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2004•Comptes Rendus MathématiqueRequires access

Absolute Lipschitz extendability

James R. Lee, Assar Naor

Open publisher page 12 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.

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What this paper is about

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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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Mathematics, Lipschitz continuity, Banach space, Metric space, Metric differential, Extension (predicate logic), Combinatorics, Discrete mathematics

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