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On quasi-isometry and choice

In this note we prove that the symmetry of the quasi-isometry relation implies the axiom of choice, even when the relation is restricted to geodesic hyperbolic spaces. We show that this result is sharp by demonstrating that symmetry of quasi-isometry in an even more restrictive setting does not imply the axiom of choice. The "Bottleneck Theorem" of Jason Fox Manning also implies choice.

preprint2016arXivOpen access
Samuel M. Corson
math.LOmath.MG
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Samuel M. Corson

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