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Uniformly continuous maps between ends of \({\mathbb{R}}\)-trees

Abstract

There is a well-known correspondence between infinite trees and ultrametric spaces which can be interpreted as an equivalence of categories and comes from considering the end space of the tree. In this equivalence, uniformly continuous maps between the end spaces are translated to some classes of coarse maps (or even classes of metrically proper Lipschitz maps) between the trees.

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Correspondence to Manuel A. Morón.

Additional information

M. A. Morón was partially supported by MTM 2006-00825.

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Martínez-Pérez, Á., Morón, M.A. Uniformly continuous maps between ends of \({\mathbb{R}}\)-trees. Math. Z. 263, 583–606 (2009). https://doi.org/10.1007/s00209-008-0431-5

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Keywords

  • Tree
  • Ultrametric
  • End space
  • Coarse map
  • Uniformly continuous
  • Non-expansive map

Mathematics Subject Classification (2000)

  • Primary 54E35
  • 53C23
  • Secondary 54C05
  • 51K05