• Title, Summary, Keyword: totally chain-transitive

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TOTALLY CHAIN-TRANSITIVE ATTRACTORS OF GENERIC HOMEOMORPHISMS ARE PERSISTENT

  • GHANE FATEMEH HELEN;FAKHARI ABBAS
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.631-638
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    • 2005
  • we prove that, given any compact metric space X, there exists a residual subset R of H(X), the space of all homeomorphisms on X, such that if $\in$ R has a totally chain-transitive attractor A, then any g sufficiently close to f has a totally chain transitive attractor A$\_{g}$ which is convergent to A in the Hausdorff topology.