On some properties of the space of upper semicontinuous functions

Abstract

For a Tychonoff space $X$, we will denote by $USC_{p}(X)$ ($B_1(X)$) a set of all real-valued upper semicontinuous functions (a set of all Baire functions of class 1) defined on $X$ endowed with the pointwise convergence topology. In this paper we describe a class of Tychonoff spaces $X$ for which the space $USC_{p}(X)$ is sequentially separable. Unexpectedly, it turns out that this class coincides with the class of spaces for which a stronger form of the sequential separability for the space $B_1(X)$ holds.