Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47886220200701Embedding topological spaces in a type of generalized topological spaces25025610982210.22034/kjm.2020.109822ENAminTalabeigiDepartment of Mathematics,
Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.0000000152325008Journal Article20190628A stack on a nonempty set $X$ is a collection of nonempty subsets of $X$ that is closed under the operation of superset.<br /> 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 $X^*$.<br /> 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.http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf