Two invariants under continuity and the incomparability of fans
Janusz Charatonik (1964)
Fundamenta Mathematicae
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Janusz Charatonik (1964)
Fundamenta Mathematicae
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J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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A. Emeryk, A. Szymański (1977)
Colloquium Mathematicae
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J. Grispolakis, E. D. Tymchatyn (1979)
Colloquium Mathematicae
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Donald Bennett (1974)
Fundamenta Mathematicae
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Mirosław Sobolewski (2015)
Fundamenta Mathematicae
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A continuum is a metric compact connected space. A continuum is chainable if it is an inverse limit of arcs. A continuum is weakly chainable if it is a continuous image of a chainable continuum. A space X is uniquely arcwise connected if any two points in X are the endpoints of a unique arc in X. D. P. Bellamy asked whether if X is a weakly chainable uniquely arcwise connected continuum then every mapping f: X → X has a fixed point. We give a counterexample.
P. Swingle (1931)
Fundamenta Mathematicae
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T. Maćkowiak (1976)
Fundamenta Mathematicae
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Charatonik, Janusz J., Spyrou, Panayotis (1994)
Mathematica Pannonica
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Roman Mańka (1987)
Colloquium Mathematicae
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J. Krasinkiewicz, Sam Nadler (1978)
Fundamenta Mathematicae
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Jack Goodykoontz, Sam Nadler (1984)
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.