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

Document Type : Original Article


Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.



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.


Main Subjects

Articles in Press, Accepted Manuscript
Available Online from 12 February 2021
  • Receive Date: 12 October 2020
  • Revise Date: 06 February 2021
  • Accept Date: 12 February 2021