A. K. Mirmostafaee

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Articles: 1

Points of joint continuity of separately continuous mappings

Alireza Kamel Mirmostafaee

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MFAT 15 (2009), no. 4, 356-360


Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $f:X \times Y \to \mathbb{R}$ be a separately continuous mapping. For each $y \in Y$, we define a game $G(Y, \{ y \})$ between players $O$ and $P$, to show that if in this game either $O$ 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 $D \times E$.

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