From 89ec2234bee47a71995098fdba720373ccfdba7c Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Tue, 30 Jun 2026 19:34:11 -0400 Subject: [PATCH] Fixed typo. --- src/topology/main/stonean.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/topology/main/stonean.tex b/src/topology/main/stonean.tex index dc3b0d3..b716e03 100644 --- a/src/topology/main/stonean.tex +++ b/src/topology/main/stonean.tex @@ -9,7 +9,7 @@ \begin{theorem}[Stone-Nakano] \label{theorem:stone-nakano-extremely-disconnected} - Let $X$ be a topological space. If $X$ is extremely disconnected, then $C(X; \real)$ is order complete. Conversely, if $X$ is ??? and $C(X; \real)$ is order complete, then $X$ is extremely disconnected. + Let $X$ be a topological space. If $X$ is extremely disconnected, then $C(X; \real)$ is order complete. Conversely, if $X$ is completely regular and $C(X; \real)$ is order complete, then $X$ is extremely disconnected. \end{theorem} \begin{proof} ($\Rightarrow$): Suppose that $X$ is extremely disconnected. Let $\cf \subset C(X; \real)$ and $F \in C(X; \real)$ be an upper bound of $\cf$. For each $q \in \real$, let