A solution of the D-space Problem

RESUMO

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; the question whether, consistently, every regular hereditarily Lindelöf space is a D-space remains open.