uniform expansivity
Let be a compact metric space and let be an expansive homeomorphism
.
Theorem (uniform expansivity). For every and there is such that for each pair of points of such that there is with such that , where is the expansivity constant of .
Proof. Let . Then K is closed, and hence compact. For each pair , there is such that . Since the mapping defined by is continuous, is also continuous and there is a neighborhood of each such that for each . Since is compact and is an open cover of , there is a finite subcover . Let . If , then , so that for some . Thus for we have and as requred.
Title | uniform expansivity |
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Canonical name | UniformExpansivity |
Date of creation | 2013-03-22 13:55:15 |
Last modified on | 2013-03-22 13:55:15 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 7 |
Author | Koro (127) |
Entry type | Theorem |
Classification | msc 37B99 |