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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Joint continuity of separately continuous functions


Author: Jens Peter Reus Christensen
Journal: Proc. Amer. Math. Soc. 82 (1981), 455-461
MSC: Primary 54C05
MathSciNet review: 612739
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Abstract: It is shown that a separately continuous function $ f:X \times Y \to Z$ from the product of a certain type of Hausdorff space $ X$ and a compact Hausdorff space $ Y$ into a metrizable space $ Z$ is jointly continuous on a set of the type $ A \times Y$, where $ A$ is a dense $ {G_\delta }$ set in $ X$. The class of Hausdorff spaces $ X$ in question is defined by a gametheoretic condition. The result improves (and simplifies the proof of) a recent result of Namioka. Many "deep" theorems in functional analysis and automatic continuity theory are easy corollaries.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0612739-1
PII: S 0002-9939(1981)0612739-1
Keywords: Separate and joint continuity, automatic continuity, denting points
Article copyright: © Copyright 1981 American Mathematical Society