| 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. |
Keywords
Compact convex sets, Extreme points, Metrizability, Monolithic.
Math Review Classification
Primary 54C05
; Secondary 22A10
Last Updated
5 February 2007
Length
25 pages
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