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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12143 |
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| _version_ | 1866914034302844928 |
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| author | Rosendal, Christian Suarez, Luis Carlos |
| author_facet | Rosendal, Christian Suarez, Luis Carlos |
| contents | A general overview of the phenomenon of automatic continuity of homomorphisms between Polish groups is given. In particular, we study variants and improvements of the closed graph theorem, applying these to the problem of continuity of universally measurable homomorphisms and also to gauge the amount of choice needed to construct discontinuous homomorphisms between Polish groups. Furthermore, we provide a simple proof of automatic continuity in the context of homeomorphism groups of compact manifolds and a complete reworking of automatic continuity theory in the context of isometry groups of highly homogeneous complete metric structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aspects of automatic continuity Rosendal, Christian Suarez, Luis Carlos Group Theory Logic 22A05, 03E15 A general overview of the phenomenon of automatic continuity of homomorphisms between Polish groups is given. In particular, we study variants and improvements of the closed graph theorem, applying these to the problem of continuity of universally measurable homomorphisms and also to gauge the amount of choice needed to construct discontinuous homomorphisms between Polish groups. Furthermore, we provide a simple proof of automatic continuity in the context of homeomorphism groups of compact manifolds and a complete reworking of automatic continuity theory in the context of isometry groups of highly homogeneous complete metric structures. |
| title | Aspects of automatic continuity |
| topic | Group Theory Logic 22A05, 03E15 |
| url | https://arxiv.org/abs/2406.12143 |