On a problem of Talagrand concerning separately continuous functions - Mykhaylyuk, Volodymyr; Pol, Roman (Cembridge University Press, 2021)
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.
Keywords: separately continuous function, Baire space, compact space, extremally disconnected space, Namioka property