id	sid	tid	token	lemma	pos
ejpam-4317	1	1	european	european	PROPN
ejpam-4317	1	2	journal	journal	PROPN
ejpam-4317	1	3	of	of	ADP
ejpam-4317	1	4	pure	pure	ADJ
ejpam-4317	1	5	and	and	CCONJ
ejpam-4317	1	6	applied	apply	VERB
ejpam-4317	1	7	mathematics	mathematic	NOUN
ejpam-4317	1	8	vol	vol	NOUN
ejpam-4317	1	9	.	.	PROPN
ejpam-4317	2	1	15	15	NUM
ejpam-4317	2	2	,	,	PUNCT
ejpam-4317	2	3	no	no	INTJ
ejpam-4317	2	4	.	.	NOUN
ejpam-4317	2	5	2	2	NUM
ejpam-4317	2	6	,	,	PUNCT
ejpam-4317	2	7	2022	2022	NUM
ejpam-4317	2	8	,	,	PUNCT
ejpam-4317	2	9	443	443	NUM
ejpam-4317	2	10	-	-	SYM
ejpam-4317	2	11	453	453	NUM
ejpam-4317	2	12	issn	issn	PROPN
ejpam-4317	2	13	1307	1307	NUM
ejpam-4317	2	14	-	-	SYM
ejpam-4317	2	15	5543	5543	NUM
ejpam-4317	2	16	–	–	PUNCT
ejpam-4317	3	1	ejpam.com	ejpam.com	X
ejpam-4317	3	2	published	publish	VERB
ejpam-4317	3	3	by	by	ADP
ejpam-4317	3	4	new	new	PROPN
ejpam-4317	3	5	york	york	PROPN
ejpam-4317	3	6	business	business	PROPN
ejpam-4317	3	7	global	global	PROPN
ejpam-4317	3	8	a	a	DET
ejpam-4317	3	9	note	note	NOUN
ejpam-4317	3	10	on	on	ADP
ejpam-4317	3	11	strongly	strongly	ADV
ejpam-4317	3	12	δθ	δθ	NOUN
ejpam-4317	3	13	-	-	PUNCT
ejpam-4317	3	14	i	i	NOUN
ejpam-4317	3	15	-	-	PUNCT
ejpam-4317	3	16	continuous	continuous	ADJ
ejpam-4317	3	17	functions	function	NOUN
ejpam-4317	3	18	josé	josé	PROPN
ejpam-4317	3	19	sanabria1,∗	sanabria1,∗	PROPN
ejpam-4317	3	20	,	,	PUNCT
ejpam-4317	3	21	rafael	rafael	PROPN
ejpam-4317	3	22	lozada	lozada	PROPN
ejpam-4317	3	23	-	-	PUNCT
ejpam-4317	3	24	yavina2,3	yavina2,3	PROPN
ejpam-4317	3	25	,	,	PUNCT
ejpam-4317	3	26	josé	josé	PROPN
ejpam-4317	3	27	tormet4	tormet4	PROPN
ejpam-4317	3	28	1	1	NUM
ejpam-4317	3	29	departamento	departamento	NOUN
ejpam-4317	3	30	de	de	PROPN
ejpam-4317	3	31	matemáticas	matemáticas	NOUN
ejpam-4317	3	32	,	,	PUNCT
ejpam-4317	3	33	facultad	facultad	PROPN
ejpam-4317	3	34	de	de	PROPN
ejpam-4317	3	35	educación	educación	PROPN
ejpam-4317	3	36	y	y	PROPN
ejpam-4317	3	37	ciencias	ciencias	PROPN
ejpam-4317	3	38	,	,	PUNCT
ejpam-4317	3	39	universidad	universidad	PROPN
ejpam-4317	3	40	de	de	X
ejpam-4317	3	41	sucre	sucre	PROPN
ejpam-4317	3	42	,	,	PUNCT
ejpam-4317	3	43	sincelejo	sincelejo	ADJ
ejpam-4317	3	44	,	,	PUNCT
ejpam-4317	3	45	colombia	colombia	PROPN
ejpam-4317	3	46	2	2	NUM
ejpam-4317	3	47	facultad	facultad	PROPN
ejpam-4317	3	48	de	de	PROPN
ejpam-4317	3	49	ciencias	ciencias	PROPN
ejpam-4317	3	50	básicas	básicas	PROPN
ejpam-4317	3	51	,	,	PUNCT
ejpam-4317	3	52	universidad	universidad	PROPN
ejpam-4317	3	53	católica	católica	PROPN
ejpam-4317	3	54	del	del	PROPN
ejpam-4317	3	55	maule	maule	PROPN
ejpam-4317	3	56	,	,	PUNCT
ejpam-4317	3	57	talca	talca	ADV
ejpam-4317	3	58	,	,	PUNCT
ejpam-4317	3	59	chile	chile	PROPN
ejpam-4317	3	60	3facultad	3facultad	PROPN
ejpam-4317	3	61	de	de	PROPN
ejpam-4317	3	62	ciencias	ciencias	PROPN
ejpam-4317	3	63	e	e	PROPN
ejpam-4317	3	64	ingeniería	ingeniería	PROPN
ejpam-4317	3	65	,	,	PUNCT
ejpam-4317	3	66	universidad	universidad	PROPN
ejpam-4317	3	67	tecnológica	tecnológica	PROPN
ejpam-4317	3	68	del	del	PROPN
ejpam-4317	3	69	perú	perú	PROPN
ejpam-4317	3	70	,	,	PUNCT
ejpam-4317	3	71	lima	lima	PROPN
ejpam-4317	3	72	,	,	PUNCT
ejpam-4317	3	73	perú	perú	VERB
ejpam-4317	3	74	4	4	NUM
ejpam-4317	3	75	departamento	departamento	PROPN
ejpam-4317	3	76	de	de	PROPN
ejpam-4317	3	77	ciencias	ciencias	PROPN
ejpam-4317	3	78	,	,	PUNCT
ejpam-4317	3	79	unidad	unidad	PROPN
ejpam-4317	3	80	de	de	PROPN
ejpam-4317	3	81	estudios	estudios	X
ejpam-4317	3	82	básicos	básicos	PROPN
ejpam-4317	3	83	,	,	PUNCT
ejpam-4317	3	84	universidad	universidad	PROPN
ejpam-4317	3	85	de	de	X
ejpam-4317	3	86	oriente	oriente	PROPN
ejpam-4317	3	87	,	,	PUNCT
ejpam-4317	3	88	puerto	puerto	PROPN
ejpam-4317	3	89	la	la	PROPN
ejpam-4317	3	90	cruz	cruz	PROPN
ejpam-4317	3	91	,	,	PUNCT
ejpam-4317	3	92	venezuela	venezuela	PROPN
ejpam-4317	3	93	abstract	abstract	NOUN
ejpam-4317	3	94	.	.	PUNCT
ejpam-4317	4	1	in	in	ADP
ejpam-4317	4	2	this	this	DET
ejpam-4317	4	3	article	article	NOUN
ejpam-4317	4	4	,	,	PUNCT
ejpam-4317	4	5	we	we	PRON
ejpam-4317	4	6	investigate	investigate	VERB
ejpam-4317	4	7	some	some	DET
ejpam-4317	4	8	properties	property	NOUN
ejpam-4317	4	9	of	of	ADP
ejpam-4317	4	10	strongly	strongly	ADV
ejpam-4317	4	11	δθ	δθ	NOUN
ejpam-4317	4	12	-	-	PUNCT
ejpam-4317	4	13	i	i	NOUN
ejpam-4317	4	14	-	-	PUNCT
ejpam-4317	4	15	continuous	continuous	ADJ
ejpam-4317	4	16	functions	function	NOUN
ejpam-4317	4	17	and	and	CCONJ
ejpam-4317	4	18	other	other	ADJ
ejpam-4317	4	19	types	type	NOUN
ejpam-4317	4	20	of	of	ADP
ejpam-4317	4	21	related	related	ADJ
ejpam-4317	4	22	functions	function	NOUN
ejpam-4317	4	23	.	.	PUNCT
ejpam-4317	5	1	specially	specially	ADV
ejpam-4317	5	2	,	,	PUNCT
ejpam-4317	5	3	we	we	PRON
ejpam-4317	5	4	characterize	characterize	VERB
ejpam-4317	5	5	strongly	strongly	ADV
ejpam-4317	5	6	δθ	δθ	NOUN
ejpam-4317	5	7	-	-	PUNCT
ejpam-4317	5	8	i	i	NOUN
ejpam-4317	5	9	-	-	PUNCT
ejpam-4317	5	10	continuous	continuous	ADJ
ejpam-4317	5	11	,	,	PUNCT
ejpam-4317	5	12	we	we	PRON
ejpam-4317	5	13	investigate	investigate	VERB
ejpam-4317	5	14	their	their	PRON
ejpam-4317	5	15	relationship	relationship	NOUN
ejpam-4317	5	16	with	with	ADP
ejpam-4317	5	17	other	other	ADJ
ejpam-4317	5	18	types	type	NOUN
ejpam-4317	5	19	of	of	ADP
ejpam-4317	5	20	functions	function	NOUN
ejpam-4317	5	21	,	,	PUNCT
ejpam-4317	5	22	and	and	CCONJ
ejpam-4317	5	23	we	we	PRON
ejpam-4317	5	24	study	study	VERB
ejpam-4317	5	25	the	the	DET
ejpam-4317	5	26	behavior	behavior	NOUN
ejpam-4317	5	27	of	of	ADP
ejpam-4317	5	28	certain	certain	ADJ
ejpam-4317	5	29	topological	topological	ADJ
ejpam-4317	5	30	notions	notion	NOUN
ejpam-4317	5	31	under	under	ADP
ejpam-4317	5	32	the	the	DET
ejpam-4317	5	33	action	action	NOUN
ejpam-4317	5	34	of	of	ADP
ejpam-4317	5	35	these	these	DET
ejpam-4317	5	36	functions	function	NOUN
ejpam-4317	5	37	.	.	PUNCT
ejpam-4317	6	1	2020	2020	NUM
ejpam-4317	6	2	mathematics	mathematic	NOUN
ejpam-4317	6	3	subject	subject	NOUN
ejpam-4317	6	4	classifications	classification	NOUN
ejpam-4317	6	5	:	:	PUNCT
ejpam-4317	6	6	54a05	54a05	NUM
ejpam-4317	6	7	,	,	PUNCT
ejpam-4317	6	8	54c10	54c10	NUM
ejpam-4317	6	9	.	.	PUNCT
ejpam-4317	7	1	key	key	ADJ
ejpam-4317	7	2	words	word	NOUN
ejpam-4317	7	3	and	and	CCONJ
ejpam-4317	7	4	phrases	phrase	NOUN
ejpam-4317	7	5	:	:	PUNCT
ejpam-4317	7	6	ideals	ideal	NOUN
ejpam-4317	7	7	,	,	PUNCT
ejpam-4317	7	8	δ	δ	NOUN
ejpam-4317	7	9	-	-	ADJ
ejpam-4317	7	10	local	local	ADJ
ejpam-4317	7	11	function	function	NOUN
ejpam-4317	7	12	,	,	PUNCT
ejpam-4317	7	13	δθ	δθ	NOUN
ejpam-4317	7	14	-	-	PUNCT
ejpam-4317	7	15	i	i	NOUN
ejpam-4317	7	16	-	-	PUNCT
ejpam-4317	7	17	open	open	ADJ
ejpam-4317	7	18	set	set	NOUN
ejpam-4317	7	19	.	.	PUNCT
ejpam-4317	8	1	1	1	X
ejpam-4317	8	2	.	.	X
ejpam-4317	8	3	introduction	introduction	NOUN
ejpam-4317	8	4	the	the	DET
ejpam-4317	8	5	concept	concept	NOUN
ejpam-4317	8	6	of	of	ADP
ejpam-4317	8	7	an	an	DET
ejpam-4317	8	8	ideal	ideal	NOUN
ejpam-4317	8	9	on	on	ADP
ejpam-4317	8	10	a	a	DET
ejpam-4317	8	11	topological	topological	ADJ
ejpam-4317	8	12	space	space	NOUN
ejpam-4317	8	13	(	(	PUNCT
ejpam-4317	8	14	nowadays	nowadays	ADV
ejpam-4317	8	15	called	call	VERB
ejpam-4317	8	16	a	a	DET
ejpam-4317	8	17	topological	topological	ADJ
ejpam-4317	8	18	ideal	ideal	NOUN
ejpam-4317	8	19	)	)	PUNCT
ejpam-4317	8	20	has	have	AUX
ejpam-4317	8	21	played	play	VERB
ejpam-4317	8	22	a	a	DET
ejpam-4317	8	23	fundamental	fundamental	ADJ
ejpam-4317	8	24	role	role	NOUN
ejpam-4317	8	25	in	in	ADP
ejpam-4317	8	26	several	several	ADJ
ejpam-4317	8	27	of	of	ADP
ejpam-4317	8	28	the	the	DET
ejpam-4317	8	29	advances	advance	NOUN
ejpam-4317	8	30	in	in	ADP
ejpam-4317	8	31	general	general	ADJ
ejpam-4317	8	32	topology	topology	NOUN
ejpam-4317	8	33	.	.	PUNCT
ejpam-4317	9	1	in	in	ADP
ejpam-4317	9	2	the	the	DET
ejpam-4317	9	3	last	last	ADJ
ejpam-4317	9	4	century	century	NOUN
ejpam-4317	9	5	,	,	PUNCT
ejpam-4317	9	6	a	a	DET
ejpam-4317	9	7	large	large	ADJ
ejpam-4317	9	8	number	number	NOUN
ejpam-4317	9	9	of	of	ADP
ejpam-4317	9	10	works	work	NOUN
ejpam-4317	9	11	have	have	AUX
ejpam-4317	9	12	arisen	arise	VERB
ejpam-4317	9	13	that	that	PRON
ejpam-4317	9	14	have	have	AUX
ejpam-4317	9	15	enriched	enrich	VERB
ejpam-4317	9	16	the	the	DET
ejpam-4317	9	17	literature	literature	NOUN
ejpam-4317	9	18	related	relate	VERB
ejpam-4317	9	19	to	to	ADP
ejpam-4317	9	20	the	the	DET
ejpam-4317	9	21	concept	concept	NOUN
ejpam-4317	9	22	of	of	ADP
ejpam-4317	9	23	topological	topological	ADJ
ejpam-4317	9	24	ideal	ideal	NOUN
ejpam-4317	9	25	.	.	PUNCT
ejpam-4317	10	1	very	very	ADV
ejpam-4317	10	2	recently	recently	ADV
ejpam-4317	10	3	,	,	PUNCT
ejpam-4317	10	4	topological	topological	ADJ
ejpam-4317	10	5	ideals	ideal	NOUN
ejpam-4317	10	6	have	have	AUX
ejpam-4317	10	7	again	again	ADV
ejpam-4317	10	8	received	receive	VERB
ejpam-4317	10	9	special	special	ADJ
ejpam-4317	10	10	attention	attention	NOUN
ejpam-4317	10	11	for	for	ADP
ejpam-4317	10	12	their	their	PRON
ejpam-4317	10	13	versatility	versatility	NOUN
ejpam-4317	10	14	in	in	ADP
ejpam-4317	10	15	tackling	tackle	VERB
ejpam-4317	10	16	topology	topology	NOUN
ejpam-4317	10	17	problems	problem	NOUN
ejpam-4317	10	18	and	and	CCONJ
ejpam-4317	10	19	in	in	ADP
ejpam-4317	10	20	studying	study	VERB
ejpam-4317	10	21	rough	rough	ADJ
ejpam-4317	10	22	set	set	NOUN
ejpam-4317	10	23	models	model	NOUN
ejpam-4317	10	24	,	,	PUNCT
ejpam-4317	10	25	as	as	SCONJ
ejpam-4317	10	26	we	we	PRON
ejpam-4317	10	27	can	can	AUX
ejpam-4317	10	28	see	see	VERB
ejpam-4317	10	29	in	in	ADP
ejpam-4317	10	30	the	the	DET
ejpam-4317	10	31	references	reference	NOUN
ejpam-4317	10	32	[	[	X
ejpam-4317	10	33	19	19	NUM
ejpam-4317	10	34	]	]	PUNCT
ejpam-4317	10	35	,	,	PUNCT
ejpam-4317	10	36	[	[	X
ejpam-4317	10	37	7	7	NUM
ejpam-4317	10	38	]	]	PUNCT
ejpam-4317	10	39	,	,	PUNCT
ejpam-4317	10	40	[	[	X
ejpam-4317	10	41	3	3	NUM
ejpam-4317	10	42	]	]	PUNCT
ejpam-4317	10	43	,	,	PUNCT
ejpam-4317	10	44	[	[	X
ejpam-4317	10	45	12	12	NUM
ejpam-4317	10	46	]	]	PUNCT
ejpam-4317	10	47	,	,	PUNCT
ejpam-4317	10	48	[	[	X
ejpam-4317	10	49	16	16	NUM
ejpam-4317	10	50	]	]	PUNCT
ejpam-4317	10	51	,	,	PUNCT
ejpam-4317	10	52	[	[	X
ejpam-4317	10	53	5	5	NUM
ejpam-4317	10	54	]	]	PUNCT
ejpam-4317	10	55	,	,	PUNCT
ejpam-4317	10	56	[	[	X
ejpam-4317	10	57	9	9	NUM
ejpam-4317	10	58	]	]	PUNCT
ejpam-4317	10	59	,	,	PUNCT
ejpam-4317	10	60	[	[	X
ejpam-4317	10	61	10	10	NUM
ejpam-4317	10	62	]	]	PUNCT
ejpam-4317	10	63	.	.	PUNCT
ejpam-4317	11	1	in	in	ADP
ejpam-4317	11	2	2014	2014	NUM
ejpam-4317	11	3	,	,	PUNCT
ejpam-4317	11	4	hatir	hatir	PROPN
ejpam-4317	11	5	and	and	CCONJ
ejpam-4317	11	6	al	al	PROPN
ejpam-4317	11	7	-	-	PUNCT
ejpam-4317	11	8	omari	omari	PROPN
ejpam-4317	11	9	[	[	X
ejpam-4317	11	10	8	8	NUM
ejpam-4317	11	11	]	]	PUNCT
ejpam-4317	11	12	introduced	introduce	VERB
ejpam-4317	11	13	the	the	DET
ejpam-4317	11	14	concept	concept	NOUN
ejpam-4317	11	15	of	of	ADP
ejpam-4317	11	16	δ	δ	PROPN
ejpam-4317	11	17	-	-	ADJ
ejpam-4317	11	18	local	local	ADJ
ejpam-4317	11	19	function	function	NOUN
ejpam-4317	11	20	and	and	CCONJ
ejpam-4317	11	21	studied	study	VERB
ejpam-4317	11	22	some	some	PRON
ejpam-4317	11	23	of	of	ADP
ejpam-4317	11	24	its	its	PRON
ejpam-4317	11	25	most	most	ADV
ejpam-4317	11	26	relevant	relevant	ADJ
ejpam-4317	11	27	properties	property	NOUN
ejpam-4317	11	28	.	.	PUNCT
ejpam-4317	12	1	the	the	DET
ejpam-4317	12	2	study	study	NOUN
ejpam-4317	12	3	carried	carry	VERB
ejpam-4317	12	4	out	out	ADP
ejpam-4317	12	5	in	in	ADP
ejpam-4317	12	6	[	[	X
ejpam-4317	12	7	8	8	NUM
ejpam-4317	12	8	]	]	PUNCT
ejpam-4317	12	9	served	serve	VERB
ejpam-4317	12	10	as	as	ADP
ejpam-4317	12	11	motivation	motivation	NOUN
ejpam-4317	12	12	to	to	PART
ejpam-4317	12	13	define	define	VERB
ejpam-4317	12	14	the	the	DET
ejpam-4317	12	15	class	class	NOUN
ejpam-4317	12	16	of	of	ADP
ejpam-4317	12	17	the	the	DET
ejpam-4317	12	18	δθ	δθ	NOUN
ejpam-4317	12	19	-	-	PUNCT
ejpam-4317	12	20	i	i	PRON
ejpam-4317	12	21	-open	-open	NOUN
ejpam-4317	12	22	sets	set	NOUN
ejpam-4317	12	23	in	in	ADP
ejpam-4317	12	24	[	[	X
ejpam-4317	12	25	11	11	NUM
ejpam-4317	12	26	]	]	PUNCT
ejpam-4317	12	27	,	,	PUNCT
ejpam-4317	12	28	which	which	PRON
ejpam-4317	12	29	was	be	AUX
ejpam-4317	12	30	later	later	ADV
ejpam-4317	12	31	used	use	VERB
ejpam-4317	12	32	in	in	ADP
ejpam-4317	12	33	[	[	X
ejpam-4317	12	34	14	14	NUM
ejpam-4317	12	35	]	]	PUNCT
ejpam-4317	12	36	to	to	PART
ejpam-4317	12	37	introduce	introduce	VERB
ejpam-4317	12	38	new	new	ADJ
ejpam-4317	12	39	variants	variant	NOUN
ejpam-4317	12	40	of	of	ADP
ejpam-4317	12	41	continuous	continuous	ADJ
ejpam-4317	12	42	functions	function	NOUN
ejpam-4317	12	43	,	,	PUNCT
ejpam-4317	12	44	called	call	VERB
ejpam-4317	12	45	δθ	δθ	NOUN
ejpam-4317	12	46	-	-	PUNCT
ejpam-4317	12	47	i	i	NOUN
ejpam-4317	12	48	-	-	PUNCT
ejpam-4317	12	49	continuous	continuous	ADJ
ejpam-4317	12	50	,	,	PUNCT
ejpam-4317	12	51	weakly	weakly	ADJ
ejpam-4317	12	52	δ	δ	PROPN
ejpam-4317	12	53	-	-	PROPN
ejpam-4317	12	54	j	j	NOUN
ejpam-4317	12	55	-continuous	-continuous	ADJ
ejpam-4317	12	56	and	and	CCONJ
ejpam-4317	12	57	strongly	strongly	ADV
ejpam-4317	12	58	δθ	δθ	NOUN
ejpam-4317	12	59	-	-	PUNCT
ejpam-4317	12	60	i	i	NOUN
ejpam-4317	12	61	-	-	PUNCT
ejpam-4317	12	62	continuous	continuous	ADJ
ejpam-4317	12	63	functions	function	NOUN
ejpam-4317	12	64	.	.	PUNCT
ejpam-4317	13	1	in	in	ADP
ejpam-4317	13	2	this	this	DET
ejpam-4317	13	3	article	article	NOUN
ejpam-4317	13	4	,	,	PUNCT
ejpam-4317	13	5	we	we	PRON
ejpam-4317	13	6	study	study	VERB
ejpam-4317	13	7	and	and	CCONJ
ejpam-4317	13	8	characterize	characterize	VERB
ejpam-4317	13	9	the	the	DET
ejpam-4317	13	10	strongly	strongly	ADV
ejpam-4317	13	11	δθ	δθ	NOUN
ejpam-4317	13	12	-	-	PUNCT
ejpam-4317	13	13	i	i	NOUN
ejpam-4317	13	14	-	-	PUNCT
ejpam-4317	13	15	continuous	continuous	ADJ
ejpam-4317	13	16	functions	function	NOUN
ejpam-4317	13	17	,	,	PUNCT
ejpam-4317	13	18	we	we	PRON
ejpam-4317	13	19	investigate	investigate	VERB
ejpam-4317	13	20	their	their	PRON
ejpam-4317	13	21	relationship	relationship	NOUN
ejpam-4317	13	22	with	with	ADP
ejpam-4317	13	23	other	other	ADJ
ejpam-4317	13	24	types	type	NOUN
ejpam-4317	13	25	of	of	ADP
ejpam-4317	13	26	functions	function	NOUN
ejpam-4317	13	27	,	,	PUNCT
ejpam-4317	13	28	and	and	CCONJ
ejpam-4317	13	29	also	also	ADV
ejpam-4317	13	30	,	,	PUNCT
ejpam-4317	13	31	we	we	PRON
ejpam-4317	13	32	explore	explore	VERB
ejpam-4317	13	33	the	the	DET
ejpam-4317	13	34	behavior	behavior	NOUN
ejpam-4317	13	35	of	of	ADP
ejpam-4317	13	36	some	some	DET
ejpam-4317	13	37	topological	topological	ADJ
ejpam-4317	13	38	notions	notion	NOUN
ejpam-4317	13	39	under	under	ADP
ejpam-4317	13	40	these	these	DET
ejpam-4317	13	41	classes	class	NOUN
ejpam-4317	13	42	of	of	ADP
ejpam-4317	13	43	functions	function	NOUN
ejpam-4317	13	44	.	.	PUNCT
ejpam-4317	14	1	∗corresponding	∗corresponde	VERB
ejpam-4317	14	2	author	author	NOUN
ejpam-4317	14	3	.	.	PUNCT
ejpam-4317	15	1	doi	doi	NOUN
ejpam-4317	15	2	:	:	PUNCT
ejpam-4317	15	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4317	https://doi.org/10.29020/nybg.ejpam.v15i2.4317	ADJ
ejpam-4317	15	4	email	email	NOUN
ejpam-4317	15	5	addresses	address	NOUN
ejpam-4317	15	6	:	:	PUNCT
ejpam-4317	16	1	jesanabri@gmail.com	jesanabri@gmail.com	PROPN
ejpam-4317	16	2	,	,	PUNCT
ejpam-4317	16	3	jose.sanabria@unisucre.edu.co	jose.sanabria@unisucre.edu.co	PROPN
ejpam-4317	16	4	(	(	PUNCT
ejpam-4317	16	5	j.	j.	PROPN
ejpam-4317	16	6	sanabria	sanabria	PROPN
ejpam-4317	16	7	)	)	PUNCT
ejpam-4317	16	8	,	,	PUNCT
ejpam-4317	16	9	trobuyo@gmail.com	trobuyo@gmail.com	X
ejpam-4317	16	10	(	(	PUNCT
ejpam-4317	16	11	r.	r.	PROPN
ejpam-4317	16	12	lozada	lozada	PROPN
ejpam-4317	16	13	-	-	PUNCT
ejpam-4317	16	14	yavina	yavina	PROPN
ejpam-4317	16	15	)	)	PUNCT
ejpam-4317	16	16	,	,	PUNCT
ejpam-4317	16	17	ajosetormet@gmail.com	ajosetormet@gmail.com	X
ejpam-4317	16	18	(	(	PUNCT
ejpam-4317	16	19	j.	j.	PROPN
ejpam-4317	16	20	tormet	tormet	PROPN
ejpam-4317	16	21	)	)	PUNCT
ejpam-4317	16	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4317	16	23	443	443	NUM
ejpam-4317	16	24	©	©	ADP
ejpam-4317	16	25	2022	2022	NUM
ejpam-4317	16	26	ejpam	ejpam	VERB
ejpam-4317	16	27	all	all	DET
ejpam-4317	16	28	rights	right	NOUN
ejpam-4317	16	29	reserved	reserve	VERB
ejpam-4317	16	30	.	.	PUNCT
ejpam-4317	17	1	j.	j.	PROPN
ejpam-4317	17	2	sanabria	sanabria	PROPN
ejpam-4317	17	3	,	,	PUNCT
ejpam-4317	17	4	r.	r.	PROPN
ejpam-4317	17	5	lozada	lozada	PROPN
ejpam-4317	17	6	-	-	PUNCT
ejpam-4317	17	7	yavina	yavina	PROPN
ejpam-4317	17	8	,	,	PUNCT
ejpam-4317	17	9	j.	j.	PROPN
ejpam-4317	17	10	tormet	tormet	PROPN
ejpam-4317	17	11	/	/	SYM
ejpam-4317	17	12	eur	eur	PROPN
ejpam-4317	17	13	.	.	PUNCT
ejpam-4317	18	1	j.	j.	PROPN
ejpam-4317	18	2	pure	pure	PROPN
ejpam-4317	18	3	appl	appl	PROPN
ejpam-4317	18	4	.	.	PROPN
ejpam-4317	18	5	math	math	PROPN
ejpam-4317	18	6	,	,	PUNCT
ejpam-4317	18	7	15	15	NUM
ejpam-4317	18	8	(	(	PUNCT
ejpam-4317	18	9	2	2	NUM
ejpam-4317	18	10	)	)	PUNCT
ejpam-4317	18	11	(	(	PUNCT
ejpam-4317	18	12	2022	2022	NUM
ejpam-4317	18	13	)	)	PUNCT
ejpam-4317	18	14	,	,	PUNCT
ejpam-4317	18	15	443	443	NUM
ejpam-4317	18	16	-	-	SYM
ejpam-4317	18	17	453	453	NUM
ejpam-4317	18	18	444	444	NUM
ejpam-4317	18	19	2	2	NUM
ejpam-4317	18	20	.	.	PUNCT
ejpam-4317	18	21	preliminaries	preliminary	NOUN
ejpam-4317	18	22	throughout	throughout	ADP
ejpam-4317	18	23	this	this	DET
ejpam-4317	18	24	paper	paper	NOUN
ejpam-4317	18	25	,	,	PUNCT
ejpam-4317	18	26	(	(	PUNCT
ejpam-4317	18	27	x	x	X
ejpam-4317	18	28	,	,	PUNCT
ejpam-4317	18	29	τ	τ	X
ejpam-4317	18	30	)	)	PUNCT
ejpam-4317	18	31	always	always	ADV
ejpam-4317	18	32	means	mean	VERB
ejpam-4317	18	33	a	a	DET
ejpam-4317	18	34	topological	topological	ADJ
ejpam-4317	18	35	space	space	NOUN
ejpam-4317	18	36	on	on	ADP
ejpam-4317	18	37	which	which	PRON
ejpam-4317	18	38	no	no	DET
ejpam-4317	18	39	separation	separation	NOUN
ejpam-4317	18	40	axioms	axiom	NOUN
ejpam-4317	18	41	are	be	AUX
ejpam-4317	18	42	assumed	assume	VERB
ejpam-4317	18	43	unless	unless	SCONJ
ejpam-4317	18	44	explicitly	explicitly	ADV
ejpam-4317	18	45	stated	state	VERB
ejpam-4317	18	46	.	.	PUNCT
ejpam-4317	19	1	if	if	SCONJ
ejpam-4317	19	2	a	a	PRON
ejpam-4317	19	3	is	be	AUX
ejpam-4317	19	4	a	a	DET
ejpam-4317	19	5	subset	subset	NOUN
ejpam-4317	19	6	of	of	ADP
ejpam-4317	19	7	x	x	PRON
ejpam-4317	19	8	,	,	PUNCT
ejpam-4317	19	9	we	we	PRON
ejpam-4317	19	10	denote	denote	VERB
ejpam-4317	19	11	the	the	DET
ejpam-4317	19	12	closure	closure	NOUN
ejpam-4317	19	13	of	of	ADP
ejpam-4317	19	14	a	a	PRON
ejpam-4317	19	15	and	and	CCONJ
ejpam-4317	19	16	the	the	DET
ejpam-4317	19	17	interior	interior	NOUN
ejpam-4317	19	18	of	of	ADP
ejpam-4317	19	19	a	a	PRON
ejpam-4317	19	20	by	by	ADP
ejpam-4317	19	21	cl(a	cl(a	NUM
ejpam-4317	19	22	)	)	PUNCT
ejpam-4317	19	23	and	and	CCONJ
ejpam-4317	19	24	int(a	int(a	PROPN
ejpam-4317	19	25	)	)	PUNCT
ejpam-4317	19	26	,	,	PUNCT
ejpam-4317	19	27	respectively	respectively	ADV
ejpam-4317	19	28	.	.	PUNCT
ejpam-4317	20	1	the	the	DET
ejpam-4317	20	2	definitions	definition	NOUN
ejpam-4317	20	3	and	and	CCONJ
ejpam-4317	20	4	results	result	NOUN
ejpam-4317	20	5	that	that	SCONJ
ejpam-4317	20	6	we	we	PRON
ejpam-4317	20	7	present	present	VERB
ejpam-4317	20	8	below	below	ADV
ejpam-4317	20	9	can	can	AUX
ejpam-4317	20	10	be	be	AUX
ejpam-4317	20	11	consulted	consult	VERB
ejpam-4317	20	12	in	in	ADP
ejpam-4317	20	13	[	[	X
ejpam-4317	20	14	8	8	NUM
ejpam-4317	20	15	]	]	PUNCT
ejpam-4317	20	16	,	,	PUNCT
ejpam-4317	20	17	[	[	X
ejpam-4317	20	18	14	14	NUM
ejpam-4317	20	19	]	]	PUNCT
ejpam-4317	20	20	and	and	CCONJ
ejpam-4317	20	21	[	[	X
ejpam-4317	20	22	11	11	NUM
ejpam-4317	20	23	]	]	PUNCT
ejpam-4317	20	24	.	.	PUNCT
ejpam-4317	21	1	a	a	DET
ejpam-4317	21	2	point	point	NOUN
ejpam-4317	21	3	x	x	X
ejpam-4317	21	4	∈	∈	NOUN
ejpam-4317	21	5	x	x	PUNCT
ejpam-4317	21	6	is	be	AUX
ejpam-4317	21	7	called	call	VERB
ejpam-4317	21	8	a	a	DET
ejpam-4317	21	9	δ	δ	NOUN
ejpam-4317	21	10	-	-	PUNCT
ejpam-4317	21	11	cluster	cluster	NOUN
ejpam-4317	21	12	(	(	PUNCT
ejpam-4317	21	13	resp	resp	NOUN
ejpam-4317	21	14	.	.	PUNCT
ejpam-4317	22	1	θ	θ	NOUN
ejpam-4317	22	2	-	-	PUNCT
ejpam-4317	22	3	cluster	cluster	NOUN
ejpam-4317	22	4	)	)	PUNCT
ejpam-4317	22	5	point	point	NOUN
ejpam-4317	22	6	of	of	ADP
ejpam-4317	22	7	a	a	DET
ejpam-4317	22	8	if	if	SCONJ
ejpam-4317	22	9	int(cl(u))∩a	int(cl(u))∩a	NOUN
ejpam-4317	22	10	6=	6=	NUM
ejpam-4317	22	11	∅	∅	NOUN
ejpam-4317	22	12	(	(	PUNCT
ejpam-4317	22	13	resp	resp	NOUN
ejpam-4317	22	14	.	.	PUNCT
ejpam-4317	23	1	cl(u)∩a	cl(u)∩a	NOUN
ejpam-4317	23	2	6=	6=	NUM
ejpam-4317	23	3	∅	∅	NOUN
ejpam-4317	23	4	)	)	PUNCT
ejpam-4317	23	5	for	for	ADP
ejpam-4317	23	6	each	each	DET
ejpam-4317	23	7	open	open	ADJ
ejpam-4317	23	8	set	set	VERB
ejpam-4317	23	9	u	u	NOUN
ejpam-4317	23	10	containing	contain	VERB
ejpam-4317	23	11	x.	x.	NOUN
ejpam-4317	23	12	the	the	DET
ejpam-4317	23	13	set	set	NOUN
ejpam-4317	23	14	of	of	ADP
ejpam-4317	23	15	all	all	DET
ejpam-4317	23	16	δ	δ	NOUN
ejpam-4317	23	17	-	-	NOUN
ejpam-4317	23	18	cluster	cluster	NOUN
ejpam-4317	23	19	(	(	PUNCT
ejpam-4317	23	20	resp	resp	NOUN
ejpam-4317	23	21	.	.	PUNCT
ejpam-4317	24	1	θ	θ	NOUN
ejpam-4317	24	2	-	-	PUNCT
ejpam-4317	24	3	cluster	cluster	NOUN
ejpam-4317	24	4	)	)	PUNCT
ejpam-4317	24	5	points	point	NOUN
ejpam-4317	24	6	of	of	ADP
ejpam-4317	24	7	a	a	PRON
ejpam-4317	24	8	is	be	AUX
ejpam-4317	24	9	called	call	VERB
ejpam-4317	24	10	the	the	DET
ejpam-4317	24	11	δ	δ	NOUN
ejpam-4317	24	12	-	-	PUNCT
ejpam-4317	24	13	closure	closure	NOUN
ejpam-4317	24	14	(	(	PUNCT
ejpam-4317	24	15	resp	resp	NOUN
ejpam-4317	24	16	.	.	PUNCT
ejpam-4317	25	1	θ	θ	X
ejpam-4317	25	2	-	-	PUNCT
ejpam-4317	25	3	closure	closure	NOUN
ejpam-4317	25	4	)	)	PUNCT
ejpam-4317	25	5	of	of	ADP
ejpam-4317	25	6	a	a	PRON
ejpam-4317	25	7	and	and	CCONJ
ejpam-4317	25	8	is	be	AUX
ejpam-4317	25	9	denoted	denote	VERB
ejpam-4317	25	10	by	by	ADP
ejpam-4317	25	11	δcl(a	δcl(a	PROPN
ejpam-4317	25	12	)	)	PUNCT
ejpam-4317	25	13	(	(	PUNCT
ejpam-4317	25	14	resp	resp	NOUN
ejpam-4317	25	15	.	.	PUNCT
ejpam-4317	26	1	clθ(a	clθ(a	NOUN
ejpam-4317	26	2	)	)	PUNCT
ejpam-4317	26	3	)	)	PUNCT
ejpam-4317	26	4	.	.	PUNCT
ejpam-4317	27	1	a	a	DET
ejpam-4317	27	2	subset	subset	NOUN
ejpam-4317	27	3	a	a	PRON
ejpam-4317	27	4	of	of	ADP
ejpam-4317	27	5	x	x	SYM
ejpam-4317	27	6	is	be	AUX
ejpam-4317	27	7	said	say	VERB
ejpam-4317	27	8	to	to	PART
ejpam-4317	27	9	be	be	AUX
ejpam-4317	27	10	δ	δ	NOUN
ejpam-4317	27	11	-	-	PUNCT
ejpam-4317	27	12	closed	closed	ADJ
ejpam-4317	27	13	(	(	PUNCT
ejpam-4317	27	14	resp	resp	NOUN
ejpam-4317	27	15	.	.	PUNCT
ejpam-4317	28	1	θ	θ	X
ejpam-4317	28	2	-	-	PUNCT
ejpam-4317	28	3	closed	closed	ADJ
ejpam-4317	28	4	)	)	PUNCT
ejpam-4317	28	5	if	if	SCONJ
ejpam-4317	28	6	a	a	DET
ejpam-4317	28	7	=	=	SYM
ejpam-4317	28	8	δcl(a	δcl(a	NOUN
ejpam-4317	28	9	)	)	PUNCT
ejpam-4317	28	10	(	(	PUNCT
ejpam-4317	28	11	resp	resp	NOUN
ejpam-4317	28	12	.	.	PUNCT
ejpam-4317	29	1	a	a	DET
ejpam-4317	29	2	=	=	ADJ
ejpam-4317	29	3	clθ(a	clθ(a	PROPN
ejpam-4317	29	4	)	)	PUNCT
ejpam-4317	29	5	)	)	PUNCT
ejpam-4317	29	6	.	.	PUNCT
ejpam-4317	30	1	the	the	DET
ejpam-4317	30	2	complement	complement	NOUN
ejpam-4317	30	3	of	of	ADP
ejpam-4317	30	4	a	a	DET
ejpam-4317	30	5	δ	δ	NOUN
ejpam-4317	30	6	-	-	PUNCT
ejpam-4317	30	7	closed	closed	ADJ
ejpam-4317	30	8	(	(	PUNCT
ejpam-4317	30	9	resp	resp	NOUN
ejpam-4317	30	10	.	.	PUNCT
ejpam-4317	31	1	θ	θ	X
ejpam-4317	31	2	-	-	PUNCT
ejpam-4317	31	3	closed	closed	ADJ
ejpam-4317	31	4	)	)	PUNCT
ejpam-4317	31	5	set	set	NOUN
ejpam-4317	31	6	is	be	AUX
ejpam-4317	31	7	said	say	VERB
ejpam-4317	31	8	to	to	PART
ejpam-4317	31	9	be	be	AUX
ejpam-4317	31	10	a	a	DET
ejpam-4317	31	11	δ	δ	NOUN
ejpam-4317	31	12	-	-	ADJ
ejpam-4317	31	13	open	open	ADJ
ejpam-4317	31	14	(	(	PUNCT
ejpam-4317	31	15	resp	resp	NOUN
ejpam-4317	31	16	.	.	PUNCT
ejpam-4317	32	1	θ	θ	X
ejpam-4317	32	2	-	-	ADJ
ejpam-4317	32	3	open	open	ADJ
ejpam-4317	32	4	)	)	PUNCT
ejpam-4317	32	5	set	set	NOUN
ejpam-4317	32	6	.	.	PUNCT
ejpam-4317	33	1	similarly	similarly	ADV
ejpam-4317	33	2	,	,	PUNCT
ejpam-4317	33	3	the	the	DET
ejpam-4317	33	4	θ	θ	NOUN
ejpam-4317	33	5	-	-	NOUN
ejpam-4317	33	6	interior	interior	NOUN
ejpam-4317	33	7	of	of	ADP
ejpam-4317	33	8	a	a	DET
ejpam-4317	33	9	subset	subset	NOUN
ejpam-4317	33	10	a	a	PRON
ejpam-4317	33	11	of	of	ADP
ejpam-4317	33	12	x	x	PRON
ejpam-4317	33	13	,	,	PUNCT
ejpam-4317	33	14	denoted	denote	VERB
ejpam-4317	33	15	by	by	ADP
ejpam-4317	33	16	intθ(a	intθ(a	NOUN
ejpam-4317	33	17	)	)	PUNCT
ejpam-4317	33	18	,	,	PUNCT
ejpam-4317	33	19	consists	consist	VERB
ejpam-4317	33	20	of	of	ADP
ejpam-4317	33	21	all	all	DET
ejpam-4317	33	22	points	point	NOUN
ejpam-4317	33	23	x	x	PUNCT
ejpam-4317	33	24	in	in	ADP
ejpam-4317	33	25	x	x	X
ejpam-4317	33	26	such	such	ADJ
ejpam-4317	33	27	that	that	PRON
ejpam-4317	33	28	for	for	ADP
ejpam-4317	33	29	some	some	DET
ejpam-4317	33	30	open	open	ADJ
ejpam-4317	33	31	set	set	NOUN
ejpam-4317	33	32	u	u	NOUN
ejpam-4317	33	33	containing	contain	VERB
ejpam-4317	33	34	x	x	X
ejpam-4317	33	35	,	,	PUNCT
ejpam-4317	33	36	cl(u	cl(u	X
ejpam-4317	33	37	)	)	PUNCT
ejpam-4317	34	1	⊂	⊂	ADJ
ejpam-4317	34	2	a.	a.	NOUN
ejpam-4317	35	1	it	it	PRON
ejpam-4317	35	2	is	be	AUX
ejpam-4317	35	3	well	well	ADV
ejpam-4317	35	4	known	know	VERB
ejpam-4317	35	5	that	that	SCONJ
ejpam-4317	35	6	,	,	PUNCT
ejpam-4317	35	7	a	a	DET
ejpam-4317	35	8	subset	subset	NOUN
ejpam-4317	35	9	a	a	PRON
ejpam-4317	35	10	of	of	ADP
ejpam-4317	35	11	x	x	NOUN
ejpam-4317	35	12	is	be	AUX
ejpam-4317	35	13	θ	θ	NOUN
ejpam-4317	35	14	-	-	ADJ
ejpam-4317	35	15	open	open	ADJ
ejpam-4317	35	16	if	if	SCONJ
ejpam-4317	35	17	and	and	CCONJ
ejpam-4317	35	18	only	only	ADV
ejpam-4317	35	19	if	if	SCONJ
ejpam-4317	35	20	a	a	DET
ejpam-4317	35	21	=	=	NOUN
ejpam-4317	35	22	intθ(a	intθ(a	NOUN
ejpam-4317	35	23	)	)	PUNCT
ejpam-4317	35	24	.	.	PUNCT
ejpam-4317	36	1	it	it	PRON
ejpam-4317	36	2	follows	follow	VERB
ejpam-4317	36	3	that	that	SCONJ
ejpam-4317	36	4	the	the	DET
ejpam-4317	36	5	collection	collection	NOUN
ejpam-4317	36	6	of	of	ADP
ejpam-4317	36	7	all	all	DET
ejpam-4317	36	8	δ	δ	NOUN
ejpam-4317	36	9	-	-	ADJ
ejpam-4317	36	10	open	open	ADJ
ejpam-4317	36	11	(	(	PUNCT
ejpam-4317	36	12	resp	resp	NOUN
ejpam-4317	36	13	.	.	PUNCT
ejpam-4317	37	1	θ	θ	X
ejpam-4317	37	2	-	-	ADJ
ejpam-4317	37	3	open	open	ADJ
ejpam-4317	37	4	)	)	PUNCT
ejpam-4317	37	5	sets	set	NOUN
ejpam-4317	37	6	in	in	ADP
ejpam-4317	37	7	a	a	DET
ejpam-4317	37	8	topological	topological	ADJ
ejpam-4317	37	9	space	space	NOUN
ejpam-4317	37	10	(	(	PUNCT
ejpam-4317	37	11	x	x	X
ejpam-4317	37	12	,	,	PUNCT
ejpam-4317	37	13	τ	τ	X
ejpam-4317	37	14	)	)	PUNCT
ejpam-4317	37	15	forms	form	VERB
ejpam-4317	37	16	a	a	DET
ejpam-4317	37	17	topology	topology	NOUN
ejpam-4317	37	18	on	on	ADP
ejpam-4317	37	19	x	x	PUNCT
ejpam-4317	37	20	which	which	PRON
ejpam-4317	37	21	is	be	AUX
ejpam-4317	37	22	denoted	denote	VERB
ejpam-4317	37	23	by	by	ADP
ejpam-4317	37	24	τδ	τδ	PROPN
ejpam-4317	37	25	(	(	PUNCT
ejpam-4317	37	26	resp	resp	NOUN
ejpam-4317	37	27	.	.	PUNCT
ejpam-4317	37	28	τθ	τθ	PROPN
ejpam-4317	37	29	)	)	PUNCT
ejpam-4317	37	30	.	.	PUNCT
ejpam-4317	38	1	from	from	ADP
ejpam-4317	38	2	the	the	DET
ejpam-4317	38	3	definitions	definition	NOUN
ejpam-4317	38	4	it	it	PRON
ejpam-4317	38	5	follows	follow	VERB
ejpam-4317	38	6	that	that	SCONJ
ejpam-4317	38	7	τθ	τθ	VERB
ejpam-4317	38	8	⊂	⊂	PROPN
ejpam-4317	38	9	τδ	τδ	ADP
ejpam-4317	38	10	⊂	⊂	PROPN
ejpam-4317	38	11	τ	τ	PROPN
ejpam-4317	38	12	.	.	PUNCT
ejpam-4317	39	1	the	the	DET
ejpam-4317	39	2	topology	topology	NOUN
ejpam-4317	39	3	τδ	τδ	ADV
ejpam-4317	39	4	is	be	AUX
ejpam-4317	39	5	called	call	VERB
ejpam-4317	39	6	the	the	DET
ejpam-4317	39	7	semi	semi	NOUN
ejpam-4317	39	8	-	-	NOUN
ejpam-4317	39	9	regularization	regularization	NOUN
ejpam-4317	39	10	of	of	ADP
ejpam-4317	39	11	τ	τ	PROPN
ejpam-4317	39	12	.	.	PUNCT
ejpam-4317	40	1	observe	observe	VERB
ejpam-4317	40	2	that	that	SCONJ
ejpam-4317	40	3	δcl	δcl	PROPN
ejpam-4317	40	4	is	be	AUX
ejpam-4317	40	5	the	the	DET
ejpam-4317	40	6	closure	closure	NOUN
ejpam-4317	40	7	operator	operator	NOUN
ejpam-4317	40	8	with	with	ADP
ejpam-4317	40	9	respect	respect	NOUN
ejpam-4317	40	10	to	to	ADP
ejpam-4317	40	11	τδ	τδ	ADP
ejpam-4317	40	12	,	,	PUNCT
ejpam-4317	40	13	but	but	CCONJ
ejpam-4317	40	14	clθ	clθ	NOUN
ejpam-4317	40	15	is	be	AUX
ejpam-4317	40	16	not	not	PART
ejpam-4317	40	17	the	the	DET
ejpam-4317	40	18	closure	closure	NOUN
ejpam-4317	40	19	operator	operator	NOUN
ejpam-4317	40	20	with	with	ADP
ejpam-4317	40	21	respect	respect	NOUN
ejpam-4317	40	22	to	to	ADP
ejpam-4317	40	23	τθ	τθ	PROPN
ejpam-4317	40	24	.	.	PUNCT
ejpam-4317	41	1	an	an	DET
ejpam-4317	41	2	ideal	ideal	NOUN
ejpam-4317	41	3	i	i	PRON
ejpam-4317	41	4	on	on	ADP
ejpam-4317	41	5	a	a	DET
ejpam-4317	41	6	topological	topological	ADJ
ejpam-4317	41	7	space	space	NOUN
ejpam-4317	41	8	(	(	PUNCT
ejpam-4317	41	9	x	x	X
ejpam-4317	41	10	,	,	PUNCT
ejpam-4317	41	11	τ	τ	X
ejpam-4317	41	12	)	)	PUNCT
ejpam-4317	41	13	is	be	AUX
ejpam-4317	41	14	a	a	DET
ejpam-4317	41	15	nonempty	nonempty	ADJ
ejpam-4317	41	16	collection	collection	NOUN
ejpam-4317	41	17	of	of	ADP
ejpam-4317	41	18	subsets	subset	NOUN
ejpam-4317	41	19	of	of	ADP
ejpam-4317	41	20	x	x	PUNCT
ejpam-4317	41	21	which	which	PRON
ejpam-4317	41	22	satisfies	satisfy	VERB
ejpam-4317	41	23	the	the	DET
ejpam-4317	41	24	following	follow	VERB
ejpam-4317	41	25	two	two	NUM
ejpam-4317	41	26	properties	property	NOUN
ejpam-4317	41	27	:	:	PUNCT
ejpam-4317	41	28	(	(	PUNCT
ejpam-4317	41	29	i	i	NOUN
ejpam-4317	41	30	)	)	PUNCT
ejpam-4317	42	1	a	a	PRON
ejpam-4317	42	2	∈	∈	NOUN
ejpam-4317	43	1	i	i	PRON
ejpam-4317	43	2	and	and	CCONJ
ejpam-4317	43	3	b	b	PROPN
ejpam-4317	43	4	⊂	⊂	PROPN
ejpam-4317	43	5	a	a	PRON
ejpam-4317	43	6	implies	imply	VERB
ejpam-4317	43	7	b	b	X
ejpam-4317	43	8	∈	∈	PROPN
ejpam-4317	44	1	i	i	PRON
ejpam-4317	44	2	;	;	PUNCT
ejpam-4317	44	3	(	(	PUNCT
ejpam-4317	44	4	ii	ii	NOUN
ejpam-4317	44	5	)	)	PUNCT
ejpam-4317	44	6	a	a	PRON
ejpam-4317	44	7	∈	∈	PROPN
ejpam-4317	45	1	i	i	PRON
ejpam-4317	45	2	and	and	CCONJ
ejpam-4317	45	3	b	b	X
ejpam-4317	45	4	∈	∈	PROPN
ejpam-4317	45	5	i	i	PRON
ejpam-4317	45	6	implies	imply	VERB
ejpam-4317	45	7	a	a	DET
ejpam-4317	45	8	∪	∪	X
ejpam-4317	45	9	b	b	PROPN
ejpam-4317	45	10	∈	∈	PROPN
ejpam-4317	45	11	i.	i.	NOUN
ejpam-4317	45	12	an	an	DET
ejpam-4317	45	13	ideal	ideal	ADJ
ejpam-4317	45	14	topological	topological	ADJ
ejpam-4317	45	15	space	space	NOUN
ejpam-4317	45	16	(	(	PUNCT
ejpam-4317	45	17	or	or	CCONJ
ejpam-4317	45	18	simply	simply	ADV
ejpam-4317	45	19	a	a	DET
ejpam-4317	45	20	space	space	NOUN
ejpam-4317	45	21	)	)	PUNCT
ejpam-4317	45	22	is	be	AUX
ejpam-4317	45	23	a	a	DET
ejpam-4317	45	24	topological	topological	ADJ
ejpam-4317	45	25	space	space	NOUN
ejpam-4317	45	26	(	(	PUNCT
ejpam-4317	45	27	x	x	X
ejpam-4317	45	28	,	,	PUNCT
ejpam-4317	45	29	τ	τ	X
ejpam-4317	45	30	)	)	PUNCT
ejpam-4317	45	31	together	together	ADV
ejpam-4317	45	32	with	with	ADP
ejpam-4317	45	33	an	an	DET
ejpam-4317	45	34	ideal	ideal	ADJ
ejpam-4317	45	35	i	i	PRON
ejpam-4317	45	36	on	on	ADP
ejpam-4317	45	37	x	x	PUNCT
ejpam-4317	45	38	and	and	CCONJ
ejpam-4317	45	39	is	be	AUX
ejpam-4317	45	40	denoted	denote	VERB
ejpam-4317	45	41	by	by	ADP
ejpam-4317	45	42	(	(	PUNCT
ejpam-4317	45	43	x	x	X
ejpam-4317	45	44	,	,	PUNCT
ejpam-4317	45	45	τ	τ	PROPN
ejpam-4317	45	46	,	,	PUNCT
ejpam-4317	45	47	i	i	PROPN
ejpam-4317	45	48	)	)	PUNCT
ejpam-4317	45	49	.	.	PUNCT
ejpam-4317	46	1	if	if	SCONJ
ejpam-4317	46	2	(	(	PUNCT
ejpam-4317	46	3	x	x	X
ejpam-4317	46	4	,	,	PUNCT
ejpam-4317	46	5	τ	τ	PROPN
ejpam-4317	46	6	,	,	PUNCT
ejpam-4317	46	7	i	i	PROPN
ejpam-4317	46	8	)	)	PUNCT
ejpam-4317	46	9	is	be	AUX
ejpam-4317	46	10	a	a	DET
ejpam-4317	46	11	space	space	NOUN
ejpam-4317	46	12	,	,	PUNCT
ejpam-4317	46	13	then	then	ADV
ejpam-4317	46	14	for	for	ADP
ejpam-4317	46	15	any	any	PRON
ejpam-4317	46	16	a	a	DET
ejpam-4317	46	17	⊂	⊂	PROPN
ejpam-4317	46	18	x	x	NOUN
ejpam-4317	46	19	,	,	PUNCT
ejpam-4317	46	20	the	the	DET
ejpam-4317	46	21	local	local	ADJ
ejpam-4317	46	22	function	function	NOUN
ejpam-4317	46	23	(	(	PUNCT
ejpam-4317	46	24	rep	rep	PROPN
ejpam-4317	46	25	.	.	PROPN
ejpam-4317	46	26	δ	δ	PROPN
ejpam-4317	46	27	-	-	ADJ
ejpam-4317	46	28	local	local	ADJ
ejpam-4317	46	29	function	function	NOUN
ejpam-4317	46	30	)	)	PUNCT
ejpam-4317	46	31	of	of	ADP
ejpam-4317	46	32	a	a	PRON
ejpam-4317	46	33	with	with	ADP
ejpam-4317	46	34	respect	respect	NOUN
ejpam-4317	46	35	to	to	ADP
ejpam-4317	46	36	i	i	PRON
ejpam-4317	46	37	and	and	CCONJ
ejpam-4317	46	38	τ	τ	PROPN
ejpam-4317	46	39	,	,	PUNCT
ejpam-4317	46	40	denoted	denote	VERB
ejpam-4317	46	41	by	by	ADP
ejpam-4317	46	42	a?(i	a?(i	PROPN
ejpam-4317	46	43	,	,	PUNCT
ejpam-4317	46	44	τ	τ	X
ejpam-4317	46	45	)	)	PUNCT
ejpam-4317	46	46	(	(	PUNCT
ejpam-4317	46	47	resp	resp	NOUN
ejpam-4317	46	48	.	.	PUNCT
ejpam-4317	46	49	aδ?(i	aδ?(i	NOUN
ejpam-4317	46	50	,	,	PUNCT
ejpam-4317	46	51	τ	τ	NOUN
ejpam-4317	46	52	)	)	PUNCT
ejpam-4317	46	53	)	)	PUNCT
ejpam-4317	46	54	,	,	PUNCT
ejpam-4317	46	55	is	be	AUX
ejpam-4317	46	56	defined	define	VERB
ejpam-4317	46	57	as	as	ADP
ejpam-4317	46	58	a?(i	a?(i	PROPN
ejpam-4317	46	59	,	,	PUNCT
ejpam-4317	46	60	τ	τ	X
ejpam-4317	46	61	)	)	PUNCT
ejpam-4317	46	62	=	=	PRON
ejpam-4317	47	1	{	{	PUNCT
ejpam-4317	47	2	x	x	PUNCT
ejpam-4317	47	3	∈	∈	PROPN
ejpam-4317	47	4	x	x	X
ejpam-4317	47	5	:	:	PUNCT
ejpam-4317	47	6	a	a	DET
ejpam-4317	47	7	∩	∩	ADJ
ejpam-4317	47	8	u	u	NOUN
ejpam-4317	47	9	/∈	/∈	PUNCT
ejpam-4317	48	1	i	i	PRON
ejpam-4317	48	2	for	for	ADP
ejpam-4317	48	3	every	every	DET
ejpam-4317	48	4	open	open	ADJ
ejpam-4317	48	5	set	set	NOUN
ejpam-4317	48	6	u	u	NOUN
ejpam-4317	48	7	containing	contain	VERB
ejpam-4317	48	8	x	x	PRON
ejpam-4317	48	9	}	}	PUNCT
ejpam-4317	48	10	(	(	PUNCT
ejpam-4317	48	11	resp	resp	NOUN
ejpam-4317	48	12	.	.	PUNCT
ejpam-4317	48	13	aδ?(i	aδ?(i	NOUN
ejpam-4317	48	14	,	,	PUNCT
ejpam-4317	48	15	τ	τ	X
ejpam-4317	48	16	)	)	PUNCT
ejpam-4317	48	17	=	=	PRON
ejpam-4317	49	1	{	{	PUNCT
ejpam-4317	49	2	x	x	PUNCT
ejpam-4317	49	3	∈	∈	PROPN
ejpam-4317	49	4	x	x	X
ejpam-4317	49	5	:	:	PUNCT
ejpam-4317	49	6	a	a	DET
ejpam-4317	49	7	∩	∩	ADJ
ejpam-4317	49	8	u	u	NOUN
ejpam-4317	49	9	/∈	/∈	PUNCT
ejpam-4317	50	1	i	i	PRON
ejpam-4317	50	2	for	for	ADP
ejpam-4317	50	3	every	every	DET
ejpam-4317	50	4	δ	δ	PROPN
ejpam-4317	50	5	-	-	ADJ
ejpam-4317	50	6	open	open	ADJ
ejpam-4317	50	7	set	set	NOUN
ejpam-4317	50	8	u	u	NOUN
ejpam-4317	50	9	containing	contain	VERB
ejpam-4317	50	10	x	x	X
ejpam-4317	50	11	}	}	PUNCT
ejpam-4317	50	12	)	)	PUNCT
ejpam-4317	50	13	.	.	PUNCT
ejpam-4317	51	1	we	we	PRON
ejpam-4317	51	2	simply	simply	ADV
ejpam-4317	51	3	write	write	VERB
ejpam-4317	51	4	a	a	PRON
ejpam-4317	51	5	?	?	PUNCT
ejpam-4317	52	1	(	(	PUNCT
ejpam-4317	52	2	resp	resp	NOUN
ejpam-4317	52	3	.	.	PUNCT
ejpam-4317	53	1	aδ	aδ	PROPN
ejpam-4317	53	2	?	?	PUNCT
ejpam-4317	53	3	)	)	PUNCT
ejpam-4317	54	1	in	in	ADP
ejpam-4317	54	2	case	case	NOUN
ejpam-4317	54	3	there	there	PRON
ejpam-4317	54	4	is	be	VERB
ejpam-4317	54	5	no	no	DET
ejpam-4317	54	6	chance	chance	NOUN
ejpam-4317	54	7	for	for	ADP
ejpam-4317	54	8	confusion	confusion	NOUN
ejpam-4317	54	9	.	.	PUNCT
ejpam-4317	55	1	in	in	ADP
ejpam-4317	55	2	general	general	ADJ
ejpam-4317	55	3	,	,	PUNCT
ejpam-4317	55	4	x	x	PRON
ejpam-4317	55	5	?	?	PROPN
ejpam-4317	55	6	is	be	AUX
ejpam-4317	55	7	a	a	DET
ejpam-4317	55	8	proper	proper	ADJ
ejpam-4317	55	9	subset	subset	NOUN
ejpam-4317	55	10	of	of	ADP
ejpam-4317	55	11	x.	x.	NOUN
ejpam-4317	55	12	the	the	DET
ejpam-4317	55	13	hypothesis	hypothesis	NOUN
ejpam-4317	55	14	x	x	X
ejpam-4317	56	1	=	=	PUNCT
ejpam-4317	56	2	x	x	X
ejpam-4317	56	3	?	?	PROPN
ejpam-4317	56	4	is	be	AUX
ejpam-4317	56	5	equivalent	equivalent	ADJ
ejpam-4317	56	6	to	to	ADP
ejpam-4317	56	7	the	the	DET
ejpam-4317	56	8	hypothesis	hypothesis	NOUN
ejpam-4317	56	9	τ	τ	PROPN
ejpam-4317	56	10	∩	∩	PROPN
ejpam-4317	56	11	i	i	PRON
ejpam-4317	56	12	=	=	SYM
ejpam-4317	56	13	{	{	PUNCT
ejpam-4317	56	14	∅	∅	NOUN
ejpam-4317	56	15	}	}	PUNCT
ejpam-4317	56	16	.	.	PUNCT
ejpam-4317	57	1	we	we	PRON
ejpam-4317	57	2	call	call	VERB
ejpam-4317	57	3	the	the	DET
ejpam-4317	57	4	ideals	ideal	NOUN
ejpam-4317	57	5	which	which	PRON
ejpam-4317	57	6	satisfy	satisfy	VERB
ejpam-4317	57	7	this	this	DET
ejpam-4317	57	8	condition	condition	NOUN
ejpam-4317	57	9	τ	τ	X
ejpam-4317	57	10	-boundary	-boundary	ADJ
ejpam-4317	57	11	ideals	ideal	NOUN
ejpam-4317	57	12	.	.	PUNCT
ejpam-4317	58	1	a	a	DET
ejpam-4317	58	2	kuratowski	kuratowski	ADJ
ejpam-4317	58	3	closure	closure	NOUN
ejpam-4317	58	4	operator	operator	NOUN
ejpam-4317	58	5	cl	cl	NOUN
ejpam-4317	58	6	?	?	PUNCT
ejpam-4317	58	7	(	(	PUNCT
ejpam-4317	58	8	.	.	PUNCT
ejpam-4317	58	9	)	)	PUNCT
ejpam-4317	59	1	(	(	PUNCT
ejpam-4317	59	2	resp	resp	NOUN
ejpam-4317	59	3	.	.	PUNCT
ejpam-4317	59	4	δcl	δcl	PROPN
ejpam-4317	59	5	?	?	PROPN
ejpam-4317	59	6	(	(	PUNCT
ejpam-4317	59	7	.	.	PUNCT
ejpam-4317	59	8	)	)	PUNCT
ejpam-4317	59	9	)	)	PUNCT
ejpam-4317	60	1	for	for	ADP
ejpam-4317	60	2	a	a	DET
ejpam-4317	60	3	topology	topology	NOUN
ejpam-4317	60	4	τ	τ	NOUN
ejpam-4317	60	5	?	?	PUNCT
ejpam-4317	60	6	(	(	PUNCT
ejpam-4317	60	7	res	re	NOUN
ejpam-4317	60	8	.	.	PUNCT
ejpam-4317	61	1	τ	τ	PROPN
ejpam-4317	61	2	δ	δ	PROPN
ejpam-4317	61	3	?	?	PUNCT
ejpam-4317	61	4	)	)	PUNCT
ejpam-4317	61	5	finer	fine	ADJ
ejpam-4317	61	6	than	than	ADP
ejpam-4317	61	7	τ	τ	PROPN
ejpam-4317	61	8	(	(	PUNCT
ejpam-4317	61	9	resp	resp	NOUN
ejpam-4317	61	10	.	.	PUNCT
ejpam-4317	62	1	τδ	τδ	X
ejpam-4317	62	2	)	)	PUNCT
ejpam-4317	63	1	,	,	PUNCT
ejpam-4317	63	2	is	be	AUX
ejpam-4317	63	3	defined	define	VERB
ejpam-4317	63	4	by	by	ADP
ejpam-4317	63	5	cl?(a	cl?(a	NOUN
ejpam-4317	63	6	)	)	PUNCT
ejpam-4317	63	7	=	=	SYM
ejpam-4317	64	1	a∪a	a∪a	ADV
ejpam-4317	64	2	?	?	PUNCT
ejpam-4317	65	1	(	(	PUNCT
ejpam-4317	65	2	resp	resp	NOUN
ejpam-4317	65	3	.	.	PUNCT
ejpam-4317	66	1	δcl?(a	δcl?(a	NOUN
ejpam-4317	66	2	)	)	PUNCT
ejpam-4317	67	1	=	=	PUNCT
ejpam-4317	67	2	a	a	PRON
ejpam-4317	67	3	∪	∪	X
ejpam-4317	67	4	aδ	aδ	PROPN
ejpam-4317	67	5	?	?	PUNCT
ejpam-4317	67	6	)	)	PUNCT
ejpam-4317	67	7	.	.	PUNCT
ejpam-4317	68	1	it	it	PRON
ejpam-4317	68	2	is	be	AUX
ejpam-4317	68	3	well	well	ADV
ejpam-4317	68	4	known	know	VERB
ejpam-4317	68	5	that	that	SCONJ
ejpam-4317	68	6	τδ	τδ	ADP
ejpam-4317	68	7	⊂	⊂	PROPN
ejpam-4317	68	8	τ	τ	PROPN
ejpam-4317	68	9	⊂	⊂	PROPN
ejpam-4317	68	10	τ	τ	PROPN
ejpam-4317	68	11	?	?	PUNCT
ejpam-4317	69	1	and	and	CCONJ
ejpam-4317	69	2	τδ	τδ	ADP
ejpam-4317	69	3	⊂	⊂	PROPN
ejpam-4317	69	4	τ?δ	τ?δ	PROPN
ejpam-4317	69	5	⊂	⊂	PROPN
ejpam-4317	69	6	τ	τ	PROPN
ejpam-4317	69	7	?	?	PUNCT
ejpam-4317	69	8	.	.	PUNCT
ejpam-4317	70	1	a	a	DET
ejpam-4317	70	2	point	point	NOUN
ejpam-4317	70	3	x	x	X
ejpam-4317	70	4	∈	∈	NOUN
ejpam-4317	70	5	x	x	PUNCT
ejpam-4317	70	6	is	be	AUX
ejpam-4317	70	7	called	call	VERB
ejpam-4317	70	8	a	a	DET
ejpam-4317	70	9	δθ	δθ	NOUN
ejpam-4317	70	10	-	-	PUNCT
ejpam-4317	70	11	i	i	NOUN
ejpam-4317	70	12	-	-	PUNCT
ejpam-4317	70	13	cluster	cluster	NOUN
ejpam-4317	70	14	point	point	NOUN
ejpam-4317	70	15	of	of	ADP
ejpam-4317	70	16	a	a	DET
ejpam-4317	70	17	if	if	SCONJ
ejpam-4317	70	18	δcl?(u	δcl?(u	PROPN
ejpam-4317	70	19	)	)	PUNCT
ejpam-4317	70	20	∩	∩	NOUN
ejpam-4317	70	21	a	a	DET
ejpam-4317	70	22	6=	6=	NOUN
ejpam-4317	70	23	∅	∅	NOUN
ejpam-4317	70	24	for	for	ADP
ejpam-4317	70	25	every	every	DET
ejpam-4317	70	26	open	open	ADJ
ejpam-4317	70	27	subset	subset	ADJ
ejpam-4317	70	28	u	u	NOUN
ejpam-4317	70	29	of	of	ADP
ejpam-4317	70	30	x	x	SYM
ejpam-4317	70	31	containing	contain	VERB
ejpam-4317	70	32	x.	x.	NOUN
ejpam-4317	70	33	the	the	DET
ejpam-4317	70	34	set	set	NOUN
ejpam-4317	70	35	of	of	ADP
ejpam-4317	70	36	all	all	DET
ejpam-4317	70	37	δθ	δθ	NOUN
ejpam-4317	70	38	-	-	PUNCT
ejpam-4317	70	39	i	i	NOUN
ejpam-4317	70	40	-	-	PUNCT
ejpam-4317	70	41	cluster	cluster	NOUN
ejpam-4317	70	42	points	point	NOUN
ejpam-4317	70	43	of	of	ADP
ejpam-4317	70	44	a	a	PRON
ejpam-4317	70	45	is	be	AUX
ejpam-4317	70	46	called	call	VERB
ejpam-4317	70	47	the	the	DET
ejpam-4317	70	48	δθ	δθ	NOUN
ejpam-4317	70	49	-	-	PUNCT
ejpam-4317	70	50	i	i	NOUN
ejpam-4317	70	51	-	-	PUNCT
ejpam-4317	70	52	closure	closure	NOUN
ejpam-4317	70	53	of	of	ADP
ejpam-4317	70	54	a	a	PRON
ejpam-4317	70	55	and	and	CCONJ
ejpam-4317	70	56	is	be	AUX
ejpam-4317	70	57	denoted	denote	VERB
ejpam-4317	70	58	by	by	ADP
ejpam-4317	70	59	δcl?θ	δcl?θ	PROPN
ejpam-4317	70	60	(	(	PUNCT
ejpam-4317	70	61	a	a	NOUN
ejpam-4317	70	62	)	)	PUNCT
ejpam-4317	70	63	.	.	PUNCT
ejpam-4317	71	1	a	a	DET
ejpam-4317	71	2	subset	subset	NOUN
ejpam-4317	71	3	a	a	PRON
ejpam-4317	71	4	of	of	ADP
ejpam-4317	71	5	x	x	SYM
ejpam-4317	71	6	is	be	AUX
ejpam-4317	71	7	said	say	VERB
ejpam-4317	71	8	to	to	PART
ejpam-4317	71	9	be	be	AUX
ejpam-4317	71	10	δθ	δθ	ADP
ejpam-4317	71	11	-	-	PUNCT
ejpam-4317	71	12	i	i	NOUN
ejpam-4317	71	13	-	-	PUNCT
ejpam-4317	71	14	closed	close	VERB
ejpam-4317	71	15	if	if	SCONJ
ejpam-4317	71	16	δcl?θ	δcl?θ	NUM
ejpam-4317	71	17	(	(	PUNCT
ejpam-4317	71	18	a	a	X
ejpam-4317	71	19	)	)	PUNCT
ejpam-4317	71	20	=	=	SYM
ejpam-4317	71	21	a.	a.	NOUN
ejpam-4317	71	22	the	the	DET
ejpam-4317	71	23	complement	complement	NOUN
ejpam-4317	71	24	of	of	ADP
ejpam-4317	71	25	a	a	DET
ejpam-4317	71	26	δθ	δθ	NOUN
ejpam-4317	71	27	-	-	PUNCT
ejpam-4317	71	28	i	i	NOUN
ejpam-4317	71	29	-	-	PUNCT
ejpam-4317	71	30	closed	close	VERB
ejpam-4317	71	31	set	set	NOUN
ejpam-4317	71	32	is	be	AUX
ejpam-4317	71	33	said	say	VERB
ejpam-4317	71	34	to	to	PART
ejpam-4317	71	35	be	be	AUX
ejpam-4317	71	36	δθ	δθ	ADP
ejpam-4317	71	37	-	-	PUNCT
ejpam-4317	71	38	i	i	NOUN
ejpam-4317	71	39	-	-	PUNCT
ejpam-4317	71	40	open	open	ADJ
ejpam-4317	71	41	set	set	NOUN
ejpam-4317	71	42	.	.	PUNCT
ejpam-4317	72	1	a	a	DET
ejpam-4317	72	2	point	point	NOUN
ejpam-4317	72	3	x	x	X
ejpam-4317	72	4	∈	∈	NOUN
ejpam-4317	72	5	x	x	PUNCT
ejpam-4317	72	6	is	be	AUX
ejpam-4317	72	7	called	call	VERB
ejpam-4317	72	8	a	a	DET
ejpam-4317	72	9	δθ	δθ	NOUN
ejpam-4317	72	10	-	-	PUNCT
ejpam-4317	72	11	i	i	NOUN
ejpam-4317	72	12	-	-	ADJ
ejpam-4317	72	13	interior	interior	ADJ
ejpam-4317	72	14	point	point	NOUN
ejpam-4317	72	15	of	of	ADP
ejpam-4317	72	16	a	a	DET
ejpam-4317	72	17	subset	subset	NOUN
ejpam-4317	72	18	a	a	PRON
ejpam-4317	72	19	of	of	ADP
ejpam-4317	72	20	x	x	PRON
ejpam-4317	72	21	if	if	SCONJ
ejpam-4317	72	22	there	there	PRON
ejpam-4317	72	23	exists	exist	VERB
ejpam-4317	72	24	an	an	DET
ejpam-4317	72	25	open	open	ADJ
ejpam-4317	72	26	set	set	NOUN
ejpam-4317	72	27	u	u	PRON
ejpam-4317	72	28	such	such	ADJ
ejpam-4317	72	29	that	that	SCONJ
ejpam-4317	72	30	x	x	SYM
ejpam-4317	72	31	∈	∈	PROPN
ejpam-4317	72	32	u	u	X
ejpam-4317	72	33	⊂	⊂	PROPN
ejpam-4317	72	34	δcl?(u	δcl?(u	PROPN
ejpam-4317	72	35	)	)	PUNCT
ejpam-4317	73	1	⊂	⊂	PROPN
ejpam-4317	73	2	a.	a.	NOUN
ejpam-4317	73	3	the	the	DET
ejpam-4317	73	4	set	set	NOUN
ejpam-4317	73	5	of	of	ADP
ejpam-4317	73	6	all	all	DET
ejpam-4317	73	7	δθ	δθ	NOUN
ejpam-4317	73	8	-	-	PUNCT
ejpam-4317	73	9	i	i	NOUN
ejpam-4317	73	10	-	-	ADJ
ejpam-4317	73	11	interior	interior	ADJ
ejpam-4317	73	12	points	point	NOUN
ejpam-4317	73	13	of	of	ADP
ejpam-4317	73	14	a	a	PRON
ejpam-4317	73	15	is	be	AUX
ejpam-4317	73	16	called	call	VERB
ejpam-4317	73	17	the	the	DET
ejpam-4317	73	18	δθ	δθ	NOUN
ejpam-4317	73	19	-	-	PUNCT
ejpam-4317	73	20	i	i	NOUN
ejpam-4317	73	21	-	-	NOUN
ejpam-4317	73	22	interior	interior	NOUN
ejpam-4317	73	23	of	of	ADP
ejpam-4317	73	24	a	a	PRON
ejpam-4317	73	25	and	and	CCONJ
ejpam-4317	73	26	is	be	AUX
ejpam-4317	73	27	denoted	denote	VERB
ejpam-4317	73	28	by	by	ADP
ejpam-4317	73	29	δint?θ	δint?θ	PROPN
ejpam-4317	73	30	(	(	PUNCT
ejpam-4317	73	31	a	a	NOUN
ejpam-4317	73	32	)	)	PUNCT
ejpam-4317	73	33	.	.	PUNCT
ejpam-4317	74	1	in	in	ADP
ejpam-4317	74	2	[	[	X
ejpam-4317	74	3	11	11	NUM
ejpam-4317	74	4	,	,	PUNCT
ejpam-4317	74	5	proposition	proposition	NOUN
ejpam-4317	74	6	4.1	4.1	NUM
ejpam-4317	74	7	]	]	PUNCT
ejpam-4317	74	8	it	it	PRON
ejpam-4317	74	9	was	be	AUX
ejpam-4317	74	10	shown	show	VERB
ejpam-4317	74	11	that	that	SCONJ
ejpam-4317	74	12	a	a	DET
ejpam-4317	74	13	subset	subset	NOUN
ejpam-4317	74	14	a	a	PRON
ejpam-4317	74	15	of	of	ADP
ejpam-4317	74	16	x	x	NOUN
ejpam-4317	74	17	is	be	AUX
ejpam-4317	74	18	δθ	δθ	ADP
ejpam-4317	74	19	-	-	PUNCT
ejpam-4317	74	20	i	i	NOUN
ejpam-4317	74	21	-	-	PUNCT
ejpam-4317	74	22	open	open	ADJ
ejpam-4317	74	23	if	if	SCONJ
ejpam-4317	74	24	and	and	CCONJ
ejpam-4317	74	25	only	only	ADV
ejpam-4317	74	26	if	if	SCONJ
ejpam-4317	74	27	a	a	DET
ejpam-4317	74	28	=	=	X
ejpam-4317	74	29	δint?θ	δint?θ	PROPN
ejpam-4317	74	30	(	(	PUNCT
ejpam-4317	74	31	a	a	NOUN
ejpam-4317	74	32	)	)	PUNCT
ejpam-4317	74	33	.	.	PUNCT
ejpam-4317	75	1	since	since	SCONJ
ejpam-4317	75	2	the	the	DET
ejpam-4317	75	3	main	main	ADJ
ejpam-4317	75	4	objective	objective	NOUN
ejpam-4317	75	5	of	of	ADP
ejpam-4317	75	6	this	this	DET
ejpam-4317	75	7	article	article	NOUN
ejpam-4317	75	8	is	be	AUX
ejpam-4317	75	9	to	to	PART
ejpam-4317	75	10	study	study	VERB
ejpam-4317	75	11	strongly	strongly	ADV
ejpam-4317	75	12	δθ	δθ	NOUN
ejpam-4317	75	13	-	-	PUNCT
ejpam-4317	75	14	i	i	NOUN
ejpam-4317	75	15	-	-	PUNCT
ejpam-4317	75	16	continuous	continuous	ADJ
ejpam-4317	75	17	functions	function	NOUN
ejpam-4317	75	18	,	,	PUNCT
ejpam-4317	75	19	now	now	ADV
ejpam-4317	75	20	we	we	PRON
ejpam-4317	75	21	will	will	AUX
ejpam-4317	75	22	recall	recall	VERB
ejpam-4317	75	23	some	some	DET
ejpam-4317	75	24	variants	variant	NOUN
ejpam-4317	75	25	of	of	ADP
ejpam-4317	75	26	continuity	continuity	NOUN
ejpam-4317	75	27	related	relate	VERB
ejpam-4317	75	28	to	to	ADP
ejpam-4317	75	29	the	the	DET
ejpam-4317	75	30	type	type	NOUN
ejpam-4317	75	31	of	of	ADP
ejpam-4317	75	32	functions	function	NOUN
ejpam-4317	75	33	that	that	PRON
ejpam-4317	75	34	we	we	PRON
ejpam-4317	75	35	will	will	AUX
ejpam-4317	75	36	study	study	VERB
ejpam-4317	75	37	.	.	PUNCT
ejpam-4317	76	1	in	in	ADP
ejpam-4317	76	2	what	what	PRON
ejpam-4317	76	3	follows	follow	VERB
ejpam-4317	76	4	,	,	PUNCT
ejpam-4317	76	5	we	we	PRON
ejpam-4317	76	6	consider	consider	VERB
ejpam-4317	76	7	that	that	PRON
ejpam-4317	76	8	(	(	PUNCT
ejpam-4317	76	9	x	x	X
ejpam-4317	76	10	,	,	PUNCT
ejpam-4317	76	11	τ	τ	PROPN
ejpam-4317	76	12	,	,	PUNCT
ejpam-4317	76	13	i	i	PROPN
ejpam-4317	76	14	)	)	PUNCT
ejpam-4317	76	15	and	and	CCONJ
ejpam-4317	76	16	(	(	PUNCT
ejpam-4317	76	17	y	y	PROPN
ejpam-4317	76	18	,	,	PUNCT
ejpam-4317	76	19	σ	σ	PROPN
ejpam-4317	76	20	,	,	PUNCT
ejpam-4317	76	21	j	j	PROPN
ejpam-4317	76	22	)	)	PUNCT
ejpam-4317	76	23	are	be	AUX
ejpam-4317	76	24	spaces	space	NOUN
ejpam-4317	76	25	.	.	PUNCT
ejpam-4317	77	1	definition	definition	NOUN
ejpam-4317	77	2	1	1	NUM
ejpam-4317	77	3	.	.	PUNCT
ejpam-4317	78	1	a	a	DET
ejpam-4317	78	2	function	function	NOUN
ejpam-4317	78	3	f	f	NOUN
ejpam-4317	78	4	:	:	PUNCT
ejpam-4317	78	5	(	(	PUNCT
ejpam-4317	78	6	x	x	X
ejpam-4317	78	7	,	,	PUNCT
ejpam-4317	78	8	τ	τ	X
ejpam-4317	78	9	)	)	PUNCT
ejpam-4317	78	10	→	→	SYM
ejpam-4317	78	11	(	(	PUNCT
ejpam-4317	78	12	y	y	PROPN
ejpam-4317	78	13	,	,	PUNCT
ejpam-4317	78	14	σ	σ	PROPN
ejpam-4317	78	15	)	)	PUNCT
ejpam-4317	78	16	is	be	AUX
ejpam-4317	78	17	said	say	VERB
ejpam-4317	78	18	to	to	PART
ejpam-4317	78	19	be	be	AUX
ejpam-4317	78	20	strongly	strongly	ADV
ejpam-4317	78	21	θ	θ	ADJ
ejpam-4317	78	22	-	-	ADJ
ejpam-4317	78	23	continuous	continuous	ADJ
ejpam-4317	78	24	[	[	X
ejpam-4317	78	25	18	18	NUM
ejpam-4317	78	26	]	]	PUNCT
ejpam-4317	78	27	,	,	PUNCT
ejpam-4317	78	28	j.	j.	PROPN
ejpam-4317	78	29	sanabria	sanabria	PROPN
ejpam-4317	78	30	,	,	PUNCT
ejpam-4317	78	31	r.	r.	PROPN
ejpam-4317	78	32	lozada	lozada	PROPN
ejpam-4317	78	33	-	-	PUNCT
ejpam-4317	78	34	yavina	yavina	PROPN
ejpam-4317	78	35	,	,	PUNCT
ejpam-4317	78	36	j.	j.	PROPN
ejpam-4317	78	37	tormet	tormet	PROPN
ejpam-4317	78	38	/	/	SYM
ejpam-4317	78	39	eur	eur	PROPN
ejpam-4317	78	40	.	.	PUNCT
ejpam-4317	79	1	j.	j.	PROPN
ejpam-4317	79	2	pure	pure	PROPN
ejpam-4317	79	3	appl	appl	PROPN
ejpam-4317	79	4	.	.	PROPN
ejpam-4317	79	5	math	math	PROPN
ejpam-4317	79	6	,	,	PUNCT
ejpam-4317	79	7	15	15	NUM
ejpam-4317	79	8	(	(	PUNCT
ejpam-4317	79	9	2	2	NUM
ejpam-4317	79	10	)	)	PUNCT
ejpam-4317	79	11	(	(	PUNCT
ejpam-4317	79	12	2022	2022	NUM
ejpam-4317	79	13	)	)	PUNCT
ejpam-4317	79	14	,	,	PUNCT
ejpam-4317	79	15	443	443	NUM
ejpam-4317	79	16	-	-	SYM
ejpam-4317	79	17	453	453	NUM
ejpam-4317	79	18	445	445	NUM
ejpam-4317	79	19	(	(	PUNCT
ejpam-4317	79	20	resp	resp	NOUN
ejpam-4317	79	21	.	.	PUNCT
ejpam-4317	80	1	weakly	weakly	ADJ
ejpam-4317	80	2	continuous	continuous	ADJ
ejpam-4317	80	3	[	[	X
ejpam-4317	80	4	13	13	NUM
ejpam-4317	80	5	]	]	PUNCT
ejpam-4317	80	6	,	,	PUNCT
ejpam-4317	80	7	θ	θ	NOUN
ejpam-4317	80	8	-	-	ADJ
ejpam-4317	80	9	continuous	continuous	ADJ
ejpam-4317	80	10	[	[	X
ejpam-4317	80	11	15	15	NUM
ejpam-4317	80	12	]	]	SYM
ejpam-4317	80	13	)	)	PUNCT
ejpam-4317	80	14	if	if	SCONJ
ejpam-4317	80	15	for	for	ADP
ejpam-4317	80	16	each	each	DET
ejpam-4317	80	17	x	x	SYM
ejpam-4317	80	18	∈	∈	PROPN
ejpam-4317	80	19	x	x	X
ejpam-4317	80	20	and	and	CCONJ
ejpam-4317	80	21	each	each	DET
ejpam-4317	80	22	open	open	ADJ
ejpam-4317	80	23	set	set	VERB
ejpam-4317	80	24	v	v	NOUN
ejpam-4317	80	25	in	in	ADP
ejpam-4317	80	26	y	y	NOUN
ejpam-4317	80	27	containing	contain	VERB
ejpam-4317	80	28	f(x	f(x	PROPN
ejpam-4317	80	29	)	)	PUNCT
ejpam-4317	80	30	,	,	PUNCT
ejpam-4317	80	31	there	there	PRON
ejpam-4317	80	32	exists	exist	VERB
ejpam-4317	80	33	an	an	DET
ejpam-4317	80	34	open	open	ADJ
ejpam-4317	80	35	set	set	NOUN
ejpam-4317	80	36	u	u	NOUN
ejpam-4317	80	37	in	in	ADP
ejpam-4317	80	38	x	x	PUNCT
ejpam-4317	80	39	containing	contain	VERB
ejpam-4317	80	40	x	x	PUNCT
ejpam-4317	80	41	such	such	ADJ
ejpam-4317	80	42	that	that	PRON
ejpam-4317	80	43	f(cl(u	f(cl(u	NOUN
ejpam-4317	80	44	)	)	PUNCT
ejpam-4317	80	45	)	)	PUNCT
ejpam-4317	81	1	⊂	⊂	PROPN
ejpam-4317	81	2	v	v	X
ejpam-4317	81	3	(	(	PUNCT
ejpam-4317	81	4	resp	resp	NOUN
ejpam-4317	81	5	.	.	PUNCT
ejpam-4317	82	1	f(u	f(u	PROPN
ejpam-4317	82	2	)	)	PUNCT
ejpam-4317	83	1	⊂	⊂	PROPN
ejpam-4317	83	2	cl(v	cl(v	NOUN
ejpam-4317	83	3	)	)	PUNCT
ejpam-4317	83	4	,	,	PUNCT
ejpam-4317	83	5	f(cl(u	f(cl(u	PROPN
ejpam-4317	83	6	)	)	PUNCT
ejpam-4317	83	7	)	)	PUNCT
ejpam-4317	84	1	⊂	⊂	PROPN
ejpam-4317	84	2	cl(v	cl(v	NOUN
ejpam-4317	84	3	)	)	PUNCT
ejpam-4317	84	4	)	)	PUNCT
ejpam-4317	84	5	.	.	PUNCT
ejpam-4317	85	1	definition	definition	NOUN
ejpam-4317	85	2	2	2	NUM
ejpam-4317	85	3	.	.	PUNCT
ejpam-4317	86	1	a	a	DET
ejpam-4317	86	2	function	function	NOUN
ejpam-4317	86	3	f	f	NOUN
ejpam-4317	86	4	:	:	PUNCT
ejpam-4317	86	5	(	(	PUNCT
ejpam-4317	86	6	x	x	X
ejpam-4317	86	7	,	,	PUNCT
ejpam-4317	86	8	τ	τ	X
ejpam-4317	86	9	)	)	PUNCT
ejpam-4317	86	10	→	→	SYM
ejpam-4317	86	11	(	(	PUNCT
ejpam-4317	86	12	y	y	PROPN
ejpam-4317	86	13	,	,	PUNCT
ejpam-4317	86	14	σ	σ	PROPN
ejpam-4317	86	15	,	,	PUNCT
ejpam-4317	86	16	j	j	PROPN
ejpam-4317	86	17	)	)	PUNCT
ejpam-4317	86	18	is	be	AUX
ejpam-4317	86	19	said	say	VERB
ejpam-4317	86	20	to	to	PART
ejpam-4317	86	21	be	be	AUX
ejpam-4317	86	22	weakly	weakly	ADJ
ejpam-4317	86	23	j	j	NOUN
ejpam-4317	86	24	-continuous	-continuous	ADJ
ejpam-4317	86	25	[	[	X
ejpam-4317	86	26	1	1	NUM
ejpam-4317	86	27	]	]	PUNCT
ejpam-4317	86	28	(	(	PUNCT
ejpam-4317	86	29	resp	resp	NOUN
ejpam-4317	86	30	.	.	PUNCT
ejpam-4317	87	1	weakly	weakly	ADJ
ejpam-4317	87	2	δ	δ	PROPN
ejpam-4317	87	3	-	-	PROPN
ejpam-4317	87	4	j	j	PROPN
ejpam-4317	87	5	-continuous	-continuous	ADJ
ejpam-4317	87	6	[	[	X
ejpam-4317	87	7	14	14	NUM
ejpam-4317	87	8	]	]	PUNCT
ejpam-4317	87	9	)	)	PUNCT
ejpam-4317	87	10	,	,	PUNCT
ejpam-4317	87	11	if	if	SCONJ
ejpam-4317	87	12	for	for	ADP
ejpam-4317	87	13	each	each	DET
ejpam-4317	87	14	x	x	SYM
ejpam-4317	87	15	∈	∈	PROPN
ejpam-4317	87	16	x	x	X
ejpam-4317	87	17	and	and	CCONJ
ejpam-4317	87	18	each	each	DET
ejpam-4317	87	19	open	open	ADJ
ejpam-4317	87	20	set	set	VERB
ejpam-4317	87	21	v	v	NOUN
ejpam-4317	87	22	in	in	ADP
ejpam-4317	87	23	y	y	NOUN
ejpam-4317	87	24	containing	contain	VERB
ejpam-4317	87	25	f(x	f(x	PROPN
ejpam-4317	87	26	)	)	PUNCT
ejpam-4317	87	27	,	,	PUNCT
ejpam-4317	87	28	there	there	PRON
ejpam-4317	87	29	exists	exist	VERB
ejpam-4317	87	30	an	an	DET
ejpam-4317	87	31	open	open	ADJ
ejpam-4317	87	32	set	set	NOUN
ejpam-4317	87	33	u	u	NOUN
ejpam-4317	87	34	in	in	ADP
ejpam-4317	87	35	x	x	PUNCT
ejpam-4317	87	36	containing	contain	VERB
ejpam-4317	87	37	x	x	PUNCT
ejpam-4317	87	38	such	such	ADJ
ejpam-4317	87	39	that	that	DET
ejpam-4317	87	40	f(u	f(u	PROPN
ejpam-4317	87	41	)	)	PUNCT
ejpam-4317	88	1	⊂	⊂	PROPN
ejpam-4317	88	2	cl?(v	cl?(v	VERB
ejpam-4317	88	3	)	)	PUNCT
ejpam-4317	88	4	(	(	PUNCT
ejpam-4317	88	5	resp	resp	NOUN
ejpam-4317	88	6	.	.	PUNCT
ejpam-4317	89	1	f(u	f(u	PROPN
ejpam-4317	89	2	)	)	PUNCT
ejpam-4317	90	1	⊂	⊂	PROPN
ejpam-4317	90	2	δcl?(v	δcl?(v	VERB
ejpam-4317	90	3	)	)	PUNCT
ejpam-4317	90	4	)	)	PUNCT
ejpam-4317	90	5	.	.	PUNCT
ejpam-4317	91	1	definition	definition	NOUN
ejpam-4317	91	2	3	3	NUM
ejpam-4317	91	3	.	.	PUNCT
ejpam-4317	92	1	a	a	DET
ejpam-4317	92	2	function	function	NOUN
ejpam-4317	92	3	f	f	NOUN
ejpam-4317	92	4	:	:	PUNCT
ejpam-4317	92	5	(	(	PUNCT
ejpam-4317	92	6	x	x	X
ejpam-4317	92	7	,	,	PUNCT
ejpam-4317	92	8	τ	τ	PROPN
ejpam-4317	92	9	,	,	PUNCT
ejpam-4317	92	10	i	i	NOUN
ejpam-4317	92	11	)	)	PUNCT
ejpam-4317	92	12	→	→	SYM
ejpam-4317	92	13	(	(	PUNCT
ejpam-4317	92	14	y	y	PROPN
ejpam-4317	92	15	,	,	PUNCT
ejpam-4317	92	16	σ	σ	PROPN
ejpam-4317	92	17	,	,	PUNCT
ejpam-4317	92	18	j	j	PROPN
ejpam-4317	92	19	)	)	PUNCT
ejpam-4317	92	20	is	be	AUX
ejpam-4317	92	21	said	say	VERB
ejpam-4317	92	22	to	to	PART
ejpam-4317	92	23	be	be	AUX
ejpam-4317	92	24	δθ	δθ	ADP
ejpam-4317	92	25	-	-	PUNCT
ejpam-4317	92	26	i	i	NOUN
ejpam-4317	92	27	-	-	NOUN
ejpam-4317	92	28	continuous	continuous	ADJ
ejpam-4317	92	29	[	[	X
ejpam-4317	92	30	14	14	NUM
ejpam-4317	92	31	]	]	X
ejpam-4317	92	32	(	(	PUNCT
ejpam-4317	92	33	resp	resp	NOUN
ejpam-4317	92	34	.	.	PUNCT
ejpam-4317	93	1	θ	θ	X
ejpam-4317	93	2	-	-	PUNCT
ejpam-4317	93	3	i	i	PRON
ejpam-4317	93	4	-	-	NOUN
ejpam-4317	93	5	continuous	continuous	ADJ
ejpam-4317	93	6	[	[	X
ejpam-4317	93	7	17	17	NUM
ejpam-4317	93	8	]	]	NUM
ejpam-4317	93	9	)	)	PUNCT
ejpam-4317	93	10	,	,	PUNCT
ejpam-4317	93	11	if	if	SCONJ
ejpam-4317	93	12	for	for	ADP
ejpam-4317	93	13	each	each	DET
ejpam-4317	93	14	x	x	SYM
ejpam-4317	93	15	∈	∈	PROPN
ejpam-4317	93	16	x	x	X
ejpam-4317	93	17	and	and	CCONJ
ejpam-4317	93	18	each	each	DET
ejpam-4317	93	19	open	open	ADJ
ejpam-4317	93	20	set	set	VERB
ejpam-4317	93	21	v	v	NOUN
ejpam-4317	93	22	in	in	ADP
ejpam-4317	93	23	y	y	NOUN
ejpam-4317	93	24	containing	contain	VERB
ejpam-4317	93	25	f(x	f(x	PROPN
ejpam-4317	93	26	)	)	PUNCT
ejpam-4317	94	1	,	,	PUNCT
ejpam-4317	94	2	there	there	PRON
ejpam-4317	94	3	exists	exist	VERB
ejpam-4317	94	4	an	an	DET
ejpam-4317	94	5	open	open	ADJ
ejpam-4317	94	6	set	set	NOUN
ejpam-4317	94	7	u	u	NOUN
ejpam-4317	94	8	containing	contain	VERB
ejpam-4317	94	9	x	x	PUNCT
ejpam-4317	94	10	such	such	ADJ
ejpam-4317	94	11	that	that	DET
ejpam-4317	94	12	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	94	13	)	)	PUNCT
ejpam-4317	94	14	)	)	PUNCT
ejpam-4317	95	1	⊂	⊂	PROPN
ejpam-4317	95	2	δcl?(v	δcl?(v	VERB
ejpam-4317	95	3	)	)	PUNCT
ejpam-4317	95	4	(	(	PUNCT
ejpam-4317	95	5	resp	resp	NOUN
ejpam-4317	95	6	.	.	PUNCT
ejpam-4317	96	1	f(cl?(u	f(cl?(u	PROPN
ejpam-4317	96	2	)	)	PUNCT
ejpam-4317	96	3	)	)	PUNCT
ejpam-4317	97	1	⊂	⊂	PROPN
ejpam-4317	97	2	cl?(v	cl?(v	VERB
ejpam-4317	97	3	)	)	PUNCT
ejpam-4317	97	4	)	)	PUNCT
ejpam-4317	97	5	.	.	PUNCT
ejpam-4317	98	1	definition	definition	NOUN
ejpam-4317	98	2	4	4	NUM
ejpam-4317	98	3	.	.	PUNCT
ejpam-4317	99	1	a	a	DET
ejpam-4317	99	2	function	function	NOUN
ejpam-4317	99	3	f	f	NOUN
ejpam-4317	99	4	:	:	PUNCT
ejpam-4317	99	5	(	(	PUNCT
ejpam-4317	99	6	x	x	X
ejpam-4317	99	7	,	,	PUNCT
ejpam-4317	99	8	τ	τ	PROPN
ejpam-4317	99	9	,	,	PUNCT
ejpam-4317	99	10	i	i	NOUN
ejpam-4317	99	11	)	)	PUNCT
ejpam-4317	99	12	→	→	SYM
ejpam-4317	99	13	(	(	PUNCT
ejpam-4317	99	14	y	y	PROPN
ejpam-4317	99	15	,	,	PUNCT
ejpam-4317	99	16	σ	σ	PROPN
ejpam-4317	99	17	)	)	PUNCT
ejpam-4317	99	18	is	be	AUX
ejpam-4317	99	19	said	say	VERB
ejpam-4317	99	20	to	to	PART
ejpam-4317	99	21	be	be	AUX
ejpam-4317	99	22	strongly	strongly	ADV
ejpam-4317	99	23	θ	θ	PROPN
ejpam-4317	99	24	-	-	PUNCT
ejpam-4317	99	25	i	i	PRON
ejpam-4317	99	26	-	-	NOUN
ejpam-4317	99	27	continuous	continuous	ADJ
ejpam-4317	99	28	[	[	X
ejpam-4317	99	29	17	17	NUM
ejpam-4317	99	30	]	]	X
ejpam-4317	99	31	(	(	PUNCT
ejpam-4317	99	32	resp	resp	NOUN
ejpam-4317	99	33	.	.	PUNCT
ejpam-4317	100	1	strongly	strongly	ADV
ejpam-4317	100	2	δθ	δθ	ADP
ejpam-4317	100	3	-	-	PUNCT
ejpam-4317	100	4	i	i	NOUN
ejpam-4317	100	5	-	-	NOUN
ejpam-4317	100	6	continuous	continuous	ADJ
ejpam-4317	100	7	[	[	X
ejpam-4317	100	8	14	14	NUM
ejpam-4317	100	9	]	]	NUM
ejpam-4317	100	10	)	)	PUNCT
ejpam-4317	100	11	,	,	PUNCT
ejpam-4317	100	12	if	if	SCONJ
ejpam-4317	100	13	for	for	ADP
ejpam-4317	100	14	each	each	DET
ejpam-4317	100	15	x	x	SYM
ejpam-4317	100	16	∈	∈	PROPN
ejpam-4317	100	17	x	x	X
ejpam-4317	100	18	and	and	CCONJ
ejpam-4317	100	19	each	each	DET
ejpam-4317	100	20	open	open	ADJ
ejpam-4317	100	21	set	set	VERB
ejpam-4317	100	22	v	v	NOUN
ejpam-4317	100	23	in	in	ADP
ejpam-4317	100	24	y	y	NOUN
ejpam-4317	100	25	containing	contain	VERB
ejpam-4317	100	26	f(x	f(x	PROPN
ejpam-4317	100	27	)	)	PUNCT
ejpam-4317	100	28	,	,	PUNCT
ejpam-4317	100	29	there	there	PRON
ejpam-4317	100	30	exists	exist	VERB
ejpam-4317	100	31	an	an	DET
ejpam-4317	100	32	open	open	ADJ
ejpam-4317	100	33	set	set	NOUN
ejpam-4317	100	34	u	u	NOUN
ejpam-4317	100	35	in	in	ADP
ejpam-4317	100	36	x	x	PUNCT
ejpam-4317	100	37	containing	contain	VERB
ejpam-4317	100	38	x	x	PUNCT
ejpam-4317	100	39	such	such	ADJ
ejpam-4317	100	40	that	that	DET
ejpam-4317	100	41	f(cl?(u	f(cl?(u	PROPN
ejpam-4317	100	42	)	)	PUNCT
ejpam-4317	100	43	)	)	PUNCT
ejpam-4317	101	1	⊂	⊂	PROPN
ejpam-4317	101	2	v	v	X
ejpam-4317	101	3	(	(	PUNCT
ejpam-4317	101	4	resp	resp	NOUN
ejpam-4317	101	5	.	.	PUNCT
ejpam-4317	102	1	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	102	2	)	)	PUNCT
ejpam-4317	102	3	)	)	PUNCT
ejpam-4317	103	1	⊂	⊂	PROPN
ejpam-4317	103	2	v	v	NOUN
ejpam-4317	103	3	)	)	PUNCT
ejpam-4317	103	4	.	.	PUNCT
ejpam-4317	104	1	remark	remark	PROPN
ejpam-4317	104	2	1	1	NUM
ejpam-4317	104	3	.	.	PUNCT
ejpam-4317	105	1	the	the	DET
ejpam-4317	105	2	following	follow	VERB
ejpam-4317	105	3	diagram	diagram	NOUN
ejpam-4317	105	4	shows	show	VERB
ejpam-4317	105	5	the	the	DET
ejpam-4317	105	6	relationship	relationship	NOUN
ejpam-4317	105	7	between	between	ADP
ejpam-4317	105	8	the	the	DET
ejpam-4317	105	9	types	type	NOUN
ejpam-4317	105	10	of	of	ADP
ejpam-4317	105	11	functions	function	NOUN
ejpam-4317	105	12	given	give	VERB
ejpam-4317	105	13	in	in	ADP
ejpam-4317	105	14	definitions	definition	NOUN
ejpam-4317	105	15	1	1	NUM
ejpam-4317	105	16	,	,	PUNCT
ejpam-4317	105	17	2	2	NUM
ejpam-4317	105	18	,	,	PUNCT
ejpam-4317	105	19	3	3	NUM
ejpam-4317	105	20	and	and	CCONJ
ejpam-4317	105	21	4	4	NUM
ejpam-4317	105	22	.	.	X
ejpam-4317	106	1	in	in	ADP
ejpam-4317	106	2	general	general	ADJ
ejpam-4317	106	3	none	none	NOUN
ejpam-4317	106	4	of	of	ADP
ejpam-4317	106	5	the	the	DET
ejpam-4317	106	6	implications	implication	NOUN
ejpam-4317	106	7	is	be	AUX
ejpam-4317	106	8	reversible	reversible	ADJ
ejpam-4317	106	9	.	.	PUNCT
ejpam-4317	107	1	weaklyδ	weaklyδ	PROPN
ejpam-4317	107	2	-	-	PUNCT
ejpam-4317	107	3	j	j	NOUN
ejpam-4317	107	4	-continuous	-continuous	ADJ
ejpam-4317	107	5	weakly	weakly	ADJ
ejpam-4317	107	6	continuous	continuous	ADJ
ejpam-4317	107	7	δθ	δθ	NOUN
ejpam-4317	107	8	-	-	PUNCT
ejpam-4317	107	9	i	i	NOUN
ejpam-4317	107	10	-	-	PUNCT
ejpam-4317	107	11	continuous	continuous	ADJ
ejpam-4317	107	12	weakly	weakly	ADJ
ejpam-4317	107	13	j	j	PROPN
ejpam-4317	107	14	-continuous	-continuous	ADJ
ejpam-4317	107	15	θ	θ	ADJ
ejpam-4317	107	16	-	-	ADJ
ejpam-4317	107	17	continuous	continuous	ADJ
ejpam-4317	107	18	strongly	strongly	ADV
ejpam-4317	107	19	δθ	δθ	NOUN
ejpam-4317	107	20	-	-	PUNCT
ejpam-4317	107	21	i	i	NOUN
ejpam-4317	107	22	-	-	PUNCT
ejpam-4317	107	23	continuous	continuous	ADJ
ejpam-4317	107	24	θ	θ	PROPN
ejpam-4317	107	25	-	-	PUNCT
ejpam-4317	107	26	i	i	NOUN
ejpam-4317	107	27	-	-	PUNCT
ejpam-4317	107	28	continuous	continuous	ADJ
ejpam-4317	107	29	continuous	continuous	ADJ
ejpam-4317	107	30	strongly	strongly	ADV
ejpam-4317	107	31	θ	θ	PROPN
ejpam-4317	107	32	-	-	PUNCT
ejpam-4317	107	33	i	i	NOUN
ejpam-4317	107	34	-	-	PUNCT
ejpam-4317	107	35	continuous	continuous	ADJ
ejpam-4317	107	36	strongly	strongly	ADV
ejpam-4317	107	37	θ	θ	NOUN
ejpam-4317	107	38	-	-	ADJ
ejpam-4317	107	39	continuous	continuous	ADJ
ejpam-4317	107	40	3	3	NUM
ejpam-4317	107	41	.	.	PUNCT
ejpam-4317	107	42	properties	property	NOUN
ejpam-4317	107	43	related	relate	VERB
ejpam-4317	107	44	to	to	ADP
ejpam-4317	107	45	strongly	strongly	ADV
ejpam-4317	107	46	δθ	δθ	ADP
ejpam-4317	107	47	-	-	PUNCT
ejpam-4317	107	48	i	i	NOUN
ejpam-4317	107	49	-	-	PUNCT
ejpam-4317	107	50	continuous	continuous	ADJ
ejpam-4317	107	51	functions	function	NOUN
ejpam-4317	107	52	in	in	ADP
ejpam-4317	107	53	this	this	DET
ejpam-4317	107	54	section	section	NOUN
ejpam-4317	107	55	,	,	PUNCT
ejpam-4317	107	56	we	we	PRON
ejpam-4317	107	57	characterize	characterize	VERB
ejpam-4317	107	58	strongly	strongly	ADV
ejpam-4317	107	59	δθ	δθ	NOUN
ejpam-4317	107	60	-	-	PUNCT
ejpam-4317	107	61	i	i	NOUN
ejpam-4317	107	62	-	-	PUNCT
ejpam-4317	107	63	continuous	continuous	ADJ
ejpam-4317	107	64	.	.	PUNCT
ejpam-4317	108	1	also	also	ADV
ejpam-4317	108	2	,	,	PUNCT
ejpam-4317	108	3	we	we	PRON
ejpam-4317	108	4	looking	look	VERB
ejpam-4317	108	5	for	for	ADP
ejpam-4317	108	6	some	some	DET
ejpam-4317	108	7	topological	topological	ADJ
ejpam-4317	108	8	conditions	condition	NOUN
ejpam-4317	108	9	in	in	ADP
ejpam-4317	108	10	order	order	NOUN
ejpam-4317	108	11	to	to	PART
ejpam-4317	108	12	find	find	VERB
ejpam-4317	108	13	the	the	DET
ejpam-4317	108	14	relationship	relationship	NOUN
ejpam-4317	108	15	between	between	ADP
ejpam-4317	108	16	the	the	DET
ejpam-4317	108	17	strongly	strongly	ADV
ejpam-4317	108	18	δθ	δθ	NOUN
ejpam-4317	108	19	-	-	PUNCT
ejpam-4317	108	20	i	i	NOUN
ejpam-4317	108	21	-	-	PUNCT
ejpam-4317	108	22	continuous	continuous	ADJ
ejpam-4317	108	23	functions	function	NOUN
ejpam-4317	108	24	,	,	PUNCT
ejpam-4317	108	25	δθ	δθ	NOUN
ejpam-4317	108	26	-	-	PUNCT
ejpam-4317	108	27	i	i	NOUN
ejpam-4317	108	28	-	-	PUNCT
ejpam-4317	108	29	continuous	continuous	ADJ
ejpam-4317	108	30	functions	function	NOUN
ejpam-4317	108	31	and	and	CCONJ
ejpam-4317	108	32	weakly	weakly	ADJ
ejpam-4317	108	33	δ	δ	PROPN
ejpam-4317	108	34	-	-	PUNCT
ejpam-4317	108	35	j	j	PROPN
ejpam-4317	108	36	-continuous	-continuous	ADJ
ejpam-4317	108	37	functions	function	NOUN
ejpam-4317	108	38	.	.	PUNCT
ejpam-4317	109	1	first	first	ADV
ejpam-4317	109	2	,	,	PUNCT
ejpam-4317	109	3	we	we	PRON
ejpam-4317	109	4	characterize	characterize	VERB
ejpam-4317	109	5	strongly	strongly	ADV
ejpam-4317	109	6	δθ	δθ	NOUN
ejpam-4317	109	7	-	-	PUNCT
ejpam-4317	109	8	i	i	NOUN
ejpam-4317	109	9	-	-	PUNCT
ejpam-4317	109	10	continuous	continuous	ADJ
ejpam-4317	109	11	functions	function	NOUN
ejpam-4317	109	12	using	use	VERB
ejpam-4317	109	13	δθ	δθ	NOUN
ejpam-4317	109	14	-	-	PUNCT
ejpam-4317	109	15	i	i	NOUN
ejpam-4317	109	16	-	-	PUNCT
ejpam-4317	109	17	open	open	ADJ
ejpam-4317	109	18	sets	set	NOUN
ejpam-4317	109	19	and	and	CCONJ
ejpam-4317	109	20	δθ	δθ	AUX
ejpam-4317	109	21	-	-	PUNCT
ejpam-4317	109	22	i	i	NOUN
ejpam-4317	109	23	-	-	PUNCT
ejpam-4317	109	24	closed	close	VERB
ejpam-4317	109	25	sets	set	NOUN
ejpam-4317	109	26	.	.	PUNCT
ejpam-4317	110	1	theorem	theorem	NOUN
ejpam-4317	110	2	1	1	NUM
ejpam-4317	110	3	.	.	PUNCT
ejpam-4317	111	1	let	let	VERB
ejpam-4317	111	2	f	f	NOUN
ejpam-4317	111	3	:	:	PUNCT
ejpam-4317	111	4	(	(	PUNCT
ejpam-4317	111	5	x	x	X
ejpam-4317	111	6	,	,	PUNCT
ejpam-4317	111	7	τ	τ	PROPN
ejpam-4317	111	8	,	,	PUNCT
ejpam-4317	111	9	i	i	NOUN
ejpam-4317	111	10	)	)	PUNCT
ejpam-4317	111	11	→	→	SYM
ejpam-4317	111	12	(	(	PUNCT
ejpam-4317	111	13	y	y	PROPN
ejpam-4317	111	14	,	,	PUNCT
ejpam-4317	111	15	σ	σ	PROPN
ejpam-4317	111	16	)	)	PUNCT
ejpam-4317	111	17	.	.	PUNCT
ejpam-4317	112	1	then	then	ADV
ejpam-4317	112	2	,	,	PUNCT
ejpam-4317	112	3	the	the	DET
ejpam-4317	112	4	following	follow	VERB
ejpam-4317	112	5	properties	property	NOUN
ejpam-4317	112	6	are	be	AUX
ejpam-4317	112	7	equivalent	equivalent	ADJ
ejpam-4317	112	8	:	:	PUNCT
ejpam-4317	112	9	(	(	PUNCT
ejpam-4317	112	10	i	i	NOUN
ejpam-4317	112	11	)	)	PUNCT
ejpam-4317	112	12	f	f	PROPN
ejpam-4317	112	13	is	be	AUX
ejpam-4317	112	14	strongly	strongly	ADV
ejpam-4317	112	15	δθ	δθ	NOUN
ejpam-4317	112	16	-	-	PUNCT
ejpam-4317	112	17	i	i	NOUN
ejpam-4317	112	18	-	-	PUNCT
ejpam-4317	112	19	continuous	continuous	ADJ
ejpam-4317	112	20	.	.	PUNCT
ejpam-4317	113	1	(	(	PUNCT
ejpam-4317	113	2	ii	ii	NOUN
ejpam-4317	113	3	)	)	PUNCT
ejpam-4317	113	4	f−1(v	f−1(v	PROPN
ejpam-4317	113	5	)	)	PUNCT
ejpam-4317	113	6	is	be	AUX
ejpam-4317	113	7	a	a	DET
ejpam-4317	113	8	δθ	δθ	NOUN
ejpam-4317	113	9	-	-	PUNCT
ejpam-4317	113	10	i	i	NOUN
ejpam-4317	113	11	-	-	PUNCT
ejpam-4317	113	12	open	open	ADJ
ejpam-4317	113	13	set	set	NOUN
ejpam-4317	113	14	in	in	ADP
ejpam-4317	113	15	x	x	NOUN
ejpam-4317	113	16	,	,	PUNCT
ejpam-4317	113	17	for	for	SCONJ
ejpam-4317	113	18	each	each	DET
ejpam-4317	113	19	open	open	ADJ
ejpam-4317	113	20	set	set	VERB
ejpam-4317	113	21	v	v	ADP
ejpam-4317	113	22	⊂	⊂	PROPN
ejpam-4317	113	23	y	y	PROPN
ejpam-4317	113	24	.	.	PUNCT
ejpam-4317	114	1	j.	j.	PROPN
ejpam-4317	114	2	sanabria	sanabria	PROPN
ejpam-4317	114	3	,	,	PUNCT
ejpam-4317	114	4	r.	r.	PROPN
ejpam-4317	114	5	lozada	lozada	PROPN
ejpam-4317	114	6	-	-	PUNCT
ejpam-4317	114	7	yavina	yavina	PROPN
ejpam-4317	114	8	,	,	PUNCT
ejpam-4317	114	9	j.	j.	PROPN
ejpam-4317	114	10	tormet	tormet	PROPN
ejpam-4317	114	11	/	/	SYM
ejpam-4317	114	12	eur	eur	PROPN
ejpam-4317	114	13	.	.	PUNCT
ejpam-4317	115	1	j.	j.	PROPN
ejpam-4317	115	2	pure	pure	PROPN
ejpam-4317	115	3	appl	appl	PROPN
ejpam-4317	115	4	.	.	PROPN
ejpam-4317	115	5	math	math	PROPN
ejpam-4317	115	6	,	,	PUNCT
ejpam-4317	115	7	15	15	NUM
ejpam-4317	115	8	(	(	PUNCT
ejpam-4317	115	9	2	2	NUM
ejpam-4317	115	10	)	)	PUNCT
ejpam-4317	115	11	(	(	PUNCT
ejpam-4317	115	12	2022	2022	NUM
ejpam-4317	115	13	)	)	PUNCT
ejpam-4317	115	14	,	,	PUNCT
ejpam-4317	115	15	443	443	NUM
ejpam-4317	115	16	-	-	SYM
ejpam-4317	115	17	453	453	NUM
ejpam-4317	115	18	446	446	NUM
ejpam-4317	115	19	(	(	PUNCT
ejpam-4317	115	20	iii	iii	NOUN
ejpam-4317	115	21	)	)	PUNCT
ejpam-4317	115	22	f−1(f	f−1(f	NOUN
ejpam-4317	115	23	)	)	PUNCT
ejpam-4317	115	24	is	be	AUX
ejpam-4317	115	25	a	a	DET
ejpam-4317	115	26	δθ	δθ	NOUN
ejpam-4317	115	27	-	-	PUNCT
ejpam-4317	115	28	i	i	NOUN
ejpam-4317	115	29	-	-	PUNCT
ejpam-4317	115	30	closed	close	VERB
ejpam-4317	115	31	set	set	NOUN
ejpam-4317	115	32	in	in	ADP
ejpam-4317	115	33	x	x	NOUN
ejpam-4317	115	34	,	,	PUNCT
ejpam-4317	115	35	for	for	ADP
ejpam-4317	115	36	each	each	DET
ejpam-4317	115	37	closed	close	VERB
ejpam-4317	115	38	set	set	VERB
ejpam-4317	115	39	f	f	PROPN
ejpam-4317	115	40	⊂	⊂	PROPN
ejpam-4317	115	41	y	y	PROPN
ejpam-4317	115	42	.	.	PUNCT
ejpam-4317	116	1	(	(	PUNCT
ejpam-4317	116	2	iv	iv	X
ejpam-4317	116	3	)	)	PUNCT
ejpam-4317	116	4	f(δcl?θ	f(δcl?θ	PROPN
ejpam-4317	117	1	(	(	PUNCT
ejpam-4317	117	2	a	a	NOUN
ejpam-4317	117	3	)	)	PUNCT
ejpam-4317	117	4	)	)	PUNCT
ejpam-4317	118	1	⊂	⊂	PROPN
ejpam-4317	118	2	cl(f(a	cl(f(a	NOUN
ejpam-4317	118	3	)	)	PUNCT
ejpam-4317	118	4	)	)	PUNCT
ejpam-4317	118	5	,	,	PUNCT
ejpam-4317	118	6	for	for	ADP
ejpam-4317	118	7	each	each	DET
ejpam-4317	118	8	a	a	PRON
ejpam-4317	118	9	⊂	⊂	PROPN
ejpam-4317	118	10	x.	x.	NOUN
ejpam-4317	118	11	(	(	PUNCT
ejpam-4317	118	12	v	v	NOUN
ejpam-4317	118	13	)	)	PUNCT
ejpam-4317	118	14	δcl?θ	δcl?θ	PROPN
ejpam-4317	118	15	(	(	PUNCT
ejpam-4317	118	16	f	f	PROPN
ejpam-4317	118	17	−1(b	−1(b	NOUN
ejpam-4317	118	18	)	)	PUNCT
ejpam-4317	118	19	)	)	PUNCT
ejpam-4317	118	20	⊂	⊂	PROPN
ejpam-4317	118	21	f−1(cl(b	f−1(cl(b	NOUN
ejpam-4317	118	22	)	)	PUNCT
ejpam-4317	118	23	)	)	PUNCT
ejpam-4317	118	24	,	,	PUNCT
ejpam-4317	118	25	for	for	ADP
ejpam-4317	118	26	each	each	DET
ejpam-4317	118	27	b	b	PROPN
ejpam-4317	118	28	⊂	⊂	PROPN
ejpam-4317	118	29	y	y	PROPN
ejpam-4317	118	30	.	.	PUNCT
ejpam-4317	119	1	proof	proof	NOUN
ejpam-4317	119	2	.	.	PUNCT
ejpam-4317	120	1	(	(	PUNCT
ejpam-4317	120	2	i	i	NOUN
ejpam-4317	120	3	)	)	PUNCT
ejpam-4317	120	4	⇒	⇒	PROPN
ejpam-4317	120	5	(	(	PUNCT
ejpam-4317	120	6	ii	ii	NOUN
ejpam-4317	120	7	)	)	PUNCT
ejpam-4317	120	8	suppose	suppose	VERB
ejpam-4317	120	9	that	that	SCONJ
ejpam-4317	120	10	v	v	NOUN
ejpam-4317	120	11	is	be	AUX
ejpam-4317	120	12	an	an	DET
ejpam-4317	120	13	open	open	ADJ
ejpam-4317	120	14	set	set	NOUN
ejpam-4317	120	15	in	in	ADP
ejpam-4317	120	16	y	y	PROPN
ejpam-4317	120	17	and	and	CCONJ
ejpam-4317	120	18	x	x	PROPN
ejpam-4317	120	19	∈	∈	PROPN
ejpam-4317	120	20	f−1(v	f−1(v	NOUN
ejpam-4317	120	21	)	)	PUNCT
ejpam-4317	120	22	.	.	PUNCT
ejpam-4317	121	1	since	since	SCONJ
ejpam-4317	121	2	f	f	PROPN
ejpam-4317	121	3	is	be	AUX
ejpam-4317	121	4	strongly	strongly	ADV
ejpam-4317	121	5	δθ	δθ	NOUN
ejpam-4317	121	6	-	-	PUNCT
ejpam-4317	121	7	i	i	NOUN
ejpam-4317	121	8	-	-	PUNCT
ejpam-4317	121	9	continuous	continuous	ADJ
ejpam-4317	121	10	,	,	PUNCT
ejpam-4317	121	11	there	there	PRON
ejpam-4317	121	12	exists	exist	VERB
ejpam-4317	121	13	an	an	DET
ejpam-4317	121	14	open	open	ADJ
ejpam-4317	121	15	set	set	NOUN
ejpam-4317	121	16	u	u	NOUN
ejpam-4317	121	17	in	in	ADP
ejpam-4317	121	18	x	x	PUNCT
ejpam-4317	121	19	containing	contain	VERB
ejpam-4317	121	20	x	x	PUNCT
ejpam-4317	121	21	such	such	ADJ
ejpam-4317	121	22	that	that	DET
ejpam-4317	121	23	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	121	24	)	)	PUNCT
ejpam-4317	121	25	)	)	PUNCT
ejpam-4317	122	1	⊂	⊂	PROPN
ejpam-4317	122	2	v	v	NOUN
ejpam-4317	122	3	.	.	PUNCT
ejpam-4317	123	1	thus	thus	ADV
ejpam-4317	123	2	,	,	PUNCT
ejpam-4317	123	3	x	x	PUNCT
ejpam-4317	123	4	∈	∈	PROPN
ejpam-4317	123	5	u	u	NOUN
ejpam-4317	123	6	⊂	⊂	PROPN
ejpam-4317	123	7	δcl?(u	δcl?(u	PROPN
ejpam-4317	123	8	)	)	PUNCT
ejpam-4317	124	1	⊂	⊂	PROPN
ejpam-4317	124	2	f−1(v	f−1(v	PROPN
ejpam-4317	124	3	)	)	PUNCT
ejpam-4317	124	4	.	.	PUNCT
ejpam-4317	125	1	consequently	consequently	ADV
ejpam-4317	125	2	,	,	PUNCT
ejpam-4317	125	3	f−1(v	f−1(v	PROPN
ejpam-4317	125	4	)	)	PUNCT
ejpam-4317	125	5	is	be	AUX
ejpam-4317	125	6	a	a	DET
ejpam-4317	125	7	δθ	δθ	NOUN
ejpam-4317	125	8	-	-	PUNCT
ejpam-4317	125	9	i	i	NOUN
ejpam-4317	125	10	-	-	PUNCT
ejpam-4317	125	11	open	open	ADJ
ejpam-4317	125	12	set	set	NOUN
ejpam-4317	125	13	in	in	ADP
ejpam-4317	125	14	x.	x.	PROPN
ejpam-4317	125	15	(	(	PUNCT
ejpam-4317	125	16	ii	ii	NOUN
ejpam-4317	125	17	)	)	PUNCT
ejpam-4317	125	18	⇒	⇒	NOUN
ejpam-4317	125	19	(	(	PUNCT
ejpam-4317	125	20	iii	iii	X
ejpam-4317	125	21	)	)	PUNCT
ejpam-4317	125	22	let	let	VERB
ejpam-4317	125	23	f	f	PRON
ejpam-4317	125	24	be	be	AUX
ejpam-4317	125	25	a	a	DET
ejpam-4317	125	26	closed	closed	ADJ
ejpam-4317	125	27	set	set	NOUN
ejpam-4317	125	28	in	in	ADP
ejpam-4317	125	29	y	y	PROPN
ejpam-4317	125	30	.	.	PUNCT
ejpam-4317	126	1	then	then	ADV
ejpam-4317	126	2	,	,	PUNCT
ejpam-4317	126	3	v	v	X
ejpam-4317	126	4	=	=	SYM
ejpam-4317	126	5	y	y	PROPN
ejpam-4317	126	6	−	−	PROPN
ejpam-4317	126	7	f	f	PROPN
ejpam-4317	126	8	is	be	AUX
ejpam-4317	126	9	an	an	DET
ejpam-4317	126	10	open	open	ADJ
ejpam-4317	126	11	set	set	NOUN
ejpam-4317	126	12	in	in	ADP
ejpam-4317	126	13	y	y	PROPN
ejpam-4317	126	14	and	and	CCONJ
ejpam-4317	126	15	by	by	ADP
ejpam-4317	126	16	(	(	PUNCT
ejpam-4317	126	17	ii	ii	NOUN
ejpam-4317	126	18	)	)	PUNCT
ejpam-4317	126	19	,	,	PUNCT
ejpam-4317	126	20	f−1(v	f−1(v	NOUN
ejpam-4317	126	21	)	)	PUNCT
ejpam-4317	127	1	=	=	PUNCT
ejpam-4317	127	2	f−1(y	f−1(y	PROPN
ejpam-4317	128	1	−	−	PROPN
ejpam-4317	128	2	f	f	PROPN
ejpam-4317	128	3	)	)	PUNCT
ejpam-4317	128	4	=	=	SYM
ejpam-4317	128	5	f−1(y	f−1(y	PROPN
ejpam-4317	128	6	)	)	PUNCT
ejpam-4317	129	1	−	−	PROPN
ejpam-4317	129	2	f−1(f	f−1(f	NOUN
ejpam-4317	129	3	)	)	PUNCT
ejpam-4317	130	1	=	=	PUNCT
ejpam-4317	130	2	x	x	PUNCT
ejpam-4317	130	3	−	−	PROPN
ejpam-4317	130	4	f−1(f	f−1(f	PROPN
ejpam-4317	130	5	)	)	PUNCT
ejpam-4317	130	6	is	be	AUX
ejpam-4317	130	7	a	a	DET
ejpam-4317	130	8	δθ	δθ	NOUN
ejpam-4317	130	9	-	-	PUNCT
ejpam-4317	130	10	i	i	NOUN
ejpam-4317	130	11	-	-	PUNCT
ejpam-4317	130	12	open	open	ADJ
ejpam-4317	130	13	set	set	NOUN
ejpam-4317	130	14	in	in	ADP
ejpam-4317	130	15	x.	x.	NOUN
ejpam-4317	130	16	therefore	therefore	ADV
ejpam-4317	130	17	,	,	PUNCT
ejpam-4317	130	18	f−1(f	f−1(f	PROPN
ejpam-4317	130	19	)	)	PUNCT
ejpam-4317	130	20	is	be	AUX
ejpam-4317	130	21	a	a	DET
ejpam-4317	130	22	δθ	δθ	NOUN
ejpam-4317	130	23	-	-	PUNCT
ejpam-4317	130	24	i	i	NOUN
ejpam-4317	130	25	-	-	PUNCT
ejpam-4317	130	26	closed	close	VERB
ejpam-4317	130	27	set	set	NOUN
ejpam-4317	130	28	in	in	ADP
ejpam-4317	130	29	x.	x.	PROPN
ejpam-4317	130	30	(	(	PUNCT
ejpam-4317	130	31	iii	iii	NOUN
ejpam-4317	130	32	)	)	PUNCT
ejpam-4317	130	33	⇒	⇒	NOUN
ejpam-4317	130	34	(	(	PUNCT
ejpam-4317	130	35	iv	iv	X
ejpam-4317	130	36	)	)	PUNCT
ejpam-4317	130	37	let	let	VERB
ejpam-4317	130	38	a	a	DET
ejpam-4317	130	39	⊂	⊂	PROPN
ejpam-4317	130	40	x.	x.	NOUN
ejpam-4317	130	41	since	since	SCONJ
ejpam-4317	130	42	cl(f(a	cl(f(a	NOUN
ejpam-4317	130	43	)	)	PUNCT
ejpam-4317	130	44	)	)	PUNCT
ejpam-4317	131	1	is	be	AUX
ejpam-4317	131	2	a	a	DET
ejpam-4317	131	3	closed	closed	ADJ
ejpam-4317	131	4	set	set	NOUN
ejpam-4317	131	5	in	in	ADP
ejpam-4317	131	6	y	y	PROPN
ejpam-4317	131	7	,	,	PUNCT
ejpam-4317	131	8	by	by	ADP
ejpam-4317	131	9	hypothesis	hypothesis	NOUN
ejpam-4317	131	10	,	,	PUNCT
ejpam-4317	131	11	it	it	PRON
ejpam-4317	131	12	follows	follow	VERB
ejpam-4317	131	13	that	that	PRON
ejpam-4317	131	14	f−1(cl(f(a	f−1(cl(f(a	NOUN
ejpam-4317	131	15	)	)	PUNCT
ejpam-4317	131	16	)	)	PUNCT
ejpam-4317	131	17	)	)	PUNCT
ejpam-4317	132	1	is	be	AUX
ejpam-4317	132	2	a	a	DET
ejpam-4317	132	3	δθ	δθ	NOUN
ejpam-4317	132	4	-	-	PUNCT
ejpam-4317	132	5	i	i	NOUN
ejpam-4317	132	6	-	-	PUNCT
ejpam-4317	132	7	closed	close	VERB
ejpam-4317	132	8	set	set	NOUN
ejpam-4317	132	9	.	.	PUNCT
ejpam-4317	133	1	then	then	ADV
ejpam-4317	133	2	,	,	PUNCT
ejpam-4317	133	3	we	we	PRON
ejpam-4317	133	4	have	have	VERB
ejpam-4317	133	5	δcl?θ	δcl?θ	NUM
ejpam-4317	133	6	(	(	PUNCT
ejpam-4317	133	7	a	a	X
ejpam-4317	133	8	)	)	PUNCT
ejpam-4317	133	9	⊂	⊂	PROPN
ejpam-4317	133	10	δcl?θ	δcl?θ	X
ejpam-4317	133	11	(	(	PUNCT
ejpam-4317	133	12	f	f	NOUN
ejpam-4317	133	13	−1(f(a	−1(f(a	ADJ
ejpam-4317	133	14	)	)	PUNCT
ejpam-4317	133	15	)	)	PUNCT
ejpam-4317	133	16	)	)	PUNCT
ejpam-4317	134	1	⊂	⊂	PROPN
ejpam-4317	134	2	δcl?θ	δcl?θ	PRON
ejpam-4317	134	3	(	(	PUNCT
ejpam-4317	134	4	f	f	PROPN
ejpam-4317	134	5	−1(cl(f(a	−1(cl(f(a	PROPN
ejpam-4317	134	6	)	)	PUNCT
ejpam-4317	134	7	)	)	PUNCT
ejpam-4317	134	8	)	)	PUNCT
ejpam-4317	134	9	)	)	PUNCT
ejpam-4317	135	1	=	=	SYM
ejpam-4317	135	2	f−1(cl(f(a	f−1(cl(f(a	PROPN
ejpam-4317	135	3	)	)	PUNCT
ejpam-4317	135	4	)	)	PUNCT
ejpam-4317	135	5	)	)	PUNCT
ejpam-4317	135	6	,	,	PUNCT
ejpam-4317	135	7	which	which	PRON
ejpam-4317	135	8	implies	imply	VERB
ejpam-4317	135	9	that	that	SCONJ
ejpam-4317	136	1	f(δcl?θ	f(δcl?θ	VERB
ejpam-4317	136	2	(	(	PUNCT
ejpam-4317	136	3	a	a	NOUN
ejpam-4317	136	4	)	)	PUNCT
ejpam-4317	136	5	)	)	PUNCT
ejpam-4317	137	1	⊂	⊂	PROPN
ejpam-4317	137	2	cl(f(a	cl(f(a	NOUN
ejpam-4317	137	3	)	)	PUNCT
ejpam-4317	137	4	)	)	PUNCT
ejpam-4317	137	5	for	for	ADP
ejpam-4317	137	6	each	each	DET
ejpam-4317	137	7	a	a	DET
ejpam-4317	137	8	⊂	⊂	X
ejpam-4317	137	9	x.	x.	NOUN
ejpam-4317	137	10	(	(	PUNCT
ejpam-4317	137	11	iv	iv	X
ejpam-4317	137	12	)	)	PUNCT
ejpam-4317	137	13	⇒	⇒	NOUN
ejpam-4317	137	14	(	(	PUNCT
ejpam-4317	137	15	v	v	NOUN
ejpam-4317	137	16	)	)	PUNCT
ejpam-4317	137	17	let	let	VERB
ejpam-4317	137	18	b	b	PROPN
ejpam-4317	137	19	⊂	⊂	PROPN
ejpam-4317	137	20	y	y	PROPN
ejpam-4317	137	21	.	.	PUNCT
ejpam-4317	138	1	by	by	ADP
ejpam-4317	138	2	hypothesis	hypothesis	NOUN
ejpam-4317	138	3	,	,	PUNCT
ejpam-4317	138	4	we	we	PRON
ejpam-4317	138	5	have	have	AUX
ejpam-4317	138	6	f(δcl?θ	f(δcl?θ	VERB
ejpam-4317	138	7	(	(	PUNCT
ejpam-4317	138	8	f	f	PROPN
ejpam-4317	138	9	−1(b	−1(b	NOUN
ejpam-4317	138	10	)	)	PUNCT
ejpam-4317	138	11	)	)	PUNCT
ejpam-4317	138	12	)	)	PUNCT
ejpam-4317	139	1	⊂	⊂	PROPN
ejpam-4317	139	2	cl(f(f−1(b	cl(f(f−1(b	PROPN
ejpam-4317	139	3	)	)	PUNCT
ejpam-4317	139	4	)	)	PUNCT
ejpam-4317	139	5	)	)	PUNCT
ejpam-4317	140	1	⊂	⊂	PROPN
ejpam-4317	140	2	cl(b	cl(b	NOUN
ejpam-4317	140	3	)	)	PUNCT
ejpam-4317	140	4	.	.	PUNCT
ejpam-4317	141	1	consequently	consequently	ADV
ejpam-4317	141	2	,	,	PUNCT
ejpam-4317	141	3	δcl?θ	δcl?θ	PROPN
ejpam-4317	141	4	(	(	PUNCT
ejpam-4317	141	5	f−1(b	f−1(b	PROPN
ejpam-4317	141	6	)	)	PUNCT
ejpam-4317	141	7	)	)	PUNCT
ejpam-4317	141	8	⊂	⊂	PROPN
ejpam-4317	141	9	f−1(cl(b	f−1(cl(b	NOUN
ejpam-4317	141	10	)	)	PUNCT
ejpam-4317	141	11	)	)	PUNCT
ejpam-4317	141	12	.	.	PUNCT
ejpam-4317	142	1	(	(	PUNCT
ejpam-4317	142	2	v	v	NOUN
ejpam-4317	142	3	)	)	PUNCT
ejpam-4317	142	4	⇒	⇒	NOUN
ejpam-4317	142	5	(	(	PUNCT
ejpam-4317	142	6	i	i	NOUN
ejpam-4317	142	7	)	)	PUNCT
ejpam-4317	142	8	let	let	VERB
ejpam-4317	142	9	x	x	PUNCT
ejpam-4317	142	10	∈	∈	PROPN
ejpam-4317	142	11	x	x	X
ejpam-4317	142	12	and	and	CCONJ
ejpam-4317	142	13	v	v	ADP
ejpam-4317	142	14	∈	∈	PROPN
ejpam-4317	142	15	σ	σ	NOUN
ejpam-4317	142	16	be	be	VERB
ejpam-4317	142	17	such	such	ADJ
ejpam-4317	142	18	that	that	SCONJ
ejpam-4317	142	19	f(x	f(x	PROPN
ejpam-4317	142	20	)	)	PUNCT
ejpam-4317	142	21	∈	∈	PROPN
ejpam-4317	142	22	v	v	NOUN
ejpam-4317	142	23	.	.	PUNCT
ejpam-4317	143	1	then	then	ADV
ejpam-4317	143	2	,	,	PUNCT
ejpam-4317	143	3	y	y	PROPN
ejpam-4317	143	4	−	−	PROPN
ejpam-4317	143	5	v	v	NOUN
ejpam-4317	143	6	is	be	AUX
ejpam-4317	143	7	a	a	DET
ejpam-4317	143	8	closed	closed	ADJ
ejpam-4317	143	9	set	set	NOUN
ejpam-4317	143	10	in	in	ADP
ejpam-4317	143	11	y	y	PROPN
ejpam-4317	143	12	and	and	CCONJ
ejpam-4317	143	13	by	by	ADP
ejpam-4317	143	14	hypothesis	hypothesis	NOUN
ejpam-4317	143	15	,	,	PUNCT
ejpam-4317	143	16	δcl?θ	δcl?θ	PROPN
ejpam-4317	143	17	(	(	PUNCT
ejpam-4317	143	18	f−1(y	f−1(y	PROPN
ejpam-4317	143	19	−	−	PROPN
ejpam-4317	143	20	v	v	NOUN
ejpam-4317	143	21	)	)	PUNCT
ejpam-4317	143	22	)	)	PUNCT
ejpam-4317	144	1	⊂	⊂	PRON
ejpam-4317	144	2	f−1(cl(y	f−1(cl(y	ADJ
ejpam-4317	144	3	−	−	PROPN
ejpam-4317	144	4	v	v	NOUN
ejpam-4317	144	5	)	)	PUNCT
ejpam-4317	144	6	)	)	PUNCT
ejpam-4317	145	1	=	=	SYM
ejpam-4317	145	2	f−1(y	f−1(y	PROPN
ejpam-4317	145	3	−	−	PROPN
ejpam-4317	145	4	v	v	NOUN
ejpam-4317	145	5	)	)	PUNCT
ejpam-4317	145	6	,	,	PUNCT
ejpam-4317	145	7	which	which	PRON
ejpam-4317	145	8	tells	tell	VERB
ejpam-4317	145	9	us	we	PRON
ejpam-4317	145	10	that	that	SCONJ
ejpam-4317	145	11	f−1(y	f−1(y	PROPN
ejpam-4317	145	12	−	−	PROPN
ejpam-4317	145	13	v	v	NOUN
ejpam-4317	145	14	)	)	PUNCT
ejpam-4317	145	15	is	be	AUX
ejpam-4317	145	16	a	a	DET
ejpam-4317	145	17	δθ	δθ	NOUN
ejpam-4317	145	18	-	-	PUNCT
ejpam-4317	145	19	i	i	NOUN
ejpam-4317	145	20	-	-	PUNCT
ejpam-4317	145	21	closed	close	VERB
ejpam-4317	145	22	set	set	NOUN
ejpam-4317	145	23	in	in	ADP
ejpam-4317	145	24	x.	x.	NOUN
ejpam-4317	145	25	since	since	SCONJ
ejpam-4317	145	26	f−1(y	f−1(y	PROPN
ejpam-4317	145	27	−	−	PROPN
ejpam-4317	145	28	v	v	NOUN
ejpam-4317	145	29	)	)	PUNCT
ejpam-4317	145	30	=	=	PUNCT
ejpam-4317	146	1	x	x	PUNCT
ejpam-4317	146	2	−	−	PROPN
ejpam-4317	146	3	f−1(v	f−1(v	PROPN
ejpam-4317	146	4	)	)	PUNCT
ejpam-4317	146	5	,	,	PUNCT
ejpam-4317	146	6	we	we	PRON
ejpam-4317	146	7	conclude	conclude	VERB
ejpam-4317	146	8	that	that	DET
ejpam-4317	146	9	f−1(v	f−1(v	PROPN
ejpam-4317	146	10	)	)	PUNCT
ejpam-4317	146	11	is	be	AUX
ejpam-4317	146	12	a	a	DET
ejpam-4317	146	13	δθ	δθ	NOUN
ejpam-4317	146	14	-	-	PUNCT
ejpam-4317	146	15	i	i	NOUN
ejpam-4317	146	16	-	-	PUNCT
ejpam-4317	146	17	open	open	ADJ
ejpam-4317	146	18	set	set	NOUN
ejpam-4317	146	19	containing	contain	VERB
ejpam-4317	146	20	x.	x.	NOUN
ejpam-4317	146	21	thus	thus	ADV
ejpam-4317	146	22	,	,	PUNCT
ejpam-4317	146	23	there	there	PRON
ejpam-4317	146	24	exists	exist	VERB
ejpam-4317	146	25	u	u	PROPN
ejpam-4317	146	26	∈	∈	PROPN
ejpam-4317	146	27	τ	τ	X
ejpam-4317	146	28	such	such	ADJ
ejpam-4317	146	29	that	that	SCONJ
ejpam-4317	146	30	x	x	SYM
ejpam-4317	146	31	∈	∈	PROPN
ejpam-4317	146	32	u	u	X
ejpam-4317	146	33	⊂	⊂	PROPN
ejpam-4317	146	34	δcl?(u	δcl?(u	PROPN
ejpam-4317	146	35	)	)	PUNCT
ejpam-4317	146	36	⊂	⊂	PROPN
ejpam-4317	146	37	f−1(v	f−1(v	PROPN
ejpam-4317	146	38	)	)	PUNCT
ejpam-4317	146	39	.	.	PUNCT
ejpam-4317	147	1	therefore	therefore	ADV
ejpam-4317	147	2	,	,	PUNCT
ejpam-4317	147	3	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	147	4	)	)	PUNCT
ejpam-4317	147	5	)	)	PUNCT
ejpam-4317	148	1	⊂	⊂	PROPN
ejpam-4317	148	2	v	v	PROPN
ejpam-4317	148	3	and	and	CCONJ
ejpam-4317	148	4	so	so	ADV
ejpam-4317	148	5	,	,	PUNCT
ejpam-4317	148	6	f	f	PROPN
ejpam-4317	148	7	is	be	AUX
ejpam-4317	148	8	a	a	DET
ejpam-4317	148	9	strongly	strongly	ADV
ejpam-4317	148	10	δθ	δθ	NOUN
ejpam-4317	148	11	-	-	PUNCT
ejpam-4317	148	12	i	i	NOUN
ejpam-4317	148	13	-	-	PUNCT
ejpam-4317	148	14	continuous	continuous	ADJ
ejpam-4317	148	15	function	function	NOUN
ejpam-4317	148	16	.	.	PUNCT
ejpam-4317	149	1	according	accord	VERB
ejpam-4317	149	2	to	to	ADP
ejpam-4317	149	3	[	[	X
ejpam-4317	149	4	14	14	NUM
ejpam-4317	149	5	]	]	PUNCT
ejpam-4317	149	6	,	,	PUNCT
ejpam-4317	149	7	we	we	PRON
ejpam-4317	149	8	say	say	VERB
ejpam-4317	149	9	that	that	SCONJ
ejpam-4317	149	10	a	a	DET
ejpam-4317	149	11	function	function	NOUN
ejpam-4317	149	12	f	f	NOUN
ejpam-4317	149	13	:	:	PUNCT
ejpam-4317	149	14	(	(	PUNCT
ejpam-4317	149	15	x	x	X
ejpam-4317	149	16	,	,	PUNCT
ejpam-4317	149	17	τ	τ	PROPN
ejpam-4317	149	18	,	,	PUNCT
ejpam-4317	149	19	i	i	NOUN
ejpam-4317	149	20	)	)	PUNCT
ejpam-4317	149	21	→	→	SYM
ejpam-4317	149	22	(	(	PUNCT
ejpam-4317	149	23	y	y	PROPN
ejpam-4317	149	24	,	,	PUNCT
ejpam-4317	149	25	σ	σ	PROPN
ejpam-4317	149	26	,	,	PUNCT
ejpam-4317	149	27	j	j	PROPN
ejpam-4317	149	28	)	)	PUNCT
ejpam-4317	149	29	is	be	AUX
ejpam-4317	149	30	δθ	δθ	ADP
ejpam-4317	149	31	-	-	PUNCT
ejpam-4317	149	32	i	i	NOUN
ejpam-4317	149	33	-	-	PUNCT
ejpam-4317	149	34	irresolute	irresolute	ADJ
ejpam-4317	149	35	,	,	PUNCT
ejpam-4317	149	36	if	if	SCONJ
ejpam-4317	149	37	f−1(v	f−1(v	PROPN
ejpam-4317	149	38	)	)	PUNCT
ejpam-4317	149	39	is	be	AUX
ejpam-4317	149	40	a	a	DET
ejpam-4317	149	41	δθ	δθ	NOUN
ejpam-4317	149	42	-	-	PUNCT
ejpam-4317	149	43	i	i	NOUN
ejpam-4317	149	44	-	-	PUNCT
ejpam-4317	149	45	open	open	ADJ
ejpam-4317	149	46	set	set	NOUN
ejpam-4317	149	47	in	in	ADP
ejpam-4317	149	48	x	x	NOUN
ejpam-4317	149	49	,	,	PUNCT
ejpam-4317	149	50	for	for	ADP
ejpam-4317	149	51	each	each	DET
ejpam-4317	149	52	δθ	δθ	NOUN
ejpam-4317	149	53	-	-	PUNCT
ejpam-4317	149	54	j	j	NOUN
ejpam-4317	149	55	-open	-open	NOUN
ejpam-4317	149	56	set	set	VERB
ejpam-4317	149	57	v	v	ADP
ejpam-4317	149	58	⊂	⊂	PROPN
ejpam-4317	149	59	y	y	PROPN
ejpam-4317	149	60	.	.	PUNCT
ejpam-4317	150	1	this	this	DET
ejpam-4317	150	2	type	type	NOUN
ejpam-4317	150	3	of	of	ADP
ejpam-4317	150	4	functions	function	NOUN
ejpam-4317	150	5	is	be	AUX
ejpam-4317	150	6	used	use	VERB
ejpam-4317	150	7	in	in	ADP
ejpam-4317	150	8	the	the	DET
ejpam-4317	150	9	following	following	NOUN
ejpam-4317	150	10	theorem	theorem	VERB
ejpam-4317	150	11	,	,	PUNCT
ejpam-4317	150	12	where	where	SCONJ
ejpam-4317	150	13	we	we	PRON
ejpam-4317	150	14	analyze	analyze	VERB
ejpam-4317	150	15	when	when	SCONJ
ejpam-4317	150	16	the	the	DET
ejpam-4317	150	17	composition	composition	NOUN
ejpam-4317	150	18	of	of	ADP
ejpam-4317	150	19	functions	function	NOUN
ejpam-4317	150	20	is	be	AUX
ejpam-4317	150	21	strongly	strongly	ADV
ejpam-4317	150	22	δθ	δθ	NOUN
ejpam-4317	150	23	-	-	PUNCT
ejpam-4317	150	24	i	i	NOUN
ejpam-4317	150	25	-	-	PUNCT
ejpam-4317	150	26	continuous	continuous	ADJ
ejpam-4317	150	27	.	.	PUNCT
ejpam-4317	151	1	theorem	theorem	NOUN
ejpam-4317	151	2	2	2	NUM
ejpam-4317	151	3	.	.	PUNCT
ejpam-4317	152	1	let	let	VERB
ejpam-4317	152	2	f	f	NOUN
ejpam-4317	152	3	:	:	PUNCT
ejpam-4317	152	4	(	(	PUNCT
ejpam-4317	152	5	x	x	X
ejpam-4317	152	6	,	,	PUNCT
ejpam-4317	152	7	τ	τ	PROPN
ejpam-4317	152	8	,	,	PUNCT
ejpam-4317	152	9	i	i	NOUN
ejpam-4317	152	10	)	)	PUNCT
ejpam-4317	152	11	→	→	SYM
ejpam-4317	152	12	(	(	PUNCT
ejpam-4317	152	13	y	y	PROPN
ejpam-4317	152	14	,	,	PUNCT
ejpam-4317	152	15	σ	σ	PROPN
ejpam-4317	152	16	,	,	PUNCT
ejpam-4317	152	17	j	j	PROPN
ejpam-4317	152	18	)	)	PUNCT
ejpam-4317	152	19	and	and	CCONJ
ejpam-4317	152	20	g	g	NOUN
ejpam-4317	152	21	:	:	PUNCT
ejpam-4317	152	22	(	(	PUNCT
ejpam-4317	152	23	y	y	PROPN
ejpam-4317	152	24	,	,	PUNCT
ejpam-4317	152	25	σ	σ	PROPN
ejpam-4317	152	26	,	,	PUNCT
ejpam-4317	152	27	j	j	PROPN
ejpam-4317	152	28	)	)	PUNCT
ejpam-4317	152	29	→	→	PUNCT
ejpam-4317	152	30	(	(	PUNCT
ejpam-4317	152	31	z,ϕ	z,ϕ	NOUN
ejpam-4317	152	32	)	)	PUNCT
ejpam-4317	152	33	be	be	AUX
ejpam-4317	152	34	two	two	NUM
ejpam-4317	152	35	functions	function	NOUN
ejpam-4317	152	36	.	.	PUNCT
ejpam-4317	153	1	then	then	ADV
ejpam-4317	153	2	,	,	PUNCT
ejpam-4317	153	3	the	the	DET
ejpam-4317	153	4	following	follow	VERB
ejpam-4317	153	5	properties	property	NOUN
ejpam-4317	153	6	hold	hold	VERB
ejpam-4317	153	7	:	:	PUNCT
ejpam-4317	153	8	(	(	PUNCT
ejpam-4317	153	9	i	i	NOUN
ejpam-4317	153	10	)	)	PUNCT
ejpam-4317	153	11	if	if	SCONJ
ejpam-4317	153	12	f	f	PROPN
ejpam-4317	153	13	is	be	AUX
ejpam-4317	153	14	strongly	strongly	ADV
ejpam-4317	153	15	δθ	δθ	NOUN
ejpam-4317	153	16	-	-	PUNCT
ejpam-4317	153	17	i	i	NOUN
ejpam-4317	153	18	-	-	PUNCT
ejpam-4317	153	19	continuous	continuous	ADJ
ejpam-4317	153	20	and	and	CCONJ
ejpam-4317	153	21	g	g	NOUN
ejpam-4317	153	22	is	be	AUX
ejpam-4317	153	23	continuous	continuous	ADJ
ejpam-4317	153	24	,	,	PUNCT
ejpam-4317	153	25	then	then	ADV
ejpam-4317	153	26	g	g	PROPN
ejpam-4317	153	27	◦	◦	NOUN
ejpam-4317	154	1	f	f	X
ejpam-4317	155	1	:	:	PUNCT
ejpam-4317	156	1	(	(	PUNCT
ejpam-4317	156	2	x	x	X
ejpam-4317	156	3	,	,	PUNCT
ejpam-4317	156	4	τ	τ	PROPN
ejpam-4317	156	5	,	,	PUNCT
ejpam-4317	156	6	i	i	NOUN
ejpam-4317	156	7	)	)	PUNCT
ejpam-4317	156	8	→	→	SYM
ejpam-4317	156	9	(	(	PUNCT
ejpam-4317	156	10	z,ϕ	z,ϕ	NOUN
ejpam-4317	156	11	)	)	PUNCT
ejpam-4317	156	12	is	be	AUX
ejpam-4317	156	13	strongly	strongly	ADV
ejpam-4317	156	14	δθ	δθ	NOUN
ejpam-4317	156	15	-	-	PUNCT
ejpam-4317	156	16	i	i	NOUN
ejpam-4317	156	17	-	-	PUNCT
ejpam-4317	156	18	continuous	continuous	ADJ
ejpam-4317	156	19	.	.	PUNCT
ejpam-4317	157	1	(	(	PUNCT
ejpam-4317	157	2	ii	ii	NOUN
ejpam-4317	157	3	)	)	PUNCT
ejpam-4317	157	4	if	if	SCONJ
ejpam-4317	157	5	f	f	PROPN
ejpam-4317	157	6	is	be	AUX
ejpam-4317	157	7	δθ	δθ	ADP
ejpam-4317	157	8	-	-	PUNCT
ejpam-4317	157	9	i	i	NOUN
ejpam-4317	157	10	-	-	PUNCT
ejpam-4317	157	11	irresolute	irresolute	ADJ
ejpam-4317	157	12	and	and	CCONJ
ejpam-4317	157	13	g	g	NOUN
ejpam-4317	157	14	is	be	AUX
ejpam-4317	157	15	strongly	strongly	ADV
ejpam-4317	157	16	δθ	δθ	NOUN
ejpam-4317	157	17	-	-	PUNCT
ejpam-4317	157	18	j	j	NOUN
ejpam-4317	157	19	-continuous	-continuous	ADJ
ejpam-4317	157	20	,	,	PUNCT
ejpam-4317	157	21	then	then	ADV
ejpam-4317	157	22	g	g	PROPN
ejpam-4317	157	23	◦	◦	NOUN
ejpam-4317	157	24	f	f	X
ejpam-4317	157	25	:	:	PUNCT
ejpam-4317	157	26	(	(	PUNCT
ejpam-4317	157	27	x	x	X
ejpam-4317	157	28	,	,	PUNCT
ejpam-4317	157	29	τ	τ	PROPN
ejpam-4317	157	30	,	,	PUNCT
ejpam-4317	157	31	i	i	NOUN
ejpam-4317	157	32	)	)	PUNCT
ejpam-4317	157	33	→	→	SYM
ejpam-4317	157	34	(	(	PUNCT
ejpam-4317	157	35	z,ϕ	z,ϕ	NOUN
ejpam-4317	157	36	)	)	PUNCT
ejpam-4317	157	37	is	be	AUX
ejpam-4317	157	38	strongly	strongly	ADV
ejpam-4317	157	39	δθ	δθ	NOUN
ejpam-4317	157	40	-	-	PUNCT
ejpam-4317	157	41	i	i	NOUN
ejpam-4317	157	42	-	-	PUNCT
ejpam-4317	157	43	continuous	continuous	ADJ
ejpam-4317	157	44	.	.	PUNCT
ejpam-4317	158	1	proof	proof	NOUN
ejpam-4317	158	2	.	.	PUNCT
ejpam-4317	159	1	(	(	PUNCT
ejpam-4317	159	2	i	i	NOUN
ejpam-4317	159	3	)	)	PUNCT
ejpam-4317	159	4	let	let	VERB
ejpam-4317	159	5	v	v	X
ejpam-4317	159	6	∈	∈	PROPN
ejpam-4317	159	7	ϕ.	ϕ.	NOUN
ejpam-4317	159	8	since	since	SCONJ
ejpam-4317	159	9	g	g	PROPN
ejpam-4317	159	10	is	be	AUX
ejpam-4317	159	11	continuous	continuous	ADJ
ejpam-4317	159	12	,	,	PUNCT
ejpam-4317	159	13	g−1(v	g−1(v	PROPN
ejpam-4317	159	14	)	)	PUNCT
ejpam-4317	159	15	is	be	AUX
ejpam-4317	159	16	an	an	DET
ejpam-4317	159	17	open	open	ADJ
ejpam-4317	159	18	set	set	NOUN
ejpam-4317	159	19	in	in	ADP
ejpam-4317	159	20	y	y	PROPN
ejpam-4317	159	21	,	,	PUNCT
ejpam-4317	159	22	and	and	CCONJ
ejpam-4317	159	23	as	as	SCONJ
ejpam-4317	159	24	f	f	PROPN
ejpam-4317	159	25	is	be	AUX
ejpam-4317	159	26	strongly	strongly	ADV
ejpam-4317	159	27	δθ	δθ	NOUN
ejpam-4317	159	28	-	-	PUNCT
ejpam-4317	159	29	i	i	NOUN
ejpam-4317	159	30	-	-	PUNCT
ejpam-4317	159	31	continuous	continuous	ADJ
ejpam-4317	159	32	,	,	PUNCT
ejpam-4317	159	33	by	by	ADP
ejpam-4317	159	34	theorem	theorem	NOUN
ejpam-4317	159	35	1	1	NUM
ejpam-4317	159	36	,	,	PUNCT
ejpam-4317	159	37	it	it	PRON
ejpam-4317	159	38	follows	follow	VERB
ejpam-4317	159	39	that	that	SCONJ
ejpam-4317	159	40	(	(	PUNCT
ejpam-4317	159	41	g	g	NOUN
ejpam-4317	159	42	◦	◦	NOUN
ejpam-4317	159	43	f)−1(v	f)−1(v	NOUN
ejpam-4317	159	44	)	)	PUNCT
ejpam-4317	160	1	=	=	SYM
ejpam-4317	160	2	f−1(g−1(v	f−1(g−1(v	PROPN
ejpam-4317	160	3	)	)	PUNCT
ejpam-4317	160	4	)	)	PUNCT
ejpam-4317	160	5	is	be	AUX
ejpam-4317	160	6	a	a	DET
ejpam-4317	160	7	δθ	δθ	NOUN
ejpam-4317	160	8	-	-	PUNCT
ejpam-4317	160	9	i	i	NOUN
ejpam-4317	160	10	-	-	PUNCT
ejpam-4317	160	11	open	open	ADJ
ejpam-4317	160	12	set	set	NOUN
ejpam-4317	160	13	in	in	ADP
ejpam-4317	160	14	x.	x.	NOUN
ejpam-4317	160	15	again	again	ADV
ejpam-4317	160	16	,	,	PUNCT
ejpam-4317	160	17	by	by	ADP
ejpam-4317	160	18	theorem	theorem	NOUN
ejpam-4317	160	19	1	1	NUM
ejpam-4317	160	20	,	,	PUNCT
ejpam-4317	160	21	we	we	PRON
ejpam-4317	160	22	get	get	VERB
ejpam-4317	160	23	that	that	DET
ejpam-4317	160	24	g	g	PROPN
ejpam-4317	160	25	◦	◦	NOUN
ejpam-4317	160	26	f	f	PROPN
ejpam-4317	160	27	is	be	AUX
ejpam-4317	160	28	a	a	DET
ejpam-4317	160	29	strongly	strongly	ADV
ejpam-4317	160	30	δθ	δθ	NOUN
ejpam-4317	160	31	-	-	PUNCT
ejpam-4317	160	32	i	i	NOUN
ejpam-4317	160	33	-	-	PUNCT
ejpam-4317	160	34	continuous	continuous	ADJ
ejpam-4317	160	35	function	function	NOUN
ejpam-4317	160	36	.	.	PUNCT
ejpam-4317	161	1	the	the	DET
ejpam-4317	161	2	proof	proof	NOUN
ejpam-4317	161	3	of	of	ADP
ejpam-4317	161	4	(	(	PUNCT
ejpam-4317	161	5	ii	ii	NOUN
ejpam-4317	161	6	)	)	PUNCT
ejpam-4317	161	7	is	be	AUX
ejpam-4317	161	8	similar	similar	ADJ
ejpam-4317	161	9	to	to	ADP
ejpam-4317	161	10	that	that	PRON
ejpam-4317	161	11	of	of	ADP
ejpam-4317	161	12	(	(	PUNCT
ejpam-4317	161	13	i	i	PROPN
ejpam-4317	161	14	)	)	PUNCT
ejpam-4317	161	15	.	.	PUNCT
ejpam-4317	162	1	j.	j.	PROPN
ejpam-4317	162	2	sanabria	sanabria	PROPN
ejpam-4317	162	3	,	,	PUNCT
ejpam-4317	162	4	r.	r.	PROPN
ejpam-4317	162	5	lozada	lozada	PROPN
ejpam-4317	162	6	-	-	PUNCT
ejpam-4317	162	7	yavina	yavina	PROPN
ejpam-4317	162	8	,	,	PUNCT
ejpam-4317	162	9	j.	j.	PROPN
ejpam-4317	162	10	tormet	tormet	PROPN
ejpam-4317	162	11	/	/	SYM
ejpam-4317	162	12	eur	eur	PROPN
ejpam-4317	162	13	.	.	PUNCT
ejpam-4317	163	1	j.	j.	PROPN
ejpam-4317	163	2	pure	pure	PROPN
ejpam-4317	163	3	appl	appl	PROPN
ejpam-4317	163	4	.	.	PROPN
ejpam-4317	163	5	math	math	PROPN
ejpam-4317	163	6	,	,	PUNCT
ejpam-4317	163	7	15	15	NUM
ejpam-4317	163	8	(	(	PUNCT
ejpam-4317	163	9	2	2	NUM
ejpam-4317	163	10	)	)	PUNCT
ejpam-4317	163	11	(	(	PUNCT
ejpam-4317	163	12	2022	2022	NUM
ejpam-4317	163	13	)	)	PUNCT
ejpam-4317	163	14	,	,	PUNCT
ejpam-4317	163	15	443	443	NUM
ejpam-4317	163	16	-	-	SYM
ejpam-4317	163	17	453	453	NUM
ejpam-4317	163	18	447	447	NUM
ejpam-4317	163	19	theorem	theorem	NOUN
ejpam-4317	163	20	3	3	X
ejpam-4317	163	21	.	.	PUNCT
ejpam-4317	164	1	let	let	VERB
ejpam-4317	164	2	{	{	PUNCT
ejpam-4317	164	3	(	(	PUNCT
ejpam-4317	164	4	yλ	yλ	INTJ
ejpam-4317	164	5	,	,	PUNCT
ejpam-4317	164	6	σλ	σλ	PROPN
ejpam-4317	164	7	)	)	PUNCT
ejpam-4317	164	8	:	:	PUNCT
ejpam-4317	165	1	λ	λ	X
ejpam-4317	165	2	∈	∈	PROPN
ejpam-4317	165	3	λ	λ	PROPN
ejpam-4317	165	4	}	}	PUNCT
ejpam-4317	165	5	be	be	VERB
ejpam-4317	165	6	a	a	DET
ejpam-4317	165	7	collection	collection	NOUN
ejpam-4317	165	8	of	of	ADP
ejpam-4317	165	9	topological	topological	ADJ
ejpam-4317	165	10	spaces	space	NOUN
ejpam-4317	165	11	and	and	CCONJ
ejpam-4317	165	12	let	let	VERB
ejpam-4317	165	13	y	y	PROPN
ejpam-4317	165	14	=	=	PRON
ejpam-4317	165	15	∏	∏	X
ejpam-4317	165	16	{	{	PUNCT
ejpam-4317	165	17	yλ	yλ	NOUN
ejpam-4317	165	18	:	:	PUNCT
ejpam-4317	165	19	λ	λ	X
ejpam-4317	165	20	∈	∈	PROPN
ejpam-4317	165	21	λ	λ	X
ejpam-4317	165	22	}	}	PUNCT
ejpam-4317	165	23	with	with	ADP
ejpam-4317	165	24	product	product	NOUN
ejpam-4317	165	25	topology	topology	NOUN
ejpam-4317	165	26	σ	σ	PROPN
ejpam-4317	165	27	=	=	SYM
ejpam-4317	165	28	∏	∏	PROPN
ejpam-4317	165	29	{	{	PUNCT
ejpam-4317	165	30	σλ	σλ	NOUN
ejpam-4317	165	31	:	:	PUNCT
ejpam-4317	165	32	λ	λ	X
ejpam-4317	165	33	∈	∈	PROPN
ejpam-4317	165	34	λ	λ	PROPN
ejpam-4317	165	35	}	}	PUNCT
ejpam-4317	165	36	induced	induce	VERB
ejpam-4317	165	37	by	by	ADP
ejpam-4317	165	38	the	the	DET
ejpam-4317	165	39	projections	projection	NOUN
ejpam-4317	165	40	pλ	pλ	INTJ
ejpam-4317	165	41	:	:	PUNCT
ejpam-4317	165	42	y	y	PROPN
ejpam-4317	165	43	→	→	SYM
ejpam-4317	165	44	yλ	yλ	PROPN
ejpam-4317	165	45	,	,	PUNCT
ejpam-4317	165	46	λ	λ	PROPN
ejpam-4317	165	47	∈	∈	PROPN
ejpam-4317	165	48	λ	λ	PROPN
ejpam-4317	165	49	.	.	PUNCT
ejpam-4317	166	1	a	a	DET
ejpam-4317	166	2	function	function	NOUN
ejpam-4317	166	3	f	f	NOUN
ejpam-4317	166	4	:	:	PUNCT
ejpam-4317	166	5	(	(	PUNCT
ejpam-4317	166	6	x	x	X
ejpam-4317	166	7	,	,	PUNCT
ejpam-4317	166	8	τ	τ	PROPN
ejpam-4317	166	9	,	,	PUNCT
ejpam-4317	166	10	i	i	NOUN
ejpam-4317	166	11	)	)	PUNCT
ejpam-4317	166	12	→	→	SYM
ejpam-4317	166	13	(	(	PUNCT
ejpam-4317	166	14	y	y	PROPN
ejpam-4317	166	15	,	,	PUNCT
ejpam-4317	166	16	σ	σ	PROPN
ejpam-4317	166	17	)	)	PUNCT
ejpam-4317	166	18	is	be	AUX
ejpam-4317	166	19	strongly	strongly	ADV
ejpam-4317	166	20	δθ	δθ	NOUN
ejpam-4317	166	21	-	-	PUNCT
ejpam-4317	166	22	i	i	NOUN
ejpam-4317	166	23	-	-	NOUN
ejpam-4317	166	24	continuous	continuous	ADJ
ejpam-4317	166	25	if	if	SCONJ
ejpam-4317	167	1	and	and	CCONJ
ejpam-4317	167	2	only	only	ADV
ejpam-4317	167	3	if	if	SCONJ
ejpam-4317	167	4	every	every	DET
ejpam-4317	167	5	composition	composition	NOUN
ejpam-4317	167	6	pλ	pλ	NOUN
ejpam-4317	167	7	◦	◦	NOUN
ejpam-4317	167	8	f	f	VERB
ejpam-4317	167	9	is	be	AUX
ejpam-4317	167	10	strongly	strongly	ADV
ejpam-4317	167	11	δθ	δθ	NOUN
ejpam-4317	167	12	-	-	PUNCT
ejpam-4317	167	13	i	i	NOUN
ejpam-4317	167	14	-	-	PUNCT
ejpam-4317	167	15	continuous	continuous	ADJ
ejpam-4317	167	16	.	.	PUNCT
ejpam-4317	168	1	proof	proof	NOUN
ejpam-4317	168	2	.	.	PUNCT
ejpam-4317	169	1	let	let	VERB
ejpam-4317	169	2	f	f	NOUN
ejpam-4317	169	3	:	:	PUNCT
ejpam-4317	169	4	(	(	PUNCT
ejpam-4317	169	5	x	x	X
ejpam-4317	169	6	,	,	PUNCT
ejpam-4317	169	7	τ	τ	PROPN
ejpam-4317	169	8	,	,	PUNCT
ejpam-4317	169	9	i	i	NOUN
ejpam-4317	169	10	)	)	PUNCT
ejpam-4317	169	11	→	→	SYM
ejpam-4317	169	12	(	(	PUNCT
ejpam-4317	169	13	y	y	PROPN
ejpam-4317	169	14	,	,	PUNCT
ejpam-4317	169	15	σ	σ	PROPN
ejpam-4317	169	16	)	)	PUNCT
ejpam-4317	169	17	be	be	AUX
ejpam-4317	169	18	a	a	DET
ejpam-4317	169	19	strongly	strongly	ADV
ejpam-4317	169	20	δθ	δθ	NOUN
ejpam-4317	169	21	-	-	PUNCT
ejpam-4317	169	22	i	i	NOUN
ejpam-4317	169	23	-	-	PUNCT
ejpam-4317	169	24	continuous	continuous	ADJ
ejpam-4317	169	25	function	function	NOUN
ejpam-4317	169	26	and	and	CCONJ
ejpam-4317	169	27	let	let	VERB
ejpam-4317	169	28	λ	λ	X
ejpam-4317	169	29	∈	∈	PROPN
ejpam-4317	169	30	λ	λ	PROPN
ejpam-4317	169	31	.	.	PUNCT
ejpam-4317	170	1	since	since	SCONJ
ejpam-4317	170	2	the	the	DET
ejpam-4317	170	3	projection	projection	NOUN
ejpam-4317	170	4	pλ	pλ	NOUN
ejpam-4317	170	5	:	:	PUNCT
ejpam-4317	170	6	y	y	X
ejpam-4317	170	7	→	→	PUNCT
ejpam-4317	170	8	yλ	yλ	PROPN
ejpam-4317	170	9	is	be	AUX
ejpam-4317	170	10	continuous	continuous	ADJ
ejpam-4317	170	11	,	,	PUNCT
ejpam-4317	170	12	by	by	ADP
ejpam-4317	170	13	theorem	theorem	NOUN
ejpam-4317	170	14	2	2	NUM
ejpam-4317	170	15	,	,	PUNCT
ejpam-4317	170	16	we	we	PRON
ejpam-4317	170	17	get	get	VERB
ejpam-4317	170	18	that	that	DET
ejpam-4317	170	19	pλ	pλ	NOUN
ejpam-4317	170	20	◦	◦	NOUN
ejpam-4317	171	1	f	f	X
ejpam-4317	171	2	:	:	PUNCT
ejpam-4317	171	3	(	(	PUNCT
ejpam-4317	171	4	x	x	X
ejpam-4317	171	5	,	,	PUNCT
ejpam-4317	171	6	τ	τ	PROPN
ejpam-4317	171	7	,	,	PUNCT
ejpam-4317	171	8	i	i	NOUN
ejpam-4317	171	9	)	)	PUNCT
ejpam-4317	171	10	→	→	SYM
ejpam-4317	171	11	(	(	PUNCT
ejpam-4317	171	12	yλ	yλ	INTJ
ejpam-4317	171	13	,	,	PUNCT
ejpam-4317	171	14	σλ	σλ	PART
ejpam-4317	171	15	)	)	PUNCT
ejpam-4317	171	16	is	be	AUX
ejpam-4317	171	17	strongly	strongly	ADV
ejpam-4317	171	18	δθ	δθ	NOUN
ejpam-4317	171	19	-	-	PUNCT
ejpam-4317	171	20	i	i	NOUN
ejpam-4317	171	21	-	-	NOUN
ejpam-4317	171	22	continuous	continuous	ADJ
ejpam-4317	171	23	for	for	ADP
ejpam-4317	171	24	every	every	DET
ejpam-4317	171	25	λ	λ	PROPN
ejpam-4317	171	26	∈	∈	PROPN
ejpam-4317	171	27	λ	λ	PROPN
ejpam-4317	171	28	.	.	PUNCT
ejpam-4317	171	29	conversely	conversely	ADV
ejpam-4317	171	30	,	,	PUNCT
ejpam-4317	171	31	suppose	suppose	VERB
ejpam-4317	171	32	that	that	SCONJ
ejpam-4317	171	33	every	every	DET
ejpam-4317	171	34	composition	composition	NOUN
ejpam-4317	171	35	pλ	pλ	NOUN
ejpam-4317	171	36	◦	◦	NOUN
ejpam-4317	171	37	f	f	X
ejpam-4317	171	38	:	:	PUNCT
ejpam-4317	171	39	(	(	PUNCT
ejpam-4317	171	40	x	x	X
ejpam-4317	171	41	,	,	PUNCT
ejpam-4317	171	42	τ	τ	PROPN
ejpam-4317	171	43	,	,	PUNCT
ejpam-4317	171	44	i	i	NOUN
ejpam-4317	171	45	)	)	PUNCT
ejpam-4317	171	46	→	→	SYM
ejpam-4317	171	47	(	(	PUNCT
ejpam-4317	171	48	yλ	yλ	INTJ
ejpam-4317	171	49	,	,	PUNCT
ejpam-4317	171	50	σλ	σλ	PART
ejpam-4317	171	51	)	)	PUNCT
ejpam-4317	171	52	is	be	AUX
ejpam-4317	171	53	strongly	strongly	ADV
ejpam-4317	171	54	δθ	δθ	NOUN
ejpam-4317	171	55	-	-	PUNCT
ejpam-4317	171	56	i	i	NOUN
ejpam-4317	171	57	-	-	PUNCT
ejpam-4317	171	58	continuous	continuous	ADJ
ejpam-4317	171	59	.	.	PUNCT
ejpam-4317	172	1	since	since	SCONJ
ejpam-4317	172	2	the	the	DET
ejpam-4317	172	3	collection	collection	NOUN
ejpam-4317	172	4	τδθ−i	τδθ−i	PROPN
ejpam-4317	172	5	of	of	ADP
ejpam-4317	172	6	all	all	DET
ejpam-4317	172	7	δθ	δθ	NOUN
ejpam-4317	172	8	-	-	PUNCT
ejpam-4317	172	9	i	i	NOUN
ejpam-4317	172	10	-	-	PUNCT
ejpam-4317	172	11	open	open	ADJ
ejpam-4317	172	12	sets	set	NOUN
ejpam-4317	172	13	in	in	ADP
ejpam-4317	172	14	x	x	SYM
ejpam-4317	172	15	is	be	AUX
ejpam-4317	172	16	a	a	DET
ejpam-4317	172	17	topology	topology	NOUN
ejpam-4317	172	18	,	,	PUNCT
ejpam-4317	172	19	it	it	PRON
ejpam-4317	172	20	suffices	suffice	VERB
ejpam-4317	172	21	to	to	PART
ejpam-4317	172	22	show	show	VERB
ejpam-4317	172	23	that	that	SCONJ
ejpam-4317	172	24	the	the	DET
ejpam-4317	172	25	inverse	inverse	NOUN
ejpam-4317	172	26	image	image	NOUN
ejpam-4317	172	27	under	under	ADP
ejpam-4317	172	28	f	f	PROPN
ejpam-4317	172	29	of	of	ADP
ejpam-4317	172	30	each	each	DET
ejpam-4317	172	31	subbasic	subbasic	ADJ
ejpam-4317	172	32	open	open	ADJ
ejpam-4317	172	33	set	set	NOUN
ejpam-4317	172	34	of	of	ADP
ejpam-4317	172	35	y	y	PROPN
ejpam-4317	172	36	=	=	SYM
ejpam-4317	172	37	∏	∏	PROPN
ejpam-4317	172	38	{	{	PUNCT
ejpam-4317	172	39	yλ	yλ	NOUN
ejpam-4317	172	40	:	:	PUNCT
ejpam-4317	172	41	λ	λ	X
ejpam-4317	172	42	∈	∈	PROPN
ejpam-4317	172	43	λ	λ	PROPN
ejpam-4317	172	44	}	}	PUNCT
ejpam-4317	172	45	is	be	AUX
ejpam-4317	172	46	a	a	DET
ejpam-4317	172	47	δθ	δθ	NOUN
ejpam-4317	172	48	-	-	PUNCT
ejpam-4317	172	49	i	i	NOUN
ejpam-4317	172	50	-	-	PUNCT
ejpam-4317	172	51	open	open	ADJ
ejpam-4317	172	52	set	set	NOUN
ejpam-4317	172	53	in	in	ADP
ejpam-4317	172	54	x.	x.	NOUN
ejpam-4317	172	55	let	let	VERB
ejpam-4317	172	56	p−1	p−1	PROPN
ejpam-4317	172	57	λ	λ	PROPN
ejpam-4317	172	58	(	(	PUNCT
ejpam-4317	172	59	vλ	vλ	PROPN
ejpam-4317	172	60	)	)	PUNCT
ejpam-4317	172	61	be	be	AUX
ejpam-4317	172	62	a	a	DET
ejpam-4317	172	63	subbasic	subbasic	ADJ
ejpam-4317	172	64	open	open	NOUN
ejpam-4317	172	65	set	set	NOUN
ejpam-4317	172	66	in	in	ADP
ejpam-4317	172	67	y	y	PROPN
ejpam-4317	172	68	.	.	PUNCT
ejpam-4317	173	1	then	then	ADV
ejpam-4317	173	2	,	,	PUNCT
ejpam-4317	173	3	vλ	vλ	INTJ
ejpam-4317	173	4	∈	∈	PROPN
ejpam-4317	173	5	σλ	σλ	VERB
ejpam-4317	173	6	and	and	CCONJ
ejpam-4317	173	7	so	so	ADV
ejpam-4317	173	8	,	,	PUNCT
ejpam-4317	173	9	f−1	f−1	PROPN
ejpam-4317	173	10	(	(	PUNCT
ejpam-4317	173	11	p−1	p−1	PROPN
ejpam-4317	173	12	λ	λ	PROPN
ejpam-4317	173	13	(	(	PUNCT
ejpam-4317	173	14	vλ	vλ	PROPN
ejpam-4317	173	15	)	)	PUNCT
ejpam-4317	173	16	)	)	PUNCT
ejpam-4317	174	1	=	=	PUNCT
ejpam-4317	174	2	(	(	PUNCT
ejpam-4317	174	3	pλ	pλ	NOUN
ejpam-4317	174	4	◦	◦	NOUN
ejpam-4317	174	5	f)−1	f)−1	NOUN
ejpam-4317	174	6	(	(	PUNCT
ejpam-4317	174	7	vλ	vλ	PROPN
ejpam-4317	174	8	)	)	PUNCT
ejpam-4317	174	9	is	be	AUX
ejpam-4317	174	10	a	a	DET
ejpam-4317	174	11	δθ	δθ	NOUN
ejpam-4317	174	12	-	-	PUNCT
ejpam-4317	174	13	i	i	NOUN
ejpam-4317	174	14	-	-	PUNCT
ejpam-4317	174	15	open	open	ADJ
ejpam-4317	174	16	set	set	NOUN
ejpam-4317	174	17	in	in	ADP
ejpam-4317	174	18	x.	x.	NOUN
ejpam-4317	174	19	therefore	therefore	ADV
ejpam-4317	174	20	,	,	PUNCT
ejpam-4317	174	21	f	f	PROPN
ejpam-4317	174	22	is	be	AUX
ejpam-4317	174	23	strongly	strongly	ADV
ejpam-4317	174	24	δθ	δθ	ADV
ejpam-4317	174	25	-	-	PUNCT
ejpam-4317	174	26	icontinuous	icontinuous	ADJ
ejpam-4317	174	27	.	.	PUNCT
ejpam-4317	175	1	corollary	corollary	ADJ
ejpam-4317	175	2	1	1	NUM
ejpam-4317	175	3	.	.	PUNCT
ejpam-4317	176	1	let	let	VERB
ejpam-4317	176	2	(	(	PUNCT
ejpam-4317	176	3	x	x	X
ejpam-4317	176	4	,	,	PUNCT
ejpam-4317	176	5	τ	τ	PROPN
ejpam-4317	176	6	,	,	PUNCT
ejpam-4317	176	7	i	i	PRON
ejpam-4317	176	8	)	)	PUNCT
ejpam-4317	176	9	be	be	VERB
ejpam-4317	176	10	a	a	DET
ejpam-4317	176	11	space	space	NOUN
ejpam-4317	176	12	,	,	PUNCT
ejpam-4317	176	13	{	{	PUNCT
ejpam-4317	176	14	(	(	PUNCT
ejpam-4317	176	15	yλ	yλ	INTJ
ejpam-4317	176	16	,	,	PUNCT
ejpam-4317	176	17	σλ	σλ	PROPN
ejpam-4317	176	18	)	)	PUNCT
ejpam-4317	176	19	:	:	PUNCT
ejpam-4317	177	1	λ	λ	X
ejpam-4317	177	2	∈	∈	PROPN
ejpam-4317	177	3	λ	λ	PROPN
ejpam-4317	177	4	}	}	PUNCT
ejpam-4317	177	5	be	be	VERB
ejpam-4317	177	6	a	a	DET
ejpam-4317	177	7	collection	collection	NOUN
ejpam-4317	177	8	of	of	ADP
ejpam-4317	177	9	topological	topological	ADJ
ejpam-4317	177	10	spaces	space	NOUN
ejpam-4317	177	11	and	and	CCONJ
ejpam-4317	177	12	fλ	fλ	INTJ
ejpam-4317	177	13	:	:	PUNCT
ejpam-4317	177	14	(	(	PUNCT
ejpam-4317	177	15	x	x	X
ejpam-4317	177	16	,	,	PUNCT
ejpam-4317	177	17	τ	τ	PROPN
ejpam-4317	177	18	,	,	PUNCT
ejpam-4317	177	19	i	i	NOUN
ejpam-4317	177	20	)	)	PUNCT
ejpam-4317	177	21	→	→	SYM
ejpam-4317	177	22	(	(	PUNCT
ejpam-4317	177	23	yλ	yλ	INTJ
ejpam-4317	177	24	,	,	PUNCT
ejpam-4317	177	25	σλ	σλ	AUX
ejpam-4317	177	26	)	)	PUNCT
ejpam-4317	177	27	be	be	AUX
ejpam-4317	177	28	a	a	DET
ejpam-4317	177	29	function	function	NOUN
ejpam-4317	177	30	for	for	ADP
ejpam-4317	177	31	every	every	DET
ejpam-4317	177	32	λ	λ	PROPN
ejpam-4317	177	33	∈	∈	PROPN
ejpam-4317	177	34	λ	λ	PROPN
ejpam-4317	177	35	.	.	PUNCT
ejpam-4317	178	1	let	let	VERB
ejpam-4317	178	2	σ	σ	NOUN
ejpam-4317	178	3	=	=	SYM
ejpam-4317	178	4	∏	∏	PROPN
ejpam-4317	178	5	{	{	PUNCT
ejpam-4317	178	6	σλ	σλ	NOUN
ejpam-4317	178	7	:	:	PUNCT
ejpam-4317	179	1	λ	λ	X
ejpam-4317	179	2	∈	∈	PROPN
ejpam-4317	179	3	λ	λ	PROPN
ejpam-4317	179	4	}	}	PUNCT
ejpam-4317	179	5	be	be	VERB
ejpam-4317	179	6	the	the	DET
ejpam-4317	179	7	product	product	NOUN
ejpam-4317	179	8	topology	topology	NOUN
ejpam-4317	179	9	on	on	ADP
ejpam-4317	179	10	y	y	PROPN
ejpam-4317	179	11	=	=	SYM
ejpam-4317	179	12	∏	∏	PROPN
ejpam-4317	179	13	{	{	PUNCT
ejpam-4317	179	14	yλ	yλ	NOUN
ejpam-4317	179	15	:	:	PUNCT
ejpam-4317	179	16	λ	λ	X
ejpam-4317	179	17	∈	∈	PROPN
ejpam-4317	179	18	λ	λ	X
ejpam-4317	179	19	}	}	PUNCT
ejpam-4317	179	20	and	and	CCONJ
ejpam-4317	179	21	f	f	NOUN
ejpam-4317	179	22	:	:	PUNCT
ejpam-4317	179	23	(	(	PUNCT
ejpam-4317	179	24	x	x	X
ejpam-4317	179	25	,	,	PUNCT
ejpam-4317	179	26	τ	τ	PROPN
ejpam-4317	179	27	,	,	PUNCT
ejpam-4317	179	28	i	i	NOUN
ejpam-4317	179	29	)	)	PUNCT
ejpam-4317	179	30	→	→	SYM
ejpam-4317	179	31	(	(	PUNCT
ejpam-4317	179	32	y	y	PROPN
ejpam-4317	179	33	,	,	PUNCT
ejpam-4317	179	34	σ	σ	PROPN
ejpam-4317	179	35	)	)	PUNCT
ejpam-4317	179	36	be	be	VERB
ejpam-4317	179	37	the	the	DET
ejpam-4317	179	38	function	function	NOUN
ejpam-4317	179	39	defined	define	VERB
ejpam-4317	179	40	by	by	ADP
ejpam-4317	179	41	f(x	f(x	PROPN
ejpam-4317	179	42	)	)	PUNCT
ejpam-4317	180	1	=	=	PUNCT
ejpam-4317	181	1	(	(	PUNCT
ejpam-4317	181	2	fλ(x))λ∈λ	fλ(x))λ∈λ	ADV
ejpam-4317	181	3	for	for	ADP
ejpam-4317	181	4	each	each	DET
ejpam-4317	181	5	x	x	SYM
ejpam-4317	181	6	∈	∈	PROPN
ejpam-4317	181	7	x.	x.	NOUN
ejpam-4317	181	8	then	then	ADV
ejpam-4317	181	9	,	,	PUNCT
ejpam-4317	181	10	f	f	PROPN
ejpam-4317	181	11	is	be	AUX
ejpam-4317	181	12	strongly	strongly	ADV
ejpam-4317	181	13	δθ	δθ	NOUN
ejpam-4317	181	14	-	-	PUNCT
ejpam-4317	181	15	i	i	NOUN
ejpam-4317	181	16	-	-	NOUN
ejpam-4317	181	17	continuous	continuous	ADJ
ejpam-4317	181	18	if	if	SCONJ
ejpam-4317	182	1	and	and	CCONJ
ejpam-4317	182	2	only	only	ADV
ejpam-4317	182	3	if	if	SCONJ
ejpam-4317	182	4	fλ	fλ	NOUN
ejpam-4317	182	5	is	be	AUX
ejpam-4317	182	6	strongly	strongly	ADV
ejpam-4317	182	7	δθ	δθ	NOUN
ejpam-4317	182	8	-	-	PUNCT
ejpam-4317	182	9	i	i	NOUN
ejpam-4317	182	10	-	-	NOUN
ejpam-4317	182	11	continuous	continuous	ADJ
ejpam-4317	182	12	for	for	ADP
ejpam-4317	182	13	every	every	DET
ejpam-4317	182	14	λ	λ	PROPN
ejpam-4317	182	15	∈	∈	PROPN
ejpam-4317	182	16	λ	λ	PROPN
ejpam-4317	182	17	.	.	PROPN
ejpam-4317	183	1	next	next	ADV
ejpam-4317	183	2	,	,	PUNCT
ejpam-4317	183	3	we	we	PRON
ejpam-4317	183	4	present	present	VERB
ejpam-4317	183	5	some	some	DET
ejpam-4317	183	6	topological	topological	ADJ
ejpam-4317	183	7	notions	notion	NOUN
ejpam-4317	183	8	to	to	PART
ejpam-4317	183	9	establish	establish	VERB
ejpam-4317	183	10	some	some	DET
ejpam-4317	183	11	properties	property	NOUN
ejpam-4317	183	12	related	relate	VERB
ejpam-4317	183	13	to	to	ADP
ejpam-4317	183	14	strongly	strongly	ADV
ejpam-4317	183	15	δθ	δθ	ADP
ejpam-4317	183	16	-	-	PUNCT
ejpam-4317	183	17	i	i	NOUN
ejpam-4317	183	18	-	-	PUNCT
ejpam-4317	183	19	continuous	continuous	ADJ
ejpam-4317	183	20	functions	function	NOUN
ejpam-4317	183	21	.	.	PUNCT
ejpam-4317	184	1	definition	definition	NOUN
ejpam-4317	184	2	5	5	NUM
ejpam-4317	184	3	.	.	PUNCT
ejpam-4317	185	1	a	a	DET
ejpam-4317	185	2	space	space	NOUN
ejpam-4317	185	3	(	(	PUNCT
ejpam-4317	185	4	x	x	X
ejpam-4317	185	5	,	,	PUNCT
ejpam-4317	185	6	τ	τ	PROPN
ejpam-4317	185	7	,	,	PUNCT
ejpam-4317	185	8	i	i	PROPN
ejpam-4317	185	9	)	)	PUNCT
ejpam-4317	185	10	is	be	AUX
ejpam-4317	185	11	said	say	VERB
ejpam-4317	185	12	to	to	PART
ejpam-4317	185	13	be	be	AUX
ejpam-4317	185	14	δ?-regular	δ?-regular	PROPN
ejpam-4317	185	15	[	[	X
ejpam-4317	185	16	14	14	NUM
ejpam-4317	185	17	]	]	X
ejpam-4317	185	18	(	(	PUNCT
ejpam-4317	185	19	resp	resp	NOUN
ejpam-4317	185	20	.	.	PUNCT
ejpam-4317	185	21	?	?	PUNCT
ejpam-4317	186	1	-regular	-regular	ADJ
ejpam-4317	186	2	[	[	X
ejpam-4317	186	3	2	2	NUM
ejpam-4317	186	4	]	]	NUM
ejpam-4317	186	5	)	)	PUNCT
ejpam-4317	186	6	,	,	PUNCT
ejpam-4317	186	7	if	if	SCONJ
ejpam-4317	186	8	for	for	ADP
ejpam-4317	186	9	each	each	DET
ejpam-4317	186	10	pair	pair	NOUN
ejpam-4317	186	11	consisting	consist	VERB
ejpam-4317	186	12	of	of	ADP
ejpam-4317	186	13	a	a	DET
ejpam-4317	186	14	closed	closed	ADJ
ejpam-4317	186	15	set	set	VERB
ejpam-4317	186	16	f	f	PROPN
ejpam-4317	186	17	and	and	CCONJ
ejpam-4317	186	18	a	a	DET
ejpam-4317	186	19	point	point	NOUN
ejpam-4317	186	20	x	x	X
ejpam-4317	186	21	/∈	/∈	PUNCT
ejpam-4317	187	1	f	f	PROPN
ejpam-4317	187	2	,	,	PUNCT
ejpam-4317	187	3	there	there	PRON
ejpam-4317	187	4	exist	exist	VERB
ejpam-4317	187	5	v	v	ADP
ejpam-4317	187	6	∈	∈	PROPN
ejpam-4317	187	7	τ	τ	X
ejpam-4317	187	8	and	and	CCONJ
ejpam-4317	187	9	u	u	PROPN
ejpam-4317	187	10	∈	∈	PROPN
ejpam-4317	187	11	τ	τ	PROPN
ejpam-4317	187	12	δ	δ	PROPN
ejpam-4317	187	13	?	?	PUNCT
ejpam-4317	188	1	(	(	PUNCT
ejpam-4317	188	2	resp	resp	NOUN
ejpam-4317	188	3	.	.	PUNCT
ejpam-4317	189	1	u	u	NOUN
ejpam-4317	189	2	∈	∈	PROPN
ejpam-4317	189	3	τ	τ	PROPN
ejpam-4317	189	4	?	?	PUNCT
ejpam-4317	189	5	)	)	PUNCT
ejpam-4317	189	6	such	such	ADJ
ejpam-4317	189	7	that	that	SCONJ
ejpam-4317	189	8	x	x	SYM
ejpam-4317	189	9	∈	∈	NOUN
ejpam-4317	189	10	v	v	NOUN
ejpam-4317	189	11	,	,	PUNCT
ejpam-4317	189	12	f	f	PROPN
ejpam-4317	189	13	⊂	⊂	PROPN
ejpam-4317	189	14	u	u	PROPN
ejpam-4317	189	15	and	and	CCONJ
ejpam-4317	189	16	u	u	PROPN
ejpam-4317	189	17	∩	∩	NOUN
ejpam-4317	189	18	v	v	NOUN
ejpam-4317	189	19	=	=	PUNCT
ejpam-4317	189	20	∅.	∅.	VERB
ejpam-4317	189	21	the	the	DET
ejpam-4317	189	22	concepts	concept	NOUN
ejpam-4317	189	23	of	of	ADP
ejpam-4317	189	24	δ?-regular	δ?-regular	ADJ
ejpam-4317	189	25	space	space	NOUN
ejpam-4317	189	26	and	and	CCONJ
ejpam-4317	189	27	?	?	PUNCT
ejpam-4317	189	28	-regular	-regular	ADJ
ejpam-4317	189	29	space	space	NOUN
ejpam-4317	189	30	are	be	AUX
ejpam-4317	189	31	related	relate	VERB
ejpam-4317	189	32	as	as	SCONJ
ejpam-4317	189	33	follows	follow	VERB
ejpam-4317	189	34	.	.	PUNCT
ejpam-4317	190	1	lemma	lemma	PROPN
ejpam-4317	190	2	1	1	NUM
ejpam-4317	190	3	.	.	PUNCT
ejpam-4317	191	1	every	every	DET
ejpam-4317	191	2	δ?-regular	δ?-regular	ADJ
ejpam-4317	191	3	space	space	NOUN
ejpam-4317	191	4	is	be	AUX
ejpam-4317	191	5	a	a	DET
ejpam-4317	191	6	?	?	ADV
ejpam-4317	191	7	-regular	-regular	ADJ
ejpam-4317	191	8	.	.	PUNCT
ejpam-4317	192	1	proof	proof	NOUN
ejpam-4317	192	2	.	.	PUNCT
ejpam-4317	193	1	suppose	suppose	VERB
ejpam-4317	193	2	that	that	SCONJ
ejpam-4317	193	3	(	(	PUNCT
ejpam-4317	193	4	x	x	X
ejpam-4317	193	5	,	,	PUNCT
ejpam-4317	193	6	τ	τ	PROPN
ejpam-4317	193	7	,	,	PUNCT
ejpam-4317	193	8	i	i	PROPN
ejpam-4317	193	9	)	)	PUNCT
ejpam-4317	193	10	is	be	AUX
ejpam-4317	193	11	a	a	DET
ejpam-4317	193	12	δ?-regular	δ?-regular	ADJ
ejpam-4317	193	13	space	space	NOUN
ejpam-4317	193	14	.	.	PUNCT
ejpam-4317	194	1	let	let	VERB
ejpam-4317	194	2	f	f	PRON
ejpam-4317	194	3	be	be	AUX
ejpam-4317	194	4	a	a	DET
ejpam-4317	194	5	closed	closed	ADJ
ejpam-4317	194	6	set	set	NOUN
ejpam-4317	194	7	and	and	CCONJ
ejpam-4317	194	8	x	x	SYM
ejpam-4317	194	9	/∈	/∈	PROPN
ejpam-4317	195	1	f	f	PROPN
ejpam-4317	195	2	.	.	PUNCT
ejpam-4317	196	1	then	then	ADV
ejpam-4317	196	2	,	,	PUNCT
ejpam-4317	196	3	there	there	PRON
ejpam-4317	196	4	exist	exist	VERB
ejpam-4317	196	5	v	v	ADP
ejpam-4317	196	6	∈	∈	PROPN
ejpam-4317	196	7	τ	τ	X
ejpam-4317	196	8	and	and	CCONJ
ejpam-4317	196	9	u	u	PROPN
ejpam-4317	196	10	∈	∈	PROPN
ejpam-4317	196	11	τ	τ	PROPN
ejpam-4317	196	12	δ	δ	PROPN
ejpam-4317	196	13	?	?	PUNCT
ejpam-4317	196	14	such	such	ADJ
ejpam-4317	196	15	that	that	SCONJ
ejpam-4317	196	16	x	x	SYM
ejpam-4317	196	17	∈	∈	NOUN
ejpam-4317	196	18	v	v	NOUN
ejpam-4317	196	19	,	,	PUNCT
ejpam-4317	196	20	f	f	PROPN
ejpam-4317	196	21	⊂	⊂	PROPN
ejpam-4317	196	22	u	u	PROPN
ejpam-4317	196	23	and	and	CCONJ
ejpam-4317	196	24	u	u	PROPN
ejpam-4317	196	25	∩	∩	NOUN
ejpam-4317	196	26	v	v	NOUN
ejpam-4317	196	27	=	=	PUNCT
ejpam-4317	196	28	∅.	∅.	NOUN
ejpam-4317	196	29	since	since	SCONJ
ejpam-4317	196	30	τ	τ	PROPN
ejpam-4317	196	31	δ	δ	PROPN
ejpam-4317	196	32	?	?	PUNCT
ejpam-4317	197	1	⊂	⊂	PROPN
ejpam-4317	197	2	τ	τ	PROPN
ejpam-4317	197	3	?	?	PROPN
ejpam-4317	197	4	,	,	PUNCT
ejpam-4317	197	5	we	we	PRON
ejpam-4317	197	6	have	have	VERB
ejpam-4317	197	7	u	u	NOUN
ejpam-4317	197	8	∈	∈	PROPN
ejpam-4317	197	9	τ	τ	PROPN
ejpam-4317	197	10	?	?	PUNCT
ejpam-4317	197	11	and	and	CCONJ
ejpam-4317	197	12	hence	hence	ADV
ejpam-4317	197	13	,	,	PUNCT
ejpam-4317	197	14	(	(	PUNCT
ejpam-4317	197	15	x	x	X
ejpam-4317	197	16	,	,	PUNCT
ejpam-4317	197	17	τ	τ	PROPN
ejpam-4317	197	18	,	,	PUNCT
ejpam-4317	197	19	i	i	PROPN
ejpam-4317	197	20	)	)	PUNCT
ejpam-4317	197	21	is	be	AUX
ejpam-4317	197	22	a	a	DET
ejpam-4317	197	23	?	?	ADV
ejpam-4317	197	24	-regular	-regular	ADJ
ejpam-4317	197	25	space	space	NOUN
ejpam-4317	197	26	.	.	PUNCT
ejpam-4317	198	1	the	the	DET
ejpam-4317	198	2	following	follow	VERB
ejpam-4317	198	3	example	example	NOUN
ejpam-4317	198	4	shows	show	VERB
ejpam-4317	198	5	that	that	SCONJ
ejpam-4317	198	6	,	,	PUNCT
ejpam-4317	198	7	in	in	ADP
ejpam-4317	198	8	general	general	ADJ
ejpam-4317	198	9	,	,	PUNCT
ejpam-4317	198	10	the	the	DET
ejpam-4317	198	11	converse	converse	NOUN
ejpam-4317	198	12	of	of	ADP
ejpam-4317	198	13	lemma	lemma	PROPN
ejpam-4317	198	14	1	1	NUM
ejpam-4317	198	15	is	be	AUX
ejpam-4317	198	16	not	not	PART
ejpam-4317	198	17	true	true	ADJ
ejpam-4317	198	18	.	.	PUNCT
ejpam-4317	199	1	example	example	NOUN
ejpam-4317	200	1	1	1	NUM
ejpam-4317	200	2	.	.	X
ejpam-4317	200	3	a	a	DET
ejpam-4317	200	4	?	?	PUNCT
ejpam-4317	200	5	-regular	-regular	ADJ
ejpam-4317	200	6	space	space	NOUN
ejpam-4317	200	7	need	need	AUX
ejpam-4317	200	8	not	not	PART
ejpam-4317	200	9	be	be	AUX
ejpam-4317	200	10	δ?-regular	δ?-regular	ADJ
ejpam-4317	200	11	space	space	NOUN
ejpam-4317	200	12	.	.	PUNCT
ejpam-4317	201	1	consider	consider	VERB
ejpam-4317	201	2	the	the	DET
ejpam-4317	201	3	space	space	NOUN
ejpam-4317	201	4	(	(	PUNCT
ejpam-4317	201	5	x	x	X
ejpam-4317	201	6	,	,	PUNCT
ejpam-4317	201	7	τ	τ	PROPN
ejpam-4317	201	8	,	,	PUNCT
ejpam-4317	201	9	i	i	PROPN
ejpam-4317	201	10	)	)	PUNCT
ejpam-4317	201	11	,	,	PUNCT
ejpam-4317	201	12	where	where	SCONJ
ejpam-4317	201	13	x	x	X
ejpam-4317	201	14	=	=	PRON
ejpam-4317	201	15	{	{	PUNCT
ejpam-4317	201	16	a	a	PRON
ejpam-4317	201	17	,	,	PUNCT
ejpam-4317	201	18	b	b	NOUN
ejpam-4317	201	19	,	,	PUNCT
ejpam-4317	201	20	c	c	NOUN
ejpam-4317	201	21	,	,	PUNCT
ejpam-4317	201	22	d	d	NOUN
ejpam-4317	201	23	}	}	PUNCT
ejpam-4317	201	24	,	,	PUNCT
ejpam-4317	201	25	τ	τ	X
ejpam-4317	201	26	=	=	PUNCT
ejpam-4317	201	27	{	{	PUNCT
ejpam-4317	201	28	∅	∅	NOUN
ejpam-4317	201	29	,	,	PUNCT
ejpam-4317	201	30	x	x	X
ejpam-4317	201	31	,	,	PUNCT
ejpam-4317	201	32	{	{	PUNCT
ejpam-4317	201	33	a	a	DET
ejpam-4317	201	34	,	,	PUNCT
ejpam-4317	201	35	b	b	NOUN
ejpam-4317	201	36	,	,	PUNCT
ejpam-4317	201	37	c	c	NOUN
ejpam-4317	201	38	}	}	PUNCT
ejpam-4317	201	39	,	,	PUNCT
ejpam-4317	201	40	{	{	PUNCT
ejpam-4317	201	41	a	a	DET
ejpam-4317	201	42	,	,	PUNCT
ejpam-4317	201	43	b	b	NOUN
ejpam-4317	201	44	,	,	PUNCT
ejpam-4317	201	45	d	d	NOUN
ejpam-4317	201	46	}	}	PUNCT
ejpam-4317	201	47	,	,	PUNCT
ejpam-4317	201	48	{	{	PUNCT
ejpam-4317	201	49	a	a	PRON
ejpam-4317	201	50	,	,	PUNCT
ejpam-4317	201	51	b	b	NOUN
ejpam-4317	201	52	}	}	PUNCT
ejpam-4317	201	53	}	}	PUNCT
ejpam-4317	201	54	and	and	CCONJ
ejpam-4317	201	55	i	i	PRON
ejpam-4317	201	56	=	=	PUNCT
ejpam-4317	201	57	{	{	PUNCT
ejpam-4317	201	58	∅	∅	NOUN
ejpam-4317	201	59	,	,	PUNCT
ejpam-4317	201	60	{	{	PUNCT
ejpam-4317	201	61	a	a	X
ejpam-4317	201	62	}	}	PUNCT
ejpam-4317	201	63	,	,	PUNCT
ejpam-4317	201	64	{	{	PUNCT
ejpam-4317	201	65	b	b	NOUN
ejpam-4317	201	66	}	}	PUNCT
ejpam-4317	201	67	,	,	PUNCT
ejpam-4317	201	68	{	{	PUNCT
ejpam-4317	201	69	a	a	PRON
ejpam-4317	201	70	,	,	PUNCT
ejpam-4317	201	71	b	b	NOUN
ejpam-4317	201	72	}	}	PUNCT
ejpam-4317	201	73	}	}	PUNCT
ejpam-4317	201	74	.	.	PUNCT
ejpam-4317	202	1	observe	observe	VERB
ejpam-4317	202	2	that	that	SCONJ
ejpam-4317	202	3	the	the	DET
ejpam-4317	202	4	collection	collection	NOUN
ejpam-4317	202	5	of	of	ADP
ejpam-4317	202	6	all	all	DET
ejpam-4317	202	7	closed	closed	ADJ
ejpam-4317	202	8	sets	set	NOUN
ejpam-4317	202	9	is	be	AUX
ejpam-4317	202	10	{	{	PUNCT
ejpam-4317	202	11	∅	∅	NOUN
ejpam-4317	202	12	,	,	PUNCT
ejpam-4317	202	13	x	x	X
ejpam-4317	202	14	,	,	PUNCT
ejpam-4317	202	15	{	{	PUNCT
ejpam-4317	202	16	c	c	NOUN
ejpam-4317	202	17	}	}	PUNCT
ejpam-4317	202	18	,	,	PUNCT
ejpam-4317	202	19	{	{	PUNCT
ejpam-4317	202	20	d	d	X
ejpam-4317	202	21	}	}	PUNCT
ejpam-4317	202	22	,	,	PUNCT
ejpam-4317	202	23	{	{	PUNCT
ejpam-4317	202	24	c	c	X
ejpam-4317	202	25	,	,	PUNCT
ejpam-4317	202	26	d	d	NOUN
ejpam-4317	202	27	}	}	PUNCT
ejpam-4317	202	28	}	}	PUNCT
ejpam-4317	202	29	.	.	PUNCT
ejpam-4317	203	1	also	also	ADV
ejpam-4317	203	2	,	,	PUNCT
ejpam-4317	203	3	τ	τ	X
ejpam-4317	203	4	?	?	PUNCT
ejpam-4317	203	5	=	=	SYM
ejpam-4317	203	6	p(x	p(x	PROPN
ejpam-4317	203	7	)	)	PUNCT
ejpam-4317	203	8	,	,	PUNCT
ejpam-4317	203	9	τδ	τδ	ADP
ejpam-4317	203	10	=	=	SYM
ejpam-4317	203	11	{	{	PUNCT
ejpam-4317	203	12	∅	∅	NOUN
ejpam-4317	203	13	,	,	PUNCT
ejpam-4317	203	14	x	x	NOUN
ejpam-4317	203	15	}	}	PUNCT
ejpam-4317	203	16	and	and	CCONJ
ejpam-4317	203	17	τ	τ	PROPN
ejpam-4317	203	18	δ	δ	PROPN
ejpam-4317	203	19	?	?	PUNCT
ejpam-4317	204	1	=	=	PRON
ejpam-4317	204	2	{	{	PUNCT
ejpam-4317	204	3	∅	∅	NOUN
ejpam-4317	204	4	,	,	PUNCT
ejpam-4317	204	5	x	x	X
ejpam-4317	204	6	,	,	PUNCT
ejpam-4317	204	7	{	{	PUNCT
ejpam-4317	204	8	c	c	X
ejpam-4317	204	9	,	,	PUNCT
ejpam-4317	204	10	d	d	NOUN
ejpam-4317	204	11	}	}	PUNCT
ejpam-4317	204	12	,	,	PUNCT
ejpam-4317	204	13	{	{	PUNCT
ejpam-4317	204	14	b	b	X
ejpam-4317	204	15	,	,	PUNCT
ejpam-4317	204	16	c	c	NOUN
ejpam-4317	204	17	,	,	PUNCT
ejpam-4317	204	18	d	d	NOUN
ejpam-4317	204	19	}	}	PUNCT
ejpam-4317	204	20	,	,	PUNCT
ejpam-4317	204	21	{	{	PUNCT
ejpam-4317	204	22	a	a	PRON
ejpam-4317	204	23	,	,	PUNCT
ejpam-4317	204	24	c	c	NOUN
ejpam-4317	204	25	,	,	PUNCT
ejpam-4317	204	26	d	d	NOUN
ejpam-4317	204	27	}	}	PUNCT
ejpam-4317	204	28	}	}	PUNCT
ejpam-4317	204	29	.	.	PUNCT
ejpam-4317	205	1	then	then	ADV
ejpam-4317	205	2	,	,	PUNCT
ejpam-4317	205	3	we	we	PRON
ejpam-4317	205	4	have	have	VERB
ejpam-4317	205	5	:	:	PUNCT
ejpam-4317	205	6	(	(	PUNCT
ejpam-4317	205	7	i	i	NOUN
ejpam-4317	205	8	)	)	PUNCT
ejpam-4317	205	9	for	for	ADP
ejpam-4317	205	10	f1	f1	NOUN
ejpam-4317	205	11	=	=	SYM
ejpam-4317	205	12	{	{	PUNCT
ejpam-4317	205	13	d	d	NOUN
ejpam-4317	205	14	}	}	PUNCT
ejpam-4317	205	15	and	and	CCONJ
ejpam-4317	205	16	a	a	DET
ejpam-4317	205	17	/∈	/∈	NOUN
ejpam-4317	205	18	f1	f1	NOUN
ejpam-4317	205	19	,	,	PUNCT
ejpam-4317	205	20	there	there	PRON
ejpam-4317	205	21	exist	exist	VERB
ejpam-4317	205	22	v1	v1	NOUN
ejpam-4317	205	23	=	=	SYM
ejpam-4317	205	24	{	{	PUNCT
ejpam-4317	205	25	a	a	PRON
ejpam-4317	205	26	,	,	PUNCT
ejpam-4317	205	27	b	b	NOUN
ejpam-4317	205	28	}	}	PUNCT
ejpam-4317	205	29	∈	∈	PROPN
ejpam-4317	205	30	τ	τ	X
ejpam-4317	205	31	and	and	CCONJ
ejpam-4317	205	32	u1	u1	PROPN
ejpam-4317	205	33	=	=	SYM
ejpam-4317	205	34	{	{	PUNCT
ejpam-4317	205	35	c	c	NOUN
ejpam-4317	205	36	,	,	PUNCT
ejpam-4317	205	37	d	d	NOUN
ejpam-4317	205	38	}	}	PUNCT
ejpam-4317	205	39	∈	∈	PROPN
ejpam-4317	205	40	τ	τ	PROPN
ejpam-4317	205	41	?	?	PUNCT
ejpam-4317	206	1	such	such	ADJ
ejpam-4317	206	2	that	that	SCONJ
ejpam-4317	206	3	a	a	DET
ejpam-4317	206	4	∈	∈	PROPN
ejpam-4317	206	5	v1	v1	NOUN
ejpam-4317	206	6	,	,	PUNCT
ejpam-4317	206	7	f1	f1	PROPN
ejpam-4317	206	8	⊂	⊂	PROPN
ejpam-4317	206	9	u1	u1	PROPN
ejpam-4317	206	10	and	and	CCONJ
ejpam-4317	206	11	v1	v1	ADJ
ejpam-4317	206	12	∩	∩	ADJ
ejpam-4317	206	13	u1	u1	NOUN
ejpam-4317	206	14	=	=	SYM
ejpam-4317	206	15	∅.	∅.	PROPN
ejpam-4317	206	16	(	(	PUNCT
ejpam-4317	206	17	ii	ii	NOUN
ejpam-4317	206	18	)	)	PUNCT
ejpam-4317	206	19	for	for	ADP
ejpam-4317	206	20	f1	f1	NOUN
ejpam-4317	206	21	=	=	SYM
ejpam-4317	206	22	{	{	PUNCT
ejpam-4317	206	23	d	d	NOUN
ejpam-4317	206	24	}	}	PUNCT
ejpam-4317	206	25	and	and	CCONJ
ejpam-4317	206	26	b	b	PROPN
ejpam-4317	206	27	/∈	/∈	PUNCT
ejpam-4317	206	28	f1	f1	NOUN
ejpam-4317	206	29	,	,	PUNCT
ejpam-4317	206	30	there	there	PRON
ejpam-4317	206	31	exist	exist	VERB
ejpam-4317	206	32	v1	v1	NOUN
ejpam-4317	206	33	=	=	SYM
ejpam-4317	206	34	{	{	PUNCT
ejpam-4317	206	35	a	a	PRON
ejpam-4317	206	36	,	,	PUNCT
ejpam-4317	206	37	b	b	NOUN
ejpam-4317	206	38	}	}	PUNCT
ejpam-4317	206	39	∈	∈	PROPN
ejpam-4317	206	40	τ	τ	X
ejpam-4317	206	41	and	and	CCONJ
ejpam-4317	206	42	u1	u1	PROPN
ejpam-4317	206	43	=	=	SYM
ejpam-4317	206	44	{	{	PUNCT
ejpam-4317	206	45	c	c	NOUN
ejpam-4317	206	46	,	,	PUNCT
ejpam-4317	206	47	d	d	NOUN
ejpam-4317	206	48	}	}	PUNCT
ejpam-4317	206	49	∈	∈	PROPN
ejpam-4317	206	50	τ	τ	PROPN
ejpam-4317	206	51	?	?	PUNCT
ejpam-4317	206	52	such	such	ADJ
ejpam-4317	206	53	that	that	DET
ejpam-4317	206	54	b	b	PROPN
ejpam-4317	206	55	∈	∈	PROPN
ejpam-4317	206	56	v1	v1	NOUN
ejpam-4317	206	57	,	,	PUNCT
ejpam-4317	206	58	f1	f1	PROPN
ejpam-4317	206	59	⊂	⊂	PROPN
ejpam-4317	206	60	u1	u1	PROPN
ejpam-4317	206	61	and	and	CCONJ
ejpam-4317	206	62	v1	v1	ADJ
ejpam-4317	206	63	∩	∩	ADJ
ejpam-4317	206	64	u1	u1	NOUN
ejpam-4317	206	65	=	=	PUNCT
ejpam-4317	206	66	∅.	∅.	PROPN
ejpam-4317	206	67	j.	j.	PROPN
ejpam-4317	206	68	sanabria	sanabria	PROPN
ejpam-4317	206	69	,	,	PUNCT
ejpam-4317	206	70	r.	r.	PROPN
ejpam-4317	206	71	lozada	lozada	PROPN
ejpam-4317	206	72	-	-	PUNCT
ejpam-4317	206	73	yavina	yavina	PROPN
ejpam-4317	206	74	,	,	PUNCT
ejpam-4317	206	75	j.	j.	PROPN
ejpam-4317	206	76	tormet	tormet	PROPN
ejpam-4317	206	77	/	/	SYM
ejpam-4317	206	78	eur	eur	PROPN
ejpam-4317	206	79	.	.	PUNCT
ejpam-4317	207	1	j.	j.	PROPN
ejpam-4317	207	2	pure	pure	PROPN
ejpam-4317	207	3	appl	appl	PROPN
ejpam-4317	207	4	.	.	PROPN
ejpam-4317	207	5	math	math	PROPN
ejpam-4317	207	6	,	,	PUNCT
ejpam-4317	207	7	15	15	NUM
ejpam-4317	207	8	(	(	PUNCT
ejpam-4317	207	9	2	2	NUM
ejpam-4317	207	10	)	)	PUNCT
ejpam-4317	207	11	(	(	PUNCT
ejpam-4317	207	12	2022	2022	NUM
ejpam-4317	207	13	)	)	PUNCT
ejpam-4317	207	14	,	,	PUNCT
ejpam-4317	207	15	443	443	NUM
ejpam-4317	207	16	-	-	SYM
ejpam-4317	207	17	453	453	NUM
ejpam-4317	207	18	448	448	NUM
ejpam-4317	207	19	(	(	PUNCT
ejpam-4317	207	20	iii	iii	NOUN
ejpam-4317	207	21	)	)	PUNCT
ejpam-4317	207	22	for	for	ADP
ejpam-4317	207	23	f1	f1	NOUN
ejpam-4317	207	24	=	=	SYM
ejpam-4317	207	25	{	{	PUNCT
ejpam-4317	207	26	d	d	NOUN
ejpam-4317	207	27	}	}	PUNCT
ejpam-4317	207	28	and	and	CCONJ
ejpam-4317	207	29	c	c	NOUN
ejpam-4317	207	30	/∈	/∈	PUNCT
ejpam-4317	208	1	f1	f1	NOUN
ejpam-4317	208	2	,	,	PUNCT
ejpam-4317	208	3	there	there	PRON
ejpam-4317	208	4	exist	exist	VERB
ejpam-4317	208	5	v2	v2	NOUN
ejpam-4317	208	6	=	=	SYM
ejpam-4317	208	7	{	{	PUNCT
ejpam-4317	208	8	a	a	PRON
ejpam-4317	208	9	,	,	PUNCT
ejpam-4317	208	10	b	b	NOUN
ejpam-4317	208	11	,	,	PUNCT
ejpam-4317	208	12	c	c	NOUN
ejpam-4317	208	13	}	}	PUNCT
ejpam-4317	208	14	∈	∈	PROPN
ejpam-4317	208	15	τ	τ	X
ejpam-4317	208	16	and	and	CCONJ
ejpam-4317	208	17	u2	u2	PROPN
ejpam-4317	208	18	=	=	SYM
ejpam-4317	208	19	{	{	PUNCT
ejpam-4317	208	20	d	d	NOUN
ejpam-4317	208	21	}	}	PUNCT
ejpam-4317	208	22	∈	∈	PROPN
ejpam-4317	208	23	τ	τ	PROPN
ejpam-4317	208	24	?	?	PUNCT
ejpam-4317	208	25	such	such	ADJ
ejpam-4317	208	26	that	that	SCONJ
ejpam-4317	208	27	c	c	PROPN
ejpam-4317	208	28	∈	∈	PROPN
ejpam-4317	208	29	v2	v2	PROPN
ejpam-4317	208	30	,	,	PUNCT
ejpam-4317	208	31	f1	f1	PROPN
ejpam-4317	208	32	⊂	⊂	PROPN
ejpam-4317	208	33	u2	u2	PROPN
ejpam-4317	208	34	and	and	CCONJ
ejpam-4317	208	35	v2	v2	PROPN
ejpam-4317	208	36	∩	∩	ADJ
ejpam-4317	208	37	u2	u2	NOUN
ejpam-4317	208	38	=	=	PROPN
ejpam-4317	208	39	∅.	∅.	X
ejpam-4317	208	40	(	(	PUNCT
ejpam-4317	208	41	iv	iv	NOUN
ejpam-4317	208	42	)	)	PUNCT
ejpam-4317	208	43	for	for	ADP
ejpam-4317	208	44	f2	f2	PROPN
ejpam-4317	208	45	=	=	SYM
ejpam-4317	208	46	{	{	PUNCT
ejpam-4317	208	47	c	c	NOUN
ejpam-4317	208	48	}	}	PUNCT
ejpam-4317	208	49	and	and	CCONJ
ejpam-4317	208	50	a	a	DET
ejpam-4317	208	51	/∈	/∈	PUNCT
ejpam-4317	208	52	f2	f2	PROPN
ejpam-4317	208	53	,	,	PUNCT
ejpam-4317	208	54	there	there	PRON
ejpam-4317	208	55	exist	exist	VERB
ejpam-4317	208	56	v1	v1	NOUN
ejpam-4317	208	57	=	=	SYM
ejpam-4317	208	58	{	{	PUNCT
ejpam-4317	208	59	a	a	PRON
ejpam-4317	208	60	,	,	PUNCT
ejpam-4317	208	61	b	b	NOUN
ejpam-4317	208	62	}	}	PUNCT
ejpam-4317	208	63	∈	∈	PROPN
ejpam-4317	208	64	τ	τ	X
ejpam-4317	208	65	and	and	CCONJ
ejpam-4317	208	66	u1	u1	PROPN
ejpam-4317	208	67	=	=	SYM
ejpam-4317	208	68	{	{	PUNCT
ejpam-4317	208	69	c	c	NOUN
ejpam-4317	208	70	,	,	PUNCT
ejpam-4317	208	71	d	d	NOUN
ejpam-4317	208	72	}	}	PUNCT
ejpam-4317	208	73	∈	∈	PROPN
ejpam-4317	208	74	τ	τ	PROPN
ejpam-4317	208	75	?	?	PUNCT
ejpam-4317	209	1	such	such	ADJ
ejpam-4317	209	2	that	that	SCONJ
ejpam-4317	209	3	a	a	DET
ejpam-4317	209	4	∈	∈	PROPN
ejpam-4317	209	5	v1	v1	NOUN
ejpam-4317	209	6	,	,	PUNCT
ejpam-4317	209	7	f2	f2	PROPN
ejpam-4317	209	8	⊂	⊂	PROPN
ejpam-4317	209	9	u1	u1	NOUN
ejpam-4317	209	10	and	and	CCONJ
ejpam-4317	209	11	v1	v1	ADJ
ejpam-4317	209	12	∩	∩	ADJ
ejpam-4317	209	13	u1	u1	NOUN
ejpam-4317	209	14	=	=	SYM
ejpam-4317	209	15	∅.	∅.	X
ejpam-4317	209	16	(	(	PUNCT
ejpam-4317	209	17	v	v	NOUN
ejpam-4317	209	18	)	)	PUNCT
ejpam-4317	209	19	for	for	ADP
ejpam-4317	209	20	f2	f2	PROPN
ejpam-4317	209	21	=	=	SYM
ejpam-4317	209	22	{	{	PUNCT
ejpam-4317	209	23	c	c	NOUN
ejpam-4317	209	24	}	}	PUNCT
ejpam-4317	209	25	and	and	CCONJ
ejpam-4317	209	26	b	b	PROPN
ejpam-4317	209	27	/∈	/∈	PUNCT
ejpam-4317	209	28	f2	f2	PROPN
ejpam-4317	209	29	,	,	PUNCT
ejpam-4317	209	30	there	there	PRON
ejpam-4317	209	31	exist	exist	VERB
ejpam-4317	209	32	v1	v1	NOUN
ejpam-4317	209	33	=	=	SYM
ejpam-4317	209	34	{	{	PUNCT
ejpam-4317	209	35	a	a	PRON
ejpam-4317	209	36	,	,	PUNCT
ejpam-4317	209	37	b	b	NOUN
ejpam-4317	209	38	}	}	PUNCT
ejpam-4317	209	39	∈	∈	PROPN
ejpam-4317	209	40	τ	τ	X
ejpam-4317	209	41	and	and	CCONJ
ejpam-4317	209	42	u1	u1	PROPN
ejpam-4317	209	43	=	=	SYM
ejpam-4317	209	44	{	{	PUNCT
ejpam-4317	209	45	c	c	NOUN
ejpam-4317	209	46	,	,	PUNCT
ejpam-4317	209	47	d	d	NOUN
ejpam-4317	209	48	}	}	PUNCT
ejpam-4317	209	49	∈	∈	PROPN
ejpam-4317	209	50	τ	τ	PROPN
ejpam-4317	209	51	?	?	PUNCT
ejpam-4317	209	52	such	such	ADJ
ejpam-4317	209	53	that	that	DET
ejpam-4317	209	54	b	b	PROPN
ejpam-4317	209	55	∈	∈	PROPN
ejpam-4317	209	56	v1	v1	NOUN
ejpam-4317	209	57	,	,	PUNCT
ejpam-4317	209	58	f2	f2	PROPN
ejpam-4317	209	59	⊂	⊂	PROPN
ejpam-4317	209	60	u1	u1	NOUN
ejpam-4317	209	61	and	and	CCONJ
ejpam-4317	209	62	v1	v1	ADJ
ejpam-4317	209	63	∩	∩	ADJ
ejpam-4317	209	64	u1	u1	NOUN
ejpam-4317	209	65	=	=	SYM
ejpam-4317	209	66	∅.	∅.	X
ejpam-4317	209	67	(	(	PUNCT
ejpam-4317	209	68	vi	vi	NOUN
ejpam-4317	209	69	)	)	PUNCT
ejpam-4317	209	70	for	for	ADP
ejpam-4317	209	71	f2	f2	PROPN
ejpam-4317	209	72	=	=	SYM
ejpam-4317	209	73	{	{	PUNCT
ejpam-4317	209	74	c	c	NOUN
ejpam-4317	209	75	}	}	PUNCT
ejpam-4317	209	76	and	and	CCONJ
ejpam-4317	209	77	d	d	PROPN
ejpam-4317	209	78	/∈	/∈	PUNCT
ejpam-4317	210	1	f2	f2	PROPN
ejpam-4317	210	2	,	,	PUNCT
ejpam-4317	210	3	there	there	PRON
ejpam-4317	210	4	exist	exist	VERB
ejpam-4317	210	5	v3	v3	PROPN
ejpam-4317	210	6	=	=	SYM
ejpam-4317	210	7	{	{	PUNCT
ejpam-4317	210	8	a	a	PRON
ejpam-4317	210	9	,	,	PUNCT
ejpam-4317	210	10	b	b	NOUN
ejpam-4317	210	11	,	,	PUNCT
ejpam-4317	210	12	d	d	NOUN
ejpam-4317	210	13	}	}	PUNCT
ejpam-4317	210	14	∈	∈	PROPN
ejpam-4317	210	15	τ	τ	X
ejpam-4317	210	16	and	and	CCONJ
ejpam-4317	210	17	u3	u3	NOUN
ejpam-4317	210	18	=	=	SYM
ejpam-4317	210	19	{	{	PUNCT
ejpam-4317	210	20	c	c	NOUN
ejpam-4317	210	21	}	}	PUNCT
ejpam-4317	210	22	∈	∈	PROPN
ejpam-4317	210	23	τ	τ	PROPN
ejpam-4317	210	24	?	?	PUNCT
ejpam-4317	210	25	such	such	ADJ
ejpam-4317	210	26	that	that	SCONJ
ejpam-4317	210	27	d	d	PROPN
ejpam-4317	210	28	∈	∈	PROPN
ejpam-4317	210	29	v3	v3	PROPN
ejpam-4317	210	30	,	,	PUNCT
ejpam-4317	210	31	f2	f2	PROPN
ejpam-4317	210	32	⊂	⊂	PROPN
ejpam-4317	210	33	u3	u3	PROPN
ejpam-4317	210	34	and	and	CCONJ
ejpam-4317	210	35	v3	v3	PROPN
ejpam-4317	210	36	∩	∩	ADJ
ejpam-4317	210	37	u3	u3	NOUN
ejpam-4317	210	38	=	=	SYM
ejpam-4317	210	39	∅.	∅.	PROPN
ejpam-4317	210	40	(	(	PUNCT
ejpam-4317	210	41	vii	vii	PROPN
ejpam-4317	210	42	)	)	PUNCT
ejpam-4317	210	43	for	for	ADP
ejpam-4317	210	44	f3	f3	ADJ
ejpam-4317	210	45	=	=	SYM
ejpam-4317	210	46	{	{	PUNCT
ejpam-4317	210	47	c	c	NOUN
ejpam-4317	210	48	,	,	PUNCT
ejpam-4317	210	49	d	d	NOUN
ejpam-4317	210	50	}	}	PUNCT
ejpam-4317	210	51	and	and	CCONJ
ejpam-4317	210	52	a	a	DET
ejpam-4317	210	53	/∈	/∈	ADJ
ejpam-4317	210	54	f3	f3	NOUN
ejpam-4317	210	55	,	,	PUNCT
ejpam-4317	210	56	there	there	PRON
ejpam-4317	210	57	exist	exist	VERB
ejpam-4317	210	58	v1	v1	NOUN
ejpam-4317	210	59	=	=	SYM
ejpam-4317	210	60	{	{	PUNCT
ejpam-4317	210	61	a	a	PRON
ejpam-4317	210	62	,	,	PUNCT
ejpam-4317	210	63	b	b	NOUN
ejpam-4317	210	64	}	}	PUNCT
ejpam-4317	210	65	∈	∈	PROPN
ejpam-4317	210	66	τ	τ	X
ejpam-4317	210	67	and	and	CCONJ
ejpam-4317	210	68	u1	u1	PROPN
ejpam-4317	210	69	=	=	SYM
ejpam-4317	210	70	{	{	PUNCT
ejpam-4317	210	71	c	c	NOUN
ejpam-4317	210	72	,	,	PUNCT
ejpam-4317	210	73	d	d	NOUN
ejpam-4317	210	74	}	}	PUNCT
ejpam-4317	210	75	∈	∈	PROPN
ejpam-4317	210	76	τ	τ	PROPN
ejpam-4317	210	77	?	?	PUNCT
ejpam-4317	211	1	such	such	ADJ
ejpam-4317	211	2	that	that	SCONJ
ejpam-4317	211	3	a	a	DET
ejpam-4317	211	4	∈	∈	PROPN
ejpam-4317	211	5	v1	v1	NOUN
ejpam-4317	211	6	,	,	PUNCT
ejpam-4317	211	7	f3	f3	PROPN
ejpam-4317	211	8	⊂	⊂	PROPN
ejpam-4317	211	9	u1	u1	PROPN
ejpam-4317	211	10	and	and	CCONJ
ejpam-4317	211	11	v1	v1	ADJ
ejpam-4317	211	12	∩	∩	ADJ
ejpam-4317	211	13	u1	u1	NOUN
ejpam-4317	211	14	=	=	SYM
ejpam-4317	211	15	∅.	∅.	X
ejpam-4317	211	16	(	(	PUNCT
ejpam-4317	211	17	viii	viii	NOUN
ejpam-4317	211	18	)	)	PUNCT
ejpam-4317	211	19	for	for	ADP
ejpam-4317	211	20	f3	f3	ADJ
ejpam-4317	211	21	=	=	SYM
ejpam-4317	211	22	{	{	PUNCT
ejpam-4317	211	23	c	c	NOUN
ejpam-4317	211	24	,	,	PUNCT
ejpam-4317	211	25	d	d	NOUN
ejpam-4317	211	26	}	}	PUNCT
ejpam-4317	211	27	and	and	CCONJ
ejpam-4317	211	28	b	b	PROPN
ejpam-4317	211	29	/∈	/∈	PUNCT
ejpam-4317	211	30	f3	f3	PROPN
ejpam-4317	211	31	,	,	PUNCT
ejpam-4317	211	32	there	there	PRON
ejpam-4317	211	33	exist	exist	VERB
ejpam-4317	211	34	v1	v1	NOUN
ejpam-4317	211	35	=	=	SYM
ejpam-4317	211	36	{	{	PUNCT
ejpam-4317	211	37	a	a	PRON
ejpam-4317	211	38	,	,	PUNCT
ejpam-4317	211	39	b	b	NOUN
ejpam-4317	211	40	}	}	PUNCT
ejpam-4317	211	41	∈	∈	PROPN
ejpam-4317	211	42	τ	τ	X
ejpam-4317	211	43	and	and	CCONJ
ejpam-4317	211	44	u1	u1	PROPN
ejpam-4317	211	45	=	=	SYM
ejpam-4317	211	46	{	{	PUNCT
ejpam-4317	211	47	c	c	NOUN
ejpam-4317	211	48	,	,	PUNCT
ejpam-4317	211	49	d	d	NOUN
ejpam-4317	211	50	}	}	PUNCT
ejpam-4317	211	51	∈	∈	PROPN
ejpam-4317	211	52	τ	τ	PROPN
ejpam-4317	211	53	?	?	PUNCT
ejpam-4317	211	54	such	such	ADJ
ejpam-4317	211	55	that	that	DET
ejpam-4317	211	56	b	b	PROPN
ejpam-4317	211	57	∈	∈	PROPN
ejpam-4317	211	58	v1	v1	NOUN
ejpam-4317	211	59	,	,	PUNCT
ejpam-4317	211	60	f3	f3	PROPN
ejpam-4317	211	61	⊂	⊂	PROPN
ejpam-4317	211	62	u1	u1	PROPN
ejpam-4317	211	63	and	and	CCONJ
ejpam-4317	211	64	v1	v1	ADJ
ejpam-4317	211	65	∩	∩	ADJ
ejpam-4317	211	66	u1	u1	NOUN
ejpam-4317	211	67	=	=	PUNCT
ejpam-4317	211	68	∅.	∅.	NOUN
ejpam-4317	211	69	by	by	ADP
ejpam-4317	211	70	(	(	PUNCT
ejpam-4317	211	71	i)-(viii	i)-(viii	NUM
ejpam-4317	211	72	)	)	PUNCT
ejpam-4317	211	73	,	,	PUNCT
ejpam-4317	211	74	we	we	PRON
ejpam-4317	211	75	deduce	deduce	VERB
ejpam-4317	211	76	that	that	SCONJ
ejpam-4317	211	77	(	(	PUNCT
ejpam-4317	211	78	x	x	X
ejpam-4317	211	79	,	,	PUNCT
ejpam-4317	211	80	τ	τ	PROPN
ejpam-4317	211	81	,	,	PUNCT
ejpam-4317	211	82	i	i	PROPN
ejpam-4317	211	83	)	)	PUNCT
ejpam-4317	211	84	is	be	AUX
ejpam-4317	211	85	a	a	DET
ejpam-4317	211	86	?	?	ADV
ejpam-4317	211	87	-regular	-regular	ADJ
ejpam-4317	211	88	space	space	NOUN
ejpam-4317	211	89	.	.	PUNCT
ejpam-4317	212	1	now	now	ADV
ejpam-4317	212	2	,	,	PUNCT
ejpam-4317	212	3	we	we	PRON
ejpam-4317	212	4	will	will	AUX
ejpam-4317	212	5	show	show	VERB
ejpam-4317	212	6	that	that	SCONJ
ejpam-4317	212	7	(	(	PUNCT
ejpam-4317	212	8	x	x	X
ejpam-4317	212	9	,	,	PUNCT
ejpam-4317	212	10	τ	τ	PROPN
ejpam-4317	212	11	,	,	PUNCT
ejpam-4317	212	12	i	i	PROPN
ejpam-4317	212	13	)	)	PUNCT
ejpam-4317	212	14	is	be	AUX
ejpam-4317	212	15	not	not	PART
ejpam-4317	212	16	a	a	DET
ejpam-4317	212	17	δ?-regular	δ?-regular	ADJ
ejpam-4317	212	18	space	space	NOUN
ejpam-4317	212	19	.	.	PUNCT
ejpam-4317	213	1	indeed	indeed	ADV
ejpam-4317	213	2	,	,	PUNCT
ejpam-4317	213	3	let	let	VERB
ejpam-4317	213	4	f	f	X
ejpam-4317	213	5	=	=	PUNCT
ejpam-4317	213	6	{	{	PUNCT
ejpam-4317	213	7	d	d	NOUN
ejpam-4317	213	8	}	}	PUNCT
ejpam-4317	213	9	.	.	PUNCT
ejpam-4317	214	1	then	then	ADV
ejpam-4317	214	2	,	,	PUNCT
ejpam-4317	214	3	f	f	PROPN
ejpam-4317	214	4	is	be	AUX
ejpam-4317	214	5	a	a	DET
ejpam-4317	214	6	closed	closed	ADJ
ejpam-4317	214	7	set	set	NOUN
ejpam-4317	214	8	and	and	CCONJ
ejpam-4317	214	9	c	c	NOUN
ejpam-4317	214	10	/∈	/∈	PUNCT
ejpam-4317	215	1	f	f	PROPN
ejpam-4317	215	2	.	.	PUNCT
ejpam-4317	216	1	observe	observe	VERB
ejpam-4317	216	2	that	that	SCONJ
ejpam-4317	216	3	the	the	DET
ejpam-4317	216	4	only	only	ADJ
ejpam-4317	216	5	open	open	ADJ
ejpam-4317	216	6	sets	set	NOUN
ejpam-4317	216	7	containing	contain	VERB
ejpam-4317	216	8	c	c	NOUN
ejpam-4317	216	9	are	be	AUX
ejpam-4317	216	10	v2	v2	PROPN
ejpam-4317	216	11	=	=	PUNCT
ejpam-4317	216	12	{	{	PUNCT
ejpam-4317	216	13	a	a	PRON
ejpam-4317	216	14	,	,	PUNCT
ejpam-4317	216	15	b	b	NOUN
ejpam-4317	216	16	,	,	PUNCT
ejpam-4317	216	17	c	c	NOUN
ejpam-4317	216	18	}	}	PUNCT
ejpam-4317	216	19	and	and	CCONJ
ejpam-4317	216	20	v4	v4	PROPN
ejpam-4317	216	21	=	=	SYM
ejpam-4317	216	22	x	x	NOUN
ejpam-4317	216	23	,	,	PUNCT
ejpam-4317	216	24	and	and	CCONJ
ejpam-4317	216	25	the	the	DET
ejpam-4317	216	26	only	only	ADJ
ejpam-4317	216	27	τ	τ	PROPN
ejpam-4317	216	28	δ?open	δ?open	PROPN
ejpam-4317	216	29	sets	set	NOUN
ejpam-4317	216	30	containing	contain	VERB
ejpam-4317	216	31	f	f	PROPN
ejpam-4317	216	32	are	be	AUX
ejpam-4317	216	33	w1	w1	NOUN
ejpam-4317	216	34	=	=	SYM
ejpam-4317	216	35	{	{	PUNCT
ejpam-4317	216	36	c	c	NOUN
ejpam-4317	216	37	,	,	PUNCT
ejpam-4317	216	38	d	d	NOUN
ejpam-4317	216	39	}	}	PUNCT
ejpam-4317	216	40	,	,	PUNCT
ejpam-4317	216	41	w2	w2	NOUN
ejpam-4317	216	42	=	=	SYM
ejpam-4317	216	43	{	{	PUNCT
ejpam-4317	216	44	b	b	PROPN
ejpam-4317	216	45	,	,	PUNCT
ejpam-4317	216	46	c	c	NOUN
ejpam-4317	216	47	,	,	PUNCT
ejpam-4317	216	48	d	d	NOUN
ejpam-4317	216	49	}	}	PUNCT
ejpam-4317	216	50	and	and	CCONJ
ejpam-4317	216	51	w3	w3	PROPN
ejpam-4317	216	52	=	=	PUNCT
ejpam-4317	216	53	{	{	PUNCT
ejpam-4317	216	54	a	a	X
ejpam-4317	216	55	,	,	PUNCT
ejpam-4317	216	56	c	c	NOUN
ejpam-4317	216	57	,	,	PUNCT
ejpam-4317	216	58	d	d	NOUN
ejpam-4317	216	59	}	}	PUNCT
ejpam-4317	216	60	.	.	PUNCT
ejpam-4317	217	1	in	in	ADP
ejpam-4317	217	2	addition	addition	NOUN
ejpam-4317	217	3	,	,	PUNCT
ejpam-4317	217	4	v2	v2	PROPN
ejpam-4317	217	5	∩	∩	ADJ
ejpam-4317	217	6	w1	w1	NOUN
ejpam-4317	217	7	=	=	SYM
ejpam-4317	217	8	{	{	PUNCT
ejpam-4317	217	9	c	c	NOUN
ejpam-4317	217	10	}	}	PUNCT
ejpam-4317	217	11	6=	6=	NOUN
ejpam-4317	217	12	∅	∅	NOUN
ejpam-4317	217	13	,	,	PUNCT
ejpam-4317	217	14	v2	v2	NOUN
ejpam-4317	217	15	∩	∩	ADJ
ejpam-4317	217	16	w2	w2	NOUN
ejpam-4317	217	17	=	=	SYM
ejpam-4317	217	18	{	{	PUNCT
ejpam-4317	217	19	b	b	PROPN
ejpam-4317	217	20	,	,	PUNCT
ejpam-4317	217	21	c	c	NOUN
ejpam-4317	217	22	}	}	PUNCT
ejpam-4317	217	23	6=	6=	NOUN
ejpam-4317	217	24	∅	∅	NOUN
ejpam-4317	217	25	,	,	PUNCT
ejpam-4317	217	26	v2	v2	PROPN
ejpam-4317	217	27	∩	∩	ADJ
ejpam-4317	217	28	w3	w3	NOUN
ejpam-4317	217	29	=	=	SYM
ejpam-4317	217	30	{	{	PUNCT
ejpam-4317	217	31	a	a	X
ejpam-4317	217	32	,	,	PUNCT
ejpam-4317	217	33	c	c	NOUN
ejpam-4317	217	34	}	}	PUNCT
ejpam-4317	217	35	6=	6=	NOUN
ejpam-4317	217	36	∅	∅	NOUN
ejpam-4317	217	37	,	,	PUNCT
ejpam-4317	217	38	v4	v4	NOUN
ejpam-4317	217	39	∩	∩	ADJ
ejpam-4317	217	40	w1	w1	NOUN
ejpam-4317	217	41	=	=	SYM
ejpam-4317	217	42	w1	w1	PROPN
ejpam-4317	217	43	6=	6=	NUM
ejpam-4317	217	44	∅	∅	NOUN
ejpam-4317	217	45	,	,	PUNCT
ejpam-4317	217	46	v4	v4	PROPN
ejpam-4317	217	47	∩w2	∩w2	NOUN
ejpam-4317	217	48	=	=	PROPN
ejpam-4317	217	49	w2	w2	PROPN
ejpam-4317	217	50	6=	6=	NUM
ejpam-4317	217	51	∅	∅	NOUN
ejpam-4317	217	52	,	,	PUNCT
ejpam-4317	217	53	v4	v4	PROPN
ejpam-4317	217	54	∩w3	∩w3	NOUN
ejpam-4317	217	55	=	=	PROPN
ejpam-4317	217	56	w3	w3	PROPN
ejpam-4317	217	57	6=	6=	PROPN
ejpam-4317	217	58	∅.	∅.	VERB
ejpam-4317	217	59	therefore	therefore	ADV
ejpam-4317	217	60	,	,	PUNCT
ejpam-4317	217	61	(	(	PUNCT
ejpam-4317	217	62	x	x	X
ejpam-4317	217	63	,	,	PUNCT
ejpam-4317	217	64	τ	τ	PROPN
ejpam-4317	217	65	,	,	PUNCT
ejpam-4317	217	66	i	i	PROPN
ejpam-4317	217	67	)	)	PUNCT
ejpam-4317	217	68	is	be	AUX
ejpam-4317	217	69	not	not	PART
ejpam-4317	217	70	a	a	DET
ejpam-4317	217	71	δ?-regular	δ?-regular	ADJ
ejpam-4317	217	72	space	space	NOUN
ejpam-4317	217	73	.	.	PUNCT
ejpam-4317	218	1	lemma	lemma	PROPN
ejpam-4317	218	2	2	2	NUM
ejpam-4317	218	3	.	.	PUNCT
ejpam-4317	219	1	[	[	X
ejpam-4317	219	2	14	14	NUM
ejpam-4317	219	3	]	]	PUNCT
ejpam-4317	219	4	a	a	DET
ejpam-4317	219	5	space	space	NOUN
ejpam-4317	219	6	(	(	PUNCT
ejpam-4317	219	7	x	x	X
ejpam-4317	219	8	,	,	PUNCT
ejpam-4317	219	9	τ	τ	PROPN
ejpam-4317	219	10	,	,	PUNCT
ejpam-4317	219	11	i	i	PROPN
ejpam-4317	219	12	)	)	PUNCT
ejpam-4317	219	13	is	be	AUX
ejpam-4317	219	14	δ?-regular	δ?-regular	ADJ
ejpam-4317	219	15	if	if	SCONJ
ejpam-4317	219	16	and	and	CCONJ
ejpam-4317	219	17	only	only	ADV
ejpam-4317	219	18	if	if	SCONJ
ejpam-4317	219	19	for	for	SCONJ
ejpam-4317	219	20	each	each	DET
ejpam-4317	219	21	x	x	SYM
ejpam-4317	219	22	∈	∈	PROPN
ejpam-4317	219	23	x	x	X
ejpam-4317	219	24	and	and	CCONJ
ejpam-4317	219	25	each	each	DET
ejpam-4317	219	26	open	open	ADJ
ejpam-4317	219	27	set	set	VERB
ejpam-4317	219	28	v	v	NOUN
ejpam-4317	219	29	containing	contain	VERB
ejpam-4317	219	30	x	x	X
ejpam-4317	219	31	,	,	PUNCT
ejpam-4317	219	32	there	there	PRON
ejpam-4317	219	33	exists	exist	VERB
ejpam-4317	219	34	an	an	DET
ejpam-4317	219	35	open	open	ADJ
ejpam-4317	219	36	set	set	NOUN
ejpam-4317	219	37	u	u	PRON
ejpam-4317	219	38	such	such	ADJ
ejpam-4317	219	39	that	that	SCONJ
ejpam-4317	219	40	x	x	SYM
ejpam-4317	219	41	∈	∈	PROPN
ejpam-4317	219	42	u	u	X
ejpam-4317	219	43	⊂	⊂	PROPN
ejpam-4317	219	44	δcl?(u	δcl?(u	PROPN
ejpam-4317	219	45	)	)	PUNCT
ejpam-4317	220	1	⊂	⊂	PROPN
ejpam-4317	220	2	v	v	NOUN
ejpam-4317	220	3	.	.	PUNCT
ejpam-4317	221	1	the	the	DET
ejpam-4317	221	2	following	follow	VERB
ejpam-4317	221	3	result	result	NOUN
ejpam-4317	221	4	shows	show	VERB
ejpam-4317	221	5	that	that	SCONJ
ejpam-4317	221	6	the	the	DET
ejpam-4317	221	7	strongly	strongly	ADV
ejpam-4317	221	8	δθ	δθ	NOUN
ejpam-4317	221	9	-	-	PUNCT
ejpam-4317	221	10	i	i	NOUN
ejpam-4317	221	11	-	-	PUNCT
ejpam-4317	221	12	continuity	continuity	NOUN
ejpam-4317	221	13	and	and	CCONJ
ejpam-4317	221	14	the	the	DET
ejpam-4317	221	15	continuity	continuity	NOUN
ejpam-4317	221	16	are	be	AUX
ejpam-4317	221	17	equivalent	equivalent	ADJ
ejpam-4317	221	18	under	under	ADP
ejpam-4317	221	19	the	the	DET
ejpam-4317	221	20	assumption	assumption	NOUN
ejpam-4317	221	21	that	that	SCONJ
ejpam-4317	221	22	the	the	DET
ejpam-4317	221	23	domain	domain	NOUN
ejpam-4317	221	24	is	be	AUX
ejpam-4317	221	25	a	a	DET
ejpam-4317	221	26	δ?-regular	δ?-regular	ADJ
ejpam-4317	221	27	space	space	NOUN
ejpam-4317	221	28	.	.	PUNCT
ejpam-4317	222	1	theorem	theorem	ADJ
ejpam-4317	222	2	4	4	NUM
ejpam-4317	222	3	.	.	PUNCT
ejpam-4317	223	1	let	let	VERB
ejpam-4317	223	2	(	(	PUNCT
ejpam-4317	223	3	x	x	X
ejpam-4317	223	4	,	,	PUNCT
ejpam-4317	223	5	τ	τ	PROPN
ejpam-4317	223	6	,	,	PUNCT
ejpam-4317	223	7	i	i	PRON
ejpam-4317	223	8	)	)	PUNCT
ejpam-4317	223	9	be	be	AUX
ejpam-4317	223	10	a	a	DET
ejpam-4317	223	11	δ?-regular	δ?-regular	ADJ
ejpam-4317	223	12	space	space	NOUN
ejpam-4317	223	13	.	.	PUNCT
ejpam-4317	224	1	a	a	DET
ejpam-4317	224	2	function	function	NOUN
ejpam-4317	224	3	f	f	NOUN
ejpam-4317	224	4	:	:	PUNCT
ejpam-4317	224	5	(	(	PUNCT
ejpam-4317	224	6	x	x	X
ejpam-4317	224	7	,	,	PUNCT
ejpam-4317	224	8	τ	τ	PROPN
ejpam-4317	224	9	,	,	PUNCT
ejpam-4317	224	10	i	i	NOUN
ejpam-4317	224	11	)	)	PUNCT
ejpam-4317	224	12	→	→	SYM
ejpam-4317	224	13	(	(	PUNCT
ejpam-4317	224	14	y	y	PROPN
ejpam-4317	224	15	,	,	PUNCT
ejpam-4317	224	16	σ	σ	PROPN
ejpam-4317	224	17	)	)	PUNCT
ejpam-4317	224	18	is	be	AUX
ejpam-4317	224	19	strongly	strongly	ADV
ejpam-4317	224	20	δθ	δθ	NOUN
ejpam-4317	224	21	-	-	PUNCT
ejpam-4317	224	22	i	i	NOUN
ejpam-4317	224	23	-	-	NOUN
ejpam-4317	224	24	continuous	continuous	ADJ
ejpam-4317	224	25	if	if	SCONJ
ejpam-4317	225	1	and	and	CCONJ
ejpam-4317	225	2	only	only	ADV
ejpam-4317	225	3	if	if	SCONJ
ejpam-4317	225	4	it	it	PRON
ejpam-4317	225	5	is	be	AUX
ejpam-4317	225	6	continuous	continuous	ADJ
ejpam-4317	225	7	.	.	PUNCT
ejpam-4317	226	1	proof	proof	NOUN
ejpam-4317	226	2	.	.	PUNCT
ejpam-4317	227	1	by	by	ADP
ejpam-4317	227	2	remark	remark	NOUN
ejpam-4317	227	3	1	1	NUM
ejpam-4317	227	4	,	,	PUNCT
ejpam-4317	227	5	if	if	SCONJ
ejpam-4317	227	6	f	f	PROPN
ejpam-4317	227	7	is	be	AUX
ejpam-4317	227	8	strongly	strongly	ADV
ejpam-4317	227	9	δθ	δθ	NOUN
ejpam-4317	227	10	-	-	PUNCT
ejpam-4317	227	11	i	i	NOUN
ejpam-4317	227	12	-	-	PUNCT
ejpam-4317	227	13	continuous	continuous	ADJ
ejpam-4317	227	14	then	then	ADV
ejpam-4317	227	15	it	it	PRON
ejpam-4317	227	16	is	be	AUX
ejpam-4317	227	17	continuous	continuous	ADJ
ejpam-4317	227	18	.	.	PUNCT
ejpam-4317	228	1	conversely	conversely	ADV
ejpam-4317	228	2	,	,	PUNCT
ejpam-4317	228	3	suppose	suppose	VERB
ejpam-4317	228	4	that	that	SCONJ
ejpam-4317	228	5	f	f	PROPN
ejpam-4317	228	6	is	be	AUX
ejpam-4317	228	7	continuous	continuous	ADJ
ejpam-4317	228	8	.	.	PUNCT
ejpam-4317	229	1	let	let	VERB
ejpam-4317	229	2	x	x	PUNCT
ejpam-4317	229	3	∈	∈	PROPN
ejpam-4317	229	4	x	x	X
ejpam-4317	229	5	and	and	CCONJ
ejpam-4317	229	6	v	v	X
ejpam-4317	229	7	be	be	AUX
ejpam-4317	229	8	any	any	DET
ejpam-4317	229	9	open	open	ADJ
ejpam-4317	229	10	set	set	NOUN
ejpam-4317	229	11	in	in	ADP
ejpam-4317	229	12	y	y	NOUN
ejpam-4317	229	13	containing	contain	VERB
ejpam-4317	229	14	f(x	f(x	PROPN
ejpam-4317	229	15	)	)	PUNCT
ejpam-4317	229	16	.	.	PUNCT
ejpam-4317	230	1	then	then	ADV
ejpam-4317	230	2	,	,	PUNCT
ejpam-4317	230	3	there	there	PRON
ejpam-4317	230	4	exists	exist	VERB
ejpam-4317	230	5	an	an	DET
ejpam-4317	230	6	open	open	ADJ
ejpam-4317	230	7	set	set	NOUN
ejpam-4317	230	8	u	u	NOUN
ejpam-4317	230	9	containing	contain	VERB
ejpam-4317	230	10	x	x	PUNCT
ejpam-4317	230	11	such	such	ADJ
ejpam-4317	230	12	that	that	DET
ejpam-4317	230	13	f(u	f(u	PROPN
ejpam-4317	230	14	)	)	PUNCT
ejpam-4317	231	1	⊂	⊂	PROPN
ejpam-4317	231	2	v	v	X
ejpam-4317	231	3	.	.	PUNCT
ejpam-4317	232	1	since	since	SCONJ
ejpam-4317	232	2	(	(	PUNCT
ejpam-4317	232	3	x	x	X
ejpam-4317	232	4	,	,	PUNCT
ejpam-4317	232	5	τ	τ	PROPN
ejpam-4317	232	6	,	,	PUNCT
ejpam-4317	232	7	i	i	PROPN
ejpam-4317	232	8	)	)	PUNCT
ejpam-4317	232	9	is	be	AUX
ejpam-4317	232	10	a	a	DET
ejpam-4317	232	11	δ?regular	δ?regular	ADJ
ejpam-4317	232	12	space	space	NOUN
ejpam-4317	232	13	,	,	PUNCT
ejpam-4317	232	14	by	by	ADP
ejpam-4317	232	15	lemma	lemma	PROPN
ejpam-4317	232	16	2	2	NUM
ejpam-4317	232	17	,	,	PUNCT
ejpam-4317	232	18	there	there	PRON
ejpam-4317	232	19	exists	exist	VERB
ejpam-4317	232	20	an	an	DET
ejpam-4317	232	21	open	open	ADJ
ejpam-4317	232	22	set	set	NOUN
ejpam-4317	232	23	w	w	ADP
ejpam-4317	232	24	such	such	ADJ
ejpam-4317	232	25	that	that	SCONJ
ejpam-4317	232	26	x	x	SYM
ejpam-4317	232	27	∈	∈	PROPN
ejpam-4317	232	28	w	w	PROPN
ejpam-4317	232	29	⊂	⊂	PROPN
ejpam-4317	232	30	δcl?(w	δcl?(w	NOUN
ejpam-4317	232	31	)	)	PUNCT
ejpam-4317	233	1	⊂	⊂	PROPN
ejpam-4317	233	2	u	u	PROPN
ejpam-4317	233	3	.	.	PUNCT
ejpam-4317	234	1	thus	thus	ADV
ejpam-4317	234	2	,	,	PUNCT
ejpam-4317	234	3	f(x	f(x	PROPN
ejpam-4317	234	4	)	)	PUNCT
ejpam-4317	234	5	∈	∈	PROPN
ejpam-4317	234	6	f(δcl?(w	f(δcl?(w	PROPN
ejpam-4317	234	7	)	)	PUNCT
ejpam-4317	234	8	)	)	PUNCT
ejpam-4317	235	1	⊂	⊂	PROPN
ejpam-4317	235	2	f(u	f(u	PROPN
ejpam-4317	235	3	)	)	PUNCT
ejpam-4317	236	1	⊂	⊂	PROPN
ejpam-4317	236	2	v	v	NOUN
ejpam-4317	236	3	,	,	PUNCT
ejpam-4317	236	4	which	which	PRON
ejpam-4317	236	5	implies	imply	VERB
ejpam-4317	236	6	that	that	SCONJ
ejpam-4317	236	7	f(δcl?(w	f(δcl?(w	NOUN
ejpam-4317	236	8	)	)	PUNCT
ejpam-4317	236	9	)	)	PUNCT
ejpam-4317	237	1	⊂	⊂	PROPN
ejpam-4317	237	2	v	v	X
ejpam-4317	237	3	.	.	PUNCT
ejpam-4317	238	1	therefore	therefore	ADV
ejpam-4317	238	2	,	,	PUNCT
ejpam-4317	238	3	f	f	PROPN
ejpam-4317	238	4	is	be	AUX
ejpam-4317	238	5	strongly	strongly	ADV
ejpam-4317	238	6	δθ	δθ	NOUN
ejpam-4317	238	7	-	-	PUNCT
ejpam-4317	238	8	i	i	NOUN
ejpam-4317	238	9	-	-	PUNCT
ejpam-4317	238	10	continuous	continuous	ADJ
ejpam-4317	238	11	.	.	PUNCT
ejpam-4317	239	1	theorem	theorem	NOUN
ejpam-4317	239	2	5	5	NUM
ejpam-4317	239	3	.	.	PUNCT
ejpam-4317	240	1	let	let	VERB
ejpam-4317	240	2	f	f	NOUN
ejpam-4317	240	3	:	:	PUNCT
ejpam-4317	240	4	(	(	PUNCT
ejpam-4317	240	5	x	x	X
ejpam-4317	240	6	,	,	PUNCT
ejpam-4317	240	7	τ	τ	PROPN
ejpam-4317	240	8	,	,	PUNCT
ejpam-4317	240	9	i	i	NOUN
ejpam-4317	240	10	)	)	PUNCT
ejpam-4317	240	11	→	→	SYM
ejpam-4317	240	12	(	(	PUNCT
ejpam-4317	240	13	y	y	PROPN
ejpam-4317	240	14	,	,	PUNCT
ejpam-4317	240	15	σ	σ	PROPN
ejpam-4317	240	16	)	)	PUNCT
ejpam-4317	240	17	be	be	AUX
ejpam-4317	240	18	a	a	DET
ejpam-4317	240	19	function	function	NOUN
ejpam-4317	240	20	and	and	CCONJ
ejpam-4317	240	21	(	(	PUNCT
ejpam-4317	240	22	x	x	X
ejpam-4317	240	23	,	,	PUNCT
ejpam-4317	240	24	τ	τ	PROPN
ejpam-4317	240	25	,	,	PUNCT
ejpam-4317	240	26	i	i	PRON
ejpam-4317	240	27	)	)	PUNCT
ejpam-4317	240	28	be	be	AUX
ejpam-4317	240	29	a	a	DET
ejpam-4317	240	30	δ?-regular	δ?-regular	ADJ
ejpam-4317	240	31	space	space	NOUN
ejpam-4317	240	32	.	.	PUNCT
ejpam-4317	241	1	if	if	SCONJ
ejpam-4317	241	2	f	f	PROPN
ejpam-4317	241	3	is	be	AUX
ejpam-4317	241	4	strongly	strongly	ADV
ejpam-4317	241	5	θ	θ	ADJ
ejpam-4317	241	6	-	-	ADJ
ejpam-4317	241	7	continuous	continuous	ADJ
ejpam-4317	241	8	,	,	PUNCT
ejpam-4317	241	9	then	then	ADV
ejpam-4317	241	10	it	it	PRON
ejpam-4317	241	11	is	be	AUX
ejpam-4317	241	12	strongly	strongly	ADV
ejpam-4317	241	13	δθ	δθ	NOUN
ejpam-4317	241	14	-	-	PUNCT
ejpam-4317	241	15	i	i	NOUN
ejpam-4317	241	16	-	-	PUNCT
ejpam-4317	241	17	continuous	continuous	ADJ
ejpam-4317	241	18	.	.	PUNCT
ejpam-4317	242	1	proof	proof	NOUN
ejpam-4317	242	2	.	.	PUNCT
ejpam-4317	243	1	the	the	DET
ejpam-4317	243	2	proof	proof	NOUN
ejpam-4317	243	3	is	be	AUX
ejpam-4317	243	4	similar	similar	ADJ
ejpam-4317	243	5	to	to	ADP
ejpam-4317	243	6	the	the	DET
ejpam-4317	243	7	part	part	NOUN
ejpam-4317	243	8	of	of	ADP
ejpam-4317	243	9	the	the	DET
ejpam-4317	243	10	proof	proof	NOUN
ejpam-4317	243	11	of	of	ADP
ejpam-4317	243	12	theorem	theorem	ADJ
ejpam-4317	243	13	4	4	NUM
ejpam-4317	243	14	,	,	PUNCT
ejpam-4317	243	15	where	where	SCONJ
ejpam-4317	243	16	it	it	PRON
ejpam-4317	243	17	was	be	AUX
ejpam-4317	243	18	proved	prove	VERB
ejpam-4317	243	19	that	that	SCONJ
ejpam-4317	243	20	if	if	SCONJ
ejpam-4317	243	21	(	(	PUNCT
ejpam-4317	243	22	x	x	NOUN
ejpam-4317	243	23	,	,	PUNCT
ejpam-4317	243	24	τ	τ	PROPN
ejpam-4317	243	25	,	,	PUNCT
ejpam-4317	243	26	i	i	PROPN
ejpam-4317	243	27	)	)	PUNCT
ejpam-4317	243	28	is	be	AUX
ejpam-4317	243	29	δ?-regular	δ?-regular	NUM
ejpam-4317	243	30	and	and	CCONJ
ejpam-4317	243	31	f	f	PROPN
ejpam-4317	243	32	is	be	AUX
ejpam-4317	243	33	continuous	continuous	ADJ
ejpam-4317	243	34	,	,	PUNCT
ejpam-4317	243	35	then	then	ADV
ejpam-4317	243	36	f	f	PROPN
ejpam-4317	243	37	is	be	AUX
ejpam-4317	243	38	strongly	strongly	ADV
ejpam-4317	243	39	δθ	δθ	NOUN
ejpam-4317	243	40	-	-	PUNCT
ejpam-4317	243	41	i	i	NOUN
ejpam-4317	243	42	-	-	PUNCT
ejpam-4317	243	43	continuous	continuous	ADJ
ejpam-4317	243	44	.	.	PUNCT
ejpam-4317	244	1	the	the	DET
ejpam-4317	244	2	following	follow	VERB
ejpam-4317	244	3	example	example	NOUN
ejpam-4317	244	4	shows	show	VERB
ejpam-4317	244	5	that	that	SCONJ
ejpam-4317	244	6	a	a	DET
ejpam-4317	244	7	strongly	strongly	ADV
ejpam-4317	244	8	δθ	δθ	NOUN
ejpam-4317	244	9	-	-	PUNCT
ejpam-4317	244	10	i	i	NOUN
ejpam-4317	244	11	-	-	PUNCT
ejpam-4317	244	12	continuous	continuous	ADJ
ejpam-4317	244	13	function	function	NOUN
ejpam-4317	244	14	is	be	AUX
ejpam-4317	244	15	not	not	PART
ejpam-4317	244	16	necessarily	necessarily	ADV
ejpam-4317	244	17	strongly	strongly	ADV
ejpam-4317	244	18	θ	θ	ADJ
ejpam-4317	244	19	-	-	ADJ
ejpam-4317	244	20	continuous	continuous	ADJ
ejpam-4317	244	21	,	,	PUNCT
ejpam-4317	244	22	even	even	ADV
ejpam-4317	244	23	though	though	SCONJ
ejpam-4317	244	24	the	the	DET
ejpam-4317	244	25	domain	domain	NOUN
ejpam-4317	244	26	is	be	AUX
ejpam-4317	244	27	a	a	DET
ejpam-4317	244	28	δ?-regular	δ?-regular	ADJ
ejpam-4317	244	29	space	space	NOUN
ejpam-4317	244	30	.	.	PUNCT
ejpam-4317	245	1	j.	j.	PROPN
ejpam-4317	245	2	sanabria	sanabria	PROPN
ejpam-4317	245	3	,	,	PUNCT
ejpam-4317	245	4	r.	r.	PROPN
ejpam-4317	245	5	lozada	lozada	PROPN
ejpam-4317	245	6	-	-	PUNCT
ejpam-4317	245	7	yavina	yavina	PROPN
ejpam-4317	245	8	,	,	PUNCT
ejpam-4317	245	9	j.	j.	PROPN
ejpam-4317	245	10	tormet	tormet	PROPN
ejpam-4317	245	11	/	/	SYM
ejpam-4317	245	12	eur	eur	PROPN
ejpam-4317	245	13	.	.	PUNCT
ejpam-4317	246	1	j.	j.	PROPN
ejpam-4317	246	2	pure	pure	PROPN
ejpam-4317	246	3	appl	appl	PROPN
ejpam-4317	246	4	.	.	PROPN
ejpam-4317	246	5	math	math	PROPN
ejpam-4317	246	6	,	,	PUNCT
ejpam-4317	246	7	15	15	NUM
ejpam-4317	246	8	(	(	PUNCT
ejpam-4317	246	9	2	2	NUM
ejpam-4317	246	10	)	)	PUNCT
ejpam-4317	246	11	(	(	PUNCT
ejpam-4317	246	12	2022	2022	NUM
ejpam-4317	246	13	)	)	PUNCT
ejpam-4317	246	14	,	,	PUNCT
ejpam-4317	246	15	443	443	NUM
ejpam-4317	246	16	-	-	SYM
ejpam-4317	246	17	453	453	NUM
ejpam-4317	246	18	449	449	NUM
ejpam-4317	246	19	example	example	NOUN
ejpam-4317	246	20	2	2	NUM
ejpam-4317	246	21	.	.	X
ejpam-4317	246	22	consider	consider	VERB
ejpam-4317	246	23	x	x	PUNCT
ejpam-4317	246	24	=	=	PRON
ejpam-4317	246	25	{	{	PUNCT
ejpam-4317	246	26	a	a	PRON
ejpam-4317	246	27	,	,	PUNCT
ejpam-4317	246	28	b	b	NOUN
ejpam-4317	246	29	,	,	PUNCT
ejpam-4317	246	30	c	c	NOUN
ejpam-4317	246	31	,	,	PUNCT
ejpam-4317	246	32	d	d	NOUN
ejpam-4317	246	33	}	}	PUNCT
ejpam-4317	246	34	with	with	ADP
ejpam-4317	246	35	the	the	DET
ejpam-4317	246	36	topology	topology	NOUN
ejpam-4317	246	37	τ	τ	X
ejpam-4317	246	38	=	=	PUNCT
ejpam-4317	246	39	{	{	PUNCT
ejpam-4317	246	40	x	x	NOUN
ejpam-4317	246	41	,	,	PUNCT
ejpam-4317	246	42	∅	∅	NOUN
ejpam-4317	246	43	,	,	PUNCT
ejpam-4317	246	44	{	{	PUNCT
ejpam-4317	246	45	a	a	DET
ejpam-4317	246	46	,	,	PUNCT
ejpam-4317	246	47	b	b	NOUN
ejpam-4317	246	48	}	}	PUNCT
ejpam-4317	246	49	,	,	PUNCT
ejpam-4317	246	50	{	{	PUNCT
ejpam-4317	246	51	a	a	DET
ejpam-4317	246	52	,	,	PUNCT
ejpam-4317	246	53	b	b	NOUN
ejpam-4317	246	54	,	,	PUNCT
ejpam-4317	246	55	c	c	NOUN
ejpam-4317	246	56	}	}	PUNCT
ejpam-4317	246	57	,	,	PUNCT
ejpam-4317	246	58	{	{	PUNCT
ejpam-4317	246	59	a	a	DET
ejpam-4317	246	60	,	,	PUNCT
ejpam-4317	246	61	b	b	NOUN
ejpam-4317	246	62	,	,	PUNCT
ejpam-4317	246	63	d	d	NOUN
ejpam-4317	246	64	}	}	PUNCT
ejpam-4317	246	65	}	}	PUNCT
ejpam-4317	246	66	and	and	CCONJ
ejpam-4317	246	67	the	the	DET
ejpam-4317	246	68	ideal	ideal	NOUN
ejpam-4317	246	69	i	i	X
ejpam-4317	246	70	=	=	SYM
ejpam-4317	246	71	{	{	PUNCT
ejpam-4317	246	72	∅	∅	NOUN
ejpam-4317	246	73	,	,	PUNCT
ejpam-4317	246	74	{	{	PUNCT
ejpam-4317	246	75	a	a	X
ejpam-4317	246	76	}	}	PUNCT
ejpam-4317	246	77	,	,	PUNCT
ejpam-4317	246	78	{	{	PUNCT
ejpam-4317	246	79	b	b	NOUN
ejpam-4317	246	80	}	}	PUNCT
ejpam-4317	246	81	,	,	PUNCT
ejpam-4317	246	82	{	{	PUNCT
ejpam-4317	246	83	a	a	DET
ejpam-4317	246	84	,	,	PUNCT
ejpam-4317	246	85	b	b	NOUN
ejpam-4317	246	86	}	}	PUNCT
ejpam-4317	246	87	}	}	PUNCT
ejpam-4317	246	88	.	.	PUNCT
ejpam-4317	247	1	let	let	VERB
ejpam-4317	247	2	us	we	PRON
ejpam-4317	247	3	define	define	VERB
ejpam-4317	247	4	a	a	DET
ejpam-4317	247	5	function	function	NOUN
ejpam-4317	247	6	f	f	NOUN
ejpam-4317	247	7	:	:	PUNCT
ejpam-4317	247	8	(	(	PUNCT
ejpam-4317	247	9	x	x	X
ejpam-4317	247	10	,	,	PUNCT
ejpam-4317	247	11	τ	τ	PROPN
ejpam-4317	247	12	,	,	PUNCT
ejpam-4317	247	13	i	i	NOUN
ejpam-4317	247	14	)	)	PUNCT
ejpam-4317	247	15	→	→	SYM
ejpam-4317	247	16	(	(	PUNCT
ejpam-4317	247	17	x	x	X
ejpam-4317	247	18	,	,	PUNCT
ejpam-4317	247	19	τ	τ	X
ejpam-4317	247	20	)	)	PUNCT
ejpam-4317	247	21	as	as	SCONJ
ejpam-4317	247	22	follows	follow	VERB
ejpam-4317	247	23	:	:	PUNCT
ejpam-4317	247	24	f(a	f(a	NOUN
ejpam-4317	247	25	)	)	PUNCT
ejpam-4317	247	26	=	=	SYM
ejpam-4317	248	1	a	a	PRON
ejpam-4317	248	2	,	,	PUNCT
ejpam-4317	248	3	f(b	f(b	PROPN
ejpam-4317	248	4	)	)	PUNCT
ejpam-4317	248	5	=	=	SYM
ejpam-4317	248	6	b	b	PROPN
ejpam-4317	248	7	,	,	PUNCT
ejpam-4317	248	8	f(c	f(c	PROPN
ejpam-4317	248	9	)	)	PUNCT
ejpam-4317	248	10	=	=	SYM
ejpam-4317	248	11	c	c	X
ejpam-4317	248	12	,	,	PUNCT
ejpam-4317	248	13	f(d	f(d	PROPN
ejpam-4317	248	14	)	)	PUNCT
ejpam-4317	248	15	=	=	SYM
ejpam-4317	248	16	b.	b.	PROPN
ejpam-4317	248	17	note	note	VERB
ejpam-4317	248	18	that	that	SCONJ
ejpam-4317	248	19	:	:	PUNCT
ejpam-4317	248	20	(	(	PUNCT
ejpam-4317	248	21	i	i	NOUN
ejpam-4317	248	22	)	)	PUNCT
ejpam-4317	248	23	the	the	DET
ejpam-4317	248	24	only	only	ADJ
ejpam-4317	248	25	open	open	ADJ
ejpam-4317	248	26	sets	set	NOUN
ejpam-4317	248	27	in	in	ADP
ejpam-4317	248	28	x	x	PUNCT
ejpam-4317	248	29	containing	contain	VERB
ejpam-4317	248	30	f(a	f(a	NOUN
ejpam-4317	248	31	)	)	PUNCT
ejpam-4317	248	32	=	=	NOUN
ejpam-4317	249	1	a	a	PRON
ejpam-4317	249	2	are	be	AUX
ejpam-4317	249	3	v1	v1	NOUN
ejpam-4317	249	4	=	=	PUNCT
ejpam-4317	249	5	{	{	PUNCT
ejpam-4317	249	6	a	a	PRON
ejpam-4317	249	7	,	,	PUNCT
ejpam-4317	249	8	b	b	NOUN
ejpam-4317	249	9	}	}	PUNCT
ejpam-4317	249	10	,	,	PUNCT
ejpam-4317	249	11	v2	v2	PROPN
ejpam-4317	249	12	=	=	SYM
ejpam-4317	249	13	{	{	PUNCT
ejpam-4317	249	14	a	a	PRON
ejpam-4317	249	15	,	,	PUNCT
ejpam-4317	249	16	b	b	NOUN
ejpam-4317	249	17	,	,	PUNCT
ejpam-4317	249	18	c	c	NOUN
ejpam-4317	249	19	}	}	PUNCT
ejpam-4317	249	20	,	,	PUNCT
ejpam-4317	249	21	v3	v3	PROPN
ejpam-4317	249	22	=	=	PUNCT
ejpam-4317	249	23	{	{	PUNCT
ejpam-4317	249	24	a	a	DET
ejpam-4317	249	25	,	,	PUNCT
ejpam-4317	249	26	b	b	NOUN
ejpam-4317	249	27	,	,	PUNCT
ejpam-4317	249	28	d	d	NOUN
ejpam-4317	249	29	}	}	PUNCT
ejpam-4317	249	30	and	and	CCONJ
ejpam-4317	249	31	v4	v4	PROPN
ejpam-4317	249	32	=	=	PUNCT
ejpam-4317	250	1	x.	x.	NOUN
ejpam-4317	250	2	in	in	ADP
ejpam-4317	250	3	addition	addition	NOUN
ejpam-4317	250	4	,	,	PUNCT
ejpam-4317	250	5	v1	v1	NOUN
ejpam-4317	250	6	satisfies	satisfie	NOUN
ejpam-4317	250	7	that	that	PRON
ejpam-4317	250	8	f(δcl?(v1	f(δcl?(v1	VERB
ejpam-4317	250	9	)	)	PUNCT
ejpam-4317	250	10	)	)	PUNCT
ejpam-4317	251	1	=	=	SYM
ejpam-4317	251	2	f(δcl?({a	f(δcl?({a	PROPN
ejpam-4317	251	3	,	,	PUNCT
ejpam-4317	251	4	b	b	NOUN
ejpam-4317	251	5	}	}	PUNCT
ejpam-4317	251	6	)	)	PUNCT
ejpam-4317	251	7	)	)	PUNCT
ejpam-4317	252	1	=	=	SYM
ejpam-4317	252	2	f({a	f({a	PROPN
ejpam-4317	252	3	,	,	PUNCT
ejpam-4317	252	4	b	b	NOUN
ejpam-4317	252	5	}	}	PUNCT
ejpam-4317	252	6	)	)	PUNCT
ejpam-4317	252	7	=	=	PRON
ejpam-4317	252	8	{	{	PUNCT
ejpam-4317	252	9	a	a	PRON
ejpam-4317	252	10	,	,	PUNCT
ejpam-4317	252	11	b	b	NOUN
ejpam-4317	252	12	}	}	PUNCT
ejpam-4317	252	13	=	=	SYM
ejpam-4317	252	14	v1	v1	NOUN
ejpam-4317	252	15	,	,	PUNCT
ejpam-4317	252	16	f(δcl?(v1	f(δcl?(v1	NOUN
ejpam-4317	252	17	)	)	PUNCT
ejpam-4317	252	18	)	)	PUNCT
ejpam-4317	253	1	=	=	SYM
ejpam-4317	253	2	v1	v1	PROPN
ejpam-4317	253	3	⊂	⊂	X
ejpam-4317	253	4	v2	v2	PROPN
ejpam-4317	253	5	,	,	PUNCT
ejpam-4317	253	6	f(δcl?(v1	f(δcl?(v1	NOUN
ejpam-4317	253	7	)	)	PUNCT
ejpam-4317	253	8	)	)	PUNCT
ejpam-4317	254	1	=	=	SYM
ejpam-4317	254	2	v1	v1	PROPN
ejpam-4317	254	3	⊂	⊂	PROPN
ejpam-4317	254	4	v3	v3	PROPN
ejpam-4317	254	5	and	and	CCONJ
ejpam-4317	254	6	f(δcl?(v1	f(δcl?(v1	NOUN
ejpam-4317	254	7	)	)	PUNCT
ejpam-4317	254	8	)	)	PUNCT
ejpam-4317	255	1	=	=	SYM
ejpam-4317	255	2	v1	v1	PROPN
ejpam-4317	255	3	⊂	⊂	X
ejpam-4317	255	4	v4	v4	PROPN
ejpam-4317	255	5	.	.	PUNCT
ejpam-4317	256	1	(	(	PUNCT
ejpam-4317	256	2	ii	ii	NOUN
ejpam-4317	256	3	)	)	PUNCT
ejpam-4317	256	4	using	use	VERB
ejpam-4317	256	5	the	the	DET
ejpam-4317	256	6	same	same	ADJ
ejpam-4317	256	7	argument	argument	NOUN
ejpam-4317	256	8	from	from	ADP
ejpam-4317	256	9	part	part	NOUN
ejpam-4317	256	10	(	(	PUNCT
ejpam-4317	256	11	1	1	NUM
ejpam-4317	256	12	)	)	PUNCT
ejpam-4317	256	13	,	,	PUNCT
ejpam-4317	256	14	we	we	PRON
ejpam-4317	256	15	get	get	VERB
ejpam-4317	256	16	the	the	DET
ejpam-4317	256	17	result	result	NOUN
ejpam-4317	256	18	for	for	ADP
ejpam-4317	256	19	f(b	f(b	PROPN
ejpam-4317	256	20	)	)	PUNCT
ejpam-4317	256	21	=	=	SYM
ejpam-4317	256	22	b.	b.	PROPN
ejpam-4317	256	23	(	(	PUNCT
ejpam-4317	256	24	iii	iii	NOUN
ejpam-4317	256	25	)	)	PUNCT
ejpam-4317	256	26	the	the	DET
ejpam-4317	256	27	only	only	ADJ
ejpam-4317	256	28	open	open	ADJ
ejpam-4317	256	29	sets	set	NOUN
ejpam-4317	256	30	in	in	ADP
ejpam-4317	256	31	x	x	PUNCT
ejpam-4317	256	32	containing	contain	VERB
ejpam-4317	256	33	f(c	f(c	PROPN
ejpam-4317	256	34	)	)	PUNCT
ejpam-4317	256	35	=	=	PUNCT
ejpam-4317	257	1	c	c	NOUN
ejpam-4317	257	2	are	be	AUX
ejpam-4317	257	3	v2	v2	NOUN
ejpam-4317	257	4	=	=	PUNCT
ejpam-4317	257	5	{	{	PUNCT
ejpam-4317	257	6	a	a	PRON
ejpam-4317	257	7	,	,	PUNCT
ejpam-4317	257	8	b	b	NOUN
ejpam-4317	257	9	,	,	PUNCT
ejpam-4317	257	10	c	c	NOUN
ejpam-4317	257	11	}	}	PUNCT
ejpam-4317	257	12	and	and	CCONJ
ejpam-4317	257	13	v4	v4	PROPN
ejpam-4317	257	14	=	=	PUNCT
ejpam-4317	258	1	x.	x.	NOUN
ejpam-4317	258	2	in	in	ADP
ejpam-4317	258	3	addition	addition	NOUN
ejpam-4317	258	4	,	,	PUNCT
ejpam-4317	258	5	v2	v2	NOUN
ejpam-4317	258	6	satisfies	satisfie	NOUN
ejpam-4317	258	7	that	that	SCONJ
ejpam-4317	258	8	f(δcl?(v2	f(δcl?(v2	NOUN
ejpam-4317	258	9	)	)	PUNCT
ejpam-4317	258	10	)	)	PUNCT
ejpam-4317	259	1	=	=	SYM
ejpam-4317	259	2	f(δcl?({a	f(δcl?({a	PROPN
ejpam-4317	259	3	,	,	PUNCT
ejpam-4317	259	4	b	b	NOUN
ejpam-4317	259	5	,	,	PUNCT
ejpam-4317	259	6	c	c	NOUN
ejpam-4317	259	7	}	}	PUNCT
ejpam-4317	259	8	)	)	PUNCT
ejpam-4317	259	9	)	)	PUNCT
ejpam-4317	260	1	=	=	SYM
ejpam-4317	260	2	f({a	f({a	PROPN
ejpam-4317	260	3	,	,	PUNCT
ejpam-4317	260	4	b	b	PROPN
ejpam-4317	260	5	,	,	PUNCT
ejpam-4317	260	6	c	c	NOUN
ejpam-4317	260	7	}	}	PUNCT
ejpam-4317	260	8	)	)	PUNCT
ejpam-4317	260	9	=	=	PRON
ejpam-4317	260	10	{	{	PUNCT
ejpam-4317	260	11	a	a	PRON
ejpam-4317	260	12	,	,	PUNCT
ejpam-4317	260	13	b	b	NOUN
ejpam-4317	260	14	,	,	PUNCT
ejpam-4317	260	15	c	c	NOUN
ejpam-4317	260	16	}	}	PUNCT
ejpam-4317	260	17	=	=	SYM
ejpam-4317	260	18	v2	v2	NOUN
ejpam-4317	260	19	and	and	CCONJ
ejpam-4317	260	20	f(δcl?(v2	f(δcl?(v2	NOUN
ejpam-4317	260	21	)	)	PUNCT
ejpam-4317	260	22	)	)	PUNCT
ejpam-4317	261	1	=	=	PUNCT
ejpam-4317	261	2	v2	v2	PROPN
ejpam-4317	261	3	⊂	⊂	X
ejpam-4317	261	4	v4	v4	PROPN
ejpam-4317	261	5	.	.	PUNCT
ejpam-4317	262	1	(	(	PUNCT
ejpam-4317	262	2	iv	iv	X
ejpam-4317	262	3	)	)	PUNCT
ejpam-4317	262	4	the	the	DET
ejpam-4317	262	5	only	only	ADJ
ejpam-4317	262	6	open	open	ADJ
ejpam-4317	262	7	sets	set	NOUN
ejpam-4317	262	8	in	in	ADP
ejpam-4317	262	9	x	x	PUNCT
ejpam-4317	262	10	containing	contain	VERB
ejpam-4317	262	11	f(d	f(d	PROPN
ejpam-4317	262	12	)	)	PUNCT
ejpam-4317	263	1	=	=	SYM
ejpam-4317	263	2	b	b	NOUN
ejpam-4317	263	3	are	be	AUX
ejpam-4317	263	4	v1	v1	NOUN
ejpam-4317	263	5	=	=	SYM
ejpam-4317	263	6	{	{	PUNCT
ejpam-4317	263	7	a	a	PRON
ejpam-4317	263	8	,	,	PUNCT
ejpam-4317	263	9	b	b	NOUN
ejpam-4317	263	10	}	}	PUNCT
ejpam-4317	263	11	,	,	PUNCT
ejpam-4317	263	12	v2	v2	PROPN
ejpam-4317	263	13	=	=	SYM
ejpam-4317	263	14	{	{	PUNCT
ejpam-4317	263	15	a	a	PRON
ejpam-4317	263	16	,	,	PUNCT
ejpam-4317	263	17	b	b	NOUN
ejpam-4317	263	18	,	,	PUNCT
ejpam-4317	263	19	c	c	NOUN
ejpam-4317	263	20	}	}	PUNCT
ejpam-4317	263	21	,	,	PUNCT
ejpam-4317	263	22	v3	v3	PROPN
ejpam-4317	263	23	=	=	PUNCT
ejpam-4317	263	24	{	{	PUNCT
ejpam-4317	263	25	a	a	DET
ejpam-4317	263	26	,	,	PUNCT
ejpam-4317	263	27	b	b	NOUN
ejpam-4317	263	28	,	,	PUNCT
ejpam-4317	263	29	d	d	NOUN
ejpam-4317	263	30	}	}	PUNCT
ejpam-4317	263	31	and	and	CCONJ
ejpam-4317	263	32	v4	v4	PROPN
ejpam-4317	263	33	=	=	PUNCT
ejpam-4317	264	1	x.	x.	NOUN
ejpam-4317	264	2	in	in	ADP
ejpam-4317	264	3	addition	addition	NOUN
ejpam-4317	264	4	,	,	PUNCT
ejpam-4317	264	5	v3	v3	PROPN
ejpam-4317	264	6	=	=	SYM
ejpam-4317	264	7	{	{	PUNCT
ejpam-4317	264	8	a	a	PRON
ejpam-4317	264	9	,	,	PUNCT
ejpam-4317	264	10	b	b	NOUN
ejpam-4317	264	11	,	,	PUNCT
ejpam-4317	264	12	d	d	NOUN
ejpam-4317	264	13	}	}	PUNCT
ejpam-4317	264	14	is	be	AUX
ejpam-4317	264	15	an	an	DET
ejpam-4317	264	16	open	open	ADJ
ejpam-4317	264	17	set	set	NOUN
ejpam-4317	264	18	in	in	ADP
ejpam-4317	264	19	x	x	PUNCT
ejpam-4317	264	20	containing	contain	VERB
ejpam-4317	264	21	d	d	PROPN
ejpam-4317	264	22	such	such	ADJ
ejpam-4317	264	23	that	that	PRON
ejpam-4317	264	24	f(δcl?(v3	f(δcl?(v3	NOUN
ejpam-4317	264	25	)	)	PUNCT
ejpam-4317	264	26	)	)	PUNCT
ejpam-4317	265	1	=	=	SYM
ejpam-4317	265	2	f(δcl?({a	f(δcl?({a	PROPN
ejpam-4317	265	3	,	,	PUNCT
ejpam-4317	265	4	b	b	NOUN
ejpam-4317	265	5	,	,	PUNCT
ejpam-4317	265	6	d	d	NOUN
ejpam-4317	265	7	}	}	PUNCT
ejpam-4317	265	8	)	)	PUNCT
ejpam-4317	265	9	)	)	PUNCT
ejpam-4317	266	1	=	=	SYM
ejpam-4317	266	2	f({a	f({a	PROPN
ejpam-4317	266	3	,	,	PUNCT
ejpam-4317	266	4	b	b	PROPN
ejpam-4317	266	5	,	,	PUNCT
ejpam-4317	266	6	d	d	NOUN
ejpam-4317	266	7	}	}	PUNCT
ejpam-4317	266	8	)	)	PUNCT
ejpam-4317	266	9	=	=	PRON
ejpam-4317	266	10	{	{	PUNCT
ejpam-4317	266	11	a	a	PRON
ejpam-4317	266	12	,	,	PUNCT
ejpam-4317	266	13	b	b	NOUN
ejpam-4317	266	14	}	}	PUNCT
ejpam-4317	266	15	=	=	SYM
ejpam-4317	266	16	v1	v1	NOUN
ejpam-4317	266	17	which	which	PRON
ejpam-4317	266	18	is	be	AUX
ejpam-4317	266	19	contained	contain	VERB
ejpam-4317	266	20	in	in	ADP
ejpam-4317	266	21	v1	v1	NOUN
ejpam-4317	266	22	,	,	PUNCT
ejpam-4317	266	23	v2	v2	PROPN
ejpam-4317	266	24	,	,	PUNCT
ejpam-4317	266	25	v3	v3	PROPN
ejpam-4317	266	26	and	and	CCONJ
ejpam-4317	266	27	v4	v4	NOUN
ejpam-4317	266	28	.	.	PUNCT
ejpam-4317	267	1	by	by	ADP
ejpam-4317	267	2	(	(	PUNCT
ejpam-4317	267	3	i)-(iv	i)-(iv	PROPN
ejpam-4317	267	4	)	)	PUNCT
ejpam-4317	267	5	,	,	PUNCT
ejpam-4317	267	6	we	we	PRON
ejpam-4317	267	7	conclude	conclude	VERB
ejpam-4317	267	8	that	that	SCONJ
ejpam-4317	267	9	f	f	PROPN
ejpam-4317	267	10	is	be	AUX
ejpam-4317	267	11	strongly	strongly	ADV
ejpam-4317	267	12	δθ	δθ	NOUN
ejpam-4317	267	13	-	-	PUNCT
ejpam-4317	267	14	i	i	NOUN
ejpam-4317	267	15	-	-	PUNCT
ejpam-4317	267	16	continuous	continuous	ADJ
ejpam-4317	267	17	.	.	PUNCT
ejpam-4317	268	1	on	on	ADP
ejpam-4317	268	2	the	the	DET
ejpam-4317	268	3	other	other	ADJ
ejpam-4317	268	4	hand	hand	NOUN
ejpam-4317	268	5	,	,	PUNCT
ejpam-4317	268	6	since	since	SCONJ
ejpam-4317	268	7	cl(v1	cl(v1	NOUN
ejpam-4317	268	8	)	)	PUNCT
ejpam-4317	268	9	=	=	SYM
ejpam-4317	268	10	cl(v2	cl(v2	NOUN
ejpam-4317	268	11	)	)	PUNCT
ejpam-4317	268	12	=	=	SYM
ejpam-4317	268	13	cl(v3	cl(v3	NOUN
ejpam-4317	268	14	)	)	PUNCT
ejpam-4317	268	15	=	=	SYM
ejpam-4317	268	16	cl(v4	cl(v4	NOUN
ejpam-4317	268	17	)	)	PUNCT
ejpam-4317	268	18	=	=	SYM
ejpam-4317	269	1	x	x	PROPN
ejpam-4317	269	2	and	and	CCONJ
ejpam-4317	269	3	f(x	f(x	PROPN
ejpam-4317	269	4	)	)	PUNCT
ejpam-4317	270	1	=	=	PUNCT
ejpam-4317	271	1	v2	v2	PROPN
ejpam-4317	271	2	6⊂	6⊂	NUM
ejpam-4317	271	3	v1	v1	NOUN
ejpam-4317	271	4	,	,	PUNCT
ejpam-4317	271	5	we	we	PRON
ejpam-4317	271	6	conclude	conclude	VERB
ejpam-4317	271	7	that	that	SCONJ
ejpam-4317	271	8	f	f	PROPN
ejpam-4317	271	9	is	be	AUX
ejpam-4317	271	10	not	not	PART
ejpam-4317	271	11	strongly	strongly	ADV
ejpam-4317	271	12	θ	θ	ADJ
ejpam-4317	271	13	-	-	ADJ
ejpam-4317	271	14	continuous	continuous	ADJ
ejpam-4317	271	15	.	.	PUNCT
ejpam-4317	272	1	observe	observe	VERB
ejpam-4317	272	2	that	that	SCONJ
ejpam-4317	272	3	(	(	PUNCT
ejpam-4317	272	4	x	x	X
ejpam-4317	272	5	,	,	PUNCT
ejpam-4317	272	6	τ	τ	PROPN
ejpam-4317	272	7	,	,	PUNCT
ejpam-4317	272	8	i	i	PROPN
ejpam-4317	272	9	)	)	PUNCT
ejpam-4317	272	10	is	be	AUX
ejpam-4317	272	11	a	a	DET
ejpam-4317	272	12	δ?-regular	δ?-regular	ADJ
ejpam-4317	272	13	space	space	NOUN
ejpam-4317	272	14	that	that	PRON
ejpam-4317	272	15	is	be	AUX
ejpam-4317	272	16	not	not	PART
ejpam-4317	272	17	regular	regular	ADJ
ejpam-4317	272	18	.	.	PUNCT
ejpam-4317	273	1	recall	recall	VERB
ejpam-4317	273	2	that	that	SCONJ
ejpam-4317	273	3	a	a	DET
ejpam-4317	273	4	function	function	NOUN
ejpam-4317	273	5	f	f	NOUN
ejpam-4317	273	6	:	:	PUNCT
ejpam-4317	273	7	(	(	PUNCT
ejpam-4317	273	8	x	x	X
ejpam-4317	273	9	,	,	PUNCT
ejpam-4317	273	10	τ	τ	X
ejpam-4317	273	11	)	)	PUNCT
ejpam-4317	273	12	→	→	SYM
ejpam-4317	273	13	(	(	PUNCT
ejpam-4317	273	14	y	y	PROPN
ejpam-4317	273	15	,	,	PUNCT
ejpam-4317	273	16	σ	σ	PROPN
ejpam-4317	273	17	)	)	PUNCT
ejpam-4317	273	18	is	be	AUX
ejpam-4317	273	19	super	super	ADJ
ejpam-4317	273	20	-	-	ADJ
ejpam-4317	273	21	continuous	continuous	ADJ
ejpam-4317	273	22	[	[	X
ejpam-4317	273	23	6	6	NUM
ejpam-4317	273	24	]	]	PUNCT
ejpam-4317	273	25	if	if	SCONJ
ejpam-4317	273	26	for	for	ADP
ejpam-4317	273	27	each	each	DET
ejpam-4317	273	28	x	x	SYM
ejpam-4317	273	29	∈	∈	PROPN
ejpam-4317	273	30	x	x	X
ejpam-4317	273	31	and	and	CCONJ
ejpam-4317	273	32	each	each	DET
ejpam-4317	273	33	open	open	ADJ
ejpam-4317	273	34	set	set	VERB
ejpam-4317	273	35	v	v	NOUN
ejpam-4317	273	36	in	in	ADP
ejpam-4317	273	37	y	y	NOUN
ejpam-4317	273	38	containing	contain	VERB
ejpam-4317	273	39	f(x	f(x	PROPN
ejpam-4317	273	40	)	)	PUNCT
ejpam-4317	273	41	,	,	PUNCT
ejpam-4317	273	42	there	there	PRON
ejpam-4317	273	43	exists	exist	VERB
ejpam-4317	273	44	an	an	DET
ejpam-4317	273	45	open	open	ADJ
ejpam-4317	273	46	set	set	NOUN
ejpam-4317	273	47	u	u	NOUN
ejpam-4317	273	48	in	in	ADP
ejpam-4317	273	49	x	x	PUNCT
ejpam-4317	273	50	containing	contain	VERB
ejpam-4317	273	51	x	x	PUNCT
ejpam-4317	273	52	such	such	ADJ
ejpam-4317	273	53	that	that	DET
ejpam-4317	273	54	f(int(cl(u	f(int(cl(u	PROPN
ejpam-4317	273	55	)	)	PUNCT
ejpam-4317	273	56	)	)	PUNCT
ejpam-4317	273	57	)	)	PUNCT
ejpam-4317	274	1	⊂	⊂	PROPN
ejpam-4317	274	2	v	v	X
ejpam-4317	274	3	.	.	PUNCT
ejpam-4317	275	1	this	this	DET
ejpam-4317	275	2	type	type	NOUN
ejpam-4317	275	3	of	of	ADP
ejpam-4317	275	4	function	function	NOUN
ejpam-4317	275	5	is	be	AUX
ejpam-4317	275	6	characterized	characterize	VERB
ejpam-4317	275	7	by	by	ADP
ejpam-4317	275	8	the	the	DET
ejpam-4317	275	9	property	property	NOUN
ejpam-4317	275	10	that	that	PRON
ejpam-4317	275	11	the	the	DET
ejpam-4317	275	12	inverse	inverse	ADJ
ejpam-4317	275	13	image	image	NOUN
ejpam-4317	275	14	of	of	ADP
ejpam-4317	275	15	each	each	DET
ejpam-4317	275	16	open	open	ADJ
ejpam-4317	275	17	set	set	NOUN
ejpam-4317	275	18	in	in	ADP
ejpam-4317	275	19	y	y	PROPN
ejpam-4317	275	20	is	be	AUX
ejpam-4317	275	21	a	a	DET
ejpam-4317	275	22	δ	δ	NOUN
ejpam-4317	275	23	-	-	ADJ
ejpam-4317	275	24	open	open	ADJ
ejpam-4317	275	25	set	set	NOUN
ejpam-4317	275	26	in	in	ADP
ejpam-4317	275	27	x.	x.	NOUN
ejpam-4317	275	28	clearly	clearly	ADV
ejpam-4317	275	29	,	,	PUNCT
ejpam-4317	275	30	every	every	DET
ejpam-4317	275	31	super	super	ADJ
ejpam-4317	275	32	-	-	ADJ
ejpam-4317	275	33	continuous	continuous	ADJ
ejpam-4317	275	34	function	function	NOUN
ejpam-4317	275	35	is	be	AUX
ejpam-4317	275	36	continuous	continuous	ADJ
ejpam-4317	275	37	,	,	PUNCT
ejpam-4317	275	38	but	but	CCONJ
ejpam-4317	275	39	the	the	DET
ejpam-4317	275	40	converse	converse	NOUN
ejpam-4317	275	41	,	,	PUNCT
ejpam-4317	275	42	in	in	ADP
ejpam-4317	275	43	general	general	ADJ
ejpam-4317	275	44	,	,	PUNCT
ejpam-4317	275	45	is	be	AUX
ejpam-4317	275	46	not	not	PART
ejpam-4317	275	47	true	true	ADJ
ejpam-4317	275	48	.	.	PUNCT
ejpam-4317	276	1	theorem	theorem	ADJ
ejpam-4317	276	2	6	6	NUM
ejpam-4317	276	3	.	.	PUNCT
ejpam-4317	277	1	let	let	AUX
ejpam-4317	277	2	(	(	PUNCT
ejpam-4317	277	3	y	y	PROPN
ejpam-4317	277	4	,	,	PUNCT
ejpam-4317	277	5	σ	σ	PROPN
ejpam-4317	277	6	)	)	PUNCT
ejpam-4317	277	7	be	be	AUX
ejpam-4317	277	8	a	a	DET
ejpam-4317	277	9	regular	regular	ADJ
ejpam-4317	277	10	space	space	NOUN
ejpam-4317	277	11	and	and	CCONJ
ejpam-4317	277	12	f	f	NOUN
ejpam-4317	277	13	:	:	PUNCT
ejpam-4317	277	14	(	(	PUNCT
ejpam-4317	277	15	x	x	X
ejpam-4317	277	16	,	,	PUNCT
ejpam-4317	277	17	τ	τ	PROPN
ejpam-4317	277	18	,	,	PUNCT
ejpam-4317	277	19	i	i	NOUN
ejpam-4317	277	20	)	)	PUNCT
ejpam-4317	277	21	→	→	SYM
ejpam-4317	277	22	(	(	PUNCT
ejpam-4317	277	23	y	y	PROPN
ejpam-4317	277	24	,	,	PUNCT
ejpam-4317	277	25	σ	σ	PROPN
ejpam-4317	277	26	)	)	PUNCT
ejpam-4317	277	27	be	be	AUX
ejpam-4317	277	28	a	a	DET
ejpam-4317	277	29	function	function	NOUN
ejpam-4317	277	30	.	.	PUNCT
ejpam-4317	278	1	if	if	SCONJ
ejpam-4317	278	2	f	f	PROPN
ejpam-4317	278	3	is	be	AUX
ejpam-4317	278	4	super	super	ADJ
ejpam-4317	278	5	-	-	ADJ
ejpam-4317	278	6	continuous	continuous	ADJ
ejpam-4317	278	7	,	,	PUNCT
ejpam-4317	278	8	then	then	ADV
ejpam-4317	278	9	it	it	PRON
ejpam-4317	278	10	is	be	AUX
ejpam-4317	278	11	strongly	strongly	ADV
ejpam-4317	278	12	δθ	δθ	NOUN
ejpam-4317	278	13	-	-	PUNCT
ejpam-4317	278	14	i	i	NOUN
ejpam-4317	278	15	-	-	PUNCT
ejpam-4317	278	16	continuous	continuous	ADJ
ejpam-4317	278	17	.	.	PUNCT
ejpam-4317	279	1	proof	proof	NOUN
ejpam-4317	279	2	.	.	PUNCT
ejpam-4317	280	1	let	let	VERB
ejpam-4317	280	2	x	x	PUNCT
ejpam-4317	280	3	∈	∈	PROPN
ejpam-4317	280	4	x	x	X
ejpam-4317	280	5	and	and	CCONJ
ejpam-4317	280	6	v	v	X
ejpam-4317	280	7	be	be	AUX
ejpam-4317	280	8	an	an	DET
ejpam-4317	280	9	open	open	ADJ
ejpam-4317	280	10	set	set	NOUN
ejpam-4317	280	11	in	in	ADP
ejpam-4317	280	12	y	y	NOUN
ejpam-4317	280	13	containing	contain	VERB
ejpam-4317	280	14	f(x	f(x	PROPN
ejpam-4317	280	15	)	)	PUNCT
ejpam-4317	280	16	.	.	PUNCT
ejpam-4317	281	1	since	since	SCONJ
ejpam-4317	281	2	y	y	PROPN
ejpam-4317	281	3	is	be	AUX
ejpam-4317	281	4	regular	regular	ADJ
ejpam-4317	281	5	,	,	PUNCT
ejpam-4317	281	6	there	there	PRON
ejpam-4317	281	7	exists	exist	VERB
ejpam-4317	281	8	an	an	DET
ejpam-4317	281	9	open	open	ADJ
ejpam-4317	281	10	set	set	NOUN
ejpam-4317	281	11	u	u	PRON
ejpam-4317	281	12	such	such	ADJ
ejpam-4317	281	13	that	that	SCONJ
ejpam-4317	281	14	f(x	f(x	PROPN
ejpam-4317	281	15	)	)	PUNCT
ejpam-4317	281	16	∈	∈	PROPN
ejpam-4317	281	17	u	u	NOUN
ejpam-4317	281	18	⊂	⊂	PROPN
ejpam-4317	281	19	cl(u	cl(u	X
ejpam-4317	281	20	)	)	PUNCT
ejpam-4317	281	21	⊂	⊂	PROPN
ejpam-4317	281	22	v	v	X
ejpam-4317	281	23	.	.	PUNCT
ejpam-4317	282	1	on	on	ADP
ejpam-4317	282	2	the	the	DET
ejpam-4317	282	3	other	other	ADJ
ejpam-4317	282	4	hand	hand	NOUN
ejpam-4317	282	5	,	,	PUNCT
ejpam-4317	282	6	as	as	SCONJ
ejpam-4317	282	7	f	f	PROPN
ejpam-4317	282	8	is	be	AUX
ejpam-4317	282	9	super	super	ADJ
ejpam-4317	282	10	-	-	ADJ
ejpam-4317	282	11	continuous	continuous	ADJ
ejpam-4317	282	12	,	,	PUNCT
ejpam-4317	282	13	there	there	PRON
ejpam-4317	282	14	exists	exist	VERB
ejpam-4317	282	15	a	a	DET
ejpam-4317	282	16	δ	δ	NOUN
ejpam-4317	282	17	-	-	ADJ
ejpam-4317	282	18	open	open	ADJ
ejpam-4317	282	19	set	set	NOUN
ejpam-4317	282	20	w	w	NOUN
ejpam-4317	282	21	containing	contain	VERB
ejpam-4317	282	22	x	x	PUNCT
ejpam-4317	282	23	such	such	ADJ
ejpam-4317	282	24	that	that	SCONJ
ejpam-4317	282	25	f(w	f(w	PROPN
ejpam-4317	282	26	)	)	PUNCT
ejpam-4317	283	1	⊂	⊂	PROPN
ejpam-4317	283	2	u	u	PROPN
ejpam-4317	283	3	.	.	PUNCT
ejpam-4317	284	1	we	we	PRON
ejpam-4317	284	2	will	will	AUX
ejpam-4317	284	3	show	show	VERB
ejpam-4317	284	4	that	that	SCONJ
ejpam-4317	284	5	f(δcl?(w	f(δcl?(w	NOUN
ejpam-4317	284	6	)	)	PUNCT
ejpam-4317	284	7	)	)	PUNCT
ejpam-4317	285	1	⊂	⊂	PROPN
ejpam-4317	285	2	cl(u	cl(u	PROPN
ejpam-4317	285	3	)	)	PUNCT
ejpam-4317	285	4	.	.	PUNCT
ejpam-4317	286	1	indeed	indeed	ADV
ejpam-4317	286	2	,	,	PUNCT
ejpam-4317	286	3	suppose	suppose	VERB
ejpam-4317	286	4	that	that	SCONJ
ejpam-4317	286	5	y	y	PROPN
ejpam-4317	286	6	/∈	/∈	PUNCT
ejpam-4317	286	7	cl(u	cl(u	PROPN
ejpam-4317	286	8	)	)	PUNCT
ejpam-4317	286	9	.	.	PUNCT
ejpam-4317	287	1	then	then	ADV
ejpam-4317	287	2	,	,	PUNCT
ejpam-4317	287	3	we	we	PRON
ejpam-4317	287	4	choose	choose	VERB
ejpam-4317	287	5	an	an	DET
ejpam-4317	287	6	open	open	ADJ
ejpam-4317	287	7	set	set	NOUN
ejpam-4317	287	8	o	o	NOUN
ejpam-4317	287	9	such	such	ADJ
ejpam-4317	287	10	that	that	SCONJ
ejpam-4317	287	11	y	y	PROPN
ejpam-4317	287	12	∈	∈	PROPN
ejpam-4317	287	13	o	o	NOUN
ejpam-4317	287	14	and	and	CCONJ
ejpam-4317	287	15	o	o	PROPN
ejpam-4317	287	16	∩	∩	ADJ
ejpam-4317	287	17	u	u	NOUN
ejpam-4317	287	18	=	=	PUNCT
ejpam-4317	287	19	∅.	∅.	NOUN
ejpam-4317	287	20	by	by	ADP
ejpam-4317	287	21	the	the	DET
ejpam-4317	287	22	super	super	NOUN
ejpam-4317	287	23	-	-	NOUN
ejpam-4317	287	24	continuity	continuity	NOUN
ejpam-4317	287	25	of	of	ADP
ejpam-4317	287	26	f	f	PROPN
ejpam-4317	287	27	,	,	PUNCT
ejpam-4317	287	28	we	we	PRON
ejpam-4317	287	29	have	have	VERB
ejpam-4317	287	30	f−1(o	f−1(o	PROPN
ejpam-4317	287	31	)	)	PUNCT
ejpam-4317	287	32	is	be	AUX
ejpam-4317	287	33	a	a	DET
ejpam-4317	287	34	δ	δ	NOUN
ejpam-4317	287	35	-	-	ADJ
ejpam-4317	287	36	open	open	ADJ
ejpam-4317	287	37	set	set	VERB
ejpam-4317	287	38	such	such	ADJ
ejpam-4317	287	39	that	that	DET
ejpam-4317	287	40	f−1(o	f−1(o	PROPN
ejpam-4317	287	41	)	)	PUNCT
ejpam-4317	287	42	∩	∩	ADJ
ejpam-4317	287	43	f−1(u	f−1(u	PROPN
ejpam-4317	287	44	)	)	PUNCT
ejpam-4317	287	45	=	=	SYM
ejpam-4317	287	46	∅	∅	NOUN
ejpam-4317	287	47	,	,	PUNCT
ejpam-4317	287	48	which	which	PRON
ejpam-4317	287	49	implies	imply	VERB
ejpam-4317	287	50	that	that	SCONJ
ejpam-4317	287	51	f−1(o	f−1(o	NOUN
ejpam-4317	287	52	)	)	PUNCT
ejpam-4317	287	53	∩w	∩w	NOUN
ejpam-4317	288	1	=	=	PUNCT
ejpam-4317	288	2	∅.	∅.	PRON
ejpam-4317	288	3	we	we	PRON
ejpam-4317	288	4	affirm	affirm	VERB
ejpam-4317	288	5	that	that	SCONJ
ejpam-4317	288	6	f−1(o	f−1(o	PROPN
ejpam-4317	288	7	)	)	PUNCT
ejpam-4317	288	8	∩	∩	NOUN
ejpam-4317	288	9	δcl?(w	δcl?(w	NOUN
ejpam-4317	288	10	)	)	PUNCT
ejpam-4317	289	1	=	=	PUNCT
ejpam-4317	289	2	∅.	∅.	VERB
ejpam-4317	289	3	otherwise	otherwise	ADV
ejpam-4317	289	4	,	,	PUNCT
ejpam-4317	289	5	there	there	PRON
ejpam-4317	289	6	exists	exist	VERB
ejpam-4317	289	7	a	a	DET
ejpam-4317	289	8	point	point	NOUN
ejpam-4317	289	9	z	z	NOUN
ejpam-4317	289	10	∈	∈	PROPN
ejpam-4317	289	11	f−1(o	f−1(o	PROPN
ejpam-4317	289	12	)	)	PUNCT
ejpam-4317	289	13	∩	∩	NOUN
ejpam-4317	289	14	δcl?(w	δcl?(w	NOUN
ejpam-4317	289	15	)	)	PUNCT
ejpam-4317	289	16	and	and	CCONJ
ejpam-4317	289	17	so	so	ADV
ejpam-4317	289	18	,	,	PUNCT
ejpam-4317	289	19	z	z	PROPN
ejpam-4317	289	20	∈	∈	PROPN
ejpam-4317	289	21	f−1(o	f−1(o	PROPN
ejpam-4317	289	22	)	)	PUNCT
ejpam-4317	289	23	and	and	CCONJ
ejpam-4317	289	24	z	z	NOUN
ejpam-4317	289	25	∈	∈	PROPN
ejpam-4317	289	26	δcl?(w	δcl?(w	NOUN
ejpam-4317	289	27	)	)	PUNCT
ejpam-4317	289	28	.	.	PUNCT
ejpam-4317	290	1	it	it	PRON
ejpam-4317	290	2	follows	follow	VERB
ejpam-4317	290	3	that	that	SCONJ
ejpam-4317	290	4	z	z	PROPN
ejpam-4317	290	5	∈	∈	PROPN
ejpam-4317	290	6	w	w	NOUN
ejpam-4317	290	7	or	or	CCONJ
ejpam-4317	290	8	z	z	NOUN
ejpam-4317	290	9	∈	∈	PROPN
ejpam-4317	290	10	w	w	PROPN
ejpam-4317	290	11	δ	δ	PROPN
ejpam-4317	290	12	?	?	PUNCT
ejpam-4317	290	13	.	.	PUNCT
ejpam-4317	291	1	if	if	SCONJ
ejpam-4317	291	2	z	z	PROPN
ejpam-4317	291	3	∈	∈	PROPN
ejpam-4317	291	4	w	w	NOUN
ejpam-4317	291	5	then	then	ADV
ejpam-4317	291	6	z	z	PROPN
ejpam-4317	291	7	∈	∈	PROPN
ejpam-4317	291	8	f−1(o	f−1(o	PROPN
ejpam-4317	291	9	)	)	PUNCT
ejpam-4317	291	10	∩	∩	PROPN
ejpam-4317	291	11	w	w	PROPN
ejpam-4317	291	12	,	,	PUNCT
ejpam-4317	291	13	which	which	PRON
ejpam-4317	291	14	is	be	AUX
ejpam-4317	291	15	a	a	DET
ejpam-4317	291	16	contradiction	contradiction	NOUN
ejpam-4317	291	17	.	.	PUNCT
ejpam-4317	292	1	if	if	SCONJ
ejpam-4317	292	2	z	z	PROPN
ejpam-4317	292	3	∈	∈	PROPN
ejpam-4317	292	4	w	w	PROPN
ejpam-4317	292	5	δ	δ	PROPN
ejpam-4317	292	6	?	?	PUNCT
ejpam-4317	293	1	then	then	ADV
ejpam-4317	293	2	g	g	PROPN
ejpam-4317	293	3	∩	∩	PROPN
ejpam-4317	293	4	w	w	PROPN
ejpam-4317	293	5	/∈	/∈	PROPN
ejpam-4317	294	1	i	i	PRON
ejpam-4317	294	2	for	for	ADP
ejpam-4317	294	3	each	each	DET
ejpam-4317	294	4	δ	δ	NOUN
ejpam-4317	294	5	-	-	ADJ
ejpam-4317	294	6	open	open	ADJ
ejpam-4317	294	7	set	set	VERB
ejpam-4317	294	8	g	g	NOUN
ejpam-4317	294	9	containing	contain	VERB
ejpam-4317	294	10	z	z	NOUN
ejpam-4317	294	11	;	;	PUNCT
ejpam-4317	294	12	in	in	ADP
ejpam-4317	294	13	particular	particular	ADJ
ejpam-4317	294	14	,	,	PUNCT
ejpam-4317	294	15	f−1(o	f−1(o	PROPN
ejpam-4317	294	16	)	)	PUNCT
ejpam-4317	294	17	∩	∩	PROPN
ejpam-4317	294	18	w	w	X
ejpam-4317	294	19	/∈	/∈	PROPN
ejpam-4317	295	1	i	i	PROPN
ejpam-4317	295	2	,	,	PUNCT
ejpam-4317	295	3	which	which	PRON
ejpam-4317	295	4	implies	imply	VERB
ejpam-4317	295	5	that	that	SCONJ
ejpam-4317	295	6	f−1(o)∩w	f−1(o)∩w	ADV
ejpam-4317	295	7	6=	6=	PUNCT
ejpam-4317	295	8	∅	∅	NOUN
ejpam-4317	295	9	,	,	PUNCT
ejpam-4317	295	10	so	so	ADV
ejpam-4317	295	11	again	again	ADV
ejpam-4317	295	12	we	we	PRON
ejpam-4317	295	13	get	get	VERB
ejpam-4317	295	14	a	a	DET
ejpam-4317	295	15	contradiction	contradiction	NOUN
ejpam-4317	295	16	.	.	PUNCT
ejpam-4317	296	1	therefore	therefore	ADV
ejpam-4317	296	2	,	,	PUNCT
ejpam-4317	296	3	we	we	PRON
ejpam-4317	296	4	deduce	deduce	VERB
ejpam-4317	296	5	that	that	PRON
ejpam-4317	296	6	f−1(o	f−1(o	NOUN
ejpam-4317	296	7	)	)	PUNCT
ejpam-4317	296	8	∩	∩	NOUN
ejpam-4317	296	9	δcl?(w	δcl?(w	NOUN
ejpam-4317	296	10	)	)	PUNCT
ejpam-4317	297	1	=	=	PUNCT
ejpam-4317	297	2	∅.	∅.	ADP
ejpam-4317	297	3	thus	thus	ADV
ejpam-4317	297	4	,	,	PUNCT
ejpam-4317	297	5	o	o	NOUN
ejpam-4317	297	6	∩	∩	ADJ
ejpam-4317	297	7	f(δcl?(w	f(δcl?(w	NOUN
ejpam-4317	297	8	)	)	PUNCT
ejpam-4317	297	9	)	)	PUNCT
ejpam-4317	298	1	=	=	NOUN
ejpam-4317	298	2	∅	∅	NOUN
ejpam-4317	298	3	and	and	CCONJ
ejpam-4317	298	4	hence	hence	ADV
ejpam-4317	298	5	,	,	PUNCT
ejpam-4317	298	6	y	y	PROPN
ejpam-4317	298	7	/∈	/∈	PUNCT
ejpam-4317	298	8	f(δcl?(w	f(δcl?(w	PROPN
ejpam-4317	298	9	)	)	PUNCT
ejpam-4317	298	10	)	)	PUNCT
ejpam-4317	298	11	.	.	PUNCT
ejpam-4317	299	1	this	this	PRON
ejpam-4317	299	2	shows	show	VERB
ejpam-4317	299	3	that	that	SCONJ
ejpam-4317	299	4	f(δcl?(w	f(δcl?(w	NOUN
ejpam-4317	299	5	)	)	PUNCT
ejpam-4317	299	6	)	)	PUNCT
ejpam-4317	300	1	⊂	⊂	PROPN
ejpam-4317	300	2	cl(u	cl(u	X
ejpam-4317	300	3	)	)	PUNCT
ejpam-4317	300	4	⊂	⊂	PROPN
ejpam-4317	300	5	v	v	PROPN
ejpam-4317	300	6	and	and	CCONJ
ejpam-4317	300	7	so	so	ADV
ejpam-4317	300	8	,	,	PUNCT
ejpam-4317	300	9	f	f	PROPN
ejpam-4317	300	10	is	be	AUX
ejpam-4317	300	11	strongly	strongly	ADV
ejpam-4317	300	12	δθ	δθ	NOUN
ejpam-4317	300	13	-	-	PUNCT
ejpam-4317	300	14	i	i	NOUN
ejpam-4317	300	15	-	-	PUNCT
ejpam-4317	300	16	continuous	continuous	ADJ
ejpam-4317	300	17	.	.	PUNCT
ejpam-4317	301	1	j.	j.	PROPN
ejpam-4317	301	2	sanabria	sanabria	PROPN
ejpam-4317	301	3	,	,	PUNCT
ejpam-4317	301	4	r.	r.	PROPN
ejpam-4317	301	5	lozada	lozada	PROPN
ejpam-4317	301	6	-	-	PUNCT
ejpam-4317	301	7	yavina	yavina	PROPN
ejpam-4317	301	8	,	,	PUNCT
ejpam-4317	301	9	j.	j.	PROPN
ejpam-4317	301	10	tormet	tormet	PROPN
ejpam-4317	301	11	/	/	SYM
ejpam-4317	301	12	eur	eur	PROPN
ejpam-4317	301	13	.	.	PUNCT
ejpam-4317	302	1	j.	j.	PROPN
ejpam-4317	302	2	pure	pure	PROPN
ejpam-4317	302	3	appl	appl	PROPN
ejpam-4317	302	4	.	.	PROPN
ejpam-4317	302	5	math	math	PROPN
ejpam-4317	302	6	,	,	PUNCT
ejpam-4317	302	7	15	15	NUM
ejpam-4317	302	8	(	(	PUNCT
ejpam-4317	302	9	2	2	NUM
ejpam-4317	302	10	)	)	PUNCT
ejpam-4317	302	11	(	(	PUNCT
ejpam-4317	302	12	2022	2022	NUM
ejpam-4317	302	13	)	)	PUNCT
ejpam-4317	302	14	,	,	PUNCT
ejpam-4317	302	15	443	443	NUM
ejpam-4317	302	16	-	-	SYM
ejpam-4317	302	17	453	453	NUM
ejpam-4317	302	18	450	450	NUM
ejpam-4317	302	19	in	in	ADP
ejpam-4317	302	20	the	the	DET
ejpam-4317	302	21	following	follow	VERB
ejpam-4317	302	22	example	example	NOUN
ejpam-4317	303	1	,	,	PUNCT
ejpam-4317	303	2	we	we	PRON
ejpam-4317	303	3	show	show	VERB
ejpam-4317	303	4	that	that	SCONJ
ejpam-4317	303	5	there	there	PRON
ejpam-4317	303	6	exists	exist	VERB
ejpam-4317	303	7	a	a	DET
ejpam-4317	303	8	strongly	strongly	ADV
ejpam-4317	303	9	δθ	δθ	NOUN
ejpam-4317	303	10	-	-	PUNCT
ejpam-4317	303	11	i	i	NOUN
ejpam-4317	303	12	-	-	PUNCT
ejpam-4317	303	13	continuous	continuous	ADJ
ejpam-4317	303	14	function	function	NOUN
ejpam-4317	303	15	that	that	PRON
ejpam-4317	303	16	is	be	AUX
ejpam-4317	303	17	not	not	PART
ejpam-4317	303	18	super	super	ADJ
ejpam-4317	303	19	-	-	ADJ
ejpam-4317	303	20	continuous	continuous	ADJ
ejpam-4317	303	21	.	.	PUNCT
ejpam-4317	303	22	example	example	NOUN
ejpam-4317	304	1	3	3	X
ejpam-4317	304	2	.	.	PUNCT
ejpam-4317	305	1	the	the	DET
ejpam-4317	305	2	function	function	NOUN
ejpam-4317	305	3	f	f	NOUN
ejpam-4317	305	4	given	give	VERB
ejpam-4317	305	5	in	in	ADP
ejpam-4317	305	6	example	example	NOUN
ejpam-4317	305	7	2	2	NUM
ejpam-4317	305	8	is	be	AUX
ejpam-4317	305	9	strongly	strongly	ADV
ejpam-4317	305	10	continuous	continuous	ADJ
ejpam-4317	305	11	,	,	PUNCT
ejpam-4317	305	12	but	but	CCONJ
ejpam-4317	305	13	it	it	PRON
ejpam-4317	305	14	is	be	AUX
ejpam-4317	305	15	not	not	PART
ejpam-4317	305	16	super	super	ADJ
ejpam-4317	305	17	-	-	ADJ
ejpam-4317	305	18	continuous	continuous	ADJ
ejpam-4317	305	19	,	,	PUNCT
ejpam-4317	305	20	because	because	SCONJ
ejpam-4317	305	21	in	in	ADP
ejpam-4317	305	22	this	this	DET
ejpam-4317	305	23	case	case	NOUN
ejpam-4317	305	24	τδ	τδ	SCONJ
ejpam-4317	305	25	=	=	PUNCT
ejpam-4317	305	26	{	{	PUNCT
ejpam-4317	305	27	∅	∅	NOUN
ejpam-4317	305	28	,	,	PUNCT
ejpam-4317	305	29	x	x	NOUN
ejpam-4317	305	30	}	}	PUNCT
ejpam-4317	305	31	and	and	CCONJ
ejpam-4317	305	32	{	{	PUNCT
ejpam-4317	305	33	a	a	DET
ejpam-4317	305	34	,	,	PUNCT
ejpam-4317	305	35	b	b	NOUN
ejpam-4317	305	36	}	}	PUNCT
ejpam-4317	305	37	is	be	AUX
ejpam-4317	305	38	an	an	DET
ejpam-4317	305	39	open	open	ADJ
ejpam-4317	305	40	set	set	NOUN
ejpam-4317	305	41	such	such	ADJ
ejpam-4317	305	42	that	that	SCONJ
ejpam-4317	305	43	f−1({a	f−1({a	NOUN
ejpam-4317	305	44	,	,	PUNCT
ejpam-4317	305	45	b	b	NOUN
ejpam-4317	305	46	}	}	PUNCT
ejpam-4317	305	47	)	)	PUNCT
ejpam-4317	306	1	=	=	PRON
ejpam-4317	306	2	{	{	PUNCT
ejpam-4317	306	3	a	a	DET
ejpam-4317	306	4	,	,	PUNCT
ejpam-4317	306	5	b	b	NOUN
ejpam-4317	306	6	}	}	PUNCT
ejpam-4317	306	7	/∈	/∈	PUNCT
ejpam-4317	307	1	τδ	τδ	INTJ
ejpam-4317	307	2	.	.	PUNCT
ejpam-4317	308	1	theorem	theorem	ADJ
ejpam-4317	308	2	7	7	NUM
ejpam-4317	308	3	.	.	PUNCT
ejpam-4317	309	1	let	let	VERB
ejpam-4317	309	2	f	f	NOUN
ejpam-4317	309	3	:	:	PUNCT
ejpam-4317	309	4	(	(	PUNCT
ejpam-4317	309	5	x	x	X
ejpam-4317	309	6	,	,	PUNCT
ejpam-4317	309	7	τ	τ	PROPN
ejpam-4317	309	8	,	,	PUNCT
ejpam-4317	309	9	i	i	NOUN
ejpam-4317	309	10	)	)	PUNCT
ejpam-4317	309	11	→	→	SYM
ejpam-4317	309	12	(	(	PUNCT
ejpam-4317	309	13	y	y	PROPN
ejpam-4317	309	14	,	,	PUNCT
ejpam-4317	309	15	σ	σ	PROPN
ejpam-4317	309	16	)	)	PUNCT
ejpam-4317	309	17	be	be	VERB
ejpam-4317	309	18	any	any	DET
ejpam-4317	309	19	function	function	NOUN
ejpam-4317	309	20	and	and	CCONJ
ejpam-4317	309	21	g	g	NOUN
ejpam-4317	309	22	:	:	PUNCT
ejpam-4317	309	23	(	(	PUNCT
ejpam-4317	309	24	x	x	X
ejpam-4317	309	25	,	,	PUNCT
ejpam-4317	309	26	τ	τ	PROPN
ejpam-4317	309	27	,	,	PUNCT
ejpam-4317	309	28	i	i	NOUN
ejpam-4317	309	29	)	)	PUNCT
ejpam-4317	309	30	→	→	PUNCT
ejpam-4317	309	31	(	(	PUNCT
ejpam-4317	309	32	x	x	SYM
ejpam-4317	309	33	×	×	PROPN
ejpam-4317	309	34	y	y	PROPN
ejpam-4317	309	35	,	,	PUNCT
ejpam-4317	309	36	τ	τ	PROPN
ejpam-4317	309	37	×	×	PROPN
ejpam-4317	309	38	σ	σ	PROPN
ejpam-4317	309	39	)	)	PUNCT
ejpam-4317	309	40	be	be	VERB
ejpam-4317	309	41	the	the	DET
ejpam-4317	309	42	graph	graph	NOUN
ejpam-4317	309	43	function	function	NOUN
ejpam-4317	309	44	of	of	ADP
ejpam-4317	309	45	f	f	PROPN
ejpam-4317	309	46	defined	define	VERB
ejpam-4317	309	47	by	by	ADP
ejpam-4317	309	48	g(x	g(x	NOUN
ejpam-4317	309	49	)	)	PUNCT
ejpam-4317	310	1	=	=	SYM
ejpam-4317	310	2	(	(	PUNCT
ejpam-4317	310	3	x	x	X
ejpam-4317	310	4	,	,	PUNCT
ejpam-4317	310	5	f(x	f(x	PROPN
ejpam-4317	310	6	)	)	PUNCT
ejpam-4317	310	7	)	)	PUNCT
ejpam-4317	311	1	for	for	ADP
ejpam-4317	311	2	every	every	DET
ejpam-4317	311	3	x	x	SYM
ejpam-4317	311	4	∈	∈	PROPN
ejpam-4317	311	5	x	x	NOUN
ejpam-4317	311	6	,	,	PUNCT
ejpam-4317	311	7	where	where	SCONJ
ejpam-4317	311	8	τ	τ	PROPN
ejpam-4317	311	9	×	×	PROPN
ejpam-4317	311	10	σ	σ	PROPN
ejpam-4317	311	11	is	be	AUX
ejpam-4317	311	12	the	the	DET
ejpam-4317	311	13	product	product	NOUN
ejpam-4317	311	14	topology	topology	NOUN
ejpam-4317	311	15	on	on	ADP
ejpam-4317	311	16	x	x	SYM
ejpam-4317	311	17	×	×	PROPN
ejpam-4317	311	18	y	y	PROPN
ejpam-4317	311	19	.	.	PUNCT
ejpam-4317	312	1	then	then	ADV
ejpam-4317	312	2	,	,	PUNCT
ejpam-4317	312	3	g	g	PROPN
ejpam-4317	312	4	is	be	AUX
ejpam-4317	312	5	strongly	strongly	ADV
ejpam-4317	312	6	δθ	δθ	NOUN
ejpam-4317	312	7	-	-	PUNCT
ejpam-4317	312	8	i	i	NOUN
ejpam-4317	312	9	-	-	NOUN
ejpam-4317	312	10	continuous	continuous	ADJ
ejpam-4317	312	11	if	if	SCONJ
ejpam-4317	313	1	and	and	CCONJ
ejpam-4317	313	2	only	only	ADV
ejpam-4317	313	3	if	if	SCONJ
ejpam-4317	313	4	f	f	PROPN
ejpam-4317	313	5	is	be	AUX
ejpam-4317	313	6	strongly	strongly	ADV
ejpam-4317	313	7	δθ	δθ	NOUN
ejpam-4317	313	8	-	-	PUNCT
ejpam-4317	313	9	i	i	NOUN
ejpam-4317	313	10	-	-	PUNCT
ejpam-4317	313	11	continuous	continuous	ADJ
ejpam-4317	313	12	and	and	CCONJ
ejpam-4317	313	13	(	(	PUNCT
ejpam-4317	313	14	x	x	X
ejpam-4317	313	15	,	,	PUNCT
ejpam-4317	313	16	τ	τ	PROPN
ejpam-4317	313	17	,	,	PUNCT
ejpam-4317	313	18	i	i	PROPN
ejpam-4317	313	19	)	)	PUNCT
ejpam-4317	313	20	is	be	AUX
ejpam-4317	313	21	δ?-regular	δ?-regular	ADJ
ejpam-4317	313	22	.	.	PUNCT
ejpam-4317	314	1	proof	proof	NOUN
ejpam-4317	314	2	.	.	PUNCT
ejpam-4317	315	1	clearly	clearly	ADV
ejpam-4317	315	2	,	,	PUNCT
ejpam-4317	315	3	g(x	g(x	NOUN
ejpam-4317	315	4	)	)	PUNCT
ejpam-4317	315	5	=	=	SYM
ejpam-4317	315	6	(	(	PUNCT
ejpam-4317	316	1	1x(x	1x(x	NUM
ejpam-4317	316	2	)	)	PUNCT
ejpam-4317	316	3	,	,	PUNCT
ejpam-4317	316	4	f(x	f(x	PROPN
ejpam-4317	316	5	)	)	PUNCT
ejpam-4317	316	6	)	)	PUNCT
ejpam-4317	316	7	for	for	ADP
ejpam-4317	316	8	every	every	DET
ejpam-4317	316	9	x	x	SYM
ejpam-4317	316	10	∈	∈	PROPN
ejpam-4317	316	11	x	x	NOUN
ejpam-4317	316	12	,	,	PUNCT
ejpam-4317	316	13	where	where	SCONJ
ejpam-4317	316	14	1x	1x	NOUN
ejpam-4317	316	15	:	:	PUNCT
ejpam-4317	316	16	(	(	PUNCT
ejpam-4317	316	17	x	x	X
ejpam-4317	316	18	,	,	PUNCT
ejpam-4317	316	19	τ	τ	PROPN
ejpam-4317	316	20	,	,	PUNCT
ejpam-4317	316	21	i	i	NOUN
ejpam-4317	316	22	)	)	PUNCT
ejpam-4317	316	23	→	→	SYM
ejpam-4317	316	24	(	(	PUNCT
ejpam-4317	316	25	x	x	X
ejpam-4317	316	26	,	,	PUNCT
ejpam-4317	316	27	τ	τ	X
ejpam-4317	316	28	)	)	PUNCT
ejpam-4317	316	29	is	be	AUX
ejpam-4317	316	30	the	the	DET
ejpam-4317	316	31	identity	identity	NOUN
ejpam-4317	316	32	function	function	NOUN
ejpam-4317	316	33	on	on	ADP
ejpam-4317	316	34	x.	x.	NOUN
ejpam-4317	316	35	then	then	ADV
ejpam-4317	316	36	,	,	PUNCT
ejpam-4317	316	37	by	by	ADP
ejpam-4317	316	38	corollary	corollary	ADJ
ejpam-4317	316	39	1	1	NUM
ejpam-4317	316	40	,	,	PUNCT
ejpam-4317	316	41	g	g	PROPN
ejpam-4317	316	42	is	be	AUX
ejpam-4317	316	43	strongly	strongly	ADV
ejpam-4317	316	44	δθ	δθ	NOUN
ejpam-4317	316	45	-	-	PUNCT
ejpam-4317	316	46	i	i	NOUN
ejpam-4317	316	47	-	-	NOUN
ejpam-4317	316	48	continuous	continuous	ADJ
ejpam-4317	316	49	if	if	SCONJ
ejpam-4317	316	50	and	and	CCONJ
ejpam-4317	316	51	only	only	ADV
ejpam-4317	316	52	if	if	SCONJ
ejpam-4317	316	53	1x	1x	NUM
ejpam-4317	316	54	and	and	CCONJ
ejpam-4317	316	55	f	f	PROPN
ejpam-4317	316	56	are	be	AUX
ejpam-4317	316	57	strongly	strongly	ADV
ejpam-4317	316	58	δθ	δθ	NOUN
ejpam-4317	316	59	-	-	PUNCT
ejpam-4317	316	60	i	i	NOUN
ejpam-4317	316	61	-	-	PUNCT
ejpam-4317	316	62	continuous	continuous	ADJ
ejpam-4317	316	63	.	.	PUNCT
ejpam-4317	317	1	in	in	ADP
ejpam-4317	317	2	addition	addition	NOUN
ejpam-4317	317	3	,	,	PUNCT
ejpam-4317	317	4	1x	1x	PROPN
ejpam-4317	317	5	is	be	AUX
ejpam-4317	317	6	strongly	strongly	ADV
ejpam-4317	317	7	δθ	δθ	NOUN
ejpam-4317	317	8	-	-	PUNCT
ejpam-4317	317	9	i	i	NOUN
ejpam-4317	317	10	-	-	NOUN
ejpam-4317	317	11	continuous	continuous	ADJ
ejpam-4317	317	12	if	if	SCONJ
ejpam-4317	317	13	and	and	CCONJ
ejpam-4317	317	14	only	only	ADV
ejpam-4317	317	15	if	if	SCONJ
ejpam-4317	317	16	for	for	SCONJ
ejpam-4317	317	17	each	each	DET
ejpam-4317	317	18	x	x	SYM
ejpam-4317	317	19	∈	∈	PROPN
ejpam-4317	317	20	x	x	X
ejpam-4317	317	21	and	and	CCONJ
ejpam-4317	317	22	each	each	DET
ejpam-4317	317	23	open	open	ADJ
ejpam-4317	317	24	set	set	VERB
ejpam-4317	317	25	v	v	NOUN
ejpam-4317	317	26	in	in	ADP
ejpam-4317	317	27	x	x	PUNCT
ejpam-4317	317	28	containing	contain	VERB
ejpam-4317	317	29	x	x	PRON
ejpam-4317	317	30	,	,	PUNCT
ejpam-4317	317	31	there	there	PRON
ejpam-4317	317	32	exists	exist	VERB
ejpam-4317	317	33	an	an	DET
ejpam-4317	317	34	open	open	ADJ
ejpam-4317	317	35	set	set	NOUN
ejpam-4317	317	36	u	u	NOUN
ejpam-4317	317	37	in	in	ADP
ejpam-4317	317	38	x	x	PUNCT
ejpam-4317	317	39	containing	contain	VERB
ejpam-4317	317	40	x	x	PUNCT
ejpam-4317	317	41	such	such	ADJ
ejpam-4317	317	42	that	that	DET
ejpam-4317	317	43	δcl?(u	δcl?(u	PROPN
ejpam-4317	317	44	)	)	PUNCT
ejpam-4317	318	1	⊂	⊂	PROPN
ejpam-4317	318	2	v	v	ADP
ejpam-4317	318	3	,	,	PUNCT
ejpam-4317	318	4	but	but	CCONJ
ejpam-4317	318	5	by	by	ADP
ejpam-4317	318	6	lemma	lemma	PROPN
ejpam-4317	318	7	2	2	NUM
ejpam-4317	318	8	,	,	PUNCT
ejpam-4317	318	9	the	the	DET
ejpam-4317	318	10	latter	latter	ADJ
ejpam-4317	318	11	is	be	AUX
ejpam-4317	318	12	equivalent	equivalent	ADJ
ejpam-4317	318	13	to	to	ADP
ejpam-4317	318	14	that	that	PRON
ejpam-4317	318	15	(	(	PUNCT
ejpam-4317	318	16	x	x	X
ejpam-4317	318	17	,	,	PUNCT
ejpam-4317	318	18	τ	τ	PROPN
ejpam-4317	318	19	,	,	PUNCT
ejpam-4317	318	20	i	i	PROPN
ejpam-4317	318	21	)	)	PUNCT
ejpam-4317	318	22	is	be	AUX
ejpam-4317	318	23	a	a	DET
ejpam-4317	318	24	δ?-regular	δ?-regular	ADJ
ejpam-4317	318	25	space	space	NOUN
ejpam-4317	318	26	.	.	PUNCT
ejpam-4317	319	1	definition	definition	NOUN
ejpam-4317	319	2	6	6	NUM
ejpam-4317	319	3	.	.	PUNCT
ejpam-4317	320	1	[	[	X
ejpam-4317	320	2	14	14	NUM
ejpam-4317	320	3	]	]	PUNCT
ejpam-4317	320	4	a	a	DET
ejpam-4317	320	5	space	space	NOUN
ejpam-4317	320	6	(	(	PUNCT
ejpam-4317	320	7	x	x	X
ejpam-4317	320	8	,	,	PUNCT
ejpam-4317	320	9	τ	τ	PROPN
ejpam-4317	320	10	,	,	PUNCT
ejpam-4317	320	11	i	i	PROPN
ejpam-4317	320	12	)	)	PUNCT
ejpam-4317	320	13	is	be	AUX
ejpam-4317	320	14	said	say	VERB
ejpam-4317	320	15	to	to	PART
ejpam-4317	320	16	be	be	AUX
ejpam-4317	320	17	δ?-urysohn	δ?-urysohn	PROPN
ejpam-4317	320	18	,	,	PUNCT
ejpam-4317	320	19	if	if	SCONJ
ejpam-4317	320	20	for	for	ADP
ejpam-4317	320	21	each	each	DET
ejpam-4317	320	22	pair	pair	NOUN
ejpam-4317	320	23	of	of	ADP
ejpam-4317	320	24	distinct	distinct	ADJ
ejpam-4317	320	25	points	point	NOUN
ejpam-4317	320	26	x	x	PUNCT
ejpam-4317	320	27	and	and	CCONJ
ejpam-4317	320	28	y	y	PROPN
ejpam-4317	320	29	in	in	ADP
ejpam-4317	320	30	x	x	SYM
ejpam-4317	320	31	,	,	PUNCT
ejpam-4317	320	32	there	there	PRON
ejpam-4317	320	33	exist	exist	VERB
ejpam-4317	320	34	two	two	NUM
ejpam-4317	320	35	open	open	ADJ
ejpam-4317	320	36	subsets	subset	NOUN
ejpam-4317	320	37	u	u	NOUN
ejpam-4317	320	38	and	and	CCONJ
ejpam-4317	320	39	v	v	NOUN
ejpam-4317	320	40	of	of	ADP
ejpam-4317	320	41	x	x	PUNCT
ejpam-4317	320	42	containing	contain	VERB
ejpam-4317	320	43	x	x	PROPN
ejpam-4317	320	44	and	and	CCONJ
ejpam-4317	320	45	y	y	PROPN
ejpam-4317	320	46	respectively	respectively	ADV
ejpam-4317	320	47	,	,	PUNCT
ejpam-4317	320	48	such	such	ADJ
ejpam-4317	320	49	that	that	DET
ejpam-4317	320	50	δcl?(u	δcl?(u	PROPN
ejpam-4317	320	51	)	)	PUNCT
ejpam-4317	320	52	∩	∩	PROPN
ejpam-4317	320	53	δcl?(v	δcl?(v	VERB
ejpam-4317	320	54	)	)	PUNCT
ejpam-4317	320	55	=	=	PUNCT
ejpam-4317	320	56	∅.	∅.	NOUN
ejpam-4317	320	57	theorem	theorem	VERB
ejpam-4317	320	58	8	8	NUM
ejpam-4317	320	59	.	.	PUNCT
ejpam-4317	321	1	if	if	SCONJ
ejpam-4317	321	2	f	f	PROPN
ejpam-4317	321	3	:	:	PUNCT
ejpam-4317	321	4	(	(	PUNCT
ejpam-4317	321	5	x	x	X
ejpam-4317	321	6	,	,	PUNCT
ejpam-4317	321	7	τ	τ	PROPN
ejpam-4317	321	8	,	,	PUNCT
ejpam-4317	321	9	i	i	NOUN
ejpam-4317	321	10	)	)	PUNCT
ejpam-4317	321	11	→	→	SYM
ejpam-4317	321	12	(	(	PUNCT
ejpam-4317	321	13	y	y	PROPN
ejpam-4317	321	14	,	,	PUNCT
ejpam-4317	321	15	σ	σ	PROPN
ejpam-4317	321	16	)	)	PUNCT
ejpam-4317	321	17	is	be	AUX
ejpam-4317	321	18	a	a	DET
ejpam-4317	321	19	strongly	strongly	ADV
ejpam-4317	321	20	δθ	δθ	NOUN
ejpam-4317	321	21	-	-	PUNCT
ejpam-4317	321	22	i	i	NOUN
ejpam-4317	321	23	-	-	PUNCT
ejpam-4317	321	24	continuous	continuous	ADJ
ejpam-4317	321	25	injective	injective	ADJ
ejpam-4317	321	26	function	function	NOUN
ejpam-4317	321	27	and	and	CCONJ
ejpam-4317	321	28	(	(	PUNCT
ejpam-4317	321	29	y	y	PROPN
ejpam-4317	321	30	,	,	PUNCT
ejpam-4317	321	31	σ	σ	PROPN
ejpam-4317	321	32	)	)	PUNCT
ejpam-4317	321	33	is	be	AUX
ejpam-4317	321	34	t2	t2	NOUN
ejpam-4317	321	35	,	,	PUNCT
ejpam-4317	321	36	then	then	ADV
ejpam-4317	321	37	(	(	PUNCT
ejpam-4317	321	38	x	x	X
ejpam-4317	321	39	,	,	PUNCT
ejpam-4317	321	40	τ	τ	PROPN
ejpam-4317	321	41	,	,	PUNCT
ejpam-4317	321	42	i	i	PROPN
ejpam-4317	321	43	)	)	PUNCT
ejpam-4317	321	44	is	be	AUX
ejpam-4317	321	45	δ?-urysohn	δ?-urysohn	PROPN
ejpam-4317	321	46	.	.	PUNCT
ejpam-4317	322	1	proof	proof	NOUN
ejpam-4317	322	2	.	.	PUNCT
ejpam-4317	323	1	let	let	VERB
ejpam-4317	323	2	x	x	PRON
ejpam-4317	323	3	and	and	CCONJ
ejpam-4317	323	4	y	y	PROPN
ejpam-4317	323	5	be	be	AUX
ejpam-4317	323	6	distinct	distinct	ADJ
ejpam-4317	323	7	points	point	NOUN
ejpam-4317	323	8	of	of	ADP
ejpam-4317	323	9	x.	x.	NOUN
ejpam-4317	323	10	then	then	ADV
ejpam-4317	323	11	,	,	PUNCT
ejpam-4317	323	12	f(x	f(x	PROPN
ejpam-4317	323	13	)	)	PUNCT
ejpam-4317	323	14	6=	6=	SYM
ejpam-4317	324	1	f(y	f(y	NOUN
ejpam-4317	324	2	)	)	PUNCT
ejpam-4317	324	3	and	and	CCONJ
ejpam-4317	324	4	as	as	ADP
ejpam-4317	324	5	(	(	PUNCT
ejpam-4317	324	6	y	y	PROPN
ejpam-4317	324	7	,	,	PUNCT
ejpam-4317	324	8	σ	σ	PROPN
ejpam-4317	324	9	)	)	PUNCT
ejpam-4317	324	10	is	be	AUX
ejpam-4317	324	11	t2	t2	NOUN
ejpam-4317	324	12	,	,	PUNCT
ejpam-4317	324	13	there	there	PRON
ejpam-4317	324	14	exist	exist	VERB
ejpam-4317	324	15	disjoint	disjoint	ADJ
ejpam-4317	324	16	open	open	ADJ
ejpam-4317	324	17	sets	set	NOUN
ejpam-4317	324	18	v	v	NOUN
ejpam-4317	324	19	and	and	CCONJ
ejpam-4317	324	20	w	w	NOUN
ejpam-4317	324	21	in	in	ADP
ejpam-4317	324	22	y	y	NOUN
ejpam-4317	324	23	containing	contain	VERB
ejpam-4317	324	24	f(x	f(x	PROPN
ejpam-4317	324	25	)	)	PUNCT
ejpam-4317	324	26	and	and	CCONJ
ejpam-4317	324	27	f(y	f(y	NOUN
ejpam-4317	324	28	)	)	PUNCT
ejpam-4317	324	29	,	,	PUNCT
ejpam-4317	324	30	respectively	respectively	ADV
ejpam-4317	324	31	.	.	PUNCT
ejpam-4317	325	1	since	since	SCONJ
ejpam-4317	325	2	f	f	PROPN
ejpam-4317	325	3	is	be	AUX
ejpam-4317	325	4	strongly	strongly	ADV
ejpam-4317	325	5	δθ	δθ	NOUN
ejpam-4317	325	6	-	-	PUNCT
ejpam-4317	325	7	i	i	NOUN
ejpam-4317	325	8	-	-	PUNCT
ejpam-4317	325	9	continuous	continuous	ADJ
ejpam-4317	325	10	,	,	PUNCT
ejpam-4317	325	11	there	there	PRON
ejpam-4317	325	12	exist	exist	VERB
ejpam-4317	325	13	two	two	NUM
ejpam-4317	325	14	open	open	ADJ
ejpam-4317	325	15	sets	set	NOUN
ejpam-4317	325	16	g	g	NOUN
ejpam-4317	325	17	and	and	CCONJ
ejpam-4317	325	18	h	h	NOUN
ejpam-4317	325	19	in	in	ADP
ejpam-4317	325	20	x	x	PUNCT
ejpam-4317	325	21	containing	contain	VERB
ejpam-4317	325	22	x	x	PROPN
ejpam-4317	325	23	and	and	CCONJ
ejpam-4317	325	24	y	y	PROPN
ejpam-4317	325	25	,	,	PUNCT
ejpam-4317	325	26	respectively	respectively	ADV
ejpam-4317	325	27	,	,	PUNCT
ejpam-4317	325	28	such	such	ADJ
ejpam-4317	325	29	that	that	SCONJ
ejpam-4317	325	30	f(δcl?(g	f(δcl?(g	NOUN
ejpam-4317	325	31	)	)	PUNCT
ejpam-4317	325	32	)	)	PUNCT
ejpam-4317	326	1	⊂	⊂	PROPN
ejpam-4317	326	2	v	v	NOUN
ejpam-4317	326	3	and	and	CCONJ
ejpam-4317	326	4	f(δcl?(h	f(δcl?(h	NOUN
ejpam-4317	326	5	)	)	PUNCT
ejpam-4317	326	6	)	)	PUNCT
ejpam-4317	327	1	⊂	⊂	PROPN
ejpam-4317	328	1	w	w	X
ejpam-4317	328	2	.	.	PUNCT
ejpam-4317	329	1	it	it	PRON
ejpam-4317	329	2	follows	follow	VERB
ejpam-4317	329	3	that	that	DET
ejpam-4317	329	4	δcl?(g	δcl?(g	NOUN
ejpam-4317	329	5	)	)	PUNCT
ejpam-4317	329	6	∩	∩	ADJ
ejpam-4317	329	7	δcl?(h	δcl?(h	NOUN
ejpam-4317	329	8	)	)	PUNCT
ejpam-4317	329	9	⊂	⊂	PROPN
ejpam-4317	329	10	f−1(f(δcl?(g	f−1(f(δcl?(g	PROPN
ejpam-4317	329	11	)	)	PUNCT
ejpam-4317	329	12	)	)	PUNCT
ejpam-4317	329	13	)	)	PUNCT
ejpam-4317	330	1	∩	∩	PROPN
ejpam-4317	330	2	f−1(f(δcl?(h	f−1(f(δcl?(h	PROPN
ejpam-4317	330	3	)	)	PUNCT
ejpam-4317	330	4	)	)	PUNCT
ejpam-4317	330	5	)	)	PUNCT
ejpam-4317	331	1	⊂	⊂	PROPN
ejpam-4317	331	2	f−1(v	f−1(v	PROPN
ejpam-4317	331	3	)	)	PUNCT
ejpam-4317	331	4	∩	∩	PROPN
ejpam-4317	331	5	f−1(w	f−1(w	PROPN
ejpam-4317	331	6	)	)	PUNCT
ejpam-4317	331	7	=	=	SYM
ejpam-4317	331	8	∅	∅	NOUN
ejpam-4317	331	9	,	,	PUNCT
ejpam-4317	331	10	and	and	CCONJ
ejpam-4317	331	11	hence	hence	ADV
ejpam-4317	331	12	,	,	PUNCT
ejpam-4317	331	13	δcl?(g	δcl?(g	NOUN
ejpam-4317	331	14	)	)	PUNCT
ejpam-4317	331	15	∩	∩	ADJ
ejpam-4317	331	16	δcl?(h	δcl?(h	NOUN
ejpam-4317	331	17	)	)	PUNCT
ejpam-4317	331	18	=	=	PUNCT
ejpam-4317	331	19	∅.	∅.	ADP
ejpam-4317	331	20	this	this	DET
ejpam-4317	331	21	shows	show	VERB
ejpam-4317	331	22	that	that	SCONJ
ejpam-4317	331	23	(	(	PUNCT
ejpam-4317	331	24	x	x	X
ejpam-4317	331	25	,	,	PUNCT
ejpam-4317	331	26	τ	τ	PROPN
ejpam-4317	331	27	,	,	PUNCT
ejpam-4317	331	28	i	i	PROPN
ejpam-4317	331	29	)	)	PUNCT
ejpam-4317	331	30	is	be	AUX
ejpam-4317	331	31	δ?-urysohn	δ?-urysohn	PROPN
ejpam-4317	331	32	.	.	PUNCT
ejpam-4317	331	33	theorem	theorem	VERB
ejpam-4317	331	34	9	9	NUM
ejpam-4317	331	35	.	.	PUNCT
ejpam-4317	332	1	if	if	SCONJ
ejpam-4317	332	2	f	f	PROPN
ejpam-4317	332	3	:	:	PUNCT
ejpam-4317	332	4	(	(	PUNCT
ejpam-4317	332	5	x	x	X
ejpam-4317	332	6	,	,	PUNCT
ejpam-4317	332	7	τ	τ	PROPN
ejpam-4317	332	8	,	,	PUNCT
ejpam-4317	332	9	i	i	NOUN
ejpam-4317	332	10	)	)	PUNCT
ejpam-4317	332	11	→	→	SYM
ejpam-4317	332	12	(	(	PUNCT
ejpam-4317	332	13	y	y	PROPN
ejpam-4317	332	14	,	,	PUNCT
ejpam-4317	332	15	σ	σ	PROPN
ejpam-4317	332	16	)	)	PUNCT
ejpam-4317	332	17	is	be	AUX
ejpam-4317	332	18	a	a	DET
ejpam-4317	332	19	strongly	strongly	ADV
ejpam-4317	332	20	δθ	δθ	NOUN
ejpam-4317	332	21	-	-	PUNCT
ejpam-4317	332	22	i	i	NOUN
ejpam-4317	332	23	-	-	PUNCT
ejpam-4317	332	24	continuous	continuous	ADJ
ejpam-4317	332	25	injective	injective	ADJ
ejpam-4317	332	26	function	function	NOUN
ejpam-4317	332	27	and	and	CCONJ
ejpam-4317	332	28	(	(	PUNCT
ejpam-4317	332	29	y	y	PROPN
ejpam-4317	332	30	,	,	PUNCT
ejpam-4317	332	31	σ	σ	PROPN
ejpam-4317	332	32	)	)	PUNCT
ejpam-4317	332	33	is	be	AUX
ejpam-4317	332	34	t0	t0	NOUN
ejpam-4317	332	35	,	,	PUNCT
ejpam-4317	332	36	then	then	ADV
ejpam-4317	332	37	(	(	PUNCT
ejpam-4317	332	38	x	x	X
ejpam-4317	332	39	,	,	PUNCT
ejpam-4317	332	40	τ	τ	X
ejpam-4317	332	41	?	?	PUNCT
ejpam-4317	332	42	)	)	PUNCT
ejpam-4317	332	43	is	be	AUX
ejpam-4317	332	44	t2	t2	NOUN
ejpam-4317	332	45	.	.	PUNCT
ejpam-4317	333	1	proof	proof	NOUN
ejpam-4317	333	2	.	.	PUNCT
ejpam-4317	334	1	let	let	VERB
ejpam-4317	334	2	x	x	PRON
ejpam-4317	334	3	and	and	CCONJ
ejpam-4317	334	4	y	y	PROPN
ejpam-4317	334	5	be	be	AUX
ejpam-4317	334	6	distinct	distinct	ADJ
ejpam-4317	334	7	points	point	NOUN
ejpam-4317	334	8	of	of	ADP
ejpam-4317	334	9	x.	x.	NOUN
ejpam-4317	334	10	then	then	ADV
ejpam-4317	334	11	,	,	PUNCT
ejpam-4317	334	12	f(x	f(x	PROPN
ejpam-4317	334	13	)	)	PUNCT
ejpam-4317	334	14	6=	6=	SYM
ejpam-4317	335	1	f(y	f(y	NOUN
ejpam-4317	335	2	)	)	PUNCT
ejpam-4317	335	3	and	and	CCONJ
ejpam-4317	335	4	as	as	SCONJ
ejpam-4317	335	5	(	(	PUNCT
ejpam-4317	335	6	y	y	PROPN
ejpam-4317	335	7	,	,	PUNCT
ejpam-4317	335	8	σ	σ	PROPN
ejpam-4317	335	9	)	)	PUNCT
ejpam-4317	335	10	is	be	AUX
ejpam-4317	335	11	t0	t0	NUM
ejpam-4317	335	12	,	,	PUNCT
ejpam-4317	335	13	there	there	PRON
ejpam-4317	335	14	exists	exist	VERB
ejpam-4317	335	15	an	an	DET
ejpam-4317	335	16	open	open	ADJ
ejpam-4317	335	17	set	set	NOUN
ejpam-4317	335	18	v	v	NOUN
ejpam-4317	335	19	in	in	ADP
ejpam-4317	335	20	y	y	NOUN
ejpam-4317	335	21	containing	contain	VERB
ejpam-4317	335	22	one	one	NUM
ejpam-4317	335	23	the	the	DET
ejpam-4317	335	24	points	point	NOUN
ejpam-4317	335	25	f(x	f(x	PROPN
ejpam-4317	335	26	)	)	PUNCT
ejpam-4317	335	27	and	and	CCONJ
ejpam-4317	335	28	f(y	f(y	NOUN
ejpam-4317	335	29	)	)	PUNCT
ejpam-4317	335	30	but	but	CCONJ
ejpam-4317	335	31	not	not	PART
ejpam-4317	335	32	both	both	PRON
ejpam-4317	335	33	.	.	PUNCT
ejpam-4317	336	1	without	without	ADP
ejpam-4317	336	2	loss	loss	NOUN
ejpam-4317	336	3	of	of	ADP
ejpam-4317	336	4	generality	generality	NOUN
ejpam-4317	336	5	,	,	PUNCT
ejpam-4317	336	6	we	we	PRON
ejpam-4317	336	7	assume	assume	VERB
ejpam-4317	336	8	that	that	SCONJ
ejpam-4317	336	9	f(x	f(x	PROPN
ejpam-4317	336	10	)	)	PUNCT
ejpam-4317	336	11	∈	∈	PROPN
ejpam-4317	336	12	v	v	NOUN
ejpam-4317	336	13	and	and	CCONJ
ejpam-4317	336	14	f(y	f(y	NOUN
ejpam-4317	336	15	)	)	PUNCT
ejpam-4317	336	16	/∈	/∈	PUNCT
ejpam-4317	337	1	v	v	INTJ
ejpam-4317	337	2	.	.	PUNCT
ejpam-4317	338	1	since	since	SCONJ
ejpam-4317	338	2	f	f	PROPN
ejpam-4317	338	3	is	be	AUX
ejpam-4317	338	4	a	a	DET
ejpam-4317	338	5	strongly	strongly	ADV
ejpam-4317	338	6	δθ	δθ	NOUN
ejpam-4317	338	7	-	-	PUNCT
ejpam-4317	338	8	i	i	NOUN
ejpam-4317	338	9	-	-	PUNCT
ejpam-4317	338	10	continuous	continuous	ADJ
ejpam-4317	338	11	function	function	NOUN
ejpam-4317	338	12	,	,	PUNCT
ejpam-4317	338	13	there	there	PRON
ejpam-4317	338	14	exists	exist	VERB
ejpam-4317	338	15	an	an	DET
ejpam-4317	338	16	open	open	ADJ
ejpam-4317	338	17	set	set	NOUN
ejpam-4317	338	18	u	u	NOUN
ejpam-4317	338	19	in	in	ADP
ejpam-4317	338	20	x	x	PUNCT
ejpam-4317	338	21	containing	contain	VERB
ejpam-4317	338	22	x	x	PUNCT
ejpam-4317	338	23	such	such	ADJ
ejpam-4317	338	24	that	that	DET
ejpam-4317	338	25	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	338	26	)	)	PUNCT
ejpam-4317	338	27	)	)	PUNCT
ejpam-4317	339	1	⊂	⊂	PROPN
ejpam-4317	339	2	v	v	X
ejpam-4317	339	3	.	.	PUNCT
ejpam-4317	340	1	thus	thus	ADV
ejpam-4317	340	2	,	,	PUNCT
ejpam-4317	340	3	we	we	PRON
ejpam-4317	340	4	obtain	obtain	VERB
ejpam-4317	340	5	that	that	SCONJ
ejpam-4317	340	6	x	x	SYM
ejpam-4317	340	7	∈	∈	PROPN
ejpam-4317	340	8	u	u	X
ejpam-4317	340	9	⊂	⊂	PROPN
ejpam-4317	340	10	δcl?(u	δcl?(u	PROPN
ejpam-4317	340	11	)	)	PUNCT
ejpam-4317	340	12	⊂	⊂	PROPN
ejpam-4317	340	13	f−1(f(δcl?(u	f−1(f(δcl?(u	PROPN
ejpam-4317	340	14	)	)	PUNCT
ejpam-4317	340	15	)	)	PUNCT
ejpam-4317	340	16	)	)	PUNCT
ejpam-4317	341	1	⊂	⊂	PROPN
ejpam-4317	341	2	f−1(v	f−1(v	PROPN
ejpam-4317	341	3	)	)	PUNCT
ejpam-4317	341	4	and	and	CCONJ
ejpam-4317	341	5	y	y	PROPN
ejpam-4317	341	6	/∈	/∈	PUNCT
ejpam-4317	341	7	δcl?(u	δcl?(u	PROPN
ejpam-4317	341	8	)	)	PUNCT
ejpam-4317	341	9	,	,	PUNCT
ejpam-4317	341	10	which	which	PRON
ejpam-4317	341	11	implies	imply	VERB
ejpam-4317	341	12	that	that	SCONJ
ejpam-4317	341	13	u	u	PROPN
ejpam-4317	341	14	and	and	CCONJ
ejpam-4317	341	15	x	x	SYM
ejpam-4317	341	16	\	\	PROPN
ejpam-4317	341	17	δcl?(u	δcl?(u	PROPN
ejpam-4317	341	18	)	)	PUNCT
ejpam-4317	341	19	are	be	AUX
ejpam-4317	341	20	two	two	NUM
ejpam-4317	341	21	disjoint	disjoint	ADJ
ejpam-4317	341	22	τ?-open	τ?-open	ADJ
ejpam-4317	341	23	sets	set	NOUN
ejpam-4317	341	24	in	in	ADP
ejpam-4317	341	25	x	x	PUNCT
ejpam-4317	341	26	containing	contain	VERB
ejpam-4317	341	27	x	x	PROPN
ejpam-4317	341	28	and	and	CCONJ
ejpam-4317	341	29	y	y	PROPN
ejpam-4317	341	30	,	,	PUNCT
ejpam-4317	341	31	respectively	respectively	ADV
ejpam-4317	341	32	.	.	PUNCT
ejpam-4317	342	1	therefore	therefore	ADV
ejpam-4317	342	2	,	,	PUNCT
ejpam-4317	342	3	(	(	PUNCT
ejpam-4317	342	4	x	x	X
ejpam-4317	342	5	,	,	PUNCT
ejpam-4317	342	6	τ	τ	X
ejpam-4317	342	7	?	?	PUNCT
ejpam-4317	342	8	)	)	PUNCT
ejpam-4317	342	9	is	be	AUX
ejpam-4317	342	10	a	a	DET
ejpam-4317	342	11	t2	t2	NOUN
ejpam-4317	342	12	-	-	PUNCT
ejpam-4317	342	13	space	space	NOUN
ejpam-4317	342	14	.	.	PUNCT
ejpam-4317	343	1	definition	definition	NOUN
ejpam-4317	343	2	7	7	NUM
ejpam-4317	343	3	.	.	PUNCT
ejpam-4317	344	1	a	a	DET
ejpam-4317	344	2	strongly	strongly	ADV
ejpam-4317	344	3	δθ	δθ	NOUN
ejpam-4317	344	4	-	-	PUNCT
ejpam-4317	344	5	i	i	NOUN
ejpam-4317	344	6	-	-	PUNCT
ejpam-4317	344	7	continuous	continuous	ADJ
ejpam-4317	344	8	retraction	retraction	NOUN
ejpam-4317	344	9	is	be	AUX
ejpam-4317	344	10	a	a	DET
ejpam-4317	344	11	strongly	strongly	ADV
ejpam-4317	344	12	δθ	δθ	NOUN
ejpam-4317	344	13	-	-	PUNCT
ejpam-4317	344	14	i	i	NOUN
ejpam-4317	344	15	-	-	PUNCT
ejpam-4317	344	16	continuous	continuous	ADJ
ejpam-4317	344	17	function	function	NOUN
ejpam-4317	344	18	f	f	NOUN
ejpam-4317	344	19	:	:	PUNCT
ejpam-4317	344	20	(	(	PUNCT
ejpam-4317	344	21	x	x	X
ejpam-4317	344	22	,	,	PUNCT
ejpam-4317	344	23	τ	τ	PROPN
ejpam-4317	344	24	,	,	PUNCT
ejpam-4317	344	25	i	i	NOUN
ejpam-4317	344	26	)	)	PUNCT
ejpam-4317	344	27	→	→	SYM
ejpam-4317	344	28	(	(	PUNCT
ejpam-4317	344	29	y	y	PROPN
ejpam-4317	344	30	,	,	PUNCT
ejpam-4317	344	31	σ	σ	PROPN
ejpam-4317	344	32	)	)	PUNCT
ejpam-4317	344	33	,	,	PUNCT
ejpam-4317	344	34	where	where	SCONJ
ejpam-4317	344	35	y	y	PROPN
ejpam-4317	344	36	⊂	⊂	PROPN
ejpam-4317	344	37	x	x	X
ejpam-4317	344	38	and	and	CCONJ
ejpam-4317	344	39	f	f	X
ejpam-4317	344	40	|y	|y	NOUN
ejpam-4317	344	41	=	=	PUNCT
ejpam-4317	344	42	1y	1y	NUM
ejpam-4317	344	43	the	the	DET
ejpam-4317	344	44	identity	identity	NOUN
ejpam-4317	344	45	function	function	NOUN
ejpam-4317	344	46	on	on	ADP
ejpam-4317	344	47	y	y	PROPN
ejpam-4317	344	48	.	.	PUNCT
ejpam-4317	345	1	j.	j.	PROPN
ejpam-4317	345	2	sanabria	sanabria	PROPN
ejpam-4317	345	3	,	,	PUNCT
ejpam-4317	345	4	r.	r.	PROPN
ejpam-4317	345	5	lozada	lozada	PROPN
ejpam-4317	345	6	-	-	PUNCT
ejpam-4317	345	7	yavina	yavina	PROPN
ejpam-4317	345	8	,	,	PUNCT
ejpam-4317	345	9	j.	j.	PROPN
ejpam-4317	345	10	tormet	tormet	PROPN
ejpam-4317	345	11	/	/	SYM
ejpam-4317	345	12	eur	eur	PROPN
ejpam-4317	345	13	.	.	PUNCT
ejpam-4317	346	1	j.	j.	PROPN
ejpam-4317	346	2	pure	pure	PROPN
ejpam-4317	346	3	appl	appl	PROPN
ejpam-4317	346	4	.	.	PROPN
ejpam-4317	346	5	math	math	PROPN
ejpam-4317	346	6	,	,	PUNCT
ejpam-4317	346	7	15	15	NUM
ejpam-4317	346	8	(	(	PUNCT
ejpam-4317	346	9	2	2	NUM
ejpam-4317	346	10	)	)	PUNCT
ejpam-4317	346	11	(	(	PUNCT
ejpam-4317	346	12	2022	2022	NUM
ejpam-4317	346	13	)	)	PUNCT
ejpam-4317	346	14	,	,	PUNCT
ejpam-4317	346	15	443	443	NUM
ejpam-4317	346	16	-	-	SYM
ejpam-4317	346	17	453	453	NUM
ejpam-4317	346	18	451	451	NUM
ejpam-4317	346	19	theorem	theorem	VERB
ejpam-4317	346	20	10	10	NUM
ejpam-4317	346	21	.	.	PUNCT
ejpam-4317	347	1	if	if	SCONJ
ejpam-4317	347	2	f	f	PROPN
ejpam-4317	347	3	:	:	PUNCT
ejpam-4317	347	4	(	(	PUNCT
ejpam-4317	347	5	x	x	X
ejpam-4317	347	6	,	,	PUNCT
ejpam-4317	347	7	τ	τ	PROPN
ejpam-4317	347	8	,	,	PUNCT
ejpam-4317	347	9	i	i	NOUN
ejpam-4317	347	10	)	)	PUNCT
ejpam-4317	347	11	→	→	SYM
ejpam-4317	347	12	(	(	PUNCT
ejpam-4317	347	13	y	y	PROPN
ejpam-4317	347	14	,	,	PUNCT
ejpam-4317	347	15	σ	σ	PROPN
ejpam-4317	347	16	)	)	PUNCT
ejpam-4317	347	17	is	be	AUX
ejpam-4317	347	18	a	a	DET
ejpam-4317	347	19	strongly	strongly	ADV
ejpam-4317	347	20	δθ	δθ	NOUN
ejpam-4317	347	21	-	-	PUNCT
ejpam-4317	347	22	i	i	NOUN
ejpam-4317	347	23	-	-	PUNCT
ejpam-4317	347	24	continuous	continuous	ADJ
ejpam-4317	347	25	retraction	retraction	NOUN
ejpam-4317	347	26	and	and	CCONJ
ejpam-4317	347	27	(	(	PUNCT
ejpam-4317	347	28	y	y	PROPN
ejpam-4317	347	29	,	,	PUNCT
ejpam-4317	347	30	σ	σ	PROPN
ejpam-4317	347	31	)	)	PUNCT
ejpam-4317	347	32	is	be	AUX
ejpam-4317	347	33	t2	t2	NOUN
ejpam-4317	347	34	,	,	PUNCT
ejpam-4317	347	35	then	then	ADV
ejpam-4317	347	36	y	y	PROPN
ejpam-4317	347	37	is	be	AUX
ejpam-4317	347	38	a	a	DET
ejpam-4317	347	39	δθ	δθ	NOUN
ejpam-4317	347	40	-	-	PUNCT
ejpam-4317	347	41	i	i	NOUN
ejpam-4317	347	42	-	-	PUNCT
ejpam-4317	347	43	closed	close	VERB
ejpam-4317	347	44	set	set	NOUN
ejpam-4317	347	45	in	in	ADP
ejpam-4317	347	46	x.	x.	NOUN
ejpam-4317	347	47	proof	proof	NOUN
ejpam-4317	347	48	.	.	PUNCT
ejpam-4317	348	1	we	we	PRON
ejpam-4317	348	2	will	will	AUX
ejpam-4317	348	3	show	show	VERB
ejpam-4317	348	4	that	that	SCONJ
ejpam-4317	348	5	x	x	PRON
ejpam-4317	348	6	\a	\a	ADJ
ejpam-4317	348	7	is	be	AUX
ejpam-4317	348	8	a	a	DET
ejpam-4317	348	9	δθ	δθ	NOUN
ejpam-4317	348	10	-	-	PUNCT
ejpam-4317	348	11	i	i	NOUN
ejpam-4317	348	12	-	-	PUNCT
ejpam-4317	348	13	open	open	ADJ
ejpam-4317	348	14	set	set	NOUN
ejpam-4317	348	15	in	in	ADP
ejpam-4317	348	16	x.	x.	NOUN
ejpam-4317	348	17	let	let	VERB
ejpam-4317	348	18	x	x	SYM
ejpam-4317	348	19	∈	∈	PROPN
ejpam-4317	348	20	x	x	SYM
ejpam-4317	348	21	\a	\a	ADJ
ejpam-4317	348	22	.	.	PUNCT
ejpam-4317	349	1	then	then	ADV
ejpam-4317	349	2	,	,	PUNCT
ejpam-4317	349	3	f(x	f(x	PROPN
ejpam-4317	349	4	)	)	PUNCT
ejpam-4317	349	5	∈	∈	PROPN
ejpam-4317	349	6	a	a	PRON
ejpam-4317	349	7	and	and	CCONJ
ejpam-4317	349	8	x	x	SYM
ejpam-4317	349	9	/∈	/∈	INTJ
ejpam-4317	350	1	a	a	PRON
ejpam-4317	350	2	because	because	SCONJ
ejpam-4317	350	3	f	f	PROPN
ejpam-4317	350	4	is	be	AUX
ejpam-4317	350	5	a	a	DET
ejpam-4317	350	6	strongly	strongly	ADV
ejpam-4317	350	7	δθ	δθ	NOUN
ejpam-4317	350	8	-	-	PUNCT
ejpam-4317	350	9	i	i	NOUN
ejpam-4317	350	10	-	-	PUNCT
ejpam-4317	350	11	continuous	continuous	ADJ
ejpam-4317	350	12	retraction	retraction	NOUN
ejpam-4317	350	13	.	.	PUNCT
ejpam-4317	351	1	since	since	SCONJ
ejpam-4317	351	2	(	(	PUNCT
ejpam-4317	351	3	y	y	PROPN
ejpam-4317	351	4	,	,	PUNCT
ejpam-4317	351	5	σ	σ	PROPN
ejpam-4317	351	6	)	)	PUNCT
ejpam-4317	351	7	is	be	AUX
ejpam-4317	351	8	t2	t2	NOUN
ejpam-4317	351	9	,	,	PUNCT
ejpam-4317	351	10	there	there	PRON
ejpam-4317	351	11	exist	exist	VERB
ejpam-4317	351	12	two	two	NUM
ejpam-4317	351	13	disjoint	disjoint	ADJ
ejpam-4317	351	14	open	open	ADJ
ejpam-4317	351	15	sets	set	NOUN
ejpam-4317	351	16	v	v	NOUN
ejpam-4317	351	17	and	and	CCONJ
ejpam-4317	351	18	w	w	NOUN
ejpam-4317	351	19	in	in	ADP
ejpam-4317	351	20	y	y	NOUN
ejpam-4317	351	21	containing	contain	VERB
ejpam-4317	351	22	x	x	PROPN
ejpam-4317	351	23	and	and	CCONJ
ejpam-4317	351	24	f(x	f(x	PROPN
ejpam-4317	351	25	)	)	PUNCT
ejpam-4317	351	26	,	,	PUNCT
ejpam-4317	351	27	respectively	respectively	ADV
ejpam-4317	351	28	.	.	PUNCT
ejpam-4317	352	1	by	by	ADP
ejpam-4317	352	2	the	the	DET
ejpam-4317	352	3	strongly	strongly	ADV
ejpam-4317	352	4	δθ	δθ	NOUN
ejpam-4317	352	5	-	-	PUNCT
ejpam-4317	352	6	i	i	NOUN
ejpam-4317	352	7	-	-	PUNCT
ejpam-4317	352	8	continuity	continuity	NOUN
ejpam-4317	352	9	of	of	ADP
ejpam-4317	352	10	f	f	PROPN
ejpam-4317	352	11	,	,	PUNCT
ejpam-4317	352	12	we	we	PRON
ejpam-4317	352	13	have	have	AUX
ejpam-4317	352	14	f−1(w	f−1(w	ADV
ejpam-4317	352	15	)	)	PUNCT
ejpam-4317	352	16	is	be	AUX
ejpam-4317	352	17	a	a	DET
ejpam-4317	352	18	δθ	δθ	NOUN
ejpam-4317	352	19	-	-	PUNCT
ejpam-4317	352	20	i	i	NOUN
ejpam-4317	352	21	-	-	PUNCT
ejpam-4317	352	22	open	open	ADJ
ejpam-4317	352	23	set	set	NOUN
ejpam-4317	352	24	in	in	ADP
ejpam-4317	352	25	x	x	PUNCT
ejpam-4317	352	26	containing	contain	VERB
ejpam-4317	352	27	x.	x.	NOUN
ejpam-4317	352	28	thus	thus	ADV
ejpam-4317	352	29	,	,	PUNCT
ejpam-4317	352	30	there	there	PRON
ejpam-4317	352	31	exists	exist	VERB
ejpam-4317	352	32	an	an	DET
ejpam-4317	352	33	open	open	ADJ
ejpam-4317	352	34	set	set	NOUN
ejpam-4317	352	35	g	g	NOUN
ejpam-4317	352	36	in	in	ADP
ejpam-4317	352	37	x	x	PUNCT
ejpam-4317	352	38	such	such	ADJ
ejpam-4317	352	39	that	that	SCONJ
ejpam-4317	352	40	x	x	SYM
ejpam-4317	352	41	∈	∈	PROPN
ejpam-4317	352	42	g	g	PROPN
ejpam-4317	352	43	⊂	⊂	PROPN
ejpam-4317	352	44	δcl?(g	δcl?(g	PROPN
ejpam-4317	352	45	)	)	PUNCT
ejpam-4317	353	1	⊂	⊂	PROPN
ejpam-4317	353	2	f−1(w	f−1(w	PROPN
ejpam-4317	353	3	)	)	PUNCT
ejpam-4317	353	4	.	.	PUNCT
ejpam-4317	354	1	let	let	VERB
ejpam-4317	354	2	us	we	PRON
ejpam-4317	354	3	observe	observe	VERB
ejpam-4317	354	4	that	that	SCONJ
ejpam-4317	354	5	u	u	NOUN
ejpam-4317	354	6	=	=	PROPN
ejpam-4317	354	7	g	g	PROPN
ejpam-4317	354	8	∩	∩	NOUN
ejpam-4317	354	9	v	v	NOUN
ejpam-4317	354	10	is	be	AUX
ejpam-4317	354	11	an	an	DET
ejpam-4317	354	12	open	open	ADJ
ejpam-4317	354	13	set	set	NOUN
ejpam-4317	354	14	in	in	ADP
ejpam-4317	354	15	x	x	PUNCT
ejpam-4317	354	16	containing	contain	VERB
ejpam-4317	354	17	x.	x.	NOUN
ejpam-4317	354	18	we	we	PRON
ejpam-4317	354	19	affirm	affirm	VERB
ejpam-4317	354	20	that	that	SCONJ
ejpam-4317	354	21	δcl?(u	δcl?(u	PROPN
ejpam-4317	354	22	)	)	PUNCT
ejpam-4317	355	1	⊂	⊂	PROPN
ejpam-4317	356	1	x	x	X
ejpam-4317	356	2	\	\	PROPN
ejpam-4317	356	3	a	a	PRON
ejpam-4317	356	4	and	and	CCONJ
ejpam-4317	356	5	so	so	ADV
ejpam-4317	356	6	,	,	PUNCT
ejpam-4317	356	7	x	x	SYM
ejpam-4317	356	8	\	\	PROPN
ejpam-4317	356	9	a	a	PRON
ejpam-4317	356	10	is	be	AUX
ejpam-4317	356	11	a	a	DET
ejpam-4317	356	12	δθ	δθ	NOUN
ejpam-4317	356	13	-	-	PUNCT
ejpam-4317	356	14	i	i	NOUN
ejpam-4317	356	15	-	-	PUNCT
ejpam-4317	356	16	open	open	ADJ
ejpam-4317	356	17	set	set	NOUN
ejpam-4317	356	18	in	in	ADP
ejpam-4317	356	19	x.	x.	NOUN
ejpam-4317	356	20	indeed	indeed	ADV
ejpam-4317	356	21	,	,	PUNCT
ejpam-4317	356	22	if	if	SCONJ
ejpam-4317	356	23	y	y	PROPN
ejpam-4317	356	24	∈	∈	PROPN
ejpam-4317	356	25	δcl?(u	δcl?(u	PROPN
ejpam-4317	356	26	)	)	PUNCT
ejpam-4317	356	27	then	then	ADV
ejpam-4317	356	28	y	y	PROPN
ejpam-4317	356	29	∈	∈	PROPN
ejpam-4317	356	30	δcl?(g	δcl?(g	NOUN
ejpam-4317	356	31	)	)	PUNCT
ejpam-4317	357	1	⊂	⊂	PROPN
ejpam-4317	357	2	f−1(w	f−1(w	PROPN
ejpam-4317	357	3	)	)	PUNCT
ejpam-4317	357	4	,	,	PUNCT
ejpam-4317	357	5	which	which	PRON
ejpam-4317	357	6	implies	imply	VERB
ejpam-4317	357	7	that	that	SCONJ
ejpam-4317	357	8	f(y	f(y	NOUN
ejpam-4317	357	9	)	)	PUNCT
ejpam-4317	357	10	∈	∈	PROPN
ejpam-4317	357	11	w	w	NOUN
ejpam-4317	357	12	,	,	PUNCT
ejpam-4317	357	13	and	and	CCONJ
ejpam-4317	357	14	as	as	ADP
ejpam-4317	357	15	v	v	NOUN
ejpam-4317	357	16	and	and	CCONJ
ejpam-4317	357	17	w	w	NOUN
ejpam-4317	357	18	are	be	AUX
ejpam-4317	357	19	disjoint	disjoint	NOUN
ejpam-4317	357	20	sets	set	NOUN
ejpam-4317	358	1	,	,	PUNCT
ejpam-4317	358	2	it	it	PRON
ejpam-4317	358	3	follows	follow	VERB
ejpam-4317	358	4	that	that	SCONJ
ejpam-4317	358	5	f(y	f(y	NOUN
ejpam-4317	358	6	)	)	PUNCT
ejpam-4317	358	7	/∈	/∈	PUNCT
ejpam-4317	359	1	v	v	NOUN
ejpam-4317	359	2	,	,	PUNCT
ejpam-4317	359	3	but	but	CCONJ
ejpam-4317	359	4	since	since	SCONJ
ejpam-4317	359	5	y	y	PROPN
ejpam-4317	359	6	∈	∈	PROPN
ejpam-4317	359	7	v	v	NOUN
ejpam-4317	359	8	,	,	PUNCT
ejpam-4317	359	9	we	we	PRON
ejpam-4317	359	10	get	get	VERB
ejpam-4317	359	11	that	that	DET
ejpam-4317	359	12	y	y	PROPN
ejpam-4317	359	13	6=	6=	SYM
ejpam-4317	359	14	f(y	f(y	PROPN
ejpam-4317	359	15	)	)	PUNCT
ejpam-4317	359	16	and	and	CCONJ
ejpam-4317	359	17	hence	hence	ADV
ejpam-4317	359	18	,	,	PUNCT
ejpam-4317	359	19	y	y	PROPN
ejpam-4317	359	20	/∈	/∈	PUNCT
ejpam-4317	359	21	a.	a.	NOUN
ejpam-4317	359	22	definition	definition	NOUN
ejpam-4317	359	23	8	8	NUM
ejpam-4317	359	24	.	.	PUNCT
ejpam-4317	360	1	the	the	DET
ejpam-4317	360	2	graph	graph	NOUN
ejpam-4317	360	3	g(f	g(f	PROPN
ejpam-4317	360	4	)	)	PUNCT
ejpam-4317	360	5	of	of	ADP
ejpam-4317	360	6	a	a	DET
ejpam-4317	360	7	function	function	NOUN
ejpam-4317	360	8	f	f	NOUN
ejpam-4317	360	9	:	:	PUNCT
ejpam-4317	360	10	(	(	PUNCT
ejpam-4317	360	11	x	x	X
ejpam-4317	360	12	,	,	PUNCT
ejpam-4317	360	13	τ	τ	PROPN
ejpam-4317	360	14	,	,	PUNCT
ejpam-4317	360	15	i	i	NOUN
ejpam-4317	360	16	)	)	PUNCT
ejpam-4317	360	17	→	→	SYM
ejpam-4317	360	18	(	(	PUNCT
ejpam-4317	360	19	y	y	PROPN
ejpam-4317	360	20	,	,	PUNCT
ejpam-4317	360	21	σ	σ	PROPN
ejpam-4317	360	22	)	)	PUNCT
ejpam-4317	360	23	is	be	AUX
ejpam-4317	360	24	said	say	VERB
ejpam-4317	360	25	to	to	PART
ejpam-4317	360	26	be	be	AUX
ejpam-4317	360	27	strongly	strongly	ADV
ejpam-4317	360	28	δθ	δθ	NOUN
ejpam-4317	360	29	-	-	PUNCT
ejpam-4317	360	30	i	i	NOUN
ejpam-4317	360	31	-	-	PUNCT
ejpam-4317	360	32	closed	close	VERB
ejpam-4317	360	33	with	with	ADP
ejpam-4317	360	34	respect	respect	NOUN
ejpam-4317	360	35	to	to	ADP
ejpam-4317	360	36	x	x	SYM
ejpam-4317	360	37	,	,	PUNCT
ejpam-4317	360	38	if	if	SCONJ
ejpam-4317	360	39	for	for	ADP
ejpam-4317	360	40	each	each	DET
ejpam-4317	360	41	(	(	PUNCT
ejpam-4317	360	42	x	x	NOUN
ejpam-4317	360	43	,	,	PUNCT
ejpam-4317	360	44	y	y	NOUN
ejpam-4317	360	45	)	)	PUNCT
ejpam-4317	360	46	∈	∈	PROPN
ejpam-4317	360	47	(	(	PUNCT
ejpam-4317	360	48	x	x	SYM
ejpam-4317	360	49	×	×	PROPN
ejpam-4317	360	50	y	y	PROPN
ejpam-4317	360	51	)	)	PUNCT
ejpam-4317	360	52	\	\	PROPN
ejpam-4317	360	53	g(f	g(f	PROPN
ejpam-4317	360	54	)	)	PUNCT
ejpam-4317	360	55	,	,	PUNCT
ejpam-4317	360	56	there	there	PRON
ejpam-4317	360	57	exist	exist	VERB
ejpam-4317	360	58	two	two	NUM
ejpam-4317	360	59	open	open	ADJ
ejpam-4317	360	60	sets	set	NOUN
ejpam-4317	360	61	u	u	NOUN
ejpam-4317	360	62	and	and	CCONJ
ejpam-4317	360	63	v	v	ADP
ejpam-4317	360	64	containing	contain	VERB
ejpam-4317	360	65	x	x	PROPN
ejpam-4317	360	66	and	and	CCONJ
ejpam-4317	360	67	y	y	PROPN
ejpam-4317	360	68	,	,	PUNCT
ejpam-4317	360	69	respectively	respectively	ADV
ejpam-4317	360	70	,	,	PUNCT
ejpam-4317	360	71	such	such	ADJ
ejpam-4317	360	72	that	that	SCONJ
ejpam-4317	360	73	(	(	PUNCT
ejpam-4317	360	74	δcl?(u)×	δcl?(u)×	PART
ejpam-4317	360	75	v	v	NOUN
ejpam-4317	360	76	)	)	PUNCT
ejpam-4317	360	77	∩g(f	∩g(f	PROPN
ejpam-4317	360	78	)	)	PUNCT
ejpam-4317	361	1	=	=	PUNCT
ejpam-4317	362	1	∅.	∅.	PRON
ejpam-4317	362	2	lemma	lemma	PROPN
ejpam-4317	362	3	3	3	NUM
ejpam-4317	362	4	.	.	PUNCT
ejpam-4317	363	1	the	the	DET
ejpam-4317	363	2	graph	graph	NOUN
ejpam-4317	363	3	g(f	g(f	PROPN
ejpam-4317	363	4	)	)	PUNCT
ejpam-4317	363	5	of	of	ADP
ejpam-4317	363	6	a	a	DET
ejpam-4317	363	7	function	function	NOUN
ejpam-4317	363	8	f	f	NOUN
ejpam-4317	363	9	:	:	PUNCT
ejpam-4317	363	10	(	(	PUNCT
ejpam-4317	363	11	x	x	X
ejpam-4317	363	12	,	,	PUNCT
ejpam-4317	363	13	τ	τ	PROPN
ejpam-4317	363	14	,	,	PUNCT
ejpam-4317	363	15	i	i	NOUN
ejpam-4317	363	16	)	)	PUNCT
ejpam-4317	363	17	→	→	SYM
ejpam-4317	363	18	(	(	PUNCT
ejpam-4317	363	19	y	y	PROPN
ejpam-4317	363	20	,	,	PUNCT
ejpam-4317	363	21	σ	σ	PROPN
ejpam-4317	363	22	)	)	PUNCT
ejpam-4317	363	23	is	be	AUX
ejpam-4317	363	24	strongly	strongly	ADV
ejpam-4317	363	25	δθ	δθ	NOUN
ejpam-4317	363	26	-	-	PUNCT
ejpam-4317	363	27	i	i	NOUN
ejpam-4317	363	28	-	-	PUNCT
ejpam-4317	363	29	closed	close	VERB
ejpam-4317	363	30	with	with	ADP
ejpam-4317	363	31	respect	respect	NOUN
ejpam-4317	363	32	to	to	ADP
ejpam-4317	363	33	x	x	PUNCT
ejpam-4317	363	34	if	if	SCONJ
ejpam-4317	364	1	and	and	CCONJ
ejpam-4317	364	2	only	only	ADV
ejpam-4317	364	3	if	if	SCONJ
ejpam-4317	364	4	for	for	ADP
ejpam-4317	364	5	each	each	DET
ejpam-4317	364	6	(	(	PUNCT
ejpam-4317	364	7	x	x	NOUN
ejpam-4317	364	8	,	,	PUNCT
ejpam-4317	364	9	y	y	NOUN
ejpam-4317	364	10	)	)	PUNCT
ejpam-4317	364	11	∈	∈	PROPN
ejpam-4317	364	12	(	(	PUNCT
ejpam-4317	364	13	x	x	SYM
ejpam-4317	364	14	×	×	PROPN
ejpam-4317	364	15	y	y	PROPN
ejpam-4317	364	16	)	)	PUNCT
ejpam-4317	364	17	\g(f	\g(f	PROPN
ejpam-4317	364	18	)	)	PUNCT
ejpam-4317	364	19	,	,	PUNCT
ejpam-4317	364	20	there	there	PRON
ejpam-4317	364	21	exist	exist	VERB
ejpam-4317	364	22	two	two	NUM
ejpam-4317	364	23	open	open	ADJ
ejpam-4317	364	24	sets	set	NOUN
ejpam-4317	364	25	u	u	NOUN
ejpam-4317	364	26	and	and	CCONJ
ejpam-4317	364	27	v	v	ADP
ejpam-4317	364	28	containing	contain	VERB
ejpam-4317	364	29	x	x	PROPN
ejpam-4317	364	30	and	and	CCONJ
ejpam-4317	364	31	y	y	PROPN
ejpam-4317	364	32	,	,	PUNCT
ejpam-4317	364	33	respectively	respectively	ADV
ejpam-4317	364	34	,	,	PUNCT
ejpam-4317	364	35	such	such	ADJ
ejpam-4317	364	36	that	that	DET
ejpam-4317	364	37	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	364	38	)	)	PUNCT
ejpam-4317	364	39	)	)	PUNCT
ejpam-4317	365	1	∩	∩	NOUN
ejpam-4317	365	2	v	v	X
ejpam-4317	365	3	=	=	SYM
ejpam-4317	365	4	∅.	∅.	NOUN
ejpam-4317	365	5	theorem	theorem	VERB
ejpam-4317	365	6	11	11	NUM
ejpam-4317	365	7	.	.	PUNCT
ejpam-4317	366	1	if	if	SCONJ
ejpam-4317	366	2	f	f	PROPN
ejpam-4317	366	3	:	:	PUNCT
ejpam-4317	366	4	(	(	PUNCT
ejpam-4317	366	5	x	x	X
ejpam-4317	366	6	,	,	PUNCT
ejpam-4317	366	7	τ	τ	PROPN
ejpam-4317	366	8	,	,	PUNCT
ejpam-4317	366	9	i	i	NOUN
ejpam-4317	366	10	)	)	PUNCT
ejpam-4317	366	11	→	→	SYM
ejpam-4317	366	12	(	(	PUNCT
ejpam-4317	366	13	y	y	PROPN
ejpam-4317	366	14	,	,	PUNCT
ejpam-4317	366	15	σ	σ	PROPN
ejpam-4317	366	16	)	)	PUNCT
ejpam-4317	366	17	is	be	AUX
ejpam-4317	366	18	strongly	strongly	ADV
ejpam-4317	366	19	δθ	δθ	NOUN
ejpam-4317	366	20	-	-	PUNCT
ejpam-4317	366	21	i	i	NOUN
ejpam-4317	366	22	-	-	PUNCT
ejpam-4317	366	23	continuous	continuous	ADJ
ejpam-4317	366	24	and	and	CCONJ
ejpam-4317	366	25	(	(	PUNCT
ejpam-4317	366	26	y	y	PROPN
ejpam-4317	366	27	,	,	PUNCT
ejpam-4317	366	28	σ	σ	PROPN
ejpam-4317	366	29	)	)	PUNCT
ejpam-4317	366	30	is	be	AUX
ejpam-4317	366	31	t2	t2	NOUN
ejpam-4317	366	32	,	,	PUNCT
ejpam-4317	366	33	then	then	ADV
ejpam-4317	366	34	g(f	g(f	PROPN
ejpam-4317	366	35	)	)	PUNCT
ejpam-4317	367	1	is	be	AUX
ejpam-4317	367	2	strongly	strongly	ADV
ejpam-4317	367	3	δθ	δθ	NOUN
ejpam-4317	367	4	-	-	PUNCT
ejpam-4317	367	5	i	i	NOUN
ejpam-4317	367	6	-	-	PUNCT
ejpam-4317	367	7	closed	close	VERB
ejpam-4317	367	8	with	with	ADP
ejpam-4317	367	9	respect	respect	NOUN
ejpam-4317	367	10	to	to	ADP
ejpam-4317	367	11	x.	x.	NOUN
ejpam-4317	367	12	proof	proof	NOUN
ejpam-4317	367	13	.	.	PUNCT
ejpam-4317	368	1	let	let	VERB
ejpam-4317	368	2	(	(	PUNCT
ejpam-4317	368	3	x	x	NOUN
ejpam-4317	368	4	,	,	PUNCT
ejpam-4317	368	5	y	y	NOUN
ejpam-4317	368	6	)	)	PUNCT
ejpam-4317	368	7	∈	∈	PROPN
ejpam-4317	368	8	(	(	PUNCT
ejpam-4317	368	9	x	x	SYM
ejpam-4317	368	10	×	×	PROPN
ejpam-4317	368	11	y	y	PROPN
ejpam-4317	368	12	)	)	PUNCT
ejpam-4317	369	1	\	\	PROPN
ejpam-4317	369	2	g(f	g(f	PROPN
ejpam-4317	369	3	)	)	PUNCT
ejpam-4317	369	4	.	.	PUNCT
ejpam-4317	370	1	then	then	ADV
ejpam-4317	370	2	,	,	PUNCT
ejpam-4317	370	3	f(x	f(x	PROPN
ejpam-4317	370	4	)	)	PUNCT
ejpam-4317	370	5	6=	6=	ADP
ejpam-4317	371	1	y	y	PROPN
ejpam-4317	371	2	and	and	CCONJ
ejpam-4317	371	3	as	as	ADP
ejpam-4317	371	4	(	(	PUNCT
ejpam-4317	371	5	y	y	PROPN
ejpam-4317	371	6	,	,	PUNCT
ejpam-4317	371	7	σ	σ	PROPN
ejpam-4317	371	8	)	)	PUNCT
ejpam-4317	371	9	is	be	AUX
ejpam-4317	371	10	t2	t2	NOUN
ejpam-4317	371	11	,	,	PUNCT
ejpam-4317	371	12	there	there	PRON
ejpam-4317	371	13	exist	exist	VERB
ejpam-4317	371	14	open	open	ADJ
ejpam-4317	371	15	sets	set	NOUN
ejpam-4317	371	16	v	v	NOUN
ejpam-4317	371	17	and	and	CCONJ
ejpam-4317	371	18	w	w	NOUN
ejpam-4317	371	19	in	in	ADP
ejpam-4317	371	20	y	y	NOUN
ejpam-4317	371	21	containing	contain	VERB
ejpam-4317	371	22	f(x	f(x	PROPN
ejpam-4317	371	23	)	)	PUNCT
ejpam-4317	371	24	and	and	CCONJ
ejpam-4317	371	25	y	y	PROPN
ejpam-4317	371	26	,	,	PUNCT
ejpam-4317	371	27	respectively	respectively	ADV
ejpam-4317	371	28	,	,	PUNCT
ejpam-4317	371	29	such	such	ADJ
ejpam-4317	371	30	that	that	DET
ejpam-4317	371	31	v	v	NOUN
ejpam-4317	371	32	∩w	∩w	NOUN
ejpam-4317	372	1	=	=	PUNCT
ejpam-4317	372	2	∅.	∅.	NOUN
ejpam-4317	372	3	since	since	SCONJ
ejpam-4317	372	4	f	f	PROPN
ejpam-4317	372	5	is	be	AUX
ejpam-4317	372	6	strongly	strongly	ADV
ejpam-4317	372	7	δθ	δθ	NOUN
ejpam-4317	372	8	-	-	PUNCT
ejpam-4317	372	9	i	i	NOUN
ejpam-4317	372	10	-	-	PUNCT
ejpam-4317	372	11	continuous	continuous	ADJ
ejpam-4317	372	12	,	,	PUNCT
ejpam-4317	372	13	there	there	PRON
ejpam-4317	372	14	exists	exist	VERB
ejpam-4317	372	15	an	an	DET
ejpam-4317	372	16	open	open	ADJ
ejpam-4317	372	17	sets	set	VERB
ejpam-4317	372	18	u	u	NOUN
ejpam-4317	372	19	in	in	ADP
ejpam-4317	372	20	x	x	PUNCT
ejpam-4317	372	21	containing	contain	VERB
ejpam-4317	372	22	x	x	PUNCT
ejpam-4317	372	23	such	such	ADJ
ejpam-4317	372	24	that	that	DET
ejpam-4317	372	25	f(δcl?(u	f(δcl?(u	NOUN
ejpam-4317	372	26	)	)	PUNCT
ejpam-4317	372	27	)	)	PUNCT
ejpam-4317	373	1	⊂	⊂	PROPN
ejpam-4317	373	2	v	v	X
ejpam-4317	373	3	,	,	PUNCT
ejpam-4317	373	4	which	which	PRON
ejpam-4317	373	5	implies	imply	VERB
ejpam-4317	373	6	that	that	SCONJ
ejpam-4317	373	7	f(δcl?(u))∩w	f(δcl?(u))∩w	ADJ
ejpam-4317	373	8	=	=	PUNCT
ejpam-4317	373	9	∅.	∅.	NOUN
ejpam-4317	373	10	by	by	ADP
ejpam-4317	373	11	lemma	lemma	PROPN
ejpam-4317	373	12	3	3	NUM
ejpam-4317	373	13	,	,	PUNCT
ejpam-4317	373	14	we	we	PRON
ejpam-4317	373	15	conclude	conclude	VERB
ejpam-4317	373	16	that	that	SCONJ
ejpam-4317	373	17	g(f	g(f	PROPN
ejpam-4317	373	18	)	)	PUNCT
ejpam-4317	373	19	is	be	AUX
ejpam-4317	373	20	strongly	strongly	ADV
ejpam-4317	373	21	δθ	δθ	NOUN
ejpam-4317	373	22	-	-	PUNCT
ejpam-4317	373	23	i	i	NOUN
ejpam-4317	373	24	-	-	PUNCT
ejpam-4317	373	25	closed	close	VERB
ejpam-4317	373	26	with	with	ADP
ejpam-4317	373	27	respect	respect	NOUN
ejpam-4317	373	28	to	to	ADP
ejpam-4317	373	29	x.	x.	PROPN
ejpam-4317	373	30	4	4	NUM
ejpam-4317	373	31	.	.	PUNCT
ejpam-4317	373	32	conclusion	conclusion	VERB
ejpam-4317	373	33	the	the	DET
ejpam-4317	373	34	notion	notion	NOUN
ejpam-4317	373	35	of	of	ADP
ejpam-4317	373	36	a	a	DET
ejpam-4317	373	37	continuous	continuous	ADJ
ejpam-4317	373	38	function	function	NOUN
ejpam-4317	373	39	and	and	CCONJ
ejpam-4317	373	40	its	its	PRON
ejpam-4317	373	41	generalizations	generalization	NOUN
ejpam-4317	373	42	have	have	VERB
ejpam-4317	373	43	important	important	ADJ
ejpam-4317	373	44	applications	application	NOUN
ejpam-4317	373	45	in	in	ADP
ejpam-4317	373	46	various	various	ADJ
ejpam-4317	373	47	areas	area	NOUN
ejpam-4317	373	48	of	of	ADP
ejpam-4317	373	49	mathematics	mathematic	NOUN
ejpam-4317	373	50	and	and	CCONJ
ejpam-4317	373	51	related	relate	VERB
ejpam-4317	373	52	sciences	science	NOUN
ejpam-4317	373	53	;	;	PUNCT
ejpam-4317	373	54	for	for	ADP
ejpam-4317	373	55	example	example	NOUN
ejpam-4317	373	56	,	,	PUNCT
ejpam-4317	373	57	this	this	DET
ejpam-4317	373	58	notion	notion	NOUN
ejpam-4317	373	59	is	be	AUX
ejpam-4317	373	60	widely	widely	ADV
ejpam-4317	373	61	used	use	VERB
ejpam-4317	373	62	in	in	ADP
ejpam-4317	373	63	physics	physics	NOUN
ejpam-4317	373	64	and	and	CCONJ
ejpam-4317	373	65	information	information	NOUN
ejpam-4317	373	66	systems	system	NOUN
ejpam-4317	373	67	,	,	PUNCT
ejpam-4317	373	68	as	as	SCONJ
ejpam-4317	373	69	described	describe	VERB
ejpam-4317	373	70	in	in	ADP
ejpam-4317	373	71	[	[	X
ejpam-4317	373	72	4	4	NUM
ejpam-4317	373	73	]	]	PUNCT
ejpam-4317	373	74	.	.	PUNCT
ejpam-4317	374	1	in	in	ADP
ejpam-4317	374	2	this	this	DET
ejpam-4317	374	3	article	article	NOUN
ejpam-4317	374	4	we	we	PRON
ejpam-4317	374	5	have	have	AUX
ejpam-4317	374	6	studied	study	VERB
ejpam-4317	374	7	a	a	DET
ejpam-4317	374	8	generalization	generalization	NOUN
ejpam-4317	374	9	of	of	ADP
ejpam-4317	374	10	continuous	continuous	ADJ
ejpam-4317	374	11	functions	function	NOUN
ejpam-4317	374	12	using	use	VERB
ejpam-4317	374	13	concepts	concept	NOUN
ejpam-4317	374	14	recently	recently	ADV
ejpam-4317	374	15	derived	derive	VERB
ejpam-4317	374	16	from	from	ADP
ejpam-4317	374	17	the	the	DET
ejpam-4317	374	18	theory	theory	NOUN
ejpam-4317	374	19	of	of	ADP
ejpam-4317	374	20	topological	topological	ADJ
ejpam-4317	374	21	ideals	ideal	NOUN
ejpam-4317	374	22	,	,	PUNCT
ejpam-4317	374	23	such	such	ADJ
ejpam-4317	374	24	as	as	ADP
ejpam-4317	374	25	δθ	δθ	NOUN
ejpam-4317	374	26	-	-	PUNCT
ejpam-4317	374	27	i	i	NOUN
ejpam-4317	374	28	-	-	PUNCT
ejpam-4317	374	29	open	open	ADJ
ejpam-4317	374	30	set	set	NOUN
ejpam-4317	374	31	and	and	CCONJ
ejpam-4317	374	32	δθ	δθ	NOUN
ejpam-4317	374	33	-	-	PUNCT
ejpam-4317	374	34	i	i	NOUN
ejpam-4317	374	35	-	-	PUNCT
ejpam-4317	374	36	closure	closure	NOUN
ejpam-4317	374	37	operator	operator	NOUN
ejpam-4317	374	38	.	.	PUNCT
ejpam-4317	375	1	this	this	DET
ejpam-4317	375	2	class	class	NOUN
ejpam-4317	375	3	of	of	ADP
ejpam-4317	375	4	functions	function	NOUN
ejpam-4317	375	5	can	can	AUX
ejpam-4317	375	6	have	have	VERB
ejpam-4317	375	7	applications	application	NOUN
ejpam-4317	375	8	in	in	ADP
ejpam-4317	375	9	computation	computation	NOUN
ejpam-4317	375	10	and	and	CCONJ
ejpam-4317	375	11	image	image	NOUN
ejpam-4317	375	12	design	design	NOUN
ejpam-4317	375	13	,	,	PUNCT
ejpam-4317	375	14	especially	especially	ADV
ejpam-4317	375	15	in	in	ADP
ejpam-4317	375	16	digital	digital	ADJ
ejpam-4317	375	17	topology	topology	NOUN
ejpam-4317	375	18	,	,	PUNCT
ejpam-4317	375	19	as	as	ADV
ejpam-4317	375	20	well	well	ADV
ejpam-4317	375	21	as	as	ADP
ejpam-4317	375	22	in	in	ADP
ejpam-4317	375	23	information	information	NOUN
ejpam-4317	375	24	systems	system	NOUN
ejpam-4317	375	25	and	and	CCONJ
ejpam-4317	375	26	quantum	quantum	NOUN
ejpam-4317	375	27	physics	physics	NOUN
ejpam-4317	375	28	.	.	PUNCT
ejpam-4317	376	1	on	on	ADP
ejpam-4317	376	2	the	the	DET
ejpam-4317	376	3	other	other	ADJ
ejpam-4317	376	4	hand	hand	NOUN
ejpam-4317	376	5	,	,	PUNCT
ejpam-4317	376	6	the	the	DET
ejpam-4317	376	7	notions	notion	NOUN
ejpam-4317	376	8	discussed	discuss	VERB
ejpam-4317	376	9	here	here	ADV
ejpam-4317	376	10	could	could	AUX
ejpam-4317	376	11	be	be	AUX
ejpam-4317	376	12	extended	extend	VERB
ejpam-4317	376	13	to	to	ADP
ejpam-4317	376	14	contexts	context	NOUN
ejpam-4317	376	15	such	such	ADJ
ejpam-4317	376	16	as	as	ADP
ejpam-4317	376	17	a	a	DET
ejpam-4317	376	18	topological	topological	ADJ
ejpam-4317	376	19	space	space	NOUN
ejpam-4317	376	20	endowed	endow	VERB
ejpam-4317	376	21	with	with	ADP
ejpam-4317	376	22	a	a	DET
ejpam-4317	376	23	hereditary	hereditary	ADJ
ejpam-4317	376	24	class	class	NOUN
ejpam-4317	376	25	,	,	PUNCT
ejpam-4317	376	26	fuzzy	fuzzy	ADJ
ejpam-4317	376	27	ideal	ideal	ADJ
ejpam-4317	376	28	topological	topological	ADJ
ejpam-4317	376	29	spaces	space	NOUN
ejpam-4317	376	30	and	and	CCONJ
ejpam-4317	376	31	soft	soft	ADJ
ejpam-4317	376	32	ideal	ideal	ADJ
ejpam-4317	376	33	topological	topological	ADJ
ejpam-4317	376	34	spaces	space	NOUN
ejpam-4317	376	35	,	,	PUNCT
ejpam-4317	376	36	where	where	SCONJ
ejpam-4317	376	37	the	the	DET
ejpam-4317	376	38	results	result	NOUN
ejpam-4317	376	39	could	could	AUX
ejpam-4317	376	40	be	be	AUX
ejpam-4317	376	41	used	use	VERB
ejpam-4317	376	42	in	in	ADP
ejpam-4317	376	43	problems	problem	NOUN
ejpam-4317	376	44	dealing	deal	VERB
ejpam-4317	376	45	with	with	ADP
ejpam-4317	376	46	uncertainty	uncertainty	NOUN
ejpam-4317	376	47	and	and	CCONJ
ejpam-4317	376	48	vagueness	vagueness	NOUN
ejpam-4317	376	49	.	.	PUNCT
ejpam-4317	377	1	references	reference	NOUN
ejpam-4317	377	2	452	452	NUM
ejpam-4317	377	3	acknowledgements	acknowledgement	NOUN
ejpam-4317	377	4	the	the	DET
ejpam-4317	377	5	authors	author	NOUN
ejpam-4317	377	6	are	be	AUX
ejpam-4317	377	7	very	very	ADV
ejpam-4317	377	8	grateful	grateful	ADJ
ejpam-4317	377	9	to	to	ADP
ejpam-4317	377	10	the	the	DET
ejpam-4317	377	11	four	four	NUM
ejpam-4317	377	12	referees	referee	NOUN
ejpam-4317	377	13	for	for	ADP
ejpam-4317	377	14	their	their	PRON
ejpam-4317	377	15	valuable	valuable	ADJ
ejpam-4317	377	16	comments	comment	NOUN
ejpam-4317	377	17	and	and	CCONJ
ejpam-4317	377	18	suggestions	suggestion	NOUN
ejpam-4317	377	19	that	that	PRON
ejpam-4317	377	20	helped	help	VERB
ejpam-4317	377	21	improve	improve	VERB
ejpam-4317	377	22	the	the	DET
ejpam-4317	377	23	quality	quality	NOUN
ejpam-4317	377	24	of	of	ADP
ejpam-4317	377	25	this	this	DET
ejpam-4317	377	26	article	article	NOUN
ejpam-4317	377	27	.	.	PUNCT
ejpam-4317	378	1	references	reference	NOUN
ejpam-4317	378	2	[	[	X
ejpam-4317	378	3	1	1	NUM
ejpam-4317	378	4	]	]	PUNCT
ejpam-4317	378	5	a.	a.	NOUN
ejpam-4317	378	6	açikgöz	açikgöz	PROPN
ejpam-4317	378	7	,	,	PUNCT
ejpam-4317	378	8	t.	t.	PROPN
ejpam-4317	378	9	noiri	noiri	PROPN
ejpam-4317	378	10	and	and	CCONJ
ejpam-4317	378	11	s.	s.	PROPN
ejpam-4317	378	12	yüksel	yüksel	PROPN
ejpam-4317	378	13	.	.	PUNCT
ejpam-4317	379	1	a	a	DET
ejpam-4317	379	2	decomposition	decomposition	NOUN
ejpam-4317	379	3	of	of	ADP
ejpam-4317	379	4	continuity	continuity	NOUN
ejpam-4317	379	5	in	in	ADP
ejpam-4317	379	6	ideal	ideal	ADJ
ejpam-4317	379	7	topological	topological	ADJ
ejpam-4317	379	8	spaces	space	NOUN
ejpam-4317	379	9	.	.	PUNCT
ejpam-4317	380	1	acta	acta	PROPN
ejpam-4317	380	2	math	math	PROPN
ejpam-4317	380	3	.	.	PUNCT
ejpam-4317	381	1	hungar	hungar	PROPN
ejpam-4317	381	2	.	.	PUNCT
ejpam-4317	381	3	,	,	PUNCT
ejpam-4317	382	1	105(4):285–289	105(4):285–289	NUM
ejpam-4317	382	2	,	,	PUNCT
ejpam-4317	382	3	2004	2004	NUM
ejpam-4317	382	4	.	.	PUNCT
ejpam-4317	383	1	[	[	X
ejpam-4317	383	2	2	2	NUM
ejpam-4317	383	3	]	]	PUNCT
ejpam-4317	383	4	a.	a.	PROPN
ejpam-4317	383	5	al	al	PROPN
ejpam-4317	383	6	-	-	PUNCT
ejpam-4317	383	7	omari	omari	PROPN
ejpam-4317	383	8	and	and	CCONJ
ejpam-4317	383	9	t.	t.	PROPN
ejpam-4317	383	10	noiri	noiri	PROPN
ejpam-4317	383	11	.	.	PUNCT
ejpam-4317	384	1	on	on	ADP
ejpam-4317	384	2	θ(i	θ(i	PROPN
ejpam-4317	384	3	,	,	PUNCT
ejpam-4317	384	4	j)-continuous	j)-continuous	ADJ
ejpam-4317	384	5	functions	function	NOUN
ejpam-4317	384	6	.	.	PUNCT
ejpam-4317	385	1	rend	rend	VERB
ejpam-4317	385	2	.	.	PUNCT
ejpam-4317	386	1	istit	istit	PROPN
ejpam-4317	386	2	.	.	PUNCT
ejpam-4317	387	1	mat	mat	NOUN
ejpam-4317	387	2	.	.	PROPN
ejpam-4317	387	3	univ	univ	PROPN
ejpam-4317	387	4	.	.	PUNCT
ejpam-4317	387	5	trieste	trieste	PROPN
ejpam-4317	387	6	,	,	PUNCT
ejpam-4317	387	7	44:399–411	44:399–411	PROPN
ejpam-4317	387	8	,	,	PUNCT
ejpam-4317	387	9	2012	2012	NUM
ejpam-4317	387	10	.	.	PUNCT
ejpam-4317	388	1	[	[	X
ejpam-4317	388	2	3	3	NUM
ejpam-4317	388	3	]	]	X
ejpam-4317	388	4	a.	a.	NOUN
ejpam-4317	388	5	guevara	guevara	PROPN
ejpam-4317	388	6	,	,	PUNCT
ejpam-4317	388	7	j.	j.	PROPN
ejpam-4317	388	8	sanabria	sanabria	PROPN
ejpam-4317	388	9	and	and	CCONJ
ejpam-4317	388	10	e.	e.	PROPN
ejpam-4317	388	11	rosas	rosas	PROPN
ejpam-4317	388	12	.	.	PUNCT
ejpam-4317	389	1	s	s	X
ejpam-4317	389	2	-	-	PUNCT
ejpam-4317	389	3	i	i	NOUN
ejpam-4317	389	4	-	-	PUNCT
ejpam-4317	389	5	convegence	convegence	NOUN
ejpam-4317	389	6	of	of	ADP
ejpam-4317	389	7	sequences	sequence	NOUN
ejpam-4317	389	8	.	.	PUNCT
ejpam-4317	390	1	trans	trans	PROPN
ejpam-4317	390	2	.	.	PUNCT
ejpam-4317	391	1	a.	a.	PROPN
ejpam-4317	391	2	radmadze	radmadze	PROPN
ejpam-4317	391	3	math	math	NOUN
ejpam-4317	391	4	.	.	PUNCT
ejpam-4317	392	1	inst	inst	PROPN
ejpam-4317	392	2	.	.	PROPN
ejpam-4317	392	3	,	,	PUNCT
ejpam-4317	392	4	174(2):75–81	174(2):75–81	NUM
ejpam-4317	392	5	,	,	PUNCT
ejpam-4317	392	6	2020	2020	NUM
ejpam-4317	392	7	.	.	PUNCT
ejpam-4317	393	1	[	[	X
ejpam-4317	393	2	4	4	NUM
ejpam-4317	393	3	]	]	PUNCT
ejpam-4317	393	4	a.	a.	NOUN
ejpam-4317	393	5	m.	m.	NOUN
ejpam-4317	393	6	farhan	farhan	PROPN
ejpam-4317	393	7	and	and	CCONJ
ejpam-4317	393	8	x.	x.	PROPN
ejpam-4317	393	9	s.	s.	PROPN
ejpam-4317	393	10	yang	yang	PROPN
ejpam-4317	393	11	.	.	PUNCT
ejpam-4317	394	1	new	new	ADJ
ejpam-4317	394	2	type	type	NOUN
ejpam-4317	394	3	of	of	ADP
ejpam-4317	394	4	strongly	strongly	ADV
ejpam-4317	394	5	continuous	continuous	ADJ
ejpam-4317	394	6	functions	function	NOUN
ejpam-4317	394	7	in	in	ADP
ejpam-4317	394	8	topological	topological	ADJ
ejpam-4317	394	9	spaces	space	NOUN
ejpam-4317	394	10	via	via	ADP
ejpam-4317	394	11	δ	δ	PROPN
ejpam-4317	394	12	-	-	PUNCT
ejpam-4317	394	13	β	β	NOUN
ejpam-4317	394	14	-	-	ADJ
ejpam-4317	394	15	open	open	ADJ
ejpam-4317	394	16	sets	set	NOUN
ejpam-4317	394	17	.	.	PUNCT
ejpam-4317	395	1	eur	eur	PROPN
ejpam-4317	395	2	.	.	PUNCT
ejpam-4317	396	1	j.	j.	PROPN
ejpam-4317	396	2	pure	pure	PROPN
ejpam-4317	396	3	appl	appl	PROPN
ejpam-4317	396	4	.	.	PUNCT
ejpam-4317	396	5	math	math	PROPN
ejpam-4317	396	6	.	.	PUNCT
ejpam-4317	396	7	,	,	PUNCT
ejpam-4317	396	8	8(2):185–200	8(2):185–200	PROPN
ejpam-4317	396	9	,	,	PUNCT
ejpam-4317	396	10	2015	2015	NUM
ejpam-4317	396	11	.	.	PUNCT
ejpam-4317	397	1	[	[	X
ejpam-4317	397	2	5	5	NUM
ejpam-4317	397	3	]	]	PUNCT
ejpam-4317	397	4	a.	a.	PROPN
ejpam-4317	397	5	s.	s.	PROPN
ejpam-4317	397	6	nawar	nawar	PROPN
ejpam-4317	397	7	,	,	PUNCT
ejpam-4317	397	8	m.	m.	NOUN
ejpam-4317	397	9	a.	a.	PROPN
ejpam-4317	397	10	el	el	PROPN
ejpam-4317	397	11	-	-	PROPN
ejpam-4317	397	12	bably	bably	PROPN
ejpam-4317	397	13	and	and	CCONJ
ejpam-4317	397	14	r.	r.	PROPN
ejpam-4317	397	15	a.	a.	PROPN
ejpam-4317	397	16	hosny	hosny	PROPN
ejpam-4317	397	17	.	.	PUNCT
ejpam-4317	398	1	θβ	θβ	NOUN
ejpam-4317	398	2	-	-	PUNCT
ejpam-4317	398	3	ideal	ideal	NOUN
ejpam-4317	398	4	approximation	approximation	NOUN
ejpam-4317	398	5	spaces	space	NOUN
ejpam-4317	398	6	and	and	CCONJ
ejpam-4317	398	7	their	their	PRON
ejpam-4317	398	8	applications	application	NOUN
ejpam-4317	398	9	.	.	PUNCT
ejpam-4317	399	1	aims	aim	VERB
ejpam-4317	399	2	mathematics	mathematic	NOUN
ejpam-4317	399	3	,	,	PUNCT
ejpam-4317	399	4	7(2):2479–2497	7(2):2479–2497	NUM
ejpam-4317	399	5	,	,	PUNCT
ejpam-4317	399	6	2022	2022	NUM
ejpam-4317	399	7	.	.	PUNCT
ejpam-4317	400	1	[	[	X
ejpam-4317	400	2	6	6	NUM
ejpam-4317	400	3	]	]	X
ejpam-4317	400	4	b.	b.	PROPN
ejpam-4317	400	5	m.	m.	PROPN
ejpam-4317	400	6	munshi	munshi	PROPN
ejpam-4317	400	7	and	and	CCONJ
ejpam-4317	400	8	d.	d.	PROPN
ejpam-4317	400	9	s.	s.	PROPN
ejpam-4317	400	10	bassan	bassan	PROPN
ejpam-4317	400	11	.	.	PUNCT
ejpam-4317	401	1	super	super	ADJ
ejpam-4317	401	2	-	-	ADJ
ejpam-4317	401	3	continuous	continuous	ADJ
ejpam-4317	401	4	mappings	mapping	NOUN
ejpam-4317	401	5	.	.	PUNCT
ejpam-4317	402	1	indian	indian	PROPN
ejpam-4317	402	2	.	.	PUNCT
ejpam-4317	403	1	j.	j.	PROPN
ejpam-4317	403	2	pure	pure	PROPN
ejpam-4317	403	3	appl	appl	PROPN
ejpam-4317	403	4	.	.	PUNCT
ejpam-4317	403	5	math	math	PROPN
ejpam-4317	403	6	.	.	PUNCT
ejpam-4317	403	7	,	,	PUNCT
ejpam-4317	404	1	13(2):229–236	13(2):229–236	NUM
ejpam-4317	404	2	,	,	PUNCT
ejpam-4317	404	3	1982	1982	NUM
ejpam-4317	404	4	.	.	PUNCT
ejpam-4317	405	1	[	[	X
ejpam-4317	405	2	7	7	X
ejpam-4317	405	3	]	]	X
ejpam-4317	405	4	c.	c.	PROPN
ejpam-4317	405	5	granados	granados	PROPN
ejpam-4317	405	6	,	,	PUNCT
ejpam-4317	405	7	j.	j.	PROPN
ejpam-4317	405	8	sanabria	sanabria	PROPN
ejpam-4317	405	9	,	,	PUNCT
ejpam-4317	405	10	e.	e.	PROPN
ejpam-4317	405	11	rosas	rosas	PROPN
ejpam-4317	405	12	and	and	CCONJ
ejpam-4317	405	13	c.	c.	PROPN
ejpam-4317	405	14	carpintero	carpintero	PROPN
ejpam-4317	405	15	.	.	PUNCT
ejpam-4317	406	1	on	on	ADP
ejpam-4317	406	2	contra	contra	PROPN
ejpam-4317	406	3	λs	λs	ADP
ejpam-4317	406	4	i	i	PROPN
ejpam-4317	406	5	-continuous	-continuous	ADJ
ejpam-4317	406	6	functions	function	NOUN
ejpam-4317	406	7	and	and	CCONJ
ejpam-4317	406	8	their	their	PRON
ejpam-4317	406	9	applications	application	NOUN
ejpam-4317	406	10	.	.	PUNCT
ejpam-4317	407	1	j.	j.	PROPN
ejpam-4317	407	2	math	math	PROPN
ejpam-4317	407	3	.	.	PUNCT
ejpam-4317	408	1	comput	comput	NOUN
ejpam-4317	408	2	.	.	PUNCT
ejpam-4317	409	1	sci	sci	PROPN
ejpam-4317	409	2	.	.	PROPN
ejpam-4317	409	3	,	,	PUNCT
ejpam-4317	409	4	11(3):2834–2846	11(3):2834–2846	NUM
ejpam-4317	409	5	,	,	PUNCT
ejpam-4317	409	6	2021	2021	NUM
ejpam-4317	409	7	.	.	PUNCT
ejpam-4317	410	1	[	[	X
ejpam-4317	410	2	8	8	NUM
ejpam-4317	410	3	]	]	X
ejpam-4317	410	4	e.	e.	PROPN
ejpam-4317	410	5	hatir	hatir	PROPN
ejpam-4317	410	6	,	,	PUNCT
ejpam-4317	410	7	a.	a.	PROPN
ejpam-4317	410	8	al	al	PROPN
ejpam-4317	410	9	-	-	PUNCT
ejpam-4317	410	10	omari	omari	PROPN
ejpam-4317	410	11	and	and	CCONJ
ejpam-4317	410	12	s.	s.	PROPN
ejpam-4317	410	13	jafari	jafari	PROPN
ejpam-4317	410	14	.	.	PUNCT
ejpam-4317	411	1	δ	δ	PROPN
ejpam-4317	411	2	-	-	ADJ
ejpam-4317	411	3	local	local	ADJ
ejpam-4317	411	4	functions	function	NOUN
ejpam-4317	411	5	and	and	CCONJ
ejpam-4317	411	6	its	its	PRON
ejpam-4317	411	7	properties	property	NOUN
ejpam-4317	411	8	in	in	ADP
ejpam-4317	411	9	ideal	ideal	ADJ
ejpam-4317	411	10	topological	topological	ADJ
ejpam-4317	411	11	spaces	space	NOUN
ejpam-4317	411	12	.	.	PUNCT
ejpam-4317	412	1	fasc	fasc	PROPN
ejpam-4317	412	2	.	.	PROPN
ejpam-4317	412	3	math	math	PROPN
ejpam-4317	412	4	.	.	PUNCT
ejpam-4317	412	5	,	,	PUNCT
ejpam-4317	413	1	no	no	INTJ
ejpam-4317	413	2	.	.	PUNCT
ejpam-4317	414	1	53:53–64	53:53–64	NUM
ejpam-4317	414	2	,	,	PUNCT
ejpam-4317	414	3	2014	2014	NUM
ejpam-4317	414	4	.	.	PUNCT
ejpam-4317	415	1	[	[	X
ejpam-4317	415	2	9	9	NUM
ejpam-4317	415	3	]	]	PUNCT
ejpam-4317	415	4	e.	e.	PROPN
ejpam-4317	415	5	rosas	rosas	PROPN
ejpam-4317	415	6	,	,	PUNCT
ejpam-4317	415	7	c.	c.	PROPN
ejpam-4317	415	8	carpintero	carpintero	PROPN
ejpam-4317	415	9	,	,	PUNCT
ejpam-4317	415	10	j.	j.	PROPN
ejpam-4317	415	11	sanabria	sanabria	PROPN
ejpam-4317	415	12	and	and	CCONJ
ejpam-4317	415	13	j.	j.	PROPN
ejpam-4317	415	14	vielma	vielma	PROPN
ejpam-4317	415	15	.	.	PUNCT
ejpam-4317	416	1	characterization	characterization	NOUN
ejpam-4317	416	2	of	of	ADP
ejpam-4317	416	3	upper	upper	ADJ
ejpam-4317	416	4	and	and	CCONJ
ejpam-4317	416	5	lower	low	ADJ
ejpam-4317	416	6	(	(	PUNCT
ejpam-4317	416	7	α	α	NOUN
ejpam-4317	416	8	,	,	PUNCT
ejpam-4317	416	9	β	β	X
ejpam-4317	416	10	,	,	PUNCT
ejpam-4317	416	11	θ	θ	PROPN
ejpam-4317	416	12	,	,	PUNCT
ejpam-4317	416	13	δ	δ	PROPN
ejpam-4317	416	14	,	,	PUNCT
ejpam-4317	416	15	i)-continuous	i)-continuous	ADJ
ejpam-4317	416	16	multifunctions	multifunction	NOUN
ejpam-4317	416	17	.	.	PUNCT
ejpam-4317	417	1	mat	mat	NOUN
ejpam-4317	417	2	.	.	NOUN
ejpam-4317	417	3	stud	stud	PROPN
ejpam-4317	417	4	.	.	PUNCT
ejpam-4317	417	5	,	,	PUNCT
ejpam-4317	417	6	55(2):206–213	55(2):206–213	NUM
ejpam-4317	417	7	,	,	PUNCT
ejpam-4317	417	8	2021	2021	NUM
ejpam-4317	417	9	.	.	PUNCT
ejpam-4317	418	1	[	[	X
ejpam-4317	418	2	10	10	NUM
ejpam-4317	418	3	]	]	X
ejpam-4317	418	4	j.	j.	PROPN
ejpam-4317	418	5	sanabria	sanabria	PROPN
ejpam-4317	418	6	,	,	PUNCT
ejpam-4317	418	7	c.	c.	PROPN
ejpam-4317	418	8	granados	granados	PROPN
ejpam-4317	418	9	,	,	PUNCT
ejpam-4317	418	10	e.	e.	PROPN
ejpam-4317	418	11	rosas	rosas	PROPN
ejpam-4317	418	12	and	and	CCONJ
ejpam-4317	418	13	c.	c.	PROPN
ejpam-4317	418	14	carpintero	carpintero	PROPN
ejpam-4317	418	15	.	.	PUNCT
ejpam-4317	419	1	contra	contra	ADJ
ejpam-4317	419	2	-	-	ADJ
ejpam-4317	419	3	continuous	continuous	ADJ
ejpam-4317	419	4	functions	function	NOUN
ejpam-4317	419	5	defined	define	VERB
ejpam-4317	419	6	through	through	ADP
ejpam-4317	419	7	λi	λi	CCONJ
ejpam-4317	419	8	-closed	-close	VERB
ejpam-4317	419	9	sets	set	NOUN
ejpam-4317	419	10	.	.	PUNCT
ejpam-4317	420	1	wseas	wseas	PROPN
ejpam-4317	420	2	trans	trans	PROPN
ejpam-4317	420	3	.	.	PROPN
ejpam-4317	420	4	math	math	PROPN
ejpam-4317	420	5	.	.	PUNCT
ejpam-4317	420	6	,	,	PUNCT
ejpam-4317	420	7	19(70):632–638	19(70):632–638	NUM
ejpam-4317	420	8	,	,	PUNCT
ejpam-4317	420	9	2020	2020	NUM
ejpam-4317	420	10	.	.	PUNCT
ejpam-4317	421	1	[	[	X
ejpam-4317	421	2	11	11	NUM
ejpam-4317	421	3	]	]	PUNCT
ejpam-4317	421	4	j.	j.	PROPN
ejpam-4317	421	5	sanabria	sanabria	PROPN
ejpam-4317	421	6	,	,	PUNCT
ejpam-4317	421	7	e.	e.	PROPN
ejpam-4317	421	8	rosas	rosas	PROPN
ejpam-4317	421	9	,	,	PUNCT
ejpam-4317	421	10	m.	m.	NOUN
ejpam-4317	421	11	salas	salas	PROPN
ejpam-4317	421	12	,	,	PUNCT
ejpam-4317	421	13	c.	c.	PROPN
ejpam-4317	421	14	carpintero	carpintero	PROPN
ejpam-4317	421	15	and	and	CCONJ
ejpam-4317	421	16	r.	r.	PROPN
ejpam-4317	421	17	lozada	lozada	PROPN
ejpam-4317	421	18	.	.	PUNCT
ejpam-4317	422	1	on	on	ADP
ejpam-4317	422	2	a	a	DET
ejpam-4317	422	3	topology	topology	NOUN
ejpam-4317	422	4	between	between	ADP
ejpam-4317	422	5	the	the	DET
ejpam-4317	422	6	topologies	topology	NOUN
ejpam-4317	422	7	τθ	τθ	VERB
ejpam-4317	422	8	and	and	CCONJ
ejpam-4317	422	9	τθ	τθ	PROPN
ejpam-4317	422	10	-	-	PUNCT
ejpam-4317	422	11	i	i	PRON
ejpam-4317	422	12	.	.	PUNCT
ejpam-4317	423	1	int	int	NOUN
ejpam-4317	423	2	.	.	PUNCT
ejpam-4317	424	1	j.	j.	PROPN
ejpam-4317	424	2	pure	pure	PROPN
ejpam-4317	424	3	appl	appl	PROPN
ejpam-4317	424	4	.	.	PUNCT
ejpam-4317	424	5	math	math	PROPN
ejpam-4317	424	6	.	.	PUNCT
ejpam-4317	424	7	,	,	PUNCT
ejpam-4317	424	8	118(1):65–76	118(1):65–76	NUM
ejpam-4317	424	9	,	,	PUNCT
ejpam-4317	424	10	2018	2018	NUM
ejpam-4317	424	11	.	.	PUNCT
ejpam-4317	425	1	[	[	X
ejpam-4317	425	2	12	12	NUM
ejpam-4317	425	3	]	]	PUNCT
ejpam-4317	425	4	m.	m.	PROPN
ejpam-4317	425	5	hosny	hosny	PROPN
ejpam-4317	425	6	.	.	PUNCT
ejpam-4317	426	1	topologies	topology	NOUN
ejpam-4317	426	2	generated	generate	VERB
ejpam-4317	426	3	by	by	ADP
ejpam-4317	426	4	two	two	NUM
ejpam-4317	426	5	ideals	ideal	NOUN
ejpam-4317	426	6	and	and	CCONJ
ejpam-4317	426	7	the	the	DET
ejpam-4317	426	8	corresponding	correspond	VERB
ejpam-4317	426	9	j	j	NOUN
ejpam-4317	426	10	-	-	PUNCT
ejpam-4317	426	11	approximations	approximation	NOUN
ejpam-4317	426	12	spaces	space	VERB
ejpam-4317	426	13	with	with	ADP
ejpam-4317	426	14	applications	application	NOUN
ejpam-4317	426	15	.	.	PUNCT
ejpam-4317	427	1	j.	j.	PROPN
ejpam-4317	427	2	math	math	PROPN
ejpam-4317	427	3	.	.	PUNCT
ejpam-4317	427	4	,	,	PUNCT
ejpam-4317	427	5	vol	vol	NOUN
ejpam-4317	427	6	.	.	NOUN
ejpam-4317	427	7	2021	2021	NUM
ejpam-4317	427	8	,	,	PUNCT
ejpam-4317	427	9	article	article	NOUN
ejpam-4317	427	10	i	i	PROPN
ejpam-4317	427	11	d	d	PROPN
ejpam-4317	427	12	6391266:13	6391266:13	NUM
ejpam-4317	427	13	pages	page	NOUN
ejpam-4317	427	14	,	,	PUNCT
ejpam-4317	427	15	2021	2021	NUM
ejpam-4317	427	16	.	.	PUNCT
ejpam-4317	428	1	[	[	X
ejpam-4317	428	2	13	13	NUM
ejpam-4317	428	3	]	]	X
ejpam-4317	428	4	n.	n.	PROPN
ejpam-4317	428	5	levine	levine	PROPN
ejpam-4317	428	6	.	.	PUNCT
ejpam-4317	429	1	a	a	DET
ejpam-4317	429	2	decomposition	decomposition	NOUN
ejpam-4317	429	3	of	of	ADP
ejpam-4317	429	4	continuity	continuity	NOUN
ejpam-4317	429	5	in	in	ADP
ejpam-4317	429	6	topological	topological	ADJ
ejpam-4317	429	7	spaces	space	NOUN
ejpam-4317	429	8	.	.	PUNCT
ejpam-4317	430	1	amer	amer	PROPN
ejpam-4317	430	2	.	.	PUNCT
ejpam-4317	430	3	math	math	PROPN
ejpam-4317	430	4	.	.	PUNCT
ejpam-4317	431	1	monthly	monthly	ADJ
ejpam-4317	431	2	,	,	PUNCT
ejpam-4317	431	3	68(1):44–46	68(1):44–46	NUM
ejpam-4317	431	4	,	,	PUNCT
ejpam-4317	431	5	1961	1961	NUM
ejpam-4317	431	6	.	.	PUNCT
ejpam-4317	432	1	[	[	X
ejpam-4317	432	2	14	14	NUM
ejpam-4317	432	3	]	]	X
ejpam-4317	432	4	r.	r.	PROPN
ejpam-4317	432	5	lozada	lozada	PROPN
ejpam-4317	432	6	,	,	PUNCT
ejpam-4317	432	7	j.	j.	PROPN
ejpam-4317	432	8	sanabria	sanabria	PROPN
ejpam-4317	432	9	,	,	PUNCT
ejpam-4317	432	10	e.	e.	PROPN
ejpam-4317	432	11	rosas	rosas	PROPN
ejpam-4317	432	12	,	,	PUNCT
ejpam-4317	432	13	c.	c.	PROPN
ejpam-4317	432	14	carpintero	carpintero	PROPN
ejpam-4317	432	15	and	and	CCONJ
ejpam-4317	432	16	m.	m.	NOUN
ejpam-4317	432	17	salas	salas	PROPN
ejpam-4317	432	18	.	.	PUNCT
ejpam-4317	433	1	on	on	ADP
ejpam-4317	433	2	δθ	δθ	ADP
ejpam-4317	433	3	-	-	PUNCT
ejpam-4317	433	4	i	i	NOUN
ejpam-4317	433	5	-	-	PUNCT
ejpam-4317	433	6	continuous	continuous	ADJ
ejpam-4317	433	7	functions	function	NOUN
ejpam-4317	433	8	.	.	PUNCT
ejpam-4317	434	1	int	int	NOUN
ejpam-4317	434	2	.	.	PUNCT
ejpam-4317	435	1	j.	j.	PROPN
ejpam-4317	435	2	pure	pure	PROPN
ejpam-4317	435	3	appl	appl	PROPN
ejpam-4317	435	4	.	.	PUNCT
ejpam-4317	435	5	math	math	PROPN
ejpam-4317	435	6	.	.	PUNCT
ejpam-4317	435	7	,	,	PUNCT
ejpam-4317	435	8	116(2):461–478	116(2):461–478	NUM
ejpam-4317	435	9	,	,	PUNCT
ejpam-4317	435	10	2017	2017	NUM
ejpam-4317	435	11	.	.	PUNCT
ejpam-4317	436	1	references	reference	NOUN
ejpam-4317	436	2	453	453	NUM
ejpam-4317	436	3	[	[	X
ejpam-4317	436	4	15	15	NUM
ejpam-4317	436	5	]	]	X
ejpam-4317	436	6	s.	s.	PROPN
ejpam-4317	436	7	fomin	fomin	PROPN
ejpam-4317	436	8	.	.	PUNCT
ejpam-4317	437	1	extension	extension	NOUN
ejpam-4317	437	2	of	of	ADP
ejpam-4317	437	3	topological	topological	ADJ
ejpam-4317	437	4	spaces	space	NOUN
ejpam-4317	437	5	.	.	PUNCT
ejpam-4317	438	1	ann	ann	PROPN
ejpam-4317	438	2	.	.	PROPN
ejpam-4317	438	3	of	of	ADP
ejpam-4317	438	4	math	math	NOUN
ejpam-4317	438	5	.	.	PUNCT
ejpam-4317	438	6	,	,	PUNCT
ejpam-4317	438	7	44:471–480	44:471–480	PROPN
ejpam-4317	438	8	,	,	PUNCT
ejpam-4317	438	9	1943	1943	NUM
ejpam-4317	438	10	.	.	PUNCT
ejpam-4317	439	1	[	[	X
ejpam-4317	439	2	16	16	NUM
ejpam-4317	439	3	]	]	PUNCT
ejpam-4317	439	4	s.	s.	PROPN
ejpam-4317	439	5	jafari	jafari	PROPN
ejpam-4317	439	6	,	,	PUNCT
ejpam-4317	439	7	t.	t.	PROPN
ejpam-4317	439	8	noiri	noiri	PROPN
ejpam-4317	439	9	and	and	CCONJ
ejpam-4317	439	10	v.	v.	ADP
ejpam-4317	439	11	popa	popa	NOUN
ejpam-4317	439	12	.	.	PUNCT
ejpam-4317	440	1	properties	property	NOUN
ejpam-4317	440	2	of	of	ADP
ejpam-4317	440	3	θ	θ	PROPN
ejpam-4317	440	4	-	-	PUNCT
ejpam-4317	440	5	i	i	NOUN
ejpam-4317	440	6	-	-	PUNCT
ejpam-4317	440	7	compact	compact	ADJ
ejpam-4317	440	8	sets	set	NOUN
ejpam-4317	440	9	in	in	ADP
ejpam-4317	440	10	ideal	ideal	ADJ
ejpam-4317	440	11	topological	topological	ADJ
ejpam-4317	440	12	spaces	space	NOUN
ejpam-4317	440	13	.	.	PUNCT
ejpam-4317	441	1	poincare	poincare	PROPN
ejpam-4317	441	2	j.	j.	PROPN
ejpam-4317	441	3	anal	anal	PROPN
ejpam-4317	441	4	.	.	PUNCT
ejpam-4317	442	1	appl	appl	PROPN
ejpam-4317	442	2	.	.	PROPN
ejpam-4317	442	3	,	,	PUNCT
ejpam-4317	442	4	8(1(i)):79–88	8(1(i)):79–88	NUM
ejpam-4317	442	5	,	,	PUNCT
ejpam-4317	442	6	2021	2021	NUM
ejpam-4317	442	7	.	.	PUNCT
ejpam-4317	443	1	[	[	X
ejpam-4317	443	2	17	17	NUM
ejpam-4317	443	3	]	]	X
ejpam-4317	443	4	s.	s.	PROPN
ejpam-4317	443	5	yüksel	yüksel	PROPN
ejpam-4317	443	6	,	,	PUNCT
ejpam-4317	443	7	a.	a.	NOUN
ejpam-4317	443	8	açikgöz	açikgöz	PROPN
ejpam-4317	443	9	and	and	CCONJ
ejpam-4317	443	10	t.	t.	PROPN
ejpam-4317	443	11	noiri	noiri	PROPN
ejpam-4317	443	12	.	.	PUNCT
ejpam-4317	444	1	δ	δ	PROPN
ejpam-4317	444	2	-	-	PUNCT
ejpam-4317	444	3	i	i	NOUN
ejpam-4317	444	4	-	-	PUNCT
ejpam-4317	444	5	continuous	continuous	ADJ
ejpam-4317	444	6	functions	function	NOUN
ejpam-4317	444	7	.	.	PUNCT
ejpam-4317	445	1	turk	turk	PROPN
ejpam-4317	445	2	.	.	PUNCT
ejpam-4317	446	1	j.	j.	PROPN
ejpam-4317	446	2	math	math	PROPN
ejpam-4317	446	3	.	.	PUNCT
ejpam-4317	446	4	,	,	PUNCT
ejpam-4317	446	5	29(1):39–51	29(1):39–51	NUM
ejpam-4317	446	6	,	,	PUNCT
ejpam-4317	446	7	2005	2005	NUM
ejpam-4317	446	8	.	.	PUNCT
ejpam-4317	447	1	[	[	X
ejpam-4317	447	2	18	18	NUM
ejpam-4317	447	3	]	]	PUNCT
ejpam-4317	447	4	t.	t.	PROPN
ejpam-4317	447	5	noiri	noiri	PROPN
ejpam-4317	447	6	.	.	PUNCT
ejpam-4317	448	1	on	on	ADP
ejpam-4317	448	2	δ	δ	PROPN
ejpam-4317	448	3	-	-	ADJ
ejpam-4317	448	4	continuous	continuous	ADJ
ejpam-4317	448	5	functions	function	NOUN
ejpam-4317	448	6	.	.	PUNCT
ejpam-4317	449	1	j.	j.	PROPN
ejpam-4317	449	2	korean	korean	PROPN
ejpam-4317	449	3	math	math	PROPN
ejpam-4317	449	4	.	.	PUNCT
ejpam-4317	450	1	soc	soc	PROPN
ejpam-4317	450	2	.	.	PUNCT
ejpam-4317	450	3	,	,	PUNCT
ejpam-4317	450	4	16(2):161–166	16(2):161–166	NUM
ejpam-4317	450	5	,	,	PUNCT
ejpam-4317	450	6	1979	1979	NUM
ejpam-4317	450	7	.	.	PUNCT
ejpam-4317	451	1	[	[	X
ejpam-4317	451	2	19	19	NUM
ejpam-4317	451	3	]	]	X
ejpam-4317	451	4	w.	w.	PROPN
ejpam-4317	451	5	al	al	PROPN
ejpam-4317	451	6	-	-	PUNCT
ejpam-4317	451	7	omeri	omeri	PROPN
ejpam-4317	451	8	and	and	CCONJ
ejpam-4317	451	9	t.	t.	PROPN
ejpam-4317	451	10	noiri	noiri	PROPN
ejpam-4317	451	11	.	.	PUNCT
ejpam-4317	452	1	on	on	ADP
ejpam-4317	452	2	almost	almost	ADV
ejpam-4317	452	3	e	e	NOUN
ejpam-4317	452	4	-	-	ADJ
ejpam-4317	452	5	i	i	NOUN
ejpam-4317	452	6	-	-	PUNCT
ejpam-4317	452	7	continuous	continuous	ADJ
ejpam-4317	452	8	functions	function	NOUN
ejpam-4317	452	9	.	.	PUNCT
ejpam-4317	453	1	demonstratio	demonstratio	PROPN
ejpam-4317	453	2	math	math	PROPN
ejpam-4317	453	3	.	.	PUNCT
ejpam-4317	453	4	,	,	PUNCT
ejpam-4317	453	5	54(1):168–177	54(1):168–177	NOUN
ejpam-4317	453	6	,	,	PUNCT
ejpam-4317	453	7	2021	2021	NUM
ejpam-4317	453	8	.	.	PUNCT