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| Authors: | Harold R. Bennett Robert W. Heath David J. Lutzer |
| Affiliation: | Department of Mathematics, Texas Tech University, Lubbock, Texas 79409 Robert W. Heath ; Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15213 David J. Lutzer ; Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187 |
| Abstract: | In this paper we study the question ``When does a perfect generalized ordered space have a |
| Keywords: | Generalized ordered space linearly ordered space perfect $sigma$-discrete dense subset $G_delta$-diagonal metrization weak monotone ortho-base Souslin line |
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-closed-discrete dense subset?' and we characterize such spaces in terms of their subspace structure, 
-mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a 
-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.