On the Statistical Variation of <i>γ</i>-covers Controlled by the Class of Weight Functions

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.