Lipschitz retraction of finite subsets of Hilbert spaces

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Finite subset spaces of a metric space X form a nested sequence under natural isometric embeddings X = X(1) ⊂ X(2) ⊂ · · ·. We prove that this sequence admits Lipschitz retractions X(n) → X(n-1) when X is a Hilbert space.

Original languageEnglish (US)
Pages (from-to)146-151
Number of pages6
JournalBulletin of the Australian Mathematical Society
Volume93
Issue number1
DOIs
StatePublished - Feb 1 2016

Keywords

  • Finite subset space
  • Hausdorff metric
  • Lipschitz retraction
  • metric space

ASJC Scopus subject areas

  • Mathematics(all)

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