Metric density and quasimöbius mappings

We study the notion of $\mu$-density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between $\mu$-density and homogeneous density is established. We also characterize $\mu$-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 $\dot{\mathbb R}_n$ in terms of $\mu$-density.