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EXPLICIT CONSTRUCTIONS OF UNIVERSAL ℝ-TREES AND ASYMPTOTIC GEOMETRY OF HYPERBOLIC SPACES
ANNA DYUBINA, IOSIF POLTEROVICH
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Source: Crossref
Published: Nov 1, 2001
DOI: 10.1112/s002460930100844x
Open original source ↗Source abstract
This paper presents explicit constructions of universal ℝ-trees as certain spaces of functions, and also proves that a 2 ℵ 0 -universal ℝ-tree can be isometrically embedded at infinity into a complete simply connected manifold of negative curvature, or into a non-abelian free group. In contrast to asymptotic cone constructions, asymptotic spaces are built without using the axiom of choice.
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