Ideal weak QN-spaces

By a result of Bukovský, Das and Šupina from [6] it is known that in the case of tall ideals I the notions of IQN-space (IwQN-space) and QN-space (wQN-space) cannot be distinguished. Answering [6, Problem 3.2], we prove that if I is a tall ideal and X is a topological space of cardinality less than cov⁎(I), then X is an IwQN-space if and only if it is a wQN-space.