Polish G-space

Definition 0.1.

Let $X$ be a topological $G$ -space (http://planetmath.org/TopologicalGSpace), 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.

Title	Polish G-space
Canonical name	PolishGspace
Date of creation	2013-03-22 18:24:37
Last modified on	2013-03-22 18:24:37
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	9
Author	bci1 (20947)
Entry type	Definition
Classification	msc 22A22
Classification	msc 22A10
Classification	msc 22A05
Classification	msc 54H05
Related topic	TopologicalGSpace
Related topic	PolishGroup
Related topic	Group
Related topic	TopologicalGroup2
Related topic	PointedTopologicalSpace
Related topic	BasicResultsInTopologicalGroups