On Closed Starshaped Sets

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