Abstract:
We study the relation between extensions of the Hewitt realcompactification type and spaces of strictly $\tau$-$F$-functions. A criterion is obtained for the realcompleteness of the space of Baire functions of class $\alpha$. It is proved that the space $B(X,G)$ of Baire functions from a $G$-$z$-normal space $X$ to a noncompact metrizable separable space $G$ is Lindel$\ddot{\mathrm o}$f if and only if $X$ is countable.
Citation:
A. V. Osipov, “On the Hewitt realcompactification and $\tau$-placedness of function spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 4, 2019, 177–183
\Bibitem{Osi19}
\by A.~V.~Osipov
\paper On the Hewitt realcompactification and $\tau$-placedness of function spaces
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 4
\pages 177--183
\mathnet{http://mi.mathnet.ru/timm1683}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-4-177-183}
\elib{https://elibrary.ru/item.asp?id=41455534}
Linking options:
https://www.mathnet.ru/eng/timm1683
https://www.mathnet.ru/eng/timm/v25/i4/p177
This publication is cited in the following 1 articles:
Mikhail Al'perin, Alexander V. Osipov, “Dieudonné completeness of function spaces”, Topology and its Applications, 2025, 109261
Citation in format AMSBIB
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