A Simple Proof of the Johnson–Lindenstrauss Extension Theorem

Manor Mendel

doi:10.1080/00029890.2019.1642071

A Simple Proof of the Johnson–Lindenstrauss Extension Theorem

Manor Mendel

Computer Science

Open University of Israel

Research output: Contribution to journal › Comment/debate

Abstract

Johnson and Lindenstrauss proved that any Lipschitz mapping from an n-point subset of a metric space into Hilbert space can be extended to the whole space, while increasing the Lipschitz constant by a factor of (Formula presented.). We present a simplification of their argument that avoids dimension reduction and the Kirszbraun theorem.

Original language	English
Pages (from-to)	838-840
Number of pages	3
Journal	American Mathematical Monthly
Volume	126
Issue number	9
DOIs	https://doi.org/10.1080/00029890.2019.1642071
State	Published - 21 Oct 2019

Keywords

54C20
MSC: Primary 46T20
Secondary 51F99

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1080/00029890.2019.1642071

Cite this

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abstract = "Johnson and Lindenstrauss proved that any Lipschitz mapping from an n-point subset of a metric space into Hilbert space can be extended to the whole space, while increasing the Lipschitz constant by a factor of (Formula presented.). We present a simplification of their argument that avoids dimension reduction and the Kirszbraun theorem.",

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AB - Johnson and Lindenstrauss proved that any Lipschitz mapping from an n-point subset of a metric space into Hilbert space can be extended to the whole space, while increasing the Lipschitz constant by a factor of (Formula presented.). We present a simplification of their argument that avoids dimension reduction and the Kirszbraun theorem.

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M3 - تعليقَ / نقاش

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JO - American Mathematical Monthly

JF - American Mathematical Monthly

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A Simple Proof of the Johnson–Lindenstrauss Extension Theorem

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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