id	sid	tid	token	lemma	pos
ejpam-6038	1	1	european	european	PROPN
ejpam-6038	1	2	journal	journal	PROPN
ejpam-6038	1	3	of	of	ADP
ejpam-6038	1	4	pure	pure	ADJ
ejpam-6038	1	5	and	and	CCONJ
ejpam-6038	1	6	applied	applied	ADJ
ejpam-6038	1	7	mathematics	mathematic	NOUN
ejpam-6038	1	8	2025	2025	NUM
ejpam-6038	1	9	,	,	PUNCT
ejpam-6038	1	10	vol	vol	NOUN
ejpam-6038	1	11	.	.	PROPN
ejpam-6038	1	12	18	18	NUM
ejpam-6038	1	13	,	,	PUNCT
ejpam-6038	1	14	issue	issue	NOUN
ejpam-6038	1	15	2	2	NUM
ejpam-6038	1	16	,	,	PUNCT
ejpam-6038	1	17	article	article	NOUN
ejpam-6038	1	18	number	number	NOUN
ejpam-6038	1	19	6038	6038	NUM
ejpam-6038	1	20	issn	issn	VERB
ejpam-6038	1	21	1307	1307	NUM
ejpam-6038	1	22	-	-	SYM
ejpam-6038	1	23	5543	5543	NUM
ejpam-6038	1	24	–	–	PUNCT
ejpam-6038	1	25	ejpam.com	ejpam.com	X
ejpam-6038	1	26	published	publish	VERB
ejpam-6038	1	27	by	by	ADP
ejpam-6038	1	28	new	new	PROPN
ejpam-6038	1	29	york	york	PROPN
ejpam-6038	1	30	business	business	PROPN
ejpam-6038	1	31	global	global	PROPN
ejpam-6038	1	32	almost	almost	ADV
ejpam-6038	1	33	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	1	34	,	,	PUNCT
ejpam-6038	1	35	τ2)p	τ2)p	NOUN
ejpam-6038	1	36	-	-	PUNCT
ejpam-6038	1	37	continuity	continuity	NOUN
ejpam-6038	1	38	for	for	ADP
ejpam-6038	1	39	functions	function	NOUN
ejpam-6038	1	40	prapart	prapart	VERB
ejpam-6038	1	41	pue	pue	PROPN
ejpam-6038	1	42	-	-	PUNCT
ejpam-6038	1	43	on1	on1	PROPN
ejpam-6038	1	44	,	,	PUNCT
ejpam-6038	1	45	areeyuth	areeyuth	NOUN
ejpam-6038	1	46	sama	sama	NOUN
ejpam-6038	1	47	-	-	PUNCT
ejpam-6038	1	48	ae2	ae2	PROPN
ejpam-6038	1	49	,	,	PUNCT
ejpam-6038	1	50	chawalit	chawalit	VERB
ejpam-6038	1	51	boonpok1,∗	boonpok1,∗	NOUN
ejpam-6038	1	52	1	1	NUM
ejpam-6038	1	53	mathematics	mathematic	NOUN
ejpam-6038	1	54	and	and	CCONJ
ejpam-6038	1	55	applied	apply	VERB
ejpam-6038	1	56	mathematics	mathematics	PROPN
ejpam-6038	1	57	research	research	NOUN
ejpam-6038	1	58	unit	unit	NOUN
ejpam-6038	1	59	,	,	PUNCT
ejpam-6038	1	60	department	department	NOUN
ejpam-6038	1	61	of	of	ADP
ejpam-6038	1	62	mathematics	mathematic	NOUN
ejpam-6038	1	63	,	,	PUNCT
ejpam-6038	1	64	faculty	faculty	NOUN
ejpam-6038	1	65	of	of	ADP
ejpam-6038	1	66	science	science	NOUN
ejpam-6038	1	67	,	,	PUNCT
ejpam-6038	1	68	mahasarakham	mahasarakham	PROPN
ejpam-6038	1	69	university	university	PROPN
ejpam-6038	1	70	,	,	PUNCT
ejpam-6038	1	71	maha	maha	PROPN
ejpam-6038	1	72	sarakham	sarakham	PROPN
ejpam-6038	1	73	,	,	PUNCT
ejpam-6038	1	74	44150	44150	NUM
ejpam-6038	1	75	,	,	PUNCT
ejpam-6038	1	76	thailand	thailand	PROPN
ejpam-6038	1	77	2	2	NUM
ejpam-6038	1	78	department	department	NOUN
ejpam-6038	1	79	of	of	ADP
ejpam-6038	1	80	mathematics	mathematic	NOUN
ejpam-6038	1	81	and	and	CCONJ
ejpam-6038	1	82	computer	computer	NOUN
ejpam-6038	1	83	science	science	NOUN
ejpam-6038	1	84	,	,	PUNCT
ejpam-6038	1	85	faculty	faculty	NOUN
ejpam-6038	1	86	of	of	ADP
ejpam-6038	1	87	science	science	NOUN
ejpam-6038	1	88	and	and	CCONJ
ejpam-6038	1	89	technology	technology	NOUN
ejpam-6038	1	90	,	,	PUNCT
ejpam-6038	1	91	prince	prince	NOUN
ejpam-6038	1	92	of	of	ADP
ejpam-6038	1	93	songkla	songkla	PROPN
ejpam-6038	1	94	university	university	PROPN
ejpam-6038	1	95	,	,	PUNCT
ejpam-6038	1	96	pattani	pattani	NOUN
ejpam-6038	1	97	campus	campus	NOUN
ejpam-6038	1	98	,	,	PUNCT
ejpam-6038	1	99	pattani	pattani	NOUN
ejpam-6038	1	100	,	,	PUNCT
ejpam-6038	1	101	94000	94000	NUM
ejpam-6038	1	102	,	,	PUNCT
ejpam-6038	1	103	thailand	thailand	PROPN
ejpam-6038	1	104	abstract	abstract	PROPN
ejpam-6038	1	105	.	.	PUNCT
ejpam-6038	2	1	this	this	DET
ejpam-6038	2	2	paper	paper	NOUN
ejpam-6038	2	3	introduces	introduce	VERB
ejpam-6038	2	4	a	a	DET
ejpam-6038	2	5	new	new	ADJ
ejpam-6038	2	6	class	class	NOUN
ejpam-6038	2	7	of	of	ADP
ejpam-6038	2	8	functions	function	NOUN
ejpam-6038	2	9	between	between	ADP
ejpam-6038	2	10	bitopological	bitopological	ADJ
ejpam-6038	2	11	spaces	space	NOUN
ejpam-6038	2	12	,	,	PUNCT
ejpam-6038	2	13	namely	namely	ADV
ejpam-6038	2	14	almost	almost	ADV
ejpam-6038	2	15	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	2	16	,	,	PUNCT
ejpam-6038	2	17	τ2)p	τ2)p	ADJ
ejpam-6038	2	18	-	-	PUNCT
ejpam-6038	2	19	continuous	continuous	ADJ
ejpam-6038	2	20	functions	function	NOUN
ejpam-6038	2	21	.	.	PUNCT
ejpam-6038	3	1	moreover	moreover	ADV
ejpam-6038	3	2	,	,	PUNCT
ejpam-6038	3	3	some	some	DET
ejpam-6038	3	4	characterizations	characterization	NOUN
ejpam-6038	3	5	and	and	CCONJ
ejpam-6038	3	6	several	several	ADJ
ejpam-6038	3	7	properties	property	NOUN
ejpam-6038	3	8	concerning	concern	VERB
ejpam-6038	3	9	almost	almost	ADV
ejpam-6038	3	10	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	3	11	,	,	PUNCT
ejpam-6038	3	12	τ2)p	τ2)p	ADJ
ejpam-6038	3	13	-	-	PUNCT
ejpam-6038	3	14	continuous	continuous	ADJ
ejpam-6038	3	15	functions	function	NOUN
ejpam-6038	3	16	are	be	AUX
ejpam-6038	3	17	established	establish	VERB
ejpam-6038	3	18	.	.	PUNCT
ejpam-6038	4	1	2020	2020	NUM
ejpam-6038	4	2	mathematics	mathematics	PROPN
ejpam-6038	4	3	subject	subject	NOUN
ejpam-6038	4	4	classifications	classification	NOUN
ejpam-6038	4	5	:	:	PUNCT
ejpam-6038	4	6	54c08	54c08	NUM
ejpam-6038	4	7	,	,	PUNCT
ejpam-6038	4	8	54e55	54e55	NUM
ejpam-6038	4	9	key	key	ADJ
ejpam-6038	4	10	words	word	NOUN
ejpam-6038	4	11	and	and	CCONJ
ejpam-6038	4	12	phrases	phrase	NOUN
ejpam-6038	4	13	:	:	PUNCT
ejpam-6038	4	14	τ1τ2	τ1τ2	ADJ
ejpam-6038	4	15	-	-	ADJ
ejpam-6038	4	16	open	open	ADJ
ejpam-6038	4	17	set	set	NOUN
ejpam-6038	4	18	,	,	PUNCT
ejpam-6038	4	19	almost	almost	ADV
ejpam-6038	4	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	4	21	,	,	PUNCT
ejpam-6038	4	22	τ2)p	τ2)p	ADJ
ejpam-6038	4	23	-	-	ADJ
ejpam-6038	4	24	continuous	continuous	ADJ
ejpam-6038	4	25	function	function	NOUN
ejpam-6038	4	26	1	1	NUM
ejpam-6038	4	27	.	.	PUNCT
ejpam-6038	4	28	introduction	introduction	NOUN
ejpam-6038	4	29	in	in	ADP
ejpam-6038	4	30	1966	1966	NUM
ejpam-6038	4	31	,	,	PUNCT
ejpam-6038	4	32	dontchev	dontchev	ADJ
ejpam-6038	4	33	[	[	X
ejpam-6038	4	34	1	1	NUM
ejpam-6038	4	35	]	]	PUNCT
ejpam-6038	4	36	introduced	introduce	VERB
ejpam-6038	4	37	the	the	DET
ejpam-6038	4	38	concepts	concept	NOUN
ejpam-6038	4	39	of	of	ADP
ejpam-6038	4	40	contra	contra	PROPN
ejpam-6038	4	41	-	-	NOUN
ejpam-6038	4	42	continuity	continuity	NOUN
ejpam-6038	4	43	and	and	CCONJ
ejpam-6038	4	44	strong	strong	ADJ
ejpam-6038	4	45	sclosedness	sclosedness	NOUN
ejpam-6038	4	46	in	in	ADP
ejpam-6038	4	47	topological	topological	ADJ
ejpam-6038	4	48	spaces	space	NOUN
ejpam-6038	4	49	.	.	PUNCT
ejpam-6038	5	1	moreover	moreover	ADV
ejpam-6038	5	2	,	,	PUNCT
ejpam-6038	5	3	dontchev	dontchev	ADJ
ejpam-6038	5	4	[	[	X
ejpam-6038	5	5	1	1	NUM
ejpam-6038	5	6	]	]	PUNCT
ejpam-6038	5	7	obtained	obtain	VERB
ejpam-6038	5	8	very	very	ADV
ejpam-6038	5	9	interesting	interesting	ADJ
ejpam-6038	5	10	and	and	CCONJ
ejpam-6038	5	11	important	important	ADJ
ejpam-6038	5	12	results	result	NOUN
ejpam-6038	5	13	concerning	concern	VERB
ejpam-6038	5	14	contra	contra	NOUN
ejpam-6038	5	15	-	-	ADJ
ejpam-6038	5	16	continuity	continuity	NOUN
ejpam-6038	5	17	,	,	PUNCT
ejpam-6038	5	18	compactness	compactness	NOUN
ejpam-6038	5	19	,	,	PUNCT
ejpam-6038	5	20	s	s	NOUN
ejpam-6038	5	21	-	-	PUNCT
ejpam-6038	5	22	closedness	closedness	ADJ
ejpam-6038	5	23	and	and	CCONJ
ejpam-6038	5	24	strong	strong	ADJ
ejpam-6038	5	25	sclosedness	sclosedness	NOUN
ejpam-6038	5	26	.	.	PUNCT
ejpam-6038	6	1	in	in	ADP
ejpam-6038	6	2	1999	1999	NUM
ejpam-6038	6	3	,	,	PUNCT
ejpam-6038	6	4	dontchev	dontchev	NOUN
ejpam-6038	6	5	et	et	PROPN
ejpam-6038	6	6	al	al	PROPN
ejpam-6038	6	7	.	.	PUNCT
ejpam-6038	7	1	[	[	X
ejpam-6038	7	2	2	2	X
ejpam-6038	7	3	]	]	PUNCT
ejpam-6038	7	4	defined	define	VERB
ejpam-6038	7	5	a	a	DET
ejpam-6038	7	6	new	new	ADJ
ejpam-6038	7	7	class	class	NOUN
ejpam-6038	7	8	of	of	ADP
ejpam-6038	7	9	functions	function	NOUN
ejpam-6038	7	10	called	call	VERB
ejpam-6038	7	11	regular	regular	ADJ
ejpam-6038	7	12	set	set	NOUN
ejpam-6038	7	13	-	-	PUNCT
ejpam-6038	7	14	connected	connect	VERB
ejpam-6038	7	15	functions	function	NOUN
ejpam-6038	7	16	.	.	PUNCT
ejpam-6038	8	1	furthermore	furthermore	ADV
ejpam-6038	8	2	,	,	PUNCT
ejpam-6038	8	3	dontchev	dontchev	ADJ
ejpam-6038	8	4	and	and	CCONJ
ejpam-6038	8	5	noiri	noiri	ADV
ejpam-6038	9	1	[	[	X
ejpam-6038	9	2	3	3	X
ejpam-6038	9	3	]	]	PUNCT
ejpam-6038	9	4	introduced	introduce	VERB
ejpam-6038	9	5	and	and	CCONJ
ejpam-6038	9	6	studied	study	VERB
ejpam-6038	9	7	the	the	DET
ejpam-6038	9	8	concept	concept	NOUN
ejpam-6038	9	9	of	of	ADP
ejpam-6038	9	10	rc	rc	NOUN
ejpam-6038	9	11	-	-	NOUN
ejpam-6038	9	12	continuity	continuity	NOUN
ejpam-6038	9	13	between	between	ADP
ejpam-6038	9	14	topological	topological	ADJ
ejpam-6038	9	15	spaces	space	NOUN
ejpam-6038	9	16	which	which	PRON
ejpam-6038	9	17	is	be	AUX
ejpam-6038	9	18	weaker	weak	ADJ
ejpam-6038	9	19	than	than	ADP
ejpam-6038	9	20	contracontinuity	contracontinuity	NOUN
ejpam-6038	9	21	.	.	PUNCT
ejpam-6038	10	1	in	in	ADP
ejpam-6038	10	2	[	[	X
ejpam-6038	10	3	4	4	NUM
ejpam-6038	10	4	]	]	PUNCT
ejpam-6038	10	5	,	,	PUNCT
ejpam-6038	10	6	the	the	DET
ejpam-6038	10	7	present	present	ADJ
ejpam-6038	10	8	authors	author	NOUN
ejpam-6038	10	9	introduced	introduce	VERB
ejpam-6038	10	10	and	and	CCONJ
ejpam-6038	10	11	investigated	investigate	VERB
ejpam-6038	10	12	a	a	DET
ejpam-6038	10	13	new	new	ADJ
ejpam-6038	10	14	class	class	NOUN
ejpam-6038	10	15	of	of	ADP
ejpam-6038	10	16	functions	function	NOUN
ejpam-6038	10	17	called	call	VERB
ejpam-6038	10	18	contra	contra	NOUN
ejpam-6038	10	19	-	-	PUNCT
ejpam-6038	10	20	super	super	ADJ
ejpam-6038	10	21	-	-	ADJ
ejpam-6038	10	22	continuous	continuous	ADJ
ejpam-6038	10	23	functions	function	NOUN
ejpam-6038	10	24	which	which	PRON
ejpam-6038	10	25	lies	lie	VERB
ejpam-6038	10	26	between	between	ADP
ejpam-6038	10	27	classes	class	NOUN
ejpam-6038	10	28	of	of	ADP
ejpam-6038	10	29	rc	rc	PROPN
ejpam-6038	10	30	-	-	ADJ
ejpam-6038	10	31	continuous	continuous	ADJ
ejpam-6038	10	32	functions	function	NOUN
ejpam-6038	10	33	and	and	CCONJ
ejpam-6038	10	34	contra	contra	ADJ
ejpam-6038	10	35	-	-	ADJ
ejpam-6038	10	36	continuous	continuous	ADJ
ejpam-6038	10	37	functions	function	NOUN
ejpam-6038	10	38	.	.	PUNCT
ejpam-6038	11	1	in	in	ADP
ejpam-6038	11	2	2002	2002	NUM
ejpam-6038	11	3	,	,	PUNCT
ejpam-6038	11	4	jafari	jafari	ADJ
ejpam-6038	11	5	and	and	CCONJ
ejpam-6038	11	6	noiri	noiri	ADV
ejpam-6038	11	7	[	[	X
ejpam-6038	11	8	5	5	NUM
ejpam-6038	11	9	]	]	PUNCT
ejpam-6038	11	10	introduced	introduce	VERB
ejpam-6038	11	11	a	a	DET
ejpam-6038	11	12	new	new	ADJ
ejpam-6038	11	13	class	class	NOUN
ejpam-6038	11	14	of	of	ADP
ejpam-6038	11	15	function	function	NOUN
ejpam-6038	11	16	called	call	VERB
ejpam-6038	11	17	contra	contra	ADJ
ejpam-6038	11	18	-	-	ADJ
ejpam-6038	11	19	precontinuous	precontinuous	ADJ
ejpam-6038	11	20	functions	function	NOUN
ejpam-6038	11	21	which	which	PRON
ejpam-6038	11	22	is	be	AUX
ejpam-6038	11	23	weaker	weak	ADJ
ejpam-6038	11	24	than	than	ADP
ejpam-6038	11	25	contra	contra	ADJ
ejpam-6038	11	26	-	-	ADJ
ejpam-6038	11	27	continuous	continuous	ADJ
ejpam-6038	11	28	functions	function	NOUN
ejpam-6038	11	29	and	and	CCONJ
ejpam-6038	11	30	studied	study	VERB
ejpam-6038	11	31	several	several	ADJ
ejpam-6038	11	32	basic	basic	ADJ
ejpam-6038	11	33	properties	property	NOUN
ejpam-6038	11	34	of	of	ADP
ejpam-6038	11	35	contra	contra	ADJ
ejpam-6038	11	36	-	-	ADJ
ejpam-6038	11	37	precontinuous	precontinuous	ADJ
ejpam-6038	11	38	functions	function	NOUN
ejpam-6038	11	39	.	.	PUNCT
ejpam-6038	12	1	in	in	ADP
ejpam-6038	12	2	particular	particular	ADJ
ejpam-6038	12	3	,	,	PUNCT
ejpam-6038	12	4	jafari	jafari	ADJ
ejpam-6038	12	5	and	and	CCONJ
ejpam-6038	12	6	noiri	noiri	ADV
ejpam-6038	12	7	[	[	X
ejpam-6038	12	8	5	5	NUM
ejpam-6038	12	9	]	]	PUNCT
ejpam-6038	12	10	defined	define	VERB
ejpam-6038	12	11	contra	contra	PROPN
ejpam-6038	12	12	-	-	ADJ
ejpam-6038	12	13	preclosed	preclose	VERB
ejpam-6038	12	14	graphs	graph	NOUN
ejpam-6038	12	15	and	and	CCONJ
ejpam-6038	12	16	investigated	investigate	VERB
ejpam-6038	12	17	relations	relation	NOUN
ejpam-6038	12	18	between	between	ADP
ejpam-6038	12	19	contra	contra	PROPN
ejpam-6038	12	20	-	-	NOUN
ejpam-6038	12	21	precontinuity	precontinuity	NOUN
ejpam-6038	12	22	and	and	CCONJ
ejpam-6038	12	23	contra	contra	PROPN
ejpam-6038	12	24	-	-	PUNCT
ejpam-6038	12	25	preclosed	preclose	VERB
ejpam-6038	12	26	graphs	graph	NOUN
ejpam-6038	12	27	.	.	PUNCT
ejpam-6038	13	1	in	in	ADP
ejpam-6038	13	2	2004	2004	NUM
ejpam-6038	13	3	,	,	PUNCT
ejpam-6038	13	4	ekici	ekici	NOUN
ejpam-6038	13	5	[	[	X
ejpam-6038	13	6	6	6	NUM
ejpam-6038	13	7	]	]	PUNCT
ejpam-6038	13	8	introduced	introduce	VERB
ejpam-6038	13	9	and	and	CCONJ
ejpam-6038	13	10	studied	study	VERB
ejpam-6038	13	11	a	a	DET
ejpam-6038	13	12	new	new	ADJ
ejpam-6038	13	13	class	class	NOUN
ejpam-6038	13	14	of	of	ADP
ejpam-6038	13	15	functions	function	NOUN
ejpam-6038	13	16	called	call	VERB
ejpam-6038	13	17	almost	almost	ADV
ejpam-6038	13	18	contra	contra	ADJ
ejpam-6038	13	19	-	-	ADJ
ejpam-6038	13	20	precontinuous	precontinuous	ADJ
ejpam-6038	13	21	functions	function	NOUN
ejpam-6038	13	22	which	which	PRON
ejpam-6038	13	23	generalize	generalize	VERB
ejpam-6038	13	24	classes	class	NOUN
ejpam-6038	13	25	of	of	ADP
ejpam-6038	13	26	regular	regular	ADJ
ejpam-6038	13	27	set	set	NOUN
ejpam-6038	13	28	-	-	PUNCT
ejpam-6038	13	29	connected	connect	VERB
ejpam-6038	13	30	functions	function	NOUN
ejpam-6038	13	31	[	[	X
ejpam-6038	13	32	2	2	NUM
ejpam-6038	13	33	]	]	PUNCT
ejpam-6038	13	34	,	,	PUNCT
ejpam-6038	13	35	contra	contra	ADJ
ejpam-6038	13	36	-	-	ADJ
ejpam-6038	13	37	precontinuous	precontinuous	ADJ
ejpam-6038	13	38	functions	function	NOUN
ejpam-6038	13	39	[	[	X
ejpam-6038	13	40	5	5	NUM
ejpam-6038	13	41	]	]	PUNCT
ejpam-6038	13	42	,	,	PUNCT
ejpam-6038	13	43	contra	contra	ADJ
ejpam-6038	13	44	-	-	ADJ
ejpam-6038	13	45	continuous	continuous	ADJ
ejpam-6038	13	46	functions	function	NOUN
ejpam-6038	13	47	[	[	X
ejpam-6038	13	48	1	1	NUM
ejpam-6038	13	49	]	]	PUNCT
ejpam-6038	13	50	,	,	PUNCT
ejpam-6038	13	51	almost	almost	ADV
ejpam-6038	13	52	s	s	NOUN
ejpam-6038	13	53	-	-	ADJ
ejpam-6038	13	54	continuous	continuous	ADJ
ejpam-6038	13	55	functions	function	NOUN
ejpam-6038	13	56	[	[	X
ejpam-6038	13	57	7	7	NUM
ejpam-6038	13	58	]	]	PUNCT
ejpam-6038	13	59	and	and	CCONJ
ejpam-6038	13	60	perfectly	perfectly	ADV
ejpam-6038	13	61	continuous	continuous	ADJ
ejpam-6038	13	62	functions	function	NOUN
ejpam-6038	13	63	[	[	X
ejpam-6038	13	64	8	8	NUM
ejpam-6038	13	65	]	]	PUNCT
ejpam-6038	13	66	.	.	PUNCT
ejpam-6038	14	1	ekici	ekici	PROPN
ejpam-6038	15	1	[	[	X
ejpam-6038	15	2	6	6	NUM
ejpam-6038	15	3	]	]	PUNCT
ejpam-6038	15	4	obtained	obtain	VERB
ejpam-6038	15	5	basic	basic	ADJ
ejpam-6038	15	6	properties	property	NOUN
ejpam-6038	15	7	and	and	CCONJ
ejpam-6038	15	8	preservation	preservation	NOUN
ejpam-6038	15	9	theorems	theorem	NOUN
ejpam-6038	15	10	of	of	ADP
ejpam-6038	15	11	almost	almost	ADV
ejpam-6038	15	12	∗corresponding	∗corresponde	VERB
ejpam-6038	15	13	author	author	NOUN
ejpam-6038	15	14	.	.	PUNCT
ejpam-6038	16	1	doi	doi	NOUN
ejpam-6038	16	2	:	:	PUNCT
ejpam-6038	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6038	https://doi.org/10.29020/nybg.ejpam.v18i2.6038	PROPN
ejpam-6038	16	4	email	email	NOUN
ejpam-6038	16	5	addresses	address	NOUN
ejpam-6038	16	6	:	:	PUNCT
ejpam-6038	16	7	prapart.p@msu.ac.th	prapart.p@msu.ac.th	PROPN
ejpam-6038	16	8	(	(	PUNCT
ejpam-6038	16	9	p.	p.	NOUN
ejpam-6038	16	10	pue	pue	NOUN
ejpam-6038	16	11	-	-	PUNCT
ejpam-6038	16	12	on	on	ADP
ejpam-6038	16	13	)	)	PUNCT
ejpam-6038	16	14	,	,	PUNCT
ejpam-6038	16	15	areeyuth.s@psu.ac.th	areeyuth.s@psu.ac.th	X
ejpam-6038	16	16	(	(	PUNCT
ejpam-6038	16	17	a.	a.	PROPN
ejpam-6038	16	18	sama	sama	PROPN
ejpam-6038	16	19	-	-	PUNCT
ejpam-6038	16	20	ae	ae	PROPN
ejpam-6038	16	21	)	)	PUNCT
ejpam-6038	16	22	,	,	PUNCT
ejpam-6038	16	23	chawalit.b@msu.ac.th	chawalit.b@msu.ac.th	PROPN
ejpam-6038	16	24	(	(	PUNCT
ejpam-6038	16	25	c.	c.	PROPN
ejpam-6038	16	26	boonpok	boonpok	PROPN
ejpam-6038	16	27	)	)	PUNCT
ejpam-6038	16	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6038	16	29	1	1	NUM
ejpam-6038	16	30	copyright	copyright	NOUN
ejpam-6038	16	31	:	:	PUNCT
ejpam-6038	16	32	©	©	PROPN
ejpam-6038	16	33	2025	2025	NUM
ejpam-6038	16	34	the	the	DET
ejpam-6038	16	35	author(s	author(s	NOUN
ejpam-6038	16	36	)	)	PUNCT
ejpam-6038	16	37	.	.	PUNCT
ejpam-6038	17	1	(	(	PUNCT
ejpam-6038	17	2	cc	cc	NOUN
ejpam-6038	17	3	by	by	ADP
ejpam-6038	17	4	-	-	PUNCT
ejpam-6038	17	5	nc	nc	PROPN
ejpam-6038	17	6	4.0	4.0	NUM
ejpam-6038	17	7	)	)	PUNCT
ejpam-6038	17	8	p.	p.	NOUN
ejpam-6038	17	9	pue	pue	NOUN
ejpam-6038	17	10	-	-	PUNCT
ejpam-6038	17	11	on	on	ADP
ejpam-6038	17	12	,	,	PUNCT
ejpam-6038	17	13	a.	a.	PROPN
ejpam-6038	17	14	sama	sama	PROPN
ejpam-6038	17	15	-	-	PUNCT
ejpam-6038	17	16	ae	ae	PROPN
ejpam-6038	17	17	,	,	PUNCT
ejpam-6038	17	18	c.	c.	PROPN
ejpam-6038	17	19	boonpok	boonpok	PROPN
ejpam-6038	17	20	/	/	SYM
ejpam-6038	17	21	eur	eur	PROPN
ejpam-6038	17	22	.	.	PUNCT
ejpam-6038	18	1	j.	j.	PROPN
ejpam-6038	18	2	pure	pure	PROPN
ejpam-6038	18	3	appl	appl	PROPN
ejpam-6038	18	4	.	.	PROPN
ejpam-6038	18	5	math	math	PROPN
ejpam-6038	18	6	,	,	PUNCT
ejpam-6038	18	7	18	18	NUM
ejpam-6038	18	8	(	(	PUNCT
ejpam-6038	18	9	2	2	NUM
ejpam-6038	18	10	)	)	PUNCT
ejpam-6038	18	11	(	(	PUNCT
ejpam-6038	18	12	2025	2025	NUM
ejpam-6038	18	13	)	)	PUNCT
ejpam-6038	18	14	,	,	PUNCT
ejpam-6038	18	15	6038	6038	NUM
ejpam-6038	18	16	2	2	NUM
ejpam-6038	18	17	of	of	ADP
ejpam-6038	18	18	11	11	NUM
ejpam-6038	18	19	contra	contra	ADJ
ejpam-6038	18	20	-	-	ADJ
ejpam-6038	18	21	precontinuous	precontinuous	ADJ
ejpam-6038	18	22	functions	function	NOUN
ejpam-6038	18	23	and	and	CCONJ
ejpam-6038	18	24	relationships	relationship	NOUN
ejpam-6038	18	25	between	between	ADP
ejpam-6038	18	26	almost	almost	ADV
ejpam-6038	18	27	contra	contra	NOUN
ejpam-6038	18	28	-	-	NOUN
ejpam-6038	18	29	precontinuity	precontinuity	NOUN
ejpam-6038	18	30	and	and	CCONJ
ejpam-6038	18	31	p	p	NOUN
ejpam-6038	18	32	-regular	-regular	ADJ
ejpam-6038	18	33	graphs	graph	NOUN
ejpam-6038	18	34	.	.	PUNCT
ejpam-6038	19	1	noiri	noiri	PROPN
ejpam-6038	19	2	and	and	CCONJ
ejpam-6038	19	3	jafari	jafari	PROPN
ejpam-6038	19	4	[	[	X
ejpam-6038	19	5	9	9	NUM
ejpam-6038	19	6	]	]	PUNCT
ejpam-6038	19	7	obtained	obtain	VERB
ejpam-6038	19	8	the	the	DET
ejpam-6038	19	9	further	further	ADJ
ejpam-6038	19	10	characterizations	characterization	NOUN
ejpam-6038	19	11	and	and	CCONJ
ejpam-6038	19	12	properties	property	NOUN
ejpam-6038	19	13	of	of	ADP
ejpam-6038	19	14	almost	almost	ADV
ejpam-6038	19	15	contra	contra	ADJ
ejpam-6038	19	16	-	-	ADJ
ejpam-6038	19	17	precontinuous	precontinuous	ADJ
ejpam-6038	19	18	functions	function	NOUN
ejpam-6038	19	19	and	and	CCONJ
ejpam-6038	19	20	showed	show	VERB
ejpam-6038	19	21	that	that	SCONJ
ejpam-6038	19	22	(	(	PUNCT
ejpam-6038	19	23	s	s	NOUN
ejpam-6038	19	24	,	,	PUNCT
ejpam-6038	19	25	p)-continuity	p)-continuity	NOUN
ejpam-6038	19	26	due	due	ADP
ejpam-6038	19	27	to	to	ADP
ejpam-6038	19	28	jafari	jafari	PROPN
ejpam-6038	19	29	[	[	X
ejpam-6038	19	30	10	10	NUM
ejpam-6038	19	31	]	]	PUNCT
ejpam-6038	19	32	is	be	AUX
ejpam-6038	19	33	equivalent	equivalent	ADJ
ejpam-6038	19	34	to	to	ADP
ejpam-6038	19	35	almost	almost	ADV
ejpam-6038	19	36	contra	contra	NOUN
ejpam-6038	19	37	-	-	NOUN
ejpam-6038	19	38	precontinuity	precontinuity	NOUN
ejpam-6038	19	39	.	.	PUNCT
ejpam-6038	20	1	in	in	ADP
ejpam-6038	20	2	2007	2007	NUM
ejpam-6038	20	3	,	,	PUNCT
ejpam-6038	20	4	al	al	PROPN
ejpam-6038	20	5	-	-	PUNCT
ejpam-6038	20	6	omari	omari	PROPN
ejpam-6038	20	7	and	and	CCONJ
ejpam-6038	20	8	noorani	noorani	ADJ
ejpam-6038	20	9	[	[	X
ejpam-6038	20	10	11	11	NUM
ejpam-6038	20	11	]	]	PUNCT
ejpam-6038	20	12	introduced	introduce	VERB
ejpam-6038	20	13	the	the	DET
ejpam-6038	20	14	concept	concept	NOUN
ejpam-6038	20	15	of	of	ADP
ejpam-6038	20	16	almost	almost	ADV
ejpam-6038	20	17	contra	contra	PROPN
ejpam-6038	20	18	ω	ω	ADJ
ejpam-6038	20	19	-	-	ADJ
ejpam-6038	20	20	continuous	continuous	ADJ
ejpam-6038	20	21	functions	function	NOUN
ejpam-6038	20	22	via	via	ADP
ejpam-6038	20	23	the	the	DET
ejpam-6038	20	24	notion	notion	NOUN
ejpam-6038	20	25	of	of	ADP
ejpam-6038	20	26	ωopen	ωopen	ADJ
ejpam-6038	20	27	sets	set	NOUN
ejpam-6038	20	28	and	and	CCONJ
ejpam-6038	20	29	investigated	investigate	VERB
ejpam-6038	20	30	several	several	ADJ
ejpam-6038	20	31	characterizations	characterization	NOUN
ejpam-6038	20	32	of	of	ADP
ejpam-6038	20	33	contra	contra	PROPN
ejpam-6038	20	34	ω	ω	PROPN
ejpam-6038	20	35	-	-	ADJ
ejpam-6038	20	36	continuous	continuous	ADJ
ejpam-6038	20	37	functions	function	NOUN
ejpam-6038	20	38	and	and	CCONJ
ejpam-6038	20	39	almost	almost	ADV
ejpam-6038	20	40	contra	contra	PROPN
ejpam-6038	20	41	ω	ω	ADJ
ejpam-6038	20	42	-	-	ADJ
ejpam-6038	20	43	continuous	continuous	ADJ
ejpam-6038	20	44	functions	function	NOUN
ejpam-6038	20	45	.	.	PUNCT
ejpam-6038	21	1	on	on	ADP
ejpam-6038	21	2	the	the	DET
ejpam-6038	21	3	other	other	ADJ
ejpam-6038	21	4	hand	hand	NOUN
ejpam-6038	21	5	,	,	PUNCT
ejpam-6038	21	6	the	the	DET
ejpam-6038	21	7	present	present	ADJ
ejpam-6038	21	8	authors	author	NOUN
ejpam-6038	21	9	introduced	introduce	VERB
ejpam-6038	21	10	and	and	CCONJ
ejpam-6038	21	11	studied	study	VERB
ejpam-6038	21	12	the	the	DET
ejpam-6038	21	13	notions	notion	NOUN
ejpam-6038	21	14	of	of	ADP
ejpam-6038	21	15	of	of	ADP
ejpam-6038	21	16	(	(	PUNCT
ejpam-6038	21	17	τ1	τ1	NOUN
ejpam-6038	21	18	,	,	PUNCT
ejpam-6038	21	19	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	20	functions	function	NOUN
ejpam-6038	21	21	[	[	X
ejpam-6038	21	22	12	12	NUM
ejpam-6038	21	23	]	]	PUNCT
ejpam-6038	21	24	,	,	PUNCT
ejpam-6038	21	25	almost	almost	ADV
ejpam-6038	21	26	(	(	PUNCT
ejpam-6038	21	27	τ1	τ1	NOUN
ejpam-6038	21	28	,	,	PUNCT
ejpam-6038	21	29	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	30	functions	function	NOUN
ejpam-6038	21	31	[	[	X
ejpam-6038	21	32	13	13	NUM
ejpam-6038	21	33	]	]	PUNCT
ejpam-6038	21	34	,	,	PUNCT
ejpam-6038	21	35	weakly	weakly	ADJ
ejpam-6038	21	36	(	(	PUNCT
ejpam-6038	21	37	τ1	τ1	NOUN
ejpam-6038	21	38	,	,	PUNCT
ejpam-6038	21	39	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	40	functions	function	NOUN
ejpam-6038	21	41	[	[	X
ejpam-6038	21	42	14	14	NUM
ejpam-6038	21	43	]	]	PUNCT
ejpam-6038	21	44	,	,	PUNCT
ejpam-6038	21	45	quasi	quasi	NOUN
ejpam-6038	21	46	θ(τ1	θ(τ1	NOUN
ejpam-6038	21	47	,	,	PUNCT
ejpam-6038	21	48	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	49	functions	function	NOUN
ejpam-6038	21	50	[	[	X
ejpam-6038	21	51	15	15	NUM
ejpam-6038	21	52	]	]	PUNCT
ejpam-6038	21	53	,	,	PUNCT
ejpam-6038	21	54	δ(τ1	δ(τ1	PROPN
ejpam-6038	21	55	,	,	PUNCT
ejpam-6038	21	56	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	57	functions	function	NOUN
ejpam-6038	21	58	[	[	X
ejpam-6038	21	59	16	16	NUM
ejpam-6038	21	60	]	]	PUNCT
ejpam-6038	21	61	,	,	PUNCT
ejpam-6038	21	62	almost	almost	ADV
ejpam-6038	21	63	quasi	quasi	NOUN
ejpam-6038	21	64	(	(	PUNCT
ejpam-6038	21	65	τ1	τ1	NOUN
ejpam-6038	21	66	,	,	PUNCT
ejpam-6038	21	67	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	68	functions	function	NOUN
ejpam-6038	21	69	[	[	X
ejpam-6038	21	70	17	17	NUM
ejpam-6038	21	71	]	]	PUNCT
ejpam-6038	21	72	,	,	PUNCT
ejpam-6038	21	73	weakly	weakly	ADJ
ejpam-6038	21	74	quasi	quasi	NOUN
ejpam-6038	21	75	(	(	PUNCT
ejpam-6038	21	76	τ1	τ1	PROPN
ejpam-6038	21	77	,	,	PUNCT
ejpam-6038	21	78	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	79	functions	function	NOUN
ejpam-6038	21	80	[	[	X
ejpam-6038	21	81	18	18	NUM
ejpam-6038	21	82	]	]	PUNCT
ejpam-6038	21	83	,	,	PUNCT
ejpam-6038	21	84	faintly	faintly	ADV
ejpam-6038	21	85	(	(	PUNCT
ejpam-6038	21	86	τ1	τ1	PROPN
ejpam-6038	21	87	,	,	PUNCT
ejpam-6038	21	88	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	89	functions	function	NOUN
ejpam-6038	21	90	[	[	X
ejpam-6038	21	91	19	19	NUM
ejpam-6038	21	92	]	]	X
ejpam-6038	21	93	,	,	PUNCT
ejpam-6038	21	94	almost	almost	ADV
ejpam-6038	21	95	nearly	nearly	ADV
ejpam-6038	21	96	(	(	PUNCT
ejpam-6038	21	97	τ1	τ1	NOUN
ejpam-6038	21	98	,	,	PUNCT
ejpam-6038	21	99	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	100	functions	function	NOUN
ejpam-6038	21	101	,	,	PUNCT
ejpam-6038	21	102	almost	almost	ADV
ejpam-6038	21	103	weakly	weakly	ADJ
ejpam-6038	21	104	(	(	PUNCT
ejpam-6038	21	105	τ1	τ1	NOUN
ejpam-6038	21	106	,	,	PUNCT
ejpam-6038	21	107	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	21	108	functions	function	NOUN
ejpam-6038	21	109	[	[	X
ejpam-6038	21	110	20	20	NUM
ejpam-6038	21	111	]	]	PUNCT
ejpam-6038	21	112	and	and	CCONJ
ejpam-6038	21	113	almost	almost	ADV
ejpam-6038	21	114	contra-(λ	contra-(λ	PROPN
ejpam-6038	21	115	,	,	PUNCT
ejpam-6038	21	116	sp)-continuous	sp)-continuous	ADJ
ejpam-6038	21	117	functions	function	NOUN
ejpam-6038	21	118	[	[	X
ejpam-6038	21	119	21	21	NUM
ejpam-6038	21	120	]	]	PUNCT
ejpam-6038	21	121	.	.	PUNCT
ejpam-6038	22	1	in	in	ADP
ejpam-6038	22	2	this	this	DET
ejpam-6038	22	3	paper	paper	NOUN
ejpam-6038	22	4	,	,	PUNCT
ejpam-6038	22	5	we	we	PRON
ejpam-6038	22	6	introduce	introduce	VERB
ejpam-6038	22	7	the	the	DET
ejpam-6038	22	8	concept	concept	NOUN
ejpam-6038	22	9	of	of	ADP
ejpam-6038	22	10	almost	almost	ADV
ejpam-6038	22	11	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	22	12	,	,	PUNCT
ejpam-6038	22	13	τ2)p	τ2)p	ADJ
ejpam-6038	22	14	-	-	PUNCT
ejpam-6038	22	15	continuous	continuous	ADJ
ejpam-6038	22	16	functions	function	NOUN
ejpam-6038	22	17	.	.	PUNCT
ejpam-6038	23	1	we	we	PRON
ejpam-6038	23	2	also	also	ADV
ejpam-6038	23	3	investigate	investigate	VERB
ejpam-6038	23	4	some	some	DET
ejpam-6038	23	5	characterizations	characterization	NOUN
ejpam-6038	23	6	of	of	ADP
ejpam-6038	23	7	almost	almost	ADV
ejpam-6038	23	8	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	23	9	,	,	PUNCT
ejpam-6038	23	10	τ2)p	τ2)p	ADJ
ejpam-6038	23	11	-	-	PUNCT
ejpam-6038	23	12	continuous	continuous	ADJ
ejpam-6038	23	13	functions	function	NOUN
ejpam-6038	23	14	.	.	PUNCT
ejpam-6038	24	1	2	2	X
ejpam-6038	24	2	.	.	NUM
ejpam-6038	24	3	preliminaries	preliminary	NOUN
ejpam-6038	24	4	throughout	throughout	ADP
ejpam-6038	24	5	the	the	DET
ejpam-6038	24	6	present	present	ADJ
ejpam-6038	24	7	paper	paper	NOUN
ejpam-6038	24	8	,	,	PUNCT
ejpam-6038	24	9	spaces	space	NOUN
ejpam-6038	24	10	(	(	PUNCT
ejpam-6038	24	11	x	x	NOUN
ejpam-6038	24	12	,	,	PUNCT
ejpam-6038	24	13	τ1	τ1	NOUN
ejpam-6038	24	14	,	,	PUNCT
ejpam-6038	24	15	τ2	τ2	NOUN
ejpam-6038	24	16	)	)	PUNCT
ejpam-6038	24	17	and	and	CCONJ
ejpam-6038	24	18	(	(	PUNCT
ejpam-6038	24	19	y	y	PROPN
ejpam-6038	24	20	,	,	PUNCT
ejpam-6038	24	21	σ1	σ1	PROPN
ejpam-6038	24	22	,	,	PUNCT
ejpam-6038	24	23	σ2	σ2	NOUN
ejpam-6038	24	24	)	)	PUNCT
ejpam-6038	24	25	(	(	PUNCT
ejpam-6038	24	26	or	or	CCONJ
ejpam-6038	24	27	simply	simply	ADV
ejpam-6038	24	28	x	x	X
ejpam-6038	24	29	and	and	CCONJ
ejpam-6038	24	30	y	y	PROPN
ejpam-6038	24	31	)	)	PUNCT
ejpam-6038	24	32	always	always	ADV
ejpam-6038	24	33	mean	mean	VERB
ejpam-6038	24	34	bitopological	bitopological	ADJ
ejpam-6038	24	35	spaces	space	NOUN
ejpam-6038	24	36	on	on	ADP
ejpam-6038	24	37	which	which	PRON
ejpam-6038	24	38	no	no	DET
ejpam-6038	24	39	separation	separation	NOUN
ejpam-6038	24	40	axioms	axiom	NOUN
ejpam-6038	24	41	are	be	AUX
ejpam-6038	24	42	assumed	assume	VERB
ejpam-6038	24	43	unless	unless	SCONJ
ejpam-6038	24	44	explicitly	explicitly	ADV
ejpam-6038	24	45	stated	state	VERB
ejpam-6038	24	46	.	.	PUNCT
ejpam-6038	25	1	let	let	VERB
ejpam-6038	25	2	a	a	DET
ejpam-6038	25	3	be	be	AUX
ejpam-6038	25	4	a	a	DET
ejpam-6038	25	5	subset	subset	NOUN
ejpam-6038	25	6	of	of	ADP
ejpam-6038	25	7	a	a	DET
ejpam-6038	25	8	bitopological	bitopological	ADJ
ejpam-6038	25	9	space	space	NOUN
ejpam-6038	25	10	(	(	PUNCT
ejpam-6038	25	11	x	x	NOUN
ejpam-6038	25	12	,	,	PUNCT
ejpam-6038	25	13	τ1	τ1	NOUN
ejpam-6038	25	14	,	,	PUNCT
ejpam-6038	25	15	τ2	τ2	NOUN
ejpam-6038	25	16	)	)	PUNCT
ejpam-6038	25	17	.	.	PUNCT
ejpam-6038	26	1	the	the	DET
ejpam-6038	26	2	closure	closure	NOUN
ejpam-6038	26	3	of	of	ADP
ejpam-6038	26	4	a	a	PRON
ejpam-6038	26	5	and	and	CCONJ
ejpam-6038	26	6	the	the	DET
ejpam-6038	26	7	interior	interior	NOUN
ejpam-6038	26	8	of	of	ADP
ejpam-6038	26	9	a	a	PRON
ejpam-6038	26	10	with	with	ADP
ejpam-6038	26	11	respect	respect	NOUN
ejpam-6038	26	12	to	to	ADP
ejpam-6038	26	13	τi	τi	PROPN
ejpam-6038	26	14	are	be	AUX
ejpam-6038	26	15	denoted	denote	VERB
ejpam-6038	26	16	by	by	ADP
ejpam-6038	26	17	τi	τi	NOUN
ejpam-6038	26	18	-	-	PUNCT
ejpam-6038	26	19	cl(a	cl(a	NUM
ejpam-6038	26	20	)	)	PUNCT
ejpam-6038	26	21	and	and	CCONJ
ejpam-6038	26	22	τi	τi	NOUN
ejpam-6038	26	23	-	-	PUNCT
ejpam-6038	26	24	int(a	int(a	NOUN
ejpam-6038	26	25	)	)	PUNCT
ejpam-6038	26	26	,	,	PUNCT
ejpam-6038	26	27	respectively	respectively	ADV
ejpam-6038	26	28	,	,	PUNCT
ejpam-6038	26	29	for	for	ADP
ejpam-6038	26	30	i	i	PROPN
ejpam-6038	26	31	=	=	SYM
ejpam-6038	26	32	1	1	NUM
ejpam-6038	26	33	,	,	PUNCT
ejpam-6038	26	34	2	2	NUM
ejpam-6038	26	35	.	.	X
ejpam-6038	26	36	a	a	DET
ejpam-6038	26	37	subset	subset	NOUN
ejpam-6038	26	38	a	a	PRON
ejpam-6038	26	39	of	of	ADP
ejpam-6038	26	40	a	a	DET
ejpam-6038	26	41	bitopological	bitopological	ADJ
ejpam-6038	26	42	space	space	NOUN
ejpam-6038	26	43	(	(	PUNCT
ejpam-6038	26	44	x	x	NOUN
ejpam-6038	26	45	,	,	PUNCT
ejpam-6038	26	46	τ1	τ1	NOUN
ejpam-6038	26	47	,	,	PUNCT
ejpam-6038	26	48	τ2	τ2	NOUN
ejpam-6038	26	49	)	)	PUNCT
ejpam-6038	26	50	is	be	AUX
ejpam-6038	26	51	called	call	VERB
ejpam-6038	26	52	τ1τ2	τ1τ2	VERB
ejpam-6038	26	53	-	-	ADJ
ejpam-6038	26	54	closed	closed	ADJ
ejpam-6038	26	55	[	[	X
ejpam-6038	26	56	22	22	NUM
ejpam-6038	26	57	]	]	PUNCT
ejpam-6038	26	58	if	if	SCONJ
ejpam-6038	26	59	a	a	DET
ejpam-6038	26	60	=	=	NOUN
ejpam-6038	26	61	τ1	τ1	NOUN
ejpam-6038	26	62	-	-	PUNCT
ejpam-6038	26	63	cl(τ2	cl(τ2	NOUN
ejpam-6038	26	64	-	-	PUNCT
ejpam-6038	26	65	cl(a	cl(a	NUM
ejpam-6038	26	66	)	)	PUNCT
ejpam-6038	26	67	)	)	PUNCT
ejpam-6038	26	68	.	.	PUNCT
ejpam-6038	27	1	the	the	DET
ejpam-6038	27	2	complement	complement	NOUN
ejpam-6038	27	3	of	of	ADP
ejpam-6038	27	4	a	a	DET
ejpam-6038	27	5	τ1τ2	τ1τ2	ADJ
ejpam-6038	27	6	-	-	ADJ
ejpam-6038	27	7	closed	closed	ADJ
ejpam-6038	27	8	set	set	NOUN
ejpam-6038	27	9	is	be	AUX
ejpam-6038	27	10	called	call	VERB
ejpam-6038	27	11	τ1τ2	τ1τ2	NOUN
ejpam-6038	27	12	-	-	ADJ
ejpam-6038	27	13	open	open	ADJ
ejpam-6038	27	14	.	.	PUNCT
ejpam-6038	28	1	the	the	DET
ejpam-6038	28	2	intersection	intersection	NOUN
ejpam-6038	28	3	of	of	ADP
ejpam-6038	28	4	all	all	DET
ejpam-6038	28	5	τ1τ2	τ1τ2	ADJ
ejpam-6038	28	6	-	-	ADJ
ejpam-6038	28	7	closed	closed	ADJ
ejpam-6038	28	8	sets	set	NOUN
ejpam-6038	28	9	of	of	ADP
ejpam-6038	28	10	x	x	PUNCT
ejpam-6038	28	11	containing	contain	VERB
ejpam-6038	28	12	a	a	PRON
ejpam-6038	28	13	is	be	AUX
ejpam-6038	28	14	called	call	VERB
ejpam-6038	28	15	the	the	DET
ejpam-6038	28	16	τ1τ2	τ1τ2	NOUN
ejpam-6038	28	17	-	-	NOUN
ejpam-6038	28	18	closure	closure	NOUN
ejpam-6038	28	19	[	[	X
ejpam-6038	28	20	22	22	NUM
ejpam-6038	28	21	]	]	PUNCT
ejpam-6038	28	22	of	of	ADP
ejpam-6038	28	23	a	a	PRON
ejpam-6038	28	24	and	and	CCONJ
ejpam-6038	28	25	is	be	AUX
ejpam-6038	28	26	denoted	denote	VERB
ejpam-6038	28	27	by	by	ADP
ejpam-6038	28	28	τ1τ2	τ1τ2	NOUN
ejpam-6038	28	29	-	-	NUM
ejpam-6038	28	30	cl(a	cl(a	NUM
ejpam-6038	28	31	)	)	PUNCT
ejpam-6038	28	32	.	.	PUNCT
ejpam-6038	29	1	the	the	DET
ejpam-6038	29	2	union	union	NOUN
ejpam-6038	29	3	of	of	ADP
ejpam-6038	29	4	all	all	DET
ejpam-6038	29	5	τ1τ2	τ1τ2	ADJ
ejpam-6038	29	6	-	-	ADJ
ejpam-6038	29	7	open	open	ADJ
ejpam-6038	29	8	sets	set	NOUN
ejpam-6038	29	9	of	of	ADP
ejpam-6038	29	10	x	x	PUNCT
ejpam-6038	29	11	contained	contain	VERB
ejpam-6038	29	12	in	in	ADP
ejpam-6038	29	13	a	a	PRON
ejpam-6038	29	14	is	be	AUX
ejpam-6038	29	15	called	call	VERB
ejpam-6038	29	16	the	the	DET
ejpam-6038	29	17	τ1τ2	τ1τ2	NOUN
ejpam-6038	29	18	-	-	ADJ
ejpam-6038	29	19	interior	interior	ADJ
ejpam-6038	29	20	[	[	X
ejpam-6038	29	21	22	22	NUM
ejpam-6038	29	22	]	]	PUNCT
ejpam-6038	29	23	of	of	ADP
ejpam-6038	29	24	a	a	PRON
ejpam-6038	29	25	and	and	CCONJ
ejpam-6038	29	26	is	be	AUX
ejpam-6038	29	27	denoted	denote	VERB
ejpam-6038	29	28	by	by	ADP
ejpam-6038	29	29	τ1τ2	τ1τ2	NOUN
ejpam-6038	29	30	-	-	ADJ
ejpam-6038	29	31	int(a	int(a	NOUN
ejpam-6038	29	32	)	)	PUNCT
ejpam-6038	29	33	.	.	PUNCT
ejpam-6038	30	1	lemma	lemma	PROPN
ejpam-6038	30	2	1	1	NUM
ejpam-6038	30	3	.	.	PUNCT
ejpam-6038	31	1	[	[	X
ejpam-6038	31	2	22	22	NUM
ejpam-6038	31	3	]	]	PUNCT
ejpam-6038	31	4	let	let	VERB
ejpam-6038	31	5	a	a	PRON
ejpam-6038	31	6	and	and	CCONJ
ejpam-6038	31	7	b	b	NOUN
ejpam-6038	31	8	be	be	AUX
ejpam-6038	31	9	subsets	subset	NOUN
ejpam-6038	31	10	of	of	ADP
ejpam-6038	31	11	a	a	DET
ejpam-6038	31	12	bitopological	bitopological	ADJ
ejpam-6038	31	13	space	space	NOUN
ejpam-6038	31	14	(	(	PUNCT
ejpam-6038	31	15	x	x	NOUN
ejpam-6038	31	16	,	,	PUNCT
ejpam-6038	31	17	τ1	τ1	NOUN
ejpam-6038	31	18	,	,	PUNCT
ejpam-6038	31	19	τ2	τ2	NOUN
ejpam-6038	31	20	)	)	PUNCT
ejpam-6038	31	21	.	.	PUNCT
ejpam-6038	32	1	for	for	ADP
ejpam-6038	32	2	the	the	DET
ejpam-6038	32	3	τ1τ2closure	τ1τ2closure	NOUN
ejpam-6038	32	4	,	,	PUNCT
ejpam-6038	32	5	the	the	DET
ejpam-6038	32	6	following	follow	VERB
ejpam-6038	32	7	properties	property	NOUN
ejpam-6038	32	8	hold	hold	VERB
ejpam-6038	32	9	:	:	PUNCT
ejpam-6038	32	10	(	(	PUNCT
ejpam-6038	32	11	1	1	X
ejpam-6038	32	12	)	)	PUNCT
ejpam-6038	32	13	a	a	DET
ejpam-6038	32	14	⊆	⊆	NUM
ejpam-6038	32	15	τ1τ2	τ1τ2	NOUN
ejpam-6038	32	16	-	-	NUM
ejpam-6038	32	17	cl(a	cl(a	NUM
ejpam-6038	32	18	)	)	PUNCT
ejpam-6038	32	19	and	and	CCONJ
ejpam-6038	32	20	τ1τ2	τ1τ2	NOUN
ejpam-6038	32	21	-	-	ADJ
ejpam-6038	32	22	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	32	23	-	-	PUNCT
ejpam-6038	32	24	cl(a	cl(a	NUM
ejpam-6038	32	25	)	)	PUNCT
ejpam-6038	32	26	)	)	PUNCT
ejpam-6038	33	1	=	=	PUNCT
ejpam-6038	33	2	τ1τ2	τ1τ2	NOUN
ejpam-6038	33	3	-	-	NUM
ejpam-6038	33	4	cl(a	cl(a	NUM
ejpam-6038	33	5	)	)	PUNCT
ejpam-6038	33	6	.	.	PUNCT
ejpam-6038	34	1	(	(	PUNCT
ejpam-6038	34	2	2	2	X
ejpam-6038	34	3	)	)	PUNCT
ejpam-6038	34	4	if	if	SCONJ
ejpam-6038	34	5	a	a	DET
ejpam-6038	34	6	⊆	⊆	NUM
ejpam-6038	34	7	b	b	NOUN
ejpam-6038	34	8	,	,	PUNCT
ejpam-6038	34	9	then	then	ADV
ejpam-6038	34	10	τ1τ2	τ1τ2	NOUN
ejpam-6038	34	11	-	-	NUM
ejpam-6038	34	12	cl(a	cl(a	NUM
ejpam-6038	34	13	)	)	PUNCT
ejpam-6038	34	14	⊆	⊆	NUM
ejpam-6038	34	15	τ1τ2	τ1τ2	NOUN
ejpam-6038	34	16	-	-	NOUN
ejpam-6038	34	17	cl(b	cl(b	NOUN
ejpam-6038	34	18	)	)	PUNCT
ejpam-6038	34	19	.	.	PUNCT
ejpam-6038	35	1	(	(	PUNCT
ejpam-6038	35	2	3	3	X
ejpam-6038	35	3	)	)	PUNCT
ejpam-6038	35	4	τ1τ2	τ1τ2	NOUN
ejpam-6038	35	5	-	-	NUM
ejpam-6038	35	6	cl(a	cl(a	NUM
ejpam-6038	35	7	)	)	PUNCT
ejpam-6038	35	8	is	be	AUX
ejpam-6038	35	9	τ1τ2	τ1τ2	NOUN
ejpam-6038	35	10	-	-	ADJ
ejpam-6038	35	11	closed	closed	ADJ
ejpam-6038	35	12	.	.	PUNCT
ejpam-6038	36	1	(	(	PUNCT
ejpam-6038	36	2	4	4	X
ejpam-6038	36	3	)	)	PUNCT
ejpam-6038	36	4	a	a	PRON
ejpam-6038	36	5	is	be	AUX
ejpam-6038	36	6	τ1τ2	τ1τ2	NOUN
ejpam-6038	36	7	-	-	ADJ
ejpam-6038	36	8	closed	closed	ADJ
ejpam-6038	36	9	if	if	SCONJ
ejpam-6038	36	10	and	and	CCONJ
ejpam-6038	36	11	only	only	ADV
ejpam-6038	36	12	if	if	SCONJ
ejpam-6038	36	13	a	a	DET
ejpam-6038	36	14	=	=	PUNCT
ejpam-6038	36	15	τ1τ2	τ1τ2	NOUN
ejpam-6038	36	16	-	-	NUM
ejpam-6038	36	17	cl(a	cl(a	NUM
ejpam-6038	36	18	)	)	PUNCT
ejpam-6038	36	19	.	.	PUNCT
ejpam-6038	37	1	(	(	PUNCT
ejpam-6038	37	2	5	5	X
ejpam-6038	37	3	)	)	PUNCT
ejpam-6038	37	4	τ1τ2	τ1τ2	NOUN
ejpam-6038	37	5	-	-	NOUN
ejpam-6038	37	6	cl(x	cl(x	X
ejpam-6038	37	7	−a	−a	NOUN
ejpam-6038	37	8	)	)	PUNCT
ejpam-6038	38	1	=	=	PUNCT
ejpam-6038	38	2	x	x	X
ejpam-6038	39	1	−	−	ADP
ejpam-6038	39	2	τ1τ2	τ1τ2	NOUN
ejpam-6038	39	3	-	-	PUNCT
ejpam-6038	39	4	int(a	int(a	NOUN
ejpam-6038	39	5	)	)	PUNCT
ejpam-6038	39	6	.	.	PUNCT
ejpam-6038	40	1	a	a	DET
ejpam-6038	40	2	subseta	subseta	NOUN
ejpam-6038	40	3	of	of	ADP
ejpam-6038	40	4	a	a	DET
ejpam-6038	40	5	bitopological	bitopological	ADJ
ejpam-6038	40	6	space	space	NOUN
ejpam-6038	40	7	(	(	PUNCT
ejpam-6038	40	8	x	x	NOUN
ejpam-6038	40	9	,	,	PUNCT
ejpam-6038	40	10	τ1	τ1	NOUN
ejpam-6038	40	11	,	,	PUNCT
ejpam-6038	40	12	τ2	τ2	NOUN
ejpam-6038	40	13	)	)	PUNCT
ejpam-6038	40	14	is	be	AUX
ejpam-6038	40	15	called	call	VERB
ejpam-6038	40	16	(	(	PUNCT
ejpam-6038	40	17	τ1	τ1	NOUN
ejpam-6038	40	18	,	,	PUNCT
ejpam-6038	40	19	τ2)r	τ2)r	NOUN
ejpam-6038	40	20	-	-	PUNCT
ejpam-6038	40	21	open	open	NOUN
ejpam-6038	40	22	[	[	X
ejpam-6038	40	23	23	23	NUM
ejpam-6038	40	24	]	]	PUNCT
ejpam-6038	40	25	(	(	PUNCT
ejpam-6038	40	26	resp	resp	NOUN
ejpam-6038	40	27	.	.	PUNCT
ejpam-6038	41	1	(	(	PUNCT
ejpam-6038	41	2	τ1	τ1	NOUN
ejpam-6038	41	3	,	,	PUNCT
ejpam-6038	41	4	τ2)sopen	τ2)sopen	VERB
ejpam-6038	41	5	[	[	X
ejpam-6038	41	6	24	24	NUM
ejpam-6038	41	7	]	]	PUNCT
ejpam-6038	41	8	,	,	PUNCT
ejpam-6038	41	9	(	(	PUNCT
ejpam-6038	41	10	τ1	τ1	NOUN
ejpam-6038	41	11	,	,	PUNCT
ejpam-6038	41	12	τ2)p	τ2)p	NOUN
ejpam-6038	41	13	-	-	ADJ
ejpam-6038	41	14	open	open	ADJ
ejpam-6038	41	15	[	[	X
ejpam-6038	41	16	24	24	NUM
ejpam-6038	41	17	]	]	PUNCT
ejpam-6038	41	18	,	,	PUNCT
ejpam-6038	41	19	(	(	PUNCT
ejpam-6038	41	20	τ1	τ1	NOUN
ejpam-6038	41	21	,	,	PUNCT
ejpam-6038	41	22	τ2)β	τ2)β	ADJ
ejpam-6038	41	23	-	-	PUNCT
ejpam-6038	41	24	open	open	NOUN
ejpam-6038	41	25	[	[	X
ejpam-6038	41	26	24	24	NUM
ejpam-6038	41	27	]	]	PUNCT
ejpam-6038	41	28	)	)	PUNCT
ejpam-6038	41	29	if	if	SCONJ
ejpam-6038	41	30	a	a	DET
ejpam-6038	41	31	=	=	PUNCT
ejpam-6038	41	32	τ1τ2	τ1τ2	NOUN
ejpam-6038	41	33	-	-	NOUN
ejpam-6038	41	34	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	41	35	-	-	PUNCT
ejpam-6038	41	36	cl(a	cl(a	NUM
ejpam-6038	41	37	)	)	PUNCT
ejpam-6038	41	38	)	)	PUNCT
ejpam-6038	41	39	(	(	PUNCT
ejpam-6038	41	40	resp	resp	NOUN
ejpam-6038	41	41	.	.	PUNCT
ejpam-6038	42	1	a	a	DET
ejpam-6038	42	2	⊆	⊆	NUM
ejpam-6038	42	3	τ1τ2	τ1τ2	NOUN
ejpam-6038	42	4	-	-	ADJ
ejpam-6038	42	5	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	42	6	-	-	PUNCT
ejpam-6038	42	7	int(a	int(a	NOUN
ejpam-6038	42	8	)	)	PUNCT
ejpam-6038	42	9	)	)	PUNCT
ejpam-6038	42	10	,	,	PUNCT
ejpam-6038	42	11	a	a	DET
ejpam-6038	42	12	⊆	⊆	NUM
ejpam-6038	42	13	τ1τ2	τ1τ2	NOUN
ejpam-6038	42	14	-	-	NOUN
ejpam-6038	42	15	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	42	16	-	-	PUNCT
ejpam-6038	42	17	cl(a	cl(a	NUM
ejpam-6038	42	18	)	)	PUNCT
ejpam-6038	42	19	)	)	PUNCT
ejpam-6038	42	20	,	,	PUNCT
ejpam-6038	42	21	a	a	DET
ejpam-6038	42	22	⊆	⊆	NUM
ejpam-6038	42	23	τ1τ2	τ1τ2	NOUN
ejpam-6038	42	24	-	-	PUNCT
ejpam-6038	42	25	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	42	26	-	-	PUNCT
ejpam-6038	42	27	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	42	28	-	-	PUNCT
ejpam-6038	42	29	cl(a	cl(a	NUM
ejpam-6038	42	30	)	)	PUNCT
ejpam-6038	42	31	)	)	PUNCT
ejpam-6038	42	32	)	)	PUNCT
ejpam-6038	42	33	)	)	PUNCT
ejpam-6038	42	34	.	.	PUNCT
ejpam-6038	43	1	the	the	DET
ejpam-6038	43	2	complement	complement	NOUN
ejpam-6038	43	3	of	of	ADP
ejpam-6038	43	4	a	a	DET
ejpam-6038	43	5	(	(	PUNCT
ejpam-6038	43	6	τ1	τ1	NOUN
ejpam-6038	43	7	,	,	PUNCT
ejpam-6038	43	8	τ2)r	τ2)r	NOUN
ejpam-6038	43	9	-	-	PUNCT
ejpam-6038	43	10	open	open	ADJ
ejpam-6038	43	11	(	(	PUNCT
ejpam-6038	43	12	resp	resp	NOUN
ejpam-6038	43	13	.	.	PUNCT
ejpam-6038	44	1	(	(	PUNCT
ejpam-6038	44	2	τ1	τ1	NOUN
ejpam-6038	44	3	,	,	PUNCT
ejpam-6038	44	4	τ2)s	τ2)s	NOUN
ejpam-6038	44	5	-	-	PUNCT
ejpam-6038	44	6	open	open	ADJ
ejpam-6038	44	7	,	,	PUNCT
ejpam-6038	44	8	(	(	PUNCT
ejpam-6038	44	9	τ1	τ1	NOUN
ejpam-6038	44	10	,	,	PUNCT
ejpam-6038	44	11	τ2)p	τ2)p	NOUN
ejpam-6038	44	12	-	-	ADJ
ejpam-6038	44	13	open	open	ADJ
ejpam-6038	44	14	,	,	PUNCT
ejpam-6038	44	15	(	(	PUNCT
ejpam-6038	44	16	τ1	τ1	NOUN
ejpam-6038	44	17	,	,	PUNCT
ejpam-6038	44	18	τ2)β	τ2)β	ADJ
ejpam-6038	44	19	-	-	PUNCT
ejpam-6038	44	20	open	open	ADJ
ejpam-6038	44	21	)	)	PUNCT
ejpam-6038	44	22	set	set	NOUN
ejpam-6038	44	23	is	be	AUX
ejpam-6038	44	24	said	say	VERB
ejpam-6038	44	25	to	to	PART
ejpam-6038	44	26	be	be	AUX
ejpam-6038	44	27	(	(	PUNCT
ejpam-6038	44	28	τ1	τ1	NOUN
ejpam-6038	44	29	,	,	PUNCT
ejpam-6038	44	30	τ2)r	τ2)r	NOUN
ejpam-6038	44	31	-	-	PUNCT
ejpam-6038	44	32	closed	closed	ADJ
ejpam-6038	44	33	(	(	PUNCT
ejpam-6038	44	34	resp	resp	NOUN
ejpam-6038	44	35	.	.	PUNCT
ejpam-6038	45	1	(	(	PUNCT
ejpam-6038	45	2	τ1	τ1	NOUN
ejpam-6038	45	3	,	,	PUNCT
ejpam-6038	45	4	τ2)s	τ2)s	NOUN
ejpam-6038	45	5	-	-	PUNCT
ejpam-6038	45	6	closed	closed	ADJ
ejpam-6038	45	7	,	,	PUNCT
ejpam-6038	45	8	(	(	PUNCT
ejpam-6038	45	9	τ1	τ1	NOUN
ejpam-6038	45	10	,	,	PUNCT
ejpam-6038	45	11	τ2)p	τ2)p	NOUN
ejpam-6038	45	12	-	-	PUNCT
ejpam-6038	45	13	closed	closed	ADJ
ejpam-6038	45	14	,	,	PUNCT
ejpam-6038	45	15	(	(	PUNCT
ejpam-6038	45	16	τ1	τ1	NOUN
ejpam-6038	45	17	,	,	PUNCT
ejpam-6038	45	18	τ2)β	τ2)β	ADJ
ejpam-6038	45	19	-	-	PUNCT
ejpam-6038	45	20	closed	closed	ADJ
ejpam-6038	45	21	)	)	PUNCT
ejpam-6038	45	22	.	.	PUNCT
ejpam-6038	46	1	a	a	DET
ejpam-6038	46	2	p.	p.	NOUN
ejpam-6038	46	3	pue	pue	NOUN
ejpam-6038	46	4	-	-	PUNCT
ejpam-6038	46	5	on	on	ADP
ejpam-6038	46	6	,	,	PUNCT
ejpam-6038	46	7	a.	a.	PROPN
ejpam-6038	46	8	sama	sama	PROPN
ejpam-6038	46	9	-	-	PUNCT
ejpam-6038	46	10	ae	ae	PROPN
ejpam-6038	46	11	,	,	PUNCT
ejpam-6038	46	12	c.	c.	PROPN
ejpam-6038	46	13	boonpok	boonpok	PROPN
ejpam-6038	46	14	/	/	SYM
ejpam-6038	46	15	eur	eur	PROPN
ejpam-6038	46	16	.	.	PUNCT
ejpam-6038	47	1	j.	j.	PROPN
ejpam-6038	47	2	pure	pure	PROPN
ejpam-6038	47	3	appl	appl	PROPN
ejpam-6038	47	4	.	.	PROPN
ejpam-6038	47	5	math	math	PROPN
ejpam-6038	47	6	,	,	PUNCT
ejpam-6038	47	7	18	18	NUM
ejpam-6038	47	8	(	(	PUNCT
ejpam-6038	47	9	2	2	NUM
ejpam-6038	47	10	)	)	PUNCT
ejpam-6038	47	11	(	(	PUNCT
ejpam-6038	47	12	2025	2025	NUM
ejpam-6038	47	13	)	)	PUNCT
ejpam-6038	47	14	,	,	PUNCT
ejpam-6038	47	15	6038	6038	NUM
ejpam-6038	47	16	3	3	NUM
ejpam-6038	47	17	of	of	ADP
ejpam-6038	47	18	11	11	NUM
ejpam-6038	47	19	subset	subset	VERB
ejpam-6038	47	20	a	a	PRON
ejpam-6038	47	21	of	of	ADP
ejpam-6038	47	22	a	a	DET
ejpam-6038	47	23	bitopological	bitopological	ADJ
ejpam-6038	47	24	space	space	NOUN
ejpam-6038	47	25	(	(	PUNCT
ejpam-6038	47	26	x	x	NOUN
ejpam-6038	47	27	,	,	PUNCT
ejpam-6038	47	28	τ1	τ1	NOUN
ejpam-6038	47	29	,	,	PUNCT
ejpam-6038	47	30	τ2	τ2	NOUN
ejpam-6038	47	31	)	)	PUNCT
ejpam-6038	47	32	is	be	AUX
ejpam-6038	47	33	said	say	VERB
ejpam-6038	47	34	to	to	PART
ejpam-6038	47	35	be	be	AUX
ejpam-6038	47	36	α(τ1	α(τ1	NOUN
ejpam-6038	47	37	,	,	PUNCT
ejpam-6038	47	38	τ2)-open	τ2)-open	ADJ
ejpam-6038	47	39	[	[	X
ejpam-6038	47	40	25	25	NUM
ejpam-6038	47	41	]	]	PUNCT
ejpam-6038	47	42	if	if	SCONJ
ejpam-6038	47	43	a	a	DET
ejpam-6038	47	44	⊆	⊆	NUM
ejpam-6038	47	45	τ1τ2	τ1τ2	NOUN
ejpam-6038	47	46	-	-	PUNCT
ejpam-6038	47	47	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	47	48	-	-	PUNCT
ejpam-6038	47	49	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	47	50	-	-	PUNCT
ejpam-6038	47	51	int(a	int(a	NOUN
ejpam-6038	47	52	)	)	PUNCT
ejpam-6038	47	53	)	)	PUNCT
ejpam-6038	47	54	)	)	PUNCT
ejpam-6038	47	55	.	.	PUNCT
ejpam-6038	48	1	the	the	DET
ejpam-6038	48	2	complement	complement	NOUN
ejpam-6038	48	3	of	of	ADP
ejpam-6038	48	4	an	an	DET
ejpam-6038	48	5	α(τ1	α(τ1	NOUN
ejpam-6038	48	6	,	,	PUNCT
ejpam-6038	48	7	τ2)-open	τ2)-open	ADJ
ejpam-6038	48	8	set	set	NOUN
ejpam-6038	48	9	is	be	AUX
ejpam-6038	48	10	said	say	VERB
ejpam-6038	48	11	to	to	PART
ejpam-6038	48	12	be	be	AUX
ejpam-6038	48	13	α(τ1	α(τ1	NOUN
ejpam-6038	48	14	,	,	PUNCT
ejpam-6038	48	15	τ2)-closed	τ2)-close	VERB
ejpam-6038	48	16	.	.	PUNCT
ejpam-6038	49	1	let	let	VERB
ejpam-6038	49	2	a	a	DET
ejpam-6038	49	3	be	be	AUX
ejpam-6038	49	4	a	a	DET
ejpam-6038	49	5	subset	subset	NOUN
ejpam-6038	49	6	of	of	ADP
ejpam-6038	49	7	a	a	DET
ejpam-6038	49	8	bitopological	bitopological	ADJ
ejpam-6038	49	9	space	space	NOUN
ejpam-6038	49	10	(	(	PUNCT
ejpam-6038	49	11	x	x	NOUN
ejpam-6038	49	12	,	,	PUNCT
ejpam-6038	49	13	τ1	τ1	NOUN
ejpam-6038	49	14	,	,	PUNCT
ejpam-6038	49	15	τ2	τ2	NOUN
ejpam-6038	49	16	)	)	PUNCT
ejpam-6038	49	17	.	.	PUNCT
ejpam-6038	50	1	the	the	DET
ejpam-6038	50	2	intersection	intersection	NOUN
ejpam-6038	50	3	of	of	ADP
ejpam-6038	50	4	all	all	DET
ejpam-6038	50	5	(	(	PUNCT
ejpam-6038	50	6	τ1	τ1	NOUN
ejpam-6038	50	7	,	,	PUNCT
ejpam-6038	50	8	τ2)p	τ2)p	NOUN
ejpam-6038	50	9	-	-	PUNCT
ejpam-6038	50	10	closed	closed	ADJ
ejpam-6038	50	11	(	(	PUNCT
ejpam-6038	50	12	resp	resp	NOUN
ejpam-6038	50	13	.	.	PUNCT
ejpam-6038	51	1	(	(	PUNCT
ejpam-6038	51	2	τ1	τ1	NOUN
ejpam-6038	51	3	,	,	PUNCT
ejpam-6038	51	4	τ2)s	τ2)s	NOUN
ejpam-6038	51	5	-	-	PUNCT
ejpam-6038	51	6	closed	closed	ADJ
ejpam-6038	51	7	,	,	PUNCT
ejpam-6038	51	8	α(τ1	α(τ1	NOUN
ejpam-6038	51	9	,	,	PUNCT
ejpam-6038	51	10	τ2)-closed	τ2)-closed	ADJ
ejpam-6038	51	11	)	)	PUNCT
ejpam-6038	51	12	sets	set	NOUN
ejpam-6038	51	13	of	of	ADP
ejpam-6038	51	14	x	x	PUNCT
ejpam-6038	51	15	containing	contain	VERB
ejpam-6038	51	16	a	a	PRON
ejpam-6038	51	17	is	be	AUX
ejpam-6038	51	18	called	call	VERB
ejpam-6038	51	19	the	the	DET
ejpam-6038	51	20	(	(	PUNCT
ejpam-6038	51	21	τ1	τ1	NOUN
ejpam-6038	51	22	,	,	PUNCT
ejpam-6038	51	23	τ2)p	τ2)p	NOUN
ejpam-6038	51	24	-	-	NOUN
ejpam-6038	51	25	closure	closure	NOUN
ejpam-6038	51	26	[	[	X
ejpam-6038	51	27	26	26	NUM
ejpam-6038	51	28	]	]	PUNCT
ejpam-6038	51	29	(	(	PUNCT
ejpam-6038	51	30	resp	resp	NOUN
ejpam-6038	51	31	.	.	PUNCT
ejpam-6038	52	1	(	(	PUNCT
ejpam-6038	52	2	τ1	τ1	NOUN
ejpam-6038	52	3	,	,	PUNCT
ejpam-6038	52	4	τ2)s	τ2)s	NOUN
ejpam-6038	52	5	-	-	PUNCT
ejpam-6038	52	6	closure	closure	NOUN
ejpam-6038	52	7	[	[	X
ejpam-6038	52	8	24	24	NUM
ejpam-6038	52	9	]	]	PUNCT
ejpam-6038	52	10	,	,	PUNCT
ejpam-6038	52	11	α(τ1	α(τ1	NOUN
ejpam-6038	52	12	,	,	PUNCT
ejpam-6038	52	13	τ2)-closure	τ2)-closure	NOUN
ejpam-6038	52	14	[	[	X
ejpam-6038	52	15	27	27	NUM
ejpam-6038	52	16	]	]	PUNCT
ejpam-6038	52	17	)	)	PUNCT
ejpam-6038	52	18	of	of	ADP
ejpam-6038	52	19	a	a	PRON
ejpam-6038	52	20	and	and	CCONJ
ejpam-6038	52	21	is	be	AUX
ejpam-6038	52	22	denoted	denote	VERB
ejpam-6038	52	23	by	by	ADP
ejpam-6038	52	24	(	(	PUNCT
ejpam-6038	52	25	τ1	τ1	NOUN
ejpam-6038	52	26	,	,	PUNCT
ejpam-6038	52	27	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6038	52	28	)	)	PUNCT
ejpam-6038	52	29	(	(	PUNCT
ejpam-6038	52	30	resp	resp	NOUN
ejpam-6038	52	31	.	.	PUNCT
ejpam-6038	53	1	(	(	PUNCT
ejpam-6038	53	2	τ1	τ1	NOUN
ejpam-6038	53	3	,	,	PUNCT
ejpam-6038	53	4	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6038	53	5	)	)	PUNCT
ejpam-6038	53	6	,	,	PUNCT
ejpam-6038	53	7	α(τ1	α(τ1	NOUN
ejpam-6038	53	8	,	,	PUNCT
ejpam-6038	53	9	τ2)-cl(a	τ2)-cl(a	NUM
ejpam-6038	53	10	)	)	PUNCT
ejpam-6038	53	11	)	)	PUNCT
ejpam-6038	53	12	.	.	PUNCT
ejpam-6038	54	1	the	the	DET
ejpam-6038	54	2	union	union	NOUN
ejpam-6038	54	3	of	of	ADP
ejpam-6038	54	4	all	all	DET
ejpam-6038	54	5	(	(	PUNCT
ejpam-6038	54	6	τ1	τ1	NOUN
ejpam-6038	54	7	,	,	PUNCT
ejpam-6038	54	8	τ2)p	τ2)p	NOUN
ejpam-6038	54	9	-	-	ADJ
ejpam-6038	54	10	open	open	ADJ
ejpam-6038	54	11	(	(	PUNCT
ejpam-6038	54	12	resp	resp	NOUN
ejpam-6038	54	13	.	.	PUNCT
ejpam-6038	55	1	(	(	PUNCT
ejpam-6038	55	2	τ1	τ1	NOUN
ejpam-6038	55	3	,	,	PUNCT
ejpam-6038	55	4	τ2)s	τ2)s	NOUN
ejpam-6038	55	5	-	-	PUNCT
ejpam-6038	55	6	open	open	ADJ
ejpam-6038	55	7	,	,	PUNCT
ejpam-6038	55	8	α(τ1	α(τ1	NOUN
ejpam-6038	55	9	,	,	PUNCT
ejpam-6038	55	10	τ2)-open	τ2)-open	ADJ
ejpam-6038	55	11	)	)	PUNCT
ejpam-6038	55	12	sets	set	NOUN
ejpam-6038	55	13	of	of	ADP
ejpam-6038	55	14	x	x	PUNCT
ejpam-6038	55	15	contained	contain	VERB
ejpam-6038	55	16	in	in	ADP
ejpam-6038	55	17	a	a	PRON
ejpam-6038	55	18	is	be	AUX
ejpam-6038	55	19	called	call	VERB
ejpam-6038	55	20	the	the	DET
ejpam-6038	55	21	(	(	PUNCT
ejpam-6038	55	22	τ1	τ1	NOUN
ejpam-6038	55	23	,	,	PUNCT
ejpam-6038	55	24	τ2)p	τ2)p	ADJ
ejpam-6038	55	25	-	-	NOUN
ejpam-6038	55	26	interior	interior	ADJ
ejpam-6038	55	27	[	[	X
ejpam-6038	55	28	26	26	NUM
ejpam-6038	55	29	]	]	PUNCT
ejpam-6038	55	30	(	(	PUNCT
ejpam-6038	55	31	resp	resp	NOUN
ejpam-6038	55	32	.	.	PUNCT
ejpam-6038	56	1	(	(	PUNCT
ejpam-6038	56	2	τ1	τ1	NOUN
ejpam-6038	56	3	,	,	PUNCT
ejpam-6038	56	4	τ2)s	τ2)s	NOUN
ejpam-6038	56	5	-	-	ADJ
ejpam-6038	56	6	interior	interior	NOUN
ejpam-6038	56	7	[	[	X
ejpam-6038	56	8	24	24	NUM
ejpam-6038	56	9	]	]	PUNCT
ejpam-6038	56	10	,	,	PUNCT
ejpam-6038	56	11	α(τ1	α(τ1	NOUN
ejpam-6038	56	12	,	,	PUNCT
ejpam-6038	56	13	τ2)-interior	τ2)-interior	PROPN
ejpam-6038	56	14	[	[	X
ejpam-6038	56	15	27	27	NUM
ejpam-6038	56	16	]	]	PUNCT
ejpam-6038	56	17	)	)	PUNCT
ejpam-6038	56	18	of	of	ADP
ejpam-6038	56	19	a	a	PRON
ejpam-6038	56	20	and	and	CCONJ
ejpam-6038	56	21	is	be	AUX
ejpam-6038	56	22	denoted	denote	VERB
ejpam-6038	56	23	by	by	ADP
ejpam-6038	56	24	(	(	PUNCT
ejpam-6038	56	25	τ1	τ1	NOUN
ejpam-6038	56	26	,	,	PUNCT
ejpam-6038	56	27	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6038	56	28	)	)	PUNCT
ejpam-6038	56	29	(	(	PUNCT
ejpam-6038	56	30	resp	resp	NOUN
ejpam-6038	56	31	.	.	PUNCT
ejpam-6038	57	1	(	(	PUNCT
ejpam-6038	57	2	τ1	τ1	NOUN
ejpam-6038	57	3	,	,	PUNCT
ejpam-6038	57	4	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6038	57	5	)	)	PUNCT
ejpam-6038	57	6	,	,	PUNCT
ejpam-6038	57	7	α(τ1	α(τ1	NOUN
ejpam-6038	57	8	,	,	PUNCT
ejpam-6038	57	9	τ2)-int(a	τ2)-int(a	NOUN
ejpam-6038	57	10	)	)	PUNCT
ejpam-6038	57	11	)	)	PUNCT
ejpam-6038	57	12	.	.	PUNCT
ejpam-6038	58	1	lemma	lemma	PROPN
ejpam-6038	58	2	2	2	NUM
ejpam-6038	58	3	.	.	X
ejpam-6038	59	1	for	for	ADP
ejpam-6038	59	2	a	a	DET
ejpam-6038	59	3	subset	subset	NOUN
ejpam-6038	59	4	a	a	PRON
ejpam-6038	59	5	of	of	ADP
ejpam-6038	59	6	a	a	DET
ejpam-6038	59	7	bitopological	bitopological	ADJ
ejpam-6038	59	8	space	space	NOUN
ejpam-6038	59	9	(	(	PUNCT
ejpam-6038	59	10	x	x	NOUN
ejpam-6038	59	11	,	,	PUNCT
ejpam-6038	59	12	τ1	τ1	NOUN
ejpam-6038	59	13	,	,	PUNCT
ejpam-6038	59	14	τ2	τ2	NOUN
ejpam-6038	59	15	)	)	PUNCT
ejpam-6038	59	16	,	,	PUNCT
ejpam-6038	59	17	the	the	DET
ejpam-6038	59	18	following	follow	VERB
ejpam-6038	59	19	properties	property	NOUN
ejpam-6038	59	20	hold	hold	VERB
ejpam-6038	59	21	:	:	PUNCT
ejpam-6038	59	22	(	(	PUNCT
ejpam-6038	59	23	1	1	X
ejpam-6038	59	24	)	)	PUNCT
ejpam-6038	59	25	(	(	PUNCT
ejpam-6038	59	26	τ1	τ1	NOUN
ejpam-6038	59	27	,	,	PUNCT
ejpam-6038	59	28	τ2)-pcl(a	τ2)-pcl(a	ADJ
ejpam-6038	59	29	)	)	PUNCT
ejpam-6038	59	30	=	=	PUNCT
ejpam-6038	60	1	τ1τ2	τ1τ2	NOUN
ejpam-6038	60	2	-	-	ADJ
ejpam-6038	60	3	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	60	4	-	-	PUNCT
ejpam-6038	60	5	int(a	int(a	NOUN
ejpam-6038	60	6	)	)	PUNCT
ejpam-6038	60	7	)	)	PUNCT
ejpam-6038	60	8	∪a	∪a	X
ejpam-6038	61	1	[	[	X
ejpam-6038	61	2	26	26	NUM
ejpam-6038	61	3	]	]	X
ejpam-6038	61	4	;	;	PUNCT
ejpam-6038	61	5	(	(	PUNCT
ejpam-6038	61	6	2	2	X
ejpam-6038	61	7	)	)	PUNCT
ejpam-6038	61	8	(	(	PUNCT
ejpam-6038	61	9	τ1	τ1	NOUN
ejpam-6038	61	10	,	,	PUNCT
ejpam-6038	61	11	τ2)-pint(a	τ2)-pint(a	PROPN
ejpam-6038	61	12	)	)	PUNCT
ejpam-6038	61	13	=	=	PUNCT
ejpam-6038	62	1	τ1τ2	τ1τ2	NOUN
ejpam-6038	62	2	-	-	NOUN
ejpam-6038	62	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	62	4	-	-	PUNCT
ejpam-6038	62	5	cl(a	cl(a	NUM
ejpam-6038	62	6	)	)	PUNCT
ejpam-6038	62	7	)	)	PUNCT
ejpam-6038	63	1	∩a	∩a	PROPN
ejpam-6038	64	1	[	[	X
ejpam-6038	64	2	20	20	NUM
ejpam-6038	64	3	]	]	PUNCT
ejpam-6038	64	4	;	;	PUNCT
ejpam-6038	64	5	(	(	PUNCT
ejpam-6038	64	6	3	3	X
ejpam-6038	64	7	)	)	PUNCT
ejpam-6038	64	8	(	(	PUNCT
ejpam-6038	64	9	τ1	τ1	NOUN
ejpam-6038	64	10	,	,	PUNCT
ejpam-6038	64	11	τ2)-scl(a	τ2)-scl(a	NOUN
ejpam-6038	64	12	)	)	PUNCT
ejpam-6038	64	13	=	=	PUNCT
ejpam-6038	65	1	τ1τ2	τ1τ2	NOUN
ejpam-6038	65	2	-	-	NOUN
ejpam-6038	65	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	65	4	-	-	PUNCT
ejpam-6038	65	5	cl(a	cl(a	NUM
ejpam-6038	65	6	)	)	PUNCT
ejpam-6038	65	7	)	)	PUNCT
ejpam-6038	65	8	∪a	∪a	X
ejpam-6038	66	1	[	[	X
ejpam-6038	66	2	24	24	NUM
ejpam-6038	66	3	]	]	PUNCT
ejpam-6038	66	4	;	;	PUNCT
ejpam-6038	66	5	(	(	PUNCT
ejpam-6038	66	6	4	4	NUM
ejpam-6038	66	7	)	)	PUNCT
ejpam-6038	66	8	(	(	PUNCT
ejpam-6038	66	9	τ1	τ1	NOUN
ejpam-6038	66	10	,	,	PUNCT
ejpam-6038	66	11	τ2)-sint(a	τ2)-sint(a	PROPN
ejpam-6038	66	12	)	)	PUNCT
ejpam-6038	67	1	=	=	PUNCT
ejpam-6038	67	2	τ1τ2	τ1τ2	NOUN
ejpam-6038	67	3	-	-	ADJ
ejpam-6038	67	4	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	67	5	-	-	PUNCT
ejpam-6038	67	6	int(a	int(a	NOUN
ejpam-6038	67	7	)	)	PUNCT
ejpam-6038	67	8	)	)	PUNCT
ejpam-6038	68	1	∩a	∩a	PROPN
ejpam-6038	69	1	[	[	X
ejpam-6038	69	2	28	28	NUM
ejpam-6038	69	3	]	]	PUNCT
ejpam-6038	69	4	.	.	PUNCT
ejpam-6038	70	1	let	let	VERB
ejpam-6038	70	2	a	a	DET
ejpam-6038	70	3	be	be	AUX
ejpam-6038	70	4	a	a	DET
ejpam-6038	70	5	subset	subset	NOUN
ejpam-6038	70	6	of	of	ADP
ejpam-6038	70	7	a	a	DET
ejpam-6038	70	8	bitopological	bitopological	ADJ
ejpam-6038	70	9	space	space	NOUN
ejpam-6038	70	10	(	(	PUNCT
ejpam-6038	70	11	x	x	NOUN
ejpam-6038	70	12	,	,	PUNCT
ejpam-6038	70	13	τ1	τ1	NOUN
ejpam-6038	70	14	,	,	PUNCT
ejpam-6038	70	15	τ2	τ2	NOUN
ejpam-6038	70	16	)	)	PUNCT
ejpam-6038	70	17	.	.	PUNCT
ejpam-6038	71	1	a	a	DET
ejpam-6038	71	2	point	point	NOUN
ejpam-6038	71	3	x	x	X
ejpam-6038	71	4	∈	∈	NOUN
ejpam-6038	71	5	x	x	PUNCT
ejpam-6038	71	6	is	be	AUX
ejpam-6038	71	7	called	call	VERB
ejpam-6038	71	8	a	a	DET
ejpam-6038	71	9	s(τ1	s(τ1	NOUN
ejpam-6038	71	10	,	,	PUNCT
ejpam-6038	71	11	τ2)θ	τ2)θ	ADJ
ejpam-6038	71	12	-	-	PUNCT
ejpam-6038	71	13	cluster	cluster	NOUN
ejpam-6038	71	14	point	point	NOUN
ejpam-6038	71	15	of	of	ADP
ejpam-6038	71	16	a	a	DET
ejpam-6038	71	17	if	if	SCONJ
ejpam-6038	71	18	τ1τ2	τ1τ2	ADJ
ejpam-6038	71	19	-	-	ADJ
ejpam-6038	71	20	cl(u)∩a	cl(u)∩a	ADJ
ejpam-6038	71	21	̸=	̸=	PROPN
ejpam-6038	71	22	∅	∅	NOUN
ejpam-6038	71	23	for	for	ADP
ejpam-6038	71	24	every	every	DET
ejpam-6038	71	25	(	(	PUNCT
ejpam-6038	71	26	τ1	τ1	NOUN
ejpam-6038	71	27	,	,	PUNCT
ejpam-6038	71	28	τ2)s	τ2)s	NOUN
ejpam-6038	71	29	-	-	PUNCT
ejpam-6038	71	30	open	open	ADJ
ejpam-6038	71	31	set	set	NOUN
ejpam-6038	71	32	u	u	NOUN
ejpam-6038	71	33	containing	contain	VERB
ejpam-6038	71	34	x.	x.	NOUN
ejpam-6038	71	35	the	the	DET
ejpam-6038	71	36	set	set	NOUN
ejpam-6038	71	37	of	of	ADP
ejpam-6038	71	38	all	all	DET
ejpam-6038	71	39	s(τ1	s(τ1	NOUN
ejpam-6038	71	40	,	,	PUNCT
ejpam-6038	71	41	τ2)θ	τ2)θ	ADJ
ejpam-6038	71	42	-	-	PUNCT
ejpam-6038	71	43	cluster	cluster	NOUN
ejpam-6038	71	44	points	point	NOUN
ejpam-6038	71	45	of	of	ADP
ejpam-6038	71	46	a	a	PRON
ejpam-6038	71	47	is	be	AUX
ejpam-6038	71	48	called	call	VERB
ejpam-6038	71	49	the	the	DET
ejpam-6038	71	50	s(τ1	s(τ1	NOUN
ejpam-6038	71	51	,	,	PUNCT
ejpam-6038	71	52	τ2)θ	τ2)θ	NOUN
ejpam-6038	71	53	-	-	PUNCT
ejpam-6038	71	54	closure	closure	NOUN
ejpam-6038	71	55	of	of	ADP
ejpam-6038	71	56	a	a	PRON
ejpam-6038	71	57	and	and	CCONJ
ejpam-6038	71	58	is	be	AUX
ejpam-6038	71	59	denoted	denote	VERB
ejpam-6038	71	60	by	by	ADP
ejpam-6038	71	61	s(τ1	s(τ1	NOUN
ejpam-6038	71	62	,	,	PUNCT
ejpam-6038	71	63	τ2)θ	τ2)θ	NOUN
ejpam-6038	71	64	-	-	PUNCT
ejpam-6038	71	65	cl(a	cl(a	NUM
ejpam-6038	71	66	)	)	PUNCT
ejpam-6038	71	67	.	.	PUNCT
ejpam-6038	72	1	a	a	DET
ejpam-6038	72	2	subset	subset	NOUN
ejpam-6038	72	3	a	a	PRON
ejpam-6038	72	4	of	of	ADP
ejpam-6038	72	5	a	a	DET
ejpam-6038	72	6	bitopological	bitopological	ADJ
ejpam-6038	72	7	space	space	NOUN
ejpam-6038	72	8	(	(	PUNCT
ejpam-6038	72	9	x	x	NOUN
ejpam-6038	72	10	,	,	PUNCT
ejpam-6038	72	11	τ1	τ1	NOUN
ejpam-6038	72	12	,	,	PUNCT
ejpam-6038	72	13	τ2	τ2	NOUN
ejpam-6038	72	14	)	)	PUNCT
ejpam-6038	72	15	is	be	AUX
ejpam-6038	72	16	called	call	VERB
ejpam-6038	72	17	s(τ1	s(τ1	NOUN
ejpam-6038	72	18	,	,	PUNCT
ejpam-6038	72	19	τ2)θ	τ2)θ	NOUN
ejpam-6038	72	20	-	-	PUNCT
ejpam-6038	72	21	closed	closed	ADJ
ejpam-6038	72	22	if	if	SCONJ
ejpam-6038	72	23	s(τ1	s(τ1	NOUN
ejpam-6038	72	24	,	,	PUNCT
ejpam-6038	72	25	τ2)θ	τ2)θ	NOUN
ejpam-6038	72	26	-	-	PUNCT
ejpam-6038	72	27	cl(a	cl(a	NUM
ejpam-6038	72	28	)	)	PUNCT
ejpam-6038	72	29	=	=	PUNCT
ejpam-6038	72	30	a.	a.	NOUN
ejpam-6038	72	31	the	the	DET
ejpam-6038	72	32	complement	complement	NOUN
ejpam-6038	72	33	of	of	ADP
ejpam-6038	72	34	a	a	DET
ejpam-6038	72	35	s(τ1	s(τ1	NOUN
ejpam-6038	72	36	,	,	PUNCT
ejpam-6038	72	37	τ2)θ	τ2)θ	ADJ
ejpam-6038	72	38	-	-	PUNCT
ejpam-6038	72	39	closed	close	VERB
ejpam-6038	72	40	set	set	NOUN
ejpam-6038	72	41	is	be	AUX
ejpam-6038	72	42	said	say	VERB
ejpam-6038	72	43	to	to	PART
ejpam-6038	72	44	be	be	AUX
ejpam-6038	72	45	s(τ1	s(τ1	NOUN
ejpam-6038	72	46	,	,	PUNCT
ejpam-6038	72	47	τ2)θ	τ2)θ	NOUN
ejpam-6038	72	48	-	-	PUNCT
ejpam-6038	72	49	open	open	ADJ
ejpam-6038	72	50	.	.	PUNCT
ejpam-6038	73	1	the	the	DET
ejpam-6038	73	2	union	union	NOUN
ejpam-6038	73	3	of	of	ADP
ejpam-6038	73	4	all	all	DET
ejpam-6038	73	5	s(τ1	s(τ1	NOUN
ejpam-6038	73	6	,	,	PUNCT
ejpam-6038	73	7	τ2)θ	τ2)θ	ADJ
ejpam-6038	73	8	-	-	PUNCT
ejpam-6038	73	9	open	open	ADJ
ejpam-6038	73	10	sets	set	NOUN
ejpam-6038	73	11	of	of	ADP
ejpam-6038	73	12	x	x	PUNCT
ejpam-6038	73	13	contained	contain	VERB
ejpam-6038	73	14	in	in	ADP
ejpam-6038	73	15	a	a	PRON
ejpam-6038	73	16	is	be	AUX
ejpam-6038	73	17	called	call	VERB
ejpam-6038	73	18	the	the	DET
ejpam-6038	73	19	s(τ1	s(τ1	NOUN
ejpam-6038	73	20	,	,	PUNCT
ejpam-6038	73	21	τ2)θ	τ2)θ	ADJ
ejpam-6038	73	22	-	-	PUNCT
ejpam-6038	73	23	interior	interior	NOUN
ejpam-6038	73	24	of	of	ADP
ejpam-6038	73	25	a	a	PRON
ejpam-6038	73	26	and	and	CCONJ
ejpam-6038	73	27	is	be	AUX
ejpam-6038	73	28	denoted	denote	VERB
ejpam-6038	73	29	by	by	ADP
ejpam-6038	73	30	s(τ1	s(τ1	NOUN
ejpam-6038	73	31	,	,	PUNCT
ejpam-6038	73	32	τ2)θ	τ2)θ	NOUN
ejpam-6038	73	33	-	-	PUNCT
ejpam-6038	73	34	int(a	int(a	NOUN
ejpam-6038	73	35	)	)	PUNCT
ejpam-6038	73	36	.	.	PUNCT
ejpam-6038	74	1	3	3	X
ejpam-6038	74	2	.	.	X
ejpam-6038	74	3	almost	almost	ADV
ejpam-6038	74	4	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	74	5	,	,	PUNCT
ejpam-6038	74	6	τ2)p	τ2)p	ADJ
ejpam-6038	74	7	-	-	PUNCT
ejpam-6038	74	8	continuous	continuous	ADJ
ejpam-6038	74	9	functions	function	NOUN
ejpam-6038	74	10	in	in	ADP
ejpam-6038	74	11	this	this	DET
ejpam-6038	74	12	section	section	NOUN
ejpam-6038	74	13	,	,	PUNCT
ejpam-6038	74	14	we	we	PRON
ejpam-6038	74	15	introduce	introduce	VERB
ejpam-6038	74	16	the	the	DET
ejpam-6038	74	17	concept	concept	NOUN
ejpam-6038	74	18	of	of	ADP
ejpam-6038	74	19	almost	almost	ADV
ejpam-6038	74	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	74	21	,	,	PUNCT
ejpam-6038	74	22	τ2)p	τ2)p	ADJ
ejpam-6038	74	23	-	-	PUNCT
ejpam-6038	74	24	continuous	continuous	ADJ
ejpam-6038	74	25	functions	function	NOUN
ejpam-6038	74	26	.	.	PUNCT
ejpam-6038	75	1	moreover	moreover	ADV
ejpam-6038	75	2	,	,	PUNCT
ejpam-6038	75	3	some	some	DET
ejpam-6038	75	4	characterizations	characterization	NOUN
ejpam-6038	75	5	of	of	ADP
ejpam-6038	75	6	almost	almost	ADV
ejpam-6038	75	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	75	8	,	,	PUNCT
ejpam-6038	75	9	τ2)p	τ2)p	ADJ
ejpam-6038	75	10	-	-	PUNCT
ejpam-6038	75	11	continuous	continuous	ADJ
ejpam-6038	75	12	functions	function	NOUN
ejpam-6038	75	13	are	be	AUX
ejpam-6038	75	14	discussed	discuss	VERB
ejpam-6038	75	15	.	.	PUNCT
ejpam-6038	76	1	definition	definition	NOUN
ejpam-6038	76	2	1	1	NUM
ejpam-6038	76	3	.	.	PUNCT
ejpam-6038	77	1	a	a	DET
ejpam-6038	77	2	function	function	NOUN
ejpam-6038	77	3	f	f	NOUN
ejpam-6038	77	4	:	:	PUNCT
ejpam-6038	77	5	(	(	PUNCT
ejpam-6038	77	6	x	x	NOUN
ejpam-6038	77	7	,	,	PUNCT
ejpam-6038	77	8	τ1	τ1	NOUN
ejpam-6038	77	9	,	,	PUNCT
ejpam-6038	77	10	τ2	τ2	NOUN
ejpam-6038	77	11	)	)	PUNCT
ejpam-6038	77	12	→	→	SYM
ejpam-6038	77	13	(	(	PUNCT
ejpam-6038	77	14	y	y	PROPN
ejpam-6038	77	15	,	,	PUNCT
ejpam-6038	77	16	σ1	σ1	PROPN
ejpam-6038	77	17	,	,	PUNCT
ejpam-6038	77	18	σ2	σ2	PROPN
ejpam-6038	77	19	)	)	PUNCT
ejpam-6038	77	20	is	be	AUX
ejpam-6038	77	21	said	say	VERB
ejpam-6038	77	22	to	to	PART
ejpam-6038	77	23	be	be	AUX
ejpam-6038	77	24	almost	almost	ADV
ejpam-6038	77	25	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	77	26	,	,	PUNCT
ejpam-6038	77	27	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6038	77	28	if	if	SCONJ
ejpam-6038	77	29	for	for	ADP
ejpam-6038	77	30	each	each	DET
ejpam-6038	77	31	x	x	SYM
ejpam-6038	77	32	∈	∈	PROPN
ejpam-6038	77	33	x	x	X
ejpam-6038	77	34	and	and	CCONJ
ejpam-6038	77	35	for	for	SCONJ
ejpam-6038	77	36	each	each	DET
ejpam-6038	77	37	(	(	PUNCT
ejpam-6038	77	38	σ1	σ1	PROPN
ejpam-6038	77	39	,	,	PUNCT
ejpam-6038	77	40	σ2)r	σ2)r	NOUN
ejpam-6038	77	41	-	-	PUNCT
ejpam-6038	77	42	closed	close	VERB
ejpam-6038	77	43	set	set	ADJ
ejpam-6038	77	44	f	f	PROPN
ejpam-6038	77	45	of	of	ADP
ejpam-6038	77	46	y	y	PROPN
ejpam-6038	77	47	containing	contain	VERB
ejpam-6038	77	48	f(x	f(x	PROPN
ejpam-6038	77	49	)	)	PUNCT
ejpam-6038	77	50	,	,	PUNCT
ejpam-6038	77	51	there	there	PRON
ejpam-6038	77	52	exists	exist	VERB
ejpam-6038	77	53	a	a	DET
ejpam-6038	77	54	(	(	PUNCT
ejpam-6038	77	55	τ1	τ1	NOUN
ejpam-6038	77	56	,	,	PUNCT
ejpam-6038	77	57	τ2)p	τ2)p	ADJ
ejpam-6038	77	58	-	-	PUNCT
ejpam-6038	77	59	open	open	ADJ
ejpam-6038	77	60	set	set	NOUN
ejpam-6038	77	61	u	u	NOUN
ejpam-6038	77	62	of	of	ADP
ejpam-6038	77	63	x	x	PUNCT
ejpam-6038	77	64	containing	contain	VERB
ejpam-6038	77	65	x	x	PUNCT
ejpam-6038	77	66	such	such	ADJ
ejpam-6038	77	67	that	that	DET
ejpam-6038	77	68	f(u	f(u	PROPN
ejpam-6038	77	69	)	)	PUNCT
ejpam-6038	77	70	⊆	⊆	NUM
ejpam-6038	77	71	f	f	PROPN
ejpam-6038	77	72	.	.	PUNCT
ejpam-6038	78	1	theorem	theorem	NOUN
ejpam-6038	78	2	1	1	NUM
ejpam-6038	78	3	.	.	X
ejpam-6038	78	4	for	for	ADP
ejpam-6038	78	5	a	a	DET
ejpam-6038	78	6	function	function	NOUN
ejpam-6038	78	7	f	f	NOUN
ejpam-6038	78	8	:	:	PUNCT
ejpam-6038	78	9	(	(	PUNCT
ejpam-6038	78	10	x	x	NOUN
ejpam-6038	78	11	,	,	PUNCT
ejpam-6038	78	12	τ1	τ1	NOUN
ejpam-6038	78	13	,	,	PUNCT
ejpam-6038	78	14	τ2	τ2	NOUN
ejpam-6038	78	15	)	)	PUNCT
ejpam-6038	78	16	→	→	SYM
ejpam-6038	78	17	(	(	PUNCT
ejpam-6038	78	18	y	y	PROPN
ejpam-6038	78	19	,	,	PUNCT
ejpam-6038	78	20	σ1	σ1	PROPN
ejpam-6038	78	21	,	,	PUNCT
ejpam-6038	78	22	σ2	σ2	NOUN
ejpam-6038	78	23	)	)	PUNCT
ejpam-6038	78	24	,	,	PUNCT
ejpam-6038	78	25	the	the	DET
ejpam-6038	78	26	following	follow	VERB
ejpam-6038	78	27	properties	property	NOUN
ejpam-6038	78	28	are	be	AUX
ejpam-6038	78	29	equivalent	equivalent	ADJ
ejpam-6038	78	30	:	:	PUNCT
ejpam-6038	78	31	(	(	PUNCT
ejpam-6038	78	32	1	1	X
ejpam-6038	78	33	)	)	PUNCT
ejpam-6038	78	34	f	f	NOUN
ejpam-6038	78	35	is	be	AUX
ejpam-6038	78	36	almost	almost	ADV
ejpam-6038	78	37	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	78	38	,	,	PUNCT
ejpam-6038	78	39	τ2)p	τ2)p	ADJ
ejpam-6038	78	40	-	-	NOUN
ejpam-6038	78	41	continuous	continuous	ADJ
ejpam-6038	78	42	;	;	PUNCT
ejpam-6038	78	43	(	(	PUNCT
ejpam-6038	78	44	2	2	X
ejpam-6038	78	45	)	)	PUNCT
ejpam-6038	78	46	f−1(f	f−1(f	NOUN
ejpam-6038	78	47	)	)	PUNCT
ejpam-6038	78	48	is	be	AUX
ejpam-6038	78	49	(	(	PUNCT
ejpam-6038	78	50	τ1	τ1	NOUN
ejpam-6038	78	51	,	,	PUNCT
ejpam-6038	78	52	τ2)p	τ2)p	NOUN
ejpam-6038	78	53	-	-	PUNCT
ejpam-6038	78	54	open	open	ADJ
ejpam-6038	78	55	in	in	ADP
ejpam-6038	78	56	x	x	PUNCT
ejpam-6038	78	57	for	for	SCONJ
ejpam-6038	78	58	every	every	DET
ejpam-6038	78	59	(	(	PUNCT
ejpam-6038	78	60	σ1	σ1	PROPN
ejpam-6038	78	61	,	,	PUNCT
ejpam-6038	78	62	σ2)r	σ2)r	NOUN
ejpam-6038	78	63	-	-	PUNCT
ejpam-6038	78	64	closed	close	VERB
ejpam-6038	78	65	set	set	ADJ
ejpam-6038	78	66	f	f	PROPN
ejpam-6038	78	67	of	of	ADP
ejpam-6038	78	68	y	y	PROPN
ejpam-6038	78	69	;	;	PUNCT
ejpam-6038	78	70	(	(	PUNCT
ejpam-6038	78	71	3	3	X
ejpam-6038	78	72	)	)	PUNCT
ejpam-6038	78	73	f−1(v	f−1(v	NOUN
ejpam-6038	78	74	)	)	PUNCT
ejpam-6038	78	75	is	be	AUX
ejpam-6038	78	76	(	(	PUNCT
ejpam-6038	78	77	τ1	τ1	NOUN
ejpam-6038	78	78	,	,	PUNCT
ejpam-6038	78	79	τ2)p	τ2)p	NOUN
ejpam-6038	78	80	-	-	PUNCT
ejpam-6038	78	81	closed	closed	ADJ
ejpam-6038	78	82	in	in	ADP
ejpam-6038	78	83	x	x	PUNCT
ejpam-6038	78	84	for	for	ADP
ejpam-6038	78	85	every	every	DET
ejpam-6038	78	86	(	(	PUNCT
ejpam-6038	78	87	σ1	σ1	PROPN
ejpam-6038	78	88	,	,	PUNCT
ejpam-6038	78	89	σ2)r	σ2)r	NOUN
ejpam-6038	78	90	-	-	PUNCT
ejpam-6038	78	91	open	open	ADJ
ejpam-6038	78	92	set	set	VERB
ejpam-6038	78	93	v	v	NOUN
ejpam-6038	78	94	of	of	ADP
ejpam-6038	78	95	y	y	PROPN
ejpam-6038	78	96	;	;	PUNCT
ejpam-6038	78	97	p.	p.	NOUN
ejpam-6038	78	98	pue	pue	PROPN
ejpam-6038	78	99	-	-	PUNCT
ejpam-6038	78	100	on	on	ADP
ejpam-6038	78	101	,	,	PUNCT
ejpam-6038	78	102	a.	a.	PROPN
ejpam-6038	78	103	sama	sama	PROPN
ejpam-6038	78	104	-	-	PUNCT
ejpam-6038	78	105	ae	ae	PROPN
ejpam-6038	78	106	,	,	PUNCT
ejpam-6038	78	107	c.	c.	PROPN
ejpam-6038	78	108	boonpok	boonpok	PROPN
ejpam-6038	78	109	/	/	SYM
ejpam-6038	78	110	eur	eur	PROPN
ejpam-6038	78	111	.	.	PUNCT
ejpam-6038	79	1	j.	j.	PROPN
ejpam-6038	79	2	pure	pure	PROPN
ejpam-6038	79	3	appl	appl	PROPN
ejpam-6038	79	4	.	.	PROPN
ejpam-6038	79	5	math	math	PROPN
ejpam-6038	79	6	,	,	PUNCT
ejpam-6038	79	7	18	18	NUM
ejpam-6038	79	8	(	(	PUNCT
ejpam-6038	79	9	2	2	NUM
ejpam-6038	79	10	)	)	PUNCT
ejpam-6038	79	11	(	(	PUNCT
ejpam-6038	79	12	2025	2025	NUM
ejpam-6038	79	13	)	)	PUNCT
ejpam-6038	79	14	,	,	PUNCT
ejpam-6038	79	15	6038	6038	NUM
ejpam-6038	79	16	4	4	NUM
ejpam-6038	79	17	of	of	ADP
ejpam-6038	79	18	11	11	NUM
ejpam-6038	79	19	(	(	PUNCT
ejpam-6038	79	20	4	4	NUM
ejpam-6038	79	21	)	)	PUNCT
ejpam-6038	79	22	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	79	23	-	-	PUNCT
ejpam-6038	79	24	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	79	25	-	-	PUNCT
ejpam-6038	79	26	cl(v	cl(v	NOUN
ejpam-6038	79	27	)	)	PUNCT
ejpam-6038	79	28	)	)	PUNCT
ejpam-6038	79	29	)	)	PUNCT
ejpam-6038	79	30	is	be	AUX
ejpam-6038	79	31	(	(	PUNCT
ejpam-6038	79	32	τ1	τ1	NOUN
ejpam-6038	79	33	,	,	PUNCT
ejpam-6038	79	34	τ2)p	τ2)p	NOUN
ejpam-6038	79	35	-	-	PUNCT
ejpam-6038	79	36	closed	closed	ADJ
ejpam-6038	79	37	in	in	ADP
ejpam-6038	79	38	x	x	PUNCT
ejpam-6038	79	39	for	for	ADP
ejpam-6038	79	40	every	every	DET
ejpam-6038	79	41	σ1σ2	σ1σ2	NOUN
ejpam-6038	79	42	-	-	ADJ
ejpam-6038	79	43	open	open	ADJ
ejpam-6038	79	44	set	set	NOUN
ejpam-6038	79	45	v	v	NOUN
ejpam-6038	79	46	of	of	ADP
ejpam-6038	79	47	y	y	PROPN
ejpam-6038	79	48	;	;	PUNCT
ejpam-6038	79	49	(	(	PUNCT
ejpam-6038	79	50	5	5	X
ejpam-6038	79	51	)	)	PUNCT
ejpam-6038	79	52	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	79	53	-	-	PUNCT
ejpam-6038	79	54	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-6038	79	55	-	-	PUNCT
ejpam-6038	79	56	int(f	int(f	PROPN
ejpam-6038	79	57	)	)	PUNCT
ejpam-6038	79	58	)	)	PUNCT
ejpam-6038	79	59	)	)	PUNCT
ejpam-6038	80	1	is	be	AUX
ejpam-6038	80	2	(	(	PUNCT
ejpam-6038	80	3	τ1	τ1	NOUN
ejpam-6038	80	4	,	,	PUNCT
ejpam-6038	80	5	τ2)p	τ2)p	NOUN
ejpam-6038	80	6	-	-	PUNCT
ejpam-6038	80	7	open	open	ADJ
ejpam-6038	80	8	in	in	ADP
ejpam-6038	80	9	x	x	PUNCT
ejpam-6038	80	10	for	for	ADP
ejpam-6038	80	11	every	every	DET
ejpam-6038	80	12	σ1σ2	σ1σ2	NUM
ejpam-6038	80	13	-	-	PUNCT
ejpam-6038	80	14	closed	closed	ADJ
ejpam-6038	80	15	set	set	ADJ
ejpam-6038	80	16	f	f	PROPN
ejpam-6038	80	17	of	of	ADP
ejpam-6038	80	18	y	y	PROPN
ejpam-6038	80	19	.	.	PUNCT
ejpam-6038	81	1	proof	proof	NOUN
ejpam-6038	81	2	.	.	PUNCT
ejpam-6038	82	1	(	(	PUNCT
ejpam-6038	82	2	1	1	X
ejpam-6038	82	3	)	)	PUNCT
ejpam-6038	82	4	⇒	⇒	NOUN
ejpam-6038	82	5	(	(	PUNCT
ejpam-6038	82	6	2	2	NUM
ejpam-6038	82	7	):	):	PUNCT
ejpam-6038	82	8	let	let	VERB
ejpam-6038	82	9	f	f	PRON
ejpam-6038	82	10	be	be	AUX
ejpam-6038	82	11	any	any	DET
ejpam-6038	82	12	(	(	PUNCT
ejpam-6038	82	13	σ1	σ1	NOUN
ejpam-6038	82	14	,	,	PUNCT
ejpam-6038	82	15	σ2)r	σ2)r	NOUN
ejpam-6038	82	16	-	-	PUNCT
ejpam-6038	82	17	closed	close	VERB
ejpam-6038	82	18	set	set	NOUN
ejpam-6038	82	19	of	of	ADP
ejpam-6038	82	20	y	y	PROPN
ejpam-6038	82	21	and	and	CCONJ
ejpam-6038	82	22	x	x	PROPN
ejpam-6038	82	23	∈	∈	PROPN
ejpam-6038	82	24	f−1(f	f−1(f	PROPN
ejpam-6038	82	25	)	)	PUNCT
ejpam-6038	82	26	.	.	PUNCT
ejpam-6038	83	1	then	then	ADV
ejpam-6038	83	2	,	,	PUNCT
ejpam-6038	83	3	f(x	f(x	PROPN
ejpam-6038	83	4	)	)	PUNCT
ejpam-6038	83	5	∈	∈	PROPN
ejpam-6038	83	6	f	f	X
ejpam-6038	83	7	.	.	PUNCT
ejpam-6038	84	1	by	by	ADP
ejpam-6038	84	2	(	(	PUNCT
ejpam-6038	84	3	1	1	NUM
ejpam-6038	84	4	)	)	PUNCT
ejpam-6038	84	5	,	,	PUNCT
ejpam-6038	84	6	there	there	PRON
ejpam-6038	84	7	exists	exist	VERB
ejpam-6038	84	8	a	a	DET
ejpam-6038	84	9	(	(	PUNCT
ejpam-6038	84	10	τ1	τ1	NOUN
ejpam-6038	84	11	,	,	PUNCT
ejpam-6038	84	12	τ2)p	τ2)p	ADJ
ejpam-6038	84	13	-	-	PUNCT
ejpam-6038	84	14	open	open	ADJ
ejpam-6038	84	15	set	set	NOUN
ejpam-6038	84	16	u	u	PRON
ejpam-6038	84	17	ofx	ofx	NOUN
ejpam-6038	84	18	containing	contain	VERB
ejpam-6038	84	19	x	x	PUNCT
ejpam-6038	84	20	such	such	ADJ
ejpam-6038	84	21	that	that	DET
ejpam-6038	84	22	f(u	f(u	PROPN
ejpam-6038	84	23	)	)	PUNCT
ejpam-6038	84	24	⊆	⊆	NUM
ejpam-6038	84	25	f	f	NOUN
ejpam-6038	84	26	.	.	PUNCT
ejpam-6038	85	1	thus	thus	ADV
ejpam-6038	85	2	,	,	PUNCT
ejpam-6038	85	3	x	x	PUNCT
ejpam-6038	85	4	∈	∈	PROPN
ejpam-6038	85	5	u	u	NOUN
ejpam-6038	85	6	⊆	⊆	NUM
ejpam-6038	85	7	f−1(f	f−1(f	PROPN
ejpam-6038	85	8	)	)	PUNCT
ejpam-6038	85	9	and	and	CCONJ
ejpam-6038	85	10	hence	hence	ADV
ejpam-6038	85	11	x	x	X
ejpam-6038	85	12	∈	∈	PROPN
ejpam-6038	85	13	(	(	PUNCT
ejpam-6038	85	14	τ1	τ1	NOUN
ejpam-6038	85	15	,	,	PUNCT
ejpam-6038	85	16	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-6038	85	17	−1(f	−1(f	NUM
ejpam-6038	85	18	)	)	PUNCT
ejpam-6038	85	19	)	)	PUNCT
ejpam-6038	85	20	.	.	PUNCT
ejpam-6038	86	1	this	this	PRON
ejpam-6038	86	2	implies	imply	VERB
ejpam-6038	86	3	that	that	SCONJ
ejpam-6038	86	4	f−1(f	f−1(f	NOUN
ejpam-6038	86	5	)	)	PUNCT
ejpam-6038	87	1	⊆	⊆	NUM
ejpam-6038	87	2	(	(	PUNCT
ejpam-6038	87	3	τ1	τ1	NOUN
ejpam-6038	87	4	,	,	PUNCT
ejpam-6038	87	5	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-6038	87	6	−1(f	−1(f	NUM
ejpam-6038	87	7	)	)	PUNCT
ejpam-6038	87	8	)	)	PUNCT
ejpam-6038	87	9	.	.	PUNCT
ejpam-6038	88	1	therefore	therefore	ADV
ejpam-6038	88	2	,	,	PUNCT
ejpam-6038	88	3	f−1(f	f−1(f	PROPN
ejpam-6038	88	4	)	)	PUNCT
ejpam-6038	88	5	is	be	AUX
ejpam-6038	88	6	(	(	PUNCT
ejpam-6038	88	7	τ1	τ1	NOUN
ejpam-6038	88	8	,	,	PUNCT
ejpam-6038	88	9	τ2)p	τ2)p	NOUN
ejpam-6038	88	10	-	-	PUNCT
ejpam-6038	88	11	open	open	ADJ
ejpam-6038	88	12	in	in	ADP
ejpam-6038	88	13	x.	x.	NOUN
ejpam-6038	88	14	(	(	PUNCT
ejpam-6038	88	15	2	2	NUM
ejpam-6038	88	16	)	)	PUNCT
ejpam-6038	88	17	⇒	⇒	NOUN
ejpam-6038	88	18	(	(	PUNCT
ejpam-6038	88	19	3	3	NUM
ejpam-6038	88	20	):	):	PUNCT
ejpam-6038	88	21	the	the	DET
ejpam-6038	88	22	proof	proof	NOUN
ejpam-6038	88	23	is	be	AUX
ejpam-6038	88	24	obvious	obvious	ADJ
ejpam-6038	88	25	.	.	PUNCT
ejpam-6038	89	1	(	(	PUNCT
ejpam-6038	89	2	3	3	X
ejpam-6038	89	3	)	)	PUNCT
ejpam-6038	89	4	⇒	⇒	NOUN
ejpam-6038	89	5	(	(	PUNCT
ejpam-6038	89	6	4	4	NUM
ejpam-6038	89	7	):	):	PUNCT
ejpam-6038	89	8	let	let	VERB
ejpam-6038	89	9	v	v	PART
ejpam-6038	89	10	be	be	AUX
ejpam-6038	89	11	any	any	DET
ejpam-6038	89	12	σ1σ2	σ1σ2	NOUN
ejpam-6038	89	13	-	-	ADJ
ejpam-6038	89	14	open	open	ADJ
ejpam-6038	89	15	set	set	NOUN
ejpam-6038	89	16	of	of	ADP
ejpam-6038	89	17	y	y	PROPN
ejpam-6038	89	18	.	.	PUNCT
ejpam-6038	90	1	then	then	ADV
ejpam-6038	90	2	,	,	PUNCT
ejpam-6038	90	3	we	we	PRON
ejpam-6038	90	4	have	have	VERB
ejpam-6038	90	5	σ1σ2	σ1σ2	NOUN
ejpam-6038	90	6	-	-	PUNCT
ejpam-6038	90	7	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	90	8	-	-	PUNCT
ejpam-6038	90	9	cl(v	cl(v	NOUN
ejpam-6038	90	10	)	)	PUNCT
ejpam-6038	90	11	)	)	PUNCT
ejpam-6038	91	1	is	be	AUX
ejpam-6038	91	2	(	(	PUNCT
ejpam-6038	91	3	σ1	σ1	NOUN
ejpam-6038	91	4	,	,	PUNCT
ejpam-6038	91	5	σ2)r	σ2)r	NOUN
ejpam-6038	91	6	-	-	PUNCT
ejpam-6038	91	7	open	open	ADJ
ejpam-6038	91	8	in	in	ADP
ejpam-6038	91	9	y	y	PROPN
ejpam-6038	91	10	.	.	PUNCT
ejpam-6038	92	1	thus	thus	ADV
ejpam-6038	92	2	by	by	ADP
ejpam-6038	92	3	(	(	PUNCT
ejpam-6038	92	4	3	3	NUM
ejpam-6038	92	5	)	)	PUNCT
ejpam-6038	92	6	,	,	PUNCT
ejpam-6038	92	7	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	92	8	-	-	PUNCT
ejpam-6038	92	9	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	92	10	-	-	PUNCT
ejpam-6038	92	11	cl(v	cl(v	NOUN
ejpam-6038	92	12	)	)	PUNCT
ejpam-6038	92	13	)	)	PUNCT
ejpam-6038	92	14	)	)	PUNCT
ejpam-6038	92	15	is	be	AUX
ejpam-6038	92	16	(	(	PUNCT
ejpam-6038	92	17	τ1	τ1	NOUN
ejpam-6038	92	18	,	,	PUNCT
ejpam-6038	92	19	τ2)p	τ2)p	NOUN
ejpam-6038	92	20	-	-	PUNCT
ejpam-6038	92	21	closed	closed	ADJ
ejpam-6038	92	22	in	in	ADP
ejpam-6038	92	23	x.	x.	NOUN
ejpam-6038	92	24	(	(	PUNCT
ejpam-6038	92	25	4	4	NUM
ejpam-6038	92	26	)	)	PUNCT
ejpam-6038	92	27	⇒	⇒	NOUN
ejpam-6038	92	28	(	(	PUNCT
ejpam-6038	92	29	5	5	NUM
ejpam-6038	92	30	):	):	PUNCT
ejpam-6038	92	31	let	let	VERB
ejpam-6038	92	32	f	f	PRON
ejpam-6038	92	33	be	be	AUX
ejpam-6038	92	34	any	any	DET
ejpam-6038	92	35	σ1σ2	σ1σ2	NUM
ejpam-6038	92	36	-	-	PUNCT
ejpam-6038	92	37	closed	closed	ADJ
ejpam-6038	92	38	set	set	NOUN
ejpam-6038	92	39	of	of	ADP
ejpam-6038	92	40	y	y	PROPN
ejpam-6038	92	41	.	.	PUNCT
ejpam-6038	93	1	then	then	ADV
ejpam-6038	93	2	,	,	PUNCT
ejpam-6038	93	3	y	y	PROPN
ejpam-6038	93	4	−	−	PROPN
ejpam-6038	94	1	f	f	PROPN
ejpam-6038	94	2	is	be	AUX
ejpam-6038	94	3	σ1σ2	σ1σ2	NOUN
ejpam-6038	94	4	-	-	ADJ
ejpam-6038	94	5	open	open	ADJ
ejpam-6038	94	6	in	in	ADP
ejpam-6038	94	7	y	y	PROPN
ejpam-6038	94	8	.	.	PUNCT
ejpam-6038	95	1	by	by	ADP
ejpam-6038	95	2	(	(	PUNCT
ejpam-6038	95	3	4	4	NUM
ejpam-6038	95	4	)	)	PUNCT
ejpam-6038	95	5	,	,	PUNCT
ejpam-6038	95	6	we	we	PRON
ejpam-6038	95	7	have	have	AUX
ejpam-6038	95	8	f−1(σ1σ2	f−1(σ1σ2	VERB
ejpam-6038	95	9	-	-	PUNCT
ejpam-6038	95	10	cl(σ1σ2	cl(σ1σ2	VERB
ejpam-6038	95	11	-	-	PUNCT
ejpam-6038	95	12	int(y	int(y	PROPN
ejpam-6038	95	13	−f	−f	NOUN
ejpam-6038	95	14	)	)	PUNCT
ejpam-6038	95	15	)	)	PUNCT
ejpam-6038	95	16	)	)	PUNCT
ejpam-6038	96	1	=	=	PUNCT
ejpam-6038	96	2	y	y	PROPN
ejpam-6038	96	3	−f−1(σ1σ2	−f−1(σ1σ2	ADV
ejpam-6038	96	4	-	-	PUNCT
ejpam-6038	96	5	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	96	6	-	-	PUNCT
ejpam-6038	96	7	cl(f	cl(f	NUM
ejpam-6038	96	8	)	)	PUNCT
ejpam-6038	96	9	)	)	PUNCT
ejpam-6038	96	10	)	)	PUNCT
ejpam-6038	97	1	is	be	AUX
ejpam-6038	97	2	(	(	PUNCT
ejpam-6038	97	3	τ1	τ1	NOUN
ejpam-6038	97	4	,	,	PUNCT
ejpam-6038	97	5	τ2)pclosed	τ2)pclose	VERB
ejpam-6038	97	6	in	in	ADP
ejpam-6038	97	7	x.	x.	NOUN
ejpam-6038	97	8	thus	thus	ADV
ejpam-6038	97	9	,	,	PUNCT
ejpam-6038	97	10	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	97	11	-	-	PUNCT
ejpam-6038	97	12	cl(σ1σ2	cl(σ1σ2	NOUN
ejpam-6038	97	13	-	-	PUNCT
ejpam-6038	97	14	int(f	int(f	PROPN
ejpam-6038	97	15	)	)	PUNCT
ejpam-6038	97	16	)	)	PUNCT
ejpam-6038	97	17	)	)	PUNCT
ejpam-6038	98	1	is	be	AUX
ejpam-6038	98	2	(	(	PUNCT
ejpam-6038	98	3	τ1	τ1	NOUN
ejpam-6038	98	4	,	,	PUNCT
ejpam-6038	98	5	τ2)p	τ2)p	NOUN
ejpam-6038	98	6	-	-	PUNCT
ejpam-6038	98	7	open	open	ADJ
ejpam-6038	98	8	in	in	ADP
ejpam-6038	98	9	x.	x.	NOUN
ejpam-6038	98	10	(	(	PUNCT
ejpam-6038	98	11	5	5	NUM
ejpam-6038	98	12	)	)	PUNCT
ejpam-6038	98	13	⇒	⇒	NOUN
ejpam-6038	98	14	(	(	PUNCT
ejpam-6038	98	15	1	1	NUM
ejpam-6038	98	16	):	):	PUNCT
ejpam-6038	98	17	let	let	VERB
ejpam-6038	98	18	f	f	PRON
ejpam-6038	98	19	be	be	AUX
ejpam-6038	98	20	any	any	DET
ejpam-6038	98	21	(	(	PUNCT
ejpam-6038	98	22	σ1	σ1	NOUN
ejpam-6038	98	23	,	,	PUNCT
ejpam-6038	98	24	σ2)r	σ2)r	NOUN
ejpam-6038	98	25	-	-	PUNCT
ejpam-6038	98	26	closed	close	VERB
ejpam-6038	98	27	set	set	NOUN
ejpam-6038	98	28	of	of	ADP
ejpam-6038	98	29	y	y	PROPN
ejpam-6038	98	30	containing	contain	VERB
ejpam-6038	98	31	f(x	f(x	PROPN
ejpam-6038	98	32	)	)	PUNCT
ejpam-6038	98	33	.	.	PUNCT
ejpam-6038	99	1	since	since	SCONJ
ejpam-6038	99	2	f	f	PROPN
ejpam-6038	99	3	is	be	AUX
ejpam-6038	99	4	σ1σ2closed	σ1σ2close	VERB
ejpam-6038	99	5	in	in	ADP
ejpam-6038	99	6	y	y	PROPN
ejpam-6038	99	7	and	and	CCONJ
ejpam-6038	99	8	by	by	ADP
ejpam-6038	99	9	(	(	PUNCT
ejpam-6038	99	10	5	5	NUM
ejpam-6038	99	11	)	)	PUNCT
ejpam-6038	99	12	,	,	PUNCT
ejpam-6038	99	13	f−1(f	f−1(f	PROPN
ejpam-6038	99	14	)	)	PUNCT
ejpam-6038	99	15	is	be	AUX
ejpam-6038	99	16	(	(	PUNCT
ejpam-6038	99	17	τ1	τ1	NOUN
ejpam-6038	99	18	,	,	PUNCT
ejpam-6038	99	19	τ2)p	τ2)p	NOUN
ejpam-6038	99	20	-	-	PUNCT
ejpam-6038	99	21	open	open	ADJ
ejpam-6038	99	22	in	in	ADP
ejpam-6038	99	23	x.	x.	NOUN
ejpam-6038	99	24	let	let	VERB
ejpam-6038	99	25	u	u	NOUN
ejpam-6038	99	26	=	=	PROPN
ejpam-6038	99	27	f−1(f	f−1(f	PROPN
ejpam-6038	99	28	)	)	PUNCT
ejpam-6038	99	29	.	.	PUNCT
ejpam-6038	100	1	then	then	ADV
ejpam-6038	100	2	,	,	PUNCT
ejpam-6038	100	3	u	u	NOUN
ejpam-6038	100	4	is	be	AUX
ejpam-6038	100	5	a	a	DET
ejpam-6038	100	6	(	(	PUNCT
ejpam-6038	100	7	τ1	τ1	NOUN
ejpam-6038	100	8	,	,	PUNCT
ejpam-6038	100	9	τ2)p	τ2)p	ADJ
ejpam-6038	100	10	-	-	PUNCT
ejpam-6038	100	11	open	open	ADJ
ejpam-6038	100	12	set	set	NOUN
ejpam-6038	100	13	u	u	NOUN
ejpam-6038	100	14	of	of	ADP
ejpam-6038	100	15	x	x	PUNCT
ejpam-6038	100	16	containing	contain	VERB
ejpam-6038	100	17	x	x	PUNCT
ejpam-6038	100	18	such	such	ADJ
ejpam-6038	100	19	that	that	DET
ejpam-6038	100	20	f(u	f(u	PROPN
ejpam-6038	100	21	)	)	PUNCT
ejpam-6038	100	22	⊆	⊆	NUM
ejpam-6038	100	23	f	f	NOUN
ejpam-6038	100	24	.	.	PUNCT
ejpam-6038	101	1	this	this	PRON
ejpam-6038	101	2	shows	show	VERB
ejpam-6038	101	3	that	that	SCONJ
ejpam-6038	101	4	f	f	PROPN
ejpam-6038	101	5	is	be	AUX
ejpam-6038	101	6	almost	almost	ADV
ejpam-6038	101	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	101	8	,	,	PUNCT
ejpam-6038	101	9	τ2)p	τ2)p	ADJ
ejpam-6038	101	10	-	-	ADJ
ejpam-6038	101	11	continuous	continuous	ADJ
ejpam-6038	101	12	.	.	PUNCT
ejpam-6038	102	1	definition	definition	NOUN
ejpam-6038	102	2	2	2	NUM
ejpam-6038	102	3	.	.	PUNCT
ejpam-6038	103	1	a	a	DET
ejpam-6038	103	2	function	function	NOUN
ejpam-6038	103	3	f	f	NOUN
ejpam-6038	103	4	:	:	PUNCT
ejpam-6038	103	5	(	(	PUNCT
ejpam-6038	103	6	x	x	NOUN
ejpam-6038	103	7	,	,	PUNCT
ejpam-6038	103	8	τ1	τ1	NOUN
ejpam-6038	103	9	,	,	PUNCT
ejpam-6038	103	10	τ2	τ2	NOUN
ejpam-6038	103	11	)	)	PUNCT
ejpam-6038	103	12	→	→	SYM
ejpam-6038	103	13	(	(	PUNCT
ejpam-6038	103	14	y	y	PROPN
ejpam-6038	103	15	,	,	PUNCT
ejpam-6038	103	16	σ1	σ1	PROPN
ejpam-6038	103	17	,	,	PUNCT
ejpam-6038	103	18	σ2	σ2	PROPN
ejpam-6038	103	19	)	)	PUNCT
ejpam-6038	103	20	is	be	AUX
ejpam-6038	103	21	said	say	VERB
ejpam-6038	103	22	to	to	PART
ejpam-6038	103	23	be	be	AUX
ejpam-6038	103	24	(	(	PUNCT
ejpam-6038	103	25	τ1	τ1	NOUN
ejpam-6038	103	26	,	,	PUNCT
ejpam-6038	103	27	τ2)p	τ2)p	NOUN
ejpam-6038	103	28	-	-	PUNCT
ejpam-6038	103	29	open	open	ADJ
ejpam-6038	103	30	if	if	SCONJ
ejpam-6038	103	31	f(u	f(u	PROPN
ejpam-6038	103	32	)	)	PUNCT
ejpam-6038	103	33	is	be	AUX
ejpam-6038	103	34	(	(	PUNCT
ejpam-6038	103	35	σ1	σ1	PROPN
ejpam-6038	103	36	,	,	PUNCT
ejpam-6038	103	37	σ2)p	σ2)p	NOUN
ejpam-6038	103	38	-	-	PUNCT
ejpam-6038	103	39	open	open	ADJ
ejpam-6038	103	40	in	in	ADP
ejpam-6038	103	41	y	y	PROPN
ejpam-6038	103	42	for	for	ADP
ejpam-6038	103	43	every	every	DET
ejpam-6038	103	44	(	(	PUNCT
ejpam-6038	103	45	τ1	τ1	NOUN
ejpam-6038	103	46	,	,	PUNCT
ejpam-6038	103	47	τ2)p	τ2)p	ADJ
ejpam-6038	103	48	-	-	PUNCT
ejpam-6038	103	49	open	open	ADJ
ejpam-6038	103	50	set	set	NOUN
ejpam-6038	103	51	u	u	PROPN
ejpam-6038	103	52	of	of	ADP
ejpam-6038	103	53	x.	x.	PROPN
ejpam-6038	103	54	theorem	theorem	VERB
ejpam-6038	103	55	2	2	NUM
ejpam-6038	103	56	.	.	PUNCT
ejpam-6038	104	1	if	if	SCONJ
ejpam-6038	104	2	f	f	PROPN
ejpam-6038	104	3	:	:	PUNCT
ejpam-6038	104	4	(	(	PUNCT
ejpam-6038	104	5	x	x	NOUN
ejpam-6038	104	6	,	,	PUNCT
ejpam-6038	104	7	τ1	τ1	NOUN
ejpam-6038	104	8	,	,	PUNCT
ejpam-6038	104	9	τ2	τ2	NOUN
ejpam-6038	104	10	)	)	PUNCT
ejpam-6038	104	11	→	→	SYM
ejpam-6038	104	12	(	(	PUNCT
ejpam-6038	104	13	y	y	PROPN
ejpam-6038	104	14	,	,	PUNCT
ejpam-6038	104	15	σ1	σ1	PROPN
ejpam-6038	104	16	,	,	PUNCT
ejpam-6038	104	17	σ2	σ2	PROPN
ejpam-6038	104	18	)	)	PUNCT
ejpam-6038	104	19	is	be	AUX
ejpam-6038	104	20	a	a	DET
ejpam-6038	104	21	(	(	PUNCT
ejpam-6038	104	22	τ1	τ1	NOUN
ejpam-6038	104	23	,	,	PUNCT
ejpam-6038	104	24	τ2)p	τ2)p	ADJ
ejpam-6038	104	25	-	-	PUNCT
ejpam-6038	104	26	open	open	ADJ
ejpam-6038	104	27	surjection	surjection	NOUN
ejpam-6038	104	28	and	and	CCONJ
ejpam-6038	104	29	g	g	NOUN
ejpam-6038	104	30	:	:	PUNCT
ejpam-6038	104	31	(	(	PUNCT
ejpam-6038	104	32	y	y	PROPN
ejpam-6038	104	33	,	,	PUNCT
ejpam-6038	104	34	σ1	σ1	PROPN
ejpam-6038	104	35	,	,	PUNCT
ejpam-6038	104	36	σ2	σ2	NOUN
ejpam-6038	104	37	)	)	PUNCT
ejpam-6038	104	38	→	→	SYM
ejpam-6038	104	39	(	(	PUNCT
ejpam-6038	104	40	z	z	NOUN
ejpam-6038	104	41	,	,	PUNCT
ejpam-6038	104	42	ρ1	ρ1	NOUN
ejpam-6038	104	43	,	,	PUNCT
ejpam-6038	104	44	ρ2	ρ2	NOUN
ejpam-6038	104	45	)	)	PUNCT
ejpam-6038	104	46	is	be	AUX
ejpam-6038	104	47	a	a	DET
ejpam-6038	104	48	function	function	NOUN
ejpam-6038	104	49	such	such	ADJ
ejpam-6038	104	50	that	that	SCONJ
ejpam-6038	104	51	g	g	PROPN
ejpam-6038	104	52	◦	◦	NOUN
ejpam-6038	104	53	f	f	NOUN
ejpam-6038	104	54	:	:	PUNCT
ejpam-6038	104	55	(	(	PUNCT
ejpam-6038	104	56	x	x	NOUN
ejpam-6038	104	57	,	,	PUNCT
ejpam-6038	104	58	τ1	τ1	NOUN
ejpam-6038	104	59	,	,	PUNCT
ejpam-6038	104	60	τ2	τ2	NOUN
ejpam-6038	104	61	)	)	PUNCT
ejpam-6038	104	62	→	→	SYM
ejpam-6038	104	63	(	(	PUNCT
ejpam-6038	104	64	z	z	NOUN
ejpam-6038	104	65	,	,	PUNCT
ejpam-6038	104	66	ρ1	ρ1	NOUN
ejpam-6038	104	67	,	,	PUNCT
ejpam-6038	104	68	ρ2	ρ2	NOUN
ejpam-6038	104	69	)	)	PUNCT
ejpam-6038	104	70	is	be	AUX
ejpam-6038	104	71	almost	almost	ADV
ejpam-6038	104	72	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	104	73	,	,	PUNCT
ejpam-6038	104	74	τ2)p	τ2)p	ADJ
ejpam-6038	104	75	-	-	ADJ
ejpam-6038	104	76	continuous	continuous	ADJ
ejpam-6038	104	77	,	,	PUNCT
ejpam-6038	104	78	then	then	ADV
ejpam-6038	104	79	g	g	PROPN
ejpam-6038	104	80	is	be	AUX
ejpam-6038	104	81	almost	almost	ADV
ejpam-6038	104	82	contra-(σ1	contra-(σ1	ADJ
ejpam-6038	104	83	,	,	PUNCT
ejpam-6038	104	84	σ2)p	σ2)p	NOUN
ejpam-6038	104	85	-	-	PUNCT
ejpam-6038	104	86	continuous	continuous	ADJ
ejpam-6038	104	87	.	.	PUNCT
ejpam-6038	105	1	proof	proof	NOUN
ejpam-6038	105	2	.	.	PUNCT
ejpam-6038	106	1	let	let	VERB
ejpam-6038	106	2	f	f	PRON
ejpam-6038	106	3	be	be	AUX
ejpam-6038	106	4	any	any	DET
ejpam-6038	106	5	(	(	PUNCT
ejpam-6038	106	6	ρ1	ρ1	NOUN
ejpam-6038	106	7	,	,	PUNCT
ejpam-6038	106	8	ρ2)r	ρ2)r	NOUN
ejpam-6038	106	9	-	-	PUNCT
ejpam-6038	106	10	closed	close	VERB
ejpam-6038	106	11	set	set	NOUN
ejpam-6038	106	12	of	of	ADP
ejpam-6038	106	13	z.	z.	PROPN
ejpam-6038	106	14	since	since	SCONJ
ejpam-6038	106	15	g	g	PROPN
ejpam-6038	106	16	◦	◦	PROPN
ejpam-6038	106	17	f	f	PROPN
ejpam-6038	106	18	is	be	AUX
ejpam-6038	106	19	almost	almost	ADV
ejpam-6038	106	20	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	106	21	,	,	PUNCT
ejpam-6038	106	22	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6038	106	23	,	,	PUNCT
ejpam-6038	106	24	by	by	ADP
ejpam-6038	106	25	theorem	theorem	NOUN
ejpam-6038	106	26	1	1	NUM
ejpam-6038	106	27	we	we	PRON
ejpam-6038	106	28	have	have	VERB
ejpam-6038	106	29	(	(	PUNCT
ejpam-6038	106	30	g	g	NOUN
ejpam-6038	106	31	◦	◦	NOUN
ejpam-6038	106	32	f)−1(f	f)−1(f	NOUN
ejpam-6038	106	33	)	)	PUNCT
ejpam-6038	107	1	=	=	SYM
ejpam-6038	107	2	f−1(g−1(f	f−1(g−1(f	NOUN
ejpam-6038	107	3	)	)	PUNCT
ejpam-6038	107	4	)	)	PUNCT
ejpam-6038	107	5	is	be	AUX
ejpam-6038	107	6	(	(	PUNCT
ejpam-6038	107	7	τ1	τ1	NOUN
ejpam-6038	107	8	,	,	PUNCT
ejpam-6038	107	9	τ2)p	τ2)p	ADJ
ejpam-6038	107	10	-	-	PUNCT
ejpam-6038	107	11	open	open	ADJ
ejpam-6038	107	12	inx	inx	NOUN
ejpam-6038	107	13	.	.	PUNCT
ejpam-6038	108	1	since	since	SCONJ
ejpam-6038	108	2	f	f	PROPN
ejpam-6038	108	3	is	be	AUX
ejpam-6038	108	4	(	(	PUNCT
ejpam-6038	108	5	τ1	τ1	NOUN
ejpam-6038	108	6	,	,	PUNCT
ejpam-6038	108	7	τ2)p	τ2)p	ADJ
ejpam-6038	108	8	-	-	PUNCT
ejpam-6038	108	9	open	open	ADJ
ejpam-6038	108	10	surjective	surjective	ADJ
ejpam-6038	108	11	,	,	PUNCT
ejpam-6038	108	12	f(f−1(g−1(f	f(f−1(g−1(f	ADJ
ejpam-6038	108	13	)	)	PUNCT
ejpam-6038	108	14	)	)	PUNCT
ejpam-6038	108	15	)	)	PUNCT
ejpam-6038	109	1	=	=	SYM
ejpam-6038	109	2	g−1(f	g−1(f	PROPN
ejpam-6038	109	3	)	)	PUNCT
ejpam-6038	109	4	is	be	AUX
ejpam-6038	109	5	(	(	PUNCT
ejpam-6038	109	6	σ1	σ1	PROPN
ejpam-6038	109	7	,	,	PUNCT
ejpam-6038	109	8	σ2)p	σ2)p	NOUN
ejpam-6038	109	9	-	-	PUNCT
ejpam-6038	109	10	open	open	ADJ
ejpam-6038	109	11	in	in	ADP
ejpam-6038	109	12	y	y	PROPN
ejpam-6038	109	13	.	.	PUNCT
ejpam-6038	110	1	thus	thus	ADV
ejpam-6038	110	2	,	,	PUNCT
ejpam-6038	110	3	g	g	PROPN
ejpam-6038	110	4	is	be	AUX
ejpam-6038	110	5	almost	almost	ADV
ejpam-6038	110	6	contra-(σ1	contra-(σ1	ADJ
ejpam-6038	110	7	,	,	PUNCT
ejpam-6038	110	8	σ2)p	σ2)p	NOUN
ejpam-6038	110	9	-	-	PUNCT
ejpam-6038	110	10	continuous	continuous	ADJ
ejpam-6038	110	11	.	.	PUNCT
ejpam-6038	111	1	definition	definition	NOUN
ejpam-6038	111	2	3	3	NUM
ejpam-6038	111	3	.	.	PUNCT
ejpam-6038	112	1	a	a	DET
ejpam-6038	112	2	function	function	NOUN
ejpam-6038	112	3	f	f	NOUN
ejpam-6038	112	4	:	:	PUNCT
ejpam-6038	112	5	(	(	PUNCT
ejpam-6038	112	6	x	x	NOUN
ejpam-6038	112	7	,	,	PUNCT
ejpam-6038	112	8	τ1	τ1	NOUN
ejpam-6038	112	9	,	,	PUNCT
ejpam-6038	112	10	τ2	τ2	NOUN
ejpam-6038	112	11	)	)	PUNCT
ejpam-6038	112	12	→	→	SYM
ejpam-6038	112	13	(	(	PUNCT
ejpam-6038	112	14	y	y	PROPN
ejpam-6038	112	15	,	,	PUNCT
ejpam-6038	112	16	σ1	σ1	PROPN
ejpam-6038	112	17	,	,	PUNCT
ejpam-6038	112	18	σ2	σ2	PROPN
ejpam-6038	112	19	)	)	PUNCT
ejpam-6038	112	20	is	be	AUX
ejpam-6038	112	21	said	say	VERB
ejpam-6038	112	22	to	to	PART
ejpam-6038	112	23	be	be	AUX
ejpam-6038	112	24	(	(	PUNCT
ejpam-6038	112	25	τ1	τ1	NOUN
ejpam-6038	112	26	,	,	PUNCT
ejpam-6038	112	27	τ2)p	τ2)p	NOUN
ejpam-6038	112	28	-	-	PUNCT
ejpam-6038	112	29	closed	closed	ADJ
ejpam-6038	112	30	if	if	SCONJ
ejpam-6038	112	31	f(k	f(k	VERB
ejpam-6038	112	32	)	)	PUNCT
ejpam-6038	112	33	is	be	AUX
ejpam-6038	112	34	(	(	PUNCT
ejpam-6038	112	35	σ1	σ1	PROPN
ejpam-6038	112	36	,	,	PUNCT
ejpam-6038	112	37	σ2)p	σ2)p	PROPN
ejpam-6038	112	38	-	-	PUNCT
ejpam-6038	112	39	closed	close	VERB
ejpam-6038	112	40	in	in	ADP
ejpam-6038	112	41	y	y	PROPN
ejpam-6038	112	42	for	for	ADP
ejpam-6038	112	43	every	every	DET
ejpam-6038	112	44	(	(	PUNCT
ejpam-6038	112	45	τ1	τ1	NOUN
ejpam-6038	112	46	,	,	PUNCT
ejpam-6038	112	47	τ2)p	τ2)p	NOUN
ejpam-6038	112	48	-	-	PUNCT
ejpam-6038	112	49	closed	closed	ADJ
ejpam-6038	112	50	set	set	NOUN
ejpam-6038	112	51	k	k	PROPN
ejpam-6038	112	52	of	of	ADP
ejpam-6038	112	53	x.	x.	PROPN
ejpam-6038	112	54	theorem	theorem	VERB
ejpam-6038	112	55	3	3	X
ejpam-6038	112	56	.	.	PUNCT
ejpam-6038	113	1	if	if	SCONJ
ejpam-6038	113	2	f	f	PROPN
ejpam-6038	113	3	:	:	PUNCT
ejpam-6038	113	4	(	(	PUNCT
ejpam-6038	113	5	x	x	NOUN
ejpam-6038	113	6	,	,	PUNCT
ejpam-6038	113	7	τ1	τ1	NOUN
ejpam-6038	113	8	,	,	PUNCT
ejpam-6038	113	9	τ2	τ2	NOUN
ejpam-6038	113	10	)	)	PUNCT
ejpam-6038	113	11	→	→	SYM
ejpam-6038	113	12	(	(	PUNCT
ejpam-6038	113	13	y	y	PROPN
ejpam-6038	113	14	,	,	PUNCT
ejpam-6038	113	15	σ1	σ1	PROPN
ejpam-6038	113	16	,	,	PUNCT
ejpam-6038	113	17	σ2	σ2	PROPN
ejpam-6038	113	18	)	)	PUNCT
ejpam-6038	113	19	is	be	AUX
ejpam-6038	113	20	a	a	DET
ejpam-6038	113	21	(	(	PUNCT
ejpam-6038	113	22	τ1	τ1	NOUN
ejpam-6038	113	23	,	,	PUNCT
ejpam-6038	113	24	τ2)p	τ2)p	NOUN
ejpam-6038	113	25	-	-	PUNCT
ejpam-6038	113	26	closed	closed	ADJ
ejpam-6038	113	27	surjection	surjection	NOUN
ejpam-6038	113	28	and	and	CCONJ
ejpam-6038	113	29	g	g	NOUN
ejpam-6038	113	30	:	:	PUNCT
ejpam-6038	113	31	(	(	PUNCT
ejpam-6038	113	32	y	y	PROPN
ejpam-6038	113	33	,	,	PUNCT
ejpam-6038	113	34	σ1	σ1	PROPN
ejpam-6038	113	35	,	,	PUNCT
ejpam-6038	113	36	σ2	σ2	NOUN
ejpam-6038	113	37	)	)	PUNCT
ejpam-6038	113	38	→	→	SYM
ejpam-6038	113	39	(	(	PUNCT
ejpam-6038	113	40	z	z	NOUN
ejpam-6038	113	41	,	,	PUNCT
ejpam-6038	113	42	ρ1	ρ1	NOUN
ejpam-6038	113	43	,	,	PUNCT
ejpam-6038	113	44	ρ2	ρ2	NOUN
ejpam-6038	113	45	)	)	PUNCT
ejpam-6038	113	46	is	be	AUX
ejpam-6038	113	47	a	a	DET
ejpam-6038	113	48	function	function	NOUN
ejpam-6038	113	49	such	such	ADJ
ejpam-6038	113	50	that	that	SCONJ
ejpam-6038	113	51	g	g	PROPN
ejpam-6038	113	52	◦	◦	NOUN
ejpam-6038	113	53	f	f	NOUN
ejpam-6038	113	54	:	:	PUNCT
ejpam-6038	113	55	(	(	PUNCT
ejpam-6038	113	56	x	x	NOUN
ejpam-6038	113	57	,	,	PUNCT
ejpam-6038	113	58	τ1	τ1	NOUN
ejpam-6038	113	59	,	,	PUNCT
ejpam-6038	113	60	τ2	τ2	NOUN
ejpam-6038	113	61	)	)	PUNCT
ejpam-6038	113	62	→	→	SYM
ejpam-6038	113	63	(	(	PUNCT
ejpam-6038	113	64	z	z	NOUN
ejpam-6038	113	65	,	,	PUNCT
ejpam-6038	113	66	ρ1	ρ1	NOUN
ejpam-6038	113	67	,	,	PUNCT
ejpam-6038	113	68	ρ2	ρ2	NOUN
ejpam-6038	113	69	)	)	PUNCT
ejpam-6038	113	70	is	be	AUX
ejpam-6038	113	71	almost	almost	ADV
ejpam-6038	113	72	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	113	73	,	,	PUNCT
ejpam-6038	113	74	τ2)p	τ2)p	ADJ
ejpam-6038	113	75	-	-	ADJ
ejpam-6038	113	76	continuous	continuous	ADJ
ejpam-6038	113	77	,	,	PUNCT
ejpam-6038	113	78	then	then	ADV
ejpam-6038	113	79	g	g	PROPN
ejpam-6038	113	80	is	be	AUX
ejpam-6038	113	81	almost	almost	ADV
ejpam-6038	113	82	contra-(σ1	contra-(σ1	ADJ
ejpam-6038	113	83	,	,	PUNCT
ejpam-6038	113	84	σ2)p	σ2)p	NOUN
ejpam-6038	113	85	-	-	PUNCT
ejpam-6038	113	86	continuous	continuous	ADJ
ejpam-6038	113	87	.	.	PUNCT
ejpam-6038	114	1	p.	p.	NOUN
ejpam-6038	114	2	pue	pue	NOUN
ejpam-6038	114	3	-	-	PUNCT
ejpam-6038	114	4	on	on	ADP
ejpam-6038	114	5	,	,	PUNCT
ejpam-6038	114	6	a.	a.	PROPN
ejpam-6038	114	7	sama	sama	PROPN
ejpam-6038	114	8	-	-	PUNCT
ejpam-6038	114	9	ae	ae	PROPN
ejpam-6038	114	10	,	,	PUNCT
ejpam-6038	114	11	c.	c.	PROPN
ejpam-6038	114	12	boonpok	boonpok	PROPN
ejpam-6038	114	13	/	/	SYM
ejpam-6038	114	14	eur	eur	PROPN
ejpam-6038	114	15	.	.	PUNCT
ejpam-6038	115	1	j.	j.	PROPN
ejpam-6038	115	2	pure	pure	PROPN
ejpam-6038	115	3	appl	appl	PROPN
ejpam-6038	115	4	.	.	PROPN
ejpam-6038	115	5	math	math	PROPN
ejpam-6038	115	6	,	,	PUNCT
ejpam-6038	115	7	18	18	NUM
ejpam-6038	115	8	(	(	PUNCT
ejpam-6038	115	9	2	2	NUM
ejpam-6038	115	10	)	)	PUNCT
ejpam-6038	115	11	(	(	PUNCT
ejpam-6038	115	12	2025	2025	NUM
ejpam-6038	115	13	)	)	PUNCT
ejpam-6038	115	14	,	,	PUNCT
ejpam-6038	115	15	6038	6038	NUM
ejpam-6038	115	16	5	5	NUM
ejpam-6038	115	17	of	of	ADP
ejpam-6038	115	18	11	11	NUM
ejpam-6038	115	19	proof	proof	NOUN
ejpam-6038	115	20	.	.	PUNCT
ejpam-6038	116	1	the	the	DET
ejpam-6038	116	2	proof	proof	NOUN
ejpam-6038	116	3	is	be	AUX
ejpam-6038	116	4	similar	similar	ADJ
ejpam-6038	116	5	to	to	ADP
ejpam-6038	116	6	that	that	PRON
ejpam-6038	116	7	of	of	ADP
ejpam-6038	116	8	theorem	theorem	NOUN
ejpam-6038	116	9	2	2	NUM
ejpam-6038	116	10	.	.	PUNCT
ejpam-6038	116	11	definition	definition	NOUN
ejpam-6038	116	12	4	4	NUM
ejpam-6038	116	13	.	.	PUNCT
ejpam-6038	117	1	a	a	DET
ejpam-6038	117	2	bitopological	bitopological	ADJ
ejpam-6038	117	3	space	space	NOUN
ejpam-6038	117	4	(	(	PUNCT
ejpam-6038	117	5	x	x	NOUN
ejpam-6038	117	6	,	,	PUNCT
ejpam-6038	117	7	τ1	τ1	NOUN
ejpam-6038	117	8	,	,	PUNCT
ejpam-6038	117	9	τ2	τ2	NOUN
ejpam-6038	117	10	)	)	PUNCT
ejpam-6038	117	11	is	be	AUX
ejpam-6038	117	12	said	say	VERB
ejpam-6038	117	13	to	to	PART
ejpam-6038	117	14	be	be	AUX
ejpam-6038	117	15	weakly	weakly	ADJ
ejpam-6038	117	16	τ1τ2	τ1τ2	NOUN
ejpam-6038	117	17	-	-	ADJ
ejpam-6038	117	18	hausdorff	hausdorff	ADJ
ejpam-6038	117	19	if	if	SCONJ
ejpam-6038	117	20	each	each	DET
ejpam-6038	117	21	element	element	NOUN
ejpam-6038	117	22	of	of	ADP
ejpam-6038	117	23	x	x	PUNCT
ejpam-6038	117	24	is	be	AUX
ejpam-6038	117	25	an	an	DET
ejpam-6038	117	26	intersection	intersection	NOUN
ejpam-6038	117	27	of	of	ADP
ejpam-6038	117	28	(	(	PUNCT
ejpam-6038	117	29	τ1	τ1	NOUN
ejpam-6038	117	30	,	,	PUNCT
ejpam-6038	117	31	τ2)r	τ2)r	NOUN
ejpam-6038	117	32	-	-	PUNCT
ejpam-6038	117	33	closed	close	VERB
ejpam-6038	117	34	sets	set	NOUN
ejpam-6038	117	35	.	.	PUNCT
ejpam-6038	118	1	definition	definition	NOUN
ejpam-6038	118	2	5	5	NUM
ejpam-6038	118	3	.	.	PUNCT
ejpam-6038	119	1	a	a	DET
ejpam-6038	119	2	bitopological	bitopological	ADJ
ejpam-6038	119	3	space	space	NOUN
ejpam-6038	119	4	(	(	PUNCT
ejpam-6038	119	5	x	x	NOUN
ejpam-6038	119	6	,	,	PUNCT
ejpam-6038	119	7	τ1	τ1	NOUN
ejpam-6038	119	8	,	,	PUNCT
ejpam-6038	119	9	τ2	τ2	NOUN
ejpam-6038	119	10	)	)	PUNCT
ejpam-6038	119	11	is	be	AUX
ejpam-6038	119	12	said	say	VERB
ejpam-6038	119	13	to	to	PART
ejpam-6038	119	14	be	be	AUX
ejpam-6038	119	15	(	(	PUNCT
ejpam-6038	119	16	τ1	τ1	NOUN
ejpam-6038	119	17	,	,	PUNCT
ejpam-6038	119	18	τ2)p	τ2)p	NOUN
ejpam-6038	119	19	-	-	NOUN
ejpam-6038	119	20	t1	t1	NOUN
ejpam-6038	119	21	if	if	SCONJ
ejpam-6038	119	22	for	for	ADP
ejpam-6038	119	23	each	each	DET
ejpam-6038	119	24	pair	pair	NOUN
ejpam-6038	119	25	of	of	ADP
ejpam-6038	119	26	distinct	distinct	ADJ
ejpam-6038	119	27	points	point	NOUN
ejpam-6038	119	28	x	x	PUNCT
ejpam-6038	119	29	and	and	CCONJ
ejpam-6038	119	30	y	y	PROPN
ejpam-6038	119	31	of	of	ADP
ejpam-6038	119	32	x	x	PRON
ejpam-6038	119	33	,	,	PUNCT
ejpam-6038	119	34	there	there	PRON
ejpam-6038	119	35	exist	exist	VERB
ejpam-6038	119	36	(	(	PUNCT
ejpam-6038	119	37	τ1	τ1	NOUN
ejpam-6038	119	38	,	,	PUNCT
ejpam-6038	119	39	τ2)p	τ2)p	ADJ
ejpam-6038	119	40	-	-	PUNCT
ejpam-6038	119	41	open	open	ADJ
ejpam-6038	119	42	sets	set	VERB
ejpam-6038	119	43	u	u	NOUN
ejpam-6038	119	44	and	and	CCONJ
ejpam-6038	119	45	v	v	ADP
ejpam-6038	119	46	containing	contain	VERB
ejpam-6038	119	47	x	x	PROPN
ejpam-6038	119	48	and	and	CCONJ
ejpam-6038	119	49	y	y	PROPN
ejpam-6038	119	50	,	,	PUNCT
ejpam-6038	119	51	respectively	respectively	ADV
ejpam-6038	119	52	,	,	PUNCT
ejpam-6038	119	53	such	such	ADJ
ejpam-6038	119	54	that	that	SCONJ
ejpam-6038	119	55	y	y	PROPN
ejpam-6038	119	56	̸∈	̸∈	PROPN
ejpam-6038	119	57	u	u	PROPN
ejpam-6038	119	58	and	and	CCONJ
ejpam-6038	119	59	x	x	PROPN
ejpam-6038	119	60	̸∈	̸∈	PROPN
ejpam-6038	119	61	v	v	PROPN
ejpam-6038	119	62	.	.	PUNCT
ejpam-6038	120	1	theorem	theorem	ADJ
ejpam-6038	120	2	4	4	NUM
ejpam-6038	120	3	.	.	PUNCT
ejpam-6038	121	1	if	if	SCONJ
ejpam-6038	121	2	f	f	PROPN
ejpam-6038	121	3	:	:	PUNCT
ejpam-6038	121	4	(	(	PUNCT
ejpam-6038	121	5	x	x	NOUN
ejpam-6038	121	6	,	,	PUNCT
ejpam-6038	121	7	τ1	τ1	NOUN
ejpam-6038	121	8	,	,	PUNCT
ejpam-6038	121	9	τ2	τ2	NOUN
ejpam-6038	121	10	)	)	PUNCT
ejpam-6038	121	11	→	→	SYM
ejpam-6038	121	12	(	(	PUNCT
ejpam-6038	121	13	y	y	PROPN
ejpam-6038	121	14	,	,	PUNCT
ejpam-6038	121	15	σ1	σ1	PROPN
ejpam-6038	121	16	,	,	PUNCT
ejpam-6038	121	17	σ2	σ2	PROPN
ejpam-6038	121	18	)	)	PUNCT
ejpam-6038	121	19	is	be	AUX
ejpam-6038	121	20	an	an	DET
ejpam-6038	121	21	almost	almost	ADV
ejpam-6038	121	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	121	23	,	,	PUNCT
ejpam-6038	121	24	τ2)p	τ2)p	ADJ
ejpam-6038	121	25	-	-	ADJ
ejpam-6038	121	26	continuous	continuous	ADJ
ejpam-6038	121	27	injection	injection	NOUN
ejpam-6038	121	28	and	and	CCONJ
ejpam-6038	121	29	(	(	PUNCT
ejpam-6038	121	30	y	y	PROPN
ejpam-6038	121	31	,	,	PUNCT
ejpam-6038	121	32	σ1	σ1	PROPN
ejpam-6038	121	33	,	,	PUNCT
ejpam-6038	121	34	σ2	σ2	NOUN
ejpam-6038	121	35	)	)	PUNCT
ejpam-6038	121	36	is	be	AUX
ejpam-6038	121	37	weakly	weakly	ADJ
ejpam-6038	121	38	σ1σ2	σ1σ2	NOUN
ejpam-6038	121	39	-	-	PUNCT
ejpam-6038	121	40	hausdorff	hausdorff	NOUN
ejpam-6038	121	41	,	,	PUNCT
ejpam-6038	121	42	then	then	ADV
ejpam-6038	121	43	(	(	PUNCT
ejpam-6038	121	44	x	x	NOUN
ejpam-6038	121	45	,	,	PUNCT
ejpam-6038	121	46	τ1	τ1	NOUN
ejpam-6038	121	47	,	,	PUNCT
ejpam-6038	121	48	τ2	τ2	NOUN
ejpam-6038	121	49	)	)	PUNCT
ejpam-6038	121	50	is	be	AUX
ejpam-6038	121	51	(	(	PUNCT
ejpam-6038	121	52	τ1	τ1	NOUN
ejpam-6038	121	53	,	,	PUNCT
ejpam-6038	121	54	τ2)p	τ2)p	NOUN
ejpam-6038	121	55	-	-	PUNCT
ejpam-6038	121	56	t1	t1	NOUN
ejpam-6038	121	57	.	.	PUNCT
ejpam-6038	122	1	proof	proof	NOUN
ejpam-6038	122	2	.	.	PUNCT
ejpam-6038	123	1	suppose	suppose	VERB
ejpam-6038	123	2	that	that	SCONJ
ejpam-6038	123	3	(	(	PUNCT
ejpam-6038	123	4	y	y	PROPN
ejpam-6038	123	5	,	,	PUNCT
ejpam-6038	123	6	σ1	σ1	PROPN
ejpam-6038	123	7	,	,	PUNCT
ejpam-6038	123	8	σ2	σ2	NOUN
ejpam-6038	123	9	)	)	PUNCT
ejpam-6038	123	10	is	be	AUX
ejpam-6038	123	11	weakly	weakly	ADJ
ejpam-6038	123	12	σ1σ2	σ1σ2	NOUN
ejpam-6038	123	13	-	-	PUNCT
ejpam-6038	123	14	hausdorff	hausdorff	NOUN
ejpam-6038	123	15	.	.	PUNCT
ejpam-6038	124	1	for	for	ADP
ejpam-6038	124	2	any	any	DET
ejpam-6038	124	3	distinct	distinct	ADJ
ejpam-6038	124	4	points	point	NOUN
ejpam-6038	124	5	x	x	PUNCT
ejpam-6038	124	6	and	and	CCONJ
ejpam-6038	124	7	y	y	PROPN
ejpam-6038	124	8	in	in	ADP
ejpam-6038	124	9	x	x	SYM
ejpam-6038	124	10	,	,	PUNCT
ejpam-6038	124	11	there	there	PRON
ejpam-6038	124	12	exist	exist	VERB
ejpam-6038	124	13	(	(	PUNCT
ejpam-6038	124	14	σ1	σ1	NOUN
ejpam-6038	124	15	,	,	PUNCT
ejpam-6038	124	16	σ2)r	σ2)r	NOUN
ejpam-6038	124	17	-	-	PUNCT
ejpam-6038	124	18	closed	close	VERB
ejpam-6038	124	19	sets	set	NOUN
ejpam-6038	124	20	h	h	NOUN
ejpam-6038	124	21	and	and	CCONJ
ejpam-6038	124	22	k	k	PROPN
ejpam-6038	124	23	of	of	ADP
ejpam-6038	124	24	y	y	PRON
ejpam-6038	124	25	such	such	ADJ
ejpam-6038	124	26	that	that	SCONJ
ejpam-6038	124	27	f(x	f(x	PROPN
ejpam-6038	124	28	)	)	PUNCT
ejpam-6038	124	29	∈	∈	PROPN
ejpam-6038	124	30	h	h	NOUN
ejpam-6038	124	31	,	,	PUNCT
ejpam-6038	124	32	f(y	f(y	NOUN
ejpam-6038	124	33	)	)	PUNCT
ejpam-6038	124	34	̸∈	̸∈	PROPN
ejpam-6038	124	35	h	h	PROPN
ejpam-6038	124	36	,	,	PUNCT
ejpam-6038	124	37	f(y	f(y	NOUN
ejpam-6038	124	38	)	)	PUNCT
ejpam-6038	124	39	∈	∈	PROPN
ejpam-6038	124	40	k	k	PROPN
ejpam-6038	124	41	and	and	CCONJ
ejpam-6038	124	42	f(x	f(x	PROPN
ejpam-6038	124	43	)	)	PUNCT
ejpam-6038	125	1	̸∈	̸∈	PROPN
ejpam-6038	125	2	k.	k.	PROPN
ejpam-6038	125	3	since	since	SCONJ
ejpam-6038	125	4	f	f	PROPN
ejpam-6038	125	5	is	be	AUX
ejpam-6038	125	6	almost	almost	ADV
ejpam-6038	125	7	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	125	8	,	,	PUNCT
ejpam-6038	125	9	τ2)p	τ2)p	ADJ
ejpam-6038	125	10	-	-	ADJ
ejpam-6038	125	11	continuous	continuous	ADJ
ejpam-6038	125	12	,	,	PUNCT
ejpam-6038	125	13	f−1(h	f−1(h	PROPN
ejpam-6038	125	14	)	)	PUNCT
ejpam-6038	125	15	and	and	CCONJ
ejpam-6038	125	16	f−1(k	f−1(k	PROPN
ejpam-6038	125	17	)	)	PUNCT
ejpam-6038	125	18	are	be	AUX
ejpam-6038	125	19	(	(	PUNCT
ejpam-6038	125	20	τ1	τ1	NOUN
ejpam-6038	125	21	,	,	PUNCT
ejpam-6038	125	22	τ2)p	τ2)p	ADJ
ejpam-6038	125	23	-	-	PUNCT
ejpam-6038	125	24	open	open	ADJ
ejpam-6038	125	25	sets	set	NOUN
ejpam-6038	125	26	of	of	ADP
ejpam-6038	125	27	x	x	SYM
ejpam-6038	125	28	such	such	ADJ
ejpam-6038	125	29	that	that	SCONJ
ejpam-6038	125	30	x	x	PROPN
ejpam-6038	125	31	∈	∈	PROPN
ejpam-6038	125	32	f−1(h	f−1(h	PROPN
ejpam-6038	125	33	)	)	PUNCT
ejpam-6038	125	34	,	,	PUNCT
ejpam-6038	125	35	y	y	PROPN
ejpam-6038	125	36	̸∈	̸∈	PROPN
ejpam-6038	125	37	f−1(h	f−1(h	PROPN
ejpam-6038	125	38	)	)	PUNCT
ejpam-6038	125	39	,	,	PUNCT
ejpam-6038	125	40	y	y	PROPN
ejpam-6038	125	41	∈	∈	PROPN
ejpam-6038	125	42	f−1(k	f−1(k	PROPN
ejpam-6038	125	43	)	)	PUNCT
ejpam-6038	125	44	and	and	CCONJ
ejpam-6038	125	45	x	x	PUNCT
ejpam-6038	125	46	̸∈	̸∈	PROPN
ejpam-6038	125	47	f−1(k	f−1(k	PROPN
ejpam-6038	125	48	)	)	PUNCT
ejpam-6038	125	49	.	.	PUNCT
ejpam-6038	126	1	this	this	PRON
ejpam-6038	126	2	shows	show	VERB
ejpam-6038	126	3	that	that	SCONJ
ejpam-6038	126	4	(	(	PUNCT
ejpam-6038	126	5	x	x	NOUN
ejpam-6038	126	6	,	,	PUNCT
ejpam-6038	126	7	τ1	τ1	NOUN
ejpam-6038	126	8	,	,	PUNCT
ejpam-6038	126	9	τ2	τ2	NOUN
ejpam-6038	126	10	)	)	PUNCT
ejpam-6038	126	11	is	be	AUX
ejpam-6038	126	12	(	(	PUNCT
ejpam-6038	126	13	τ1	τ1	NOUN
ejpam-6038	126	14	,	,	PUNCT
ejpam-6038	126	15	τ2)p	τ2)p	PROPN
ejpam-6038	126	16	-	-	PUNCT
ejpam-6038	126	17	t1	t1	NOUN
ejpam-6038	126	18	.	.	PUNCT
ejpam-6038	127	1	recall	recall	VERB
ejpam-6038	127	2	that	that	SCONJ
ejpam-6038	127	3	a	a	DET
ejpam-6038	127	4	bitopological	bitopological	ADJ
ejpam-6038	127	5	space	space	NOUN
ejpam-6038	127	6	(	(	PUNCT
ejpam-6038	127	7	x	x	NOUN
ejpam-6038	127	8	,	,	PUNCT
ejpam-6038	127	9	τ1	τ1	NOUN
ejpam-6038	127	10	,	,	PUNCT
ejpam-6038	127	11	τ2	τ2	NOUN
ejpam-6038	127	12	)	)	PUNCT
ejpam-6038	127	13	is	be	AUX
ejpam-6038	127	14	said	say	VERB
ejpam-6038	127	15	to	to	PART
ejpam-6038	127	16	be	be	AUX
ejpam-6038	127	17	τ1τ2	τ1τ2	NOUN
ejpam-6038	127	18	-	-	ADJ
ejpam-6038	127	19	connected	connected	ADJ
ejpam-6038	128	1	[	[	X
ejpam-6038	128	2	22	22	NUM
ejpam-6038	128	3	]	]	PUNCT
ejpam-6038	128	4	if	if	SCONJ
ejpam-6038	128	5	x	x	PRON
ejpam-6038	128	6	can	can	AUX
ejpam-6038	128	7	not	not	PART
ejpam-6038	128	8	be	be	AUX
ejpam-6038	128	9	written	write	VERB
ejpam-6038	128	10	as	as	ADP
ejpam-6038	128	11	the	the	DET
ejpam-6038	128	12	union	union	NOUN
ejpam-6038	128	13	of	of	ADP
ejpam-6038	128	14	two	two	NUM
ejpam-6038	128	15	nonempty	nonempty	ADV
ejpam-6038	128	16	disjoint	disjoint	NOUN
ejpam-6038	128	17	τ1τ2	τ1τ2	ADJ
ejpam-6038	128	18	-	-	ADJ
ejpam-6038	128	19	open	open	ADJ
ejpam-6038	128	20	sets	set	NOUN
ejpam-6038	128	21	.	.	PUNCT
ejpam-6038	129	1	definition	definition	NOUN
ejpam-6038	129	2	6	6	NUM
ejpam-6038	129	3	.	.	PUNCT
ejpam-6038	130	1	a	a	DET
ejpam-6038	130	2	bitopological	bitopological	ADJ
ejpam-6038	130	3	space	space	NOUN
ejpam-6038	130	4	(	(	PUNCT
ejpam-6038	130	5	x	x	NOUN
ejpam-6038	130	6	,	,	PUNCT
ejpam-6038	130	7	τ1	τ1	NOUN
ejpam-6038	130	8	,	,	PUNCT
ejpam-6038	130	9	τ2	τ2	NOUN
ejpam-6038	130	10	)	)	PUNCT
ejpam-6038	130	11	is	be	AUX
ejpam-6038	130	12	said	say	VERB
ejpam-6038	130	13	to	to	PART
ejpam-6038	130	14	be	be	AUX
ejpam-6038	130	15	(	(	PUNCT
ejpam-6038	130	16	τ1	τ1	NOUN
ejpam-6038	130	17	,	,	PUNCT
ejpam-6038	130	18	τ2)p	τ2)p	NOUN
ejpam-6038	130	19	-	-	PUNCT
ejpam-6038	130	20	connected	connected	ADJ
ejpam-6038	130	21	if	if	SCONJ
ejpam-6038	130	22	x	x	PRON
ejpam-6038	130	23	can	can	AUX
ejpam-6038	130	24	not	not	PART
ejpam-6038	130	25	be	be	AUX
ejpam-6038	130	26	written	write	VERB
ejpam-6038	130	27	as	as	ADP
ejpam-6038	130	28	the	the	DET
ejpam-6038	130	29	union	union	NOUN
ejpam-6038	130	30	of	of	ADP
ejpam-6038	130	31	two	two	NUM
ejpam-6038	130	32	nonempty	nonempty	ADJ
ejpam-6038	130	33	disjoint	disjoint	NOUN
ejpam-6038	130	34	(	(	PUNCT
ejpam-6038	130	35	τ1	τ1	NOUN
ejpam-6038	130	36	,	,	PUNCT
ejpam-6038	130	37	τ2)p	τ2)p	ADJ
ejpam-6038	130	38	-	-	PUNCT
ejpam-6038	130	39	open	open	ADJ
ejpam-6038	130	40	sets	set	NOUN
ejpam-6038	130	41	.	.	PUNCT
ejpam-6038	131	1	theorem	theorem	NOUN
ejpam-6038	131	2	5	5	NUM
ejpam-6038	131	3	.	.	PUNCT
ejpam-6038	132	1	if	if	SCONJ
ejpam-6038	132	2	f	f	PROPN
ejpam-6038	132	3	:	:	PUNCT
ejpam-6038	132	4	(	(	PUNCT
ejpam-6038	132	5	x	x	NOUN
ejpam-6038	132	6	,	,	PUNCT
ejpam-6038	132	7	τ1	τ1	NOUN
ejpam-6038	132	8	,	,	PUNCT
ejpam-6038	132	9	τ2	τ2	NOUN
ejpam-6038	132	10	)	)	PUNCT
ejpam-6038	132	11	→	→	SYM
ejpam-6038	132	12	(	(	PUNCT
ejpam-6038	132	13	y	y	PROPN
ejpam-6038	132	14	,	,	PUNCT
ejpam-6038	132	15	σ1	σ1	PROPN
ejpam-6038	132	16	,	,	PUNCT
ejpam-6038	132	17	σ2	σ2	PROPN
ejpam-6038	132	18	)	)	PUNCT
ejpam-6038	132	19	is	be	AUX
ejpam-6038	132	20	an	an	DET
ejpam-6038	132	21	almost	almost	ADV
ejpam-6038	132	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	132	23	,	,	PUNCT
ejpam-6038	132	24	τ2)p	τ2)p	ADJ
ejpam-6038	132	25	-	-	ADJ
ejpam-6038	132	26	continuous	continuous	ADJ
ejpam-6038	132	27	surjection	surjection	NOUN
ejpam-6038	132	28	and	and	CCONJ
ejpam-6038	132	29	(	(	PUNCT
ejpam-6038	132	30	x	x	NOUN
ejpam-6038	132	31	,	,	PUNCT
ejpam-6038	132	32	τ1	τ1	NOUN
ejpam-6038	132	33	,	,	PUNCT
ejpam-6038	132	34	τ2	τ2	NOUN
ejpam-6038	132	35	)	)	PUNCT
ejpam-6038	132	36	is	be	AUX
ejpam-6038	132	37	(	(	PUNCT
ejpam-6038	132	38	τ1	τ1	NOUN
ejpam-6038	132	39	,	,	PUNCT
ejpam-6038	132	40	τ2)p	τ2)p	NOUN
ejpam-6038	132	41	-	-	PUNCT
ejpam-6038	132	42	connected	connect	VERB
ejpam-6038	132	43	,	,	PUNCT
ejpam-6038	132	44	then	then	ADV
ejpam-6038	132	45	(	(	PUNCT
ejpam-6038	132	46	y	y	PROPN
ejpam-6038	132	47	,	,	PUNCT
ejpam-6038	132	48	σ1	σ1	PROPN
ejpam-6038	132	49	,	,	PUNCT
ejpam-6038	132	50	σ2	σ2	PROPN
ejpam-6038	132	51	)	)	PUNCT
ejpam-6038	132	52	is	be	AUX
ejpam-6038	132	53	σ1σ2	σ1σ2	NOUN
ejpam-6038	132	54	-	-	PUNCT
ejpam-6038	132	55	connected	connected	ADJ
ejpam-6038	132	56	.	.	PUNCT
ejpam-6038	133	1	proof	proof	NOUN
ejpam-6038	133	2	.	.	PUNCT
ejpam-6038	134	1	suppose	suppose	VERB
ejpam-6038	134	2	that	that	SCONJ
ejpam-6038	134	3	(	(	PUNCT
ejpam-6038	134	4	y	y	PROPN
ejpam-6038	134	5	,	,	PUNCT
ejpam-6038	134	6	σ1	σ1	PROPN
ejpam-6038	134	7	,	,	PUNCT
ejpam-6038	134	8	σ2	σ2	PROPN
ejpam-6038	134	9	)	)	PUNCT
ejpam-6038	134	10	is	be	AUX
ejpam-6038	134	11	not	not	PART
ejpam-6038	134	12	σ1σ2	σ1σ2	VERB
ejpam-6038	134	13	-	-	PUNCT
ejpam-6038	134	14	connected	connect	VERB
ejpam-6038	134	15	.	.	PUNCT
ejpam-6038	135	1	then	then	ADV
ejpam-6038	135	2	,	,	PUNCT
ejpam-6038	135	3	there	there	PRON
ejpam-6038	135	4	exist	exist	VERB
ejpam-6038	135	5	nonempty	nonempty	ADV
ejpam-6038	135	6	σ1σ2	σ1σ2	NOUN
ejpam-6038	135	7	-	-	ADJ
ejpam-6038	135	8	open	open	ADJ
ejpam-6038	135	9	sets	set	NOUN
ejpam-6038	135	10	v	v	ADP
ejpam-6038	135	11	and	and	CCONJ
ejpam-6038	135	12	w	w	ADP
ejpam-6038	135	13	such	such	ADJ
ejpam-6038	135	14	that	that	SCONJ
ejpam-6038	135	15	y	y	PROPN
ejpam-6038	135	16	=	=	SYM
ejpam-6038	135	17	v	v	PROPN
ejpam-6038	135	18	∪w	∪w	PROPN
ejpam-6038	135	19	.	.	PUNCT
ejpam-6038	136	1	therefore	therefore	ADV
ejpam-6038	136	2	,	,	PUNCT
ejpam-6038	136	3	v	v	NOUN
ejpam-6038	136	4	and	and	CCONJ
ejpam-6038	136	5	w	w	NOUN
ejpam-6038	136	6	are	be	AUX
ejpam-6038	136	7	σ1σ2	σ1σ2	NOUN
ejpam-6038	136	8	-	-	PUNCT
ejpam-6038	136	9	clopen	clopen	ADJ
ejpam-6038	136	10	in	in	ADP
ejpam-6038	136	11	y	y	PROPN
ejpam-6038	136	12	.	.	PUNCT
ejpam-6038	137	1	since	since	SCONJ
ejpam-6038	137	2	f	f	PROPN
ejpam-6038	137	3	is	be	AUX
ejpam-6038	137	4	almost	almost	ADV
ejpam-6038	137	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	137	6	,	,	PUNCT
ejpam-6038	137	7	τ2)p	τ2)p	ADJ
ejpam-6038	137	8	-	-	ADJ
ejpam-6038	137	9	continuous	continuous	ADJ
ejpam-6038	137	10	,	,	PUNCT
ejpam-6038	137	11	f	f	PROPN
ejpam-6038	137	12	−1(v	−1(v	PROPN
ejpam-6038	137	13	)	)	PUNCT
ejpam-6038	137	14	and	and	CCONJ
ejpam-6038	137	15	f−1(w	f−1(w	ADV
ejpam-6038	137	16	)	)	PUNCT
ejpam-6038	137	17	are	be	AUX
ejpam-6038	137	18	(	(	PUNCT
ejpam-6038	137	19	τ1	τ1	NOUN
ejpam-6038	137	20	,	,	PUNCT
ejpam-6038	137	21	τ2)p	τ2)p	NOUN
ejpam-6038	137	22	-	-	PUNCT
ejpam-6038	137	23	open	open	ADJ
ejpam-6038	137	24	in	in	ADP
ejpam-6038	137	25	x.	x.	NOUN
ejpam-6038	137	26	furthermore	furthermore	ADV
ejpam-6038	137	27	,	,	PUNCT
ejpam-6038	137	28	f−1(v	f−1(v	PROPN
ejpam-6038	137	29	)	)	PUNCT
ejpam-6038	137	30	and	and	CCONJ
ejpam-6038	137	31	f−1(w	f−1(w	ADV
ejpam-6038	137	32	)	)	PUNCT
ejpam-6038	137	33	are	be	AUX
ejpam-6038	137	34	nonempty	nonempty	X
ejpam-6038	137	35	disjoint	disjoint	NOUN
ejpam-6038	137	36	and	and	CCONJ
ejpam-6038	137	37	x	x	X
ejpam-6038	137	38	=	=	SYM
ejpam-6038	137	39	f−1(v	f−1(v	NOUN
ejpam-6038	137	40	)	)	PUNCT
ejpam-6038	137	41	∪	∪	ADP
ejpam-6038	137	42	f−1(w	f−1(w	PROPN
ejpam-6038	137	43	)	)	PUNCT
ejpam-6038	137	44	.	.	PUNCT
ejpam-6038	138	1	this	this	PRON
ejpam-6038	138	2	shows	show	VERB
ejpam-6038	138	3	that	that	SCONJ
ejpam-6038	138	4	(	(	PUNCT
ejpam-6038	138	5	x	x	NOUN
ejpam-6038	138	6	,	,	PUNCT
ejpam-6038	138	7	τ1	τ1	NOUN
ejpam-6038	138	8	,	,	PUNCT
ejpam-6038	138	9	τ2	τ2	NOUN
ejpam-6038	138	10	)	)	PUNCT
ejpam-6038	138	11	is	be	AUX
ejpam-6038	138	12	not	not	PART
ejpam-6038	138	13	(	(	PUNCT
ejpam-6038	138	14	τ1	τ1	NOUN
ejpam-6038	138	15	,	,	PUNCT
ejpam-6038	138	16	τ2)p	τ2)p	NOUN
ejpam-6038	138	17	-	-	PUNCT
ejpam-6038	138	18	connected	connect	VERB
ejpam-6038	138	19	.	.	PUNCT
ejpam-6038	139	1	this	this	PRON
ejpam-6038	139	2	is	be	AUX
ejpam-6038	139	3	a	a	DET
ejpam-6038	139	4	contradiction	contradiction	NOUN
ejpam-6038	139	5	.	.	PUNCT
ejpam-6038	140	1	thus	thus	ADV
ejpam-6038	140	2	,	,	PUNCT
ejpam-6038	140	3	(	(	PUNCT
ejpam-6038	140	4	y	y	PROPN
ejpam-6038	140	5	,	,	PUNCT
ejpam-6038	140	6	σ1	σ1	PROPN
ejpam-6038	140	7	,	,	PUNCT
ejpam-6038	140	8	σ2	σ2	PROPN
ejpam-6038	140	9	)	)	PUNCT
ejpam-6038	140	10	is	be	AUX
ejpam-6038	140	11	σ1σ2	σ1σ2	NOUN
ejpam-6038	140	12	-	-	PUNCT
ejpam-6038	140	13	connected	connect	VERB
ejpam-6038	140	14	.	.	PUNCT
ejpam-6038	141	1	definition	definition	NOUN
ejpam-6038	141	2	7	7	NUM
ejpam-6038	141	3	.	.	PUNCT
ejpam-6038	142	1	a	a	DET
ejpam-6038	142	2	bitopological	bitopological	ADJ
ejpam-6038	142	3	space	space	NOUN
ejpam-6038	142	4	(	(	PUNCT
ejpam-6038	142	5	x	x	NOUN
ejpam-6038	142	6	,	,	PUNCT
ejpam-6038	142	7	τ1	τ1	NOUN
ejpam-6038	142	8	,	,	PUNCT
ejpam-6038	142	9	τ2	τ2	NOUN
ejpam-6038	142	10	)	)	PUNCT
ejpam-6038	142	11	is	be	AUX
ejpam-6038	142	12	said	say	VERB
ejpam-6038	142	13	to	to	PART
ejpam-6038	142	14	be	be	AUX
ejpam-6038	142	15	(	(	PUNCT
ejpam-6038	142	16	τ1	τ1	NOUN
ejpam-6038	142	17	,	,	PUNCT
ejpam-6038	142	18	τ2)p	τ2)p	ADJ
ejpam-6038	142	19	-	-	ADJ
ejpam-6038	142	20	compact	compact	ADJ
ejpam-6038	142	21	if	if	SCONJ
ejpam-6038	142	22	every	every	DET
ejpam-6038	142	23	(	(	PUNCT
ejpam-6038	142	24	τ1	τ1	NOUN
ejpam-6038	142	25	,	,	PUNCT
ejpam-6038	142	26	τ2)p	τ2)p	ADJ
ejpam-6038	142	27	-	-	PUNCT
ejpam-6038	142	28	open	open	ADJ
ejpam-6038	142	29	cover	cover	NOUN
ejpam-6038	142	30	of	of	ADP
ejpam-6038	142	31	x	x	PUNCT
ejpam-6038	142	32	has	have	VERB
ejpam-6038	142	33	a	a	DET
ejpam-6038	142	34	finite	finite	ADJ
ejpam-6038	142	35	subcover	subcover	PROPN
ejpam-6038	142	36	.	.	PUNCT
ejpam-6038	143	1	definition	definition	NOUN
ejpam-6038	143	2	8	8	NUM
ejpam-6038	143	3	.	.	PUNCT
ejpam-6038	144	1	a	a	DET
ejpam-6038	144	2	bitopological	bitopological	ADJ
ejpam-6038	144	3	space	space	NOUN
ejpam-6038	144	4	(	(	PUNCT
ejpam-6038	144	5	x	x	NOUN
ejpam-6038	144	6	,	,	PUNCT
ejpam-6038	144	7	τ1	τ1	NOUN
ejpam-6038	144	8	,	,	PUNCT
ejpam-6038	144	9	τ2	τ2	NOUN
ejpam-6038	144	10	)	)	PUNCT
ejpam-6038	144	11	is	be	AUX
ejpam-6038	144	12	said	say	VERB
ejpam-6038	144	13	to	to	PART
ejpam-6038	144	14	be	be	AUX
ejpam-6038	144	15	s	s	NOUN
ejpam-6038	144	16	-	-	PUNCT
ejpam-6038	144	17	τ1τ2	τ1τ2	ADJ
ejpam-6038	144	18	-	-	ADJ
ejpam-6038	144	19	closed	closed	ADJ
ejpam-6038	144	20	if	if	SCONJ
ejpam-6038	144	21	every	every	DET
ejpam-6038	144	22	(	(	PUNCT
ejpam-6038	144	23	τ1	τ1	NOUN
ejpam-6038	144	24	,	,	PUNCT
ejpam-6038	144	25	τ2)rclosed	τ2)rclosed	ADJ
ejpam-6038	144	26	cover	cover	NOUN
ejpam-6038	144	27	of	of	ADP
ejpam-6038	144	28	x	x	PUNCT
ejpam-6038	144	29	has	have	VERB
ejpam-6038	144	30	a	a	DET
ejpam-6038	144	31	finite	finite	ADJ
ejpam-6038	144	32	subcover	subcover	PROPN
ejpam-6038	144	33	.	.	PUNCT
ejpam-6038	145	1	theorem	theorem	VERB
ejpam-6038	145	2	6	6	NUM
ejpam-6038	145	3	.	.	PUNCT
ejpam-6038	146	1	if	if	SCONJ
ejpam-6038	146	2	f	f	PROPN
ejpam-6038	146	3	:	:	PUNCT
ejpam-6038	146	4	(	(	PUNCT
ejpam-6038	146	5	x	x	NOUN
ejpam-6038	146	6	,	,	PUNCT
ejpam-6038	146	7	τ1	τ1	NOUN
ejpam-6038	146	8	,	,	PUNCT
ejpam-6038	146	9	τ2	τ2	NOUN
ejpam-6038	146	10	)	)	PUNCT
ejpam-6038	146	11	→	→	SYM
ejpam-6038	146	12	(	(	PUNCT
ejpam-6038	146	13	y	y	PROPN
ejpam-6038	146	14	,	,	PUNCT
ejpam-6038	146	15	σ1	σ1	PROPN
ejpam-6038	146	16	,	,	PUNCT
ejpam-6038	146	17	σ2	σ2	PROPN
ejpam-6038	146	18	)	)	PUNCT
ejpam-6038	146	19	is	be	AUX
ejpam-6038	146	20	an	an	DET
ejpam-6038	146	21	almost	almost	ADV
ejpam-6038	146	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	146	23	,	,	PUNCT
ejpam-6038	146	24	τ2)p	τ2)p	ADJ
ejpam-6038	146	25	-	-	ADJ
ejpam-6038	146	26	continuous	continuous	ADJ
ejpam-6038	146	27	surjection	surjection	NOUN
ejpam-6038	146	28	and	and	CCONJ
ejpam-6038	146	29	(	(	PUNCT
ejpam-6038	146	30	x	x	NOUN
ejpam-6038	146	31	,	,	PUNCT
ejpam-6038	146	32	τ1	τ1	NOUN
ejpam-6038	146	33	,	,	PUNCT
ejpam-6038	146	34	τ2	τ2	NOUN
ejpam-6038	146	35	)	)	PUNCT
ejpam-6038	146	36	is	be	AUX
ejpam-6038	146	37	(	(	PUNCT
ejpam-6038	146	38	τ1	τ1	NOUN
ejpam-6038	146	39	,	,	PUNCT
ejpam-6038	146	40	τ2)p	τ2)p	ADJ
ejpam-6038	146	41	-	-	ADJ
ejpam-6038	146	42	compact	compact	ADJ
ejpam-6038	146	43	,	,	PUNCT
ejpam-6038	146	44	then	then	ADV
ejpam-6038	146	45	(	(	PUNCT
ejpam-6038	146	46	y	y	PROPN
ejpam-6038	146	47	,	,	PUNCT
ejpam-6038	146	48	σ1	σ1	PROPN
ejpam-6038	146	49	,	,	PUNCT
ejpam-6038	146	50	σ2	σ2	PROPN
ejpam-6038	146	51	)	)	PUNCT
ejpam-6038	146	52	is	be	AUX
ejpam-6038	146	53	s	s	NOUN
ejpam-6038	146	54	-	-	PUNCT
ejpam-6038	146	55	σ1σ2	σ1σ2	VERB
ejpam-6038	146	56	-	-	PUNCT
ejpam-6038	146	57	closed	closed	ADJ
ejpam-6038	146	58	.	.	PUNCT
ejpam-6038	147	1	proof	proof	NOUN
ejpam-6038	147	2	.	.	PUNCT
ejpam-6038	148	1	let	let	VERB
ejpam-6038	148	2	{	{	PUNCT
ejpam-6038	148	3	vγ	vγ	VERB
ejpam-6038	148	4	|	|	ADV
ejpam-6038	148	5	γ	γ	X
ejpam-6038	148	6	∈	∈	PROPN
ejpam-6038	148	7	∇	∇	X
ejpam-6038	148	8	}	}	PUNCT
ejpam-6038	148	9	be	be	VERB
ejpam-6038	148	10	any	any	DET
ejpam-6038	148	11	(	(	PUNCT
ejpam-6038	148	12	σ1	σ1	NOUN
ejpam-6038	148	13	,	,	PUNCT
ejpam-6038	148	14	σ2)r	σ2)r	NOUN
ejpam-6038	148	15	-	-	PUNCT
ejpam-6038	148	16	closed	close	VERB
ejpam-6038	148	17	cover	cover	NOUN
ejpam-6038	148	18	of	of	ADP
ejpam-6038	148	19	y	y	PROPN
ejpam-6038	148	20	.	.	PUNCT
ejpam-6038	149	1	since	since	SCONJ
ejpam-6038	149	2	f	f	PROPN
ejpam-6038	149	3	is	be	AUX
ejpam-6038	149	4	almost	almost	ADV
ejpam-6038	149	5	contra(τ1	contra(τ1	NOUN
ejpam-6038	149	6	,	,	PUNCT
ejpam-6038	149	7	τ2)p	τ2)p	ADJ
ejpam-6038	149	8	-	-	NOUN
ejpam-6038	149	9	continuous	continuous	ADJ
ejpam-6038	149	10	,	,	PUNCT
ejpam-6038	149	11	we	we	PRON
ejpam-6038	149	12	have	have	AUX
ejpam-6038	149	13	{	{	PUNCT
ejpam-6038	149	14	f−1(vγ	f−1(vγ	PROPN
ejpam-6038	149	15	)	)	PUNCT
ejpam-6038	149	16	|	|	ADV
ejpam-6038	149	17	γ	γ	PROPN
ejpam-6038	149	18	∈	∈	PROPN
ejpam-6038	149	19	∇	∇	X
ejpam-6038	149	20	}	}	PUNCT
ejpam-6038	149	21	is	be	AUX
ejpam-6038	149	22	a	a	DET
ejpam-6038	149	23	(	(	PUNCT
ejpam-6038	149	24	τ1	τ1	NOUN
ejpam-6038	149	25	,	,	PUNCT
ejpam-6038	149	26	τ2)p	τ2)p	ADJ
ejpam-6038	149	27	-	-	PUNCT
ejpam-6038	149	28	open	open	ADJ
ejpam-6038	149	29	cover	cover	NOUN
ejpam-6038	149	30	ofx	ofx	NOUN
ejpam-6038	149	31	and	and	CCONJ
ejpam-6038	149	32	therefore	therefore	ADV
ejpam-6038	149	33	there	there	PRON
ejpam-6038	149	34	exists	exist	VERB
ejpam-6038	149	35	a	a	DET
ejpam-6038	149	36	finite	finite	NOUN
ejpam-6038	149	37	subset	subset	NOUN
ejpam-6038	149	38	∇0	∇0	NUM
ejpam-6038	149	39	of	of	ADP
ejpam-6038	149	40	∇	∇	NOUN
ejpam-6038	149	41	such	such	ADJ
ejpam-6038	149	42	that	that	SCONJ
ejpam-6038	149	43	x	x	SYM
ejpam-6038	149	44	=	=	SYM
ejpam-6038	149	45	∪{f−1(vγ	∪{f−1(vγ	PROPN
ejpam-6038	149	46	)	)	PUNCT
ejpam-6038	149	47	|	|	ADV
ejpam-6038	149	48	γ	γ	X
ejpam-6038	149	49	∈	∈	NOUN
ejpam-6038	149	50	∇0	∇0	NOUN
ejpam-6038	149	51	}	}	PUNCT
ejpam-6038	149	52	.	.	PUNCT
ejpam-6038	150	1	thus	thus	ADV
ejpam-6038	150	2	,	,	PUNCT
ejpam-6038	150	3	we	we	PRON
ejpam-6038	150	4	have	have	VERB
ejpam-6038	150	5	y	y	PROPN
ejpam-6038	150	6	=	=	SYM
ejpam-6038	150	7	∪{vγ	∪{vγ	PROPN
ejpam-6038	150	8	|	|	ADV
ejpam-6038	150	9	γ	γ	X
ejpam-6038	150	10	∈	∈	NOUN
ejpam-6038	150	11	∇0	∇0	VERB
ejpam-6038	150	12	}	}	PUNCT
ejpam-6038	150	13	and	and	CCONJ
ejpam-6038	150	14	hence	hence	ADV
ejpam-6038	150	15	(	(	PUNCT
ejpam-6038	150	16	y	y	PROPN
ejpam-6038	150	17	,	,	PUNCT
ejpam-6038	150	18	σ1	σ1	PROPN
ejpam-6038	150	19	,	,	PUNCT
ejpam-6038	150	20	σ2	σ2	PROPN
ejpam-6038	150	21	)	)	PUNCT
ejpam-6038	150	22	is	be	AUX
ejpam-6038	150	23	s	s	NOUN
ejpam-6038	150	24	-	-	PUNCT
ejpam-6038	150	25	σ1σ2	σ1σ2	VERB
ejpam-6038	150	26	-	-	PUNCT
ejpam-6038	150	27	closed	closed	ADJ
ejpam-6038	150	28	.	.	PUNCT
ejpam-6038	151	1	p.	p.	NOUN
ejpam-6038	151	2	pue	pue	NOUN
ejpam-6038	151	3	-	-	PUNCT
ejpam-6038	151	4	on	on	ADP
ejpam-6038	151	5	,	,	PUNCT
ejpam-6038	151	6	a.	a.	PROPN
ejpam-6038	151	7	sama	sama	PROPN
ejpam-6038	151	8	-	-	PUNCT
ejpam-6038	151	9	ae	ae	PROPN
ejpam-6038	151	10	,	,	PUNCT
ejpam-6038	151	11	c.	c.	PROPN
ejpam-6038	151	12	boonpok	boonpok	PROPN
ejpam-6038	151	13	/	/	SYM
ejpam-6038	151	14	eur	eur	PROPN
ejpam-6038	151	15	.	.	PUNCT
ejpam-6038	152	1	j.	j.	PROPN
ejpam-6038	152	2	pure	pure	PROPN
ejpam-6038	152	3	appl	appl	PROPN
ejpam-6038	152	4	.	.	PROPN
ejpam-6038	152	5	math	math	PROPN
ejpam-6038	152	6	,	,	PUNCT
ejpam-6038	152	7	18	18	NUM
ejpam-6038	152	8	(	(	PUNCT
ejpam-6038	152	9	2	2	NUM
ejpam-6038	152	10	)	)	PUNCT
ejpam-6038	152	11	(	(	PUNCT
ejpam-6038	152	12	2025	2025	NUM
ejpam-6038	152	13	)	)	PUNCT
ejpam-6038	152	14	,	,	PUNCT
ejpam-6038	152	15	6038	6038	NUM
ejpam-6038	152	16	6	6	NUM
ejpam-6038	152	17	of	of	ADP
ejpam-6038	152	18	11	11	NUM
ejpam-6038	152	19	definition	definition	NOUN
ejpam-6038	152	20	9	9	NUM
ejpam-6038	152	21	.	.	PUNCT
ejpam-6038	153	1	a	a	DET
ejpam-6038	153	2	bitopological	bitopological	ADJ
ejpam-6038	153	3	space	space	NOUN
ejpam-6038	153	4	(	(	PUNCT
ejpam-6038	153	5	x	x	NOUN
ejpam-6038	153	6	,	,	PUNCT
ejpam-6038	153	7	τ1	τ1	NOUN
ejpam-6038	153	8	,	,	PUNCT
ejpam-6038	153	9	τ2	τ2	NOUN
ejpam-6038	153	10	)	)	PUNCT
ejpam-6038	153	11	is	be	AUX
ejpam-6038	153	12	said	say	VERB
ejpam-6038	153	13	to	to	PART
ejpam-6038	153	14	be	be	AUX
ejpam-6038	153	15	p	p	ADJ
ejpam-6038	153	16	-	-	PUNCT
ejpam-6038	153	17	τ1τ2	τ1τ2	NOUN
ejpam-6038	153	18	-	-	ADJ
ejpam-6038	153	19	closed	closed	ADJ
ejpam-6038	153	20	if	if	SCONJ
ejpam-6038	153	21	every	every	DET
ejpam-6038	153	22	(	(	PUNCT
ejpam-6038	153	23	τ1	τ1	NOUN
ejpam-6038	153	24	,	,	PUNCT
ejpam-6038	153	25	τ2)pclosed	τ2)pclose	VERB
ejpam-6038	153	26	cover	cover	NOUN
ejpam-6038	153	27	of	of	ADP
ejpam-6038	153	28	x	x	PUNCT
ejpam-6038	153	29	has	have	VERB
ejpam-6038	153	30	a	a	DET
ejpam-6038	153	31	finite	finite	ADJ
ejpam-6038	153	32	subcover	subcover	PROPN
ejpam-6038	153	33	.	.	PUNCT
ejpam-6038	154	1	definition	definition	NOUN
ejpam-6038	154	2	10	10	NUM
ejpam-6038	154	3	.	.	PUNCT
ejpam-6038	155	1	a	a	DET
ejpam-6038	155	2	bitopological	bitopological	ADJ
ejpam-6038	155	3	space	space	NOUN
ejpam-6038	155	4	(	(	PUNCT
ejpam-6038	155	5	x	x	NOUN
ejpam-6038	155	6	,	,	PUNCT
ejpam-6038	155	7	τ1	τ1	NOUN
ejpam-6038	155	8	,	,	PUNCT
ejpam-6038	155	9	τ2	τ2	NOUN
ejpam-6038	155	10	)	)	PUNCT
ejpam-6038	155	11	is	be	AUX
ejpam-6038	155	12	said	say	VERB
ejpam-6038	155	13	to	to	PART
ejpam-6038	155	14	be	be	AUX
ejpam-6038	155	15	(	(	PUNCT
ejpam-6038	155	16	τ1	τ1	NOUN
ejpam-6038	155	17	,	,	PUNCT
ejpam-6038	155	18	τ2)r	τ2)r	ADJ
ejpam-6038	155	19	-	-	PUNCT
ejpam-6038	155	20	compact	compact	ADJ
ejpam-6038	155	21	if	if	SCONJ
ejpam-6038	155	22	every	every	DET
ejpam-6038	155	23	(	(	PUNCT
ejpam-6038	155	24	τ1	τ1	NOUN
ejpam-6038	155	25	,	,	PUNCT
ejpam-6038	155	26	τ2)r	τ2)r	ADJ
ejpam-6038	155	27	-	-	PUNCT
ejpam-6038	155	28	open	open	ADJ
ejpam-6038	155	29	cover	cover	NOUN
ejpam-6038	155	30	of	of	ADP
ejpam-6038	155	31	x	x	PUNCT
ejpam-6038	155	32	has	have	VERB
ejpam-6038	155	33	a	a	DET
ejpam-6038	155	34	finite	finite	ADJ
ejpam-6038	155	35	subcover	subcover	PROPN
ejpam-6038	155	36	.	.	PUNCT
ejpam-6038	156	1	theorem	theorem	VERB
ejpam-6038	156	2	7	7	NUM
ejpam-6038	156	3	.	.	PUNCT
ejpam-6038	157	1	if	if	SCONJ
ejpam-6038	157	2	f	f	PROPN
ejpam-6038	157	3	:	:	PUNCT
ejpam-6038	157	4	(	(	PUNCT
ejpam-6038	157	5	x	x	NOUN
ejpam-6038	157	6	,	,	PUNCT
ejpam-6038	157	7	τ1	τ1	NOUN
ejpam-6038	157	8	,	,	PUNCT
ejpam-6038	157	9	τ2	τ2	NOUN
ejpam-6038	157	10	)	)	PUNCT
ejpam-6038	157	11	→	→	SYM
ejpam-6038	157	12	(	(	PUNCT
ejpam-6038	157	13	y	y	PROPN
ejpam-6038	157	14	,	,	PUNCT
ejpam-6038	157	15	σ1	σ1	PROPN
ejpam-6038	157	16	,	,	PUNCT
ejpam-6038	157	17	σ2	σ2	PROPN
ejpam-6038	157	18	)	)	PUNCT
ejpam-6038	157	19	is	be	AUX
ejpam-6038	157	20	an	an	DET
ejpam-6038	157	21	almost	almost	ADV
ejpam-6038	157	22	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	157	23	,	,	PUNCT
ejpam-6038	157	24	τ2)p	τ2)p	ADJ
ejpam-6038	157	25	-	-	ADJ
ejpam-6038	157	26	continuous	continuous	ADJ
ejpam-6038	157	27	surjection	surjection	NOUN
ejpam-6038	157	28	and	and	CCONJ
ejpam-6038	157	29	(	(	PUNCT
ejpam-6038	157	30	x	x	NOUN
ejpam-6038	157	31	,	,	PUNCT
ejpam-6038	157	32	τ1	τ1	NOUN
ejpam-6038	157	33	,	,	PUNCT
ejpam-6038	157	34	τ2	τ2	NOUN
ejpam-6038	157	35	)	)	PUNCT
ejpam-6038	157	36	is	be	AUX
ejpam-6038	157	37	p	p	ADJ
ejpam-6038	157	38	-	-	PUNCT
ejpam-6038	157	39	τ1τ2	τ1τ2	NOUN
ejpam-6038	157	40	-	-	ADJ
ejpam-6038	157	41	closed	closed	ADJ
ejpam-6038	157	42	,	,	PUNCT
ejpam-6038	157	43	then	then	ADV
ejpam-6038	157	44	(	(	PUNCT
ejpam-6038	157	45	y	y	PROPN
ejpam-6038	157	46	,	,	PUNCT
ejpam-6038	157	47	σ1	σ1	PROPN
ejpam-6038	157	48	,	,	PUNCT
ejpam-6038	157	49	σ2	σ2	PROPN
ejpam-6038	157	50	)	)	PUNCT
ejpam-6038	157	51	is	be	AUX
ejpam-6038	157	52	(	(	PUNCT
ejpam-6038	157	53	σ1	σ1	NOUN
ejpam-6038	157	54	,	,	PUNCT
ejpam-6038	157	55	σ2)r	σ2)r	NOUN
ejpam-6038	157	56	-	-	PUNCT
ejpam-6038	157	57	compact	compact	ADJ
ejpam-6038	157	58	.	.	PUNCT
ejpam-6038	158	1	proof	proof	NOUN
ejpam-6038	158	2	.	.	PUNCT
ejpam-6038	159	1	let	let	VERB
ejpam-6038	159	2	{	{	PUNCT
ejpam-6038	159	3	vγ	vγ	VERB
ejpam-6038	159	4	|	|	ADV
ejpam-6038	159	5	γ	γ	X
ejpam-6038	159	6	∈	∈	PROPN
ejpam-6038	159	7	∇	∇	X
ejpam-6038	159	8	}	}	PUNCT
ejpam-6038	159	9	be	be	VERB
ejpam-6038	159	10	any	any	DET
ejpam-6038	159	11	(	(	PUNCT
ejpam-6038	159	12	σ1	σ1	NOUN
ejpam-6038	159	13	,	,	PUNCT
ejpam-6038	159	14	σ2)r	σ2)r	NOUN
ejpam-6038	159	15	-	-	PUNCT
ejpam-6038	159	16	open	open	ADJ
ejpam-6038	159	17	cover	cover	NOUN
ejpam-6038	159	18	of	of	ADP
ejpam-6038	159	19	y	y	PROPN
ejpam-6038	159	20	.	.	PUNCT
ejpam-6038	160	1	since	since	SCONJ
ejpam-6038	160	2	f	f	PROPN
ejpam-6038	160	3	is	be	AUX
ejpam-6038	160	4	almost	almost	ADV
ejpam-6038	160	5	contra(τ1	contra(τ1	NOUN
ejpam-6038	160	6	,	,	PUNCT
ejpam-6038	160	7	τ2)p	τ2)p	ADJ
ejpam-6038	160	8	-	-	NOUN
ejpam-6038	160	9	continuous	continuous	ADJ
ejpam-6038	160	10	,	,	PUNCT
ejpam-6038	160	11	we	we	PRON
ejpam-6038	160	12	have	have	AUX
ejpam-6038	160	13	{	{	PUNCT
ejpam-6038	160	14	f−1(vγ	f−1(vγ	PROPN
ejpam-6038	160	15	)	)	PUNCT
ejpam-6038	160	16	|	|	ADV
ejpam-6038	160	17	γ	γ	PROPN
ejpam-6038	160	18	∈	∈	PROPN
ejpam-6038	160	19	∇	∇	X
ejpam-6038	160	20	}	}	PUNCT
ejpam-6038	160	21	is	be	AUX
ejpam-6038	160	22	a	a	DET
ejpam-6038	160	23	(	(	PUNCT
ejpam-6038	160	24	τ1	τ1	NOUN
ejpam-6038	160	25	,	,	PUNCT
ejpam-6038	160	26	τ2)p	τ2)p	NOUN
ejpam-6038	160	27	-	-	PUNCT
ejpam-6038	160	28	closed	closed	ADJ
ejpam-6038	160	29	cover	cover	NOUN
ejpam-6038	160	30	of	of	ADP
ejpam-6038	160	31	x.	x.	NOUN
ejpam-6038	160	32	since	since	SCONJ
ejpam-6038	160	33	(	(	PUNCT
ejpam-6038	160	34	x	x	NOUN
ejpam-6038	160	35	,	,	PUNCT
ejpam-6038	160	36	τ1	τ1	NOUN
ejpam-6038	160	37	,	,	PUNCT
ejpam-6038	160	38	τ2	τ2	NOUN
ejpam-6038	160	39	)	)	PUNCT
ejpam-6038	160	40	is	be	AUX
ejpam-6038	160	41	p	p	ADJ
ejpam-6038	160	42	-	-	PUNCT
ejpam-6038	160	43	τ1τ2	τ1τ2	NOUN
ejpam-6038	160	44	-	-	ADJ
ejpam-6038	160	45	closed	closed	ADJ
ejpam-6038	160	46	,	,	PUNCT
ejpam-6038	160	47	there	there	PRON
ejpam-6038	160	48	exists	exist	VERB
ejpam-6038	160	49	a	a	DET
ejpam-6038	160	50	finite	finite	NOUN
ejpam-6038	160	51	subset	subset	NOUN
ejpam-6038	160	52	∇0	∇0	NUM
ejpam-6038	160	53	of	of	ADP
ejpam-6038	160	54	∇	∇	NOUN
ejpam-6038	160	55	such	such	ADJ
ejpam-6038	160	56	that	that	SCONJ
ejpam-6038	160	57	x	x	SYM
ejpam-6038	160	58	=	=	SYM
ejpam-6038	160	59	∪{f−1(vγ	∪{f−1(vγ	PROPN
ejpam-6038	160	60	)	)	PUNCT
ejpam-6038	160	61	|	|	ADV
ejpam-6038	160	62	γ	γ	X
ejpam-6038	160	63	∈	∈	NOUN
ejpam-6038	160	64	∇0	∇0	NOUN
ejpam-6038	160	65	}	}	PUNCT
ejpam-6038	160	66	.	.	PUNCT
ejpam-6038	161	1	thus	thus	ADV
ejpam-6038	161	2	,	,	PUNCT
ejpam-6038	161	3	we	we	PRON
ejpam-6038	161	4	have	have	VERB
ejpam-6038	161	5	y	y	PROPN
ejpam-6038	161	6	=	=	SYM
ejpam-6038	161	7	∪{vγ	∪{vγ	PROPN
ejpam-6038	161	8	|	|	ADV
ejpam-6038	161	9	γ	γ	X
ejpam-6038	161	10	∈	∈	NOUN
ejpam-6038	161	11	∇0	∇0	VERB
ejpam-6038	161	12	}	}	PUNCT
ejpam-6038	161	13	and	and	CCONJ
ejpam-6038	161	14	hence	hence	ADV
ejpam-6038	161	15	(	(	PUNCT
ejpam-6038	161	16	y	y	PROPN
ejpam-6038	161	17	,	,	PUNCT
ejpam-6038	161	18	σ1	σ1	PROPN
ejpam-6038	161	19	,	,	PUNCT
ejpam-6038	161	20	σ2	σ2	PROPN
ejpam-6038	161	21	)	)	PUNCT
ejpam-6038	161	22	is	be	AUX
ejpam-6038	161	23	(	(	PUNCT
ejpam-6038	161	24	σ1	σ1	NOUN
ejpam-6038	161	25	,	,	PUNCT
ejpam-6038	161	26	σ2)r	σ2)r	NOUN
ejpam-6038	161	27	-	-	PUNCT
ejpam-6038	161	28	compact	compact	ADJ
ejpam-6038	161	29	.	.	PUNCT
ejpam-6038	162	1	let	let	VERB
ejpam-6038	162	2	a	a	DET
ejpam-6038	162	3	be	be	AUX
ejpam-6038	162	4	a	a	DET
ejpam-6038	162	5	subset	subset	NOUN
ejpam-6038	162	6	of	of	ADP
ejpam-6038	162	7	a	a	DET
ejpam-6038	162	8	bitopological	bitopological	ADJ
ejpam-6038	162	9	space	space	NOUN
ejpam-6038	162	10	(	(	PUNCT
ejpam-6038	162	11	x	x	NOUN
ejpam-6038	162	12	,	,	PUNCT
ejpam-6038	162	13	τ1	τ1	NOUN
ejpam-6038	162	14	,	,	PUNCT
ejpam-6038	162	15	τ2	τ2	NOUN
ejpam-6038	162	16	)	)	PUNCT
ejpam-6038	162	17	.	.	PUNCT
ejpam-6038	163	1	a	a	DET
ejpam-6038	163	2	point	point	NOUN
ejpam-6038	163	3	x	x	X
ejpam-6038	163	4	∈	∈	NOUN
ejpam-6038	163	5	x	x	PUNCT
ejpam-6038	163	6	is	be	AUX
ejpam-6038	163	7	called	call	VERB
ejpam-6038	163	8	a	a	DET
ejpam-6038	163	9	s(τ1	s(τ1	NOUN
ejpam-6038	163	10	,	,	PUNCT
ejpam-6038	163	11	τ2)θ	τ2)θ	ADJ
ejpam-6038	163	12	-	-	PUNCT
ejpam-6038	163	13	cluster	cluster	NOUN
ejpam-6038	163	14	point	point	NOUN
ejpam-6038	163	15	of	of	ADP
ejpam-6038	163	16	a	a	DET
ejpam-6038	163	17	if	if	SCONJ
ejpam-6038	163	18	τ1τ2	τ1τ2	ADJ
ejpam-6038	163	19	-	-	ADJ
ejpam-6038	163	20	cl(u)∩a	cl(u)∩a	ADJ
ejpam-6038	163	21	̸=	̸=	PROPN
ejpam-6038	163	22	∅	∅	NOUN
ejpam-6038	163	23	for	for	ADP
ejpam-6038	163	24	every	every	DET
ejpam-6038	163	25	(	(	PUNCT
ejpam-6038	163	26	τ1	τ1	NOUN
ejpam-6038	163	27	,	,	PUNCT
ejpam-6038	163	28	τ2)s	τ2)s	NOUN
ejpam-6038	163	29	-	-	PUNCT
ejpam-6038	163	30	open	open	ADJ
ejpam-6038	163	31	set	set	NOUN
ejpam-6038	163	32	u	u	NOUN
ejpam-6038	163	33	containing	contain	VERB
ejpam-6038	163	34	x.	x.	NOUN
ejpam-6038	163	35	the	the	DET
ejpam-6038	163	36	set	set	NOUN
ejpam-6038	163	37	of	of	ADP
ejpam-6038	163	38	all	all	DET
ejpam-6038	163	39	s(τ1	s(τ1	NOUN
ejpam-6038	163	40	,	,	PUNCT
ejpam-6038	163	41	τ2)θ	τ2)θ	ADJ
ejpam-6038	163	42	-	-	PUNCT
ejpam-6038	163	43	cluster	cluster	NOUN
ejpam-6038	163	44	points	point	NOUN
ejpam-6038	163	45	of	of	ADP
ejpam-6038	163	46	a	a	PRON
ejpam-6038	163	47	is	be	AUX
ejpam-6038	163	48	called	call	VERB
ejpam-6038	163	49	the	the	DET
ejpam-6038	163	50	s(τ1	s(τ1	NOUN
ejpam-6038	163	51	,	,	PUNCT
ejpam-6038	163	52	τ2)θ	τ2)θ	NOUN
ejpam-6038	163	53	-	-	PUNCT
ejpam-6038	163	54	closure	closure	NOUN
ejpam-6038	163	55	of	of	ADP
ejpam-6038	163	56	a	a	PRON
ejpam-6038	163	57	and	and	CCONJ
ejpam-6038	163	58	is	be	AUX
ejpam-6038	163	59	denoted	denote	VERB
ejpam-6038	163	60	by	by	ADP
ejpam-6038	163	61	s(τ1	s(τ1	NOUN
ejpam-6038	163	62	,	,	PUNCT
ejpam-6038	163	63	τ2)θ	τ2)θ	NOUN
ejpam-6038	163	64	-	-	PUNCT
ejpam-6038	163	65	cl(a	cl(a	NUM
ejpam-6038	163	66	)	)	PUNCT
ejpam-6038	163	67	.	.	PUNCT
ejpam-6038	164	1	a	a	DET
ejpam-6038	164	2	subset	subset	NOUN
ejpam-6038	164	3	a	a	PRON
ejpam-6038	164	4	of	of	ADP
ejpam-6038	164	5	a	a	DET
ejpam-6038	164	6	bitopological	bitopological	ADJ
ejpam-6038	164	7	space	space	NOUN
ejpam-6038	164	8	(	(	PUNCT
ejpam-6038	164	9	x	x	NOUN
ejpam-6038	164	10	,	,	PUNCT
ejpam-6038	164	11	τ1	τ1	NOUN
ejpam-6038	164	12	,	,	PUNCT
ejpam-6038	164	13	τ2	τ2	NOUN
ejpam-6038	164	14	)	)	PUNCT
ejpam-6038	164	15	is	be	AUX
ejpam-6038	164	16	called	call	VERB
ejpam-6038	164	17	s(τ1	s(τ1	NOUN
ejpam-6038	164	18	,	,	PUNCT
ejpam-6038	164	19	τ2)θ	τ2)θ	NOUN
ejpam-6038	164	20	-	-	PUNCT
ejpam-6038	164	21	closed	closed	ADJ
ejpam-6038	164	22	if	if	SCONJ
ejpam-6038	164	23	s(τ1	s(τ1	NOUN
ejpam-6038	164	24	,	,	PUNCT
ejpam-6038	164	25	τ2)θ	τ2)θ	NOUN
ejpam-6038	164	26	-	-	PUNCT
ejpam-6038	164	27	cl(a	cl(a	NUM
ejpam-6038	164	28	)	)	PUNCT
ejpam-6038	164	29	=	=	PUNCT
ejpam-6038	164	30	a.	a.	NOUN
ejpam-6038	164	31	the	the	DET
ejpam-6038	164	32	complement	complement	NOUN
ejpam-6038	164	33	of	of	ADP
ejpam-6038	164	34	a	a	DET
ejpam-6038	164	35	s(τ1	s(τ1	NOUN
ejpam-6038	164	36	,	,	PUNCT
ejpam-6038	164	37	τ2)θ	τ2)θ	ADJ
ejpam-6038	164	38	-	-	PUNCT
ejpam-6038	164	39	closed	close	VERB
ejpam-6038	164	40	set	set	NOUN
ejpam-6038	164	41	is	be	AUX
ejpam-6038	164	42	said	say	VERB
ejpam-6038	164	43	to	to	PART
ejpam-6038	164	44	be	be	AUX
ejpam-6038	164	45	s(τ1	s(τ1	NOUN
ejpam-6038	164	46	,	,	PUNCT
ejpam-6038	164	47	τ2)θ	τ2)θ	NOUN
ejpam-6038	164	48	-	-	PUNCT
ejpam-6038	164	49	open	open	ADJ
ejpam-6038	164	50	.	.	PUNCT
ejpam-6038	165	1	the	the	DET
ejpam-6038	165	2	union	union	NOUN
ejpam-6038	165	3	of	of	ADP
ejpam-6038	165	4	all	all	DET
ejpam-6038	165	5	s(τ1	s(τ1	NOUN
ejpam-6038	165	6	,	,	PUNCT
ejpam-6038	165	7	τ2)θ	τ2)θ	ADJ
ejpam-6038	165	8	-	-	PUNCT
ejpam-6038	165	9	open	open	ADJ
ejpam-6038	165	10	sets	set	NOUN
ejpam-6038	165	11	of	of	ADP
ejpam-6038	165	12	x	x	PUNCT
ejpam-6038	165	13	contained	contain	VERB
ejpam-6038	165	14	in	in	ADP
ejpam-6038	165	15	a	a	PRON
ejpam-6038	165	16	is	be	AUX
ejpam-6038	165	17	called	call	VERB
ejpam-6038	165	18	the	the	DET
ejpam-6038	165	19	s(τ1	s(τ1	NOUN
ejpam-6038	165	20	,	,	PUNCT
ejpam-6038	165	21	τ2)θ	τ2)θ	ADJ
ejpam-6038	165	22	-	-	PUNCT
ejpam-6038	165	23	interior	interior	NOUN
ejpam-6038	165	24	of	of	ADP
ejpam-6038	165	25	a	a	PRON
ejpam-6038	165	26	and	and	CCONJ
ejpam-6038	165	27	is	be	AUX
ejpam-6038	165	28	denoted	denote	VERB
ejpam-6038	165	29	by	by	ADP
ejpam-6038	165	30	s(τ1	s(τ1	NOUN
ejpam-6038	165	31	,	,	PUNCT
ejpam-6038	165	32	τ2)θ	τ2)θ	NOUN
ejpam-6038	165	33	-	-	PUNCT
ejpam-6038	165	34	int(a	int(a	NOUN
ejpam-6038	165	35	)	)	PUNCT
ejpam-6038	165	36	.	.	PUNCT
ejpam-6038	166	1	definition	definition	NOUN
ejpam-6038	166	2	11	11	NUM
ejpam-6038	166	3	.	.	PUNCT
ejpam-6038	167	1	a	a	DET
ejpam-6038	167	2	function	function	NOUN
ejpam-6038	167	3	f	f	NOUN
ejpam-6038	167	4	:	:	PUNCT
ejpam-6038	167	5	(	(	PUNCT
ejpam-6038	167	6	x	x	NOUN
ejpam-6038	167	7	,	,	PUNCT
ejpam-6038	167	8	τ1	τ1	NOUN
ejpam-6038	167	9	,	,	PUNCT
ejpam-6038	167	10	τ2	τ2	NOUN
ejpam-6038	167	11	)	)	PUNCT
ejpam-6038	167	12	→	→	SYM
ejpam-6038	167	13	(	(	PUNCT
ejpam-6038	167	14	y	y	PROPN
ejpam-6038	167	15	,	,	PUNCT
ejpam-6038	167	16	σ1	σ1	PROPN
ejpam-6038	167	17	,	,	PUNCT
ejpam-6038	167	18	σ2	σ2	PROPN
ejpam-6038	167	19	)	)	PUNCT
ejpam-6038	167	20	is	be	AUX
ejpam-6038	167	21	said	say	VERB
ejpam-6038	167	22	to	to	PART
ejpam-6038	167	23	be	be	AUX
ejpam-6038	167	24	p(τ1	p(τ1	NOUN
ejpam-6038	167	25	,	,	PUNCT
ejpam-6038	167	26	τ2)s	τ2)s	NOUN
ejpam-6038	167	27	-	-	ADJ
ejpam-6038	167	28	continuous	continuous	ADJ
ejpam-6038	167	29	if	if	SCONJ
ejpam-6038	167	30	for	for	ADP
ejpam-6038	167	31	each	each	DET
ejpam-6038	167	32	x	x	SYM
ejpam-6038	167	33	∈	∈	PROPN
ejpam-6038	167	34	x	x	X
ejpam-6038	167	35	and	and	CCONJ
ejpam-6038	167	36	for	for	ADP
ejpam-6038	167	37	each	each	DET
ejpam-6038	167	38	(	(	PUNCT
ejpam-6038	167	39	σ1	σ1	PROPN
ejpam-6038	167	40	,	,	PUNCT
ejpam-6038	167	41	σ2)s	σ2)s	NOUN
ejpam-6038	167	42	-	-	PUNCT
ejpam-6038	167	43	open	open	NOUN
ejpam-6038	167	44	set	set	NOUN
ejpam-6038	167	45	v	v	NOUN
ejpam-6038	167	46	of	of	ADP
ejpam-6038	167	47	y	y	NOUN
ejpam-6038	167	48	containing	contain	VERB
ejpam-6038	167	49	f(x	f(x	PROPN
ejpam-6038	167	50	)	)	PUNCT
ejpam-6038	167	51	,	,	PUNCT
ejpam-6038	167	52	there	there	PRON
ejpam-6038	167	53	exists	exist	VERB
ejpam-6038	167	54	a	a	DET
ejpam-6038	167	55	(	(	PUNCT
ejpam-6038	167	56	τ1	τ1	NOUN
ejpam-6038	167	57	,	,	PUNCT
ejpam-6038	167	58	τ2)p	τ2)p	ADJ
ejpam-6038	167	59	-	-	PUNCT
ejpam-6038	167	60	open	open	ADJ
ejpam-6038	167	61	set	set	NOUN
ejpam-6038	167	62	u	u	NOUN
ejpam-6038	167	63	of	of	ADP
ejpam-6038	167	64	x	x	PUNCT
ejpam-6038	167	65	containing	contain	VERB
ejpam-6038	167	66	x	x	PUNCT
ejpam-6038	167	67	such	such	ADJ
ejpam-6038	167	68	that	that	DET
ejpam-6038	167	69	f(u	f(u	PROPN
ejpam-6038	167	70	)	)	PUNCT
ejpam-6038	167	71	⊆	⊆	NUM
ejpam-6038	167	72	σ1σ2	σ1σ2	NOUN
ejpam-6038	167	73	-	-	NUM
ejpam-6038	167	74	cl(v	cl(v	NOUN
ejpam-6038	167	75	)	)	PUNCT
ejpam-6038	167	76	.	.	PUNCT
ejpam-6038	168	1	theorem	theorem	ADJ
ejpam-6038	168	2	8	8	NUM
ejpam-6038	168	3	.	.	PUNCT
ejpam-6038	169	1	for	for	ADP
ejpam-6038	169	2	a	a	DET
ejpam-6038	169	3	function	function	NOUN
ejpam-6038	169	4	f	f	NOUN
ejpam-6038	169	5	:	:	PUNCT
ejpam-6038	169	6	(	(	PUNCT
ejpam-6038	169	7	x	x	NOUN
ejpam-6038	169	8	,	,	PUNCT
ejpam-6038	169	9	τ1	τ1	NOUN
ejpam-6038	169	10	,	,	PUNCT
ejpam-6038	169	11	τ2	τ2	NOUN
ejpam-6038	169	12	)	)	PUNCT
ejpam-6038	169	13	→	→	SYM
ejpam-6038	169	14	(	(	PUNCT
ejpam-6038	169	15	y	y	PROPN
ejpam-6038	169	16	,	,	PUNCT
ejpam-6038	169	17	σ1	σ1	PROPN
ejpam-6038	169	18	,	,	PUNCT
ejpam-6038	169	19	σ2	σ2	NOUN
ejpam-6038	169	20	)	)	PUNCT
ejpam-6038	169	21	,	,	PUNCT
ejpam-6038	169	22	the	the	DET
ejpam-6038	169	23	following	follow	VERB
ejpam-6038	169	24	properties	property	NOUN
ejpam-6038	169	25	are	be	AUX
ejpam-6038	169	26	equivalent	equivalent	ADJ
ejpam-6038	169	27	:	:	PUNCT
ejpam-6038	169	28	(	(	PUNCT
ejpam-6038	169	29	1	1	X
ejpam-6038	169	30	)	)	PUNCT
ejpam-6038	169	31	f	f	PROPN
ejpam-6038	169	32	is	be	AUX
ejpam-6038	169	33	p(τ1	p(τ1	NOUN
ejpam-6038	169	34	,	,	PUNCT
ejpam-6038	169	35	τ2)s	τ2)s	NOUN
ejpam-6038	169	36	-	-	PUNCT
ejpam-6038	169	37	continuous	continuous	ADJ
ejpam-6038	169	38	;	;	PUNCT
ejpam-6038	169	39	(	(	PUNCT
ejpam-6038	169	40	2	2	X
ejpam-6038	169	41	)	)	PUNCT
ejpam-6038	169	42	f	f	PROPN
ejpam-6038	169	43	is	be	AUX
ejpam-6038	169	44	almost	almost	ADV
ejpam-6038	169	45	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	169	46	,	,	PUNCT
ejpam-6038	169	47	τ2)p	τ2)p	ADJ
ejpam-6038	169	48	-	-	NOUN
ejpam-6038	169	49	continuous	continuous	ADJ
ejpam-6038	169	50	;	;	PUNCT
ejpam-6038	169	51	(	(	PUNCT
ejpam-6038	169	52	3	3	X
ejpam-6038	169	53	)	)	PUNCT
ejpam-6038	169	54	f−1(v	f−1(v	NOUN
ejpam-6038	169	55	)	)	PUNCT
ejpam-6038	169	56	is	be	AUX
ejpam-6038	169	57	(	(	PUNCT
ejpam-6038	169	58	τ1	τ1	NOUN
ejpam-6038	169	59	,	,	PUNCT
ejpam-6038	169	60	τ2)p	τ2)p	NOUN
ejpam-6038	169	61	-	-	PUNCT
ejpam-6038	169	62	open	open	ADJ
ejpam-6038	169	63	in	in	ADP
ejpam-6038	169	64	x	x	PUNCT
ejpam-6038	169	65	for	for	ADP
ejpam-6038	169	66	each	each	DET
ejpam-6038	169	67	s(σ1	s(σ1	NOUN
ejpam-6038	169	68	,	,	PUNCT
ejpam-6038	169	69	σ2)θ	σ2)θ	NOUN
ejpam-6038	169	70	-	-	PUNCT
ejpam-6038	169	71	open	open	ADJ
ejpam-6038	169	72	set	set	NOUN
ejpam-6038	169	73	v	v	NOUN
ejpam-6038	169	74	of	of	ADP
ejpam-6038	169	75	y	y	PROPN
ejpam-6038	169	76	;	;	PUNCT
ejpam-6038	169	77	(	(	PUNCT
ejpam-6038	169	78	4	4	X
ejpam-6038	169	79	)	)	PUNCT
ejpam-6038	169	80	f−1(f	f−1(f	NOUN
ejpam-6038	169	81	)	)	PUNCT
ejpam-6038	169	82	is	be	AUX
ejpam-6038	169	83	(	(	PUNCT
ejpam-6038	169	84	τ1	τ1	NOUN
ejpam-6038	169	85	,	,	PUNCT
ejpam-6038	169	86	τ2)p	τ2)p	NOUN
ejpam-6038	169	87	-	-	PUNCT
ejpam-6038	169	88	closed	closed	ADJ
ejpam-6038	169	89	in	in	ADP
ejpam-6038	169	90	x	x	PUNCT
ejpam-6038	169	91	for	for	ADP
ejpam-6038	169	92	each	each	DET
ejpam-6038	169	93	s(σ1	s(σ1	NOUN
ejpam-6038	169	94	,	,	PUNCT
ejpam-6038	169	95	σ2)θ	σ2)θ	NOUN
ejpam-6038	169	96	-	-	PUNCT
ejpam-6038	169	97	closed	close	VERB
ejpam-6038	169	98	set	set	ADJ
ejpam-6038	169	99	f	f	PROPN
ejpam-6038	169	100	of	of	ADP
ejpam-6038	169	101	y	y	PROPN
ejpam-6038	169	102	.	.	PUNCT
ejpam-6038	170	1	proof	proof	NOUN
ejpam-6038	170	2	.	.	PUNCT
ejpam-6038	171	1	(	(	PUNCT
ejpam-6038	171	2	1	1	X
ejpam-6038	171	3	)	)	PUNCT
ejpam-6038	171	4	⇒	⇒	NOUN
ejpam-6038	171	5	(	(	PUNCT
ejpam-6038	171	6	2	2	NUM
ejpam-6038	171	7	):	):	PUNCT
ejpam-6038	171	8	let	let	VERB
ejpam-6038	171	9	f	f	PRON
ejpam-6038	171	10	be	be	AUX
ejpam-6038	171	11	any	any	DET
ejpam-6038	171	12	(	(	PUNCT
ejpam-6038	171	13	σ1	σ1	NOUN
ejpam-6038	171	14	,	,	PUNCT
ejpam-6038	171	15	σ2)r	σ2)r	NOUN
ejpam-6038	171	16	-	-	PUNCT
ejpam-6038	171	17	closed	close	VERB
ejpam-6038	171	18	set	set	NOUN
ejpam-6038	171	19	of	of	ADP
ejpam-6038	171	20	y	y	PROPN
ejpam-6038	171	21	and	and	CCONJ
ejpam-6038	171	22	x	x	PROPN
ejpam-6038	171	23	∈	∈	PROPN
ejpam-6038	171	24	f−1(f	f−1(f	PROPN
ejpam-6038	171	25	)	)	PUNCT
ejpam-6038	171	26	.	.	PUNCT
ejpam-6038	172	1	then	then	ADV
ejpam-6038	172	2	,	,	PUNCT
ejpam-6038	172	3	f(x	f(x	PROPN
ejpam-6038	172	4	)	)	PUNCT
ejpam-6038	172	5	∈	∈	PROPN
ejpam-6038	172	6	f	f	PROPN
ejpam-6038	172	7	and	and	CCONJ
ejpam-6038	172	8	f	f	PROPN
ejpam-6038	172	9	is	be	AUX
ejpam-6038	172	10	(	(	PUNCT
ejpam-6038	172	11	σ1	σ1	PROPN
ejpam-6038	172	12	,	,	PUNCT
ejpam-6038	172	13	σ2)s	σ2)s	NOUN
ejpam-6038	172	14	-	-	PUNCT
ejpam-6038	172	15	open	open	ADJ
ejpam-6038	172	16	.	.	PUNCT
ejpam-6038	173	1	since	since	SCONJ
ejpam-6038	173	2	f	f	PROPN
ejpam-6038	173	3	is	be	AUX
ejpam-6038	173	4	p(τ1	p(τ1	NOUN
ejpam-6038	173	5	,	,	PUNCT
ejpam-6038	173	6	τ2)s	τ2)s	NOUN
ejpam-6038	173	7	-	-	PUNCT
ejpam-6038	173	8	continuous	continuous	ADJ
ejpam-6038	173	9	,	,	PUNCT
ejpam-6038	173	10	there	there	PRON
ejpam-6038	173	11	exists	exist	VERB
ejpam-6038	173	12	a	a	DET
ejpam-6038	173	13	(	(	PUNCT
ejpam-6038	173	14	τ1	τ1	NOUN
ejpam-6038	173	15	,	,	PUNCT
ejpam-6038	173	16	τ2)popen	τ2)popen	ADJ
ejpam-6038	173	17	set	set	VERB
ejpam-6038	173	18	u	u	NOUN
ejpam-6038	173	19	of	of	ADP
ejpam-6038	173	20	x	x	PUNCT
ejpam-6038	173	21	containing	contain	VERB
ejpam-6038	173	22	x	x	PUNCT
ejpam-6038	173	23	such	such	ADJ
ejpam-6038	173	24	that	that	DET
ejpam-6038	173	25	f(u	f(u	PROPN
ejpam-6038	173	26	)	)	PUNCT
ejpam-6038	173	27	⊆	⊆	NUM
ejpam-6038	173	28	σ1σ2	σ1σ2	NOUN
ejpam-6038	173	29	-	-	NUM
ejpam-6038	173	30	cl(f	cl(f	NUM
ejpam-6038	173	31	)	)	PUNCT
ejpam-6038	174	1	=	=	PUNCT
ejpam-6038	174	2	f	f	PROPN
ejpam-6038	174	3	.	.	PUNCT
ejpam-6038	175	1	therefore	therefore	ADV
ejpam-6038	175	2	,	,	PUNCT
ejpam-6038	175	3	we	we	PRON
ejpam-6038	175	4	have	have	VERB
ejpam-6038	175	5	x	x	X
ejpam-6038	175	6	∈	∈	PROPN
ejpam-6038	175	7	u	u	NOUN
ejpam-6038	175	8	⊆	⊆	NUM
ejpam-6038	175	9	f−1(f	f−1(f	PROPN
ejpam-6038	175	10	)	)	PUNCT
ejpam-6038	175	11	which	which	PRON
ejpam-6038	175	12	implies	imply	VERB
ejpam-6038	175	13	that	that	SCONJ
ejpam-6038	175	14	x	x	SYM
ejpam-6038	175	15	∈	∈	PROPN
ejpam-6038	175	16	(	(	PUNCT
ejpam-6038	175	17	τ1	τ1	NOUN
ejpam-6038	175	18	,	,	PUNCT
ejpam-6038	175	19	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-6038	175	20	−1(f	−1(f	NUM
ejpam-6038	175	21	)	)	PUNCT
ejpam-6038	175	22	)	)	PUNCT
ejpam-6038	175	23	.	.	PUNCT
ejpam-6038	176	1	thus	thus	ADV
ejpam-6038	176	2	,	,	PUNCT
ejpam-6038	176	3	f−1(f	f−1(f	PROPN
ejpam-6038	176	4	)	)	PUNCT
ejpam-6038	177	1	⊆	⊆	NUM
ejpam-6038	177	2	(	(	PUNCT
ejpam-6038	177	3	τ1	τ1	NOUN
ejpam-6038	177	4	,	,	PUNCT
ejpam-6038	177	5	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-6038	177	6	−1(f	−1(f	NUM
ejpam-6038	177	7	)	)	PUNCT
ejpam-6038	177	8	)	)	PUNCT
ejpam-6038	177	9	and	and	CCONJ
ejpam-6038	177	10	hence	hence	ADV
ejpam-6038	177	11	f−1(f	f−1(f	PROPN
ejpam-6038	177	12	)	)	PUNCT
ejpam-6038	177	13	=	=	PUNCT
ejpam-6038	178	1	(	(	PUNCT
ejpam-6038	178	2	τ1	τ1	PROPN
ejpam-6038	178	3	,	,	PUNCT
ejpam-6038	178	4	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-6038	178	5	−1(f	−1(f	NUM
ejpam-6038	178	6	)	)	PUNCT
ejpam-6038	178	7	)	)	PUNCT
ejpam-6038	178	8	.	.	PUNCT
ejpam-6038	179	1	this	this	PRON
ejpam-6038	179	2	shows	show	VERB
ejpam-6038	179	3	that	that	SCONJ
ejpam-6038	179	4	f−1(f	f−1(f	PROPN
ejpam-6038	179	5	)	)	PUNCT
ejpam-6038	179	6	is	be	AUX
ejpam-6038	179	7	(	(	PUNCT
ejpam-6038	179	8	τ1	τ1	NOUN
ejpam-6038	179	9	,	,	PUNCT
ejpam-6038	179	10	τ2)p	τ2)p	NOUN
ejpam-6038	179	11	-	-	PUNCT
ejpam-6038	179	12	open	open	ADJ
ejpam-6038	179	13	in	in	ADP
ejpam-6038	179	14	x.	x.	NOUN
ejpam-6038	179	15	it	it	PRON
ejpam-6038	179	16	follows	follow	VERB
ejpam-6038	179	17	from	from	ADP
ejpam-6038	179	18	theorem	theorem	ADJ
ejpam-6038	179	19	1	1	NUM
ejpam-6038	179	20	that	that	SCONJ
ejpam-6038	179	21	f	f	PROPN
ejpam-6038	179	22	is	be	AUX
ejpam-6038	179	23	almost	almost	ADV
ejpam-6038	179	24	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	179	25	,	,	PUNCT
ejpam-6038	179	26	τ2)p	τ2)p	ADJ
ejpam-6038	179	27	-	-	NOUN
ejpam-6038	179	28	continuous	continuous	ADJ
ejpam-6038	179	29	.	.	PUNCT
ejpam-6038	180	1	p.	p.	NOUN
ejpam-6038	180	2	pue	pue	NOUN
ejpam-6038	180	3	-	-	PUNCT
ejpam-6038	180	4	on	on	ADP
ejpam-6038	180	5	,	,	PUNCT
ejpam-6038	180	6	a.	a.	PROPN
ejpam-6038	180	7	sama	sama	PROPN
ejpam-6038	180	8	-	-	PUNCT
ejpam-6038	180	9	ae	ae	PROPN
ejpam-6038	180	10	,	,	PUNCT
ejpam-6038	180	11	c.	c.	PROPN
ejpam-6038	180	12	boonpok	boonpok	PROPN
ejpam-6038	180	13	/	/	SYM
ejpam-6038	180	14	eur	eur	PROPN
ejpam-6038	180	15	.	.	PUNCT
ejpam-6038	181	1	j.	j.	PROPN
ejpam-6038	181	2	pure	pure	PROPN
ejpam-6038	181	3	appl	appl	PROPN
ejpam-6038	181	4	.	.	PROPN
ejpam-6038	181	5	math	math	PROPN
ejpam-6038	181	6	,	,	PUNCT
ejpam-6038	181	7	18	18	NUM
ejpam-6038	181	8	(	(	PUNCT
ejpam-6038	181	9	2	2	NUM
ejpam-6038	181	10	)	)	PUNCT
ejpam-6038	181	11	(	(	PUNCT
ejpam-6038	181	12	2025	2025	NUM
ejpam-6038	181	13	)	)	PUNCT
ejpam-6038	181	14	,	,	PUNCT
ejpam-6038	181	15	6038	6038	NUM
ejpam-6038	181	16	7	7	NUM
ejpam-6038	181	17	of	of	ADP
ejpam-6038	181	18	11	11	NUM
ejpam-6038	181	19	(	(	PUNCT
ejpam-6038	181	20	2	2	NUM
ejpam-6038	181	21	)	)	PUNCT
ejpam-6038	181	22	⇒	⇒	NOUN
ejpam-6038	181	23	(	(	PUNCT
ejpam-6038	181	24	3	3	NUM
ejpam-6038	181	25	):	):	PUNCT
ejpam-6038	181	26	this	this	PRON
ejpam-6038	181	27	follows	follow	VERB
ejpam-6038	181	28	from	from	ADP
ejpam-6038	181	29	the	the	DET
ejpam-6038	181	30	fact	fact	NOUN
ejpam-6038	181	31	that	that	SCONJ
ejpam-6038	181	32	every	every	DET
ejpam-6038	181	33	s(σ1	s(σ1	NOUN
ejpam-6038	181	34	,	,	PUNCT
ejpam-6038	181	35	σ2)θ	σ2)θ	ADJ
ejpam-6038	181	36	-	-	PUNCT
ejpam-6038	181	37	open	open	ADJ
ejpam-6038	181	38	set	set	NOUN
ejpam-6038	181	39	is	be	AUX
ejpam-6038	181	40	the	the	DET
ejpam-6038	181	41	union	union	NOUN
ejpam-6038	181	42	of	of	ADP
ejpam-6038	181	43	(	(	PUNCT
ejpam-6038	181	44	σ1	σ1	PROPN
ejpam-6038	181	45	,	,	PUNCT
ejpam-6038	181	46	σ2)r	σ2)r	NOUN
ejpam-6038	181	47	-	-	PUNCT
ejpam-6038	181	48	closed	close	VERB
ejpam-6038	181	49	sets	set	NOUN
ejpam-6038	181	50	.	.	PUNCT
ejpam-6038	182	1	(	(	PUNCT
ejpam-6038	182	2	3	3	X
ejpam-6038	182	3	)	)	PUNCT
ejpam-6038	182	4	⇔	⇔	X
ejpam-6038	182	5	(	(	PUNCT
ejpam-6038	182	6	4	4	NUM
ejpam-6038	182	7	):	):	PUNCT
ejpam-6038	182	8	this	this	PRON
ejpam-6038	182	9	is	be	AUX
ejpam-6038	182	10	obvious	obvious	ADJ
ejpam-6038	182	11	.	.	PUNCT
ejpam-6038	183	1	(	(	PUNCT
ejpam-6038	183	2	4	4	X
ejpam-6038	183	3	)	)	PUNCT
ejpam-6038	183	4	⇒	⇒	NOUN
ejpam-6038	183	5	(	(	PUNCT
ejpam-6038	183	6	1	1	NUM
ejpam-6038	183	7	):	):	PUNCT
ejpam-6038	183	8	let	let	VERB
ejpam-6038	183	9	x	x	PUNCT
ejpam-6038	183	10	∈	∈	PROPN
ejpam-6038	183	11	x	x	X
ejpam-6038	183	12	and	and	CCONJ
ejpam-6038	183	13	v	v	AUX
ejpam-6038	183	14	be	be	AUX
ejpam-6038	183	15	any	any	DET
ejpam-6038	183	16	(	(	PUNCT
ejpam-6038	183	17	σ1	σ1	NOUN
ejpam-6038	183	18	,	,	PUNCT
ejpam-6038	183	19	σ2)s	σ2)s	NOUN
ejpam-6038	183	20	-	-	PUNCT
ejpam-6038	183	21	open	open	ADJ
ejpam-6038	183	22	set	set	NOUN
ejpam-6038	183	23	of	of	ADP
ejpam-6038	183	24	y	y	PROPN
ejpam-6038	183	25	containing	contain	VERB
ejpam-6038	183	26	f(x	f(x	PROPN
ejpam-6038	183	27	)	)	PUNCT
ejpam-6038	183	28	.	.	PUNCT
ejpam-6038	184	1	since	since	SCONJ
ejpam-6038	184	2	σ1σ2	σ1σ2	NOUN
ejpam-6038	184	3	-	-	NOUN
ejpam-6038	184	4	cl(v	cl(v	NOUN
ejpam-6038	184	5	)	)	PUNCT
ejpam-6038	184	6	is	be	AUX
ejpam-6038	184	7	(	(	PUNCT
ejpam-6038	184	8	σ1	σ1	NOUN
ejpam-6038	184	9	,	,	PUNCT
ejpam-6038	184	10	σ2)r	σ2)r	NOUN
ejpam-6038	184	11	-	-	PUNCT
ejpam-6038	184	12	closed	closed	ADJ
ejpam-6038	184	13	,	,	PUNCT
ejpam-6038	184	14	we	we	PRON
ejpam-6038	184	15	have	have	VERB
ejpam-6038	184	16	σ1σ2	σ1σ2	NOUN
ejpam-6038	184	17	-	-	NUM
ejpam-6038	184	18	cl(v	cl(v	NOUN
ejpam-6038	184	19	)	)	PUNCT
ejpam-6038	184	20	is	be	AUX
ejpam-6038	184	21	s(σ1	s(σ1	ADV
ejpam-6038	184	22	,	,	PUNCT
ejpam-6038	184	23	σ2)θ	σ2)θ	NOUN
ejpam-6038	184	24	-	-	PUNCT
ejpam-6038	184	25	open	open	ADJ
ejpam-6038	184	26	.	.	PUNCT
ejpam-6038	185	1	thus	thus	ADV
ejpam-6038	185	2	by	by	ADP
ejpam-6038	185	3	(	(	PUNCT
ejpam-6038	185	4	4	4	NUM
ejpam-6038	185	5	)	)	PUNCT
ejpam-6038	185	6	,	,	PUNCT
ejpam-6038	185	7	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	185	8	-	-	PUNCT
ejpam-6038	185	9	cl(v	cl(v	NOUN
ejpam-6038	185	10	)	)	PUNCT
ejpam-6038	185	11	)	)	PUNCT
ejpam-6038	185	12	is	be	AUX
ejpam-6038	185	13	(	(	PUNCT
ejpam-6038	185	14	τ1	τ1	NOUN
ejpam-6038	185	15	,	,	PUNCT
ejpam-6038	185	16	τ2)p	τ2)p	NOUN
ejpam-6038	185	17	-	-	PUNCT
ejpam-6038	185	18	open	open	ADJ
ejpam-6038	185	19	in	in	ADP
ejpam-6038	185	20	x.	x.	NOUN
ejpam-6038	185	21	now	now	ADV
ejpam-6038	185	22	,	,	PUNCT
ejpam-6038	185	23	put	put	VERB
ejpam-6038	185	24	u	u	NOUN
ejpam-6038	185	25	=	=	PRON
ejpam-6038	185	26	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	185	27	-	-	PUNCT
ejpam-6038	185	28	cl(v	cl(v	NOUN
ejpam-6038	185	29	)	)	PUNCT
ejpam-6038	185	30	)	)	PUNCT
ejpam-6038	185	31	.	.	PUNCT
ejpam-6038	186	1	then	then	ADV
ejpam-6038	186	2	,	,	PUNCT
ejpam-6038	186	3	u	u	NOUN
ejpam-6038	186	4	is	be	AUX
ejpam-6038	186	5	a	a	DET
ejpam-6038	186	6	(	(	PUNCT
ejpam-6038	186	7	τ1	τ1	NOUN
ejpam-6038	186	8	,	,	PUNCT
ejpam-6038	186	9	τ2)p	τ2)p	ADJ
ejpam-6038	186	10	-	-	PUNCT
ejpam-6038	186	11	open	open	ADJ
ejpam-6038	186	12	set	set	NOUN
ejpam-6038	186	13	of	of	ADP
ejpam-6038	186	14	x	x	PUNCT
ejpam-6038	186	15	containing	contain	VERB
ejpam-6038	186	16	x	x	PROPN
ejpam-6038	186	17	and	and	CCONJ
ejpam-6038	186	18	f(u	f(u	PROPN
ejpam-6038	186	19	)	)	PUNCT
ejpam-6038	186	20	⊆	⊆	NUM
ejpam-6038	186	21	σ1σ2	σ1σ2	NOUN
ejpam-6038	186	22	-	-	NUM
ejpam-6038	186	23	cl(v	cl(v	NOUN
ejpam-6038	186	24	)	)	PUNCT
ejpam-6038	186	25	.	.	PUNCT
ejpam-6038	187	1	this	this	PRON
ejpam-6038	187	2	shows	show	VERB
ejpam-6038	187	3	that	that	SCONJ
ejpam-6038	187	4	f	f	PROPN
ejpam-6038	187	5	is	be	AUX
ejpam-6038	187	6	p(τ1	p(τ1	NOUN
ejpam-6038	187	7	,	,	PUNCT
ejpam-6038	187	8	τ2)s	τ2)s	NOUN
ejpam-6038	187	9	-	-	PUNCT
ejpam-6038	187	10	continuous	continuous	ADJ
ejpam-6038	187	11	.	.	PUNCT
ejpam-6038	188	1	theorem	theorem	NOUN
ejpam-6038	188	2	9	9	NUM
ejpam-6038	188	3	.	.	PUNCT
ejpam-6038	188	4	for	for	ADP
ejpam-6038	188	5	a	a	DET
ejpam-6038	188	6	function	function	NOUN
ejpam-6038	188	7	f	f	NOUN
ejpam-6038	188	8	:	:	PUNCT
ejpam-6038	188	9	(	(	PUNCT
ejpam-6038	188	10	x	x	NOUN
ejpam-6038	188	11	,	,	PUNCT
ejpam-6038	188	12	τ1	τ1	NOUN
ejpam-6038	188	13	,	,	PUNCT
ejpam-6038	188	14	τ2	τ2	NOUN
ejpam-6038	188	15	)	)	PUNCT
ejpam-6038	188	16	→	→	SYM
ejpam-6038	188	17	(	(	PUNCT
ejpam-6038	188	18	y	y	PROPN
ejpam-6038	188	19	,	,	PUNCT
ejpam-6038	188	20	σ1	σ1	PROPN
ejpam-6038	188	21	,	,	PUNCT
ejpam-6038	188	22	σ2	σ2	NOUN
ejpam-6038	188	23	)	)	PUNCT
ejpam-6038	188	24	,	,	PUNCT
ejpam-6038	188	25	the	the	DET
ejpam-6038	188	26	following	follow	VERB
ejpam-6038	188	27	properties	property	NOUN
ejpam-6038	188	28	are	be	AUX
ejpam-6038	188	29	equivalent	equivalent	ADJ
ejpam-6038	188	30	:	:	PUNCT
ejpam-6038	188	31	(	(	PUNCT
ejpam-6038	188	32	1	1	X
ejpam-6038	188	33	)	)	PUNCT
ejpam-6038	188	34	f	f	NOUN
ejpam-6038	188	35	is	be	AUX
ejpam-6038	188	36	almost	almost	ADV
ejpam-6038	188	37	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	188	38	,	,	PUNCT
ejpam-6038	188	39	τ2)p	τ2)p	ADJ
ejpam-6038	189	1	-	-	NOUN
ejpam-6038	189	2	continuous	continuous	ADJ
ejpam-6038	189	3	;	;	PUNCT
ejpam-6038	189	4	(	(	PUNCT
ejpam-6038	189	5	2	2	X
ejpam-6038	189	6	)	)	PUNCT
ejpam-6038	189	7	f((τ1	f((τ1	PROPN
ejpam-6038	189	8	,	,	PUNCT
ejpam-6038	189	9	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6038	189	10	)	)	PUNCT
ejpam-6038	189	11	)	)	PUNCT
ejpam-6038	190	1	⊆	⊆	NUM
ejpam-6038	190	2	s(σ1	s(σ1	NOUN
ejpam-6038	190	3	,	,	PUNCT
ejpam-6038	190	4	σ2)θ	σ2)θ	ADJ
ejpam-6038	190	5	-	-	PUNCT
ejpam-6038	190	6	cl(f(a	cl(f(a	NOUN
ejpam-6038	190	7	)	)	PUNCT
ejpam-6038	190	8	)	)	PUNCT
ejpam-6038	190	9	for	for	ADP
ejpam-6038	190	10	every	every	DET
ejpam-6038	190	11	subset	subset	NOUN
ejpam-6038	190	12	a	a	PRON
ejpam-6038	190	13	of	of	ADP
ejpam-6038	190	14	x	x	PRON
ejpam-6038	190	15	;	;	PUNCT
ejpam-6038	190	16	(	(	PUNCT
ejpam-6038	190	17	3	3	X
ejpam-6038	190	18	)	)	PUNCT
ejpam-6038	190	19	(	(	PUNCT
ejpam-6038	190	20	τ1	τ1	NOUN
ejpam-6038	190	21	,	,	PUNCT
ejpam-6038	190	22	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6038	190	23	−1(b	−1(b	NOUN
ejpam-6038	190	24	)	)	PUNCT
ejpam-6038	190	25	)	)	PUNCT
ejpam-6038	191	1	⊆	⊆	NUM
ejpam-6038	191	2	f−1(s(σ1	f−1(s(σ1	NOUN
ejpam-6038	191	3	,	,	PUNCT
ejpam-6038	191	4	σ2)θ	σ2)θ	NOUN
ejpam-6038	191	5	-	-	PUNCT
ejpam-6038	191	6	cl(b	cl(b	NOUN
ejpam-6038	191	7	)	)	PUNCT
ejpam-6038	191	8	)	)	PUNCT
ejpam-6038	191	9	for	for	ADP
ejpam-6038	191	10	every	every	DET
ejpam-6038	191	11	subset	subset	NOUN
ejpam-6038	191	12	b	b	PROPN
ejpam-6038	191	13	of	of	ADP
ejpam-6038	191	14	y	y	PROPN
ejpam-6038	191	15	.	.	PUNCT
ejpam-6038	192	1	proof	proof	NOUN
ejpam-6038	192	2	.	.	PUNCT
ejpam-6038	193	1	(	(	PUNCT
ejpam-6038	193	2	1	1	X
ejpam-6038	193	3	)	)	PUNCT
ejpam-6038	193	4	⇒	⇒	NOUN
ejpam-6038	193	5	(	(	PUNCT
ejpam-6038	193	6	2	2	NUM
ejpam-6038	193	7	):	):	PUNCT
ejpam-6038	193	8	let	let	VERB
ejpam-6038	193	9	a	a	DET
ejpam-6038	193	10	be	be	AUX
ejpam-6038	193	11	any	any	DET
ejpam-6038	193	12	subset	subset	NOUN
ejpam-6038	193	13	of	of	ADP
ejpam-6038	193	14	x.	x.	NOUN
ejpam-6038	193	15	let	let	VERB
ejpam-6038	193	16	x	x	X
ejpam-6038	193	17	∈	∈	PROPN
ejpam-6038	193	18	(	(	PUNCT
ejpam-6038	193	19	τ1	τ1	NOUN
ejpam-6038	193	20	,	,	PUNCT
ejpam-6038	193	21	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6038	193	22	)	)	PUNCT
ejpam-6038	193	23	and	and	CCONJ
ejpam-6038	193	24	v	v	AUX
ejpam-6038	193	25	be	be	AUX
ejpam-6038	193	26	any	any	DET
ejpam-6038	193	27	(	(	PUNCT
ejpam-6038	193	28	σ1	σ1	NOUN
ejpam-6038	193	29	,	,	PUNCT
ejpam-6038	193	30	σ2)s	σ2)s	NOUN
ejpam-6038	193	31	-	-	PUNCT
ejpam-6038	193	32	open	open	ADJ
ejpam-6038	193	33	set	set	NOUN
ejpam-6038	193	34	of	of	ADP
ejpam-6038	193	35	y	y	PROPN
ejpam-6038	193	36	containing	contain	VERB
ejpam-6038	193	37	f(x	f(x	PROPN
ejpam-6038	193	38	)	)	PUNCT
ejpam-6038	193	39	.	.	PUNCT
ejpam-6038	194	1	since	since	SCONJ
ejpam-6038	194	2	f	f	PROPN
ejpam-6038	194	3	is	be	AUX
ejpam-6038	194	4	almost	almost	ADV
ejpam-6038	194	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	194	6	,	,	PUNCT
ejpam-6038	194	7	τ2)p	τ2)p	ADJ
ejpam-6038	194	8	-	-	ADJ
ejpam-6038	194	9	continuous	continuous	ADJ
ejpam-6038	194	10	,	,	PUNCT
ejpam-6038	194	11	by	by	ADP
ejpam-6038	194	12	theorem	theorem	NOUN
ejpam-6038	194	13	8	8	NUM
ejpam-6038	194	14	there	there	PRON
ejpam-6038	194	15	exists	exist	VERB
ejpam-6038	194	16	a	a	DET
ejpam-6038	194	17	(	(	PUNCT
ejpam-6038	194	18	τ1	τ1	NOUN
ejpam-6038	194	19	,	,	PUNCT
ejpam-6038	194	20	τ2)p	τ2)p	ADJ
ejpam-6038	194	21	-	-	PUNCT
ejpam-6038	194	22	open	open	ADJ
ejpam-6038	194	23	set	set	NOUN
ejpam-6038	194	24	u	u	NOUN
ejpam-6038	194	25	of	of	ADP
ejpam-6038	194	26	x	x	PUNCT
ejpam-6038	194	27	containing	contain	VERB
ejpam-6038	194	28	x	x	PUNCT
ejpam-6038	194	29	such	such	ADJ
ejpam-6038	194	30	that	that	DET
ejpam-6038	194	31	f(u	f(u	PROPN
ejpam-6038	194	32	)	)	PUNCT
ejpam-6038	194	33	⊆	⊆	NUM
ejpam-6038	194	34	σ1σ2	σ1σ2	NOUN
ejpam-6038	194	35	-	-	NUM
ejpam-6038	194	36	cl(v	cl(v	NOUN
ejpam-6038	194	37	)	)	PUNCT
ejpam-6038	194	38	.	.	PUNCT
ejpam-6038	195	1	since	since	SCONJ
ejpam-6038	195	2	x	x	PROPN
ejpam-6038	195	3	∈	∈	PROPN
ejpam-6038	195	4	(	(	PUNCT
ejpam-6038	195	5	τ1	τ1	NOUN
ejpam-6038	195	6	,	,	PUNCT
ejpam-6038	195	7	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6038	195	8	)	)	PUNCT
ejpam-6038	195	9	,	,	PUNCT
ejpam-6038	195	10	we	we	PRON
ejpam-6038	195	11	have	have	VERB
ejpam-6038	195	12	u	u	NOUN
ejpam-6038	195	13	∩a	∩a	PROPN
ejpam-6038	195	14	̸=	̸=	PROPN
ejpam-6038	195	15	∅	∅	NOUN
ejpam-6038	195	16	and	and	CCONJ
ejpam-6038	195	17	hence	hence	ADV
ejpam-6038	195	18	∅	∅	NOUN
ejpam-6038	195	19	=	=	NOUN
ejpam-6038	195	20	̸	̸	X
ejpam-6038	195	21	f(u	f(u	ADJ
ejpam-6038	195	22	)	)	PUNCT
ejpam-6038	195	23	∩	∩	ADJ
ejpam-6038	195	24	f(a	f(a	NOUN
ejpam-6038	195	25	)	)	PUNCT
ejpam-6038	195	26	⊆	⊆	NUM
ejpam-6038	195	27	σ1σ2	σ1σ2	NOUN
ejpam-6038	195	28	-	-	PUNCT
ejpam-6038	195	29	cl(v	cl(v	NOUN
ejpam-6038	195	30	)	)	PUNCT
ejpam-6038	195	31	∩	∩	ADJ
ejpam-6038	195	32	f(a	f(a	NOUN
ejpam-6038	195	33	)	)	PUNCT
ejpam-6038	195	34	.	.	PUNCT
ejpam-6038	196	1	therefore	therefore	ADV
ejpam-6038	196	2	,	,	PUNCT
ejpam-6038	196	3	f(x	f(x	PROPN
ejpam-6038	196	4	)	)	PUNCT
ejpam-6038	196	5	∈	∈	PROPN
ejpam-6038	196	6	s(σ1	s(σ1	NOUN
ejpam-6038	196	7	,	,	PUNCT
ejpam-6038	196	8	σ2)θ	σ2)θ	ADJ
ejpam-6038	196	9	-	-	PUNCT
ejpam-6038	196	10	cl(f(a	cl(f(a	NOUN
ejpam-6038	196	11	)	)	PUNCT
ejpam-6038	196	12	)	)	PUNCT
ejpam-6038	196	13	.	.	PUNCT
ejpam-6038	197	1	thus	thus	ADV
ejpam-6038	197	2	,	,	PUNCT
ejpam-6038	197	3	f((τ1	f((τ1	PROPN
ejpam-6038	197	4	,	,	PUNCT
ejpam-6038	197	5	τ2)-pcl(a	τ2)-pcl(a	NOUN
ejpam-6038	197	6	)	)	PUNCT
ejpam-6038	197	7	)	)	PUNCT
ejpam-6038	198	1	⊆	⊆	NUM
ejpam-6038	198	2	s(σ1	s(σ1	NOUN
ejpam-6038	198	3	,	,	PUNCT
ejpam-6038	198	4	σ2)θ	σ2)θ	ADJ
ejpam-6038	198	5	-	-	PUNCT
ejpam-6038	198	6	cl(f(a	cl(f(a	NOUN
ejpam-6038	198	7	)	)	PUNCT
ejpam-6038	198	8	)	)	PUNCT
ejpam-6038	198	9	.	.	PUNCT
ejpam-6038	199	1	(	(	PUNCT
ejpam-6038	199	2	2	2	X
ejpam-6038	199	3	)	)	PUNCT
ejpam-6038	199	4	⇒	⇒	NOUN
ejpam-6038	199	5	(	(	PUNCT
ejpam-6038	199	6	3	3	NUM
ejpam-6038	199	7	):	):	PUNCT
ejpam-6038	199	8	let	let	VERB
ejpam-6038	199	9	b	b	X
ejpam-6038	199	10	be	be	AUX
ejpam-6038	199	11	any	any	DET
ejpam-6038	199	12	subset	subset	NOUN
ejpam-6038	199	13	of	of	ADP
ejpam-6038	199	14	y	y	PROPN
ejpam-6038	199	15	.	.	PUNCT
ejpam-6038	200	1	by	by	ADP
ejpam-6038	200	2	(	(	PUNCT
ejpam-6038	200	3	2	2	NUM
ejpam-6038	200	4	)	)	PUNCT
ejpam-6038	200	5	,	,	PUNCT
ejpam-6038	200	6	we	we	PRON
ejpam-6038	200	7	have	have	AUX
ejpam-6038	200	8	f((τ1	f((τ1	VERB
ejpam-6038	200	9	,	,	PUNCT
ejpam-6038	200	10	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6038	200	11	−1(b	−1(b	NOUN
ejpam-6038	200	12	)	)	PUNCT
ejpam-6038	200	13	)	)	PUNCT
ejpam-6038	200	14	)	)	PUNCT
ejpam-6038	201	1	⊆	⊆	NUM
ejpam-6038	201	2	s(σ1	s(σ1	NOUN
ejpam-6038	201	3	,	,	PUNCT
ejpam-6038	201	4	σ2)θ	σ2)θ	ADJ
ejpam-6038	201	5	-	-	PUNCT
ejpam-6038	201	6	cl(f(f	cl(f(f	ADJ
ejpam-6038	201	7	−1(b	−1(b	NOUN
ejpam-6038	201	8	)	)	PUNCT
ejpam-6038	201	9	)	)	PUNCT
ejpam-6038	201	10	)	)	PUNCT
ejpam-6038	202	1	⊆	⊆	NUM
ejpam-6038	202	2	s(σ1	s(σ1	NOUN
ejpam-6038	202	3	,	,	PUNCT
ejpam-6038	202	4	σ2)θ	σ2)θ	NOUN
ejpam-6038	202	5	-	-	PUNCT
ejpam-6038	202	6	cl(b	cl(b	NOUN
ejpam-6038	202	7	)	)	PUNCT
ejpam-6038	202	8	and	and	CCONJ
ejpam-6038	202	9	hence	hence	ADV
ejpam-6038	202	10	(	(	PUNCT
ejpam-6038	202	11	τ1	τ1	PROPN
ejpam-6038	202	12	,	,	PUNCT
ejpam-6038	202	13	τ2)-pcl(f	τ2)-pcl(f	NOUN
ejpam-6038	202	14	−1(b	−1(b	NOUN
ejpam-6038	202	15	)	)	PUNCT
ejpam-6038	202	16	)	)	PUNCT
ejpam-6038	203	1	⊆	⊆	NUM
ejpam-6038	203	2	f−1(s(σ1	f−1(s(σ1	NOUN
ejpam-6038	203	3	,	,	PUNCT
ejpam-6038	203	4	σ2)θ	σ2)θ	NOUN
ejpam-6038	203	5	-	-	PUNCT
ejpam-6038	203	6	cl(b	cl(b	NOUN
ejpam-6038	203	7	)	)	PUNCT
ejpam-6038	203	8	)	)	PUNCT
ejpam-6038	203	9	.	.	PUNCT
ejpam-6038	204	1	(	(	PUNCT
ejpam-6038	204	2	3	3	X
ejpam-6038	204	3	)	)	PUNCT
ejpam-6038	204	4	⇒	⇒	NOUN
ejpam-6038	204	5	(	(	PUNCT
ejpam-6038	204	6	1	1	NUM
ejpam-6038	204	7	):	):	PUNCT
ejpam-6038	204	8	let	let	VERB
ejpam-6038	204	9	v	v	PART
ejpam-6038	204	10	be	be	AUX
ejpam-6038	204	11	any	any	DET
ejpam-6038	204	12	(	(	PUNCT
ejpam-6038	204	13	σ1	σ1	NOUN
ejpam-6038	204	14	,	,	PUNCT
ejpam-6038	204	15	σ2)s	σ2)s	NOUN
ejpam-6038	204	16	-	-	PUNCT
ejpam-6038	204	17	open	open	ADJ
ejpam-6038	204	18	set	set	NOUN
ejpam-6038	204	19	of	of	ADP
ejpam-6038	204	20	y	y	PROPN
ejpam-6038	204	21	containing	contain	VERB
ejpam-6038	204	22	f(x	f(x	PROPN
ejpam-6038	204	23	)	)	PUNCT
ejpam-6038	204	24	.	.	PUNCT
ejpam-6038	205	1	since	since	SCONJ
ejpam-6038	205	2	σ1σ2	σ1σ2	NOUN
ejpam-6038	205	3	-	-	PUNCT
ejpam-6038	205	4	cl(v	cl(v	NOUN
ejpam-6038	205	5	)	)	PUNCT
ejpam-6038	205	6	∩	∩	NOUN
ejpam-6038	205	7	(	(	PUNCT
ejpam-6038	205	8	y	y	PROPN
ejpam-6038	205	9	−	−	PROPN
ejpam-6038	205	10	σ1σ2	σ1σ2	NOUN
ejpam-6038	205	11	-	-	NUM
ejpam-6038	205	12	cl(v	cl(v	NOUN
ejpam-6038	205	13	)	)	PUNCT
ejpam-6038	205	14	)	)	PUNCT
ejpam-6038	205	15	=	=	SYM
ejpam-6038	205	16	∅	∅	NOUN
ejpam-6038	205	17	,	,	PUNCT
ejpam-6038	205	18	we	we	PRON
ejpam-6038	205	19	have	have	VERB
ejpam-6038	205	20	f(x	f(x	PROPN
ejpam-6038	205	21	)	)	PUNCT
ejpam-6038	205	22	̸∈	̸∈	PROPN
ejpam-6038	205	23	s(σ1	s(σ1	ADV
ejpam-6038	205	24	,	,	PUNCT
ejpam-6038	205	25	σ2)θ	σ2)θ	ADJ
ejpam-6038	205	26	-	-	PUNCT
ejpam-6038	205	27	cl(y	cl(y	NOUN
ejpam-6038	205	28	−	−	NOUN
ejpam-6038	205	29	σ1σ2	σ1σ2	NOUN
ejpam-6038	205	30	-	-	NUM
ejpam-6038	205	31	cl(v	cl(v	NOUN
ejpam-6038	205	32	)	)	PUNCT
ejpam-6038	205	33	)	)	PUNCT
ejpam-6038	205	34	and	and	CCONJ
ejpam-6038	205	35	hence	hence	ADV
ejpam-6038	205	36	x	x	X
ejpam-6038	205	37	̸∈	̸∈	PROPN
ejpam-6038	205	38	f−1(s(σ1	f−1(s(σ1	PROPN
ejpam-6038	205	39	,	,	PUNCT
ejpam-6038	205	40	σ2)θ	σ2)θ	ADJ
ejpam-6038	205	41	-	-	PUNCT
ejpam-6038	205	42	cl(y	cl(y	NOUN
ejpam-6038	205	43	−	−	NOUN
ejpam-6038	205	44	σ1σ2	σ1σ2	NOUN
ejpam-6038	205	45	-	-	NUM
ejpam-6038	205	46	cl(v	cl(v	NOUN
ejpam-6038	205	47	)	)	PUNCT
ejpam-6038	205	48	)	)	PUNCT
ejpam-6038	205	49	)	)	PUNCT
ejpam-6038	205	50	.	.	PUNCT
ejpam-6038	206	1	by	by	ADP
ejpam-6038	206	2	(	(	PUNCT
ejpam-6038	206	3	3	3	NUM
ejpam-6038	206	4	)	)	PUNCT
ejpam-6038	206	5	,	,	PUNCT
ejpam-6038	206	6	x	x	PROPN
ejpam-6038	206	7	̸∈	̸∈	PROPN
ejpam-6038	206	8	(	(	PUNCT
ejpam-6038	206	9	τ1	τ1	PROPN
ejpam-6038	206	10	,	,	PUNCT
ejpam-6038	206	11	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6038	206	12	−1(y	−1(y	PUNCT
ejpam-6038	206	13	−	−	PUNCT
ejpam-6038	206	14	σ1σ2	σ1σ2	NOUN
ejpam-6038	206	15	-	-	NUM
ejpam-6038	206	16	cl(v	cl(v	NOUN
ejpam-6038	206	17	)	)	PUNCT
ejpam-6038	206	18	)	)	PUNCT
ejpam-6038	206	19	)	)	PUNCT
ejpam-6038	206	20	.	.	PUNCT
ejpam-6038	207	1	there	there	PRON
ejpam-6038	207	2	exists	exist	VERB
ejpam-6038	207	3	a	a	DET
ejpam-6038	207	4	(	(	PUNCT
ejpam-6038	207	5	τ1	τ1	NOUN
ejpam-6038	207	6	,	,	PUNCT
ejpam-6038	207	7	τ2)p	τ2)p	ADJ
ejpam-6038	207	8	-	-	PUNCT
ejpam-6038	207	9	open	open	ADJ
ejpam-6038	207	10	set	set	NOUN
ejpam-6038	207	11	u	u	NOUN
ejpam-6038	207	12	of	of	ADP
ejpam-6038	207	13	x	x	PUNCT
ejpam-6038	207	14	containing	contain	VERB
ejpam-6038	207	15	x	x	PUNCT
ejpam-6038	207	16	such	such	ADJ
ejpam-6038	207	17	that	that	SCONJ
ejpam-6038	207	18	u	u	PRON
ejpam-6038	207	19	∩f−1(y	∩f−1(y	PUNCT
ejpam-6038	207	20	−σ1σ2	−σ1σ2	NOUN
ejpam-6038	207	21	-	-	NOUN
ejpam-6038	207	22	cl(v	cl(v	NOUN
ejpam-6038	207	23	)	)	PUNCT
ejpam-6038	207	24	)	)	PUNCT
ejpam-6038	208	1	=	=	NOUN
ejpam-6038	208	2	∅	∅	NOUN
ejpam-6038	208	3	;	;	PUNCT
ejpam-6038	208	4	hence	hence	ADV
ejpam-6038	208	5	f(u)∩	f(u)∩	PROPN
ejpam-6038	208	6	(	(	PUNCT
ejpam-6038	208	7	y	y	PROPN
ejpam-6038	208	8	−σ1σ2	−σ1σ2	PROPN
ejpam-6038	208	9	-	-	PUNCT
ejpam-6038	208	10	cl(v	cl(v	NOUN
ejpam-6038	208	11	)	)	PUNCT
ejpam-6038	208	12	)	)	PUNCT
ejpam-6038	209	1	=	=	PUNCT
ejpam-6038	209	2	∅.	∅.	ADP
ejpam-6038	209	3	this	this	PRON
ejpam-6038	209	4	shows	show	VERB
ejpam-6038	209	5	that	that	SCONJ
ejpam-6038	209	6	f(u	f(u	PROPN
ejpam-6038	209	7	)	)	PUNCT
ejpam-6038	209	8	⊆	⊆	NUM
ejpam-6038	209	9	σ1σ2	σ1σ2	NOUN
ejpam-6038	209	10	-	-	NUM
ejpam-6038	209	11	cl(v	cl(v	NOUN
ejpam-6038	209	12	)	)	PUNCT
ejpam-6038	209	13	.	.	PUNCT
ejpam-6038	210	1	thus	thus	ADV
ejpam-6038	210	2	by	by	ADP
ejpam-6038	210	3	theorem	theorem	NOUN
ejpam-6038	210	4	8	8	NUM
ejpam-6038	210	5	,	,	PUNCT
ejpam-6038	210	6	f	f	PROPN
ejpam-6038	210	7	is	be	AUX
ejpam-6038	210	8	almost	almost	ADV
ejpam-6038	210	9	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	210	10	,	,	PUNCT
ejpam-6038	210	11	τ2)pcontinuous	τ2)pcontinuous	ADJ
ejpam-6038	210	12	.	.	PUNCT
ejpam-6038	211	1	p.	p.	NOUN
ejpam-6038	211	2	pue	pue	NOUN
ejpam-6038	211	3	-	-	PUNCT
ejpam-6038	211	4	on	on	ADP
ejpam-6038	211	5	,	,	PUNCT
ejpam-6038	211	6	a.	a.	PROPN
ejpam-6038	211	7	sama	sama	PROPN
ejpam-6038	211	8	-	-	PUNCT
ejpam-6038	211	9	ae	ae	PROPN
ejpam-6038	211	10	,	,	PUNCT
ejpam-6038	211	11	c.	c.	PROPN
ejpam-6038	211	12	boonpok	boonpok	PROPN
ejpam-6038	211	13	/	/	SYM
ejpam-6038	211	14	eur	eur	PROPN
ejpam-6038	211	15	.	.	PUNCT
ejpam-6038	212	1	j.	j.	PROPN
ejpam-6038	212	2	pure	pure	PROPN
ejpam-6038	212	3	appl	appl	PROPN
ejpam-6038	212	4	.	.	PROPN
ejpam-6038	212	5	math	math	PROPN
ejpam-6038	212	6	,	,	PUNCT
ejpam-6038	212	7	18	18	NUM
ejpam-6038	212	8	(	(	PUNCT
ejpam-6038	212	9	2	2	NUM
ejpam-6038	212	10	)	)	PUNCT
ejpam-6038	212	11	(	(	PUNCT
ejpam-6038	212	12	2025	2025	NUM
ejpam-6038	212	13	)	)	PUNCT
ejpam-6038	212	14	,	,	PUNCT
ejpam-6038	212	15	6038	6038	NUM
ejpam-6038	212	16	8	8	NUM
ejpam-6038	212	17	of	of	ADP
ejpam-6038	212	18	11	11	NUM
ejpam-6038	212	19	theorem	theorem	VERB
ejpam-6038	212	20	10	10	NUM
ejpam-6038	212	21	.	.	PUNCT
ejpam-6038	213	1	for	for	ADP
ejpam-6038	213	2	a	a	DET
ejpam-6038	213	3	function	function	NOUN
ejpam-6038	213	4	f	f	NOUN
ejpam-6038	213	5	:	:	PUNCT
ejpam-6038	213	6	(	(	PUNCT
ejpam-6038	213	7	x	x	NOUN
ejpam-6038	213	8	,	,	PUNCT
ejpam-6038	213	9	τ1	τ1	NOUN
ejpam-6038	213	10	,	,	PUNCT
ejpam-6038	213	11	τ2	τ2	NOUN
ejpam-6038	213	12	)	)	PUNCT
ejpam-6038	213	13	→	→	SYM
ejpam-6038	213	14	(	(	PUNCT
ejpam-6038	213	15	y	y	PROPN
ejpam-6038	213	16	,	,	PUNCT
ejpam-6038	213	17	σ1	σ1	PROPN
ejpam-6038	213	18	,	,	PUNCT
ejpam-6038	213	19	σ2	σ2	NOUN
ejpam-6038	213	20	)	)	PUNCT
ejpam-6038	213	21	,	,	PUNCT
ejpam-6038	213	22	the	the	DET
ejpam-6038	213	23	following	follow	VERB
ejpam-6038	213	24	properties	property	NOUN
ejpam-6038	213	25	are	be	AUX
ejpam-6038	213	26	equivalent	equivalent	ADJ
ejpam-6038	213	27	:	:	PUNCT
ejpam-6038	213	28	(	(	PUNCT
ejpam-6038	213	29	1	1	X
ejpam-6038	213	30	)	)	PUNCT
ejpam-6038	213	31	f	f	NOUN
ejpam-6038	213	32	is	be	AUX
ejpam-6038	213	33	almost	almost	ADV
ejpam-6038	213	34	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	213	35	,	,	PUNCT
ejpam-6038	213	36	τ2)p	τ2)p	ADJ
ejpam-6038	213	37	-	-	NOUN
ejpam-6038	213	38	continuous	continuous	ADJ
ejpam-6038	213	39	;	;	PUNCT
ejpam-6038	213	40	(	(	PUNCT
ejpam-6038	213	41	2	2	X
ejpam-6038	213	42	)	)	PUNCT
ejpam-6038	213	43	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	213	44	-	-	PUNCT
ejpam-6038	213	45	cl(v	cl(v	NOUN
ejpam-6038	213	46	)	)	PUNCT
ejpam-6038	213	47	)	)	PUNCT
ejpam-6038	214	1	is	be	AUX
ejpam-6038	214	2	(	(	PUNCT
ejpam-6038	214	3	τ1	τ1	NOUN
ejpam-6038	214	4	,	,	PUNCT
ejpam-6038	214	5	τ2)p	τ2)p	NOUN
ejpam-6038	214	6	-	-	PUNCT
ejpam-6038	214	7	open	open	ADJ
ejpam-6038	214	8	in	in	ADP
ejpam-6038	214	9	x	x	PUNCT
ejpam-6038	214	10	for	for	ADP
ejpam-6038	214	11	every	every	DET
ejpam-6038	214	12	(	(	PUNCT
ejpam-6038	214	13	σ1	σ1	PROPN
ejpam-6038	214	14	,	,	PUNCT
ejpam-6038	214	15	σ2)β	σ2)β	NOUN
ejpam-6038	214	16	-	-	PUNCT
ejpam-6038	214	17	open	open	NOUN
ejpam-6038	214	18	set	set	NOUN
ejpam-6038	214	19	v	v	NOUN
ejpam-6038	214	20	of	of	ADP
ejpam-6038	214	21	y	y	PROPN
ejpam-6038	214	22	;	;	PUNCT
ejpam-6038	214	23	(	(	PUNCT
ejpam-6038	214	24	3	3	X
ejpam-6038	214	25	)	)	PUNCT
ejpam-6038	214	26	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	214	27	-	-	PUNCT
ejpam-6038	214	28	cl(v	cl(v	NOUN
ejpam-6038	214	29	)	)	PUNCT
ejpam-6038	214	30	)	)	PUNCT
ejpam-6038	215	1	is	be	AUX
ejpam-6038	215	2	(	(	PUNCT
ejpam-6038	215	3	τ1	τ1	NOUN
ejpam-6038	215	4	,	,	PUNCT
ejpam-6038	215	5	τ2)p	τ2)p	NOUN
ejpam-6038	215	6	-	-	PUNCT
ejpam-6038	215	7	open	open	ADJ
ejpam-6038	215	8	in	in	ADP
ejpam-6038	215	9	x	x	PUNCT
ejpam-6038	215	10	for	for	ADP
ejpam-6038	215	11	every	every	DET
ejpam-6038	215	12	(	(	PUNCT
ejpam-6038	215	13	σ1	σ1	PROPN
ejpam-6038	215	14	,	,	PUNCT
ejpam-6038	215	15	σ2)s	σ2)s	NOUN
ejpam-6038	215	16	-	-	PUNCT
ejpam-6038	215	17	open	open	NOUN
ejpam-6038	215	18	set	set	NOUN
ejpam-6038	215	19	v	v	NOUN
ejpam-6038	215	20	of	of	ADP
ejpam-6038	215	21	y	y	PROPN
ejpam-6038	215	22	;	;	PUNCT
ejpam-6038	215	23	(	(	PUNCT
ejpam-6038	215	24	4	4	X
ejpam-6038	215	25	)	)	PUNCT
ejpam-6038	215	26	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	215	27	-	-	PUNCT
ejpam-6038	215	28	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	215	29	-	-	PUNCT
ejpam-6038	215	30	cl(v	cl(v	NOUN
ejpam-6038	215	31	)	)	PUNCT
ejpam-6038	215	32	)	)	PUNCT
ejpam-6038	215	33	)	)	PUNCT
ejpam-6038	216	1	is	be	AUX
ejpam-6038	216	2	(	(	PUNCT
ejpam-6038	216	3	τ1	τ1	NOUN
ejpam-6038	216	4	,	,	PUNCT
ejpam-6038	216	5	τ2)p	τ2)p	NOUN
ejpam-6038	216	6	-	-	PUNCT
ejpam-6038	216	7	closed	closed	ADJ
ejpam-6038	216	8	in	in	ADP
ejpam-6038	216	9	x	x	PUNCT
ejpam-6038	216	10	for	for	ADP
ejpam-6038	216	11	every	every	DET
ejpam-6038	216	12	(	(	PUNCT
ejpam-6038	216	13	σ1	σ1	PROPN
ejpam-6038	216	14	,	,	PUNCT
ejpam-6038	216	15	σ2)p	σ2)p	NOUN
ejpam-6038	216	16	-	-	PUNCT
ejpam-6038	216	17	open	open	NOUN
ejpam-6038	216	18	set	set	NOUN
ejpam-6038	216	19	v	v	NOUN
ejpam-6038	216	20	of	of	ADP
ejpam-6038	216	21	y	y	PROPN
ejpam-6038	216	22	.	.	PUNCT
ejpam-6038	217	1	proof	proof	NOUN
ejpam-6038	217	2	.	.	PUNCT
ejpam-6038	218	1	(	(	PUNCT
ejpam-6038	218	2	1	1	X
ejpam-6038	218	3	)	)	PUNCT
ejpam-6038	218	4	⇒	⇒	NOUN
ejpam-6038	218	5	(	(	PUNCT
ejpam-6038	218	6	2	2	NUM
ejpam-6038	218	7	):	):	PUNCT
ejpam-6038	218	8	let	let	VERB
ejpam-6038	218	9	v	v	PART
ejpam-6038	218	10	be	be	AUX
ejpam-6038	218	11	any	any	DET
ejpam-6038	218	12	(	(	PUNCT
ejpam-6038	218	13	σ1	σ1	PROPN
ejpam-6038	218	14	,	,	PUNCT
ejpam-6038	218	15	σ2)β	σ2)β	NOUN
ejpam-6038	218	16	-	-	PUNCT
ejpam-6038	218	17	open	open	ADJ
ejpam-6038	218	18	set	set	NOUN
ejpam-6038	218	19	of	of	ADP
ejpam-6038	218	20	y	y	PROPN
ejpam-6038	218	21	.	.	PUNCT
ejpam-6038	219	1	then	then	ADV
ejpam-6038	219	2	,	,	PUNCT
ejpam-6038	219	3	σ1σ2	σ1σ2	NOUN
ejpam-6038	219	4	-	-	NUM
ejpam-6038	219	5	cl(v	cl(v	NOUN
ejpam-6038	219	6	)	)	PUNCT
ejpam-6038	219	7	is	be	AUX
ejpam-6038	219	8	(	(	PUNCT
ejpam-6038	219	9	σ1	σ1	PROPN
ejpam-6038	219	10	,	,	PUNCT
ejpam-6038	219	11	σ2)rclosed	σ2)rclose	VERB
ejpam-6038	219	12	in	in	ADP
ejpam-6038	219	13	y	y	PROPN
ejpam-6038	219	14	,	,	PUNCT
ejpam-6038	219	15	by	by	ADP
ejpam-6038	219	16	theorem	theorem	NOUN
ejpam-6038	219	17	1	1	NUM
ejpam-6038	219	18	we	we	PRON
ejpam-6038	219	19	have	have	AUX
ejpam-6038	219	20	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	219	21	-	-	PUNCT
ejpam-6038	219	22	cl(v	cl(v	NOUN
ejpam-6038	219	23	)	)	PUNCT
ejpam-6038	219	24	)	)	PUNCT
ejpam-6038	220	1	is	be	AUX
ejpam-6038	220	2	(	(	PUNCT
ejpam-6038	220	3	τ1	τ1	NOUN
ejpam-6038	220	4	,	,	PUNCT
ejpam-6038	220	5	τ2)p	τ2)p	NOUN
ejpam-6038	220	6	-	-	PUNCT
ejpam-6038	220	7	open	open	ADJ
ejpam-6038	220	8	in	in	ADP
ejpam-6038	220	9	x.	x.	NOUN
ejpam-6038	220	10	(	(	PUNCT
ejpam-6038	220	11	2	2	NUM
ejpam-6038	220	12	)	)	PUNCT
ejpam-6038	220	13	⇒	⇒	NOUN
ejpam-6038	220	14	(	(	PUNCT
ejpam-6038	220	15	3	3	NUM
ejpam-6038	220	16	):	):	PUNCT
ejpam-6038	220	17	this	this	PRON
ejpam-6038	220	18	is	be	AUX
ejpam-6038	220	19	obvious	obvious	ADJ
ejpam-6038	220	20	since	since	SCONJ
ejpam-6038	220	21	every	every	DET
ejpam-6038	220	22	(	(	PUNCT
ejpam-6038	220	23	σ1	σ1	PROPN
ejpam-6038	220	24	,	,	PUNCT
ejpam-6038	220	25	σ2)s	σ2)s	NOUN
ejpam-6038	220	26	-	-	PUNCT
ejpam-6038	220	27	open	open	ADJ
ejpam-6038	220	28	set	set	NOUN
ejpam-6038	220	29	is	be	AUX
ejpam-6038	220	30	(	(	PUNCT
ejpam-6038	220	31	σ1	σ1	PROPN
ejpam-6038	220	32	,	,	PUNCT
ejpam-6038	220	33	σ2)β	σ2)β	NOUN
ejpam-6038	220	34	-	-	PUNCT
ejpam-6038	220	35	open	open	ADJ
ejpam-6038	220	36	.	.	PUNCT
ejpam-6038	221	1	(	(	PUNCT
ejpam-6038	221	2	3	3	X
ejpam-6038	221	3	)	)	PUNCT
ejpam-6038	221	4	⇒	⇒	NOUN
ejpam-6038	221	5	(	(	PUNCT
ejpam-6038	221	6	4	4	NUM
ejpam-6038	221	7	):	):	PUNCT
ejpam-6038	221	8	let	let	VERB
ejpam-6038	221	9	v	v	PART
ejpam-6038	221	10	be	be	AUX
ejpam-6038	221	11	any	any	DET
ejpam-6038	221	12	(	(	PUNCT
ejpam-6038	221	13	σ1	σ1	PROPN
ejpam-6038	221	14	,	,	PUNCT
ejpam-6038	221	15	σ2)p	σ2)p	NOUN
ejpam-6038	221	16	-	-	PUNCT
ejpam-6038	221	17	open	open	ADJ
ejpam-6038	221	18	set	set	NOUN
ejpam-6038	221	19	of	of	ADP
ejpam-6038	221	20	y	y	PROPN
ejpam-6038	221	21	.	.	PUNCT
ejpam-6038	222	1	then	then	ADV
ejpam-6038	222	2	,	,	PUNCT
ejpam-6038	222	3	y	y	PROPN
ejpam-6038	222	4	−	−	NUM
ejpam-6038	222	5	σ1σ2	σ1σ2	NOUN
ejpam-6038	222	6	-	-	NUM
ejpam-6038	222	7	cl(v	cl(v	NOUN
ejpam-6038	222	8	)	)	PUNCT
ejpam-6038	222	9	is	be	AUX
ejpam-6038	222	10	(	(	PUNCT
ejpam-6038	222	11	σ1	σ1	PROPN
ejpam-6038	222	12	,	,	PUNCT
ejpam-6038	222	13	σ2)rclosed	σ2)rclose	VERB
ejpam-6038	222	14	and	and	CCONJ
ejpam-6038	222	15	hence	hence	ADV
ejpam-6038	222	16	y	y	NOUN
ejpam-6038	222	17	−	−	NUM
ejpam-6038	222	18	σ1σ2	σ1σ2	NOUN
ejpam-6038	222	19	-	-	NUM
ejpam-6038	222	20	cl(v	cl(v	NOUN
ejpam-6038	222	21	)	)	PUNCT
ejpam-6038	222	22	is	be	AUX
ejpam-6038	222	23	(	(	PUNCT
ejpam-6038	222	24	σ1	σ1	PROPN
ejpam-6038	222	25	,	,	PUNCT
ejpam-6038	222	26	σ2)s	σ2)s	NOUN
ejpam-6038	222	27	-	-	PUNCT
ejpam-6038	222	28	open	open	ADJ
ejpam-6038	222	29	.	.	PUNCT
ejpam-6038	223	1	thus	thus	ADV
ejpam-6038	223	2	by	by	ADP
ejpam-6038	223	3	(	(	PUNCT
ejpam-6038	223	4	3	3	NUM
ejpam-6038	223	5	)	)	PUNCT
ejpam-6038	223	6	,	,	PUNCT
ejpam-6038	223	7	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	223	8	-	-	PUNCT
ejpam-6038	223	9	cl(y	cl(y	NOUN
ejpam-6038	223	10	−	−	NOUN
ejpam-6038	223	11	σ1σ2	σ1σ2	NUM
ejpam-6038	223	12	-	-	PUNCT
ejpam-6038	223	13	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	223	14	-	-	PUNCT
ejpam-6038	223	15	cl(v	cl(v	NOUN
ejpam-6038	223	16	)	)	PUNCT
ejpam-6038	223	17	)	)	PUNCT
ejpam-6038	223	18	)	)	PUNCT
ejpam-6038	223	19	)	)	PUNCT
ejpam-6038	224	1	is	be	AUX
ejpam-6038	224	2	(	(	PUNCT
ejpam-6038	224	3	τ1	τ1	NOUN
ejpam-6038	224	4	,	,	PUNCT
ejpam-6038	224	5	τ2)p	τ2)p	NOUN
ejpam-6038	224	6	-	-	PUNCT
ejpam-6038	224	7	open	open	ADJ
ejpam-6038	224	8	in	in	ADP
ejpam-6038	224	9	x.	x.	NOUN
ejpam-6038	224	10	since	since	SCONJ
ejpam-6038	224	11	x	x	PROPN
ejpam-6038	224	12	−	−	PRON
ejpam-6038	224	13	f−1(σ1σ2	f−1(σ1σ2	VERB
ejpam-6038	224	14	-	-	PUNCT
ejpam-6038	224	15	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	224	16	-	-	PUNCT
ejpam-6038	224	17	cl(v	cl(v	NOUN
ejpam-6038	224	18	)	)	PUNCT
ejpam-6038	224	19	)	)	PUNCT
ejpam-6038	224	20	)	)	PUNCT
ejpam-6038	225	1	=	=	PUNCT
ejpam-6038	225	2	f−1(y	f−1(y	PROPN
ejpam-6038	225	3	−	−	NOUN
ejpam-6038	225	4	σ1σ2	σ1σ2	X
ejpam-6038	225	5	-	-	PUNCT
ejpam-6038	225	6	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	225	7	-	-	PUNCT
ejpam-6038	225	8	cl(v	cl(v	NOUN
ejpam-6038	225	9	)	)	PUNCT
ejpam-6038	225	10	)	)	PUNCT
ejpam-6038	225	11	)	)	PUNCT
ejpam-6038	226	1	=	=	SYM
ejpam-6038	226	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	226	3	-	-	PUNCT
ejpam-6038	226	4	cl(y	cl(y	NOUN
ejpam-6038	226	5	−	−	NOUN
ejpam-6038	226	6	σ1σ2	σ1σ2	NUM
ejpam-6038	226	7	-	-	PUNCT
ejpam-6038	226	8	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	226	9	-	-	PUNCT
ejpam-6038	226	10	cl(v	cl(v	NOUN
ejpam-6038	226	11	)	)	PUNCT
ejpam-6038	226	12	)	)	PUNCT
ejpam-6038	226	13	)	)	PUNCT
ejpam-6038	226	14	)	)	PUNCT
ejpam-6038	226	15	,	,	PUNCT
ejpam-6038	226	16	we	we	PRON
ejpam-6038	226	17	have	have	AUX
ejpam-6038	226	18	f−1(σ1σ2	f−1(σ1σ2	VERB
ejpam-6038	226	19	-	-	PUNCT
ejpam-6038	226	20	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	226	21	-	-	PUNCT
ejpam-6038	226	22	cl(v	cl(v	NOUN
ejpam-6038	226	23	)	)	PUNCT
ejpam-6038	226	24	)	)	PUNCT
ejpam-6038	226	25	)	)	PUNCT
ejpam-6038	227	1	is	be	AUX
ejpam-6038	227	2	(	(	PUNCT
ejpam-6038	227	3	τ1	τ1	NOUN
ejpam-6038	227	4	,	,	PUNCT
ejpam-6038	227	5	τ2)p	τ2)p	NOUN
ejpam-6038	227	6	-	-	PUNCT
ejpam-6038	227	7	closed	closed	ADJ
ejpam-6038	227	8	in	in	ADP
ejpam-6038	227	9	x.	x.	NOUN
ejpam-6038	227	10	(	(	PUNCT
ejpam-6038	227	11	4	4	NUM
ejpam-6038	227	12	)	)	PUNCT
ejpam-6038	227	13	⇒	⇒	NOUN
ejpam-6038	227	14	(	(	PUNCT
ejpam-6038	227	15	1	1	NUM
ejpam-6038	227	16	):	):	PUNCT
ejpam-6038	227	17	let	let	VERB
ejpam-6038	227	18	v	v	PART
ejpam-6038	227	19	be	be	AUX
ejpam-6038	227	20	any	any	DET
ejpam-6038	227	21	(	(	PUNCT
ejpam-6038	227	22	σ1	σ1	NOUN
ejpam-6038	227	23	,	,	PUNCT
ejpam-6038	227	24	σ2)r	σ2)r	NOUN
ejpam-6038	227	25	-	-	PUNCT
ejpam-6038	227	26	open	open	ADJ
ejpam-6038	227	27	set	set	NOUN
ejpam-6038	227	28	of	of	ADP
ejpam-6038	227	29	y	y	PROPN
ejpam-6038	227	30	.	.	PUNCT
ejpam-6038	228	1	then	then	ADV
ejpam-6038	228	2	,	,	PUNCT
ejpam-6038	228	3	v	v	NOUN
ejpam-6038	228	4	is	be	AUX
ejpam-6038	228	5	(	(	PUNCT
ejpam-6038	228	6	σ1	σ1	PROPN
ejpam-6038	228	7	,	,	PUNCT
ejpam-6038	228	8	σ2)p	σ2)p	NOUN
ejpam-6038	228	9	-	-	PUNCT
ejpam-6038	228	10	open	open	ADJ
ejpam-6038	228	11	in	in	ADP
ejpam-6038	228	12	y	y	PROPN
ejpam-6038	228	13	.	.	PUNCT
ejpam-6038	229	1	by	by	ADP
ejpam-6038	229	2	(	(	PUNCT
ejpam-6038	229	3	4	4	NUM
ejpam-6038	229	4	)	)	PUNCT
ejpam-6038	229	5	,	,	PUNCT
ejpam-6038	229	6	we	we	PRON
ejpam-6038	229	7	have	have	VERB
ejpam-6038	229	8	f−1(v	f−1(v	NOUN
ejpam-6038	229	9	)	)	PUNCT
ejpam-6038	230	1	=	=	SYM
ejpam-6038	230	2	f−1(σ1σ2	f−1(σ1σ2	VERB
ejpam-6038	230	3	-	-	PUNCT
ejpam-6038	230	4	int(σ1σ2	int(σ1σ2	NOUN
ejpam-6038	230	5	-	-	PUNCT
ejpam-6038	230	6	cl(v	cl(v	NOUN
ejpam-6038	230	7	)	)	PUNCT
ejpam-6038	230	8	)	)	PUNCT
ejpam-6038	230	9	)	)	PUNCT
ejpam-6038	231	1	is	be	AUX
ejpam-6038	231	2	(	(	PUNCT
ejpam-6038	231	3	τ1	τ1	NOUN
ejpam-6038	231	4	,	,	PUNCT
ejpam-6038	231	5	τ2)p	τ2)p	NOUN
ejpam-6038	231	6	-	-	PUNCT
ejpam-6038	231	7	closed	closed	ADJ
ejpam-6038	231	8	in	in	ADP
ejpam-6038	231	9	x.	x.	NOUN
ejpam-6038	231	10	it	it	PRON
ejpam-6038	231	11	follows	follow	VERB
ejpam-6038	231	12	from	from	ADP
ejpam-6038	231	13	theorem	theorem	ADJ
ejpam-6038	231	14	1	1	NUM
ejpam-6038	231	15	that	that	SCONJ
ejpam-6038	231	16	f	f	PROPN
ejpam-6038	231	17	is	be	AUX
ejpam-6038	231	18	almost	almost	ADV
ejpam-6038	231	19	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	231	20	,	,	PUNCT
ejpam-6038	231	21	τ2)p	τ2)p	ADJ
ejpam-6038	231	22	-	-	NOUN
ejpam-6038	231	23	continuous	continuous	ADJ
ejpam-6038	231	24	.	.	PUNCT
ejpam-6038	232	1	lemma	lemma	PROPN
ejpam-6038	232	2	3	3	X
ejpam-6038	232	3	.	.	PUNCT
ejpam-6038	233	1	for	for	ADP
ejpam-6038	233	2	a	a	DET
ejpam-6038	233	3	bitopological	bitopological	ADJ
ejpam-6038	233	4	space	space	NOUN
ejpam-6038	233	5	(	(	PUNCT
ejpam-6038	233	6	x	x	NOUN
ejpam-6038	233	7	,	,	PUNCT
ejpam-6038	233	8	τ1	τ1	NOUN
ejpam-6038	233	9	,	,	PUNCT
ejpam-6038	233	10	τ2	τ2	NOUN
ejpam-6038	233	11	)	)	PUNCT
ejpam-6038	233	12	,	,	PUNCT
ejpam-6038	233	13	the	the	DET
ejpam-6038	233	14	following	follow	VERB
ejpam-6038	233	15	properties	property	NOUN
ejpam-6038	233	16	hold	hold	VERB
ejpam-6038	233	17	:	:	PUNCT
ejpam-6038	233	18	(	(	PUNCT
ejpam-6038	233	19	1	1	X
ejpam-6038	233	20	)	)	PUNCT
ejpam-6038	233	21	α(τ1	α(τ1	NOUN
ejpam-6038	233	22	,	,	PUNCT
ejpam-6038	233	23	τ2)-cl(v	τ2)-cl(v	NOUN
ejpam-6038	233	24	)	)	PUNCT
ejpam-6038	233	25	=	=	PUNCT
ejpam-6038	234	1	τ1τ2	τ1τ2	NOUN
ejpam-6038	234	2	-	-	NOUN
ejpam-6038	234	3	cl(v	cl(v	X
ejpam-6038	234	4	)	)	PUNCT
ejpam-6038	234	5	for	for	ADP
ejpam-6038	234	6	every	every	DET
ejpam-6038	234	7	(	(	PUNCT
ejpam-6038	234	8	τ1	τ1	NOUN
ejpam-6038	234	9	,	,	PUNCT
ejpam-6038	234	10	τ2)β	τ2)β	ADJ
ejpam-6038	234	11	-	-	PUNCT
ejpam-6038	234	12	open	open	NOUN
ejpam-6038	234	13	set	set	NOUN
ejpam-6038	234	14	v	v	NOUN
ejpam-6038	234	15	of	of	ADP
ejpam-6038	234	16	x	x	PRON
ejpam-6038	234	17	;	;	PUNCT
ejpam-6038	234	18	(	(	PUNCT
ejpam-6038	234	19	2	2	X
ejpam-6038	234	20	)	)	PUNCT
ejpam-6038	234	21	(	(	PUNCT
ejpam-6038	234	22	τ1	τ1	NOUN
ejpam-6038	234	23	,	,	PUNCT
ejpam-6038	234	24	τ2)-pcl(v	τ2)-pcl(v	NOUN
ejpam-6038	234	25	)	)	PUNCT
ejpam-6038	234	26	=	=	PUNCT
ejpam-6038	235	1	τ1τ2	τ1τ2	NOUN
ejpam-6038	235	2	-	-	NOUN
ejpam-6038	235	3	cl(v	cl(v	X
ejpam-6038	235	4	)	)	PUNCT
ejpam-6038	235	5	for	for	ADP
ejpam-6038	235	6	every	every	DET
ejpam-6038	235	7	(	(	PUNCT
ejpam-6038	235	8	τ1	τ1	NOUN
ejpam-6038	235	9	,	,	PUNCT
ejpam-6038	235	10	τ2)s	τ2)s	NOUN
ejpam-6038	235	11	-	-	PUNCT
ejpam-6038	235	12	open	open	ADJ
ejpam-6038	235	13	set	set	NOUN
ejpam-6038	235	14	v	v	NOUN
ejpam-6038	235	15	of	of	ADP
ejpam-6038	235	16	x	x	PRON
ejpam-6038	235	17	;	;	PUNCT
ejpam-6038	235	18	(	(	PUNCT
ejpam-6038	235	19	3	3	X
ejpam-6038	235	20	)	)	PUNCT
ejpam-6038	235	21	(	(	PUNCT
ejpam-6038	235	22	τ1	τ1	NOUN
ejpam-6038	235	23	,	,	PUNCT
ejpam-6038	235	24	τ2)-scl(v	τ2)-scl(v	NOUN
ejpam-6038	235	25	)	)	PUNCT
ejpam-6038	236	1	=	=	PUNCT
ejpam-6038	237	1	τ1τ2	τ1τ2	NOUN
ejpam-6038	237	2	-	-	NOUN
ejpam-6038	237	3	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	237	4	-	-	PUNCT
ejpam-6038	237	5	cl(v	cl(v	NOUN
ejpam-6038	237	6	)	)	PUNCT
ejpam-6038	237	7	)	)	PUNCT
ejpam-6038	237	8	for	for	ADP
ejpam-6038	237	9	every	every	DET
ejpam-6038	237	10	(	(	PUNCT
ejpam-6038	237	11	τ1	τ1	NOUN
ejpam-6038	237	12	,	,	PUNCT
ejpam-6038	237	13	τ2)p	τ2)p	ADJ
ejpam-6038	237	14	-	-	PUNCT
ejpam-6038	237	15	open	open	ADJ
ejpam-6038	237	16	set	set	NOUN
ejpam-6038	237	17	v	v	NOUN
ejpam-6038	237	18	of	of	ADP
ejpam-6038	237	19	x.	x.	NOUN
ejpam-6038	237	20	corollary	corollary	NOUN
ejpam-6038	237	21	1	1	NUM
ejpam-6038	237	22	.	.	PUNCT
ejpam-6038	237	23	for	for	ADP
ejpam-6038	237	24	a	a	DET
ejpam-6038	237	25	function	function	NOUN
ejpam-6038	237	26	f	f	NOUN
ejpam-6038	237	27	:	:	PUNCT
ejpam-6038	237	28	(	(	PUNCT
ejpam-6038	237	29	x	x	NOUN
ejpam-6038	237	30	,	,	PUNCT
ejpam-6038	237	31	τ1	τ1	NOUN
ejpam-6038	237	32	,	,	PUNCT
ejpam-6038	237	33	τ2	τ2	NOUN
ejpam-6038	237	34	)	)	PUNCT
ejpam-6038	237	35	→	→	SYM
ejpam-6038	237	36	(	(	PUNCT
ejpam-6038	237	37	y	y	PROPN
ejpam-6038	237	38	,	,	PUNCT
ejpam-6038	237	39	σ1	σ1	PROPN
ejpam-6038	237	40	,	,	PUNCT
ejpam-6038	237	41	σ2	σ2	NOUN
ejpam-6038	237	42	)	)	PUNCT
ejpam-6038	237	43	,	,	PUNCT
ejpam-6038	237	44	the	the	DET
ejpam-6038	237	45	following	follow	VERB
ejpam-6038	237	46	properties	property	NOUN
ejpam-6038	237	47	are	be	AUX
ejpam-6038	237	48	equivalent	equivalent	ADJ
ejpam-6038	237	49	:	:	PUNCT
ejpam-6038	237	50	(	(	PUNCT
ejpam-6038	237	51	1	1	X
ejpam-6038	237	52	)	)	PUNCT
ejpam-6038	237	53	f	f	NOUN
ejpam-6038	237	54	is	be	AUX
ejpam-6038	237	55	almost	almost	ADV
ejpam-6038	237	56	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	237	57	,	,	PUNCT
ejpam-6038	237	58	τ2)p	τ2)p	ADJ
ejpam-6038	237	59	-	-	NOUN
ejpam-6038	237	60	continuous	continuous	ADJ
ejpam-6038	237	61	;	;	PUNCT
ejpam-6038	237	62	(	(	PUNCT
ejpam-6038	237	63	2	2	X
ejpam-6038	237	64	)	)	PUNCT
ejpam-6038	237	65	f−1(α(σ1	f−1(α(σ1	PROPN
ejpam-6038	237	66	,	,	PUNCT
ejpam-6038	237	67	σ2)-cl(v	σ2)-cl(v	NOUN
ejpam-6038	237	68	)	)	PUNCT
ejpam-6038	237	69	)	)	PUNCT
ejpam-6038	237	70	is	be	AUX
ejpam-6038	237	71	(	(	PUNCT
ejpam-6038	237	72	τ1	τ1	NOUN
ejpam-6038	237	73	,	,	PUNCT
ejpam-6038	237	74	τ2)p	τ2)p	NOUN
ejpam-6038	237	75	-	-	PUNCT
ejpam-6038	237	76	open	open	ADJ
ejpam-6038	237	77	in	in	ADP
ejpam-6038	237	78	x	x	PUNCT
ejpam-6038	237	79	for	for	ADP
ejpam-6038	237	80	every	every	DET
ejpam-6038	237	81	(	(	PUNCT
ejpam-6038	237	82	σ1	σ1	PROPN
ejpam-6038	237	83	,	,	PUNCT
ejpam-6038	237	84	σ2)β	σ2)β	NOUN
ejpam-6038	237	85	-	-	PUNCT
ejpam-6038	237	86	open	open	NOUN
ejpam-6038	237	87	set	set	NOUN
ejpam-6038	237	88	v	v	NOUN
ejpam-6038	237	89	of	of	ADP
ejpam-6038	237	90	y	y	PROPN
ejpam-6038	237	91	;	;	PUNCT
ejpam-6038	237	92	(	(	PUNCT
ejpam-6038	237	93	3	3	X
ejpam-6038	237	94	)	)	PUNCT
ejpam-6038	237	95	f−1((σ1	f−1((σ1	NOUN
ejpam-6038	237	96	,	,	PUNCT
ejpam-6038	237	97	σ2)-pcl(v	σ2)-pcl(v	NOUN
ejpam-6038	237	98	)	)	PUNCT
ejpam-6038	237	99	)	)	PUNCT
ejpam-6038	238	1	is	be	AUX
ejpam-6038	238	2	(	(	PUNCT
ejpam-6038	238	3	τ1	τ1	NOUN
ejpam-6038	238	4	,	,	PUNCT
ejpam-6038	238	5	τ2)p	τ2)p	NOUN
ejpam-6038	238	6	-	-	PUNCT
ejpam-6038	238	7	open	open	ADJ
ejpam-6038	238	8	in	in	ADP
ejpam-6038	238	9	x	x	PUNCT
ejpam-6038	238	10	for	for	ADP
ejpam-6038	238	11	every	every	DET
ejpam-6038	238	12	(	(	PUNCT
ejpam-6038	238	13	σ1	σ1	PROPN
ejpam-6038	238	14	,	,	PUNCT
ejpam-6038	238	15	σ2)s	σ2)s	NOUN
ejpam-6038	238	16	-	-	PUNCT
ejpam-6038	238	17	open	open	NOUN
ejpam-6038	238	18	set	set	NOUN
ejpam-6038	238	19	v	v	NOUN
ejpam-6038	238	20	of	of	ADP
ejpam-6038	238	21	y	y	PROPN
ejpam-6038	238	22	;	;	PUNCT
ejpam-6038	238	23	(	(	PUNCT
ejpam-6038	238	24	4	4	X
ejpam-6038	238	25	)	)	PUNCT
ejpam-6038	238	26	f−1((σ1	f−1((σ1	NOUN
ejpam-6038	238	27	,	,	PUNCT
ejpam-6038	238	28	σ2)-scl(v	σ2)-scl(v	NOUN
ejpam-6038	238	29	)	)	PUNCT
ejpam-6038	238	30	)	)	PUNCT
ejpam-6038	239	1	is	be	AUX
ejpam-6038	239	2	(	(	PUNCT
ejpam-6038	239	3	τ1	τ1	NOUN
ejpam-6038	239	4	,	,	PUNCT
ejpam-6038	239	5	τ2)p	τ2)p	NOUN
ejpam-6038	239	6	-	-	PUNCT
ejpam-6038	239	7	closed	closed	ADJ
ejpam-6038	239	8	in	in	ADP
ejpam-6038	239	9	x	x	PUNCT
ejpam-6038	239	10	for	for	ADP
ejpam-6038	239	11	every	every	DET
ejpam-6038	239	12	(	(	PUNCT
ejpam-6038	239	13	σ1	σ1	PROPN
ejpam-6038	239	14	,	,	PUNCT
ejpam-6038	239	15	σ2)p	σ2)p	NOUN
ejpam-6038	239	16	-	-	PUNCT
ejpam-6038	239	17	open	open	NOUN
ejpam-6038	239	18	set	set	NOUN
ejpam-6038	239	19	v	v	NOUN
ejpam-6038	239	20	of	of	ADP
ejpam-6038	239	21	y	y	PROPN
ejpam-6038	239	22	.	.	PUNCT
ejpam-6038	240	1	p.	p.	NOUN
ejpam-6038	240	2	pue	pue	NOUN
ejpam-6038	240	3	-	-	PUNCT
ejpam-6038	240	4	on	on	ADP
ejpam-6038	240	5	,	,	PUNCT
ejpam-6038	240	6	a.	a.	PROPN
ejpam-6038	240	7	sama	sama	PROPN
ejpam-6038	240	8	-	-	PUNCT
ejpam-6038	240	9	ae	ae	PROPN
ejpam-6038	240	10	,	,	PUNCT
ejpam-6038	240	11	c.	c.	PROPN
ejpam-6038	240	12	boonpok	boonpok	PROPN
ejpam-6038	240	13	/	/	SYM
ejpam-6038	240	14	eur	eur	PROPN
ejpam-6038	240	15	.	.	PUNCT
ejpam-6038	241	1	j.	j.	PROPN
ejpam-6038	241	2	pure	pure	PROPN
ejpam-6038	241	3	appl	appl	PROPN
ejpam-6038	241	4	.	.	PROPN
ejpam-6038	241	5	math	math	PROPN
ejpam-6038	241	6	,	,	PUNCT
ejpam-6038	241	7	18	18	NUM
ejpam-6038	241	8	(	(	PUNCT
ejpam-6038	241	9	2	2	NUM
ejpam-6038	241	10	)	)	PUNCT
ejpam-6038	241	11	(	(	PUNCT
ejpam-6038	241	12	2025	2025	NUM
ejpam-6038	241	13	)	)	PUNCT
ejpam-6038	241	14	,	,	PUNCT
ejpam-6038	241	15	6038	6038	NUM
ejpam-6038	241	16	9	9	NUM
ejpam-6038	241	17	of	of	ADP
ejpam-6038	241	18	11	11	NUM
ejpam-6038	241	19	proof	proof	NOUN
ejpam-6038	241	20	.	.	PUNCT
ejpam-6038	242	1	this	this	PRON
ejpam-6038	242	2	is	be	AUX
ejpam-6038	242	3	an	an	DET
ejpam-6038	242	4	immediate	immediate	ADJ
ejpam-6038	242	5	consequence	consequence	NOUN
ejpam-6038	242	6	of	of	ADP
ejpam-6038	242	7	theorem	theorem	ADJ
ejpam-6038	242	8	10	10	NUM
ejpam-6038	242	9	and	and	CCONJ
ejpam-6038	242	10	lemma	lemma	PROPN
ejpam-6038	242	11	3	3	X
ejpam-6038	242	12	.	.	PUNCT
ejpam-6038	242	13	definition	definition	NOUN
ejpam-6038	242	14	12	12	NUM
ejpam-6038	242	15	.	.	PUNCT
ejpam-6038	243	1	[	[	X
ejpam-6038	243	2	20	20	NUM
ejpam-6038	243	3	]	]	PUNCT
ejpam-6038	243	4	a	a	DET
ejpam-6038	243	5	function	function	NOUN
ejpam-6038	243	6	f	f	NOUN
ejpam-6038	243	7	:	:	PUNCT
ejpam-6038	243	8	(	(	PUNCT
ejpam-6038	243	9	x	x	NOUN
ejpam-6038	243	10	,	,	PUNCT
ejpam-6038	243	11	τ1	τ1	NOUN
ejpam-6038	243	12	,	,	PUNCT
ejpam-6038	243	13	τ2	τ2	NOUN
ejpam-6038	243	14	)	)	PUNCT
ejpam-6038	243	15	→	→	SYM
ejpam-6038	243	16	(	(	PUNCT
ejpam-6038	243	17	y	y	PROPN
ejpam-6038	243	18	,	,	PUNCT
ejpam-6038	243	19	σ1	σ1	PROPN
ejpam-6038	243	20	,	,	PUNCT
ejpam-6038	243	21	σ2	σ2	PROPN
ejpam-6038	243	22	)	)	PUNCT
ejpam-6038	243	23	is	be	AUX
ejpam-6038	243	24	said	say	VERB
ejpam-6038	243	25	to	to	PART
ejpam-6038	243	26	be	be	AUX
ejpam-6038	243	27	almost	almost	ADV
ejpam-6038	243	28	weakly	weakly	ADJ
ejpam-6038	243	29	(	(	PUNCT
ejpam-6038	243	30	τ1	τ1	NOUN
ejpam-6038	243	31	,	,	PUNCT
ejpam-6038	243	32	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	243	33	if	if	SCONJ
ejpam-6038	243	34	for	for	ADP
ejpam-6038	243	35	each	each	DET
ejpam-6038	243	36	x	x	SYM
ejpam-6038	243	37	∈	∈	PROPN
ejpam-6038	243	38	x	x	X
ejpam-6038	243	39	and	and	CCONJ
ejpam-6038	243	40	each	each	DET
ejpam-6038	243	41	σ1σ2	σ1σ2	VERB
ejpam-6038	243	42	-	-	ADJ
ejpam-6038	243	43	open	open	ADJ
ejpam-6038	243	44	set	set	NOUN
ejpam-6038	243	45	v	v	NOUN
ejpam-6038	243	46	of	of	ADP
ejpam-6038	243	47	y	y	NOUN
ejpam-6038	243	48	containing	contain	VERB
ejpam-6038	243	49	f(x	f(x	PROPN
ejpam-6038	243	50	)	)	PUNCT
ejpam-6038	243	51	,	,	PUNCT
ejpam-6038	243	52	x	x	PUNCT
ejpam-6038	243	53	∈	∈	ADP
ejpam-6038	243	54	τ1τ2	τ1τ2	NOUN
ejpam-6038	243	55	-	-	NOUN
ejpam-6038	243	56	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	243	57	-	-	PUNCT
ejpam-6038	243	58	cl(f	cl(f	NOUN
ejpam-6038	243	59	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6038	243	60	-	-	PUNCT
ejpam-6038	243	61	cl(v	cl(v	NOUN
ejpam-6038	243	62	)	)	PUNCT
ejpam-6038	243	63	)	)	PUNCT
ejpam-6038	243	64	)	)	PUNCT
ejpam-6038	243	65	)	)	PUNCT
ejpam-6038	243	66	.	.	PUNCT
ejpam-6038	244	1	lemma	lemma	PROPN
ejpam-6038	244	2	4	4	NUM
ejpam-6038	244	3	.	.	PUNCT
ejpam-6038	245	1	[	[	X
ejpam-6038	245	2	20	20	NUM
ejpam-6038	245	3	]	]	PUNCT
ejpam-6038	245	4	for	for	ADP
ejpam-6038	245	5	a	a	DET
ejpam-6038	245	6	function	function	NOUN
ejpam-6038	245	7	f	f	NOUN
ejpam-6038	245	8	:	:	PUNCT
ejpam-6038	245	9	(	(	PUNCT
ejpam-6038	245	10	x	x	NOUN
ejpam-6038	245	11	,	,	PUNCT
ejpam-6038	245	12	τ1	τ1	NOUN
ejpam-6038	245	13	,	,	PUNCT
ejpam-6038	245	14	τ2	τ2	NOUN
ejpam-6038	245	15	)	)	PUNCT
ejpam-6038	245	16	→	→	SYM
ejpam-6038	245	17	(	(	PUNCT
ejpam-6038	245	18	y	y	PROPN
ejpam-6038	245	19	,	,	PUNCT
ejpam-6038	245	20	σ1	σ1	PROPN
ejpam-6038	245	21	,	,	PUNCT
ejpam-6038	245	22	σ2	σ2	NOUN
ejpam-6038	245	23	)	)	PUNCT
ejpam-6038	245	24	,	,	PUNCT
ejpam-6038	245	25	the	the	DET
ejpam-6038	245	26	following	follow	VERB
ejpam-6038	245	27	properties	property	NOUN
ejpam-6038	245	28	are	be	AUX
ejpam-6038	245	29	equivalent	equivalent	ADJ
ejpam-6038	245	30	:	:	PUNCT
ejpam-6038	245	31	(	(	PUNCT
ejpam-6038	245	32	1	1	X
ejpam-6038	245	33	)	)	PUNCT
ejpam-6038	245	34	f	f	NOUN
ejpam-6038	245	35	is	be	AUX
ejpam-6038	245	36	almost	almost	ADV
ejpam-6038	245	37	weakly	weakly	ADJ
ejpam-6038	245	38	(	(	PUNCT
ejpam-6038	245	39	τ1	τ1	NOUN
ejpam-6038	245	40	,	,	PUNCT
ejpam-6038	245	41	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	245	42	;	;	PUNCT
ejpam-6038	245	43	(	(	PUNCT
ejpam-6038	245	44	2	2	X
ejpam-6038	245	45	)	)	PUNCT
ejpam-6038	245	46	f−1(v	f−1(v	NOUN
ejpam-6038	245	47	)	)	PUNCT
ejpam-6038	246	1	⊆	⊆	X
ejpam-6038	246	2	τ1τ2	τ1τ2	NOUN
ejpam-6038	246	3	-	-	NOUN
ejpam-6038	246	4	int(τ1τ2	int(τ1τ2	NOUN
ejpam-6038	246	5	-	-	PUNCT
ejpam-6038	246	6	cl(f	cl(f	NOUN
ejpam-6038	246	7	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6038	246	8	-	-	PUNCT
ejpam-6038	246	9	cl(v	cl(v	NOUN
ejpam-6038	246	10	)	)	PUNCT
ejpam-6038	246	11	)	)	PUNCT
ejpam-6038	246	12	)	)	PUNCT
ejpam-6038	246	13	)	)	PUNCT
ejpam-6038	246	14	for	for	ADP
ejpam-6038	246	15	every	every	DET
ejpam-6038	246	16	σ1σ2	σ1σ2	NOUN
ejpam-6038	246	17	-	-	ADJ
ejpam-6038	246	18	open	open	ADJ
ejpam-6038	246	19	set	set	NOUN
ejpam-6038	246	20	v	v	NOUN
ejpam-6038	246	21	of	of	ADP
ejpam-6038	246	22	y	y	PROPN
ejpam-6038	246	23	;	;	PUNCT
ejpam-6038	246	24	(	(	PUNCT
ejpam-6038	246	25	3	3	X
ejpam-6038	246	26	)	)	PUNCT
ejpam-6038	246	27	τ1τ2	τ1τ2	NOUN
ejpam-6038	246	28	-	-	NOUN
ejpam-6038	246	29	cl(τ1τ2	cl(τ1τ2	NOUN
ejpam-6038	246	30	-	-	PUNCT
ejpam-6038	246	31	int(f	int(f	PROPN
ejpam-6038	246	32	−1(v	−1(v	NOUN
ejpam-6038	246	33	)	)	PUNCT
ejpam-6038	246	34	)	)	PUNCT
ejpam-6038	246	35	)	)	PUNCT
ejpam-6038	247	1	⊆	⊆	NUM
ejpam-6038	247	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	247	3	-	-	PUNCT
ejpam-6038	247	4	cl(v	cl(v	NOUN
ejpam-6038	247	5	)	)	PUNCT
ejpam-6038	247	6	)	)	PUNCT
ejpam-6038	247	7	for	for	ADP
ejpam-6038	247	8	every	every	DET
ejpam-6038	247	9	σ1σ2	σ1σ2	NOUN
ejpam-6038	247	10	-	-	ADJ
ejpam-6038	247	11	open	open	ADJ
ejpam-6038	247	12	set	set	NOUN
ejpam-6038	247	13	v	v	NOUN
ejpam-6038	247	14	of	of	ADP
ejpam-6038	247	15	y	y	PROPN
ejpam-6038	247	16	;	;	PUNCT
ejpam-6038	247	17	(	(	PUNCT
ejpam-6038	247	18	4	4	X
ejpam-6038	247	19	)	)	PUNCT
ejpam-6038	247	20	(	(	PUNCT
ejpam-6038	247	21	τ1	τ1	NOUN
ejpam-6038	247	22	,	,	PUNCT
ejpam-6038	247	23	τ2)-pcl(f	τ2)-pcl(f	PROPN
ejpam-6038	247	24	−1(v	−1(v	PROPN
ejpam-6038	247	25	)	)	PUNCT
ejpam-6038	247	26	)	)	PUNCT
ejpam-6038	248	1	⊆	⊆	NUM
ejpam-6038	248	2	f−1(σ1σ2	f−1(σ1σ2	NOUN
ejpam-6038	248	3	-	-	PUNCT
ejpam-6038	248	4	cl(v	cl(v	NOUN
ejpam-6038	248	5	)	)	PUNCT
ejpam-6038	248	6	)	)	PUNCT
ejpam-6038	248	7	for	for	ADP
ejpam-6038	248	8	every	every	DET
ejpam-6038	248	9	σ1σ2	σ1σ2	NOUN
ejpam-6038	248	10	-	-	ADJ
ejpam-6038	248	11	open	open	ADJ
ejpam-6038	248	12	set	set	NOUN
ejpam-6038	248	13	v	v	NOUN
ejpam-6038	248	14	of	of	ADP
ejpam-6038	248	15	y	y	PROPN
ejpam-6038	248	16	;	;	PUNCT
ejpam-6038	248	17	(	(	PUNCT
ejpam-6038	248	18	5	5	X
ejpam-6038	248	19	)	)	PUNCT
ejpam-6038	248	20	f−1(v	f−1(v	NOUN
ejpam-6038	248	21	)	)	PUNCT
ejpam-6038	249	1	⊆	⊆	NUM
ejpam-6038	249	2	(	(	PUNCT
ejpam-6038	249	3	τ1	τ1	NOUN
ejpam-6038	249	4	,	,	PUNCT
ejpam-6038	249	5	τ2)-pint(f	τ2)-pint(f	PROPN
ejpam-6038	249	6	−1(σ1σ2	−1(σ1σ2	NOUN
ejpam-6038	249	7	-	-	PUNCT
ejpam-6038	249	8	cl(v	cl(v	NOUN
ejpam-6038	249	9	)	)	PUNCT
ejpam-6038	249	10	)	)	PUNCT
ejpam-6038	249	11	)	)	PUNCT
ejpam-6038	249	12	for	for	ADP
ejpam-6038	249	13	every	every	DET
ejpam-6038	249	14	σ1σ2	σ1σ2	NOUN
ejpam-6038	249	15	-	-	ADJ
ejpam-6038	249	16	open	open	ADJ
ejpam-6038	249	17	set	set	NOUN
ejpam-6038	249	18	v	v	NOUN
ejpam-6038	249	19	of	of	ADP
ejpam-6038	249	20	y	y	PROPN
ejpam-6038	249	21	;	;	PUNCT
ejpam-6038	249	22	(	(	PUNCT
ejpam-6038	249	23	6	6	NUM
ejpam-6038	249	24	)	)	PUNCT
ejpam-6038	249	25	for	for	ADP
ejpam-6038	249	26	each	each	DET
ejpam-6038	249	27	x	x	SYM
ejpam-6038	249	28	∈	∈	PROPN
ejpam-6038	249	29	x	x	X
ejpam-6038	249	30	and	and	CCONJ
ejpam-6038	249	31	each	each	DET
ejpam-6038	249	32	σ1σ2	σ1σ2	VERB
ejpam-6038	249	33	-	-	ADJ
ejpam-6038	249	34	open	open	ADJ
ejpam-6038	249	35	set	set	NOUN
ejpam-6038	249	36	v	v	NOUN
ejpam-6038	249	37	of	of	ADP
ejpam-6038	249	38	y	y	NOUN
ejpam-6038	249	39	containing	contain	VERB
ejpam-6038	249	40	f(x	f(x	PROPN
ejpam-6038	249	41	)	)	PUNCT
ejpam-6038	249	42	,	,	PUNCT
ejpam-6038	249	43	there	there	PRON
ejpam-6038	249	44	exists	exist	VERB
ejpam-6038	249	45	a	a	DET
ejpam-6038	249	46	(	(	PUNCT
ejpam-6038	249	47	τ1	τ1	NOUN
ejpam-6038	249	48	,	,	PUNCT
ejpam-6038	249	49	τ2)p	τ2)p	ADJ
ejpam-6038	249	50	-	-	PUNCT
ejpam-6038	249	51	open	open	ADJ
ejpam-6038	249	52	set	set	NOUN
ejpam-6038	249	53	u	u	NOUN
ejpam-6038	249	54	of	of	ADP
ejpam-6038	249	55	x	x	PUNCT
ejpam-6038	249	56	containing	contain	VERB
ejpam-6038	249	57	x	x	PUNCT
ejpam-6038	249	58	such	such	ADJ
ejpam-6038	249	59	that	that	DET
ejpam-6038	249	60	f(u	f(u	PROPN
ejpam-6038	249	61	)	)	PUNCT
ejpam-6038	249	62	⊆	⊆	NUM
ejpam-6038	249	63	σ1σ2	σ1σ2	NOUN
ejpam-6038	249	64	-	-	NUM
ejpam-6038	249	65	cl(v	cl(v	NOUN
ejpam-6038	249	66	)	)	PUNCT
ejpam-6038	249	67	.	.	PUNCT
ejpam-6038	250	1	theorem	theorem	VERB
ejpam-6038	250	2	11	11	NUM
ejpam-6038	250	3	.	.	PUNCT
ejpam-6038	251	1	if	if	SCONJ
ejpam-6038	251	2	a	a	DET
ejpam-6038	251	3	function	function	NOUN
ejpam-6038	251	4	f	f	X
ejpam-6038	251	5	:	:	PUNCT
ejpam-6038	251	6	(	(	PUNCT
ejpam-6038	251	7	x	x	NOUN
ejpam-6038	251	8	,	,	PUNCT
ejpam-6038	251	9	τ1	τ1	NOUN
ejpam-6038	251	10	,	,	PUNCT
ejpam-6038	251	11	τ2	τ2	NOUN
ejpam-6038	251	12	)	)	PUNCT
ejpam-6038	251	13	→	→	SYM
ejpam-6038	251	14	(	(	PUNCT
ejpam-6038	251	15	y	y	PROPN
ejpam-6038	251	16	,	,	PUNCT
ejpam-6038	251	17	σ1	σ1	PROPN
ejpam-6038	251	18	,	,	PUNCT
ejpam-6038	251	19	σ2	σ2	PROPN
ejpam-6038	251	20	)	)	PUNCT
ejpam-6038	251	21	is	be	AUX
ejpam-6038	251	22	almost	almost	ADV
ejpam-6038	251	23	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	251	24	,	,	PUNCT
ejpam-6038	251	25	τ2)p	τ2)p	ADJ
ejpam-6038	251	26	-	-	ADJ
ejpam-6038	251	27	continuous	continuous	ADJ
ejpam-6038	251	28	,	,	PUNCT
ejpam-6038	251	29	then	then	ADV
ejpam-6038	251	30	f	f	PROPN
ejpam-6038	251	31	is	be	AUX
ejpam-6038	251	32	almost	almost	ADV
ejpam-6038	251	33	weakly	weakly	ADJ
ejpam-6038	251	34	(	(	PUNCT
ejpam-6038	251	35	τ1	τ1	NOUN
ejpam-6038	251	36	,	,	PUNCT
ejpam-6038	251	37	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	251	38	.	.	PUNCT
ejpam-6038	252	1	proof	proof	NOUN
ejpam-6038	252	2	.	.	PUNCT
ejpam-6038	253	1	let	let	VERB
ejpam-6038	253	2	x	x	PUNCT
ejpam-6038	253	3	∈	∈	PROPN
ejpam-6038	253	4	x	x	X
ejpam-6038	253	5	and	and	CCONJ
ejpam-6038	253	6	v	v	X
ejpam-6038	253	7	be	be	AUX
ejpam-6038	253	8	any	any	DET
ejpam-6038	253	9	σ1σ2	σ1σ2	NOUN
ejpam-6038	253	10	-	-	ADJ
ejpam-6038	253	11	open	open	ADJ
ejpam-6038	253	12	set	set	NOUN
ejpam-6038	253	13	of	of	ADP
ejpam-6038	253	14	y	y	PROPN
ejpam-6038	253	15	containing	contain	VERB
ejpam-6038	253	16	f(x	f(x	PROPN
ejpam-6038	253	17	)	)	PUNCT
ejpam-6038	253	18	.	.	PUNCT
ejpam-6038	254	1	then	then	ADV
ejpam-6038	254	2	,	,	PUNCT
ejpam-6038	254	3	σ1σ2	σ1σ2	NOUN
ejpam-6038	254	4	-	-	NUM
ejpam-6038	254	5	cl(v	cl(v	NOUN
ejpam-6038	254	6	)	)	PUNCT
ejpam-6038	254	7	is	be	AUX
ejpam-6038	254	8	a	a	DET
ejpam-6038	254	9	(	(	PUNCT
ejpam-6038	254	10	σ1	σ1	NOUN
ejpam-6038	254	11	,	,	PUNCT
ejpam-6038	254	12	σ2)r	σ2)r	NOUN
ejpam-6038	254	13	-	-	PUNCT
ejpam-6038	254	14	closed	close	VERB
ejpam-6038	254	15	set	set	NOUN
ejpam-6038	254	16	of	of	ADP
ejpam-6038	254	17	y	y	PROPN
ejpam-6038	254	18	containing	contain	VERB
ejpam-6038	254	19	f(x	f(x	PROPN
ejpam-6038	254	20	)	)	PUNCT
ejpam-6038	254	21	.	.	PUNCT
ejpam-6038	255	1	since	since	SCONJ
ejpam-6038	255	2	f	f	PROPN
ejpam-6038	255	3	is	be	AUX
ejpam-6038	255	4	almost	almost	ADV
ejpam-6038	255	5	contra-(τ1	contra-(τ1	NOUN
ejpam-6038	255	6	,	,	PUNCT
ejpam-6038	255	7	τ2)p	τ2)p	ADJ
ejpam-6038	255	8	-	-	ADJ
ejpam-6038	255	9	continuous	continuous	ADJ
ejpam-6038	255	10	,	,	PUNCT
ejpam-6038	255	11	there	there	PRON
ejpam-6038	255	12	exists	exist	VERB
ejpam-6038	255	13	a	a	DET
ejpam-6038	255	14	(	(	PUNCT
ejpam-6038	255	15	τ1	τ1	NOUN
ejpam-6038	255	16	,	,	PUNCT
ejpam-6038	255	17	τ2)p	τ2)p	ADJ
ejpam-6038	255	18	-	-	PUNCT
ejpam-6038	255	19	open	open	ADJ
ejpam-6038	255	20	set	set	NOUN
ejpam-6038	255	21	u	u	NOUN
ejpam-6038	255	22	of	of	ADP
ejpam-6038	255	23	x	x	PUNCT
ejpam-6038	255	24	containing	contain	VERB
ejpam-6038	255	25	x	x	PUNCT
ejpam-6038	255	26	such	such	ADJ
ejpam-6038	255	27	that	that	DET
ejpam-6038	255	28	f(u	f(u	PROPN
ejpam-6038	255	29	)	)	PUNCT
ejpam-6038	255	30	⊆	⊆	NUM
ejpam-6038	255	31	σ1σ2	σ1σ2	NOUN
ejpam-6038	255	32	-	-	NUM
ejpam-6038	255	33	cl(v	cl(v	NOUN
ejpam-6038	255	34	)	)	PUNCT
ejpam-6038	255	35	.	.	PUNCT
ejpam-6038	256	1	by	by	ADP
ejpam-6038	256	2	lemma	lemma	PROPN
ejpam-6038	256	3	4	4	NUM
ejpam-6038	256	4	,	,	PUNCT
ejpam-6038	256	5	f	f	PROPN
ejpam-6038	256	6	is	be	AUX
ejpam-6038	256	7	almost	almost	ADV
ejpam-6038	256	8	weakly	weakly	ADJ
ejpam-6038	256	9	(	(	PUNCT
ejpam-6038	256	10	τ1	τ1	NOUN
ejpam-6038	256	11	,	,	PUNCT
ejpam-6038	256	12	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	256	13	.	.	PUNCT
ejpam-6038	257	1	acknowledgements	acknowledgement	NOUN
ejpam-6038	257	2	this	this	DET
ejpam-6038	257	3	research	research	NOUN
ejpam-6038	257	4	project	project	NOUN
ejpam-6038	257	5	was	be	AUX
ejpam-6038	257	6	financially	financially	ADV
ejpam-6038	257	7	supported	support	VERB
ejpam-6038	257	8	by	by	ADP
ejpam-6038	257	9	mahasarakham	mahasarakham	PROPN
ejpam-6038	257	10	university	university	PROPN
ejpam-6038	257	11	.	.	PUNCT
ejpam-6038	258	1	references	reference	NOUN
ejpam-6038	258	2	[	[	X
ejpam-6038	258	3	1	1	X
ejpam-6038	258	4	]	]	PUNCT
ejpam-6038	258	5	j.	j.	PROPN
ejpam-6038	258	6	dontchev	dontchev	PROPN
ejpam-6038	258	7	.	.	PUNCT
ejpam-6038	259	1	contra	contra	ADJ
ejpam-6038	259	2	-	-	ADJ
ejpam-6038	259	3	continuous	continuous	ADJ
ejpam-6038	259	4	functions	function	NOUN
ejpam-6038	259	5	and	and	CCONJ
ejpam-6038	259	6	strongly	strongly	ADV
ejpam-6038	259	7	s	s	NOUN
ejpam-6038	259	8	-	-	PUNCT
ejpam-6038	259	9	closed	closed	ADJ
ejpam-6038	259	10	spaces	space	NOUN
ejpam-6038	259	11	.	.	PUNCT
ejpam-6038	260	1	international	international	ADJ
ejpam-6038	260	2	journal	journal	PROPN
ejpam-6038	260	3	of	of	ADP
ejpam-6038	260	4	mathematics	mathematics	PROPN
ejpam-6038	260	5	and	and	CCONJ
ejpam-6038	260	6	mathematical	mathematical	ADJ
ejpam-6038	260	7	sciences	science	NOUN
ejpam-6038	260	8	,	,	PUNCT
ejpam-6038	260	9	19:303–310	19:303–310	PROPN
ejpam-6038	260	10	,	,	PUNCT
ejpam-6038	260	11	1966	1966	NUM
ejpam-6038	260	12	.	.	PUNCT
ejpam-6038	261	1	[	[	X
ejpam-6038	261	2	2	2	X
ejpam-6038	261	3	]	]	PUNCT
ejpam-6038	261	4	j.	j.	PROPN
ejpam-6038	261	5	dontchev	dontchev	PROPN
ejpam-6038	261	6	,	,	PUNCT
ejpam-6038	261	7	m.	m.	NOUN
ejpam-6038	261	8	ganster	ganster	NOUN
ejpam-6038	261	9	,	,	PUNCT
ejpam-6038	261	10	and	and	CCONJ
ejpam-6038	261	11	i.	i.	PROPN
ejpam-6038	261	12	reilly	reilly	PROPN
ejpam-6038	261	13	.	.	PUNCT
ejpam-6038	262	1	more	more	ADV
ejpam-6038	262	2	on	on	ADP
ejpam-6038	262	3	almost	almost	ADV
ejpam-6038	262	4	s	s	NOUN
ejpam-6038	262	5	-	-	NOUN
ejpam-6038	262	6	continuity	continuity	NOUN
ejpam-6038	262	7	.	.	PUNCT
ejpam-6038	263	1	indian	indian	ADJ
ejpam-6038	263	2	journal	journal	PROPN
ejpam-6038	263	3	of	of	ADP
ejpam-6038	263	4	mathematics	mathematics	PROPN
ejpam-6038	263	5	,	,	PUNCT
ejpam-6038	263	6	41:139–146	41:139–146	PROPN
ejpam-6038	263	7	,	,	PUNCT
ejpam-6038	263	8	1999	1999	NUM
ejpam-6038	263	9	.	.	PUNCT
ejpam-6038	264	1	[	[	X
ejpam-6038	264	2	3	3	X
ejpam-6038	264	3	]	]	X
ejpam-6038	264	4	j.	j.	PROPN
ejpam-6038	264	5	dontchev	dontchev	PROPN
ejpam-6038	264	6	and	and	CCONJ
ejpam-6038	264	7	t.	t.	PROPN
ejpam-6038	264	8	noiri	noiri	PROPN
ejpam-6038	264	9	.	.	PUNCT
ejpam-6038	265	1	contra	contra	ADJ
ejpam-6038	265	2	-	-	ADJ
ejpam-6038	265	3	semicontinuous	semicontinuous	ADJ
ejpam-6038	265	4	functions	function	NOUN
ejpam-6038	265	5	.	.	PUNCT
ejpam-6038	266	1	mathematica	mathematica	PROPN
ejpam-6038	266	2	pannonica	pannonica	PROPN
ejpam-6038	266	3	,	,	PUNCT
ejpam-6038	266	4	10:159–168	10:159–168	NOUN
ejpam-6038	266	5	,	,	PUNCT
ejpam-6038	266	6	1999	1999	NUM
ejpam-6038	266	7	.	.	PUNCT
ejpam-6038	267	1	[	[	X
ejpam-6038	267	2	4	4	X
ejpam-6038	267	3	]	]	PUNCT
ejpam-6038	267	4	s.	s.	PROPN
ejpam-6038	267	5	jafari	jafari	PROPN
ejpam-6038	267	6	and	and	CCONJ
ejpam-6038	267	7	t.	t.	PROPN
ejpam-6038	267	8	noiri	noiri	PROPN
ejpam-6038	267	9	.	.	PUNCT
ejpam-6038	268	1	contra	contra	PROPN
ejpam-6038	268	2	-	-	ADJ
ejpam-6038	268	3	super	super	ADJ
ejpam-6038	268	4	-	-	ADJ
ejpam-6038	268	5	continuous	continuous	ADJ
ejpam-6038	268	6	functions	function	NOUN
ejpam-6038	268	7	.	.	PUNCT
ejpam-6038	269	1	annales	annales	PROPN
ejpam-6038	269	2	universitatis	universitatis	PROPN
ejpam-6038	269	3	scientiarum	scientiarum	PROPN
ejpam-6038	269	4	budapestinensis	budapestinensis	PROPN
ejpam-6038	269	5	de	de	PROPN
ejpam-6038	269	6	rolando	rolando	PROPN
ejpam-6038	269	7	eötvös	eötvös	PROPN
ejpam-6038	269	8	,	,	PUNCT
ejpam-6038	269	9	sectio	sectio	PROPN
ejpam-6038	269	10	mathematica	mathematica	PROPN
ejpam-6038	269	11	,	,	PUNCT
ejpam-6038	269	12	42:27–34	42:27–34	PROPN
ejpam-6038	269	13	,	,	PUNCT
ejpam-6038	269	14	1999	1999	NUM
ejpam-6038	269	15	.	.	PUNCT
ejpam-6038	270	1	p.	p.	NOUN
ejpam-6038	270	2	pue	pue	NOUN
ejpam-6038	270	3	-	-	PUNCT
ejpam-6038	270	4	on	on	ADP
ejpam-6038	270	5	,	,	PUNCT
ejpam-6038	270	6	a.	a.	PROPN
ejpam-6038	270	7	sama	sama	PROPN
ejpam-6038	270	8	-	-	PUNCT
ejpam-6038	270	9	ae	ae	PROPN
ejpam-6038	270	10	,	,	PUNCT
ejpam-6038	270	11	c.	c.	PROPN
ejpam-6038	270	12	boonpok	boonpok	PROPN
ejpam-6038	270	13	/	/	SYM
ejpam-6038	270	14	eur	eur	PROPN
ejpam-6038	270	15	.	.	PUNCT
ejpam-6038	271	1	j.	j.	PROPN
ejpam-6038	271	2	pure	pure	PROPN
ejpam-6038	271	3	appl	appl	PROPN
ejpam-6038	271	4	.	.	PROPN
ejpam-6038	271	5	math	math	PROPN
ejpam-6038	271	6	,	,	PUNCT
ejpam-6038	271	7	18	18	NUM
ejpam-6038	271	8	(	(	PUNCT
ejpam-6038	271	9	2	2	NUM
ejpam-6038	271	10	)	)	PUNCT
ejpam-6038	271	11	(	(	PUNCT
ejpam-6038	271	12	2025	2025	NUM
ejpam-6038	271	13	)	)	PUNCT
ejpam-6038	271	14	,	,	PUNCT
ejpam-6038	271	15	6038	6038	NUM
ejpam-6038	271	16	10	10	NUM
ejpam-6038	271	17	of	of	ADP
ejpam-6038	271	18	11	11	NUM
ejpam-6038	272	1	[	[	SYM
ejpam-6038	272	2	5	5	NUM
ejpam-6038	272	3	]	]	PUNCT
ejpam-6038	273	1	s.	s.	PROPN
ejpam-6038	273	2	jafari	jafari	PROPN
ejpam-6038	273	3	and	and	CCONJ
ejpam-6038	273	4	t.	t.	PROPN
ejpam-6038	273	5	noiri	noiri	PROPN
ejpam-6038	273	6	.	.	PUNCT
ejpam-6038	274	1	on	on	ADP
ejpam-6038	274	2	contra	contra	ADJ
ejpam-6038	274	3	-	-	ADJ
ejpam-6038	274	4	precontinuous	precontinuous	ADJ
ejpam-6038	274	5	functions	function	NOUN
ejpam-6038	274	6	.	.	PUNCT
ejpam-6038	275	1	bulletin	bulletin	NOUN
ejpam-6038	275	2	of	of	ADP
ejpam-6038	275	3	the	the	DET
ejpam-6038	275	4	malaysian	malaysian	PROPN
ejpam-6038	275	5	mathematical	mathematical	PROPN
ejpam-6038	275	6	sciences	sciences	PROPN
ejpam-6038	275	7	society	society	NOUN
ejpam-6038	275	8	,	,	PUNCT
ejpam-6038	275	9	25:115–128	25:115–128	PROPN
ejpam-6038	275	10	,	,	PUNCT
ejpam-6038	275	11	2002	2002	NUM
ejpam-6038	275	12	.	.	PUNCT
ejpam-6038	276	1	[	[	X
ejpam-6038	276	2	6	6	NUM
ejpam-6038	276	3	]	]	PUNCT
ejpam-6038	276	4	e.	e.	PROPN
ejpam-6038	276	5	ekici	ekici	PROPN
ejpam-6038	276	6	.	.	PUNCT
ejpam-6038	277	1	almost	almost	ADV
ejpam-6038	277	2	contra	contra	ADJ
ejpam-6038	277	3	-	-	ADJ
ejpam-6038	277	4	precontinuous	precontinuous	ADJ
ejpam-6038	277	5	functions	function	NOUN
ejpam-6038	277	6	.	.	PUNCT
ejpam-6038	278	1	bulletin	bulletin	NOUN
ejpam-6038	278	2	of	of	ADP
ejpam-6038	278	3	the	the	DET
ejpam-6038	278	4	malaysian	malaysian	PROPN
ejpam-6038	278	5	mathematical	mathematical	PROPN
ejpam-6038	278	6	sciences	sciences	PROPN
ejpam-6038	278	7	society	society	NOUN
ejpam-6038	278	8	,	,	PUNCT
ejpam-6038	278	9	27:53–65	27:53–65	NUM
ejpam-6038	278	10	,	,	PUNCT
ejpam-6038	278	11	2004	2004	NUM
ejpam-6038	278	12	.	.	PUNCT
ejpam-6038	279	1	[	[	X
ejpam-6038	279	2	7	7	X
ejpam-6038	279	3	]	]	X
ejpam-6038	279	4	t.	t.	PROPN
ejpam-6038	279	5	noiri	noiri	PROPN
ejpam-6038	279	6	,	,	PUNCT
ejpam-6038	279	7	b.	b.	PROPN
ejpam-6038	279	8	ahmad	ahmad	PROPN
ejpam-6038	279	9	,	,	PUNCT
ejpam-6038	279	10	and	and	CCONJ
ejpam-6038	279	11	m.	m.	PROPN
ejpam-6038	279	12	khan	khan	PROPN
ejpam-6038	279	13	.	.	PUNCT
ejpam-6038	280	1	almost	almost	ADV
ejpam-6038	280	2	s	s	NOUN
ejpam-6038	280	3	-	-	PUNCT
ejpam-6038	280	4	continuous	continuous	ADJ
ejpam-6038	280	5	functions	function	NOUN
ejpam-6038	280	6	.	.	PUNCT
ejpam-6038	281	1	kyungpook	kyungpook	PROPN
ejpam-6038	281	2	mathematical	mathematical	PROPN
ejpam-6038	281	3	journal	journal	PROPN
ejpam-6038	281	4	,	,	PUNCT
ejpam-6038	281	5	35:311–322	35:311–322	PROPN
ejpam-6038	281	6	,	,	PUNCT
ejpam-6038	281	7	1995	1995	NUM
ejpam-6038	281	8	.	.	PUNCT
ejpam-6038	282	1	[	[	X
ejpam-6038	282	2	8	8	X
ejpam-6038	282	3	]	]	PUNCT
ejpam-6038	282	4	t.	t.	PROPN
ejpam-6038	282	5	noiri	noiri	PROPN
ejpam-6038	282	6	.	.	PUNCT
ejpam-6038	283	1	super	super	ADJ
ejpam-6038	283	2	-	-	NOUN
ejpam-6038	283	3	continuity	continuity	NOUN
ejpam-6038	283	4	and	and	CCONJ
ejpam-6038	283	5	some	some	DET
ejpam-6038	283	6	strong	strong	ADJ
ejpam-6038	283	7	forms	form	NOUN
ejpam-6038	283	8	of	of	ADP
ejpam-6038	283	9	continuity	continuity	NOUN
ejpam-6038	283	10	.	.	PUNCT
ejpam-6038	284	1	indian	indian	ADJ
ejpam-6038	284	2	journal	journal	PROPN
ejpam-6038	284	3	of	of	ADP
ejpam-6038	284	4	pure	pure	ADJ
ejpam-6038	284	5	and	and	CCONJ
ejpam-6038	284	6	applied	applied	ADJ
ejpam-6038	284	7	mathematics	mathematic	NOUN
ejpam-6038	284	8	,	,	PUNCT
ejpam-6038	284	9	15:241–250	15:241–250	NUM
ejpam-6038	284	10	,	,	PUNCT
ejpam-6038	284	11	1984	1984	NUM
ejpam-6038	284	12	.	.	PUNCT
ejpam-6038	285	1	[	[	X
ejpam-6038	285	2	9	9	NUM
ejpam-6038	285	3	]	]	PUNCT
ejpam-6038	285	4	t.	t.	PROPN
ejpam-6038	285	5	noiri	noiri	PROPN
ejpam-6038	285	6	and	and	CCONJ
ejpam-6038	285	7	s.	s.	PROPN
ejpam-6038	285	8	jafari	jafari	PROPN
ejpam-6038	285	9	.	.	PUNCT
ejpam-6038	286	1	some	some	DET
ejpam-6038	286	2	properties	property	NOUN
ejpam-6038	286	3	of	of	ADP
ejpam-6038	286	4	almost	almost	ADV
ejpam-6038	286	5	contra	contra	ADJ
ejpam-6038	286	6	-	-	ADJ
ejpam-6038	286	7	precontinuous	precontinuous	ADJ
ejpam-6038	286	8	functions	function	NOUN
ejpam-6038	286	9	.	.	PUNCT
ejpam-6038	287	1	bulletin	bulletin	NOUN
ejpam-6038	287	2	of	of	ADP
ejpam-6038	287	3	the	the	DET
ejpam-6038	287	4	malaysian	malaysian	PROPN
ejpam-6038	287	5	mathematical	mathematical	PROPN
ejpam-6038	287	6	sciences	sciences	PROPN
ejpam-6038	287	7	society	society	NOUN
ejpam-6038	287	8	,	,	PUNCT
ejpam-6038	287	9	28:107–116	28:107–116	PROPN
ejpam-6038	287	10	,	,	PUNCT
ejpam-6038	287	11	2005	2005	NUM
ejpam-6038	287	12	.	.	PUNCT
ejpam-6038	288	1	[	[	X
ejpam-6038	288	2	10	10	NUM
ejpam-6038	288	3	]	]	PUNCT
ejpam-6038	288	4	s.	s.	PROPN
ejpam-6038	288	5	jafari	jafari	PROPN
ejpam-6038	288	6	.	.	PUNCT
ejpam-6038	289	1	on	on	ADP
ejpam-6038	289	2	semi	semi	ADJ
ejpam-6038	289	3	-	-	ADJ
ejpam-6038	289	4	pre	pre	ADJ
ejpam-6038	289	5	-	-	ADJ
ejpam-6038	289	6	irresolute	irresolute	ADJ
ejpam-6038	289	7	functions	function	NOUN
ejpam-6038	289	8	.	.	PUNCT
ejpam-6038	290	1	far	far	PROPN
ejpam-6038	290	2	east	east	PROPN
ejpam-6038	290	3	journal	journal	PROPN
ejpam-6038	290	4	of	of	ADP
ejpam-6038	290	5	mathematical	mathematical	ADJ
ejpam-6038	290	6	sciences	science	NOUN
ejpam-6038	290	7	,	,	PUNCT
ejpam-6038	290	8	6:1003–1010	6:1003–1010	NUM
ejpam-6038	290	9	,	,	PUNCT
ejpam-6038	290	10	1998	1998	NUM
ejpam-6038	290	11	.	.	PUNCT
ejpam-6038	291	1	[	[	X
ejpam-6038	291	2	11	11	NUM
ejpam-6038	291	3	]	]	PUNCT
ejpam-6038	291	4	a.	a.	PROPN
ejpam-6038	291	5	al	al	PROPN
ejpam-6038	291	6	-	-	PUNCT
ejpam-6038	291	7	omari	omari	PROPN
ejpam-6038	291	8	and	and	CCONJ
ejpam-6038	291	9	m.	m.	PROPN
ejpam-6038	291	10	s.	s.	PROPN
ejpam-6038	291	11	m.	m.	PROPN
ejpam-6038	291	12	noorani	noorani	PROPN
ejpam-6038	291	13	.	.	PUNCT
ejpam-6038	292	1	contra	contra	PROPN
ejpam-6038	292	2	ω	ω	PROPN
ejpam-6038	292	3	-	-	ADJ
ejpam-6038	292	4	continuous	continuous	ADJ
ejpam-6038	292	5	and	and	CCONJ
ejpam-6038	292	6	almost	almost	ADV
ejpam-6038	292	7	contra	contra	PROPN
ejpam-6038	292	8	ωcontinuous	ωcontinuous	ADJ
ejpam-6038	292	9	functions	function	NOUN
ejpam-6038	292	10	.	.	PUNCT
ejpam-6038	293	1	international	international	ADJ
ejpam-6038	293	2	journal	journal	PROPN
ejpam-6038	293	3	of	of	ADP
ejpam-6038	293	4	mathematics	mathematics	PROPN
ejpam-6038	293	5	and	and	CCONJ
ejpam-6038	293	6	mathematical	mathematical	ADJ
ejpam-6038	293	7	sciences	science	NOUN
ejpam-6038	293	8	,	,	PUNCT
ejpam-6038	293	9	2007:40469	2007:40469	NUM
ejpam-6038	293	10	,	,	PUNCT
ejpam-6038	293	11	2007	2007	NUM
ejpam-6038	293	12	.	.	PUNCT
ejpam-6038	294	1	[	[	X
ejpam-6038	294	2	12	12	NUM
ejpam-6038	294	3	]	]	X
ejpam-6038	294	4	c.	c.	PROPN
ejpam-6038	294	5	boonpok	boonpok	PROPN
ejpam-6038	294	6	and	and	CCONJ
ejpam-6038	294	7	n.	n.	PROPN
ejpam-6038	294	8	srisarakham	srisarakham	PROPN
ejpam-6038	294	9	.	.	PUNCT
ejpam-6038	295	1	(	(	PUNCT
ejpam-6038	295	2	τ1	τ1	NOUN
ejpam-6038	295	3	,	,	PUNCT
ejpam-6038	295	4	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6038	295	5	for	for	ADP
ejpam-6038	295	6	functions	function	NOUN
ejpam-6038	295	7	.	.	PUNCT
ejpam-6038	296	1	asia	asia	PROPN
ejpam-6038	296	2	pacific	pacific	PROPN
ejpam-6038	296	3	journal	journal	PROPN
ejpam-6038	296	4	of	of	ADP
ejpam-6038	296	5	mathematics	mathematic	NOUN
ejpam-6038	296	6	,	,	PUNCT
ejpam-6038	296	7	11:21	11:21	NUM
ejpam-6038	296	8	,	,	PUNCT
ejpam-6038	296	9	2024	2024	NUM
ejpam-6038	296	10	.	.	PUNCT
ejpam-6038	297	1	[	[	X
ejpam-6038	297	2	13	13	NUM
ejpam-6038	297	3	]	]	PUNCT
ejpam-6038	297	4	c.	c.	PROPN
ejpam-6038	297	5	boonpok	boonpok	PROPN
ejpam-6038	297	6	and	and	CCONJ
ejpam-6038	297	7	p.	p.	NOUN
ejpam-6038	297	8	pue	pue	NOUN
ejpam-6038	297	9	-	-	PUNCT
ejpam-6038	297	10	on	on	ADP
ejpam-6038	297	11	.	.	PUNCT
ejpam-6038	298	1	characterizations	characterization	NOUN
ejpam-6038	298	2	of	of	ADP
ejpam-6038	298	3	almost	almost	ADV
ejpam-6038	298	4	(	(	PUNCT
ejpam-6038	298	5	τ1	τ1	NOUN
ejpam-6038	298	6	,	,	PUNCT
ejpam-6038	298	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	298	8	functions	function	NOUN
ejpam-6038	298	9	.	.	PUNCT
ejpam-6038	299	1	international	international	ADJ
ejpam-6038	299	2	journal	journal	NOUN
ejpam-6038	299	3	of	of	ADP
ejpam-6038	299	4	analysis	analysis	NOUN
ejpam-6038	299	5	and	and	CCONJ
ejpam-6038	299	6	applications	application	NOUN
ejpam-6038	299	7	,	,	PUNCT
ejpam-6038	299	8	22:33	22:33	NUM
ejpam-6038	299	9	,	,	PUNCT
ejpam-6038	299	10	2024	2024	NUM
ejpam-6038	299	11	.	.	PUNCT
ejpam-6038	300	1	[	[	X
ejpam-6038	300	2	14	14	NUM
ejpam-6038	300	3	]	]	X
ejpam-6038	300	4	c.	c.	PROPN
ejpam-6038	300	5	boonpok	boonpok	PROPN
ejpam-6038	300	6	and	and	CCONJ
ejpam-6038	300	7	c.	c.	PROPN
ejpam-6038	300	8	klanarong	klanarong	PROPN
ejpam-6038	300	9	.	.	PUNCT
ejpam-6038	301	1	on	on	ADP
ejpam-6038	301	2	weakly	weakly	ADJ
ejpam-6038	301	3	(	(	PUNCT
ejpam-6038	301	4	τ1	τ1	NOUN
ejpam-6038	301	5	,	,	PUNCT
ejpam-6038	301	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	301	7	functions	function	NOUN
ejpam-6038	301	8	.	.	PUNCT
ejpam-6038	302	1	european	european	ADJ
ejpam-6038	302	2	journal	journal	PROPN
ejpam-6038	302	3	of	of	ADP
ejpam-6038	302	4	pure	pure	ADJ
ejpam-6038	302	5	and	and	CCONJ
ejpam-6038	302	6	applied	applied	ADJ
ejpam-6038	302	7	mathematics	mathematic	NOUN
ejpam-6038	302	8	,	,	PUNCT
ejpam-6038	302	9	17(1):416–425	17(1):416–425	NUM
ejpam-6038	302	10	,	,	PUNCT
ejpam-6038	302	11	2024	2024	NUM
ejpam-6038	302	12	.	.	PUNCT
ejpam-6038	303	1	[	[	X
ejpam-6038	303	2	15	15	NUM
ejpam-6038	303	3	]	]	X
ejpam-6038	303	4	n.	n.	NOUN
ejpam-6038	303	5	srisarakham	srisarakham	PROPN
ejpam-6038	303	6	,	,	PUNCT
ejpam-6038	303	7	s.	s.	PROPN
ejpam-6038	303	8	sompong	sompong	PROPN
ejpam-6038	303	9	,	,	PUNCT
ejpam-6038	303	10	and	and	CCONJ
ejpam-6038	303	11	c.	c.	PROPN
ejpam-6038	303	12	boonpok	boonpok	PROPN
ejpam-6038	303	13	.	.	PUNCT
ejpam-6038	304	1	quasi	quasi	PROPN
ejpam-6038	304	2	θ(τ1	θ(τ1	PROPN
ejpam-6038	304	3	,	,	PUNCT
ejpam-6038	304	4	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	304	5	functions	function	NOUN
ejpam-6038	304	6	.	.	PUNCT
ejpam-6038	305	1	european	european	ADJ
ejpam-6038	305	2	journal	journal	PROPN
ejpam-6038	305	3	of	of	ADP
ejpam-6038	305	4	pure	pure	ADJ
ejpam-6038	305	5	and	and	CCONJ
ejpam-6038	305	6	applied	applied	ADJ
ejpam-6038	305	7	mathematics	mathematic	NOUN
ejpam-6038	305	8	,	,	PUNCT
ejpam-6038	305	9	18(1):5722	18(1):5722	NUM
ejpam-6038	305	10	,	,	PUNCT
ejpam-6038	305	11	2025	2025	NUM
ejpam-6038	305	12	.	.	PUNCT
ejpam-6038	306	1	[	[	X
ejpam-6038	306	2	16	16	NUM
ejpam-6038	306	3	]	]	X
ejpam-6038	306	4	c.	c.	PROPN
ejpam-6038	306	5	prachanpol	prachanpol	NOUN
ejpam-6038	306	6	,	,	PUNCT
ejpam-6038	306	7	c.	c.	PROPN
ejpam-6038	306	8	boonpok	boonpok	PROPN
ejpam-6038	306	9	,	,	PUNCT
ejpam-6038	306	10	and	and	CCONJ
ejpam-6038	306	11	c.	c.	PROPN
ejpam-6038	306	12	viriyapong	viriyapong	PROPN
ejpam-6038	306	13	.	.	PUNCT
ejpam-6038	307	1	δ(τ1	δ(τ1	PROPN
ejpam-6038	307	2	,	,	PUNCT
ejpam-6038	307	3	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	307	4	functions	function	NOUN
ejpam-6038	307	5	.	.	PUNCT
ejpam-6038	308	1	european	european	ADJ
ejpam-6038	308	2	journal	journal	PROPN
ejpam-6038	308	3	of	of	ADP
ejpam-6038	308	4	pure	pure	ADJ
ejpam-6038	308	5	and	and	CCONJ
ejpam-6038	308	6	applied	applied	ADJ
ejpam-6038	308	7	mathematics	mathematic	NOUN
ejpam-6038	308	8	,	,	PUNCT
ejpam-6038	308	9	17(4):3730–3742	17(4):3730–3742	NUM
ejpam-6038	308	10	,	,	PUNCT
ejpam-6038	308	11	2024	2024	NUM
ejpam-6038	308	12	.	.	PUNCT
ejpam-6038	309	1	[	[	X
ejpam-6038	309	2	17	17	NUM
ejpam-6038	309	3	]	]	X
ejpam-6038	309	4	b.	b.	PROPN
ejpam-6038	309	5	kong	kong	PROPN
ejpam-6038	309	6	-	-	PUNCT
ejpam-6038	309	7	ied	ied	PROPN
ejpam-6038	309	8	,	,	PUNCT
ejpam-6038	309	9	s.	s.	PROPN
ejpam-6038	309	10	sompong	sompong	PROPN
ejpam-6038	309	11	,	,	PUNCT
ejpam-6038	309	12	and	and	CCONJ
ejpam-6038	309	13	c.	c.	PROPN
ejpam-6038	309	14	boonpok	boonpok	PROPN
ejpam-6038	309	15	.	.	PUNCT
ejpam-6038	310	1	almost	almost	ADV
ejpam-6038	310	2	quasi	quasi	X
ejpam-6038	310	3	(	(	PUNCT
ejpam-6038	310	4	τ1	τ1	NOUN
ejpam-6038	310	5	,	,	PUNCT
ejpam-6038	310	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	310	7	functions	function	NOUN
ejpam-6038	310	8	.	.	PUNCT
ejpam-6038	311	1	asia	asia	PROPN
ejpam-6038	311	2	pacific	pacific	PROPN
ejpam-6038	311	3	journal	journal	PROPN
ejpam-6038	311	4	of	of	ADP
ejpam-6038	311	5	mathematics	mathematic	NOUN
ejpam-6038	311	6	,	,	PUNCT
ejpam-6038	311	7	11:64	11:64	NUM
ejpam-6038	311	8	,	,	PUNCT
ejpam-6038	311	9	2024	2024	NUM
ejpam-6038	311	10	.	.	PUNCT
ejpam-6038	312	1	[	[	X
ejpam-6038	312	2	18	18	NUM
ejpam-6038	312	3	]	]	PUNCT
ejpam-6038	312	4	m.	m.	NOUN
ejpam-6038	312	5	chiangpradit	chiangpradit	NOUN
ejpam-6038	312	6	,	,	PUNCT
ejpam-6038	312	7	s.	s.	PROPN
ejpam-6038	312	8	sompong	sompong	PROPN
ejpam-6038	312	9	,	,	PUNCT
ejpam-6038	312	10	and	and	CCONJ
ejpam-6038	312	11	c.	c.	PROPN
ejpam-6038	312	12	boonpok	boonpok	PROPN
ejpam-6038	312	13	.	.	PUNCT
ejpam-6038	313	1	weakly	weakly	ADJ
ejpam-6038	313	2	quasi	quasi	NOUN
ejpam-6038	313	3	(	(	PUNCT
ejpam-6038	313	4	τ1	τ1	PROPN
ejpam-6038	313	5	,	,	PUNCT
ejpam-6038	313	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	313	7	functions	function	NOUN
ejpam-6038	313	8	.	.	PUNCT
ejpam-6038	314	1	international	international	ADJ
ejpam-6038	314	2	journal	journal	NOUN
ejpam-6038	314	3	of	of	ADP
ejpam-6038	314	4	analysis	analysis	NOUN
ejpam-6038	314	5	and	and	CCONJ
ejpam-6038	314	6	applications	application	NOUN
ejpam-6038	314	7	,	,	PUNCT
ejpam-6038	314	8	22:125	22:125	NUM
ejpam-6038	314	9	,	,	PUNCT
ejpam-6038	314	10	2024	2024	NUM
ejpam-6038	314	11	.	.	PUNCT
ejpam-6038	315	1	[	[	X
ejpam-6038	315	2	19	19	NUM
ejpam-6038	315	3	]	]	X
ejpam-6038	315	4	n.	n.	NOUN
ejpam-6038	315	5	srisarakham	srisarakham	PROPN
ejpam-6038	315	6	,	,	PUNCT
ejpam-6038	315	7	a.	a.	PROPN
ejpam-6038	315	8	sama	sama	PROPN
ejpam-6038	315	9	-	-	PUNCT
ejpam-6038	315	10	ae	ae	PROPN
ejpam-6038	315	11	,	,	PUNCT
ejpam-6038	315	12	and	and	CCONJ
ejpam-6038	315	13	c.	c.	PROPN
ejpam-6038	315	14	boonpok	boonpok	PROPN
ejpam-6038	315	15	.	.	PUNCT
ejpam-6038	316	1	characterizations	characterization	NOUN
ejpam-6038	316	2	of	of	ADP
ejpam-6038	316	3	faintly	faintly	ADV
ejpam-6038	316	4	(	(	PUNCT
ejpam-6038	316	5	τ1	τ1	PROPN
ejpam-6038	316	6	,	,	PUNCT
ejpam-6038	316	7	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	316	8	functions	function	NOUN
ejpam-6038	316	9	.	.	PUNCT
ejpam-6038	317	1	european	european	ADJ
ejpam-6038	317	2	journal	journal	PROPN
ejpam-6038	317	3	of	of	ADP
ejpam-6038	317	4	pure	pure	ADJ
ejpam-6038	317	5	and	and	CCONJ
ejpam-6038	317	6	applied	applied	ADJ
ejpam-6038	317	7	mathematics	mathematic	NOUN
ejpam-6038	317	8	,	,	PUNCT
ejpam-6038	317	9	17(4):2753–2762	17(4):2753–2762	NUM
ejpam-6038	317	10	,	,	PUNCT
ejpam-6038	317	11	2024	2024	NUM
ejpam-6038	317	12	.	.	PUNCT
ejpam-6038	318	1	[	[	X
ejpam-6038	318	2	20	20	NUM
ejpam-6038	318	3	]	]	X
ejpam-6038	318	4	j.	j.	PROPN
ejpam-6038	318	5	khampakdee	khampakdee	PROPN
ejpam-6038	318	6	,	,	PUNCT
ejpam-6038	318	7	s.	s.	PROPN
ejpam-6038	318	8	sompong	sompong	PROPN
ejpam-6038	318	9	,	,	PUNCT
ejpam-6038	318	10	and	and	CCONJ
ejpam-6038	318	11	c.	c.	PROPN
ejpam-6038	318	12	boonpok	boonpok	PROPN
ejpam-6038	318	13	.	.	PUNCT
ejpam-6038	319	1	almost	almost	ADV
ejpam-6038	319	2	weakly	weakly	ADJ
ejpam-6038	319	3	(	(	PUNCT
ejpam-6038	319	4	τ1	τ1	NOUN
ejpam-6038	319	5	,	,	PUNCT
ejpam-6038	319	6	τ2)-continuous	τ2)-continuous	ADJ
ejpam-6038	319	7	functions	function	NOUN
ejpam-6038	319	8	.	.	PUNCT
ejpam-6038	320	1	european	european	ADJ
ejpam-6038	320	2	journal	journal	PROPN
ejpam-6038	320	3	of	of	ADP
ejpam-6038	320	4	pure	pure	ADJ
ejpam-6038	320	5	and	and	CCONJ
ejpam-6038	320	6	applied	applied	ADJ
ejpam-6038	320	7	mathematics	mathematic	NOUN
ejpam-6038	320	8	,	,	PUNCT
ejpam-6038	320	9	18(1):5721	18(1):5721	NUM
ejpam-6038	320	10	,	,	PUNCT
ejpam-6038	320	11	2025	2025	NUM
ejpam-6038	320	12	.	.	PUNCT
ejpam-6038	321	1	[	[	X
ejpam-6038	321	2	21	21	NUM
ejpam-6038	321	3	]	]	X
ejpam-6038	321	4	c.	c.	PROPN
ejpam-6038	321	5	boonpok	boonpok	PROPN
ejpam-6038	321	6	and	and	CCONJ
ejpam-6038	321	7	j.	j.	PROPN
ejpam-6038	321	8	khampakdee	khampakdee	PROPN
ejpam-6038	321	9	.	.	PUNCT
ejpam-6038	322	1	upper	upper	ADJ
ejpam-6038	322	2	and	and	CCONJ
ejpam-6038	322	3	lower	low	ADJ
ejpam-6038	322	4	almost	almost	ADV
ejpam-6038	322	5	contra-(λ	contra-(λ	PROPN
ejpam-6038	322	6	,	,	PUNCT
ejpam-6038	322	7	sp)-continuity	sp)-continuity	NOUN
ejpam-6038	322	8	.	.	PUNCT
ejpam-6038	323	1	european	european	PROPN
ejpam-6038	323	2	journal	journal	PROPN
ejpam-6038	323	3	of	of	ADP
ejpam-6038	323	4	pure	pure	ADJ
ejpam-6038	323	5	and	and	CCONJ
ejpam-6038	323	6	applied	applied	ADJ
ejpam-6038	323	7	mathematics	mathematic	NOUN
ejpam-6038	323	8	,	,	PUNCT
ejpam-6038	323	9	16(1):156–168	16(1):156–168	PROPN
ejpam-6038	323	10	,	,	PUNCT
ejpam-6038	323	11	2023	2023	NUM
ejpam-6038	323	12	.	.	PUNCT
ejpam-6038	324	1	[	[	X
ejpam-6038	324	2	22	22	NUM
ejpam-6038	324	3	]	]	PUNCT
ejpam-6038	324	4	c.	c.	PROPN
ejpam-6038	324	5	boonpok	boonpok	PROPN
ejpam-6038	324	6	,	,	PUNCT
ejpam-6038	324	7	c.	c.	PROPN
ejpam-6038	324	8	viriyapong	viriyapong	PROPN
ejpam-6038	324	9	,	,	PUNCT
ejpam-6038	324	10	and	and	CCONJ
ejpam-6038	324	11	m.	m.	NOUN
ejpam-6038	324	12	thongmoon	thongmoon	NOUN
ejpam-6038	324	13	.	.	PUNCT
ejpam-6038	325	1	on	on	ADP
ejpam-6038	325	2	upper	upper	ADJ
ejpam-6038	325	3	and	and	CCONJ
ejpam-6038	325	4	lower	low	ADJ
ejpam-6038	325	5	(	(	PUNCT
ejpam-6038	325	6	τ1	τ1	NOUN
ejpam-6038	325	7	,	,	PUNCT
ejpam-6038	325	8	τ2)precontinuous	τ2)precontinuous	ADJ
ejpam-6038	325	9	multifunctions	multifunction	NOUN
ejpam-6038	325	10	.	.	PUNCT
ejpam-6038	326	1	journal	journal	PROPN
ejpam-6038	326	2	of	of	ADP
ejpam-6038	326	3	mathematics	mathematics	PROPN
ejpam-6038	326	4	and	and	CCONJ
ejpam-6038	326	5	computer	computer	NOUN
ejpam-6038	326	6	science	science	NOUN
ejpam-6038	326	7	,	,	PUNCT
ejpam-6038	326	8	18:282–293	18:282–293	NUM
ejpam-6038	326	9	,	,	PUNCT
ejpam-6038	326	10	2018	2018	NUM
ejpam-6038	326	11	.	.	PUNCT
ejpam-6038	327	1	[	[	X
ejpam-6038	327	2	23	23	NUM
ejpam-6038	327	3	]	]	X
ejpam-6038	327	4	c.	c.	PROPN
ejpam-6038	327	5	viriyapong	viriyapong	PROPN
ejpam-6038	327	6	and	and	CCONJ
ejpam-6038	327	7	c.	c.	PROPN
ejpam-6038	327	8	boonpok	boonpok	PROPN
ejpam-6038	327	9	.	.	PUNCT
ejpam-6038	328	1	(	(	PUNCT
ejpam-6038	328	2	τ1	τ1	NOUN
ejpam-6038	328	3	,	,	PUNCT
ejpam-6038	328	4	τ2)α	τ2)α	NOUN
ejpam-6038	328	5	-	-	PUNCT
ejpam-6038	328	6	continuity	continuity	NOUN
ejpam-6038	328	7	for	for	ADP
ejpam-6038	328	8	multifunctions	multifunction	NOUN
ejpam-6038	328	9	.	.	PUNCT
ejpam-6038	329	1	journal	journal	PROPN
ejpam-6038	329	2	of	of	ADP
ejpam-6038	329	3	mathematics	mathematic	NOUN
ejpam-6038	329	4	,	,	PUNCT
ejpam-6038	329	5	2020:6285763	2020:6285763	NUM
ejpam-6038	329	6	,	,	PUNCT
ejpam-6038	329	7	2020	2020	NUM
ejpam-6038	329	8	.	.	PUNCT
ejpam-6038	330	1	[	[	X
ejpam-6038	330	2	24	24	NUM
ejpam-6038	330	3	]	]	PUNCT
ejpam-6038	330	4	c.	c.	PROPN
ejpam-6038	330	5	boonpok	boonpok	PROPN
ejpam-6038	330	6	.	.	PUNCT
ejpam-6038	331	1	(	(	PUNCT
ejpam-6038	331	2	τ1	τ1	NOUN
ejpam-6038	331	3	,	,	PUNCT
ejpam-6038	331	4	τ2)δ	τ2)δ	ADJ
ejpam-6038	331	5	-	-	PUNCT
ejpam-6038	331	6	semicontinuous	semicontinuous	ADJ
ejpam-6038	331	7	multifunctions	multifunction	NOUN
ejpam-6038	331	8	.	.	PUNCT
ejpam-6038	332	1	heliyon	heliyon	NOUN
ejpam-6038	332	2	,	,	PUNCT
ejpam-6038	332	3	6	6	NUM
ejpam-6038	332	4	:	:	SYM
ejpam-6038	332	5	e05367	e05367	PROPN
ejpam-6038	332	6	,	,	PUNCT
ejpam-6038	332	7	2020	2020	NUM
ejpam-6038	332	8	.	.	PUNCT
ejpam-6038	333	1	[	[	X
ejpam-6038	333	2	25	25	NUM
ejpam-6038	333	3	]	]	X
ejpam-6038	333	4	n.	n.	PROPN
ejpam-6038	333	5	viriyapong	viriyapong	PROPN
ejpam-6038	333	6	,	,	PUNCT
ejpam-6038	333	7	s.	s.	PROPN
ejpam-6038	333	8	sompong	sompong	PROPN
ejpam-6038	333	9	,	,	PUNCT
ejpam-6038	333	10	and	and	CCONJ
ejpam-6038	333	11	c.	c.	PROPN
ejpam-6038	333	12	boonpok	boonpok	PROPN
ejpam-6038	333	13	.	.	PUNCT
ejpam-6038	334	1	(	(	PUNCT
ejpam-6038	334	2	τ1	τ1	NOUN
ejpam-6038	334	3	,	,	PUNCT
ejpam-6038	334	4	τ2)-extremal	τ2)-extremal	ADJ
ejpam-6038	334	5	disconnectedness	disconnectedness	NOUN
ejpam-6038	334	6	in	in	ADP
ejpam-6038	334	7	p.	p.	NOUN
ejpam-6038	334	8	pue	pue	NOUN
ejpam-6038	334	9	-	-	PUNCT
ejpam-6038	334	10	on	on	ADP
ejpam-6038	334	11	,	,	PUNCT
ejpam-6038	334	12	a.	a.	PROPN
ejpam-6038	334	13	sama	sama	PROPN
ejpam-6038	334	14	-	-	PUNCT
ejpam-6038	334	15	ae	ae	PROPN
ejpam-6038	334	16	,	,	PUNCT
ejpam-6038	334	17	c.	c.	PROPN
ejpam-6038	334	18	boonpok	boonpok	PROPN
ejpam-6038	334	19	/	/	SYM
ejpam-6038	334	20	eur	eur	PROPN
ejpam-6038	334	21	.	.	PUNCT
ejpam-6038	335	1	j.	j.	PROPN
ejpam-6038	335	2	pure	pure	PROPN
ejpam-6038	335	3	appl	appl	PROPN
ejpam-6038	335	4	.	.	PROPN
ejpam-6038	335	5	math	math	PROPN
ejpam-6038	335	6	,	,	PUNCT
ejpam-6038	335	7	18	18	NUM
ejpam-6038	335	8	(	(	PUNCT
ejpam-6038	335	9	2	2	NUM
ejpam-6038	335	10	)	)	PUNCT
ejpam-6038	335	11	(	(	PUNCT
ejpam-6038	335	12	2025	2025	NUM
ejpam-6038	335	13	)	)	PUNCT
ejpam-6038	335	14	,	,	PUNCT
ejpam-6038	335	15	6038	6038	NUM
ejpam-6038	335	16	11	11	NUM
ejpam-6038	335	17	of	of	ADP
ejpam-6038	335	18	11	11	NUM
ejpam-6038	335	19	bitopological	bitopological	ADJ
ejpam-6038	335	20	spaces	space	NOUN
ejpam-6038	335	21	.	.	PUNCT
ejpam-6038	336	1	international	international	ADJ
ejpam-6038	336	2	journal	journal	PROPN
ejpam-6038	336	3	of	of	ADP
ejpam-6038	336	4	mathematics	mathematic	NOUN
ejpam-6038	336	5	and	and	CCONJ
ejpam-6038	336	6	computer	computer	NOUN
ejpam-6038	336	7	science	science	NOUN
ejpam-6038	336	8	,	,	PUNCT
ejpam-6038	336	9	19(3):855–860	19(3):855–860	PROPN
ejpam-6038	336	10	,	,	PUNCT
ejpam-6038	336	11	2024	2024	NUM
ejpam-6038	336	12	.	.	PUNCT
ejpam-6038	337	1	[	[	X
ejpam-6038	337	2	26	26	NUM
ejpam-6038	337	3	]	]	X
ejpam-6038	337	4	n.	n.	PROPN
ejpam-6038	337	5	viriyapong	viriyapong	PROPN
ejpam-6038	337	6	,	,	PUNCT
ejpam-6038	337	7	s.	s.	PROPN
ejpam-6038	337	8	sompong	sompong	PROPN
ejpam-6038	337	9	,	,	PUNCT
ejpam-6038	337	10	and	and	CCONJ
ejpam-6038	337	11	c.	c.	PROPN
ejpam-6038	337	12	boonpok	boonpok	PROPN
ejpam-6038	337	13	.	.	PUNCT
ejpam-6038	338	1	upper	upper	ADJ
ejpam-6038	338	2	and	and	CCONJ
ejpam-6038	338	3	lower	low	ADJ
ejpam-6038	338	4	s-(τ1	s-(τ1	NOUN
ejpam-6038	338	5	,	,	PUNCT
ejpam-6038	338	6	τ2)p	τ2)p	ADJ
ejpam-6038	338	7	-	-	PUNCT
ejpam-6038	338	8	continuous	continuous	ADJ
ejpam-6038	338	9	multifunctions	multifunction	NOUN
ejpam-6038	338	10	.	.	PUNCT
ejpam-6038	339	1	european	european	ADJ
ejpam-6038	339	2	journal	journal	PROPN
ejpam-6038	339	3	of	of	ADP
ejpam-6038	339	4	pure	pure	ADJ
ejpam-6038	339	5	and	and	CCONJ
ejpam-6038	339	6	applied	applied	ADJ
ejpam-6038	339	7	mathematics	mathematic	NOUN
ejpam-6038	339	8	,	,	PUNCT
ejpam-6038	339	9	17(3):2210–2220	17(3):2210–2220	NUM
ejpam-6038	339	10	,	,	PUNCT
ejpam-6038	339	11	2024	2024	NUM
ejpam-6038	339	12	.	.	PUNCT
ejpam-6038	340	1	[	[	X
ejpam-6038	340	2	27	27	NUM
ejpam-6038	340	3	]	]	X
ejpam-6038	340	4	c.	c.	PROPN
ejpam-6038	340	5	viriyapong	viriyapong	PROPN
ejpam-6038	340	6	,	,	PUNCT
ejpam-6038	340	7	s.	s.	PROPN
ejpam-6038	340	8	sompong	sompong	PROPN
ejpam-6038	340	9	,	,	PUNCT
ejpam-6038	340	10	and	and	CCONJ
ejpam-6038	340	11	c.	c.	PROPN
ejpam-6038	340	12	boonpok	boonpok	PROPN
ejpam-6038	340	13	.	.	PUNCT
ejpam-6038	341	1	upper	upper	ADJ
ejpam-6038	341	2	and	and	CCONJ
ejpam-6038	341	3	lower	low	ADJ
ejpam-6038	341	4	slight	slight	ADJ
ejpam-6038	341	5	α(τ1	α(τ1	NOUN
ejpam-6038	341	6	,	,	PUNCT
ejpam-6038	341	7	τ2)continuity	τ2)continuity	PROPN
ejpam-6038	341	8	.	.	PUNCT
ejpam-6038	342	1	european	european	PROPN
ejpam-6038	342	2	journal	journal	PROPN
ejpam-6038	342	3	of	of	ADP
ejpam-6038	342	4	pure	pure	ADJ
ejpam-6038	342	5	and	and	CCONJ
ejpam-6038	342	6	applied	applied	ADJ
ejpam-6038	342	7	mathematics	mathematic	NOUN
ejpam-6038	342	8	,	,	PUNCT
ejpam-6038	342	9	17(3):2142–2154	17(3):2142–2154	NUM
ejpam-6038	342	10	,	,	PUNCT
ejpam-6038	342	11	2024	2024	NUM
ejpam-6038	342	12	.	.	PUNCT
ejpam-6038	343	1	[	[	X
ejpam-6038	343	2	28	28	NUM
ejpam-6038	343	3	]	]	X
ejpam-6038	343	4	p.	p.	NOUN
ejpam-6038	343	5	pue	pue	NOUN
ejpam-6038	343	6	-	-	PUNCT
ejpam-6038	343	7	on	on	ADP
ejpam-6038	343	8	,	,	PUNCT
ejpam-6038	343	9	s.	s.	PROPN
ejpam-6038	343	10	sompong	sompong	PROPN
ejpam-6038	343	11	,	,	PUNCT
ejpam-6038	343	12	and	and	CCONJ
ejpam-6038	343	13	c.	c.	PROPN
ejpam-6038	343	14	boonpok	boonpok	PROPN
ejpam-6038	343	15	.	.	PUNCT
ejpam-6038	344	1	almost	almost	ADV
ejpam-6038	344	2	quasi	quasi	X
ejpam-6038	344	3	(	(	PUNCT
ejpam-6038	344	4	τ1	τ1	NOUN
ejpam-6038	344	5	,	,	PUNCT
ejpam-6038	344	6	τ2)-continuity	τ2)-continuity	NOUN
ejpam-6038	344	7	for	for	ADP
ejpam-6038	344	8	multifunctions	multifunction	NOUN
ejpam-6038	344	9	.	.	PUNCT
ejpam-6038	345	1	international	international	ADJ
ejpam-6038	345	2	journal	journal	NOUN
ejpam-6038	345	3	of	of	ADP
ejpam-6038	345	4	analysis	analysis	NOUN
ejpam-6038	345	5	and	and	CCONJ
ejpam-6038	345	6	applications	application	NOUN
ejpam-6038	345	7	,	,	PUNCT
ejpam-6038	345	8	22:97	22:97	NUM
ejpam-6038	345	9	,	,	PUNCT
ejpam-6038	345	10	2024	2024	NUM
ejpam-6038	345	11	.	.	PUNCT