2021/09/10 by Ігор Протасов, Igor Protasov, Protasov, Igor
Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #math.GN
paper · pdf · doi:10.48550/arxiv.2110.01377
linearly ordered coarse space, asymptotic dimension, selector. arXiv admin note: text overlap with arXiv:2102.02053
arxiv created 2021/09/10 · openalex publication_date 2021/09/10 · arxiv updated 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A coarse space X, endowed with a linear order compatible with the coarse structure of X, is called linearly ordered. We prove that every linearly ordered coarse space X is locally convex and the asymptotic dimension of X is either 0 or 1. If X is metrizable then the family of all right bounded subsets of X has a selector.