Joint Continuity of Separately Continuous Functions

It is shown that a separately continuous function <!-- MATH $f:X \times Y \to Z$ --> from the product of a certain type of Hausdorff space and a compact Hausdorff space into a metrizable space is jointly continuous on a set of the type <!-- MATH $A \times Y$ --> , where is a dense <!-- MATH ${G_\delta }$ --> set in . The class of Hausdorff spaces in question is defined by a gametheoretic condition. The result improves (and simplifies the proof of) a recent result of Namioka. Many "deep" theorems in functional analysis and automatic continuity theory are easy corollaries.