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 language||English (US)|
|Number of pages||9|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - 2015|
ASJC Scopus subject areas
- Applied Mathematics