 A point set \(P\) is closed iff its derived set \(P' \subseteq P\), and perfect iff \(P = P'\). The Cantor-Bendixson theorem then states that a closed point set can be decomposed into two subsets \(R\) and \(S\), such that \(R\) is denumerable and \(S\) is perfect (indeed, \(S\) is the \(a\)th derived set of \(P\), for a countable ordinal \(a\)). Because of this, closed sets are said to have the perfect set property. Furthermore, Cantor was able to prove that perfect sets have the power of the continuum (1884). Both results implied that the Continuum Hypothesis is valid for all closed point sets. Many years later, in 1916, Pavel Aleksandrov and Felix Hausdorff were able to show that the broader class of Borel sets have the perfect set property too.