The orderability of nonarchimedean spaces |
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Authors: | S. Purisch |
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Affiliation: | Department of Mathematics, Lafayette College, Easton, PA 18042, USA |
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Abstract: | Let X be a nonarchimedean space and C be the union of all compact open subsets of X. The following conditions are listed in increasing order of generality. (Conditions 2 and 3 are equivalent.) 1. X is perfect; 2. C is an Fσ in X; 3. C? is metrizable; 4. X is orderable. It is also shown that X is orderable if is scattered or X is a GO space with countably many pseudogaps. An example is given of a non-orderable, totally disconnected, GO space with just one pseudogap. |
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Keywords: | Primary 54F05, 54E15, 06A05 Secondary 54E35, 54D45, 54C20, 06A10 |
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