Points of joint continuity of separately continuous mappings - Mirmostafaee, A. K. (Methods of Functional Analysis and Topology, 2009)
Let X be a Baire space, Y be a compact Hausdorff space and f:X × Y → R be a separately continuous mapping. For each y Y, we define a game G(Y, { y }) between players O and P, to show that if in this game either O player has a winning strategy or X is α-favorable and P player does not have a winning strategy, then for each countable subset E of Y, there exists a dense G_δ subset D of X such that f is jointly continuous on D × E.