Supra topological quotients and their structural properties

Network topology is a fundamental component of data communication systems, determining the structural and functional relationships among network nodes. Mathematical modeling of such structures provides deeper insight into information flow and connectivity. In this paper, we introduce the notion of quotient supra topology and investigate its fundamental properties. Using this construction, we develop the concept of a quotient supra space defined on quotient sets induced by equivalence relations. Further, we introduce a new class of supra topologies called vivid supra topologies, establish their existence and uniqueness, and prove their universal property. These constructions provide a flexible framework for modeling layered physical and logical network structures.