Definition:Uniformity

Definition
Let $S$ be a set.

A uniformity on $S$ is a set of subsets $\UU$ of the cartesian product $S \times S$ satisfying the quasiuniformity axioms:

and also:
 * $(\text U 5): \forall u \in \UU: \exists u^{-1} \in \UU$ where $u^{-1}$ is defined as:
 * $u^{-1} := \set {\tuple {y, x}: \tuple {x, y} \in u}$
 * That is, all elements of $\UU$ are symmetric.

These five axioms are together known as the uniformity axioms.

Also see

 * Definition:Quasiuniformity
 * Definition:Entourage