广义仿拓扑群的若干性质研究  

A Study of Some Properties of Generalized Paratopological Groups

作　　者：叶珮琪 蔡长勇 YE Pei-qi;CAI Zhang-yong(School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530100

出　　处：《南宁师范大学学报（自然科学版）》2021年第2期27-36,共10页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金(11861018,11961004)。

摘　　要：该文探讨广义仿拓扑群的广义邻域基、闭包运算、广义分离性、商群、同态映射、广义乘积、广义紧性等问题,建立了任意一个抽象群上的广义仿拓扑群化定理和广义仿拓扑群的一个广义拓扑同构定理,证明了每一广义仿拓扑群中单位元的广义开邻域生成的子群是广义开子群以及一族强广义仿拓扑群的广义乘积仍是广义仿拓扑群,并提出了一些问题.We study generalized paratopological groups and mainly discuss their generalized neighborhood bases,closure operations,generalized separation,quotient groups,homomorphism,generalized products and generalized compactness.We establish a generalized paratopologization theorem on an abstract group and a generalized topological isomorphism theorem for generalized paratopological groups,and prove that the subgroup generated by ageneralized open neighborhood of the neutral element in a generalized paratopological group is a generalized open subgroup and the generalized product of a family of strong generalized paratopological groups is also a generalized paratopological group.Some questions of generalized paratopological groups are posed.

关 键 词：广义仿拓扑群 广义邻域基 闭包运算 广义分离性 商群 同态映射 广义乘积 广义紧性 

分 类 号：O189[理学—数学]