# Cantor-Bendixson theorem

Any closed subset $X$ of the reals can be written as a disjoint union

 $X=C\cup P,$

where $C$ is countable and $P$ is a perfect set (hence this theorem is also known as the CUP theorem).

Title Cantor-Bendixson theorem CantorBendixsonTheorem 2013-03-22 15:01:40 2013-03-22 15:01:40 CWoo (3771) CWoo (3771) 6 CWoo (3771) Theorem msc 03E15 msc 54H05 CUP theorem