On the Hewitt realcompactification and τ-placedness of function spaces

Abstract

We study the relation between extensions of the Hewitt realcompactification type and spaces of strictly τ -F - functions. A criterion is obtained for the realcompleteness of the space of Baire functions of class α. 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 Lindelöf if and only if X is countable. © 2019 Krasovskii Institute of Mathematics and Mechanics. All right reserved.