On some variants of compactness

Abstract

Three weak variants of compactness were introduced and studied by Kohli and Singh [ Acta Math. Hungar. 106 (2005), 317-329 ]. These three properties are reconsidered from the change of topology perspective. In particular, it is shown that each of these properties is equivalent to compactness with respect to another topology on the underlying set. Some consequences of this situation are investigated.