On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms

Abstract

A wireless network system is a pair $(U;\mathcal{B})$, where $\mathcal{B}$ is a family of some base stations and $U$ is a set of their users. To investigate the connectivity of wireless network systems, this paper takes covering approximation spaces as mathematical models of wireless network systems. With the help of covering approximation operators, this paper characterizes the connectivity of covering approximation spaces by their definable subsets. Furthermore, it is obtained that a wireless network system is connected if and only if the relevant covering approximation space has no nonempty definable proper subset. As an application of this result, the connectivity of a teacher-student interactive platform is discussed, which is established in the School of Mathematical Sciences of Soochow University. This application further demonstrates the usefulness of rough set theory in pedagogy and makes it possible to research education by logical methods and mathematical methods.