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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quarter-stratifiability in ordered spaces
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by Harold R. Bennett and David J. Lutzer
Proc. Amer. Math. Soc. 134 (2006), 1835-1847
DOI: https://doi.org/10.1090/S0002-9939-05-08306-1
Published electronically: December 5, 2005
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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.
References
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Bibliographic 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
  • Received by editor(s): January 12, 2005
  • Published electronically: December 5, 2005
  • Communicated by: Alexander N. Dranishnikov
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2207501