GO-spaces with 𝜎-closed discrete dense subsets

Bennett, Harold; Heath, Robert; Lutzer, David

doi:10.1090/S0002-9939-00-05582-9

GO-spaces with $\sigma$-closed discrete dense subsets
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by Harold R. Bennett, Robert W. Heath and David J. Lutzer PDF

Proc. Amer. Math. Soc. 129 (2001), 931-939 Request permission

Abstract:

In this paper we study the question “When does a perfect generalized ordered space have a $\sigma$-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 $\sigma$-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.

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