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Points de continuité d'une fonction séparément continue

Author: Gabriel Debs
Journal: Proc. Amer. Math. Soc. 97 (1986), 167-176
MSC: Primary 54C05
MathSciNet review: 831408
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Abstract: Let $ f:X \times Y \to {\mathbf{R}}$ be a separately continuous function defined on the product of a Baire space $ X$ and a Hausdorff compact space $ Y$. We prove that $ f$ is jointly continuous at any point of $ G \times Y$, for a dense $ {G_\delta }$ subset $ G$ of $ X$, under one of the following assumptions: (i) If the Banach space $ \mathcal{C}(Y)$ is weakly $ \mathcal{K}$-analytic; or (ii) if $ X$ contains a dense subset which is $ \mathcal{K}$-analytic.

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Keywords: Separate and joint continuity, Baire spaces, $ \mathcal{K}$-analytic sets, topological games
Article copyright: © Copyright 1986 American Mathematical Society

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