The space of selections of a dendrite (Q924267)

If \(X\) is a continuum (that is, a compact connected metrizable space), denote by \(C(X)\) the space of all nonempty subcontinua of X equipped with the Vietoris topology. A continuous function \(\sigma :C(X)\rightarrow X\) is a selection if it satisfies \(\sigma (K)\in K\) for all \(K\in C(X)\). Let \(\Sigma(X)\) be the space of all selections of \(X\) endowed with the topology of uniform convergence. The author proves that if \(D\) is a nondegenerate dendrite then \(\Sigma (D)\) is homeomorphic to \(l^2\).