Definition:Entourage

Definition
Let $S$ be a set.

Let $\mathcal U \subseteq \mathcal P \left({S \times S}\right)$ be a quasiuniformity on $S$.

An element $u \in \mathcal U$ of such a quasiuniformity is known as an entourage (or relation) of $\mathcal U$.

Note that an entourage of $\mathcal U$ actually is a relation on $S$.