Abstract
In this paper we study the question "When does a perfect generalized ordered space have a ω-closed-discrete dense subset?" and we characterize such spaces in terms of their subspace structure, s-mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a ω-closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.
Original language | English |
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Pages (from-to) | 931-939 |
Number of pages | 9 |
Journal | Proceedings of the American Mathematical Society |
Volume | 129 |
Issue number | 3 |
DOIs | |
State | Published - 2001 |
Keywords
- G-diagonal
- Generalized ordered space
- Linearly ordered space
- Metrization
- Perfect, ω-discrete dense subset
- Souslin line
- Weak monotone ortho-base