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Zig-zag chains and metric equivalences between ultrametric spaces
Authors:Álvaro Martínez-Pérez
Institution:Departamento de Geometría y Topología, Universidad Complutense de Madrid, Madrid 28040, Spain
Abstract:We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (bi-uniform equivalences). Using a combinatoric approach we consider every ultrametric space as the end space of a chain and prove that all these equivalences can be characterized by the existence of a common zig-zag chain.
Keywords:primary  18B30  37F20  secondary  54E35
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