仿拓扑群嵌入性质的一点注记  

A note on properties of embedding paratopological groups into topological products

作　　者：郭伟业 GUO Weiye(School of Mathematics and Computational Science,Wuyi University,Jiangmen,Guangdong 529020,China)

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《闽南师范大学学报（自然科学版）》2020年第4期9-14,共6页Journal of Minnan Normal University：Natural Science

基　　金：国家自然科学基金青年科学基金资助项目(11601393,11861018)。

摘　　要：对特征小于等于κ以及权势小于等于κ的仿拓扑群乘积空间的子群进行刻画,得到如下结论:1)设仿拓扑群G满足T2(正则)分离公理,则G拓扑同构于一族满足特征小于等于κ且满足T2(正则)分离公理仿拓扑群乘积空间的子群当且仅当G是κ—balanced且Hs(G)≤(κIr(G)≤κ);2)设仿拓扑群G满足T2(正则)分离公理,则G拓扑同构于一族满足权势小于等于κ且满足T2(正则)分离公理仿拓扑群乘积空间的子群当且仅当G是完全κ—narrow且Hs(G)≤(κIr(G)≤κ).By discussing a subgroup of topological product of paratopological groups satisfying character or weight not larger thanκ,we obtain the following results:1)Let G be a T2(regular)paratopological group,then G can be topological embedded as a subgroup into a topological product of T2(regular)paratopological groups of character less than or equal toκif and only if G is κ—balanced and Hs(G)≤κ(Ir(G)≤κ);2)Let G be a T2(regular)paratopological group,then G can be topological embedded as a subgroup into a topological product of T2(regular)paratopological groups of weight less than or equal toκif and only if G is totally κ—narrow and Hs(G)≤κ(Ir(G)≤κ).

关 键 词：仿拓扑群 Hausdorff数 正则数 

分 类 号：O189.1[理学—数学]