Polish G-space

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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.

References

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

Type of Math Object:

Definition

Major Section:

Reference

Parent:

topological G-space

Groups audience:

Editing Group for PolishGSpace

Mathematics Subject Classification

22A22 Topological groupoids (including differentiable and Lie groupoids)
22A10 Analysis on general topological groups
22A05 Structure of general topological groups
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)

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