On finitely equivalent continua.
Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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J. Krasinkiewicz, Sam Nadler (1978)
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.
J. Grispolakis, E. D. Tymchatyn (1979)
Colloquium Mathematicae
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T. Maćkowiak (1976)
Fundamenta Mathematicae
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Sam Nadler, J. Quinn (1973)
Fundamenta Mathematicae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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Janusz Charatonik (1964)
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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Wojciech Dębski, J. Heath, J. Mioduszewski (1992)
Fundamenta Mathematicae
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It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated...
Jerzy Krzempek (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
Hisao Kato (1988)
Compositio Mathematica
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Hatch, Jonathan, Stanojević, Č.V. (2003)
Publications de l'Institut Mathématique. Nouvelle Série
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