A counterexample in the theory of $D$-spaces
  Assuming $\diamondsuit$, we construct a $T_2$ example of a hereditarily Lindel\"of space of size $\omega_1$ which is not a $D$-space. The example has the property that all finite powers are also Lindel\"of. 
Daniel T. Soukup, Paul J. Szeptycki
math.GN