Regular $\Gamma$-irresolvable spaces

Abstract

In this paper by using regular open sets and $\Gamma$-local functions, we introduce and investigate the notions of $\mathcal{I}_R$-dense sets, $\mathcal{I}_R$-hyperconnectedness, $\mathcal{I}^*_R$-hyperconnectedness, $\Gamma$-resolbablity and regular $\Gamma$-irresobability in ideal topological spaces.