POINTS OF JOINT CONTINUITY OF SEPARATELY CONTINUOUS MAPPINGS

Let X be a Baire space, Y be a compact Hausdorff space and f : X xY -> R be a separately continuous mapping. For each y is an element of Y, we define a game G(Y, {y}) between players 0 and P, to show that if in this game either 0 player has a winning strategy or X is alpha-favorable and P player does not have a winning strategy, then for each countable subset E of Y, there exists a dense G(delta) subset D of X such that f is jointly continuous on D x E.