Mathematics – Geometric Topology
Scientific paper
2008-10-24
Mathematics
Geometric Topology
16 pages. In the new version, the property on the homeomorphism originally used to characterize quasi-isometry between the hyp
Scientific paper
We prove that a PQ-symmetric homeomorphism between two complete metric spaces
can be extended to a quasi-isometry between their hyperbolic approximations.
This result is used to prove that two visual Gromov hyperbolic spaces are
quasi-isometric if and only if there is a PQ-symmetric homeomorphism between
their boundaries.
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