2024/06/11 by Jean F. Du Plessis, Plessis, J. F. Du, Zurab Janelidze +3
Computer Science · #06A06 #06B23 #06D22 #18A40 #54D05 #Cellular Automata and Applications #Cooperative Communication and Network Coding #Distributed systems and fault tolerance #FOS: Mathematics #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2406.16923
openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.