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

## TL;DR

This paper proves that expansive actions with the weak specification property of an amenable group on a compact space have the Myhill property, meaning pre-injective maps commuting with the action are surjective, extending previous metrizable results.

## Contribution

It extends the Myhill property to expansive actions with weak specification on non-metrizable compact spaces for amenable groups.

## Key findings

- Pre-injective maps are surjective under the given conditions.
- The result generalizes previous metrizable space cases.
- It links expansive actions, weak specification, 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.