sequential compactness

Mar 2010
4
0
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.
 

Plato

MHF Helper
Aug 2006
22,461
8,633
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.
Is it possible that there is an infinite subset of \(\displaystyle E\) with no accumulation point in \(\displaystyle X\)?