Geodesic
Some Invariant Properties of Quasi-Möbius Maps
Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 69-77.

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We investigate properties which remain invariant under the action of quasi-Möbius maps of quasimetric spaces. A metric space is called doubling with constant D if every ball of finite radius can be covered by at most D balls of half the radius. It is shown that the doubling property is an invariant property for (quasi-)Möbius maps. Additionally it is shown that the property of uniform disconnectedness is an invariant for (quasi-)Möbius maps as well.
Mots-clés : Möbius structures, doubling property, quasi-Möbius maps, uniform disconnectedness 
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Heer, Loreno. Some Invariant Properties of Quasi-Möbius Maps. Analysis and Geometry in Metric Spaces, Tome 5 (2017) no. 1, pp. 69-77. http://geodesic.mathdoc.fr/item/AGMS_2017_5_1_a3/