Special Session 7: Topological and combinatorial dynamics

Contents

Let $G$ be a complete separable metric group and $X$ be a separable metric space. Suppose that $G \times X \to X$ is a continuous action by $G$ on $X$. Let $C$ be a metric compactification of $X$. Suppose that for each $g \in G$ the homeomorphism associated with $g$ has an extension to a homeomorphism on $C$. Then the action $G \times C \to C$ is also continuous.
This theorem has implications for the Hilbert-Smith Conjecture. There are also applications to topological group actions in many settings. We will discuss these in this talk.