Preserving affine Baire classes by perfect affine maps

Abstract

Let $\phi :X\to Y$ be an affine continuous surjection between compact convex sets. Suppose that the canonical copy of the space of real-valued affine continuous functions on $Y$ in the space of real-valued affine continuous functions on $X$ is complemented. We show that if $F$ is a topological vector space, then $f:Y\to F$ is of affine Baire class $\alpha$ whenever the composition $f\circ \phi$ is of affine Baire class $\alpha$. This abstract result is applied to extend known results on affine Baire classes of strongly affine Baire mappings.

10 pages

References in corpus (2)

• Complementation in Spaces of Continuous Functions on Compact Lines
• Baire classes of affine vector-valued functions

Cited by in corpus (1)

• Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces