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.
- Generalized ordered space
- Linearly ordered space
- Perfect, ω-discrete dense subset
- Souslin line
- Weak monotone ortho-base