Given metric continuum X we consider the n-th symmetric product, Fn(X) defined as the hyperspace of nonempty subsets with at most n elements. The continuum X is an Fn-coselection space (n≥2) if for each ε > 0, there exists a mapping gε : X →Fn(X) \F1(X) such that x ∈ gε(x) and diameter(gε(x)) <ε for each x∈X. Answering two questions by Patricia Pellicer-Covarrubias, in this talk we present two significant examples:

(a) we prove that a Cook continuum is not an Fn-coselection space for any n ≥2, and

(b) there exist two no homeomorphic compactifications of the ray [0,∞) with remainder a simple closed curve which are F2-coselection spaces.