Fixed typos and migrated to new version.

src/fa/tvs/quotient.tex

@@ -23,7 +23,7 @@
 \begin{proof}
     Let $\td E = E/M$ be the algebraic quotient of $E$ by $M$, and equip it with the quotient topology by $\pi$.
 
-    (1): By \autoref{definition:quotient-topology}, for each $\pi(U) \subset E/M$, $\pi(U)$ is open if and only if $U$ is open. Since the topology on $E$ is translation-invariant, so is the quotient topology on $E/M$. Let
+    (1): For each $U \subset E$ open, $\pi^{-1}\pi(U) = U + M$ is open, so $\pi(U)$ is open as well by \autoref{definition:quotient-topology}. Since the topology on $E$ is translation-invariant, so is the quotient topology on $E/M$. Let
     \[
     \fB = \bracs{\pi(U)| U \in \cn(0) \text{ circled and radial}}
     \]