Quarter-stratifiability in ordered spaces

Harold R. Bennett; David J. Lutzer

doi:10.1090/S0002-9939-05-08306-1

Quarter-stratifiability in ordered spaces

Harold R. Bennett, David J. Lutzer

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-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 G_δ-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 language	English
Pages (from-to)	1835-1847
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	134
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-05-08306-1
State	Published - Jun 2006

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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.",

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AB - 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.

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Quarter-stratifiability in ordered spaces

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