The Steiner Ratio and the Embedding of Spaces

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

Abstract

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.

Keywords

Unit Ball Isometric Embedding Affine Space Mathematical Question Steiner Ratio 
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

© 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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