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Andrzej Szymanski - On a class of special Namioka spaces



ANDRZEJ SZYMANSKI, Slippery Rock University of Pennsylvania
On a class of special Namioka spaces


If $f\colon X\times Y \rightarrow M$ is a separately continuous function on the product of a compact space Y and a strongly countably complete space X into a metric space M, then there exists a dense $G\delta \subset A$ of X such that f is jointly continuous at each point of $A\times Y$.

We introduce a game-theoretic description of a class of topological spaces that is substantially wider than, for example, the class of strongly countably complete spaces or the class of metric Baire spaces, yet the conclusion of the Namioka theorem holds for spaces from this class. The class itself is also closed under perfect preimages. We apply our results to the theory of semitopological groups.


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