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.
@article{bwmeta1.element.doi-10_1515_agms-2017-0004,
author = {Loreno Heer},
title = {Some Invariant Properties of Quasi-M\"obius Maps},
journal = {Analysis and Geometry in Metric Spaces},
volume = {5},
year = {2017},
pages = {69-77},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0004}
}
Loreno Heer. Some Invariant Properties of Quasi-Möbius Maps. Analysis and Geometry in Metric Spaces, Tome 5 (2017) pp. 69-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0004/