The nonexistence of expansive homeomorphisms of chainable continua
Fundamenta Mathematicae, Tome 149 (1996) no. 2, pp. 119-126
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_fm_149_2_119_126,
author = {Hisao Kato},
title = {The nonexistence of expansive homeomorphisms of chainable continua},
journal = {Fundamenta Mathematicae},
pages = {119--126},
publisher = {mathdoc},
volume = {149},
number = {2},
year = {1996},
doi = {10.4064/fm-149-2-119-126},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-149-2-119-126/}
}
TY - JOUR AU - Hisao Kato TI - The nonexistence of expansive homeomorphisms of chainable continua JO - Fundamenta Mathematicae PY - 1996 SP - 119 EP - 126 VL - 149 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-149-2-119-126/ DO - 10.4064/fm-149-2-119-126 LA - en ID - 10_4064_fm_149_2_119_126 ER -
Hisao Kato. The nonexistence of expansive homeomorphisms of chainable continua. Fundamenta Mathematicae, Tome 149 (1996) no. 2, pp. 119-126. doi: 10.4064/fm-149-2-119-126
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