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Symmetric products of the line: Embeddings and retractions


Author: Leonid V. Kovalev
Journal: Proc. Amer. Math. Soc. 143 (2015), 801-809
MSC (2010): Primary 30L05; Secondary 54E40, 54B20, 54C15, 54C25
Published electronically: October 15, 2014
MathSciNet review: 3283666
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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
Email: lvkovale@syr.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12280-5
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
Article copyright: © Copyright 2014 American Mathematical Society