|
This article is cited in 13 scientific papers (total 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.
Received: 05.09.2018 Revised: 15.11.2018 Accepted: 19.12.2018
Citation:
A. A. Zaitov, “Geometrical and topological properties of a subspace $P_f(X)$ of probability measures”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 10, 28–37; Russian Math. (Iz. VUZ), 63:10 (2019), 24–32
Linking options:
https://www.mathnet.ru/eng/ivm9504 https://www.mathnet.ru/eng/ivm/y2019/i10/p28
|
Statistics & downloads: |
Abstract page: | 245 | Full-text PDF : | 120 | References: | 35 | First page: | 7 |
|