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math104-f21:compactness [2022/01/11 08:36] pzhou ↷ Page moved from math104:compactness to math104-f21:compactness |
math104-f21:compactness [2022/01/21 21:33] (current) pzhou [Sequential Compactness $\Rightarrow$ Compactness] |
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Assume $K$ is sequentially compact, we will prove the following two lemma. | Assume $K$ is sequentially compact, we will prove the following two lemma. | ||
- | === Lemma 1 === Assume $K$ is sequentially compact, then for any $\epsilon> | + | === Lemma 1 === |
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+ | Assume $K$ is sequentially compact, then for any $\epsilon> | ||
$K \In \bigcup_{x \in S} B_\epsilon(x). $ | $K \In \bigcup_{x \in S} B_\epsilon(x). $ | ||