Esakia order-compactifications and locally Esakia spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908732916498432 |
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| author | Almeida, Rodrigo Nicolau Bezhanishvili, Guram Bezhanishvili, Nick |
| author_facet | Almeida, Rodrigo Nicolau Bezhanishvili, Guram Bezhanishvili, Nick |
| contents | We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characterizing Esakia order-compactifications by means of special rings of upsets. These considerations naturally lead to the notion of a locally Esakia space, for which we prove that taking the largest Esakia order-compacification is functorial, thus obtaining an analog of Banaschewski's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Esakia order-compactifications and locally Esakia spaces Almeida, Rodrigo Nicolau Bezhanishvili, Guram Bezhanishvili, Nick Logic General Topology 54F05, 06F30, 54D35, 06E15, 06D50, 06D20 We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characterizing Esakia order-compactifications by means of special rings of upsets. These considerations naturally lead to the notion of a locally Esakia space, for which we prove that taking the largest Esakia order-compacification is functorial, thus obtaining an analog of Banaschewski's theorem. |
| title | Esakia order-compactifications and locally Esakia spaces |
| topic | Logic General Topology 54F05, 06F30, 54D35, 06E15, 06D50, 06D20 |
| url | https://arxiv.org/abs/2512.22042 |