0000000000249489

AUTHOR

Ellen Veomett

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SPACES OF SMALL METRIC COTYPE

2010

Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result.

Mathematics::Functional AnalysisPure mathematics30L05 46B85010102 general mathematicsBanach spaceMetric Geometry (math.MG)0102 computer and information sciences16. Peace & justice01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMetric spaceMathematics - Metric Geometry010201 computation theory & mathematicsConverseMetric (mathematics)FOS: MathematicsMathematics::Metric GeometryGeometry and Topology0101 mathematicsIsoperimetric inequalityUltrametric spaceAnalysisMathematicsJournal of Topology and Analysis
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