Symmetric products of the line: embeddings and retractions

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.

10 pages

Cited by in corpus (3)

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