Points de continuité d’une fonction séparément continue

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.