On a problem of Talagrand concerning separately continuous functions

Abstract

We construct a separately continuous function e:E×K→{0,1} on the product of a Baire space E and a compact space K such that no restriction of e to any non-meagre Borel set in E×K is continuous. The function e has no points of joint continuity, and, hence, it provides a negative solution of Talagrand’s problem in Talagrand.