Applications of the Gelfand--Naimark duality
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910049427783680 |
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| author | Farah, Ilijas |
| author_facet | Farah, Ilijas |
| contents | Stone duality is an indispensable tool for the study of compact, zero-dimensional, Hausdorff spaces. In the case of general compact Hausdorff spaces one can get quite a bit of mileage by considering the `Wallman duality' between compact spaces and lattices of closed sets. I will argue that the Gelfand--Naimark duality between compact Hausdorff spaces and unital, commutative \cstar-algebras provides great insight into compact Hausdorff spaces, and \v Cech--Stone remainders and their autohomeomorphisms in particular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10957 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Applications of the Gelfand--Naimark duality Farah, Ilijas Logic Operator Algebras Stone duality is an indispensable tool for the study of compact, zero-dimensional, Hausdorff spaces. In the case of general compact Hausdorff spaces one can get quite a bit of mileage by considering the `Wallman duality' between compact spaces and lattices of closed sets. I will argue that the Gelfand--Naimark duality between compact Hausdorff spaces and unital, commutative \cstar-algebras provides great insight into compact Hausdorff spaces, and \v Cech--Stone remainders and their autohomeomorphisms in particular. |
| title | Applications of the Gelfand--Naimark duality |
| topic | Logic Operator Algebras |
| url | https://arxiv.org/abs/2603.10957 |