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topological G-space (Definition)

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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See Also: Polish G-space, Polish group, variable topology

Other names:  G-space
Keywords:  topolgical G-space, topological group G, action of a group on a topological space

Cross-references: topological, group, topological group
There are 3 references to this object.

This is version 1 of topological G-space, born on 2009-04-19.
Object id is 675, canonical name is TopologicalGSpace.
Accessed 509 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
Pending Errata and Addenda
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