Una primitiva asociada a la derivada de Cantor-Bendixson en espacios polacos.

Abstract

In this paper we study polish spaces, their most important properties, and the Cantor-Bendixson derivative associated to them. For a proper understanding of the Cantor-Bendixson derivative, together with its most relevant properties, it is necessary to study ordinal numbers, for this reason, several results are presented in this work. In addition, we prove that there is a primitive associated with the Cantor-Bendixson derivative in polish spaces, starting, first, from primitives for singletones, with this, we find a primitive for countable compact subsets of a polish space and, then, taking advantage of the separability of polish spaces, the condition of countability is removed.