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.