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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]
Line 18: Line 18:
 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 $\epsilon>0$, there exists a finite subset $S \In K$, such that+=== Lemma 1 ===  
 + 
 +Assume $K$ is sequentially compact, then for any $\epsilon>0$, there exists a finite subset $S \In K$, such that
 $K \In \bigcup_{x \in S} B_\epsilon(x). $ $K \In \bigcup_{x \in S} B_\epsilon(x). $
  
math104-f21/compactness.1641918978.txt.gz · Last modified: 2022/01/11 08:36 by pzhou