S — Compactness Via Ideals

Abstract

Compactness modulo as an ideal has not been widely studied. Many new sorts of weak compactness have been introduced to topological spaces in the last twenty years but have not been studied using ideals. So, the main aim of our work is to study relations between ideals and some types of weak compactness. We initiate types of compactness modulo an ideal that generalize semi-compactness, S-closeness, S-Lindelofness and other types of compactness. Moreover, we study some of their properties and characterizations.