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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
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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