Discrete subsets in Hausdorff topologies (Q1124157)
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scientific article; zbMATH DE number 4111556
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Discrete subsets in Hausdorff topologies |
scientific article; zbMATH DE number 4111556 |
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Discrete subsets in Hausdorff topologies (English)
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1987
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It is shown that the problem of recovering a Hausdorff topology from the family of its discrete subspaces has a negative answer in general (there exist uncountably many pairwise incomparable Hausdorff topologies on the real line with the same discrete subsets). A sufficient condition in terms of neighborhood bases is given (for example, first countable and order Hausdorff topologies are determined by their discrete subsets).
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