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namioka property

Journal of the Institute of Mathematics of Jussieu (1)

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ON A PROBLEM OF TALAGRAND CONCERNING SEPARATELY CONTINUOUS FUNCTIONS
Part of
Volodymyr Mykhaylyuk, Roman Pol
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 5 / September 2021

Published online by Cambridge University Press:

06 February 2020, pp. 1719-1728

Print publication:

September 2021
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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].