Abstract
This chapter discusses convex compact sets and their extremal points. It reviews the theorems of Krein–Milman and Choquet on extremal points and barycentric representation. A topological vector space (H, ▪) is called separated if it is Hausdorff and locally convex if there is a neighborhood base for ▪ at every x ∈ H that consists of convex sets. If (H, ▪) be a separated topological vector space, then for a set H0 ⊆ H0, the following statements are equivalent. (1) H0is a closed hyper plane of H. (2) There is a continuous linear form▪ and a real number α such that ▪ and ▪.
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