Shadowing is generic: a continuous map case

Abstract

We prove that shadowing (the pseudo-orbit tracing property), pe- riodic shadowing (tracing periodic pseudo-orbits with periodic real trajecto- ries), and inverse shadowing with respect to certain families of methods (tracing all real orbits of the system with pseudo-orbits generated by arbitrary methods from these families) are all generic in the class of continuous maps and in the class of continuous onto maps on compact topological manifolds (with or with- out boundary) that admit a decomposition (including triangulable manifolds and manifolds with handlebody).