Definition:Entourage

Definition
Let $S$ be a set and 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 $S$.

Linguistic Note
The word entourage is a French one, meaning neighborhood or surroundings.

In (natural language) English the word has come to mean the people one surrounds oneself with, usually in the context of celebrity lifestyles.