On some properties of the space of upper semicontinuous functions

Alexander V. Osipov; Evgenii G. Pytkeev

paper

On some properties of the space of upper semicontinuous functions

arXiv:1807.01895

Abstract

For a Tychonoff space $X$ , we will denote by $U S C_{p} (X)$ ( $B_{1} (X)$ ) 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 $U S C_{p} (X)$ 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.

7 pages