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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2000
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| 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 |
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| Sumario: | 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. |
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