-6017	39	14	τ1	τ1	NOUN
ejpam-6017	39	15	,	,	PUNCT
ejpam-6017	39	16	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	17	functions	function	NOUN
ejpam-6017	39	18	,	,	PUNCT
ejpam-6017	39	19	weakly	weakly	ADJ
ejpam-6017	39	20	(	(	PUNCT
ejpam-6017	39	21	τ1	τ1	NOUN
ejpam-6017	39	22	,	,	PUNCT
ejpam-6017	39	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	24	functions	function	NOUN
ejpam-6017	39	25	,	,	PUNCT
ejpam-6017	39	26	almost	almost	ADV
ejpam-6017	39	27	weakly	weakly	ADJ
ejpam-6017	39	28	(	(	PUNCT
ejpam-6017	39	29	τ1	τ1	NOUN
ejpam-6017	39	30	,	,	PUNCT
ejpam-6017	39	31	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	32	functions	function	NOUN
ejpam-6017	39	33	,	,	PUNCT
ejpam-6017	39	34	faintly	faintly	ADV
ejpam-6017	39	35	(	(	PUNCT
ejpam-6017	39	36	τ1	τ1	PROPN
ejpam-6017	39	37	,	,	PUNCT
ejpam-6017	39	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	39	functions	function	NOUN
ejpam-6017	39	40	,	,	PUNCT
ejpam-6017	39	41	weakly	weakly	ADJ
ejpam-6017	39	42	quasi	quasi	NOUN
ejpam-6017	39	43	(	(	PUNCT
ejpam-6017	39	44	τ1	τ1	NOUN
ejpam-6017	39	45	,	,	PUNCT
ejpam-6017	39	46	τ2)continuous	τ2)continuous	ADJ
ejpam-6017	39	47	functions	function	NOUN
ejpam-6017	39	48	,	,	PUNCT
ejpam-6017	39	49	almost	almost	ADV
ejpam-6017	39	50	quasi	quasi	NOUN
ejpam-6017	39	51	(	(	PUNCT
ejpam-6017	39	52	τ1	τ1	NOUN
ejpam-6017	39	53	,	,	PUNCT
ejpam-6017	39	54	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	55	functions	function	NOUN
ejpam-6017	39	56	,	,	PUNCT
ejpam-6017	39	57	δ(τ1	δ(τ1	NOUN
ejpam-6017	39	58	,	,	PUNCT
ejpam-6017	39	59	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	60	functions	function	NOUN
ejpam-6017	39	61	and	and	CCONJ
ejpam-6017	39	62	quasi	quasi	NOUN
ejpam-6017	39	63	θ(τ1	θ(τ1	NOUN
ejpam-6017	39	64	,	,	PUNCT
ejpam-6017	39	65	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	39	66	functions	function	NOUN
ejpam-6017	39	67	were	be	AUX
ejpam-6017	39	68	established	establish	VERB
ejpam-6017	39	69	in	in	ADP
ejpam-6017	39	70	[	[	X
ejpam-6017	39	71	18	18	NUM
ejpam-6017	39	72	]	]	PUNCT
ejpam-6017	39	73	,	,	PUNCT
ejpam-6017	39	74	[	[	X
ejpam-6017	39	75	19	19	NUM
ejpam-6017	39	76	]	]	PUNCT
ejpam-6017	39	77	,	,	PUNCT
ejpam-6017	39	78	[	[	X
ejpam-6017	39	79	20	20	NUM
ejpam-6017	39	80	]	]	PUNCT
ejpam-6017	39	81	,	,	PUNCT
ejpam-6017	39	82	[	[	X
ejpam-6017	39	83	21	21	NUM
ejpam-6017	39	84	]	]	PUNCT
ejpam-6017	39	85	,	,	PUNCT
ejpam-6017	39	86	[	[	X
ejpam-6017	39	87	22	22	NUM
ejpam-6017	39	88	]	]	PUNCT
ejpam-6017	39	89	,	,	PUNCT
ejpam-6017	39	90	[	[	X
ejpam-6017	39	91	23	23	NUM
ejpam-6017	39	92	]	]	PUNCT
ejpam-6017	39	93	,	,	PUNCT
ejpam-6017	39	94	[	[	X
ejpam-6017	39	95	24	24	NUM
ejpam-6017	39	96	]	]	PUNCT
ejpam-6017	39	97	,	,	PUNCT
ejpam-6017	39	98	[	[	X
ejpam-6017	39	99	25	25	NUM
ejpam-6017	39	100	]	]	PUNCT
ejpam-6017	39	101	and	and	CCONJ
ejpam-6017	39	102	[	[	X
ejpam-6017	39	103	26	26	NUM
ejpam-6017	39	104	]	]	X
ejpam-6017	39	105	,	,	PUNCT
ejpam-6017	39	106	respectively	respectively	ADV
ejpam-6017	39	107	.	.	PUNCT
ejpam-6017	40	1	in	in	ADP
ejpam-6017	40	2	this	this	DET
ejpam-6017	40	3	paper	paper	NOUN
ejpam-6017	40	4	,	,	PUNCT
ejpam-6017	40	5	we	we	PRON
ejpam-6017	40	6	introduce	introduce	VERB
ejpam-6017	40	7	the	the	DET
ejpam-6017	40	8	concept	concept	NOUN
ejpam-6017	40	9	of	of	ADP
ejpam-6017	40	10	strongly	strongly	ADV
ejpam-6017	40	11	θ(τ1	θ(τ1	NOUN
ejpam-6017	40	12	,	,	PUNCT
ejpam-6017	40	13	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	40	14	functions	function	NOUN
ejpam-6017	40	15	.	.	PUNCT
ejpam-6017	41	1	we	we	PRON
ejpam-6017	41	2	also	also	ADV
ejpam-6017	41	3	investigate	investigate	VERB
ejpam-6017	41	4	several	several	ADJ
ejpam-6017	41	5	characterizations	characterization	NOUN
ejpam-6017	41	6	of	of	ADP
ejpam-6017	41	7	strongly	strongly	ADV
ejpam-6017	41	8	θ(τ1	θ(τ1	NOUN
ejpam-6017	41	9	,	,	PUNCT
ejpam-6017	41	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	41	11	functions	function	NOUN
ejpam-6017	41	12	.	.	PUNCT
ejpam-6017	42	1	2	2	X
ejpam-6017	42	2	.	.	NUM
ejpam-6017	42	3	preliminaries	preliminary	NOUN
ejpam-6017	42	4	throughout	throughout	ADP
ejpam-6017	42	5	the	the	DET
ejpam-6017	42	6	present	present	ADJ
ejpam-6017	42	7	paper	paper	NOUN
ejpam-6017	42	8	,	,	PUNCT
ejpam-6017	42	9	spaces	space	NOUN
ejpam-6017	42	10	(	(	PUNCT
ejpam-6017	42	11	x	x	NOUN
ejpam-6017	42	12	,	,	PUNCT
ejpam-6017	42	13	τ1	τ1	NOUN
ejpam-6017	42	14	,	,	PUNCT
ejpam-6017	42	15	τ2	τ2	NOUN
ejpam-6017	42	16	)	)	PUNCT
ejpam-6017	42	17	and	and	CCONJ
ejpam-6017	42	18	(	(	PUNCT
ejpam-6017	42	19	y	y	PROPN
ejpam-6017	42	20	,	,	PUNCT
ejpam-6017	42	21	σ1	σ1	PROPN
ejpam-6017	42	22	,	,	PUNCT
ejpam-6017	42	23	σ2	σ2	NOUN
ejpam-6017	42	24	)	)	PUNCT
ejpam-6017	42	25	(	(	PUNCT
ejpam-6017	42	26	or	or	CCONJ
ejpam-6017	42	27	simply	simply	ADV
ejpam-6017	42	28	x	x	X
ejpam-6017	42	29	and	and	CCONJ
ejpam-6017	42	30	y	y	PROPN
ejpam-6017	42	31	)	)	PUNCT
ejpam-6017	42	32	always	always	ADV
ejpam-6017	42	33	mean	mean	VERB
ejpam-6017	42	34	bitopological	bitopological	ADJ
ejpam-6017	42	35	spaces	space	NOUN
ejpam-6017	42	36	on	on	ADP
ejpam-6017	42	37	which	which	PRON
ejpam-6017	42	38	no	no	DET
ejpam-6017	42	39	separation	separation	NOUN
ejpam-6017	42	40	axioms	axiom	NOUN
ejpam-6017	42	41	are	be	AUX
ejpam-6017	42	42	assumed	assume	VERB
ejpam-6017	42	43	unless	unless	SCONJ
ejpam-6017	42	44	explicitly	explicitly	ADV
ejpam-6017	42	45	stated	state	VERB
ejpam-6017	42	46	.	.	PUNCT
ejpam-6017	43	1	let	let	VERB
ejpam-6017	43	2	a	a	DET
ejpam-6017	43	3	be	be	AUX
ejpam-6017	43	4	a	a	DET
ejpam-6017	43	5	subset	subset	NOUN
ejpam-6017	43	6	of	of	ADP
ejpam-6017	43	7	a	a	DET
ejpam-6017	43	8	bitopological	bitopological	ADJ
ejpam-6017	43	9	space	space	NOUN
ejpam-6017	43	10	(	(	PUNCT
ejpam-6017	43	11	x	x	NOUN
ejpam-6017	43	12	,	,	PUNCT
ejpam-6017	43	13	τ1	τ1	NOUN
ejpam-6017	43	14	,	,	PUNCT
ejpam-6017	43	15	τ2	τ2	NOUN
ejpam-6017	43	16	)	)	PUNCT
ejpam-6017	43	17	.	.	PUNCT
ejpam-6017	44	1	the	the	DET
ejpam-6017	44	2	closure	closure	NOUN
ejpam-6017	44	3	of	of	ADP
ejpam-6017	44	4	a	a	PRON
ejpam-6017	44	5	and	and	CCONJ
ejpam-6017	44	6	the	the	DET
ejpam-6017	44	7	interior	interior	NOUN
ejpam-6017	44	8	of	of	ADP
ejpam-6017	44	9	a	a	PRON
ejpam-6017	44	10	with	with	ADP
ejpam-6017	44	11	respect	respect	NOUN
ejpam-6017	44	12	to	to	ADP
ejpam-6017	44	13	τi	τi	PROPN
ejpam-6017	44	14	are	be	AUX
ejpam-6017	44	15	denoted	denote	VERB
ejpam-6017	44	16	by	by	ADP
ejpam-6017	44	17	τi	τi	NOUN
ejpam-6017	44	18	-	-	PUNCT
ejpam-6017	44	19	cl(a	cl(a	NUM
ejpam-6017	44	20	)	)	PUNCT
ejpam-6017	44	21	and	and	CCONJ
ejpam-6017	44	22	τi	τi	NOUN
ejpam-6017	44	23	-	-	PUNCT
ejpam-6017	44	24	int(a	int(a	NOUN
ejpam-6017	44	25	)	)	PUNCT
ejpam-6017	44	26	,	,	PUNCT
ejpam-6017	44	27	respectively	respectively	ADV
ejpam-6017	44	28	,	,	PUNCT
ejpam-6017	44	29	for	for	ADP
ejpam-6017	44	30	i	i	PROPN
ejpam-6017	44	31	=	=	SYM
ejpam-6017	44	32	1	1	NUM
ejpam-6017	44	33	,	,	PUNCT
ejpam-6017	44	34	2	2	NUM
ejpam-6017	44	35	.	.	X
ejpam-6017	44	36	a	a	DET
ejpam-6017	44	37	subset	subset	NOUN
ejpam-6017	44	38	a	a	PRON
ejpam-6017	44	39	of	of	ADP
ejpam-6017	44	40	a	a	DET
ejpam-6017	44	41	bitopological	bitopological	ADJ
ejpam-6017	44	42	space	space	NOUN
ejpam-6017	44	43	(	(	PUNCT
ejpam-6017	44	44	x	x	NOUN
ejpam-6017	44	45	,	,	PUNCT
ejpam-6017	44	46	τ1	τ1	NOUN
ejpam-6017	44	47	,	,	PUNCT
ejpam-6017	44	48	τ2	τ2	NOUN
ejpam-6017	44	49	)	)	PUNCT
ejpam-6017	44	50	is	be	AUX
ejpam-6017	44	51	called	call	VERB
ejpam-6017	44	52	τ1τ2	τ1τ2	VERB
ejpam-6017	44	53	-	-	ADJ
ejpam-6017	44	54	closed	closed	ADJ
ejpam-6017	44	55	[	[	X
ejpam-6017	44	56	27	27	NUM
ejpam-6017	44	57	]	]	X
ejpam-6017	44	58	if	if	SCONJ
ejpam-6017	44	59	a	a	DET
ejpam-6017	44	60	=	=	NOUN
ejpam-6017	44	61	τ1	τ1	NOUN
ejpam-6017	44	62	-	-	PUNCT
ejpam-6017	44	63	cl(τ2	cl(τ2	NOUN
ejpam-6017	44	64	-	-	PUNCT
ejpam-6017	44	65	cl(a	cl(a	NUM
ejpam-6017	44	66	)	)	PUNCT
ejpam-6017	44	67	)	)	PUNCT
ejpam-6017	44	68	.	.	PUNCT
ejpam-6017	45	1	the	the	DET
ejpam-6017	45	2	complement	complement	NOUN
ejpam-6017	45	3	of	of	ADP
ejpam-6017	45	4	a	a	DET
ejpam-6017	45	5	τ1τ2	τ1τ2	ADJ
ejpam-6017	45	6	-	-	ADJ
ejpam-6017	45	7	closed	closed	ADJ
ejpam-6017	45	8	set	set	NOUN
ejpam-6017	45	9	is	be	AUX
ejpam-6017	45	10	called	call	VERB
ejpam-6017	45	11	τ1τ2	τ1τ2	NOUN
ejpam-6017	45	12	-	-	ADJ
ejpam-6017	45	13	open	open	ADJ
ejpam-6017	45	14	.	.	PUNCT
ejpam-6017	46	1	the	the	DET
ejpam-6017	46	2	intersection	intersection	NOUN
ejpam-6017	46	3	of	of	ADP
ejpam-6017	46	4	all	all	DET
ejpam-6017	46	5	τ1τ2	τ1τ2	ADJ
ejpam-6017	46	6	-	-	ADJ
ejpam-6017	46	7	closed	closed	ADJ
ejpam-6017	46	8	sets	set	NOUN
ejpam-6017	46	9	of	of	ADP
ejpam-6017	46	10	x	x	PUNCT
ejpam-6017	46	11	containing	contain	VERB
ejpam-6017	46	12	a	a	PRON
ejpam-6017	46	13	is	be	AUX
ejpam-6017	46	14	called	call	VERB
ejpam-6017	46	15	the	the	DET
ejpam-6017	46	16	τ1τ2	τ1τ2	NOUN
ejpam-6017	46	17	-	-	NOUN
ejpam-6017	46	18	closure	closure	NOUN
ejpam-6017	46	19	[	[	X
ejpam-6017	46	20	27	27	NUM
ejpam-6017	46	21	]	]	PUNCT
ejpam-6017	46	22	of	of	ADP
ejpam-6017	46	23	a	a	PRON
ejpam-6017	46	24	and	and	CCONJ
ejpam-6017	46	25	is	be	AUX
ejpam-6017	46	26	denoted	denote	VERB
ejpam-6017	46	27	by	by	ADP
ejpam-6017	46	28	τ1τ2	τ1τ2	NOUN
ejpam-6017	46	29	-	-	NUM
ejpam-6017	46	30	cl(a	cl(a	NUM
ejpam-6017	46	31	)	)	PUNCT
ejpam-6017	46	32	.	.	PUNCT
ejpam-6017	47	1	the	the	DET
ejpam-6017	47	2	union	union	NOUN
ejpam-6017	47	3	of	of	ADP
ejpam-6017	47	4	all	all	DET
ejpam-6017	47	5	τ1τ2	τ1τ2	ADJ
ejpam-6017	47	6	-	-	ADJ
ejpam-6017	47	7	open	open	ADJ
ejpam-6017	47	8	sets	set	NOUN
ejpam-6017	47	9	of	of	ADP
ejpam-6017	47	10	x	x	PUNCT
ejpam-6017	47	11	contained	contain	VERB
ejpam-6017	47	12	in	in	ADP
ejpam-6017	47	13	a	a	PRON
ejpam-6017	47	14	is	be	AUX
ejpam-6017	47	15	called	call	VERB
ejpam-6017	47	16	the	the	DET
ejpam-6017	47	17	τ1τ2	τ1τ2	NOUN
ejpam-6017	47	18	-	-	ADJ
ejpam-6017	47	19	interior	interior	ADJ
ejpam-6017	47	20	[	[	X
ejpam-6017	47	21	27	27	NUM
ejpam-6017	47	22	]	]	PUNCT
ejpam-6017	47	23	of	of	ADP
ejpam-6017	47	24	a	a	PRON
ejpam-6017	47	25	and	and	CCONJ
ejpam-6017	47	26	is	be	AUX
ejpam-6017	47	27	denoted	denote	VERB
ejpam-6017	47	28	by	by	ADP
ejpam-6017	47	29	τ1τ2	τ1τ2	NOUN
ejpam-6017	47	30	-	-	ADJ
ejpam-6017	47	31	int(a	int(a	NOUN
ejpam-6017	47	32	)	)	PUNCT
ejpam-6017	47	33	.	.	PUNCT
ejpam-6017	48	1	lemma	lemma	PROPN
ejpam-6017	48	2	1	1	NUM
ejpam-6017	48	3	.	.	PUNCT
ejpam-6017	49	1	[	[	X
ejpam-6017	49	2	27	27	NUM
ejpam-6017	49	3	]	]	PUNCT
ejpam-6017	49	4	let	let	VERB
ejpam-6017	49	5	a	a	PRON
ejpam-6017	49	6	and	and	CCONJ
ejpam-6017	49	7	b	b	NOUN
ejpam-6017	49	8	be	be	AUX
ejpam-6017	49	9	subsets	subset	NOUN
ejpam-6017	49	10	of	of	ADP
ejpam-6017	49	11	a	a	DET
ejpam-6017	49	12	bitopological	bitopological	ADJ
ejpam-6017	49	13	space	space	NOUN
ejpam-6017	49	14	(	(	PUNCT
ejpam-6017	49	15	x	x	NOUN
ejpam-6017	49	16	,	,	PUNCT
ejpam-6017	49	17	τ1	τ1	NOUN
ejpam-6017	49	18	,	,	PUNCT
ejpam-6017	49	19	τ2	τ2	NOUN
ejpam-6017	49	20	)	)	PUNCT
ejpam-6017	49	21	.	.	PUNCT
ejpam-6017	50	1	for	for	ADP
ejpam-6017	50	2	the	the	DET
ejpam-6017	50	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-6017	50	4	,	,	PUNCT
ejpam-6017	50	5	the	the	DET
ejpam-6017	50	6	following	follow	VERB
ejpam-6017	50	7	properties	property	NOUN
ejpam-6017	50	8	hold	hold	VERB
ejpam-6017	50	9	:	:	PUNCT
ejpam-6017	50	10	(	(	PUNCT
ejpam-6017	50	11	1	1	X
ejpam-6017	50	12	)	)	PUNCT
ejpam-6017	50	13	a	a	DET
ejpam-6017	50	14	⊆	⊆	NUM
ejpam-6017	50	15	τ1τ2	τ1τ2	NOUN
ejpam-6017	50	16	-	-	NUM
ejpam-6017	50	17	cl(a	cl(a	NUM
ejpam-6017	50	18	)	)	PUNCT
ejpam-6017	50	19	and	and	CCONJ
ejpam-6017	50	20	τ1τ2	τ1τ2	NOUN
ejpam-6017	50	21	-	-	ADJ
ejpam-6017	50	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6017	50	23	-	-	PUNCT
ejpam-6017	50	24	cl(a	cl(a	NUM
ejpam-6017	50	25	)	)	PUNCT
ejpam-6017	50	26	)	)	PUNCT
ejpam-6017	51	1	=	=	PUNCT
ejpam-6017	51	2	τ1τ2	τ1τ2	NOUN
ejpam-6017	51	3	-	-	NUM
ejpam-6017	51	4	cl(a	cl(a	NUM
ejpam-6017	51	5	)	)	PUNCT
ejpam-6017	51	6	.	.	PUNCT
ejpam-6017	52	1	(	(	PUNCT
ejpam-6017	52	2	2	2	X
ejpam-6017	52	3	)	)	PUNCT
ejpam-6017	52	4	if	if	SCONJ
ejpam-6017	52	5	a	a	DET
ejpam-6017	52	6	⊆	⊆	NUM
ejpam-6017	52	7	b	b	NOUN
ejpam-6017	52	8	,	,	PUNCT
ejpam-6017	52	9	then	then	ADV
ejpam-6017	52	10	τ1τ2	τ1τ2	NOUN
ejpam-6017	52	11	-	-	NUM
ejpam-6017	52	12	cl(a	cl(a	NUM
ejpam-6017	52	13	)	)	PUNCT
ejpam-6017	52	14	⊆	⊆	NUM
ejpam-6017	52	15	τ1τ2	τ1τ2	NOUN
ejpam-6017	52	16	-	-	NOUN
ejpam-6017	52	17	cl(b	cl(b	NOUN
ejpam-6017	52	18	)	)	PUNCT
ejpam-6017	52	19	.	.	PUNCT
ejpam-6017	53	1	(	(	PUNCT
ejpam-6017	53	2	3	3	X
ejpam-6017	53	3	)	)	PUNCT
ejpam-6017	53	4	τ1τ2	τ1τ2	NOUN
ejpam-6017	53	5	-	-	NUM
ejpam-6017	53	6	cl(a	cl(a	NUM
ejpam-6017	53	7	)	)	PUNCT
ejpam-6017	53	8	is	be	AUX
ejpam-6017	53	9	τ1τ2	τ1τ2	NOUN
ejpam-6017	53	10	-	-	ADJ
ejpam-6017	53	11	closed	closed	ADJ
ejpam-6017	53	12	.	.	PUNCT
ejpam-6017	54	1	(	(	PUNCT
ejpam-6017	54	2	4	4	X
ejpam-6017	54	3	)	)	PUNCT
ejpam-6017	54	4	a	a	PRON
ejpam-6017	54	5	is	be	AUX
ejpam-6017	54	6	τ1τ2	τ1τ2	NOUN
ejpam-6017	54	7	-	-	ADJ
ejpam-6017	54	8	closed	closed	ADJ
ejpam-6017	54	9	if	if	SCONJ
ejpam-6017	54	10	and	and	CCONJ
ejpam-6017	54	11	only	only	ADV
ejpam-6017	54	12	if	if	SCONJ
ejpam-6017	54	13	a	a	DET
ejpam-6017	54	14	=	=	PUNCT
ejpam-6017	54	15	τ1τ2	τ1τ2	NOUN
ejpam-6017	54	16	-	-	NUM
ejpam-6017	54	17	cl(a	cl(a	NUM
ejpam-6017	54	18	)	)	PUNCT
ejpam-6017	54	19	.	.	PUNCT
ejpam-6017	55	1	(	(	PUNCT
ejpam-6017	55	2	5	5	X
ejpam-6017	55	3	)	)	PUNCT
ejpam-6017	55	4	τ1τ2	τ1τ2	NOUN
ejpam-6017	55	5	-	-	NOUN
ejpam-6017	55	6	cl(x	cl(x	X
ejpam-6017	55	7	−a	−a	NOUN
ejpam-6017	55	8	)	)	PUNCT
ejpam-6017	56	1	=	=	PUNCT
ejpam-6017	56	2	x	x	X
ejpam-6017	57	1	−	−	ADP
ejpam-6017	57	2	τ1τ2	τ1τ2	NOUN
ejpam-6017	57	3	-	-	PUNCT
ejpam-6017	57	4	int(a	int(a	NOUN
ejpam-6017	57	5	)	)	PUNCT
ejpam-6017	57	6	.	.	PUNCT
ejpam-6017	58	1	a	a	DET
ejpam-6017	58	2	subset	subset	NOUN
ejpam-6017	58	3	a	a	PRON
ejpam-6017	58	4	of	of	ADP
ejpam-6017	58	5	a	a	DET
ejpam-6017	58	6	bitopological	bitopological	ADJ
ejpam-6017	58	7	space	space	NOUN
ejpam-6017	58	8	(	(	PUNCT
ejpam-6017	58	9	x	x	NOUN
ejpam-6017	58	10	,	,	PUNCT
ejpam-6017	58	11	τ1	τ1	NOUN
ejpam-6017	58	12	,	,	PUNCT
ejpam-6017	58	13	τ2	τ2	NOUN
ejpam-6017	58	14	)	)	PUNCT
ejpam-6017	58	15	is	be	AUX
ejpam-6017	58	16	said	say	VERB
ejpam-6017	58	17	to	to	PART
ejpam-6017	58	18	be	be	AUX
ejpam-6017	58	19	(	(	PUNCT
ejpam-6017	58	20	τ1	τ1	NOUN
ejpam-6017	58	21	,	,	PUNCT
ejpam-6017	58	22	τ2)r	τ2)r	NOUN
ejpam-6017	58	23	-	-	PUNCT
ejpam-6017	58	24	open	open	NOUN
ejpam-6017	58	25	[	[	X
ejpam-6017	58	26	28	28	NUM
ejpam-6017	58	27	]	]	X
ejpam-6017	58	28	(	(	PUNCT
ejpam-6017	58	29	resp	resp	NOUN
ejpam-6017	58	30	.	.	PUNCT
ejpam-6017	59	1	(	(	PUNCT
ejpam-6017	59	2	τ1	τ1	NOUN
ejpam-6017	59	3	,	,	PUNCT
ejpam-6017	59	4	τ2)s	τ2)s	NOUN
ejpam-6017	59	5	-	-	PUNCT
ejpam-6017	59	6	open	open	ADJ
ejpam-6017	59	7	[	[	X
ejpam-6017	59	8	29	29	NUM
ejpam-6017	59	9	]	]	NUM
ejpam-6017	59	10	,	,	PUNCT
ejpam-6017	59	11	(	(	PUNCT
ejpam-6017	59	12	τ1	τ1	NOUN
ejpam-6017	59	13	,	,	PUNCT
ejpam-6017	59	14	τ2)p	τ2)p	NOUN
ejpam-6017	59	15	-	-	ADJ
ejpam-6017	59	16	open	open	ADJ
ejpam-6017	59	17	[	[	X
ejpam-6017	59	18	29	29	NUM
ejpam-6017	59	19	]	]	NUM
ejpam-6017	59	20	,	,	PUNCT
ejpam-6017	59	21	(	(	PUNCT
ejpam-6017	59	22	τ1	τ1	NOUN
ejpam-6017	59	23	,	,	PUNCT
ejpam-6017	59	24	τ2)β	τ2)β	ADJ
ejpam-6017	59	25	-	-	PUNCT
ejpam-6017	59	26	open	open	NOUN
ejpam-6017	59	27	[	[	X
ejpam-6017	59	28	29	29	NUM
ejpam-6017	59	29	]	]	SYM
ejpam-6017	59	30	)	)	PUNCT
ejpam-6017	59	31	if	if	SCONJ
ejpam-6017	59	32	a	a	DET
ejpam-6017	59	33	=	=	PUNCT
ejpam-6017	59	34	τ1τ2	τ1τ2	NOUN
ejpam-6017	59	35	-	-	NOUN
ejpam-6017	59	36	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6017	59	37	-	-	PUNCT
ejpam-6017	59	38	cl(a	cl(a	NUM
ejpam-6017	59	39	)	)	PUNCT
ejpam-6017	59	40	)	)	PUNCT
ejpam-6017	59	41	(	(	PUNCT
ejpam-6017	59	42	resp	resp	NOUN
ejpam-6017	59	43	.	.	PUNCT
ejpam-6017	60	1	a	a	DET
ejpam-6017	60	2	⊆	⊆	NUM
ejpam-6017	60	3	τ1τ2	τ1τ2	NOUN
ejpam-6017	60	4	-	-	ADJ
ejpam-6017	60	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6017	60	6	-	-	PUNCT
ejpam-6017	60	7	int(a	int(a	NOUN
ejpam-6017	60	8	)	)	PUNCT
ejpam-6017	60	9	)	)	PUNCT
ejpam-6017	60	10	,	,	PUNCT
ejpam-6017	60	11	a	a	DET
ejpam-6017	60	12	⊆	⊆	NUM
ejpam-6017	60	13	τ1τ2	τ1τ2	NOUN
ejpam-6017	60	14	-	-	NOUN
ejpam-6017	60	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6017	60	16	-	-	PUNCT
ejpam-6017	60	17	cl(a	cl(a	NUM
ejpam-6017	60	18	)	)	PUNCT
ejpam-6017	60	19	)	)	PUNCT
ejpam-6017	60	20	,	,	PUNCT
ejpam-6017	60	21	a	a	DET
ejpam-6017	60	22	⊆	⊆	NUM
ejpam-6017	60	23	τ1τ2	τ1τ2	NOUN
ejpam-6017	60	24	-	-	PUNCT
ejpam-6017	60	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6017	60	26	-	-	PUNCT
ejpam-6017	60	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6017	60	28	-	-	PUNCT
ejpam-6017	60	29	cl(a	cl(a	NUM
ejpam-6017	60	30	)	)	PUNCT
ejpam-6017	60	31	)	)	PUNCT
ejpam-6017	60	32	)	)	PUNCT
ejpam-6017	60	33	)	)	PUNCT
ejpam-6017	60	34	.	.	PUNCT
ejpam-6017	61	1	the	the	DET
ejpam-6017	61	2	complement	complement	NOUN
ejpam-6017	61	3	of	of	ADP
ejpam-6017	61	4	a	a	DET
ejpam-6017	61	5	(	(	PUNCT
ejpam-6017	61	6	τ1	τ1	NOUN
ejpam-6017	61	7	,	,	PUNCT
ejpam-6017	61	8	τ2)r	τ2)r	NOUN
ejpam-6017	61	9	-	-	PUNCT
ejpam-6017	61	10	open	open	ADJ
ejpam-6017	61	11	(	(	PUNCT
ejpam-6017	61	12	resp	resp	NOUN
ejpam-6017	61	13	.	.	PUNCT
ejpam-6017	62	1	(	(	PUNCT
ejpam-6017	62	2	τ1	τ1	NOUN
ejpam-6017	62	3	,	,	PUNCT
ejpam-6017	62	4	τ2)s	τ2)s	NOUN
ejpam-6017	62	5	-	-	PUNCT
ejpam-6017	62	6	open	open	ADJ
ejpam-6017	62	7	,	,	PUNCT
ejpam-6017	62	8	(	(	PUNCT
ejpam-6017	62	9	τ1	τ1	NOUN
ejpam-6017	62	10	,	,	PUNCT
ejpam-6017	62	11	τ2)p	τ2)p	NOUN
ejpam-6017	62	12	-	-	ADJ
ejpam-6017	62	13	open	open	ADJ
ejpam-6017	62	14	,	,	PUNCT
ejpam-6017	62	15	(	(	PUNCT
ejpam-6017	62	16	τ1	τ1	NOUN
ejpam-6017	62	17	,	,	PUNCT
ejpam-6017	62	18	τ2)β	τ2)β	ADJ
ejpam-6017	62	19	-	-	PUNCT
ejpam-6017	62	20	open	open	ADJ
ejpam-6017	62	21	)	)	PUNCT
ejpam-6017	62	22	set	set	NOUN
ejpam-6017	62	23	is	be	AUX
ejpam-6017	62	24	called	call	VERB
ejpam-6017	62	25	(	(	PUNCT
ejpam-6017	62	26	τ1	τ1	NOUN
ejpam-6017	62	27	,	,	PUNCT
ejpam-6017	62	28	τ2)r	τ2)r	NOUN
ejpam-6017	62	29	-	-	PUNCT
ejpam-6017	62	30	closed	closed	ADJ
ejpam-6017	62	31	(	(	PUNCT
ejpam-6017	62	32	resp	resp	NOUN
ejpam-6017	62	33	.	.	PUNCT
ejpam-6017	63	1	(	(	PUNCT
ejpam-6017	63	2	τ1	τ1	NOUN
ejpam-6017	63	3	,	,	PUNCT
ejpam-6017	63	4	τ2)s	τ2)s	NOUN
ejpam-6017	63	5	-	-	PUNCT
ejpam-6017	63	6	closed	closed	ADJ
ejpam-6017	63	7	,	,	PUNCT
ejpam-6017	63	8	(	(	PUNCT
ejpam-6017	63	9	τ1	τ1	NOUN
ejpam-6017	63	10	,	,	PUNCT
ejpam-6017	63	11	τ2)p	τ2)p	NOUN
ejpam-6017	63	12	-	-	PUNCT
ejpam-6017	63	13	closed	closed	ADJ
ejpam-6017	63	14	,	,	PUNCT
ejpam-6017	63	15	(	(	PUNCT
ejpam-6017	63	16	τ1	τ1	NOUN
ejpam-6017	63	17	,	,	PUNCT
ejpam-6017	63	18	τ2)β	τ2)β	ADJ
ejpam-6017	63	19	-	-	PUNCT
ejpam-6017	63	20	closed	closed	ADJ
ejpam-6017	63	21	)	)	PUNCT
ejpam-6017	63	22	.	.	PUNCT
ejpam-6017	64	1	a	a	DET
ejpam-6017	64	2	subset	subset	NOUN
ejpam-6017	64	3	a	a	PRON
ejpam-6017	64	4	of	of	ADP
ejpam-6017	64	5	a	a	DET
ejpam-6017	64	6	bitopological	bitopological	ADJ
ejpam-6017	64	7	space	space	NOUN
ejpam-6017	64	8	(	(	PUNCT
ejpam-6017	64	9	x	x	NOUN
ejpam-6017	64	10	,	,	PUNCT
ejpam-6017	64	11	τ1	τ1	NOUN
ejpam-6017	64	12	,	,	PUNCT
ejpam-6017	64	13	τ2	τ2	NOUN
ejpam-6017	64	14	)	)	PUNCT
ejpam-6017	64	15	is	be	AUX
ejpam-6017	64	16	said	say	VERB
ejpam-6017	64	17	to	to	PART
ejpam-6017	64	18	be	be	AUX
ejpam-6017	64	19	α(τ1	α(τ1	NOUN
ejpam-6017	64	20	,	,	PUNCT
ejpam-6017	64	21	τ2)-open	τ2)-open	ADJ
ejpam-6017	64	22	[	[	X
ejpam-6017	64	23	30	30	NUM
ejpam-6017	64	24	]	]	X
ejpam-6017	64	25	if	if	SCONJ
ejpam-6017	64	26	a	a	DET
ejpam-6017	64	27	⊆	⊆	NUM
ejpam-6017	64	28	τ1τ2	τ1τ2	NOUN
ejpam-6017	64	29	-	-	PUNCT
ejpam-6017	64	30	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6017	64	31	-	-	PUNCT
ejpam-6017	64	32	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6017	64	33	-	-	PUNCT
ejpam-6017	64	34	int(a	int(a	NOUN
ejpam-6017	64	35	)	)	PUNCT
ejpam-6017	64	36	)	)	PUNCT
ejpam-6017	64	37	)	)	PUNCT
ejpam-6017	64	38	.	.	PUNCT
ejpam-6017	65	1	the	the	DET
ejpam-6017	65	2	complement	complement	NOUN
ejpam-6017	65	3	of	of	ADP
ejpam-6017	65	4	an	an	DET
ejpam-6017	65	5	α(τ1	α(τ1	NOUN
ejpam-6017	65	6	,	,	PUNCT
ejpam-6017	65	7	τ2)-open	τ2)-open	ADJ
ejpam-6017	65	8	set	set	NOUN
ejpam-6017	65	9	is	be	AUX
ejpam-6017	65	10	said	say	VERB
ejpam-6017	65	11	to	to	PART
ejpam-6017	65	12	be	be	AUX
ejpam-6017	65	13	p.	p.	NOUN
ejpam-6017	65	14	pue	pue	NOUN
ejpam-6017	65	15	-	-	PUNCT
ejpam-6017	65	16	on	on	ADP
ejpam-6017	65	17	,	,	PUNCT
ejpam-6017	65	18	s.	s.	PROPN
ejpam-6017	65	19	sompong	sompong	PROPN
ejpam-6017	65	20	,	,	PUNCT
ejpam-6017	65	21	c.	c.	PROPN
ejpam-6017	65	22	boonpok	boonpok	PROPN
ejpam-6017	65	23	/	/	SYM
ejpam-6017	65	24	eur	eur	PROPN
ejpam-6017	65	25	.	.	PUNCT
ejpam-6017	66	1	j.	j.	PROPN
ejpam-6017	66	2	pure	pure	PROPN
ejpam-6017	66	3	appl	appl	PROPN
ejpam-6017	66	4	.	.	PROPN
ejpam-6017	66	5	math	math	PROPN
ejpam-6017	66	6	,	,	PUNCT
ejpam-6017	66	7	18	18	NUM
ejpam-6017	66	8	(	(	PUNCT
ejpam-6017	66	9	2	2	NUM
ejpam-6017	66	10	)	)	PUNCT
ejpam-6017	66	11	(	(	PUNCT
ejpam-6017	66	12	2025	2025	NUM
ejpam-6017	66	13	)	)	PUNCT
ejpam-6017	66	14	,	,	PUNCT
ejpam-6017	66	15	6017	6017	NUM
ejpam-6017	66	16	3	3	NUM
ejpam-6017	66	17	of	of	ADP
ejpam-6017	66	18	11	11	NUM
ejpam-6017	66	19	α(τ1	α(τ1	NOUN
ejpam-6017	66	20	,	,	PUNCT
ejpam-6017	66	21	τ2)-closed	τ2)-closed	PROPN
ejpam-6017	66	22	.	.	PUNCT
ejpam-6017	67	1	for	for	ADP
ejpam-6017	67	2	a	a	DET
ejpam-6017	67	3	subset	subset	NOUN
ejpam-6017	67	4	a	a	PRON
ejpam-6017	67	5	of	of	ADP
ejpam-6017	67	6	a	a	DET
ejpam-6017	67	7	bitopological	bitopological	ADJ
ejpam-6017	67	8	space	space	NOUN
ejpam-6017	67	9	(	(	PUNCT
ejpam-6017	67	10	x	x	NOUN
ejpam-6017	67	11	,	,	PUNCT
ejpam-6017	67	12	τ1	τ1	NOUN
ejpam-6017	67	13	,	,	PUNCT
ejpam-6017	67	14	τ2	τ2	PROPN
ejpam-6017	67	15	)	)	PUNCT
ejpam-6017	67	16	,	,	PUNCT
ejpam-6017	67	17	a	a	DET
ejpam-6017	67	18	point	point	NOUN
ejpam-6017	67	19	x	x	X
ejpam-6017	67	20	∈	∈	NOUN
ejpam-6017	67	21	x	x	PUNCT
ejpam-6017	67	22	is	be	AUX
ejpam-6017	67	23	called	call	VERB
ejpam-6017	67	24	a	a	DET
ejpam-6017	67	25	(	(	PUNCT
ejpam-6017	67	26	τ1	τ1	NOUN
ejpam-6017	67	27	,	,	PUNCT
ejpam-6017	67	28	τ2)θ	τ2)θ	ADJ
ejpam-6017	67	29	-	-	PUNCT
ejpam-6017	67	30	cluster	cluster	NOUN
ejpam-6017	67	31	point	point	NOUN
ejpam-6017	67	32	[	[	X
ejpam-6017	67	33	28	28	NUM
ejpam-6017	67	34	]	]	PUNCT
ejpam-6017	67	35	of	of	ADP
ejpam-6017	67	36	a	a	DET
ejpam-6017	67	37	if	if	SCONJ
ejpam-6017	67	38	τ1τ2	τ1τ2	ADJ
ejpam-6017	67	39	-	-	ADJ
ejpam-6017	67	40	cl(u)∩a	cl(u)∩a	ADJ
ejpam-6017	67	41	̸=	̸=	PROPN
ejpam-6017	67	42	∅	∅	NOUN
ejpam-6017	67	43	for	for	ADP
ejpam-6017	67	44	every	every	DET
ejpam-6017	67	45	τ1τ2	τ1τ2	ADJ
ejpam-6017	67	46	-	-	ADJ
ejpam-6017	67	47	open	open	ADJ
ejpam-6017	67	48	set	set	NOUN
ejpam-6017	67	49	u	u	NOUN
ejpam-6017	67	50	containing	contain	VERB
ejpam-6017	67	51	x.	x.	NOUN
ejpam-6017	67	52	the	the	DET
ejpam-6017	67	53	set	set	NOUN
ejpam-6017	67	54	of	of	ADP
ejpam-6017	67	55	all	all	DET
ejpam-6017	67	56	(	(	PUNCT
ejpam-6017	67	57	τ1	τ1	NOUN
ejpam-6017	67	58	,	,	PUNCT
ejpam-6017	67	59	τ2)θ	τ2)θ	ADJ
ejpam-6017	67	60	-	-	PUNCT
ejpam-6017	67	61	cluster	cluster	NOUN
ejpam-6017	67	62	points	point	NOUN
ejpam-6017	67	63	of	of	ADP
ejpam-6017	67	64	a	a	PRON
ejpam-6017	67	65	is	be	AUX
ejpam-6017	67	66	called	call	VERB
ejpam-6017	67	67	the	the	DET
ejpam-6017	67	68	(	(	PUNCT
ejpam-6017	67	69	τ1	τ1	NOUN
ejpam-6017	67	70	,	,	PUNCT
ejpam-6017	67	71	τ2)θ	τ2)θ	ADJ
ejpam-6017	67	72	-	-	PUNCT
ejpam-6017	67	73	closure	closure	NOUN
ejpam-6017	67	74	[	[	X
ejpam-6017	67	75	28	28	NUM
ejpam-6017	67	76	]	]	PUNCT
ejpam-6017	67	77	of	of	ADP
ejpam-6017	67	78	a	a	PRON
ejpam-6017	67	79	and	and	CCONJ
ejpam-6017	67	80	is	be	AUX
ejpam-6017	67	81	denoted	denote	VERB
ejpam-6017	67	82	by	by	ADP
ejpam-6017	67	83	(	(	PUNCT
ejpam-6017	67	84	τ1	τ1	NOUN
ejpam-6017	67	85	,	,	PUNCT
ejpam-6017	67	86	τ2)θ	τ2)θ	NOUN
ejpam-6017	67	87	-	-	PUNCT
ejpam-6017	67	88	cl(a	cl(a	NUM
ejpam-6017	67	89	)	)	PUNCT
ejpam-6017	67	90	.	.	PUNCT
ejpam-6017	68	1	a	a	DET
ejpam-6017	68	2	subset	subset	NOUN
ejpam-6017	68	3	a	a	PRON
ejpam-6017	68	4	of	of	ADP
ejpam-6017	68	5	a	a	DET
ejpam-6017	68	6	bitopological	bitopological	ADJ
ejpam-6017	68	7	space	space	NOUN
ejpam-6017	68	8	(	(	PUNCT
ejpam-6017	68	9	x	x	NOUN
ejpam-6017	68	10	,	,	PUNCT
ejpam-6017	68	11	τ1	τ1	NOUN
ejpam-6017	68	12	,	,	PUNCT
ejpam-6017	68	13	τ2	τ2	NOUN
ejpam-6017	68	14	)	)	PUNCT
ejpam-6017	68	15	is	be	AUX
ejpam-6017	68	16	said	say	VERB
ejpam-6017	68	17	to	to	PART
ejpam-6017	68	18	be	be	AUX
ejpam-6017	68	19	(	(	PUNCT
ejpam-6017	68	20	τ1	τ1	NOUN
ejpam-6017	68	21	,	,	PUNCT
ejpam-6017	68	22	τ2)θ	τ2)θ	NOUN
ejpam-6017	68	23	-	-	PUNCT
ejpam-6017	68	24	closed	closed	ADJ
ejpam-6017	68	25	[	[	X
ejpam-6017	68	26	28	28	NUM
ejpam-6017	68	27	]	]	X
ejpam-6017	68	28	if	if	SCONJ
ejpam-6017	68	29	a	a	PRON
ejpam-6017	68	30	=	=	X
ejpam-6017	68	31	(	(	PUNCT
ejpam-6017	68	32	τ1	τ1	NOUN
ejpam-6017	68	33	,	,	PUNCT
ejpam-6017	68	34	τ2)θ	τ2)θ	NOUN
ejpam-6017	68	35	-	-	PUNCT
ejpam-6017	68	36	cl(a	cl(a	NUM
ejpam-6017	68	37	)	)	PUNCT
ejpam-6017	68	38	.	.	PUNCT
ejpam-6017	69	1	the	the	DET
ejpam-6017	69	2	complement	complement	NOUN
ejpam-6017	69	3	of	of	ADP
ejpam-6017	69	4	a	a	DET
ejpam-6017	69	5	(	(	PUNCT
ejpam-6017	69	6	τ1	τ1	NOUN
ejpam-6017	69	7	,	,	PUNCT
ejpam-6017	69	8	τ2)θ	τ2)θ	ADJ
ejpam-6017	69	9	-	-	PUNCT
ejpam-6017	69	10	closed	close	VERB
ejpam-6017	69	11	set	set	NOUN
ejpam-6017	69	12	is	be	AUX
ejpam-6017	69	13	said	say	VERB
ejpam-6017	69	14	to	to	PART
ejpam-6017	69	15	be	be	AUX
ejpam-6017	69	16	(	(	PUNCT
ejpam-6017	69	17	τ1	τ1	NOUN
ejpam-6017	69	18	,	,	PUNCT
ejpam-6017	69	19	τ2)θ	τ2)θ	NOUN
ejpam-6017	69	20	-	-	PUNCT
ejpam-6017	69	21	open	open	ADJ
ejpam-6017	69	22	.	.	PUNCT
ejpam-6017	70	1	the	the	DET
ejpam-6017	70	2	union	union	NOUN
ejpam-6017	70	3	of	of	ADP
ejpam-6017	70	4	all	all	DET
ejpam-6017	70	5	(	(	PUNCT
ejpam-6017	70	6	τ1	τ1	NOUN
ejpam-6017	70	7	,	,	PUNCT
ejpam-6017	70	8	τ2)θ	τ2)θ	ADJ
ejpam-6017	70	9	-	-	PUNCT
ejpam-6017	70	10	open	open	ADJ
ejpam-6017	70	11	sets	set	NOUN
ejpam-6017	70	12	contained	contain	VERB
ejpam-6017	70	13	in	in	ADP
ejpam-6017	70	14	a	a	PRON
ejpam-6017	70	15	is	be	AUX
ejpam-6017	70	16	called	call	VERB
ejpam-6017	70	17	the	the	DET
ejpam-6017	70	18	(	(	PUNCT
ejpam-6017	70	19	τ1	τ1	NOUN
ejpam-6017	70	20	,	,	PUNCT
ejpam-6017	70	21	τ2)θ	τ2)θ	ADJ
ejpam-6017	70	22	-	-	PUNCT
ejpam-6017	70	23	interior	interior	NOUN
ejpam-6017	70	24	[	[	X
ejpam-6017	70	25	28	28	NUM
ejpam-6017	70	26	]	]	PUNCT
ejpam-6017	70	27	of	of	ADP
ejpam-6017	70	28	a	a	PRON
ejpam-6017	70	29	and	and	CCONJ
ejpam-6017	70	30	is	be	AUX
ejpam-6017	70	31	denoted	denote	VERB
ejpam-6017	70	32	by	by	ADP
ejpam-6017	70	33	(	(	PUNCT
ejpam-6017	70	34	τ1	τ1	NOUN
ejpam-6017	70	35	,	,	PUNCT
ejpam-6017	70	36	τ2)θ	τ2)θ	NOUN
ejpam-6017	70	37	-	-	PUNCT
ejpam-6017	70	38	int(a	int(a	NOUN
ejpam-6017	70	39	)	)	PUNCT
ejpam-6017	70	40	.	.	PUNCT
ejpam-6017	71	1	lemma	lemma	PROPN
ejpam-6017	71	2	2	2	NUM
ejpam-6017	71	3	.	.	PUNCT
ejpam-6017	72	1	[	[	X
ejpam-6017	72	2	28	28	NUM
ejpam-6017	72	3	]	]	PUNCT
ejpam-6017	72	4	for	for	ADP
ejpam-6017	72	5	a	a	DET
ejpam-6017	72	6	subset	subset	NOUN
ejpam-6017	72	7	a	a	PRON
ejpam-6017	72	8	of	of	ADP
ejpam-6017	72	9	a	a	DET
ejpam-6017	72	10	bitopological	bitopological	ADJ
ejpam-6017	72	11	space	space	NOUN
ejpam-6017	72	12	(	(	PUNCT
ejpam-6017	72	13	x	x	NOUN
ejpam-6017	72	14	,	,	PUNCT
ejpam-6017	72	15	τ1	τ1	NOUN
ejpam-6017	72	16	,	,	PUNCT
ejpam-6017	72	17	τ2	τ2	NOUN
ejpam-6017	72	18	)	)	PUNCT
ejpam-6017	72	19	,	,	PUNCT
ejpam-6017	72	20	the	the	DET
ejpam-6017	72	21	following	follow	VERB
ejpam-6017	72	22	properties	property	NOUN
ejpam-6017	72	23	hold	hold	VERB
ejpam-6017	72	24	:	:	PUNCT
ejpam-6017	72	25	(	(	PUNCT
ejpam-6017	72	26	1	1	X
ejpam-6017	72	27	)	)	PUNCT
ejpam-6017	72	28	if	if	SCONJ
ejpam-6017	72	29	a	a	PRON
ejpam-6017	72	30	is	be	AUX
ejpam-6017	72	31	τ2τ2	τ2τ2	VERB
ejpam-6017	72	32	-	-	VERB
ejpam-6017	72	33	open	open	ADJ
ejpam-6017	72	34	in	in	ADP
ejpam-6017	72	35	x	x	NOUN
ejpam-6017	72	36	,	,	PUNCT
ejpam-6017	72	37	then	then	ADV
ejpam-6017	72	38	τ1τ2	τ1τ2	NOUN
ejpam-6017	72	39	-	-	NUM
ejpam-6017	72	40	cl(a	cl(a	NUM
ejpam-6017	72	41	)	)	PUNCT
ejpam-6017	72	42	=	=	PUNCT
ejpam-6017	72	43	(	(	PUNCT
ejpam-6017	72	44	τ1	τ1	NOUN
ejpam-6017	72	45	,	,	PUNCT
ejpam-6017	72	46	τ2)θ	τ2)θ	NOUN
ejpam-6017	72	47	-	-	PUNCT
ejpam-6017	72	48	cl(a	cl(a	NUM
ejpam-6017	72	49	)	)	PUNCT
ejpam-6017	72	50	.	.	PUNCT
ejpam-6017	73	1	(	(	PUNCT
ejpam-6017	73	2	2	2	X
ejpam-6017	73	3	)	)	PUNCT
ejpam-6017	73	4	(	(	PUNCT
ejpam-6017	73	5	τ1	τ1	NOUN
ejpam-6017	73	6	,	,	PUNCT
ejpam-6017	73	7	τ2)θ	τ2)θ	NOUN
ejpam-6017	73	8	-	-	PUNCT
ejpam-6017	73	9	cl(a	cl(a	NUM
ejpam-6017	73	10	)	)	PUNCT
ejpam-6017	73	11	is	be	AUX
ejpam-6017	73	12	τ1τ2	τ1τ2	NOUN
ejpam-6017	73	13	-	-	ADJ
ejpam-6017	73	14	closed	closed	ADJ
ejpam-6017	73	15	in	in	ADP
ejpam-6017	73	16	x.	x.	NOUN
ejpam-6017	73	17	3	3	NUM
ejpam-6017	73	18	.	.	PUNCT
ejpam-6017	74	1	on	on	ADP
ejpam-6017	74	2	strongly	strongly	ADV
ejpam-6017	74	3	θ(τ1	θ(τ1	NOUN
ejpam-6017	74	4	,	,	PUNCT
ejpam-6017	74	5	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	74	6	functions	function	NOUN
ejpam-6017	74	7	in	in	ADP
ejpam-6017	74	8	this	this	DET
ejpam-6017	74	9	section	section	NOUN
ejpam-6017	74	10	,	,	PUNCT
ejpam-6017	74	11	we	we	PRON
ejpam-6017	74	12	introduce	introduce	VERB
ejpam-6017	74	13	the	the	DET
ejpam-6017	74	14	concept	concept	NOUN
ejpam-6017	74	15	of	of	ADP
ejpam-6017	74	16	strongly	strongly	ADV
ejpam-6017	74	17	θ(τ1	θ(τ1	NOUN
ejpam-6017	74	18	,	,	PUNCT
ejpam-6017	74	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	74	20	functions	function	NOUN
ejpam-6017	74	21	.	.	PUNCT
ejpam-6017	75	1	moreover	moreover	ADV
ejpam-6017	75	2	,	,	PUNCT
ejpam-6017	75	3	some	some	DET
ejpam-6017	75	4	characterizations	characterization	NOUN
ejpam-6017	75	5	of	of	ADP
ejpam-6017	75	6	strongly	strongly	ADV
ejpam-6017	75	7	θ(τ1	θ(τ1	NOUN
ejpam-6017	75	8	,	,	PUNCT
ejpam-6017	75	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	75	10	functions	function	NOUN
ejpam-6017	75	11	are	be	AUX
ejpam-6017	75	12	discussed	discuss	VERB
ejpam-6017	75	13	.	.	PUNCT
ejpam-6017	76	1	definition	definition	NOUN
ejpam-6017	76	2	1	1	NUM
ejpam-6017	76	3	.	.	PUNCT
ejpam-6017	77	1	a	a	DET
ejpam-6017	77	2	function	function	NOUN
ejpam-6017	77	3	f	f	NOUN
ejpam-6017	77	4	:	:	PUNCT
ejpam-6017	77	5	(	(	PUNCT
ejpam-6017	77	6	x	x	NOUN
ejpam-6017	77	7	,	,	PUNCT
ejpam-6017	77	8	τ1	τ1	NOUN
ejpam-6017	77	9	,	,	PUNCT
ejpam-6017	77	10	τ2	τ2	NOUN
ejpam-6017	77	11	)	)	PUNCT
ejpam-6017	77	12	→	→	SYM
ejpam-6017	77	13	(	(	PUNCT
ejpam-6017	77	14	y	y	PROPN
ejpam-6017	77	15	,	,	PUNCT
ejpam-6017	77	16	σ1	σ1	PROPN
ejpam-6017	77	17	,	,	PUNCT
ejpam-6017	77	18	σ2	σ2	PROPN
ejpam-6017	77	19	)	)	PUNCT
ejpam-6017	77	20	is	be	AUX
ejpam-6017	77	21	said	say	VERB
ejpam-6017	77	22	to	to	PART
ejpam-6017	77	23	be	be	AUX
ejpam-6017	77	24	strongly	strongly	ADV
ejpam-6017	77	25	θ(τ1	θ(τ1	ADJ
ejpam-6017	77	26	,	,	PUNCT
ejpam-6017	77	27	τ2)continuous	τ2)continuous	ADJ
ejpam-6017	77	28	at	at	ADP
ejpam-6017	77	29	a	a	DET
ejpam-6017	77	30	point	point	NOUN
ejpam-6017	77	31	x	x	SYM
ejpam-6017	77	32	∈	∈	NOUN
ejpam-6017	77	33	x	x	PUNCT
ejpam-6017	77	34	if	if	SCONJ
ejpam-6017	77	35	for	for	ADP
ejpam-6017	77	36	each	each	DET
ejpam-6017	77	37	σ1σ2	σ1σ2	VERB
ejpam-6017	77	38	-	-	ADJ
ejpam-6017	77	39	open	open	ADJ
ejpam-6017	77	40	set	set	NOUN
ejpam-6017	77	41	v	v	NOUN
ejpam-6017	77	42	of	of	ADP
ejpam-6017	77	43	y	y	NOUN
ejpam-6017	77	44	containing	contain	VERB
ejpam-6017	77	45	f(x	f(x	PROPN
ejpam-6017	77	46	)	)	PUNCT
ejpam-6017	77	47	,	,	PUNCT
ejpam-6017	77	48	there	there	PRON
ejpam-6017	77	49	exists	exist	VERB
ejpam-6017	77	50	a	a	DET
ejpam-6017	77	51	τ1τ2	τ1τ2	NOUN
ejpam-6017	77	52	-	-	ADJ
ejpam-6017	77	53	open	open	ADJ
ejpam-6017	77	54	set	set	ADJ
ejpam-6017	77	55	u	u	NOUN
ejpam-6017	77	56	of	of	ADP
ejpam-6017	77	57	x	x	PUNCT
ejpam-6017	77	58	containing	contain	VERB
ejpam-6017	77	59	x	x	PUNCT
ejpam-6017	77	60	such	such	ADJ
ejpam-6017	77	61	that	that	SCONJ
ejpam-6017	77	62	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	77	63	-	-	PUNCT
ejpam-6017	77	64	cl(u	cl(u	NOUN
ejpam-6017	77	65	)	)	PUNCT
ejpam-6017	77	66	)	)	PUNCT
ejpam-6017	78	1	⊆	⊆	NUM
ejpam-6017	78	2	v	v	NOUN
ejpam-6017	78	3	.	.	PUNCT
ejpam-6017	79	1	a	a	DET
ejpam-6017	79	2	function	function	NOUN
ejpam-6017	79	3	f	f	NOUN
ejpam-6017	79	4	:	:	PUNCT
ejpam-6017	79	5	(	(	PUNCT
ejpam-6017	79	6	x	x	NOUN
ejpam-6017	79	7	,	,	PUNCT
ejpam-6017	79	8	τ1	τ1	NOUN
ejpam-6017	79	9	,	,	PUNCT
ejpam-6017	79	10	τ2	τ2	NOUN
ejpam-6017	79	11	)	)	PUNCT
ejpam-6017	79	12	→	→	SYM
ejpam-6017	79	13	(	(	PUNCT
ejpam-6017	79	14	y	y	PROPN
ejpam-6017	79	15	,	,	PUNCT
ejpam-6017	79	16	σ1	σ1	PROPN
ejpam-6017	79	17	,	,	PUNCT
ejpam-6017	79	18	σ2	σ2	PROPN
ejpam-6017	79	19	)	)	PUNCT
ejpam-6017	79	20	is	be	AUX
ejpam-6017	79	21	said	say	VERB
ejpam-6017	79	22	to	to	PART
ejpam-6017	79	23	be	be	AUX
ejpam-6017	79	24	strongly	strongly	ADV
ejpam-6017	79	25	θ(τ1	θ(τ1	ADJ
ejpam-6017	79	26	,	,	PUNCT
ejpam-6017	79	27	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	79	28	if	if	SCONJ
ejpam-6017	79	29	f	f	PROPN
ejpam-6017	79	30	is	be	AUX
ejpam-6017	79	31	strongly	strongly	ADV
ejpam-6017	79	32	θ(τ1	θ(τ1	ADJ
ejpam-6017	79	33	,	,	PUNCT
ejpam-6017	79	34	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	79	35	at	at	ADP
ejpam-6017	79	36	each	each	DET
ejpam-6017	79	37	point	point	NOUN
ejpam-6017	79	38	x	x	PUNCT
ejpam-6017	79	39	of	of	ADP
ejpam-6017	79	40	x.	x.	PROPN
ejpam-6017	79	41	theorem	theorem	VERB
ejpam-6017	79	42	1	1	NUM
ejpam-6017	79	43	.	.	PUNCT
ejpam-6017	80	1	a	a	DET
ejpam-6017	80	2	function	function	NOUN
ejpam-6017	80	3	f	f	NOUN
ejpam-6017	80	4	:	:	PUNCT
ejpam-6017	80	5	(	(	PUNCT
ejpam-6017	80	6	x	x	NOUN
ejpam-6017	80	7	,	,	PUNCT
ejpam-6017	80	8	τ1	τ1	NOUN
ejpam-6017	80	9	,	,	PUNCT
ejpam-6017	80	10	τ2	τ2	NOUN
ejpam-6017	80	11	)	)	PUNCT
ejpam-6017	80	12	→	→	SYM
ejpam-6017	80	13	(	(	PUNCT
ejpam-6017	80	14	y	y	PROPN
ejpam-6017	80	15	,	,	PUNCT
ejpam-6017	80	16	σ1	σ1	PROPN
ejpam-6017	80	17	,	,	PUNCT
ejpam-6017	80	18	σ2	σ2	PROPN
ejpam-6017	80	19	)	)	PUNCT
ejpam-6017	80	20	is	be	AUX
ejpam-6017	80	21	strongly	strongly	ADV
ejpam-6017	80	22	θ(τ1	θ(τ1	ADJ
ejpam-6017	80	23	,	,	PUNCT
ejpam-6017	80	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	80	25	at	at	ADP
ejpam-6017	80	26	x	x	X
ejpam-6017	80	27	∈	∈	PROPN
ejpam-6017	80	28	x	x	SYM
ejpam-6017	80	29	if	if	SCONJ
ejpam-6017	81	1	and	and	CCONJ
ejpam-6017	81	2	only	only	ADV
ejpam-6017	81	3	if	if	SCONJ
ejpam-6017	81	4	for	for	ADP
ejpam-6017	81	5	each	each	DET
ejpam-6017	81	6	σ1σ2	σ1σ2	VERB
ejpam-6017	81	7	-	-	ADJ
ejpam-6017	81	8	open	open	ADJ
ejpam-6017	81	9	set	set	NOUN
ejpam-6017	81	10	v	v	NOUN
ejpam-6017	81	11	of	of	ADP
ejpam-6017	81	12	y	y	NOUN
ejpam-6017	81	13	containing	contain	VERB
ejpam-6017	81	14	f(x	f(x	PROPN
ejpam-6017	81	15	)	)	PUNCT
ejpam-6017	81	16	,	,	PUNCT
ejpam-6017	81	17	x	x	PUNCT
ejpam-6017	81	18	∈	∈	PROPN
ejpam-6017	81	19	(	(	PUNCT
ejpam-6017	81	20	τ1	τ1	NOUN
ejpam-6017	81	21	,	,	PUNCT
ejpam-6017	81	22	τ2)θ	τ2)θ	NOUN
ejpam-6017	81	23	-	-	PUNCT
ejpam-6017	81	24	int(f	int(f	PROPN
ejpam-6017	81	25	−1(v	−1(v	NOUN
ejpam-6017	81	26	)	)	PUNCT
ejpam-6017	81	27	)	)	PUNCT
ejpam-6017	81	28	.	.	PUNCT
ejpam-6017	82	1	proof	proof	NOUN
ejpam-6017	82	2	.	.	PUNCT
ejpam-6017	83	1	suppose	suppose	VERB
ejpam-6017	83	2	that	that	SCONJ
ejpam-6017	83	3	f	f	PROPN
ejpam-6017	83	4	is	be	AUX
ejpam-6017	83	5	strongly	strongly	ADV
ejpam-6017	83	6	θ(τ1	θ(τ1	ADJ
ejpam-6017	83	7	,	,	PUNCT
ejpam-6017	83	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	83	9	at	at	ADP
ejpam-6017	83	10	x	x	SYM
ejpam-6017	83	11	∈	∈	PROPN
ejpam-6017	83	12	x.	x.	NOUN
ejpam-6017	83	13	let	let	VERB
ejpam-6017	83	14	v	v	PART
ejpam-6017	83	15	be	be	AUX
ejpam-6017	83	16	any	any	DET
ejpam-6017	83	17	σ1σ2open	σ1σ2open	ADJ
ejpam-6017	83	18	set	set	NOUN
ejpam-6017	83	19	of	of	ADP
ejpam-6017	83	20	y	y	PROPN
ejpam-6017	83	21	containing	contain	VERB
ejpam-6017	83	22	f(x	f(x	PROPN
ejpam-6017	83	23	)	)	PUNCT
ejpam-6017	83	24	.	.	PUNCT
ejpam-6017	84	1	then	then	ADV
ejpam-6017	84	2	,	,	PUNCT
ejpam-6017	84	3	there	there	PRON
ejpam-6017	84	4	exists	exist	VERB
ejpam-6017	84	5	a	a	DET
ejpam-6017	84	6	τ1τ2	τ1τ2	NOUN
ejpam-6017	84	7	-	-	ADJ
ejpam-6017	84	8	open	open	ADJ
ejpam-6017	84	9	set	set	ADJ
ejpam-6017	84	10	u	u	NOUN
ejpam-6017	84	11	of	of	ADP
ejpam-6017	84	12	x	x	PUNCT
ejpam-6017	84	13	containing	contain	VERB
ejpam-6017	84	14	x	x	PUNCT
ejpam-6017	84	15	such	such	ADJ
ejpam-6017	84	16	that	that	SCONJ
ejpam-6017	84	17	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	84	18	-	-	PUNCT
ejpam-6017	84	19	cl(u	cl(u	NOUN
ejpam-6017	84	20	)	)	PUNCT
ejpam-6017	84	21	)	)	PUNCT
ejpam-6017	85	1	⊆	⊆	NUM
ejpam-6017	85	2	v	v	NOUN
ejpam-6017	85	3	.	.	PUNCT
ejpam-6017	86	1	thus	thus	ADV
ejpam-6017	86	2	,	,	PUNCT
ejpam-6017	86	3	τ1τ2	τ1τ2	NOUN
ejpam-6017	86	4	-	-	NOUN
ejpam-6017	86	5	cl(u	cl(u	ADJ
ejpam-6017	86	6	)	)	PUNCT
ejpam-6017	86	7	⊆	⊆	NUM
ejpam-6017	86	8	f−1(v	f−1(v	NOUN
ejpam-6017	86	9	)	)	PUNCT
ejpam-6017	86	10	and	and	CCONJ
ejpam-6017	86	11	hence	hence	ADV
ejpam-6017	86	12	x	x	X
ejpam-6017	86	13	∈	∈	PROPN
ejpam-6017	86	14	(	(	PUNCT
ejpam-6017	86	15	τ1	τ1	NOUN
ejpam-6017	86	16	,	,	PUNCT
ejpam-6017	86	17	τ2)θ	τ2)θ	NOUN
ejpam-6017	86	18	-	-	PUNCT
ejpam-6017	86	19	int(f	int(f	PROPN
ejpam-6017	86	20	−1(v	−1(v	NOUN
ejpam-6017	86	21	)	)	PUNCT
ejpam-6017	86	22	)	)	PUNCT
ejpam-6017	86	23	.	.	PUNCT
ejpam-6017	87	1	conversely	conversely	ADV
ejpam-6017	87	2	,	,	PUNCT
ejpam-6017	87	3	let	let	VERB
ejpam-6017	87	4	v	v	PART
ejpam-6017	87	5	be	be	AUX
ejpam-6017	87	6	any	any	DET
ejpam-6017	87	7	σ1σ2	σ1σ2	NOUN
ejpam-6017	87	8	-	-	ADJ
ejpam-6017	87	9	open	open	ADJ
ejpam-6017	87	10	set	set	NOUN
ejpam-6017	87	11	of	of	ADP
ejpam-6017	87	12	y	y	PROPN
ejpam-6017	87	13	containing	contain	VERB
ejpam-6017	87	14	f(x	f(x	PROPN
ejpam-6017	87	15	)	)	PUNCT
ejpam-6017	87	16	.	.	PUNCT
ejpam-6017	88	1	then	then	ADV
ejpam-6017	88	2	,	,	PUNCT
ejpam-6017	88	3	by	by	ADP
ejpam-6017	88	4	the	the	DET
ejpam-6017	88	5	hypothesis	hypothesis	NOUN
ejpam-6017	88	6	we	we	PRON
ejpam-6017	88	7	have	have	VERB
ejpam-6017	88	8	x	x	X
ejpam-6017	88	9	∈	∈	PROPN
ejpam-6017	88	10	(	(	PUNCT
ejpam-6017	88	11	τ1	τ1	NOUN
ejpam-6017	88	12	,	,	PUNCT
ejpam-6017	88	13	τ2)θ	τ2)θ	NOUN
ejpam-6017	88	14	-	-	PUNCT
ejpam-6017	88	15	int(f	int(f	PROPN
ejpam-6017	88	16	−1(v	−1(v	NOUN
ejpam-6017	88	17	)	)	PUNCT
ejpam-6017	88	18	)	)	PUNCT
ejpam-6017	88	19	.	.	PUNCT
ejpam-6017	89	1	there	there	PRON
ejpam-6017	89	2	exists	exist	VERB
ejpam-6017	89	3	a	a	DET
ejpam-6017	89	4	τ1τ2	τ1τ2	NOUN
ejpam-6017	89	5	-	-	ADJ
ejpam-6017	89	6	open	open	ADJ
ejpam-6017	89	7	set	set	ADJ
ejpam-6017	89	8	u	u	NOUN
ejpam-6017	89	9	of	of	ADP
ejpam-6017	89	10	x	x	SYM
ejpam-6017	89	11	such	such	ADJ
ejpam-6017	89	12	that	that	SCONJ
ejpam-6017	89	13	x	x	SYM
ejpam-6017	89	14	∈	∈	PROPN
ejpam-6017	89	15	u	u	NOUN
ejpam-6017	89	16	⊆	⊆	NUM
ejpam-6017	89	17	τ1τ2	τ1τ2	NOUN
ejpam-6017	89	18	-	-	NOUN
ejpam-6017	89	19	cl(u	cl(u	ADJ
ejpam-6017	89	20	)	)	PUNCT
ejpam-6017	89	21	⊆	⊆	NUM
ejpam-6017	89	22	f−1(v	f−1(v	NOUN
ejpam-6017	89	23	)	)	PUNCT
ejpam-6017	89	24	;	;	PUNCT
ejpam-6017	89	25	hence	hence	ADV
ejpam-6017	89	26	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	89	27	-	-	PUNCT
ejpam-6017	89	28	cl(u	cl(u	NOUN
ejpam-6017	89	29	)	)	PUNCT
ejpam-6017	89	30	)	)	PUNCT
ejpam-6017	90	1	⊆	⊆	NUM
ejpam-6017	90	2	v	v	NOUN
ejpam-6017	90	3	.	.	PUNCT
ejpam-6017	91	1	this	this	PRON
ejpam-6017	91	2	shows	show	VERB
ejpam-6017	91	3	that	that	SCONJ
ejpam-6017	91	4	f	f	PROPN
ejpam-6017	91	5	is	be	AUX
ejpam-6017	91	6	strongly	strongly	ADV
ejpam-6017	91	7	θ(τ1	θ(τ1	ADJ
ejpam-6017	91	8	,	,	PUNCT
ejpam-6017	91	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	91	10	at	at	ADP
ejpam-6017	91	11	x	x	SYM
ejpam-6017	91	12	∈	∈	PROPN
ejpam-6017	91	13	x.	x.	NOUN
ejpam-6017	91	14	theorem	theorem	VERB
ejpam-6017	91	15	2	2	NUM
ejpam-6017	91	16	.	.	X
ejpam-6017	91	17	for	for	ADP
ejpam-6017	91	18	a	a	DET
ejpam-6017	91	19	function	function	NOUN
ejpam-6017	91	20	(	(	PUNCT
ejpam-6017	91	21	x	x	NOUN
ejpam-6017	91	22	,	,	PUNCT
ejpam-6017	91	23	τ1	τ1	NOUN
ejpam-6017	91	24	,	,	PUNCT
ejpam-6017	91	25	τ2	τ2	NOUN
ejpam-6017	91	26	)	)	PUNCT
ejpam-6017	91	27	→	→	SYM
ejpam-6017	91	28	(	(	PUNCT
ejpam-6017	91	29	y	y	PROPN
ejpam-6017	91	30	,	,	PUNCT
ejpam-6017	91	31	σ1	σ1	PROPN
ejpam-6017	91	32	,	,	PUNCT
ejpam-6017	91	33	σ2	σ2	NOUN
ejpam-6017	91	34	)	)	PUNCT
ejpam-6017	91	35	,	,	PUNCT
ejpam-6017	91	36	the	the	DET
ejpam-6017	91	37	following	follow	VERB
ejpam-6017	91	38	properties	property	NOUN
ejpam-6017	91	39	are	be	AUX
ejpam-6017	91	40	equivalent	equivalent	ADJ
ejpam-6017	91	41	:	:	PUNCT
ejpam-6017	91	42	(	(	PUNCT
ejpam-6017	91	43	1	1	X
ejpam-6017	91	44	)	)	PUNCT
ejpam-6017	91	45	f	f	PROPN
ejpam-6017	91	46	is	be	AUX
ejpam-6017	91	47	strongly	strongly	ADV
ejpam-6017	91	48	θ(τ1	θ(τ1	ADJ
ejpam-6017	91	49	,	,	PUNCT
ejpam-6017	91	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	91	51	;	;	PUNCT
ejpam-6017	91	52	(	(	PUNCT
ejpam-6017	91	53	2	2	X
ejpam-6017	91	54	)	)	PUNCT
ejpam-6017	91	55	f−1(v	f−1(v	NOUN
ejpam-6017	91	56	)	)	PUNCT
ejpam-6017	91	57	is	be	AUX
ejpam-6017	91	58	(	(	PUNCT
ejpam-6017	91	59	τ1	τ1	NOUN
ejpam-6017	91	60	,	,	PUNCT
ejpam-6017	91	61	τ2)θ	τ2)θ	NOUN
ejpam-6017	91	62	-	-	PUNCT
ejpam-6017	91	63	open	open	ADJ
ejpam-6017	91	64	in	in	ADP
ejpam-6017	91	65	x	x	PUNCT
ejpam-6017	91	66	for	for	ADP
ejpam-6017	91	67	every	every	DET
ejpam-6017	91	68	σ1σ2	σ1σ2	NOUN
ejpam-6017	91	69	-	-	ADJ
ejpam-6017	91	70	open	open	ADJ
ejpam-6017	91	71	set	set	NOUN
ejpam-6017	91	72	v	v	NOUN
ejpam-6017	91	73	of	of	ADP
ejpam-6017	91	74	y	y	PROPN
ejpam-6017	91	75	;	;	PUNCT
ejpam-6017	91	76	p.	p.	NOUN
ejpam-6017	91	77	pue	pue	PROPN
ejpam-6017	91	78	-	-	PUNCT
ejpam-6017	91	79	on	on	ADP
ejpam-6017	91	80	,	,	PUNCT
ejpam-6017	91	81	s.	s.	PROPN
ejpam-6017	91	82	sompong	sompong	PROPN
ejpam-6017	91	83	,	,	PUNCT
ejpam-6017	91	84	c.	c.	PROPN
ejpam-6017	91	85	boonpok	boonpok	PROPN
ejpam-6017	91	86	/	/	SYM
ejpam-6017	91	87	eur	eur	PROPN
ejpam-6017	91	88	.	.	PUNCT
ejpam-6017	92	1	j.	j.	PROPN
ejpam-6017	92	2	pure	pure	PROPN
ejpam-6017	92	3	appl	appl	PROPN
ejpam-6017	92	4	.	.	PROPN
ejpam-6017	92	5	math	math	PROPN
ejpam-6017	92	6	,	,	PUNCT
ejpam-6017	92	7	18	18	NUM
ejpam-6017	92	8	(	(	PUNCT
ejpam-6017	92	9	2	2	NUM
ejpam-6017	92	10	)	)	PUNCT
ejpam-6017	92	11	(	(	PUNCT
ejpam-6017	92	12	2025	2025	NUM
ejpam-6017	92	13	)	)	PUNCT
ejpam-6017	92	14	,	,	PUNCT
ejpam-6017	92	15	6017	6017	NUM
ejpam-6017	92	16	4	4	NUM
ejpam-6017	92	17	of	of	ADP
ejpam-6017	92	18	11	11	NUM
ejpam-6017	92	19	(	(	PUNCT
ejpam-6017	92	20	3	3	NUM
ejpam-6017	92	21	)	)	PUNCT
ejpam-6017	92	22	f−1(f	f−1(f	NOUN
ejpam-6017	92	23	)	)	PUNCT
ejpam-6017	92	24	is	be	AUX
ejpam-6017	92	25	(	(	PUNCT
ejpam-6017	92	26	τ1	τ1	NOUN
ejpam-6017	92	27	,	,	PUNCT
ejpam-6017	92	28	τ2)θ	τ2)θ	NOUN
ejpam-6017	92	29	-	-	PUNCT
ejpam-6017	92	30	closed	closed	ADJ
ejpam-6017	92	31	in	in	ADP
ejpam-6017	92	32	x	x	PUNCT
ejpam-6017	92	33	for	for	ADP
ejpam-6017	92	34	every	every	DET
ejpam-6017	92	35	σ1σ2	σ1σ2	NUM
ejpam-6017	92	36	-	-	PUNCT
ejpam-6017	92	37	closed	closed	ADJ
ejpam-6017	92	38	set	set	ADJ
ejpam-6017	92	39	f	f	PROPN
ejpam-6017	92	40	of	of	ADP
ejpam-6017	92	41	y	y	PROPN
ejpam-6017	92	42	;	;	PUNCT
ejpam-6017	92	43	(	(	PUNCT
ejpam-6017	92	44	4	4	X
ejpam-6017	92	45	)	)	PUNCT
ejpam-6017	92	46	f((τ1	f((τ1	PROPN
ejpam-6017	92	47	,	,	PUNCT
ejpam-6017	92	48	τ2)θ	τ2)θ	NOUN
ejpam-6017	92	49	-	-	PUNCT
ejpam-6017	92	50	cl(a	cl(a	NUM
ejpam-6017	92	51	)	)	PUNCT
ejpam-6017	92	52	)	)	PUNCT
ejpam-6017	93	1	⊆	⊆	X
ejpam-6017	93	2	σ1σ2	σ1σ2	NUM
ejpam-6017	93	3	-	-	PUNCT
ejpam-6017	93	4	cl(f(a	cl(f(a	NOUN
ejpam-6017	93	5	)	)	PUNCT
ejpam-6017	93	6	)	)	PUNCT
ejpam-6017	93	7	for	for	ADP
ejpam-6017	93	8	every	every	DET
ejpam-6017	93	9	subset	subset	NOUN
ejpam-6017	93	10	a	a	PRON
ejpam-6017	93	11	of	of	ADP
ejpam-6017	93	12	x	x	PRON
ejpam-6017	93	13	;	;	PUNCT
ejpam-6017	93	14	(	(	PUNCT
ejpam-6017	93	15	5	5	NUM
ejpam-6017	93	16	)	)	PUNCT
ejpam-6017	93	17	(	(	PUNCT
ejpam-6017	93	18	τ1	τ1	NOUN
ejpam-6017	93	19	,	,	PUNCT
ejpam-6017	93	20	τ2)θ	τ2)θ	PROPN
ejpam-6017	93	21	-	-	PUNCT
ejpam-6017	93	22	cl(f	cl(f	NOUN
ejpam-6017	93	23	−1(b	−1(b	NOUN
ejpam-6017	93	24	)	)	PUNCT
ejpam-6017	93	25	)	)	PUNCT
ejpam-6017	94	1	⊆	⊆	NUM
ejpam-6017	94	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6017	94	3	-	-	PUNCT
ejpam-6017	94	4	cl(b	cl(b	NOUN
ejpam-6017	94	5	)	)	PUNCT
ejpam-6017	94	6	)	)	PUNCT
ejpam-6017	94	7	for	for	ADP
ejpam-6017	94	8	every	every	DET
ejpam-6017	94	9	subset	subset	NOUN
ejpam-6017	94	10	b	b	PROPN
ejpam-6017	94	11	of	of	ADP
ejpam-6017	94	12	y	y	PROPN
ejpam-6017	94	13	.	.	PUNCT
ejpam-6017	95	1	proof	proof	NOUN
ejpam-6017	95	2	.	.	PUNCT
ejpam-6017	96	1	(	(	PUNCT
ejpam-6017	96	2	1	1	X
ejpam-6017	96	3	)	)	PUNCT
ejpam-6017	96	4	⇒	⇒	NOUN
ejpam-6017	96	5	(	(	PUNCT
ejpam-6017	96	6	2	2	NUM
ejpam-6017	96	7	):	):	PUNCT
ejpam-6017	96	8	let	let	VERB
ejpam-6017	96	9	v	v	PART
ejpam-6017	96	10	be	be	AUX
ejpam-6017	96	11	any	any	DET
ejpam-6017	96	12	σ1σ2	σ1σ2	NOUN
ejpam-6017	96	13	-	-	ADJ
ejpam-6017	96	14	open	open	ADJ
ejpam-6017	96	15	set	set	NOUN
ejpam-6017	96	16	of	of	ADP
ejpam-6017	96	17	y	y	PROPN
ejpam-6017	96	18	and	and	CCONJ
ejpam-6017	96	19	x	x	PROPN
ejpam-6017	96	20	∈	∈	PROPN
ejpam-6017	96	21	f−1(v	f−1(v	NOUN
ejpam-6017	96	22	)	)	PUNCT
ejpam-6017	96	23	.	.	PUNCT
ejpam-6017	97	1	then	then	ADV
ejpam-6017	97	2	,	,	PUNCT
ejpam-6017	97	3	f(x	f(x	PROPN
ejpam-6017	97	4	)	)	PUNCT
ejpam-6017	97	5	∈	∈	PROPN
ejpam-6017	97	6	v	v	NOUN
ejpam-6017	97	7	.	.	PUNCT
ejpam-6017	98	1	since	since	SCONJ
ejpam-6017	98	2	f	f	PROPN
ejpam-6017	98	3	is	be	AUX
ejpam-6017	98	4	strongly	strongly	ADV
ejpam-6017	98	5	θ(τ1	θ(τ1	ADJ
ejpam-6017	98	6	,	,	PUNCT
ejpam-6017	98	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	98	8	,	,	PUNCT
ejpam-6017	98	9	by	by	ADP
ejpam-6017	98	10	theorem	theorem	NOUN
ejpam-6017	98	11	1	1	NUM
ejpam-6017	98	12	we	we	PRON
ejpam-6017	98	13	have	have	VERB
ejpam-6017	98	14	x	x	X
ejpam-6017	98	15	∈	∈	PROPN
ejpam-6017	98	16	(	(	PUNCT
ejpam-6017	98	17	τ1	τ1	NOUN
ejpam-6017	98	18	,	,	PUNCT
ejpam-6017	98	19	τ2)θ	τ2)θ	NOUN
ejpam-6017	98	20	-	-	PUNCT
ejpam-6017	98	21	int(f	int(f	PROPN
ejpam-6017	98	22	−1(v	−1(v	NOUN
ejpam-6017	98	23	)	)	PUNCT
ejpam-6017	98	24	)	)	PUNCT
ejpam-6017	98	25	.	.	PUNCT
ejpam-6017	99	1	thus	thus	ADV
ejpam-6017	99	2	,	,	PUNCT
ejpam-6017	99	3	f−1(v	f−1(v	PROPN
ejpam-6017	99	4	)	)	PUNCT
ejpam-6017	100	1	⊆	⊆	NUM
ejpam-6017	100	2	(	(	PUNCT
ejpam-6017	100	3	τ1	τ1	NOUN
ejpam-6017	100	4	,	,	PUNCT
ejpam-6017	100	5	τ2)θ	τ2)θ	NOUN
ejpam-6017	100	6	-	-	PUNCT
ejpam-6017	100	7	int(f	int(f	PROPN
ejpam-6017	100	8	−1(v	−1(v	NOUN
ejpam-6017	100	9	)	)	PUNCT
ejpam-6017	100	10	)	)	PUNCT
ejpam-6017	100	11	and	and	CCONJ
ejpam-6017	100	12	hence	hence	ADV
ejpam-6017	100	13	f−1(v	f−1(v	NOUN
ejpam-6017	100	14	)	)	PUNCT
ejpam-6017	101	1	=	=	PUNCT
ejpam-6017	101	2	(	(	PUNCT
ejpam-6017	101	3	τ1	τ1	NOUN
ejpam-6017	101	4	,	,	PUNCT
ejpam-6017	101	5	τ2)θ	τ2)θ	NOUN
ejpam-6017	101	6	-	-	PUNCT
ejpam-6017	101	7	int(f	int(f	PROPN
ejpam-6017	101	8	−1(v	−1(v	NOUN
ejpam-6017	101	9	)	)	PUNCT
ejpam-6017	101	10	)	)	PUNCT
ejpam-6017	101	11	.	.	PUNCT
ejpam-6017	102	1	this	this	PRON
ejpam-6017	102	2	shows	show	VERB
ejpam-6017	102	3	that	that	DET
ejpam-6017	102	4	f−1(v	f−1(v	PROPN
ejpam-6017	102	5	)	)	PUNCT
ejpam-6017	102	6	is	be	AUX
ejpam-6017	102	7	(	(	PUNCT
ejpam-6017	102	8	τ1	τ1	NOUN
ejpam-6017	102	9	,	,	PUNCT
ejpam-6017	102	10	τ2)θ	τ2)θ	NOUN
ejpam-6017	102	11	-	-	PUNCT
ejpam-6017	102	12	open	open	ADJ
ejpam-6017	102	13	in	in	ADP
ejpam-6017	102	14	x.	x.	NOUN
ejpam-6017	102	15	(	(	PUNCT
ejpam-6017	102	16	2	2	NUM
ejpam-6017	102	17	)	)	PUNCT
ejpam-6017	102	18	⇒	⇒	NOUN
ejpam-6017	102	19	(	(	PUNCT
ejpam-6017	102	20	3	3	NUM
ejpam-6017	102	21	):	):	PUNCT
ejpam-6017	102	22	the	the	DET
ejpam-6017	102	23	proof	proof	NOUN
ejpam-6017	102	24	is	be	AUX
ejpam-6017	102	25	obvious	obvious	ADJ
ejpam-6017	102	26	.	.	PUNCT
ejpam-6017	103	1	(	(	PUNCT
ejpam-6017	103	2	3	3	X
ejpam-6017	103	3	)	)	PUNCT
ejpam-6017	103	4	⇒	⇒	NOUN
ejpam-6017	103	5	(	(	PUNCT
ejpam-6017	103	6	1	1	NUM
ejpam-6017	103	7	):	):	PUNCT
ejpam-6017	103	8	let	let	VERB
ejpam-6017	103	9	x	x	PUNCT
ejpam-6017	103	10	∈	∈	PROPN
ejpam-6017	103	11	x	x	X
ejpam-6017	103	12	and	and	CCONJ
ejpam-6017	103	13	v	v	X
ejpam-6017	103	14	be	be	AUX
ejpam-6017	103	15	any	any	DET
ejpam-6017	103	16	σ1σ2	σ1σ2	NOUN
ejpam-6017	103	17	-	-	ADJ
ejpam-6017	103	18	open	open	ADJ
ejpam-6017	103	19	set	set	NOUN
ejpam-6017	103	20	of	of	ADP
ejpam-6017	103	21	y	y	PROPN
ejpam-6017	103	22	containing	contain	VERB
ejpam-6017	103	23	f(x	f(x	PROPN
ejpam-6017	103	24	)	)	PUNCT
ejpam-6017	103	25	.	.	PUNCT
ejpam-6017	104	1	by	by	ADP
ejpam-6017	104	2	(	(	PUNCT
ejpam-6017	104	3	3	3	NUM
ejpam-6017	104	4	)	)	PUNCT
ejpam-6017	104	5	,	,	PUNCT
ejpam-6017	104	6	f−1(y	f−1(y	PROPN
ejpam-6017	104	7	−	−	PROPN
ejpam-6017	104	8	v	v	NOUN
ejpam-6017	104	9	)	)	PUNCT
ejpam-6017	104	10	is	be	AUX
ejpam-6017	104	11	(	(	PUNCT
ejpam-6017	104	12	τ1	τ1	NOUN
ejpam-6017	104	13	,	,	PUNCT
ejpam-6017	104	14	τ2)θ	τ2)θ	NOUN
ejpam-6017	104	15	-	-	PUNCT
ejpam-6017	104	16	closed	close	VERB
ejpam-6017	104	17	and	and	CCONJ
ejpam-6017	104	18	so	so	ADV
ejpam-6017	104	19	f−1(v	f−1(v	PROPN
ejpam-6017	104	20	)	)	PUNCT
ejpam-6017	105	1	is	be	AUX
ejpam-6017	105	2	(	(	PUNCT
ejpam-6017	105	3	τ1	τ1	NOUN
ejpam-6017	105	4	,	,	PUNCT
ejpam-6017	105	5	τ2)θ	τ2)θ	NOUN
ejpam-6017	105	6	-	-	PUNCT
ejpam-6017	105	7	open	open	ADJ
ejpam-6017	105	8	.	.	PUNCT
ejpam-6017	106	1	then	then	ADV
ejpam-6017	106	2	,	,	PUNCT
ejpam-6017	106	3	there	there	PRON
ejpam-6017	106	4	exists	exist	VERB
ejpam-6017	106	5	a	a	DET
ejpam-6017	106	6	τ1τ2open	τ1τ2open	ADJ
ejpam-6017	106	7	set	set	NOUN
ejpam-6017	106	8	u	u	NOUN
ejpam-6017	106	9	of	of	ADP
ejpam-6017	106	10	x	x	SYM
ejpam-6017	106	11	such	such	ADJ
ejpam-6017	106	12	that	that	SCONJ
ejpam-6017	106	13	x	x	SYM
ejpam-6017	106	14	∈	∈	PROPN
ejpam-6017	106	15	u	u	NOUN
ejpam-6017	106	16	⊆	⊆	NUM
ejpam-6017	106	17	τ1τ2	τ1τ2	NOUN
ejpam-6017	106	18	-	-	NOUN
ejpam-6017	106	19	cl(u	cl(u	ADJ
ejpam-6017	106	20	)	)	PUNCT
ejpam-6017	106	21	⊆	⊆	NUM
ejpam-6017	106	22	f−1(v	f−1(v	NOUN
ejpam-6017	106	23	)	)	PUNCT
ejpam-6017	106	24	.	.	PUNCT
ejpam-6017	107	1	thus	thus	ADV
ejpam-6017	107	2	,	,	PUNCT
ejpam-6017	107	3	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	107	4	-	-	PUNCT
ejpam-6017	107	5	cl(u	cl(u	NOUN
ejpam-6017	107	6	)	)	PUNCT
ejpam-6017	107	7	)	)	PUNCT
ejpam-6017	108	1	⊆	⊆	NUM
ejpam-6017	108	2	v	v	NOUN
ejpam-6017	108	3	.	.	PUNCT
ejpam-6017	109	1	this	this	PRON
ejpam-6017	109	2	shows	show	VERB
ejpam-6017	109	3	that	that	SCONJ
ejpam-6017	109	4	f	f	PROPN
ejpam-6017	109	5	is	be	AUX
ejpam-6017	109	6	strongly	strongly	ADV
ejpam-6017	109	7	θ(τ1	θ(τ1	ADJ
ejpam-6017	109	8	,	,	PUNCT
ejpam-6017	109	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	109	10	.	.	PUNCT
ejpam-6017	110	1	(	(	PUNCT
ejpam-6017	110	2	1	1	X
ejpam-6017	110	3	)	)	PUNCT
ejpam-6017	110	4	⇒	⇒	NOUN
ejpam-6017	110	5	(	(	PUNCT
ejpam-6017	110	6	4	4	NUM
ejpam-6017	110	7	):	):	PUNCT
ejpam-6017	110	8	let	let	VERB
ejpam-6017	110	9	a	a	DET
ejpam-6017	110	10	be	be	AUX
ejpam-6017	110	11	any	any	DET
ejpam-6017	110	12	subset	subset	NOUN
ejpam-6017	110	13	of	of	ADP
ejpam-6017	110	14	x.	x.	NOUN
ejpam-6017	110	15	let	let	VERB
ejpam-6017	110	16	x	x	X
ejpam-6017	110	17	∈	∈	PROPN
ejpam-6017	110	18	(	(	PUNCT
ejpam-6017	110	19	τ1	τ1	NOUN
ejpam-6017	110	20	,	,	PUNCT
ejpam-6017	110	21	τ2)θ	τ2)θ	NOUN
ejpam-6017	110	22	-	-	PUNCT
ejpam-6017	110	23	cl(a	cl(a	NUM
ejpam-6017	110	24	)	)	PUNCT
ejpam-6017	110	25	and	and	CCONJ
ejpam-6017	110	26	v	v	AUX
ejpam-6017	110	27	be	be	AUX
ejpam-6017	110	28	any	any	DET
ejpam-6017	110	29	σ1σ2open	σ1σ2open	ADJ
ejpam-6017	110	30	set	set	NOUN
ejpam-6017	110	31	of	of	ADP
ejpam-6017	110	32	y	y	PROPN
ejpam-6017	110	33	containing	contain	VERB
ejpam-6017	110	34	f(x	f(x	PROPN
ejpam-6017	110	35	)	)	PUNCT
ejpam-6017	110	36	.	.	PUNCT
ejpam-6017	111	1	since	since	SCONJ
ejpam-6017	111	2	f	f	PROPN
ejpam-6017	111	3	is	be	AUX
ejpam-6017	111	4	strongly	strongly	ADV
ejpam-6017	111	5	θ(τ1	θ(τ1	ADJ
ejpam-6017	111	6	,	,	PUNCT
ejpam-6017	111	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	111	8	,	,	PUNCT
ejpam-6017	111	9	there	there	PRON
ejpam-6017	111	10	exists	exist	VERB
ejpam-6017	111	11	a	a	DET
ejpam-6017	111	12	τ1τ2	τ1τ2	NOUN
ejpam-6017	111	13	-	-	ADJ
ejpam-6017	111	14	open	open	ADJ
ejpam-6017	111	15	set	set	ADJ
ejpam-6017	111	16	u	u	NOUN
ejpam-6017	111	17	of	of	ADP
ejpam-6017	111	18	x	x	SYM
ejpam-6017	111	19	such	such	ADJ
ejpam-6017	111	20	that	that	SCONJ
ejpam-6017	111	21	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	111	22	-	-	PUNCT
ejpam-6017	111	23	cl(u	cl(u	NOUN
ejpam-6017	111	24	)	)	PUNCT
ejpam-6017	111	25	)	)	PUNCT
ejpam-6017	112	1	⊆	⊆	NUM
ejpam-6017	112	2	v	v	NOUN
ejpam-6017	112	3	.	.	PUNCT
ejpam-6017	113	1	since	since	SCONJ
ejpam-6017	113	2	x	x	PROPN
ejpam-6017	113	3	∈	∈	PROPN
ejpam-6017	113	4	(	(	PUNCT
ejpam-6017	113	5	τ1	τ1	NOUN
ejpam-6017	113	6	,	,	PUNCT
ejpam-6017	113	7	τ2)θ	τ2)θ	NOUN
ejpam-6017	113	8	-	-	PUNCT
ejpam-6017	113	9	cl(a	cl(a	NUM
ejpam-6017	113	10	)	)	PUNCT
ejpam-6017	113	11	,	,	PUNCT
ejpam-6017	113	12	we	we	PRON
ejpam-6017	113	13	have	have	VERB
ejpam-6017	113	14	τ1τ2	τ1τ2	NOUN
ejpam-6017	113	15	-	-	NOUN
ejpam-6017	113	16	cl(u	cl(u	NOUN
ejpam-6017	113	17	)	)	PUNCT
ejpam-6017	113	18	∩	∩	NOUN
ejpam-6017	113	19	a	a	DET
ejpam-6017	113	20	̸=	̸=	PROPN
ejpam-6017	113	21	∅.	∅.	NOUN
ejpam-6017	113	22	it	it	PRON
ejpam-6017	113	23	follows	follow	VERB
ejpam-6017	113	24	that	that	SCONJ
ejpam-6017	113	25	∅	∅	NOUN
ejpam-6017	113	26	̸=	̸=	PROPN
ejpam-6017	113	27	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	113	28	-	-	PUNCT
ejpam-6017	113	29	cl(u	cl(u	NOUN
ejpam-6017	113	30	)	)	PUNCT
ejpam-6017	113	31	)	)	PUNCT
ejpam-6017	113	32	∩	∩	NOUN
ejpam-6017	113	33	f(a	f(a	NOUN
ejpam-6017	113	34	)	)	PUNCT
ejpam-6017	113	35	⊆	⊆	NUM
ejpam-6017	113	36	v	v	ADP
ejpam-6017	113	37	∩	∩	ADJ
ejpam-6017	113	38	f(a	f(a	NOUN
ejpam-6017	113	39	)	)	PUNCT
ejpam-6017	113	40	.	.	PUNCT
ejpam-6017	114	1	thus	thus	ADV
ejpam-6017	114	2	,	,	PUNCT
ejpam-6017	114	3	f(x	f(x	PROPN
ejpam-6017	114	4	)	)	PUNCT
ejpam-6017	114	5	∈	∈	PROPN
ejpam-6017	114	6	σ1σ2	σ1σ2	NOUN
ejpam-6017	114	7	-	-	PUNCT
ejpam-6017	114	8	cl(f(a	cl(f(a	NOUN
ejpam-6017	114	9	)	)	PUNCT
ejpam-6017	114	10	)	)	PUNCT
ejpam-6017	114	11	.	.	PUNCT
ejpam-6017	115	1	(	(	PUNCT
ejpam-6017	115	2	4	4	X
ejpam-6017	115	3	)	)	PUNCT
ejpam-6017	115	4	⇒	⇒	NOUN
ejpam-6017	115	5	(	(	PUNCT
ejpam-6017	115	6	5	5	NUM
ejpam-6017	115	7	):	):	PUNCT
ejpam-6017	115	8	let	let	VERB
ejpam-6017	115	9	b	b	X
ejpam-6017	115	10	be	be	AUX
ejpam-6017	115	11	any	any	DET
ejpam-6017	115	12	subset	subset	NOUN
ejpam-6017	115	13	of	of	ADP
ejpam-6017	115	14	y	y	PROPN
ejpam-6017	115	15	.	.	PUNCT
ejpam-6017	116	1	by	by	ADP
ejpam-6017	116	2	(	(	PUNCT
ejpam-6017	116	3	4	4	NUM
ejpam-6017	116	4	)	)	PUNCT
ejpam-6017	116	5	,	,	PUNCT
ejpam-6017	116	6	we	we	PRON
ejpam-6017	116	7	have	have	AUX
ejpam-6017	116	8	f((τ1	f((τ1	NOUN
ejpam-6017	116	9	,	,	PUNCT
ejpam-6017	116	10	τ2)θ	τ2)θ	ADJ
ejpam-6017	116	11	-	-	PUNCT
ejpam-6017	116	12	cl(f	cl(f	NOUN
ejpam-6017	116	13	−1(b	−1(b	NOUN
ejpam-6017	116	14	)	)	PUNCT
ejpam-6017	116	15	)	)	PUNCT
ejpam-6017	116	16	)	)	PUNCT
ejpam-6017	117	1	⊆	⊆	X
ejpam-6017	117	2	σ1σ2	σ1σ2	NUM
ejpam-6017	117	3	-	-	PUNCT
ejpam-6017	117	4	cl(f(f	cl(f(f	ADJ
ejpam-6017	117	5	−1(b	−1(b	NOUN
ejpam-6017	117	6	)	)	PUNCT
ejpam-6017	117	7	)	)	PUNCT
ejpam-6017	117	8	)	)	PUNCT
ejpam-6017	117	9	⊆	⊆	X
ejpam-6017	117	10	σ1σ2	σ1σ2	NUM
ejpam-6017	117	11	-	-	PUNCT
ejpam-6017	117	12	cl(b	cl(b	NOUN
ejpam-6017	117	13	)	)	PUNCT
ejpam-6017	117	14	and	and	CCONJ
ejpam-6017	117	15	hence	hence	ADV
ejpam-6017	117	16	(	(	PUNCT
ejpam-6017	117	17	τ1	τ1	NOUN
ejpam-6017	117	18	,	,	PUNCT
ejpam-6017	117	19	τ2)θ	τ2)θ	PROPN
ejpam-6017	117	20	-	-	PUNCT
ejpam-6017	117	21	cl(f	cl(f	NOUN
ejpam-6017	117	22	−1(b	−1(b	NOUN
ejpam-6017	117	23	)	)	PUNCT
ejpam-6017	117	24	)	)	PUNCT
ejpam-6017	117	25	⊆	⊆	NUM
ejpam-6017	117	26	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6017	117	27	-	-	PUNCT
ejpam-6017	117	28	cl(b	cl(b	NOUN
ejpam-6017	117	29	)	)	PUNCT
ejpam-6017	117	30	)	)	PUNCT
ejpam-6017	117	31	.	.	PUNCT
ejpam-6017	118	1	(	(	PUNCT
ejpam-6017	118	2	5	5	X
ejpam-6017	118	3	)	)	PUNCT
ejpam-6017	118	4	⇒	⇒	NOUN
ejpam-6017	118	5	(	(	PUNCT
ejpam-6017	118	6	1	1	NUM
ejpam-6017	118	7	):	):	PUNCT
ejpam-6017	118	8	let	let	VERB
ejpam-6017	118	9	x	x	PUNCT
ejpam-6017	118	10	∈	∈	PROPN
ejpam-6017	118	11	x	x	X
ejpam-6017	118	12	and	and	CCONJ
ejpam-6017	118	13	v	v	X
ejpam-6017	118	14	be	be	AUX
ejpam-6017	118	15	any	any	DET
ejpam-6017	118	16	σ1σ2	σ1σ2	NOUN
ejpam-6017	118	17	-	-	ADJ
ejpam-6017	118	18	open	open	ADJ
ejpam-6017	118	19	set	set	NOUN
ejpam-6017	118	20	of	of	ADP
ejpam-6017	118	21	y	y	PROPN
ejpam-6017	118	22	containing	contain	VERB
ejpam-6017	118	23	f(x	f(x	PROPN
ejpam-6017	118	24	)	)	PUNCT
ejpam-6017	118	25	.	.	PUNCT
ejpam-6017	119	1	since	since	SCONJ
ejpam-6017	119	2	v	v	NUM
ejpam-6017	119	3	∩(y	∩(y	PROPN
ejpam-6017	119	4	−v	−v	NOUN
ejpam-6017	119	5	)	)	PUNCT
ejpam-6017	119	6	=	=	SYM
ejpam-6017	119	7	∅	∅	NOUN
ejpam-6017	119	8	,	,	PUNCT
ejpam-6017	119	9	f(x	f(x	PROPN
ejpam-6017	119	10	)	)	PUNCT
ejpam-6017	119	11	̸∈	̸∈	PROPN
ejpam-6017	119	12	σ1σ2	σ1σ2	NUM
ejpam-6017	119	13	-	-	PUNCT
ejpam-6017	119	14	cl(y	cl(y	NOUN
ejpam-6017	119	15	−v	−v	NOUN
ejpam-6017	119	16	)	)	PUNCT
ejpam-6017	119	17	and	and	CCONJ
ejpam-6017	119	18	so	so	ADV
ejpam-6017	119	19	x	x	PUNCT
ejpam-6017	119	20	̸∈	̸∈	PROPN
ejpam-6017	119	21	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6017	119	22	-	-	PUNCT
ejpam-6017	119	23	cl(y	cl(y	NOUN
ejpam-6017	119	24	−v	−v	NOUN
ejpam-6017	119	25	)	)	PUNCT
ejpam-6017	119	26	)	)	PUNCT
ejpam-6017	119	27	.	.	PUNCT
ejpam-6017	120	1	by	by	ADP
ejpam-6017	120	2	(	(	PUNCT
ejpam-6017	120	3	5	5	NUM
ejpam-6017	120	4	)	)	PUNCT
ejpam-6017	120	5	,	,	PUNCT
ejpam-6017	120	6	we	we	PRON
ejpam-6017	120	7	have	have	VERB
ejpam-6017	120	8	x	x	PROPN
ejpam-6017	120	9	̸∈	̸∈	PROPN
ejpam-6017	120	10	(	(	PUNCT
ejpam-6017	120	11	τ1	τ1	PROPN
ejpam-6017	120	12	,	,	PUNCT
ejpam-6017	120	13	τ2)θ	τ2)θ	PROPN
ejpam-6017	120	14	-	-	PUNCT
ejpam-6017	120	15	cl(f	cl(f	NOUN
ejpam-6017	120	16	−1(y	−1(y	NOUN
ejpam-6017	120	17	−v	−v	NOUN
ejpam-6017	120	18	)	)	PUNCT
ejpam-6017	120	19	)	)	PUNCT
ejpam-6017	121	1	=	=	SYM
ejpam-6017	121	2	x−(τ1	x−(τ1	PROPN
ejpam-6017	121	3	,	,	PUNCT
ejpam-6017	121	4	τ2)θ	τ2)θ	NOUN
ejpam-6017	121	5	-	-	PUNCT
ejpam-6017	121	6	int(f	int(f	PROPN
ejpam-6017	121	7	−1(v	−1(v	NOUN
ejpam-6017	121	8	)	)	PUNCT
ejpam-6017	121	9	)	)	PUNCT
ejpam-6017	121	10	.	.	PUNCT
ejpam-6017	122	1	thus	thus	ADV
ejpam-6017	122	2	,	,	PUNCT
ejpam-6017	122	3	x	x	SYM
ejpam-6017	122	4	∈	∈	PROPN
ejpam-6017	122	5	(	(	PUNCT
ejpam-6017	122	6	τ1	τ1	NOUN
ejpam-6017	122	7	,	,	PUNCT
ejpam-6017	122	8	τ2)θ	τ2)θ	NOUN
ejpam-6017	122	9	-	-	PUNCT
ejpam-6017	122	10	int(f	int(f	PROPN
ejpam-6017	122	11	−1(v	−1(v	NOUN
ejpam-6017	122	12	)	)	PUNCT
ejpam-6017	122	13	)	)	PUNCT
ejpam-6017	122	14	.	.	PUNCT
ejpam-6017	123	1	then	then	ADV
ejpam-6017	123	2	,	,	PUNCT
ejpam-6017	123	3	there	there	PRON
ejpam-6017	123	4	exists	exist	VERB
ejpam-6017	123	5	a	a	DET
ejpam-6017	123	6	τ1τ2	τ1τ2	NOUN
ejpam-6017	123	7	-	-	ADJ
ejpam-6017	123	8	open	open	ADJ
ejpam-6017	123	9	set	set	ADJ
ejpam-6017	123	10	u	u	NOUN
ejpam-6017	123	11	of	of	ADP
ejpam-6017	123	12	x	x	SYM
ejpam-6017	123	13	such	such	ADJ
ejpam-6017	123	14	that	that	SCONJ
ejpam-6017	123	15	τ1τ2	τ1τ2	NOUN
ejpam-6017	123	16	-	-	NOUN
ejpam-6017	123	17	cl(u	cl(u	ADJ
ejpam-6017	123	18	)	)	PUNCT
ejpam-6017	123	19	⊆	⊆	NUM
ejpam-6017	123	20	f−1(v	f−1(v	NOUN
ejpam-6017	123	21	)	)	PUNCT
ejpam-6017	123	22	;	;	PUNCT
ejpam-6017	123	23	hence	hence	ADV
ejpam-6017	123	24	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	123	25	-	-	PUNCT
ejpam-6017	123	26	cl(u	cl(u	NOUN
ejpam-6017	123	27	)	)	PUNCT
ejpam-6017	123	28	)	)	PUNCT
ejpam-6017	124	1	⊆	⊆	NUM
ejpam-6017	124	2	v.	v.	ADP
ejpam-6017	124	3	this	this	PRON
ejpam-6017	124	4	shows	show	VERB
ejpam-6017	124	5	that	that	SCONJ
ejpam-6017	124	6	f	f	PROPN
ejpam-6017	124	7	is	be	AUX
ejpam-6017	124	8	strongly	strongly	ADV
ejpam-6017	124	9	θ(τ1	θ(τ1	ADJ
ejpam-6017	124	10	,	,	PUNCT
ejpam-6017	124	11	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	124	12	.	.	PUNCT
ejpam-6017	125	1	definition	definition	NOUN
ejpam-6017	125	2	2	2	NUM
ejpam-6017	125	3	.	.	PUNCT
ejpam-6017	126	1	[	[	X
ejpam-6017	126	2	18	18	NUM
ejpam-6017	126	3	]	]	PUNCT
ejpam-6017	126	4	a	a	DET
ejpam-6017	126	5	function	function	NOUN
ejpam-6017	126	6	f	f	NOUN
ejpam-6017	126	7	:	:	PUNCT
ejpam-6017	126	8	(	(	PUNCT
ejpam-6017	126	9	x	x	NOUN
ejpam-6017	126	10	,	,	PUNCT
ejpam-6017	126	11	τ1	τ1	NOUN
ejpam-6017	126	12	,	,	PUNCT
ejpam-6017	126	13	τ2	τ2	NOUN
ejpam-6017	126	14	)	)	PUNCT
ejpam-6017	126	15	→	→	SYM
ejpam-6017	126	16	(	(	PUNCT
ejpam-6017	126	17	y	y	PROPN
ejpam-6017	126	18	,	,	PUNCT
ejpam-6017	126	19	σ1	σ1	PROPN
ejpam-6017	126	20	,	,	PUNCT
ejpam-6017	126	21	σ2	σ2	PROPN
ejpam-6017	126	22	)	)	PUNCT
ejpam-6017	126	23	is	be	AUX
ejpam-6017	126	24	called	call	VERB
ejpam-6017	126	25	(	(	PUNCT
ejpam-6017	126	26	τ1	τ1	NOUN
ejpam-6017	126	27	,	,	PUNCT
ejpam-6017	126	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	126	29	at	at	ADP
ejpam-6017	126	30	a	a	DET
ejpam-6017	126	31	point	point	NOUN
ejpam-6017	126	32	x	x	SYM
ejpam-6017	126	33	∈	∈	NOUN
ejpam-6017	126	34	x	x	PUNCT
ejpam-6017	126	35	if	if	SCONJ
ejpam-6017	126	36	for	for	ADP
ejpam-6017	126	37	each	each	DET
ejpam-6017	126	38	σ1σ2	σ1σ2	VERB
ejpam-6017	126	39	-	-	ADJ
ejpam-6017	126	40	open	open	ADJ
ejpam-6017	126	41	set	set	NOUN
ejpam-6017	126	42	v	v	NOUN
ejpam-6017	126	43	of	of	ADP
ejpam-6017	126	44	y	y	NOUN
ejpam-6017	126	45	containing	contain	VERB
ejpam-6017	126	46	f(x	f(x	PROPN
ejpam-6017	126	47	)	)	PUNCT
ejpam-6017	126	48	,	,	PUNCT
ejpam-6017	126	49	there	there	PRON
ejpam-6017	126	50	exists	exist	VERB
ejpam-6017	126	51	a	a	DET
ejpam-6017	126	52	τ1τ2	τ1τ2	NOUN
ejpam-6017	126	53	-	-	ADJ
ejpam-6017	126	54	open	open	ADJ
ejpam-6017	126	55	set	set	ADJ
ejpam-6017	126	56	u	u	NOUN
ejpam-6017	126	57	of	of	ADP
ejpam-6017	126	58	x	x	PUNCT
ejpam-6017	126	59	containing	contain	VERB
ejpam-6017	126	60	x	x	PUNCT
ejpam-6017	126	61	such	such	ADJ
ejpam-6017	126	62	that	that	DET
ejpam-6017	126	63	f(u	f(u	PROPN
ejpam-6017	126	64	)	)	PUNCT
ejpam-6017	126	65	⊆	⊆	NUM
ejpam-6017	126	66	v	v	NOUN
ejpam-6017	126	67	.	.	PUNCT
ejpam-6017	127	1	a	a	DET
ejpam-6017	127	2	function	function	NOUN
ejpam-6017	127	3	f	f	NOUN
ejpam-6017	127	4	:	:	PUNCT
ejpam-6017	127	5	(	(	PUNCT
ejpam-6017	127	6	x	x	NOUN
ejpam-6017	127	7	,	,	PUNCT
ejpam-6017	127	8	τ1	τ1	NOUN
ejpam-6017	127	9	,	,	PUNCT
ejpam-6017	127	10	τ2	τ2	NOUN
ejpam-6017	127	11	)	)	PUNCT
ejpam-6017	127	12	→	→	SYM
ejpam-6017	127	13	(	(	PUNCT
ejpam-6017	127	14	y	y	PROPN
ejpam-6017	127	15	,	,	PUNCT
ejpam-6017	127	16	σ1	σ1	PROPN
ejpam-6017	127	17	,	,	PUNCT
ejpam-6017	127	18	σ2	σ2	PROPN
ejpam-6017	127	19	)	)	PUNCT
ejpam-6017	127	20	is	be	AUX
ejpam-6017	127	21	called	call	VERB
ejpam-6017	127	22	(	(	PUNCT
ejpam-6017	127	23	τ1	τ1	NOUN
ejpam-6017	127	24	,	,	PUNCT
ejpam-6017	127	25	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	127	26	if	if	SCONJ
ejpam-6017	127	27	f	f	PROPN
ejpam-6017	127	28	has	have	VERB
ejpam-6017	127	29	this	this	DET
ejpam-6017	127	30	property	property	NOUN
ejpam-6017	127	31	at	at	ADP
ejpam-6017	127	32	each	each	DET
ejpam-6017	127	33	point	point	NOUN
ejpam-6017	127	34	of	of	ADP
ejpam-6017	127	35	x.	x.	PROPN
ejpam-6017	127	36	lemma	lemma	PROPN
ejpam-6017	128	1	3	3	X
ejpam-6017	128	2	.	.	PUNCT
ejpam-6017	129	1	[	[	X
ejpam-6017	129	2	18	18	NUM
ejpam-6017	129	3	]	]	PUNCT
ejpam-6017	129	4	for	for	ADP
ejpam-6017	129	5	a	a	DET
ejpam-6017	129	6	function	function	NOUN
ejpam-6017	129	7	(	(	PUNCT
ejpam-6017	129	8	x	x	NOUN
ejpam-6017	129	9	,	,	PUNCT
ejpam-6017	129	10	τ1	τ1	NOUN
ejpam-6017	129	11	,	,	PUNCT
ejpam-6017	129	12	τ2	τ2	NOUN
ejpam-6017	129	13	)	)	PUNCT
ejpam-6017	129	14	→	→	SYM
ejpam-6017	129	15	(	(	PUNCT
ejpam-6017	129	16	y	y	PROPN
ejpam-6017	129	17	,	,	PUNCT
ejpam-6017	129	18	σ1	σ1	PROPN
ejpam-6017	129	19	,	,	PUNCT
ejpam-6017	129	20	σ2	σ2	NOUN
ejpam-6017	129	21	)	)	PUNCT
ejpam-6017	129	22	,	,	PUNCT
ejpam-6017	129	23	the	the	DET
ejpam-6017	129	24	following	follow	VERB
ejpam-6017	129	25	properties	property	NOUN
ejpam-6017	129	26	are	be	AUX
ejpam-6017	129	27	equivalent	equivalent	ADJ
ejpam-6017	129	28	:	:	PUNCT
ejpam-6017	129	29	(	(	PUNCT
ejpam-6017	129	30	1	1	X
ejpam-6017	129	31	)	)	PUNCT
ejpam-6017	129	32	f	f	PROPN
ejpam-6017	129	33	is	be	AUX
ejpam-6017	129	34	(	(	PUNCT
ejpam-6017	129	35	τ1	τ1	NOUN
ejpam-6017	129	36	,	,	PUNCT
ejpam-6017	129	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	129	38	;	;	PUNCT
ejpam-6017	129	39	(	(	PUNCT
ejpam-6017	129	40	2	2	X
ejpam-6017	129	41	)	)	PUNCT
ejpam-6017	129	42	f−1(v	f−1(v	NOUN
ejpam-6017	129	43	)	)	PUNCT
ejpam-6017	129	44	is	be	AUX
ejpam-6017	129	45	τ1τ2	τ1τ2	NOUN
ejpam-6017	129	46	-	-	ADJ
ejpam-6017	129	47	open	open	ADJ
ejpam-6017	129	48	in	in	ADP
ejpam-6017	129	49	x	x	PUNCT
ejpam-6017	129	50	for	for	ADP
ejpam-6017	129	51	every	every	DET
ejpam-6017	129	52	σ1σ2	σ1σ2	NOUN
ejpam-6017	129	53	-	-	ADJ
ejpam-6017	129	54	open	open	ADJ
ejpam-6017	129	55	set	set	NOUN
ejpam-6017	129	56	v	v	NOUN
ejpam-6017	129	57	of	of	ADP
ejpam-6017	129	58	y	y	PROPN
ejpam-6017	129	59	;	;	PUNCT
ejpam-6017	129	60	(	(	PUNCT
ejpam-6017	129	61	3	3	X
ejpam-6017	129	62	)	)	PUNCT
ejpam-6017	129	63	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	129	64	-	-	PUNCT
ejpam-6017	129	65	cl(a	cl(a	NUM
ejpam-6017	129	66	)	)	PUNCT
ejpam-6017	129	67	)	)	PUNCT
ejpam-6017	130	1	⊆	⊆	X
ejpam-6017	130	2	σ1σ2	σ1σ2	NUM
ejpam-6017	130	3	-	-	PUNCT
ejpam-6017	130	4	cl(f(a	cl(f(a	NOUN
ejpam-6017	130	5	)	)	PUNCT
ejpam-6017	130	6	)	)	PUNCT
ejpam-6017	130	7	for	for	ADP
ejpam-6017	130	8	every	every	DET
ejpam-6017	130	9	subset	subset	NOUN
ejpam-6017	130	10	a	a	PRON
ejpam-6017	130	11	of	of	ADP
ejpam-6017	130	12	x	x	PRON
ejpam-6017	130	13	;	;	PUNCT
ejpam-6017	130	14	p.	p.	NOUN
ejpam-6017	130	15	pue	pue	NOUN
ejpam-6017	130	16	-	-	PUNCT
ejpam-6017	130	17	on	on	ADP
ejpam-6017	130	18	,	,	PUNCT
ejpam-6017	130	19	s.	s.	PROPN
ejpam-6017	130	20	sompong	sompong	PROPN
ejpam-6017	130	21	,	,	PUNCT
ejpam-6017	130	22	c.	c.	PROPN
ejpam-6017	130	23	boonpok	boonpok	PROPN
ejpam-6017	130	24	/	/	SYM
ejpam-6017	130	25	eur	eur	PROPN
ejpam-6017	130	26	.	.	PUNCT
ejpam-6017	131	1	j.	j.	PROPN
ejpam-6017	131	2	pure	pure	PROPN
ejpam-6017	131	3	appl	appl	PROPN
ejpam-6017	131	4	.	.	PROPN
ejpam-6017	131	5	math	math	PROPN
ejpam-6017	131	6	,	,	PUNCT
ejpam-6017	131	7	18	18	NUM
ejpam-6017	131	8	(	(	PUNCT
ejpam-6017	131	9	2	2	NUM
ejpam-6017	131	10	)	)	PUNCT
ejpam-6017	131	11	(	(	PUNCT
ejpam-6017	131	12	2025	2025	NUM
ejpam-6017	131	13	)	)	PUNCT
ejpam-6017	131	14	,	,	PUNCT
ejpam-6017	131	15	6017	6017	NUM
ejpam-6017	131	16	5	5	NUM
ejpam-6017	131	17	of	of	ADP
ejpam-6017	131	18	11	11	NUM
ejpam-6017	131	19	(	(	PUNCT
ejpam-6017	131	20	4	4	NUM
ejpam-6017	131	21	)	)	PUNCT
ejpam-6017	131	22	τ1τ2	τ1τ2	NOUN
ejpam-6017	131	23	-	-	NOUN
ejpam-6017	131	24	cl(f	cl(f	NOUN
ejpam-6017	131	25	−1(b	−1(b	NOUN
ejpam-6017	131	26	)	)	PUNCT
ejpam-6017	131	27	)	)	PUNCT
ejpam-6017	132	1	⊆	⊆	NUM
ejpam-6017	132	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6017	132	3	-	-	PUNCT
ejpam-6017	132	4	cl(b	cl(b	NOUN
ejpam-6017	132	5	)	)	PUNCT
ejpam-6017	132	6	)	)	PUNCT
ejpam-6017	132	7	for	for	ADP
ejpam-6017	132	8	every	every	DET
ejpam-6017	132	9	subset	subset	NOUN
ejpam-6017	132	10	b	b	PROPN
ejpam-6017	132	11	of	of	ADP
ejpam-6017	132	12	y	y	PROPN
ejpam-6017	132	13	;	;	PUNCT
ejpam-6017	132	14	(	(	PUNCT
ejpam-6017	132	15	5	5	X
ejpam-6017	132	16	)	)	PUNCT
ejpam-6017	132	17	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6017	132	18	-	-	PUNCT
ejpam-6017	132	19	int(b	int(b	NOUN
ejpam-6017	132	20	)	)	PUNCT
ejpam-6017	132	21	)	)	PUNCT
ejpam-6017	133	1	⊆	⊆	X
ejpam-6017	133	2	τ1τ2	τ1τ2	NOUN
ejpam-6017	133	3	-	-	NUM
ejpam-6017	133	4	int(f	int(f	NOUN
ejpam-6017	133	5	−1(b	−1(b	NOUN
ejpam-6017	133	6	)	)	PUNCT
ejpam-6017	133	7	)	)	PUNCT
ejpam-6017	133	8	for	for	ADP
ejpam-6017	133	9	every	every	DET
ejpam-6017	133	10	subset	subset	NOUN
ejpam-6017	133	11	b	b	PROPN
ejpam-6017	133	12	of	of	ADP
ejpam-6017	133	13	y	y	PROPN
ejpam-6017	133	14	;	;	PUNCT
ejpam-6017	133	15	(	(	PUNCT
ejpam-6017	133	16	6	6	X
ejpam-6017	133	17	)	)	PUNCT
ejpam-6017	133	18	f−1(k	f−1(k	PROPN
ejpam-6017	133	19	)	)	PUNCT
ejpam-6017	133	20	is	be	AUX
ejpam-6017	133	21	τ1τ2	τ1τ2	NOUN
ejpam-6017	133	22	-	-	ADJ
ejpam-6017	133	23	closed	closed	ADJ
ejpam-6017	133	24	in	in	ADP
ejpam-6017	133	25	x	x	PUNCT
ejpam-6017	133	26	for	for	ADP
ejpam-6017	133	27	every	every	DET
ejpam-6017	133	28	σ1σ2	σ1σ2	NUM
ejpam-6017	133	29	-	-	PUNCT
ejpam-6017	133	30	closed	closed	ADJ
ejpam-6017	133	31	set	set	NOUN
ejpam-6017	133	32	k	k	PROPN
ejpam-6017	133	33	of	of	ADP
ejpam-6017	133	34	y	y	PROPN
ejpam-6017	133	35	.	.	PUNCT
ejpam-6017	134	1	definition	definition	NOUN
ejpam-6017	134	2	3	3	NUM
ejpam-6017	134	3	.	.	PUNCT
ejpam-6017	135	1	[	[	X
ejpam-6017	135	2	20	20	NUM
ejpam-6017	135	3	]	]	PUNCT
ejpam-6017	135	4	a	a	DET
ejpam-6017	135	5	function	function	NOUN
ejpam-6017	135	6	f	f	NOUN
ejpam-6017	135	7	:	:	PUNCT
ejpam-6017	135	8	(	(	PUNCT
ejpam-6017	135	9	x	x	NOUN
ejpam-6017	135	10	,	,	PUNCT
ejpam-6017	135	11	τ1	τ1	NOUN
ejpam-6017	135	12	,	,	PUNCT
ejpam-6017	135	13	τ2	τ2	NOUN
ejpam-6017	135	14	)	)	PUNCT
ejpam-6017	135	15	→	→	SYM
ejpam-6017	135	16	(	(	PUNCT
ejpam-6017	135	17	y	y	PROPN
ejpam-6017	135	18	,	,	PUNCT
ejpam-6017	135	19	σ1	σ1	PROPN
ejpam-6017	135	20	,	,	PUNCT
ejpam-6017	135	21	σ2	σ2	PROPN
ejpam-6017	135	22	)	)	PUNCT
ejpam-6017	135	23	is	be	AUX
ejpam-6017	135	24	said	say	VERB
ejpam-6017	135	25	to	to	PART
ejpam-6017	135	26	be	be	AUX
ejpam-6017	135	27	weakly	weakly	ADJ
ejpam-6017	135	28	(	(	PUNCT
ejpam-6017	135	29	τ1	τ1	NOUN
ejpam-6017	135	30	,	,	PUNCT
ejpam-6017	135	31	τ2)continuous	τ2)continuous	ADJ
ejpam-6017	135	32	at	at	ADP
ejpam-6017	135	33	a	a	DET
ejpam-6017	135	34	point	point	NOUN
ejpam-6017	135	35	x	x	SYM
ejpam-6017	135	36	∈	∈	NOUN
ejpam-6017	135	37	x	x	PUNCT
ejpam-6017	135	38	if	if	SCONJ
ejpam-6017	135	39	for	for	ADP
ejpam-6017	135	40	each	each	DET
ejpam-6017	135	41	τ1τ2	τ1τ2	ADJ
ejpam-6017	135	42	-	-	ADJ
ejpam-6017	135	43	open	open	ADJ
ejpam-6017	135	44	set	set	VERB
ejpam-6017	135	45	v	v	NOUN
ejpam-6017	135	46	of	of	ADP
ejpam-6017	135	47	y	y	NOUN
ejpam-6017	135	48	containing	contain	VERB
ejpam-6017	135	49	f(x	f(x	PROPN
ejpam-6017	135	50	)	)	PUNCT
ejpam-6017	135	51	,	,	PUNCT
ejpam-6017	135	52	there	there	PRON
ejpam-6017	135	53	exists	exist	VERB
ejpam-6017	135	54	a	a	DET
ejpam-6017	135	55	τ1τ2	τ1τ2	NOUN
ejpam-6017	135	56	-	-	ADJ
ejpam-6017	135	57	open	open	ADJ
ejpam-6017	135	58	set	set	ADJ
ejpam-6017	135	59	u	u	NOUN
ejpam-6017	135	60	of	of	ADP
ejpam-6017	135	61	x	x	PUNCT
ejpam-6017	135	62	containing	contain	VERB
ejpam-6017	135	63	x	x	PUNCT
ejpam-6017	135	64	such	such	ADJ
ejpam-6017	135	65	that	that	DET
ejpam-6017	135	66	f(u	f(u	PROPN
ejpam-6017	135	67	)	)	PUNCT
ejpam-6017	135	68	⊆	⊆	NUM
ejpam-6017	135	69	σ1σ2	σ1σ2	NOUN
ejpam-6017	135	70	-	-	NUM
ejpam-6017	135	71	cl(v	cl(v	NOUN
ejpam-6017	135	72	)	)	PUNCT
ejpam-6017	135	73	.	.	PUNCT
ejpam-6017	136	1	a	a	DET
ejpam-6017	136	2	function	function	NOUN
ejpam-6017	136	3	f	f	NOUN
ejpam-6017	136	4	:	:	PUNCT
ejpam-6017	136	5	(	(	PUNCT
ejpam-6017	136	6	x	x	NOUN
ejpam-6017	136	7	,	,	PUNCT
ejpam-6017	136	8	τ1	τ1	NOUN
ejpam-6017	136	9	,	,	PUNCT
ejpam-6017	136	10	τ2	τ2	NOUN
ejpam-6017	136	11	)	)	PUNCT
ejpam-6017	136	12	→	→	SYM
ejpam-6017	136	13	(	(	PUNCT
ejpam-6017	136	14	y	y	PROPN
ejpam-6017	136	15	,	,	PUNCT
ejpam-6017	136	16	σ1	σ1	PROPN
ejpam-6017	136	17	,	,	PUNCT
ejpam-6017	136	18	σ2	σ2	PROPN
ejpam-6017	136	19	)	)	PUNCT
ejpam-6017	136	20	is	be	AUX
ejpam-6017	136	21	said	say	VERB
ejpam-6017	136	22	to	to	PART
ejpam-6017	136	23	be	be	AUX
ejpam-6017	136	24	weakly	weakly	ADJ
ejpam-6017	136	25	(	(	PUNCT
ejpam-6017	136	26	τ1	τ1	NOUN
ejpam-6017	136	27	,	,	PUNCT
ejpam-6017	136	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	136	29	if	if	SCONJ
ejpam-6017	136	30	f	f	PROPN
ejpam-6017	136	31	has	have	VERB
ejpam-6017	136	32	this	this	DET
ejpam-6017	136	33	property	property	NOUN
ejpam-6017	136	34	at	at	ADP
ejpam-6017	136	35	each	each	DET
ejpam-6017	136	36	point	point	NOUN
ejpam-6017	136	37	of	of	ADP
ejpam-6017	136	38	x.	x.	PROPN
ejpam-6017	136	39	lemma	lemma	PROPN
ejpam-6017	136	40	4	4	NUM
ejpam-6017	136	41	.	.	PUNCT
ejpam-6017	137	1	[	[	X
ejpam-6017	137	2	20	20	NUM
ejpam-6017	137	3	]	]	PUNCT
ejpam-6017	137	4	for	for	ADP
ejpam-6017	137	5	a	a	DET
ejpam-6017	137	6	function	function	NOUN
ejpam-6017	137	7	(	(	PUNCT
ejpam-6017	137	8	x	x	NOUN
ejpam-6017	137	9	,	,	PUNCT
ejpam-6017	137	10	τ1	τ1	NOUN
ejpam-6017	137	11	,	,	PUNCT
ejpam-6017	137	12	τ2	τ2	NOUN
ejpam-6017	137	13	)	)	PUNCT
ejpam-6017	137	14	→	→	SYM
ejpam-6017	137	15	(	(	PUNCT
ejpam-6017	137	16	y	y	PROPN
ejpam-6017	137	17	,	,	PUNCT
ejpam-6017	137	18	σ1	σ1	PROPN
ejpam-6017	137	19	,	,	PUNCT
ejpam-6017	137	20	σ2	σ2	NOUN
ejpam-6017	137	21	)	)	PUNCT
ejpam-6017	137	22	,	,	PUNCT
ejpam-6017	137	23	the	the	DET
ejpam-6017	137	24	following	follow	VERB
ejpam-6017	137	25	properties	property	NOUN
ejpam-6017	137	26	are	be	AUX
ejpam-6017	137	27	equivalent	equivalent	ADJ
ejpam-6017	137	28	:	:	PUNCT
ejpam-6017	137	29	(	(	PUNCT
ejpam-6017	137	30	1	1	X
ejpam-6017	137	31	)	)	PUNCT
ejpam-6017	137	32	f	f	PROPN
ejpam-6017	137	33	is	be	AUX
ejpam-6017	137	34	weakly	weakly	ADJ
ejpam-6017	137	35	(	(	PUNCT
ejpam-6017	137	36	τ1	τ1	NOUN
ejpam-6017	137	37	,	,	PUNCT
ejpam-6017	137	38	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	137	39	;	;	PUNCT
ejpam-6017	137	40	(	(	PUNCT
ejpam-6017	137	41	2	2	X
ejpam-6017	137	42	)	)	PUNCT
ejpam-6017	137	43	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	137	44	-	-	PUNCT
ejpam-6017	137	45	cl(a	cl(a	NUM
ejpam-6017	137	46	)	)	PUNCT
ejpam-6017	137	47	)	)	PUNCT
ejpam-6017	138	1	⊆	⊆	NUM
ejpam-6017	138	2	(	(	PUNCT
ejpam-6017	138	3	σ1	σ1	PROPN
ejpam-6017	138	4	,	,	PUNCT
ejpam-6017	138	5	σ2)θ	σ2)θ	NOUN
ejpam-6017	138	6	-	-	PUNCT
ejpam-6017	138	7	cl(f(a	cl(f(a	NOUN
ejpam-6017	138	8	)	)	PUNCT
ejpam-6017	138	9	)	)	PUNCT
ejpam-6017	138	10	for	for	ADP
ejpam-6017	138	11	every	every	DET
ejpam-6017	138	12	subset	subset	NOUN
ejpam-6017	138	13	a	a	PRON
ejpam-6017	138	14	of	of	ADP
ejpam-6017	138	15	x	x	PRON
ejpam-6017	138	16	;	;	PUNCT
ejpam-6017	138	17	(	(	PUNCT
ejpam-6017	138	18	3	3	X
ejpam-6017	138	19	)	)	PUNCT
ejpam-6017	138	20	τ1τ2	τ1τ2	NOUN
ejpam-6017	138	21	-	-	NOUN
ejpam-6017	138	22	cl(f	cl(f	NOUN
ejpam-6017	138	23	−1(b	−1(b	NOUN
ejpam-6017	138	24	)	)	PUNCT
ejpam-6017	138	25	)	)	PUNCT
ejpam-6017	139	1	⊆	⊆	NUM
ejpam-6017	139	2	f−1((σ1	f−1((σ1	NOUN
ejpam-6017	139	3	,	,	PUNCT
ejpam-6017	139	4	σ2)θ	σ2)θ	NOUN
ejpam-6017	139	5	-	-	PUNCT
ejpam-6017	139	6	cl(b	cl(b	NOUN
ejpam-6017	139	7	)	)	PUNCT
ejpam-6017	139	8	)	)	PUNCT
ejpam-6017	139	9	for	for	ADP
ejpam-6017	139	10	every	every	DET
ejpam-6017	139	11	subset	subset	NOUN
ejpam-6017	139	12	b	b	PROPN
ejpam-6017	139	13	of	of	ADP
ejpam-6017	139	14	y	y	PROPN
ejpam-6017	139	15	.	.	PUNCT
ejpam-6017	140	1	definition	definition	NOUN
ejpam-6017	140	2	4	4	NUM
ejpam-6017	140	3	.	.	PUNCT
ejpam-6017	141	1	[	[	X
ejpam-6017	141	2	31	31	NUM
ejpam-6017	141	3	]	]	PUNCT
ejpam-6017	141	4	a	a	DET
ejpam-6017	141	5	function	function	NOUN
ejpam-6017	141	6	f	f	NOUN
ejpam-6017	141	7	:	:	PUNCT
ejpam-6017	141	8	(	(	PUNCT
ejpam-6017	141	9	x	x	NOUN
ejpam-6017	141	10	,	,	PUNCT
ejpam-6017	141	11	τ1	τ1	NOUN
ejpam-6017	141	12	,	,	PUNCT
ejpam-6017	141	13	τ2	τ2	NOUN
ejpam-6017	141	14	)	)	PUNCT
ejpam-6017	141	15	→	→	SYM
ejpam-6017	141	16	(	(	PUNCT
ejpam-6017	141	17	y	y	PROPN
ejpam-6017	141	18	,	,	PUNCT
ejpam-6017	141	19	σ1	σ1	PROPN
ejpam-6017	141	20	,	,	PUNCT
ejpam-6017	141	21	σ2	σ2	PROPN
ejpam-6017	141	22	)	)	PUNCT
ejpam-6017	141	23	is	be	AUX
ejpam-6017	141	24	called	call	VERB
ejpam-6017	141	25	faintly	faintly	ADV
ejpam-6017	141	26	(	(	PUNCT
ejpam-6017	141	27	τ1	τ1	NOUN
ejpam-6017	141	28	,	,	PUNCT
ejpam-6017	141	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	141	30	at	at	ADP
ejpam-6017	141	31	a	a	DET
ejpam-6017	141	32	point	point	NOUN
ejpam-6017	141	33	x	x	SYM
ejpam-6017	141	34	∈	∈	NOUN
ejpam-6017	141	35	x	x	INTJ
ejpam-6017	141	36	if	if	SCONJ
ejpam-6017	141	37	for	for	SCONJ
ejpam-6017	141	38	each	each	DET
ejpam-6017	141	39	(	(	PUNCT
ejpam-6017	141	40	σ1	σ1	PROPN
ejpam-6017	141	41	,	,	PUNCT
ejpam-6017	141	42	σ2)θ	σ2)θ	NOUN
ejpam-6017	141	43	-	-	PUNCT
ejpam-6017	141	44	open	open	ADJ
ejpam-6017	141	45	set	set	NOUN
ejpam-6017	141	46	v	v	NOUN
ejpam-6017	141	47	of	of	ADP
ejpam-6017	141	48	y	y	NOUN
ejpam-6017	141	49	containing	contain	VERB
ejpam-6017	141	50	f(x	f(x	PROPN
ejpam-6017	141	51	)	)	PUNCT
ejpam-6017	141	52	,	,	PUNCT
ejpam-6017	141	53	there	there	PRON
ejpam-6017	141	54	exists	exist	VERB
ejpam-6017	141	55	a	a	DET
ejpam-6017	141	56	τ1τ2open	τ1τ2open	ADJ
ejpam-6017	141	57	set	set	NOUN
ejpam-6017	141	58	u	u	NOUN
ejpam-6017	141	59	of	of	ADP
ejpam-6017	141	60	x	x	PUNCT
ejpam-6017	141	61	containing	contain	VERB
ejpam-6017	141	62	x	x	PUNCT
ejpam-6017	141	63	such	such	ADJ
ejpam-6017	141	64	that	that	DET
ejpam-6017	141	65	f(u	f(u	PROPN
ejpam-6017	141	66	)	)	PUNCT
ejpam-6017	141	67	⊆	⊆	NUM
ejpam-6017	141	68	v	v	NOUN
ejpam-6017	141	69	.	.	PUNCT
ejpam-6017	142	1	a	a	DET
ejpam-6017	142	2	function	function	NOUN
ejpam-6017	142	3	f	f	NOUN
ejpam-6017	142	4	:	:	PUNCT
ejpam-6017	142	5	(	(	PUNCT
ejpam-6017	142	6	x	x	NOUN
ejpam-6017	142	7	,	,	PUNCT
ejpam-6017	142	8	τ1	τ1	NOUN
ejpam-6017	142	9	,	,	PUNCT
ejpam-6017	142	10	τ2	τ2	NOUN
ejpam-6017	142	11	)	)	PUNCT
ejpam-6017	142	12	→	→	SYM
ejpam-6017	142	13	(	(	PUNCT
ejpam-6017	142	14	y	y	PROPN
ejpam-6017	142	15	,	,	PUNCT
ejpam-6017	142	16	σ1	σ1	PROPN
ejpam-6017	142	17	,	,	PUNCT
ejpam-6017	142	18	σ2	σ2	PROPN
ejpam-6017	142	19	)	)	PUNCT
ejpam-6017	142	20	is	be	AUX
ejpam-6017	142	21	called	call	VERB
ejpam-6017	142	22	faintly	faintly	ADV
ejpam-6017	142	23	(	(	PUNCT
ejpam-6017	142	24	τ1	τ1	NOUN
ejpam-6017	142	25	,	,	PUNCT
ejpam-6017	142	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	142	27	if	if	SCONJ
ejpam-6017	142	28	f	f	PROPN
ejpam-6017	142	29	has	have	VERB
ejpam-6017	142	30	this	this	DET
ejpam-6017	142	31	property	property	NOUN
ejpam-6017	142	32	at	at	ADP
ejpam-6017	142	33	every	every	DET
ejpam-6017	142	34	point	point	NOUN
ejpam-6017	142	35	of	of	ADP
ejpam-6017	142	36	x.	x.	NOUN
ejpam-6017	142	37	lemma	lemma	PROPN
ejpam-6017	142	38	5	5	NUM
ejpam-6017	142	39	.	.	PUNCT
ejpam-6017	143	1	[	[	X
ejpam-6017	143	2	31	31	NUM
ejpam-6017	143	3	]	]	PUNCT
ejpam-6017	143	4	for	for	ADP
ejpam-6017	143	5	a	a	DET
ejpam-6017	143	6	function	function	NOUN
ejpam-6017	143	7	f	f	NOUN
ejpam-6017	143	8	:	:	PUNCT
ejpam-6017	143	9	(	(	PUNCT
ejpam-6017	143	10	x	x	NOUN
ejpam-6017	143	11	,	,	PUNCT
ejpam-6017	143	12	τ1	τ1	NOUN
ejpam-6017	143	13	,	,	PUNCT
ejpam-6017	143	14	τ2	τ2	NOUN
ejpam-6017	143	15	)	)	PUNCT
ejpam-6017	143	16	→	→	SYM
ejpam-6017	143	17	(	(	PUNCT
ejpam-6017	143	18	y	y	PROPN
ejpam-6017	143	19	,	,	PUNCT
ejpam-6017	143	20	σ1	σ1	PROPN
ejpam-6017	143	21	,	,	PUNCT
ejpam-6017	143	22	σ2	σ2	NOUN
ejpam-6017	143	23	)	)	PUNCT
ejpam-6017	143	24	,	,	PUNCT
ejpam-6017	143	25	the	the	DET
ejpam-6017	143	26	following	follow	VERB
ejpam-6017	143	27	properties	property	NOUN
ejpam-6017	143	28	are	be	AUX
ejpam-6017	143	29	equivalent	equivalent	ADJ
ejpam-6017	143	30	:	:	PUNCT
ejpam-6017	143	31	(	(	PUNCT
ejpam-6017	143	32	1	1	X
ejpam-6017	143	33	)	)	PUNCT
ejpam-6017	143	34	f	f	PROPN
ejpam-6017	143	35	is	be	AUX
ejpam-6017	143	36	faintly	faintly	ADV
ejpam-6017	143	37	(	(	PUNCT
ejpam-6017	143	38	τ1	τ1	NOUN
ejpam-6017	143	39	,	,	PUNCT
ejpam-6017	143	40	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	143	41	;	;	PUNCT
ejpam-6017	143	42	(	(	PUNCT
ejpam-6017	143	43	2	2	X
ejpam-6017	143	44	)	)	PUNCT
ejpam-6017	143	45	f−1(v	f−1(v	NOUN
ejpam-6017	143	46	)	)	PUNCT
ejpam-6017	143	47	is	be	AUX
ejpam-6017	143	48	τ1τ2	τ1τ2	NOUN
ejpam-6017	143	49	-	-	ADJ
ejpam-6017	143	50	open	open	ADJ
ejpam-6017	143	51	in	in	ADP
ejpam-6017	143	52	x	x	PUNCT
ejpam-6017	143	53	for	for	ADP
ejpam-6017	143	54	each	each	DET
ejpam-6017	143	55	(	(	PUNCT
ejpam-6017	143	56	σ1	σ1	PROPN
ejpam-6017	143	57	,	,	PUNCT
ejpam-6017	143	58	σ2)θ	σ2)θ	NOUN
ejpam-6017	143	59	-	-	PUNCT
ejpam-6017	143	60	open	open	ADJ
ejpam-6017	143	61	set	set	NOUN
ejpam-6017	143	62	v	v	NOUN
ejpam-6017	143	63	of	of	ADP
ejpam-6017	143	64	y	y	PROPN
ejpam-6017	143	65	;	;	PUNCT
ejpam-6017	143	66	(	(	PUNCT
ejpam-6017	143	67	3	3	X
ejpam-6017	143	68	)	)	PUNCT
ejpam-6017	143	69	f−1(k	f−1(k	PROPN
ejpam-6017	143	70	)	)	PUNCT
ejpam-6017	143	71	is	be	AUX
ejpam-6017	143	72	τ1τ2	τ1τ2	NOUN
ejpam-6017	143	73	-	-	ADJ
ejpam-6017	143	74	closed	closed	ADJ
ejpam-6017	143	75	in	in	ADP
ejpam-6017	143	76	x	x	PUNCT
ejpam-6017	143	77	for	for	ADP
ejpam-6017	143	78	each	each	DET
ejpam-6017	143	79	(	(	PUNCT
ejpam-6017	143	80	σ1	σ1	PROPN
ejpam-6017	143	81	,	,	PUNCT
ejpam-6017	143	82	σ2)θ	σ2)θ	NOUN
ejpam-6017	143	83	-	-	PUNCT
ejpam-6017	143	84	closed	close	VERB
ejpam-6017	143	85	set	set	NOUN
ejpam-6017	143	86	k	k	PROPN
ejpam-6017	143	87	of	of	ADP
ejpam-6017	143	88	y	y	PROPN
ejpam-6017	143	89	.	.	PUNCT
ejpam-6017	144	1	recall	recall	VERB
ejpam-6017	144	2	that	that	SCONJ
ejpam-6017	144	3	a	a	DET
ejpam-6017	144	4	bitopological	bitopological	ADJ
ejpam-6017	144	5	space	space	NOUN
ejpam-6017	144	6	(	(	PUNCT
ejpam-6017	144	7	x	x	NOUN
ejpam-6017	144	8	,	,	PUNCT
ejpam-6017	144	9	τ1	τ1	NOUN
ejpam-6017	144	10	,	,	PUNCT
ejpam-6017	144	11	τ2	τ2	NOUN
ejpam-6017	144	12	)	)	PUNCT
ejpam-6017	144	13	is	be	AUX
ejpam-6017	144	14	said	say	VERB
ejpam-6017	144	15	to	to	PART
ejpam-6017	144	16	be	be	AUX
ejpam-6017	144	17	(	(	PUNCT
ejpam-6017	144	18	τ1	τ1	NOUN
ejpam-6017	144	19	,	,	PUNCT
ejpam-6017	145	1	τ2)-regular	τ2)-regular	ADJ
ejpam-6017	145	2	[	[	X
ejpam-6017	145	3	32	32	NUM
ejpam-6017	145	4	]	]	PUNCT
ejpam-6017	145	5	if	if	SCONJ
ejpam-6017	145	6	for	for	ADP
ejpam-6017	145	7	each	each	DET
ejpam-6017	145	8	τ1τ2	τ1τ2	ADJ
ejpam-6017	145	9	-	-	ADJ
ejpam-6017	145	10	closed	closed	ADJ
ejpam-6017	145	11	set	set	VERB
ejpam-6017	145	12	f	f	NOUN
ejpam-6017	145	13	and	and	CCONJ
ejpam-6017	145	14	each	each	DET
ejpam-6017	145	15	x	x	PROPN
ejpam-6017	145	16	̸∈	̸∈	PROPN
ejpam-6017	145	17	f	f	PROPN
ejpam-6017	145	18	,	,	PUNCT
ejpam-6017	145	19	there	there	PRON
ejpam-6017	145	20	exist	exist	VERB
ejpam-6017	145	21	disjoint	disjoint	ADJ
ejpam-6017	145	22	τ1τ2	τ1τ2	ADJ
ejpam-6017	145	23	-	-	ADJ
ejpam-6017	145	24	open	open	ADJ
ejpam-6017	145	25	sets	set	NOUN
ejpam-6017	145	26	u	u	NOUN
ejpam-6017	145	27	and	and	CCONJ
ejpam-6017	145	28	v	v	ADP
ejpam-6017	145	29	such	such	ADJ
ejpam-6017	145	30	that	that	SCONJ
ejpam-6017	145	31	x	x	SYM
ejpam-6017	145	32	∈	∈	PROPN
ejpam-6017	145	33	u	u	NOUN
ejpam-6017	145	34	and	and	CCONJ
ejpam-6017	145	35	f	f	PROPN
ejpam-6017	145	36	⊆	⊆	NUM
ejpam-6017	145	37	v	v	NOUN
ejpam-6017	145	38	.	.	PUNCT
ejpam-6017	146	1	lemma	lemma	PROPN
ejpam-6017	146	2	6	6	NUM
ejpam-6017	146	3	.	.	PUNCT
ejpam-6017	147	1	[	[	X
ejpam-6017	147	2	33	33	NUM
ejpam-6017	147	3	]	]	PUNCT
ejpam-6017	147	4	a	a	DET
ejpam-6017	147	5	bitopological	bitopological	ADJ
ejpam-6017	147	6	space	space	NOUN
ejpam-6017	147	7	(	(	PUNCT
ejpam-6017	147	8	x	x	NOUN
ejpam-6017	147	9	,	,	PUNCT
ejpam-6017	147	10	τ1	τ1	NOUN
ejpam-6017	147	11	,	,	PUNCT
ejpam-6017	147	12	τ2	τ2	NOUN
ejpam-6017	147	13	)	)	PUNCT
ejpam-6017	147	14	is	be	AUX
ejpam-6017	147	15	(	(	PUNCT
ejpam-6017	147	16	τ1	τ1	NOUN
ejpam-6017	147	17	,	,	PUNCT
ejpam-6017	147	18	τ2)-regular	τ2)-regular	ADJ
ejpam-6017	147	19	if	if	SCONJ
ejpam-6017	147	20	and	and	CCONJ
ejpam-6017	147	21	only	only	ADV
ejpam-6017	147	22	if	if	SCONJ
ejpam-6017	147	23	for	for	ADP
ejpam-6017	147	24	each	each	DET
ejpam-6017	147	25	x	x	SYM
ejpam-6017	147	26	∈	∈	PROPN
ejpam-6017	147	27	x	x	X
ejpam-6017	147	28	and	and	CCONJ
ejpam-6017	147	29	each	each	DET
ejpam-6017	147	30	τ1τ2	τ1τ2	ADJ
ejpam-6017	147	31	-	-	ADJ
ejpam-6017	147	32	open	open	ADJ
ejpam-6017	147	33	set	set	NOUN
ejpam-6017	147	34	u	u	NOUN
ejpam-6017	147	35	containing	contain	VERB
ejpam-6017	147	36	x	x	PRON
ejpam-6017	147	37	,	,	PUNCT
ejpam-6017	147	38	there	there	PRON
ejpam-6017	147	39	exists	exist	VERB
ejpam-6017	147	40	a	a	DET
ejpam-6017	147	41	τ1τ2	τ1τ2	NOUN
ejpam-6017	147	42	-	-	ADJ
ejpam-6017	147	43	open	open	ADJ
ejpam-6017	147	44	set	set	VERB
ejpam-6017	147	45	v	v	ADP
ejpam-6017	147	46	such	such	ADJ
ejpam-6017	147	47	that	that	SCONJ
ejpam-6017	147	48	x	x	SYM
ejpam-6017	147	49	∈	∈	NOUN
ejpam-6017	147	50	v	v	ADP
ejpam-6017	147	51	⊆	⊆	NUM
ejpam-6017	147	52	τ1τ2	τ1τ2	NOUN
ejpam-6017	147	53	-	-	NOUN
ejpam-6017	147	54	cl(v	cl(v	X
ejpam-6017	147	55	)	)	PUNCT
ejpam-6017	147	56	⊆	⊆	NUM
ejpam-6017	147	57	u	u	NOUN
ejpam-6017	147	58	.	.	PUNCT
ejpam-6017	148	1	lemma	lemma	PROPN
ejpam-6017	148	2	7	7	NUM
ejpam-6017	148	3	.	.	PUNCT
ejpam-6017	149	1	[	[	X
ejpam-6017	149	2	33	33	NUM
ejpam-6017	149	3	]	]	PUNCT
ejpam-6017	149	4	let	let	VERB
ejpam-6017	149	5	(	(	PUNCT
ejpam-6017	149	6	x	x	NOUN
ejpam-6017	149	7	,	,	PUNCT
ejpam-6017	149	8	τ1	τ1	NOUN
ejpam-6017	149	9	,	,	PUNCT
ejpam-6017	149	10	τ2	τ2	PROPN
ejpam-6017	149	11	)	)	PUNCT
ejpam-6017	149	12	be	be	VERB
ejpam-6017	149	13	a	a	DET
ejpam-6017	149	14	(	(	PUNCT
ejpam-6017	149	15	τ1	τ1	NOUN
ejpam-6017	149	16	,	,	PUNCT
ejpam-6017	149	17	τ2)-regular	τ2)-regular	ADJ
ejpam-6017	149	18	space	space	NOUN
ejpam-6017	149	19	.	.	PUNCT
ejpam-6017	150	1	then	then	ADV
ejpam-6017	150	2	,	,	PUNCT
ejpam-6017	150	3	the	the	DET
ejpam-6017	150	4	following	follow	VERB
ejpam-6017	150	5	properties	property	NOUN
ejpam-6017	150	6	hold	hold	VERB
ejpam-6017	150	7	:	:	PUNCT
ejpam-6017	150	8	(	(	PUNCT
ejpam-6017	150	9	1	1	X
ejpam-6017	150	10	)	)	PUNCT
ejpam-6017	150	11	τ1τ2	τ1τ2	NOUN
ejpam-6017	150	12	-	-	NUM
ejpam-6017	150	13	cl(a	cl(a	NUM
ejpam-6017	150	14	)	)	PUNCT
ejpam-6017	150	15	=	=	PUNCT
ejpam-6017	150	16	(	(	PUNCT
ejpam-6017	150	17	τ1	τ1	NOUN
ejpam-6017	150	18	,	,	PUNCT
ejpam-6017	150	19	τ2)θ	τ2)θ	NOUN
ejpam-6017	150	20	-	-	PUNCT
ejpam-6017	150	21	cl(a	cl(a	NUM
ejpam-6017	150	22	)	)	PUNCT
ejpam-6017	150	23	for	for	ADP
ejpam-6017	150	24	every	every	DET
ejpam-6017	150	25	subset	subset	NOUN
ejpam-6017	150	26	a	a	PRON
ejpam-6017	150	27	of	of	ADP
ejpam-6017	150	28	x.	x.	NOUN
ejpam-6017	150	29	(	(	PUNCT
ejpam-6017	150	30	2	2	NUM
ejpam-6017	150	31	)	)	PUNCT
ejpam-6017	150	32	every	every	DET
ejpam-6017	150	33	τ1τ2	τ1τ2	NOUN
ejpam-6017	150	34	-	-	ADJ
ejpam-6017	150	35	open	open	ADJ
ejpam-6017	150	36	set	set	NOUN
ejpam-6017	150	37	is	be	AUX
ejpam-6017	150	38	(	(	PUNCT
ejpam-6017	150	39	τ1	τ1	NOUN
ejpam-6017	150	40	,	,	PUNCT
ejpam-6017	150	41	τ2)θ	τ2)θ	NOUN
ejpam-6017	150	42	-	-	PUNCT
ejpam-6017	150	43	open	open	ADJ
ejpam-6017	150	44	.	.	PUNCT
ejpam-6017	151	1	p.	p.	NOUN
ejpam-6017	151	2	pue	pue	NOUN
ejpam-6017	151	3	-	-	PUNCT
ejpam-6017	151	4	on	on	ADP
ejpam-6017	151	5	,	,	PUNCT
ejpam-6017	151	6	s.	s.	PROPN
ejpam-6017	151	7	sompong	sompong	PROPN
ejpam-6017	151	8	,	,	PUNCT
ejpam-6017	151	9	c.	c.	PROPN
ejpam-6017	151	10	boonpok	boonpok	PROPN
ejpam-6017	151	11	/	/	SYM
ejpam-6017	151	12	eur	eur	PROPN
ejpam-6017	151	13	.	.	PUNCT
ejpam-6017	152	1	j.	j.	PROPN
ejpam-6017	152	2	pure	pure	PROPN
ejpam-6017	152	3	appl	appl	PROPN
ejpam-6017	152	4	.	.	PROPN
ejpam-6017	152	5	math	math	PROPN
ejpam-6017	152	6	,	,	PUNCT
ejpam-6017	152	7	18	18	NUM
ejpam-6017	152	8	(	(	PUNCT
ejpam-6017	152	9	2	2	NUM
ejpam-6017	152	10	)	)	PUNCT
ejpam-6017	152	11	(	(	PUNCT
ejpam-6017	152	12	2025	2025	NUM
ejpam-6017	152	13	)	)	PUNCT
ejpam-6017	152	14	,	,	PUNCT
ejpam-6017	152	15	6017	6017	NUM
ejpam-6017	152	16	6	6	NUM
ejpam-6017	152	17	of	of	ADP
ejpam-6017	152	18	11	11	NUM
ejpam-6017	152	19	theorem	theorem	NOUN
ejpam-6017	152	20	3	3	NUM
ejpam-6017	152	21	.	.	X
ejpam-6017	153	1	for	for	ADP
ejpam-6017	153	2	a	a	DET
ejpam-6017	153	3	function	function	NOUN
ejpam-6017	153	4	f	f	NOUN
ejpam-6017	153	5	:	:	PUNCT
ejpam-6017	153	6	(	(	PUNCT
ejpam-6017	153	7	x	x	NOUN
ejpam-6017	153	8	,	,	PUNCT
ejpam-6017	153	9	τ1	τ1	NOUN
ejpam-6017	153	10	,	,	PUNCT
ejpam-6017	153	11	τ2	τ2	NOUN
ejpam-6017	153	12	)	)	PUNCT
ejpam-6017	153	13	→	→	SYM
ejpam-6017	153	14	(	(	PUNCT
ejpam-6017	153	15	y	y	PROPN
ejpam-6017	153	16	,	,	PUNCT
ejpam-6017	153	17	σ1	σ1	PROPN
ejpam-6017	153	18	,	,	PUNCT
ejpam-6017	153	19	σ2	σ2	NOUN
ejpam-6017	153	20	)	)	PUNCT
ejpam-6017	153	21	,	,	PUNCT
ejpam-6017	153	22	where	where	SCONJ
ejpam-6017	153	23	(	(	PUNCT
ejpam-6017	153	24	y	y	PROPN
ejpam-6017	153	25	,	,	PUNCT
ejpam-6017	153	26	σ1	σ1	PROPN
ejpam-6017	153	27	,	,	PUNCT
ejpam-6017	153	28	σ2	σ2	PROPN
ejpam-6017	153	29	)	)	PUNCT
ejpam-6017	153	30	is	be	AUX
ejpam-6017	153	31	(	(	PUNCT
ejpam-6017	153	32	σ1	σ1	PROPN
ejpam-6017	153	33	,	,	PUNCT
ejpam-6017	153	34	σ2)regular	σ2)regular	PROPN
ejpam-6017	153	35	,	,	PUNCT
ejpam-6017	153	36	the	the	DET
ejpam-6017	153	37	following	follow	VERB
ejpam-6017	153	38	properties	property	NOUN
ejpam-6017	153	39	are	be	AUX
ejpam-6017	153	40	equivalent	equivalent	ADJ
ejpam-6017	153	41	:	:	PUNCT
ejpam-6017	153	42	(	(	PUNCT
ejpam-6017	153	43	1	1	X
ejpam-6017	153	44	)	)	PUNCT
ejpam-6017	153	45	f	f	PROPN
ejpam-6017	153	46	is	be	AUX
ejpam-6017	153	47	(	(	PUNCT
ejpam-6017	153	48	τ1	τ1	NOUN
ejpam-6017	153	49	,	,	PUNCT
ejpam-6017	153	50	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	153	51	;	;	PUNCT
ejpam-6017	153	52	(	(	PUNCT
ejpam-6017	153	53	2	2	X
ejpam-6017	153	54	)	)	PUNCT
ejpam-6017	153	55	f	f	PROPN
ejpam-6017	153	56	is	be	AUX
ejpam-6017	153	57	weakly	weakly	ADJ
ejpam-6017	153	58	(	(	PUNCT
ejpam-6017	153	59	τ1	τ1	NOUN
ejpam-6017	153	60	,	,	PUNCT
ejpam-6017	153	61	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	153	62	;	;	PUNCT
ejpam-6017	153	63	(	(	PUNCT
ejpam-6017	153	64	3	3	X
ejpam-6017	153	65	)	)	PUNCT
ejpam-6017	153	66	f	f	PROPN
ejpam-6017	153	67	is	be	AUX
ejpam-6017	153	68	faintly	faintly	ADV
ejpam-6017	153	69	(	(	PUNCT
ejpam-6017	153	70	τ1	τ1	NOUN
ejpam-6017	153	71	,	,	PUNCT
ejpam-6017	153	72	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	153	73	;	;	PUNCT
ejpam-6017	153	74	(	(	PUNCT
ejpam-6017	153	75	4	4	X
ejpam-6017	153	76	)	)	PUNCT
ejpam-6017	153	77	f	f	PROPN
ejpam-6017	153	78	is	be	AUX
ejpam-6017	153	79	strongly	strongly	ADV
ejpam-6017	153	80	θ(τ1	θ(τ1	ADJ
ejpam-6017	153	81	,	,	PUNCT
ejpam-6017	153	82	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	153	83	.	.	PUNCT
ejpam-6017	154	1	proof	proof	NOUN
ejpam-6017	154	2	.	.	PUNCT
ejpam-6017	155	1	(	(	PUNCT
ejpam-6017	155	2	1	1	X
ejpam-6017	155	3	)	)	PUNCT
ejpam-6017	155	4	⇒	⇒	NOUN
ejpam-6017	155	5	(	(	PUNCT
ejpam-6017	155	6	2	2	NUM
ejpam-6017	155	7	):	):	PUNCT
ejpam-6017	155	8	the	the	DET
ejpam-6017	155	9	proof	proof	NOUN
ejpam-6017	155	10	is	be	AUX
ejpam-6017	155	11	obvious	obvious	ADJ
ejpam-6017	155	12	.	.	PUNCT
ejpam-6017	156	1	(	(	PUNCT
ejpam-6017	156	2	2	2	X
ejpam-6017	156	3	)	)	PUNCT
ejpam-6017	156	4	⇒	⇒	NOUN
ejpam-6017	156	5	(	(	PUNCT
ejpam-6017	156	6	3	3	NUM
ejpam-6017	156	7	):	):	PUNCT
ejpam-6017	156	8	let	let	VERB
ejpam-6017	156	9	k	k	PRON
ejpam-6017	156	10	be	be	AUX
ejpam-6017	156	11	any	any	DET
ejpam-6017	156	12	θ(σ1	θ(σ1	NOUN
ejpam-6017	156	13	,	,	PUNCT
ejpam-6017	156	14	σ2)-closed	σ2)-close	VERB
ejpam-6017	156	15	set	set	NOUN
ejpam-6017	156	16	of	of	ADP
ejpam-6017	156	17	y	y	PROPN
ejpam-6017	156	18	.	.	PUNCT
ejpam-6017	157	1	by	by	ADP
ejpam-6017	157	2	lemma	lemma	PROPN
ejpam-6017	157	3	4	4	NUM
ejpam-6017	157	4	,	,	PUNCT
ejpam-6017	157	5	we	we	PRON
ejpam-6017	157	6	have	have	VERB
ejpam-6017	157	7	τ1τ2	τ1τ2	NOUN
ejpam-6017	157	8	-	-	NOUN
ejpam-6017	157	9	cl(f	cl(f	NUM
ejpam-6017	157	10	−1(k	−1(k	NOUN
ejpam-6017	157	11	)	)	PUNCT
ejpam-6017	157	12	)	)	PUNCT
ejpam-6017	158	1	⊆	⊆	NUM
ejpam-6017	158	2	f−1((σ1	f−1((σ1	NOUN
ejpam-6017	158	3	,	,	PUNCT
ejpam-6017	158	4	σ2)θ	σ2)θ	NOUN
ejpam-6017	158	5	-	-	PUNCT
ejpam-6017	158	6	cl(k	cl(k	NOUN
ejpam-6017	158	7	)	)	PUNCT
ejpam-6017	158	8	)	)	PUNCT
ejpam-6017	158	9	=	=	PUNCT
ejpam-6017	158	10	f−1(k	f−1(k	PROPN
ejpam-6017	158	11	)	)	PUNCT
ejpam-6017	158	12	and	and	CCONJ
ejpam-6017	158	13	hence	hence	ADV
ejpam-6017	158	14	f−1(k	f−1(k	PROPN
ejpam-6017	158	15	)	)	PUNCT
ejpam-6017	158	16	is	be	AUX
ejpam-6017	158	17	τ1τ2	τ1τ2	NOUN
ejpam-6017	158	18	-	-	ADJ
ejpam-6017	158	19	closed	closed	ADJ
ejpam-6017	158	20	in	in	ADP
ejpam-6017	158	21	x.	x.	NOUN
ejpam-6017	158	22	thus	thus	ADV
ejpam-6017	158	23	by	by	ADP
ejpam-6017	158	24	lemma	lemma	PROPN
ejpam-6017	158	25	5	5	NUM
ejpam-6017	158	26	,	,	PUNCT
ejpam-6017	158	27	f	f	PROPN
ejpam-6017	158	28	is	be	AUX
ejpam-6017	158	29	faintly	faintly	ADV
ejpam-6017	158	30	(	(	PUNCT
ejpam-6017	158	31	τ1	τ1	NOUN
ejpam-6017	158	32	,	,	PUNCT
ejpam-6017	158	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	158	34	.	.	PUNCT
ejpam-6017	159	1	(	(	PUNCT
ejpam-6017	159	2	3	3	X
ejpam-6017	159	3	)	)	PUNCT
ejpam-6017	159	4	⇒	⇒	NOUN
ejpam-6017	159	5	(	(	PUNCT
ejpam-6017	159	6	1	1	NUM
ejpam-6017	159	7	):	):	PUNCT
ejpam-6017	159	8	let	let	VERB
ejpam-6017	159	9	x	x	PUNCT
ejpam-6017	159	10	∈	∈	PROPN
ejpam-6017	159	11	x	x	X
ejpam-6017	159	12	and	and	CCONJ
ejpam-6017	159	13	v	v	X
ejpam-6017	159	14	be	be	AUX
ejpam-6017	159	15	any	any	DET
ejpam-6017	159	16	σ1σ2	σ1σ2	NOUN
ejpam-6017	159	17	-	-	ADJ
ejpam-6017	159	18	open	open	ADJ
ejpam-6017	159	19	set	set	NOUN
ejpam-6017	159	20	of	of	ADP
ejpam-6017	159	21	y	y	PROPN
ejpam-6017	159	22	containing	contain	VERB
ejpam-6017	159	23	f(x	f(x	PROPN
ejpam-6017	159	24	)	)	PUNCT
ejpam-6017	159	25	.	.	PUNCT
ejpam-6017	160	1	since	since	SCONJ
ejpam-6017	160	2	(	(	PUNCT
ejpam-6017	160	3	y	y	PROPN
ejpam-6017	160	4	,	,	PUNCT
ejpam-6017	160	5	σ1	σ1	PROPN
ejpam-6017	160	6	,	,	PUNCT
ejpam-6017	160	7	σ2	σ2	PROPN
ejpam-6017	160	8	)	)	PUNCT
ejpam-6017	160	9	is	be	AUX
ejpam-6017	160	10	(	(	PUNCT
ejpam-6017	160	11	σ1	σ1	NOUN
ejpam-6017	160	12	,	,	PUNCT
ejpam-6017	160	13	σ2)-regular	σ2)-regular	ADJ
ejpam-6017	160	14	,	,	PUNCT
ejpam-6017	160	15	by	by	ADP
ejpam-6017	160	16	lemma	lemma	PROPN
ejpam-6017	160	17	7	7	NUM
ejpam-6017	160	18	we	we	PRON
ejpam-6017	160	19	have	have	VERB
ejpam-6017	160	20	v	v	NOUN
ejpam-6017	160	21	is	be	AUX
ejpam-6017	160	22	a	a	DET
ejpam-6017	160	23	θ(τ1	θ(τ1	NOUN
ejpam-6017	160	24	,	,	PUNCT
ejpam-6017	160	25	τ2)-open	τ2)-open	ADJ
ejpam-6017	160	26	set	set	NOUN
ejpam-6017	160	27	of	of	ADP
ejpam-6017	160	28	y	y	PROPN
ejpam-6017	160	29	.	.	PUNCT
ejpam-6017	161	1	since	since	SCONJ
ejpam-6017	161	2	f	f	PROPN
ejpam-6017	161	3	is	be	AUX
ejpam-6017	161	4	faintly	faintly	ADV
ejpam-6017	161	5	(	(	PUNCT
ejpam-6017	161	6	τ1	τ1	NOUN
ejpam-6017	161	7	,	,	PUNCT
ejpam-6017	161	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	161	9	,	,	PUNCT
ejpam-6017	161	10	by	by	ADP
ejpam-6017	161	11	lemma	lemma	PROPN
ejpam-6017	161	12	5	5	NUM
ejpam-6017	161	13	we	we	PRON
ejpam-6017	161	14	have	have	VERB
ejpam-6017	161	15	f−1(v	f−1(v	PROPN
ejpam-6017	161	16	)	)	PUNCT
ejpam-6017	161	17	is	be	AUX
ejpam-6017	161	18	τ1τ2	τ1τ2	NOUN
ejpam-6017	161	19	-	-	ADJ
ejpam-6017	161	20	open	open	ADJ
ejpam-6017	161	21	in	in	ADP
ejpam-6017	161	22	x.	x.	NOUN
ejpam-6017	161	23	then	then	ADV
ejpam-6017	161	24	by	by	ADP
ejpam-6017	161	25	lemma	lemma	PROPN
ejpam-6017	161	26	3	3	NUM
ejpam-6017	161	27	,	,	PUNCT
ejpam-6017	161	28	f	f	PROPN
ejpam-6017	161	29	is	be	AUX
ejpam-6017	161	30	(	(	PUNCT
ejpam-6017	161	31	τ1	τ1	NOUN
ejpam-6017	161	32	,	,	PUNCT
ejpam-6017	161	33	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	161	34	.	.	PUNCT
ejpam-6017	162	1	(	(	PUNCT
ejpam-6017	162	2	1	1	X
ejpam-6017	162	3	)	)	PUNCT
ejpam-6017	162	4	⇒	⇒	NOUN
ejpam-6017	162	5	(	(	PUNCT
ejpam-6017	162	6	4	4	NUM
ejpam-6017	162	7	):	):	PUNCT
ejpam-6017	162	8	let	let	VERB
ejpam-6017	162	9	x	x	PUNCT
ejpam-6017	162	10	∈	∈	PROPN
ejpam-6017	162	11	x	x	X
ejpam-6017	162	12	and	and	CCONJ
ejpam-6017	162	13	v	v	X
ejpam-6017	162	14	be	be	AUX
ejpam-6017	162	15	any	any	DET
ejpam-6017	162	16	σ1σ2	σ1σ2	NOUN
ejpam-6017	162	17	-	-	ADJ
ejpam-6017	162	18	open	open	ADJ
ejpam-6017	162	19	set	set	NOUN
ejpam-6017	162	20	of	of	ADP
ejpam-6017	162	21	y	y	PROPN
ejpam-6017	162	22	containing	contain	VERB
ejpam-6017	162	23	f(x	f(x	PROPN
ejpam-6017	162	24	)	)	PUNCT
ejpam-6017	162	25	.	.	PUNCT
ejpam-6017	163	1	since	since	SCONJ
ejpam-6017	163	2	(	(	PUNCT
ejpam-6017	163	3	y	y	PROPN
ejpam-6017	163	4	,	,	PUNCT
ejpam-6017	163	5	σ1	σ1	PROPN
ejpam-6017	163	6	,	,	PUNCT
ejpam-6017	163	7	σ2	σ2	PROPN
ejpam-6017	163	8	)	)	PUNCT
ejpam-6017	163	9	is	be	AUX
ejpam-6017	163	10	(	(	PUNCT
ejpam-6017	163	11	σ1	σ1	NOUN
ejpam-6017	163	12	,	,	PUNCT
ejpam-6017	163	13	σ2)-regular	σ2)-regular	ADJ
ejpam-6017	163	14	,	,	PUNCT
ejpam-6017	163	15	by	by	ADP
ejpam-6017	163	16	lemma	lemma	PROPN
ejpam-6017	163	17	6	6	NUM
ejpam-6017	163	18	there	there	ADV
ejpam-6017	163	19	exists	exist	VERB
ejpam-6017	163	20	a	a	DET
ejpam-6017	163	21	σ1σ2	σ1σ2	NUM
ejpam-6017	163	22	-	-	ADJ
ejpam-6017	163	23	open	open	ADJ
ejpam-6017	163	24	set	set	NOUN
ejpam-6017	163	25	w	w	PROPN
ejpam-6017	163	26	of	of	ADP
ejpam-6017	163	27	y	y	PRON
ejpam-6017	163	28	such	such	ADJ
ejpam-6017	163	29	that	that	SCONJ
ejpam-6017	163	30	f(x	f(x	PROPN
ejpam-6017	163	31	)	)	PUNCT
ejpam-6017	163	32	∈	∈	PROPN
ejpam-6017	164	1	w	w	ADP
ejpam-6017	164	2	⊆	⊆	NUM
ejpam-6017	164	3	σ1σ2	σ1σ2	NOUN
ejpam-6017	164	4	-	-	PUNCT
ejpam-6017	164	5	cl(w	cl(w	NOUN
ejpam-6017	164	6	)	)	PUNCT
ejpam-6017	164	7	⊆	⊆	NUM
ejpam-6017	164	8	v	v	NOUN
ejpam-6017	164	9	.	.	PUNCT
ejpam-6017	165	1	since	since	SCONJ
ejpam-6017	165	2	f	f	PROPN
ejpam-6017	165	3	is	be	AUX
ejpam-6017	165	4	(	(	PUNCT
ejpam-6017	165	5	τ1	τ1	NOUN
ejpam-6017	165	6	,	,	PUNCT
ejpam-6017	165	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	165	8	,	,	PUNCT
ejpam-6017	165	9	there	there	PRON
ejpam-6017	165	10	exists	exist	VERB
ejpam-6017	165	11	a	a	DET
ejpam-6017	165	12	τ1τ2	τ1τ2	NOUN
ejpam-6017	165	13	-	-	ADJ
ejpam-6017	165	14	open	open	ADJ
ejpam-6017	165	15	set	set	ADJ
ejpam-6017	165	16	u	u	NOUN
ejpam-6017	165	17	of	of	ADP
ejpam-6017	165	18	x	x	PUNCT
ejpam-6017	165	19	containing	contain	VERB
ejpam-6017	165	20	x	x	PUNCT
ejpam-6017	165	21	such	such	ADJ
ejpam-6017	165	22	that	that	DET
ejpam-6017	165	23	f(u	f(u	PROPN
ejpam-6017	165	24	)	)	PUNCT
ejpam-6017	165	25	⊆	⊆	NUM
ejpam-6017	165	26	v	v	NOUN
ejpam-6017	165	27	.	.	PUNCT
ejpam-6017	166	1	now	now	ADV
ejpam-6017	166	2	,	,	PUNCT
ejpam-6017	166	3	we	we	PRON
ejpam-6017	166	4	shall	shall	AUX
ejpam-6017	166	5	show	show	VERB
ejpam-6017	166	6	that	that	SCONJ
ejpam-6017	166	7	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	166	8	-	-	PUNCT
ejpam-6017	166	9	cl(u	cl(u	NOUN
ejpam-6017	166	10	)	)	PUNCT
ejpam-6017	166	11	)	)	PUNCT
ejpam-6017	167	1	⊆	⊆	X
ejpam-6017	167	2	σ1σ2	σ1σ2	NOUN
ejpam-6017	167	3	-	-	PUNCT
ejpam-6017	167	4	cl(w	cl(w	NOUN
ejpam-6017	167	5	)	)	PUNCT
ejpam-6017	167	6	.	.	PUNCT
ejpam-6017	168	1	suppose	suppose	VERB
ejpam-6017	168	2	that	that	SCONJ
ejpam-6017	168	3	y	y	PROPN
ejpam-6017	168	4	̸∈	̸∈	PROPN
ejpam-6017	168	5	σ1σ2	σ1σ2	NOUN
ejpam-6017	168	6	-	-	PUNCT
ejpam-6017	168	7	cl(w	cl(w	NOUN
ejpam-6017	168	8	)	)	PUNCT
ejpam-6017	168	9	.	.	PUNCT
ejpam-6017	169	1	then	then	ADV
ejpam-6017	169	2	,	,	PUNCT
ejpam-6017	169	3	there	there	PRON
ejpam-6017	169	4	exists	exist	VERB
ejpam-6017	169	5	a	a	DET
ejpam-6017	169	6	σ1σ2	σ1σ2	NUM
ejpam-6017	169	7	-	-	ADJ
ejpam-6017	169	8	open	open	ADJ
ejpam-6017	169	9	set	set	NOUN
ejpam-6017	169	10	g	g	NOUN
ejpam-6017	169	11	of	of	ADP
ejpam-6017	169	12	y	y	PROPN
ejpam-6017	169	13	containing	contain	VERB
ejpam-6017	169	14	y	y	PRON
ejpam-6017	169	15	such	such	ADJ
ejpam-6017	169	16	that	that	SCONJ
ejpam-6017	169	17	g	g	PROPN
ejpam-6017	169	18	∩	∩	NOUN
ejpam-6017	169	19	w	w	NOUN
ejpam-6017	169	20	=	=	PUNCT
ejpam-6017	169	21	∅.	∅.	NOUN
ejpam-6017	169	22	since	since	SCONJ
ejpam-6017	169	23	f	f	PROPN
ejpam-6017	169	24	is	be	AUX
ejpam-6017	169	25	(	(	PUNCT
ejpam-6017	169	26	τ1	τ1	NOUN
ejpam-6017	169	27	,	,	PUNCT
ejpam-6017	169	28	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	169	29	,	,	PUNCT
ejpam-6017	169	30	by	by	ADP
ejpam-6017	169	31	lemma	lemma	PROPN
ejpam-6017	169	32	3	3	NUM
ejpam-6017	169	33	we	we	PRON
ejpam-6017	169	34	have	have	AUX
ejpam-6017	169	35	f−1(g	f−1(g	PROPN
ejpam-6017	169	36	)	)	PUNCT
ejpam-6017	169	37	is	be	AUX
ejpam-6017	169	38	τ1τ2	τ1τ2	NOUN
ejpam-6017	169	39	-	-	ADJ
ejpam-6017	169	40	open	open	ADJ
ejpam-6017	169	41	in	in	ADP
ejpam-6017	169	42	x	x	X
ejpam-6017	169	43	and	and	CCONJ
ejpam-6017	169	44	f−1(g	f−1(g	NUM
ejpam-6017	169	45	)	)	PUNCT
ejpam-6017	169	46	∩	∩	NOUN
ejpam-6017	169	47	u	u	NOUN
ejpam-6017	169	48	=	=	NOUN
ejpam-6017	169	49	∅	∅	NOUN
ejpam-6017	169	50	,	,	PUNCT
ejpam-6017	169	51	which	which	PRON
ejpam-6017	169	52	implies	imply	VERB
ejpam-6017	169	53	that	that	PRON
ejpam-6017	169	54	f−1(g	f−1(g	PROPN
ejpam-6017	169	55	)	)	PUNCT
ejpam-6017	169	56	∩	∩	NOUN
ejpam-6017	169	57	τ1τ2	τ1τ2	NOUN
ejpam-6017	169	58	-	-	NOUN
ejpam-6017	169	59	cl(u	cl(u	NOUN
ejpam-6017	169	60	)	)	PUNCT
ejpam-6017	169	61	=	=	PUNCT
ejpam-6017	169	62	∅.	∅.	VERB
ejpam-6017	169	63	if	if	SCONJ
ejpam-6017	169	64	f−1(g	f−1(g	PROPN
ejpam-6017	169	65	)	)	PUNCT
ejpam-6017	169	66	∩	∩	NOUN
ejpam-6017	169	67	τ1τ2	τ1τ2	NOUN
ejpam-6017	169	68	-	-	NOUN
ejpam-6017	169	69	cl(u	cl(u	NOUN
ejpam-6017	169	70	)	)	PUNCT
ejpam-6017	169	71	̸=	̸=	NOUN
ejpam-6017	169	72	∅	∅	NOUN
ejpam-6017	169	73	,	,	PUNCT
ejpam-6017	169	74	then	then	ADV
ejpam-6017	169	75	τ1τ2	τ1τ2	NOUN
ejpam-6017	169	76	-	-	ADJ
ejpam-6017	169	77	int(f	int(f	NUM
ejpam-6017	169	78	−1(g	−1(g	NOUN
ejpam-6017	169	79	)	)	PUNCT
ejpam-6017	169	80	)	)	PUNCT
ejpam-6017	170	1	∩	∩	NOUN
ejpam-6017	170	2	τ1τ2	τ1τ2	NOUN
ejpam-6017	170	3	-	-	NOUN
ejpam-6017	170	4	cl(u	cl(u	NOUN
ejpam-6017	170	5	)	)	PUNCT
ejpam-6017	170	6	̸=	̸=	PROPN
ejpam-6017	170	7	∅.	∅.	ADV
ejpam-6017	170	8	let	let	VERB
ejpam-6017	170	9	z	z	NOUN
ejpam-6017	170	10	∈	∈	PROPN
ejpam-6017	170	11	τ1τ2	τ1τ2	PROPN
ejpam-6017	170	12	-	-	ADJ
ejpam-6017	170	13	int(f	int(f	NUM
ejpam-6017	170	14	−1(g	−1(g	NOUN
ejpam-6017	170	15	)	)	PUNCT
ejpam-6017	170	16	)	)	PUNCT
ejpam-6017	171	1	∩	∩	NOUN
ejpam-6017	171	2	τ1τ2	τ1τ2	NOUN
ejpam-6017	171	3	-	-	NOUN
ejpam-6017	171	4	cl(u	cl(u	NUM
ejpam-6017	171	5	)	)	PUNCT
ejpam-6017	171	6	.	.	PUNCT
ejpam-6017	172	1	then	then	ADV
ejpam-6017	172	2	,	,	PUNCT
ejpam-6017	172	3	z	z	PROPN
ejpam-6017	172	4	∈	∈	PROPN
ejpam-6017	172	5	τ1τ2	τ1τ2	NOUN
ejpam-6017	172	6	-	-	ADJ
ejpam-6017	172	7	int(f	int(f	NUM
ejpam-6017	172	8	−1(g	−1(g	NOUN
ejpam-6017	172	9	)	)	PUNCT
ejpam-6017	172	10	)	)	PUNCT
ejpam-6017	173	1	and	and	CCONJ
ejpam-6017	173	2	z	z	NOUN
ejpam-6017	173	3	∈	∈	PROPN
ejpam-6017	173	4	τ1τ2	τ1τ2	NOUN
ejpam-6017	173	5	-	-	NOUN
ejpam-6017	173	6	cl(u	cl(u	NUM
ejpam-6017	173	7	)	)	PUNCT
ejpam-6017	173	8	.	.	PUNCT
ejpam-6017	174	1	there	there	PRON
ejpam-6017	174	2	exists	exist	VERB
ejpam-6017	174	3	a	a	DET
ejpam-6017	174	4	τ1τ2	τ1τ2	ADJ
ejpam-6017	174	5	-	-	ADJ
ejpam-6017	174	6	open	open	ADJ
ejpam-6017	174	7	set	set	ADJ
ejpam-6017	174	8	u0	u0	NOUN
ejpam-6017	174	9	of	of	ADP
ejpam-6017	174	10	x	x	PUNCT
ejpam-6017	174	11	containing	contain	VERB
ejpam-6017	174	12	x	x	PUNCT
ejpam-6017	174	13	such	such	ADJ
ejpam-6017	174	14	that	that	DET
ejpam-6017	174	15	u0	u0	ADJ
ejpam-6017	174	16	⊆	⊆	NUM
ejpam-6017	174	17	f−1(g	f−1(g	NUM
ejpam-6017	174	18	)	)	PUNCT
ejpam-6017	174	19	.	.	PUNCT
ejpam-6017	175	1	since	since	SCONJ
ejpam-6017	175	2	z	z	PROPN
ejpam-6017	175	3	∈	∈	PROPN
ejpam-6017	175	4	τ1τ2	τ1τ2	NOUN
ejpam-6017	175	5	-	-	NOUN
ejpam-6017	175	6	cl(u	cl(u	NOUN
ejpam-6017	175	7	)	)	PUNCT
ejpam-6017	175	8	,	,	PUNCT
ejpam-6017	175	9	we	we	PRON
ejpam-6017	175	10	have	have	VERB
ejpam-6017	175	11	u0∩u	u0∩u	NOUN
ejpam-6017	175	12	̸=	̸=	PROPN
ejpam-6017	175	13	∅	∅	NOUN
ejpam-6017	175	14	and	and	CCONJ
ejpam-6017	175	15	so	so	ADV
ejpam-6017	175	16	f−1(g)∩u	f−1(g)∩u	NOUN
ejpam-6017	175	17	̸=	̸=	PROPN
ejpam-6017	175	18	∅.	∅.	ADP
ejpam-6017	175	19	this	this	PRON
ejpam-6017	175	20	is	be	AUX
ejpam-6017	175	21	a	a	DET
ejpam-6017	175	22	contradiction	contradiction	NOUN
ejpam-6017	175	23	.	.	PUNCT
ejpam-6017	176	1	therefore	therefore	ADV
ejpam-6017	176	2	,	,	PUNCT
ejpam-6017	176	3	f−1(g	f−1(g	PROPN
ejpam-6017	176	4	)	)	PUNCT
ejpam-6017	176	5	∩	∩	NOUN
ejpam-6017	176	6	τ1τ2	τ1τ2	NOUN
ejpam-6017	176	7	-	-	NOUN
ejpam-6017	176	8	cl(u	cl(u	NOUN
ejpam-6017	176	9	)	)	PUNCT
ejpam-6017	176	10	=	=	SYM
ejpam-6017	176	11	∅	∅	NOUN
ejpam-6017	176	12	which	which	PRON
ejpam-6017	176	13	implies	imply	VERB
ejpam-6017	176	14	that	that	SCONJ
ejpam-6017	176	15	g	g	PROPN
ejpam-6017	176	16	∩	∩	NOUN
ejpam-6017	176	17	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	176	18	-	-	NOUN
ejpam-6017	176	19	cl(u	cl(u	NOUN
ejpam-6017	176	20	)	)	PUNCT
ejpam-6017	176	21	)	)	PUNCT
ejpam-6017	177	1	=	=	PUNCT
ejpam-6017	177	2	∅.	∅.	VERB
ejpam-6017	177	3	thus	thus	ADV
ejpam-6017	177	4	,	,	PUNCT
ejpam-6017	177	5	y	y	PROPN
ejpam-6017	177	6	̸∈	̸∈	PROPN
ejpam-6017	177	7	f(τ1τ2	f(τ1τ2	PROPN
ejpam-6017	177	8	-	-	PUNCT
ejpam-6017	177	9	cl(u	cl(u	NOUN
ejpam-6017	177	10	)	)	PUNCT
ejpam-6017	177	11	)	)	PUNCT
ejpam-6017	177	12	and	and	CCONJ
ejpam-6017	177	13	hence	hence	ADV
ejpam-6017	177	14	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	177	15	-	-	PUNCT
ejpam-6017	177	16	cl(u	cl(u	NOUN
ejpam-6017	177	17	)	)	PUNCT
ejpam-6017	177	18	)	)	PUNCT
ejpam-6017	178	1	⊆	⊆	X
ejpam-6017	178	2	σ1σ2	σ1σ2	NOUN
ejpam-6017	178	3	-	-	PUNCT
ejpam-6017	178	4	cl(w	cl(w	NOUN
ejpam-6017	178	5	)	)	PUNCT
ejpam-6017	178	6	⊆	⊆	NUM
ejpam-6017	178	7	v	v	NOUN
ejpam-6017	178	8	.	.	PUNCT
ejpam-6017	179	1	this	this	PRON
ejpam-6017	179	2	shows	show	VERB
ejpam-6017	179	3	that	that	SCONJ
ejpam-6017	179	4	f	f	PROPN
ejpam-6017	179	5	is	be	AUX
ejpam-6017	179	6	strongly	strongly	ADV
ejpam-6017	179	7	θ(τ1	θ(τ1	ADJ
ejpam-6017	179	8	,	,	PUNCT
ejpam-6017	179	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	179	10	.	.	PUNCT
ejpam-6017	180	1	(	(	PUNCT
ejpam-6017	180	2	4	4	X
ejpam-6017	180	3	)	)	PUNCT
ejpam-6017	180	4	⇒	⇒	NOUN
ejpam-6017	180	5	(	(	PUNCT
ejpam-6017	180	6	1	1	NUM
ejpam-6017	180	7	):	):	PUNCT
ejpam-6017	180	8	the	the	DET
ejpam-6017	180	9	proof	proof	NOUN
ejpam-6017	180	10	is	be	AUX
ejpam-6017	180	11	obvious	obvious	ADJ
ejpam-6017	180	12	.	.	PUNCT
ejpam-6017	181	1	theorem	theorem	ADJ
ejpam-6017	181	2	4	4	NUM
ejpam-6017	181	3	.	.	PUNCT
ejpam-6017	182	1	let	let	VERB
ejpam-6017	182	2	(	(	PUNCT
ejpam-6017	182	3	x	x	NOUN
ejpam-6017	182	4	,	,	PUNCT
ejpam-6017	182	5	τ1	τ1	NOUN
ejpam-6017	182	6	,	,	PUNCT
ejpam-6017	182	7	τ2	τ2	PROPN
ejpam-6017	182	8	)	)	PUNCT
ejpam-6017	182	9	be	be	AUX
ejpam-6017	182	10	(	(	PUNCT
ejpam-6017	182	11	τ1	τ1	NOUN
ejpam-6017	182	12	,	,	PUNCT
ejpam-6017	182	13	τ2)-regular	τ2)-regular	PROPN
ejpam-6017	182	14	.	.	PUNCT
ejpam-6017	183	1	then	then	ADV
ejpam-6017	183	2	,	,	PUNCT
ejpam-6017	183	3	a	a	DET
ejpam-6017	183	4	function	function	NOUN
ejpam-6017	183	5	f	f	NOUN
ejpam-6017	183	6	:	:	PUNCT
ejpam-6017	183	7	(	(	PUNCT
ejpam-6017	183	8	x	x	NOUN
ejpam-6017	183	9	,	,	PUNCT
ejpam-6017	183	10	τ1	τ1	NOUN
ejpam-6017	183	11	,	,	PUNCT
ejpam-6017	183	12	τ2	τ2	NOUN
ejpam-6017	183	13	)	)	PUNCT
ejpam-6017	183	14	→	→	SYM
ejpam-6017	183	15	(	(	PUNCT
ejpam-6017	183	16	y	y	PROPN
ejpam-6017	183	17	,	,	PUNCT
ejpam-6017	183	18	σ1	σ1	PROPN
ejpam-6017	183	19	,	,	PUNCT
ejpam-6017	183	20	σ2	σ2	PROPN
ejpam-6017	183	21	)	)	PUNCT
ejpam-6017	183	22	is	be	AUX
ejpam-6017	183	23	strongly	strongly	ADV
ejpam-6017	183	24	θ(τ1	θ(τ1	ADJ
ejpam-6017	183	25	,	,	PUNCT
ejpam-6017	183	26	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	183	27	if	if	SCONJ
ejpam-6017	183	28	and	and	CCONJ
ejpam-6017	183	29	only	only	ADV
ejpam-6017	183	30	if	if	SCONJ
ejpam-6017	183	31	f	f	PROPN
ejpam-6017	183	32	is	be	AUX
ejpam-6017	183	33	(	(	PUNCT
ejpam-6017	183	34	τ1	τ1	NOUN
ejpam-6017	183	35	,	,	PUNCT
ejpam-6017	183	36	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	183	37	.	.	PUNCT
ejpam-6017	184	1	p.	p.	NOUN
ejpam-6017	184	2	pue	pue	NOUN
ejpam-6017	184	3	-	-	PUNCT
ejpam-6017	184	4	on	on	ADP
ejpam-6017	184	5	,	,	PUNCT
ejpam-6017	184	6	s.	s.	PROPN
ejpam-6017	184	7	sompong	sompong	PROPN
ejpam-6017	184	8	,	,	PUNCT
ejpam-6017	184	9	c.	c.	PROPN
ejpam-6017	184	10	boonpok	boonpok	PROPN
ejpam-6017	184	11	/	/	SYM
ejpam-6017	184	12	eur	eur	PROPN
ejpam-6017	184	13	.	.	PUNCT
ejpam-6017	185	1	j.	j.	PROPN
ejpam-6017	185	2	pure	pure	PROPN
ejpam-6017	185	3	appl	appl	PROPN
ejpam-6017	185	4	.	.	PROPN
ejpam-6017	185	5	math	math	PROPN
ejpam-6017	185	6	,	,	PUNCT
ejpam-6017	185	7	18	18	NUM
ejpam-6017	185	8	(	(	PUNCT
ejpam-6017	185	9	2	2	NUM
ejpam-6017	185	10	)	)	PUNCT
ejpam-6017	185	11	(	(	PUNCT
ejpam-6017	185	12	2025	2025	NUM
ejpam-6017	185	13	)	)	PUNCT
ejpam-6017	185	14	,	,	PUNCT
ejpam-6017	185	15	6017	6017	NUM
ejpam-6017	185	16	7	7	NUM
ejpam-6017	185	17	of	of	ADP
ejpam-6017	185	18	11	11	NUM
ejpam-6017	185	19	proof	proof	NOUN
ejpam-6017	185	20	.	.	PUNCT
ejpam-6017	186	1	we	we	PRON
ejpam-6017	186	2	prove	prove	VERB
ejpam-6017	186	3	only	only	ADV
ejpam-6017	186	4	the	the	DET
ejpam-6017	186	5	sufficiency	sufficiency	NOUN
ejpam-6017	186	6	.	.	PUNCT
ejpam-6017	187	1	suppose	suppose	VERB
ejpam-6017	187	2	that	that	SCONJ
ejpam-6017	187	3	f	f	PROPN
ejpam-6017	187	4	is	be	AUX
ejpam-6017	187	5	(	(	PUNCT
ejpam-6017	187	6	τ1	τ1	NOUN
ejpam-6017	187	7	,	,	PUNCT
ejpam-6017	187	8	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	187	9	.	.	PUNCT
ejpam-6017	188	1	let	let	VERB
ejpam-6017	188	2	x	x	PUNCT
ejpam-6017	188	3	∈	∈	PROPN
ejpam-6017	188	4	x	x	X
ejpam-6017	188	5	and	and	CCONJ
ejpam-6017	188	6	v	v	X
ejpam-6017	188	7	be	be	AUX
ejpam-6017	188	8	any	any	DET
ejpam-6017	188	9	σ1σ2	σ1σ2	NOUN
ejpam-6017	188	10	-	-	ADJ
ejpam-6017	188	11	open	open	ADJ
ejpam-6017	188	12	set	set	NOUN
ejpam-6017	188	13	of	of	ADP
ejpam-6017	188	14	y	y	PROPN
ejpam-6017	188	15	containing	contain	VERB
ejpam-6017	188	16	f(x	f(x	PROPN
ejpam-6017	188	17	)	)	PUNCT
ejpam-6017	188	18	.	.	PUNCT
ejpam-6017	189	1	then	then	ADV
ejpam-6017	189	2	,	,	PUNCT
ejpam-6017	189	3	there	there	PRON
ejpam-6017	189	4	exists	exist	VERB
ejpam-6017	189	5	a	a	DET
ejpam-6017	189	6	τ1τ2	τ1τ2	NOUN
ejpam-6017	189	7	-	-	ADJ
ejpam-6017	189	8	open	open	ADJ
ejpam-6017	189	9	set	set	NOUN
ejpam-6017	189	10	g	g	NOUN
ejpam-6017	189	11	of	of	ADP
ejpam-6017	189	12	x	x	PUNCT
ejpam-6017	189	13	containing	contain	VERB
ejpam-6017	189	14	x	x	PUNCT
ejpam-6017	189	15	such	such	ADJ
ejpam-6017	189	16	that	that	DET
ejpam-6017	189	17	f(g	f(g	NOUN
ejpam-6017	189	18	)	)	PUNCT
ejpam-6017	189	19	⊆	⊆	NUM
ejpam-6017	189	20	v	v	NOUN
ejpam-6017	189	21	.	.	PUNCT
ejpam-6017	190	1	since	since	SCONJ
ejpam-6017	190	2	(	(	PUNCT
ejpam-6017	190	3	x	x	NOUN
ejpam-6017	190	4	,	,	PUNCT
ejpam-6017	190	5	τ1	τ1	NOUN
ejpam-6017	190	6	,	,	PUNCT
ejpam-6017	190	7	τ2	τ2	NOUN
ejpam-6017	190	8	)	)	PUNCT
ejpam-6017	190	9	is	be	AUX
ejpam-6017	190	10	(	(	PUNCT
ejpam-6017	190	11	τ1	τ1	NOUN
ejpam-6017	190	12	,	,	PUNCT
ejpam-6017	190	13	τ2)-regular	τ2)-regular	ADJ
ejpam-6017	190	14	,	,	PUNCT
ejpam-6017	190	15	by	by	ADP
ejpam-6017	190	16	lemma	lemma	PROPN
ejpam-6017	190	17	6	6	NUM
ejpam-6017	190	18	there	there	ADV
ejpam-6017	190	19	exists	exist	VERB
ejpam-6017	190	20	a	a	DET
ejpam-6017	190	21	τ1τ2	τ1τ2	NOUN
ejpam-6017	190	22	-	-	ADJ
ejpam-6017	190	23	open	open	ADJ
ejpam-6017	190	24	set	set	ADJ
ejpam-6017	190	25	u	u	NOUN
ejpam-6017	190	26	of	of	ADP
ejpam-6017	190	27	x	x	SYM
ejpam-6017	190	28	such	such	ADJ
ejpam-6017	190	29	that	that	SCONJ
ejpam-6017	190	30	x	x	SYM
ejpam-6017	190	31	∈	∈	PROPN
ejpam-6017	190	32	u	u	NOUN
ejpam-6017	190	33	⊆	⊆	NUM
ejpam-6017	190	34	τ1τ2	τ1τ2	NOUN
ejpam-6017	190	35	-	-	NOUN
ejpam-6017	190	36	cl(u	cl(u	ADJ
ejpam-6017	190	37	)	)	PUNCT
ejpam-6017	190	38	⊆	⊆	NUM
ejpam-6017	190	39	g.	g.	NOUN
ejpam-6017	190	40	thus	thus	ADV
ejpam-6017	190	41	,	,	PUNCT
ejpam-6017	190	42	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	190	43	-	-	PUNCT
ejpam-6017	190	44	cl(u	cl(u	NOUN
ejpam-6017	190	45	)	)	PUNCT
ejpam-6017	190	46	)	)	PUNCT
ejpam-6017	191	1	⊆	⊆	NUM
ejpam-6017	191	2	v	v	NOUN
ejpam-6017	191	3	.	.	PUNCT
ejpam-6017	192	1	this	this	PRON
ejpam-6017	192	2	shows	show	VERB
ejpam-6017	192	3	that	that	SCONJ
ejpam-6017	192	4	f	f	PROPN
ejpam-6017	192	5	is	be	AUX
ejpam-6017	192	6	strongly	strongly	ADV
ejpam-6017	192	7	θ(τ1	θ(τ1	ADJ
ejpam-6017	192	8	,	,	PUNCT
ejpam-6017	192	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	192	10	.	.	NOUN
ejpam-6017	193	1	4	4	X
ejpam-6017	193	2	.	.	X
ejpam-6017	194	1	some	some	DET
ejpam-6017	194	2	results	result	NOUN
ejpam-6017	194	3	on	on	ADP
ejpam-6017	194	4	strong	strong	ADJ
ejpam-6017	194	5	θ(τ1	θ(τ1	NOUN
ejpam-6017	194	6	,	,	PUNCT
ejpam-6017	194	7	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6017	194	8	recall	recall	VERB
ejpam-6017	194	9	that	that	SCONJ
ejpam-6017	194	10	a	a	DET
ejpam-6017	194	11	bitopological	bitopological	ADJ
ejpam-6017	194	12	space	space	NOUN
ejpam-6017	194	13	(	(	PUNCT
ejpam-6017	194	14	x	x	NOUN
ejpam-6017	194	15	,	,	PUNCT
ejpam-6017	194	16	τ1	τ1	NOUN
ejpam-6017	194	17	,	,	PUNCT
ejpam-6017	194	18	τ2	τ2	NOUN
ejpam-6017	194	19	)	)	PUNCT
ejpam-6017	194	20	is	be	AUX
ejpam-6017	194	21	said	say	VERB
ejpam-6017	194	22	to	to	PART
ejpam-6017	194	23	be	be	AUX
ejpam-6017	194	24	(	(	PUNCT
ejpam-6017	194	25	τ1	τ1	NOUN
ejpam-6017	194	26	,	,	PUNCT
ejpam-6017	194	27	τ2)-t0	τ2)-t0	PRON
ejpam-6017	195	1	[	[	X
ejpam-6017	195	2	34	34	NUM
ejpam-6017	195	3	]	]	X
ejpam-6017	195	4	if	if	SCONJ
ejpam-6017	195	5	for	for	ADP
ejpam-6017	195	6	any	any	DET
ejpam-6017	195	7	pair	pair	NOUN
ejpam-6017	195	8	of	of	ADP
ejpam-6017	195	9	distinct	distinct	ADJ
ejpam-6017	195	10	points	point	NOUN
ejpam-6017	195	11	in	in	ADP
ejpam-6017	195	12	x	x	NOUN
ejpam-6017	195	13	,	,	PUNCT
ejpam-6017	195	14	there	there	PRON
ejpam-6017	195	15	exists	exist	VERB
ejpam-6017	195	16	a	a	DET
ejpam-6017	195	17	τ1τ2	τ1τ2	NOUN
ejpam-6017	195	18	-	-	ADJ
ejpam-6017	195	19	open	open	ADJ
ejpam-6017	195	20	set	set	NOUN
ejpam-6017	195	21	of	of	ADP
ejpam-6017	195	22	x	x	PUNCT
ejpam-6017	195	23	containing	contain	VERB
ejpam-6017	195	24	one	one	NUM
ejpam-6017	195	25	of	of	ADP
ejpam-6017	195	26	the	the	DET
ejpam-6017	195	27	points	point	NOUN
ejpam-6017	195	28	but	but	CCONJ
ejpam-6017	195	29	not	not	PART
ejpam-6017	195	30	the	the	DET
ejpam-6017	195	31	other	other	ADJ
ejpam-6017	195	32	.	.	PUNCT
ejpam-6017	196	1	definition	definition	NOUN
ejpam-6017	196	2	5	5	NUM
ejpam-6017	196	3	.	.	PUNCT
ejpam-6017	197	1	[	[	X
ejpam-6017	197	2	35	35	NUM
ejpam-6017	197	3	]	]	PUNCT
ejpam-6017	197	4	a	a	DET
ejpam-6017	197	5	bitopological	bitopological	ADJ
ejpam-6017	197	6	space	space	NOUN
ejpam-6017	197	7	(	(	PUNCT
ejpam-6017	197	8	x	x	NOUN
ejpam-6017	197	9	,	,	PUNCT
ejpam-6017	197	10	τ1	τ1	NOUN
ejpam-6017	197	11	,	,	PUNCT
ejpam-6017	197	12	τ2	τ2	NOUN
ejpam-6017	197	13	)	)	PUNCT
ejpam-6017	197	14	is	be	AUX
ejpam-6017	197	15	said	say	VERB
ejpam-6017	197	16	to	to	PART
ejpam-6017	197	17	be	be	AUX
ejpam-6017	197	18	(	(	PUNCT
ejpam-6017	197	19	τ1	τ1	NOUN
ejpam-6017	197	20	,	,	PUNCT
ejpam-6017	197	21	τ2)-t2	τ2)-t2	ADJ
ejpam-6017	197	22	if	if	SCONJ
ejpam-6017	197	23	for	for	ADP
ejpam-6017	197	24	any	any	DET
ejpam-6017	197	25	pair	pair	NOUN
ejpam-6017	197	26	of	of	ADP
ejpam-6017	197	27	distinct	distinct	ADJ
ejpam-6017	197	28	points	point	NOUN
ejpam-6017	197	29	x	x	X
ejpam-6017	197	30	,	,	PUNCT
ejpam-6017	197	31	y	y	PROPN
ejpam-6017	197	32	in	in	ADP
ejpam-6017	197	33	x	x	SYM
ejpam-6017	197	34	,	,	PUNCT
ejpam-6017	197	35	there	there	PRON
ejpam-6017	197	36	exist	exist	VERB
ejpam-6017	197	37	disjoint	disjoint	ADJ
ejpam-6017	197	38	τ1τ2	τ1τ2	ADJ
ejpam-6017	197	39	-	-	ADJ
ejpam-6017	197	40	open	open	ADJ
ejpam-6017	197	41	sets	set	NOUN
ejpam-6017	197	42	u	u	NOUN
ejpam-6017	197	43	and	and	CCONJ
ejpam-6017	197	44	v	v	NOUN
ejpam-6017	197	45	of	of	ADP
ejpam-6017	197	46	x	x	PUNCT
ejpam-6017	197	47	containing	contain	VERB
ejpam-6017	197	48	x	x	PROPN
ejpam-6017	197	49	and	and	CCONJ
ejpam-6017	197	50	y	y	PROPN
ejpam-6017	197	51	,	,	PUNCT
ejpam-6017	197	52	respectively	respectively	ADV
ejpam-6017	197	53	.	.	PUNCT
ejpam-6017	198	1	theorem	theorem	VERB
ejpam-6017	198	2	5	5	NUM
ejpam-6017	198	3	.	.	PUNCT
ejpam-6017	199	1	if	if	SCONJ
ejpam-6017	199	2	f	f	PROPN
ejpam-6017	199	3	:	:	PUNCT
ejpam-6017	199	4	(	(	PUNCT
ejpam-6017	199	5	x	x	NOUN
ejpam-6017	199	6	,	,	PUNCT
ejpam-6017	199	7	τ1	τ1	NOUN
ejpam-6017	199	8	,	,	PUNCT
ejpam-6017	199	9	τ2	τ2	NOUN
ejpam-6017	199	10	)	)	PUNCT
ejpam-6017	199	11	→	→	SYM
ejpam-6017	199	12	(	(	PUNCT
ejpam-6017	199	13	y	y	PROPN
ejpam-6017	199	14	,	,	PUNCT
ejpam-6017	199	15	σ1	σ1	PROPN
ejpam-6017	199	16	,	,	PUNCT
ejpam-6017	199	17	σ2	σ2	PROPN
ejpam-6017	199	18	)	)	PUNCT
ejpam-6017	199	19	is	be	AUX
ejpam-6017	199	20	a	a	DET
ejpam-6017	199	21	strongly	strongly	ADV
ejpam-6017	199	22	θ(τ1	θ(τ1	NOUN
ejpam-6017	199	23	,	,	PUNCT
ejpam-6017	199	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	199	25	injection	injection	NOUN
ejpam-6017	199	26	and	and	CCONJ
ejpam-6017	199	27	(	(	PUNCT
ejpam-6017	199	28	y	y	PROPN
ejpam-6017	199	29	,	,	PUNCT
ejpam-6017	199	30	σ1	σ1	PROPN
ejpam-6017	199	31	,	,	PUNCT
ejpam-6017	199	32	σ2	σ2	PROPN
ejpam-6017	199	33	)	)	PUNCT
ejpam-6017	199	34	is	be	AUX
ejpam-6017	199	35	(	(	PUNCT
ejpam-6017	199	36	σ1	σ1	PROPN
ejpam-6017	199	37	,	,	PUNCT
ejpam-6017	199	38	σ2)-t0	σ2)-t0	PRON
ejpam-6017	199	39	,	,	PUNCT
ejpam-6017	199	40	then	then	ADV
ejpam-6017	199	41	(	(	PUNCT
ejpam-6017	199	42	x	x	NOUN
ejpam-6017	199	43	,	,	PUNCT
ejpam-6017	199	44	τ1	τ1	NOUN
ejpam-6017	199	45	,	,	PUNCT
ejpam-6017	199	46	τ2	τ2	NOUN
ejpam-6017	199	47	)	)	PUNCT
ejpam-6017	199	48	is	be	AUX
ejpam-6017	199	49	(	(	PUNCT
ejpam-6017	199	50	τ1	τ1	NOUN
ejpam-6017	199	51	,	,	PUNCT
ejpam-6017	199	52	τ2)-t2	τ2)-t2	PROPN
ejpam-6017	199	53	.	.	PUNCT
ejpam-6017	200	1	proof	proof	NOUN
ejpam-6017	200	2	.	.	PUNCT
ejpam-6017	201	1	suppose	suppose	VERB
ejpam-6017	201	2	that	that	SCONJ
ejpam-6017	201	3	(	(	PUNCT
ejpam-6017	201	4	y	y	PROPN
ejpam-6017	201	5	,	,	PUNCT
ejpam-6017	201	6	σ1	σ1	PROPN
ejpam-6017	201	7	,	,	PUNCT
ejpam-6017	201	8	σ2	σ2	PROPN
ejpam-6017	201	9	)	)	PUNCT
ejpam-6017	201	10	is	be	AUX
ejpam-6017	201	11	(	(	PUNCT
ejpam-6017	201	12	σ1	σ1	PROPN
ejpam-6017	201	13	,	,	PUNCT
ejpam-6017	201	14	σ2)-t0	σ2)-t0	PROPN
ejpam-6017	201	15	.	.	PUNCT
ejpam-6017	202	1	let	let	VERB
ejpam-6017	202	2	x	x	PRON
ejpam-6017	202	3	and	and	CCONJ
ejpam-6017	202	4	y	y	PROPN
ejpam-6017	202	5	be	be	AUX
ejpam-6017	202	6	any	any	DET
ejpam-6017	202	7	distinct	distinct	ADJ
ejpam-6017	202	8	points	point	NOUN
ejpam-6017	202	9	of	of	ADP
ejpam-6017	202	10	x.	x.	NOUN
ejpam-6017	202	11	since	since	SCONJ
ejpam-6017	202	12	f	f	PROPN
ejpam-6017	202	13	is	be	AUX
ejpam-6017	202	14	injective	injective	ADJ
ejpam-6017	202	15	,	,	PUNCT
ejpam-6017	202	16	f(x	f(x	PROPN
ejpam-6017	202	17	)	)	PUNCT
ejpam-6017	202	18	̸=	̸=	PROPN
ejpam-6017	202	19	f(y	f(y	NOUN
ejpam-6017	202	20	)	)	PUNCT
ejpam-6017	202	21	.	.	PUNCT
ejpam-6017	203	1	since	since	SCONJ
ejpam-6017	203	2	(	(	PUNCT
ejpam-6017	203	3	y	y	PROPN
ejpam-6017	203	4	,	,	PUNCT
ejpam-6017	203	5	σ1	σ1	PROPN
ejpam-6017	203	6	,	,	PUNCT
ejpam-6017	203	7	σ2	σ2	PROPN
ejpam-6017	203	8	)	)	PUNCT
ejpam-6017	203	9	is	be	AUX
ejpam-6017	203	10	(	(	PUNCT
ejpam-6017	203	11	σ1	σ1	PROPN
ejpam-6017	203	12	,	,	PUNCT
ejpam-6017	203	13	σ2)-t0	σ2)-t0	PRON
ejpam-6017	203	14	,	,	PUNCT
ejpam-6017	203	15	there	there	PRON
ejpam-6017	203	16	exists	exist	VERB
ejpam-6017	203	17	a	a	DET
ejpam-6017	203	18	σ1σ2open	σ1σ2open	NOUN
ejpam-6017	203	19	set	set	NOUN
ejpam-6017	203	20	v	v	NOUN
ejpam-6017	203	21	of	of	ADP
ejpam-6017	203	22	y	y	PRON
ejpam-6017	203	23	which	which	PRON
ejpam-6017	203	24	either	either	CCONJ
ejpam-6017	203	25	contains	contain	VERB
ejpam-6017	203	26	f(x	f(x	PROPN
ejpam-6017	203	27	)	)	PUNCT
ejpam-6017	203	28	and	and	CCONJ
ejpam-6017	203	29	not	not	PART
ejpam-6017	203	30	f(y	f(y	NOUN
ejpam-6017	203	31	)	)	PUNCT
ejpam-6017	203	32	or	or	CCONJ
ejpam-6017	203	33	contains	contain	VERB
ejpam-6017	203	34	f(y	f(y	NOUN
ejpam-6017	203	35	)	)	PUNCT
ejpam-6017	203	36	and	and	CCONJ
ejpam-6017	203	37	not	not	PART
ejpam-6017	203	38	f(x	f(x	PROPN
ejpam-6017	203	39	)	)	PUNCT
ejpam-6017	203	40	.	.	PUNCT
ejpam-6017	204	1	if	if	SCONJ
ejpam-6017	204	2	the	the	DET
ejpam-6017	204	3	first	first	ADJ
ejpam-6017	204	4	case	case	NOUN
ejpam-6017	204	5	holds	hold	VERB
ejpam-6017	204	6	,	,	PUNCT
ejpam-6017	204	7	then	then	ADV
ejpam-6017	204	8	there	there	PRON
ejpam-6017	204	9	exists	exist	VERB
ejpam-6017	204	10	a	a	DET
ejpam-6017	204	11	τ1τ2	τ1τ2	NOUN
ejpam-6017	204	12	-	-	ADJ
ejpam-6017	204	13	open	open	ADJ
ejpam-6017	204	14	set	set	ADJ
ejpam-6017	204	15	u	u	NOUN
ejpam-6017	204	16	of	of	ADP
ejpam-6017	204	17	x	x	PUNCT
ejpam-6017	204	18	containing	contain	VERB
ejpam-6017	204	19	x	x	PUNCT
ejpam-6017	204	20	such	such	ADJ
ejpam-6017	204	21	that	that	SCONJ
ejpam-6017	204	22	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	204	23	-	-	PUNCT
ejpam-6017	204	24	cl(u	cl(u	NOUN
ejpam-6017	204	25	)	)	PUNCT
ejpam-6017	204	26	)	)	PUNCT
ejpam-6017	205	1	⊆	⊆	NUM
ejpam-6017	205	2	v	v	NOUN
ejpam-6017	205	3	.	.	PUNCT
ejpam-6017	206	1	thus	thus	ADV
ejpam-6017	206	2	,	,	PUNCT
ejpam-6017	206	3	f(y	f(y	NOUN
ejpam-6017	206	4	)	)	PUNCT
ejpam-6017	207	1	̸∈	̸∈	PROPN
ejpam-6017	207	2	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	207	3	-	-	PUNCT
ejpam-6017	207	4	cl(u	cl(u	NOUN
ejpam-6017	207	5	)	)	PUNCT
ejpam-6017	207	6	)	)	PUNCT
ejpam-6017	207	7	and	and	CCONJ
ejpam-6017	207	8	hence	hence	ADV
ejpam-6017	207	9	y	y	PROPN
ejpam-6017	207	10	∈	∈	PROPN
ejpam-6017	207	11	x	x	PUNCT
ejpam-6017	207	12	−	−	ADP
ejpam-6017	207	13	τ1τ2	τ1τ2	NOUN
ejpam-6017	207	14	-	-	NOUN
ejpam-6017	207	15	cl(u	cl(u	NOUN
ejpam-6017	207	16	)	)	PUNCT
ejpam-6017	207	17	=	=	PUNCT
ejpam-6017	207	18	τ1τ2	τ1τ2	NOUN
ejpam-6017	207	19	-	-	ADJ
ejpam-6017	207	20	int(x	int(x	ADJ
ejpam-6017	207	21	−	−	PROPN
ejpam-6017	207	22	u	u	NOUN
ejpam-6017	207	23	)	)	PUNCT
ejpam-6017	207	24	.	.	PUNCT
ejpam-6017	208	1	then	then	ADV
ejpam-6017	208	2	,	,	PUNCT
ejpam-6017	208	3	there	there	PRON
ejpam-6017	208	4	exists	exist	VERB
ejpam-6017	208	5	a	a	DET
ejpam-6017	208	6	τ1τ2	τ1τ2	NOUN
ejpam-6017	208	7	-	-	ADJ
ejpam-6017	208	8	open	open	ADJ
ejpam-6017	208	9	set	set	NOUN
ejpam-6017	208	10	w	w	NOUN
ejpam-6017	208	11	of	of	ADP
ejpam-6017	208	12	x	x	SYM
ejpam-6017	208	13	such	such	ADJ
ejpam-6017	208	14	that	that	SCONJ
ejpam-6017	208	15	y	y	PROPN
ejpam-6017	208	16	∈	∈	PROPN
ejpam-6017	208	17	w	w	ADP
ejpam-6017	208	18	⊆	⊆	NUM
ejpam-6017	209	1	x	x	SYM
ejpam-6017	209	2	−	−	PROPN
ejpam-6017	209	3	u	u	NOUN
ejpam-6017	209	4	.	.	PUNCT
ejpam-6017	210	1	therefore	therefore	ADV
ejpam-6017	210	2	,	,	PUNCT
ejpam-6017	210	3	u	u	NOUN
ejpam-6017	210	4	∩w	∩w	NOUN
ejpam-6017	210	5	=	=	PUNCT
ejpam-6017	210	6	∅.	∅.	ADP
ejpam-6017	210	7	this	this	PRON
ejpam-6017	210	8	shows	show	VERB
ejpam-6017	210	9	that	that	SCONJ
ejpam-6017	210	10	(	(	PUNCT
ejpam-6017	210	11	x	x	NOUN
ejpam-6017	210	12	,	,	PUNCT
ejpam-6017	210	13	τ1	τ1	NOUN
ejpam-6017	210	14	,	,	PUNCT
ejpam-6017	210	15	τ2	τ2	NOUN
ejpam-6017	210	16	)	)	PUNCT
ejpam-6017	210	17	is	be	AUX
ejpam-6017	210	18	(	(	PUNCT
ejpam-6017	210	19	τ1	τ1	NOUN
ejpam-6017	210	20	,	,	PUNCT
ejpam-6017	210	21	τ2)-t2	τ2)-t2	PROPN
ejpam-6017	210	22	.	.	PUNCT
ejpam-6017	211	1	definition	definition	NOUN
ejpam-6017	211	2	6	6	NUM
ejpam-6017	211	3	.	.	PUNCT
ejpam-6017	212	1	[	[	X
ejpam-6017	212	2	36	36	NUM
ejpam-6017	212	3	]	]	PUNCT
ejpam-6017	212	4	a	a	DET
ejpam-6017	212	5	bitopological	bitopological	ADJ
ejpam-6017	212	6	space	space	NOUN
ejpam-6017	212	7	(	(	PUNCT
ejpam-6017	212	8	x	x	NOUN
ejpam-6017	212	9	,	,	PUNCT
ejpam-6017	212	10	τ1	τ1	NOUN
ejpam-6017	212	11	,	,	PUNCT
ejpam-6017	212	12	τ2	τ2	NOUN
ejpam-6017	212	13	)	)	PUNCT
ejpam-6017	212	14	is	be	AUX
ejpam-6017	212	15	said	say	VERB
ejpam-6017	212	16	to	to	PART
ejpam-6017	212	17	be	be	AUX
ejpam-6017	212	18	τ1τ2	τ1τ2	NOUN
ejpam-6017	212	19	-	-	ADJ
ejpam-6017	212	20	urysohn	urysohn	ADJ
ejpam-6017	212	21	if	if	SCONJ
ejpam-6017	212	22	for	for	ADP
ejpam-6017	212	23	each	each	DET
ejpam-6017	212	24	pair	pair	NOUN
ejpam-6017	212	25	of	of	ADP
ejpam-6017	212	26	distinct	distinct	ADJ
ejpam-6017	212	27	points	point	NOUN
ejpam-6017	212	28	x	x	PUNCT
ejpam-6017	212	29	and	and	CCONJ
ejpam-6017	212	30	y	y	PROPN
ejpam-6017	212	31	in	in	ADP
ejpam-6017	212	32	x	x	SYM
ejpam-6017	212	33	,	,	PUNCT
ejpam-6017	212	34	there	there	PRON
ejpam-6017	212	35	exist	exist	VERB
ejpam-6017	212	36	τ1τ2	τ1τ2	ADJ
ejpam-6017	212	37	-	-	ADJ
ejpam-6017	212	38	open	open	ADJ
ejpam-6017	212	39	sets	set	NOUN
ejpam-6017	212	40	u	u	NOUN
ejpam-6017	212	41	and	and	CCONJ
ejpam-6017	212	42	v	v	ADP
ejpam-6017	212	43	such	such	ADJ
ejpam-6017	212	44	that	that	SCONJ
ejpam-6017	212	45	x	x	SYM
ejpam-6017	212	46	∈	∈	PROPN
ejpam-6017	212	47	u	u	NOUN
ejpam-6017	212	48	,	,	PUNCT
ejpam-6017	212	49	y	y	PROPN
ejpam-6017	212	50	∈	∈	PROPN
ejpam-6017	212	51	v	v	NOUN
ejpam-6017	212	52	and	and	CCONJ
ejpam-6017	212	53	τ1τ2	τ1τ2	NOUN
ejpam-6017	212	54	-	-	NOUN
ejpam-6017	212	55	cl(u	cl(u	NOUN
ejpam-6017	212	56	)	)	PUNCT
ejpam-6017	212	57	∩	∩	NOUN
ejpam-6017	212	58	τ1τ2	τ1τ2	NOUN
ejpam-6017	212	59	-	-	NOUN
ejpam-6017	212	60	cl(v	cl(v	X
ejpam-6017	212	61	)	)	PUNCT
ejpam-6017	212	62	=	=	PUNCT
ejpam-6017	212	63	∅.	∅.	NOUN
ejpam-6017	212	64	theorem	theorem	VERB
ejpam-6017	212	65	6	6	NUM
ejpam-6017	212	66	.	.	PUNCT
ejpam-6017	213	1	if	if	SCONJ
ejpam-6017	213	2	f	f	PROPN
ejpam-6017	213	3	:	:	PUNCT
ejpam-6017	213	4	(	(	PUNCT
ejpam-6017	213	5	x	x	NOUN
ejpam-6017	213	6	,	,	PUNCT
ejpam-6017	213	7	τ1	τ1	NOUN
ejpam-6017	213	8	,	,	PUNCT
ejpam-6017	213	9	τ2	τ2	NOUN
ejpam-6017	213	10	)	)	PUNCT
ejpam-6017	213	11	→	→	SYM
ejpam-6017	213	12	(	(	PUNCT
ejpam-6017	213	13	y	y	PROPN
ejpam-6017	213	14	,	,	PUNCT
ejpam-6017	213	15	σ1	σ1	PROPN
ejpam-6017	213	16	,	,	PUNCT
ejpam-6017	213	17	σ2	σ2	PROPN
ejpam-6017	213	18	)	)	PUNCT
ejpam-6017	213	19	is	be	AUX
ejpam-6017	213	20	a	a	DET
ejpam-6017	213	21	strongly	strongly	ADV
ejpam-6017	213	22	θ(τ1	θ(τ1	NOUN
ejpam-6017	213	23	,	,	PUNCT
ejpam-6017	213	24	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	213	25	injection	injection	NOUN
ejpam-6017	213	26	and	and	CCONJ
ejpam-6017	213	27	(	(	PUNCT
ejpam-6017	213	28	y	y	PROPN
ejpam-6017	213	29	,	,	PUNCT
ejpam-6017	213	30	σ1	σ1	PROPN
ejpam-6017	213	31	,	,	PUNCT
ejpam-6017	213	32	σ2	σ2	PROPN
ejpam-6017	213	33	)	)	PUNCT
ejpam-6017	213	34	is	be	AUX
ejpam-6017	213	35	(	(	PUNCT
ejpam-6017	213	36	σ1	σ1	PROPN
ejpam-6017	213	37	,	,	PUNCT
ejpam-6017	213	38	σ2)-t2	σ2)-t2	PROPN
ejpam-6017	213	39	,	,	PUNCT
ejpam-6017	213	40	then	then	ADV
ejpam-6017	213	41	(	(	PUNCT
ejpam-6017	213	42	x	x	NOUN
ejpam-6017	213	43	,	,	PUNCT
ejpam-6017	213	44	τ1	τ1	NOUN
ejpam-6017	213	45	,	,	PUNCT
ejpam-6017	213	46	τ2	τ2	NOUN
ejpam-6017	213	47	)	)	PUNCT
ejpam-6017	213	48	is	be	AUX
ejpam-6017	213	49	τ1τ2	τ1τ2	NOUN
ejpam-6017	213	50	-	-	ADJ
ejpam-6017	213	51	urysohn	urysohn	ADJ
ejpam-6017	213	52	.	.	PUNCT
ejpam-6017	214	1	proof	proof	NOUN
ejpam-6017	214	2	.	.	PUNCT
ejpam-6017	215	1	suppose	suppose	VERB
ejpam-6017	215	2	that	that	SCONJ
ejpam-6017	215	3	(	(	PUNCT
ejpam-6017	215	4	y	y	PROPN
ejpam-6017	215	5	,	,	PUNCT
ejpam-6017	215	6	σ1	σ1	PROPN
ejpam-6017	215	7	,	,	PUNCT
ejpam-6017	215	8	σ2	σ2	PROPN
ejpam-6017	215	9	)	)	PUNCT
ejpam-6017	215	10	is	be	AUX
ejpam-6017	215	11	(	(	PUNCT
ejpam-6017	215	12	σ1	σ1	PROPN
ejpam-6017	215	13	,	,	PUNCT
ejpam-6017	215	14	σ2)-t2	σ2)-t2	PROPN
ejpam-6017	215	15	.	.	PUNCT
ejpam-6017	216	1	let	let	VERB
ejpam-6017	216	2	x	x	PRON
ejpam-6017	216	3	and	and	CCONJ
ejpam-6017	216	4	y	y	PROPN
ejpam-6017	216	5	be	be	AUX
ejpam-6017	216	6	any	any	DET
ejpam-6017	216	7	distinct	distinct	ADJ
ejpam-6017	216	8	points	point	NOUN
ejpam-6017	216	9	of	of	ADP
ejpam-6017	216	10	x.	x.	NOUN
ejpam-6017	216	11	since	since	SCONJ
ejpam-6017	216	12	f	f	PROPN
ejpam-6017	216	13	is	be	AUX
ejpam-6017	216	14	injective	injective	ADJ
ejpam-6017	216	15	,	,	PUNCT
ejpam-6017	216	16	f(x	f(x	PROPN
ejpam-6017	216	17	)	)	PUNCT
ejpam-6017	216	18	̸=	̸=	PROPN
ejpam-6017	216	19	f(y	f(y	NOUN
ejpam-6017	216	20	)	)	PUNCT
ejpam-6017	216	21	.	.	PUNCT
ejpam-6017	217	1	since	since	SCONJ
ejpam-6017	217	2	(	(	PUNCT
ejpam-6017	217	3	y	y	PROPN
ejpam-6017	217	4	,	,	PUNCT
ejpam-6017	217	5	σ1	σ1	PROPN
ejpam-6017	217	6	,	,	PUNCT
ejpam-6017	217	7	σ2	σ2	PROPN
ejpam-6017	217	8	)	)	PUNCT
ejpam-6017	217	9	is	be	AUX
ejpam-6017	217	10	(	(	PUNCT
ejpam-6017	217	11	σ1	σ1	PROPN
ejpam-6017	217	12	,	,	PUNCT
ejpam-6017	217	13	σ2)-t2	σ2)-t2	PROPN
ejpam-6017	217	14	,	,	PUNCT
ejpam-6017	217	15	there	there	PRON
ejpam-6017	217	16	exist	exist	VERB
ejpam-6017	217	17	σ1σ2	σ1σ2	NOUN
ejpam-6017	217	18	-	-	ADJ
ejpam-6017	217	19	open	open	ADJ
ejpam-6017	217	20	sets	set	NOUN
ejpam-6017	217	21	v	v	ADP
ejpam-6017	217	22	and	and	CCONJ
ejpam-6017	217	23	w	w	PROPN
ejpam-6017	217	24	of	of	ADP
ejpam-6017	217	25	y	y	PROPN
ejpam-6017	217	26	containing	contain	VERB
ejpam-6017	217	27	f(x	f(x	PROPN
ejpam-6017	217	28	)	)	PUNCT
ejpam-6017	217	29	and	and	CCONJ
ejpam-6017	217	30	f(y	f(y	NOUN
ejpam-6017	217	31	)	)	PUNCT
ejpam-6017	217	32	,	,	PUNCT
ejpam-6017	217	33	respectively	respectively	ADV
ejpam-6017	217	34	,	,	PUNCT
ejpam-6017	217	35	such	such	ADJ
ejpam-6017	217	36	that	that	DET
ejpam-6017	217	37	v	v	NOUN
ejpam-6017	217	38	∩w	∩w	NOUN
ejpam-6017	217	39	=	=	PUNCT
ejpam-6017	217	40	∅.	∅.	NOUN
ejpam-6017	217	41	since	since	SCONJ
ejpam-6017	217	42	f	f	PROPN
ejpam-6017	217	43	is	be	AUX
ejpam-6017	217	44	strongly	strongly	ADV
ejpam-6017	217	45	θ(τ1	θ(τ1	ADJ
ejpam-6017	217	46	,	,	PUNCT
ejpam-6017	217	47	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	217	48	,	,	PUNCT
ejpam-6017	217	49	there	there	PRON
ejpam-6017	217	50	exist	exist	VERB
ejpam-6017	217	51	τ1τ2	τ1τ2	ADJ
ejpam-6017	217	52	-	-	ADJ
ejpam-6017	217	53	open	open	ADJ
ejpam-6017	217	54	sets	set	NOUN
ejpam-6017	217	55	u	u	NOUN
ejpam-6017	217	56	and	and	CCONJ
ejpam-6017	217	57	g	g	PROPN
ejpam-6017	217	58	of	of	ADP
ejpam-6017	217	59	x	x	PUNCT
ejpam-6017	217	60	containing	contain	VERB
ejpam-6017	217	61	x	x	PROPN
ejpam-6017	217	62	and	and	CCONJ
ejpam-6017	217	63	y	y	PROPN
ejpam-6017	217	64	,	,	PUNCT
ejpam-6017	217	65	respectively	respectively	ADV
ejpam-6017	217	66	,	,	PUNCT
ejpam-6017	217	67	such	such	ADJ
ejpam-6017	217	68	that	that	SCONJ
ejpam-6017	217	69	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	217	70	-	-	PUNCT
ejpam-6017	217	71	cl(u	cl(u	NOUN
ejpam-6017	217	72	)	)	PUNCT
ejpam-6017	217	73	)	)	PUNCT
ejpam-6017	218	1	⊆	⊆	NUM
ejpam-6017	218	2	v	v	NOUN
ejpam-6017	218	3	and	and	CCONJ
ejpam-6017	218	4	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	218	5	-	-	PUNCT
ejpam-6017	218	6	cl(g	cl(g	NOUN
ejpam-6017	218	7	)	)	PUNCT
ejpam-6017	218	8	)	)	PUNCT
ejpam-6017	219	1	⊆	⊆	NUM
ejpam-6017	219	2	w	w	NOUN
ejpam-6017	219	3	.	.	PUNCT
ejpam-6017	220	1	it	it	PRON
ejpam-6017	220	2	follows	follow	VERB
ejpam-6017	220	3	that	that	SCONJ
ejpam-6017	220	4	τ1τ2	τ1τ2	NOUN
ejpam-6017	220	5	-	-	NOUN
ejpam-6017	220	6	cl(u	cl(u	NOUN
ejpam-6017	220	7	)	)	PUNCT
ejpam-6017	220	8	∩	∩	NOUN
ejpam-6017	220	9	τ1τ2	τ1τ2	NOUN
ejpam-6017	220	10	-	-	ADJ
ejpam-6017	220	11	cl(g	cl(g	ADJ
ejpam-6017	220	12	)	)	PUNCT
ejpam-6017	220	13	=	=	NOUN
ejpam-6017	220	14	∅.	∅.	ADP
ejpam-6017	220	15	thus	thus	ADV
ejpam-6017	220	16	,	,	PUNCT
ejpam-6017	220	17	(	(	PUNCT
ejpam-6017	220	18	x	x	NOUN
ejpam-6017	220	19	,	,	PUNCT
ejpam-6017	220	20	τ1	τ1	NOUN
ejpam-6017	220	21	,	,	PUNCT
ejpam-6017	220	22	τ2	τ2	NOUN
ejpam-6017	220	23	)	)	PUNCT
ejpam-6017	220	24	is	be	AUX
ejpam-6017	220	25	τ1τ2	τ1τ2	NOUN
ejpam-6017	220	26	-	-	ADJ
ejpam-6017	220	27	urysohn	urysohn	ADJ
ejpam-6017	220	28	.	.	PUNCT
ejpam-6017	221	1	p.	p.	NOUN
ejpam-6017	221	2	pue	pue	NOUN
ejpam-6017	221	3	-	-	PUNCT
ejpam-6017	221	4	on	on	ADP
ejpam-6017	221	5	,	,	PUNCT
ejpam-6017	221	6	s.	s.	PROPN
ejpam-6017	221	7	sompong	sompong	PROPN
ejpam-6017	221	8	,	,	PUNCT
ejpam-6017	221	9	c.	c.	PROPN
ejpam-6017	221	10	boonpok	boonpok	PROPN
ejpam-6017	221	11	/	/	SYM
ejpam-6017	221	12	eur	eur	PROPN
ejpam-6017	221	13	.	.	PUNCT
ejpam-6017	222	1	j.	j.	PROPN
ejpam-6017	222	2	pure	pure	PROPN
ejpam-6017	222	3	appl	appl	PROPN
ejpam-6017	222	4	.	.	PROPN
ejpam-6017	222	5	math	math	PROPN
ejpam-6017	222	6	,	,	PUNCT
ejpam-6017	222	7	18	18	NUM
ejpam-6017	222	8	(	(	PUNCT
ejpam-6017	222	9	2	2	NUM
ejpam-6017	222	10	)	)	PUNCT
ejpam-6017	222	11	(	(	PUNCT
ejpam-6017	222	12	2025	2025	NUM
ejpam-6017	222	13	)	)	PUNCT
ejpam-6017	222	14	,	,	PUNCT
ejpam-6017	222	15	6017	6017	NUM
ejpam-6017	222	16	8	8	NUM
ejpam-6017	222	17	of	of	ADP
ejpam-6017	222	18	11	11	NUM
ejpam-6017	222	19	definition	definition	NOUN
ejpam-6017	222	20	7	7	NUM
ejpam-6017	222	21	.	.	PUNCT
ejpam-6017	223	1	a	a	DET
ejpam-6017	223	2	function	function	NOUN
ejpam-6017	223	3	f	f	NOUN
ejpam-6017	223	4	:	:	PUNCT
ejpam-6017	223	5	(	(	PUNCT
ejpam-6017	223	6	x	x	NOUN
ejpam-6017	223	7	,	,	PUNCT
ejpam-6017	223	8	τ1	τ1	NOUN
ejpam-6017	223	9	,	,	PUNCT
ejpam-6017	223	10	τ2	τ2	NOUN
ejpam-6017	223	11	)	)	PUNCT
ejpam-6017	223	12	→	→	SYM
ejpam-6017	223	13	(	(	PUNCT
ejpam-6017	223	14	y	y	PROPN
ejpam-6017	223	15	,	,	PUNCT
ejpam-6017	223	16	σ1	σ1	PROPN
ejpam-6017	223	17	,	,	PUNCT
ejpam-6017	223	18	σ2	σ2	PROPN
ejpam-6017	223	19	)	)	PUNCT
ejpam-6017	223	20	is	be	AUX
ejpam-6017	223	21	said	say	VERB
ejpam-6017	223	22	to	to	PART
ejpam-6017	223	23	have	have	VERB
ejpam-6017	223	24	a	a	DET
ejpam-6017	223	25	strongly	strongly	ADV
ejpam-6017	223	26	θ(τ1	θ(τ1	NOUN
ejpam-6017	223	27	,	,	PUNCT
ejpam-6017	223	28	τ2)closed	τ2)closed	ADJ
ejpam-6017	223	29	graph	graph	NOUN
ejpam-6017	223	30	with	with	ADP
ejpam-6017	223	31	respect	respect	NOUN
ejpam-6017	223	32	to	to	ADP
ejpam-6017	223	33	x	x	PRON
ejpam-6017	223	34	if	if	SCONJ
ejpam-6017	223	35	for	for	ADP
ejpam-6017	223	36	each	each	DET
ejpam-6017	223	37	(	(	PUNCT
ejpam-6017	223	38	x	x	NOUN
ejpam-6017	223	39	,	,	PUNCT
ejpam-6017	223	40	y	y	NOUN
ejpam-6017	223	41	)	)	PUNCT
ejpam-6017	223	42	∈	∈	PROPN
ejpam-6017	223	43	(	(	PUNCT
ejpam-6017	223	44	x	x	SYM
ejpam-6017	223	45	×	×	PROPN
ejpam-6017	223	46	y	y	PROPN
ejpam-6017	223	47	)	)	PUNCT
ejpam-6017	223	48	−g(f	−g(f	NOUN
ejpam-6017	223	49	)	)	PUNCT
ejpam-6017	223	50	,	,	PUNCT
ejpam-6017	223	51	there	there	PRON
ejpam-6017	223	52	exist	exist	VERB
ejpam-6017	223	53	a	a	DET
ejpam-6017	223	54	τ1τ2	τ1τ2	NOUN
ejpam-6017	223	55	-	-	ADJ
ejpam-6017	223	56	open	open	ADJ
ejpam-6017	223	57	set	set	ADJ
ejpam-6017	223	58	u	u	NOUN
ejpam-6017	223	59	of	of	ADP
ejpam-6017	223	60	x	x	PUNCT
ejpam-6017	223	61	containing	contain	VERB
ejpam-6017	223	62	x	x	X
ejpam-6017	223	63	and	and	CCONJ
ejpam-6017	223	64	a	a	DET
ejpam-6017	223	65	σ1σ2	σ1σ2	NUM
ejpam-6017	223	66	-	-	ADJ
ejpam-6017	223	67	open	open	ADJ
ejpam-6017	223	68	set	set	NOUN
ejpam-6017	223	69	v	v	NOUN
ejpam-6017	223	70	of	of	ADP
ejpam-6017	223	71	y	y	PROPN
ejpam-6017	223	72	containing	contain	VERB
ejpam-6017	223	73	y	y	PRON
ejpam-6017	223	74	such	such	ADJ
ejpam-6017	223	75	that	that	SCONJ
ejpam-6017	224	1	[	[	X
ejpam-6017	224	2	τ1τ2	τ1τ2	NOUN
ejpam-6017	224	3	-	-	ADJ
ejpam-6017	224	4	cl(u)×	cl(u)×	NOUN
ejpam-6017	224	5	v	v	NOUN
ejpam-6017	224	6	]	]	PUNCT
ejpam-6017	224	7	∩g(f	∩g(f	PROPN
ejpam-6017	224	8	)	)	PUNCT
ejpam-6017	224	9	=	=	PUNCT
ejpam-6017	224	10	∅.	∅.	PRON
ejpam-6017	224	11	lemma	lemma	PROPN
ejpam-6017	224	12	8	8	NUM
ejpam-6017	224	13	.	.	PUNCT
ejpam-6017	225	1	a	a	DET
ejpam-6017	225	2	function	function	NOUN
ejpam-6017	225	3	f	f	NOUN
ejpam-6017	225	4	:	:	PUNCT
ejpam-6017	225	5	(	(	PUNCT
ejpam-6017	225	6	x	x	NOUN
ejpam-6017	225	7	,	,	PUNCT
ejpam-6017	225	8	τ1	τ1	NOUN
ejpam-6017	225	9	,	,	PUNCT
ejpam-6017	225	10	τ2	τ2	NOUN
ejpam-6017	225	11	)	)	PUNCT
ejpam-6017	225	12	→	→	SYM
ejpam-6017	225	13	(	(	PUNCT
ejpam-6017	225	14	y	y	PROPN
ejpam-6017	225	15	,	,	PUNCT
ejpam-6017	225	16	σ1	σ1	PROPN
ejpam-6017	225	17	,	,	PUNCT
ejpam-6017	225	18	σ2	σ2	NOUN
ejpam-6017	225	19	)	)	PUNCT
ejpam-6017	225	20	has	have	VERB
ejpam-6017	225	21	a	a	DET
ejpam-6017	225	22	strongly	strongly	ADV
ejpam-6017	225	23	θ(τ1	θ(τ1	NOUN
ejpam-6017	225	24	,	,	PUNCT
ejpam-6017	225	25	τ2)-closed	τ2)-close	VERB
ejpam-6017	225	26	graph	graph	NOUN
ejpam-6017	225	27	with	with	ADP
ejpam-6017	225	28	respect	respect	NOUN
ejpam-6017	225	29	to	to	ADP
ejpam-6017	225	30	x	x	PUNCT
ejpam-6017	225	31	if	if	SCONJ
ejpam-6017	226	1	and	and	CCONJ
ejpam-6017	226	2	only	only	ADV
ejpam-6017	226	3	if	if	SCONJ
ejpam-6017	226	4	for	for	ADP
ejpam-6017	226	5	each	each	DET
ejpam-6017	226	6	(	(	PUNCT
ejpam-6017	226	7	x	x	NOUN
ejpam-6017	226	8	,	,	PUNCT
ejpam-6017	226	9	y	y	NOUN
ejpam-6017	226	10	)	)	PUNCT
ejpam-6017	226	11	∈	∈	PROPN
ejpam-6017	226	12	(	(	PUNCT
ejpam-6017	226	13	x	x	SYM
ejpam-6017	226	14	×	×	PROPN
ejpam-6017	226	15	y	y	PROPN
ejpam-6017	226	16	)	)	PUNCT
ejpam-6017	226	17	−g(f	−g(f	NOUN
ejpam-6017	226	18	)	)	PUNCT
ejpam-6017	226	19	,	,	PUNCT
ejpam-6017	226	20	there	there	PRON
ejpam-6017	226	21	exist	exist	VERB
ejpam-6017	226	22	a	a	DET
ejpam-6017	226	23	τ1τ2	τ1τ2	NOUN
ejpam-6017	226	24	-	-	ADJ
ejpam-6017	226	25	open	open	ADJ
ejpam-6017	226	26	set	set	ADJ
ejpam-6017	226	27	u	u	NOUN
ejpam-6017	226	28	of	of	ADP
ejpam-6017	226	29	x	x	PUNCT
ejpam-6017	226	30	containing	contain	VERB
ejpam-6017	226	31	x	x	X
ejpam-6017	226	32	and	and	CCONJ
ejpam-6017	226	33	a	a	DET
ejpam-6017	226	34	σ1σ2	σ1σ2	NUM
ejpam-6017	226	35	-	-	ADJ
ejpam-6017	226	36	open	open	ADJ
ejpam-6017	226	37	set	set	NOUN
ejpam-6017	226	38	v	v	NOUN
ejpam-6017	226	39	of	of	ADP
ejpam-6017	226	40	y	y	PROPN
ejpam-6017	226	41	containing	contain	VERB
ejpam-6017	226	42	y	y	PRON
ejpam-6017	226	43	such	such	ADJ
ejpam-6017	226	44	that	that	SCONJ
ejpam-6017	226	45	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	226	46	-	-	PUNCT
ejpam-6017	226	47	cl(u	cl(u	NOUN
ejpam-6017	226	48	)	)	PUNCT
ejpam-6017	226	49	)	)	PUNCT
ejpam-6017	227	1	∩	∩	NOUN
ejpam-6017	227	2	v	v	X
ejpam-6017	227	3	=	=	SYM
ejpam-6017	227	4	∅.	∅.	NOUN
ejpam-6017	227	5	theorem	theorem	VERB
ejpam-6017	227	6	7	7	NUM
ejpam-6017	227	7	.	.	PUNCT
ejpam-6017	228	1	if	if	SCONJ
ejpam-6017	228	2	f	f	PROPN
ejpam-6017	228	3	:	:	PUNCT
ejpam-6017	228	4	(	(	PUNCT
ejpam-6017	228	5	x	x	NOUN
ejpam-6017	228	6	,	,	PUNCT
ejpam-6017	228	7	τ1	τ1	NOUN
ejpam-6017	228	8	,	,	PUNCT
ejpam-6017	228	9	τ2	τ2	NOUN
ejpam-6017	228	10	)	)	PUNCT
ejpam-6017	228	11	→	→	SYM
ejpam-6017	228	12	(	(	PUNCT
ejpam-6017	228	13	y	y	PROPN
ejpam-6017	228	14	,	,	PUNCT
ejpam-6017	228	15	σ1	σ1	PROPN
ejpam-6017	228	16	,	,	PUNCT
ejpam-6017	228	17	σ2	σ2	PROPN
ejpam-6017	228	18	)	)	PUNCT
ejpam-6017	228	19	is	be	AUX
ejpam-6017	228	20	strongly	strongly	ADV
ejpam-6017	228	21	θ(τ1	θ(τ1	ADJ
ejpam-6017	228	22	,	,	PUNCT
ejpam-6017	228	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	228	24	and	and	CCONJ
ejpam-6017	228	25	(	(	PUNCT
ejpam-6017	228	26	y	y	PROPN
ejpam-6017	228	27	,	,	PUNCT
ejpam-6017	228	28	σ1	σ1	PROPN
ejpam-6017	228	29	,	,	PUNCT
ejpam-6017	228	30	σ2	σ2	PROPN
ejpam-6017	228	31	)	)	PUNCT
ejpam-6017	228	32	is	be	AUX
ejpam-6017	228	33	(	(	PUNCT
ejpam-6017	228	34	σ1	σ1	PROPN
ejpam-6017	228	35	,	,	PUNCT
ejpam-6017	228	36	σ2)-t2	σ2)-t2	PROPN
ejpam-6017	228	37	,	,	PUNCT
ejpam-6017	228	38	then	then	ADV
ejpam-6017	228	39	g(f	g(f	PROPN
ejpam-6017	228	40	)	)	PUNCT
ejpam-6017	228	41	is	be	AUX
ejpam-6017	228	42	strongly	strongly	ADV
ejpam-6017	228	43	θ(τ1	θ(τ1	ADJ
ejpam-6017	228	44	,	,	PUNCT
ejpam-6017	228	45	τ2)-closed	τ2)-close	VERB
ejpam-6017	228	46	graph	graph	NOUN
ejpam-6017	228	47	with	with	ADP
ejpam-6017	228	48	respect	respect	NOUN
ejpam-6017	228	49	to	to	ADP
ejpam-6017	228	50	x.	x.	NOUN
ejpam-6017	228	51	proof	proof	NOUN
ejpam-6017	228	52	.	.	PUNCT
ejpam-6017	229	1	let	let	VERB
ejpam-6017	229	2	(	(	PUNCT
ejpam-6017	229	3	x	x	NOUN
ejpam-6017	229	4	,	,	PUNCT
ejpam-6017	229	5	y	y	NOUN
ejpam-6017	229	6	)	)	PUNCT
ejpam-6017	229	7	∈	∈	PROPN
ejpam-6017	229	8	(	(	PUNCT
ejpam-6017	229	9	x	x	SYM
ejpam-6017	229	10	×	×	PROPN
ejpam-6017	229	11	y	y	PROPN
ejpam-6017	229	12	)	)	PUNCT
ejpam-6017	230	1	−	−	PROPN
ejpam-6017	230	2	g(f	g(f	NOUN
ejpam-6017	230	3	)	)	PUNCT
ejpam-6017	230	4	.	.	PUNCT
ejpam-6017	231	1	then	then	ADV
ejpam-6017	231	2	,	,	PUNCT
ejpam-6017	231	3	y	y	PROPN
ejpam-6017	231	4	̸=	̸=	PROPN
ejpam-6017	231	5	f(x	f(x	PROPN
ejpam-6017	231	6	)	)	PUNCT
ejpam-6017	231	7	.	.	PUNCT
ejpam-6017	232	1	since	since	SCONJ
ejpam-6017	232	2	(	(	PUNCT
ejpam-6017	232	3	y	y	PROPN
ejpam-6017	232	4	,	,	PUNCT
ejpam-6017	232	5	σ1	σ1	PROPN
ejpam-6017	232	6	,	,	PUNCT
ejpam-6017	232	7	σ2	σ2	PROPN
ejpam-6017	232	8	)	)	PUNCT
ejpam-6017	232	9	is	be	AUX
ejpam-6017	232	10	(	(	PUNCT
ejpam-6017	232	11	σ1	σ1	PROPN
ejpam-6017	232	12	,	,	PUNCT
ejpam-6017	232	13	σ2)-t2	σ2)-t2	PROPN
ejpam-6017	232	14	,	,	PUNCT
ejpam-6017	232	15	there	there	PRON
ejpam-6017	232	16	exist	exist	VERB
ejpam-6017	232	17	σ1σ2	σ1σ2	NOUN
ejpam-6017	232	18	-	-	ADJ
ejpam-6017	232	19	open	open	ADJ
ejpam-6017	232	20	sets	set	NOUN
ejpam-6017	232	21	v	v	ADP
ejpam-6017	232	22	and	and	CCONJ
ejpam-6017	232	23	w	w	PROPN
ejpam-6017	232	24	of	of	ADP
ejpam-6017	232	25	y	y	PROPN
ejpam-6017	232	26	containing	contain	VERB
ejpam-6017	232	27	f(x	f(x	PROPN
ejpam-6017	232	28	)	)	PUNCT
ejpam-6017	232	29	and	and	CCONJ
ejpam-6017	232	30	f(y	f(y	NOUN
ejpam-6017	232	31	)	)	PUNCT
ejpam-6017	232	32	,	,	PUNCT
ejpam-6017	232	33	respectively	respectively	ADV
ejpam-6017	232	34	,	,	PUNCT
ejpam-6017	232	35	such	such	ADJ
ejpam-6017	232	36	that	that	PRON
ejpam-6017	232	37	v	v	ADP
ejpam-6017	232	38	∩	∩	NOUN
ejpam-6017	232	39	w	w	NOUN
ejpam-6017	232	40	=	=	PUNCT
ejpam-6017	232	41	∅.	∅.	NOUN
ejpam-6017	232	42	since	since	SCONJ
ejpam-6017	232	43	f	f	PROPN
ejpam-6017	232	44	is	be	AUX
ejpam-6017	232	45	strongly	strongly	ADV
ejpam-6017	232	46	θ(τ1	θ(τ1	ADJ
ejpam-6017	232	47	,	,	PUNCT
ejpam-6017	232	48	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	232	49	,	,	PUNCT
ejpam-6017	232	50	there	there	PRON
ejpam-6017	232	51	exist	exist	VERB
ejpam-6017	232	52	a	a	DET
ejpam-6017	232	53	τ1τ2	τ1τ2	NOUN
ejpam-6017	232	54	-	-	ADJ
ejpam-6017	232	55	open	open	ADJ
ejpam-6017	232	56	set	set	ADJ
ejpam-6017	232	57	u	u	NOUN
ejpam-6017	232	58	of	of	ADP
ejpam-6017	232	59	x	x	PUNCT
ejpam-6017	232	60	containing	contain	VERB
ejpam-6017	232	61	x	x	PUNCT
ejpam-6017	232	62	such	such	ADJ
ejpam-6017	232	63	that	that	SCONJ
ejpam-6017	232	64	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	232	65	-	-	PUNCT
ejpam-6017	232	66	cl(u	cl(u	NOUN
ejpam-6017	232	67	)	)	PUNCT
ejpam-6017	232	68	)	)	PUNCT
ejpam-6017	233	1	⊆	⊆	NUM
ejpam-6017	233	2	w	w	NOUN
ejpam-6017	233	3	.	.	PUNCT
ejpam-6017	234	1	this	this	PRON
ejpam-6017	234	2	implies	imply	VERB
ejpam-6017	234	3	that	that	SCONJ
ejpam-6017	234	4	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	234	5	-	-	PUNCT
ejpam-6017	234	6	cl(u	cl(u	NOUN
ejpam-6017	234	7	)	)	PUNCT
ejpam-6017	234	8	)	)	PUNCT
ejpam-6017	234	9	∩	∩	NOUN
ejpam-6017	234	10	v	v	NOUN
ejpam-6017	234	11	=	=	NOUN
ejpam-6017	234	12	∅	∅	NOUN
ejpam-6017	234	13	and	and	CCONJ
ejpam-6017	234	14	by	by	ADP
ejpam-6017	234	15	lemma	lemma	PROPN
ejpam-6017	234	16	8	8	NUM
ejpam-6017	234	17	,	,	PUNCT
ejpam-6017	234	18	g(f	g(f	PROPN
ejpam-6017	234	19	)	)	PUNCT
ejpam-6017	234	20	is	be	AUX
ejpam-6017	234	21	strongly	strongly	ADV
ejpam-6017	234	22	θ(τ1	θ(τ1	ADJ
ejpam-6017	234	23	,	,	PUNCT
ejpam-6017	234	24	τ2)-closed	τ2)-close	VERB
ejpam-6017	234	25	graph	graph	NOUN
ejpam-6017	234	26	with	with	ADP
ejpam-6017	234	27	respect	respect	NOUN
ejpam-6017	234	28	to	to	ADP
ejpam-6017	234	29	x.	x.	NOUN
ejpam-6017	234	30	definition	definition	NOUN
ejpam-6017	234	31	8	8	NUM
ejpam-6017	234	32	.	.	PUNCT
ejpam-6017	235	1	[	[	X
ejpam-6017	235	2	37	37	NUM
ejpam-6017	235	3	]	]	PUNCT
ejpam-6017	235	4	let	let	VERB
ejpam-6017	235	5	a	a	PRON
ejpam-6017	235	6	be	be	AUX
ejpam-6017	235	7	a	a	DET
ejpam-6017	235	8	subset	subset	NOUN
ejpam-6017	235	9	of	of	ADP
ejpam-6017	235	10	a	a	DET
ejpam-6017	235	11	bitopological	bitopological	ADJ
ejpam-6017	235	12	space	space	NOUN
ejpam-6017	235	13	(	(	PUNCT
ejpam-6017	235	14	x	x	NOUN
ejpam-6017	235	15	,	,	PUNCT
ejpam-6017	235	16	τ1	τ1	NOUN
ejpam-6017	235	17	,	,	PUNCT
ejpam-6017	235	18	τ2	τ2	NOUN
ejpam-6017	235	19	)	)	PUNCT
ejpam-6017	235	20	.	.	PUNCT
ejpam-6017	236	1	the	the	DET
ejpam-6017	236	2	(	(	PUNCT
ejpam-6017	236	3	τ1	τ1	NOUN
ejpam-6017	236	4	,	,	PUNCT
ejpam-6017	236	5	τ2)θfrontier	τ2)θfrontier	NOUN
ejpam-6017	236	6	of	of	ADP
ejpam-6017	236	7	a	a	DET
ejpam-6017	236	8	,	,	PUNCT
ejpam-6017	236	9	(	(	PUNCT
ejpam-6017	236	10	τ1	τ1	NOUN
ejpam-6017	236	11	,	,	PUNCT
ejpam-6017	236	12	τ2)θ	τ2)θ	NOUN
ejpam-6017	236	13	-	-	PUNCT
ejpam-6017	236	14	fr(a	fr(a	NUM
ejpam-6017	236	15	)	)	PUNCT
ejpam-6017	236	16	,	,	PUNCT
ejpam-6017	236	17	is	be	AUX
ejpam-6017	236	18	defined	define	VERB
ejpam-6017	236	19	by	by	ADP
ejpam-6017	236	20	(	(	PUNCT
ejpam-6017	236	21	τ1	τ1	NOUN
ejpam-6017	236	22	,	,	PUNCT
ejpam-6017	236	23	τ2)θ	τ2)θ	NOUN
ejpam-6017	236	24	-	-	PUNCT
ejpam-6017	236	25	fr(a	fr(a	NUM
ejpam-6017	236	26	)	)	PUNCT
ejpam-6017	236	27	=	=	SYM
ejpam-6017	236	28	(	(	PUNCT
ejpam-6017	236	29	τ1	τ1	NOUN
ejpam-6017	236	30	,	,	PUNCT
ejpam-6017	236	31	τ2)θ	τ2)θ	NOUN
ejpam-6017	236	32	-	-	PUNCT
ejpam-6017	236	33	cl(a	cl(a	NUM
ejpam-6017	236	34	)	)	PUNCT
ejpam-6017	236	35	∩	∩	NOUN
ejpam-6017	236	36	(	(	PUNCT
ejpam-6017	236	37	τ1	τ1	NOUN
ejpam-6017	236	38	,	,	PUNCT
ejpam-6017	236	39	τ2)θ	τ2)θ	ADJ
ejpam-6017	236	40	-	-	PUNCT
ejpam-6017	236	41	cl(x	cl(x	NOUN
ejpam-6017	236	42	−a	−a	NOUN
ejpam-6017	236	43	)	)	PUNCT
ejpam-6017	236	44	.	.	PUNCT
ejpam-6017	237	1	theorem	theorem	ADJ
ejpam-6017	237	2	8	8	NUM
ejpam-6017	237	3	.	.	PUNCT
ejpam-6017	238	1	the	the	DET
ejpam-6017	238	2	set	set	NOUN
ejpam-6017	238	3	of	of	ADP
ejpam-6017	238	4	all	all	DET
ejpam-6017	238	5	points	point	NOUN
ejpam-6017	238	6	x	x	X
ejpam-6017	238	7	∈	∈	NOUN
ejpam-6017	238	8	x	x	PUNCT
ejpam-6017	238	9	at	at	ADP
ejpam-6017	238	10	which	which	PRON
ejpam-6017	238	11	a	a	DET
ejpam-6017	238	12	function	function	NOUN
ejpam-6017	238	13	f	f	NOUN
ejpam-6017	238	14	:	:	PUNCT
ejpam-6017	238	15	(	(	PUNCT
ejpam-6017	238	16	x	x	NOUN
ejpam-6017	238	17	,	,	PUNCT
ejpam-6017	238	18	τ1	τ1	NOUN
ejpam-6017	238	19	,	,	PUNCT
ejpam-6017	238	20	τ2	τ2	NOUN
ejpam-6017	238	21	)	)	PUNCT
ejpam-6017	238	22	→	→	SYM
ejpam-6017	238	23	(	(	PUNCT
ejpam-6017	238	24	y	y	PROPN
ejpam-6017	238	25	,	,	PUNCT
ejpam-6017	238	26	σ1	σ1	PROPN
ejpam-6017	238	27	,	,	PUNCT
ejpam-6017	238	28	σ2	σ2	PROPN
ejpam-6017	238	29	)	)	PUNCT
ejpam-6017	238	30	is	be	AUX
ejpam-6017	238	31	not	not	PART
ejpam-6017	238	32	strongly	strongly	ADV
ejpam-6017	238	33	θ(τ1	θ(τ1	NOUN
ejpam-6017	238	34	,	,	PUNCT
ejpam-6017	238	35	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	238	36	is	be	AUX
ejpam-6017	238	37	identical	identical	ADJ
ejpam-6017	238	38	with	with	ADP
ejpam-6017	238	39	the	the	DET
ejpam-6017	238	40	union	union	NOUN
ejpam-6017	238	41	of	of	ADP
ejpam-6017	238	42	the	the	DET
ejpam-6017	238	43	(	(	PUNCT
ejpam-6017	238	44	τ1	τ1	NOUN
ejpam-6017	238	45	,	,	PUNCT
ejpam-6017	238	46	τ2)θ	τ2)θ	ADJ
ejpam-6017	238	47	-	-	PUNCT
ejpam-6017	238	48	frontier	frontier	NOUN
ejpam-6017	238	49	of	of	ADP
ejpam-6017	238	50	the	the	DET
ejpam-6017	238	51	inverse	inverse	NOUN
ejpam-6017	238	52	images	image	NOUN
ejpam-6017	238	53	of	of	ADP
ejpam-6017	238	54	σ1σ2	σ1σ2	NOUN
ejpam-6017	238	55	-	-	PUNCT
ejpam-6017	238	56	open	open	ADJ
ejpam-6017	238	57	sets	set	NOUN
ejpam-6017	238	58	containing	contain	VERB
ejpam-6017	238	59	f(x	f(x	PROPN
ejpam-6017	238	60	)	)	PUNCT
ejpam-6017	238	61	.	.	PUNCT
ejpam-6017	239	1	proof	proof	NOUN
ejpam-6017	239	2	.	.	PUNCT
ejpam-6017	240	1	suppose	suppose	VERB
ejpam-6017	240	2	that	that	SCONJ
ejpam-6017	240	3	f	f	PROPN
ejpam-6017	240	4	is	be	AUX
ejpam-6017	240	5	not	not	PART
ejpam-6017	240	6	strongly	strongly	ADV
ejpam-6017	240	7	θ(τ1	θ(τ1	NOUN
ejpam-6017	240	8	,	,	PUNCT
ejpam-6017	240	9	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	240	10	.	.	PUNCT
ejpam-6017	241	1	then	then	ADV
ejpam-6017	241	2	,	,	PUNCT
ejpam-6017	241	3	there	there	PRON
ejpam-6017	241	4	exists	exist	VERB
ejpam-6017	241	5	a	a	DET
ejpam-6017	241	6	σ1σ2open	σ1σ2open	NOUN
ejpam-6017	241	7	set	set	NOUN
ejpam-6017	241	8	v	v	NOUN
ejpam-6017	241	9	of	of	ADP
ejpam-6017	241	10	y	y	NOUN
ejpam-6017	241	11	containing	contain	VERB
ejpam-6017	241	12	f(x	f(x	PROPN
ejpam-6017	241	13	)	)	PUNCT
ejpam-6017	241	14	such	such	ADJ
ejpam-6017	241	15	that	that	SCONJ
ejpam-6017	241	16	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	241	17	-	-	PUNCT
ejpam-6017	241	18	cl(u	cl(u	NOUN
ejpam-6017	241	19	)	)	PUNCT
ejpam-6017	241	20	)	)	PUNCT
ejpam-6017	241	21	is	be	AUX
ejpam-6017	241	22	not	not	PART
ejpam-6017	241	23	contained	contain	VERB
ejpam-6017	241	24	in	in	ADP
ejpam-6017	241	25	v	v	NOUN
ejpam-6017	241	26	for	for	ADP
ejpam-6017	241	27	every	every	DET
ejpam-6017	241	28	τ1τ2	τ1τ2	ADJ
ejpam-6017	241	29	-	-	ADJ
ejpam-6017	241	30	open	open	ADJ
ejpam-6017	241	31	set	set	ADJ
ejpam-6017	241	32	u	u	NOUN
ejpam-6017	241	33	of	of	ADP
ejpam-6017	241	34	x	x	SYM
ejpam-6017	241	35	containing	contain	VERB
ejpam-6017	241	36	x.	x.	NOUN
ejpam-6017	241	37	then	then	ADV
ejpam-6017	241	38	,	,	PUNCT
ejpam-6017	241	39	τ1τ2	τ1τ2	NOUN
ejpam-6017	241	40	-	-	NOUN
ejpam-6017	241	41	cl(u	cl(u	ADJ
ejpam-6017	241	42	)	)	PUNCT
ejpam-6017	241	43	∩	∩	NOUN
ejpam-6017	241	44	(	(	PUNCT
ejpam-6017	241	45	x	x	SYM
ejpam-6017	241	46	−	−	PROPN
ejpam-6017	241	47	f−1(v	f−1(v	NOUN
ejpam-6017	241	48	)	)	PUNCT
ejpam-6017	241	49	)	)	PUNCT
ejpam-6017	242	1	̸=	̸=	NOUN
ejpam-6017	242	2	∅	∅	NOUN
ejpam-6017	242	3	for	for	ADP
ejpam-6017	242	4	every	every	DET
ejpam-6017	242	5	τ1τ2open	τ1τ2open	NUM
ejpam-6017	242	6	set	set	VERB
ejpam-6017	242	7	u	u	NOUN
ejpam-6017	242	8	of	of	ADP
ejpam-6017	242	9	x	x	SYM
ejpam-6017	242	10	containing	contain	VERB
ejpam-6017	242	11	x.	x.	NOUN
ejpam-6017	242	12	thus	thus	ADV
ejpam-6017	242	13	,	,	PUNCT
ejpam-6017	242	14	x	x	SYM
ejpam-6017	242	15	∈	∈	PROPN
ejpam-6017	242	16	(	(	PUNCT
ejpam-6017	242	17	τ1	τ1	NOUN
ejpam-6017	242	18	,	,	PUNCT
ejpam-6017	242	19	τ2)θ	τ2)θ	ADJ
ejpam-6017	242	20	-	-	PUNCT
ejpam-6017	242	21	cl(x	cl(x	PUNCT
ejpam-6017	242	22	−	−	PROPN
ejpam-6017	242	23	f−1(v	f−1(v	PROPN
ejpam-6017	242	24	)	)	PUNCT
ejpam-6017	242	25	)	)	PUNCT
ejpam-6017	242	26	.	.	PUNCT
ejpam-6017	243	1	on	on	ADP
ejpam-6017	243	2	the	the	DET
ejpam-6017	243	3	other	other	ADJ
ejpam-6017	243	4	hand	hand	NOUN
ejpam-6017	243	5	,	,	PUNCT
ejpam-6017	243	6	we	we	PRON
ejpam-6017	243	7	have	have	VERB
ejpam-6017	243	8	x	x	X
ejpam-6017	243	9	∈	∈	PROPN
ejpam-6017	243	10	f−1(v	f−1(v	NOUN
ejpam-6017	243	11	)	)	PUNCT
ejpam-6017	244	1	⊆	⊆	NUM
ejpam-6017	244	2	(	(	PUNCT
ejpam-6017	244	3	τ1	τ1	NOUN
ejpam-6017	244	4	,	,	PUNCT
ejpam-6017	244	5	τ2)θ	τ2)θ	PROPN
ejpam-6017	244	6	-	-	PUNCT
ejpam-6017	244	7	cl(f	cl(f	PROPN
ejpam-6017	244	8	−1(v	−1(v	PROPN
ejpam-6017	244	9	)	)	PUNCT
ejpam-6017	244	10	)	)	PUNCT
ejpam-6017	244	11	and	and	CCONJ
ejpam-6017	244	12	hence	hence	ADV
ejpam-6017	244	13	x	x	X
ejpam-6017	244	14	∈	∈	PROPN
ejpam-6017	244	15	(	(	PUNCT
ejpam-6017	244	16	τ1	τ1	NOUN
ejpam-6017	244	17	,	,	PUNCT
ejpam-6017	244	18	τ2)θ	τ2)θ	ADJ
ejpam-6017	244	19	-	-	PUNCT
ejpam-6017	244	20	fr(f	fr(f	NOUN
ejpam-6017	244	21	−1(v	−1(v	NOUN
ejpam-6017	244	22	)	)	PUNCT
ejpam-6017	244	23	)	)	PUNCT
ejpam-6017	244	24	.	.	PUNCT
ejpam-6017	245	1	conversely	conversely	ADV
ejpam-6017	245	2	,	,	PUNCT
ejpam-6017	245	3	suppose	suppose	VERB
ejpam-6017	245	4	that	that	SCONJ
ejpam-6017	245	5	f	f	PROPN
ejpam-6017	245	6	is	be	AUX
ejpam-6017	245	7	strongly	strongly	ADV
ejpam-6017	245	8	θ(τ1	θ(τ1	ADJ
ejpam-6017	245	9	,	,	PUNCT
ejpam-6017	245	10	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	245	11	at	at	ADP
ejpam-6017	245	12	x	x	SYM
ejpam-6017	245	13	∈	∈	PROPN
ejpam-6017	245	14	x.	x.	NOUN
ejpam-6017	245	15	let	let	VERB
ejpam-6017	245	16	v	v	PART
ejpam-6017	245	17	be	be	AUX
ejpam-6017	245	18	any	any	DET
ejpam-6017	245	19	σ1σ2	σ1σ2	NOUN
ejpam-6017	245	20	-	-	ADJ
ejpam-6017	245	21	open	open	ADJ
ejpam-6017	245	22	set	set	NOUN
ejpam-6017	245	23	of	of	ADP
ejpam-6017	245	24	y	y	PROPN
ejpam-6017	245	25	containing	contain	VERB
ejpam-6017	245	26	f(x	f(x	PROPN
ejpam-6017	245	27	)	)	PUNCT
ejpam-6017	245	28	.	.	PUNCT
ejpam-6017	246	1	by	by	ADP
ejpam-6017	246	2	theorem	theorem	NOUN
ejpam-6017	246	3	1	1	NUM
ejpam-6017	246	4	,	,	PUNCT
ejpam-6017	246	5	x	x	SYM
ejpam-6017	246	6	∈	∈	PROPN
ejpam-6017	246	7	(	(	PUNCT
ejpam-6017	246	8	τ1	τ1	NOUN
ejpam-6017	246	9	,	,	PUNCT
ejpam-6017	246	10	τ2)θ	τ2)θ	NOUN
ejpam-6017	246	11	-	-	PUNCT
ejpam-6017	246	12	int(f	int(f	PROPN
ejpam-6017	246	13	−1(v	−1(v	NOUN
ejpam-6017	246	14	)	)	PUNCT
ejpam-6017	246	15	)	)	PUNCT
ejpam-6017	246	16	.	.	PUNCT
ejpam-6017	247	1	thus	thus	ADV
ejpam-6017	247	2	,	,	PUNCT
ejpam-6017	247	3	x	x	PROPN
ejpam-6017	247	4	̸∈	̸∈	PROPN
ejpam-6017	247	5	(	(	PUNCT
ejpam-6017	247	6	τ1	τ1	PROPN
ejpam-6017	247	7	,	,	PUNCT
ejpam-6017	247	8	τ2)θ	τ2)θ	ADJ
ejpam-6017	247	9	-	-	PUNCT
ejpam-6017	247	10	fr(f	fr(f	NOUN
ejpam-6017	247	11	−1(v	−1(v	NOUN
ejpam-6017	247	12	)	)	PUNCT
ejpam-6017	247	13	)	)	PUNCT
ejpam-6017	247	14	for	for	ADP
ejpam-6017	247	15	every	every	DET
ejpam-6017	247	16	σ1σ2	σ1σ2	NOUN
ejpam-6017	247	17	-	-	ADJ
ejpam-6017	247	18	open	open	ADJ
ejpam-6017	247	19	set	set	NOUN
ejpam-6017	247	20	v	v	NOUN
ejpam-6017	247	21	of	of	ADP
ejpam-6017	247	22	y	y	NOUN
ejpam-6017	247	23	containing	contain	VERB
ejpam-6017	247	24	f(x	f(x	PROPN
ejpam-6017	247	25	)	)	PUNCT
ejpam-6017	247	26	.	.	PUNCT
ejpam-6017	248	1	this	this	PRON
ejpam-6017	248	2	completes	complete	VERB
ejpam-6017	248	3	the	the	DET
ejpam-6017	248	4	proof	proof	NOUN
ejpam-6017	248	5	.	.	PUNCT
ejpam-6017	249	1	recall	recall	VERB
ejpam-6017	249	2	that	that	SCONJ
ejpam-6017	249	3	a	a	DET
ejpam-6017	249	4	bitopological	bitopological	ADJ
ejpam-6017	249	5	space	space	NOUN
ejpam-6017	249	6	(	(	PUNCT
ejpam-6017	249	7	x	x	NOUN
ejpam-6017	249	8	,	,	PUNCT
ejpam-6017	249	9	τ1	τ1	NOUN
ejpam-6017	249	10	,	,	PUNCT
ejpam-6017	249	11	τ2	τ2	NOUN
ejpam-6017	249	12	)	)	PUNCT
ejpam-6017	249	13	is	be	AUX
ejpam-6017	249	14	said	say	VERB
ejpam-6017	249	15	to	to	PART
ejpam-6017	249	16	be	be	AUX
ejpam-6017	249	17	quasi	quasi	X
ejpam-6017	249	18	(	(	PUNCT
ejpam-6017	249	19	τ1	τ1	NOUN
ejpam-6017	249	20	,	,	PUNCT
ejpam-6017	249	21	τ2)-h	τ2)-h	PUNCT
ejpam-6017	249	22	-closed	-closed	ADJ
ejpam-6017	250	1	[	[	PUNCT
ejpam-6017	250	2	38	38	NUM
ejpam-6017	250	3	]	]	PUNCT
ejpam-6017	250	4	if	if	SCONJ
ejpam-6017	250	5	every	every	DET
ejpam-6017	250	6	τ1τ2	τ1τ2	ADJ
ejpam-6017	250	7	-	-	ADJ
ejpam-6017	250	8	open	open	ADJ
ejpam-6017	250	9	cover	cover	NOUN
ejpam-6017	250	10	{	{	PUNCT
ejpam-6017	250	11	uγ	uγ	ADV
ejpam-6017	250	12	|	|	ADV
ejpam-6017	250	13	γ	γ	X
ejpam-6017	250	14	∈	∈	PROPN
ejpam-6017	250	15	γ	γ	X
ejpam-6017	250	16	}	}	PUNCT
ejpam-6017	250	17	,	,	PUNCT
ejpam-6017	250	18	there	there	PRON
ejpam-6017	250	19	exists	exist	VERB
ejpam-6017	250	20	a	a	DET
ejpam-6017	250	21	finite	finite	NOUN
ejpam-6017	250	22	subset	subset	NOUN
ejpam-6017	250	23	γ0	γ0	NOUN
ejpam-6017	250	24	of	of	ADP
ejpam-6017	250	25	γ	γ	NOUN
ejpam-6017	251	1	such	such	ADJ
ejpam-6017	251	2	that	that	SCONJ
ejpam-6017	251	3	x	x	X
ejpam-6017	251	4	=	=	PUNCT
ejpam-6017	251	5	∪{τ1τ2	∪{τ1τ2	NOUN
ejpam-6017	251	6	-	-	NOUN
ejpam-6017	251	7	cl(uγ	cl(uγ	NOUN
ejpam-6017	251	8	)	)	PUNCT
ejpam-6017	251	9	|	|	ADV
ejpam-6017	251	10	γ	γ	PROPN
ejpam-6017	251	11	∈	∈	PROPN
ejpam-6017	251	12	γ0	γ0	PROPN
ejpam-6017	251	13	}	}	PUNCT
ejpam-6017	251	14	.	.	PUNCT
ejpam-6017	252	1	a	a	DET
ejpam-6017	252	2	subset	subset	NOUN
ejpam-6017	252	3	k	k	NOUN
ejpam-6017	252	4	of	of	ADP
ejpam-6017	252	5	a	a	DET
ejpam-6017	252	6	bitopological	bitopological	ADJ
ejpam-6017	252	7	space	space	NOUN
ejpam-6017	252	8	(	(	PUNCT
ejpam-6017	252	9	x	x	NOUN
ejpam-6017	252	10	,	,	PUNCT
ejpam-6017	252	11	τ1	τ1	NOUN
ejpam-6017	252	12	,	,	PUNCT
ejpam-6017	252	13	τ2	τ2	NOUN
ejpam-6017	252	14	)	)	PUNCT
ejpam-6017	252	15	is	be	AUX
ejpam-6017	252	16	said	say	VERB
ejpam-6017	252	17	to	to	PART
ejpam-6017	252	18	be	be	AUX
ejpam-6017	252	19	quasi	quasi	X
ejpam-6017	252	20	(	(	PUNCT
ejpam-6017	252	21	τ1	τ1	NOUN
ejpam-6017	252	22	,	,	PUNCT
ejpam-6017	252	23	τ2)-h	τ2)-h	NOUN
ejpam-6017	252	24	-closed	-close	VERB
ejpam-6017	252	25	relative	relative	ADJ
ejpam-6017	252	26	to	to	ADP
ejpam-6017	252	27	(	(	PUNCT
ejpam-6017	252	28	x	x	NOUN
ejpam-6017	252	29	,	,	PUNCT
ejpam-6017	252	30	τ1	τ1	NOUN
ejpam-6017	252	31	,	,	PUNCT
ejpam-6017	252	32	τ2	τ2	NOUN
ejpam-6017	252	33	)	)	PUNCT
ejpam-6017	252	34	if	if	SCONJ
ejpam-6017	252	35	for	for	ADP
ejpam-6017	252	36	any	any	DET
ejpam-6017	252	37	cover	cover	NOUN
ejpam-6017	252	38	{	{	PUNCT
ejpam-6017	252	39	vγ	vγ	NOUN
ejpam-6017	252	40	|	|	ADV
ejpam-6017	252	41	γ	γ	PROPN
ejpam-6017	252	42	∈	∈	PROPN
ejpam-6017	252	43	γ	γ	X
ejpam-6017	252	44	}	}	PUNCT
ejpam-6017	252	45	by	by	ADP
ejpam-6017	252	46	τ1τ2	τ1τ2	ADJ
ejpam-6017	252	47	-	-	ADJ
ejpam-6017	252	48	open	open	ADJ
ejpam-6017	252	49	sets	set	NOUN
ejpam-6017	252	50	of	of	ADP
ejpam-6017	252	51	x	x	NOUN
ejpam-6017	252	52	,	,	PUNCT
ejpam-6017	252	53	there	there	PRON
ejpam-6017	252	54	exists	exist	VERB
ejpam-6017	252	55	a	a	DET
ejpam-6017	252	56	finite	finite	NOUN
ejpam-6017	252	57	subset	subset	NOUN
ejpam-6017	252	58	γ0	γ0	NOUN
ejpam-6017	252	59	of	of	ADP
ejpam-6017	252	60	γ	γ	PRON
ejpam-6017	252	61	such	such	ADJ
ejpam-6017	252	62	that	that	SCONJ
ejpam-6017	252	63	k	k	PROPN
ejpam-6017	252	64	⊆	⊆	NUM
ejpam-6017	252	65	∪{τ1τ2	∪{τ1τ2	ADJ
ejpam-6017	252	66	-	-	ADJ
ejpam-6017	252	67	cl(vγ	cl(vγ	ADJ
ejpam-6017	252	68	)	)	PUNCT
ejpam-6017	252	69	|	|	ADV
ejpam-6017	252	70	γ	γ	PROPN
ejpam-6017	252	71	∈	∈	PROPN
ejpam-6017	252	72	γ0	γ0	PROPN
ejpam-6017	252	73	}	}	PUNCT
ejpam-6017	252	74	.	.	PUNCT
ejpam-6017	253	1	a	a	DET
ejpam-6017	253	2	subset	subset	NOUN
ejpam-6017	253	3	k	k	NOUN
ejpam-6017	253	4	of	of	ADP
ejpam-6017	253	5	a	a	DET
ejpam-6017	253	6	bitopological	bitopological	ADJ
ejpam-6017	253	7	space	space	NOUN
ejpam-6017	253	8	(	(	PUNCT
ejpam-6017	253	9	x	x	NOUN
ejpam-6017	253	10	,	,	PUNCT
ejpam-6017	253	11	τ1	τ1	NOUN
ejpam-6017	253	12	,	,	PUNCT
ejpam-6017	253	13	τ2	τ2	NOUN
ejpam-6017	253	14	)	)	PUNCT
ejpam-6017	253	15	is	be	AUX
ejpam-6017	253	16	said	say	VERB
ejpam-6017	253	17	to	to	PART
ejpam-6017	253	18	be	be	AUX
ejpam-6017	253	19	τ1τ2	τ1τ2	ADJ
ejpam-6017	253	20	-	-	ADJ
ejpam-6017	253	21	compact	compact	ADJ
ejpam-6017	253	22	relative	relative	NOUN
ejpam-6017	253	23	to	to	ADP
ejpam-6017	253	24	(	(	PUNCT
ejpam-6017	253	25	x	x	NOUN
ejpam-6017	253	26	,	,	PUNCT
ejpam-6017	253	27	τ1	τ1	NOUN
ejpam-6017	253	28	,	,	PUNCT
ejpam-6017	253	29	τ2	τ2	NOUN
ejpam-6017	253	30	)	)	PUNCT
ejpam-6017	253	31	if	if	SCONJ
ejpam-6017	253	32	for	for	ADP
ejpam-6017	253	33	p.	p.	NOUN
ejpam-6017	253	34	pue	pue	NOUN
ejpam-6017	253	35	-	-	PUNCT
ejpam-6017	253	36	on	on	ADP
ejpam-6017	253	37	,	,	PUNCT
ejpam-6017	253	38	s.	s.	PROPN
ejpam-6017	253	39	sompong	sompong	PROPN
ejpam-6017	253	40	,	,	PUNCT
ejpam-6017	253	41	c.	c.	PROPN
ejpam-6017	253	42	boonpok	boonpok	PROPN
ejpam-6017	253	43	/	/	SYM
ejpam-6017	253	44	eur	eur	PROPN
ejpam-6017	253	45	.	.	PUNCT
ejpam-6017	254	1	j.	j.	PROPN
ejpam-6017	254	2	pure	pure	PROPN
ejpam-6017	254	3	appl	appl	PROPN
ejpam-6017	254	4	.	.	PROPN
ejpam-6017	254	5	math	math	PROPN
ejpam-6017	254	6	,	,	PUNCT
ejpam-6017	254	7	18	18	NUM
ejpam-6017	254	8	(	(	PUNCT
ejpam-6017	254	9	2	2	NUM
ejpam-6017	254	10	)	)	PUNCT
ejpam-6017	254	11	(	(	PUNCT
ejpam-6017	254	12	2025	2025	NUM
ejpam-6017	254	13	)	)	PUNCT
ejpam-6017	254	14	,	,	PUNCT
ejpam-6017	254	15	6017	6017	NUM
ejpam-6017	254	16	9	9	NUM
ejpam-6017	254	17	of	of	ADP
ejpam-6017	254	18	11	11	NUM
ejpam-6017	254	19	any	any	DET
ejpam-6017	254	20	cover	cover	NOUN
ejpam-6017	254	21	{	{	PUNCT
ejpam-6017	254	22	vγ	vγ	NOUN
ejpam-6017	254	23	|	|	ADV
ejpam-6017	254	24	γ	γ	PROPN
ejpam-6017	254	25	∈	∈	PROPN
ejpam-6017	254	26	γ	γ	X
ejpam-6017	254	27	}	}	PUNCT
ejpam-6017	254	28	by	by	ADP
ejpam-6017	254	29	τ1τ2	τ1τ2	ADJ
ejpam-6017	254	30	-	-	ADJ
ejpam-6017	254	31	open	open	ADJ
ejpam-6017	254	32	sets	set	NOUN
ejpam-6017	254	33	of	of	ADP
ejpam-6017	254	34	x	x	NOUN
ejpam-6017	254	35	,	,	PUNCT
ejpam-6017	254	36	there	there	PRON
ejpam-6017	254	37	exists	exist	VERB
ejpam-6017	254	38	a	a	DET
ejpam-6017	254	39	finite	finite	NOUN
ejpam-6017	254	40	subset	subset	NOUN
ejpam-6017	254	41	γ0	γ0	NOUN
ejpam-6017	254	42	of	of	ADP
ejpam-6017	254	43	γ	γ	PRON
ejpam-6017	254	44	such	such	ADJ
ejpam-6017	254	45	that	that	SCONJ
ejpam-6017	255	1	k	k	PROPN
ejpam-6017	255	2	⊆	⊆	NUM
ejpam-6017	255	3	∪{vγ	∪{vγ	PROPN
ejpam-6017	255	4	|	|	ADV
ejpam-6017	255	5	γ	γ	PROPN
ejpam-6017	255	6	∈	∈	PROPN
ejpam-6017	255	7	γ0	γ0	NOUN
ejpam-6017	255	8	}	}	PUNCT
ejpam-6017	255	9	.	.	PUNCT
ejpam-6017	256	1	if	if	SCONJ
ejpam-6017	256	2	x	x	PRON
ejpam-6017	256	3	is	be	AUX
ejpam-6017	256	4	τ1τ2	τ1τ2	ADJ
ejpam-6017	256	5	-	-	ADJ
ejpam-6017	256	6	compact	compact	ADJ
ejpam-6017	256	7	relative	relative	NOUN
ejpam-6017	256	8	to	to	ADP
ejpam-6017	256	9	(	(	PUNCT
ejpam-6017	256	10	x	x	NOUN
ejpam-6017	256	11	,	,	PUNCT
ejpam-6017	256	12	τ1	τ1	NOUN
ejpam-6017	256	13	,	,	PUNCT
ejpam-6017	256	14	τ2	τ2	NOUN
ejpam-6017	256	15	)	)	PUNCT
ejpam-6017	256	16	,	,	PUNCT
ejpam-6017	256	17	then	then	ADV
ejpam-6017	256	18	(	(	PUNCT
ejpam-6017	256	19	x	x	NOUN
ejpam-6017	256	20	,	,	PUNCT
ejpam-6017	256	21	τ1	τ1	NOUN
ejpam-6017	256	22	,	,	PUNCT
ejpam-6017	256	23	τ2	τ2	NOUN
ejpam-6017	256	24	)	)	PUNCT
ejpam-6017	256	25	is	be	AUX
ejpam-6017	256	26	said	say	VERB
ejpam-6017	256	27	to	to	PART
ejpam-6017	256	28	be	be	AUX
ejpam-6017	256	29	τ1τ2	τ1τ2	NOUN
ejpam-6017	256	30	-	-	ADJ
ejpam-6017	256	31	compact	compact	ADJ
ejpam-6017	256	32	[	[	X
ejpam-6017	256	33	27	27	NUM
ejpam-6017	256	34	]	]	PUNCT
ejpam-6017	256	35	.	.	PUNCT
ejpam-6017	257	1	theorem	theorem	VERB
ejpam-6017	257	2	9	9	NUM
ejpam-6017	257	3	.	.	PUNCT
ejpam-6017	258	1	if	if	SCONJ
ejpam-6017	258	2	f	f	PROPN
ejpam-6017	258	3	:	:	PUNCT
ejpam-6017	258	4	(	(	PUNCT
ejpam-6017	258	5	x	x	NOUN
ejpam-6017	258	6	,	,	PUNCT
ejpam-6017	258	7	τ1	τ1	NOUN
ejpam-6017	258	8	,	,	PUNCT
ejpam-6017	258	9	τ2	τ2	NOUN
ejpam-6017	258	10	)	)	PUNCT
ejpam-6017	258	11	→	→	SYM
ejpam-6017	258	12	(	(	PUNCT
ejpam-6017	258	13	y	y	PROPN
ejpam-6017	258	14	,	,	PUNCT
ejpam-6017	258	15	σ1	σ1	PROPN
ejpam-6017	258	16	,	,	PUNCT
ejpam-6017	258	17	σ2	σ2	PROPN
ejpam-6017	258	18	)	)	PUNCT
ejpam-6017	258	19	is	be	AUX
ejpam-6017	258	20	strongly	strongly	ADV
ejpam-6017	258	21	θ(τ1	θ(τ1	ADJ
ejpam-6017	258	22	,	,	PUNCT
ejpam-6017	258	23	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	258	24	and	and	CCONJ
ejpam-6017	258	25	k	k	PROPN
ejpam-6017	258	26	is	be	AUX
ejpam-6017	258	27	quasi	quasi	NOUN
ejpam-6017	258	28	(	(	PUNCT
ejpam-6017	258	29	τ1	τ1	NOUN
ejpam-6017	258	30	,	,	PUNCT
ejpam-6017	258	31	τ2)-h	τ2)-h	NOUN
ejpam-6017	258	32	-closed	-close	VERB
ejpam-6017	258	33	relative	relative	ADJ
ejpam-6017	258	34	to	to	ADP
ejpam-6017	258	35	(	(	PUNCT
ejpam-6017	258	36	x	x	NOUN
ejpam-6017	258	37	,	,	PUNCT
ejpam-6017	258	38	τ1	τ1	NOUN
ejpam-6017	258	39	,	,	PUNCT
ejpam-6017	258	40	τ2	τ2	NOUN
ejpam-6017	258	41	)	)	PUNCT
ejpam-6017	258	42	,	,	PUNCT
ejpam-6017	258	43	then	then	ADV
ejpam-6017	258	44	f(k	f(k	VERB
ejpam-6017	258	45	)	)	PUNCT
ejpam-6017	258	46	is	be	AUX
ejpam-6017	258	47	σ1σ2	σ1σ2	NOUN
ejpam-6017	258	48	-	-	ADJ
ejpam-6017	258	49	compact	compact	ADJ
ejpam-6017	258	50	relative	relative	NOUN
ejpam-6017	258	51	to	to	ADP
ejpam-6017	258	52	(	(	PUNCT
ejpam-6017	258	53	y	y	PROPN
ejpam-6017	258	54	,	,	PUNCT
ejpam-6017	258	55	σ1	σ1	PROPN
ejpam-6017	258	56	,	,	PUNCT
ejpam-6017	258	57	σ2	σ2	NOUN
ejpam-6017	258	58	)	)	PUNCT
ejpam-6017	258	59	.	.	PUNCT
ejpam-6017	259	1	proof	proof	NOUN
ejpam-6017	259	2	.	.	PUNCT
ejpam-6017	260	1	let	let	VERB
ejpam-6017	260	2	k	k	X
ejpam-6017	260	3	be	be	AUX
ejpam-6017	260	4	quasi	quasi	X
ejpam-6017	260	5	(	(	PUNCT
ejpam-6017	260	6	τ1	τ1	NOUN
ejpam-6017	260	7	,	,	PUNCT
ejpam-6017	260	8	τ2)-h	τ2)-h	NOUN
ejpam-6017	260	9	-closed	-close	VERB
ejpam-6017	260	10	relative	relative	ADJ
ejpam-6017	260	11	to	to	ADP
ejpam-6017	260	12	(	(	PUNCT
ejpam-6017	260	13	x	x	NOUN
ejpam-6017	260	14	,	,	PUNCT
ejpam-6017	260	15	τ1	τ1	NOUN
ejpam-6017	260	16	,	,	PUNCT
ejpam-6017	260	17	τ2	τ2	NOUN
ejpam-6017	260	18	)	)	PUNCT
ejpam-6017	260	19	.	.	PUNCT
ejpam-6017	261	1	let	let	VERB
ejpam-6017	261	2	{	{	PUNCT
ejpam-6017	261	3	vγ	vγ	VERB
ejpam-6017	261	4	|	|	ADV
ejpam-6017	261	5	γ	γ	PROPN
ejpam-6017	261	6	∈	∈	PROPN
ejpam-6017	261	7	γ	γ	AUX
ejpam-6017	261	8	}	}	PUNCT
ejpam-6017	261	9	be	be	VERB
ejpam-6017	261	10	any	any	DET
ejpam-6017	261	11	cover	cover	NOUN
ejpam-6017	261	12	of	of	ADP
ejpam-6017	261	13	f(k	f(k	VERB
ejpam-6017	261	14	)	)	PUNCT
ejpam-6017	261	15	by	by	ADP
ejpam-6017	261	16	σ1σ2	σ1σ2	NOUN
ejpam-6017	261	17	-	-	PUNCT
ejpam-6017	261	18	open	open	ADJ
ejpam-6017	261	19	sets	set	NOUN
ejpam-6017	261	20	of	of	ADP
ejpam-6017	261	21	y	y	PROPN
ejpam-6017	261	22	.	.	PUNCT
ejpam-6017	262	1	for	for	ADP
ejpam-6017	262	2	each	each	DET
ejpam-6017	262	3	x	x	SYM
ejpam-6017	262	4	∈	∈	PROPN
ejpam-6017	262	5	k	k	NOUN
ejpam-6017	262	6	,	,	PUNCT
ejpam-6017	262	7	there	there	PRON
ejpam-6017	262	8	exists	exist	VERB
ejpam-6017	262	9	γ(x	γ(x	NOUN
ejpam-6017	262	10	)	)	PUNCT
ejpam-6017	262	11	∈	∈	PROPN
ejpam-6017	262	12	γ	γ	NOUN
ejpam-6017	262	13	such	such	ADJ
ejpam-6017	262	14	that	that	SCONJ
ejpam-6017	262	15	f(x	f(x	PROPN
ejpam-6017	262	16	)	)	PUNCT
ejpam-6017	262	17	∈	∈	PROPN
ejpam-6017	262	18	vγ(x	vγ(x	NOUN
ejpam-6017	262	19	)	)	PUNCT
ejpam-6017	262	20	.	.	PUNCT
ejpam-6017	263	1	since	since	SCONJ
ejpam-6017	263	2	f	f	PROPN
ejpam-6017	263	3	is	be	AUX
ejpam-6017	263	4	strongly	strongly	ADV
ejpam-6017	263	5	θ(τ1	θ(τ1	ADJ
ejpam-6017	263	6	,	,	PUNCT
ejpam-6017	263	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	263	8	,	,	PUNCT
ejpam-6017	263	9	there	there	PRON
ejpam-6017	263	10	exists	exist	VERB
ejpam-6017	263	11	a	a	DET
ejpam-6017	263	12	τ1τ2	τ1τ2	NOUN
ejpam-6017	263	13	-	-	ADJ
ejpam-6017	263	14	open	open	ADJ
ejpam-6017	263	15	set	set	ADJ
ejpam-6017	263	16	u(x	u(x	NOUN
ejpam-6017	263	17	)	)	PUNCT
ejpam-6017	263	18	of	of	ADP
ejpam-6017	263	19	x	x	SYM
ejpam-6017	263	20	containing	contain	VERB
ejpam-6017	263	21	x	x	PUNCT
ejpam-6017	263	22	such	such	ADJ
ejpam-6017	263	23	that	that	SCONJ
ejpam-6017	263	24	f(τ1τ2	f(τ1τ2	NOUN
ejpam-6017	263	25	-	-	PUNCT
ejpam-6017	263	26	cl(u(x	cl(u(x	NOUN
ejpam-6017	263	27	)	)	PUNCT
ejpam-6017	263	28	)	)	PUNCT
ejpam-6017	263	29	)	)	PUNCT
ejpam-6017	264	1	⊆	⊆	X
ejpam-6017	264	2	σ1σ2	σ1σ2	NUM
ejpam-6017	264	3	-	-	PUNCT
ejpam-6017	264	4	cl(vγ(x	cl(vγ(x	NOUN
ejpam-6017	264	5	)	)	PUNCT
ejpam-6017	264	6	)	)	PUNCT
ejpam-6017	264	7	.	.	PUNCT
ejpam-6017	265	1	the	the	DET
ejpam-6017	265	2	family	family	NOUN
ejpam-6017	265	3	{	{	PUNCT
ejpam-6017	265	4	u(x	u(x	PROPN
ejpam-6017	265	5	)	)	PUNCT
ejpam-6017	265	6	|	|	ADV
ejpam-6017	265	7	x	x	SYM
ejpam-6017	265	8	∈	∈	PROPN
ejpam-6017	265	9	k	k	NOUN
ejpam-6017	265	10	}	}	PUNCT
ejpam-6017	265	11	is	be	AUX
ejpam-6017	265	12	a	a	DET
ejpam-6017	265	13	cover	cover	NOUN
ejpam-6017	265	14	of	of	ADP
ejpam-6017	265	15	k	k	X
ejpam-6017	265	16	by	by	ADP
ejpam-6017	265	17	τ1τ2	τ1τ2	ADJ
ejpam-6017	265	18	-	-	ADJ
ejpam-6017	265	19	open	open	ADJ
ejpam-6017	265	20	sets	set	NOUN
ejpam-6017	265	21	of	of	ADP
ejpam-6017	265	22	x.	x.	NOUN
ejpam-6017	265	23	since	since	SCONJ
ejpam-6017	265	24	k	k	PROPN
ejpam-6017	265	25	is	be	AUX
ejpam-6017	265	26	quasi	quasi	NOUN
ejpam-6017	265	27	(	(	PUNCT
ejpam-6017	265	28	τ1	τ1	NOUN
ejpam-6017	265	29	,	,	PUNCT
ejpam-6017	265	30	τ2)-h	τ2)-h	NOUN
ejpam-6017	265	31	-closed	-close	VERB
ejpam-6017	265	32	relative	relative	ADJ
ejpam-6017	265	33	to	to	ADP
ejpam-6017	265	34	(	(	PUNCT
ejpam-6017	265	35	x	x	NOUN
ejpam-6017	265	36	,	,	PUNCT
ejpam-6017	265	37	τ1	τ1	NOUN
ejpam-6017	265	38	,	,	PUNCT
ejpam-6017	265	39	τ2	τ2	NOUN
ejpam-6017	265	40	)	)	PUNCT
ejpam-6017	265	41	,	,	PUNCT
ejpam-6017	265	42	there	there	PRON
ejpam-6017	265	43	exists	exist	VERB
ejpam-6017	265	44	a	a	DET
ejpam-6017	265	45	finite	finite	ADJ
ejpam-6017	265	46	number	number	NOUN
ejpam-6017	265	47	of	of	ADP
ejpam-6017	265	48	points	point	NOUN
ejpam-6017	265	49	,	,	PUNCT
ejpam-6017	265	50	say	say	INTJ
ejpam-6017	265	51	,	,	PUNCT
ejpam-6017	265	52	x1	x1	PROPN
ejpam-6017	265	53	,	,	PUNCT
ejpam-6017	265	54	x2	x2	PROPN
ejpam-6017	265	55	,	,	PUNCT
ejpam-6017	265	56	x3	x3	ADJ
ejpam-6017	265	57	,	,	PUNCT
ejpam-6017	265	58	...	...	PUNCT
ejpam-6017	265	59	,	,	PUNCT
ejpam-6017	265	60	xn	xn	PROPN
ejpam-6017	266	1	in	in	ADP
ejpam-6017	266	2	k	k	PROPN
ejpam-6017	266	3	such	such	ADJ
ejpam-6017	266	4	that	that	SCONJ
ejpam-6017	266	5	k	k	PROPN
ejpam-6017	266	6	⊆	⊆	NUM
ejpam-6017	266	7	∪{τ1τ2	∪{τ1τ2	NOUN
ejpam-6017	266	8	-	-	PUNCT
ejpam-6017	266	9	cl(u(xk	cl(u(xk	NUM
ejpam-6017	266	10	)	)	PUNCT
ejpam-6017	266	11	)	)	PUNCT
ejpam-6017	266	12	|	|	ADV
ejpam-6017	266	13	xk	xk	PROPN
ejpam-6017	266	14	∈	∈	PROPN
ejpam-6017	266	15	k	k	PROPN
ejpam-6017	266	16	;	;	PUNCT
ejpam-6017	266	17	1	1	NUM
ejpam-6017	266	18	≤	≤	NUM
ejpam-6017	266	19	k	k	X
ejpam-6017	266	20	≤	≤	PROPN
ejpam-6017	266	21	n	n	CCONJ
ejpam-6017	266	22	}	}	PUNCT
ejpam-6017	266	23	.	.	PUNCT
ejpam-6017	267	1	thus	thus	ADV
ejpam-6017	267	2	,	,	PUNCT
ejpam-6017	267	3	f(k	f(k	VERB
ejpam-6017	267	4	)	)	PUNCT
ejpam-6017	267	5	⊆	⊆	X
ejpam-6017	267	6	∪{f(τ1τ2	∪{f(τ1τ2	NOUN
ejpam-6017	267	7	-	-	PUNCT
ejpam-6017	267	8	cl(u(xk	cl(u(xk	NOUN
ejpam-6017	267	9	)	)	PUNCT
ejpam-6017	267	10	)	)	PUNCT
ejpam-6017	267	11	)	)	PUNCT
ejpam-6017	268	1	|	|	ADV
ejpam-6017	268	2	xk	xk	PROPN
ejpam-6017	268	3	∈	∈	PROPN
ejpam-6017	268	4	k	k	PROPN
ejpam-6017	268	5	;	;	PUNCT
ejpam-6017	268	6	1	1	NUM
ejpam-6017	268	7	≤	≤	NUM
ejpam-6017	268	8	k	k	X
ejpam-6017	268	9	≤	≤	PROPN
ejpam-6017	268	10	n	n	CCONJ
ejpam-6017	268	11	}	}	PUNCT
ejpam-6017	268	12	⊆	⊆	NUM
ejpam-6017	268	13	∪{vγ(xk	∪{vγ(xk	NOUN
ejpam-6017	268	14	)	)	PUNCT
ejpam-6017	268	15	|	|	ADV
ejpam-6017	268	16	xk	xk	PROPN
ejpam-6017	268	17	∈	∈	PROPN
ejpam-6017	268	18	k	k	PROPN
ejpam-6017	268	19	;	;	PUNCT
ejpam-6017	268	20	1	1	NUM
ejpam-6017	268	21	≤	≤	NUM
ejpam-6017	268	22	k	k	X
ejpam-6017	268	23	≤	≤	PROPN
ejpam-6017	268	24	n	n	CCONJ
ejpam-6017	268	25	}	}	PUNCT
ejpam-6017	268	26	.	.	PUNCT
ejpam-6017	269	1	this	this	PRON
ejpam-6017	269	2	shows	show	VERB
ejpam-6017	269	3	that	that	SCONJ
ejpam-6017	269	4	f(k	f(k	VERB
ejpam-6017	269	5	)	)	PUNCT
ejpam-6017	269	6	is	be	AUX
ejpam-6017	269	7	σ1σ2	σ1σ2	NOUN
ejpam-6017	269	8	-	-	ADJ
ejpam-6017	269	9	compact	compact	ADJ
ejpam-6017	269	10	relative	relative	NOUN
ejpam-6017	269	11	to	to	ADP
ejpam-6017	269	12	(	(	PUNCT
ejpam-6017	269	13	y	y	PROPN
ejpam-6017	269	14	,	,	PUNCT
ejpam-6017	269	15	σ1	σ1	PROPN
ejpam-6017	269	16	,	,	PUNCT
ejpam-6017	269	17	σ2	σ2	NOUN
ejpam-6017	269	18	)	)	PUNCT
ejpam-6017	269	19	.	.	PUNCT
ejpam-6017	270	1	acknowledgements	acknowledgement	NOUN
ejpam-6017	270	2	this	this	DET
ejpam-6017	270	3	research	research	NOUN
ejpam-6017	270	4	project	project	NOUN
ejpam-6017	270	5	was	be	AUX
ejpam-6017	270	6	financially	financially	ADV
ejpam-6017	270	7	supported	support	VERB
ejpam-6017	270	8	by	by	ADP
ejpam-6017	270	9	mahasarakham	mahasarakham	PROPN
ejpam-6017	270	10	university	university	PROPN
ejpam-6017	270	11	.	.	PUNCT
ejpam-6017	271	1	references	reference	NOUN
ejpam-6017	271	2	[	[	X
ejpam-6017	271	3	1	1	X
ejpam-6017	271	4	]	]	PUNCT
ejpam-6017	271	5	s.	s.	PROPN
ejpam-6017	271	6	fomin	fomin	PROPN
ejpam-6017	271	7	.	.	PUNCT
ejpam-6017	272	1	extensions	extension	NOUN
ejpam-6017	272	2	of	of	ADP
ejpam-6017	272	3	topological	topological	ADJ
ejpam-6017	272	4	spaces	space	NOUN
ejpam-6017	272	5	.	.	PUNCT
ejpam-6017	273	1	doklady	doklady	PROPN
ejpam-6017	273	2	akademii	akademii	NOUN
ejpam-6017	273	3	nauk	nauk	NOUN
ejpam-6017	273	4	sssr	sssr	NOUN
ejpam-6017	273	5	,	,	PUNCT
ejpam-6017	273	6	32:114	32:114	NUM
ejpam-6017	273	7	–	–	PUNCT
ejpam-6017	273	8	116	116	NUM
ejpam-6017	273	9	,	,	PUNCT
ejpam-6017	273	10	1941	1941	NUM
ejpam-6017	273	11	.	.	PUNCT
ejpam-6017	274	1	[	[	X
ejpam-6017	274	2	2	2	X
ejpam-6017	274	3	]	]	PUNCT
ejpam-6017	274	4	t.	t.	PROPN
ejpam-6017	274	5	noiri	noiri	PROPN
ejpam-6017	274	6	.	.	PUNCT
ejpam-6017	275	1	properties	property	NOUN
ejpam-6017	275	2	of	of	ADP
ejpam-6017	275	3	θ	θ	ADJ
ejpam-6017	275	4	-	-	ADJ
ejpam-6017	275	5	continuous	continuous	ADJ
ejpam-6017	275	6	functions	function	NOUN
ejpam-6017	275	7	.	.	PUNCT
ejpam-6017	276	1	atti	atti	PROPN
ejpam-6017	276	2	della	della	PROPN
ejpam-6017	276	3	accademia	accademia	PROPN
ejpam-6017	276	4	nazionale	nazionale	PROPN
ejpam-6017	276	5	dei	dei	PROPN
ejpam-6017	276	6	lincei	lincei	NOUN
ejpam-6017	276	7	,	,	PUNCT
ejpam-6017	276	8	classe	classe	PROPN
ejpam-6017	276	9	di	di	PROPN
ejpam-6017	276	10	scienze	scienze	PROPN
ejpam-6017	276	11	fisiche	fisiche	PROPN
ejpam-6017	276	12	,	,	PUNCT
ejpam-6017	276	13	matematiche	matematiche	PROPN
ejpam-6017	276	14	e	e	X
ejpam-6017	276	15	naturali	naturali	X
ejpam-6017	276	16	.	.	PUNCT
ejpam-6017	277	1	rendiconti	rendiconti	PROPN
ejpam-6017	277	2	,	,	PUNCT
ejpam-6017	277	3	series	series	NOUN
ejpam-6017	277	4	(	(	PUNCT
ejpam-6017	277	5	8)	8)	NUM
ejpam-6017	277	6	,	,	PUNCT
ejpam-6017	277	7	58:887–891	58:887–891	NUM
ejpam-6017	277	8	,	,	PUNCT
ejpam-6017	277	9	1975	1975	NUM
ejpam-6017	277	10	.	.	PUNCT
ejpam-6017	278	1	[	[	X
ejpam-6017	278	2	3	3	X
ejpam-6017	278	3	]	]	PUNCT
ejpam-6017	278	4	v.	v.	CCONJ
ejpam-6017	278	5	popa	popa	NOUN
ejpam-6017	278	6	.	.	PUNCT
ejpam-6017	279	1	characterizations	characterization	NOUN
ejpam-6017	279	2	of	of	ADP
ejpam-6017	279	3	θ	θ	ADJ
ejpam-6017	279	4	-	-	ADJ
ejpam-6017	279	5	continuous	continuous	ADJ
ejpam-6017	279	6	functions	function	NOUN
ejpam-6017	279	7	.	.	PUNCT
ejpam-6017	280	1	studii	studii	PROPN
ejpam-6017	280	2	şi	şi	PROPN
ejpam-6017	280	3	cercetări	cercetări	PROPN
ejpam-6017	280	4	ştiinţifice	ştiinţifice	PROPN
ejpam-6017	280	5	.	.	PUNCT
ejpam-6017	281	1	seria	seria	PROPN
ejpam-6017	281	2	matematică	matematică	PROPN
ejpam-6017	281	3	,	,	PUNCT
ejpam-6017	281	4	32:113–119	32:113–119	PROPN
ejpam-6017	281	5	,	,	PUNCT
ejpam-6017	281	6	1980	1980	NUM
ejpam-6017	281	7	.	.	PUNCT
ejpam-6017	282	1	[	[	X
ejpam-6017	282	2	4	4	X
ejpam-6017	282	3	]	]	PUNCT
ejpam-6017	282	4	s.	s.	PROPN
ejpam-6017	282	5	p.	p.	PROPN
ejpam-6017	282	6	arya	arya	PROPN
ejpam-6017	282	7	and	and	CCONJ
ejpam-6017	282	8	m.	m.	PROPN
ejpam-6017	282	9	p.	p.	PROPN
ejpam-6017	282	10	bhamini	bhamini	PROPN
ejpam-6017	282	11	.	.	PUNCT
ejpam-6017	283	1	some	some	DET
ejpam-6017	283	2	weaker	weak	ADJ
ejpam-6017	283	3	forms	form	NOUN
ejpam-6017	283	4	of	of	ADP
ejpam-6017	283	5	semi	semi	ADJ
ejpam-6017	283	6	-	-	ADJ
ejpam-6017	283	7	continuous	continuous	ADJ
ejpam-6017	283	8	functions	function	NOUN
ejpam-6017	283	9	.	.	PUNCT
ejpam-6017	284	1	ganita	ganita	NOUN
ejpam-6017	284	2	,	,	PUNCT
ejpam-6017	284	3	33:124–134	33:124–134	NUM
ejpam-6017	284	4	,	,	PUNCT
ejpam-6017	284	5	1982	1982	NUM
ejpam-6017	284	6	.	.	PUNCT
ejpam-6017	285	1	[	[	X
ejpam-6017	285	2	5	5	X
ejpam-6017	285	3	]	]	PUNCT
ejpam-6017	285	4	s.	s.	PROPN
ejpam-6017	285	5	jafari	jafari	PROPN
ejpam-6017	285	6	and	and	CCONJ
ejpam-6017	285	7	t.	t.	PROPN
ejpam-6017	285	8	noiri	noiri	PROPN
ejpam-6017	285	9	.	.	PUNCT
ejpam-6017	286	1	properties	property	NOUN
ejpam-6017	286	2	of	of	ADP
ejpam-6017	286	3	θ	θ	NOUN
ejpam-6017	286	4	-	-	PUNCT
ejpam-6017	286	5	semi	semi	ADJ
ejpam-6017	286	6	-	-	ADJ
ejpam-6017	286	7	continuous	continuous	ADJ
ejpam-6017	286	8	functions	function	NOUN
ejpam-6017	286	9	.	.	PUNCT
ejpam-6017	287	1	journal	journal	PROPN
ejpam-6017	287	2	of	of	ADP
ejpam-6017	287	3	institute	institute	PROPN
ejpam-6017	287	4	of	of	ADP
ejpam-6017	287	5	mathematics	mathematics	PROPN
ejpam-6017	287	6	and	and	CCONJ
ejpam-6017	287	7	computer	computer	NOUN
ejpam-6017	287	8	sciences	science	NOUN
ejpam-6017	287	9	,	,	PUNCT
ejpam-6017	287	10	mathematics	mathematic	NOUN
ejpam-6017	287	11	series	series	NOUN
ejpam-6017	287	12	,	,	PUNCT
ejpam-6017	287	13	13:123–128	13:123–128	NUM
ejpam-6017	287	14	,	,	PUNCT
ejpam-6017	287	15	2000	2000	NUM
ejpam-6017	287	16	.	.	PUNCT
ejpam-6017	288	1	[	[	X
ejpam-6017	288	2	6	6	NUM
ejpam-6017	288	3	]	]	PUNCT
ejpam-6017	288	4	t.	t.	PROPN
ejpam-6017	288	5	noiri	noiri	PROPN
ejpam-6017	288	6	.	.	PUNCT
ejpam-6017	289	1	on	on	ADP
ejpam-6017	289	2	θ	θ	ADJ
ejpam-6017	289	3	-	-	ADJ
ejpam-6017	289	4	precontinuous	precontinuous	ADJ
ejpam-6017	289	5	functions	function	NOUN
ejpam-6017	289	6	.	.	PUNCT
ejpam-6017	290	1	international	international	ADJ
ejpam-6017	290	2	journal	journal	PROPN
ejpam-6017	290	3	of	of	ADP
ejpam-6017	290	4	mathematics	mathematics	PROPN
ejpam-6017	290	5	and	and	CCONJ
ejpam-6017	290	6	mathematical	mathematical	ADJ
ejpam-6017	290	7	sciences	science	NOUN
ejpam-6017	290	8	,	,	PUNCT
ejpam-6017	290	9	28:285–292	28:285–292	NUM
ejpam-6017	290	10	,	,	PUNCT
ejpam-6017	290	11	2001	2001	NUM
ejpam-6017	290	12	.	.	PUNCT
ejpam-6017	291	1	[	[	X
ejpam-6017	291	2	7	7	X
ejpam-6017	291	3	]	]	PUNCT
ejpam-6017	291	4	p.	p.	NOUN
ejpam-6017	291	5	e.	e.	PROPN
ejpam-6017	292	1	long	long	PROPN
ejpam-6017	292	2	and	and	CCONJ
ejpam-6017	292	3	l.	l.	PROPN
ejpam-6017	292	4	l.	l.	PROPN
ejpam-6017	292	5	herrington	herrington	PROPN
ejpam-6017	292	6	.	.	PUNCT
ejpam-6017	293	1	strongly	strongly	ADV
ejpam-6017	293	2	θ	θ	ADJ
ejpam-6017	293	3	-	-	ADJ
ejpam-6017	293	4	continuous	continuous	ADJ
ejpam-6017	293	5	functions	function	NOUN
ejpam-6017	293	6	.	.	PUNCT
ejpam-6017	294	1	journal	journal	NOUN
ejpam-6017	294	2	of	of	ADP
ejpam-6017	294	3	the	the	DET
ejpam-6017	294	4	korean	korean	PROPN
ejpam-6017	294	5	mathematical	mathematical	ADJ
ejpam-6017	294	6	society	society	NOUN
ejpam-6017	294	7	,	,	PUNCT
ejpam-6017	294	8	18:21–28	18:21–28	NUM
ejpam-6017	294	9	,	,	PUNCT
ejpam-6017	294	10	1981	1981	NUM
ejpam-6017	294	11	.	.	PUNCT
ejpam-6017	295	1	[	[	X
ejpam-6017	295	2	8	8	X
ejpam-6017	295	3	]	]	PUNCT
ejpam-6017	295	4	s.	s.	PROPN
ejpam-6017	295	5	jafari	jafari	PROPN
ejpam-6017	295	6	and	and	CCONJ
ejpam-6017	295	7	t.	t.	PROPN
ejpam-6017	295	8	noiri	noiri	PROPN
ejpam-6017	295	9	.	.	PUNCT
ejpam-6017	296	1	strongly	strongly	ADV
ejpam-6017	296	2	θ	θ	VERB
ejpam-6017	296	3	-	-	PUNCT
ejpam-6017	296	4	semi	semi	ADJ
ejpam-6017	296	5	-	-	ADJ
ejpam-6017	296	6	continuous	continuous	ADJ
ejpam-6017	296	7	functions	function	NOUN
ejpam-6017	296	8	.	.	PUNCT
ejpam-6017	297	1	indian	indian	ADJ
ejpam-6017	297	2	journal	journal	PROPN
ejpam-6017	297	3	of	of	ADP
ejpam-6017	297	4	pure	pure	ADJ
ejpam-6017	297	5	and	and	CCONJ
ejpam-6017	297	6	applied	applied	ADJ
ejpam-6017	297	7	mathematics	mathematic	NOUN
ejpam-6017	297	8	,	,	PUNCT
ejpam-6017	297	9	29:1195–1201	29:1195–1201	NUM
ejpam-6017	297	10	,	,	PUNCT
ejpam-6017	297	11	1998	1998	NUM
ejpam-6017	297	12	.	.	PUNCT
ejpam-6017	298	1	p.	p.	NOUN
ejpam-6017	298	2	pue	pue	NOUN
ejpam-6017	298	3	-	-	PUNCT
ejpam-6017	298	4	on	on	ADP
ejpam-6017	298	5	,	,	PUNCT
ejpam-6017	298	6	s.	s.	PROPN
ejpam-6017	298	7	sompong	sompong	PROPN
ejpam-6017	298	8	,	,	PUNCT
ejpam-6017	298	9	c.	c.	PROPN
ejpam-6017	298	10	boonpok	boonpok	PROPN
ejpam-6017	298	11	/	/	SYM
ejpam-6017	298	12	eur	eur	PROPN
ejpam-6017	298	13	.	.	PUNCT
ejpam-6017	299	1	j.	j.	PROPN
ejpam-6017	299	2	pure	pure	PROPN
ejpam-6017	299	3	appl	appl	PROPN
ejpam-6017	299	4	.	.	PROPN
ejpam-6017	299	5	math	math	PROPN
ejpam-6017	299	6	,	,	PUNCT
ejpam-6017	299	7	18	18	NUM
ejpam-6017	299	8	(	(	PUNCT
ejpam-6017	299	9	2	2	NUM
ejpam-6017	299	10	)	)	PUNCT
ejpam-6017	299	11	(	(	PUNCT
ejpam-6017	299	12	2025	2025	NUM
ejpam-6017	299	13	)	)	PUNCT
ejpam-6017	299	14	,	,	PUNCT
ejpam-6017	299	15	6017	6017	NUM
ejpam-6017	299	16	10	10	NUM
ejpam-6017	299	17	of	of	ADP
ejpam-6017	299	18	11	11	NUM
ejpam-6017	299	19	[	[	X
ejpam-6017	299	20	9	9	NUM
ejpam-6017	299	21	]	]	PUNCT
ejpam-6017	299	22	t.	t.	PROPN
ejpam-6017	299	23	noiri	noiri	PROPN
ejpam-6017	299	24	.	.	PUNCT
ejpam-6017	300	1	strongly	strongly	ADV
ejpam-6017	300	2	θ	θ	ADJ
ejpam-6017	300	3	-	-	ADJ
ejpam-6017	300	4	precontinuous	precontinuous	ADJ
ejpam-6017	300	5	functions	function	NOUN
ejpam-6017	300	6	.	.	PUNCT
ejpam-6017	301	1	acta	acta	PROPN
ejpam-6017	301	2	mathematica	mathematica	PROPN
ejpam-6017	301	3	hungarica	hungarica	PROPN
ejpam-6017	301	4	,	,	PUNCT
ejpam-6017	301	5	90(4):307–316	90(4):307–316	NUM
ejpam-6017	301	6	,	,	PUNCT
ejpam-6017	301	7	2001	2001	NUM
ejpam-6017	301	8	.	.	PUNCT
ejpam-6017	302	1	[	[	X
ejpam-6017	302	2	10	10	NUM
ejpam-6017	302	3	]	]	PUNCT
ejpam-6017	302	4	t.	t.	PROPN
ejpam-6017	302	5	noiri	noiri	PROPN
ejpam-6017	302	6	and	and	CCONJ
ejpam-6017	302	7	v.	v.	ADP
ejpam-6017	302	8	popa	popa	NOUN
ejpam-6017	302	9	.	.	PUNCT
ejpam-6017	303	1	strongly	strongly	ADV
ejpam-6017	303	2	θ	θ	VERB
ejpam-6017	303	3	-	-	PUNCT
ejpam-6017	303	4	β	β	ADJ
ejpam-6017	303	5	-	-	ADJ
ejpam-6017	303	6	continuous	continuous	ADJ
ejpam-6017	303	7	functions	function	NOUN
ejpam-6017	303	8	.	.	PUNCT
ejpam-6017	304	1	journal	journal	NOUN
ejpam-6017	304	2	of	of	ADP
ejpam-6017	304	3	pure	pure	ADJ
ejpam-6017	304	4	mathematics	mathematic	NOUN
ejpam-6017	304	5	,	,	PUNCT
ejpam-6017	304	6	19:31–39	19:31–39	NUM
ejpam-6017	304	7	,	,	PUNCT
ejpam-6017	304	8	2002	2002	NUM
ejpam-6017	304	9	.	.	PUNCT
ejpam-6017	305	1	[	[	X
ejpam-6017	305	2	11	11	NUM
ejpam-6017	305	3	]	]	X
ejpam-6017	305	4	g.	g.	PROPN
ejpam-6017	305	5	di	di	PROPN
ejpam-6017	305	6	maio	maio	PROPN
ejpam-6017	305	7	and	and	CCONJ
ejpam-6017	305	8	t.	t.	PROPN
ejpam-6017	305	9	noiri	noiri	PROPN
ejpam-6017	305	10	.	.	PUNCT
ejpam-6017	306	1	weak	weak	ADJ
ejpam-6017	306	2	and	and	CCONJ
ejpam-6017	306	3	strong	strong	ADJ
ejpam-6017	306	4	forms	form	NOUN
ejpam-6017	306	5	of	of	ADP
ejpam-6017	306	6	irresolute	irresolute	ADJ
ejpam-6017	306	7	functions	function	NOUN
ejpam-6017	306	8	.	.	PUNCT
ejpam-6017	307	1	rendiconti	rendiconti	ADJ
ejpam-6017	307	2	del	del	PROPN
ejpam-6017	307	3	circolo	circolo	PROPN
ejpam-6017	307	4	matematico	matematico	NOUN
ejpam-6017	307	5	di	di	X
ejpam-6017	307	6	palermo	palermo	NOUN
ejpam-6017	307	7	(	(	PUNCT
ejpam-6017	307	8	2	2	NUM
ejpam-6017	307	9	)	)	PUNCT
ejpam-6017	307	10	,	,	PUNCT
ejpam-6017	307	11	supplemento	supplemento	NOUN
ejpam-6017	307	12	,	,	PUNCT
ejpam-6017	307	13	18:255–273	18:255–273	NUM
ejpam-6017	307	14	,	,	PUNCT
ejpam-6017	307	15	1988	1988	NUM
ejpam-6017	307	16	.	.	PUNCT
ejpam-6017	308	1	[	[	X
ejpam-6017	308	2	12	12	NUM
ejpam-6017	308	3	]	]	PUNCT
ejpam-6017	308	4	m.	m.	NOUN
ejpam-6017	308	5	c.	c.	PROPN
ejpam-6017	308	6	pal	pal	PROPN
ejpam-6017	308	7	and	and	CCONJ
ejpam-6017	308	8	p.	p.	NOUN
ejpam-6017	308	9	bhattacharyya	bhattacharyya	ADJ
ejpam-6017	308	10	.	.	PUNCT
ejpam-6017	309	1	feeble	feeble	ADJ
ejpam-6017	309	2	and	and	CCONJ
ejpam-6017	309	3	strong	strong	ADJ
ejpam-6017	309	4	forms	form	NOUN
ejpam-6017	309	5	of	of	ADP
ejpam-6017	309	6	preirresolute	preirresolute	ADJ
ejpam-6017	309	7	functions	function	NOUN
ejpam-6017	309	8	.	.	PUNCT
ejpam-6017	310	1	bulletin	bulletin	NOUN
ejpam-6017	310	2	of	of	ADP
ejpam-6017	310	3	the	the	DET
ejpam-6017	310	4	malaysian	malaysian	PROPN
ejpam-6017	310	5	mathematical	mathematical	PROPN
ejpam-6017	310	6	sciences	sciences	PROPN
ejpam-6017	310	7	society	society	NOUN
ejpam-6017	310	8	,	,	PUNCT
ejpam-6017	310	9	19:63–75	19:63–75	NUM
ejpam-6017	310	10	,	,	PUNCT
ejpam-6017	310	11	1996	1996	NUM
ejpam-6017	310	12	.	.	PUNCT
ejpam-6017	311	1	[	[	X
ejpam-6017	311	2	13	13	NUM
ejpam-6017	311	3	]	]	PUNCT
ejpam-6017	311	4	t.	t.	PROPN
ejpam-6017	311	5	noiri	noiri	PROPN
ejpam-6017	311	6	.	.	PUNCT
ejpam-6017	312	1	weak	weak	ADJ
ejpam-6017	312	2	and	and	CCONJ
ejpam-6017	312	3	strong	strong	ADJ
ejpam-6017	312	4	forms	form	NOUN
ejpam-6017	312	5	of	of	ADP
ejpam-6017	312	6	β	β	NOUN
ejpam-6017	312	7	-	-	ADJ
ejpam-6017	312	8	irresolute	irresolute	ADJ
ejpam-6017	312	9	functions	function	NOUN
ejpam-6017	312	10	.	.	PUNCT
ejpam-6017	313	1	acta	acta	PROPN
ejpam-6017	313	2	mathematica	mathematica	PROPN
ejpam-6017	313	3	hungarica	hungarica	PROPN
ejpam-6017	313	4	,	,	PUNCT
ejpam-6017	313	5	99(4):315–328	99(4):315–328	PROPN
ejpam-6017	313	6	,	,	PUNCT
ejpam-6017	313	7	2003	2003	NUM
ejpam-6017	313	8	.	.	PUNCT
ejpam-6017	314	1	[	[	X
ejpam-6017	314	2	14	14	NUM
ejpam-6017	314	3	]	]	X
ejpam-6017	314	4	s.	s.	PROPN
ejpam-6017	314	5	jafari	jafari	PROPN
ejpam-6017	314	6	and	and	CCONJ
ejpam-6017	314	7	t.	t.	PROPN
ejpam-6017	314	8	noiri	noiri	PROPN
ejpam-6017	314	9	.	.	PUNCT
ejpam-6017	315	1	strongly	strongly	ADV
ejpam-6017	315	2	sober	sober	ADJ
ejpam-6017	315	3	θ	θ	ADJ
ejpam-6017	315	4	-	-	ADJ
ejpam-6017	315	5	continuous	continuous	ADJ
ejpam-6017	315	6	functions	function	NOUN
ejpam-6017	315	7	.	.	PUNCT
ejpam-6017	316	1	journal	journal	NOUN
ejpam-6017	316	2	of	of	ADP
ejpam-6017	316	3	pure	pure	ADJ
ejpam-6017	316	4	mathematics	mathematic	NOUN
ejpam-6017	316	5	,	,	PUNCT
ejpam-6017	316	6	16:9–17	16:9–17	NUM
ejpam-6017	316	7	,	,	PUNCT
ejpam-6017	316	8	1999	1999	NUM
ejpam-6017	316	9	.	.	PUNCT
ejpam-6017	317	1	[	[	X
ejpam-6017	317	2	15	15	NUM
ejpam-6017	317	3	]	]	X
ejpam-6017	317	4	t.	t.	PROPN
ejpam-6017	317	5	noiri	noiri	PROPN
ejpam-6017	317	6	and	and	CCONJ
ejpam-6017	317	7	v.	v.	ADP
ejpam-6017	317	8	popa	popa	NOUN
ejpam-6017	317	9	.	.	PUNCT
ejpam-6017	318	1	a	a	DET
ejpam-6017	318	2	unified	unified	ADJ
ejpam-6017	318	3	theory	theory	NOUN
ejpam-6017	318	4	for	for	ADP
ejpam-6017	318	5	strongly	strongly	ADV
ejpam-6017	318	6	θcontinuity	θcontinuity	NOUN
ejpam-6017	318	7	for	for	ADP
ejpam-6017	318	8	functions	function	NOUN
ejpam-6017	318	9	.	.	PUNCT
ejpam-6017	319	1	acta	acta	PROPN
ejpam-6017	319	2	mathematica	mathematica	PROPN
ejpam-6017	319	3	hungarica	hungarica	PROPN
ejpam-6017	319	4	,	,	PUNCT
ejpam-6017	319	5	106(3):167–186	106(3):167–186	NUM
ejpam-6017	319	6	,	,	PUNCT
ejpam-6017	319	7	2005	2005	NUM
ejpam-6017	319	8	.	.	PUNCT
ejpam-6017	320	1	[	[	X
ejpam-6017	320	2	16	16	NUM
ejpam-6017	320	3	]	]	PUNCT
ejpam-6017	320	4	m.	m.	NOUN
ejpam-6017	320	5	thongmoon	thongmoon	NOUN
ejpam-6017	320	6	and	and	CCONJ
ejpam-6017	320	7	c.	c.	PROPN
ejpam-6017	320	8	boonpok	boonpok	PROPN
ejpam-6017	320	9	.	.	PUNCT
ejpam-6017	321	1	strongly	strongly	ADV
ejpam-6017	321	2	θ(λ	θ(λ	PROPN
ejpam-6017	321	3	,	,	PUNCT
ejpam-6017	321	4	p)-continuous	p)-continuous	ADJ
ejpam-6017	321	5	functions	function	NOUN
ejpam-6017	321	6	.	.	PUNCT
ejpam-6017	322	1	international	international	ADJ
ejpam-6017	322	2	journal	journal	PROPN
ejpam-6017	322	3	of	of	ADP
ejpam-6017	322	4	mathematics	mathematic	NOUN
ejpam-6017	322	5	and	and	CCONJ
ejpam-6017	322	6	computer	computer	NOUN
ejpam-6017	322	7	science	science	NOUN
ejpam-6017	322	8	,	,	PUNCT
ejpam-6017	322	9	19(2):475–479	19(2):475–479	PROPN
ejpam-6017	322	10	,	,	PUNCT
ejpam-6017	322	11	2024	2024	NUM
ejpam-6017	322	12	.	.	PUNCT
ejpam-6017	323	1	[	[	X
ejpam-6017	323	2	17	17	NUM
ejpam-6017	323	3	]	]	X
ejpam-6017	323	4	j.	j.	PROPN
ejpam-6017	323	5	khampakdee	khampakdee	PROPN
ejpam-6017	323	6	and	and	CCONJ
ejpam-6017	323	7	c.	c.	PROPN
ejpam-6017	323	8	boonpok	boonpok	PROPN
ejpam-6017	323	9	.	.	PUNCT
ejpam-6017	324	1	almost	almost	ADV
ejpam-6017	324	2	strong	strong	ADJ
ejpam-6017	324	3	θ(λ	θ(λ	PROPN
ejpam-6017	324	4	,	,	PUNCT
ejpam-6017	324	5	p)-continuity	p)-continuity	NOUN
ejpam-6017	324	6	for	for	ADP
ejpam-6017	324	7	functions	function	NOUN
ejpam-6017	324	8	.	.	PUNCT
ejpam-6017	325	1	european	european	ADJ
ejpam-6017	325	2	journal	journal	PROPN
ejpam-6017	325	3	of	of	ADP
ejpam-6017	325	4	pure	pure	ADJ
ejpam-6017	325	5	and	and	CCONJ
ejpam-6017	325	6	applied	applied	ADJ
ejpam-6017	325	7	mathematics	mathematic	NOUN
ejpam-6017	325	8	,	,	PUNCT
ejpam-6017	325	9	17(1):300–309	17(1):300–309	PROPN
ejpam-6017	325	10	,	,	PUNCT
ejpam-6017	325	11	2024	2024	NUM
ejpam-6017	325	12	.	.	PUNCT
ejpam-6017	326	1	[	[	X
ejpam-6017	326	2	18	18	NUM
ejpam-6017	326	3	]	]	PUNCT
ejpam-6017	326	4	c.	c.	PROPN
ejpam-6017	326	5	boonpok	boonpok	PROPN
ejpam-6017	326	6	and	and	CCONJ
ejpam-6017	326	7	n.	n.	PROPN
ejpam-6017	326	8	srisarakham	srisarakham	PROPN
ejpam-6017	326	9	.	.	PUNCT
ejpam-6017	327	1	(	(	PUNCT
ejpam-6017	327	2	τ1	τ1	NOUN
ejpam-6017	327	3	,	,	PUNCT
ejpam-6017	327	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6017	327	5	for	for	ADP
ejpam-6017	327	6	functions	function	NOUN
ejpam-6017	327	7	.	.	PUNCT
ejpam-6017	328	1	asia	asia	PROPN
ejpam-6017	328	2	pacific	pacific	PROPN
ejpam-6017	328	3	journal	journal	PROPN
ejpam-6017	328	4	of	of	ADP
ejpam-6017	328	5	mathematics	mathematic	NOUN
ejpam-6017	328	6	,	,	PUNCT
ejpam-6017	328	7	11:21	11:21	NUM
ejpam-6017	328	8	,	,	PUNCT
ejpam-6017	328	9	2024	2024	NUM
ejpam-6017	328	10	.	.	PUNCT
ejpam-6017	329	1	[	[	X
ejpam-6017	329	2	19	19	NUM
ejpam-6017	329	3	]	]	X
ejpam-6017	329	4	c.	c.	PROPN
ejpam-6017	329	5	boonpok	boonpok	PROPN
ejpam-6017	329	6	and	and	CCONJ
ejpam-6017	329	7	p.	p.	NOUN
ejpam-6017	329	8	pue	pue	NOUN
ejpam-6017	329	9	-	-	PUNCT
ejpam-6017	329	10	on	on	ADP
ejpam-6017	329	11	.	.	PUNCT
ejpam-6017	330	1	characterizations	characterization	NOUN
ejpam-6017	330	2	of	of	ADP
ejpam-6017	330	3	almost	almost	ADV
ejpam-6017	330	4	(	(	PUNCT
ejpam-6017	330	5	τ1	τ1	NOUN
ejpam-6017	330	6	,	,	PUNCT
ejpam-6017	330	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	330	8	functions	function	NOUN
ejpam-6017	330	9	.	.	PUNCT
ejpam-6017	331	1	international	international	ADJ
ejpam-6017	331	2	journal	journal	NOUN
ejpam-6017	331	3	of	of	ADP
ejpam-6017	331	4	analysis	analysis	NOUN
ejpam-6017	331	5	and	and	CCONJ
ejpam-6017	331	6	applications	application	NOUN
ejpam-6017	331	7	,	,	PUNCT
ejpam-6017	331	8	22:33	22:33	NUM
ejpam-6017	331	9	,	,	PUNCT
ejpam-6017	331	10	2024	2024	NUM
ejpam-6017	331	11	.	.	PUNCT
ejpam-6017	332	1	[	[	X
ejpam-6017	332	2	20	20	NUM
ejpam-6017	332	3	]	]	PUNCT
ejpam-6017	332	4	c.	c.	PROPN
ejpam-6017	332	5	boonpok	boonpok	PROPN
ejpam-6017	332	6	and	and	CCONJ
ejpam-6017	332	7	c.	c.	PROPN
ejpam-6017	332	8	klanarong	klanarong	PROPN
ejpam-6017	332	9	.	.	PUNCT
ejpam-6017	333	1	on	on	ADP
ejpam-6017	333	2	weakly	weakly	ADJ
ejpam-6017	333	3	(	(	PUNCT
ejpam-6017	333	4	τ1	τ1	NOUN
ejpam-6017	333	5	,	,	PUNCT
ejpam-6017	333	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	333	7	functions	function	NOUN
ejpam-6017	333	8	.	.	PUNCT
ejpam-6017	334	1	european	european	ADJ
ejpam-6017	334	2	journal	journal	PROPN
ejpam-6017	334	3	of	of	ADP
ejpam-6017	334	4	pure	pure	ADJ
ejpam-6017	334	5	and	and	CCONJ
ejpam-6017	334	6	applied	applied	ADJ
ejpam-6017	334	7	mathematics	mathematic	NOUN
ejpam-6017	334	8	,	,	PUNCT
ejpam-6017	334	9	17(1):416–425	17(1):416–425	NUM
ejpam-6017	334	10	,	,	PUNCT
ejpam-6017	334	11	2024	2024	NUM
ejpam-6017	334	12	.	.	PUNCT
ejpam-6017	335	1	[	[	X
ejpam-6017	335	2	21	21	NUM
ejpam-6017	335	3	]	]	X
ejpam-6017	335	4	j.	j.	PROPN
ejpam-6017	335	5	khampakdee	khampakdee	PROPN
ejpam-6017	335	6	,	,	PUNCT
ejpam-6017	335	7	s.	s.	PROPN
ejpam-6017	335	8	sompong	sompong	PROPN
ejpam-6017	335	9	,	,	PUNCT
ejpam-6017	335	10	and	and	CCONJ
ejpam-6017	335	11	c.	c.	PROPN
ejpam-6017	335	12	boonpok	boonpok	PROPN
ejpam-6017	335	13	.	.	PUNCT
ejpam-6017	336	1	almost	almost	ADV
ejpam-6017	336	2	weakly	weakly	ADJ
ejpam-6017	336	3	(	(	PUNCT
ejpam-6017	336	4	τ1	τ1	NOUN
ejpam-6017	336	5	,	,	PUNCT
ejpam-6017	336	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	336	7	functions	function	NOUN
ejpam-6017	336	8	.	.	PUNCT
ejpam-6017	337	1	european	european	ADJ
ejpam-6017	337	2	journal	journal	PROPN
ejpam-6017	337	3	of	of	ADP
ejpam-6017	337	4	pure	pure	ADJ
ejpam-6017	337	5	and	and	CCONJ
ejpam-6017	337	6	applied	applied	ADJ
ejpam-6017	337	7	mathematics	mathematic	NOUN
ejpam-6017	337	8	,	,	PUNCT
ejpam-6017	337	9	18(1):5721	18(1):5721	NUM
ejpam-6017	337	10	,	,	PUNCT
ejpam-6017	337	11	2025	2025	NUM
ejpam-6017	337	12	.	.	PUNCT
ejpam-6017	338	1	[	[	X
ejpam-6017	338	2	22	22	NUM
ejpam-6017	338	3	]	]	X
ejpam-6017	338	4	n.	n.	NOUN
ejpam-6017	338	5	srisarakham	srisarakham	PROPN
ejpam-6017	338	6	,	,	PUNCT
ejpam-6017	338	7	a.	a.	PROPN
ejpam-6017	338	8	sama	sama	PROPN
ejpam-6017	338	9	-	-	PUNCT
ejpam-6017	338	10	ae	ae	PROPN
ejpam-6017	338	11	,	,	PUNCT
ejpam-6017	338	12	and	and	CCONJ
ejpam-6017	338	13	c.	c.	PROPN
ejpam-6017	338	14	boonpok	boonpok	PROPN
ejpam-6017	338	15	.	.	PUNCT
ejpam-6017	339	1	characterizations	characterization	NOUN
ejpam-6017	339	2	of	of	ADP
ejpam-6017	339	3	faintly	faintly	ADV
ejpam-6017	339	4	(	(	PUNCT
ejpam-6017	339	5	τ1	τ1	PROPN
ejpam-6017	339	6	,	,	PUNCT
ejpam-6017	339	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	339	8	functions	function	NOUN
ejpam-6017	339	9	.	.	PUNCT
ejpam-6017	340	1	european	european	ADJ
ejpam-6017	340	2	journal	journal	PROPN
ejpam-6017	340	3	of	of	ADP
ejpam-6017	340	4	pure	pure	ADJ
ejpam-6017	340	5	and	and	CCONJ
ejpam-6017	340	6	applied	applied	ADJ
ejpam-6017	340	7	mathematics	mathematic	NOUN
ejpam-6017	340	8	,	,	PUNCT
ejpam-6017	340	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-6017	340	10	,	,	PUNCT
ejpam-6017	340	11	2024	2024	NUM
ejpam-6017	340	12	.	.	PUNCT
ejpam-6017	341	1	[	[	X
ejpam-6017	341	2	23	23	NUM
ejpam-6017	341	3	]	]	PUNCT
ejpam-6017	341	4	m.	m.	NOUN
ejpam-6017	341	5	chiangpradit	chiangpradit	NOUN
ejpam-6017	341	6	,	,	PUNCT
ejpam-6017	341	7	s.	s.	PROPN
ejpam-6017	341	8	sompong	sompong	PROPN
ejpam-6017	341	9	,	,	PUNCT
ejpam-6017	341	10	and	and	CCONJ
ejpam-6017	341	11	c.	c.	PROPN
ejpam-6017	341	12	boonpok	boonpok	PROPN
ejpam-6017	341	13	.	.	PUNCT
ejpam-6017	342	1	weakly	weakly	ADJ
ejpam-6017	342	2	quasi	quasi	NOUN
ejpam-6017	342	3	(	(	PUNCT
ejpam-6017	342	4	τ1	τ1	PROPN
ejpam-6017	342	5	,	,	PUNCT
ejpam-6017	342	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	342	7	functions	function	NOUN
ejpam-6017	342	8	.	.	PUNCT
ejpam-6017	343	1	international	international	ADJ
ejpam-6017	343	2	journal	journal	NOUN
ejpam-6017	343	3	of	of	ADP
ejpam-6017	343	4	analysis	analysis	NOUN
ejpam-6017	343	5	and	and	CCONJ
ejpam-6017	343	6	applications	application	NOUN
ejpam-6017	343	7	,	,	PUNCT
ejpam-6017	343	8	22:125	22:125	NUM
ejpam-6017	343	9	,	,	PUNCT
ejpam-6017	343	10	2024	2024	NUM
ejpam-6017	343	11	.	.	PUNCT
ejpam-6017	344	1	[	[	X
ejpam-6017	344	2	24	24	NUM
ejpam-6017	344	3	]	]	PUNCT
ejpam-6017	344	4	b.	b.	PROPN
ejpam-6017	344	5	kong	kong	PROPN
ejpam-6017	344	6	-	-	PUNCT
ejpam-6017	344	7	ied	ied	PROPN
ejpam-6017	344	8	,	,	PUNCT
ejpam-6017	344	9	s.	s.	PROPN
ejpam-6017	344	10	sompong	sompong	PROPN
ejpam-6017	344	11	,	,	PUNCT
ejpam-6017	344	12	and	and	CCONJ
ejpam-6017	344	13	c.	c.	PROPN
ejpam-6017	344	14	boonpok	boonpok	PROPN
ejpam-6017	344	15	.	.	PUNCT
ejpam-6017	345	1	almost	almost	ADV
ejpam-6017	345	2	quasi	quasi	X
ejpam-6017	345	3	(	(	PUNCT
ejpam-6017	345	4	τ1	τ1	NOUN
ejpam-6017	345	5	,	,	PUNCT
ejpam-6017	345	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	345	7	functions	function	NOUN
ejpam-6017	345	8	.	.	PUNCT
ejpam-6017	346	1	asia	asia	PROPN
ejpam-6017	346	2	pacific	pacific	PROPN
ejpam-6017	346	3	journal	journal	PROPN
ejpam-6017	346	4	of	of	ADP
ejpam-6017	346	5	mathematics	mathematic	NOUN
ejpam-6017	346	6	,	,	PUNCT
ejpam-6017	346	7	11:64	11:64	NUM
ejpam-6017	346	8	,	,	PUNCT
ejpam-6017	346	9	2024	2024	NUM
ejpam-6017	346	10	.	.	PUNCT
ejpam-6017	347	1	[	[	X
ejpam-6017	347	2	25	25	NUM
ejpam-6017	347	3	]	]	PUNCT
ejpam-6017	347	4	c.	c.	NOUN
ejpam-6017	347	5	prachanpol	prachanpol	NOUN
ejpam-6017	347	6	,	,	PUNCT
ejpam-6017	347	7	c.	c.	PROPN
ejpam-6017	347	8	boonpok	boonpok	PROPN
ejpam-6017	347	9	,	,	PUNCT
ejpam-6017	347	10	and	and	CCONJ
ejpam-6017	347	11	c.	c.	PROPN
ejpam-6017	347	12	viriyapong	viriyapong	PROPN
ejpam-6017	347	13	.	.	PUNCT
ejpam-6017	348	1	δ(τ1	δ(τ1	PROPN
ejpam-6017	348	2	,	,	PUNCT
ejpam-6017	348	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	348	4	functions	function	NOUN
ejpam-6017	348	5	.	.	PUNCT
ejpam-6017	349	1	european	european	ADJ
ejpam-6017	349	2	journal	journal	PROPN
ejpam-6017	349	3	of	of	ADP
ejpam-6017	349	4	pure	pure	ADJ
ejpam-6017	349	5	and	and	CCONJ
ejpam-6017	349	6	applied	applied	ADJ
ejpam-6017	349	7	mathematics	mathematic	NOUN
ejpam-6017	349	8	,	,	PUNCT
ejpam-6017	349	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-6017	349	10	,	,	PUNCT
ejpam-6017	349	11	2024	2024	NUM
ejpam-6017	349	12	.	.	PUNCT
ejpam-6017	350	1	[	[	X
ejpam-6017	350	2	26	26	NUM
ejpam-6017	350	3	]	]	X
ejpam-6017	350	4	n.	n.	PROPN
ejpam-6017	350	5	srisarakham	srisarakham	PROPN
ejpam-6017	350	6	,	,	PUNCT
ejpam-6017	350	7	s.	s.	PROPN
ejpam-6017	350	8	sompong	sompong	PROPN
ejpam-6017	350	9	,	,	PUNCT
ejpam-6017	350	10	and	and	CCONJ
ejpam-6017	350	11	c.	c.	PROPN
ejpam-6017	350	12	boonpok	boonpok	PROPN
ejpam-6017	350	13	.	.	PUNCT
ejpam-6017	351	1	quasi	quasi	PROPN
ejpam-6017	351	2	θ(τ1	θ(τ1	PROPN
ejpam-6017	351	3	,	,	PUNCT
ejpam-6017	351	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6017	351	5	functions	function	NOUN
ejpam-6017	351	6	.	.	PUNCT
ejpam-6017	352	1	european	european	ADJ
ejpam-6017	352	2	journal	journal	PROPN
ejpam-6017	352	3	of	of	ADP
ejpam-6017	352	4	pure	pure	ADJ
ejpam-6017	352	5	and	and	CCONJ
ejpam-6017	352	6	applied	applied	ADJ
ejpam-6017	352	7	mathematics	mathematic	NOUN
ejpam-6017	352	8	,	,	PUNCT
ejpam-6017	352	9	18(1):5722	18(1):5722	NUM
ejpam-6017	352	10	,	,	PUNCT
ejpam-6017	352	11	2025	2025	NUM
ejpam-6017	352	12	.	.	PUNCT
ejpam-6017	353	1	[	[	X
ejpam-6017	353	2	27	27	NUM
ejpam-6017	353	3	]	]	X
ejpam-6017	353	4	c.	c.	PROPN
ejpam-6017	353	5	boonpok	boonpok	PROPN
ejpam-6017	353	6	,	,	PUNCT
ejpam-6017	353	7	c.	c.	PROPN
ejpam-6017	353	8	viriyapong	viriyapong	PROPN
ejpam-6017	353	9	,	,	PUNCT
ejpam-6017	353	10	and	and	CCONJ
ejpam-6017	353	11	m.	m.	NOUN
ejpam-6017	353	12	thongmoon	thongmoon	NOUN
ejpam-6017	353	13	.	.	PUNCT
ejpam-6017	354	1	on	on	ADP
ejpam-6017	354	2	upper	upper	ADJ
ejpam-6017	354	3	and	and	CCONJ
ejpam-6017	354	4	lower	low	ADJ
ejpam-6017	354	5	(	(	PUNCT
ejpam-6017	354	6	τ1	τ1	NOUN
ejpam-6017	354	7	,	,	PUNCT
ejpam-6017	354	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6017	354	9	multifunctions	multifunction	NOUN
ejpam-6017	354	10	.	.	PUNCT
ejpam-6017	355	1	journal	journal	PROPN
ejpam-6017	355	2	of	of	ADP
ejpam-6017	355	3	mathematics	mathematics	PROPN
ejpam-6017	355	4	and	and	CCONJ
ejpam-6017	355	5	computer	computer	NOUN
ejpam-6017	355	6	science	science	NOUN
ejpam-6017	355	7	,	,	PUNCT
ejpam-6017	355	8	18:282–293	18:282–293	NUM
ejpam-6017	355	9	,	,	PUNCT
ejpam-6017	355	10	2018	2018	NUM
ejpam-6017	355	11	.	.	PUNCT
ejpam-6017	356	1	[	[	X
ejpam-6017	356	2	28	28	NUM
ejpam-6017	356	3	]	]	X
ejpam-6017	356	4	n.	n.	PROPN
ejpam-6017	356	5	viriyapong	viriyapong	PROPN
ejpam-6017	356	6	and	and	CCONJ
ejpam-6017	356	7	c.	c.	PROPN
ejpam-6017	356	8	boonpok	boonpok	PROPN
ejpam-6017	356	9	.	.	PUNCT
ejpam-6017	357	1	(	(	PUNCT
ejpam-6017	357	2	τ1	τ1	NOUN
ejpam-6017	357	3	,	,	PUNCT
ejpam-6017	357	4	τ2)α	τ2)α	NOUN
ejpam-6017	357	5	-	-	PUNCT
ejpam-6017	357	6	continuity	continuity	NOUN
ejpam-6017	357	7	for	for	ADP
ejpam-6017	357	8	multifunctions	multifunction	NOUN
ejpam-6017	357	9	.	.	PUNCT
ejpam-6017	358	1	journal	journal	PROPN
ejpam-6017	358	2	of	of	ADP
ejpam-6017	358	3	mathematics	mathematic	NOUN
ejpam-6017	358	4	,	,	PUNCT
ejpam-6017	358	5	2020:6285763	2020:6285763	NUM
ejpam-6017	358	6	,	,	PUNCT
ejpam-6017	358	7	2020	2020	NUM
ejpam-6017	358	8	.	.	PUNCT
ejpam-6017	359	1	[	[	X
ejpam-6017	359	2	29	29	NUM
ejpam-6017	359	3	]	]	X
ejpam-6017	359	4	c.	c.	PROPN
ejpam-6017	359	5	boonpok	boonpok	PROPN
ejpam-6017	359	6	.	.	PUNCT
ejpam-6017	360	1	(	(	PUNCT
ejpam-6017	360	2	τ1	τ1	NOUN
ejpam-6017	360	3	,	,	PUNCT
ejpam-6017	360	4	τ2)δ	τ2)δ	ADJ
ejpam-6017	360	5	-	-	PUNCT
ejpam-6017	360	6	semicontinuous	semicontinuous	ADJ
ejpam-6017	360	7	multifunctions	multifunction	NOUN
ejpam-6017	360	8	.	.	PUNCT
ejpam-6017	361	1	heliyon	heliyon	NOUN
ejpam-6017	361	2	,	,	PUNCT
ejpam-6017	361	3	6	6	NUM
ejpam-6017	361	4	:	:	SYM
ejpam-6017	361	5	e05367	e05367	PROPN
ejpam-6017	361	6	,	,	PUNCT
ejpam-6017	361	7	2020	2020	NUM
ejpam-6017	361	8	.	.	PUNCT
ejpam-6017	362	1	p.	p.	NOUN
ejpam-6017	362	2	pue	pue	NOUN
ejpam-6017	362	3	-	-	PUNCT
ejpam-6017	362	4	on	on	ADP
ejpam-6017	362	5	,	,	PUNCT
ejpam-6017	362	6	s.	s.	PROPN
ejpam-6017	362	7	sompong	sompong	PROPN
ejpam-6017	362	8	,	,	PUNCT
ejpam-6017	362	9	c.	c.	PROPN
ejpam-6017	362	10	boonpok	boonpok	PROPN
ejpam-6017	362	11	/	/	SYM
ejpam-6017	362	12	eur	eur	PROPN
ejpam-6017	362	13	.	.	PUNCT
ejpam-6017	363	1	j.	j.	PROPN
ejpam-6017	363	2	pure	pure	PROPN
ejpam-6017	363	3	appl	appl	PROPN
ejpam-6017	363	4	.	.	PROPN
ejpam-6017	363	5	math	math	PROPN
ejpam-6017	363	6	,	,	PUNCT
ejpam-6017	363	7	18	18	NUM
ejpam-6017	363	8	(	(	PUNCT
ejpam-6017	363	9	2	2	NUM
ejpam-6017	363	10	)	)	PUNCT
ejpam-6017	363	11	(	(	PUNCT
ejpam-6017	363	12	2025	2025	NUM
ejpam-6017	363	13	)	)	PUNCT
ejpam-6017	363	14	,	,	PUNCT
ejpam-6017	363	15	6017	6017	NUM
ejpam-6017	363	16	11	11	NUM
ejpam-6017	363	17	of	of	ADP
ejpam-6017	363	18	11	11	NUM
ejpam-6017	363	19	[	[	SYM
ejpam-6017	363	20	30	30	NUM
ejpam-6017	363	21	]	]	X
ejpam-6017	363	22	n.	n.	PROPN
ejpam-6017	363	23	viriyapong	viriyapong	PROPN
ejpam-6017	363	24	,	,	PUNCT
ejpam-6017	363	25	s.	s.	PROPN
ejpam-6017	363	26	sompong	sompong	PROPN
ejpam-6017	363	27	,	,	PUNCT
ejpam-6017	363	28	and	and	CCONJ
ejpam-6017	363	29	c.	c.	PROPN
ejpam-6017	363	30	boonpok	boonpok	PROPN
ejpam-6017	363	31	.	.	PUNCT
ejpam-6017	364	1	(	(	PUNCT
ejpam-6017	364	2	τ1	τ1	NOUN
ejpam-6017	364	3	,	,	PUNCT
ejpam-6017	364	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6017	364	5	disconnectedness	disconnectedness	NOUN
ejpam-6017	364	6	in	in	ADP
ejpam-6017	364	7	bitopological	bitopological	ADJ
ejpam-6017	364	8	spaces	space	NOUN
ejpam-6017	364	9	.	.	PUNCT
ejpam-6017	365	1	international	international	ADJ
ejpam-6017	365	2	journal	journal	PROPN
ejpam-6017	365	3	of	of	ADP
ejpam-6017	365	4	mathematics	mathematic	NOUN
ejpam-6017	365	5	and	and	CCONJ
ejpam-6017	365	6	computer	computer	NOUN
ejpam-6017	365	7	science	science	NOUN
ejpam-6017	365	8	,	,	PUNCT
ejpam-6017	365	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6017	365	10	,	,	PUNCT
ejpam-6017	365	11	2024	2024	NUM
ejpam-6017	365	12	.	.	PUNCT
ejpam-6017	366	1	[	[	X
ejpam-6017	366	2	31	31	NUM
ejpam-6017	366	3	]	]	PUNCT
ejpam-6017	366	4	p.	p.	NOUN
ejpam-6017	366	5	pue	pue	NOUN
ejpam-6017	366	6	-	-	PUNCT
ejpam-6017	366	7	on	on	ADP
ejpam-6017	366	8	,	,	PUNCT
ejpam-6017	366	9	s.	s.	PROPN
ejpam-6017	366	10	sompong	sompong	PROPN
ejpam-6017	366	11	,	,	PUNCT
ejpam-6017	366	12	and	and	CCONJ
ejpam-6017	366	13	c.	c.	PROPN
ejpam-6017	366	14	boonpok	boonpok	PROPN
ejpam-6017	366	15	.	.	PUNCT
ejpam-6017	367	1	upper	upper	ADJ
ejpam-6017	367	2	and	and	CCONJ
ejpam-6017	367	3	lower	low	ADJ
ejpam-6017	367	4	faint	faint	ADJ
ejpam-6017	367	5	(	(	PUNCT
ejpam-6017	367	6	τ1	τ1	NOUN
ejpam-6017	367	7	,	,	PUNCT
ejpam-6017	367	8	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6017	367	9	.	.	PUNCT
ejpam-6017	368	1	international	international	ADJ
ejpam-6017	368	2	journal	journal	NOUN
ejpam-6017	368	3	of	of	ADP
ejpam-6017	368	4	analysis	analysis	NOUN
ejpam-6017	368	5	and	and	CCONJ
ejpam-6017	368	6	applications	application	NOUN
ejpam-6017	368	7	,	,	PUNCT
ejpam-6017	368	8	22:169	22:169	NUM
ejpam-6017	368	9	,	,	PUNCT
ejpam-6017	368	10	2024	2024	NUM
ejpam-6017	368	11	.	.	PUNCT
ejpam-6017	369	1	[	[	X
ejpam-6017	369	2	32	32	NUM
ejpam-6017	369	3	]	]	PUNCT
ejpam-6017	369	4	m.	m.	NOUN
ejpam-6017	369	5	chiangpradit	chiangpradit	NOUN
ejpam-6017	369	6	,	,	PUNCT
ejpam-6017	369	7	s.	s.	PROPN
ejpam-6017	369	8	sompong	sompong	PROPN
ejpam-6017	369	9	,	,	PUNCT
ejpam-6017	369	10	and	and	CCONJ
ejpam-6017	369	11	c.	c.	PROPN
ejpam-6017	369	12	boonpok	boonpok	PROPN
ejpam-6017	369	13	.	.	PUNCT
ejpam-6017	370	1	on	on	ADP
ejpam-6017	370	2	characterizations	characterization	NOUN
ejpam-6017	370	3	of	of	ADP
ejpam-6017	370	4	(	(	PUNCT
ejpam-6017	370	5	τ1	τ1	NOUN
ejpam-6017	370	6	,	,	PUNCT
ejpam-6017	370	7	τ2)regular	τ2)regular	ADJ
ejpam-6017	370	8	spaces	space	NOUN
ejpam-6017	370	9	.	.	PUNCT
ejpam-6017	371	1	international	international	ADJ
ejpam-6017	371	2	journal	journal	PROPN
ejpam-6017	371	3	of	of	ADP
ejpam-6017	371	4	mathematics	mathematic	NOUN
ejpam-6017	371	5	and	and	CCONJ
ejpam-6017	371	6	computer	computer	NOUN
ejpam-6017	371	7	science	science	NOUN
ejpam-6017	371	8	,	,	PUNCT
ejpam-6017	371	9	19(4):1229–1334	19(4):1229–1334	NUM
ejpam-6017	371	10	,	,	PUNCT
ejpam-6017	371	11	2024	2024	NUM
ejpam-6017	371	12	.	.	PUNCT
ejpam-6017	372	1	[	[	X
ejpam-6017	372	2	33	33	NUM
ejpam-6017	372	3	]	]	PUNCT
ejpam-6017	372	4	c.	c.	PROPN
ejpam-6017	372	5	klanarong	klanarong	PROPN
ejpam-6017	372	6	,	,	PUNCT
ejpam-6017	372	7	s.	s.	PROPN
ejpam-6017	372	8	sompong	sompong	PROPN
ejpam-6017	372	9	,	,	PUNCT
ejpam-6017	372	10	and	and	CCONJ
ejpam-6017	372	11	c.	c.	PROPN
ejpam-6017	372	12	boonpok	boonpok	PROPN
ejpam-6017	372	13	.	.	PUNCT
ejpam-6017	373	1	(	(	PUNCT
ejpam-6017	373	2	τ1	τ1	NOUN
ejpam-6017	373	3	,	,	PUNCT
ejpam-6017	373	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6017	373	5	and	and	CCONJ
ejpam-6017	373	6	(	(	PUNCT
ejpam-6017	373	7	τ1	τ1	NOUN
ejpam-6017	373	8	,	,	PUNCT
ejpam-6017	373	9	τ2)θ	τ2)θ	ADJ
ejpam-6017	373	10	-	-	PUNCT
ejpam-6017	373	11	closed	close	VERB
ejpam-6017	373	12	sets	set	NOUN
ejpam-6017	373	13	.	.	PUNCT
ejpam-6017	374	1	international	international	ADJ
ejpam-6017	374	2	journal	journal	NOUN
ejpam-6017	374	3	of	of	ADP
ejpam-6017	374	4	mathematics	mathematic	NOUN
ejpam-6017	374	5	and	and	CCONJ
ejpam-6017	374	6	computer	computer	NOUN
ejpam-6017	374	7	science	science	NOUN
ejpam-6017	374	8	,	,	PUNCT
ejpam-6017	374	9	19(4):1299–1304	19(4):1299–1304	NUM
ejpam-6017	374	10	,	,	PUNCT
ejpam-6017	374	11	2024	2024	NUM
ejpam-6017	374	12	.	.	PUNCT
ejpam-6017	375	1	[	[	X
ejpam-6017	375	2	34	34	NUM
ejpam-6017	375	3	]	]	PUNCT
ejpam-6017	375	4	m.	m.	NOUN
ejpam-6017	375	5	chiangpradit	chiangpradit	NOUN
ejpam-6017	375	6	,	,	PUNCT
ejpam-6017	375	7	s.	s.	PROPN
ejpam-6017	375	8	sompong	sompong	PROPN
ejpam-6017	375	9	,	,	PUNCT
ejpam-6017	375	10	and	and	CCONJ
ejpam-6017	375	11	c.	c.	PROPN
ejpam-6017	375	12	boonpok	boonpok	PROPN
ejpam-6017	375	13	.	.	PUNCT
ejpam-6017	376	1	λ(τ1,τ2)-sets	λ(τ1,τ2)-set	NOUN
ejpam-6017	376	2	and	and	CCONJ
ejpam-6017	376	3	related	relate	VERB
ejpam-6017	376	4	topological	topological	ADJ
ejpam-6017	376	5	spaces	space	NOUN
ejpam-6017	376	6	.	.	PUNCT
ejpam-6017	377	1	asia	asia	PROPN
ejpam-6017	377	2	pacific	pacific	PROPN
ejpam-6017	377	3	journal	journal	PROPN
ejpam-6017	377	4	of	of	ADP
ejpam-6017	377	5	mathematics	mathematic	NOUN
ejpam-6017	377	6	,	,	PUNCT
ejpam-6017	377	7	11:49	11:49	NUM
ejpam-6017	377	8	,	,	PUNCT
ejpam-6017	377	9	2024	2024	NUM
ejpam-6017	377	10	.	.	PUNCT
ejpam-6017	378	1	[	[	X
ejpam-6017	378	2	35	35	NUM
ejpam-6017	378	3	]	]	X
ejpam-6017	378	4	n.	n.	NOUN
ejpam-6017	378	5	chutiman	chutiman	NOUN
ejpam-6017	378	6	,	,	PUNCT
ejpam-6017	378	7	s.	s.	PROPN
ejpam-6017	378	8	sompong	sompong	PROPN
ejpam-6017	378	9	,	,	PUNCT
ejpam-6017	378	10	and	and	CCONJ
ejpam-6017	378	11	c.	c.	PROPN
ejpam-6017	378	12	boonpok	boonpok	PROPN
ejpam-6017	378	13	.	.	PUNCT
ejpam-6017	379	1	on	on	ADP
ejpam-6017	379	2	some	some	DET
ejpam-6017	379	3	separation	separation	NOUN
ejpam-6017	379	4	axioms	axiom	NOUN
ejpam-6017	379	5	in	in	ADP
ejpam-6017	379	6	bitopological	bitopological	ADJ
ejpam-6017	379	7	spaces	space	NOUN
ejpam-6017	379	8	.	.	PUNCT
ejpam-6017	380	1	asia	asia	PROPN
ejpam-6017	380	2	pacific	pacific	PROPN
ejpam-6017	380	3	journal	journal	PROPN
ejpam-6017	380	4	of	of	ADP
ejpam-6017	380	5	mathematics	mathematic	NOUN
ejpam-6017	380	6	,	,	PUNCT
ejpam-6017	380	7	11:41	11:41	NUM
ejpam-6017	380	8	,	,	PUNCT
ejpam-6017	380	9	2024	2024	NUM
ejpam-6017	380	10	.	.	PUNCT
ejpam-6017	381	1	[	[	X
ejpam-6017	381	2	36	36	NUM
ejpam-6017	381	3	]	]	X
ejpam-6017	381	4	p.	p.	NOUN
ejpam-6017	381	5	pue	pue	NOUN
ejpam-6017	381	6	-	-	PUNCT
ejpam-6017	381	7	on	on	ADP
ejpam-6017	381	8	,	,	PUNCT
ejpam-6017	381	9	a.	a.	PROPN
ejpam-6017	381	10	sama	sama	PROPN
ejpam-6017	381	11	-	-	PUNCT
ejpam-6017	381	12	ae	ae	PROPN
ejpam-6017	381	13	,	,	PUNCT
ejpam-6017	381	14	and	and	CCONJ
ejpam-6017	381	15	c.	c.	PROPN
ejpam-6017	381	16	boonpok	boonpok	PROPN
ejpam-6017	381	17	.	.	PUNCT
ejpam-6017	382	1	characterizations	characterization	NOUN
ejpam-6017	382	2	of	of	ADP
ejpam-6017	382	3	quasi	quasi	NOUN
ejpam-6017	382	4	θ(τ1	θ(τ1	NOUN
ejpam-6017	382	5	,	,	PUNCT
ejpam-6017	382	6	τ2)continuous	τ2)continuous	ADJ
ejpam-6017	382	7	multifunctions	multifunction	NOUN
ejpam-6017	382	8	.	.	PUNCT
ejpam-6017	383	1	international	international	ADJ
ejpam-6017	383	2	journal	journal	NOUN
ejpam-6017	383	3	of	of	ADP
ejpam-6017	383	4	analysis	analysis	NOUN
ejpam-6017	383	5	and	and	CCONJ
ejpam-6017	383	6	applications	application	NOUN
ejpam-6017	383	7	,	,	PUNCT
ejpam-6017	383	8	23:59	23:59	NUM
ejpam-6017	383	9	,	,	PUNCT
ejpam-6017	383	10	2025	2025	NUM
ejpam-6017	383	11	.	.	PUNCT
ejpam-6017	384	1	[	[	X
ejpam-6017	384	2	37	37	NUM
ejpam-6017	384	3	]	]	PUNCT
ejpam-6017	384	4	m.	m.	NOUN
ejpam-6017	384	5	thongmoon	thongmoon	NOUN
ejpam-6017	384	6	,	,	PUNCT
ejpam-6017	384	7	s.	s.	PROPN
ejpam-6017	384	8	sompong	sompong	PROPN
ejpam-6017	384	9	,	,	PUNCT
ejpam-6017	384	10	and	and	CCONJ
ejpam-6017	384	11	c.	c.	PROPN
ejpam-6017	384	12	boonpok	boonpok	PROPN
ejpam-6017	384	13	.	.	PUNCT
ejpam-6017	384	14	θ(τ1	θ(τ1	PROPN
ejpam-6017	384	15	,	,	PUNCT
ejpam-6017	384	16	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6017	384	17	for	for	ADP
ejpam-6017	384	18	functions	function	NOUN
ejpam-6017	384	19	.	.	PUNCT
ejpam-6017	385	1	(	(	PUNCT
ejpam-6017	385	2	submitted	submit	VERB
ejpam-6017	385	3	)	)	PUNCT
ejpam-6017	385	4	.	.	PUNCT
ejpam-6017	386	1	[	[	X
ejpam-6017	386	2	38	38	NUM
ejpam-6017	386	3	]	]	PUNCT
ejpam-6017	386	4	m.	m.	NOUN
ejpam-6017	386	5	thongmoon	thongmoon	NOUN
ejpam-6017	386	6	,	,	PUNCT
ejpam-6017	386	7	s.	s.	PROPN
ejpam-6017	386	8	sompong	sompong	PROPN
ejpam-6017	386	9	,	,	PUNCT
ejpam-6017	386	10	and	and	CCONJ
ejpam-6017	386	11	c.	c.	PROPN
ejpam-6017	386	12	boonpok	boonpok	PROPN
ejpam-6017	386	13	.	.	PUNCT
ejpam-6017	387	1	upper	upper	ADJ
ejpam-6017	387	2	and	and	CCONJ
ejpam-6017	387	3	lower	low	ADJ
ejpam-6017	387	4	weak	weak	ADJ
ejpam-6017	387	5	(	(	PUNCT
ejpam-6017	387	6	τ1	τ1	NOUN
ejpam-6017	387	7	,	,	PUNCT
ejpam-6017	387	8	τ2)continuity	τ2)continuity	PROPN
ejpam-6017	387	9	.	.	PUNCT
ejpam-6017	388	1	european	european	PROPN
ejpam-6017	388	2	journal	journal	PROPN
ejpam-6017	388	3	of	of	ADP
ejpam-6017	388	4	pure	pure	ADJ
ejpam-6017	388	5	and	and	CCONJ
ejpam-6017	388	6	applied	applied	ADJ
ejpam-6017	388	7	mathematics	mathematic	NOUN
ejpam-6017	388	8	,	,	PUNCT
ejpam-6017	388	9	17(3):1705–1716	17(3):1705–1716	NUM
ejpam-6017	388	10	,	,	PUNCT
ejpam-6017	388	11	2024	2024	NUM
ejpam-6017	388	12	.	.	PUNCT