Definition:Uniformity

Definition
Let $S$ be a set.

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

... and also:
 * $(U5)$: $\forall u \in \mathcal U: \exists u^{-1} \in \mathcal U$ where $u^{-1}$ is defined as:
 * $u^{-1} := \left\{{\left({y, x}\right): \left({x, y}\right) \in u}\right\}$
 * That is, all elements of $\mathcal U$ are symmetric.

These five axioms are together known as the uniformity axioms.

Also see

 * Quasiuniformity


 * Entourage