2021/07/23 by Pedro J. Chocano, Manuel A. Morón, Francisco R. Ruiz del Portal
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic number #Approximations of π #Combinatorics #Compact space #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Inverse #Inverse limit #Limit (mathematics) #Mathematical analysis #Mathematics #Metric (unit) #Metric space #Pure mathematics #Retract #Sequence (biology) #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AT #math.CO #math.GT
paper · pdf · doi:10.1016/j.physd.2022.133168
arxiv created 2021/07/23 · openalex publication_date 2022/02/12 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given a compact metric space X, we associate to it an inverse sequence of finite T0 topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of X that is a strong deformation retract. We provide a method to approximate the homology groups of X and other algebraic invariants. Finally, we study computational aspects and the implementation of this method.