M\"obius structures, quasi-metrics, and completeness
Metric Geometry
2024-07-24 v2
Abstract
We study cross ratios from an axiomatic viewpoint, also known as the study of M\"obius spaces. We characterise cross ratios induced by quasi-metrics in terms of topological properties of their image. Furthermore, we generalise the notions of Cauchy-sequences and completeness to M\"obius spaces and prove the existence of a unique completion under an extra assumption that, again, can be expressed in terms of the image of the cross ratio.
Cite
@article{arxiv.1706.10166,
title = {M\"obius structures, quasi-metrics, and completeness},
author = {Merlin Incerti-Medici},
journal= {arXiv preprint arXiv:1706.10166},
year = {2024}
}
Comments
Revised version: The paper has been restructured and some proofs shortened. Various typos etc. corrected