Acta Mathematica Hungarica

, Volume 157, Issue 2, pp 459–464 | Cite as

On some properties of the space of upper semicontinuous functions

  • A. V. OsipovEmail author
  • E. G. Pytkeev


For a Tychonoff space X, we will denote by USCp(X) (B1(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 USCp(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 B1(X) holds.

Key words and phrases

sequentially separable function space continuous function upper semicontinuous function Baire function of class 1 

Mathematics Subject Classification

54C35 54C30 54A20 54H05 


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The authors are grateful to Sergey V. Medvedev and the anonymous referee for making several suggestions which improved this paper.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsUral Federal UniversityEkaterinburgRussia
  2. 2.Ural State University of EconomicsEkaterinburgRussia

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