 Completely Ramsey-null set

A set $N$ is completely Ramsey-null when every Ellentuck topology neighborhood $[s,A]$ has a refinement $[s,B]$ disjoint from $N$, with the same finite stem $s$. Assuming open Ellentuck sets are completely Ramsey, every star-nowhere dense set is completely Ramsey-null: apply the open-set property to the dense complement of its closure. The Ellentuck meagre-set fusion lemma shows that countable unions retain this avoidance property.