Abstract
In this article, we introduce and study the concepts of γij -semi-I-open sets and γij -βI-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 -semi-I-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.
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