0.1 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)
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.
