The points of local nonconvexity of starshaped sets

The notion of point of local nonconvexity has been an important tool in the study of the geometry of nonconvex sets, since Tietze characterized, more than fifty years ago, the convex subsets of En as those connected sets without points of local nonconvexity. It is proved here that for each convex co...

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Autor principal: Toranzos, F.A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00308730_v101_n1_p209_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_00308730_v101_n1_p209_Toranzos2023-10-03T14:40:44Z The points of local nonconvexity of starshaped sets Toranzos, F.A. The notion of point of local nonconvexity has been an important tool in the study of the geometry of nonconvex sets, since Tietze characterized, more than fifty years ago, the convex subsets of En as those connected sets without points of local nonconvexity. It is proved here that for each convex component K of a closed connected set S in a locally convex space there exist points of local nonconvexity of S arbitrarily close to K, unless S itself be convex. Klee’s generalization of the just quoted Tietze’s theorem follows immediately. The notion of “higher visibility” is introduced in the last section, and three Erasnosselsky-type theorems involving the points of local nonconvexity are proved. © 1982, University of California, Berkeley. All Rights Reserved. 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_00308730_v101_n1_p209_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 point of local nonconvexity has been an important tool in the study of the geometry of nonconvex sets, since Tietze characterized, more than fifty years ago, the convex subsets of En as those connected sets without points of local nonconvexity. It is proved here that for each convex component K of a closed connected set S in a locally convex space there exist points of local nonconvexity of S arbitrarily close to K, unless S itself be convex. Klee’s generalization of the just quoted Tietze’s theorem follows immediately. The notion of “higher visibility” is introduced in the last section, and three Erasnosselsky-type theorems involving the points of local nonconvexity are proved. © 1982, University of California, Berkeley. All Rights Reserved.
format JOUR
author Toranzos, F.A.
spellingShingle Toranzos, F.A.
The points of local nonconvexity of starshaped sets
author_facet Toranzos, F.A.
author_sort Toranzos, F.A.
title The points of local nonconvexity of starshaped sets
title_short The points of local nonconvexity of starshaped sets
title_full The points of local nonconvexity of starshaped sets
title_fullStr The points of local nonconvexity of starshaped sets
title_full_unstemmed The points of local nonconvexity of starshaped sets
title_sort points of local nonconvexity of starshaped sets
url http://hdl.handle.net/20.500.12110/paper_00308730_v101_n1_p209_Toranzos
work_keys_str_mv AT toranzosfa thepointsoflocalnonconvexityofstarshapedsets
AT toranzosfa pointsoflocalnonconvexityofstarshapedsets
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