### 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

CLC Number:

• O157.5
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