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Isometric approximation property of unbounded sets

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Abstract

We give a necessary and sufficient quantitative geometric condition for an unbounded set A ⊂ Rn to have the following property with a given c > 0: For every ε ≥ 0 and for every map f: A → Rn such that , there is an isometry T: A → Rn such that ¦Tx−fx¦ ≤ cε for all x ∈ A.

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  1. Matematiikan laitos, Helsingin yliopisto, PL 4, Yliopistonkatu 5, 00014, Helsinki, Finland

    Jussi Väisälä

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  1. Jussi Väisälä
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Correspondence to Jussi Väisälä.

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Väisälä, J. Isometric approximation property of unbounded sets. Results. Math. 43, 359–372 (2003). https://doi.org/10.1007/BF03322748

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