Definition:Continuous Group Action

Definition
Let $G$ be a topological group.

Let $X$ be a topological space.

A group action $\phi: G \times X \to X$ is defined as continuous $\phi$ is continuous.

Also see

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