Metric Density and Quasimobius Mappings

Abstract

We study the notion of μ-density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between μ-density and homogeneous density is established. We also characterize μ-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 μ-density.