度量空间的非标准特征（Ⅰ）

The Nonstandard Character of Metric Spaces

本文首先引进度量空间非标准包的定义，然后将讨论非标准包的许多性质。在此基础上，用非标准方法来刻划度量空间中的各种紧性。最后应用这些结果，将证明ＡｒｚｅｌａＡｓｃｏｌｉ定理，并在较弱的条件下，得到Ｂａｎａｃｈ不动点定理。

In the paper,We first introduce the definition of the nonstandard hull of a metric space. Many properties of the nonstandard hull are obtained. After that,with the nonstandard method,We describe a few of compact properties in a metric space.Finally with these conclusions,Arzela-Ascoli theorem is proved,and Banach fixed pointed theorem is obtained under the weaker conditions.