Generic isomorphism classes of abelian groups
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912460605227008 |
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| author | Darji, Udayan B. Elekes, Márton Kátay, Tamás Kocsis, Anett Pálfy, Máté |
| author_facet | Darji, Udayan B. Elekes, Márton Kátay, Tamás Kocsis, Anett Pálfy, Máté |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05214 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generic isomorphism classes of abelian groups Darji, Udayan B. Elekes, Márton Kátay, Tamás Kocsis, Anett Pálfy, Máté Logic General Topology Group Theory Primary 22B99, 54E52, Secondary 22C05, 54H05, 03E15 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. |
| title | Generic isomorphism classes of abelian groups |
| topic | Logic General Topology Group Theory Primary 22B99, 54E52, Secondary 22C05, 54H05, 03E15 |
| url | https://arxiv.org/abs/2306.05214 |