Symmetric products of the line: Embeddings and retractions

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish (US)
Pages (from-to)801-809
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - 2015

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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