Definition:Symmetric Filter Basis

Definition
Let $S$ be a set.

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

From the definition, a quasiuniformity on $S$ is also a filter on the cartesian product $S \times S$.

Let $\mathcal B \subset \mathcal P \left({S \times S}\right)$ be a filter basis of $\mathcal U$.

Then $\mathcal B$ is a symmetric filter basis of $\mathcal U$ iff every element of $\mathcal B$ is symmetric.