Whitney’s example by way of Assouad’s embedding

Hajłasz, Piotr

doi:10.1090/S0002-9939-03-06913-2

Whitney’s example by way of Assouad’s embedding
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by Piotr Hajłasz

Proc. Amer. Math. Soc. 131 (2003), 3463-3467

DOI: https://doi.org/10.1090/S0002-9939-03-06913-2

Published electronically: February 6, 2003

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Abstract:

In this note we show how to use the Assouad embedding theorem (about almost bi-Lipschitz embeddings) to construct examples of $C^m$ functions which are not constant on a critical set homeomorphic to the $n$-dimensional cube. This extends the famous example of Whitney. Our examples are shown to be sharp.

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