Quarter-stratifiability in Ordered Spaces
نویسندگان
چکیده
In this paper we study Banakh’s quarter-stratifiability among generalized ordered (GO)-spaces. All quarterstratifiable GO-spaces have a σ-closed-discrete dense set and therefore are perfect, and have a Gδ-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 Gδ-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. MR Classifications: Primary 54F05; Secondary 54E20, 54H05
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