2021/09/17 by Shunsuke Ichiki, Ichiki, Shunsuke
Mathematics · #FOS: Mathematics #Functional Equations Stability Results #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2109.08760
openalex publication_date 2021/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Around 1970, Mather established a significant theory on the stability of C^∞ mappings and gave a characterization of the density of proper stable mappings in the set of all proper mappings. The result yields a characterization of the density of stable mappings in the set of all mappings in the case where the source manifold is compact. The aim of this paper is to complement Mather's result. Namely, we show that the set of stable mappings in the set of all mappings is never dense if the source manifold is non-compact. Moreover, as a corollary of Mather's result and the main theorem of this paper, we give a characterization of the density of stable mappings in the set of all mappings in the case where the source manifold is not necessarily compact.