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)) the set of all real-valued upper semicontinuous functions (the 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. © 2019, Akadémiai Kiadó, Budapest, Hungary.