Slight adjustment to topological groups.

src/topology/groups/definition.tex

@@ -10,7 +10,7 @@
         \item The inversion map $G \to G$ with $g \mapsto g^{-1}$ is continuous. 
     \end{enumerate}
     
-    then the pair $(E, \mathcal{T})$ is a \textbf{topological group}. 
+    then the pair $(G, \mathcal{T})$ is a \textbf{topological group}. 
 \end{definition}
 
 \begin{definition}[Translation-Invariant Topology]
@@ -128,4 +128,21 @@
     \]
 
     so $x \in yB \subset AB$.
-\end{proof}
+\end{proof}
+
+\begin{definition}[Symmetric Neighbourhood]
+\label{definition:tg-symmetric-neighbourhood}
+    Let $G$ be a topological group and $U \in \cn_G(1)$, then $U$ is \textbf{symmetric} if $U = U^{-1}$. 
+\end{definition}
+
+\begin{proposition}
+\label{proposition:tg-good-neighbourhood-base}
+    Let $G$ be a topological group, then
+    \begin{enumerate}
+        \item $G$ admits a fundamental system of neighbourhoods at $0$ consisting of symmetric sets.
+        \item The system in (1) may be taken to be open or closed. 
+    \end{enumerate}
+\end{proposition}
+% Obvious so proof omitted.
+
+