Embedding cones in hyperspaces

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 continua X that are cone-embeddable in C ( X ) .