Replaced mentions of normed spaces to normed vector spaces.

src/fa/norm/separable.tex

@@ -1,9 +1,9 @@
-\section{Separable Normed Spaces}
+\section{Separable Normed Vector Spaces}
 \label{section:separable-banach-space}
 
 \begin{proposition}
 \label{proposition:separable-dual}
-    Let $E$ be a separable normed space, then $E^*$ is separable with respect to the weak*-topology. 
+    Let $E$ be a separable normed vector space, then $E^*$ is separable with respect to the weak*-topology. 
 \end{proposition}
 \begin{proof}
     Let $\seq{x_n} \subset E$ be a dense subset and $S = \bracsn{\phi \in E^*| \norm{\phi}_{E^*} \le 1}$. For each $N \in \natp$, let
@@ -23,7 +23,7 @@
 
 \begin{proposition}
 \label{proposition:separable-banach-borel-sigma-algebra}
-    Let $E$ be a separable normed space, then the Borel $\sigma$-algebra on $E$ is generated by the following families of sets:
+    Let $E$ be a separable normed vector space, then the Borel $\sigma$-algebra on $E$ is generated by the following families of sets:
     \begin{enumerate}
         \item Open sets in $E$ with respect to the strong topology. 
         \item $\bracs{B(x, r)|x \in E, r > 0}$.