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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Guardado en:
Detalles Bibliográficos
Publicado: 2000
Materias:
Cone of recession
Convex components
Finitely starshapod sets
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez
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 paper:paper_00029939_v128_n5_p1433_Rodriguez
record_format dspace
spelling paper:paper_00029939_v128_n5_p1433_Rodriguez2023-06-08T14:23:25Z Structure of closed finitely starshaped sets mabel 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. 2000 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez 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
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.
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
publishDate 2000
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez
http://hdl.handle.net/20.500.12110/paper_00029939_v128_n5_p1433_Rodriguez
_version_ 1768543062707929088

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