On local density and local weak density of the hyperspace of sets with finitely many components-Reference-Cited by-同舟云学术

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

Published:2023 Issue:14 Volume:37 Page:4659-4669
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Beshimov R.B.¹,Georgiou D.N.²,Mamadaliev N.K.¹,Sereti F.³

Affiliation:

1. National University of Uzbekistan named after Mirzo Ulugbek, str. University, Tashkent, Uzbeksitan

2. University of Patras, Department of Mathematics, Patras, Greece

3. University of Western Macedonia, Department of Mathematics, Kastoria, Greece

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.

Publisher

National Library of Serbia

Reference20 articles.

1. A.V. Archangel’skii, Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978) 33-96.

2. A.V. Archangel’skii, A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolin. 36 (1995) 303-325.

3. R.B. Beshimov, On weakly additive functionals, Math.i Studii 18 (2002) 179-186.

4. R.B. Beshimov, On weakly density of topological spaces, DAN RUz 11 (2000) 10-13.

5. R.B. Beshimov, Some properties of the functor Oβ, J. Math. Sci. 133 (2006) 1599-1601.