Cells in hyperspaces

AbstractLet C(X) denote the hyperspace of subcontinua of a continuum X. For A∈C(X), define the hyperspace C(A,X)={B∈C(X):A⊂B}. Let k∈N, k⩾2. We prove that A is contained in the core of a k-od if and only if C(A,X) contains a k-cell