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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.11188 |
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| _version_ | 1866912634301841408 |
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| author | Rodríguez, Sebastián Caicedo, Xavier |
| author_facet | Rodríguez, Sebastián Caicedo, Xavier |
| contents | We characterize those algebras over a disconnected uniformly complete topological field which are representable as algebras of continuous functions on compact topological spaces, generalizing thus Gelfand duality for non-archimedean normed fields (Van der Put theorem). More generally, we establish for any topological field F a (dual) adjunction between the category of compact F-Tychonoff spaces and a natural category of commutative F-algebras, which becomes a duality for fields satisfying the Stone-Weierstrass theorem. To obtain these results we do not utilize analytic tools, but the canonical group uniformity of the field and intrinsic properties of the algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Totally Disconnected (non-metric) Gelfand Duality Rodríguez, Sebastián Caicedo, Xavier General Topology Logic Rings and Algebras We characterize those algebras over a disconnected uniformly complete topological field which are representable as algebras of continuous functions on compact topological spaces, generalizing thus Gelfand duality for non-archimedean normed fields (Van der Put theorem). More generally, we establish for any topological field F a (dual) adjunction between the category of compact F-Tychonoff spaces and a natural category of commutative F-algebras, which becomes a duality for fields satisfying the Stone-Weierstrass theorem. To obtain these results we do not utilize analytic tools, but the canonical group uniformity of the field and intrinsic properties of the algebras. |
| title | Totally Disconnected (non-metric) Gelfand Duality |
| topic | General Topology Logic Rings and Algebras |
| url | https://arxiv.org/abs/2508.11188 |