TY - JOUR
ID - 4296
TI - Extracting some supra topologies from the topology of a topological space using stacks
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Talabeigi, Amin
AD - Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran
Y1 - 2022
PY - 2022
VL - 3
IS - 1
SP - 45
EP - 52
KW - supra closure operator
KW - supra topology
KW - supra topological space
KW - stack
DO - 10.22060/ajmc.2021.19123.1042
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4296.html
L1 - https://ajmc.aut.ac.ir/article_4296_7e967a99aed521365e5048b79e71c0e5.pdf
ER -