In mathematics, a real tree, or an -tree, is a metric space (M,d) such thatfor any x, y in M there is a unique arc from x to y and this arc is a geodesic segment. Here by an arc from x to y we mean the image in M of a topological embedding f from an interval [a,b] to M such that f(a)=x and f(b)=y.

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dbpedia-owl:abstract
  • In mathematics, a real tree, or an -tree, is a metric space (M,d) such thatfor any x, y in M there is a unique arc from x to y and this arc is a geodesic segment. Here by an arc from x to y we mean the image in M of a topological embedding f from an interval [a,b] to M such that f(a)=x and f(b)=y. The condition that the arc is a geodesic segment means that the map f above can be chosen to be an isometric embedding, that is it can be chosen so that for every z, t in [a,b] we have d(f(z), f(t))=|z-t| and that f(a)=x, f(b)=y.Equivalently, a geodesic metric space M is a real tree if and only if M is a δ-hyperbolic space with δ=0.Complete real trees are injective metric spaces (Kirk 1998).There is a theory of group actions on R-trees, known as the Rips machine, which is part of geometric group theory.
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  • 2003 (xsd:integer)
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  • 978 (xsd:integer)
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  • Oxford University Press
prop-fr:nom
  • Semple
prop-fr:prénom
  • Charles
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  • Phylogenetics
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  • http://books.google.fr/books?id=uR8i2qetjSAC
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  • OUP
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rdfs:comment
  • In mathematics, a real tree, or an -tree, is a metric space (M,d) such thatfor any x, y in M there is a unique arc from x to y and this arc is a geodesic segment. Here by an arc from x to y we mean the image in M of a topological embedding f from an interval [a,b] to M such that f(a)=x and f(b)=y.
rdfs:label
  • Arbre réel
  • Real tree
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