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.