TY - JOUR
ID - 109822
TI - Embedding topological spaces in a type of generalized topological spaces
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Talabeigi, Amin
AD - Department of Mathematics,
Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.
Y1 - 2020
PY - 2020
VL - 6
IS - 2
SP - 250
EP - 256
KW - Generalized topology
KW - generalized extension
KW - one-point generalized extension
KW - strong generalized topology
KW - Stack
DO - 10.22034/kjm.2020.109822
N2 - 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.
UR - http://www.kjm-math.org/article_109822.html
L1 - http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf
ER -