Extracting some supra topologies from the topology of a topological space using stacks

A collection μ of subsets of a nonempty set X is a supra topology on X whenever ∅ and X belong to μ, and also μ is closed under arbitrary unions. Also, a nonempty collection S of nonempty subsets of a nonempty set X is called a stack on X whenever it is closed under operation superset. In this paper, we are going to introduce an approach to extract some supra topologies from the topology of a topological space. For this purpose, we consider a topological space (X, τ) with a closed set P of its subsets. Using a stack S on the space (X, τ) and the closure operator cl associated with τ, we define a supra closure operator λP on X to create the desired supra topology. We then characterize the form of this resulting supra topology and also determine its relationship to the initial topology of the space.