Metric Density and Quasimobius Mappings

We study the notion of -density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between -density and homogeneous density is established. We also characterize -dense spaces as arcwise connected metric spaces in which arcs are the quasimobius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of ⁿ in terms of -density.