Concerning the relation between separability and the proposition that every uncountable point set has a limit point
Robert Moore (1926)
Fundamenta Mathematicae
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The purpose of this paper is to establish two theorems: Theoreme: In order that every subclass of a given class D of Fréchet should be separable it is necessary and sufficient that every uncountable subclass of that class D should have a limit point. Theoreme: If D_s is a separable class D then every uncountable subclass of D_s contains a point of condensation.