Some New Sets and Topologies in Ideal Topological Spaces

Abstract

An ideal topological space is a triplet ( , , I), where is a nonempty set, is a topology on , and I is an ideal of subsets of . In this paper, we introduce * -perfect, * -perfect, and * -perfect sets in ideal spaces and study their properties. We obtained a characterization for compatible ideals via * -perfect sets. Also, we obtain a generalized topology via ideals which is finer than using * -perfect sets on a finite set.

Ideals on Generalized Topological Spaces

“…In 1990 Jankovic and Hamlett [13] wrote a paper in which they, among their results, included many other results in this area using modern notation, and logically and systematically arranging them. This paper rekindled the interest in this topic, resulting in many generalizations of the ideal topological space and many generalizations of the notion of open sets, like in papers of Jafari and Rajesh [11], and Manoharan and Thangavelu [16].…”

Soft Semi Local Functions in Soft Ideal Topological Spaces

“…In 1990 Jankovic and Hamlett [6] wrote a paper in which they, among their results, included many other results in this area using modern notation, and logically and systematically arranging them. This paper rekindled the interest in this topic, resulting in many generalizations of the ideal topological space and many generalizations of the notion of open sets, like in papers of Jafari and Rajesh [5] and Manoharan and Thangavelu [22]. In 1966, Velicko [30] introduced the notions of θ-open and θ-closed sets, and also a θ-closure, examining H-closed spaces in terms of an arbitrary filter base.…”

Local function versus local closure function in ideal topological spaces

“…In 1990 Janković and Hamlett [12] wrote a paper in which they, among their results, included many other results in this area using modern notation, and logically and systematically arranging them. This paper rekindled the interest in this topic, resulting in many generalizations of the ideal topological space and many generalizations of the notion of open sets, like in papers of Jafari and Rajesh [10], and Manoharan and Thangavelu [15].…”