COUNTABLE COMPACTNESS MODULO AN IDEAL OF NATURAL NUMBERS

Abstract

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.