Quarter-stratifiability in ordered spaces

Harold R. Bennett, David J. Lutzer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper we study Banakh's quarter-stratifiability among generalized ordered (GO)-spaces. All quarter-stratifiable GO-spaces have a σ-closed-discrete dense set and therefore are perfect, and have a G δ-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.

Original languageEnglish
Pages (from-to)1835-1847
Number of pages13
JournalProceedings of the American Mathematical Society
Volume134
Issue number6
DOIs
StatePublished - Jun 2006

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