Article

Homotopy Properties of the Space If(X) of Idempotent Probability Measures

A. A. ZaitovTashkent Institute of Architecture and Civil Engineering, Tashkent, 100011, UzbekistanA. Ya. IshmetovTashkent Institute of Architecture and Civil Engineering, Tashkent, 100011, Uzbekistan

Mathematical Notesjournal2019en

ABI

Abstract

A subspace If(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 If(X) is a contractible compact space as well. It is shown that the shapes of the compact spaces X and If(X) are equal. It is also proved that, given a compact space X, the compact space If(X) is an absolute neighborhood retract if and only if so is X.

Topics

Advanced Topology and Set Theory Mathematical and Theoretical Analysis

Identifiers

DOI: 10.1134/s0001434619090244

Citations and references

Cited by 8 19 references

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