Symmetric products of the line: Embeddings and retractions

Leonid V. Kovalev

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

Symmetric products of the line: Embeddings and retractions

Leonid V. Kovalev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The nth 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.

Original language	English (US)
Pages (from-to)	801-809
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2014-12280-5
State	Published - 2015

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "The nth 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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AB - The nth 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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Symmetric products of the line: Embeddings and retractions

Abstract

ASJC Scopus subject areas

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