D-space

In mathematics, a topological space formula_1 is a D-space if for any family formula_2 of open sets such that formula_3 for all points formula_4, there is a closed discrete subset formula_5 of the space formula_1 such that formula_7.
History.
The notion of D-spaces was introduced by Eric Karel van Douwen and E.A. Michael. It first appeared in a 1979 paper by van Douwen and Washek Frantisek Pfeffer in the Pacific Journal of Mathematics. Whether every Lindelöf and regular topological space is a D-space is known as the D-space problem. This problem is among twenty of the most important problems of set theoretic topology.