关于$\mathcal{B}$ -开集
On $\mathcal{B}$-Open Sets
摘要：
定义并研究了$\mathcal{B}$ -开集及其相关性质。粗略地说，$\mathcal{B}$ -开集是$b$ -开集的推广，而开集又是预开集和半开集的推广。利用$\mathcal{B}$ -开集，我们引入了$\mathcal{B}$ -稠密，$\mathcal{B}$ -Frechet，反$\mathcal{B}$ -闭图和反$\mathcal{B}$ -连续等概念.定义了一个双算子拓扑空间$(X, τ, T_1, T_2)$，它包含两个算子$T_1$和$T_2$，它们用于定义$\mathcal{B}$ -开集.
英文摘要：
The aim of this paper is to define and study $\mathcal{B}$-open sets and related properties. A $\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is in turn a generalization of a pre-open set and a semi-open set. Using $\mathcal{B}$-open sets, we introduce a number of concepts such as $\mathcal{B}$-dense, $\mathcal{B}$-Frechet, contra-$\mathcal{B}$-closed graph and contra-$\mathcal{B}$-continuity. Also, we define a bi-operator topological space $(X, τ, T_1, T_2)$ which involves two operators $T_1$ and $T_2$, which are used to define $\mathcal{B}$-open sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
