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.
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