2020/03/12 by John F. Jardine, Jardine, J. F. · 1 citation
Computer Science · Mathematics · #55U10 #62H30 #68R10 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2003.06285
openalex publication_date 2020/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hierarchy poset and branch point poset for a data set both admit a calculus of least upper bounds. A method involving upper bounds is used to show that the map of branch points associated to the inclusion of data sets is a controlled homotopy equivalence, where the control is expressed by an upper bound relation that is constrained by Hausdorff distance.