关于连通在图论与拓扑学中的关系研究

Research the Relationship of Connectivity between the Graph and the Topology

本文主要通过在简单无向连通图中建立距离概念,构造出一个拓扑空间,在此拓扑空间上证明了图论中的连通可以推导出拓扑学中的连通;反之,证明了拓扑学中的连通也可以推导出图论中的连通;从而说明图论中的连通与拓扑学中的连通可以相互转化.

This article mainly used a simple and connected graph to create the concept of distance, and construct a topological space. Then prove that the connectivity of graph could translate into topologies on the base of the distance. On the other hand, proves that the connectivity of topology also could translate into graphs. Thus we can conclude that the connectivity of graph＇s and topologies could translate from each others.