PlanetPhysics/Polish G Space

Let $$X$$ be a topological $G$-space, and $$G$$ its associated topological group (that is, such that an action $$a$$ of $$G$$ on $$X$$ is continuous if $$a : G \times X \to X$$ is continuous). If $$G$$ is a Polish group and $$X$$ is also a Polish space, then $$X$$ is called a Polish G-space.