分形列的收敛特性

对于完备度量空间(X,d)及相应的分形空间(H(X)，h)，我们曾得到结论如果(H(X)，h)中的分形列{A

Convergent Characteristic of Sequence of Fractals

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.