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Abstract

In this study, the notion of the star operator and the class of weight functions defined on the entire natural number set ℕ have been used to develop a version of the statistical cover of a topological space. In this version of statistical γ-cover, the pace of statistical convergence is mostly controlled by the selected weight function. A map g defined as g:ℕ→[0,∞)such that limn→∞g(n)=∞ and limn→∞⁄ng(n)≠0is called a weight function. Relationships between several γ-cover variants have been established, and many counter instances have been offered to help differentiate between them. It has been established that every sg-γcover of a space is an sg-St-γ cover for that space; every sg-St-γcover is an s-St-γcover but the converse of these relations does not hold. The nature of weighted statistical γ-covers under various topological procedures and topological sub-spaces is investigated. The idea of an sg-St-dense subset has been presented and it is observed that sg-dense subset of an sg-γ-cover is an sg-γ-cover. An unsolved open problem is proposed to analyze the potential that an sg-dense subset of an sg-St-cover may not be an sg-St-cover.

Keywords

γ-cover, Natural density, Sg-γ-cover, Weight function, Weighted statistical convergence

Subject Area

Mathematics

Article Type

Article

First Page

3493

Last Page

3502

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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