On some generalized open sets in ideal bitopological spaces

Generalized open sets play a very important role in general topology and they are now the research topic of many topologists worldwide. Indeed, an important subject in general topology and real analysis concerns the various modified forms of continuity, separation axioms, etc., with the use of generalized open sets. This research area (which is fertile in information) still takes a significant part of the investigations because it has a clear effect on the development of the topological space through the experience of many theories and characteristics of different types of open sets. In this thesis, we introduce and study the concepts of γ_ij-T-open sets ,γ_ij-semi-T-open sets ,γ_ij-pre-T- open sets,γ_ij-b-T-open sets, γ_ij-β-T-open sets by generalizing (i,j)-T- open, (i,j)-preT- open, (i,j)-bT- open,(i,j)-semi-T- open and (i,j)-β-T- open sets, respectively, in ideal bitopological spaces with an operation γ:T_ →P(X).Further, we describe and study (〖γ,δ)〗_ij-Continuous functions in ideal bitoplogical spaces through this generalized open sets, and their related notions. In addition, various examples and counterexamples are given for answers to some questions raised in this study.