The orderability of nonarchimedean spaces (Q791919)
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scientific article; zbMATH DE number 3852004
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The orderability of nonarchimedean spaces |
scientific article; zbMATH DE number 3852004 |
Statements
The orderability of nonarchimedean spaces (English)
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1983
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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 \(F_{\sigma}\) in X; (3) \(\bar C\) is metrizable; (4) X is orderable. It is also shown that X is orderable if \(\bar C\)-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.
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linearly uniformizable space
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tree base
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perfect spaces
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suborderable space
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F-sigma-set
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nonarchimedean space
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union of all compact open subsets
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non-orderable, totally disconnected, GO-space
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pseudogap
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