Symmetric products of the line: Embeddings and retractions

Kovalev, Leonid

doi:10.1090/S0002-9939-2014-12280-5

Symmetric products of the line: Embeddings and retractions
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by Leonid V. Kovalev

Proc. Amer. Math. Soc. 143 (2015), 801-809

DOI: https://doi.org/10.1090/S0002-9939-2014-12280-5

Published electronically: October 15, 2014

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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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