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 $S$.

Linguistic Note

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

Its pronunciation is something similar to on-too-rahzh, but the vowel sounds have subtleties.

In (natural language) English the word has come to mean the people one surrounds oneself with, usually in the context of celebrity lifestyles (although I learn that it became the fashionable term for posse or gang among pretentious teenagers in the early 2010's).

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces: Uniformities