Generic isomorphism classes of abelian groups
We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: \((\mathbb{Q},+)\), which is the dual of the universal solenoid, is the generic countably infinite tors...
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Veröffentlicht in: | arXiv.org 2023-06 |
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Hauptverfasser: | , , , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: \((\mathbb{Q},+)\), which is the dual of the universal solenoid, is the generic countably infinite torsion-free abelian group. |
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ISSN: | 2331-8422 |