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.
References
- 1 Howard Becker, Alexander S. Kechris. 1996. The Descriptive Set Theory of Polish Group Actions Cambridge University Press: Cambridge, UK, p.14.
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 |