Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.
10.22060/ajmc.2021.19123.1042
Abstract
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.
Talabeigi, A. (2021). Extracting some supra topologies from the topology of a topological space using stacks. AUT Journal of Mathematics and Computing, (), -. doi: 10.22060/ajmc.2021.19123.1042
MLA
Amin Talabeigi. "Extracting some supra topologies from the topology of a topological space using stacks". AUT Journal of Mathematics and Computing, , , 2021, -. doi: 10.22060/ajmc.2021.19123.1042
HARVARD
Talabeigi, A. (2021). 'Extracting some supra topologies from the topology of a topological space using stacks', AUT Journal of Mathematics and Computing, (), pp. -. doi: 10.22060/ajmc.2021.19123.1042
VANCOUVER
Talabeigi, A. Extracting some supra topologies from the topology of a topological space using stacks. AUT Journal of Mathematics and Computing, 2021; (): -. doi: 10.22060/ajmc.2021.19123.1042
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