Fixed typos and migrated to new version.

src/fa/lc/hahn-banach.tex

@@ -77,7 +77,7 @@
 \begin{proof}
     By translation, assume without loss of generality that $0 \in A$. In which case, $A \in \cn^o(0)$ is convex.
 
-    Let $[\cdot]_A: E \to [0, \infty)$ be the \hyperref[gaugeg]{definition:gauge} of $A$, then $[\cdot]_A$ is a sublinear functional on $E$. For any $y, z \in E$ and $t > 0$ with $y, z \in tA$,
+    Let $[\cdot]_A: E \to [0, \infty)$ be the \hyperref[gauge]{definition:gauge} of $A$, then $[\cdot]_A$ is a sublinear functional on $E$. For any $y, z \in E$ and $t > 0$ with $y, z \in tA$,
     \[
     \abs{[y]_A - [z]_A} \le [y - z]_A \le t
     \]

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
     \[
     \fB = \bracs{\pi(U)| U \in \cn(0) \text{ circled and radial}}
     \]