Polish G-space

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 \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.

Bibliography

1
Howard Becker, Alexander S. Kechris. 1996. The Descriptive Set Theory of Polish Group Actions Cambridge University Press: Cambridge, UK, p.14.



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