Replaced mentions of normed spaces to normed vector spaces.

src/fa/norm/normed.tex

@@ -34,7 +34,7 @@
 
 \begin{theorem}[Successive Approximation]
 \label{theorem:successive-approximation}
-    Let $E, F$ be normed spaces, $T \in L(E; F)$, $C \ge 0$, and $\gamma \in (0, 1)$. If for all $y \in F$, there exists $x \in E$ such that:
+    Let $E, F$ be normed vector spaces, $T \in L(E; F)$, $C \ge 0$, and $\gamma \in (0, 1)$. If for all $y \in F$, there exists $x \in E$ such that:
     \begin{enumerate}
         \item[(a)] $\norm{x}_E \le C\norm{y}_F$.
         \item[(b)] $\norm{y - Tx}_F \le \gamma \norm{y}_F$.
@@ -69,7 +69,7 @@
 
 \begin{theorem}[Uniform Boundedness Principle]
 \label{theorem:uniform-boundedness}
-    Let $E, F$ be normed spaces and $\mathcal{T} \subset L(E; F)$. If
+    Let $E, F$ be normed vector spaces and $\mathcal{T} \subset L(E; F)$. If
     \begin{enumerate}
         \item For every $x \in E$, $\sup_{T \in \mathcal{T}}\norm{Tx}_F < \infty$.
         \item $E$ is a Banach space.
@@ -90,7 +90,7 @@
 
 \begin{proposition}
 \label{proposition:dual-norm}
-    Let $E$ be a normed space, then for any $x \in E$, 
+    Let $E$ be a normed vector space, then for any $x \in E$, 
     \[
     \norm{x}_E = \sup_{\substack{\phi \in E^* \\ \norm{\phi}_{E^*} = 1}}\dpn{x, \phi}{E}
     \]