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ON EMBEDDINGS OF FINITE METRIC SPACES IN ln∞

Part of: Graph theory General convexity

Published online by Cambridge University Press:  10 December 2009

F. V. Petrov ,
D. M. Stolyarov  and
P. B. Zatitskiy
F. V. Petrov
Affiliation:
St. Petersburg Department of Steklov Mathematical Institute RAS 27, Fontanka, 191023 St. Petersburg, Russia
D. M. Stolyarov
Affiliation:
Saint-Petersburg State University, Mathematics and Mechanics Faculty, Universitetsky prospekt, 28, 198504, St. Petersburg, Russia
P. B. Zatitskiy
Affiliation:
Saint-Petersburg State University, Mathematics and Mechanics Faculty, Universitetsky prospekt, 28, 198504, St. Petersburg, Russia
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Abstract

We prove that for any given integer c≥0 any metric space on n points may be isometrically embedded into ln−c∞ provided n is large enough.

MSC classification

Secondary: 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.) 05C55: Generalized Ramsey theory
Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 135 - 139
Copyright
Copyright © University College London 2010

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References

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