Definition:Entourage

Definition
Let $S$ be a set.

Let $\UU \subseteq \powerset {S \times S}$ be a quasiuniformity on $S$.

An element $u \in \UU$ of such a quasiuniformity is known as an entourage of $\UU$'''.

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

Also known as
An entourage of $\UU$ is also known as a relation of $\UU$.

It is to be noted that an entourage of $\UU$ actually is a relation (technically an endorelation) on $S$.