Countable compactness modulo an ideal of natural numbers

In this article, we introduce the idea of $I$-compactness as a covering property through ideals of $\mathbb N$ and regardless of the $I$-convergent sequences of points. The frameworks of $s$-compactness, compactness and sequential compactness are compared to the structure of $I$-compact space. We began our research by looking at some fundamental characteristics, such as the nature of a subspace of an $I$-compact space, then investigated its attributes in regular and separable space. Finally, various features resembling finite intersection property have been investigated, and a connection between $I$-compactness and sequential $I$-compactness has been established.