  We consider the class of compact countable subsets of the real numbers
$\mathbb{R}$. By using an appropriate partition, up to homeomorphism, of this
class we give a detailed proof of a result shown by S. Mazurkiewicz and W.
Sierpinski related to the cardinality of this partition. Furthermore, for any
compact subset of $\mathbb{R}$, we show the existence of a "primitive" related
to its Cantor-Bendixson derivative.
