Definition:Symmetric Filter Basis

Definition
Let $S$ be a set.

Let $\UU$ be a quasiuniformity on $S$.

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

Let $\BB \subset \powerset {S \times S}$ be a filter basis of $\UU$.

Then $\BB$ is a symmetric filter basis of $\UU$ every element of $\BB$ is symmetric.