On local density and local weak density of the hyperspace of sets with finitely many components

This paper is devoted to the investigation of cardinal invariants such as the local density, the local weak density and the relation between the tightness of the space Cn(X) of closed sets with finitely many components and the density of a topological space itself. Moreover, it is shown that the functor Cn : Comp ? Comp preserves the local density and the local weak density of compact spaces. As a result, criteria for locally separability and locally weakly separability of compact spaces are obtained.