This article is cited in 13 papers

Geometrical and topological properties of a subspace $P_f(X)$ of probability measures

A. A. Zaitov

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

Abstract: We prove that for a compact $X$ the space $P_{f}(X)$ is an absolute neighbourhood retract if and only if $X$ is an absolute neighbourhood retract. Futher, we demonstrate that a functor $P_{f}$ preserves the property of a compact to be $Q$-manifold or Hilbert cube, preserves the propetry of a map to be absolute neighbourhood retract in a class of compact, to be $Q$-manifold or Hilbetr cube (finite sum of Hilbert cube).

Keywords: propability measure, compact Hausdorff space (compact), retract, $A(N)R$-space.

UDC: 515.12

Received: 05.09.2018
Revised: 15.11.2018
Accepted: 19.12.2018

DOI: 10.26907/0021-3446-2019-10-28-37

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:10, 24–32

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