7元素集合上T_(0)拓扑数计算  

Calculation of the T_(0)-Topological Number on a 7-Element Set

作　　者：刘生云 王小霞[1] 王玉焕 LIU Sheng-yun;WANG Xiao-xia;WANG Yu-huan(College of Mathematics and Computer Science,Yan’an University,Yan’an,Shaanxi,716000)

机构地区：[1]延安大学数学与计算机学院,陕西延安716000

出　　处：《韩山师范学院学报》2024年第3期1-10,共10页Journal of Hanshan Normal University

基　　金：国家自然科学地区基金项目(项目编号:12261090);陕西省自然科学基础研究计划项目(项目编号:2018JM1042).

摘　　要：主要借助序与拓扑交叉的方法,得出拓扑空间上的T_(0)拓扑数与偏序之间的一一对应关系,通过对极小元和极大元的个数进行分类讨论,结合Hasse图和层级配比数,进而采用纯数学的方法计算得出7元素集合上T_(0)拓扑数为7544798.This paper mainly uses the method of order and topological intersection to obtain the one-to-one correspondence between topological numbers and partial orders in topological space.By classifying and discussing the number of the minimal element and maximal element,combining Hasse graph and hierarchical matching number,the T_(0)-topological number on a 7-element set is calculated as 7544798 through pure mathematical methods.

关 键 词：偏序集 极小元 极大元 T_(0)拓扑数 

分 类 号：O189.1[理学—数学]