  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.
