Definition:Symmetric Entourage

Definition
Let $S$ be a set.

Let $\mathcal U$ be a quasiuniformity on $S$.

Let $u \in \mathcal U$ be an entourage of $\mathcal U$ such that:
 * $u = u^{-1}$

where $u^{-1}$ is the inverse of $u$.

Then $u$ is symmetric.

Also see

 * Symmetric relation, which is consistent with this definition: see Relation equals Inverse iff Symmetric.