On some properties of the space of upper semicontinuous functions
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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 phrasessequentially separable function space continuous function upper semicontinuous function Baire function of class 1
Mathematics Subject Classification54C35 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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