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topological G-space∗
bci1†
2013-03-22 1:45:12
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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) 7→ xy −1 is continuous, 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 × X → X is continuous; with these
conditions, X is defined to be a topological G-space.
References
[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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