Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces

  title={Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces},
  author={A. Dress},
  journal={Advances in Mathematics},
  • A. Dress
  • Published 1984
  • Mathematics
  • Advances in Mathematics
Abstract The concept of tight extensions of a metric space is introduced, the existence of an essentially unique maximal tight extension T x —the “tight span,” being an abstract analogon of the convex hull—is established for any given metric space X and its properties are studied. Applications with respect to (1) the existence of embeddings of a metric space into trees, (2) optimal graphs realizing a metric space, and (3) the cohomological dimension of groups with specific length functions are… Expand
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