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Typo fix.
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Bokuan Li
2026-03-20 15:18:08 -04:00
parent 780d5d362e
commit d7d5db5f90
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src/topology/uniform/complete.tex
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@@ -37,7 +37,7 @@
\begin{proposition}[{{\cite[Proposition 2.3.11]{Bourbaki}}}] \begin{proposition}[{{\cite[Proposition 2.3.11]{Bourbaki}}}]
\label{proposition:uniformextension} \label{proposition:uniformextension}
Let $X$ be a topological space, $Y$ be a complete Hausdorff uniform space, $A \subset X$ be a dense subset, and $f \in C(A; Y)$ be a continuous function, then the following are equivalent: Let $X$ be a uniform space, $Y$ be a complete Hausdorff uniform space, $A \subset X$ be a dense subset, and $f \in C(A; Y)$ be a continuous function, then the following are equivalent:
\begin{enumerate} \begin{enumerate}
\item There exists a continuous function $F \in C(X; Y)$ such that $F|_A = f$. \item There exists a continuous function $F \in C(X; Y)$ such that $F|_A = f$.
\item $f$ is Cauchy continuous. \item $f$ is Cauchy continuous.