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 language | English |
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Pages (from-to) | 1835-1847 |
Number of pages | 13 |
Journal | Proceedings of the American Mathematical Society |
Volume | 134 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2006 |