On a Topological Operator via Local Closure Function

Authors : Ayşe Nur Tunç, Sena Özen Yildirim

Pages : 227-236

Doi:10.47000/tjmcs.1195540

View : 64 | Download : 80

Publication Date : 2023-12-31

Article Type : Research

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.
Keywords : Operator $Bd^{\\Gamma}$, local closure function, ideal topological space, $\\Im_{\\theta}$-open set