LAUSR

Abstract The class of cellular-Lindelof spaces was introduced and studied by A. Bella and S. Spadaro (2017) [4] . We say that a topological space X is cellular-Lindelof if for every family U of pairwise disjoint non-empty open sets of X there is a Lindelof subspace L ⊂ X such that U ∩ L ≠ ∅ , for every U ∈ U . In this paper, we first study topological properties of cellular-Lindelof spaces, and the relations between cellular-Lindelof spaces and related spaces. In particular, we obtain a Tychonoff example of a weakly Lindelof space which is not cellular-Lindelof, which gives a positive answer to a question of A. Bella and S. Spadaro ( [4, Question 2] ). We also prove that every monotonically normal W-space is cellular-Lindelof if and only if it is Lindelof. Finally, by using Erdos–Rado's theorem, we establish some cardinal inequalities for cellular-Lindelof spaces. Some new questions are also posed.