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ArticleOriginal scientific text

Title

The nonexistence of expansive homeomorphisms of chainable continua

Authors 1

Affiliations

  1. Institute of Mathematics, University of Tsukuba, Ibaraki, 305 Japan

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(fn(x),fn(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.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm149/fm14922.pdf

Fundamenta Mathematicae
1996/149/2
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Pages:
119-126
Main language of publication
English
Received
1994-07-19
Published
1996
Exact and natural sciences