Supra Regularity and Supra Normality Inspired by Supra-$\epsilon$-Open Sets

Abstract

In this article, as an extension of the concepts of supra-E-T2-space, supra-E-T1-space, and supra-E-T0-space, we present the notion of supra-E completely space. Furthermore, we demonstrate that for any STS (γ; θ), the concepts of supra-E-T2-space and supra-E- completely-space are the same if  γ less than or equal  4. We also explore the behavior of this notion with respect to specific forms of supra functions. We demonstrate that, under a bijective supra E-open function, the image of any supra-E- completely -space is a supra-E- completely. Additionally, we demonstrate that every supra subspace of supra-E- completely -space is supra-E-completely. Moreover, four new versions of separation axioms that utilize supra E-open sets are introduced namely: supra-E -regular-space, supra-E-normal-space, supra-E-T3-space, and supra-E-T4-space. We also give a general illustration of their key traits and look at the prerequisites for a number of similar links between them. We also propose a figure 1 graphic that shows these linkages. Furthermore, we demonstrate that every supra-E-R-space (γ; θ) is supra-E-N-space if  γ less than or equal  4. This implies that the approaches of supra-E-T3-space and supra-E-T4-space are the same in this case. The necessary counterexamples that validate our findings are finally presented