New Topologies from Old via Ideals

On e-I-open sets, e-I-continuous functions and decomposition of continuity

“…Jankovic and Hamlett [11] investigated further properties of ideal space. The importance of continuity and generalized continuity is significant in various areas of mathematics and related sciences.…”

“…Applications to various fields were further investigated by Jankovic and Hamlett [11] Dontchev et al [3]; Mukherjee et al [13]; Arenas et al [2]; et al Nasef and Mahmoud [18], etc. Given a topological space (X, τ ) with an ideal I on X and if ℘(X) is the set of all subsets of X, a set operator (.)…”

“…Given a topological space (X, τ ) with an ideal I on X and if ℘(X) is the set of all subsets of X, a set operator (.) * : ℘(X) → ℘(X), called a local function [24,11] of A with respect to τ and I is defined as follows: for A ⊆ X,…”

Soft Generalized Closed Sets with Respect to an Ideal in Soft Topological Spaces

“…Indeed ideals are very important tools in general topology. It was the works of Newcomb [19], Rancin [20], Samuels [21] and Hamlet Jankovic [22,23] which motivated the research in applying topological ideals to generalize the most basic properties in general Topology. Jafari and Rajesh [24] introduced the concept of g-closed sets with respect to an ideal which is a extension of the concept of g-closed sets.…”

A Class of Continuous Mappings in Ideal Topological Spaces

“…In 1990, T.R.Hamlett and D.Jankovic [1], introduced the concept of ideals in topological spaces and after that [2,3,4,5,6] several authors turned their attention towards generalizations of various concepts of topology by considering ideal topological spaces. A non-empty collection I of subsets on a topological space (X, τ) is called a topological ideal if it satisfies the following two conditions: (i) If A I and B A implies B I (heredity)…”