%0 Journal Article
%T Extracting some supra topologies from the topology of a topological space using stacks
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Talabeigi, Amin
%D 2022
%\ 02/01/2022
%V 3
%N 1
%P 45-52
%! Extracting some supra topologies from the topology of a topological space using stacks
%K supra closure operator
%K supra topology
%K supra topological space
%K stack
%R 10.22060/ajmc.2021.19123.1042
%X A collection $\mu$ of subsets of a nonempty set $X$ is a supra topology on $X$ whenever $\emptyset$ and $X$ belong to $\mu$, and also $\mu$ is closed under arbitrary unions. Also, a nonempty collection $\mathcal{S}$ 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 $(X, \tau)$ with a closed set $P$ of its subsets. Using a stack $\mathcal{S}$ on the space $(X, \tau)$ and the closure operator $cl$ associated with $\tau$, we define a supra closure operator $\lambda_P$ 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.
%U https://ajmc.aut.ac.ir/article_4296_7e967a99aed521365e5048b79e71c0e5.pdf