Geometrical properties of the space P_f(X) of probability measures

2018/09/06 by A. A. Zaitov, Zaitov, A. A.
Mathematics · #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1809.03331

openalex publication_date 2018/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that for a compact space X inclusion P_f(X)∈ ANR holds if and only if X∈ ANR. Further, it is shown that the functor P_f preserves property of a compact to be Q-manifold or a Hilbert cube, properties of maps fibres to be ANR-compact, Q-manifold, Hilbert cube (the finite of Hilbert cube).

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