### 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.

Language | English (US) |
---|---|

Pages | 801-809 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 2 |

DOIs | |

State | Published - 2015 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Symmetric products of the line : Embeddings and retractions.** / Kovalev, Leonid Vladimirovich.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 143, no. 2, pp. 801-809. https://doi.org/10.1090/S0002-9939-2014-12280-5

}

TY - JOUR

T1 - Symmetric products of the line

T2 - Proceedings of the American Mathematical Society

AU - Kovalev, Leonid Vladimirovich

PY - 2015

Y1 - 2015

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84919362794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919362794&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2014-12280-5

DO - 10.1090/S0002-9939-2014-12280-5

M3 - Article

VL - 143

SP - 801

EP - 809

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -