Definition:Group Action by Homeomorphisms

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 for all $g\in G$, the map
 * $\phi_g : X \to X : x \mapsto \phi(g,x)$

is a homeomorphism.

Also see

 * Definition:Continuous Group Action
 * Definition:Homeomorphism Group
 * Discrete Group Acts Continuously iff Acts by Homeomorphisms