# 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