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 EquationSource % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafSyhHeQbai% aaaaa!3766! n in terms of μ-density.
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Ibragimov, Z. Metric Density and Quasimobius Mappings. Siberian Mathematical Journal 43, 812–821 (2002). https://doi.org/10.1023/A:1020194404901
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DOI: https://doi.org/10.1023/A:1020194404901