# sequential compactness

Printable View

• May 11th 2010, 08:36 AM
Alex314
sequential compactness
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.
• May 11th 2010, 08:56 AM
Plato
Quote:

Originally Posted by Alex314
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 $E$ with no accumulation point in $X$?