度量空间X与H(X)空间的连续映射

度量空间是用距离来定义拓扑结构的特殊拓扑空间，度量空间的完备性是度量空间的一个独有的性质．在完备度量空间上建立分形空间H(X)，如果函数在完备度量空间上连续，则函数在分形空间H(X)空间上连续。由局部基的覆盖来刻划紧空间，用H(X)表示X中的全体非空紧集构成的集族．在此集族中定义豪斯道夫距离，连续映射的定理在分形空间成立。

The continuous mapping of tolerance space X and H(X) space

Tolerance space is a special topology space determined by distance,and the completeness of tolerance space is a unique characteristic of tolerance space,on complete tolerance space,establishing divided shape space H(X),if function on complete tolerance space continuous,function on divided shape space H(X) continuous.Determining compact space by covering of local base H(X) representing all the compact spaces no empty on X dominating.Hausdorff distance in the family space,continuum theorem is applicable on divided shape space.