Added the support function.
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\section{Equicontinuous Families of Linear Maps}
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\label{section:equicontinuous-linear}
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\begin{proposition}[{{\cite[IV.4.2]{SchaeferWolff}}}]
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\begin{proposition}
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\label{proposition:equicontinuous-linear}
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Let $E, F$ be TVSs over $K \in RC$ and $\alg \subset \hom(E; F)$, then the following are equivalent:
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\begin{enumerate}
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\item For each $V \in \cn_F(0)$, $\bigcap_{T \in \alg}T^{-1}(V) \in \cn_E(0)$.
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\end{enumerate}
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\end{proposition}
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\begin{proof}
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\begin{proof}[Proof, {{\cite[IV.4.2]{SchaeferWolff}}}. ]
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(5) $\Rightarrow$ (1): Let $V \in \cn_F(0)$, then $U = \bigcap_{T \in \alg}T^{-1}(V) \in \cn_E(0)$. Thus for any $x, y \in E$ with $x - y \in U$, $Tx - Ty \in V$ for all $T \in \alg$.
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\end{proof}
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