Cantor-Bendixson theorem

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


where C is countableMathworldPlanetmath and P is a perfect setMathworldPlanetmath (hence this theorem is also known as the CUP theorem).

Title Cantor-Bendixson theorem
Canonical name CantorBendixsonTheorem
Date of creation 2013-03-22 15:01:40
Last modified on 2013-03-22 15:01:40
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Theorem
Classification msc 03E15
Classification msc 54H05
Synonym CUP theorem