摘要
一个有限集上能生成几个拓扑?这一问题一直未得到解决本文利用上半拓扑,下半拓扑[1]等概念给出了如何由X_n+{a_1,a_2,…,a_n}的拓扑构造出X_(n+1)={a_1,a_2,…,a_(n+1)}上全部拓扑的方法。本文还证明了不存在阶为4的自同余拓扑,给出了T的阶为4,maxacT的阶为2的拓扑T的结构。
No one knows how many topologies can bc constructed on a finite set X_n with n points, except the cases n=1,2,3.In this parper, we find out a method of constructing all the topologics on X(n+1) from topologies on X_n, by using supcr-scmitopology, and infcrior-semitopology(theorem 2). We also find that the self-complement topology with order 4 does not exist(theorem 3), and give the structure of the topology with order 4 which has the maximum self-complement topology with order 2.
出处
《云南师范大学学报(自然科学版)》
1992年第4期19-22,共4页
Journal of Yunnan Normal University:Natural Sciences Edition
关键词
自同余拓扑
有限集
拓扑结构
Supcr-scmilopology Infcrior-scmitopology Sclf-complcmcnt topology Topological order.