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topological G-space
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(Definition)
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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.
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- 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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"topological G-space" is owned by bci1.
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Cross-references: action, product topology, continuous, topology, group, topological group
There are 3 references to this entry.
This is version 6 of topological G-space, born on 2008-09-21, modified 2009-04-19.
Object id is 11057, canonical name is TopologicalGSpace.
Accessed 639 times total.
Classification:
| AMS MSC: | 22A05 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Structure of general topological groups) | | | 54H05 (General topology :: Connections with other structures, applications :: Descriptive set theory ) | | | 22A10 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Analysis on general topological groups) | | | 22A22 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Topological groupoids ) | | | 22A25 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Representations of general topological groups and semigroups) | | | 22A15 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Structure of topological semigroups) |
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Pending Errata and Addenda
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