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Zheyuan Wu
2025-01-16 12:57:26 -06:00
parent 35de983451
commit 5e35ab79b1
3 changed files with 606 additions and 1 deletions

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@@ -27,7 +27,7 @@ $K$ is compact if $\forall$ open cover, $\exists \{G_{\alpha_i}\}_{i=1}^n$ that
$\mathbb{R}$ is not compact since we can build a open cover $\{(x,x+2):x\in \mathbb{Z}\}$ such that we cannot find a finite subcover of $\mathbb{R}$
$\{1,2\}$ is compact let $ $\{G_{\alpha}\}_{\alpha\in A}$ be an open cover of $\{1,2\}$
$\{1,2\}$ is compact let $\{G_{\alpha}\}_{\alpha\in A}$ be an open cover of $\{1,2\}$
Ironically, $[0,1]$ is compact. This will follow from Theorem 2.40.