Topological groups in which each nowhere dense subset is closed (Q1282527)
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scientific article; zbMATH DE number 1274232
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topological groups in which each nowhere dense subset is closed |
scientific article; zbMATH DE number 1274232 |
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Topological groups in which each nowhere dense subset is closed (English)
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12 July 1999
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It is proved under the combinatorial principle \(p=\mathfrak c\) (which is also called Booth lemma) that any nondiscrete metrizable group topology on an Abelian group can be strengthened to a nondiscrete group topology such that each nowhere dense subset is closed. Recall that the Martin's axiom (and therefore also the continuum hypothesis) implies the validity of the combinatorial principle \(p=\mathfrak c\).
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Abelian group
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metrizable topology
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Booth lemma
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continuum hypothesis
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nowhere dense set
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Martin's axiom
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nondiscrete topology
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