The nonexistence of expansive homeomorphisms of chainable continua

Volume 149 / 1996

Hisao Kato Fundamenta Mathematicae 149 (1996), 119-126 DOI: 10.4064/fm-149-2-119-126

Abstract

A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that $d(f^n(x),f^n(y)) > c$. In this paper, we prove that if a homeomorphism f:X → X of a continuum X can be lifted to an onto map h:P → P of the pseudo-arc P, then f is not expansive. As a corollary, we prove that there are no expansive homeomorphisms on chainable continua. This is an affirmative answer to one of Williams' conjectures.

Authors

  • Hisao Kato

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