Lipschitz retraction of finite subsets of Hilbert spaces

Leonid V. Kovalev

doi:10.1017/S0004972715000672

Lipschitz retraction of finite subsets of Hilbert spaces

Leonid V. Kovalev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English (US)
Pages (from-to)	146-151
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	93
Issue number	1
DOIs	https://doi.org/10.1017/S0004972715000672
State	Published - Feb 1 2016

Keywords

Finite subset space
Hausdorff metric
Lipschitz retraction
metric space

ASJC Scopus subject areas

General Mathematics

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10.1017/S0004972715000672

Cite this

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title = "Lipschitz retraction of finite subsets of Hilbert spaces",

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.",

keywords = "Finite subset space, Hausdorff metric, Lipschitz retraction, metric space",

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year = "2016",

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AB - 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.

KW - Finite subset space

KW - Hausdorff metric

KW - Lipschitz retraction

KW - metric space

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Lipschitz retraction of finite subsets of Hilbert spaces

Abstract

Keywords

ASJC Scopus subject areas

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