Minimal Base for Finite Topological Space by Matrix Method

Abstract

Topological base plays a foundational role in topology theory. However, few works have been done to find the minimal base, which would make us difficult to interpret the internal structure of topological spaces. To address this issue, we provide a method to convert the finite topological space into Boolean matrix and some properties of minimal base are investigated. According to the properties, an algorithm(URMB) is proposed. Subsequently, the relationship between topological space and its sub-space with respect to the base is concentrated on by Boolean matrix. Then, a fast algorithm(MMB) is presented, which can avoid a mass of redundant computations. Finally, some numerical experiments are given to show the advantage and the effectiveness of MMB compared with URMB.