topological G-space

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.

Bibliography

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



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