On a problem of Talagrand concerning separately continuous functions

Volodymyr Mykhaylyuk; Roman Pol

doi:10.1017/S1474748019000677

paper

On a problem of Talagrand concerning separately continuous functions

arXiv:1809.05799 · doi:10.1017/S1474748019000677

Abstract

We construct a separately continuous function $e : E \times K \to {0, 1}$ on the product of a Baire space $E$ and a zero-dimensional compact space $K$ such that no restriction of $e$ to any non-meager Borel set in $E \times K$ is continuous. The function $e$ provides a negative solution of Talagrand's problem in \cite{T}.