The topological definition implies the statement that if two Lie groups are isomorphic as topological groups, then they are isomorphic as Lie groups. In fact, it states the general principle that, to a large extent, the topology of a Lie group together with the group law determines the geometry of the group.
The topological definition implies the statement that if two Lie groups are isomorphic as topological groups, then they are isomorphic as Lie groups In fact, it states the general principle that, to a large extent, the topology of a Lie group together with the group law determines the geometry of the group.