Symmetric products of the line: Embeddings and retractions

Research output: Research - peer-reviewArticle

  • 3 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.

LanguageEnglish (US)
Pages801-809
Number of pages9
JournalProceedings of the American Mathematical Society
Volume143
Issue number2
DOIs
StatePublished - 2015

Fingerprint

Symmetric Product
Retraction
Lipschitz
Line
Hausdorff Metric
Retract
Higher Dimensions
Metric space
Euclidean space
Cardinality
Subset

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 143, No. 2, 2015, p. 801-809.

Research output: Research - peer-reviewArticle

@article{d2f2288c2831424195e39adfa34aac74,
title = "Symmetric products of the line: Embeddings and retractions",
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.",
author = "Kovalev, {Leonid V.}",
year = "2015",
doi = "10.1090/S0002-9939-2014-12280-5",
volume = "143",
pages = "801--809",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "2",

}

TY - JOUR

T1 - Symmetric products of the line

T2 - Proceedings of the American Mathematical Society

AU - Kovalev,Leonid V.

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 -