Quasi compactness with respect to an Ideal

الملخص EN

Given a nonempty set X, an ideal I on X is a collection of subsets of X closed under finite union and subset operations.

Newcomb (1967) and Ranğin (1972) defined a generalization of compactness (I-compactness) which requires that an open cover of a space have a finite subcollection which covers all the space except for a set in the ideal.

In this paper we introduce and study two different notions of generalized compactness namely, quasi I-compactness and countable quasi /-compactness.

Classical results concerning quasi H-closed and lightly compact spaces are obtained by letting I.

{ϕ}.

Some results in [1, 2] are improved.