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 $(x,y)\mapsto x{y}^{-1}$ 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.

Title	topological G-space
Canonical name	TopologicalGspace
Date of creation	2013-03-22 18:24:32
Last modified on	2013-03-22 18:24:32
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	9
Author	bci1 (20947)
Entry type	Definition
Classification	msc 22A15
Classification	msc 22A25
Classification	msc 22A22
Classification	msc 22A10
Classification	msc 54H05
Classification	msc 22A05
Synonym	G-space
Related topic	PolishSpace
Related topic	PolishGSpace
Related topic	PolishGroup