On the hyperspace, elements of which have finitely many components

In this talk we consider categorical and topological properties of the functor $C_n (X)$. We state that the functor $C_n\colon Comp \to Comp$ preserves the density and weak density of topological spaces. As well as, we investigate several categorical properties of this functor. We proved that the functor $C_n$ satisfies all properties of normality except preserving surjections.