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Quarter-stratifiability in ordered spaces


Authors: Harold R. Bennett and David J. Lutzer
Journal: Proc. Amer. Math. Soc. 134 (2006), 1835-1847
MSC (2000): Primary 54F05; Secondary 54E20, 54H05
DOI: https://doi.org/10.1090/S0002-9939-05-08306-1
Published electronically: December 5, 2005
MathSciNet review: 2207501
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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 $ \sigma$-closed-discrete dense set and therefore are perfect, and have a $ 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_\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.


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Additional Information

Harold R. Bennett
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
Email: bennett@math.ttu.edu

David J. Lutzer
Affiliation: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23187
Email: lutzer@math.wm.edu

DOI: https://doi.org/10.1090/S0002-9939-05-08306-1
Received by editor(s): January 12, 2005
Published electronically: December 5, 2005
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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