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 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.