有限拓扑的有向图表示

doi:10.6040/j.issn.1671-9352.0.2016.362

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (4): 100-104.doi: 10.6040/j.issn.1671-9352.0.2016.362

有限拓扑的有向图表示

马海成^1,2,李生刚²

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-cheng^1,2, LI Sheng-gang²

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

摘要/Abstract

摘要： 对每一个有限拓扑定义了一个被称为拓扑图的有向图。拓扑的元之间规定了一个等价关系,因而产生等价类,利用等价类的闭包之间的包含关系定义这个有向图。证明了拓扑和拓扑图是相互唯一确定的, 利用拓扑图很容易计算一个集合的闭包、导集、内部和边界等运算。证明了拓扑的连通性与拓扑图的连通性是一致的, 利用拓扑图计算了只有1≤n≤4个元的不同胚拓扑的个数。

关键词: 有向图, 闭包公理, 有限拓扑

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

中图分类号:

O157.5

马海成,李生刚. 有限拓扑的有向图表示[J]. 山东大学学报（理学版）, 2017, 52(4): 100-104.

MA Hai-cheng, LI Sheng-gang. The digraphs representation of finite topologies[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 100-104.

参考文献

[1] DIESTEL R, KH(¨overU)N D. Topological paths, cycles and spanning trees in infinite graphs[J]. European Journal of Combinatorics, 2004, 25:835-862.
[2] DIESTEL R. The cycle space of an infinite graph[J]. Combin Probab Comput, 2005, 14:59-79.
[3] DIESTEL R. End spaces and spanning trees[J]. Journal of Combinatorial Theory, Series B, 2006, 96:846-854.
[4] AGELOS GEORGAKOPOULOS. Graph topologies induced by edge lengths[J]. Discrete Mathematics, 2011, 311:1523-1542.
[5] DIESTEL R, KH(¨overU)N D. Topological paths, cycles and spanning trees in infinite graphs[J]. European Journal of Combinatorics, 2004, 25:835-862.
[6] RICHTER BRUCE R. Graph-like spaces: an introduction[J]. Discrete Mathematics, 2011, 311:1390-1396.
[7] DIESTEL R. Locally finite graphs with ends: a topological approach. I. basic theory[J]. Discrete Mathematics, 2011, 311:1423-1447.
[8] DIESTEL R. Locally finite graphs with ends: a topological approach, II. applications[J]. Discrete Mathematics, 2010, 310:2750-2765.
[9] DIESTEL R, SPR(¨overU)SSEL P. Locally finite graphs with ends: a topological approach. III. fundamental group and homology[J]. Discrete Mathematics, 2012, 312:21-29.
[10] 熊金城. 点集拓扑讲义[M]. 3rd. 北京:高等教育出版社,2003. XIONG Jincheng. Poing set topology[M]. 3rd. Beijing: Higher Education Press, 2003.
[11] BONDY J A, MURTY U S R. Graph theory with applications[M]. New York: The Macmillan Press, 1976.

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