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

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.