Definition 9.1.2 (Translation-Invariant Topology).label Let $G$ be a group and $\topo \subset 2^{G}$ be a topology, then $\topo$ is left translation-invariant if for every $U \in \topo$ and $g \in G$, $gU \in \topo$, and right translation-invariant if for every $U \in \topo$ and $g \in G$, $Ug \in \topo$. If $\topo$ is both left and right translation-invariant, then $\topo$ is translation-invariant.