The Steiner Ratio and the Embedding of Spaces

  • Dietmar Cieslik
Part of the Combinatorial Optimization book series (COOP, volume 10)


Assume that we know the Steiner ratio of a metric space (X′, ρ′) and we have that (X′, ρ′) is a subspace of (X, ρ). Then m(X, ρ) must be less or equal than m(X′, ρ′). This observation is the core of the present chapter, but in a less weak form: We consider functions which map the space (X′, ρ′) into (X, ρ) which preserve the distance between points.


Unit Ball Isometric Embedding Affine Space Mathematical Question Steiner Ratio 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Dietmar Cieslik
    • 1
  1. 1.Institute of Mathematics and C.S.University of GreifswaldGermany

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