A characterization of dendroids by the n-connectedness of the Whitney levels
Volume 140 / 1992
Fundamenta Mathematicae 140 (1992), 157-174
DOI: 10.4064/fm-140-2-157-174
Abstract
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).
