Definition:Inverse 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 $\UU$.
Then the inverse entourage $u^{-1}$ is defined as:
- $u^{-1} := \set {\tuple {y, x}: \tuple {x, y} \in u}$
Also see
- Definition:Inverse Relation, which is consistent with this definition.
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