Moreover, multiplication, and inversion in are analytic since these operations are analytic in and restriction to a submanifold ( embedded or immersed ) with the relative topology again yield analytic operations and.
12.
The surface described above, given the relative topology from stereographically projecting the topological torus into "'R "'3 from the north pole of " S " 3.
13.
There are also examples of groups for which one can find points in an arbitrarily small neighborhood ( in the relative topology ) of the identity that are " not " exponentials of elements of.
14.
The example shows that for some groups one can find points in an arbitrarily small neighborhood in the relative topology of the identity that are exponentials of elements of, yet they cannot be connected to the identity with a path staying in.
