关于准isometry及其选择

摘要：

本文证明了拟等距关系的对称性蕴涵选择公理，即使该关系仅限于测地线双曲空间。我们表明，这一结果是尖锐的，证明对称性的准等距在一个更严格的设置并不意味着选择公理。詹森·福克斯·曼宁的“瓶颈定理”也意味着选择。

英文摘要：

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.

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