Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property

Abstract

We prove that every expansive continuous action with the weak specification property of an amenable group $G$ on a compact Hausdorff space $X$ has the Myhill property, i.e., every pre-injective continuous self-mapping of $X$ commuting with the action of $G$ on $X$ is surjective. This extends a result previously obtained by Hanfeng Li in the case when $X$ is metrizable.

We have corrected a few typos and removed part (iii) of Theorem 4.2. It is accepted for publication in the Journal of Dynamical and Control Systems

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• Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity