On the hyperspaces of snake-like and circle-like continua
J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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George W. Henderson (1971)
Colloquium Mathematicae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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James Davis, W. Ingram (1988)
Fundamenta Mathematicae
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Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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Mirosław Sobolewski (1984)
Fundamenta Mathematicae
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Acosta, Gerardo, Charatonik, Janusz J. (2004)
Mathematica Pannonica
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Hisao Kato (1988)
Compositio Mathematica
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Hisao Kato (1996)
Fundamenta Mathematicae
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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 . A homeomorphism f: X → X is continuum-wise expansive if there is c > 0 such that if A is a nondegenerate subcontinuum of X, then there is an integer n ∈ ℤ such that . Clearly, every expansive homeomorphism is continuum-wise expansive, but the converse assertion is not true. In [6], we defined the notion of chaotic continua...
H. Stratton (1970)
Fundamenta Mathematicae
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Jo Heath, Van C. Nall (2003)
Fundamenta Mathematicae
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In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.