A note on expansive homeomorphisms.
SHI Enhui~1, ZHOU Lizhen~1,2 (1.Department of Mathematics, Zhejiang University, Hangzhou 310027, China; 2. Department of Mathematics, Suzhou University, Suzhou 215006, China)
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 , XA has only finite connected components with diameter of each component less than c , then X=∪+∞n=∞fn(A) . As an application of this conclusion, a new proof of the nonexistence of expansive homeomorphisms on the closed unit interval is given.


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