Embedding hyperspaces

For a metric continuum X, we consider the hyperspaces C ( X ) and F 2 ( 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 F 2 ( 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 R 4 and we prove a similar result for R 5 .