Definition:Group Action by Homeomorphisms
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Definition
Let $G$ be a group.
Let $X$ be a topological space.
Let $\phi: G \times X \to X$ be a group action
Then $G$ acts by homeomorphisms if and only if for all $g \in G$, the mapping:
- $\phi_g : X \to X : x \mapsto \phi \left({g, x}\right)$
is a homeomorphism.