摘要
本文通过定义距离空间(X,d)上的自相似空间的概念,给出相关命题的同时证E(kk=1,2,…,m)多于两个点的紧致距离空间(X,d)中的压缩Lipschitz道路,且X=km=1Ek。如果存在非扩张Lipschitz满射gi:X→[0,1(]1燮i燮m),则X为自相似空间;作为应用得知:有限个有公共交点的Lipschitz道路之并是自相似空间;平面上任一连通图与树都是自相似空间。
In this paper,it defines the conception of self-similar space on a distance space X,and some topics are given.It is proved that if Ek（k=1,2,…,m） are Lipschitz paths in a connected compact metric space（X,d） that has at least two points such that X=Uk=1^mEk,then X is a self-similar space.As applications,we conclude that every non-disjoint union of two Lipschitz paths,every planar connected graph and each tree are self-similar spaces.
出处
《价值工程》
2012年第1期241-242,共2页
Value Engineering
