Maximal $d$-spectra via Priestley duality
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918220074582016 |
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| author | Bezhanishvili, G. Bhattacharjee, P. Melzer, S. D. |
| author_facet | Bezhanishvili, G. Bhattacharjee, P. Melzer, S. D. |
| contents | We use Priestley duality as a new tool to study maximal $d$-spectra of arithmetic frames, both with and without units. We pay special attention to when the maximal $d$-spectrum is compact or Hausdorff. Various necessary and sufficient conditions are given, including a construction of an arithmetic frame with a unit whose maximal $d$-spectrum is not Hausdorff, thus resolving an open problem in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal $d$-spectra via Priestley duality Bezhanishvili, G. Bhattacharjee, P. Melzer, S. D. General Topology 18F70, 06D22, 06E15, 06F20, 54D10, 54D30 We use Priestley duality as a new tool to study maximal $d$-spectra of arithmetic frames, both with and without units. We pay special attention to when the maximal $d$-spectrum is compact or Hausdorff. Various necessary and sufficient conditions are given, including a construction of an arithmetic frame with a unit whose maximal $d$-spectrum is not Hausdorff, thus resolving an open problem in the literature. |
| title | Maximal $d$-spectra via Priestley duality |
| topic | General Topology 18F70, 06D22, 06E15, 06F20, 54D10, 54D30 |
| url | https://arxiv.org/abs/2501.07673 |