A Note on Generic Properties of Continuous Maps

Part of the Progress in Mathematics book series (PM, volume 21)


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.


Periodic Point Open Ball Compact Manifold Genericity Theorem Technical Error 
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Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  1. 1.Wesleyan UniversityMiddletownUSA
  2. 2.Tufts UniversityMedfordUSA

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