A counterexample in the theory of \(D\)-spaces
``\(D\)-space'' is a covering property: \(X\) is a \(D\)-space iff, given an open cover \(\{u_x: x \in X\}\) where each \(x \in u_x\), there is a closed discrete subset \(D \subset X\) such that \(\{u_x: x \in D\}\) covers \(X\). Many properties imply \(D\)-space, for example, metrizability. It is not known whether a number of other strong properties imply \(D\)-space, in particular, whether every regular Lindelöf space is a \(D\)-space.NEWLINENEWLINEIn this paper, using a delicate \(\diamondsuit\) construction, the authors show the consistency of the existence of a hereditarily Lindelöf Hausdorff space, all of whose finite powers are Lindelöf, which is not a \(D\)-space.
scientific article; zbMATH DE number 6049353
scientific article