topological G-space

0.1 Essential data

Let us recall the definition of a topological groupMathworldPlanetmath; this is a group (G,.,e) together with a topologyMathworldPlanetmathPlanetmath on G such that (x,y)xy-1 is continuousPlanetmathPlanetmath, i.e., from G×G into G. Note also that G×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×XX 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