On Baire classification of strongly separately continuous functions

Abstract

We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to \mathbb{R}$ which is not Baire measurable. We show that if $X$ is a product of normed spaces $X_n$, $a\in X$ and $\sigma (a)=\{x\in X:|\{n\in \mathbb{N}:x_n\ne a_n\}|<{\aleph }_0\}$ is a subspace of $X$, equipped with the Tychonoff topology, then for any open set $G\subseteq \sigma (a)$ there is a strongly separately continuous function $f:\sigma (a)\to \mathbb{R}$ such that the discontinuity point set of $f$ is equal to~$G$.

arXiv commentarXiv admin note: text overlap with arXiv:1411.6886