In topology, a continuous group action on a topological space X is a group action of a topological group G that is continuous: i.e., is a continuous map. Together with the group action, X is called a Gspace. If is a continuous group homomorphism of topological groups and if X is a Gspace, then H can act on X by restriction: , making X a Hspace. Often f is either an inclusion or a quotient map. In particular, any topological space may be thought of as a Gspace via (and G would act trivially.)
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