Supra ϵ-open Sets: Features, Operators and Applications

In supra topological spaces, we provide supra ϵ-open sets, an extremely broad class of open sets. We demonstrate that, the previously comparable concepts of supra regular (respectively, α-, semi-, pre-, b-, β-, and R-) open sets are contained in this new category of open sets. To further illustrate the key concepts discussed in the study, we have included a geometric topological diagram [see Diagram 1]. Also, we outline this class’s primary characteristics. Specifically, we show that our new category forms a supra topology rather than a topological space. Utilizing our recently introduced category of supra open sets, we define new kinds of operators called supra ϵ-interior (closure, accumulation, exterior, and boundary, respectively). Moreover, we highlight the deviations between these new operators and their corresponding operators. Furthermore, we also give some key examples and counterexamples to illustrate the importance of our new operators. In addition, we highlight the advantages and distinctions of our work in comparison to similar studies in the field.