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


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