Parameterized Statistical Compactness of Topological Spaces

In this research, we present the notion of statistical compactness restricted up to order $\alpha$, where $\alpha \in (0,1]$. There exist statistically compact spaces that are not compact. So the parameter $\alpha$ became the measurement of non compactness. Additionally, we looked for the continued existence of order $\alpha$ statistical compactness under open continuous surjection and sub-space topology. A finite intersection-like characterization for $\alpha$ statistical compactness has also been established.