Prove that if a set contains each of its accumulation points, then it must be a closed set.
February 4th 2010, 11:57 AM
Plato
Quote:
Originally Posted by LCopper2010
Prove that if a set contains each of its accumulation points, then it must be a closed set.
Suppose that is such a set.
If , the complement, then is not a limit point of .
Therefore, the is an open set, that contains no point of .
Now show the complement is open.