Critical visibility and outward rays

The notion of clear visibility has appeared recently in the literature concerning the geometry of starshaped sets. A somewhat converse notion, that of critical visibility, is explored here. As a by-product it is proved that the points of local nonconvexity of a closed connected set S determine the n...

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Autor principal: Toranzos, F.A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00472468_v33_n1-2_p155_Toranzos
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00472468_v33_n1-2_p155_Toranzos2023-10-03T14:52:19Z Critical visibility and outward rays Toranzos, F.A. The notion of clear visibility has appeared recently in the literature concerning the geometry of starshaped sets. A somewhat converse notion, that of critical visibility, is explored here. As a by-product it is proved that the points of local nonconvexity of a closed connected set S determine the nontrivial portions of the boundary of the star of a point in S. Paragraph 4 is devoted to the study of the concepts of outward ray through a boundary point and inner stem of that point. A new characterization of the convex kernel of a starshaped set results from this study, and Krasnoselsky-type theorems are obtained in the planar case. © 1988 Birkhäuser Verlag. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00472468_v33_n1-2_p155_Toranzos
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 notion of clear visibility has appeared recently in the literature concerning the geometry of starshaped sets. A somewhat converse notion, that of critical visibility, is explored here. As a by-product it is proved that the points of local nonconvexity of a closed connected set S determine the nontrivial portions of the boundary of the star of a point in S. Paragraph 4 is devoted to the study of the concepts of outward ray through a boundary point and inner stem of that point. A new characterization of the convex kernel of a starshaped set results from this study, and Krasnoselsky-type theorems are obtained in the planar case. © 1988 Birkhäuser Verlag.
format JOUR
author Toranzos, F.A.
spellingShingle Toranzos, F.A.
Critical visibility and outward rays
author_facet Toranzos, F.A.
author_sort Toranzos, F.A.
title Critical visibility and outward rays
title_short Critical visibility and outward rays
title_full Critical visibility and outward rays
title_fullStr Critical visibility and outward rays
title_full_unstemmed Critical visibility and outward rays
title_sort critical visibility and outward rays
url http://hdl.handle.net/20.500.12110/paper_00472468_v33_n1-2_p155_Toranzos
work_keys_str_mv AT toranzosfa criticalvisibilityandoutwardrays
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