A study of cellular-Lindelöf spaces.

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