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Positivity

, Volume 19, Issue 2, pp 395–417 | Cite as

Additive combination spaces

  • Stephen SánchezEmail author
Article

Abstract

We introduce a class of metric spaces called \(p\)-additive combinations and show that for such spaces we may deduce information about their \(p\)-negative type behaviour by focusing on a relatively small collection of almost disjoint metric subspaces, which we call the components. In particular we deduce a formula for the \(p\)-negative type gap of the space in terms of the \(p\)-negative type gaps of the components, independent of how the components are arranged in the ambient space. This generalizes earlier work on metric trees by Doust and Weston. The results hold for semi-metric spaces as well, as the triangle inequality is not used.

Keywords

Negative type Generalized roundness Additive combination  Metric embedding 

Mathematics Subject Classification

46B85 46T99 05C12 

Notes

Acknowledgments

The author wishes to thank the assistance provided by Ian Doust and Tony Weston during the editing and preparation of this document.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUNSWSydneyAustralia

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