Definition 0.1. 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 × X → X is continuous). If
G is a Polish group and X is also a Polish space, then X is called a Polish G-space.
References
[1] Howard Becker, Alexander S. Kechris. 1996. The Descriptive Set Theory of Polish
Group Actions Cambridge University Press: Cambridge, UK, p.14.
