The visibility function revisited

The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain....

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Autores principales: Cunto, A.F., Losada, M.P., Toranzos, F.A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00472468_v65_n1-2_p101_Cunto
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spelling todo:paper_00472468_v65_n1-2_p101_Cunto2023-10-03T14:52:19Z The visibility function revisited Cunto, A.F. Losada, M.P. Toranzos, F.A. The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. The basic intention of this paper is to extend this characterization to a compact subset of Ed. Under certain assumptions, it is proved here that the visibility function of such a set is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. © Birkhäuser Verlag, 1999. Fil:Toranzos, F.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. The basic intention of this paper is to extend this characterization to a compact subset of Ed. Under certain assumptions, it is proved here that the visibility function of such a set is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. © Birkhäuser Verlag, 1999.
format JOUR
author Cunto, A.F.
Losada, M.P.
Toranzos, F.A.
spellingShingle Cunto, A.F.
Losada, M.P.
Toranzos, F.A.
The visibility function revisited
author_facet Cunto, A.F.
Losada, M.P.
Toranzos, F.A.
author_sort Cunto, A.F.
title The visibility function revisited
title_short The visibility function revisited
title_full The visibility function revisited
title_fullStr The visibility function revisited
title_full_unstemmed The visibility function revisited
title_sort visibility function revisited
url http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto
work_keys_str_mv AT cuntoaf thevisibilityfunctionrevisited
AT losadamp thevisibilityfunctionrevisited
AT toranzosfa thevisibilityfunctionrevisited
AT cuntoaf visibilityfunctionrevisited
AT losadamp visibilityfunctionrevisited
AT toranzosfa visibilityfunctionrevisited
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