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On Projectively Inductively Closed Subfunctors of the Functor P of Probability Measures

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Abstract

In this paper, we examine topological and dimensional properties of metric, Tychonoff, and compact C-spaces under the action of the covariant subfunctor Pf of the functor P of probability measures in the category of metric, compact, and paracompact spaces and continuous self-mappings. We consider geometric properties of spaces under the action of the subfunctor Pf of the functor P of probability measures and show that this functor Pf is an open σ-p.i.c. functor that preserves soft mappings and various types of topological spaces.

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Authors and Affiliations

  1. Uzbekistan Academy of Sciences, V. I. Romanovskiy Institute of Mathematics, Tashkent, Uzbekistan

    Sh. A. Ayupov

  2. Tashkent State Pedagogical University named after Nizami, Tashkent, Uzbekistan

    T. F. Zhuraev

Authors
  1. Sh. A. Ayupov
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  2. T. F. Zhuraev
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Correspondence to Sh. A. Ayupov.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 144, Proceedings of the Conference “Problems of Modern Topology and Its Applications” (May 11–12, 2017), Tashkent, Uzbekistan, 2018.

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Ayupov, S.A., Zhuraev, T.F. On Projectively Inductively Closed Subfunctors of the Functor P of Probability Measures. J Math Sci 245, 382–389 (2020). https://doi.org/10.1007/s10958-020-04700-9

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  • DOI: https://doi.org/10.1007/s10958-020-04700-9

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