2020/04/30 by David J. Fernández-Bretón, David Fernández-Bretón, Nicholas G. Vlamis +1
Mathematics · #Advanced Topology and Set Theory #Combinatorics #Countable set #Generalization #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Mathematics and Applications #Metrization theorem #Pure mathematics #Separable space #Topology (electrical circuits) #math.GN #math.GT #math.LO #msc:03E75 #msc:54D40 #msc:54D99 #msc:57N99
paper · pdf · doi:10.1016/j.topol.2022.108017
published as Topology and its Applications 310 (2022), 108017 · 39 pages, 4 figures. Main paper written by the first two authors, Appendix B written by all three
openalex publication_date 2022/01/19 · arxiv created 2022/01/26 · arxiv updated 2022/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizable manifold plus a countable number of "long pipes" in terms of their spaces of ends; this is a direct generalization of Nyikos's bagpipe theorem.