Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24493120220201Extracting some supra topologies from the topology of a topological space using stacks4552429610.22060/ajmc.2021.19123.1042ENAminTalabeigiDepartment of Mathematics, Payame Noor University, P.O. Box, 19395-3697,
Tehran, Iran.Journal Article20201012A 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<br />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.<br />In this paper, we are going to introduce an approach to extract some supra topologies from the topology of a topological space. <br />For this purpose, we consider a topological space $(X, tau)$ with a closed set $P$ of its subsets.<br />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_f6cd295ba698dcd2118d82b638b329dd.pdf