集合$\tau$-标准部分的闭性

The Closeness of the $\tau$-Standard Part of a Set

中文关键词:  扩大模型  饱和模型  $\tau$-标准部分  $\tau$-闭集.

英文关键词:enlarged models  saturated models  $\tau$-standard part  $\tau$-closed set.

中文摘要:

      本文讨论了集合$\tau$-标准部分的闭性.首先给出了拓扑空间中集合$\tau$-邻域系,集合$\tau$-单子和集合$\tau$-标准部分有关命题和结论.在此基础上,给出了非标准扩大模型和饱和模型的充要条件.最后证明了在非标准扩大模型和饱和模型下集合$\tau$-标准部分是闭集的充分条件.

英文摘要:

      In this paper, the closeness of the $\tau$-standard part of a set is discussed. Some related propositions of the $\tau$-neighborhood system of a set are given. And then some related conclusions of the $\tau$-monad of a set and the $\tau$-standard part of a set are presented. And based on it, the necessary and sufficient conditions of the enlarged model and the saturated model are showed. Finally, some sufficient conditions that the $\tau$-standard part of a set is closed are proved in the enlarged model and the saturated model.