Borel measurability of separately continuous functions, II

Abstract

This paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29–65] into the measurability properties of separately continuous functions. We sharpen several results from that paper.

• If X is any product of countably compact Dedekind complete linearly ordered spaces, then there is a network for the norm topology on C(X) which is σ-isolated in the topology of pointwise convergence.

• If X is a nonseparable ccc space, then the evaluation map $\text{X×C}{}_{\mathrm{p}}\text{(X)→}\text{R}$ is not a Baire function.

• If X_i, i<κ, are nondegenerate subspaces of separable linearly ordered spaces and X=∏_i<κX_i, then the evaluation map $\text{X×C}{}_{\mathrm{p}}\text{(X)→}\text{R}$ is F_σ-measurable if and only if $\text{κ⩽}\text{c}$.