Removed parts from Zhu citations.

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Bokuan Li
2026-07-07 11:39:54 -04:00
parent 86aba8ee4b
commit f613e65d10
11 changed files with 17 additions and 10 deletions

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@@ -40,7 +40,7 @@
so $g \le F$. As this holds for all upper bounds of $\cf$, $g$ is the supremum of $\cf$ in $C(X; \real)$.
($\Leftarrow$, \cite[Theorem II.9.6]{Zhu}): Suppose that $X$ is completely regular and $C(X; \real)$ is order complete. Let $U \subset X$ be open and
($\Leftarrow$, \cite[Theorem 9.6]{Zhu}): Suppose that $X$ is completely regular and $C(X; \real)$ is order complete. Let $U \subset X$ be open and
\[
\cf = \bracs{f \in C(X; [0, 1])| 0 \le f \le \one_U}
\]