Results in Mathematics

, Volume 43, Issue 3–4, pp 359–372 | Cite as

Isometric approximation property of unbounded sets



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 Open image in new window , there is an isometry T: A → Rn such that ¦Tx−fx¦ ≤ cε for all x ∈ A.

2000 Mathematics Subject Classification

46C05 46B20 30C65 

Key Words

nearisometry Hyers-Ulam isometric approximation 


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Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.Matematiikan laitosHelsingin yliopistoHelsinkiFinland

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