Absolute Lipschitz extendability

James R. Lee; Assar Naor

doi:10.1016/j.crma.2004.03.005

Absolute Lipschitz extendability

James R. Lee
, Assar Naor

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

12 Scopus citations

Abstract

A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y X, where the loss in the Lipschitz constant in the extension is independent of Y, Z, and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable.

Original language	English (US)
Pages (from-to)	859-862
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	338
Issue number	11
DOIs	https://doi.org/10.1016/j.crma.2004.03.005
State	Published - Jun 1 2004
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2004.03.005

Cite this

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title = "Absolute Lipschitz extendability",

abstract = "A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y X, where the loss in the Lipschitz constant in the extension is independent of Y, Z, and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable.",

author = "Lee, \{James R.\} and Assar Naor",

note = "Funding Information: E-mail addresses: [email protected] (J.R. Lee), [email protected] (A. Naor). 1 The first author was partially supported by NSF grant CCR-0121555 and an NSF Graduate Research Fellowship.",

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PY - 2004/6/1

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N2 - A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y X, where the loss in the Lipschitz constant in the extension is independent of Y, Z, and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable.

AB - A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y X, where the loss in the Lipschitz constant in the extension is independent of Y, Z, and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable.

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U2 - 10.1016/j.crma.2004.03.005

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M3 - Article

AN - SCOPUS:2342442684

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SP - 859

EP - 862

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 11

ER -

Absolute Lipschitz extendability

Abstract

All Science Journal Classification (ASJC) codes

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