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Isometric approximation property of unbounded sets

Jussi Vaisala
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Abstract

Necessary and sufficient quantitative geometric conditions are given for an unbounded set A in a euclidean space R^n to have the following property with a given c > 0: For every s > 0 and for every s-nearisometry f: A -> R^n there is an isometry T: A -> R^n such that |Tx - fx| \le cs for all x in A.

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Jussi Vaisala. 2002-01-04. Isometric approximation property of unbounded sets. https://arxiv.org/abs/math/0201023

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