Product topology in the hyperspace of subcontinua

Let X be a metric continuum. Let C(X) be the hyperespace of subcontinua of X . Given two finite subsets P and Q of X , let U(P,Q)={A∈C(X):P⊂A and A∩Q=∅} . In this paper we consider C(X) with the topology τP which have the sets U(P,Q) as a basis. In this paper we show that, for a dendroid X , some topological properties of X are very closely related to the topological structure of (C(X),τP) .