A Note on Generic Properties of Continuous Maps

Abstract

Let M be a compact manifold, with or without boundary. The genericity theorem of J. Palis, C. Pugh, M. Shub and D. Sullivan [PPSS] asserts that, among others, the property $\Omega = \overline {\text{P}}$ (the set of non-wandering points is the closure of the set of periodic points) is C⁰-generic, i.e., holds for all homeomorphisms in some residual subset of the space Homeo(M) of all homeomorphisms of M to itself. This note points out and corrects a technical error in their proof, and extends the result to the space C⁰ (M, M) of all continuous maps of M to itself.