浅论距离空间的距离函数与诱导距离函数的关系

SHALLOWLY DISCUSSION ON THE RELATION OF METRIC FUNCTION AND REDUCED METRIC FUNCTION IN METRIC SPACE

本文主要研究的是距离空间的距离函数何有到距离函数的关系,文中给出了分割,分割的加密,可求长曲线以及曲线长度的定义及其相关性质,并对这些性质予以了证明。仿照黎曼几何的做法,通过距离空间的距离函数给出了距离空间的诱导距离函数的概念,并证明了在距离空间中,两点间的诱导距离不小于这两点的距离。

This paper mainly studies the relation of metric function and reduced metric functionin in metric space.This paper defines the concept and characteristic of partition,densification partition,rectifiable curve and curve length.Ulteriorly,the paper proves these characteristic.Imitating Riemannian geometry,the paper defines reduced metric in metric space via metric function in metric space.Finally,the paper prove reduced distance is not less than distance between two points in metric space.