Compactifications whose cone can be embedded into their hyperspace of subcontinua

Given a metric continuum X, let C(X) be the hyperspace of subcontinua of X and Cone(X) the topological cone of X. We say that a continuum X is cone-embeddable in C(X) provided that there is an embedding h from Cone(X) into C(X) such that h(x, 0) = {x} for each x in X. In this paper, we present some results concerning compactifications X of rays, union of two rays, and real lines which are cone-embeddable in C(X). (C) 2015 Elsevier B.V. All rights reserved.