Must the visibility function of an open set be continuous?

The visibility function of a set S was defined in 1972 by G. Beer. This function evaluates the Lebesgue outer measure of the star of each point of S. The continuity of this function for compact sets was studied by its creator. Recently, the present authors settled the problem of continuity in the bo...

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Detalles Bibliográficos
Autor principal: Toranzos, Fausto Alfredo
Publicado: 2008
Materias:
Visibility function
Visibility in open sets
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17835720_v77_n_p1_Losada
http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_17835720_v77_n_p1_Losada
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spelling paper:paper_17835720_v77_n_p1_Losada2025-07-30T19:04:42Z Must the visibility function of an open set be continuous? Toranzos, Fausto Alfredo Visibility function Visibility in open sets The visibility function of a set S was defined in 1972 by G. Beer. This function evaluates the Lebesgue outer measure of the star of each point of S. The continuity of this function for compact sets was studied by its creator. Recently, the present authors settled the problem of continuity in the boundary of a compact set S. The question of the continuity in the case where S is an open bounded set - proposed by G. Beer - is still unsettled. We show here that the continuity of the visibility function does not depend on the boundedness of the open set S. Fil:Toranzos, F.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17835720_v77_n_p1_Losada http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Visibility function
Visibility in open sets
spellingShingle Visibility function
Visibility in open sets
Toranzos, Fausto Alfredo
Must the visibility function of an open set be continuous?
topic_facet Visibility function
Visibility in open sets
description The visibility function of a set S was defined in 1972 by G. Beer. This function evaluates the Lebesgue outer measure of the star of each point of S. The continuity of this function for compact sets was studied by its creator. Recently, the present authors settled the problem of continuity in the boundary of a compact set S. The question of the continuity in the case where S is an open bounded set - proposed by G. Beer - is still unsettled. We show here that the continuity of the visibility function does not depend on the boundedness of the open set S.
author Toranzos, Fausto Alfredo
author_facet Toranzos, Fausto Alfredo
author_sort Toranzos, Fausto Alfredo
title Must the visibility function of an open set be continuous?
title_short Must the visibility function of an open set be continuous?
title_full Must the visibility function of an open set be continuous?
title_fullStr Must the visibility function of an open set be continuous?
title_full_unstemmed Must the visibility function of an open set be continuous?
title_sort must the visibility function of an open set be continuous?
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17835720_v77_n_p1_Losada
http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada
work_keys_str_mv AT toranzosfaustoalfredo mustthevisibilityfunctionofanopensetbecontinuous
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