Isomorphisms of spaces of continuous affine functions on compact convex sets with Lindelöf boundaries

Abstract

Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and both ext X and ext Y are Lindelof spaces. We prove that, if there exists a special isomorphism T, then ext X is homeomorphic to ext Y.

This generalizes results of H. B.

Cohen and C. H.

Chu.

Keywords

• Isomorphisms
• spaces
• continuous
• affine
• functions
• compact
• convex
• sets
• with
• Lindelöf
• boundaries