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

Abstract

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 $C_n(X)$ of closed sets with
finitely many components and the density of a topological space
itself. Moreover, it is shown that the functor $C_n\colon Comp
\rightarrow Comp$ 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.