Let us recall the definition of a topological group; this is a group
together
with a topology on
such that
is continuous, i.e., from
into
.
Note also that
is regarded as a topological space defined by the product topology.
Definition 0.1
Consider
to be a topological group with the above notations, and also let
be a topological space, such that an action
of
on
is
continuous if
is continuous; with these conditions,
is defined to be
a topological G-space.