Separate continuity, joint continuity and the Lindelöf property

Abstract

In this paper we prove a theorem more general than the following. Suppose that X X is Lindelöf and α \alpha -favourable and Y Y is Lindelöf and Čech-complete. Then for each separately continuous function f : X × Y → R f:X\times Y \rightarrow \mathbb {R} there exists a residual set R R in X X such that f f is jointly continuous at each point of R × Y R\times Y .