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\begin{enumerate}
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\item For each $i \in I$, $T_i \in L(E; F_i)$.
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\item[(U)] If $\mathfrak{V}$ is a uniformity on $E$ satisfying $(1)$, then $\mathfrak{V} \supset \fU$.
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\end\{enumerate\}
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\end{enumerate}
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Moreover,
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\begin{enumerate}
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@@ -20,7 +20,7 @@
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\]
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is a fundamental system of neighbourhoods for $E$ at $0$.
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\end\{enumerate\}
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\end{enumerate}
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The uniformity $\fU$ and its topology are the \textbf{projective uniformity/topology} induced by $\seqi{T}$.
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@@ -76,7 +76,7 @@
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for all $i \in I$.
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\item For any TVS $F$ over $K$ and $S \in \hom(F; E)$, $S \in L(F; E)$ if and only if $T^E_i \circ S \in L(F; E_i)$ for all $i \in I$.
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\end\{enumerate\}
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\end{enumerate}
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The pair $(E, \bracsn{T^E_i}_{i \in I})$ is the \textbf{projective 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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