Separate continuity, joint continuity and the Lindelöf property

Kenderov, Petar; Moors, Warren

doi:10.1090/S0002-9939-05-08499-6

Separate continuity, joint continuity and the Lindelöf property
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by Petar S. Kenderov and Warren B. Moors PDF

Proc. Amer. Math. Soc. 134 (2006), 1503-1512 Request permission

Abstract:

In this paper we prove a theorem more general than the following. Suppose that $X$ is Lindelöf and $\alpha$-favourable and $Y$ is Lindelöf and Čech-complete. Then for each separately continuous function $f:X\times Y \rightarrow \mathbb {R}$ there exists a residual set $R$ in $X$ such that $f$ is jointly continuous at each point of $R\times Y$.

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