The Tits metric on X(∞)

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


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.


Accumulation Point Length Space Geodesic Segment Unit Speed Antipodal Point 
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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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