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arXiv · 1008.0180

Comparability of clopen sets in a zero-dimensional dynamical system

Hisatoshi Yuasa
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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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Hisatoshi Yuasa. 2010-08-01. Comparability of clopen sets in a zero-dimensional dynamical system. https://arxiv.org/abs/1008.0180

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