The nonexistence of expansive homeomorphisms of chainable continua
Kato, Hisao
Fundamenta Mathematicae, Tome 149 (1996), p. 119-126 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:212111 
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     year = {1996},
     pages = {119-126},
     zbl = {0868.54032},
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Kato, Hisao. The nonexistence of expansive homeomorphisms of chainable continua. Fundamenta Mathematicae, Tome 149 (1996) pp. 119-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p119bwm/

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