Complementability of spaces of affine continuous functions on simplices

Abstract

We construct metrizable simplices X-1 and X-2 and a homeornorphism phi (ext X-1) over bar -} (ext X-2) over bar such that phi(ext X-1) = ext X-2, the space U(X-1) U(X-2) is not complemented in any C(K) space. This shows that complementability of U(X) cannot be determined by topological properties of the couple (ext X, (ext X) over bar).

Keywords

• Complementability
• spaces
• affine
• continuous
• functions
• simplices