Separable subspaces of affine function spaces on convex compact sets

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.