High Quality Content by WIKIPEDIA articles! A real tree, or an R-tree, is a metric space (M,d) such that for 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. A real tree is also sometimes referred to as a metric tree.

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