Typo fixes.

src/topology/main/c0.tex

@@ -5,7 +5,7 @@
 \label{definition:vanish-at-infinity}
     Let $X$ be a topological space, $E$ be a TVS over $K \in \RC$, and $f \in C(X; E)$, then $f$ \textbf{vanishes at infinity} if for every $U \in \cn_E^o(0)$, $\bracs{f \not\in U}$ is compact.
 
-    The set $C_0(X; \complex)$ is the space of all functions that vanish at infinity. 
+    The set $C_0(X; E)$ is the space of all functions that vanish at infinity. 
 \end{definition}
 
 \begin{proposition}
@@ -35,6 +35,6 @@
     \[
     (\phi f - f)(X) = \underbrace{(\phi f - f)(\bracs{f \not\in U})}_{0} + \underbrace{(\phi f - f)(\bracs{f \in U})}_{\in U} \in U
     \]
-    
+
     so $f \in \ol{C_c(X; E)}$. 
 \end{proof}

src/topology/uniform/metric.tex

@@ -70,15 +70,16 @@ The axioms of uniform spaces strongly resembles working in a metric space. In fa
     \begin{enumerate}
         \item[(FB1)] For any $J, J' \subset I$ finite and $r, r' > 0$,
         \[
-        \bigcap_{j \in J \cup J'}E(d_j, \min(r,r')E(d_j, r \wedge r') \subset \paren{\bigcap_{j \in J}E(d_j, r)} \cap \paren{\bigcap_{j \in J'}E(d_j, r')}
+        \bigcap_{j \in J \cup J'}E(d_j, r \wedge r') \subset \paren{\bigcap_{j \in J}E(d_j, r)} \cap \paren{\bigcap_{j \in J'}E(d_j, r')}
         \]
 
         \item[(UB1)] For each $i \in I$, $d(x, x) = 0$ for all $x \in X$. Thus for any $i \in I$ and $r > 0$, $E(d_i, r)$ contains the diagonal.
         \item[(UB2)] For each $J \subset I$ finite and $r > 0$,
-        \[
-        \paren{\bigcap_{j \in J}E(d_j, r/2)} \circ \paren{\bigcap_{j \in J}E(d_j, r)} \subset \bigcap_{j \in J}E(d_j, r/2) \circ E(d_j, r/2) \subset \bigcap_{j \in J}E(d_j, r)
-        \]
-
+        \begin{align*}
+        \paren{\bigcap_{j \in J}E(d_j, r/2)} \circ \paren{\bigcap_{j \in J}E(d_j, r)} &\subset \bigcap_{j \in J}E(d_j, r/2) \circ E(d_j, r/2) \\
+        &\subset \bigcap_{j \in J}E(d_j, r)
+        \end{align*}
+        
         by the triangle inequality.
     \end{enumerate}