Updated Schaefer & Wolff citations.

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Bokuan Li
2026-01-27 14:10:21 -05:00
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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}