| 6元素集合上T0拓扑总数的计算 |
| |
| 引用本文： | 曾佳泓,赵浩.6元素集合上T0拓扑总数的计算[J].高校应用数学学报(A辑),2022(1):91-100. |
| |
| 作者姓名： | 曾佳泓 赵浩 |
| |
| 作者单位： | 华南师范大学数学科学学院 |
| |
| 基金项目： | 国家自然科学基金(12171165)；;广东省自然科学基金(2020A1515011008; 2021A1515010374)； |
| |
| 摘 要： | 文中证明了有限预序集与有限偏序集的一些性质,并基于有限集上的拓扑和其上预序的一一对应关系,利用这些性质通过对极小元和极大元个数进行分类讨论,以一种有别于计算机算法而又容易理解的计算方法得出6元素集合上的T0拓扑总数为130023.
|
| 关 键 词： | 偏序集 有限集 T0拓扑总数 |
Calculating of the total number of T0-topologies on a 6-element set |
| |
| ZENG Jia-hong,ZHAO Hao.Calculating of the total number of T0-topologies on a 6-element set[J].Applied Mathematics A Journal of Chinese Universities,2022(1):91-100. |
| |
| Authors: | ZENG Jia-hong ZHAO Hao |
| |
| Institution: | (School of Math.Sci.,South China Normal Univ.,Guangzhou 510631,China) |
| |
| Abstract: | In this paper, some lemmas of a finite preordered set and a finite partial ordered set are proved. Based on the one-to-one correspondence between the topologies and the preorders on the finite set, it is shown that the total number of T0 topologies on a 6-element set is 130023 by classifying and discussing the number of minimal elements. The method used in this paper is different from the computer algorithm and easy to be understood. |
| |
| Keywords: | partial ordered set finite set total number of T0 topologies |
| 本文献已被 维普 等数据库收录！ |
