Updated Schaefer & Wolff citations.

src/fa/tvs/bounded.tex

@@ -6,7 +6,7 @@
     Let $E$ be a TVS over $K \in \RC$ and $B \subset E$, then $B$ is \textbf{bounded} if for every $U \in \cn(0)$, there exists $\lambda \in K$ such that $\lambda U \supset B$. The collection $B(E)$ is the set of all bounded sets of $E$.
 \end{definition}
 
-\begin{proposition}[{{\cite[1.5.1]{SchaeferWolff}}}]
+\begin{proposition}[{{\cite[I.5.1]{SchaeferWolff}}}]
 \label{proposition:bounded-operations}
     Let $E$ be a TVS over $K \in \RC$ and $A, B \in B(E)$, then the following sets are bounded:
     \begin{enumerate}

src/fa/tvs/completion.tex

@@ -29,6 +29,6 @@
     By continuity and the density of $\iota(E)$ in $E$, $\wh E$ with these operations forms a TVS, and $T$ is linear.
 \end{proof}
 
-\begin{remark}[{{\cite[Section 1.1]{SchaeferWolff}}}]
+\begin{remark}[{{\cite[Section I.1]{SchaeferWolff}}}]
 	The Hausdorff completion works in general with arbitrary valuated fields. Though the completion yields a TVS over the completion of the field, the field need not to be complete.
 \end{remark}

src/fa/tvs/definition.tex

@@ -43,7 +43,7 @@
 \end{proof}
 
 
-\begin{proposition}[{{\cite[1.1.4]{SchaeferWolff}}}]
+\begin{proposition}[{{\cite[I.1.4]{SchaeferWolff}}}]
 \label{proposition:tvs-uniform}
     Let $E$ be a TVS over $K \in \bracs{\real, \complex}$, then:
     \begin{enumerate}
@@ -85,7 +85,7 @@
     \]
 \end{proof}
 
-\begin{proposition}[{{\cite[1.1.1]{SchaeferWolff}}}]
+\begin{proposition}[{{\cite[I.1.1]{SchaeferWolff}}}]
 \label{proposition:tvs-set-operations}
     Let $E$ be a TVS over $K \in \RC$ and $A, B \subset E$, then:
     \begin{enumerate}
@@ -148,7 +148,7 @@
     Let $U \in \cn(0)$ be closed, then there exists a balanced neighbourhood $V \in \cn^o(0)$ such that $V \subset U$. In which case, for any $\lambda \in K$ with $0 < \abs{\lambda} \le 1$, $\lambda \overline{V} = \overline{\lambda V} \subset \overline{V}$ by (TVS2). Therefore $\overline{V} \subset U$ is balanced as well.
 \end{proof}
 
-\begin{proposition}[{{\cite[1.2]{SchaeferWolff}}}]
+\begin{proposition}[{{\cite[I.1.2]{SchaeferWolff}}}]
 \label{proposition:tvs-0-neighbourhood-base}
     Let $E$ be a vector space over $K \in \RC$, and $\topo$ be a vector space topology on $E$, then there exists a fundamental system of neighbourhoods $\fB \subset \cn_E(0)$ such that:
     \begin{enumerate}

src/fa/tvs/metric.tex

@@ -71,7 +71,7 @@
     $(4) \Rightarrow (1)$: By \ref{definition:tvs-pseudonorm-topology}, for each $r > 0$, $\rho^{-1}([0, r)) \in \cn_E(0)$. Thus for any $x, y \in E$, if $x - y \in \rho^{-1}([0, r))$, then $\abs{\rho(x) - \rho(y)} \le r$. Therefore $\rho \in UC(E; [0, \infty))$.
 \end{proof}
 
-\begin{lemma}[{{\cite[Theorem 1.6.1]{SchaeferWolff}}}]
+\begin{lemma}[{{\cite[Theorem I.6.1]{SchaeferWolff}}}]
 \label{lemma:tvs-sequence-pseudonorm}
     Let $E$ be a vector space over $K \in \RC$, $\seq{U_n} \subset 2^E$ such that
     \begin{enumerate}
@@ -143,7 +143,7 @@
     Let $E$ be a TVS over $K \in \RC$, then $E$ is \textbf{locally bounded} if there exists $U \in \cn^o(0)$ bounded.
 \end{definition}
 
-\begin{proposition}[{{\cite[1.6.2]{SchaeferWolff}}}]
+\begin{proposition}[{{\cite[I.6.2]{SchaeferWolff}}}]
 \label{proposition:locally-bounded-metrisable}
     Let $E$ be a locally bounded TVS over $K \in \RC$, then there exists a pseudonorm $\rho: E \to [0, \infty)$ that induces the topology on $E$.
 \end{proposition}

src/fa/tvs/spaces-of-linear.tex

@@ -1,7 +1,7 @@
 \section{Vector-Valued Function Spaces}
 \label{section:spaces-linear-map}
 
-\begin{proposition}[{{\cite[3.3.1]{SchaeferWolff}}}]
+\begin{proposition}[{{\cite[III.3.1]{SchaeferWolff}}}]
 \label{proposition:tvs-set-uniformity}
     Let $T$ be a set, $\mathfrak{S} \subset 2^T$ be an upward-directed system of sets, $F$ be a TVS over $K \in \RC$, then
     \begin{enumerate}