Oopsies daisies.

src/op/banach/multiplicative.tex

@@ -37,7 +37,7 @@
     Let $A$ be a Banach algebra, then $\Omega(A)$ is the \textbf{space of multiplicative linear functionals}, and with respect to the weak-* topology, 
     \begin{enumerate}
         \item If $A$ is unital, then $\Omega(A)$ is a compact Hausdorff space. 
-        \item $\Omega(A) \cup \bracs{0}$ is a compact Hausdorff space, and $\Omega(A)$ is a LCH space.
+        \item $\Omega(A) \cup \bracs{0}$ is a compact Hausdorff space, and $\Omega(A)$ is an LCH space.
     \end{enumerate}
 \end{definition}
 \begin{proof}

src/op/example/c0.tex

@@ -3,12 +3,12 @@
 
 \begin{definition}[$C_0(X)$]
 \label{definition:vanishing-infinity-algebra}
-    Let $X$ be a LCH space, then $C_0(X; \complex)$ equipped with pointwise operations and the uniform norm is a $C^*$-algebra. 
+    Let $X$ be an LCH space, then $C_0(X; \complex)$ equipped with pointwise operations and the uniform norm is a $C^*$-algebra. 
 \end{definition}
 
 \begin{theorem}
 \label{theorem:vanishing-infinity-multiplicative-functional}
-    Let $X$ be a LCH space, then the mapping
+    Let $X$ be an LCH space, then the mapping
     \[
     E: X \to \Omega(C_0(X)) \quad E(x)(f) = f(x)
     \]