Displaying similar documents to “An acyclic continuum that admits no mean”

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

Alejandro Illanes (1992)

Fundamenta Mathematicae

Similarity:

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).