Fixed regex incident.
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This commit is contained in:
Bokuan Li
2026-05-05 02:00:05 -04:00
parent 0f2e69d1f9
commit 97372173e1
78 changed files with 172 additions and 172 deletions

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@@ -21,7 +21,7 @@
\]
is a fundamental system of neighbourhoods for $E$ at $0$.
\end\{enumerate\}
\end{enumerate}
The topology $\topo$ is the \textbf{inductive locally convex topology} on $E$ induced by $\seqi{T}$.
\end{definition}
@@ -65,7 +65,7 @@
\]
is a fundamental system of neighbourhoods for $E$ at $0$.
\end\{enumerate\}
\end{enumerate}
The space $E = \bigoplus_{i \in I}E_i$ is the \textbf{locally convex direct sum} of $\seqi{E}$.
@@ -112,7 +112,7 @@
\]
is a fundamental system of neighbourhoods for $E$ at $0$.
\end\{enumerate\}
\end{enumerate}
The pair $(E, \bracsn{T^i_E}_{i \in I})$ is the \textbf{inductive limit} of $(\seqi{E}, \bracsn{T^i_j| i, j \in I, i \lesssim j})$.
\end{definition}
@@ -177,7 +177,7 @@
\begin{enumerate}
\item[(a)] $B$ is bounded.
\item[(b)] There exists $n \in \natp$ such that $B \subset E_n$ is bounded.
\end\{enumerate\}
\end{enumerate}
\item If $E_n$ is complete for each $n \in \natp$, then $E$ is also complete.
\end{enumerate}
@@ -194,7 +194,7 @@
\item For each $k \in \natp$, $U_k \in \cn_{E_{n_k}}(0)$.
\item For each $k \in \natp$, $U_k = U_{k+1} \cap E_{n_k}$.
\item For each $k \in \natp$, $n^{-1}x_k \not\in U_k$.
\end\{enumerate\}
\end{enumerate}
then $V = \bigcup_{k \in \natp}U_k \in \cn_E(0)$ with $V \cap E_{n_k} = U_k$ for all $k \in \natp$. For any $n \in \natp$, $x_k \not\in nU_k = nV \cap E_{n_k}$. Therefore $B$ is not bounded.