Delta Set Spaces vs Q Set Spaces

The concept of a ∆-set of reals was originally defined by G.M. Reed. An equivalent version was defined by Eric van Douwen and later on was generalized to an arbitrary topology space, (∆-space) . Historically, this notion arose in the study of the normal Moore space conjecture, where Q-sets were used to construct important

counterexamples to the conjecture: For example, the tangent disc topology over a set X is normal if, and only if, X is a Q-set while the space is countably paracompact if, and only if, X is a ∆-set.  
I will prove two of my results that Moore's L space (a hereditarily Lindelöf but not separable space in ZFC) is not a Q-set space and if Aronszajn tree naturally associated with Moore’s L-space is special Moore's L-space will not be ∆-space.