Ordered spaces with special bases

Volume 158 / 1998

Harold Bennett, David Lutzer Fundamenta Mathematicae 158 (1998), 289-299 DOI: 10.4064/fm-158-3-289-299


We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a $G_δ$-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.


  • Harold Bennett
  • David Lutzer

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