$\mathcal{I}_\mathbf{g}^*$-closed Sets via Ideal Topological Spaces

Abstract

In this paper, aspects of generalized continuity and generalized closedness are explored. The standard material on the notions of $*g$-open, $\mathbf{g}$-open sets and some definitions and results that are needed are presented first. Then the class of $\mathcal{I}_\mathbf{g}^*$-closed sets is introduced and its fundamental properties are studied. Also, $\mathcal{I}_\mathbf{g}^*$-regular, $^*$-additive, $^*$-multiplicative, $\mathcal{I}_\mathbf{g}^*$-additive, and $\mathcal{I}_\mathbf{g}^*$-multiplicative spaces are introduced and their properties are investigated.