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 $\operatorname{ext} X$ is homeomorphic to $\operatorname{ext} Y$ provided there exists a small-bound isomorphism of the space $\mathfrak{A}(X,\mathbb{C} )$ of continuous affine complex functions on $X$ onto $\mathfrak{A}(Y,\mathbb{C} )$. Further, we generalize a result of Cengiz to the context of compact convex sets.