This article is cited in 14 papers

Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures

A. A. Zaitov, A. Ya. Ishmetov

Tashkent Institute of Architecture and Civil Engineering

Abstract: A subspace $I_f(X)$ of the space of idempotent probability measures on a given compact space $X$ is constructed. It is proved that if the initial compact space $X$ is contractible, then $I_f(X)$ is a contractible compact space as well. It is shown that the shapes of the compact spaces $X$ and $I_f(X)$ are equal. It is also proved that, given a compact space $X$, the compact space $I_f(X)$ is an absolute neighborhood retract if and only if so is $X$.

Keywords: idempotent measure, compact space, absolute neighborhood retract, shape.

UDC: 515.12

PACS: 02.40.Pc

Received: 29.08.2018
Revised: 10.02.2019

DOI: 10.4213/mzm12166

 English version: Mathematical Notes, 2019, 106:4, 562–571

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