Definition:Separated Quasiuniformity
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Definition
Let $\UU$ be a quasiuniformity on a set $S$.
Then $\UU$ is separated if and only if:
- $\forall u, v \in \UU: u \cap v = \Delta_S$
That is, if and only if the intersection of all its entourages is the diagonal relation.
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