关于膨胀同胚的一个注记

A note on expansive homeomorphisms.

利用符号法则证明了如下结论:设X是Peano连续统,f是X上的膨胀同胚,膨胀常数为c.如果A是X的闭子集,X-A有有限个连通分支,且每个分支的直径小于c,那么X=∪+∞fn(A).作为应用给出了单位闭区间上n=-∞不存在膨胀同胚的一个新的证明.

Using the symbolic method, the following conclusion is given: If X is a Peano continuum, f is an expansive homeomorphism on X with expansive constant c . If A is a closed subset of X , X-A has only finite connected components with diameter of each component less than c , then X=∪+∞n=-∞fn(A) . As an application of this conclusion, a new proof of the nonexistence of expansive homeomorphisms on the closed unit interval is given.