Geodesic
On the Hewitt realcompactification and $\tau$-placedness of function spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 177-183

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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. 
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     author = {A. V. Osipov},
     title = {On the {Hewitt} realcompactification and $\tau$-placedness of function spaces},
     journal = {Trudy Instituta matematiki i mehaniki},
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A. V. Osipov. On the Hewitt realcompactification and $\tau$-placedness of function spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 177-183. http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a18/