Updated Schaefer & Wolff citations.
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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 $E$.
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\end{definition}
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\begin{proposition}[{{\cite[1.5.1]{SchaeferWolff}}}]
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\begin{proposition}[{{\cite[I.5.1]{SchaeferWolff}}}]
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\label{proposition:bounded-operations}
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Let $E$ be a TVS over $K \in \RC$ and $A, B \in B(E)$, then the following sets are bounded:
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\begin{enumerate}
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