Separable subspaces of affine function spaces on convex compact sets

摘要

Let K be a compact convex subset of a separated locally convex space (over R) and let A_p(K) denote the space of all continuous real-valued affine mappings defined on K, endowed with the topology of pointwise convergence on the extreme points of K. In this paper we shall examine some topological properties of A_p(K). For example, we shall consider when A_p(K) is monolithic and when separable compact subsets of A_p(K) are metrizable.