伪-γ空间的若干等价刻画  

Some Characterizations of Pseudo-γ Spaces

作　　者：吴代龙[1] WU Dai-long(Maanshan Teachers College,Maanshan Anhui 243041,China)

机构地区：[1]马鞍山师范高等专科学校,安徽马鞍山243041

出　　处：《淮阴师范学院学报（自然科学版）》2018年第4期298-301,共4页Journal of Huaiyin Teachers College;Natural Science Edition

基　　金：安徽省高校自然科学基金资助项目(KJ2017A851)

摘　　要：讨论了一类重要的广义度量空间-伪-γ空间的等价刻画问题,利用o-度量及局部拟一致结构给出对伪-γ空间的若干等价刻画.得到X为伪-γ空间当且仅当存在与X上拓扑相容的具有可数基的局部拟一致结构和X为伪-γ空间当且仅当存在与X上拓扑相容的o-度量d使得对X的任一紧集K及任一闭集F,若K∩F=O,则d(K,F)> 0.The main purpose of this paper is to discuss the characterization of an important class of generalized metric spaces,i.e.,pseudo-γspaces.We use the notions of o-metrics and local quasi-uniformities to give some characterizations of pseudo-γspaces.The main results are:1.X is a pseudo-γspace if and only if it admits a compatible local quasi-uniformity with a countable base;2.X is a pseudo-γspace if and only if it admits a compatible o-metric d such that for each compact subset K and closed subset F of X,if K∩F=,then d(K,F)>0.

关 键 词：弱基g-函数 伪-γ空间 o-度量 局部拟一致结构 

分 类 号：O189.1[理学—数学]