The Baire property and precompact duality
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909189338562560 |
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| author | Ferrer, M. Hernández, S. Sepúlveda, I. Trigos-Arrieta, F. J. |
| author_facet | Ferrer, M. Hernández, S. Sepúlveda, I. Trigos-Arrieta, F. J. |
| contents | We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au$β$enhofer and Dikranjan.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Baire property and precompact duality Ferrer, M. Hernández, S. Sepúlveda, I. Trigos-Arrieta, F. J. Group Theory Commutative Algebra General Topology We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco, Domínguez and Tkachenko. {Among other consequences, we obtain an example of a group that is $g$-dense in its completion but is not $g$-barrelled. This solves a question proposed by Au$β$enhofer and Dikranjan.} |
| title | The Baire property and precompact duality |
| topic | Group Theory Commutative Algebra General Topology |
| url | https://arxiv.org/abs/2405.02624 |