For the present, this notation will be used although it is usually reserved for sets with a finite number of
elements. Later in this section, differentiable manifolds
are discussed, for which
is the symbol for
the group that is analogous to
. As in the case of
, invariance under
holds in
the absence of any other geometrical structures on
. A study of the subgroups of
and their
relation to each other is thus equivalent to a study of all possible geometries on
and their relation to each
other.