On local density and local weak density of the hyperspace of sets with finitely many components
R. B. BeshimovNational University of Uzbekistan named after Mirzo Ulugbek, str. University, Tashkent, UzbeksitanD.N. GeorgiouUniversity of Patras, Department of Mathematics, Patras, GreeceN.K. MamadalievNational University of Uzbekistan named after Mirzo Ulugbek, str. University, Tashkent, UzbeksitanF. SeretiUniversity of Western Macedonia, Department of Mathematics, Kastoria, Greece
ABI
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 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.
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