Supra Topological Spaces Via Delta-Semi-Open Sets

Abstract

The significance of supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extensions to supra open sets, including supra semi-open sets, supra delta-open sets and others. In this paper, the concept of supra delta-semi-open set was introduced within the generalizations of the supra topology of sets. Our investigation involves harnessing this category of sets to introduce new notions in these spaces, specifically supra delta-semi-limit points, supra delta-semi-derive points and examining their relationship with supra semi-open. Building upon this set classification, we introduce several additional concepts such as supra delta-semi-symmetric, supra (delta, delta) semi-generalized closed, supra delta-semi-continuous functions, supra semi-kernel-delta sets, supra delta-semi-separation axioms, supra temperate delta-semi ₀, ₁ spaces and supra delta-semi rho₀, ₁ spaces, and we have presented several theories that demonstrate cases of equivalence among these ideas under specific conditions. Additionally, we have proven a collection of useful relationships and properties for the aforementioned ideas. Furthermore, the research was enhanced with illustrative and refuting examples.