On Strong $(i,j)$-Semi$^{*}$-$\Gamma $-Open Sets in Ideal Bitopological Space

Abstract

In this study, we introduce the concepts of $(i,j)$-semi$^{*}$-$\Gamma $-open sets within the context of ideal bitopological spaces. This concept is demonstrated to be weaker than the established the notion of $(i,j)$-semi-$\Gamma $-open sets. Subsequently, we define strong $(i,j)$-semi$^{*}$-$\Gamma $-open sets in ideal bitopological spaces, elucidating some of their essential characteristics. Furthermore, leveraging this newly introduced concept, we establish the notions of strong $(i,j)$-semi$^{*}$-$\Gamma $-interior and strong $(i,j)$-semi$^{*}$-$\Gamma $-closure.