概率度量空间的拓扑

TOPOLOGY FOR PROBABILISTIC METRIC SPACES

本文在用轮廓函数构造PM空间的闭包算子族(在Cech意义上)这一新的拓扑结构的基础上,讨论PM空间成为Hausdorff空间的条件,讨论了PM空间的收敛性和连续性。

Profile functions are used to construct a family of closure operators (in the sense of Cvch) on a probabilistic metric space. The suitable conditions under which probabilistic metric space becomes Hausdorff space are studied. Finally, convergence and continuance on PM spaces are discussed.