\begin{definition}[Definition:Discrete Uniformity]
Let $S$ be a set.
The '''discrete uniformity''' on $S$ is the uniformity $\UU$ defined as:
:$\UU := \set {u \subseteq S \times S: \Delta_S \subseteq u}$
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 $S$.
\end{definition}