Definition:Symmetric Filter Basis

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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 $\UU$ if and only if every element of $\BB$ is symmetric.


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