Basic Concepts

  • Martin R. Bridson
  • André Haefliger
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 319)


The fundamental concept with which we shall be concerned throughout this book is that of distance. We shall explore the geometry of spaces whose distance functions possess various properties that compare favourably to those of the distance function in Euclidean space. If such properties are identified and articulated clearly, then by proceeding in simple steps from these defining properties one can recover much of the elegant structure of classical geometry, now adapted to a wider context.


Triangle Inequality Cayley Graph Geodesic Segment Geodesic Path Normed Vector Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Martin R. Bridson
    • 1
  • André Haefliger
    • 2
  1. 1.Mathematical InstituteUniversity of OxfodOxfordGreat Britain
  2. 2.Section de MathématiquesUniversité de GenèveGenève 24Switzerland

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