Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 3 1 2022 02 01 Extracting some supra topologies from the topology of a topological space using stacks 45 52 4296 10.22060/ajmc.2021.19123.1042 EN Amin Talabeigi Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran Journal Article 2020 10 12 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. https://ajmc.aut.ac.ir/article_4296_beda24c1e1b46055dff2c39c98fd6fc1.pdf