(untitled) (European Journal of Pure and Applied Mathematics, 2018)
The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ÏIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ÏIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that Iclosed and closed-I are independent concepts, as well as Iâˆ—-closed sets and closed-I concepts.