English

Symmetric products of the line: embeddings and retractions

Metric Geometry 2018-07-10 v1

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.

Keywords

Cite

@article{arxiv.1212.1698,
  title  = {Symmetric products of the line: embeddings and retractions},
  author = {Leonid V. Kovalev},
  journal= {arXiv preprint arXiv:1212.1698},
  year   = {2018}
}

Comments

10 pages