On uniquely arcwise connected curves
Roman Mańka (1987)
Colloquium Mathematicae
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Roman Mańka (1987)
Colloquium Mathematicae
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Roman Mańka (1987)
Colloquium Mathematicae
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Gordon Whyburn (1929)
Fundamenta Mathematicae
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J. Grispolakis, E. D. Tymchatyn (1979)
Colloquium Mathematicae
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Janusz Charatonik (1964)
Fundamenta Mathematicae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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D. Daniel, C. Islas, R. Leonel, E. D. Tymchatyn (2015)
Colloquium Mathematicae
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We revisit an old question of Knaster by demonstrating that each non-degenerate plane hereditarily unicoherent continuum X contains a proper, non-degenerate subcontinuum which does not separate X.
J. Roberts (1929)
Fundamenta Mathematicae
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R. Moore (1925)
Fundamenta Mathematicae
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The purpose of this paper is to prove: Théorème: In order that a continuum M should be a continuous curve it is necessary and sufficient that for every two distinct points A and B of M there should exist a subset of M which consists of a finite number of continua and which separates A from B in M. Théorème: In order that a bounded continuum M should be a continuous curve which contains no domain and does not separate the plane it is necessary and sufficient that for every two distinct...
J. Krasinkiewicz (1974)
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.
J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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A. Emeryk, A. Szymański (1977)
Colloquium 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.
Mirosław Sobolewski (1984)
Fundamenta Mathematicae
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