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Extracting some supra topologies from the topology of a topological space using stacks | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 6، دوره 3، شماره 1، اردیبهشت 2022، صفحه 45-52 اصل مقاله (307.38 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2021.19123.1042 | ||
| نویسنده | ||
| Amin Talabeigi* | ||
| Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Supra closure operator؛ Supra topology؛ Supra topological space؛ Stack | ||
| مراجع | ||
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