Abstract

This paper deals with problems on LQ𝒰 spaces which have a nested base; among others we give conditions so that a space (X,τ1,τ2) admits an LQ𝒰𝒰 which generates τ1 and 𝒰−1τ2, and give necessary and sufficient conditions for a space to be quasi-metrizable, related to concrete covering properties. We also give a Stone's type characterization of pairwise paracompactness for some categories of LQ𝒰 spaces with nested bases.