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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.

Keywords:

topological G-space, Polish group

Related:

TopologicalGSpace, PolishGroup,Group,TopologicalGroup2,PointedTopologicalSpace, BasicResultsInTopologicalGroups

Type of Math Object:

Definition

Major Section:

Reference

Parent:

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## Mathematics Subject Classification

22A22*no label found*22A10

*no label found*22A05

*no label found*54H05

*no label found*

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