石油化工高等学校学报2001，Vol.14Issue(1)：82-84,3.
分形列的收敛特性
Convergent Characteristic of Sequence of Fractals
摘要
Abstract
Let (X,d) be a complete metric space and (H(X),h) be the corresponding f r actal space. The following facts were already known to us: (1) If a sequence of fractals {An} in (H(X),h) is convergent, then ∪∞n=1[ DD )〗An is totally bounded, and limn→∞An=∩ ∞n=1∪∞m=nAm; (2) If {An} is mono tone increasing, the totally bound of ∪∞n=1An a lso become the sufficient condition for convergence of {An}. Under the con di tion of omitting the monotonicity of {An}, the problem of seeking necessar y and sufficient condition for convergence of {An} was further studied in th is paper, and the convergent characteristic of {An} was obtained, i.e., { An} is convergent if and only if ∪∞n=1An is to tall y bounded in (X,d) and ∩∞n=1∪∞m=nAm=∩{Ani}∈S∪∞i=1A ni , where S is the set of all subsequence of {An} and “——” denotes t he closure of a set.关键词
分形空间/分形列/收敛性/完全有界集分类
数理科学引用本文复制引用
沈晨..分形列的收敛特性[J].石油化工高等学校学报,2001,14(1):82-84,3.
