A solution of the D-space Problem

Abstract

Settling a central problem in set-theoretic topology, and many related problems, we prove that there is, consistently, a regular Lindelöf space of cardinality ${\aleph }_1$ that is not a D-space. The existence of such a space is independent of ZFC; we establish its equivalence to a weak form of the Continuum Hypothesis. The proof of the main theorem is adjustable to produce consistent examples with a variety of stronger properties.

Major revision. Proof uses CH instead of diamond. We announce additional results that were obtained but are not yet polished