Definition:Uniformity/Mistake

Source Work

 * Part $\text I$: Basic Definitions
 * Section $5$. Metric Spaces
 * Uniformities
 * 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 $u^{-1} = \set {\tuple {y, x}: \tuple {x, y} \in u}$.