可分离公理的三空间性  

The three space property of separated axioms

作　　者：张国芳[1] 王跃超[1] ZHANG Guo-fang;WANG Yue-chao(College of Mathematics,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《吉林师范大学学报（自然科学版）》2018年第2期63-65,共3页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(71501082);吉林省教育厅"十三五"科学技术研究规划项目(2018年)

摘　　要：在拓扑代数一些基本定义及基本性质的基础上,讨论了拓扑群中的群扩张理论,研究了可分离公理的三空间性质.利用逆纤维性质,得出了满足T_1公理是三空间性质;给出了T_2公理和T_3公理成为三空间性质的条件.结果表明:T_2T_3公理在不变子群是既开又闭的条件下可以扩张到整个拓扑群上.On the basis of some basal definitions and properties in the topology algebraic,the theory of group extensions was discussed and the three space property of separated axioms was studied.Using the inverse fiber property,the theorem that being T1 space is a three space property was proved and the conditions that make being T2 space and being T3 space to three space properties were given.It is show that,T2 axiom and T3 axiom can be expanded into the whole group in the condition that the invariant subgroup is closed and open.

关 键 词：拓扑群 三空间性质 逆纤维性质 分离公理 

分 类 号：O189[理学—数学]