Embedding metric spaces into normed spaces and estimates of metric capacity |
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Authors: | Gennadiy Averkov Nico Düvelmeyer |
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Institution: | (1) University of Technology, Chemnitz, Germany |
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Abstract: | Let
be an arbitrary real normed space of finite dimension d ≥ 2. We define the metric capacity of
as the maximal
such that every m-point metric space is isometric to some subset of
(with metric induced by
). We obtain that the metric capacity of
lies in the range from 3 to
, where the lower bound is sharp for all d, and the upper bound is shown to be sharp for d ∈ {2, 3}. Thus, the unknown sharp upper bound is asymptotically linear, since it lies in the range from d + 2 to
.
Research supported by the German Research Foundation, Project AV 85/1-1. |
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Keywords: | 2000 Mathematics Subject Classification: 52A21 52B10 52C10 |
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