Definition:Symmetric Entourage
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Definition
Let $S$ be a set.
Let $\UU$ be a quasiuniformity on $S$.
Let $u \in \UU$ be an entourage of $\UU$ such that:
- $u = u^{-1}$
where $u^{-1}$ is the inverse of $u$.
Then $u$ is symmetric.
Also see
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