Covering properties for LQ𝒰s with nested bases

Abstract

Abstract. This paper deals with problems on LQᐁ spaces which have a nested base; among others we give conditions so that a space (X, τ 1 ,τ 2 ) admits an LQᐁ ᐁ which generates τ 1 and ᐁ −1 τ 2 , 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 LQᐁ spaces with nested bases.2000 Mathematics Subject Classification. Primary 54E15, 54E55, 54E25.