A Primer on Chainmails: Structures for Point-free Connectivity

J. F. Du Plessis; Zurab Janelidze; Bernardus A. Wessels

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arXiv · 2406.16923

A Primer on Chainmails: Structures for Point-free Connectivity

J. F. Du Plessis·Zurab Janelidze·Bernardus A. Wessels

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Abstract

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.

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BibTeX RIS

J. F. Du Plessis, Zurab Janelidze, Bernardus A. Wessels. 2024-06-11. A Primer on Chainmails: Structures for Point-free Connectivity. https://arxiv.org/abs/2406.16923

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