1994/08/21 by Aristophanes Dimakis, A. Dimakis, Folkert Müller-Hoissen +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Countable set #Differentiable function #Differential (mechanical device) #Differential geometry #Differential topology #Dynamical systems theory #Geometry #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Quantum chaos and dynamical systems #Ricci-flat manifold #Space (punctuation) #Topological and Geometric Data Analysis #Topology (electrical circuits) #advanced mathematical theories #gr-qc #hep-th
paper · pdf · doi:10.1063/1.530996
published as J.Math.Phys. 36 (1995) 3771-3791 · 26 pages, LaTeX (RevTex), GOET-TP 88/94
arxiv created 1994/08/21 · openalex publication_date 1995/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A discrete differential manifold is a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides a convenient framework for the formulation of dynamical models on networks and physical theories with discrete space and time. Several examples are presented and a notion of differentiability of maps between discrete differential manifolds is introduced. Particular attention is given to differentiable curves in such spaces. Every discrete differentiable manifold carries a topology and we show that differentiability of a map implies continuity.