On a Topological Operator via Local Closure Function

Abstract

In this paper, we define and study the new topological operator called \Gamma-boundary operator Bd^{\Gamma} by using local closure function in ideal topological spaces. We investigate important properties of this operator and we specialize \Gamma-boundary of some special sets, such as \theta-open, I_{\Gamma}-perfect and I_{\Gamma}-dense. Moreover, we examine the properties of this operator in the topology which is formed by using local closure function. Furthermore, we compare \Gamma-boundary operator with the boundary operator and the *-boundary operator. We also showed that under what conditions \Gamma-boundary operator, boundary operator and *-boundary operator are coincide.