距离空间的距离函数与诱导距离函数的关系以及应用

摘要

主要研究的是距离空间的距离函数和诱导距离函数的关系,并给出了分割、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,最后给出这个结论相关应用以及举例。%In this paper,we investigate the relation of metric function and induced distance function in the metric space, we put forword the definition of metric space , the continuous mapping, the continuous curve. By way of imitating Riemann geometry, we put forword the definition of induced distance function through distance function in metric space . Also, we prove that the two points of induced distance is not shorter than the distance of two points in metric space. Finally, we use three examples as the properties of the application