Injective Metric Space - Examples

Examples

Examples of hyperconvex metric spaces include

  • The real line
  • Any vector space Rd with the L∞ distance
  • Manhattan distance (L1) in the plane (which is equivalent up to rotation and scaling to the L∞), but not in higher dimensions
  • The tight span of a metric space
  • Any real tree
  • Aim(X) – see Metric space aimed at its subspace

Due to the equivalence between hyperconvexity and injectivity, these spaces are all also injective.

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