Supra Regularity and Supra Normality Inspired by Supra-ϵ-Open Sets

In this article, as an extension of the concepts of supra-ϵ-T₂-space, supra-ϵ-T₁-space, and supra-ϵ-T₀-space, we present the notion of supra-ϵ-completely space. Furthermore, we demonstrate that for any STS (γ, θ), the concepts of supra-ϵ-T₂-space and supra-ϵ-completely-space are the same if |γ| ⩽ 4. We also explore the behavior of this notion with respect to specific forms of supra functions. We demonstrate that, under a bijective supra ϵ^∗-open function, the image of any supra-ϵ-(Formula Presented)-space is a supra-ϵ-(Formula Presented). Additionally, we demonstrate that every supra subspace of supra-ϵ-(Formula Presented)-space is supra-ϵ-(Formula Presented). Moreover, four new versions of separation axioms that utilize 2 supra ϵ-open sets are introduced namely: supra-ϵ-regular-space, supra-ϵ-normal-space, supra-ϵ-T₃-space, and supra-ϵ-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-ϵ-R-space (γ, θ) is supra-ϵ-N-space if |γ| ⩽ 4. This implies that the approaches of supra-ϵ-T₃-space and supra-ϵ-T₄-space are the same in this case. The necessary counterexamples that validate our findings are finally presented.