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On some properties of the space of upper semicontinuous functions

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, 620219, Ekaterinburg, Russia

    A. V. Osipov & E. G. Pytkeev

  2. Ural State University of Economics, 620144, Ekaterinburg, Russia

    A. V. Osipov

Authors
  1. A. V. Osipov
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  2. E. G. Pytkeev
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Correspondence to A. V. Osipov.

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Osipov, A.V., Pytkeev, E.G. On some properties of the space of upper semicontinuous functions. Acta Math. Hungar. 157, 459–464 (2019). https://doi.org/10.1007/s10474-018-00906-1

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  • DOI: https://doi.org/10.1007/s10474-018-00906-1

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