## Abstract

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.

Original language | English |
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Pages (from-to) | 289-299 |

Number of pages | 11 |

Journal | Fundamenta Mathematicae |

Volume | 158 |

Issue number | 3 |

State | Published - 1999 |

## Keywords

- Generalized ordered space
- Linearly ordered space
- Metrizable space
- Open-in-finite base
- Point-countable base
- Quasi-developable space
- Sharp base
- Weakly uniform base
- ω-in-ω base