Comparability of clopen sets in a zero-dimensional dynamical system

2010/08/01 by Hisatoshi Yuasa, Yuasa, Hisatoshi
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #math.DS

paper · pdf · doi:10.48550/arxiv.1008.0180

4 pages

arxiv created 2010/08/01 · openalex publication_date 2010/08/01 · arxiv updated 2010/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a homeomorphism on a totally disconnected, compact metric space and define a binary relation on the family of clopen subsets. We will show that the comparability of any clopen sets with respect to the relation is equivalent to the unique ergodicity of the homeomorphism.

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