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ON A PROBLEM OF TALAGRAND CONCERNING SEPARATELY CONTINUOUS FUNCTIONS

Part of: Linear function spaces and their duals Peculiar spaces Spaces with richer structures

Published online by Cambridge University Press:  06 February 2020

Volodymyr Mykhaylyuk Open the ORCID record for Volodymyr Mykhaylyuk [Opens in a new window]  and
Roman Pol Open the ORCID record for Roman Pol [Opens in a new window]
Volodymyr Mykhaylyuk
Affiliation:
Jan Kochanowski University in Kielce, Poland Yurii Fedkovych Chernivtsi National University, Ukraine ([email protected])
Roman Pol
Affiliation:
University of Warsaw, Poland ([email protected])
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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

separately continuous functionBaire spacecompact spaceextremally disconnected spaceNamioka property

MSC classification

Primary: 54E52: Baire category, Baire spaces 54G05: Extremally disconnected spaces, $F$-spaces, etc. 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 5 , September 2021 , pp. 1719 - 1728
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Copyright
© Cambridge University Press 2020

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