Another application of the Effros theorem to the pseudo-arc
Kazuhiro Kawamura, Janusz Prajs (1991)
Fundamenta Mathematicae
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Kazuhiro Kawamura, Janusz Prajs (1991)
Fundamenta Mathematicae
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Hisao Kato (1993)
Fundamenta Mathematicae
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We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions and of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, ...
Beverly Brechner (1969)
Fundamenta Mathematicae
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Lex Oversteegen, E. Tymchatyn (1984)
Fundamenta Mathematicae
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A. Lelek (1970)
Fundamenta Mathematicae
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Wayne Lewis (1983)
Fundamenta Mathematicae
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Judy Kennedy (1988)
Colloquium Mathematicae
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Hisao Kuto (1991)
Fundamenta Mathematicae
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Hisao Kato (1990)
Fundamenta Mathematicae
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Christopher Mouron (2009)
Fundamenta Mathematicae
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A homeomorphism h:X → X of a compactum X is expansive provided that for some fixed c > 0 and any distinct x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a circle-like continuum that admits an expansive homeomorphism, then X is homeomorphic to a solenoid.
L. G. Oversteegen, E. D. Tymchatyn (1986)
Banach Center Publications
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Nelly Kroonenberg (1976)
Compositio Mathematica
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