On the Complexity of Collaring Theorem in the Lipschitz Category
نویسنده
چکیده
We prove that, if a compact subspace of a metric space can be covered by a family C of bi–Lipschitz local collars, then it admits also a bi–Lipschitz global collar, whose complexity, measured by the so–called weak bi–Lipschitz constant, depends only on C. If the compactness condition is dropped, a slightly weaker version of this result remains valid, provided C is uniform in a suitable natural sense. Applications to topological and Lipschitz manifolds are given. 2000 Mathematics Subject Classification: 30L05, 57N35, 57N45, 57N40.
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تاریخ انتشار 2010