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 Gδ-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 |
|---|---|
| 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