Quarter-stratifiability in ordered spaces

Abstract

In this paper we study Banakh’s quarter-stratifiability among generalized ordered (GO)-spaces. All quarter-stratifiable GO-spaces have a σ \sigma -closed-discrete dense set and therefore are perfect, and have a G δ G_\delta -diagonal. We characterize quarter-stratifiability among GO-spaces and show that, unlike the situation in general topological spaces, quarter-stratifiability is a hereditary property in GO-spaces. We give examples showing that a separable perfect GO-space with a G δ G_\delta -diagonal can fail to be quarter-stratifiable and that any GO-space constructed on a Q-set in the real line must be quarter-stratifiable.