Abstract
In this paper we use a metric space V due to A. H. Stone and one of its completions X to construct a linearly ordered topological space E = E(Y,X) that is Čecil complete, has a tr-closed-discrete dense subset, is perfect, hereditarily paracompact, first-countable, and has the property that each of its subspaces has a σ-minimal base for its relative topology. However, E is not metrizable and is not quasi-developable. The construction of E(Y, X) is a point-splitting process that is familiar in ordered spaces, and an orderability theorem of Herrlich is the link between Stone's metric space and our construction.
Original language | English |
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Pages (from-to) | 2191-2196 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 126 |
Issue number | 7 |
DOIs | |
State | Published - 1998 |
Keywords
- Cech complete
- Cr-minimal base
- Generalized ordered space
- Linearly ordered space
- Metrization theory
- Paracompact
- Perfect space