On Minimal R − I−open Sets and Continuous Functions in Ideal Topological Space

Aims/Objectives: This paper introduces novel classes of sets and continuous functions in ideal topological spaces by incorporating the concepts of minimal open sets and R −I−open sets. These newly defined classes provide a broader framework for studying continuity and topological structures in ideal spaces. Furthermore, the paper defines and characterizes the R−I −Tmin and R−I −Tmax spaces, establishing their fundamental properties and examining their behavior. The relationships between these newly introduced continuous functions and several existing classes of continuous functions available in the literature are also investigated, highlighting similarities, distinctions, and generalizations. Study Design: Theoretical. Place and Duration of Study: Department of Mathematics, St. Joseph’s College (Autonomous) Devagiri, Calicut-673008, India. Methodology: The application of logical reasoning to deduce new theorems from established principles. Conclusion: This paper proposed a class of sets and continuous functions in R − I−space called minimal R − I−open sets and minimal R − I−continuous functions. A small discussion on minimal R − I−open sets, minimal R − I−continuous functions, and minimal R − I−open sets, minimal R − I−continuous functions is given. The relation between these continuous functions and some continuous functions that are already in literature is studied. Also, this paper surveyed R − I − Tmin and R − I − Tmax spaces and obtained that R − I − Tmin (resp. R − I − Tmax) and R − I − Ti i = 0, 1, 2 spaces are independent of each other. Similarly, R−I−Tmin (resp. R−I−Tmax) and R−I−door spaces are independent of each other.