Definition:Uniformity/Mistake
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Source Work
1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.):
- Part $\text I$: Basic Definitions
- Section $5$. Metric Spaces
- Uniformities
- Section $5$. Metric Spaces
Mistake
- The quasiuniformity $\UU$ is a uniformity if the following additional condition is satisfied:
- $\text U 5$: If $u \in \UU$, then $u^{-1} \in \UU$ where $u^{-1} = \set {\tuple {y, x}: \tuple {x, y} \in \UU}$.
Correction
That should read:
- $\text U 5$: If $u \in \UU$, then $u^{-1} \in \UU$ where $u^{-1} = \set {\tuple {y, x}: \tuple {x, y} \in u}$.
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