On generalized β-open sets in ideal bitopological space

Abstract

In this article, we introduce and study the concepts of γij-semi-I-open sets and γijβI-open sets by generalizing (i, j)-semi-I-open sets and (ij)-βI-open sets, respectively, in ideal bitopological spaces with an operation γ: τ → P(X). Further, we describe and study (γ, δ)ij-semiI-continuous and (γ, δ)ij-βI-continuous functions in ideal bitopological spaces and their related notions. In addition, various examples and counterexamples are given for answers to some questions raised in this study.