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
Received June 3, 2019
Revised August 12, 2019
Accepted September 5, 2019
Alexander Vladimirovich Osipov, Dr. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620083 Russia; Ural State University of Economicis, Yekaterinburg, 620144 Russia, e-mail: OAB@list.ru
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Cite this article as: A.V.Osipov. On the Hewitt realcompactification and τ-placedness of function spaces, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 177-183.
