Quasi-Möbius映射的一些不变性

Pub Date : 2016-03-24 DOI:10.1515/agms-2017-0004

Loreno Heer

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引用次数: 9

摘要

摘要研究了在quasi-Möbius拟度量空间映射作用下保持不变的性质。如果每个有限半径的球可以被最多D个半径为一半的球覆盖，则度量空间称为常数D倍。证明了加倍性质是(拟)Möbius映射的一个不变性质。此外，还证明了(拟)Möbius映射的一致不连通性是一个不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some Invariant Properties of Quasi-Möbius Maps

Abstract 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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