A generalization of 𝐹-spaces and some topological characterizations of GCH

Abstract

Several topological characterizations involving F F -spaces of the continuum hypothesis are due to R. G Woods and E. K. van Douwen. We extend this work by defining a space X X to be an F α {F_\alpha } -space if the union of > α > \alpha cozero-sets is C ∗ {C^{\ast }} -embedded in X X and by giving, for every infinite cardinal α \alpha , topological characterizations involving F α {F_\alpha } -spaces of the cardinal equality 2 α = α + {2^\alpha } = {\alpha ^ + } .