基于拟拓扑的有限集上拓扑构建递推算法  

Recursive algorithm based on quasi-topology to construct topologies on a finite set

作　　者：赵婷婷[1] 梁立[1] 高云[2] 

机构地区：[1]云南师范大学信息学院,云南昆明650500 [2]云南师范大学学报编辑部,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2013年第6期744-749,共6页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(61262071);云南省应用基础研究计划面上项目(2011FB044)

摘　　要：为了更好地解决拓扑计数问题,提出利用递推算法来构建拓扑.该算法从拓扑的结构性质出发,研究了拓扑间的递推关系;基于封闭性提出了拟拓扑的概念,并将其应用于拓扑的构建,生成所有的拓扑.实验测试表明:随着元素个数不断增加,该算法相对于传统的穷举算法所表现出来的优势越来越明显.The recursive algorithm is applied to solve the topologies counting problem. By researching topolo gical structure properties, a recursive pattern is found. Using closed property, the article defines quasi - topology as a new concept and uses it to construct topology. All the topologies are generated by this method. When increas ing the number of elements, this algorithm shows more and more obvious advantage compared with the traditional enumeration method.

关 键 词：有限集 拟拓扑 拓扑构建 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]