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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• Charles
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• Phylogenetics
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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.
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• Arbre réel
• Real tree
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