$h^{\Gamma}$-Open Sets in Ideal Topological Spaces

This paper first introduces $h^{\Gamma}$-open sets by utilizing the local closure function in an ideal topological space. Afterward, it researches the relation between $h^{\Gamma}$-open sets and $h^{\star}$-open sets. Then, it concludes that $h^{\Gamma}$-open sets coincide with $h^{\star}$-open sets. Therefore, the present paper obtains that $h^{\Gamma}$-open sets have the properties which are satisfied by $h^{\star}$-open sets. Additionally, it defines the notion of the $h^{\star}$-kernel of a set via $h\mathfrak{I}$-open sets and investigates some of its basic properties.