Added the fundamental theorem of calculus.
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Bokuan Li
2026-03-22 17:12:22 -04:00
parent 156c9e8728
commit af1fa61668
6 changed files with 246 additions and 40 deletions

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@@ -47,7 +47,7 @@
As $\ol{W}$ is compact, it is normal by \autoref{proposition:compact-hausdorff-normal}. Since $X$ is Hausdorff, $K \subset \ol{W}$ is closed by \autoref{proposition:compact-closed}.
By \hyperref[Urysohn's lemma]{lemma:lch-urysohn}, there exists $f \in C(\ol{V}; [0, 1])$ such that $f|_K = 1$ and $f|_{\ol{W} \setminus V} = 0$. Let
By \hyperref[Urysohn's lemma]{lemma:urysohn}, there exists $f \in C(\ol{V}; [0, 1])$ such that $f|_K = 1$ and $f|_{\ol{W} \setminus V} = 0$. Let
\[
F: X \to [0, 1] \quad x \mapsto \begin{cases}
f(x) &x \in W \\