uniform structure of a topological group
Let be a topological group. There is a natural uniform structure on which induces its topology. We define a subset of the Cartesian product to be an entourage if and only if it contains a subset of the form
for some neighborhood of the identity element. This is called the right uniformity of the topological group, with which multiplication becomes a uniformly continuous map. The left uniformity is defined in a fashion, but in general they don’t coincide, although they both induce the same topology on .
|Title||uniform structure of a topological group|
|Date of creation||2013-03-22 12:47:21|
|Last modified on||2013-03-22 12:47:21|
|Last modified by||mps (409)|