Statistical compactness of topological spaces confined by weight functions

Abstract

A mapping of the form $\varrho:\mathbb{N}\longrightarrow[0,\infty)$ satisfying $\lim_{n\to\infty}\varrho(n)=\infty$ and $\lim_{n\to\infty}\frac{n}{\varrho(n)}\neq0$ is called a weight function. By incorporating weight functions into the statistical framework, we come up with a new notion called weighted statistical compactness that extends the traditional notion of compactness. The paper involves studying the compactness properties via sequences and relationship between compactness variations. We also look into the nature of weighted statistical compactness with in sub-space and under open continuous onto maps. Weighted statistical compactness has also been given a finite intersection-like characterization.