| 理想拓扑扩张的正则性 |
| |
| 引用本文： | 程瑜,张旼旼. 理想拓扑扩张的正则性[J]. 淮海工学院学报, 2013, 0(4): 1-2 |
| |
| 作者姓名： | 程瑜 张旼旼 |
| |
| 作者单位： | [1]徐州工程学院数学与物理科学学院,江苏徐州221111 [2]东南大学医学院,江苏南京210009 |
| |
| 基金项目： | 徐州工程学院青年基金资助项目（XKY2012301） |
| |
| 摘 要： | 理想可以扩展为一个拓扑空间，此种扩展拓扑空间的正则性有非常重要的研究价值．对一类特殊的理想I来说，经此理想扩展的拓扑空间是不能正则的，除非扩展的拓扑与原拓扑一致，即对任何无孤立点的拓扑空间（X，T）和X上的一个理想J，如果J中每个元素内部为空，那么由{U＼I：U∈T，I∈I）生成的理想拓扑T。是正则的当且仅当I中的每个元都是（X，T）中的闲集（或者等价地T=T）．
|
| 关 键 词： | 一般拓扑学 理想 正则 理想拓扑空间 |
Regularity of Ideal Topological Expansions |
| |
| Affiliation: | CHENG Yu1 , ZHANG Min-min2 College of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou 221111, China; 2. School of Medicine, Sotitheast University, Nanjing 210009, China) |
| |
| Abstract: | In literature one the concept of ideal topology was studied, and the properties of topolo- gical expansions via ideals have been investigated in other literatures. In this paper, the regularity of such topological expansions is studied. It is proved that for the special type of ideal ! on X, the topological expansion via I is not regular, unless the expanded topology is equal to the original to- pology, i. e. , the statement that for a crowded topological space （X,T）, and an ideal ! on X, if each element of I has empty interior, then the ideal topology T generated by {U/I.UE T ,IEI } is regular if and only if each element in I is closed in T （or equivalently T ：T）. |
| |
| Keywords: | general topology ideal regular expansion ideal topological space |
| 本文献已被 维普 等数据库收录！ |
|
