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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Symmetric products of the line: Embeddings and retractions
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by Leonid V. Kovalev PDF
Proc. Amer. Math. Soc. 143 (2015), 801-809 Request permission

Abstract:

The $n$th symmetric product of a metric space is the set of its nonempty subsets with cardinality at most $n$, equipped with the Hausdorff metric. We prove that every symmetric product of the line is an absolute Lipschitz retract and admits a bi-Lipschitz embedding into a Euclidean space of sufficiently high dimension.
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Additional Information
  • Leonid V. Kovalev
  • Affiliation: Department of Mathematics, 215 Carnegie, Syracuse University, Syracuse, New York 13244-1150
  • MR Author ID: 641917
  • Email: lvkovale@syr.edu
  • Received by editor(s): December 7, 2012
  • Received by editor(s) in revised form: June 5, 2013
  • Published electronically: October 15, 2014
  • Additional Notes: This research was supported by the NSF grant DMS-0968756.
  • Communicated by: Jeremy Tyson
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 801-809
  • MSC (2010): Primary 30L05; Secondary 54E40, 54B20, 54C15, 54C25
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12280-5
  • MathSciNet review: 3283666