@article {
author = {Talabeigi, Amin},
title = {Embedding topological spaces in a type of generalized topological spaces},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {250-256},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {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.},
keywords = {Generalized topology,generalized extension,one-point generalized extension,strong generalized topology,Stack},
url = {https://www.kjm-math.org/article_109822.html},
eprint = {https://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf}
}