由度量空间诱导的*-拓扑T~*和s-拓扑T^s（英文）

*-Topology T~* and s-topology T^s induced bymetric space

在多饱和模型下研究了由度量空间诱导的*-拓扑T~*和s-拓扑T^s.首先,为了构造*-拓扑T~*,提出了有限点集的概念.其次,在此拓扑空间中证明了每个内集是紧集,每个开集是饱和集,以及标准部分映射是连续映射.最后,在s-拓扑T^s中讨论了闭包算子、内部算子和*映射.

This paper studies*-topology■and s-topology■in polysaturated nonstandard model,which are induced by metric space on two nonstandard sets.In order to construct*-topology■,the set of finite points is introduced.It shows that every internal set is compact,every open set is saturated and standard part mapping is continuous.Finally,the closure operator,interior operator and mapping*are discussed under s-topology■.