Separate continuity, joint continuity, the Lindelof property and p-spaces

In this paper we prove a theorem more general than the following. Suppose that X is Cech-complete and Y is a closed subset of a product of a separable metric space with a compact Hausdorff space. Then for each separately continuous function f : X x Y --> R there exists a residual set R in X such that f is jointly continuous at each point of R x Y. This confirms the suspicions of S. Mercourakis and S. Negrepontis from 1991. (C) 2006 Elsevier B.V. All rights reserved.