We show how all topological full groups coming from a one-sided irreducible shift of finite type, as studied by Matui, can be re-interpreted as groups of colour-preserving tree almost automorphisms. As an application, we show that they admit t.d.l.c. completions of arbitrary finite local prime content. This applies in particular to Thompson's $V$.

中文翻译：

---

汤普森 V 的拓扑全群和 tdlc 补全

我们展示了所有来自有限类型的单边不可约移位的拓扑完整群，如 Matui 所研究的，可以重新解释为几乎自同构的保色树群。作为一个应用，我们证明他们承认任意有限局部素数内容的 tdlc 补全。这尤其适用于汤普森的 $V$。