Tree-like continua do not admit expansive homeomorphisms
Tree-like continua do not admit expansive homeomorphisms
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DOI：
10.1090/s0002-9939-02-06447-x
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发表时间：
2002-05
期刊：
影响因子：
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通讯作者：
C. Mouron
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文献类型：
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作者：
C. Mouron
如果对某固定的c > 0和每一个X， y∈X存在一个只依赖于X和y的整数n，使得d(h n (X), h n (y)) > c，则称同纯h: X→X是可扩展的。证明了如果X是一个树状连续体，则h不能是可扩展的。
A homeomorphism h: X → X is called expansive provided that for some fixed c > 0 and every x, y ∈ X there exists an integer n, dependent only on x and y, such that d(h n (x), h n (y)) > c. It is shown that if X is a tree-like continuum, then h cannot be expansive.