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The Tits metric on X(∞)

  • Werner Ballmann
  • Mikhael Gromov
  • Viktor Schroeder
Part of the Progress in Mathematics book series (PM, volume 61)

Abstract

In this chapter we will define a metric on the ideal boundary X(∞). We first fix our terminology: a metric (or distance) d on a set M is a map d: M × M → [0,∞) ∪ {∞} which satisfies d(x,y) = 0 ⇔ x = y, d(x,y) = d(y,x), d(x,y) + d(y.z) ≥ d(x,z). We allow that points have infinite distance.

Keywords

Accumulation Point Length Space Geodesic Segment Unit Speed Antipodal Point 
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 New York 1985

Authors and Affiliations

  • Werner Ballmann
    • 1
    • 2
  • Mikhael Gromov
    • 3
  • Viktor Schroeder
    • 4
    • 5
  1. 1.Dept. of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Math. Institut der UniversitätBonnWest Germany
  3. 3.Inst. des Hautes Etudes ScientifiquesBures-sur-YvetteFrance
  4. 4.Math. Institut der UniversitätMünsterGermany
  5. 5.Math. Institut der UniversitätBaselSwitzerland

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