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Hometopological G-space

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# topological G-space

# 0.1 Essential data

Let us recall the definition of a *topological group*; this is a group $(G,.,e)$ together
with a topology on $G$ such that $(x,y)\mapsto xy^{{-1}}$ is continuous, i.e., from $G\times G$ into $G$.
Note also that $G\times G$ is regarded as a topological space defined by the product topology.

###### Definition 0.1.

Consider $G$ to be a topological group with the above notations, and also let
$X$ be a topological space, such that an action $a$ of $G$ on $X$ is
continuous if $a:G\times X\to X$ is continuous; with these conditions, $X$ is defined to be
a *topological 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:

topolgical G-space, topological group G, action of a group on a topological space

Related:

PolishSpace, PolishGSpace, PolishGroup

Synonym:

G-space

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

22A15*no label found*22A25

*no label found*22A22

*no label found*22A10

*no label found*54H05

*no label found*22A05

*no label found*

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