A Primer on Chainmails: Structures for Point-free Connectivity
| Autor: | Plessis, J. F. Du, Janelidze, Zurab, Wessels, Bernardus A. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 11 pages, 4 figures |
| Databáze: | arXiv |
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