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Metric density and quasimöbius mappings. (Russian, English) Zbl 1018.30015

Sib. Mat. Zh. 43, No. 5, 1007-1019 (2002); translation in Sib. Math. J. 43, No. 5, 812-821 (2002).
Summary: We study the notion of \(\mu\)-density of metric spaces which was introduced by V. V. Aseev and D. A. Trotsenko. An interrelation between the \(\mu\)-density and homogeneous density is established. We also characterize \(\mu\)-dense spaces as “arcwise” connected metric spaces in which “arcs” are the quasimöbius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of \(\dot{\mathbb R}^n\) in terms of the \(\mu\)-density.

MSC:

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
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