On quasi-isometry and choice
Logic
2016-09-07 v1 Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1609.01353,
title = {On quasi-isometry and choice},
author = {Samuel M. Corson},
journal= {arXiv preprint arXiv:1609.01353},
year = {2016}
}