Journal of Convex Analysis 17 (2010), No. 2, 659--671
Copyright Heldermann Verlag 2010
On Closed Starshaped Sets
Guillermo Hansen
Universidad de Luján, Argentina
Horst Martini
Fakultät für Mathematik, Technische Universität, 09107 Chemnitz, Germany
horst.martini@mathematik.tu-chemnitz.de
We present several new results on closed starshaped sets in Rd which mainly refer to the kernel and the boundary structure of such sets. In particular, we introduce so-called dispensable points which, in a certain sense, play the same role for closed starshaped sets that extreme points play for convex sets. Based on this notion we prove an analogue of the famous Krein-Milman theorem.
Keywords: Asymptotic structure, cone, dispensable point, extreme point, kernel, Krein-Milman theorem, Minkowski's theorem, starshaped set, support cone.
MSC: 52-99, 52A01, 52A30
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