概率度量空间的拓扑结构和度量化问题及其应用

Topological Structure and Metrization Problem of Probabilistic Metric Spaces and Application

本文研究了概率度量空间的拓扑结构和度量化的问題,得到了一种充分条件,给出其具体度量函数的形式,并由此得到了概率度量空间中的Ekeland变分原理和Caristi定理,以及概率度量空间和非阿基米德概率度量空间中映象的不动点定理。

In this paper, we study topological structure and metrization problem of probabilistic metric spaces, obtain a kind of sufficient conditions and give the form of concretely metric function. And then we obtain Ekeland varia tional pr-inciple and Caristi theorem on probabilistic metric spaces,and the fixed points theorem of mapping on probabilistic metric spaces andnon-Archimedean probabilistic spaces.