Crowded spaces with nowhere dense tightness: resolvability

Determine whether every crowded topological space X that has nowhere dense tightness—meaning that for every subset A ⊆ X and every point x that is an accumulation point of A, there exists a subset N ⊆ A such that N is nowhere dense in X and x is an accumulation point of N—is resolvable (i.e., contains two disjoint dense subsets).

Background

Bella and Malykhin proved that every countable crowded space with nowhere dense tightness (NDT) is ω-resolvable. This result raises the natural question of whether resolvability extends beyond the countable case. The paper reiterates this longstanding question and investigates related constructions and tightness notions, including strongly discrete tightness, but does not settle the general case.