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有限集上的拓扑结构 被引量:3

THE STRUCTURE OF TOPOLOGIES ON A FINITE SET
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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.
作者 郭志勇
机构地区 云南师大数学系
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.
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