Separable subspaces of affine function spaces on convex compact sets

W.B.Moors and E.Reznichenko


Let $K$ be a compact convex subset of a separated locally convex space
(over $mathbb{R}$) 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.

Compact convex sets, Extreme points, Metrizability, Monolithic.

Math Review Classification
Primary 54C05 ; Secondary 22A10

Last Updated
5 February 2007

25 pages

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