\begin{definition}[Definition:Cantor-Bendixson Rank]
Let $\struct {X, \tau}$ be a topological space.
Let $S \subseteq X$.
For each ordinal $\alpha$, let $S^{\paren \alpha}$ be the $\alpha$th Cantor-Bendixson derivative of $S$.
Then the '''Cantor-Bendixson rank''' of $S$ is the least ordinal $\alpha$ such that:
:$S^{\paren {\alpha^+} } = S^{\paren \alpha}$
if such an ordinal exists.
{{LinkWanted|Definition:Smallest Ordinal, to replace least ordinal}}
{{NamedforDef|Georg Cantor|name2 = Ivar Otto Bendixson|cat = Cantor|cat2 = Bendixson}}
\end{definition}