关于区间向量空间上的度量及其完备性

About The Metric on Interval Vector Space and Its Completeess

首先,利用度量的公理化定义,讨论了区间向量空间的度量化问题,给出了区间向量空间中度量的一般表示形式;其次,分析区间向量空间中度量的一般表示形式的同时举例说明了根据一般表示形式构造具体度量公式的方法;然后,讨论了区间向量空间上度量的完备性问题,给出了几种刻画完备性的定理。

Firstly, utilizing axiomatic definition of metric, we discusse the metrization problem of interval vector space, give the general representation of metric on interval vector space. Secondly, at the same time of analysing general representation of metric on interval vector space, it illustrates that we can construct specific metric fotmulas according to the general representation. Then, we discusse the completeness problem of the metric on interval vector space, and give several theorems of characterizing completeness.