Polished A-A and added new lines for broken enumerates.
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Bokuan Li
2026-05-05 01:50:35 -04:00
parent 47a7e1de68
commit 0f2e69d1f9
81 changed files with 441 additions and 185 deletions

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@@ -7,7 +7,8 @@
\begin{enumerate}
\item For each $i \in I$, $T_i \in L(E; F_i)$.
\item[(U)] If $\mathfrak{V}$ is a uniformity on $E$ satisfying $(1)$, then $\mathfrak{V} \supset \fU$.
\end{enumerate}
\end\{enumerate\}
Moreover,
\begin{enumerate}
\item[(3)] $\fU$ is translation-invariant.
@@ -19,7 +20,8 @@
\]
is a fundamental system of neighbourhoods for $E$ at $0$.
\end{enumerate}
\end\{enumerate\}
The uniformity $\fU$ and its topology are the \textbf{projective uniformity/topology} induced by $\seqi{T}$.
\end{definition}
@@ -74,7 +76,8 @@
for all $i \in I$.
\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 $i \in I$.
\end{enumerate}
\end\{enumerate\}
The pair $(E, \bracsn{T^E_i}_{i \in I})$ is the \textbf{projective limit} of $(\seqi{E}, \bracsn{T^i_j|i, j \in I, i \lesssim j})$.
\end{definition}
\begin{proof}