Polished A-A and added new lines for broken enumerates.
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@@ -9,7 +9,8 @@
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\item For each $i \in I$, $T_i \in L(E_i; E)$.
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\item[(U)] For any topology $\mathcal{S}$ on $E$ satisfying (1) and (2), $\mathcal{S} \subset T$.
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\item For any TVS $F$ and $T \in \hom(E; F)$, $T \in L(E; F)$ if and only if $T \circ T_i \in L(E_i; F)$ for all $i \in I$.
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\end{enumerate}
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\end\{enumerate\}
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The topology $\topo$ is the \textbf{inductive topology} on $E$ induced by $\seqi{T}$.
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\end{definition}
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\begin{proof}
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@@ -61,7 +62,8 @@
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for all $i \in I$.
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\item For any TVS $F$ and $T \in \hom(E; F)$, $T \in L(E; F)$ if and only if $T \circ T^i_E \in L(E_i; F)$ for all $i \in I$.
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\end{enumerate}
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\end\{enumerate\}
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The pair $(E, \bracsn{T^i_E}_{i \in I})$ is the \textbf{inductive limit} of $(\seqi{E}, \bracsn{T^i_j| i, j \in I, i \lesssim j})$.
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\end{definition}
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\begin{proof}
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