ISOMORPHISMS OF SPACES OF AFFINE CONTINUOUS COMPLEX FUNCTIONS

Abstract

Let X and Y be compact convex sets such that their each extreme point is a weak peak point. We show that ext X is homeomorphic to ext Y provided there exists a small-bound isomorphism of the space A(X, C) of continuous affine complex functions on X onto A(Y, C).

Further, we generalize a result of Cengiz to the context of compact convex sets.

Keywords

• compact convex set
• Banach-Stone theorem
• weak peak point