On star statistically compactness

In a space X, if for every countable open cover \(\mathcal {U} =\{U_n:n \in \textbf{N}\}\) of X, we can find a subcover \({\mathcal {V}} = \{U_{m_k}:k \in \textbf{N}\}\) such that \(\delta (\{m_k: U_{m_k} \in {\mathcal {V}} \})=0\) then the space is called a statistically compact space. Extending the recent works of Sarkar, Bal, and Rakshit on statistically compactness, we investigate statistically compactness of a topological space in the star-operator’s background. The concept of star statistically compactness is contrasted to other topological features. This study explains the attributes of star statistically compactness and its subspaces under diverse circumstances, especially under open continuous surjection.