Selectors and scattered spaces (Q5928998)
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scientific article; zbMATH DE number 1587932
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Selectors and scattered spaces |
scientific article; zbMATH DE number 1587932 |
Statements
Selectors and scattered spaces (English)
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29 November 2001
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Vietoris topology
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topologically well-orderable space
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measurable cardinal
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The paper develops the research area initiated in [\textit{R. Engelking}, \textit{R. W. Heath}, and \textit{E. Michael}, Invent. Math. 6, 150-158 (1968; Zbl 0167.20504)]. Let \(X\) be a non-Archimedean space in which every countable subset is closed. Then the following conditions are proved to be equivalent: (i) \(X\) is scattered; (ii) \(X\) is topologically well-orderable; (iii) there exists a continuous selector on the hyperspace of nonempty closed subsets of \(X\).NEWLINENEWLINENEWLINEThe existence of continuous selectors for the hyperspaces of ultracompact scattered spaces and of spaces with a unique accumulation point is also investigated.
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