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### 有限拓扑的有向图表示

1. 1.青海民族大学数学学院, 青海 西宁 810007;(2.陕西师范大学数学与信息科学学院, 陕西 西安 710062
• 收稿日期:2016-07-23 出版日期:2017-04-20 发布日期:2017-04-11
• 作者简介:马海成(1965— ),男,教授,研究方向为代数图论. E-mail:qhmymhc@163.com
• 基金资助:
国家自然科学基金资助项目(11561056,11661066);青海省自然科学基金资助项目(2016-ZJ-914);青海民族大学科研基金资助项目(2015G02)

### The digraphs representation of finite topologies

MA Hai-cheng1,2, LI Sheng-gang2

1. 1. Department of Mathematics, Qinghai University for Nationalities, Xining 810007, Qinghai, China;
2. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
• Received:2016-07-23 Online:2017-04-20 Published:2017-04-11

Abstract: A digraph which is called topology graph is defined for each finite topology space. First, an equivalence relation between elements is defined, and then, the equivalence classes is came into being. These digraphs is defined by using the inclusion relation between equivalence classes. Topological space and its topology graph to determine each other is proved. It is easy to calculate the closure, the derived set, the interior and border of a set by using the topology graph. The connectedness consistent of the topological space and its topology graph is proved. The number of non-homeomorphism topology with 1≤n≤4 elements is calculated by using the topology graph.

Key words: finite topology, closure axioms, digraph

• O157.5
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