摘要
本文定义了半线性拓扑空间及局部凸半线性拓扑空间,研究了这些空间的性质.并给出了半线性拓扑空间之拓扑由所谓弱半范数,分离弱半范数及范数引出之条件,把线性拓扑空间中某些结论推广到半线性拓扑空间.
In this paper the definition of semi-linear topological space and locally convex semi-linear topological space is given.Further,the properties of those spaces are studied and the conditions of the topology on semi-linear topological space X are induced by weak semi-norm,seperating weak sé-mi-norm or norm.finally,some
conclusions of linear topological space are applied to semi-linear topo-ogical space.
出处
《晓庄学院自然科学学报》
CAS
1993年第1期1-6,共6页
Journal of Natural Science of Hunan Normal University
关键词
半线性
拓扑空间
半范数
T1空间
semi-linear topological space
semi-norm
T_1-space
convex set
