%0 Journal Article
%T Embedding topological spaces in a type of generalized topological spaces
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Talabeigi, Amin
%D 2020
%\ 07/01/2020
%V 6
%N 2
%P 250-256
%! Embedding topological spaces in a type of generalized topological spaces
%K Generalized topology
%K generalized extension
%K one-point generalized extension
%K strong generalized topology
%K Stack
%R 10.22034/kjm.2020.109822
%X 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.
%U http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf