COMPACTNESS OF S(n)-CLOSED SPACES

Abstract

The aim of this paper is to study compactness of the \(S(n)\)-closed spaces. It is proved that \(S(n)\)-closed space \((X,\tau)\) is compact if every closed subset of \((X,\tau)\) is \(S(n)\)-set and that sequentially \(S(n)\)-closed space \(X\) is countably compact if every closed subset of \(X\) is \(\theta^n\)-closed.