Embedding topological spaces in a type of generalized topological spaces

[摘要] 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.

[学科分类] 公共、环境与职业健康