"Uniform groups" (similar to topological groups)? Why have I heard about topological groups, but nothing about "uniform groups" (uniform spaces endowed with a group)?

A topological group is a uniform space in two ways... one by left translation, the other by right translation.  Replace $x\cdot y^{-1}$ in Owen's answer by $y^{-1}\cdot x$ to switch.  The two are equivalent in abelian groups, compact groups, and in many others.  But not all.  
I have heard it said that the notion of "uniform space" was originally given as a common generalization of "metric space" and "topological group".
