A Note on the Connectedness of the Hyperspace with Hausdorff Metric

Abstract:

      In this note, some examples and propositions are given to answer the open question posed by E . Klein & A . C . Thompson in [ 1 ] . The main results in this note is that : if X is a metric space and there exists an arc in X, then ( 1 ) there exists an order arc a in P(X) such that α(0) is connected and (?) is not connected ;( 2 ) there exists a point x∈X and an are β in F(X- {x}) such that β(0)∈C(X- {x}) and ∪β∈C(X- {x}).