A solution of the D-space Problem

We prove that there is, consistently, a regular Lindelöf space of cardinality ${\mathrm{\aleph }}_1$ that is not a D-space. This settles a central problem in set-theoretic topology, and many related problems. The existence of such a space is independent of ZFC@. The question whether, consistently, every regular hereditarily Lindelöf space is a D-space remains open.