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

 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