PlanetPhysics/Topological G Space

Essential Data

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Let us recall the definition of a topological group; this is a group together with a topology on such that is continuous, i.e., from into . Note also that is regarded as a topological space defined by the product topology.

Definition: Topological Group

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Consider   to be a topological group with the above notations, and also let   be a topological space, such that an action   of   on   is continuous if   is continuous; with these conditions,   is defined to be a topological G-space .

All Sources

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[1]

References

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