Structure of closed finitely starshaped sets |
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Authors: | Mabel A Rodriguez Fausto A Toranzos |
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Institution: | Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, Roca 850, (1663) San Miguel, Argentina ; Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, (1428) Buenos Aires, Argentina |
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Abstract: | A set is finitely starshaped if any finite subset of is totally visible from some point of . 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. |
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Keywords: | Finitely starshaped sets cone of recession convex components |
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