### Abstract

It is shown that for every K > 0 and ε ∈ (0, 1/2) there exist N = N(K) ∈ N and D = D(K, ε) ∈ (1,∞) with the following properties. For every metric space (X, d) with doubling constant at most K, themetric space (X, d^{1-ε}) admits a bi-Lipschitz embedding into R^{N} with distortion at most D. The classical Assouad embedding theorem makes the same assertion, but with N →∞ as ε → 0.

Original language | English (US) |
---|---|

Pages (from-to) | 1123-1142 |

Number of pages | 20 |

Journal | Revista Matematica Iberoamericana |

Volume | 28 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- Assouad's theorem
- Doubling metric spaces

## Fingerprint Dive into the research topics of 'Assouad's theorem with dimension independent of the snowflaking'. Together they form a unique fingerprint.

## Cite this

Naor, A., & Neiman, O. (2012). Assouad's theorem with dimension independent of the snowflaking.

*Revista Matematica Iberoamericana*,*28*(4), 1123-1142. https://doi.org/10.4171/rmi/706