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The orderability of nonarchimedean spaces
Authors:S Purisch
Institution:Department of Mathematics, Lafayette College, Easton, PA 18042, USA
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 C??C 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.
Keywords:Primary 54F05  54E15  06A05  Secondary 54E35  54D45  54C20  06A10
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