Abstract

We present several new results on closed starshaped sets in Rd\mathbb{R}^d 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.

Author information

Contact details are reproduced from the original publication and may be historical.

Guillermo Hansen

Universidad de Luján, Argentina

Keywords

  • Asymptotic structure
  • cone
  • dispensable point
  • extreme point
  • kernel
  • Krein-Milman theorem
  • Minkowski's theorem
  • starshaped set
  • support cone

Mathematics Subject Classification

52-99, 52A01, 52A30

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Suggested citation

G. Hansen, H. Martini. “On Closed Starshaped Sets.” Journal of Convex Analysis 17 (2010), No. 2, 659–671. https://doi.org/10.68381/jca17044

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.