2014/02/23 by Aleksey A. Petrov, Petrov, Aleksey A., Sergei Yu. Pilyugin +1
Mathematics · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1402.5636
In 1994, Sakai introduced the property of C0 transversality for two smooth curves in a two-dimensional manifold. This property was related to various shadowing properties of dynamical systems. In this short note, we generalize this property to arbitrary continuous mappings of topological spaces into topological manifolds. We prove a sufficient condition for the C0 transversality of two submanifolds of a topological manifold and a necessary condition of C0 transversality for mappings of metric spaces into ℝn.