论文标题
拓扑粗糙组的一些拓扑特性
Some topological properties of topological rough groups
论文作者
论文摘要
令$（u，r）$为近似空间，$ u $是非空置的，$ r $是$ u $的等价关系，让$ \ overline {g} $和$ \ upessuessline {g} $是上近似值，是$ u $ u $ u $ u $ u $ u $的$ g $ g $的下近似值。 A topological rough group $G$ is a rough group $G=(\underline{G}, \overline{G})$ endowed with a topology, which is induced from the upper approximation space $\overline{G}$, such that the product mapping $f: G\times G\rightarrow \overline{G}$ and the inverse mapping are continuous.在拓扑粗糙组的类别中，获得了一些分离公理的关系，研究了粗糙的身份元素和拓扑粗糙亚组的某些基本特性。特别是，提供了一些拓扑粗糙组的例子，以阐明有关拓扑粗糙群体的一些事实。此外，获得了拓扑粗糙组类别中的开放映射定理的版本。此外，提出了一些有趣的开放问题。
Let $(U, R)$ be an approximation space with $U$ being non-empty set and $R$ being an equivalence relation on $U$, and let $\overline{G}$ and $\underline{G}$ be the upper approximation and the lower approximation of subset $G$ of $U$. A topological rough group $G$ is a rough group $G=(\underline{G}, \overline{G})$ endowed with a topology, which is induced from the upper approximation space $\overline{G}$, such that the product mapping $f: G\times G\rightarrow \overline{G}$ and the inverse mapping are continuous. In the class of topological rough groups, the relations of some separation axioms are obtained, some basic properties of the neighborhoods of the rough identity element and topological rough subgroups are investigated. In particular, some examples of topological rough groups are provided to clarify some facts about topological rough groups. Moreover, the version of open mapping theorem in the class of topological rough group is obtained. Further, some interesting open questions are posed.
