On a Topological Operator via Local Closure Function

Abstract

In this research, we define and study the new topological operator called $\Gamma$-boundary operator $Bd^{\Gamma}$ by merging local closure function in ideal topological spaces. We research essential properties of this operator and we specialize $\Gamma$-boundary of some special sets, such as $\theta$-open, $\Im_{\Gamma}$-perfect and $\Im_{\Gamma}$-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 show that under what conditions $\Gamma$-boundary operator, boundary operator and $*$-boundary operator are coincide.