A metric space of a.h. stone and an example concerning σ-minimal bases

In this paper we use a metric space V due to A. H. Stone and one of its completions X to construct a linearly ordered topological space E = E(Y,X) that is Čecil complete, has a tr-closed-discrete dense subset, is perfect, hereditarily paracompact, first-countable, and has the property that each of its subspaces has a σ-minimal base for its relative topology. However, E is not metrizable and is not quasi-developable. The construction of E(Y, X) is a point-splitting process that is familiar in ordered spaces, and an orderability theorem of Herrlich is the link between Stone's metric space and our construction.