Lie subgroup

Summary

A Lie subgroup of a Lie group $G$ is a subgroup with its own Lie group structure. The inclusion into $G$ must be a smooth immersion. Its topology may be finer than the subspace topology, so a Lie subgroup need not be closed or embedded. The connected Lie subgroups of $G$ correspond exactly to the Lie subalgebras of the Lie algebra of $G$.