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Fixed missing citation.
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Bokuan Li
2026-06-03 17:13:07 -04:00
parent 6c9c479198
commit 677a396e24
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src/op/example/bc.tex
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@@ -17,7 +17,7 @@
is a homeomorphism. Under the identification $\beta X = \Omega(BC(X; \complex))$, $\Gamma_{BC(X; \complex)} = \beta$. is a homeomorphism. Under the identification $\beta X = \Omega(BC(X; \complex))$, $\Gamma_{BC(X; \complex)} = \beta$.
\end{theorem} \end{theorem}
\begin{proof} \begin{proof}{Proof, {{\cite[Theorem I.6.4]{Zhu}}}. }
Let $\phi \in BC(X; \complex)^* \setminus \ol{E(X)}$, then there exists $\seqf{f_k} \subset BC(X; \complex)$ and $\eps > 0$ such that for every $x \in X$, Let $\phi \in BC(X; \complex)^* \setminus \ol{E(X)}$, then there exists $\seqf{f_k} \subset BC(X; \complex)$ and $\eps > 0$ such that for every $x \in X$,
\[ \[
f(x) = \sum_{k = 1}^n |f_k(x) - \dpn{f_k, \phi}{BC(X; \complex)}|^2 \ge \eps^2 f(x) = \sum_{k = 1}^n |f_k(x) - \dpn{f_k, \phi}{BC(X; \complex)}|^2 \ge \eps^2