Lipschitz retraction of finite subsets of Hilbert spaces

Research output: Research - peer-reviewArticle

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Abstract

Finite subset spaces of a metric space (Formula presented.) form a nested sequence under natural isometric embeddings (Formula presented.). We prove that this sequence admits Lipschitz retractions (Formula presented.) when (Formula presented.) is a Hilbert space.

LanguageEnglish (US)
JournalBulletin of the Australian Mathematical Society
DOIs
StateAccepted/In press - Jul 8 2015

Fingerprint

Retraction
Lipschitz
Hilbert space
Subset
Isometric Embedding
Metric space

Keywords

  • finite subset space
  • Hausdorff metric
  • Lipschitz retraction
  • metric space

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Lipschitz retraction of finite subsets of Hilbert spaces",
abstract = "Finite subset spaces of a metric space (Formula presented.) form a nested sequence under natural isometric embeddings (Formula presented.). We prove that this sequence admits Lipschitz retractions (Formula presented.) when (Formula presented.) is a Hilbert space.",
keywords = "finite subset space, Hausdorff metric, Lipschitz retraction, metric space",
author = "Kovalev, {Leonid V.}",
year = "2015",
month = "7",
doi = "10.1017/S0004972715000672",
journal = "Bulletin of the Australian Mathematical Society",
issn = "0004-9727",
publisher = "Cambridge University Press",

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KW - metric space

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