Embedding hyperspaces

For a metric continuum X, we consider the hyperspaces C(X) and F2(X) of all subcontinua and of all nonempty subsets of X with at most two points, respectively. In this paper we study classes of continua X for which F2(X) can be embedded in C(X) and we also characterize locally connected continua X for which C(X) can be embedded in the Euclidean space R4 and we prove a similar result for R5.