A Alex314 Mar 2010 4 0 May 11, 2010 #1 How do you prove the following theorem? If X is a metric space and E a subset of X is compact, then E is sequentially compact.

How do you prove the following theorem? If X is a metric space and E a subset of X is compact, then E is sequentially compact.

P Plato MHF Helper Aug 2006 22,461 8,633 May 11, 2010 #2 Alex314 said: How do you prove the following theorem? If X is a metric space and E a subset of X is compact, then E is sequentially compact. Click to expand... Is it possible that there is an infinite subset of \(\displaystyle E\) with no accumulation point in \(\displaystyle X\)?

Alex314 said: How do you prove the following theorem? If X is a metric space and E a subset of X is compact, then E is sequentially compact. Click to expand... Is it possible that there is an infinite subset of \(\displaystyle E\) with no accumulation point in \(\displaystyle X\)?