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Trudy Inst. Mat. i Mekh. UrO RAN, 2019, Volume 25, Number 4, Pages 177–183 (Mi timm1683)  

On the Hewitt realcompactification and $\tau$-placedness of function spaces

A. V. Osipovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

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.

Keywords: realcomplete spaces, weak functional tightness, Baire function, $\tau$-placedness, Hewitt realcompactification.

DOI: https://doi.org/10.21538/0134-4889-2019-25-4-177-183

Full text: PDF file (184 kB)
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Bibliographic databases:

UDC: 515.122+517.982
MSC: 54C35 54C25
Received: 03.06.2019
Revised: 12.08.2019
Accepted:12.09.2019

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

Citation in format AMSBIB
\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}


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