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Israel Journal of Mathematics

, Volume 128, Issue 1, pp 1–27 | Cite as

Isometric approximation property in euclidean spaces

  • Jussi Väisälä
Article

Abstract

We give a necessary and sufficient quantitative geometric condition for a compact setA⊂R n to have the following property with a givenc≥1: For everyɛ>0 and for every mapf: A→R n such that\(\left| {\left| {fx - fy} \right| - \left| {x - y} \right|} \right| \leqslant \varepsilon for all x,y \in A\) there is an isometryS: A→R n such that |Sxfx|≤ for allxA.

Keywords

EUCLIDEAN Space Solar System Orthogonal Projection Piecewise Linear Function Maximal Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2002

Authors and Affiliations

  • Jussi Väisälä
    • 1
  1. 1.Matematiikan laitosHelsingin yliopistoHelsinkiFinland

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