Concerning the relation between separability and the proposition that every uncountable point set has a limit point

The purpose of this paper is to establish two theorems: Theoreme: In order that every subclass of a given class ${\displaystyle D}$ of Fréchet should be separable it is necessary and sufficient that every uncountable subclass of that class ${\displaystyle D}$ should have a limit point. Theoreme: If ${\displaystyle D_s}$ is a separable class ${\displaystyle D}$ then every uncountable subclass of ${\displaystyle D_s}$ contains a point of condensation.