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...
Guardado en:
Autores principales: | , |
---|---|
Formato: | JOUR |
Materias: | |
Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00029939_v128_n5_p1433_Rodriguez |
Aporte de: |
id |
todo:paper_00029939_v128_n5_p1433_Rodriguez |
---|---|
record_format |
dspace |
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 |
_version_ |
1782025959061323776 |