Abstract
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 I∗-closed sets and closed-I concepts.
Highlights
Introduction and preliminariesThe g-closed sets, which is a extension of closed sets, was introduced by Levine and the Ig-closed sets, which is a generalization of g-closed sets, was defined by Jafari-Rajesh, in terms of ideals
In this paper we introduce and study new intermediate concepts between closed and Ig-closed sets, via ideals
(1) If U is the usual topology in the set R, all A ⊆ R is ρIg-closed in the ideal space (R, U, I = P(R)), but (0, 1) is not g-closed
Summary
Introduction and preliminariesThe g-closed sets, which is a extension of closed sets, was introduced by Levine and the Ig-closed sets, which is a generalization of g-closed sets, was defined by Jafari-Rajesh, in terms of ideals. An ideal space (X, τ, I) is defined to be I-normal [1] if for every pair of disjoint closed subsets F and G, there exist disjoint open sets U and V such that F \U ∈ I and G\V ∈ I. If (X, τ, I) is an ideal topological space and A ⊆ X A is said to be ρIg-closed if for each U ∈ τ , if A\U ∈ I A\U ∈ I.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
