摘要
应用非标准方法研究由内集E上的超实度量d所导出的Q-拓扑与S-拓扑,给出这两种拓扑的一些重要性质:(E,Q)是完全不连通的且其紧子集都是有限集;G(x)/■关于E上的S-拓扑的商拓扑是可度量化且完备的;G(x)的有界子集A若满足A/■是S-拓扑的商空间G(x)/■的闭子集,则A是S-紧的。进而讨论了S-拓扑在构造完备度量空间中的应用。
We use Nonstandard methods to study the Q-topology and S-topology derived from an internal hyperreal metric d on an internal set E.The space （E,Q） is totally disconnected and its compact subset is finite; With respect to S-topology,the quotient topology on G（x）/≌ metrizable and complete, and each bounded subset A of G （x） with A/≌ closed is S-compact. Furthermore,the application of S-topology in the construction of complete metric space is discussed.
出处
《咸阳师范学院学报》
2007年第4期6-8,共3页
Journal of Xianyang Normal University
关键词
内超实度量空间
内定义原理
持续性原理
Q-拓扑
S-拓扑
internal hyperreal metric space
internal definition principle
Permanence principle
Q-topology
S-topology
