Analysis and Geometry in Metric Spaces (Sep 2017)

Some Invariant Properties of Quasi-Möbius Maps

  • Heer Loreno

DOI
https://doi.org/10.1515/agms-2017-0004
Journal volume & issue
Vol. 5, no. 1
pp. 69 – 77

Abstract

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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.

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