Definition:Discrete Uniformity

Definition
Let $S$ be a set.

The discrete uniformity on $S$ is the uniformity $\mathcal U$ defined as:
 * $\mathcal U := \left\{{u \subseteq S \times S: \Delta_S \subseteq u}\right\}$

that is, all subsets of the cartesian product on $S$ which contain the diagonal relation on $S$. Hence from Relation Contains Diagonal Relation iff Reflexive it can be considered as the set of all reflexive relations on $S$.