Menger 概率度量空间的拓扑和紧性

TOPOLOGIES AND COMPACTNESS ON SOME KINDS OF MENGER PM SPACES

本文应用“轮廓函数”规定 Menger 概率度量空间的拓扑,引进邻域系{N_p(φ;ε,λ)},推广了常用邻域系{N_p(ε,λ)},提出了概率预紧、概率列紧、概率稠密和概率可分的概念,讨论了它们之间的关系。

This paper uses “the profile function” to determine the topological struc- tures of some kinds of Menger PM space,brings forward the concept of the probabilistic precompactness,probabilistic compactaess,probabilisticdense, Probabiliitic separability,and studies the relation between probabilistic prec- ompactness and probabilistic eompactness. We also prove Du(x)=D_A(x)in a special Menger PM Space.