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Geometrical and Topological Properties of a Subspace Pf(X) of Probability Measures

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Abstract

We prove that for a compact X, the space Pf(X) is an absolute neighbourhood retract if and only if X is an absolute neighbourhood retract. Further, we demonstrate that a functor Pf preserves the property of a compact to be Q-manifold or Hilbert cube, preserves the property for leaves of maps to be absolute neighbourhood retracts in the class of compacts, to be Q-manifold or Hilbert cube (finite sum of Hilbert cubes).

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Acknowledgments

The author expresses his deep appreciation to the reviewer for the help in correction of imperfections in the paper, and his useful advices.

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Authors and Affiliations

  1. Tashkent Institute of Architecture and Civil Engineering, 13 Navoi str., Tashkent, 100011, Uzbekistan

    A. A. Zaitov

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  1. A. A. Zaitov
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Correspondence to A. A. Zaitov.

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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 10, pp. 28–37.

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Zaitov, A.A. Geometrical and Topological Properties of a Subspace Pf(X) of Probability Measures. Russ Math. 63, 24–32 (2019). https://doi.org/10.3103/S1066369X19100049

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  • DOI: https://doi.org/10.3103/S1066369X19100049

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