Editing Topological group (section)

=== Uniform space ===

Every topological group can be viewed as a [[uniform space]] in two ways; the ''left uniformity'' turns all left multiplications into uniformly continuous maps while the ''right uniformity'' turns all right multiplications into uniformly continuous maps.{{sfn|Bourbaki|1998|loc=section III.3}}
If {{mvar|G}} is not abelian, then these two need not coincide. 
The uniform structures allow one to talk about notions such as [[completeness (topology)|completeness]], [[uniformly continuous|uniform continuity]] and [[uniform convergence]] on topological groups.