Monotone relations which preserve arcs and acyclicity
Jane Day (1966)
Fundamenta Mathematicae
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Jane Day (1966)
Fundamenta Mathematicae
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J. Cornette, J. Girolo (1967)
Fundamenta Mathematicae
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J. Carruth (1970)
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E. Tymchatyn (1978)
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Nikiel, J., Treybig, L.B., Tuncali, H.M. (1997)
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J. Krasinkiewicz, Piotr Minc (1979)
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Charatonik, Janusz J., Illanes, Alejandro (2002)
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H. Berkowitz (1972)
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Alejandro Illanes (1992)
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Let X be a continuum. Let C(X) denote the hyperspace of all subcontinua of X. In this paper we prove that the following assertions are equivalent: (a) X is a dendroid, (b) each positive Whitney level in C(X) is 2-connected, and (c) each positive Whitney level in C(X) is ∞-connected (n-connected for each n ≥ 0).