Definition 9.1.3 (Translation-Invariant Uniformity).label Let $G$ be a group, $\fU$ be a uniformity on $G$, and $U \in \fU$, then $U$ is left translation-invariant if for every $z \in G$,
\[U = zU = \bracs{(zx, zy)|(x, y) \in U}\]
and right translation-invariant if for every $z \in G$,
\[U = Uz = \bracs{(xz, yz)|(x, y) \in U}\]
The uniformity $\fU$ is left/right translation-invariant if it admits a fundamental system of left/right translation-invariant entourages.
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