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Journal of Convex Analysis 17 (2010), No. 2, 659--671
Copyright Heldermann Verlag 2010

On Closed Starshaped Sets

Guillermo Hansen
Universidad de LujŠn, Argentina

Horst Martini
Fakultšt fŁr Mathematik, Technische Universitšt, 09107 Chemnitz, Germany

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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