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ON A PROBLEM OF TALAGRAND CONCERNING SEPARATELY CONTINUOUS FUNCTIONS
Published online by Cambridge University Press: 06 February 2020
Abstract
We construct a separately continuous function $e:E\times K\rightarrow \{0,1\}$ on the product of a Baire space
$E$ and a compact space
$K$ such that no restriction of
$e$ to any non-meagre Borel set in
$E\times K$ is continuous. The function
$e$ has no points of joint continuity, and, hence, it provides a negative solution of Talagrand’s problem in Talagrand [Espaces de Baire et espaces de Namioka, Math. Ann.270 (1985), 159–164].
Keywords
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 5 , September 2021 , pp. 1719 - 1728
- Copyright
- © Cambridge University Press 2020
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