Continua and their open subsets with connected complements
J. Krasinkiewicz, Piotr Minc (1979)
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J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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Donald Bennett (1974)
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R. Dickamn (1973)
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J. Cornette (1966)
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E. Tymchatyn (1978)
Fundamenta Mathematicae
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J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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P. Mostert (1964)
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Lee Mohler (1984)
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Charatonik, Janusz J., Illanes, Alejandro (2002)
Mathematica Pannonica
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Nikiel, J., Treybig, L.B., Tuncali, H.M. (1997)
International Journal of Mathematics and Mathematical Sciences
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R. Dickamn, Leonard Rubin (1973)
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A. Emeryk, A. Szymański (1977)
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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).