Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.
10.22034/kjm.2020.109822
Abstract
A stack on a nonempty set $X$ is a collection of nonempty subsets of $X$ that is closed under the operation of superset. Let $(X, \tau)$ be an arbitrary topological space with a stack $\mathcal{S}$, and let $X^*=X \cup \{p\}$ for $p \notin X$. In the present paper, using the stack $\mathcal{S}$ and the topological closure operator associated to the space $(X, \tau)$, we define an envelope operator on $X^*$ to construct a generalized topology $\mu_\mathcal{S}$ on $X^*$. We then show that the space $(X^*, \mu_\mathcal{S})$ is the generalized extension of the space $(X, \tau)$. We also provide conditions under which $(X^*, \mu_\mathcal{S})$ becomes a generalized Hausdorff space.
Talabeigi, A. (2020). Embedding topological spaces in a type of generalized topological spaces. Khayyam Journal of Mathematics, 6(2), 250-256. doi: 10.22034/kjm.2020.109822
MLA
Amin Talabeigi. "Embedding topological spaces in a type of generalized topological spaces". Khayyam Journal of Mathematics, 6, 2, 2020, 250-256. doi: 10.22034/kjm.2020.109822
HARVARD
Talabeigi, A. (2020). 'Embedding topological spaces in a type of generalized topological spaces', Khayyam Journal of Mathematics, 6(2), pp. 250-256. doi: 10.22034/kjm.2020.109822
VANCOUVER
Talabeigi, A. Embedding topological spaces in a type of generalized topological spaces. Khayyam Journal of Mathematics, 2020; 6(2): 250-256. doi: 10.22034/kjm.2020.109822
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