The union of two $D$-spaces need not be $D$
Fundamenta Mathematicae 220 (2013), 129-137 MSC: Primary 54D20; Secondary 54A35, 54G20. DOI: 10.4064/fm220-2-3
We construct from $\diamondsuit $ a $T_2$ example of a hereditarily Lindelöf space $X$ that is not a $D$-space but is the union of two subspaces both of which are $D$-spaces. This answers a question of Arhangel'skii.