Structure of closed finitely starshaped sets mabel

A set S is finitely starshaped if any finite subset of S is totally visible from some point of S. It is well known that in a finite-dimensional linear space, a closed finitely starshaped set which is not starshaped must be unbounded. It is proved here that such a set must admit at least one directio...

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Detalles Bibliográficos
Autores principales: Rodriguez, A., Toranzos, F.A.
Formato: JOUR
Materias:
Cone of recession
Convex components
Finitely starshapod sets
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029939_v128_n5_p1433_Rodriguez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00029939_v128_n5_p1433_Rodriguez
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spelling todo:paper_00029939_v128_n5_p1433_Rodriguez2023-10-03T13:55:05Z Structure of closed finitely starshaped sets mabel Rodriguez, A. Toranzos, F.A. Cone of recession Convex components Finitely starshapod sets A set S is finitely starshaped if any finite subset of S is totally visible from some point of S. It is well known that in a finite-dimensional linear space, a closed finitely starshaped set which is not starshaped must be unbounded. It is proved here that such a set must admit at least one direction of recession. This fact clarifies the structure of such sets and allows the study of properties of their visibility elements, well known in the case of starshaped sets. A characterization of planar finitely starshaped sets by means of its convex components is obtained. Some plausible conjectures are disproved by means of counterexamples. ©2000 American Mathematical Society. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00029939_v128_n5_p1433_Rodriguez
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cone of recession
Convex components
Finitely starshapod sets
spellingShingle Cone of recession
Convex components
Finitely starshapod sets
Rodriguez, A.
Toranzos, F.A.
Structure of closed finitely starshaped sets mabel
topic_facet Cone of recession
Convex components
Finitely starshapod sets
description A set S is finitely starshaped if any finite subset of S is totally visible from some point of S. It is well known that in a finite-dimensional linear space, a closed finitely starshaped set which is not starshaped must be unbounded. It is proved here that such a set must admit at least one direction of recession. This fact clarifies the structure of such sets and allows the study of properties of their visibility elements, well known in the case of starshaped sets. A characterization of planar finitely starshaped sets by means of its convex components is obtained. Some plausible conjectures are disproved by means of counterexamples. ©2000 American Mathematical Society.
format JOUR
author Rodriguez, A.
Toranzos, F.A.
author_facet Rodriguez, A.
Toranzos, F.A.
author_sort Rodriguez, A.
title Structure of closed finitely starshaped sets mabel
title_short Structure of closed finitely starshaped sets mabel
title_full Structure of closed finitely starshaped sets mabel
title_fullStr Structure of closed finitely starshaped sets mabel
title_full_unstemmed Structure of closed finitely starshaped sets mabel
title_sort structure of closed finitely starshaped sets mabel
url http://hdl.handle.net/20.500.12110/paper_00029939_v128_n5_p1433_Rodriguez
work_keys_str_mv AT rodrigueza structureofclosedfinitelystarshapedsetsmabel
AT toranzosfa structureofclosedfinitelystarshapedsetsmabel
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