2017/12/13 by A. Batubenge, Yael Karshon, Batubenge, Augustin +3 · 3 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.1712.04576
openalex publication_date 2017/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Differential calculus on Euclidean spaces has many generalisations. In particular, on a set X, a diffeological structure is given by maps from open subsets of Euclidean spaces to X, a differential structure is given by maps from X to ℝ, and a Frölicher structure is given by maps from ℝ to X as well as maps from X to ℝ. We illustrate the relations between these structures through examples.