PlanetMath: Polish G-space

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Polish G-space

(Definition)

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.

"Polish G-space" is owned by bci1.

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Keywords:

topological G-space, Polish group

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Cross-references: Polish space, Polish group, continuous, action, topological group

This is version 6 of Polish G-space, born on 2008-09-21, modified 2009-02-02.
Object id is 11059, canonical name is PolishGSpace.
Accessed 349 times total.

Classification:

AMS MSC:	22A05 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Structure of general topological groups)
	54H05 (General topology :: Connections with other structures, applications :: Descriptive set theory )
	22A10 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Analysis on general topological groups)
	22A22 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Topological groupoids )

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