A Primer on Chainmails: Structures for Point-free Connectivity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909472278970368 |
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| author | Plessis, J. F. Du Janelidze, Zurab Wessels, Bernardus A. |
| author_facet | Plessis, J. F. Du Janelidze, Zurab Wessels, Bernardus A. |
| contents | In point-free topology, one abstracts the poset of open subsets of a topological space, by replacing it with a frame (a complete lattice, where meet distributes over arbitrary join). In this paper we propose a similar abstraction of the posets of connected subsets in various space-like structures. The analogue of a frame is called a chainmail, which is defined as a poset admitting joins of its mails, i.e., subsets having a lower bound. The main result of the paper is an equivalence between a subcategory of the category of complete join-semilattices and the category of chainmails. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_16923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Primer on Chainmails: Structures for Point-free Connectivity Plessis, J. F. Du Janelidze, Zurab Wessels, Bernardus A. General Mathematics 54D05, 06A06, 06B23, 18A40, 06D22 In point-free topology, one abstracts the poset of open subsets of a topological space, by replacing it with a frame (a complete lattice, where meet distributes over arbitrary join). In this paper we propose a similar abstraction of the posets of connected subsets in various space-like structures. The analogue of a frame is called a chainmail, which is defined as a poset admitting joins of its mails, i.e., subsets having a lower bound. The main result of the paper is an equivalence between a subcategory of the category of complete join-semilattices and the category of chainmails. |
| title | A Primer on Chainmails: Structures for Point-free Connectivity |
| topic | General Mathematics 54D05, 06A06, 06B23, 18A40, 06D22 |
| url | https://arxiv.org/abs/2406.16923 |