A characterization of dendroids by the n-connectedness of the Whitney levels

Volume 140 / 1992

Alejandro Illanes Fundamenta Mathematicae 140 (1992), 157-174 DOI: 10.4064/fm-140-2-157-174


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).


  • Alejandro Illanes

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