LAUSR

A space X is said to be cellular-Lindelöf if, for every family $$\mathcal U$$ U of disjoint non-empty open sets of X , there is a Lindelöf subspace $$L\subset X$$ L ⊂ X , such that $$U\cap L \not = \emptyset $$ U ∩ L ≠ ∅ for every $$U\in \mathcal U$$ U ∈ U . This class of spaces was introduced by Bella and Spadaro in 2007. In this paper, our main result is to show that the Pixley–Roy space $$\mathcal F[X]$$ F [ X ] is cellular-Lindelöf if and only if it is CCC. We also establish a cardinal inequality for cellular-Lindelöf spaces which have a symmetric g -function. Some open questions are posed.